LMFDB - Embedded newform 151.2.k.a.90.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(5,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(150))

chi = DirichletCharacter(H, H._module([112]))

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

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

chi := DirichletCharacter("151.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.k (of order $75$, degree $40$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$12$ over $\Q(\zeta_{75})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{75}]$

Embedding invariants

Embedding label			90.10
Character	$\chi$	$=$	151.90
Dual form			151.2.k.a.99.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.200615 - 1.90872i) q^{2} +(-1.50561 + 1.41386i) q^{3} +(-1.64668 - 0.350012i) q^{4} +(-3.54627 + 1.76038i) q^{5} +(2.39661 + 3.15742i) q^{6} +(-1.71178 + 3.27434i) q^{7} +(0.187730 - 0.577774i) q^{8} +(0.0794829 - 1.26334i) q^{9} +O(q^{10})$	\(q+(0.200615 - 1.90872i) q^{2} +(-1.50561 + 1.41386i) q^{3} +(-1.64668 - 0.350012i) q^{4} +(-3.54627 + 1.76038i) q^{5} +(2.39661 + 3.15742i) q^{6} +(-1.71178 + 3.27434i) q^{7} +(0.187730 - 0.577774i) q^{8} +(0.0794829 - 1.26334i) q^{9} +(2.64865 + 7.12200i) q^{10} +(0.717405 - 3.05867i) q^{11} +(2.97411 - 1.80119i) q^{12} +(-2.96441 - 0.248928i) q^{13} +(5.90639 + 3.92420i) q^{14} +(2.85035 - 7.66437i) q^{15} +(-4.14099 - 1.84369i) q^{16} +(-0.0397401 - 0.00166560i) q^{17} +(-2.39543 - 0.405156i) q^{18} +(2.13806 + 6.58029i) q^{19} +(6.45571 - 1.65755i) q^{20} +(-2.05218 - 7.35008i) q^{21} +(-5.69423 - 1.98294i) q^{22} +(0.529130 - 0.587659i) q^{23} +(0.534243 + 1.13532i) q^{24} +(6.45409 - 8.50295i) q^{25} +(-1.06984 + 5.60829i) q^{26} +(-2.28307 - 2.75976i) q^{27} +(3.96481 - 4.79263i) q^{28} +(1.40777 + 7.37979i) q^{29} +(-14.0573 - 6.97811i) q^{30} +(0.618885 + 0.490522i) q^{31} +(-3.74232 + 6.48189i) q^{32} +(3.24440 + 5.61946i) q^{33} +(-0.0111516 + 0.0755186i) q^{34} +(0.306352 - 14.6251i) q^{35} +(-0.573068 + 2.05250i) q^{36} +(-4.57150 + 6.57753i) q^{37} +(12.9889 - 2.76087i) q^{38} +(4.81518 - 3.81646i) q^{39} +(0.351363 + 2.37942i) q^{40} +(-3.38149 + 0.427182i) q^{41} +(-14.4410 + 2.44251i) q^{42} +(-0.00513286 - 0.00981826i) q^{43} +(-2.25190 + 4.78554i) q^{44} +(1.94210 + 4.62008i) q^{45} +(-1.01553 - 1.12786i) q^{46} +(1.58003 - 3.75875i) q^{47} +(8.84141 - 3.07890i) q^{48} +(-3.79611 - 5.46188i) q^{49} +(-14.9350 - 14.0249i) q^{50} +(0.0621878 - 0.0536791i) q^{51} +(4.79429 + 1.44748i) q^{52} +(-8.31300 + 4.57011i) q^{53} +(-5.72563 + 3.80410i) q^{54} +(2.84032 + 12.1098i) q^{55} +(1.57048 + 1.60372i) q^{56} +(-12.5227 - 6.88440i) q^{57} +(14.3684 - 1.20655i) q^{58} +(9.85592 - 7.16074i) q^{59} +(-7.37623 + 11.6231i) q^{60} +(-3.35463 + 1.01282i) q^{61} +(1.06043 - 1.08287i) q^{62} +(4.00056 + 2.42283i) q^{63} +(4.28701 + 3.11469i) q^{64} +(10.9508 - 4.33573i) q^{65} +(11.3769 - 5.06530i) q^{66} +(-0.00118771 - 0.0188781i) q^{67} +(0.0648561 + 0.0166522i) q^{68} +(0.0342043 + 1.63290i) q^{69} +(-27.8538 - 3.51875i) q^{70} +(12.9868 - 0.544308i) q^{71} +(-0.715007 - 0.283091i) q^{72} +(7.81699 + 12.3176i) q^{73} +(11.6376 + 10.0453i) q^{74} +(2.30465 + 21.9273i) q^{75} +(-1.21752 - 11.5839i) q^{76} +(8.78709 + 7.58481i) q^{77} +(-6.31857 - 9.95647i) q^{78} +(0.356166 + 0.141016i) q^{79} +(17.9307 - 0.751518i) q^{80} +(11.1069 + 1.40313i) q^{81} +(0.136994 + 6.54003i) q^{82} +(-5.75181 - 1.47681i) q^{83} +(0.806660 + 12.8215i) q^{84} +(0.143861 - 0.0640511i) q^{85} +(-0.0197700 + 0.00782751i) q^{86} +(-12.5535 - 9.12067i) q^{87} +(-1.63254 - 0.988703i) q^{88} +(-3.78755 + 3.86772i) q^{89} +(9.20807 - 2.78008i) q^{90} +(5.88950 - 9.28036i) q^{91} +(-1.07699 + 0.782481i) q^{92} +(-1.62533 + 0.136482i) q^{93} +(-6.85744 - 3.76991i) q^{94} +(-19.1660 - 19.5717i) q^{95} +(-3.53001 - 15.0503i) q^{96} +(-2.26011 + 1.50162i) q^{97} +(-11.1868 + 6.14997i) q^{98} +(-3.80713 - 1.14944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) $ 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{22}{75}\right)$

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 $

