LMFDB - Embedded newform 225.2.q.a.31.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.21
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.21

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955162 - 1.06081i) q^{2} +(-1.72633 - 0.140638i) q^{3} +(-0.00393676 - 0.0374558i) q^{4} +(0.397449 + 2.20046i) q^{5} +(-1.79812 + 1.69699i) q^{6} +(1.20474 + 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(2.96044 + 0.485576i) q^{9} +O(q^{10})$	\(q+(0.955162 - 1.06081i) q^{2} +(-1.72633 - 0.140638i) q^{3} +(-0.00393676 - 0.0374558i) q^{4} +(0.397449 + 2.20046i) q^{5} +(-1.79812 + 1.69699i) q^{6} +(1.20474 + 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(2.96044 + 0.485576i) q^{9} +(2.71391 + 1.68018i) q^{10} +(-0.0211445 + 0.0234833i) q^{11} +(0.00152844 + 0.0652148i) q^{12} +(-4.22250 - 4.68956i) q^{13} +(3.36428 + 0.715100i) q^{14} +(-0.376660 - 3.85462i) q^{15} +(3.98488 - 0.847013i) q^{16} +(2.72065 + 1.97667i) q^{17} +(3.34281 - 2.67668i) q^{18} +(1.81267 + 1.31698i) q^{19} +(0.0808554 - 0.0235495i) q^{20} +(-1.78631 - 3.77171i) q^{21} +(0.00471506 + 0.0448608i) q^{22} +(-1.88117 - 0.399856i) q^{23} +(-3.68065 - 3.16110i) q^{24} +(-4.68407 + 1.74914i) q^{25} -9.00793 q^{26} +(-5.04241 - 1.25462i) q^{27} +(0.0734149 - 0.0533391i) q^{28} +(8.54224 + 3.80325i) q^{29} +(-4.44881 - 3.28222i) q^{30} +(-3.43471 + 1.52923i) q^{31} +(0.106511 - 0.184482i) q^{32} +(0.0398050 - 0.0375663i) q^{33} +(4.69554 - 0.998067i) q^{34} +(-4.11281 + 3.48032i) q^{35} +(0.00653309 - 0.112797i) q^{36} +(3.22975 - 9.94014i) q^{37} +(3.12847 - 0.664976i) q^{38} +(6.62990 + 8.68958i) q^{39} +(-2.72234 + 5.64107i) q^{40} +(1.08631 + 1.20647i) q^{41} +(-5.70730 - 1.70765i) q^{42} +(-5.58816 - 9.67898i) q^{43} +(0.000962828 + 0.000699535i) q^{44} +(0.108132 + 6.70733i) q^{45} +(-2.22100 + 1.61365i) q^{46} +(-2.88640 - 1.28511i) q^{47} +(-6.99835 + 0.901798i) q^{48} +(0.597221 - 1.03442i) q^{49} +(-2.61853 + 6.63964i) q^{50} +(-4.41875 - 3.79501i) q^{51} +(-0.159028 + 0.176619i) q^{52} +(1.23376 - 0.896379i) q^{53} +(-6.14724 + 4.15070i) q^{54} +(-0.0600780 - 0.0371942i) q^{55} +(-0.705499 + 6.71237i) q^{56} +(-2.94405 - 2.52848i) q^{57} +(12.1938 - 5.42901i) q^{58} +(-8.58158 - 9.53081i) q^{59} +(-0.142895 + 0.0292828i) q^{60} +(7.10677 - 7.89287i) q^{61} +(-1.65848 + 5.10426i) q^{62} +(2.55332 + 6.76244i) q^{63} +(2.42385 + 7.45983i) q^{64} +(8.64097 - 11.1553i) q^{65} +(-0.00183061 - 0.0781077i) q^{66} +(-2.07993 + 0.926044i) q^{67} +(0.0633271 - 0.109686i) q^{68} +(3.19129 + 0.954848i) q^{69} +(-0.236421 + 7.68719i) q^{70} +(-3.63556 + 2.64139i) q^{71} +(5.90945 + 5.97474i) q^{72} +(0.380414 + 1.17080i) q^{73} +(-7.45971 - 12.9206i) q^{74} +(8.33225 - 2.36084i) q^{75} +(0.0421926 - 0.0730797i) q^{76} +(-0.0744753 - 0.0158302i) q^{77} +(15.5507 + 1.26686i) q^{78} +(0.840545 + 0.374235i) q^{79} +(3.44761 + 8.43194i) q^{80} +(8.52843 + 2.87504i) q^{81} +2.31745 q^{82} +(-0.581163 + 5.52940i) q^{83} +(-0.134240 + 0.0817560i) q^{84} +(-3.26826 + 6.77231i) q^{85} +(-15.6052 - 3.31699i) q^{86} +(-14.2119 - 7.76704i) q^{87} +(-0.0865826 + 0.0184037i) q^{88} +(-0.932477 - 2.86987i) q^{89} +(7.21852 + 6.29188i) q^{90} +(4.69854 - 14.4606i) q^{91} +(-0.00757118 + 0.0720350i) q^{92} +(6.14453 - 2.15691i) q^{93} +(-4.12024 + 1.83445i) q^{94} +(-2.17753 + 4.51214i) q^{95} +(-0.209818 + 0.303497i) q^{96} +(-9.49506 - 4.22747i) q^{97} +(-0.526882 - 1.62158i) q^{98} +(-0.0739999 + 0.0592538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.955162	−	1.06081i	0.675401	−	0.750109i	−0.303859	−	0.952717i	$-0.598275\pi$
$2$	0.955162	−	1.06081i	0.675401	−	0.750109i	0.979260	+	0.202608i	$0.0649417\pi$
$3$	−1.72633	−	0.140638i	−0.996698	−	0.0811975i
$3$	−1.72633	−	0.140638i	−0.996698	−	0.0811975i
$4$	−0.00393676	−	0.0374558i	−0.00196838	−	0.0187279i
$5$	0.397449	+	2.20046i	0.177745	+	0.984077i
$5$	0.397449	+	2.20046i	0.177745	+	0.984077i
$6$	−1.79812	+	1.69699i	−0.734078	+	0.692792i
$7$	1.20474	+	2.08666i	0.455348	+	0.788685i	0.998708	−	0.0508144i	$-0.0161817\pi$
$7$	1.20474	+	2.08666i	0.455348	+	0.788685i	−0.543361	+	0.839499i	$0.682848\pi$
$8$	2.26620	+	1.64649i	0.801221	+	0.582121i
$9$	2.96044	+	0.485576i	0.986814	+	0.161859i
$10$	2.71391	+	1.68018i	0.858214	+	0.531319i
$11$	−0.0211445	+	0.0234833i	−0.00637530	+	0.00708049i	−0.746324	−	0.665583i	$-0.768183\pi$
$11$	−0.0211445	+	0.0234833i	−0.00637530	+	0.00708049i	0.739949	+	0.672663i	$0.234850\pi$
$12$	0.00152844	+	0.0652148i	0.000441224	+	0.0188259i
$13$	−4.22250	−	4.68956i	−1.17111	−	1.30065i	−0.945196	−	0.326503i	$-0.894130\pi$
$13$	−4.22250	−	4.68956i	−1.17111	−	1.30065i	−0.225914	−	0.974147i	$-0.572537\pi$
$14$	3.36428	+	0.715100i	0.899142	+	0.191119i
$15$	−0.376660	−	3.85462i	−0.0972531	−	0.995260i
$16$	3.98488	−	0.847013i	0.996220	−	0.211753i
$17$	2.72065	+	1.97667i	0.659854	+	0.479412i	0.866614	−	0.498980i	$-0.166292\pi$
$17$	2.72065	+	1.97667i	0.659854	+	0.479412i	−0.206760	+	0.978392i	$0.566292\pi$
$18$	3.34281	−	2.67668i	0.787907	−	0.630899i
$19$	1.81267	+	1.31698i	0.415855	+	0.302136i	0.775968	−	0.630772i	$-0.217262\pi$
$19$	1.81267	+	1.31698i	0.415855	+	0.302136i	−0.360113	+	0.932909i	$0.617262\pi$
$20$	0.0808554	−	0.0235495i	0.0180798	−	0.00526582i
$21$	−1.78631	−	3.77171i	−0.389805	−	0.823054i
$22$	0.00471506	+	0.0448608i	0.00100525	+	0.00956434i
$23$	−1.88117	−	0.399856i	−0.392252	−	0.0833756i	0.00756369	−	0.999971i	$-0.497592\pi$
$23$	−1.88117	−	0.399856i	−0.392252	−	0.0833756i	−0.399815	+	0.916596i	$0.630926\pi$
$24$	−3.68065	−	3.16110i	−0.751309	−	0.645256i
$25$	−4.68407	+	1.74914i	−0.936814	+	0.349829i
$26$	−9.00793			−1.76660
$27$	−5.04241	−	1.25462i	−0.970413	−	0.241451i
$28$	0.0734149	−	0.0533391i	0.0138741	−	0.0100801i
$29$	8.54224	+	3.80325i	1.58625	+	0.706246i	0.994966	−	0.100215i	$-0.0319530\pi$
$29$	8.54224	+	3.80325i	1.58625	+	0.706246i	0.591288	+	0.806460i	$0.298620\pi$
$30$	−4.44881	−	3.28222i	−0.812238	−	0.599249i
$31$	−3.43471	+	1.52923i	−0.616893	+	0.274658i	−0.691298	−	0.722570i	$-0.742961\pi$
$31$	−3.43471	+	1.52923i	−0.616893	+	0.274658i	0.0744052	+	0.997228i	$0.476294\pi$
$32$	0.106511	−	0.184482i	0.0188286	−	0.0326121i
$33$	0.0398050	−	0.0375663i	0.00692917	−	0.00653945i
$34$	4.69554	−	0.998067i	0.805278	−	0.171167i
$35$	−4.11281	+	3.48032i	−0.695191	+	0.588281i
$36$	0.00653309	−	0.112797i	0.00108885	−	0.0187996i
$37$	3.22975	−	9.94014i	0.530967	−	1.63415i	−0.221238	−	0.975220i	$-0.571010\pi$
$37$	3.22975	−	9.94014i	0.530967	−	1.63415i	0.752205	−	0.658929i	$-0.228990\pi$
$38$	3.12847	−	0.664976i	0.507504	−	0.107873i
$39$	6.62990	+	8.68958i	1.06163	+	1.39145i
$40$	−2.72234	+	5.64107i	−0.430439	+	0.891932i
$41$	1.08631	+	1.20647i	0.169654	+	0.188420i	0.821976	−	0.569522i	$-0.192872\pi$
$41$	1.08631	+	1.20647i	0.169654	+	0.188420i	−0.652322	+	0.757942i	$0.726205\pi$
$42$	−5.70730	−	1.70765i	−0.880655	−	0.263496i
$43$	−5.58816	−	9.67898i	−0.852186	−	1.47603i	−0.879231	−	0.476396i	$-0.841943\pi$
$43$	−5.58816	−	9.67898i	−0.852186	−	1.47603i	0.0270444	−	0.999634i	$-0.491390\pi$
$44$	0.000962828	0	0.000699535i	0.000145152	0	0.000105459i
$45$	0.108132	+	6.70733i	0.0161194	+	0.999870i
$46$	−2.22100	+	1.61365i	−0.327468	+	0.237919i
$47$	−2.88640	−	1.28511i	−0.421025	−	0.187452i	0.185278	−	0.982686i	$-0.440681\pi$
$47$	−2.88640	−	1.28511i	−0.421025	−	0.187452i	−0.606303	+	0.795234i	$0.707348\pi$
$48$	−6.99835	+	0.901798i	−1.01012	+	0.130163i
$49$	0.597221	−	1.03442i	0.0853173	−	0.147774i
$50$	−2.61853	+	6.63964i	−0.370316	+	0.938987i
$51$	−4.41875	−	3.79501i	−0.618748	−	0.531408i
$52$	−0.159028	+	0.176619i	−0.0220533	+	0.0244926i
$53$	1.23376	−	0.896379i	0.169470	−	0.123127i	−0.499817	−	0.866131i	$-0.666600\pi$
$53$	1.23376	−	0.896379i	0.169470	−	0.123127i	0.669287	+	0.743004i	$0.266600\pi$
$54$	−6.14724	+	4.15070i	−0.836533	+	0.564839i
$55$	−0.0600780	−	0.0371942i	−0.00810092	−	0.00501527i
$56$	−0.705499	+	6.71237i	−0.0942763	+	0.896979i
$57$	−2.94405	−	2.52848i	−0.389949	−	0.334905i
$58$	12.1938	−	5.42901i	1.60112	−	0.712864i
$59$	−8.58158	−	9.53081i	−1.11723	−	1.24081i	−0.967715	−	0.252046i	$-0.918897\pi$
$59$	−8.58158	−	9.53081i	−1.11723	−	1.24081i	−0.149511	−	0.988760i	$-0.547770\pi$
$60$	−0.142895	+	0.0292828i	−0.0184477	+	0.00378040i
$61$	7.10677	−	7.89287i	0.909929	−	1.01058i	−0.0899640	−	0.995945i	$-0.528675\pi$
$61$	7.10677	−	7.89287i	0.909929	−	1.01058i	0.999893	−	0.0146335i	$-0.00465815\pi$
$62$	−1.65848	+	5.10426i	−0.210627	+	0.648242i
$63$	2.55332	+	6.76244i	0.321688	+	0.851987i
$64$	2.42385	+	7.45983i	0.302981	+	0.932479i
$65$	8.64097	−	11.1553i	1.07178	−	1.38365i
$66$	−0.00183061	−	0.0781077i	−0.000225333	−	0.00961439i
$67$	−2.07993	+	0.926044i	−0.254104	+	0.113134i	−0.529836	−	0.848100i	$-0.677746\pi$
$67$	−2.07993	+	0.926044i	−0.254104	+	0.113134i	0.275732	+	0.961235i	$0.411080\pi$
$68$	0.0633271	−	0.109686i	0.00767954	−	0.0133014i
$69$	3.19129	+	0.954848i	0.384186	+	0.114950i
$70$	−0.236421	+	7.68719i	−0.0282577	+	0.918795i
$71$	−3.63556	+	2.64139i	−0.431462	+	0.313475i	−0.782233	−	0.622986i	$-0.785919\pi$
$71$	−3.63556	+	2.64139i	−0.431462	+	0.313475i	0.350771	+	0.936461i	$0.385919\pi$
$72$	5.90945	+	5.97474i	0.696435	+	0.704130i
$73$	0.380414	+	1.17080i	0.0445241	+	0.137031i	0.970847	−	0.239698i	$-0.0770486\pi$
$73$	0.380414	+	1.17080i	0.0445241	+	0.137031i	−0.926323	+	0.376730i	$0.877049\pi$
$74$	−7.45971	−	12.9206i	−0.867174	−	1.50199i
$75$	8.33225	−	2.36084i	0.962126	−	0.272606i
$76$	0.0421926	−	0.0730797i	0.00483982	−	0.00838281i
