LMFDB - Embedded newform 225.2.q.a.211.9

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			211.9
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23977 - 0.551980i) q^{2} +(1.19364 + 1.25508i) q^{3} +(-0.105919 - 0.117635i) q^{4} +(-2.19872 - 0.406964i) q^{5} +(-0.787056 - 2.21487i) q^{6} +(-1.81169 - 3.13794i) q^{7} +(0.905114 + 2.78565i) q^{8} +(-0.150451 + 2.99623i) q^{9} +O(q^{10})$	\(q+(-1.23977 - 0.551980i) q^{2} +(1.19364 + 1.25508i) q^{3} +(-0.105919 - 0.117635i) q^{4} +(-2.19872 - 0.406964i) q^{5} +(-0.787056 - 2.21487i) q^{6} +(-1.81169 - 3.13794i) q^{7} +(0.905114 + 2.78565i) q^{8} +(-0.150451 + 2.99623i) q^{9} +(2.50127 + 1.71819i) q^{10} +(-5.29383 - 2.35697i) q^{11} +(0.0212123 - 0.273352i) q^{12} +(-0.742899 + 0.330760i) q^{13} +(0.513995 + 4.89034i) q^{14} +(-2.11371 - 3.24534i) q^{15} +(0.382402 - 3.63831i) q^{16} +(0.527788 + 1.62436i) q^{17} +(1.84038 - 3.63158i) q^{18} +(-2.00045 - 6.15676i) q^{19} +(0.185014 + 0.301753i) q^{20} +(1.77586 - 6.01939i) q^{21} +(5.26212 + 5.84418i) q^{22} +(-0.197808 - 1.88202i) q^{23} +(-2.41584 + 4.46105i) q^{24} +(4.66876 + 1.78960i) q^{25} +1.10360 q^{26} +(-3.94009 + 3.38758i) q^{27} +(-0.177240 + 0.545488i) q^{28} +(-7.33067 + 1.55818i) q^{29} +(0.829145 + 5.19019i) q^{30} +(-1.47849 - 0.314262i) q^{31} +(0.446643 - 0.773608i) q^{32} +(-3.36074 - 9.45755i) q^{33} +(0.242282 - 2.30516i) q^{34} +(2.70638 + 7.63676i) q^{35} +(0.368398 - 0.299660i) q^{36} +(2.11767 + 1.53858i) q^{37} +(-0.918313 + 8.73716i) q^{38} +(-1.30188 - 0.537590i) q^{39} +(-0.856434 - 6.49323i) q^{40} +(-3.60811 + 1.60644i) q^{41} +(-5.52424 + 6.48240i) q^{42} +(4.09520 + 7.09310i) q^{43} +(0.283457 + 0.872391i) q^{44} +(1.55016 - 6.52664i) q^{45} +(-0.793600 + 2.44245i) q^{46} +(10.8737 - 2.31128i) q^{47} +(5.02282 - 3.86289i) q^{48} +(-3.06445 + 5.30779i) q^{49} +(-4.80035 - 4.79575i) q^{50} +(-1.40872 + 2.60132i) q^{51} +(0.117597 + 0.0523574i) q^{52} +(2.97637 - 9.16031i) q^{53} +(6.75467 - 2.02497i) q^{54} +(10.6805 + 7.33671i) q^{55} +(7.10143 - 7.88694i) q^{56} +(5.33941 - 9.85968i) q^{57} +(9.94842 + 2.11460i) q^{58} +(2.50272 - 1.11428i) q^{59} +(-0.157884 + 0.592392i) q^{60} +(1.04900 + 0.467045i) q^{61} +(1.65951 + 1.20571i) q^{62} +(9.67455 - 4.95613i) q^{63} +(-6.90009 + 5.01321i) q^{64} +(1.76804 - 0.424917i) q^{65} +(-1.05384 + 13.5802i) q^{66} +(-3.12703 - 0.664670i) q^{67} +(0.135180 - 0.234138i) q^{68} +(2.12597 - 2.49471i) q^{69} +(0.860057 - 10.9617i) q^{70} +(2.75915 - 8.49180i) q^{71} +(-8.48262 + 2.29282i) q^{72} +(-6.96422 + 5.05980i) q^{73} +(-1.77615 - 3.07639i) q^{74} +(3.32672 + 7.99581i) q^{75} +(-0.512367 + 0.887445i) q^{76} +(2.19477 + 20.8818i) q^{77} +(1.31729 + 1.38510i) q^{78} +(3.47196 - 0.737989i) q^{79} +(-2.32146 + 7.84402i) q^{80} +(-8.95473 - 0.901572i) q^{81} +5.35994 q^{82} +(-6.17496 + 6.85798i) q^{83} +(-0.896192 + 0.428666i) q^{84} +(-0.499402 - 3.78632i) q^{85} +(-1.16185 - 11.0543i) q^{86} +(-10.7058 - 7.34067i) q^{87} +(1.77417 - 16.8801i) q^{88} +(-0.00564656 + 0.00410246i) q^{89} +(-5.52441 + 7.23586i) q^{90} +(2.38381 + 1.73194i) q^{91} +(-0.200440 + 0.222612i) q^{92} +(-1.37035 - 2.23073i) q^{93} +(-14.7566 - 3.13662i) q^{94} +(1.89286 + 14.3511i) q^{95} +(1.50407 - 0.362836i) q^{96} +(0.0365021 - 0.00775876i) q^{97} +(6.72900 - 4.88891i) q^{98} +(7.85846 - 15.5069i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.23977	−	0.551980i	−0.876648	−	0.390309i	−0.0814635	−	0.996676i	$-0.525959\pi$
$2$	−1.23977	−	0.551980i	−0.876648	−	0.390309i	−0.795185	+	0.606367i	$0.792626\pi$
$3$	1.19364	+	1.25508i	0.689148	+	0.724621i
$3$	1.19364	+	1.25508i	0.689148	+	0.724621i
$4$	−0.105919	−	0.117635i	−0.0529597	−	0.0588177i
$5$	−2.19872	−	0.406964i	−0.983299	−	0.182000i
$5$	−2.19872	−	0.406964i	−0.983299	−	0.182000i
$6$	−0.787056	−	2.21487i	−0.321314	−	0.904218i
$7$	−1.81169	−	3.13794i	−0.684755	−	1.18603i	−0.973514	−	0.228629i	$-0.926576\pi$
$7$	−1.81169	−	3.13794i	−0.684755	−	1.18603i	0.288759	−	0.957402i	$-0.406757\pi$
$8$	0.905114	+	2.78565i	0.320006	+	0.984877i
$9$	−0.150451	+	2.99623i	−0.0501505	+	0.998742i
$10$	2.50127	+	1.71819i	0.790971	+	0.543340i
$11$	−5.29383	−	2.35697i	−1.59615	−	0.710652i	−0.600140	−	0.799895i	$-0.704889\pi$
$11$	−5.29383	−	2.35697i	−1.59615	−	0.710652i	−0.996010	+	0.0892428i	$0.971555\pi$
$12$	0.0212123	−	0.273352i	0.00612347	−	0.0789098i
$13$	−0.742899	+	0.330760i	−0.206043	+	0.0917363i	−0.507164	−	0.861850i	$-0.669306\pi$
$13$	−0.742899	+	0.330760i	−0.206043	+	0.0917363i	0.301120	+	0.953586i	$0.402639\pi$
$14$	0.513995	+	4.89034i	0.137371	+	1.30700i
$15$	−2.11371	−	3.24534i	−0.545757	−	0.837943i
$16$	0.382402	−	3.63831i	0.0956005	−	0.909578i
$17$	0.527788	+	1.62436i	0.128007	+	0.393966i	0.994437	−	0.105333i	$-0.0335908\pi$
$17$	0.527788	+	1.62436i	0.128007	+	0.393966i	−0.866430	+	0.499299i	$0.833591\pi$
$18$	1.84038	−	3.63158i	0.433782	−	0.855971i
$19$	−2.00045	−	6.15676i	−0.458935	−	1.41246i	−0.866452	−	0.499260i	$-0.833605\pi$
$19$	−2.00045	−	6.15676i	−0.458935	−	1.41246i	0.407517	−	0.913198i	$-0.366395\pi$
$20$	0.185014	+	0.301753i	0.0413704	+	0.0674741i
$21$	1.77586	−	6.01939i	0.387525	−	1.31354i
$22$	5.26212	+	5.84418i	1.12189	+	1.24598i
$23$	−0.197808	−	1.88202i	−0.0412458	−	0.392428i	−0.995597	−	0.0937400i	$-0.970118\pi$
$23$	−0.197808	−	1.88202i	−0.0412458	−	0.392428i	0.954351	−	0.298688i	$-0.0965489\pi$
$24$	−2.41584	+	4.46105i	−0.493131	+	0.910609i
$25$	4.66876	+	1.78960i	0.933752	+	0.357920i
$26$	1.10360			0.216433
$27$	−3.94009	+	3.38758i	−0.758270	+	0.651941i
$28$	−0.177240	+	0.545488i	−0.0334952	+	0.103088i
$29$	−7.33067	+	1.55818i	−1.36127	+	0.289347i	−0.829957	−	0.557827i	$-0.811635\pi$
$29$	−7.33067	+	1.55818i	−1.36127	+	0.289347i	−0.531315	+	0.847175i	$0.678302\pi$
$30$	0.829145	+	5.19019i	0.151380	+	0.947595i
$31$	−1.47849	−	0.314262i	−0.265544	−	0.0564431i	0.0732155	−	0.997316i	$-0.476674\pi$
$31$	−1.47849	−	0.314262i	−0.265544	−	0.0564431i	−0.338759	+	0.940873i	$0.610007\pi$
$32$	0.446643	−	0.773608i	0.0789560	−	0.136756i
$33$	−3.36074	−	9.45755i	−0.585030	−	1.64635i
$34$	0.242282	−	2.30516i	0.0415511	−	0.395332i
$35$	2.70638	+	7.63676i	0.457461	+	1.29085i
$36$	0.368398	−	0.299660i	0.0613997	−	0.0499433i
$37$	2.11767	+	1.53858i	0.348143	+	0.252940i	0.748089	−	0.663598i	$-0.230971\pi$
$37$	2.11767	+	1.53858i	0.348143	+	0.252940i	−0.399947	+	0.916538i	$0.630971\pi$
$38$	−0.918313	+	8.73716i	−0.148970	+	1.41736i
$39$	−1.30188	−	0.537590i	−0.208468	−	0.0860833i
$40$	−0.856434	−	6.49323i	−0.135414	−	1.02667i
$41$	−3.60811	+	1.60644i	−0.563493	+	0.250883i	−0.668656	−	0.743572i	$-0.733130\pi$
$41$	−3.60811	+	1.60644i	−0.563493	+	0.250883i	0.105163	+	0.994455i	$0.466463\pi$
$42$	−5.52424	+	6.48240i	−0.852408	+	1.00026i
$43$	4.09520	+	7.09310i	0.624513	+	1.08169i	0.988635	+	0.150336i	$0.0480357\pi$
$43$	4.09520	+	7.09310i	0.624513	+	1.08169i	−0.364122	+	0.931351i	$0.618631\pi$
$44$	0.283457	+	0.872391i	0.0427327	+	0.131518i
$45$	1.55016	−	6.52664i	0.231084	−	0.972934i
$46$	−0.793600	+	2.44245i	−0.117010	+	0.360120i
$47$	10.8737	−	2.31128i	1.58609	−	0.337134i	0.671339	−	0.741150i	$-0.265719\pi$
$47$	10.8737	−	2.31128i	1.58609	−	0.337134i	0.914752	+	0.404016i	$0.132386\pi$
$48$	5.02282	−	3.86289i	0.724982	−	0.557560i
$49$	−3.06445	+	5.30779i	−0.437779	+	0.758255i
$50$	−4.80035	−	4.79575i	−0.678873	−	0.678222i
$51$	−1.40872	+	2.60132i	−0.197260	+	0.364258i
$52$	0.117597	+	0.0523574i	0.0163077	+	0.00726066i
$53$	2.97637	−	9.16031i	0.408835	−	1.25827i	−0.508815	−	0.860876i	$-0.669916\pi$
$53$	2.97637	−	9.16031i	0.408835	−	1.25827i	0.917650	−	0.397390i	$-0.130084\pi$
$54$	6.75467	−	2.02497i	0.919194	−	0.275563i
$55$	10.6805	+	7.33671i	1.44015	+	0.989282i
$56$	7.10143	−	7.88694i	0.948969	−	1.05394i
$57$	5.33941	−	9.85968i	0.707222	−	1.30595i
$58$	9.94842	+	2.11460i	1.30629	+	0.277661i
$59$	2.50272	−	1.11428i	0.325826	−	0.145067i	−0.237304	−	0.971435i	$-0.576264\pi$
$59$	2.50272	−	1.11428i	0.325826	−	0.145067i	0.563130	+	0.826368i	$0.309597\pi$
$60$	−0.157884	+	0.592392i	−0.0203828	+	0.0764775i
$61$	1.04900	+	0.467045i	0.134311	+	0.0597990i	0.472792	−	0.881174i	$-0.343246\pi$
$61$	1.04900	+	0.467045i	0.134311	+	0.0597990i	−0.338481	+	0.940973i	$0.609913\pi$
$62$	1.65951	+	1.20571i	0.210758	+	0.153125i
$63$	9.67455	−	4.95613i	1.21888	−	0.624413i
$64$	−6.90009	+	5.01321i	−0.862511	+	0.626651i
$65$	1.76804	−	0.424917i	0.219298	−	0.0527044i
$66$	−1.05384	+	13.5802i	−0.129718	+	1.67161i
$67$	−3.12703	−	0.664670i	−0.382027	−	0.0812024i	0.0128953	−	0.999917i	$-0.495895\pi$
$67$	−3.12703	−	0.664670i	−0.382027	−	0.0812024i	−0.394922	+	0.918714i	$0.629229\pi$
$68$	0.135180	−	0.234138i	0.0163930	−	0.0283935i
$69$	2.12597	−	2.49471i	0.255937	−	0.300328i
$70$	0.860057	−	10.9617i	0.102797	−	1.31017i
$71$	2.75915	−	8.49180i	0.327451	−	1.00779i	−0.642871	−	0.765975i	$-0.722257\pi$
$71$	2.75915	−	8.49180i	0.327451	−	1.00779i	0.970322	−	0.241817i	$-0.0777432\pi$
$72$	−8.48262	+	2.29282i	−0.999686	+	0.270211i
$73$	−6.96422	+	5.05980i	−0.815101	+	0.592205i	−0.915305	−	0.402762i	$-0.868050\pi$
$73$	−6.96422	+	5.05980i	−0.815101	+	0.592205i	0.100204	+	0.994967i	$0.468050\pi$
$74$	−1.77615	−	3.07639i	−0.206474	−	0.357623i
$75$	3.32672	+	7.99581i	0.384137	+	0.923276i
$76$	−0.512367	+	0.887445i	−0.0587725	+	0.101797i
$77$	2.19477	+	20.8818i	0.250117	+	2.37971i