$2$	0.200615	−	1.90872i	0.141856	−	1.34967i	−0.659600	−	0.751617i	$-0.729274\pi$
$2$	0.200615	−	1.90872i	0.141856	−	1.34967i	0.801456	−	0.598053i	$-0.204059\pi$
$3$	−1.50561	+	1.41386i	−0.869262	+	0.816291i	−0.984196	−	0.177082i	$-0.943334\pi$
$3$	−1.50561	+	1.41386i	−0.869262	+	0.816291i	0.114934	+	0.993373i	$0.463334\pi$
$4$	−1.64668	−	0.350012i	−0.823338	−	0.175006i
$5$	−3.54627	+	1.76038i	−1.58594	+	0.787268i	−0.999738	−	0.0228966i	$-0.992711\pi$
$5$	−3.54627	+	1.76038i	−1.58594	+	0.787268i	−0.586203	+	0.810164i	$0.699378\pi$
$6$	2.39661	+	3.15742i	0.978414	+	1.28901i
$7$	−1.71178	+	3.27434i	−0.646993	+	1.23758i	0.310895	+	0.950444i	$0.399371\pi$
$7$	−1.71178	+	3.27434i	−0.646993	+	1.23758i	−0.957889	+	0.287140i	$0.907295\pi$
$8$	0.187730	−	0.577774i	0.0663727	−	0.204274i
$9$	0.0794829	−	1.26334i	0.0264943	−	0.421115i
$10$	2.64865	+	7.12200i	0.837576	+	2.25217i
$11$	0.717405	−	3.05867i	0.216306	−	0.922224i	−0.749304	−	0.662227i	$-0.769612\pi$
$11$	0.717405	−	3.05867i	0.216306	−	0.922224i	0.965609	−	0.259997i	$-0.0837217\pi$
$12$	2.97411	−	1.80119i	0.858552	−	0.519958i
$13$	−2.96441	−	0.248928i	−0.822178	−	0.0690403i	−0.334864	−	0.942267i	$-0.608690\pi$
$13$	−2.96441	−	0.248928i	−0.822178	−	0.0690403i	−0.487315	+	0.873226i	$0.662024\pi$
$14$	5.90639	+	3.92420i	1.57855	+	1.04879i
$15$	2.85035	−	7.66437i	0.735958	−	1.97893i
$16$	−4.14099	−	1.84369i	−1.03525	−	0.460922i
$17$	−0.0397401	−	0.00166560i	−0.00963839	−	0.000403968i	0.0370560	−	0.999313i	$-0.488202\pi$
$17$	−0.0397401	−	0.00166560i	−0.00963839	−	0.000403968i	−0.0466944	+	0.998909i	$0.514869\pi$
$18$	−2.39543	−	0.405156i	−0.564608	−	0.0954962i
$19$	2.13806	+	6.58029i	0.490506	+	1.50962i	0.823845	+	0.566815i	$0.191824\pi$
$19$	2.13806	+	6.58029i	0.490506	+	1.50962i	−0.333340	+	0.942807i	$0.608176\pi$
$20$	6.45571	−	1.65755i	1.44354	−	0.370638i
$21$	−2.05218	−	7.35008i	−0.447822	−	1.60392i
$22$	−5.69423	−	1.98294i	−1.21401	−	0.422764i
$23$	0.529130	−	0.587659i	0.110331	−	0.122535i	−0.685449	−	0.728120i	$-0.740394\pi$
$23$	0.529130	−	0.587659i	0.110331	−	0.122535i	0.795781	+	0.605585i	$0.207061\pi$
$24$	0.534243	+	1.13532i	0.109052	+	0.231747i
$25$	6.45409	−	8.50295i	1.29082	−	1.70059i
$26$	−1.06984	+	5.60829i	−0.209813	+	1.09988i
$27$	−2.28307	−	2.75976i	−0.439377	−	0.531116i
$28$	3.96481	−	4.79263i	0.749279	−	0.905722i
$29$	1.40777	+	7.37979i	0.261417	+	1.37039i	0.834550	+	0.550932i	$0.185727\pi$
$29$	1.40777	+	7.37979i	0.261417	+	1.37039i	−0.573134	+	0.819462i	$0.694273\pi$
$30$	−14.0573	−	6.97811i	−2.56650	−	1.27402i
$31$	0.618885	+	0.490522i	0.111155	+	0.0881004i	0.675161	−	0.737670i	$-0.264074\pi$
$31$	0.618885	+	0.490522i	0.111155	+	0.0881004i	−0.564006	+	0.825770i	$0.690741\pi$
$32$	−3.74232	+	6.48189i	−0.661555	+	1.14585i
$33$	3.24440	+	5.61946i	0.564777	+	0.978223i
$34$	−0.0111516	+	0.0755186i	−0.00191249	+	0.0129513i
$35$	0.306352	−	14.6251i	0.0517830	−	2.47209i
$36$	−0.573068	+	2.05250i	−0.0955113	+	0.342083i
$37$	−4.57150	+	6.57753i	−0.751550	+	1.08134i	0.242256	+	0.970212i	$0.422113\pi$
$37$	−4.57150	+	6.57753i	−0.751550	+	1.08134i	−0.993806	+	0.111127i	$0.964554\pi$
$38$	12.9889	−	2.76087i	2.10707	−	0.447872i
$39$	4.81518	−	3.81646i	0.771045	−	0.611123i
$40$	0.351363	+	2.37942i	0.0555553	+	0.376220i
$41$	−3.38149	+	0.427182i	−0.528101	+	0.0667146i	−0.384863	−	0.922974i	$-0.625751\pi$
$41$	−3.38149	+	0.427182i	−0.528101	+	0.0667146i	−0.143238	+	0.989688i	$0.545751\pi$
$42$	−14.4410	+	2.44251i	−2.22829	+	0.376887i
$43$	−0.00513286	−	0.00981826i	−0.000782754	−	0.00149727i	0.885812	−	0.464045i	$-0.153602\pi$
$43$	−0.00513286	−	0.00981826i	−0.000782754	−	0.00149727i	−0.886595	+	0.462547i	$0.846936\pi$
$44$	−2.25190	+	4.78554i	−0.339487	+	0.721447i
$45$	1.94210	+	4.62008i	0.289512	+	0.688721i
$46$	−1.01553	−	1.12786i	−0.149731	−	0.166293i
$47$	1.58003	−	3.75875i	0.230472	−	0.548271i	−0.764924	−	0.644120i	$-0.777224\pi$
$47$	1.58003	−	3.75875i	0.230472	−	0.548271i	0.995396	+	0.0958499i	$0.0305569\pi$
$48$	8.84141	−	3.07890i	1.27615	−	0.444402i
$49$	−3.79611	−	5.46188i	−0.542301	−	0.780269i
$50$	−14.9350	−	14.0249i	−2.11212	−	1.98342i