$77$	−0.0744753	−	0.0158302i	−0.00848725	−	0.00180402i
$78$	15.5507	+	1.26686i	1.76077	+	0.143443i
$79$	0.840545	+	0.374235i	0.0945687	+	0.0421047i	0.453476	−	0.891269i	$-0.350184\pi$
$79$	0.840545	+	0.374235i	0.0945687	+	0.0421047i	−0.358907	+	0.933373i	$0.616851\pi$
$80$	3.44761	+	8.43194i	0.385454	+	0.942719i
$81$	8.52843	+	2.87504i	0.947603	+	0.319449i
$82$	2.31745			0.255920
$83$	−0.581163	+	5.52940i	−0.0637909	+	0.606930i	0.915196	+	0.403008i	$0.132035\pi$
$83$	−0.581163	+	5.52940i	−0.0637909	+	0.606930i	−0.978987	+	0.203922i	$0.934631\pi$
$84$	−0.134240	+	0.0817560i	−0.0146468	+	0.00892031i
$85$	−3.26826	+	6.77231i	−0.354493	+	0.734560i
$86$	−15.6052	−	3.31699i	−1.68275	−	0.357680i
$87$	−14.2119	−	7.76704i	−1.52367	−	0.832714i
$88$	−0.0865826	+	0.0184037i	−0.00922973	+	0.00196184i
$89$	−0.932477	−	2.86987i	−0.0988424	−	0.304206i	0.889394	−	0.457142i	$-0.151127\pi$
$89$	−0.932477	−	2.86987i	−0.0988424	−	0.304206i	−0.988236	+	0.152937i	$0.951127\pi$
$90$	7.21852	+	6.29188i	0.760899	+	0.663222i
$91$	4.69854	−	14.4606i	0.492541	−	1.51589i
$92$	−0.00757118	+	0.0720350i	−0.000789350	+	0.00751017i
$93$	6.14453	−	2.15691i	0.637158	−	0.223661i
$94$	−4.12024	+	1.83445i	−0.424971	+	0.189209i
$95$	−2.17753	+	4.51214i	−0.223409	+	0.462936i
$96$	−0.209818	+	0.303497i	−0.0214144	+	0.0309755i
$97$	−9.49506	−	4.22747i	−0.964077	−	0.429235i	−0.136533	−	0.990636i	$-0.543596\pi$
$97$	−9.49506	−	4.22747i	−0.964077	−	0.429235i	−0.827544	+	0.561401i	$0.810263\pi$
$98$	−0.526882	−	1.62158i	−0.0532232	−	0.163804i
$99$	−0.0739999	+	0.0592538i	−0.00743727	+	0.00595523i
$100$	0.0839556	+	0.168560i	0.00839556	+	0.0168560i
$101$	2.74091	+	4.74740i	0.272731	+	0.472384i	0.969560	−	0.244853i	$-0.0787398\pi$
$101$	2.74091	+	4.74740i	0.272731	+	0.472384i	−0.696829	+	0.717237i	$0.745406\pi$
$102$	−8.24642	+	1.06262i	−0.816517	+	0.105215i
$103$	0.191572	+	1.82268i	0.0188761	+	0.179594i	0.999898	−	0.0143043i	$-0.00455337\pi$
$103$	0.191572	+	1.82268i	0.0188761	+	0.179594i	−0.981022	+	0.193899i	$0.937887\pi$
$104$	−1.84771	−	17.5798i	−0.181183	−	1.72384i
$105$	7.58953	−	5.42977i	0.740662	−	0.529891i
$106$	0.227548	−	2.16498i	0.0221014	−	0.210281i
$107$	18.4750			1.78604			0.893021	−	0.450014i	$-0.148581\pi$
$107$	18.4750			1.78604			0.893021	+	0.450014i	$0.148581\pi$
$108$	−0.0271419	+	0.193807i	−0.00261173	+	0.0186491i
$109$	1.39665	−	4.29846i	0.133775	−	0.411718i	−0.861622	−	0.507550i	$-0.830551\pi$
$109$	1.39665	−	4.29846i	0.133775	−	0.411718i	0.995397	+	0.0958324i	$0.0305513\pi$
$110$	−0.0968404	+	0.0282052i	−0.00923337	+	0.00268926i
$111$	−6.97358	+	16.7057i	−0.661903	+	1.58564i
$112$	6.56816	+	7.29468i	0.620633	+	0.689283i
$113$	2.49461	+	2.77055i	0.234673	+	0.260631i	0.848966	−	0.528447i	$-0.177225\pi$
$113$	2.49461	+	2.77055i	0.234673	+	0.260631i	−0.614293	+	0.789078i	$0.710559\pi$
$114$	−5.49429	+	0.707987i	−0.514588	+	0.0663091i
$115$	0.132197	−	4.29837i	0.0123274	−	0.400825i
$116$	0.108825	−	0.334929i	0.0101041	−	0.0310974i
$117$	−10.2233	−	15.9335i	−0.945147	−	1.47305i
$118$	−18.3072			−1.68532
$119$	−0.846976	+	8.05844i	−0.0776422	+	0.738716i
$120$	5.49301	−	9.35550i	0.501441	−	0.854036i
$121$	1.14971	+	10.9387i	0.104519	+	0.994432i
$122$	−1.58476	−	15.0779i	−0.143477	−	1.36509i
$123$	−1.70566	−	2.23555i	−0.153794	−	0.201573i
$124$	0.0708003	+	0.122630i	0.00635806	+	0.0110125i
$125$	−5.71060	−	9.61192i	−0.510772	−	0.859716i
$126$	9.61253	+	3.75063i	0.856352	+	0.334133i
$127$	3.06084	+	9.42031i	0.271606	+	0.835917i	0.990098	+	0.140381i	$0.0448329\pi$
$127$	3.06084	+	9.42031i	0.271606	+	0.835917i	−0.718492	+	0.695536i	$0.755167\pi$
$128$	10.6179	+	4.72738i	0.938496	+	0.417845i
$129$	8.28578	+	17.4950i	0.729523	+	1.54035i
$130$	−3.58019	−	19.8216i	−0.314003	−	1.73847i
$131$	0.808980	−	0.360181i	0.0706809	−	0.0314692i	−0.371092	−	0.928596i	$-0.621016\pi$
$131$	0.808980	−	0.360181i	0.0706809	−	0.0314692i	0.441773	+	0.897127i	$0.354350\pi$
$132$	−0.00156378	−	0.00134304i	−0.000136109	−	0.000116897i
$133$	−0.564310	+	5.36905i	−0.0489319	+	0.465556i
$134$	−1.00431	+	3.09094i	−0.0867590	+	0.267017i
$135$	0.756635	−	11.5943i	0.0651208	−	0.997877i
$136$	2.91097	+	8.95903i	0.249613	+	0.768230i
$137$	10.9483	−	2.32714i	0.935378	−	0.198821i	0.285083	−	0.958503i	$-0.407979\pi$
$137$	10.9483	−	2.32714i	0.935378	−	0.198821i	0.650295	+	0.759682i	$0.274645\pi$
$138$	4.06112	−	2.47334i	0.345705	−	0.210544i
$139$	0.0394061	+	0.00837602i	0.00334238	+	0.000710445i	0.209583	−	0.977791i	$-0.432789\pi$
$139$	0.0394061	+	0.00837602i	0.00334238	+	0.000710445i	−0.206240	+	0.978501i	$0.566123\pi$
$140$	0.146549	+	0.140347i	0.0123857	+	0.0118615i
$141$	4.80215	+	2.62446i	0.404414	+	0.221020i
$142$	−0.670525	+	6.37962i	−0.0562692	+	0.535365i
$143$	0.199409			0.0166754
$144$	12.2083	−	0.572568i	1.01736	−	0.0477140i
$145$	−4.97380	+	20.3085i	−0.413052	+	1.68653i
$146$	1.60535	+	0.714750i	0.132860	+	0.0591531i
$147$	−1.17648	+	1.70176i	−0.0970345	+	0.140358i
$148$	−0.385031	−	0.0818408i	−0.0316493	−	0.00672727i
$149$	4.04741	−	7.01032i	0.331577	−	0.574308i	−0.651245	−	0.758868i	$-0.725753\pi$
$149$	4.04741	−	7.01032i	0.331577	−	0.574308i	0.982821	+	0.184560i	$0.0590861\pi$
$150$	5.45423	−	11.0940i	0.445336	−	0.905818i
$151$	−4.63305	−	8.02468i	−0.377032	−	0.653039i	0.613597	−	0.789620i	$-0.289722\pi$
$151$	−4.63305	−	8.02468i	−0.377032	−	0.653039i	−0.990629	+	0.136580i	$0.956389\pi$
$152$	1.93947	+	5.96908i	0.157312	+	0.484156i
$153$	7.09450	+	7.17289i	0.573556	+	0.579894i
$154$	−0.0879289	+	0.0638841i	−0.00708552	+	0.00514793i
$155$	−4.73014	−	6.95017i	−0.379934	−	0.558251i
$156$	0.299375	−	0.282537i	0.0239692	−	0.0226211i
$157$	−5.80545	+	10.0553i	−0.463326	+	0.802503i	−0.999124	−	0.0418424i	$-0.986677\pi$
$157$	−5.80545	+	10.0553i	−0.463326	+	0.802503i	0.535799	+	0.844346i	$0.320011\pi$
$158$	1.19985	−	0.534208i	0.0954549	−	0.0424993i
$159$	−2.25594	+	1.37393i	−0.178908	+	0.108960i
$160$	0.448277	+	0.161050i	0.0354394	+	0.0127321i
$161$	−1.43195	−	4.40710i	−0.112854	−	0.347328i
$162$	11.1959	−	6.30096i	0.879634	−	0.495050i
$163$	−1.85642	+	5.71348i	−0.145406	+	0.447515i	−0.997063	−	0.0765854i	$-0.975598\pi$
$163$	−1.85642	+	5.71348i	−0.145406	+	0.447515i	0.851657	+	0.524100i	$0.175598\pi$
$164$	0.0409129	−	0.0454384i	0.00319476	−	0.00354814i
$165$	0.0984837	+	0.0726588i	0.00766694	+	0.00565648i
$166$	5.31056	+	5.89797i	0.412179	+	0.457772i
$167$	12.3524	−	5.49964i	0.955857	−	0.425575i	0.131293	−	0.991344i	$-0.458087\pi$
$167$	12.3524	−	5.49964i	0.955857	−	0.425575i	0.824564	+	0.565769i	$0.191420\pi$
$168$	2.16194	−	11.4886i	0.166797	−	0.886362i
$169$	−2.80361	+	26.6745i	−0.215662	+	2.05189i
$170$	4.06245	+	9.93567i	0.311575	+	0.762031i
$171$	4.72681	+	4.77904i	0.361468	+	0.365462i
$172$	−0.340535	+	0.247413i	−0.0259655	+	0.0188651i
$173$	−4.52702	+	5.02776i	−0.344183	+	0.382254i	−0.890238	−	0.455495i	$-0.849462\pi$
$173$	−4.52702	+	5.02776i	−0.344183	+	0.382254i	0.546055	+	0.837749i	$0.316129\pi$
$174$	−21.8140	+	7.65737i	−1.65372	+	0.580504i
$175$	−9.29294	−	7.66682i	−0.702480	−	0.579557i
$176$	−0.0643676	+	0.111488i	−0.00485189	+	0.00840372i
$177$	13.4743	+	17.6602i	1.01279	+	1.32742i
$178$	−3.93507	−	1.75200i	−0.294946	−	0.131318i
$179$	5.82355	−	4.23106i	0.435272	−	0.316244i	−0.348481	−	0.937316i	$-0.613302\pi$
$179$	5.82355	−	4.23106i	0.435272	−	0.316244i	0.783754	+	0.621072i	$0.213302\pi$
$180$	0.250803	−	0.0304554i	0.0186937	−	0.00227001i
$181$	−5.56870	−	4.04590i	−0.413918	−	0.300729i	0.361268	−	0.932462i	$-0.382344\pi$
$181$	−5.56870	−	4.04590i	−0.413918	−	0.300729i	−0.775186	+	0.631733i	$0.782344\pi$
$182$	−10.8522	−	18.7965i	−0.804417	−	1.39329i
$183$	−13.3787	+	12.6262i	−0.988981	+	0.933358i
$184$	−3.60475	−	4.00348i	−0.265746	−	0.295140i
$185$	23.1566	+	3.15624i	1.70250	+	0.232051i
$186$	3.58093	−	8.57840i	0.262567	−	0.628999i
$187$	−0.103945	+	0.0220943i	−0.00760124	+	0.00161569i
$188$	−0.0367717	+	0.113172i	−0.00268185	+	0.00825389i
$189$	−3.45681	−	12.0333i	−0.251446	−	0.875294i
$190$	2.70666	+	6.61978i	0.196362	+	0.480249i
$191$	−11.0464	+	2.34798i	−0.799289	+	0.169894i	−0.589411	−	0.807834i	$-0.700640\pi$
$191$	−11.0464	+	2.34798i	−0.799289	+	0.169894i	−0.209878	+	0.977728i	$0.567307\pi$
$192$	−3.13523	−	13.2190i	−0.226265	−	0.954001i
$193$	11.1617	−	19.3326i	0.803434	−	1.39159i	−0.113909	−	0.993491i	$-0.536337\pi$
$193$	11.1617	−	19.3326i	0.803434	−	1.39159i	0.917343	−	0.398098i	$-0.130330\pi$
$194$	−13.5539	+	6.03458i	−0.973112	+	0.433257i
$195$	−16.4860	+	18.0425i	−1.18059	+	1.29205i
$196$	−0.0410961	−	0.0182971i	−0.00293543	−	0.00130694i
$197$	−21.1964	+	15.4001i	−1.51018	+	1.09721i	−0.544083	+	0.839031i	$0.683122\pi$
$197$	−21.1964	+	15.4001i	−1.51018	+	1.09721i	−0.966097	+	0.258179i	$0.916878\pi$
$198$	−0.00782467	+	0.135097i	−0.000556075	+	0.00960094i
$199$	−16.6094			−1.17741			−0.588703	−	0.808349i	$-0.700361\pi$
$199$	−16.6094			−1.17741			−0.588703	+	0.808349i	$0.700361\pi$
$200$	−13.4950	−	3.74836i	−0.954238	−	0.265049i
$201$	3.72088	−	1.30614i	0.262451	−	0.0921281i
$202$	7.65412	+	1.62693i	0.538542	+	0.114471i
$203$	2.35504	+	22.4067i	0.165291	+	1.57264i
$204$	−0.124750	+	0.180448i	−0.00873422	+	0.0126339i
$205$	−2.22305	+	2.86991i	−0.155264	+	0.200443i
$206$	2.11651	+	1.53774i	0.147464	+	0.107139i
$207$	−5.37494	−	2.09720i	−0.373584	−	0.145766i
$208$	−20.7983	−	15.1108i	−1.44210	−	1.04775i
$209$	−0.0692551	+	0.0147206i	−0.00479047	+	0.00101825i
$210$	1.48925	−	13.2374i	0.102768	−	0.913467i