$78$	1.31729	+	1.38510i	0.149154	+	0.156832i
$79$	3.47196	−	0.737989i	0.390627	−	0.0830302i	−0.00841147	−	0.999965i	$-0.502677\pi$
$79$	3.47196	−	0.737989i	0.390627	−	0.0830302i	0.399038	+	0.916934i	$0.369344\pi$
$80$	−2.32146	+	7.84402i	−0.259547	+	0.876988i
$81$	−8.95473	−	0.901572i	−0.994970	−	0.100175i
$82$	5.35994			0.591907
$83$	−6.17496	+	6.85798i	−0.677790	+	0.752762i	−0.979677	−	0.200582i	$-0.935717\pi$
$83$	−6.17496	+	6.85798i	−0.677790	+	0.752762i	0.301887	+	0.953344i	$0.402383\pi$
$84$	−0.896192	+	0.428666i	−0.0977825	+	0.0467713i
$85$	−0.499402	−	3.78632i	−0.0541677	−	0.410684i
$86$	−1.16185	−	11.0543i	−0.125286	−	1.19201i
$87$	−10.7058	−	7.34067i	−1.14778	−	0.787003i
$88$	1.77417	−	16.8801i	0.189127	−	1.79942i
$89$	−0.00564656	+	0.00410246i	−0.000598534	+	0.000434860i	−0.588084	−	0.808800i	$-0.700118\pi$
$89$	−0.00564656	+	0.00410246i	−0.000598534	+	0.000434860i	0.587486	+	0.809234i	$0.300118\pi$
$90$	−5.52441	+	7.23586i	−0.582324	+	0.762727i
$91$	2.38381	+	1.73194i	0.249891	+	0.181557i
$92$	−0.200440	+	0.222612i	−0.0208973	+	0.0232089i
$93$	−1.37035	−	2.23073i	−0.142099	−	0.231316i
$94$	−14.7566	−	3.13662i	−1.52203	−	0.323518i
$95$	1.89286	+	14.3511i	0.194204	+	1.47239i
$96$	1.50407	−	0.362836i	0.153508	−	0.0370318i
$97$	0.0365021	−	0.00775876i	0.00370623	−	0.000787783i	−0.206058	−	0.978540i	$-0.566064\pi$
$97$	0.0365021	−	0.00775876i	0.00370623	−	0.000787783i	0.209764	+	0.977752i	$0.432730\pi$
$98$	6.72900	−	4.88891i	0.679732	−	0.493854i
$99$	7.85846	−	15.5069i	0.789805	−	1.55850i
$100$	−0.283992	−	0.738765i	−0.0283992	−	0.0738765i
$101$	−5.04199	−	8.73298i	−0.501696	−	0.868964i	−0.999998	−	0.00196000i	$-0.999376\pi$
$101$	−5.04199	−	8.73298i	−0.501696	−	0.868964i	0.498302	−	0.867004i	$-0.333957\pi$
$102$	3.18236	−	2.44745i	0.315101	−	0.242334i
$103$	−7.45712	−	8.28197i	−0.734772	−	0.816046i	0.253727	−	0.967276i	$-0.418343\pi$
$103$	−7.45712	−	8.28197i	−0.734772	−	0.816046i	−0.988499	+	0.151229i	$0.951677\pi$
$104$	−1.59379	−	1.77008i	−0.156284	−	0.173571i
$105$	−6.35430	+	12.5123i	−0.620116	+	1.22107i
$106$	−8.74631	+	9.71377i	−0.849517	+	0.943484i
$107$	3.33860			0.322754			0.161377	−	0.986893i	$-0.448406\pi$
$107$	3.33860			0.322754			0.161377	+	0.986893i	$0.448406\pi$
$108$	0.815832	+	0.104683i	0.0785034	+	0.0100731i
$109$	−7.34425	−	5.33591i	−0.703451	−	0.511087i	0.177603	−	0.984102i	$-0.443166\pi$
$109$	−7.34425	−	5.33591i	−0.703451	−	0.511087i	−0.881054	+	0.473015i	$0.843166\pi$
$110$	−9.19158	−	14.9912i	−0.876383	−	1.42936i
$111$	0.596696	+	4.49435i	0.0566359	+	0.426585i
$112$	−12.1096	+	5.39155i	−1.14425	+	0.509453i
$113$	−5.25363	+	2.33907i	−0.494220	+	0.220041i	−0.638684	−	0.769469i	$-0.720521\pi$
$113$	−5.25363	+	2.33907i	−0.494220	+	0.220041i	0.144464	+	0.989510i	$0.453854\pi$
$114$	−12.0620	+	9.27647i	−1.12971	+	0.868821i
$115$	−0.330988	+	4.21854i	−0.0308648	+	0.393380i
$116$	0.959758	+	0.697305i	0.0891113	+	0.0647432i
$117$	−0.879262	−	2.27566i	−0.0812878	−	0.210385i
$118$	−3.71785			−0.342255
$119$	4.14097	−	4.59902i	0.379602	−	0.421591i
$120$	7.12725	−	8.82546i	0.650626	−	0.805651i
$121$	15.1089	+	16.7802i	1.37354	+	1.52547i
$122$	−1.04272	−	1.15805i	−0.0944031	−	0.104845i
$123$	−6.32299	−	2.61097i	−0.570125	−	0.235423i
$124$	0.119632	+	0.207209i	0.0107433	+	0.0186079i
$125$	−9.53701	−	5.83485i	−0.853016	−	0.521885i
$126$	−14.7299	+	0.804287i	−1.31224	+	0.0716516i
$127$	−7.75165	+	5.63190i	−0.687847	+	0.499750i	−0.875952	−	0.482399i	$-0.839766\pi$
$127$	−7.75165	+	5.63190i	−0.687847	+	0.499750i	0.188104	+	0.982149i	$0.439766\pi$
$128$	9.57417	−	2.03505i	0.846245	−	0.179875i
$129$	−4.01421	+	13.6064i	−0.353432	+	1.19798i
$130$	−2.42650	−	0.449123i	−0.212818	−	0.0393907i
$131$	−4.63169	−	0.984497i	−0.404673	−	0.0860159i	0.00107841	−	0.999999i	$-0.499657\pi$
$131$	−4.63169	−	0.984497i	−0.404673	−	0.0860159i	−0.405751	+	0.913984i	$0.632990\pi$
$132$	−0.756575	+	1.39708i	−0.0658514	+	0.121600i
$133$	−15.6954	+	17.4315i	−1.36096	+	1.51150i
$134$	3.50990	+	2.55009i	0.303209	+	0.220294i
$135$	10.0418	−	5.84488i	0.864259	−	0.503047i
$136$	−4.04721	+	2.94047i	−0.347045	+	0.252143i
$137$	0.843300	−	8.02346i	0.0720480	−	0.685491i	−0.897571	−	0.440870i	$-0.854670\pi$
$137$	0.843300	−	8.02346i	0.0720480	−	0.685491i	0.969619	−	0.244620i	$-0.0786634\pi$
$138$	−4.01274	+	1.91937i	−0.341587	+	0.163388i
$139$	−1.18925	−	11.3149i	−0.100871	−	0.959721i	−0.921531	−	0.388305i	$-0.873061\pi$
$139$	−1.18925	−	11.3149i	−0.100871	−	0.959721i	0.820660	−	0.571417i	$-0.193606\pi$
$140$	0.611695	−	1.12725i	0.0516977	−	0.0952698i
$141$	15.8801	+	10.8885i	1.33735	+	0.916979i
$142$	−8.10801	+	9.00486i	−0.680409	+	0.755671i
$143$	4.71237			0.394069
$144$	10.8437	+	1.69315i	0.903640	+	0.141096i
$145$	16.7522	−	0.442693i	1.39120	−	0.0367636i
$146$	11.4269	−	2.42887i	0.945699	−	0.201015i
$147$	−10.3195	+	2.48945i	−0.851142	+	0.205326i
$148$	−0.0433112	−	0.412078i	−0.00356016	−	0.0338726i
$149$	7.57401	−	13.1186i	0.620487	−	1.07471i	−0.368908	−	0.929466i	$-0.620268\pi$
$149$	7.57401	−	13.1186i	0.620487	−	1.07471i	0.989395	−	0.145249i	$-0.0463983\pi$
$150$	0.289162	−	11.7492i	0.0236099	−	0.959320i
$151$	1.63784	+	2.83682i	0.133285	+	0.230857i	0.924941	−	0.380110i	$-0.124114\pi$
$151$	1.63784	+	2.83682i	0.133285	+	0.230857i	−0.791656	+	0.610967i	$0.790781\pi$
$152$	15.3400	−	11.1451i	1.24424	−	0.903990i
$153$	−4.94637	+	1.33698i	−0.399890	+	0.108089i
$154$	8.80535	−	27.1001i	0.709555	−	2.18379i
$155$	3.12289	+	1.29266i	0.250836	+	0.103829i
$156$	0.0746552	+	0.210089i	0.00597720	+	0.0168206i
$157$	3.26548	−	5.65597i	0.260614	−	0.451396i	−0.705792	−	0.708420i	$-0.749408\pi$
$157$	3.26548	−	5.65597i	0.260614	−	0.451396i	0.966405	+	0.257024i	$0.0827418\pi$
$158$	−4.71178	−	1.00152i	−0.374849	−	0.0796767i
$159$	15.0496	−	7.19853i	1.19351	−	0.570881i
$160$	−1.29687	+	1.51918i	−0.102527	+	0.120102i
$161$	−5.54729	+	4.03035i	−0.437188	+	0.317636i
$162$	10.6041	+	6.06057i	0.833139	+	0.476164i
$163$	−16.9298	−	12.3002i	−1.32605	−	0.963429i	−0.999836	−	0.0181320i	$-0.994228\pi$
$163$	−16.9298	−	12.3002i	−1.32605	−	0.963429i	−0.326211	−	0.945297i	$-0.605772\pi$
$164$	0.571143	+	0.254289i	0.0445988	+	0.0198567i
$165$	3.54046	+	22.1622i	0.275625	+	1.72533i
$166$	11.4410	−	5.09385i	0.887993	−	0.395360i
$167$	−1.61166	−	0.342569i	−0.124714	−	0.0265088i	0.145132	−	0.989412i	$-0.453639\pi$
$167$	−1.61166	−	0.342569i	−0.124714	−	0.0265088i	−0.269846	+	0.962904i	$0.586973\pi$
$168$	18.3753	−	0.501294i	1.41768	−	0.0386757i
$169$	−8.25620	+	9.16944i	−0.635092	+	0.705342i
$170$	−1.47083	+	4.96981i	−0.112808	+	0.381167i
$171$	18.7480	−	5.06751i	1.43370	−	0.387523i
$172$	0.400638	−	1.23304i	0.0305484	−	0.0940183i
$173$	−17.6770	−	7.87029i	−1.34395	−	0.598367i	−0.396434	−	0.918063i	$-0.629753\pi$
$173$	−17.6770	−	7.87029i	−1.34395	−	0.598367i	−0.947520	+	0.319696i	$0.896419\pi$
$174$	9.22083	+	15.0101i	0.699029	+	1.13791i
$175$	−2.84269	−	17.8925i	−0.214887	−	1.35255i
$176$	−10.5998	+	18.3593i	−0.798987	+	1.38389i
$177$	4.38585	+	1.81106i	0.329661	+	0.136128i
$178$	0.00926489	−	0.00196931i	0.000694433	−	0.000147606i
$179$	−5.48463	+	16.8800i	−0.409941	+	1.26167i	0.506758	+	0.862089i	$0.330844\pi$
$179$	−5.48463	+	16.8800i	−0.409941	+	1.26167i	−0.916698	+	0.399580i	$0.869156\pi$
$180$	−0.931956	+	0.508945i	−0.0694639	+	0.0379345i
$181$	−1.01795	−	3.13292i	−0.0756633	−	0.232868i	0.906071	−	0.423126i	$-0.139067\pi$
$181$	−1.01795	−	3.13292i	−0.0756633	−	0.232868i	−0.981734	+	0.190259i	$0.939067\pi$
$182$	−1.99937	−	3.46302i	−0.148204	−	0.256696i
$183$	0.665949	+	1.87406i	0.0492284	+	0.138535i
$184$	5.06361	−	2.25446i	0.373294	−	0.166201i
$185$	−4.03002	−	4.24472i	−0.296293	−	0.312078i
$186$	0.467601	+	3.52200i	0.0342862	+	0.258245i
$187$	1.03455	−	9.84309i	0.0756538	−	0.719798i
$188$	−1.42362	−	1.03432i	−0.103828	−	0.0754358i
$189$	17.7683	+	6.22651i	1.29245	+	0.452912i
$190$	5.57482	−	18.8369i	0.404440	−	1.36657i
$191$	2.35882	−	22.4427i	0.170678	−	1.62389i	−0.488957	−	0.872308i	$-0.662622\pi$
$191$	2.35882	−	22.4427i	0.170678	−	1.62389i	0.659635	−	0.751586i	$-0.270711\pi$
$192$	−14.5282	−	2.67620i	−1.04848	−	0.193138i
$193$	−7.18794	+	12.4499i	−0.517399	+	0.896161i	0.482397	+	0.875953i	$0.339766\pi$
$193$	−7.18794	+	12.4499i	−0.517399	+	0.896161i	−0.999796	+	0.0202084i	$0.993567\pi$
$194$	−0.0495368	−	0.0105294i	−0.00355653	−	0.000755965i
$195$	2.64370	+	1.71183i	0.189319	+	0.122587i
$196$	0.948969	−	0.201710i	0.0677835	−	0.0144078i
$197$	3.42186	−	10.5314i	0.243798	−	0.750332i	−0.752034	−	0.659124i	$-0.770927\pi$
$197$	3.42186	−	10.5314i	0.243798	−	0.750332i	0.995832	−	0.0912078i	$-0.0290728\pi$
$198$	−18.3022	+	14.8872i	−1.30068	+	1.05799i
$199$	13.9667			0.990073			0.495037	−	0.868872i	$-0.335155\pi$
$199$	13.9667			0.990073			0.495037	+	0.868872i	$0.335155\pi$
$200$	−0.759448	+	14.6253i	−0.0537011	+	1.03417i
$201$	−2.89833	−	4.71804i	−0.204432	−	0.332785i
$202$	1.43046	+	13.6099i	0.100647	+	0.957592i
$203$	18.1704	+	20.1803i	1.27531	+	1.41638i
$204$	0.455218	−	0.109815i	0.0318717	−	0.00768860i
$205$	8.58700	−	2.06373i	0.599742	−	0.144137i
$206$	4.67361	+	14.3839i	0.325626	+	1.00217i
$207$	5.66871	−	0.309525i	0.394003	−	0.0215135i
$208$	0.919323	+	2.82938i	0.0637436	+	0.196183i
$209$	−3.92121	+	37.3079i	−0.271236	+	2.58064i
$210$	14.7844	−	12.0048i	1.02022	−	0.828412i
$211$	−2.79668	−	26.6087i	−0.192532	−	1.83182i	−0.483805	−	0.875176i	$-0.660746\pi$