$51$	0.0621878	−	0.0536791i	0.00870804	−	0.00751658i
$52$	4.79429	+	1.44748i	0.664848	+	0.200730i
$53$	−8.31300	+	4.57011i	−1.14188	+	0.627753i	−0.936409	−	0.350911i	$-0.885872\pi$
$53$	−8.31300	+	4.57011i	−1.14188	+	0.627753i	−0.205469	+	0.978664i	$0.565872\pi$
$54$	−5.72563	+	3.80410i	−0.779159	+	0.517672i
$55$	2.84032	+	12.1098i	0.382989	+	1.63288i
$56$	1.57048	+	1.60372i	0.209864	+	0.214306i
$57$	−12.5227	−	6.88440i	−1.65867	−	0.911861i
$58$	14.3684	−	1.20655i	1.88666	−	0.158427i
$59$	9.85592	−	7.16074i	1.28313	−	0.932249i	0.283488	−	0.958976i	$-0.408508\pi$
$59$	9.85592	−	7.16074i	1.28313	−	0.932249i	0.999643	+	0.0267266i	$0.00850836\pi$
$60$	−7.37623	+	11.6231i	−0.952267	+	1.50053i
$61$	−3.35463	+	1.01282i	−0.429516	+	0.129679i	−0.496423	−	0.868081i	$-0.665354\pi$
$61$	−3.35463	+	1.01282i	−0.429516	+	0.129679i	0.0669071	+	0.997759i	$0.478687\pi$
$62$	1.06043	−	1.08287i	0.134674	−	0.137525i
$63$	4.00056	+	2.42283i	0.504024	+	0.305248i
$64$	4.28701	+	3.11469i	0.535876	+	0.389337i
$65$	10.9508	−	4.33573i	1.35828	−	0.537781i
$66$	11.3769	−	5.06530i	1.40039	−	0.623496i
$67$	−0.00118771	−	0.0188781i	−0.000145101	−	0.00230632i	0.997954	−	0.0639436i	$-0.0203678\pi$
$67$	−0.00118771	−	0.0188781i	−0.000145101	−	0.00230632i	−0.998099	+	0.0616373i	$0.980368\pi$
$68$	0.0648561	+	0.0166522i	0.00786495	+	0.00201938i
$69$	0.0342043	+	1.63290i	0.00411772	+	0.196578i
$70$	−27.8538	−	3.51875i	−3.32916	−	0.420571i
$71$	12.9868	−	0.544308i	1.54125	−	0.0645975i	0.743972	−	0.668211i	$-0.232939\pi$
$71$	12.9868	−	0.544308i	1.54125	−	0.0645975i	0.797277	+	0.603613i	$0.206273\pi$
$72$	−0.715007	−	0.283091i	−0.0842644	−	0.0333626i
$73$	7.81699	+	12.3176i	0.914909	+	1.44167i	0.897102	+	0.441824i	$0.145669\pi$
$73$	7.81699	+	12.3176i	0.914909	+	1.44167i	0.0178074	+	0.999841i	$0.494331\pi$
$74$	11.6376	+	10.0453i	1.35284	+	1.16774i
$75$	2.30465	+	21.9273i	0.266118	+	2.53194i
$76$	−1.21752	−	11.5839i	−0.139659	−	1.32877i
$77$	8.78709	+	7.58481i	1.00138	+	0.864369i
$78$	−6.31857	−	9.95647i	−0.715437	−	1.12735i
$79$	0.356166	+	0.141016i	0.0400718	+	0.0158656i	0.388075	−	0.921628i	$-0.373140\pi$
$79$	0.356166	+	0.141016i	0.0400718	+	0.0158656i	−0.348003	+	0.937493i	$0.613140\pi$
$80$	17.9307	−	0.751518i	2.00471	−	0.0840222i
$81$	11.1069	+	1.40313i	1.23410	+	0.155903i
$82$	0.136994	+	6.54003i	0.0151285	+	0.722225i
$83$	−5.75181	−	1.47681i	−0.631343	−	0.162101i	−0.0805599	−	0.996750i	$-0.525671\pi$
$83$	−5.75181	−	1.47681i	−0.631343	−	0.162101i	−0.550783	+	0.834648i	$0.685671\pi$
$84$	0.806660	+	12.8215i	0.0880138	+	1.39894i
$85$	0.143861	−	0.0640511i	0.0156039	−	0.00694732i
$86$	−0.0197700	+	0.00782751i	−0.00213186	+	0.000844062i
$87$	−12.5535	−	9.12067i	−1.34588	−	0.977839i
$88$	−1.63254	−	0.988703i	−0.174030	−	0.105396i
$89$	−3.78755	+	3.86772i	−0.401480	+	0.409978i	−0.885175	−	0.465259i	$-0.845961\pi$
$89$	−3.78755	+	3.86772i	−0.401480	+	0.409978i	0.483695	+	0.875237i	$0.339295\pi$
$90$	9.20807	−	2.78008i	0.970615	−	0.293046i
$91$	5.88950	−	9.28036i	0.617387	−	0.972847i
$92$	−1.07699	+	0.782481i	−0.112284	+	0.0815793i
$93$	−1.62533	+	0.136482i	−0.168538	+	0.0141526i
$94$	−6.85744	−	3.76991i	−0.707290	−	0.388836i
$95$	−19.1660	−	19.5717i	−1.96639	−	2.00801i
$96$	−3.53001	−	15.0503i	−0.360280	−	1.53606i
$97$	−2.26011	+	1.50162i	−0.229480	+	0.152466i	−0.662856	−	0.748747i	$-0.730656\pi$
$97$	−2.26011	+	1.50162i	−0.229480	+	0.152466i	0.433376	+	0.901213i	$0.357322\pi$
$98$	−11.1868	+	6.14997i	−1.13003	+	0.621241i
$99$	−3.80713	−	1.14944i	−0.382631	−	0.115523i
$100$	−13.6039	+	11.7426i	−1.36039	+	1.17426i
$101$	−13.3256	−	12.5136i	−1.32595	−	1.24515i	−0.947589	−	0.319493i	$-0.896488\pi$
$101$	−13.3256	−	12.5136i	−1.32595	−	1.24515i	−0.378362	−	0.925658i	$-0.623512\pi$
$102$	−0.0899826	−	0.129468i	−0.00890961	−	0.0128192i
$103$	−9.70251	+	3.37877i	−0.956017	+	0.332920i	−0.761635	−	0.648006i	$-0.775603\pi$
$103$	−9.70251	+	3.37877i	−0.956017	+	0.332920i	−0.194381	+	0.980926i	$0.562270\pi$
$104$	−0.700333	+	1.66603i	−0.0686733	+	0.163367i
$105$	20.2166	+	22.4528i	1.97293	+	2.19117i
$106$	7.05535	+	16.7840i	0.685277	+	1.63021i