$211$	9.41180	+	2.00054i	0.647935	+	0.137723i	0.520145	−	0.854078i	$-0.325878\pi$
$211$	9.41180	+	2.00054i	0.647935	+	0.137723i	0.127791	+	0.991801i	$0.459211\pi$
$212$	−0.0384316	−	0.0426826i	−0.00263949	−	0.00293146i
$213$	6.64767	−	4.04862i	0.455491	−	0.277407i
$214$	17.6466	−	19.5985i	1.20630	−	1.33973i
$215$	19.0772	−	16.1434i	1.30106	−	1.10097i
$216$	−9.36139	−	11.1455i	−0.636962	−	0.758354i
$217$	−7.32892	−	5.32477i	−0.497520	−	0.361469i
$218$	−3.22584	−	5.58731i	−0.218481	−	0.378421i
$219$	−0.492063	−	2.07468i	−0.0332505	−	0.140194i
$220$	−0.00115663	+	0.00239670i	−7.79797e−5	+	0.000161585i
$221$	−2.21824	−	21.1051i	−0.149215	−	1.41968i
$222$	11.0608	+	23.3544i	0.742353	+	1.56744i
$223$	−17.3409	+	19.2591i	−1.16124	+	1.28968i	−0.211235	+	0.977435i	$0.567749\pi$
$223$	−17.3409	+	19.2591i	−1.16124	+	1.28968i	−0.950001	+	0.312248i	$0.898918\pi$
$224$	0.513268			0.0342942
$225$	−14.7163	+	2.90376i	−0.981084	+	0.193584i
$226$	5.32179			0.354000
$227$	13.4978	−	14.9908i	0.895881	−	0.994977i	−0.104119	−	0.994565i	$-0.533202\pi$
$227$	13.4978	−	14.9908i	0.895881	−	0.994977i	1.00000		0.000411914i	$-0.000131116\pi$
$228$	−0.0831162	+	0.120226i	−0.00550450	+	0.00796215i
$229$	0.727435	+	6.92109i	0.0480703	+	0.457358i	0.991909	+	0.126951i	$0.0405193\pi$
$229$	0.727435	+	6.92109i	0.0480703	+	0.457358i	−0.943839	+	0.330407i	$0.892814\pi$
$230$	−4.43351	−	4.24588i	−0.292337	−	0.279965i
$231$	0.126343	+	0.0378023i	0.00831275	+	0.00248721i
$232$	13.0964	+	22.6836i	0.859820	+	1.48925i
$233$	−22.8409	−	16.5949i	−1.49636	−	1.08717i	−0.971805	−	0.235787i	$-0.924233\pi$
$233$	−22.8409	−	16.5949i	−1.49636	−	1.08717i	−0.524551	−	0.851379i	$-0.675767\pi$
$234$	−26.6674	−	4.37404i	−1.74330	−	0.285940i
$235$	1.68064	−	6.86218i	0.109633	−	0.447639i
$236$	−0.323201	+	0.358951i	−0.0210386	+	0.0233657i
$237$	−1.39843	−	0.764266i	−0.0908376	−	0.0496444i
$238$	7.73951	+	8.59560i	0.501678	+	0.557170i
$239$	−4.35020	−	0.924664i	−0.281391	−	0.0598115i	0.0650541	−	0.997882i	$-0.479278\pi$
$239$	−4.35020	−	0.924664i	−0.281391	−	0.0598115i	−0.346445	+	0.938070i	$0.612611\pi$
$240$	−4.76586	−	15.0412i	−0.307635	−	0.970904i
$241$	−14.8371	+	3.15373i	−0.955743	+	0.203149i	−0.659282	−	0.751895i	$-0.729140\pi$
$241$	−14.8371	+	3.15373i	−0.955743	+	0.203149i	−0.296461	+	0.955045i	$0.595806\pi$
$242$	12.7021	+	9.22865i	0.816525	+	0.593240i
$243$	−14.3186	−	6.16270i	−0.918536	−	0.395337i
$244$	−0.323612	−	0.235118i	−0.0207171	−	0.0150519i
$245$	2.51356	+	0.903035i	0.160586	+	0.0576928i
$246$	−4.00069	−	0.325922i	−0.255075	−	0.0207800i
$247$	−1.47793	−	14.0616i	−0.0940385	−	0.894717i
$248$	−10.3016	−	2.18967i	−0.654152	−	0.139044i
$249$	1.78092	−	9.46384i	0.112861	−	0.599746i
$250$	−15.6510	−	3.12305i	−0.989857	−	0.197519i
$251$	−14.0348			−0.885869			−0.442935	−	0.896554i	$-0.646063\pi$
$251$	−14.0348			−0.885869			−0.442935	+	0.896554i	$0.646063\pi$
$252$	0.243241	−	0.122259i	0.0153227	−	0.00770157i
$253$	0.0491663	−	0.0357214i	0.00309106	−	0.00224579i
$254$	12.9168	+	5.75093i	0.810472	+	0.360845i
$255$	6.59455	−	11.2316i	0.412967	−	0.703351i
$256$	0.825455	−	0.367516i	0.0515909	−	0.0229698i
$257$	−4.76132	+	8.24684i	−0.297003	+	0.514424i	−0.975449	−	0.220226i	$-0.929320\pi$
$257$	−4.76132	+	8.24684i	−0.297003	+	0.514424i	0.678446	+	0.734650i	$0.262654\pi$
$258$	26.4733	+	7.92091i	1.64815	+	0.493134i
$259$	24.6327	−	5.23585i	1.53060	−	0.325340i
$260$	−0.451849	−	0.279739i	−0.0280225	−	0.0173487i
$261$	23.4420	+	15.4072i	1.45103	+	0.953682i
$262$	0.390622	−	1.20221i	0.0241327	−	0.0742728i
$263$	−23.7423	+	5.04659i	−1.46402	+	0.311186i	−0.869914	−	0.493204i	$-0.835826\pi$
$263$	−23.7423	+	5.04659i	−1.46402	+	0.311186i	−0.594101	+	0.804390i	$0.702492\pi$
$264$	0.152058	−	0.0195941i	0.00935855	−	0.00120593i
$265$	2.46280	+	2.35858i	0.151289	+	0.144886i
$266$	5.15656	+	5.72694i	0.316169	+	0.351141i
$267$	1.20615	+	5.08549i	0.0738153	+	0.311227i
$268$	0.0428739	+	0.0742598i	0.00261894	+	0.00453614i
$269$	−12.9182	−	9.38564i	−0.787638	−	0.572252i	0.119624	−	0.992819i	$-0.461831\pi$
$269$	−12.9182	−	9.38564i	−0.787638	−	0.572252i	−0.907262	+	0.420567i	$0.861831\pi$
$270$	−11.5767	−	11.8771i	−0.704534	−	0.722816i
$271$	11.6010	−	8.42860i	0.704709	−	0.512001i	−0.176754	−	0.984255i	$-0.556560\pi$
$271$	11.6010	−	8.42860i	0.704709	−	0.512001i	0.881462	+	0.472254i	$0.156560\pi$
$272$	12.5157	+	5.57236i	0.758877	+	0.337874i
$273$	−10.1450	+	24.3030i	−0.614001	+	1.47089i
$274$	7.98875	−	13.8369i	0.482618	−	0.835919i
$275$	0.0579665	−	0.146982i	0.00349551	−	0.00886336i
$276$	0.0232012	−	0.123291i	0.00139655	−	0.00742127i
$277$	−10.5642	+	11.7327i	−0.634740	+	0.704950i	−0.971607	−	0.236602i	$-0.923966\pi$
$277$	−10.5642	+	11.7327i	−0.634740	+	0.704950i	0.336867	+	0.941552i	$0.390633\pi$
$278$	0.0465246	−	0.0338021i	0.00279036	−	0.00202732i
$279$	−10.9108	+	2.85939i	−0.653214	+	0.171187i
$280$	−15.0507	+	1.11540i	−0.899453	+	0.0666580i
$281$	0.154395	−	1.46897i	0.00921045	−	0.0876316i	−0.988951	−	0.148243i	$-0.952638\pi$
$281$	0.154395	−	1.46897i	0.00921045	−	0.0876316i	0.998161	+	0.0606112i	$0.0193050\pi$
$282$	7.37090	−	2.58741i	0.438931	−	0.154078i
$283$	−12.4438	+	5.54033i	−0.739706	+	0.329338i	−0.741765	−	0.670660i	$-0.766011\pi$
$283$	−12.4438	+	5.54033i	−0.739706	+	0.329338i	0.00205936	+	0.999998i	$0.499344\pi$
$284$	0.113248	+	0.125774i	0.00672002	+	0.00746334i
$285$	4.39371	−	7.48321i	0.260261	−	0.443267i
$286$	0.190468	−	0.211536i	0.0112626	−	0.0125084i
$287$	−1.20879	+	3.72026i	−0.0713523	+	0.219600i
$288$	0.404898	−	0.494428i	0.0238588	−	0.0291345i
$289$	−1.75857	−	5.41233i	−0.103445	−	0.318372i
$290$	16.7927	+	24.6742i	0.986104	+	1.44892i
$291$	15.7971	+	8.63339i	0.926041	+	0.506098i
$292$	0.0423555	−	0.0188579i	0.00247867	−	0.00110357i
$293$	−8.13530	+	14.0908i	−0.475270	+	0.823191i	−0.999599	−	0.0283246i	$-0.990983\pi$
$293$	−8.13530	+	14.0908i	−0.475270	+	0.823191i	0.524329	+	0.851516i	$0.324316\pi$
$294$	0.681518	+	2.87348i	0.0397469	+	0.167585i
$295$	17.5615	−	22.6715i	1.02247	−	1.31998i
$296$	23.6856	−	17.2086i	1.37669	−	1.00023i
$297$	0.136082	−	0.0918844i	0.00789627	−	0.00533167i
$298$	−3.57072	−	10.9895i	−0.206846	−	0.636607i
$299$	6.06810	+	10.5103i	0.350927	+	0.607824i
$300$	−0.121229	−	0.302797i	−0.00699918	−	0.0174820i
$301$	13.4645	−	23.3212i	0.776082	−	1.34421i
$302$	−12.9380	−	2.75006i	−0.744499	−	0.158248i
$303$	−4.06406	−	8.58106i	−0.233474	−	0.492969i
$304$	8.33877	+	3.71266i	0.478262	+	0.212936i
$305$	20.1925	+	12.5012i	1.15622	+	0.715815i
$306$	14.3855	−	0.674678i	0.822364	−	0.0385688i
$307$	14.3507			0.819040			0.409520	−	0.912301i	$-0.365696\pi$
$307$	14.3507			0.819040			0.409520	+	0.912301i	$0.365696\pi$
$308$	−0.000299742		0.00285185i	−1.70794e−5		0.000162499i
$309$	−0.0743775	−	3.17350i	−0.00423119	−	0.180534i
$310$	−11.8909	−	1.62073i	−0.675357	−	0.0920512i
$311$	21.9008	+	4.65515i	1.24188	+	0.263970i	0.781586	−	0.623797i	$-0.214411\pi$
$311$	21.9008	+	4.65515i	1.24188	+	0.263970i	0.460293	+	0.887767i	$0.347744\pi$
$312$	0.717370	+	30.6084i	0.0406131	+	1.73286i
$313$	23.9037	−	5.08090i	1.35112	−	0.287189i	0.525200	−	0.850979i	$-0.323990\pi$
$313$	23.9037	−	5.08090i	1.35112	−	0.287189i	0.825919	+	0.563789i	$0.190657\pi$
$314$	5.12170	+	15.7630i	0.289035	+	0.889557i
$315$	−13.8657	+	8.30620i	−0.781243	+	0.468001i
$316$	0.0107082	−	0.0329566i	0.000602385	−	0.00185395i
$317$	−1.80810	+	17.2029i	−0.101553	+	0.966213i	0.818523	+	0.574474i	$0.194793\pi$
$317$	−1.80810	+	17.2029i	−0.101553	+	0.966213i	−0.920076	+	0.391740i	$0.871873\pi$
$318$	−0.697302	+	3.70547i	−0.0391028	+	0.207792i
$319$	−0.269934	+	0.120182i	−0.0151134	+	0.00672892i
$320$	−15.4517	+	8.29848i	−0.863778	+	0.463899i
$321$	−31.8939	−	2.59829i	−1.78015	−	0.145022i
$322$	−6.04286	−	2.69045i	−0.336755	−	0.149933i
$323$	2.32840	+	7.16609i	0.129556	+	0.398732i
$324$	0.0741126	−	0.330758i	0.00411736	−	0.0183754i
$325$	27.9812	+	14.5805i	1.55212	+	0.808779i
$326$	4.28776	+	7.42662i	0.237477	+	0.411323i
$327$	−3.01561	+	7.22414i	−0.166764	+	0.399496i
$328$	0.475356	+	4.52271i	0.0262472	+	0.249725i
$329$	−0.795762	−	7.57117i	−0.0438718	−	0.417412i
$330$	0.171145	−	0.0350720i	0.00942124	−	0.00193065i
$331$	2.74019	−	26.0711i	0.150614	−	1.43300i	−0.614404	−	0.788991i	$-0.710604\pi$
$331$	2.74019	−	26.0711i	0.150614	−	1.43300i	0.765019	−	0.644008i	$-0.222730\pi$
$332$	0.209396			0.0114921
$333$	14.3882	−	27.8589i	0.788467	−	1.52666i
$334$	5.96444	−	18.3567i	0.326360	−	1.00443i
$335$	−2.86439	−	4.20875i	−0.156498	−	0.229949i
$336$	−10.3129	−	13.5168i	−0.562616	−	0.737401i
$337$	10.8044	+	11.9995i	0.588553	+	0.653654i	0.961696	−	0.274120i	$-0.0883864\pi$
$337$	10.8044	+	11.9995i	0.588553	+	0.653654i	−0.373143	+	0.927774i	$0.621720\pi$
$338$	25.6189	+	28.4526i	1.39348	+	1.54762i
$339$	−3.91688	−	5.13372i	−0.212736	−	0.278825i
$340$	0.266529	+	0.0957544i	0.0144545	+	0.00519301i
$341$	0.0367138	−	0.112993i	0.00198816	−	0.00611893i
$342$	9.58454	−	0.449514i	0.518273	−	0.0243069i
$343$	19.7443			1.06609
$344$	3.27245	−	31.1353i	0.176439	−	1.67870i
$345$	−0.832731	+	7.40182i	−0.0448327	+	0.398501i
$346$	1.00949	+	9.60465i	0.0542705	+	0.516349i
$347$	1.95974	+	18.6457i	0.105205	+	1.00095i	0.912019	+	0.410149i	$0.134523\pi$
$347$	1.95974	+	18.6457i	0.105205	+	1.00095i	−0.806814	+	0.590806i	$0.798810\pi$
$348$	−0.234972	+	0.562894i	−0.0125958	+	0.0301743i
$349$	−0.899591	−	1.55814i	−0.0481540	−	0.0834051i	0.840944	−	0.541123i	$-0.182000\pi$