$211$	−2.79668	−	26.6087i	−0.192532	−	1.83182i	0.291273	−	0.956640i	$-0.405921\pi$
$212$	−1.39283	+	0.620129i	−0.0956602	+	0.0425906i
$213$	13.9513	−	6.67319i	0.955929	−	0.457239i
$214$	−4.13908	−	1.84284i	−0.282942	−	0.125974i
$215$	−6.11758	−	17.2624i	−0.417216	−	1.17728i
$216$	−13.0029	−	7.90957i	−0.884732	−	0.538178i
$217$	1.69242	+	5.20875i	0.114889	+	0.353593i
$218$	6.15985	+	10.6692i	0.417197	+	0.722607i
$219$	−14.6632	−	2.70108i	−0.990849	−	0.182522i
$220$	−0.268212	−	2.03350i	−0.0180828	−	0.137099i
$221$	−0.929369	−	1.03217i	−0.0625161	−	0.0694312i
$222$	1.74103	−	5.90131i	0.116850	−	0.396070i
$223$	22.3244	+	9.93945i	1.49495	+	0.665595i	0.981314	−	0.192414i	$-0.0616315\pi$
$223$	22.3244	+	9.93945i	1.49495	+	0.665595i	0.513636	+	0.858008i	$0.328298\pi$
$224$	−3.23671			−0.216262
$225$	−6.06447	+	13.7194i	−0.404298	+	0.914627i
$226$	7.80440			0.519141
$227$	−1.59524	−	0.710248i	−0.105880	−	0.0471408i	0.353113	−	0.935581i	$-0.385123\pi$
$227$	−1.59524	−	0.710248i	−0.105880	−	0.0471408i	−0.458993	+	0.888440i	$0.651790\pi$
$228$	−1.72540	+	0.416228i	−0.114267	+	0.0275654i
$229$	13.0970	+	14.5457i	0.865474	+	0.961206i	0.999557	−	0.0297638i	$-0.00947551\pi$
$229$	13.0970	+	14.5457i	0.865474	+	0.961206i	−0.134083	+	0.990970i	$0.542809\pi$
$230$	2.73890	−	5.04730i	0.180597	−	0.332809i
$231$	−23.5886	+	27.6800i	−1.55202	+	1.82121i
$232$	−10.9756	−	19.0104i	−0.720587	−	1.24809i
$233$	1.68425	+	5.18360i	0.110339	+	0.339589i	0.990946	−	0.134258i	$-0.0428650\pi$
$233$	1.68425	+	5.18360i	0.110339	+	0.339589i	−0.880607	+	0.473847i	$0.842865\pi$
$234$	−0.166037	+	3.30662i	−0.0108542	+	0.216161i
$235$	−24.8488	+	0.656653i	−1.62096	+	0.0428353i
$236$	−0.396165	−	0.176384i	−0.0257882	−	0.0114816i
$237$	5.07051	+	3.47670i	0.329365	+	0.225836i
$238$	−7.67241	+	3.41598i	−0.497328	+	0.221425i
$239$	−0.382646	−	3.64063i	−0.0247513	−	0.235493i	−0.999903	−	0.0139533i	$-0.995558\pi$
$239$	−0.382646	−	3.64063i	−0.0247513	−	0.235493i	0.975151	−	0.221540i	$-0.0711083\pi$
$240$	−12.6159	+	6.44931i	−0.814350	+	0.416301i
$241$	−1.95702	+	18.6198i	−0.126063	+	1.19941i	0.730333	+	0.683091i	$0.239365\pi$
$241$	−1.95702	+	18.6198i	−0.126063	+	1.19941i	−0.856397	+	0.516319i	$0.827302\pi$
$242$	−9.46924	−	29.1433i	−0.608706	−	1.87340i
$243$	−9.55717	−	12.3151i	−0.613093	−	0.790011i
$244$	−0.0561685	−	0.172869i	−0.00359582	−	0.0110668i
$245$	8.89796	−	10.4232i	0.568470	−	0.665916i
$246$	6.39784	+	6.72716i	0.407911	+	0.428908i
$247$	3.52255	+	3.91218i	0.224134	+	0.248926i
$248$	−0.462773	−	4.40299i	−0.0293861	−	0.279590i
$249$	−15.9780	+	0.435894i	−1.01256	+	0.0276236i
$250$	8.60295	+	12.4981i	0.544098	+	0.790449i
$251$	−8.85291			−0.558791			−0.279395	−	0.960176i	$-0.590134\pi$
$251$	−8.85291			−0.558791			−0.279395	+	0.960176i	$0.590134\pi$
$252$	−1.60774	−	0.613120i	−0.101278	−	0.0386229i
$253$	−3.38869	+	10.4293i	−0.213045	+	0.655685i
$254$	12.7189	−	2.70349i	0.798057	−	0.169632i
$255$	4.15603	−	5.14629i	0.260260	−	0.322273i
$256$	3.69215	+	0.784790i	0.230759	+	0.0490494i
$257$	4.67379	−	8.09525i	0.291543	−	0.504968i	−0.682632	−	0.730763i	$-0.739165\pi$
$257$	4.67379	−	8.09525i	0.291543	−	0.504968i	0.974175	+	0.225795i	$0.0724979\pi$
$258$	12.4872	−	14.6530i	0.777417	−	0.912257i
$259$	0.991401	−	9.43255i	0.0616026	−	0.586110i
$260$	−0.237255	−	0.162977i	−0.0147139	−	0.0101074i
$261$	−3.56576	−	22.1988i	−0.220715	−	1.37407i
$262$	5.19880	+	3.77715i	0.321183	+	0.233353i
$263$	−1.12680	+	10.7208i	−0.0694817	+	0.661075i	0.903246	+	0.429124i	$0.141178\pi$
$263$	−1.12680	+	10.7208i	−0.0694817	+	0.661075i	−0.972727	+	0.231951i	$0.925489\pi$
$264$	23.3036	−	17.9220i	1.43424	−	1.10302i
$265$	−10.2721	+	18.9297i	−0.631011	+	1.16284i
$266$	29.0804	−	12.9474i	1.78303	−	0.793858i
$267$	−0.0118889	−	0.00219002i	−0.000727587	−	0.000134027i
$268$	0.253024	+	0.438251i	0.0154559	+	0.0267704i
$269$	0.431845	+	1.32908i	0.0263301	+	0.0810356i	0.963358	−	0.268219i	$-0.0864350\pi$
$269$	0.431845	+	1.32908i	0.0263301	+	0.0810356i	−0.937028	+	0.349254i	$0.886435\pi$
$270$	−15.6757	+	1.70343i	−0.953995	+	0.103668i
$271$	0.0702470	−	0.216198i	0.00426720	−	0.0131331i	−0.948900	−	0.315576i	$-0.897802\pi$
$271$	0.0702470	−	0.216198i	0.00426720	−	0.0131331i	0.953167	+	0.302443i	$0.0978022\pi$
$272$	6.11178	−	1.29910i	0.370581	−	0.0787694i
$273$	0.671687	+	5.05918i	0.0406523	+	0.306196i
$274$	−5.47429	+	9.48174i	−0.330714	+	0.572813i
$275$	−20.4976	−	20.4780i	−1.23605	−	1.23487i
$276$	−0.518649	+	0.0141492i	−0.0312190	+	0.000851682i
$277$	9.08110	+	4.04317i	0.545630	+	0.242930i	0.660992	−	0.750393i	$-0.270136\pi$
$277$	9.08110	+	4.04317i	0.545630	+	0.242930i	−0.115361	+	0.993324i	$0.536803\pi$
$278$	−4.77123	+	14.6844i	−0.286160	+	0.880709i
$279$	1.16404	−	4.38259i	0.0696892	−	0.262379i
$280$	−18.8238	+	14.4512i	−1.12494	+	0.863622i
$281$	−1.01002	+	1.12174i	−0.0602529	+	0.0669176i	−0.772518	−	0.634993i	$-0.781003\pi$
$281$	−1.01002	+	1.12174i	−0.0602529	+	0.0669176i	0.712265	+	0.701911i	$0.247670\pi$
$282$	−13.6774	−	22.2647i	−0.814477	−	1.32585i
$283$	1.19385	+	0.253761i	0.0709671	+	0.0150845i	0.243258	−	0.969962i	$-0.421784\pi$
$283$	1.19385	+	0.253761i	0.0709671	+	0.0150845i	−0.172291	+	0.985046i	$0.555117\pi$
$284$	−1.29118	+	0.574873i	−0.0766177	+	0.0341124i
$285$	−15.7524	+	19.5058i	−0.933092	+	1.15542i
$286$	−5.84225	−	2.60114i	−0.345459	−	0.153808i
$287$	11.5777	+	8.41168i	0.683409	+	0.496526i
$288$	2.25070	+	1.45463i	0.132624	+	0.0857150i
$289$	11.3933	−	8.27771i	0.670193	−	0.486924i
$290$	−21.0132	−	8.69807i	−1.23394	−	0.510768i
$291$	0.0533082	+	0.0365519i	0.00312498	+	0.00214271i
$292$	1.33286	+	0.283308i	0.0779997	+	0.0165793i
$293$	−9.32859	+	16.1576i	−0.544982	+	0.943937i	0.453626	+	0.891192i	$0.350130\pi$
$293$	−9.32859	+	16.1576i	−0.544982	+	0.943937i	−0.998608	+	0.0527445i	$0.983203\pi$
$294$	14.1680	+	2.60985i	0.826293	+	0.152209i
$295$	−5.95625	+	1.43148i	−0.346786	+	0.0833440i
$296$	−2.36921	+	7.29168i	−0.137708	+	0.423820i
$297$	28.8426	−	8.64664i	1.67362	−	0.501729i
$298$	−16.6312	+	12.0833i	−0.963419	+	0.699965i
$299$	0.769448	+	1.33272i	0.0444983	+	0.0770733i
$300$	0.588226	−	1.23825i	0.0339612	−	0.0714905i
$301$	14.8385	−	25.7010i	0.855276	−	1.48138i
$302$	−0.464671	−	4.42105i	−0.0267388	−	0.254403i
$303$	4.94227	−	16.7521i	0.283926	−	0.962384i
$304$	−23.1652	+	4.92392i	−1.32862	+	0.282406i
$305$	−2.11639	−	1.45381i	−0.121184	−	0.0832448i
$306$	6.87034	+	1.07275i	0.392751	+	0.0613249i
$307$	16.1713			0.922948			0.461474	−	0.887154i	$-0.347321\pi$
$307$	16.1713			0.922948			0.461474	+	0.887154i	$0.347321\pi$
$308$	2.22398	−	2.46997i	0.126723	−	0.140740i
$309$	1.49342	−	19.2450i	0.0849580	−	1.09481i
$310$	−3.15813	−	3.32637i	−0.179370	−	0.188925i
$311$	2.17268	+	20.6717i	0.123202	+	1.17218i	0.865074	+	0.501644i	$0.167271\pi$
$311$	2.17268	+	20.6717i	0.123202	+	1.17218i	−0.741873	+	0.670541i	$0.766062\pi$
$312$	0.319186	−	4.11318i	0.0180704	−	0.232863i
$313$	1.30223	−	12.3899i	0.0736064	−	0.700318i	−0.894036	−	0.447994i	$-0.852138\pi$
$313$	1.30223	−	12.3899i	0.0736064	−	0.700318i	0.967643	−	0.252324i	$-0.0811949\pi$
$314$	−7.17042	+	5.20962i	−0.404650	+	0.293996i
$315$	−23.2886	+	6.95996i	−1.31216	+	0.392149i
$316$	−0.454562	−	0.330259i	−0.0255711	−	0.0185785i
$317$	−15.4630	+	17.1734i	−0.868488	+	0.964554i	−0.999641	−	0.0268081i	$-0.991466\pi$
$317$	−15.4630	+	17.1734i	−0.868488	+	0.964554i	0.131152	+	0.991362i	$0.458132\pi$
$318$	−22.6315	+	0.617407i	−1.26911	+	0.0346225i
$319$	42.4799	+	9.02939i	2.37842	+	0.505549i
$320$	17.2116	−	8.21457i	0.962157	−	0.459208i
$321$	3.98508	+	4.19020i	0.222425	+	0.233874i
$322$	9.10203	−	1.93470i	0.507236	−	0.107816i
$323$	8.94501	−	6.49893i	0.497714	−	0.361610i
$324$	0.842423	+	1.14889i	0.0468013	+	0.0638271i
$325$	−4.06035	+	0.214747i	−0.225228	+	0.0119120i
$326$	14.1996	+	24.5944i	0.786441	+	1.36216i
$327$	−2.06939	−	15.5868i	−0.114438	−	0.861950i
$328$	−7.74073	−	8.59695i	−0.427410	−	0.474687i
$329$	−26.9524	−	29.9337i	−1.48594	−	1.65030i
$330$	7.84376	−	29.4303i	0.431785	−	1.62008i
$331$	5.37570	−	5.97032i	0.295475	−	0.328159i	−0.577067	−	0.816697i	$-0.695803\pi$
$331$	5.37570	−	5.97032i	0.295475	−	0.328159i	0.872543	+	0.488538i	$0.162470\pi$
$332$	1.46079			0.0801713
$333$	−4.92853	+	6.11353i	−0.270082	+	0.335019i
$334$	1.80899	+	1.31431i	0.0989836	+	0.0719158i
$335$	6.60497	+	2.73401i	0.360868	+	0.149375i
$336$	−21.2213	−	8.76297i	−1.15772	−	0.478059i
$337$	17.2811	−	7.69405i	0.941363	−	0.419122i	0.122086	−	0.992520i	$-0.461042\pi$
$337$	17.2811	−	7.69405i	0.941363	−	0.419122i	0.819277	+	0.573398i	$0.194375\pi$
$338$	15.2971	−	6.81072i	0.832054	−	0.370454i
$339$	−9.20665	−	3.80172i	−0.500037	−	0.206481i
$340$	−0.392509	+	0.459792i	−0.0212868	+	0.0249357i
$341$	7.08615	+	5.14839i	0.383736	+	0.278801i
$342$	−26.0403	−	4.06599i	−1.40810	−	0.219864i
$343$	−3.15631			−0.170425
$344$	−16.0523	+	17.8279i	−0.865482	+	0.961215i
$345$	−5.68968	+	4.61999i	−0.306322	+	0.248732i
$346$	17.5711	+	19.5147i	0.944627	+	1.04911i
$347$	7.90347	+	8.77770i	0.424281	+	0.471211i	0.916948	−	0.399006i	$-0.130645\pi$
$347$	7.90347	+	8.77770i	0.424281	+	0.471211i	−0.492668	+	0.870218i	$0.663978\pi$
$348$	0.270431	+	2.03690i	0.0144966	+	0.109190i
$349$	−4.49549	−	7.78642i	−0.240638	−	0.416797i	0.720258	−	0.693706i	$-0.244023\pi$