$107$	−4.56778	+	9.70703i	−0.441584	+	0.938414i	0.552873	+	0.833266i	$0.313532\pi$
$107$	−4.56778	+	9.70703i	−0.441584	+	0.938414i	−0.994457	+	0.105148i	$0.966468\pi$
$108$	2.79353	+	5.34353i	0.268807	+	0.514181i
$109$	−1.17414	+	0.198592i	−0.112463	+	0.0190216i	−0.222729	−	0.974880i	$-0.571496\pi$
$109$	−1.17414	+	0.198592i	−0.112463	+	0.0190216i	0.110266	+	0.993902i	$0.464830\pi$
$110$	23.6840	−	2.99199i	2.25818	−	0.285275i
$111$	−2.41681	−	16.3666i	−0.229394	−	1.55345i
$112$	13.1253	−	10.4030i	1.24023	−	0.982993i
$113$	−0.00677854	+	0.00144082i	−0.000637671	+	0.000135541i	−0.208231	−	0.978080i	$-0.566770\pi$
$113$	−0.00677854	+	0.00144082i	−0.000637671	+	0.000135541i	0.207593	+	0.978215i	$0.433437\pi$
$114$	−15.6526	+	22.5212i	−1.46600	+	2.10930i
$115$	−0.841934	+	3.01547i	−0.0785108	+	0.281194i
$116$	0.264872	−	12.6449i	0.0245928	−	1.17405i
$117$	−0.550102	+	3.72528i	−0.0508569	+	0.344402i
$118$	−11.6906	−	20.2487i	−1.07621	−	1.86405i
$119$	0.0734802	−	0.127271i	0.00673592	−	0.0116670i
$120$	−3.89318	−	3.08570i	−0.355397	−	0.281684i
$121$	1.01203	+	0.502376i	0.0920027	+	0.0456705i
$122$	1.26021	+	6.60624i	0.114094	+	0.598101i
$123$	4.48722	−	5.42412i	0.404599	−	0.489076i
$124$	−0.847414	−	1.02435i	−0.0761001	−	0.0919892i
$125$	−4.21013	+	22.0703i	−0.376565	+	1.97402i
$126$	5.42707	−	7.14991i	0.483482	−	0.636964i
$127$	1.34580	+	2.85998i	0.119421	+	0.253782i	0.955596	−	0.294681i	$-0.0952133\pi$
$127$	1.34580	+	2.85998i	0.119421	+	0.253782i	−0.836175	+	0.548463i	$0.815213\pi$
$128$	−3.21129	+	3.56650i	−0.283840	+	0.315237i
$129$	0.0216097	+	0.00752529i	0.00190263	+	0.000662565i
$130$	−6.07881	−	21.7718i	−0.533146	−	1.90952i
$131$	−13.3989	+	3.44026i	−1.17067	+	0.300577i	−0.783477	−	0.621421i	$-0.786556\pi$
$131$	−13.3989	+	3.44026i	−1.17067	+	0.300577i	−0.387194	+	0.921998i	$0.626556\pi$
$132$	−3.37559	−	10.3890i	−0.293808	−	0.904247i
$133$	−25.2060	−	4.26328i	−2.18564	−	0.369673i
$134$	−0.0362712	−	0.00152021i	−0.00313336	−	0.000131327i
$135$	12.9546	+	5.76777i	1.11496	+	0.496411i
$136$	−0.00842276	+	0.0226481i	−0.000722246	+	0.00194206i
$137$	−9.13530	−	6.06948i	−0.780481	−	0.518551i	0.0986545	−	0.995122i	$-0.468546\pi$
$137$	−9.13530	−	6.06948i	−0.780481	−	0.518551i	−0.879136	+	0.476571i	$0.841879\pi$
$138$	3.12361	+	0.262297i	0.265899	+	0.0223282i
$139$	11.2375	−	6.80566i	0.953151	−	0.577249i	0.0464032	−	0.998923i	$-0.485224\pi$
$139$	11.2375	−	6.80566i	0.953151	−	0.577249i	0.906747	+	0.421674i	$0.138557\pi$
$140$	−5.62342	+	23.9756i	−0.475266	+	2.02630i
$141$	2.93543	+	7.89315i	0.247208	+	0.664723i
$142$	1.56641	−	24.8974i	0.131450	−	2.08934i
$143$	−2.88807	+	8.88856i	−0.241512	+	0.743299i
$144$	−2.65835	+	5.08496i	−0.221529	+	0.423746i
$145$	−17.9836	−	23.6925i	−1.49346	−	1.96756i
$146$	25.0791	−	12.4494i	2.07556	−	1.03032i
$147$	13.4378	+	2.85628i	1.10833	+	0.235582i
$148$	9.82999	−	9.23098i	0.808020	−	0.758782i
$149$	−1.26089	+	11.9966i	−0.103296	+	0.982800i	0.812990	+	0.582277i	$0.197838\pi$
$149$	−1.26089	+	11.9966i	−0.103296	+	0.982800i	−0.916287	+	0.400523i	$0.868829\pi$
$150$	42.3154			3.45504
$151$	5.82290	−	10.8210i	0.473861	−	0.880600i
$151$	5.82290	−	10.8210i	0.473861	−	0.880600i
$152$	4.20330			0.340933
$153$	−0.00526289	+	0.0500730i	−0.000425479	+	0.00404817i
$154$	16.2401	−	15.2505i	1.30867	−	1.22892i
$155$	−3.05824	−	0.650049i	−0.245644	−	0.0522132i
$156$	−9.26484	+	4.59911i	−0.741781	+	0.368223i
$157$	9.79166	+	12.9000i	0.781459	+	1.02953i	0.998574	+	0.0533884i	$0.0170022\pi$
$157$	9.79166	+	12.9000i	0.781459	+	1.02953i	−0.217115	+	0.976146i	$0.569665\pi$
$158$	0.340613	−	0.651532i	0.0270977	−	0.0518331i
$159$	6.05461	−	18.6342i	0.480162	−	1.47779i
$160$	1.86067	−	29.5745i	0.147099	−	2.33807i
$161$	1.01844	+	2.73850i	0.0802641	+	0.215824i
$162$	4.90638	−	20.9185i	0.385482	−	1.64351i
$163$	4.45664	−	2.69904i	0.349071	−	0.211405i	−0.332593	−	0.943071i	$-0.607923\pi$
$163$	4.45664	−	2.69904i	0.349071	−	0.211405i	0.681664	+	0.731666i	$0.261257\pi$
$164$	5.71774	+	0.480132i	0.446481	+	0.0374920i
$165$	−21.3979	−	14.2167i	−1.66583	−	1.10677i
$166$	−3.97272	+	10.6823i	−0.308343	+	0.829109i