$349$	−0.899591	−	1.55814i	−0.0481540	−	0.0834051i	−0.889098	+	0.457717i	$0.848667\pi$
$350$	−17.0093	+	2.53503i	−0.909188	+	0.135503i
$351$	15.4080	+	28.9443i	0.822417	+	1.54493i
$352$	0.00208013	+	0.00640199i	0.000110871	+	0.000341227i
$353$	−1.67743	−	0.746839i	−0.0892805	−	0.0397502i	0.361610	−	0.932329i	$-0.382227\pi$
$353$	−1.67743	−	0.746839i	−0.0892805	−	0.0397502i	−0.450891	+	0.892579i	$0.648894\pi$
$354$	31.6043	+	2.57469i	1.67975	+	0.136843i
$355$	−7.25723	−	6.95010i	−0.385174	−	0.368873i
$356$	−0.103822	+	0.0462247i	−0.00550257	+	0.00244990i
$357$	2.59549	−	13.7924i	0.137368	−	0.729973i
$358$	1.07407	−	10.2190i	0.0567661	−	0.540093i
$359$	−10.8516	+	33.3977i	−0.572724	+	1.76266i	0.0710775	+	0.997471i	$0.477356\pi$
$359$	−10.8516	+	33.3977i	−0.572724	+	1.76266i	−0.643802	+	0.765192i	$0.722644\pi$
$360$	−10.7985	+	15.3782i	−0.569131	+	0.810501i
$361$	−4.31999	−	13.2956i	−0.227368	−	0.699767i
$362$	−9.61096	+	2.04287i	−0.505141	+	0.107371i
$363$	−0.446373	−	19.0456i	−0.0234285	−	0.999635i
$364$	−0.560131	−	0.119060i	−0.0293589	−	0.00624042i
$365$	−2.42510	+	1.30242i	−0.126935	+	0.0681717i
$366$	0.615279	+	26.2524i	0.0321612	+	1.37223i
$367$	−2.51317	+	23.9112i	−0.131186	+	1.24815i	0.708747	+	0.705463i	$0.249261\pi$
$367$	−2.51317	+	23.9112i	−0.131186	+	1.24815i	−0.839933	+	0.542690i	$0.817406\pi$
$368$	−7.83493			−0.408424
$369$	2.63014	+	4.09919i	0.136919	+	0.213395i
$370$	25.4664	−	21.5501i	1.32394	−	1.12034i
$371$	3.35680	+	1.49454i	0.174276	+	0.0775928i
$372$	−0.104978	−	0.221657i	−0.00544288	−	0.0114924i
$373$	−1.97274	−	0.419319i	−0.102145	−	0.0217115i	0.156556	−	0.987669i	$-0.449961\pi$
$373$	−1.97274	−	0.419319i	−0.102145	−	0.0217115i	−0.258700	+	0.965958i	$0.583294\pi$
$374$	−0.0758467	+	0.131370i	−0.00392194	+	0.00679300i
$375$	8.50659	+	17.3965i	0.439278	+	0.898351i
$376$	−4.42524	−	7.66473i	−0.228214	−	0.395278i
$377$	−18.2340	−	56.1186i	−0.939100	−	2.89025i
$378$	−16.0669	−	7.82672i	−0.826394	−	0.402563i
$379$	−15.2526	+	11.0817i	−0.783474	+	0.569227i	−0.906020	−	0.423236i	$-0.860894\pi$
$379$	−15.2526	+	11.0817i	−0.783474	+	0.569227i	0.122546	+	0.992463i	$0.460894\pi$
$380$	0.177578	+	0.0637977i	0.00910958	+	0.00327275i
$381$	−3.95918	−	16.6930i	−0.202835	−	0.855211i
$382$	−8.06032	+	13.9609i	−0.412402	+	0.714301i
$383$	10.1089	−	4.50077i	0.516541	−	0.229979i	−0.131873	−	0.991267i	$-0.542099\pi$
$383$	10.1089	−	4.50077i	0.516541	−	0.229979i	0.648414	+	0.761288i	$0.275433\pi$
$384$	−17.6651	−	9.65431i	−0.901469	−	0.492669i
$385$	0.00523367	−	0.170172i	0.000266732	−	0.00867276i
$386$	−9.84708	−	30.3062i	−0.501203	−	1.54254i
$387$	−11.8435	−	31.3675i	−0.602041	−	1.59450i
$388$	−0.120964	+	0.372288i	−0.00614100	+	0.0189000i
$389$	−14.4803	+	16.0820i	−0.734181	+	0.815391i	−0.988419	−	0.151751i	$-0.951509\pi$
$389$	−14.4803	+	16.0820i	−0.734181	+	0.815391i	0.254238	+	0.967142i	$0.418175\pi$
$390$	3.39292	+	34.7222i	0.171807	+	1.75823i
$391$	−4.32763	−	4.80632i	−0.218858	−	0.243066i
$392$	3.05658	−	1.36088i	0.154380	−	0.0687346i
$393$	−1.44722	+	0.508019i	−0.0730028	+	0.0256262i
$394$	−3.90935	+	37.1950i	−0.196950	+	1.87386i
$395$	−0.489416	+	1.99833i	−0.0246252	+	0.100547i
$396$	0.00251072	+	0.00253846i	0.000126168	+	0.000127562i
$397$	6.42510	−	4.66811i	0.322467	−	0.234286i	−0.414761	−	0.909931i	$-0.636135\pi$
$397$	6.42510	−	4.66811i	0.322467	−	0.234286i	0.737227	+	0.675645i	$0.236135\pi$
$398$	−15.8646	+	17.6195i	−0.795222	+	0.883184i
$399$	1.72928	−	9.18940i	0.0865722	−	0.460045i
$400$	−17.1839	+	10.9376i	−0.859196	+	0.546880i
$401$	6.27204	−	10.8635i	0.313211	−	0.542497i	−0.665845	−	0.746090i	$-0.731929\pi$
$401$	6.27204	−	10.8635i	0.313211	−	0.542497i	0.979056	+	0.203593i	$0.0652621\pi$
$402$	2.16847	−	5.19474i	0.108154	−	0.259090i
$403$	21.6745	+	9.65011i	1.07968	+	0.480706i
$404$	0.167027	−	0.121352i	0.00830992	−	0.00603751i
$405$	−2.93680	+	19.9092i	−0.145931	+	0.989295i
$406$	26.0188	+	18.9038i	1.29129	+	0.938178i
$407$	0.165136	+	0.286024i	0.00818549	+	0.0141777i
$408$	−3.76531	−	15.8756i	−0.186411	−	0.785962i
$409$	−2.96912	−	3.29754i	−0.146813	−	0.163053i	0.665253	−	0.746618i	$-0.268324\pi$
$409$	−2.96912	−	3.29754i	−0.146813	−	0.163053i	−0.812066	+	0.583565i	$0.801657\pi$
$410$	0.921069	+	5.09947i	0.0454884	+	0.251845i
$411$	−19.2277	+	2.47766i	−0.948433	+	0.122214i
$412$	0.0675159	−	0.0143510i	0.00332627	−	0.000707021i
$413$	9.54906	−	29.3890i	0.469879	−	1.44614i
$414$	−7.35868	+	3.69865i	−0.361659	+	0.181779i
$415$	−12.3982	+	0.918825i	−0.608604	+	0.0451034i
$416$	−1.31488	+	0.279486i	−0.0644672	+	0.0137029i
$417$	−0.0668500	−	0.0200018i	−0.00327366	−	0.000979492i
$418$	−0.0505340	+	0.0875274i	−0.00247170	+	0.00428110i
$419$	−6.70380	+	2.98472i	−0.327502	+	0.145813i	−0.563900	−	0.825843i	$-0.690700\pi$
$419$	−6.70380	+	2.98472i	−0.327502	+	0.145813i	0.236398	+	0.971656i	$0.424033\pi$
$420$	−0.233255	−	0.262896i	−0.0113817	−	0.0128280i
$421$	−7.15154	−	3.18407i	−0.348545	−	0.155182i	0.224995	−	0.974360i	$-0.427763\pi$
$421$	−7.15154	−	3.18407i	−0.348545	−	0.155182i	−0.573540	+	0.819178i	$0.694430\pi$
$422$	11.1120	−	8.07334i	0.540924	−	0.393004i
$423$	−7.92101	−	5.20606i	−0.385132	−	0.253127i
$424$	4.27182			0.207458
$425$	−16.2012	−	4.50004i	−0.785872	−	0.218284i
$426$	2.05477	−	10.9190i	0.0995537	−	0.529029i
$427$	25.0316	+	5.32062i	1.21136	+	0.257483i
$428$	−0.0727316	−	0.691995i	−0.00351562	−	0.0334488i
$429$	−0.344246	−	0.0280445i	−0.0166204	−	0.00135400i
$430$	1.09664	−	35.6570i	0.0528845	−	1.71953i
$431$	10.2026	+	7.41261i	0.491441	+	0.357053i	0.805738	−	0.592272i	$-0.201769\pi$
$431$	10.2026	+	7.41261i	0.491441	+	0.357053i	−0.314297	+	0.949325i	$0.601769\pi$
$432$	−21.1561	−	0.728511i	−1.01787	−	0.0350505i
$433$	30.3440	+	22.0462i	1.45824	+	1.05947i	0.983817	+	0.179179i	$0.0573441\pi$
$433$	30.3440	+	22.0462i	1.45824	+	1.05947i	0.474425	+	0.880296i	$0.342656\pi$
$434$	−12.6489	+	2.68861i	−0.607167	+	0.129057i
$435$	11.4426	−	34.3596i	0.548630	−	1.64742i
$436$	−0.166501	−	0.0353908i	−0.00797393	−	0.00169491i
$437$	−2.88334	−	3.20228i	−0.137929	−	0.153186i
$438$	−2.67085	−	1.45967i	−0.127618	−	0.0697457i
$439$	23.3463	−	25.9287i	1.11426	−	1.23751i	0.145536	−	0.989353i	$-0.453509\pi$
$439$	23.3463	−	25.9287i	1.11426	−	1.23751i	0.968721	−	0.248154i	$-0.0798239\pi$
$440$	−0.0749088	−	0.183207i	−0.00357114	−	0.00873406i
$441$	2.27033	−	2.77234i	0.108111	−	0.132016i
$442$	−24.5074	−	17.8057i	−1.16570	−	0.846929i
$443$	−12.2771	−	21.2646i	−0.583304	−	1.01031i	−0.995085	−	0.0990295i	$-0.968426\pi$
$443$	−12.2771	−	21.2646i	−0.583304	−	1.01031i	0.411780	−	0.911283i	$-0.364907\pi$
$444$	0.653181	+	0.195434i	0.0309986	+	0.00927490i
$445$	5.94443	−	3.19251i	0.281793	−	0.151339i
$446$	3.86690	+	36.7911i	0.183103	+	1.74211i
$447$	−7.97309	+	11.5329i	−0.377114	+	0.545488i
$448$	−12.6461	+	14.0449i	−0.597471	+	0.663558i
$449$	5.69752			0.268882			0.134441	−	0.990922i	$-0.457076\pi$
$449$	5.69752			0.268882			0.134441	+	0.990922i	$0.457076\pi$
$450$	−10.9761	+	18.3848i	−0.517416	+	0.866667i
$451$	−0.0513016			−0.00241570
$452$	0.0939523	−	0.104345i	0.00441915	−	0.00490796i
$453$	6.86961	+	14.5048i	0.322762	+	0.681497i
$454$	−3.00991	−	28.6374i	−0.141262	−	1.34402i
$455$	33.6875	+	4.59160i	1.57929	+	0.215258i
$456$	−2.50869	−	10.5774i	−0.117480	−	0.495331i
$457$	−14.9907	−	25.9647i	−0.701238	−	1.21458i	−0.968032	−	0.250826i	$-0.919298\pi$
$457$	−14.9907	−	25.9647i	−0.701238	−	1.21458i	0.266795	−	0.963753i	$-0.414035\pi$
$458$	8.03681	+	5.83908i	0.375535	+	0.272842i
$459$	−11.2387	−	13.3805i	−0.524576	−	0.624550i
$460$	−0.161519	+	0.0119701i	−0.00753088	+	0.000558110i
$461$	−3.32317	+	3.69076i	−0.154776	+	0.171896i	−0.815546	−	0.578693i	$-0.803563\pi$
$461$	−3.32317	+	3.69076i	−0.154776	+	0.171896i	0.660770	+	0.750588i	$0.270230\pi$
$462$	0.160779	−	0.0979190i	0.00748012	−	0.00455560i
$463$	7.65307	+	8.49959i	0.355668	+	0.395009i	0.894253	−	0.447562i	$-0.147708\pi$
$463$	7.65307	+	8.49959i	0.355668	+	0.395009i	−0.538585	+	0.842571i	$0.681041\pi$
$464$	37.2612	+	7.92011i	1.72981	+	0.367682i
$465$	7.18834	+	12.6635i	0.333351	+	0.587257i
$466$	−39.4208	+	8.37915i	−1.82613	+	0.388157i
$467$	21.2823	+	15.4625i	0.984827	+	0.715518i	0.958782	−	0.284142i	$-0.0917088\pi$
$467$	21.2823	+	15.4625i	0.984827	+	0.715518i	0.0260445	+	0.999661i	$0.491709\pi$
$468$	−0.556556	+	0.445649i	−0.0257268	+	0.0206002i
$469$	−4.43811	−	3.22447i	−0.204933	−	0.148892i
$470$	−5.67422	−	8.33734i	−0.261732	−	0.384573i
$471$	11.4363	−	16.5424i	0.526957	−	0.762233i
$472$	−3.75518	−	35.7282i	−0.172846	−	1.64452i
$473$	0.345453	+	0.0734284i	0.0158840	+	0.00337624i
$474$	−2.14647	+	0.753475i	−0.0985906	+	0.0346082i
$475$	−10.7943	−	2.99821i	−0.495275	−	0.137568i
$476$	0.305170			0.0139874
$477$	4.08773	−	2.05459i	0.187164	−	0.0940733i
$478$	−5.13604	+	3.73155i	−0.234917	+	0.170677i
$479$	0.427614	+	0.190386i	0.0195382	+	0.00869896i	0.416482	−	0.909144i	$-0.363263\pi$
$479$	0.427614	+	0.190386i	0.0195382	+	0.00869896i	−0.396944	+	0.917843i	$0.629929\pi$
$480$	−0.751225	−	0.341071i	−0.0342886	−	0.0155677i
$481$	−60.2525	+	26.8261i	−2.74728	+	1.22317i
$482$	−10.8263	+	18.7518i	−0.493126	+	0.854119i
$483$	1.85222	+	7.80950i	0.0842789	+	0.355344i
$484$	0.405194	−	0.0861265i	0.0184179	−	0.00391484i
$485$	5.52859	−	22.5737i	0.251041	−	1.02502i
$486$	−20.2140	+	9.30297i	−0.916927	+	0.421991i
$487$	1.55836	−	4.79614i	0.0706160	−	0.217334i	−0.909520	−	0.415660i	$-0.863551\pi$
$487$	1.55836	−	4.79614i	0.0706160	−	0.217334i	0.980136	+	0.198326i	$0.0635506\pi$