$349$	−4.49549	−	7.78642i	−0.240638	−	0.416797i	−0.960896	+	0.276909i	$0.910690\pi$
$350$	−6.35203	+	23.7517i	−0.339530	+	1.26958i
$351$	1.80661	−	3.81986i	0.0964297	−	0.203889i
$352$	−4.18782	+	3.04263i	−0.223211	+	0.162173i
$353$	26.8537	−	5.70792i	1.42928	−	0.303802i	0.572676	−	0.819782i	$-0.305905\pi$
$353$	26.8537	−	5.70792i	1.42928	−	0.303802i	0.856601	+	0.515980i	$0.172572\pi$
$354$	−4.43777	−	4.66619i	−0.235865	−	0.248005i
$355$	−9.52247	+	17.5482i	−0.505400	+	0.931364i
$356$	0.00108068		0.000229705i	5.72757e−5		1.21743e-5i
$357$	10.7150	−	0.292314i	0.567096	−	0.0154709i
$358$	16.1171	−	17.8998i	0.851814	−	0.946036i
$359$	−23.8073	−	17.2970i	−1.25650	−	0.912901i	−0.257920	−	0.966166i	$-0.583037\pi$
$359$	−23.8073	−	17.2970i	−1.25650	−	0.912901i	−0.998580	+	0.0532656i	$0.983037\pi$
$360$	19.5840	−	1.58915i	1.03217	−	0.0837557i
$361$	−18.5326	+	13.4647i	−0.975399	+	0.708669i
$362$	−0.467291	+	4.44597i	−0.0245603	+	0.233675i
$363$	−3.02584	+	38.9924i	−0.158815	+	2.04657i
$364$	−0.0487544	−	0.463867i	−0.00255542	−	0.0243132i
$365$	17.3715	−	8.29092i	0.909268	−	0.433966i
$366$	0.208823	−	2.69099i	0.0109154	−	0.140660i
$367$	5.56358	−	6.17898i	0.290416	−	0.322540i	−0.580227	−	0.814455i	$-0.697036\pi$
$367$	5.56358	−	6.17898i	0.290416	−	0.322540i	0.870643	+	0.491915i	$0.163703\pi$
$368$	−6.92301			−0.360887
$369$	−4.27040	−	11.0524i	−0.222308	−	0.575366i
$370$	2.65329	+	7.48695i	0.137938	+	0.389228i
$371$	−34.1368	+	7.25600i	−1.77229	+	0.376713i
$372$	−0.117266	+	0.397480i	−0.00607996	+	0.0206084i
$373$	−0.387360	−	3.68548i	−0.0200567	−	0.190827i	0.979906	−	0.199460i	$-0.0639187\pi$
$373$	−0.387360	−	3.68548i	−0.0200567	−	0.190827i	−0.999963	+	0.00863278i	$0.997252\pi$
$374$	−6.71579	+	11.6321i	−0.347265	+	0.601481i
$375$	−4.06054	−	18.9344i	−0.209685	−	0.977769i
$376$	16.2803	+	28.1984i	0.839595	+	1.45422i
$377$	4.93057	−	3.58227i	0.253937	−	0.184496i
$378$	−18.5916	−	17.5271i	−0.956249	−	0.901499i
$379$	−1.43560	+	4.41832i	−0.0737419	+	0.226954i	−0.981133	−	0.193332i	$-0.938070\pi$
$379$	−1.43560	+	4.41832i	−0.0737419	+	0.226954i	0.907391	+	0.420286i	$0.138070\pi$
$380$	1.48771	−	1.74273i	0.0763179	−	0.0894002i
$381$	−16.3212	−	3.00648i	−0.836158	−	0.154027i
$382$	−15.3123	+	26.5217i	−0.783445	+	1.35697i
$383$	18.6644	+	3.96724i	0.953707	+	0.202717i	0.658385	−	0.752681i	$-0.271240\pi$
$383$	18.6644	+	3.96724i	0.953707	+	0.202717i	0.295322	+	0.955398i	$0.404573\pi$
$384$	13.9823	+	9.58723i	0.713529	+	0.489246i
$385$	3.67246	−	46.8065i	0.187166	−	2.38548i
$386$	15.7834	−	11.4673i	0.803356	−	0.583673i
$387$	−21.8687	+	11.2030i	−1.11165	+	0.569480i
$388$	−0.00477899	−	0.00347214i	−0.000242616	−	0.000176271i
$389$	3.47141	+	1.54557i	0.176007	+	0.0783635i	0.492849	−	0.870115i	$-0.335956\pi$
$389$	3.47141	+	1.54557i	0.176007	+	0.0783635i	−0.316841	+	0.948479i	$0.602622\pi$
$390$	−2.33268	−	3.58154i	−0.118120	−	0.181359i
$391$	2.95268	−	1.31462i	0.149324	−	0.0664831i
$392$	−17.5593	−	3.73235i	−0.886880	−	0.188512i
$393$	−4.29295	−	6.98828i	−0.216551	−	0.352512i
$394$	−10.0554	+	11.1677i	−0.506586	+	0.562621i
$395$	−7.93422	+	0.209669i	−0.399214	+	0.0105496i
$396$	−2.65653	+	0.718049i	−0.133495	+	0.0360833i
$397$	−6.50617	+	20.0239i	−0.326535	+	1.00497i	0.644207	+	0.764851i	$0.277187\pi$
$397$	−6.50617	+	20.0239i	−0.326535	+	1.00497i	−0.970743	+	0.240122i	$0.922813\pi$
$398$	−17.3155	−	7.70934i	−0.867946	−	0.386434i
$399$	−40.6125	+	1.10794i	−2.03317	+	0.0554666i
$400$	8.29647	−	16.3021i	0.414824	−	0.815104i
$401$	−11.2925	+	19.5592i	−0.563922	+	0.976741i	0.433228	+	0.901285i	$0.357375\pi$
$401$	−11.2925	+	19.5592i	−0.563922	+	0.976741i	−0.997149	+	0.0754562i	$0.975959\pi$
$402$	0.988985	+	7.44910i	0.0493261	+	0.371527i
$403$	1.20231	−	0.255559i	0.0598914	−	0.0127303i
$404$	−0.493263	+	1.51811i	−0.0245408	+	0.0755287i
$405$	19.3221	+	5.62656i	0.960121	+	0.279586i
$406$	−11.3880	−	35.0486i	−0.565175	−	1.73943i
$407$	−7.58421	−	13.1362i	−0.375935	−	0.651139i
$408$	−8.52143	−	1.56971i	−0.421874	−	0.0777123i
$409$	−22.5846	+	10.0553i	−1.11674	+	0.497203i	−0.880287	−	0.474441i	$-0.842650\pi$
$409$	−22.5846	+	10.0553i	−1.11674	+	0.497203i	−0.236449	+	0.971644i	$0.575984\pi$
$410$	−11.7850	−	2.18130i	−0.582021	−	0.107727i
$411$	11.0767	−	8.51871i	0.546372	−	0.420197i
$412$	−0.184399	+	1.75444i	−0.00908471	+	0.0864352i
$413$	−8.03070	−	5.83464i	−0.395165	−	0.287104i
$414$	−7.19873	−	2.74528i	−0.353798	−	0.134923i
$415$	16.3680	−	12.5658i	0.803472	−	0.616832i
$416$	−0.0759320	+	0.722444i	−0.00372287	+	0.0354207i
$417$	12.7816	−	14.9986i	0.625919	−	0.734483i
$418$	25.4546	−	44.0886i	1.24502	−	2.15645i
$419$	38.1667	+	8.11259i	1.86457	+	0.396326i	0.995202	−	0.0978459i	$-0.0311952\pi$
$419$	38.1667	+	8.11259i	1.86457	+	0.396326i	0.869364	+	0.494172i	$0.164529\pi$
$420$	2.14493	−	0.577800i	0.104662	−	0.0281937i
$421$	−22.2800	+	4.73576i	−1.08586	+	0.230807i	−0.715874	−	0.698230i	$-0.753971\pi$
$421$	−22.2800	+	4.73576i	−1.08586	+	0.230807i	−0.369988	+	0.929037i	$0.620638\pi$
$422$	−11.2202	+	34.5323i	−0.546191	+	1.68100i
$423$	5.28914	+	32.9278i	0.257167	+	1.60100i
$424$	28.2114			1.37007
$425$	−0.442848	+	8.52830i	−0.0214813	+	0.413683i
$426$	−20.9799	+	0.572349i	−1.01648	+	0.0277304i
$427$	−0.434905	−	4.13784i	−0.0210465	−	0.200244i
$428$	−0.353622	−	0.392737i	−0.0170930	−	0.0189837i
$429$	5.62487	+	5.91441i	0.271572	+	0.285550i
$430$	−1.94410	+	24.7781i	−0.0937528	+	1.19491i
$431$	−9.46750	−	29.1380i	−0.456033	−	1.40353i	−0.869918	−	0.493197i	$-0.835828\pi$
$431$	−9.46750	−	29.1380i	−0.456033	−	1.40353i	0.413885	−	0.910329i	$-0.364172\pi$
$432$	10.8184	+	15.6307i	0.520500	+	0.752032i
$433$	−3.87801	−	11.9353i	−0.186365	−	0.573573i	0.813604	−	0.581419i	$-0.197502\pi$
$433$	−3.87801	−	11.9353i	−0.186365	−	0.573573i	−0.999969	+	0.00784636i	$0.997502\pi$
$434$	0.776912	−	7.39182i	0.0372930	−	0.354819i
$435$	20.5517	+	20.4970i	0.985381	+	0.982755i
$436$	0.150207	+	1.42912i	0.00719359	+	0.0684425i
$437$	−11.1914	+	4.98275i	−0.535359	+	0.238357i
$438$	16.6881	+	11.4425i	0.797386	+	0.546745i
$439$	8.61888	+	3.83737i	0.411357	+	0.183148i	0.601972	−	0.798517i	$-0.294382\pi$
$439$	8.61888	+	3.83737i	0.411357	+	0.183148i	−0.190616	+	0.981665i	$0.561048\pi$
$440$	−10.7705	+	36.3926i	−0.513463	+	1.73495i
$441$	−15.4423	−	9.98035i	−0.735346	−	0.475255i
$442$	0.582465	+	1.79264i	0.0277050	+	0.0852673i
$443$	1.34165	+	2.32381i	0.0637439	+	0.110408i	0.896136	−	0.443779i	$-0.146363\pi$
$443$	1.34165	+	2.32381i	0.0637439	+	0.110408i	−0.832392	+	0.554187i	$0.813029\pi$
$444$	0.465493	−	0.546232i	0.0220913	−	0.0259230i
$445$	0.0140848	−	0.00672223i	0.000667682	−	0.000318664i
$446$	−22.1906	−	24.6452i	−1.05076	−	1.16698i
$447$	25.5055	−	6.15285i	1.20637	−	0.291020i
$448$	28.2320	+	12.5697i	1.33384	+	0.593862i
$449$	16.6360			0.785100			0.392550	−	0.919731i	$-0.371593\pi$
$449$	16.6360			0.785100			0.392550	+	0.919731i	$0.371593\pi$
$450$	15.0914	−	13.6614i	0.711414	−	0.644005i
$451$	22.8871			1.07771
$452$	0.831619	+	0.370261i	0.0391161	+	0.0174156i
$453$	−1.60544	+	5.44175i	−0.0754304	+	0.255676i
$454$	1.58569	+	1.76109i	0.0744201	+	0.0826518i
$455$	−4.53650	−	4.77818i	−0.212674	−	0.224004i
$456$	32.2984	+	5.94961i	1.51251	+	0.278616i
$457$	−6.85895	−	11.8801i	−0.320848	−	0.555725i	0.659815	−	0.751428i	$-0.270635\pi$
$457$	−6.85895	−	11.8801i	−0.320848	−	0.555725i	−0.980663	+	0.195703i	$0.937301\pi$
$458$	−8.20830	−	25.2626i	−0.383549	−	1.18044i
$459$	−7.58220	−	4.61221i	−0.353907	−	0.215280i
$460$	0.531307	−	0.407889i	0.0247723	−	0.0190179i
$461$	4.82680	+	2.14903i	0.224806	+	0.100090i	0.516049	−	0.856559i	$-0.327402\pi$
$461$	4.82680	+	2.14903i	0.224806	+	0.100090i	−0.291243	+	0.956649i	$0.594069\pi$
$462$	44.5232	−	21.2963i	2.07141	−	0.990794i
$463$	−28.6434	+	12.7529i	−1.33117	+	0.592677i	−0.944187	−	0.329409i	$-0.893151\pi$
$463$	−28.6434	+	12.7529i	−1.33117	+	0.592677i	−0.386986	+	0.922085i	$0.626484\pi$
$464$	2.86589	+	27.2671i	0.133046	+	1.26585i
$465$	2.10520	+	5.46245i	0.0976264	+	0.253315i
$466$	0.773161	−	7.35614i	0.0358160	−	0.340767i
$467$	6.16817	+	18.9837i	0.285429	+	0.878459i	0.986270	+	0.165142i	$0.0528082\pi$
$467$	6.16817	+	18.9837i	0.285429	+	0.878459i	−0.700841	+	0.713317i	$0.747192\pi$
$468$	−0.174567	+	0.344469i	−0.00806937	+	0.0159231i
$469$	3.57951	+	11.0166i	0.165286	+	0.508699i
$470$	31.1692	+	12.9020i	1.43773	+	0.595124i
$471$	10.9965	−	2.65276i	0.506692	−	0.122233i
$472$	5.36924	+	5.96315i	0.247139	+	0.274476i
$473$	−4.96112	−	47.2019i	−0.228113	−	2.17035i
$474$	−4.36718	−	7.10912i	−0.200591	−	0.326533i
$475$	1.67851	−	32.3245i	0.0770152	−	1.48315i
$476$	−0.979617			−0.0449007
$477$	26.9986	+	10.2960i	1.23618	+	0.471424i
$478$	−1.53517	+	4.72475i	−0.0702168	+	0.216105i
$479$	6.25719	−	1.33001i	0.285898	−	0.0607696i	−0.0627302	−	0.998031i	$-0.519981\pi$
$479$	6.25719	−	1.33001i	0.285898	−	0.0607696i	0.348629	+	0.937261i	$0.386647\pi$
$480$	−3.45469	+	0.185674i	−0.157684	+	0.00847483i
$481$	−2.08211	−	0.442567i	−0.0949363	−	0.0201793i
$482$	12.7040	−	22.0040i	0.578653	−	1.00226i
$483$	−11.6799	−	2.15152i	−0.531453	−	0.0978976i
$484$	0.373613	−	3.55469i	0.0169824	−	0.161577i
$485$	−0.0834155	+	0.00220433i	−0.00378770	+	0.000100093i
$486$	5.05101	+	20.5432i	0.229118	+	0.931857i
$487$	0.699919	+	0.508521i	0.0317164	+	0.0230433i	0.603530	−	0.797340i	$-0.293760\pi$