$167$	8.75619	+	3.89851i	0.677575	+	0.301676i	0.716521	−	0.697566i	$-0.245733\pi$
$167$	8.75619	+	3.89851i	0.677575	+	0.301676i	−0.0389462	+	0.999241i	$0.512400\pi$
$168$	−4.63195	−	0.194136i	−0.357362	−	0.0149779i
$169$	−4.09221	−	0.692145i	−0.314785	−	0.0532419i
$170$	−0.0933951	−	0.287441i	−0.00716308	−	0.0220457i
$171$	8.48311	−	2.17809i	0.648720	−	0.166563i
$172$	0.00501565	+	0.0179640i	0.000382440	+	0.00136975i
$173$	3.96167	+	1.37960i	0.301200	+	0.104889i	0.475258	−	0.879846i	$-0.342355\pi$
$173$	3.96167	+	1.37960i	0.301200	+	0.104889i	−0.174058	+	0.984735i	$0.555688\pi$
$174$	−19.9272	+	22.1314i	−1.51068	+	1.67778i
$175$	16.7935	+	35.6881i	1.26947	+	2.69777i
$176$	−8.61000	+	11.3433i	−0.649003	+	0.855030i
$177$	−4.71485	+	24.7161i	−0.354390	+	1.85778i
$178$	6.62257	+	8.00531i	0.496382	+	0.600023i
$179$	−5.87476	+	7.10137i	−0.439100	+	0.530781i	−0.942916	−	0.333030i	$-0.891929\pi$
$179$	−5.87476	+	7.10137i	−0.439100	+	0.530781i	0.503816	+	0.863811i	$0.331929\pi$
$180$	−1.58093	−	8.28754i	−0.117836	−	0.617717i
$181$	−5.72628	−	2.84255i	−0.425631	−	0.211285i	0.219087	−	0.975705i	$-0.429692\pi$
$181$	−5.72628	−	2.84255i	−0.425631	−	0.211285i	−0.644719	+	0.764420i	$0.723025\pi$
$182$	−16.5321	−	13.1032i	−1.22544	−	0.971273i
$183$	3.61876	−	6.26788i	0.267506	−	0.463335i
$184$	−0.240200	−	0.416039i	−0.0177078	−	0.0306708i
$185$	4.63281	−	31.3733i	0.340611	−	2.30661i
$186$	−0.0655573	+	3.12967i	−0.00480690	+	0.229479i
$187$	−0.0336043	+	0.120357i	−0.00245739	+	0.00880137i
$188$	−3.91741	+	5.63642i	−0.285707	+	0.411078i
$189$	12.9445	−	2.75144i	0.941575	−	0.200138i
$190$	−41.2018	+	32.6562i	−2.98910	+	2.36913i
$191$	−0.813960	−	5.51212i	−0.0588961	−	0.398843i	−0.998412	−	0.0563375i	$-0.982058\pi$
$191$	−0.813960	−	5.51212i	−0.0588961	−	0.398843i	0.939516	−	0.342506i	$-0.111276\pi$
$192$	−10.8583	+	1.37172i	−0.783629	+	0.0989953i
$193$	25.5141	−	4.31539i	1.83655	−	0.310629i	0.857534	−	0.514427i	$-0.171995\pi$
$193$	25.5141	−	4.31539i	1.83655	−	0.310629i	0.979013	+	0.203798i	$0.0653286\pi$
$194$	2.41276	+	4.61517i	0.173226	+	0.331350i
$195$	−10.3575	+	22.0108i	−0.741715	+	1.57622i
$196$	4.33923	+	10.3226i	0.309945	+	0.737331i
$197$	−1.43486	−	1.59357i	−0.102229	−	0.113537i	0.689859	−	0.723944i	$-0.257673\pi$
$197$	−1.43486	−	1.59357i	−0.102229	−	0.113537i	−0.792088	+	0.610407i	$0.791006\pi$
$198$	−2.95773	+	7.03616i	−0.210197	+	0.500038i
$199$	−5.01874	+	1.74771i	−0.355769	+	0.123892i	−0.500864	−	0.865526i	$-0.666984\pi$
$199$	−5.01874	+	1.74771i	−0.355769	+	0.123892i	0.145095	+	0.989418i	$0.453651\pi$
$200$	−3.70116	−	5.32527i	−0.261711	−	0.376553i
$201$	0.0284791	+	0.0267437i	0.00200876	+	0.00188635i
$202$	−26.5583	+	22.9245i	−1.86864	+	1.61296i
$203$	−26.5738	−	8.02309i	−1.86511	−	0.563111i
$204$	−0.121192	+	0.0666256i	−0.00848510	+	0.00466472i
$205$	11.2397	−	7.46763i	0.785014	−	0.521562i
$206$	4.50267	+	19.1972i	0.313716	+	1.33753i
$207$	−0.700359	−	0.715183i	−0.0486783	−	0.0497086i
$208$	11.8166	+	6.49625i	0.819336	+	0.450434i
$209$	21.6608	−	1.81891i	1.49831	−	0.125816i
$210$	46.9118	−	34.0834i	3.23722	−	2.35198i
$211$	0.0979190	−	0.154296i	0.00674102	−	0.0106221i	−0.840941	−	0.541127i	$-0.817998\pi$
$211$	0.0979190	−	0.154296i	0.00674102	−	0.0106221i	0.847682	+	0.530505i	$0.177998\pi$
$212$	15.2884	−	4.61584i	1.05001	−	0.317017i
$213$	−18.7834	+	19.1810i	−1.28702	+	1.31426i
$214$	17.6116	+	10.6660i	1.20391	+	0.729112i
$215$	0.0354864	+	0.0257824i	0.00242015	+	0.00175834i
$216$	−2.02312	+	0.801010i	−0.137656	+	0.0545018i
$217$	−2.66553	+	1.18677i	−0.180948	+	0.0805634i
$218$	0.143505	+	2.28095i	0.00971941	+	0.154486i
$219$	−29.1846	−	7.49334i	−1.97211	−	0.506353i
$220$	−0.438527	−	20.9350i	−0.0295655	−	1.41144i
$221$	0.117391	+	0.0148300i	0.00789658	+	0.000997571i
$222$	−31.7242	+	1.32964i	−2.12919	+	0.0892393i
$223$	4.36068	+	1.72652i	0.292013	+	0.115616i	0.509564	−	0.860433i	$-0.329807\pi$
$223$	4.36068	+	1.72652i	0.292013	+	0.115616i	−0.217551	+	0.976049i	$0.569807\pi$
$224$	−14.8179	−	23.3492i	−0.990061	−	1.56009i
$225$	−10.2292	−	8.82958i	−0.681944	−	0.588639i