$488$	29.1009	−	6.18558i	1.31733	−	0.280008i
$489$	4.00834	−	9.60229i	0.181263	−	0.434230i
$490$	3.35881	−	1.80388i	0.151736	−	0.0814909i
$491$	−5.02924	−	5.58554i	−0.226966	−	0.252072i	0.618896	−	0.785473i	$-0.287580\pi$
$491$	−5.02924	−	5.58554i	−0.226966	−	0.252072i	−0.845862	+	0.533401i	$0.820914\pi$
$492$	−0.0770197	+	0.0726878i	−0.00347231	+	0.00327702i
$493$	15.7227	+	27.2325i	0.708113	+	1.22649i
$494$	−16.3284	−	11.8633i	−0.734649	−	0.533754i
$495$	−0.159797	−	0.139284i	−0.00718233	−	0.00626034i
$496$	−12.3916	+	9.00306i	−0.556401	+	0.404249i
$497$	−9.89159	−	4.40402i	−0.443699	−	0.197547i
$498$	−8.33831	−	10.9287i	−0.373648	−	0.489728i
$499$	4.05527	−	7.02394i	0.181539	−	0.314435i	−0.760866	−	0.648909i	$-0.775225\pi$
$499$	4.05527	−	7.02394i	0.181539	−	0.314435i	0.942405	+	0.334474i	$0.108559\pi$
$500$	−0.337541	+	0.251735i	−0.0150953	+	0.0112579i
$501$	−22.0978	+	7.75699i	−0.987257	+	0.346557i
$502$	−13.4055	+	14.8883i	−0.598317	+	0.664499i
$503$	−16.3455	+	11.8757i	−0.728812	+	0.529513i	−0.889187	−	0.457543i	$-0.848729\pi$
$503$	−16.3455	+	11.8757i	−0.728812	+	0.529513i	0.160376	+	0.987056i	$0.448729\pi$
$504$	−5.34796	+	19.5290i	−0.238217	+	0.869892i
$505$	−9.35710	+	7.91812i	−0.416385	+	0.352352i
$506$	0.00906799	−	0.0862761i	0.000403121	−	0.00383544i
$507$	8.59142	−	45.6548i	0.381558	−	2.02760i
$508$	0.340795	−	0.151732i	0.0151204	−	0.00673201i
$509$	14.0043	+	15.5533i	0.620728	+	0.689389i	0.968733	−	0.248104i	$-0.0798075\pi$
$509$	14.0043	+	15.5533i	0.620728	+	0.689389i	−0.348005	+	0.937493i	$0.613141\pi$
$510$	−5.61579	−	17.7236i	−0.248671	−	0.784814i
$511$	−1.98476	+	2.20430i	−0.0878005	+	0.0975124i
$512$	−6.78465	+	20.8810i	−0.299842	+	0.922819i
$513$	−7.48792	−	8.91497i	−0.330600	−	0.393606i
$514$	4.20054	+	12.9279i	0.185278	+	0.570227i
$515$	−3.93461	+	1.14597i	−0.173379	+	0.0504975i
$516$	0.622671	−	0.379225i	0.0274116	−	0.0166944i
$517$	0.0912101	−	0.0406093i	0.00401141	−	0.00178600i
$518$	17.9740	−	31.1318i	0.789731	−	1.36785i
$519$	8.52223	−	8.04291i	0.374084	−	0.353045i
$520$	37.9492	−	11.0529i	1.66418	−	0.484700i
$521$	5.09658	−	3.70289i	0.223285	−	0.162226i	−0.470519	−	0.882390i	$-0.655933\pi$
$521$	5.09658	−	3.70289i	0.223285	−	0.162226i	0.693804	+	0.720164i	$0.255933\pi$
$522$	38.7351	−	10.1513i	1.69539	−	0.444309i
$523$	−6.61794	−	20.3679i	−0.289382	−	0.890628i	−0.985051	−	0.172264i	$-0.944892\pi$
$523$	−6.61794	−	20.3679i	−0.289382	−	0.890628i	0.695668	−	0.718363i	$-0.255108\pi$
$524$	−0.0166756	−	0.0288831i	−0.000728479	−	0.00126176i
$525$	14.9644	+	14.5424i	0.653102	+	0.634683i
$526$	−17.3243	+	30.0065i	−0.755374	+	1.30835i
$527$	−12.3674	−	2.62878i	−0.538734	−	0.114511i
$528$	0.126799	−	0.183413i	0.00551823	−	0.00798201i
$529$	−17.6326	−	7.85055i	−0.766636	−	0.341328i
$530$	4.85439	−	0.359756i	0.210861	−	0.0156268i
$531$	−20.7773	−	32.3824i	−0.901660	−	1.40528i
$532$	0.203324			0.00881520
$533$	1.07087	−	10.1887i	0.0463847	−	0.441321i
$534$	6.54683	+	3.57796i	0.283309	+	0.154834i
$535$	7.34286	+	40.6535i	0.317459	+	1.75760i
$536$	−6.23825	−	1.32598i	−0.269451	−	0.0572736i
$537$	−10.6484	+	6.48519i	−0.459513	+	0.279857i
$538$	−22.2954	+	4.73904i	−0.961224	+	0.204314i
$539$	0.0116636	+	0.0358970i	0.000502388	+	0.00154619i
$540$	−0.437252	+	0.0173036i	−0.0188163	+	0.000744628i
$541$	2.06074	−	6.34232i	0.0885983	−	0.272678i	−0.896934	−	0.442164i	$-0.854211\pi$
$541$	2.06074	−	6.34232i	0.0885983	−	0.272678i	0.985533	+	0.169486i	$0.0542109\pi$
$542$	2.13962	−	20.3572i	0.0919047	−	0.874415i
$543$	9.04442	+	7.76774i	0.388133	+	0.333345i
$544$	0.654436	−	0.291374i	0.0280587	−	0.0124925i
$545$	10.0137	+	1.36487i	0.428939	+	0.0584644i
$546$	16.0909	+	33.9753i	0.688629	+	1.45401i
$547$	−28.9519	−	12.8902i	−1.23790	−	0.551147i	−0.319792	−	0.947488i	$-0.603613\pi$
$547$	−28.9519	−	12.8902i	−1.23790	−	0.551147i	−0.918103	+	0.396341i	$0.870280\pi$
$548$	−0.130266	−	0.400917i	−0.00556467	−	0.0171263i
$549$	24.8718	−	19.9155i	1.06150	−	0.849973i
$550$	−0.100553	−	0.201884i	−0.00428762	−	0.00860834i
$551$	10.4754	+	18.1440i	0.446269	+	0.772961i
$552$	5.65995	+	7.41830i	0.240903	+	0.315744i
$553$	0.231733	+	2.20479i	0.00985427	+	0.0937571i
$554$	2.35573	+	22.4133i	0.100085	+	0.952248i
$555$	−39.5320	−	8.70541i	−1.67804	−	0.369524i
$556$	0.000158598	−	0.00150896i	6.72606e−6	−	6.39942e-5i
$557$	−23.0896			−0.978337			−0.489168	−	0.872189i	$-0.662700\pi$
$557$	−23.0896			−0.978337			−0.489168	+	0.872189i	$0.662700\pi$
$558$	−7.38833	+	14.3056i	−0.312773	+	0.605602i
$559$	−21.7941	+	67.0755i	−0.921794	+	2.83699i
$560$	−13.4412	+	17.3523i	−0.567993	+	0.733267i
$561$	0.182552	−	0.0235234i	0.00770733	−	0.000993157i
$562$	−1.41084	−	1.56689i	−0.0595125	−	0.0660953i
$563$	−24.5755	−	27.2938i	−1.03573	−	1.15030i	−0.988470	−	0.151414i	$-0.951617\pi$
$563$	−24.5755	−	27.2938i	−1.03573	−	1.15030i	−0.0472616	−	0.998883i	$-0.515049\pi$
$564$	0.0793964	−	0.190200i	0.00334319	−	0.00800888i
$565$	−5.10500	+	6.59045i	−0.214769	+	0.277262i
$566$	−6.00856	+	18.4925i	−0.252559	+	0.777296i
$567$	4.27527	+	21.2596i	0.179544	+	0.892821i
$568$	−12.5879			−0.528177
$569$	−1.66757	+	15.8659i	−0.0699083	+	0.665133i	0.902315	+	0.431077i	$0.141866\pi$
$569$	−1.66757	+	15.8659i	−0.0699083	+	0.665133i	−0.972223	+	0.234055i	$0.924800\pi$
$570$	−3.74160	−	11.8086i	−0.156718	−	0.494608i
$571$	−0.299358	−	2.84820i	−0.0125277	−	0.119193i	0.986471	−	0.163937i	$-0.0524195\pi$
$571$	−0.299358	−	2.84820i	−0.0125277	−	0.119193i	−0.998998	+	0.0447439i	$0.985753\pi$
$572$	−0.000785026	−	0.00746903i	−3.28236e−5	−	0.000312296i
$573$	19.3999	−	2.49985i	0.810445	−	0.104433i
$574$	2.79192	+	4.83575i	0.116532	+	0.201840i
$575$	9.51094	−	1.41749i	0.396634	−	0.0591133i
$576$	3.55334	+	23.2614i	0.148056	+	0.969223i
$577$	2.14710	+	6.60811i	0.0893851	+	0.275099i	0.985750	−	0.168218i	$-0.0538014\pi$
$577$	2.14710	+	6.60811i	0.0893851	+	0.275099i	−0.896365	+	0.443318i	$0.853801\pi$
$578$	−7.42120	−	3.30413i	−0.308681	−	0.137434i
$579$	−21.9876	+	31.8047i	−0.913775	+	1.32176i
$580$	0.780251	+	0.106348i	0.0323982	+	0.00441587i
$581$	−12.2381	+	5.44877i	−0.507724	+	0.226053i
$582$	24.2472	−	8.51149i	1.00508	−	0.352813i
$583$	−0.00503725	+	0.0479262i	−0.000208622	+	0.00198490i
$584$	−1.06561	+	3.27960i	−0.0440951	+	0.135711i
$585$	30.9979	−	28.8288i	1.28160	−	1.19192i
$586$	7.17715	+	22.0890i	0.296485	+	0.912489i
$587$	−0.784085	+	0.166662i	−0.0323626	+	0.00687889i	−0.224065	−	0.974574i	$-0.571933\pi$
$587$	−0.784085	+	0.166662i	−0.0323626	+	0.00687889i	0.191702	+	0.981453i	$0.438599\pi$
$588$	0.0683722	+	0.0373666i	0.00281962	+	0.00154097i
$589$	−8.23998	−	1.75146i	−0.339522	−	0.0721677i
$590$	−7.27619	−	40.2844i	−0.299556	−	1.65848i
$591$	38.7578	−	23.6046i	1.59428	−	0.970964i
$592$	4.45073	−	42.3459i	0.182924	−	1.74041i
$593$	19.9879			0.820804			0.410402	−	0.911905i	$-0.365388\pi$
$593$	19.9879			0.820804			0.410402	+	0.911905i	$0.365388\pi$
$594$	0.0325078	−	0.232122i	0.00133381	−	0.00952408i
$595$	−18.0689	+	1.33908i	−0.740754	+	0.0548969i
$596$	−0.278511	−	0.124001i	−0.0114082	−	0.00507928i
$597$	28.6733	+	2.33591i	1.17352	+	0.0956025i
$598$	16.9455	+	3.60187i	0.692951	+	0.147291i
$599$	1.80743	−	3.13056i	0.0738495	−	0.127911i	−0.826736	−	0.562590i	$-0.809805\pi$
$599$	1.80743	−	3.13056i	0.0738495	−	0.127911i	0.900585	+	0.434679i	$0.143138\pi$
$600$	22.7696	+	8.36882i	0.929566	+	0.341656i
$601$	18.5936	+	32.2050i	0.758449	+	1.31367i	0.943642	+	0.330969i	$0.107376\pi$
$601$	18.5936	+	32.2050i	0.758449	+	1.31367i	−0.185193	+	0.982702i	$0.559291\pi$
$602$	−11.8787	−	36.5589i	−0.484140	−	1.49003i
$603$	−6.60717	+	1.73154i	−0.269065	+	0.0705136i
$604$	−0.282332	+	0.205126i	−0.0114879	+	0.00834646i
$605$	−23.6134	+	6.87748i	−0.960019	+	0.279609i
$606$	−12.9847	−	3.88509i	−0.527469	−	0.157821i
$607$	−16.6597	+	28.8555i	−0.676197	+	1.17121i	0.299920	+	0.953964i	$0.403040\pi$
$607$	−16.6597	+	28.8555i	−0.676197	+	1.17121i	−0.976117	+	0.217244i	$0.930293\pi$
$608$	0.436027	−	0.194132i	0.0176832	−	0.00787309i
$609$	−0.914341	−	39.0126i	−0.0370510	−	1.58087i
$610$	32.5486	−	9.47990i	1.31785	−	0.383830i
$611$	6.16123	+	18.9623i	0.249257	+	0.767134i
$612$	0.240737	−	0.293968i	0.00973122	−	0.0118830i
$613$	1.94595	−	5.98902i	0.0785962	−	0.241894i	−0.904037	−	0.427455i	$-0.859410\pi$
$613$	1.94595	−	5.98902i	0.0785962	−	0.241894i	0.982633	+	0.185561i	$0.0594102\pi$
$614$	13.7073	−	15.2235i	0.553181	−	0.614370i
$615$	4.24134	−	4.64177i	0.171027	−	0.187174i
$616$	−0.142711	−	0.158497i	−0.00575001	−	0.00638603i
$617$	24.1693	−	10.7608i	0.973018	−	0.433215i	0.142248	−	0.989831i	$-0.454567\pi$
$617$	24.1693	−	10.7608i	0.973018	−	0.433215i	0.830770	+	0.556616i	$0.187900\pi$
$618$	−3.43754	−	2.95230i	−0.138278	−	0.118759i
$619$	1.63835	−	15.5879i	0.0658508	−	0.626529i	−0.910970	−	0.412472i	$-0.864666\pi$
$619$	1.63835	−	15.5879i	0.0658508	−	0.626529i	0.976821	−	0.214057i	$-0.0686678\pi$
$620$	−0.241703	+	0.204533i	−0.00970701	+	0.00821423i
$621$	8.98398	+	4.37639i	0.360515	+	0.175618i
$622$	25.8570	−	18.7862i	1.03677	−	0.753260i
$623$	4.86507	−	5.40320i	0.194915	−	0.216475i
$624$	33.7796	+	29.0113i	1.35226	+	1.16138i
$625$	18.8810	−	16.3862i	0.755240	−	0.655448i
$626$	17.4420	−	30.2105i	0.697124	−	1.20745i
$627$	0.121628	−	0.0156728i	0.00485733	−	0.000625910i
$628$	0.399486	+	0.177862i	0.0159412	+	0.00709748i
$629$	28.4353	−	20.6595i	1.13379	−	0.823748i
$630$	−4.43263	+	22.6427i	−0.176600	+	0.902106i