$487$	0.699919	+	0.508521i	0.0317164	+	0.0230433i	−0.571814	+	0.820383i	$0.693760\pi$
$488$	−0.351561	+	3.34488i	−0.0159144	+	0.151416i
$489$	−4.77032	−	35.9303i	−0.215721	−	1.62483i
$490$	−16.7848	+	8.01089i	−0.758261	+	0.361895i
$491$	−3.54920	+	1.58021i	−0.160173	+	0.0713137i	−0.485257	−	0.874371i	$-0.661274\pi$
$491$	−3.54920	+	1.58021i	−0.160173	+	0.0713137i	0.325084	+	0.945685i	$0.394607\pi$
$492$	0.362585	+	1.02036i	0.0163466	+	0.0460014i
$493$	−6.40010	−	11.0853i	−0.288246	−	0.499257i
$494$	−2.20769	−	6.79458i	−0.0993287	−	0.305702i
$495$	−23.5893	+	30.8973i	−1.06026	+	1.38873i
$496$	−1.70876	+	5.25902i	−0.0767256	+	0.236137i
$497$	−31.6455	+	6.72646i	−1.41950	+	0.301723i
$498$	20.0496	+	8.27913i	0.898444	+	0.370996i
$499$	−3.51395	+	6.08634i	−0.157306	+	0.272462i	−0.933896	−	0.357544i	$-0.883614\pi$
$499$	−3.51395	+	6.08634i	−0.157306	+	0.272462i	0.776590	+	0.630006i	$0.216948\pi$
$500$	0.323769	+	1.73991i	0.0144794	+	0.0778113i
$501$	−1.49379	−	2.43166i	−0.0667375	−	0.108639i
$502$	10.9756	+	4.88663i	0.489863	+	0.218101i
$503$	−8.35675	+	25.7194i	−0.372609	+	1.14677i	0.572468	+	0.819927i	$0.305986\pi$
$503$	−8.35675	+	25.7194i	−0.372609	+	1.14677i	−0.945078	+	0.326846i	$0.894014\pi$
$504$	22.5626	+	22.4641i	1.00502	+	1.00063i
$505$	7.53192	+	21.2533i	0.335166	+	0.945759i
$506$	9.95796	−	11.0594i	0.442685	−	0.491652i
$507$	−21.3633	+	0.582810i	−0.948778	+	0.0258835i
$508$	1.48356	+	0.315341i	0.0658224	+	0.0139910i
$509$	2.73606	−	1.21817i	0.121274	−	0.0539945i	−0.345203	−	0.938528i	$-0.612190\pi$
$509$	2.73606	−	1.21817i	0.121274	−	0.0539945i	0.466477	+	0.884534i	$0.345523\pi$
$510$	−7.99315	+	4.08616i	−0.353943	+	0.180938i
$511$	28.4944	+	12.6865i	1.26052	+	0.561219i
$512$	−19.9816	−	14.5175i	−0.883072	−	0.641589i
$513$	28.7385	+	17.4815i	1.26884	+	0.771826i
$514$	−10.2628	+	7.45639i	−0.452674	+	0.328887i
$515$	13.0257	+	21.2445i	0.573980	+	0.936146i
$516$	2.02578	−	0.968970i	0.0891800	−	0.0426565i
$517$	−63.0111	−	13.3934i	−2.77123	−	0.589042i
$518$	−6.43569	+	11.1469i	−0.282768	+	0.489768i
$519$	−11.2221	−	31.5803i	−0.492594	−	1.38622i
$520$	2.78394	+	4.54054i	0.122084	+	0.199116i
$521$	−2.86656	+	8.82235i	−0.125586	+	0.386514i	−0.994007	−	0.109313i	$-0.965135\pi$
$521$	−2.86656	+	8.82235i	−0.125586	+	0.386514i	0.868421	+	0.495827i	$0.165135\pi$
$522$	−7.83257	+	29.4896i	−0.342822	+	1.29072i
$523$	27.2717	−	19.8140i	1.19251	−	0.866406i	0.198979	−	0.980004i	$-0.436237\pi$
$523$	27.2717	−	19.8140i	1.19251	−	0.866406i	0.993527	+	0.113597i	$0.0362374\pi$
$524$	0.374775	+	0.649129i	0.0163721	+	0.0283573i
$525$	19.0634	−	24.9250i	0.831994	−	1.08782i
$526$	7.31466	−	12.6694i	0.318934	−	0.552410i
$527$	−0.269851	−	2.56746i	−0.0117549	−	0.111840i
$528$	−35.6947	+	8.61085i	−1.55341	+	0.374739i
$529$	18.9945	−	4.03741i	0.825849	−	0.175540i
$530$	23.1839	−	17.7984i	1.00704	−	0.773115i
$531$	2.96210	+	7.66634i	0.128544	+	0.332691i
$532$	3.71300			0.160979
$533$	2.14912	−	2.38684i	0.0930887	−	0.103386i
$534$	0.0135306	+	0.00927753i	0.000585526	+	0.000401478i
$535$	−7.34064	−	1.35869i	−0.317364	−	0.0587412i
$536$	−0.978774	−	9.31241i	−0.0422766	−	0.402235i
$537$	−27.7324	+	13.2649i	−1.19674	+	0.572424i
$538$	0.198240	−	1.88612i	0.00854671	−	0.0813166i
$539$	28.7330	−	20.8757i	1.23762	−	0.899181i
$540$	−1.75119	−	0.562183i	−0.0753590	−	0.0241925i
$541$	−34.5832	−	25.1262i	−1.48685	−	1.08026i	−0.975269	−	0.221023i	$-0.929060\pi$
$541$	−34.5832	−	25.1262i	−1.48685	−	1.08026i	−0.511580	−	0.859236i	$-0.670940\pi$
$542$	−0.206427	+	0.229261i	−0.00886680	+	0.00984758i
$543$	2.71700	−	5.01717i	0.116598	−	0.215308i
$544$	1.49235	+	0.317210i	0.0639841	+	0.0136002i
$545$	13.9764	+	14.7210i	0.598685	+	0.630579i
$546$	1.95983	−	6.64297i	0.0838731	−	0.284293i
$547$	−31.4809	+	6.69148i	−1.34603	+	0.286107i	−0.823888	−	0.566753i	$-0.808199\pi$
$547$	−31.4809	+	6.69148i	−1.34603	+	0.286107i	−0.522140	+	0.852860i	$0.674866\pi$
$548$	−1.03317	+	0.750639i	−0.0441346	+	0.0320657i
$549$	−1.55720	+	3.07277i	−0.0664595	+	0.131143i
$550$	14.1088	+	36.7022i	0.601603	+	1.56499i
$551$	24.2580	+	42.0161i	1.03343	+	1.78995i
$552$	8.87366	+	3.66422i	0.377688	+	0.155960i
$553$	−8.60589	−	9.55781i	−0.365960	−	0.406440i
$554$	−9.02670	−	10.0252i	−0.383508	−	0.425929i
$555$	0.517069	−	10.1247i	0.0219483	−	0.429768i
$556$	−1.20507	+	1.33837i	−0.0511066	+	0.0567596i
$557$	0.690059			0.0292387			0.0146194	−	0.999893i	$-0.495346\pi$
$557$	0.690059			0.0292387			0.0146194	+	0.999893i	$0.495346\pi$
$558$	−3.86224	+	4.79087i	−0.163502	+	0.202814i
$559$	−5.38844	−	3.91493i	−0.227907	−	0.165584i
$560$	28.8198	−	6.92634i	1.21786	−	0.292691i
$561$	13.5887	−	10.4507i	0.573717	−	0.441227i
$562$	1.87137	−	0.833189i	0.0789391	−	0.0351460i
$563$	24.9057	−	11.0887i	1.04965	−	0.467335i	0.191908	−	0.981413i	$-0.438533\pi$
$563$	24.9057	−	11.0887i	1.04965	−	0.467335i	0.857743	+	0.514078i	$0.171866\pi$
$564$	−0.401135	−	3.02137i	−0.0168908	−	0.127223i
$565$	12.5032	−	3.00492i	0.526013	−	0.126418i
$566$	−1.34003	−	0.973587i	−0.0563255	−	0.0409229i
$567$	13.3941	+	29.7328i	0.562500	+	1.24866i
$568$	26.1526			1.09734
$569$	−1.82199	+	2.02353i	−0.0763818	+	0.0848306i	−0.780124	−	0.625625i	$-0.784844\pi$
$569$	−1.82199	+	2.02353i	−0.0763818	+	0.0848306i	0.703742	+	0.710455i	$0.251511\pi$
$570$	30.2961	−	15.4876i	1.26896	−	0.648704i
$571$	−8.49408	−	9.43363i	−0.355466	−	0.394785i	0.538717	−	0.842487i	$-0.318909\pi$
$571$	−8.49408	−	9.43363i	−0.355466	−	0.394785i	−0.894183	+	0.447702i	$0.852243\pi$
$572$	−0.499132	−	0.554342i	−0.0208698	−	0.0231782i
$573$	30.9829	−	23.8279i	1.29433	−	0.995426i
$574$	−9.71056	−	16.8192i	−0.405311	−	0.702019i
$575$	2.44454	−	9.14069i	0.101944	−	0.381193i
$576$	−13.9826	−	21.4285i	−0.582607	−	0.892853i
$577$	16.0147	−	11.6353i	0.666699	−	0.484386i	−0.202219	−	0.979340i	$-0.564815\pi$
$577$	16.0147	−	11.6353i	0.666699	−	0.484386i	0.868919	+	0.494955i	$0.164815\pi$
$578$	−18.6942	+	3.97357i	−0.777575	+	0.165279i
$579$	−24.2054	+	5.83922i	−1.00594	+	0.242670i
$580$	−1.82646	−	1.92377i	−0.0758398	−	0.0798801i
$581$	32.7071	+	6.95210i	1.35692	+	0.288422i
$582$	−0.0459138	−	0.0747409i	−0.00190319	−	0.00309811i
$583$	−37.3469	+	41.4780i	−1.54675	+	1.71784i
$584$	−20.3983	−	14.8202i	−0.844086	−	0.613265i
$585$	1.00714	+	5.36137i	0.0416402	+	0.221665i
$586$	20.4840	−	14.8825i	0.846184	−	0.614789i
$587$	0.882137	−	8.39297i	0.0364097	−	0.346415i	−0.961118	−	0.276138i	$-0.910945\pi$
$587$	0.882137	−	8.39297i	0.0364097	−	0.346415i	0.997528	−	0.0702765i	$-0.0223882\pi$
$588$	1.38589	+	0.950264i	0.0571531	+	0.0391882i
$589$	1.02281	+	9.73135i	0.0421440	+	0.400973i
$590$	8.17451	+	1.51303i	0.336539	+	0.0622904i
$591$	17.3022	−	8.27599i	0.711719	−	0.340429i
$592$	6.40763	−	7.11639i	0.263352	−	0.292482i
$593$	12.9618			0.532277			0.266139	−	0.963935i	$-0.414252\pi$
$593$	12.9618			0.532277			0.266139	+	0.963935i	$0.414252\pi$
$594$	−40.5309	−	5.20070i	−1.66300	−	0.213387i
$595$	−10.9765	+	8.42673i	−0.449992	+	0.345462i
$596$	−2.34544	+	0.498539i	−0.0960731	+	0.0204210i
$597$	16.6712	+	17.5293i	0.682307	+	0.717427i
$598$	−0.218300	−	2.07699i	−0.00892695	−	0.0849343i
$599$	−1.18552	+	2.05337i	−0.0484389	+	0.0838986i	−0.889228	−	0.457464i	$-0.848758\pi$
$599$	−1.18552	+	2.05337i	−0.0484389	+	0.0838986i	0.840789	+	0.541362i	$0.182091\pi$
$600$	−19.2625	+	16.5042i	−0.786388	+	0.673782i
$601$	−10.9399	−	18.9484i	−0.446247	−	0.772922i	0.551892	−	0.833916i	$-0.313906\pi$
$601$	−10.9399	−	18.9484i	−0.446247	−	0.772922i	−0.998138	+	0.0609941i	$0.980573\pi$
$602$	−32.5827	+	23.6727i	−1.32797	+	0.964829i
$603$	2.46197	−	9.26927i	0.100259	−	0.377474i
$604$	0.160231	−	0.493142i	0.00651972	−	0.0200656i
$605$	−26.3914	−	43.0437i	−1.07296	−	1.74998i
$606$	−15.3741	+	18.0407i	−0.624530	+	0.732853i
$607$	−3.49108	+	6.04672i	−0.141698	+	0.245429i	−0.928136	−	0.372240i	$-0.878590\pi$
$607$	−3.49108	+	6.04672i	−0.141698	+	0.245429i	0.786438	+	0.617669i	$0.211923\pi$
$608$	−5.65641	−	1.20231i	−0.229398	−	0.0487600i
$609$	−3.63896	+	46.8933i	−0.147458	+	1.90021i
$610$	1.82136	+	2.97059i	0.0737447	+	0.120276i
$611$	−7.31358	+	5.31363i	−0.295876	+	0.214966i
$612$	0.681193	+	0.440256i	0.0275356	+	0.0177963i
$613$	−8.10328	−	5.88738i	−0.327289	−	0.237789i	0.411991	−	0.911188i	$-0.364834\pi$
$613$	−8.10328	−	5.88738i	−0.327289	−	0.237789i	−0.739279	+	0.673399i	$0.764834\pi$
$614$	−20.0487	−	8.92626i	−0.809100	−	0.360235i
$615$	12.8399	+	8.31402i	0.517756	+	0.335254i
$616$	−56.1830	+	25.0143i	−2.26368	+	1.00785i
$617$	14.7266	+	3.13023i	0.592870	+	0.126018i	0.494569	−	0.869138i	$-0.335326\pi$
$617$	14.7266	+	3.13023i	0.592870	+	0.126018i	0.0983008	+	0.995157i	$0.468659\pi$
$618$	−12.4743	+	23.0349i	−0.501791	+	0.926601i
$619$	−17.8559	+	19.8310i	−0.717688	+	0.797073i	−0.986086	−	0.166235i	$-0.946839\pi$
$619$	−17.8559	+	19.8310i	−0.717688	+	0.797073i	0.268398	+	0.963308i	$0.413506\pi$
$620$	−0.178711	−	0.504280i	−0.00717721	−	0.0202524i
$621$	7.15487	+	6.74522i	0.287115	+	0.270676i
$622$	8.71674	−	26.8274i	0.349510	−	1.07568i
$623$	0.0231031	+	0.0102862i	0.000925606	+	0.000412107i
$624$	−2.45376	+	4.53109i	−0.0982292	+	0.181389i
$625$	18.5947	+	16.7104i	0.743786	+	0.668417i
$626$	−8.45344	+	14.6418i	−0.337867	+	0.585204i
$627$	−51.5049	+	39.6107i	−2.05691	+	1.58190i
$628$	−1.01122	+	0.214942i	−0.0403521	+	0.00857711i
$629$	−1.38153	+	4.25191i	−0.0550852	+	0.169535i