$226$	0.00139025	+	0.0132274i	9.24783e−5	+	0.000879873i
$227$	−1.26025	−	11.9905i	−0.0836457	−	0.795836i	−0.953270	−	0.302121i	$-0.902305\pi$
$227$	−1.26025	−	11.9905i	−0.0836457	−	0.795836i	0.869624	−	0.493715i	$-0.164361\pi$
$228$	18.2112	+	15.7195i	1.20606	+	1.04105i
$229$	−6.08667	−	9.59106i	−0.402218	−	0.633795i	0.581493	−	0.813552i	$-0.302469\pi$
$229$	−6.08667	−	9.59106i	−0.402218	−	0.633795i	−0.983711	+	0.179757i	$0.942469\pi$
$230$	5.58679	+	2.21197i	0.368382	+	0.145853i
$231$	−23.9537	+	1.00396i	−1.57604	+	0.0660557i
$232$	4.52814	+	0.572037i	0.297287	+	0.0375561i
$233$	0.215442	+	10.2851i	0.0141141	+	0.673798i	0.948365	+	0.317181i	$0.102736\pi$
$233$	0.215442	+	10.2851i	0.0141141	+	0.673798i	−0.934251	+	0.356617i	$0.883930\pi$
$234$	7.00017	+	1.79734i	0.457615	+	0.117496i
$235$	1.01362	+	16.1110i	0.0661213	+	1.05097i
$236$	−18.7358	+	8.34173i	−1.21960	+	0.543001i
$237$	−0.735623	+	0.291254i	−0.0477838	+	0.0189190i
$238$	−0.228184	−	0.165786i	−0.0147910	−	0.0107463i
$239$	18.1890	+	11.0156i	1.17655	+	0.712543i	0.964336	−	0.264681i	$-0.0852666\pi$
$239$	18.1890	+	11.0156i	1.17655	+	0.712543i	0.212212	+	0.977224i	$0.431933\pi$
$240$	−25.9340	+	26.4829i	−1.67403	+	1.70946i
$241$	4.57172	−	1.38028i	0.294490	−	0.0889118i	−0.138347	−	0.990384i	$-0.544179\pi$
$241$	4.57172	−	1.38028i	0.294490	−	0.0889118i	0.432838	+	0.901472i	$0.357512\pi$
$242$	1.16192	−	1.83090i	0.0746913	−	0.117695i
$243$	−10.0134	+	7.27518i	−0.642361	+	0.466703i
$244$	5.87848	−	0.493630i	0.376331	−	0.0316014i
$245$	23.0770	+	12.6867i	1.47434	+	0.810524i
$246$	−9.45293	−	9.65302i	−0.602697	−	0.615454i
$247$	−4.70007	−	20.0389i	−0.299059	−	1.27504i
$248$	0.399595	−	0.265490i	0.0253743	−	0.0168586i
$249$	10.7480	−	5.90874i	0.681124	−	0.374451i
$250$	41.2814	+	12.4636i	2.61086	+	0.788266i
$251$	−7.28723	+	6.29017i	−0.459966	+	0.397032i	−0.852518	−	0.522698i	$-0.824926\pi$
$251$	−7.28723	+	6.29017i	−0.459966	+	0.397032i	0.392552	+	0.919730i	$0.371592\pi$
$252$	−5.73961	−	5.38985i	−0.361562	−	0.339529i
$253$	−1.41785	−	2.04002i	−0.0891397	−	0.128255i
$254$	5.72889	−	1.99501i	0.359462	−	0.125178i
$255$	−0.126039	+	0.299835i	−0.00789287	+	0.0187764i
$256$	13.2547	+	14.7208i	0.828419	+	0.920053i
$257$	−9.79547	−	23.3025i	−0.611025	−	1.45357i	−0.872623	−	0.488394i	$-0.837583\pi$
$257$	−9.79547	−	23.3025i	−0.611025	−	1.45357i	0.261599	−	0.965177i	$-0.415750\pi$
$258$	0.0186989	−	0.0397372i	0.00116414	−	0.00247393i
$259$	−13.7116	−	26.2280i	−0.852000	−	1.62973i
$260$	−19.5500	+	3.30663i	−1.21244	+	0.205068i
$261$	9.43512	−	1.19193i	0.584019	−	0.0737788i
$262$	3.87848	+	26.2650i	0.239613	+	1.62266i
$263$	8.18684	−	6.48881i	0.504822	−	0.400117i	−0.335638	−	0.941991i	$-0.608952\pi$
$263$	8.18684	−	6.48881i	0.504822	−	0.400117i	0.840460	+	0.541874i	$0.182285\pi$
$264$	3.85585	−	0.819587i	0.237311	−	0.0504421i
$265$	21.4350	−	30.8409i	1.31674	−	1.89454i
$266$	−13.1941	+	47.2560i	−0.808982	+	2.89745i
$267$	0.234153	−	11.1783i	0.0143299	−	0.684103i
$268$	−0.00465177	+	0.0315018i	−0.000284152	+	0.00192428i
$269$	8.39645	+	14.5431i	0.511941	+	0.886707i	0.999904	+	0.0138433i	$0.00440660\pi$
$269$	8.39645	+	14.5431i	0.511941	+	0.886707i	−0.487963	+	0.872864i	$0.662260\pi$
$270$	13.6080	−	23.5697i	0.828154	−	1.43440i
$271$	23.1581	+	18.3549i	1.40675	+	1.11498i	0.977293	+	0.211894i	$0.0679631\pi$
$271$	23.1581	+	18.3549i	1.40675	+	1.11498i	0.429461	+	0.903085i	$0.358704\pi$
$272$	0.161492	+	0.0801655i	0.00979192	+	0.00486075i
$273$	4.25385	+	22.2995i	0.257455	+	1.34963i
$274$	−13.4176	+	16.2191i	−0.810588	+	0.979833i
$275$	−21.3775	−	25.8410i	−1.28911	−	1.55827i
$276$	0.515210	−	2.70082i	0.0310120	−	0.162570i
$277$	−6.44467	+	8.49055i	−0.387223	+	0.510147i	−0.948196	−	0.317687i	$-0.897094\pi$
$277$	−6.44467	+	8.49055i	−0.387223	+	0.510147i	0.560973	+	0.827834i	$0.310427\pi$
$278$	−10.7357	−	22.8145i	−0.643885	−	1.36832i
$279$	0.668889	−	0.742877i	0.0400454	−	0.0444749i
$280$	−8.39249	−	2.92258i	−0.501547	−	0.174657i
$281$	1.93343	+	6.92478i	0.115339	+	0.413097i	0.998424	−	0.0561148i	$-0.0178713\pi$
$281$	1.93343	+	6.92478i	0.115339	+	0.413097i	−0.883085	+	0.469212i	$0.844538\pi$