$631$	1.57126	+	1.14159i	0.0625508	+	0.0454458i	0.618621	−	0.785689i	$-0.287692\pi$
$631$	1.57126	+	1.14159i	0.0625508	+	0.0454458i	−0.556070	+	0.831135i	$0.687692\pi$
$632$	1.28867	+	2.23204i	0.0512604	+	0.0887856i
$633$	−15.9665	−	4.77726i	−0.634613	−	0.189879i
$634$	16.5221	+	18.3497i	0.656176	+	0.728758i
$635$	−19.5125	+	10.4794i	−0.774330	+	0.415861i
$636$	0.0603429	+	0.0790893i	0.00239275	+	0.00313610i
$637$	−7.37273	+	1.56712i	−0.292118	+	0.0620916i
$638$	−0.130340	+	0.401144i	−0.00516019	+	0.0158814i
$639$	−12.0455	+	6.05434i	−0.476511	+	0.239506i
$640$	−6.18236	+	25.2431i	−0.244379	+	0.997822i
$641$	−16.3424	+	3.47368i	−0.645484	+	0.137202i	−0.519010	−	0.854768i	$-0.673699\pi$
$641$	−16.3424	+	3.47368i	−0.645484	+	0.137202i	−0.126474	+	0.991970i	$0.540366\pi$
$642$	−33.2202	+	31.3518i	−1.31110	+	1.23736i
$643$	15.9436	−	27.6151i	0.628753	−	1.08903i	−0.359050	−	0.933319i	$-0.616899\pi$
$643$	15.9436	−	27.6151i	0.628753	−	1.08903i	0.987802	−	0.155713i	$-0.0497676\pi$
$644$	−0.159434	+	0.0709846i	−0.00628258	+	0.00279719i
$645$	−35.2040	+	25.1859i	−1.38616	+	0.991695i
$646$	9.82589	+	4.37477i	0.386595	+	0.172123i
$647$	16.4808	−	11.9740i	0.647928	−	0.470747i	−0.214637	−	0.976694i	$-0.568857\pi$
$647$	16.4808	−	11.9740i	0.647928	−	0.470747i	0.862565	+	0.505947i	$0.168857\pi$
$648$	14.5934	+	20.5574i	0.573282	+	0.807570i
$649$	0.405268			0.0159082
$650$	42.1937	−	15.7561i	1.65497	−	0.618007i
$651$	11.9033	+	10.2231i	0.466526	+	0.400673i
$652$	0.221312	+	0.0470412i	0.00866723	+	0.00184228i
$653$	−3.91951	−	37.2917i	−0.153382	−	1.45934i	−0.752456	−	0.658642i	$-0.771131\pi$
$653$	−3.91951	−	37.2917i	−0.153382	−	1.45934i	0.599074	−	0.800694i	$-0.295536\pi$
$654$	4.78307	+	10.0992i	0.187033	+	0.394911i
$655$	1.11409	+	1.63698i	0.0435312	+	0.0639620i
$656$	5.35073	+	3.88754i	0.208911	+	0.151783i
$657$	0.557684	+	3.65079i	0.0217573	+	0.142431i
$658$	−8.79169	−	6.38754i	−0.342736	−	0.249012i
$659$	−24.0150	+	5.10455i	−0.935492	+	0.198845i	−0.650345	−	0.759639i	$-0.725376\pi$
$659$	−24.0150	+	5.10455i	−0.935492	+	0.198845i	−0.285147	+	0.958484i	$0.592042\pi$
$660$	0.00233379	−	0.00397483i	9.08426e−5	−	0.000154720i
$661$	6.52118	+	1.38612i	0.253645	+	0.0539138i	0.332979	−	0.942934i	$-0.391946\pi$
$661$	6.52118	+	1.38612i	0.253645	+	0.0539138i	−0.0793344	+	0.996848i	$0.525279\pi$
$662$	−25.0393	−	27.8090i	−0.973181	−	1.08083i
$663$	0.861228	+	36.7464i	0.0334473	+	1.42711i
$664$	−10.4211	+	11.5738i	−0.404418	+	0.449151i
$665$	−12.0387	+	0.892180i	−0.466840	+	0.0345973i
$666$	−15.8101	−	41.8729i	−0.612629	−	1.62254i
$667$	−14.5487	−	10.5702i	−0.563327	−	0.409281i
$668$	−0.254622	−	0.441018i	−0.00985162	−	0.0170635i
$669$	32.6448	−	30.8088i	1.26212	−	1.19114i
$670$	−7.20066	−	0.981450i	−0.278186	−	0.0379167i
$671$	0.0350818	+	0.333781i	0.00135432	+	0.0128855i
$672$	−0.886071	−	0.0721851i	−0.0341809	−	0.00278460i
$673$	8.06200	−	8.95376i	0.310767	−	0.345142i	−0.567446	−	0.823410i	$-0.692069\pi$
$673$	8.06200	−	8.95376i	0.310767	−	0.345142i	0.878214	+	0.478268i	$0.158735\pi$
$674$	23.0492			0.887822
$675$	25.8135	−	2.94319i	0.993563	−	0.113283i
$676$	1.01015			0.0388521
$677$	−16.8244	+	18.6854i	−0.646613	+	0.718137i	−0.973948	−	0.226772i	$-0.927183\pi$
$677$	−16.8244	+	18.6854i	−0.646613	+	0.718137i	0.327335	+	0.944908i	$0.393849\pi$
$678$	−9.18718	−	0.748447i	−0.352831	−	0.0287439i
$679$	−2.61773	−	24.9060i	−0.100459	−	0.955804i
$680$	−18.5570	+	9.96623i	−0.711630	+	0.382187i
$681$	−25.4100	+	23.9808i	−0.973713	+	0.918948i
$682$	−0.0847974	−	0.146873i	−0.00324706	−	0.00562408i
$683$	29.2073	+	21.2203i	1.11758	+	0.811973i	0.983841	−	0.179043i	$-0.0573002\pi$
$683$	29.2073	+	21.2203i	1.11758	+	0.811973i	0.133743	+	0.991016i	$0.457300\pi$
$684$	0.160394	−	0.195860i	0.00613283	−	0.00748891i
$685$	9.47217	+	23.1664i	0.361913	+	0.885144i
$686$	18.8590	−	20.9450i	0.720039	−	0.799685i
$687$	−0.282426	−	12.0504i	−0.0107752	−	0.459751i
$688$	−30.4664	−	33.8363i	−1.16152	−	1.29000i
$689$	−9.41317	−	2.00083i	−0.358613	−	0.0762256i
$690$	7.05657	+	7.95331i	0.268639	+	0.302777i
$691$	−7.37700	+	1.56803i	−0.280634	+	0.0596506i	−0.346078	−	0.938206i	$-0.612487\pi$
$691$	−7.37700	+	1.56803i	−0.280634	+	0.0596506i	0.0654442	+	0.997856i	$0.479154\pi$
$692$	0.206141	+	0.149770i	0.00783629	+	0.00569340i
$693$	−0.212793	−	0.0830279i	−0.00808334	−	0.00315397i
$694$	21.6515	+	15.7308i	0.821881	+	0.597131i
$695$	−0.00276922	+	0.0900406i	−0.000105042	+	0.00341544i
$696$	−19.4185	−	41.0013i	−0.736057	−	1.55415i
$697$	0.570682	+	5.42968i	0.0216161	+	0.205664i
$698$	−2.51215	−	0.533974i	−0.0950862	−	0.0202112i
$699$	37.0971	+	31.8605i	1.40314	+	1.20508i
$700$	−0.250583	+	0.378257i	−0.00947115	+	0.0142968i
$701$	−41.9293			−1.58365			−0.791824	−	0.610749i	$-0.790868\pi$
$701$	−41.9293			−1.58365			−0.791824	+	0.610749i	$0.790868\pi$
$702$	45.4217	+	11.3015i	1.71433	+	0.426547i
$703$	18.9454	−	13.7647i	0.714541	−	0.519144i
$704$	−0.226433	−	0.100814i	−0.00853400	−	0.00379958i
$705$	−3.86642	+	11.6100i	−0.145618	+	0.437259i
$706$	−2.39447	+	1.06609i	−0.0901172	+	0.0401228i
$707$	−6.60415	+	11.4387i	−0.248375	+	0.430197i
$708$	0.608434	−	0.574214i	0.0228663	−	0.0215803i
$709$	0.535037	−	0.113726i	0.0200937	−	0.00427105i	−0.197854	−	0.980232i	$-0.563397\pi$
$709$	0.535037	−	0.113726i	0.0200937	−	0.00427105i	0.217948	+	0.975960i	$0.430064\pi$
$710$	−14.3046	+	1.06011i	−0.536842	+	0.0397851i
$711$	2.30666	+	1.51605i	0.0865067	+	0.0568563i
$712$	2.61203	−	8.03900i	0.0978899	−	0.301274i
$713$	7.07276	−	1.50336i	0.264877	−	0.0563014i
$714$	−12.1521	−	15.9273i	−0.454781	−	0.596065i
$715$	0.0792549	+	0.438792i	0.00296397	+	0.0164099i
$716$	−0.181404	−	0.201469i	−0.00677937	−	0.00752925i
$717$	7.37984	+	2.20808i	0.275605	+	0.0824623i
$718$	25.0638	+	43.4117i	0.935371	+	1.62011i
$719$	−23.1267	−	16.8026i	−0.862482	−	0.626630i	0.0660771	−	0.997815i	$-0.478952\pi$
$719$	−23.1267	−	16.8026i	−0.862482	−	0.626630i	−0.928559	+	0.371185i	$0.878952\pi$
$720$	6.11209	+	26.6363i	0.227784	+	0.992678i
$721$	−3.57254	+	2.59560i	−0.133048	+	0.0966651i
$722$	−18.2304	−	8.11671i	−0.678466	−	0.302073i
$723$	26.0573	−	3.35771i	0.969083	−	0.124875i
$724$	−0.129620	+	0.224508i	−0.00481728	+	0.00834378i
$725$	−46.6649	−	2.87309i	−1.73309	−	0.106704i
$726$	−20.6302	−	17.7181i	−0.765659	−	0.657581i
$727$	26.0768	−	28.9613i	0.967136	−	1.07411i	−0.0300799	−	0.999547i	$-0.509576\pi$
$727$	26.0768	−	28.9613i	0.967136	−	1.07411i	0.997216	−	0.0745661i	$-0.0237572\pi$
$728$	34.4571	−	25.0345i	1.27706	−	0.927841i
$729$	23.8519	+	12.6526i	0.883403	+	0.468615i
$730$	−0.934734	+	3.81660i	−0.0345960	+	0.141259i
$731$	3.92869	−	37.3790i	0.145308	−	1.38251i
$732$	0.525594	+	0.451403i	0.0194265	+	0.0166843i
$733$	9.18772	−	4.09063i	0.339356	−	0.151091i	−0.229981	−	0.973195i	$-0.573867\pi$
$733$	9.18772	−	4.09063i	0.339356	−	0.151091i	0.569337	+	0.822104i	$0.307200\pi$
$734$	22.9649	+	25.5051i	0.847648	+	0.941409i
$735$	−4.21224	−	1.91244i	−0.155371	−	0.0705414i
$736$	−0.274131	+	0.304453i	−0.0101046	+	0.0112223i
$737$	0.0222324	−	0.0684244i	0.000818942	−	0.00252044i
$738$	6.86068	+	1.12530i	0.252545	+	0.0414229i
$739$	−12.4137	−	38.2054i	−0.456645	−	1.40541i	−0.869193	−	0.494473i	$-0.835361\pi$
$739$	−12.4137	−	38.2054i	−0.456645	−	1.40541i	0.412548	−	0.910936i	$-0.364639\pi$
$740$	0.0270576	−	0.879773i	0.000994656	−	0.0323411i
$741$	0.573805	+	24.4828i	0.0210793	+	0.899398i
$742$	4.79172	−	2.13341i	0.175909	−	0.0783199i
$743$	6.57831	−	11.3940i	0.241335	−	0.418004i	−0.719760	−	0.694223i	$-0.755748\pi$
$743$	6.57831	−	11.3940i	0.241335	−	0.418004i	0.961095	+	0.276219i	$0.0890815\pi$
$744$	17.4760	+	5.22890i	0.640702	+	0.191701i
$745$	17.0346	+	6.11993i	0.624099	+	0.224217i
$746$	−2.32911	+	1.69220i	−0.0852747	+	0.0619557i
$747$	−4.40544	+	16.0873i	−0.161187	+	0.588602i
$748$	0.00123677	+	0.00380638i	4.52207e−5	+	0.000139175i
$749$	22.2575	+	38.5511i	0.813270	+	1.40863i
$750$	26.5796	+	7.59255i	0.970551	+	0.277241i
$751$	6.07148	−	10.5161i	0.221552	−	0.383738i	−0.733728	−	0.679444i	$-0.762221\pi$
$751$	6.07148	−	10.5161i	0.221552	−	0.383738i	0.955279	+	0.295705i	$0.0955546\pi$
$752$	−12.5905	−	2.67619i	−0.459127	−	0.0975905i
$753$	24.2287	+	1.97383i	0.882944	+	0.0719304i
$754$	−76.9478	−	34.2594i	−2.80228	−	1.24765i
$755$	15.8166	−	13.3843i	0.575625	−	0.487103i
$756$	−0.437109	+	0.176850i	−0.0158975	+	0.00643198i
$757$	−10.4368			−0.379330			−0.189665	−	0.981849i	$-0.560740\pi$
$757$	−10.4368			−0.379330			−0.189665	+	0.981849i	$0.560740\pi$
$758$	−2.81311	+	26.7650i	−0.102177	+	0.972148i
$759$	−0.0899012	+	0.0547524i	−0.00326321	+	0.00198739i
$760$	−12.3639	+	6.64014i	−0.448485	+	0.240863i
$761$	3.64738	+	0.775275i	0.132218	+	0.0281037i	0.273545	−	0.961859i	$-0.411804\pi$
$761$	3.64738	+	0.775275i	0.132218	+	0.0281037i	−0.141328	+	0.989963i	$0.545137\pi$
$762$	−21.4899	−	11.7446i	−0.778496	−	0.425462i
$763$	10.6520	−	2.26416i	0.385630	−	0.0819681i
$764$	0.131433	+	0.404508i	0.00475507	+	0.0146346i
$765$	−12.9640	+	18.4620i	−0.468713	+	0.667496i
$766$	4.88115	−	15.0226i	0.176363	−	0.542790i
$767$	−8.45960	+	80.4877i	−0.305458	+	2.90624i
$768$	−1.47670	+	0.518364i	−0.0532856	+	0.0187049i
$769$	−28.2623	+	12.5832i	−1.01916	+	0.453761i	−0.847162	−	0.531335i	$-0.821690\pi$
$769$	−28.2623	+	12.5832i	−1.01916	+	0.453761i	−0.172003	+	0.985097i	$0.555024\pi$
$770$	−0.175522	−	0.168094i	−0.00632537	−	0.00605767i
$771$	9.37943	−	13.5672i	0.337792	−	0.488609i
$772$	−0.768058	−	0.341961i	−0.0276430	−	0.0123075i