$630$	32.7142	+	4.22612i	1.30337	+	0.168373i
$631$	−12.8840	−	39.6527i	−0.512902	−	1.57855i	−0.787067	−	0.616868i	$-0.788401\pi$
$631$	−12.8840	−	39.6527i	−0.512902	−	1.57855i	0.274165	−	0.961683i	$-0.411599\pi$
$632$	5.19830	+	9.00373i	0.206777	+	0.358149i
$633$	30.0578	−	35.2712i	1.19469	−	1.40190i
$634$	28.6499	−	12.7558i	1.13783	−	0.506596i
$635$	19.3357	−	9.22835i	0.767314	−	0.366216i
$636$	−2.44085	−	1.00791i	−0.0967861	−	0.0399661i
$637$	0.520975	−	4.95675i	0.0206418	−	0.196394i
$638$	−47.6812	−	34.6424i	−1.88772	−	1.37151i
$639$	25.0282	+	9.54465i	0.990101	+	0.377580i
$640$	−21.8791	+	0.578176i	−0.864849	+	0.0228544i
$641$	1.83139	−	17.4245i	0.0723356	−	0.688227i	−0.896924	−	0.442185i	$-0.854203\pi$
$641$	1.83139	−	17.4245i	0.0723356	−	0.688227i	0.969259	−	0.246042i	$-0.0791300\pi$
$642$	−2.62766	−	7.39456i	−0.103706	−	0.291840i
$643$	21.8712	−	37.8820i	0.862514	−	1.49392i	−0.00698031	−	0.999976i	$-0.502222\pi$
$643$	21.8712	−	37.8820i	0.862514	−	1.49392i	0.869494	−	0.493943i	$-0.164445\pi$
$644$	1.06168	+	0.225667i	0.0418360	+	0.00889251i
$645$	14.3635	−	28.2831i	0.565561	−	1.11365i
$646$	−14.6770	+	3.11970i	−0.577460	+	0.122743i
$647$	1.45484	−	4.47752i	0.0571955	−	0.176030i	−0.918377	−	0.395706i	$-0.870500\pi$
$647$	1.45484	−	4.47752i	0.0571955	−	0.176030i	0.975573	+	0.219676i	$0.0705000\pi$
$648$	−5.59358	−	25.7608i	−0.219737	−	1.01198i
$649$	−15.8753			−0.623159
$650$	5.15242	+	1.97500i	0.202095	+	0.0774657i
$651$	−4.51725	+	8.34149i	−0.177045	+	0.326929i
$652$	0.346254	+	3.29438i	0.0135603	+	0.129018i
$653$	−7.88400	−	8.75607i	−0.308525	−	0.342651i	0.568864	−	0.822432i	$-0.307383\pi$
$653$	−7.88400	−	8.75607i	−0.308525	−	0.342651i	−0.877389	+	0.479780i	$0.840716\pi$
$654$	−6.03802	+	20.4662i	−0.236105	+	0.800293i
$655$	9.78315	+	4.04957i	0.382259	+	0.158230i
$656$	4.46497	+	13.7418i	0.174328	+	0.536525i
$657$	−14.1125	−	21.6276i	−0.550582	−	0.843774i
$658$	16.8919	+	51.9880i	0.658516	+	2.02670i
$659$	4.56492	−	43.4323i	0.177824	−	1.69188i	−0.434020	−	0.900903i	$-0.642905\pi$
$659$	4.56492	−	43.4323i	0.177824	−	1.69188i	0.611844	−	0.790978i	$-0.290428\pi$
$660$	2.23206	−	2.76389i	0.0868828	−	0.107584i
$661$	3.09245	+	29.4227i	0.120282	+	1.14441i	0.873563	+	0.486711i	$0.161803\pi$
$661$	3.09245	+	29.4227i	0.120282	+	1.14441i	−0.753281	+	0.657699i	$0.771530\pi$
$662$	−9.96012	+	4.43453i	−0.387111	+	0.172353i
$663$	0.186123	−	2.39847i	0.00722842	−	0.0931488i
$664$	−24.6930	−	10.9940i	−0.958275	−	0.426651i
$665$	41.6037	−	31.9395i	1.61332	−	1.23856i
$666$	9.48478	−	4.85891i	0.367528	−	0.188279i
$667$	4.38259	+	13.4882i	0.169695	+	0.522267i
$668$	0.130408	+	0.225873i	0.00504563	+	0.00873928i
$669$	14.1724	+	39.8830i	0.547938	+	1.54196i
$670$	−6.67950	−	7.03535i	−0.258052	−	0.271799i
$671$	−4.45242	−	4.94491i	−0.171884	−	0.190896i
$672$	−3.86347	−	4.06234i	−0.149037	−	0.156708i
$673$	−9.48138	−	4.22138i	−0.365480	−	0.162722i	0.215776	−	0.976443i	$-0.430772\pi$
$673$	−9.48138	−	4.22138i	−0.365480	−	0.162722i	−0.581256	+	0.813721i	$0.697439\pi$
$674$	−25.6715			−0.988831
$675$	−24.4577	+	8.76463i	−0.941379	+	0.337351i
$676$	1.95314			0.0751209
$677$	12.2593	+	5.45819i	0.471163	+	0.209775i	0.628561	−	0.777760i	$-0.283644\pi$
$677$	12.2593	+	5.45819i	0.471163	+	0.209775i	−0.157399	+	0.987535i	$0.550311\pi$
$678$	9.31564	+	9.79514i	0.357765	+	0.376180i
$679$	−0.0904771	−	0.100485i	−0.00347219	−	0.00385626i
$680$	10.0954	−	4.81821i	0.387139	−	0.184770i
$681$	−1.01273	−	2.84994i	−0.0388078	−	0.109210i
$682$	−5.94337	−	10.2942i	−0.227583	−	0.394186i
$683$	−6.23742	−	19.1968i	−0.238668	−	0.734546i	−0.996614	−	0.0822274i	$-0.973797\pi$
$683$	−6.23742	−	19.1968i	−0.238668	−	0.734546i	0.757945	−	0.652318i	$-0.226203\pi$
$684$	−2.58190	−	1.66868i	−0.0987214	−	0.0638037i
$685$	−5.11944	+	17.2982i	−0.195604	+	0.660929i
$686$	3.91310	+	1.74222i	0.149403	+	0.0665184i
$687$	−2.62291	+	33.8001i	−0.100070	+	1.28955i
$688$	27.3729	−	12.1872i	1.04358	−	0.464633i
$689$	0.818726	+	7.78965i	0.0311910	+	0.296762i
$690$	9.60402	−	2.58713i	0.365619	−	0.0984902i
$691$	5.21851	−	49.6508i	0.198522	−	1.88881i	−0.212471	−	0.977167i	$-0.568151\pi$
$691$	5.21851	−	49.6508i	0.198522	−	1.88881i	0.410992	−	0.911639i	$-0.365182\pi$
$692$	0.946509	+	2.91305i	0.0359809	+	0.110738i
$693$	−62.8969	+	3.43432i	−2.38925	+	0.130459i
$694$	−4.95336	−	15.2449i	−0.188027	−	0.578687i
$695$	−1.98995	+	25.3624i	−0.0754830	+	0.962051i
$696$	10.7586	−	36.4669i	0.407803	−	1.38227i
$697$	−4.51376	−	5.01304i	−0.170971	−	0.189882i
$698$	1.27542	+	12.1348i	0.0482752	+	0.459308i
$699$	−4.49544	+	8.30123i	−0.170033	+	0.313981i
$700$	−1.80370	+	2.22957i	−0.0681733	+	0.0842697i
$701$	−14.3384			−0.541556			−0.270778	−	0.962642i	$-0.587281\pi$
$701$	−14.3384			−0.541556			−0.270778	+	0.962642i	$0.587281\pi$
$702$	−4.34826	+	3.73852i	−0.164115	+	0.141101i
$703$	5.23635	−	16.1158i	0.197493	−	0.607820i
$704$	48.3439	−	10.2758i	1.82203	−	0.387284i
$705$	−30.4847	−	30.4035i	−1.14812	−	1.14506i
$706$	−36.4430	−	7.74619i	−1.37155	−	0.291532i
$707$	−18.2690	+	31.6429i	−0.687078	+	1.19005i
$708$	−0.251502	−	0.707758i	−0.00945203	−	0.0265992i
$709$	−0.419476	+	3.99104i	−0.0157537	+	0.149887i	−0.999571	−	0.0292879i	$-0.990676\pi$
$709$	−0.419476	+	3.99104i	−0.0157537	+	0.149887i	0.983817	+	0.179175i	$0.0573427\pi$
$710$	21.4919	−	16.4995i	0.806578	−	0.619216i
$711$	1.68882	+	10.5138i	0.0633357	+	0.394299i
$712$	−0.0165388	−	0.0120162i	−0.000619818	−	0.000450324i
$713$	−0.298990	+	2.84470i	−0.0111973	+	0.106535i
$714$	−13.4454	−	5.55204i	−0.503182	−	0.207780i
$715$	−10.3612	−	1.91777i	−0.387487	−	0.0717204i
$716$	2.56661	−	1.14273i	0.0959188	−	0.0427058i
$717$	4.11255	−	4.82586i	0.153586	−	0.180225i
$718$	19.9679	+	34.5854i	0.745195	+	1.29072i
$719$	−8.19802	−	25.2309i	−0.305734	−	0.940954i	−0.979402	−	0.201919i	$-0.935282\pi$
$719$	−8.19802	−	25.2309i	−0.305734	−	0.940954i	0.673668	−	0.739034i	$-0.264718\pi$
$720$	−23.1532	−	8.13575i	−0.862868	−	0.303202i
$721$	−12.4783	+	38.4044i	−0.464717	+	1.43025i
$722$	30.4083	−	6.46349i	1.13168	−	0.240546i
$723$	−25.7054	+	19.7691i	−0.955993	+	0.735223i
$724$	−0.260722	+	0.451583i	−0.00968965	+	0.0167830i
$725$	−37.0137	−	5.84420i	−1.37465	−	0.217048i
$726$	25.2744	−	46.6713i	0.938019	−	1.73213i
$727$	−38.3332	−	17.0671i	−1.42170	−	0.632982i	−0.455374	−	0.890300i	$-0.650495\pi$
$727$	−38.3332	−	17.0671i	−1.42170	−	0.632982i	−0.966327	+	0.257318i	$0.917161\pi$
$728$	−2.66696	+	8.20807i	−0.0988443	+	0.304211i
$729$	4.04856	−	26.6947i	0.149947	−	0.988694i
$730$	−26.1131	+	0.690062i	−0.966489	+	0.0255403i
$731$	−9.36038	+	10.3958i	−0.346206	+	0.384501i
$732$	0.149919	−	0.276839i	0.00554117	−	0.0102323i
$733$	5.15459	+	1.09564i	0.190389	+	0.0404685i	0.302119	−	0.953270i	$-0.402306\pi$
$733$	5.15459	+	1.09564i	0.190389	+	0.0404685i	−0.111730	+	0.993739i	$0.535639\pi$
$734$	−10.3082	+	4.58951i	−0.380483	+	0.169402i
$735$	23.7029	−	1.27393i	0.874296	−	0.0469895i
$736$	−1.54429	−	0.687564i	−0.0569234	−	0.0253439i
$737$	14.9873	+	10.8889i	0.552066	+	0.401099i
$738$	−0.806411	+	16.0596i	−0.0296844	+	0.591162i
$739$	−40.7402	+	29.5995i	−1.49865	+	1.08884i	−0.527739	+	0.849406i	$0.676960\pi$
$739$	−40.7402	+	29.5995i	−1.49865	+	1.08884i	−0.970914	+	0.239429i	$0.923040\pi$
$740$	−0.0724717	+	0.923672i	−0.00266411	+	0.0339548i
$741$	−0.705455	+	9.09081i	−0.0259155	+	0.333959i
$742$	46.3269	+	9.84708i	1.70071	+	0.361498i
$743$	4.77119	−	8.26395i	0.175038	−	0.303175i	−0.765136	−	0.643868i	$-0.777328\pi$
$743$	4.77119	−	8.26395i	0.175038	−	0.303175i	0.940174	+	0.340693i	$0.110662\pi$
$744$	4.97372	−	5.83640i	0.182345	−	0.213973i
$745$	−21.9919	+	25.7617i	−0.805722	+	0.943837i
$746$	−1.55408	+	4.78296i	−0.0568988	+	0.175116i
$747$	−19.6190	−	19.5334i	−0.717823	−	0.714688i
$748$	−1.26748	+	0.920875i	−0.0463435	+	0.0336705i
$749$	−6.04850	−	10.4763i	−0.221008	−	0.382796i
$750$	−5.41730	+	25.7156i	−0.197812	+	0.939001i
$751$	−2.21298	+	3.83300i	−0.0807530	+	0.139868i	−0.903574	−	0.428433i	$-0.859066\pi$
$751$	−2.21298	+	3.83300i	−0.0807530	+	0.139868i	0.822821	+	0.568301i	$0.192399\pi$
$752$	−4.25102	−	40.4458i	−0.155019	−	1.47490i
$753$	−10.5672	−	11.1111i	−0.385090	−	0.404911i
$754$	−8.09010	+	1.71960i	−0.294624	+	0.0626243i
$755$	−2.44667	−	6.90391i	−0.0890433	−	0.251259i
$756$	−1.14955	−	2.74969i	−0.0418086	−	0.100005i
$757$	17.6362			0.640999			0.320499	−	0.947249i	$-0.396149\pi$
$757$	17.6362			0.640999			0.320499	+	0.947249i	$0.396149\pi$
$758$	4.21864	−	4.68527i	0.153228	−	0.170177i
$759$	−17.1345	+	8.19576i	−0.621943	+	0.297487i
$760$	−38.2640	+	18.2623i	−1.38798	+	0.662442i
$761$	−4.73869	−	45.0856i	−0.171777	−	1.63435i	−0.652719	−	0.757600i	$-0.726372\pi$
$761$	−4.73869	−	45.0856i	−0.171777	−	1.63435i	0.480942	−	0.876753i	$-0.340295\pi$
$762$	18.5749	+	12.7363i	0.672898	+	0.461387i
$763$	−3.43826	+	32.7128i	−0.124473	+	1.18428i
$764$	−2.88990	+	2.09963i	−0.104553	+	0.0759621i
$765$	11.4198	−	0.926664i	0.412884	−	0.0335036i
$766$	−20.9497	−	15.2208i	−0.756943	−	0.549951i
$767$	−1.49071	+	1.65560i	−0.0538263	+	0.0597801i
$768$	3.42212	+	5.57070i	0.123485	+	0.201015i
$769$	16.9322	+	3.59905i	0.610591	+	0.129785i	0.502821	−	0.864391i	$-0.332296\pi$
$769$	16.9322	+	3.59905i	0.610591	+	0.129785i	0.107770	+	0.994176i	$0.465629\pi$
$770$	−30.3893	+	56.0021i	−1.09515	+	2.01818i
$771$	15.7390	−	3.79682i	0.566826	−	0.136739i