$282$	15.6547	−	4.01945i	0.932224	−	0.239355i
$283$	4.57613	+	14.0839i	0.272023	+	0.837200i	0.989992	+	0.141125i	$0.0450720\pi$
$283$	4.57613	+	14.0839i	0.272023	+	0.837200i	−0.717969	+	0.696075i	$0.754928\pi$
$284$	−21.5756	−	3.64923i	−1.28027	−	0.216542i
$285$	56.5280	+	2.36922i	3.34843	+	0.140341i
$286$	16.3864	+	7.29570i	0.968948	+	0.431404i
$287$	4.38965	−	11.8034i	0.259113	−	0.696733i
$288$	7.89141	+	5.24304i	0.465006	+	0.308949i
$289$	−16.9388	−	1.42239i	−0.996400	−	0.0836701i
$290$	−48.8302	+	29.5726i	−2.86741	+	1.73656i
$291$	1.27977	−	5.45632i	0.0750214	−	0.319855i
$292$	−8.56074	−	23.0191i	−0.500979	−	1.34709i
$293$	1.39268	−	22.1360i	0.0813613	−	1.29320i	−0.719560	−	0.694430i	$-0.755656\pi$
$293$	1.39268	−	22.1360i	0.0813613	−	1.29320i	0.800921	−	0.598770i	$-0.204344\pi$
$294$	8.14766	−	25.0759i	0.475181	−	1.46246i
$295$	−22.3461	+	42.7441i	−1.30104	+	2.48866i
$296$	2.94212	+	3.87610i	0.171007	+	0.225294i
$297$	−10.0791	+	5.00330i	−0.584847	+	0.290321i
$298$	22.6452	+	4.81339i	1.31180	+	0.278832i
$299$	−1.71484	+	1.61034i	−0.0991719	+	0.0931286i
$300$	3.87979	−	36.9137i	0.224000	−	2.13122i
$301$	0.0409347			0.00235943
$302$	−19.4861	−	13.2851i	−1.12130	−	0.764474i
$303$	37.7556			2.16900
$304$	3.27829	−	31.1908i	0.188023	−	1.78892i
$305$	10.1135	−	9.49717i	0.579095	−	0.543807i
$306$	0.0945197	+	0.0200908i	0.00540333	+	0.00114851i
$307$	23.5549	−	11.6927i	1.34435	−	0.667340i	0.378295	−	0.925685i	$-0.376511\pi$
$307$	23.5549	−	11.6927i	1.34435	−	0.667340i	0.966053	+	0.258345i	$0.0831773\pi$
$308$	−11.8147	−	15.5653i	−0.673206	−	0.886916i
$309$	9.83105	−	18.8051i	0.559269	−	1.06978i
$310$	−1.85429	+	5.70692i	−0.105317	+	0.324131i
$311$	−1.90766	+	30.3214i	−0.108174	+	1.71937i	0.452865	+	0.891579i	$0.350402\pi$
$311$	−1.90766	+	30.3214i	−0.108174	+	1.71937i	−0.561039	+	0.827790i	$0.689598\pi$
$312$	−1.30110	−	3.49855i	−0.0736603	−	0.198066i
$313$	2.49978	−	10.6578i	0.141296	−	0.602417i	−0.855165	−	0.518356i	$-0.826544\pi$
$313$	2.49978	−	10.6578i	0.141296	−	0.602417i	0.996461	−	0.0840612i	$-0.0267891\pi$
$314$	26.5869	−	16.1016i	1.50039	−	0.908666i
$315$	−18.4522	−	1.54947i	−1.03966	−	0.0873029i
$316$	−0.537133	−	0.356870i	−0.0302161	−	0.0200755i
$317$	4.04098	−	10.8659i	0.226964	−	0.610288i	−0.772737	−	0.634726i	$-0.781113\pi$
$317$	4.04098	−	10.8659i	0.226964	−	0.610288i	0.999701	+	0.0244380i	$0.00777965\pi$
$318$	−34.3528	−	15.2949i	−1.92641	−	0.857693i
$319$	23.5823	+	0.988391i	1.32036	+	0.0553393i
$320$	−20.6859	−	3.49877i	−1.15638	−	0.195587i
$321$	−6.84708	−	21.0731i	−0.382167	−	1.17619i
$322$	5.43134	−	1.39453i	0.302677	−	0.0777142i
$323$	−0.0740067	−	0.265062i	−0.00411785	−	0.0147485i
$324$	−17.7983	−	6.19804i	−0.988797	−	0.344335i
$325$	−21.2492	+	23.5996i	−1.17869	+	1.30907i
$326$	−4.25764	−	9.04795i	−0.235809	−	0.501120i
$327$	1.48702	−	1.95907i	0.0822322	−	0.108337i
$328$	−0.387994	+	2.03394i	−0.0214234	+	0.112305i
$329$	9.60276	+	11.6077i	0.529417	+	0.639956i
$330$	−31.4285	+	37.9906i	−1.73008	+	2.09131i
$331$	1.57044	+	8.23255i	0.0863194	+	0.452502i	0.999036	+	0.0439079i	$0.0139808\pi$
$331$	1.57044	+	8.23255i	0.0863194	+	0.452502i	−0.912716	+	0.408594i	$0.866019\pi$
$332$	8.95446	+	4.44503i	0.491440	+	0.243953i
$333$	7.94633	+	6.29818i	0.435456	+	0.345138i
$334$	9.19779	−	15.9310i	0.503281	−	0.871708i
$335$	0.0374446	+	0.0648559i	0.00204582	+	0.00354346i
$336$	−5.05320	+	34.2202i	−0.275675	+	1.86687i
$337$	−0.158374	+	7.56070i	−0.00862719	+	0.411858i	0.974029	+	0.226422i	$0.0727029\pi$
$337$	−0.158374	+	7.56070i	−0.00862719	+	0.411858i	−0.982656	+	0.185436i	$0.940630\pi$
$338$	−2.14207	+	7.67203i	−0.116513	+	0.417303i
$339$	0.00816868	−	0.0117532i	0.000443662	−	0.000638346i
$340$	−0.259311	+	0.0551183i	−0.0140631	+	0.00298921i
$341$	1.94434	−	1.54106i	0.105292	−	0.0834532i
$342$	−2.45554	−	16.6289i	−0.132780	−	0.899185i
$343$	−1.27745	+	0.161380i	−0.0689761	+	0.00871370i
$344$	−0.00663633	+	0.00112245i	−0.000357807	+	6.05185e-5i
$345$	−2.99582	−	5.73048i	−0.161290	−	0.308519i
$346$	3.42804	−	7.28496i	0.184293	−	0.391642i