$773$	−1.07567	−	3.31057i	−0.0386891	−	0.119073i	0.929847	−	0.367947i	$-0.119939\pi$
$773$	−1.07567	−	3.31057i	−0.0386891	−	0.119073i	−0.968536	+	0.248874i	$0.919939\pi$
$774$	−44.5876	−	17.3973i	−1.60267	−	0.625332i
$775$	13.4136	−	13.1708i	0.481830	−	0.473111i
$776$	−14.5572	−	25.2138i	−0.522572	−	0.905122i
$777$	−43.2606	+	5.57451i	−1.55197	+	0.199984i
$778$	3.22900	+	30.7219i	0.115765	+	1.10143i
$779$	0.380225	+	3.61760i	0.0136230	+	0.129614i
$780$	0.740699	+	0.546469i	0.0265213	+	0.0195667i
$781$	0.0148434	−	0.141226i	0.000531140	−	0.00505346i
$782$	−9.23220			−0.330143
$783$	−38.3019	−	29.8948i	−1.36880	−	1.06835i
$784$	1.50369	−	4.62788i	0.0537032	−	0.165282i
$785$	−24.4338	−	8.77820i	−0.872078	−	0.313307i
$786$	−0.843419	+	2.02048i	−0.0300838	+	0.0720680i
$787$	31.5111	+	34.9966i	1.12325	+	1.24749i	0.965609	+	0.259998i	$0.0837218\pi$
$787$	31.5111	+	34.9966i	1.12325	+	1.24749i	0.157640	+	0.987497i	$0.449612\pi$
$788$	0.660268	+	0.733301i	0.0235211	+	0.0261228i
$789$	41.6969	−	5.37301i	1.48445	−	0.191284i
$790$	1.65238	+	2.42790i	0.0587891	+	0.0863810i
$791$	−2.77585	+	8.54319i	−0.0986979	+	0.303761i
$792$	−0.265259	+	0.0124406i	−0.00942557	+	0.000442058i
$793$	−67.0224			−2.38004
$794$	1.18501	−	11.2746i	0.0420545	−	0.400122i
$795$	−3.91991	−	4.41805i	−0.139025	−	0.156692i
$796$	0.0653872	+	0.622117i	0.00231759	+	0.0220504i
$797$	3.29146	+	31.3161i	0.116589	+	1.10927i	0.883795	+	0.467873i	$0.154980\pi$
$797$	3.29146	+	31.3161i	0.116589	+	1.10927i	−0.767206	+	0.641401i	$0.778354\pi$
$798$	−8.09651	−	10.6118i	−0.286613	−	0.375654i
$799$	−5.31265	−	9.20178i	−0.187948	−	0.325536i
$800$	−0.176218	+	1.05043i	−0.00623024	+	0.0371382i
$801$	−1.36700	−	8.94887i	−0.0483007	−	0.316193i
$802$	−5.53334	−	17.0299i	−0.195389	−	0.601345i
$803$	−0.0355378	−	0.0158225i	−0.00125410	−	0.000558363i
$804$	−0.0635708	−	0.134227i	−0.00224197	−	0.00473381i
$805$	9.12852	−	4.90255i	0.321738	−	0.172792i
$806$	30.9397	−	13.7752i	1.08980	−	0.485211i
$807$	20.9812	+	18.0195i	0.738572	+	0.634317i
$808$	−1.60509	+	15.2714i	−0.0564669	+	0.537246i
$809$	−8.49171	+	26.1348i	−0.298553	+	0.918851i	0.683452	+	0.729995i	$0.260478\pi$
$809$	−8.49171	+	26.1348i	−0.298553	+	0.918851i	−0.982005	+	0.188856i	$0.939522\pi$
$810$	18.3148	+	22.1319i	0.643517	+	0.777635i
$811$	−2.41545	−	7.43400i	−0.0848180	−	0.261043i	0.899649	−	0.436615i	$-0.143823\pi$
$811$	−2.41545	−	7.43400i	−0.0848180	−	0.261043i	−0.984467	+	0.175572i	$0.943823\pi$
$812$	0.829990	−	0.176420i	0.0291269	−	0.00619112i
$813$	−21.2125	+	12.9190i	−0.743955	+	0.453090i
$814$	0.461150	+	0.0980206i	0.0161633	+	0.00343562i
$815$	−13.3101	−	1.81417i	−0.466234	−	0.0635477i
$816$	−20.8226	−	11.3799i	−0.728937	−	0.398377i
$817$	2.61755	−	24.9043i	0.0915764	−	0.871291i
$818$	−6.33407			−0.221466
$819$	20.9315	−	40.5283i	0.731406	−	1.41617i
$820$	0.116246	+	0.0719679i	0.00405950	+	0.00251323i
$821$	−19.5212	−	8.69141i	−0.681295	−	0.303332i	0.0367542	−	0.999324i	$-0.488298\pi$
$821$	−19.5212	−	8.69141i	−0.681295	−	0.303332i	−0.718049	+	0.695992i	$0.754965\pi$
$822$	−15.7372	+	22.7636i	−0.548899	+	0.793972i
$823$	30.8456	+	6.55643i	1.07521	+	0.228543i	0.711298	−	0.702891i	$-0.248108\pi$
$823$	30.8456	+	6.55643i	1.07521	+	0.228543i	0.363911	+	0.931434i	$0.381441\pi$
$824$	−2.56689	+	4.44598i	−0.0894217	+	0.154883i
$825$	−0.120741	+	0.245588i	−0.00420365	+	0.00855027i
$826$	−22.0554	−	38.2010i	−0.767405	−	1.32918i
$827$	0.0456076	+	0.140366i	0.00158593	+	0.00488099i	0.951846	−	0.306575i	$-0.0991832\pi$
$827$	0.0456076	+	0.140366i	0.00158593	+	0.00488099i	−0.950260	+	0.311456i	$0.899183\pi$
$828$	−0.0573925	+	0.209579i	−0.00199453	+	0.00728337i
$829$	−31.5635	+	22.9322i	−1.09625	+	0.796469i	−0.980443	−	0.196803i	$-0.936944\pi$
$829$	−31.5635	+	22.9322i	−1.09625	+	0.796469i	−0.115802	+	0.993272i	$0.536944\pi$
$830$	−10.8676	+	14.0298i	−0.377220	+	0.486982i
$831$	19.8873	−	18.7688i	0.689884	−	0.651083i
$832$	24.7486	−	42.8659i	0.858005	−	1.48611i
$833$	3.66953	−	1.63378i	0.127142	−	0.0566071i
$834$	−0.0850707	+	0.0518105i	−0.00294576	+	0.00179405i
$835$	17.0112	+	24.9952i	0.588697	+	0.864993i
$836$	0.000824014		0.00253605i	2.84991e−5		8.77112e-5i
$837$	19.2379	−	3.40178i	0.664958	−	0.117583i
$838$	−3.23698	+	9.96239i	−0.111819	+	0.344145i
$839$	25.7166	−	28.5612i	0.887836	−	0.986042i	−0.112135	−	0.993693i	$-0.535769\pi$
$839$	25.7166	−	28.5612i	0.887836	−	0.986042i	0.999971	+	0.00765121i	$0.00243548\pi$
$840$	26.1394	+	0.191153i	0.901895	+	0.00659542i
$841$	39.1003	+	43.4253i	1.34829	+	1.49743i
$842$	−10.2086	+	4.54515i	−0.351811	+	0.156636i
$843$	−0.473131	+	2.51422i	−0.0162955	+	0.0865944i
$844$	0.0378798	−	0.360402i	0.00130388	−	0.0124056i
$845$	−59.8106	+	4.43254i	−2.05755	+	0.152484i
$846$	−13.0885	+	3.43009i	−0.449992	+	0.117929i
$847$	−21.4404	+	15.5774i	−0.736701	+	0.535244i
$848$	4.15714	−	4.61697i	0.142757	−	0.158547i
$849$	22.2613	−	7.81437i	0.764005	−	0.268189i
$850$	−20.2485	+	12.8882i	−0.694516	+	0.442061i
$851$	−10.0503	+	17.4077i	−0.344521	+	0.596728i
$852$	−0.177815	−	0.233055i	−0.00609183	−	0.00798435i
$853$	−27.6057	−	12.2909i	−0.945202	−	0.420831i	−0.124520	−	0.992217i	$-0.539739\pi$
$853$	−27.6057	−	12.2909i	−0.945202	−	0.420831i	−0.820681	+	0.571386i	$0.806406\pi$
$854$	29.5534	−	21.4718i	1.01130	−	0.734750i
$855$	−8.63743	+	12.3006i	−0.295394	+	0.420671i
$856$	41.8679	+	30.4188i	1.43102	+	1.03969i
$857$	−3.63200	−	6.29081i	−0.124067	−	0.214890i	0.797301	−	0.603582i	$-0.206260\pi$
$857$	−3.63200	−	6.29081i	−0.124067	−	0.214890i	−0.921368	+	0.388692i	$0.872927\pi$
$858$	−0.358561	+	0.338394i	−0.0122411	+	0.0115526i
$859$	−21.0773	−	23.4088i	−0.719149	−	0.798696i	0.267151	−	0.963655i	$-0.413918\pi$
$859$	−21.0773	−	23.4088i	−0.719149	−	0.798696i	−0.986301	+	0.164958i	$0.947251\pi$
$860$	−0.679768	−	0.651000i	−0.0231799	−	0.0221989i
$861$	2.60997	−	6.25240i	0.0889477	−	0.213081i
$862$	17.6085	−	3.74281i	0.599749	−	0.127481i
$863$	−14.1918	+	43.6780i	−0.483096	+	1.48682i	0.351623	+	0.936142i	$0.385630\pi$
$863$	−14.1918	+	43.6780i	−0.483096	+	1.48682i	−0.834719	+	0.550675i	$0.814370\pi$
$864$	−0.768524	+	0.796603i	−0.0261457	+	0.0271010i
$865$	−12.8627	−	7.96325i	−0.437344	−	0.270759i
$866$	52.3705	−	11.1317i	1.77962	−	0.378270i
$867$	2.27470	+	9.59080i	0.0772528	+	0.325721i
$868$	−0.170591	+	0.295473i	−0.00579025	+	0.0100290i
$869$	−0.0265612	+	0.0118258i	−0.000901025	+	0.000401162i
$870$	−25.5197	−	44.9575i	−0.865199	−	1.52420i
$871$	13.1252	+	5.84373i	0.444732	+	0.198007i
$872$	10.2424	−	7.44158i	0.346853	−	0.252004i
$873$	−26.0568	−	17.1258i	−0.881889	−	0.579619i
$874$	−6.15108			−0.208063
$875$	13.1771	−	23.4959i	0.445467	−	0.794308i
$876$	−0.0757718	+	0.0265982i	−0.00256009	+	0.000898668i
$877$	−15.3320	−	3.25891i	−0.517724	−	0.110046i	−0.0583633	−	0.998295i	$-0.518588\pi$
$877$	−15.3320	−	3.25891i	−0.517724	−	0.110046i	−0.459361	+	0.888250i	$0.651922\pi$
$878$	−5.20604	−	49.5321i	−0.175695	−	1.67163i
$879$	16.0259	−	23.1812i	0.540541	−	0.781882i
$880$	−0.270908	−	0.0973277i	−0.00913230	−	0.00328091i
$881$	36.7061	+	26.6685i	1.23666	+	0.898486i	0.997371	−	0.0724624i	$-0.0230857\pi$
$881$	36.7061	+	26.6685i	1.23666	+	0.898486i	0.239289	+	0.970948i	$0.423086\pi$
$882$	−0.772405	−	5.05643i	−0.0260082	−	0.170259i
$883$	2.12115	+	1.54110i	0.0713823	+	0.0518623i	0.622904	−	0.782298i	$-0.285953\pi$
$883$	2.12115	+	1.54110i	0.0713823	+	0.0518623i	−0.551522	+	0.834160i	$0.685953\pi$
$884$	−0.781777	+	0.166172i	−0.0262940	+	0.00558896i
$885$	−33.5054	+	36.6686i	−1.12627	+	1.23260i
$886$	−34.2845	−	7.28739i	−1.15181	−	0.244825i
$887$	21.0513	+	23.3798i	0.706833	+	0.785017i	0.984448	−	0.175675i	$-0.0562108\pi$
$887$	21.0513	+	23.3798i	0.706833	+	0.785017i	−0.277615	+	0.960692i	$0.589544\pi$
$888$	−43.3093	+	26.3766i	−1.45337	+	0.885140i
$889$	−15.9695	+	17.7359i	−0.535600	+	0.594844i
$890$	2.29123	−	9.35530i	0.0768023	−	0.313590i
$891$	−0.247845	+	0.139485i	−0.00830311	+	0.00467291i
$892$	0.789632	+	0.573701i	0.0264388	+	0.0192089i
$893$	−3.53963	−	6.13082i	−0.118449	−	0.205160i
$894$	4.61869	+	19.4738i	0.154472	+	0.651300i
$895$	11.6248	+	11.1329i	0.388576	+	0.372131i
$896$	2.92728	+	27.8512i	0.0977935	+	0.930443i
$897$	−8.99741	−	18.9976i	−0.300415	−	0.634311i
$898$	5.44205	−	6.04401i	0.181604	−	0.201691i
$899$	−35.1562			−1.17253
$900$	0.166697	+	0.539778i	0.00555657	+	0.0179926i
$901$	5.12847			0.170854
$902$	−0.0490013	+	0.0544215i	−0.00163157	+	0.00181204i
$903$	−26.5241	+	38.3666i	−0.882666	+	1.27676i
$904$	1.09161	+	10.3859i	0.0363063	+	0.345431i
$905$	6.68957	−	13.8618i	0.222369	−	0.460780i
$906$	21.9485	+	6.56709i	0.729191	+	0.218177i
$907$	19.4248	+	33.6448i	0.644991	+	1.11716i	0.984304	+	0.176484i	$0.0564724\pi$
$907$	19.4248	+	33.6448i	0.644991	+	1.11716i	−0.339312	+	0.940674i	$0.610194\pi$
$908$	−0.614632	−	0.446556i	−0.0203973	−	0.0148195i
$909$	5.80908	+	15.3853i	0.192675	+	0.510299i
$910$	37.0478	−	31.3505i	1.22812	−	1.03926i
$911$	−16.0647	+	17.8417i	−0.532248	+	0.591121i	−0.947966	−	0.318373i	$-0.896864\pi$
$911$	−16.0647	+	17.8417i	−0.532248	+	0.591121i	0.415718	+	0.909494i	$0.363530\pi$
$912$	−13.8733	−	7.58204i	−0.459392	−	0.251066i
$913$	−0.117560	−	0.130564i	−0.00389067	−	0.00432103i
$914$	−41.8624	−	8.89812i	−1.38468	−	0.294324i
$915$	−33.1009	−	24.4210i	−1.09428	−	0.807334i
$916$	0.256371	−	0.0544934i	0.00847074	−	0.00180051i
$917$	1.72619	+	1.25415i	0.0570037	+	0.0414156i
$918$	−24.9290	−	0.858432i	−0.822781	−	0.0283325i