$772$	2.22589	−	0.473127i	0.0801115	−	0.0170282i
$773$	−3.80040	+	2.76115i	−0.136691	+	0.0993117i	−0.654029	−	0.756469i	$-0.726923\pi$
$773$	−3.80040	+	2.76115i	−0.136691	+	0.0993117i	0.517339	+	0.855781i	$0.326923\pi$
$774$	33.2959	−	1.81804i	1.19680	−	0.0653479i
$775$	−6.34029	−	4.11311i	−0.227750	−	0.147747i
$776$	0.0546517	+	0.0946596i	0.00196188	+	0.00339808i
$777$	13.0220	−	10.0148i	0.467161	−	0.359278i
$778$	−3.45061	−	3.83229i	−0.123710	−	0.137394i
$779$	17.1083	+	19.0007i	0.612969	+	0.680771i
$780$	−0.0786475	−	0.492309i	−0.00281603	−	0.0176275i
$781$	−34.6214	+	38.4509i	−1.23885	+	1.37588i
$782$	−4.38628			−0.156853
$783$	23.6050	−	30.9726i	0.843574	−	1.10687i
$784$	18.1395	+	13.1791i	0.647841	+	0.470684i
$785$	−9.48166	+	11.1070i	−0.338415	+	0.396425i
$786$	1.46487	+	11.0335i	0.0522501	+	0.393551i
$787$	−1.11096	+	0.494633i	−0.0396016	+	0.0176318i	−0.426442	−	0.904515i	$-0.640233\pi$
$787$	−1.11096	+	0.494633i	−0.0396016	+	0.0176318i	0.386840	+	0.922147i	$0.373566\pi$
$788$	−1.60131	+	0.712949i	−0.0570443	+	0.0253977i
$789$	−14.8005	+	11.3826i	−0.526912	+	0.405230i
$790$	9.95232	+	4.11959i	0.354088	+	0.146568i
$791$	16.8578	+	12.2479i	0.599395	+	0.435486i
$792$	50.3097	+	7.85545i	1.78768	+	0.279131i
$793$	−0.933781			−0.0331595
$794$	19.1190	−	21.2337i	0.678506	−	0.753558i
$795$	−36.0195	+	9.70292i	−1.27748	+	0.344127i
$796$	−1.47935	−	1.64298i	−0.0524340	−	0.0582339i
$797$	6.79857	+	7.55057i	0.240818	+	0.267455i	0.851423	−	0.524480i	$-0.175740\pi$
$797$	6.79857	+	7.55057i	0.240818	+	0.267455i	−0.610605	+	0.791935i	$0.709074\pi$
$798$	50.9616	+	21.0437i	1.80402	+	0.744938i
$799$	9.49336	+	16.4430i	0.335851	+	0.581711i
$800$	3.46972	−	2.81248i	0.122673	−	0.0994361i
$801$	−0.0114424	−	0.0175356i	−0.000404296	−	0.000619589i
$802$	24.7964	−	18.0156i	0.875591	−	0.636154i
$803$	48.7932	−	10.3713i	1.72187	−	0.365996i
$804$	−0.248020	+	0.840679i	−0.00874700	+	0.0296485i
$805$	13.8372	−	6.60406i	0.487696	−	0.232763i
$806$	−1.63165	−	0.346818i	−0.0574724	−	0.0122161i
$807$	−1.15264	+	2.12845i	−0.0405748	+	0.0749248i
$808$	19.7635	−	21.9496i	0.695277	−	0.772183i
$809$	23.4603	+	17.0449i	0.824822	+	0.599268i	0.918090	−	0.396373i	$-0.129731\pi$
$809$	23.4603	+	17.0449i	0.824822	+	0.599268i	−0.0932678	+	0.995641i	$0.529731\pi$
$810$	−20.8491	−	17.6410i	−0.732563	−	0.619842i
$811$	6.79475	−	4.93668i	0.238596	−	0.173350i	−0.462062	−	0.886848i	$-0.652890\pi$
$811$	6.79475	−	4.93668i	0.238596	−	0.173350i	0.700658	+	0.713498i	$0.252890\pi$
$812$	0.449317	−	4.27497i	0.0157679	−	0.150022i
$813$	0.355196	−	0.169897i	0.0124573	−	0.00595855i
$814$	2.15172	+	20.4722i	0.0754176	+	0.717551i
$815$	32.2182	+	33.9346i	1.12856	+	1.18868i
$816$	8.92573	+	6.12011i	0.312463	+	0.214247i
$817$	35.4783	−	39.4026i	1.24123	−	1.37852i
$818$	33.5500			1.17305
$819$	−5.54793	+	6.88186i	−0.193860	+	0.240472i
$820$	−1.15230	−	0.791546i	−0.0402400	−	0.0276420i
$821$	−29.5317	+	6.27717i	−1.03066	+	0.219075i	−0.692049	−	0.721850i	$-0.743292\pi$
$821$	−29.5317	+	6.27717i	−1.03066	+	0.219075i	−0.338616	+	0.940925i	$0.609959\pi$
$822$	−18.4347	+	4.44711i	−0.642983	+	0.155111i
$823$	4.02282	+	38.2746i	0.140227	+	1.33417i	0.807726	+	0.589557i	$0.200698\pi$
$823$	4.02282	+	38.2746i	0.140227	+	1.33417i	−0.667500	+	0.744610i	$0.732636\pi$
$824$	16.3212	−	28.2691i	0.568574	−	0.984800i
$825$	1.23473	−	50.1694i	0.0429876	−	1.74668i
$826$	6.73559	+	11.6664i	0.234361	+	0.405925i
$827$	−13.9655	+	10.1465i	−0.485629	+	0.352830i	−0.803501	−	0.595304i	$-0.797032\pi$
$827$	−13.9655	+	10.1465i	−0.485629	+	0.352830i	0.317872	+	0.948134i	$0.397032\pi$
$828$	−0.636838	−	0.634057i	−0.0221316	−	0.0220350i
$829$	0.316717	−	0.974753i	0.0110000	−	0.0338546i	−0.945406	−	0.325895i	$-0.894334\pi$
$829$	0.316717	−	0.974753i	0.0110000	−	0.0338546i	0.956406	+	0.292041i	$0.0943343\pi$
$830$	−27.2286	+	6.54391i	−0.945117	+	0.227142i
$831$	5.76506	+	16.2236i	0.199988	+	0.562790i
$832$	3.46790	−	6.00659i	0.120228	−	0.208241i
$833$	−10.2392	−	2.17640i	−0.354766	−	0.0754078i
$834$	−24.1252	+	11.5395i	−0.835386	+	0.399581i
$835$	3.40418	+	1.40910i	0.117806	+	0.0487639i
$836$	4.80406	−	3.49035i	0.166152	−	0.120716i
$837$	6.88995	−	3.77027i	0.238151	−	0.130320i
$838$	−42.8399	−	31.1250i	−1.47988	−	1.07519i
$839$	22.7924	+	10.1478i	0.786882	+	0.350343i	0.760524	−	0.649310i	$-0.224942\pi$
$839$	22.7924	+	10.1478i	0.786882	+	0.350343i	0.0263585	+	0.999653i	$0.491609\pi$
$840$	−40.6062	−	6.37587i	−1.40105	−	0.219988i
$841$	24.8180	−	11.0497i	0.855794	−	0.381024i
$842$	30.2361	+	6.42688i	1.04200	+	0.221485i
$843$	−2.61348	+	0.0712981i	−0.0900130	+	0.00245564i
$844$	−2.83390	+	3.14736i	−0.0975468	+	0.108337i
$845$	21.8847	−	16.8011i	0.752857	−	0.577975i
$846$	11.6182	−	43.7423i	0.399441	−	1.50389i
$847$	25.2825	−	77.8114i	0.868716	−	2.67363i
$848$	−32.1899	−	14.3319i	−1.10541	−	0.492159i
$849$	1.10654	+	1.80128i	0.0379763	+	0.0618197i
$850$	5.25648	−	10.3287i	0.180296	−	0.354270i
$851$	2.47674	−	4.28983i	0.0849014	−	0.147054i
$852$	−2.26272	−	0.934350i	−0.0775195	−	0.0320103i
$853$	47.2914	−	10.0521i	1.61923	−	0.344177i	0.692939	−	0.720996i	$-0.256315\pi$
$853$	47.2914	−	10.0521i	1.61923	−	0.344177i	0.926287	+	0.376819i	$0.122982\pi$
$854$	−1.74483	+	5.37002i	−0.0597067	+	0.183758i
$855$	−43.2840	+	3.51230i	−1.48028	+	0.120118i
$856$	3.02181	+	9.30017i	0.103283	+	0.317873i
$857$	5.39440	+	9.34338i	0.184269	+	0.319164i	0.943330	−	0.331856i	$-0.107675\pi$
$857$	5.39440	+	9.34338i	0.184269	+	0.319164i	−0.759061	+	0.651020i	$0.774341\pi$
$858$	−3.70890	−	10.4373i	−0.126620	−	0.356324i
$859$	−29.5585	+	13.1603i	−1.00852	+	0.449024i	−0.843421	−	0.537253i	$-0.819462\pi$
$859$	−29.5585	+	13.1603i	−1.00852	+	0.449024i	−0.165102	+	0.986276i	$0.552795\pi$
$860$	−1.38269	+	2.54806i	−0.0471495	+	0.0868883i
$861$	3.26225	+	24.5714i	0.111177	+	0.837393i
$862$	−4.34608	+	41.3502i	−0.148028	+	1.40839i
$863$	42.3313	+	30.7555i	1.44098	+	1.04693i	0.987838	+	0.155489i	$0.0496954\pi$
$863$	42.3313	+	30.7555i	1.44098	+	1.04693i	0.453138	+	0.891441i	$0.350305\pi$
$864$	0.860850	+	4.56112i	0.0292867	+	0.155172i
$865$	35.6638	+	24.4985i	1.21261	+	0.832973i
$866$	−1.78021	+	16.9376i	−0.0604940	+	0.575562i
$867$	23.9887	+	4.41889i	0.814698	+	0.150073i
$868$	0.433473	−	0.750797i	0.0147130	−	0.0254837i
$869$	−20.1194	−	4.27651i	−0.682504	−	0.145071i
$870$	−14.1655	−	36.7557i	−0.480254	−	1.24613i
$871$	2.54291	−	0.540513i	0.0861633	−	0.0183146i
$872$	8.21661	−	25.2881i	0.278250	−	0.856364i
$873$	0.0177552	+	0.110536i	0.000600922	+	0.00374107i
$874$	16.6251			0.562354
$875$	−1.03131	+	40.4975i	−0.0348647	+	1.36907i
$876$	1.23538	+	2.01101i	0.0417396	+	0.0679458i
$877$	−0.395513	−	3.76306i	−0.0133555	−	0.127069i	0.985813	−	0.167850i	$-0.0536823\pi$
$877$	−0.395513	−	3.76306i	−0.0133555	−	0.127069i	−0.999168	+	0.0407802i	$0.987016\pi$
$878$	−8.56726	−	9.51490i	−0.289131	−	0.321112i
$879$	−31.4140	+	7.57821i	−1.05957	+	0.255607i
$880$	30.7775	−	36.0533i	1.03751	−	1.21536i
$881$	11.3121	+	34.8150i	0.381114	+	1.17295i	0.939261	+	0.343205i	$0.111513\pi$
$881$	11.3121	+	34.8150i	0.381114	+	1.17295i	−0.558147	+	0.829742i	$0.688487\pi$
$882$	13.6359	+	20.8971i	0.459144	+	0.703643i
$883$	14.4473	+	44.4642i	0.486191	+	1.49634i	0.830249	+	0.557393i	$0.188198\pi$
$883$	14.4473	+	44.4642i	0.486191	+	1.49634i	−0.344058	+	0.938948i	$0.611802\pi$
$884$	−0.0229814	+	0.218653i	−0.000772948	+	0.00735411i
$885$	−8.90623	−	5.76690i	−0.299380	−	0.193852i
$886$	−0.380640	−	3.62155i	−0.0127879	−	0.121668i
$887$	24.4031	−	10.8650i	0.819376	−	0.364810i	0.0461455	−	0.998935i	$-0.485306\pi$
$887$	24.4031	−	10.8650i	0.819376	−	0.364810i	0.773231	+	0.634125i	$0.218640\pi$
$888$	−11.9796	+	5.73008i	−0.402010	+	0.192289i
$889$	31.7162	+	14.1209i	1.06373	+	0.473601i
$890$	−0.0211724		0.000559499i	−0.000709700		1.87544e-5i
$891$	45.2799	+	25.8788i	1.51693	+	0.866971i
$892$	−1.19535	−	3.67892i	−0.0400234	−	0.123179i
$893$	−35.9823	−	62.3232i	−1.20410	−	2.08556i
$894$	−35.0171	−	6.45042i	−1.17115	−	0.215734i
$895$	18.9287	−	34.8823i	0.632718	−	1.16599i
$896$	−23.7313	−	26.3563i	−0.792808	−	0.880502i
$897$	−0.754231	+	2.55651i	−0.0251830	+	0.0853593i
$898$	−20.6247	−	9.18273i	−0.688256	−	0.306432i
$899$	11.3280			0.377809
$900$	2.25623	−	0.739756i	0.0752078	−	0.0246585i
$901$	16.4506			0.548048
$902$	−28.3746	−	12.6332i	−0.944772	−	0.420640i
$903$	49.9686	−	12.0542i	1.66285	−	0.401140i
$904$	−11.2710	−	12.5177i	−0.374867	−	0.416332i
$905$	0.963198	+	7.30268i	0.0320178	+	0.242749i
$906$	4.99412	−	5.86033i	0.165918	−	0.194696i
$907$	21.1942	+	36.7094i	0.703742	+	1.21892i	0.967144	+	0.254231i	$0.0818222\pi$
$907$	21.1942	+	36.7094i	0.703742	+	1.21892i	−0.263402	+	0.964686i	$0.584844\pi$
$908$	0.0854169	+	0.262886i	0.00283466	+	0.00872419i
$909$	26.9245	−	13.7930i	0.893031	−	0.457486i
$910$	2.98675	+	8.42789i	0.0990097	+	0.279382i
$911$	−1.54647	−	0.688534i	−0.0512369	−	0.0228122i	0.380958	−	0.924592i	$-0.375594\pi$
$911$	−1.54647	−	0.688534i	−0.0512369	−	0.0228122i	−0.432195	+	0.901780i	$0.642261\pi$
$912$	−33.8308	−	23.1968i	−1.12025	−	0.768123i
$913$	48.8532	−	21.7509i	1.61681	−	0.719848i
$914$	1.94595	+	18.5145i	0.0643664	+	0.612405i
$915$	−0.701561	−	4.39156i	−0.0231929	−	0.145180i
$916$	0.323862	−	3.08134i	0.0107007	−	0.101810i
$917$	5.30190	+	16.3176i	0.175084	+	0.538854i
$918$	6.85432	+	9.90330i	0.226226	+	0.326857i
$919$	−18.5418	−	57.0659i	−0.611639	−	1.88243i	−0.442284	−	0.896875i	$-0.645832\pi$
$919$	−18.5418	−	57.0659i	−0.611639	−	1.88243i	−0.169354	−	0.985555i	$-0.554168\pi$
$920$	−12.0510	+	2.89624i	−0.397308	+	0.0954861i
$921$	19.3028	+	20.2963i	0.636047	+	0.668787i
$922$	−4.79789	−	5.32859i	−0.158010	−	0.175488i
$923$	0.758976	+	7.22117i	0.0249820	+	0.237688i
$924$	5.75464	−	0.156992i	0.189314	−	0.00516465i
$925$	7.13345	+	10.9730i	0.234546	+	0.360791i
$926$	42.5506			1.39830
$927$	25.9366	−	21.0972i	0.851869	−	0.692922i
$928$	−2.06877	+	6.36702i	−0.0679107	+	0.209008i
$929$	−10.1741	+	2.16258i	−0.333802	+	0.0709518i	−0.371764	−	0.928327i	$-0.621247\pi$
$929$	−10.1741	+	2.16258i	−0.333802	+	0.0709518i	0.0379617	+	0.999279i	$0.487914\pi$
$930$	0.405201	−	7.93419i	0.0132871	−	0.260172i
$931$	38.8091	+	8.24912i	1.27192	+	0.270354i
$932$	0.431380	−	0.747173i	0.0141303	−	0.0244745i
$933$	−23.3512	+	27.4014i	−0.764485	+	0.897083i
$934$	2.83151	−	26.9400i	0.0926499	−	0.881505i
$935$	−6.28047	+	21.2212i	−0.205393	+	0.694008i
$936$	5.54336	−	4.50905i	0.181190	−	0.147383i
$937$	−26.6086	−	19.3323i	−0.869264	−	0.631557i	0.0611254	−	0.998130i	$-0.480531\pi$
$937$	−26.6086	−	19.3323i	−0.869264	−	0.631557i	−0.930389	+	0.366573i	$0.880531\pi$
$938$	1.64318	−	15.6338i	0.0536518	−	0.510463i
$939$	17.1047	−	13.1547i	0.558191	−	0.429286i
$940$	2.70922	+	2.85355i	0.0883651	+	0.0930726i
$941$	−26.1372	+	11.6370i	−0.852048	+	0.379356i	−0.785825	−	0.618449i	$-0.787761\pi$
$941$	−26.1372	+	11.6370i	−0.852048	+	0.379356i	−0.0662226	+	0.997805i	$0.521095\pi$
$942$	−15.0974	−	2.78105i	−0.491899	−	0.0906115i
$943$	3.73705	+	6.47277i	0.121695	+	0.210782i
$944$	−3.09706	−	9.53177i	−0.100801	−	0.310233i
$945$	−36.5335	−	20.9214i	−1.18844	−	0.680573i
$946$	−19.9039	+	61.2579i	−0.647131	+	1.99167i
$947$	−39.8598	+	8.47246i	−1.29527	+	0.275318i	−0.803446	−	0.595378i	$-0.797002\pi$
$947$	−39.8598	+	8.47246i	−1.29527	+	0.275318i	−0.491823	+	0.870695i	$0.663669\pi$
$948$	−0.128082	−	0.964722i	−0.00415991	−	0.0313327i
$949$	3.50013	−	6.06241i	0.113619	−	0.196794i
$950$	−19.9234	+	39.1483i	−0.646401	+	1.27014i
$951$	−40.0112	+	1.09154i	−1.29745	+	0.0353957i
$952$	16.5593	+	7.37268i	0.536691	+	0.238950i
$953$	−15.8582	+	48.8064i	−0.513697	+	1.58100i	0.271944	+	0.962313i	$0.412333\pi$
$953$	−15.8582	+	48.8064i	−0.513697	+	1.58100i	−0.785641	+	0.618683i	$0.787667\pi$
$954$	−27.7887	−	27.6674i	−0.899693	−	0.895764i
$955$	−14.3197	+	48.3852i	−0.463376	+	1.56571i
$956$	−0.387738	+	0.430627i	−0.0125403	+	0.0139275i
$957$	39.3731	+	64.0935i	1.27275	+	2.07185i
$958$	−8.49160	−	1.80495i	−0.274351	−	0.0583152i
$959$	−26.7050	+	11.8898i	−0.862348	+	0.383942i
$960$	30.8544	+	11.7967i	0.995820	+	0.380736i
$961$	−26.2328	−	11.6796i	−0.846218	−	0.376760i
$962$	2.33705	+	1.69797i	0.0753495	+	0.0547446i
$963$	−0.502296	+	10.0032i	−0.0161863	+	0.322348i
$964$	2.39764	−	1.74199i	0.0772228	−	0.0561057i
$965$	20.8709	−	24.4486i	0.671859	−	0.787028i
$966$	13.2927	+	9.11444i	0.427687	+	0.293252i
$967$	−48.9177	−	10.3978i	−1.57309	−	0.334370i	−0.662945	−	0.748668i	$-0.730694\pi$
$967$	−48.9177	−	10.3978i	−1.57309	−	0.334370i	−0.910141	+	0.414298i	$0.864027\pi$
$968$	−33.0684	+	57.2762i	−1.06286	+	1.84093i
$969$	18.8338	+	3.46933i	0.605029	+	0.111451i
$970$	0.104633	+	0.0433108i	0.00335955	+	0.00139063i
$971$	7.19668	−	22.1491i	0.230953	−	0.710799i	−0.766680	−	0.642029i	$-0.778093\pi$
$971$	7.19668	−	22.1491i	0.230953	−	0.710799i	0.997633	−	0.0687694i	$-0.0219073\pi$
$972$	−0.436397	+	2.42867i	−0.0139974	+	0.0778995i
$973$	−33.3511	+	24.2310i	−1.06919	+	0.776810i
$974$	−0.587043	−	1.01679i	−0.0188101	−	0.0325800i
$975$	−5.11611	−	4.83973i	−0.163847	−	0.154995i
$976$	2.10040	−	3.63799i	0.0672320	−	0.116449i
$977$	2.13598	+	20.3224i	0.0683359	+	0.650173i	0.974058	+	0.226300i	$0.0726630\pi$
$977$	2.13598	+	20.3224i	0.0683359	+	0.650173i	−0.905722	+	0.423873i	$0.860670\pi$
$978$	−13.9187	+	47.1784i	−0.445072	+	1.50860i
$979$	0.0395613	−	0.00840901i	0.00126438	−	0.000268753i
$980$	−2.16861	+	0.0573074i	−0.0692736	+	0.00183062i
$981$	17.0925	−	21.2022i	0.545723	−	0.676935i
$982$	5.27243			0.168250
$983$	−10.3699	+	11.5170i	−0.330750	+	0.367335i	−0.885466	−	0.464705i	$-0.846160\pi$
$983$	−10.3699	+	11.5170i	−0.330750	+	0.367335i	0.554716	+	0.832040i	$0.312827\pi$
$984$	1.55022	−	19.9769i	0.0494193	−	0.636840i
$985$	−11.8096	+	21.7631i	−0.376286	+	0.693429i
$986$	1.81577	+	17.2759i	0.0578260	+	0.550177i
$987$	5.39772	−	69.5575i	0.171811	−	2.21404i
$988$	0.0871054	−	0.828753i	0.00277119	−	0.0263661i
$989$	12.5393	−	9.11032i	0.398726	−	0.289691i
$990$	46.3000	−	25.2846i	1.47151	−	0.803597i
$991$	−45.2960	−	32.9095i	−1.43887	−	1.04540i	−0.988276	−	0.152677i	$-0.951211\pi$
$991$	−45.2960	−	32.9095i	−1.43887	−	1.04540i	−0.450599	−	0.892727i	$-0.648789\pi$
$992$	−0.903470	+	1.00341i	−0.0286852	+	0.0318581i
$993$	13.9099	−	0.379474i	0.441417	−	0.0120422i
$994$	42.9460	+	9.12844i	1.36216	+	0.289537i
$995$	−30.7089	−	5.68394i	−0.973537	−	0.180193i
$996$	1.74366	+	1.83341i	0.0552499	+	0.0580938i
$997$	−23.5934	+	5.01494i	−0.747211	+	0.158825i	−0.565754	−	0.824574i	$-0.691415\pi$
$997$	−23.5934	+	5.01494i	−0.747211	+	0.158825i	−0.181457	+	0.983399i	$0.558081\pi$
$998$	7.71602	−	5.60601i	0.244246	−	0.177455i
$999$	−13.5559	+	1.11165i	−0.428888	+	0.0351712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.9	yes	224
3.2	odd	2		675.2.r.a.361.20		224
9.2	odd	6		675.2.r.a.586.9		224
9.7	even	3	inner	225.2.q.a.61.20	yes	224
25.16	even	5	inner	225.2.q.a.166.20	yes	224
75.41	odd	10		675.2.r.a.91.9		224
225.16	even	15	inner	225.2.q.a.16.9	✓	224
225.191	odd	30		675.2.r.a.316.20		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.9	✓	224	225.16	even	15	inner
225.2.q.a.61.20	yes	224	9.7	even	3	inner
225.2.q.a.166.20	yes	224	25.16	even	5	inner
225.2.q.a.211.9	yes	224	1.1	even	1	trivial
675.2.r.a.91.9		224	75.41	odd	10
675.2.r.a.316.20		224	225.191	odd	30
675.2.r.a.361.20		224	3.2	odd	2
675.2.r.a.586.9		224	9.2	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.23977 - 0.551980i) q^{2} +(1.19364 + 1.25508i) q^{3} +(-0.105919 - 0.117635i) q^{4} +(-2.19872 - 0.406964i) q^{5} +(-0.787056 - 2.21487i) q^{6} +(-1.81169 - 3.13794i) q^{7} +(0.905114 + 2.78565i) q^{8} +(-0.150451 + 2.99623i) q^{9} +O(q^{10})\)	\(q+(-1.23977 - 0.551980i) q^{2} +(1.19364 + 1.25508i) q^{3} +(-0.105919 - 0.117635i) q^{4} +(-2.19872 - 0.406964i) q^{5} +(-0.787056 - 2.21487i) q^{6} +(-1.81169 - 3.13794i) q^{7} +(0.905114 + 2.78565i) q^{8} +(-0.150451 + 2.99623i) q^{9} +(2.50127 + 1.71819i) q^{10} +(-5.29383 - 2.35697i) q^{11} +(0.0212123 - 0.273352i) q^{12} +(-0.742899 + 0.330760i) q^{13} +(0.513995 + 4.89034i) q^{14} +(-2.11371 - 3.24534i) q^{15} +(0.382402 - 3.63831i) q^{16} +(0.527788 + 1.62436i) q^{17} +(1.84038 - 3.63158i) q^{18} +(-2.00045 - 6.15676i) q^{19} +(0.185014 + 0.301753i) q^{20} +(1.77586 - 6.01939i) q^{21} +(5.26212 + 5.84418i) q^{22} +(-0.197808 - 1.88202i) q^{23} +(-2.41584 + 4.46105i) q^{24} +(4.66876 + 1.78960i) q^{25} +1.10360 q^{26} +(-3.94009 + 3.38758i) q^{27} +(-0.177240 + 0.545488i) q^{28} +(-7.33067 + 1.55818i) q^{29} +(0.829145 + 5.19019i) q^{30} +(-1.47849 - 0.314262i) q^{31} +(0.446643 - 0.773608i) q^{32} +(-3.36074 - 9.45755i) q^{33} +(0.242282 - 2.30516i) q^{34} +(2.70638 + 7.63676i) q^{35} +(0.368398 - 0.299660i) q^{36} +(2.11767 + 1.53858i) q^{37} +(-0.918313 + 8.73716i) q^{38} +(-1.30188 - 0.537590i) q^{39} +(-0.856434 - 6.49323i) q^{40} +(-3.60811 + 1.60644i) q^{41} +(-5.52424 + 6.48240i) q^{42} +(4.09520 + 7.09310i) q^{43} +(0.283457 + 0.872391i) q^{44} +(1.55016 - 6.52664i) q^{45} +(-0.793600 + 2.44245i) q^{46} +(10.8737 - 2.31128i) q^{47} +(5.02282 - 3.86289i) q^{48} +(-3.06445 + 5.30779i) q^{49} +(-4.80035 - 4.79575i) q^{50} +(-1.40872 + 2.60132i) q^{51} +(0.117597 + 0.0523574i) q^{52} +(2.97637 - 9.16031i) q^{53} +(6.75467 - 2.02497i) q^{54} +(10.6805 + 7.33671i) q^{55} +(7.10143 - 7.88694i) q^{56} +(5.33941 - 9.85968i) q^{57} +(9.94842 + 2.11460i) q^{58} +(2.50272 - 1.11428i) q^{59} +(-0.157884 + 0.592392i) q^{60} +(1.04900 + 0.467045i) q^{61} +(1.65951 + 1.20571i) q^{62} +(9.67455 - 4.95613i) q^{63} +(-6.90009 + 5.01321i) q^{64} +(1.76804 - 0.424917i) q^{65} +(-1.05384 + 13.5802i) q^{66} +(-3.12703 - 0.664670i) q^{67} +(0.135180 - 0.234138i) q^{68} +(2.12597 - 2.49471i) q^{69} +(0.860057 - 10.9617i) q^{70} +(2.75915 - 8.49180i) q^{71} +(-8.48262 + 2.29282i) q^{72} +(-6.96422 + 5.05980i) q^{73} +(-1.77615 - 3.07639i) q^{74} +(3.32672 + 7.99581i) q^{75} +(-0.512367 + 0.887445i) q^{76} +(2.19477 + 20.8818i) q^{77} +(1.31729 + 1.38510i) q^{78} +(3.47196 - 0.737989i) q^{79} +(-2.32146 + 7.84402i) q^{80} +(-8.95473 - 0.901572i) q^{81} +5.35994 q^{82} +(-6.17496 + 6.85798i) q^{83} +(-0.896192 + 0.428666i) q^{84} +(-0.499402 - 3.78632i) q^{85} +(-1.16185 - 11.0543i) q^{86} +(-10.7058 - 7.34067i) q^{87} +(1.77417 - 16.8801i) q^{88} +(-0.00564656 + 0.00410246i) q^{89} +(-5.52441 + 7.23586i) q^{90} +(2.38381 + 1.73194i) q^{91} +(-0.200440 + 0.222612i) q^{92} +(-1.37035 - 2.23073i) q^{93} +(-14.7566 - 3.13662i) q^{94} +(1.89286 + 14.3511i) q^{95} +(1.50407 - 0.362836i) q^{96} +(0.0365021 - 0.00775876i) q^{97} +(6.72900 - 4.88891i) q^{98} +(7.85846 - 15.5069i) 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

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