$919$	34.1266	+	24.7944i	1.12573	+	0.817892i	0.985068	−	0.172165i	$-0.0550762\pi$
$919$	34.1266	+	24.7944i	1.12573	+	0.817892i	0.140664	+	0.990057i	$0.455076\pi$
$920$	7.37680	−	9.52329i	0.243206	−	0.313974i
$921$	−24.7741	−	2.01826i	−0.816336	−	0.0665040i
$922$	0.741042	+	7.05054i	0.0244049	+	0.232197i
$923$	27.7381	+	5.89592i	0.913012	+	0.194067i
$924$	0.000918534	−	0.00488109i	3.02175e−5	−	0.000160576i
$925$	2.25836	+	52.2096i	0.0742545	+	1.71664i
$926$	16.3264			0.536519
$927$	−0.317915	+	5.48897i	−0.0104417	+	0.180281i
$928$	1.61147	−	1.17080i	0.0528990	−	0.0384334i
$929$	3.60542	+	1.60523i	0.118290	+	0.0526660i	0.465028	−	0.885296i	$-0.346044\pi$
$929$	3.60542	+	1.60523i	0.118290	+	0.0526660i	−0.346738	+	0.937962i	$0.612711\pi$
$930$	20.2997	+	4.47023i	0.665653	+	0.146585i
$931$	2.44487	−	1.08853i	0.0801275	−	0.0356751i
$932$	−0.531655	+	0.920854i	−0.0174149	+	0.0301636i
$933$	−37.1533	−	11.1164i	−1.21634	−	0.363935i
$934$	36.7309	−	7.80738i	1.20187	−	0.255465i
$935$	−0.0899306	−	0.219947i	−0.00294105	−	0.00719302i
$936$	3.06628	−	52.9411i	0.100225	−	1.73043i
$937$	9.87834	−	30.4024i	0.322711	−	0.993204i	−0.649752	−	0.760147i	$-0.725127\pi$
$937$	9.87834	−	30.4024i	0.322711	−	0.993204i	0.972463	−	0.233057i	$-0.0748729\pi$
$938$	−7.65968	+	1.62812i	−0.250097	+	0.0531599i
$939$	−41.9803	+	5.40953i	−1.36998	+	0.176533i
$940$	−0.263645	−	0.0359348i	−0.00859915	−	0.00117206i
$941$	9.66246	+	10.7313i	0.314987	+	0.349829i	0.879760	−	0.475417i	$-0.157703\pi$
$941$	9.66246	+	10.7313i	0.314987	+	0.349829i	−0.564773	+	0.825246i	$0.691036\pi$
$942$	−6.62488	−	27.9324i	−0.215850	−	0.910088i
$943$	−1.56113	−	2.70396i	−0.0508374	−	0.0880529i
$944$	−42.2693	−	30.7104i	−1.37575	−	0.999540i
$945$	25.1049	−	12.3892i	0.816664	−	0.403021i
$946$	0.407858	−	0.296326i	0.0132606	−	0.00963439i
$947$	43.6238	+	19.4226i	1.41758	+	0.631149i	0.965399	−	0.260776i	$-0.0839784\pi$
$947$	43.6238	+	19.4226i	1.41758	+	0.631149i	0.452184	+	0.891925i	$0.350645\pi$
$948$	−0.0231209	+	0.0553880i	−0.000750932	+	0.00179892i
$949$	3.88422	−	6.72766i	0.126087	−	0.218389i
$950$	−13.4908	+	8.58693i	−0.437700	+	0.278597i
$951$	5.54077	−	29.4437i	0.179672	−	0.954777i
$952$	−15.1875	+	16.8675i	−0.492231	+	0.546678i
$953$	−14.1198	+	10.2587i	−0.457387	+	0.332311i	−0.792505	−	0.609865i	$-0.791224\pi$
$953$	−14.1198	+	10.2587i	−0.457387	+	0.332311i	0.335119	+	0.942176i	$0.391224\pi$
$954$	1.72490	−	6.29880i	0.0558459	−	0.203931i
$955$	−9.55702	−	23.3740i	−0.309258	−	0.756364i
$956$	−0.0175083	+	0.166580i	−0.000566259	+	0.00538760i
$957$	0.482898	−	0.169512i	0.0156099	−	0.00547953i
$958$	0.610405	−	0.271770i	0.0197213	−	0.00878048i
$959$	18.0458	+	20.0419i	0.582729	+	0.647186i
$960$	27.8419	−	12.1528i	0.898593	−	0.392231i
$961$	−11.2843	+	12.5325i	−0.364011	+	0.404275i
$962$	−29.0933	+	89.5400i	−0.938006	+	2.88689i
$963$	54.6941	+	8.97101i	1.76249	+	0.289087i
$964$	0.176536	+	0.543321i	0.00568583	+	0.0174992i
$965$	46.9768	+	16.8771i	1.51224	+	0.543294i
$966$	10.0536	+	5.49447i	0.323469	+	0.176782i
$967$	23.4521	−	10.4416i	0.754170	−	0.335778i	0.00661483	−	0.999978i	$-0.497894\pi$
$967$	23.4521	−	10.4416i	0.754170	−	0.335778i	0.747555	+	0.664200i	$0.231228\pi$
$968$	−15.4051	+	26.6823i	−0.495137	+	0.857603i
$969$	−3.01177	−	12.6985i	−0.0967520	−	0.407935i
$970$	−18.6658	−	27.4264i	−0.599324	−	0.880608i
$971$	−0.505556	+	0.367308i	−0.0162241	+	0.0117875i	−0.595868	−	0.803083i	$-0.703192\pi$
$971$	−0.505556	+	0.367308i	−0.0162241	+	0.0117875i	0.579644	+	0.814870i	$0.303192\pi$
$972$	−0.174460	+	0.560574i	−0.00559581	+	0.0179804i
$973$	0.0299960	+	0.0923182i	0.000961627	+	0.00295958i
$974$	−3.59933	−	6.23422i	−0.115330	−	0.199757i
$975$	−46.2542	−	29.1060i	−1.48132	−	0.932136i
$976$	21.6343	−	37.4717i	0.692497	−	1.19944i
$977$	36.0526	+	7.66322i	1.15342	+	0.245168i	0.744642	−	0.667464i	$-0.232620\pi$
$977$	36.0526	+	7.66322i	1.15342	+	0.245168i	0.408783	+	0.912632i	$0.365953\pi$
$978$	−6.35764	−	13.4238i	−0.203295	−	0.429247i
$979$	0.0871108	+	0.0387842i	0.00278407	+	0.00123955i
$980$	0.0239286	−	0.0977025i	0.000764371	−	0.00312099i
$981$	6.22194	−	12.0472i	0.198651	−	0.384636i
$982$	−10.7290			−0.342375
$983$	2.98616	−	28.4114i	0.0952436	−	0.906182i	−0.837693	−	0.546141i	$-0.816096\pi$
$983$	2.98616	−	28.4114i	0.0952436	−	0.906182i	0.932937	−	0.360041i	$-0.117237\pi$
$984$	−0.184556	−	7.87455i	−0.00588344	−	0.251032i
$985$	−42.3118	−	40.5211i	−1.34817	−	1.29111i
$986$	43.9063	+	9.33257i	1.39826	+	0.297210i
$987$	0.308953	+	13.1823i	0.00983410	+	0.419596i
$988$	−0.520870	+	0.110714i	−0.0165711	+	0.00352229i
$989$	6.64210	+	20.4423i	0.211206	+	0.650027i
$990$	−0.300386	+	0.0364763i	−0.00954690	+	0.00115929i
$991$	18.1246	−	55.7817i	0.575746	−	1.77196i	−0.0578809	−	0.998323i	$-0.518434\pi$
$991$	18.1246	−	55.7817i	0.575746	−	1.77196i	0.633626	−	0.773639i	$-0.281566\pi$
$992$	−0.0837177	+	0.796521i	−0.00265804	+	0.0252896i
$993$	−8.39707	+	44.6221i	−0.266473	+	1.41604i
$994$	−14.1199	+	6.28659i	−0.447857	+	0.199399i
$995$	−6.60137	−	36.5483i	−0.209278	−	1.15866i
$996$	−0.361487	−	0.0294491i	−0.0114541	−	0.000933129i
$997$	−45.5343	−	20.2732i	−1.44209	−	0.642058i	−0.471293	−	0.881977i	$-0.656213\pi$
$997$	−45.5343	−	20.2732i	−1.44209	−	0.642058i	−0.970793	+	0.239919i	$0.922879\pi$
$998$	−3.57766	−	11.0109i	−0.113249	−	0.348544i
$999$	−28.7568	+	46.0702i	−0.909824	+	1.45760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.21	✓	224
3.2	odd	2		675.2.r.a.631.8		224
9.2	odd	6		675.2.r.a.181.21		224
9.7	even	3	inner	225.2.q.a.106.8	yes	224
25.21	even	5	inner	225.2.q.a.121.8	yes	224
75.71	odd	10		675.2.r.a.496.21		224
225.146	odd	30		675.2.r.a.46.8		224
225.196	even	15	inner	225.2.q.a.196.21	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.21	✓	224	1.1	even	1	trivial
225.2.q.a.106.8	yes	224	9.7	even	3	inner
225.2.q.a.121.8	yes	224	25.21	even	5	inner
225.2.q.a.196.21	yes	224	225.196	even	15	inner
675.2.r.a.46.8		224	225.146	odd	30
675.2.r.a.181.21		224	9.2	odd	6
675.2.r.a.496.21		224	75.71	odd	10
675.2.r.a.631.8		224	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.955162 - 1.06081i) q^{2} +(-1.72633 - 0.140638i) q^{3} +(-0.00393676 - 0.0374558i) q^{4} +(0.397449 + 2.20046i) q^{5} +(-1.79812 + 1.69699i) q^{6} +(1.20474 + 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(2.96044 + 0.485576i) q^{9} +O(q^{10})\)	\(q+(0.955162 - 1.06081i) q^{2} +(-1.72633 - 0.140638i) q^{3} +(-0.00393676 - 0.0374558i) q^{4} +(0.397449 + 2.20046i) q^{5} +(-1.79812 + 1.69699i) q^{6} +(1.20474 + 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(2.96044 + 0.485576i) q^{9} +(2.71391 + 1.68018i) q^{10} +(-0.0211445 + 0.0234833i) q^{11} +(0.00152844 + 0.0652148i) q^{12} +(-4.22250 - 4.68956i) q^{13} +(3.36428 + 0.715100i) q^{14} +(-0.376660 - 3.85462i) q^{15} +(3.98488 - 0.847013i) q^{16} +(2.72065 + 1.97667i) q^{17} +(3.34281 - 2.67668i) q^{18} +(1.81267 + 1.31698i) q^{19} +(0.0808554 - 0.0235495i) q^{20} +(-1.78631 - 3.77171i) q^{21} +(0.00471506 + 0.0448608i) q^{22} +(-1.88117 - 0.399856i) q^{23} +(-3.68065 - 3.16110i) q^{24} +(-4.68407 + 1.74914i) q^{25} -9.00793 q^{26} +(-5.04241 - 1.25462i) q^{27} +(0.0734149 - 0.0533391i) q^{28} +(8.54224 + 3.80325i) q^{29} +(-4.44881 - 3.28222i) q^{30} +(-3.43471 + 1.52923i) q^{31} +(0.106511 - 0.184482i) q^{32} +(0.0398050 - 0.0375663i) q^{33} +(4.69554 - 0.998067i) q^{34} +(-4.11281 + 3.48032i) q^{35} +(0.00653309 - 0.112797i) q^{36} +(3.22975 - 9.94014i) q^{37} +(3.12847 - 0.664976i) q^{38} +(6.62990 + 8.68958i) q^{39} +(-2.72234 + 5.64107i) q^{40} +(1.08631 + 1.20647i) q^{41} +(-5.70730 - 1.70765i) q^{42} +(-5.58816 - 9.67898i) q^{43} +(0.000962828 + 0.000699535i) q^{44} +(0.108132 + 6.70733i) q^{45} +(-2.22100 + 1.61365i) q^{46} +(-2.88640 - 1.28511i) q^{47} +(-6.99835 + 0.901798i) q^{48} +(0.597221 - 1.03442i) q^{49} +(-2.61853 + 6.63964i) q^{50} +(-4.41875 - 3.79501i) q^{51} +(-0.159028 + 0.176619i) q^{52} +(1.23376 - 0.896379i) q^{53} +(-6.14724 + 4.15070i) q^{54} +(-0.0600780 - 0.0371942i) q^{55} +(-0.705499 + 6.71237i) q^{56} +(-2.94405 - 2.52848i) q^{57} +(12.1938 - 5.42901i) q^{58} +(-8.58158 - 9.53081i) q^{59} +(-0.142895 + 0.0292828i) q^{60} +(7.10677 - 7.89287i) q^{61} +(-1.65848 + 5.10426i) q^{62} +(2.55332 + 6.76244i) q^{63} +(2.42385 + 7.45983i) q^{64} +(8.64097 - 11.1553i) q^{65} +(-0.00183061 - 0.0781077i) q^{66} +(-2.07993 + 0.926044i) q^{67} +(0.0633271 - 0.109686i) q^{68} +(3.19129 + 0.954848i) q^{69} +(-0.236421 + 7.68719i) q^{70} +(-3.63556 + 2.64139i) q^{71} +(5.90945 + 5.97474i) q^{72} +(0.380414 + 1.17080i) q^{73} +(-7.45971 - 12.9206i) q^{74} +(8.33225 - 2.36084i) q^{75} +(0.0421926 - 0.0730797i) q^{76} +(-0.0744753 - 0.0158302i) q^{77} +(15.5507 + 1.26686i) q^{78} +(0.840545 + 0.374235i) q^{79} +(3.44761 + 8.43194i) q^{80} +(8.52843 + 2.87504i) q^{81} +2.31745 q^{82} +(-0.581163 + 5.52940i) q^{83} +(-0.134240 + 0.0817560i) q^{84} +(-3.26826 + 6.77231i) q^{85} +(-15.6052 - 3.31699i) q^{86} +(-14.2119 - 7.76704i) q^{87} +(-0.0865826 + 0.0184037i) q^{88} +(-0.932477 - 2.86987i) q^{89} +(7.21852 + 6.29188i) q^{90} +(4.69854 - 14.4606i) q^{91} +(-0.00757118 + 0.0720350i) q^{92} +(6.14453 - 2.15691i) q^{93} +(-4.12024 + 1.83445i) q^{94} +(-2.17753 + 4.51214i) q^{95} +(-0.209818 + 0.303497i) q^{96} +(-9.49506 - 4.22747i) q^{97} +(-0.526882 - 1.62158i) q^{98} +(-0.0739999 + 0.0592538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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