$347$	2.43204	+	5.78559i	0.130559	+	0.310587i	0.973968	−	0.226684i	$-0.0727886\pi$
$347$	2.43204	+	5.78559i	0.130559	+	0.310587i	−0.843410	+	0.537271i	$0.819455\pi$
$348$	17.4792	+	19.4127i	0.936986	+	1.04063i
$349$	4.64386	−	11.0473i	0.248580	−	0.591348i	−0.748870	−	0.662717i	$-0.769403\pi$
$349$	4.64386	−	11.0473i	0.248580	−	0.591348i	0.997450	+	0.0713686i	$0.0227367\pi$
$350$	71.4877	−	24.8946i	3.82118	−	1.33067i
$351$	6.08097	+	8.74937i	0.324578	+	0.467007i
$352$	17.1412	+	16.0967i	0.913630	+	0.857955i
$353$	−12.6196	+	10.8930i	−0.671674	+	0.579774i	−0.921434	−	0.388534i	$-0.872982\pi$
$353$	−12.6196	+	10.8930i	−0.671674	+	0.579774i	0.249760	+	0.968308i	$0.419648\pi$
$354$	46.2303	+	13.9578i	2.45711	+	0.741846i
$355$	−45.0965	+	24.7920i	−2.39347	+	1.31582i
$356$	7.59062	−	5.04320i	0.402302	−	0.267289i
$357$	0.0693115	+	0.295511i	0.00366835	+	0.0156401i
$358$	12.3760	+	12.6379i	0.654090	+	0.667935i
$359$	−12.9159	−	7.10059i	−0.681677	−	0.374755i	0.102982	−	0.994683i	$-0.467162\pi$
$359$	−12.9159	−	7.10059i	−0.681677	−	0.374755i	−0.784658	+	0.619928i	$0.787162\pi$
$360$	3.03396	−	0.254769i	0.159904	−	0.0134275i
$361$	−23.3575	+	16.9702i	−1.22934	+	0.893171i
$362$	−6.57442	+	10.3596i	−0.345544	+	0.544490i
$363$	−2.23401	+	0.674486i	−0.117255	+	0.0354013i
$364$	−12.9463	+	13.2204i	−0.678572	+	0.692935i
$365$	−49.4049	−	29.9206i	−2.58597	−	1.56612i
$366$	−11.2377	−	8.16463i	−0.587402	−	0.426772i
$367$	13.5230	−	5.35413i	0.705895	−	0.279483i	0.0123773	−	0.999923i	$-0.496060\pi$
$367$	13.5230	−	5.35413i	0.705895	−	0.279483i	0.693517	+	0.720440i	$0.256060\pi$
$368$	−3.27458	+	1.45794i	−0.170699	+	0.0760003i
$369$	0.270907	+	4.30595i	0.0141029	+	0.224159i
$370$	−58.9535	−	15.1367i	−3.06484	−	0.786918i
$371$	−0.734038	−	35.0426i	−0.0381094	−	1.81932i
$372$	2.72415	+	0.344141i	0.141241	+	0.0178429i
$373$	5.34766	−	0.224133i	0.276891	−	0.0116052i	0.0969740	−	0.995287i	$-0.469084\pi$
$373$	5.34766	−	0.224133i	0.276891	−	0.0116052i	0.179917	+	0.983682i	$0.442417\pi$
$374$	0.222986	+	0.0882866i	0.0115304	+	0.00456519i
$375$	−24.8654	−	39.1816i	−1.28404	−	2.02333i
$376$	−1.87509	−	1.61854i	−0.0967005	−	0.0834696i
$377$	−2.33617	−	22.2271i	−0.120319	−	1.14476i
$378$	−2.65487	−	25.2594i	−0.136552	−	1.29921i
$379$	2.30138	+	1.98650i	0.118214	+	0.102039i	0.710533	−	0.703664i	$-0.248454\pi$
$379$	2.30138	+	1.98650i	0.118214	+	0.102039i	−0.592319	+	0.805704i	$0.701787\pi$
$380$	24.7099	+	38.9365i	1.26759	+	1.99740i
$381$	−6.06985	−	2.40322i	−0.310968	−	0.123121i
$382$	−10.6844	+	0.447809i	−0.546662	+	0.0229119i
$383$	−10.5335	−	1.33069i	−0.538237	−	0.0679951i	−0.148484	−	0.988915i	$-0.547439\pi$
$383$	−10.5335	−	1.33069i	−0.538237	−	0.0679951i	−0.389753	+	0.920920i	$0.627439\pi$
$384$	−0.207586	−	9.91004i	−0.0105933	−	0.505720i
$385$	−44.5136	−	11.4291i	−2.26862	−	0.582483i
$386$	−3.11837	−	49.5651i	−0.158721	−	2.52280i
$387$	−0.0128118	+	0.00570419i	−0.000651261	+	0.000289960i
$388$	4.24726	−	1.68161i	0.215622	−	0.0853707i
$389$	9.63446	+	6.99985i	0.488487	+	0.354906i	0.804602	−	0.593814i	$-0.202379\pi$
$389$	9.63446	+	6.99985i	0.488487	+	0.354906i	−0.316115	+	0.948721i	$0.602379\pi$
$390$	39.9346	+	24.1852i	2.02217	+	1.22467i
$391$	−0.0220065	+	0.0224723i	−0.00111292	+	0.00113647i
$392$	−3.86838	+	1.16793i	−0.195383	+	0.0589895i
$393$	15.3095	−	24.1239i	0.772261	−	1.21689i
$394$	−3.32954	+	2.41905i	−0.167740	+	0.121870i
$395$	−1.51130	+	0.126908i	−0.0760420	+	0.00638542i
$396$	5.86680	+	3.22530i	0.294818	+	0.162077i
$397$	11.2369	+	11.4748i	0.563965	+	0.575902i	0.935860	−	0.352373i	$-0.114625\pi$
$397$	11.2369	+	11.4748i	0.563965	+	0.575902i	−0.371895	+	0.928275i	$0.621292\pi$
$398$	2.32906	+	9.92999i	0.116745	+	0.497745i
$399$	43.9780	−	29.2189i	2.20165	−	1.46277i
$400$	−42.4031	+	23.3113i	−2.12016	+	1.16557i
$401$	5.54624	+	1.67451i	0.276966	+	0.0836209i	0.424475	−	0.905440i	$-0.360459\pi$
$401$	5.54624	+	1.67451i	0.276966	+	0.0836209i	−0.147509	+	0.989061i	$0.547125\pi$
$402$	0.0567595	−	0.0489935i	0.00283091	−	0.00244357i
$403$	−1.71252	−	1.60817i	−0.0853068	−	0.0801084i
$404$	17.5631	+	25.2700i	0.873797	+	1.25723i
$405$	−41.8581	+	14.5765i	−2.07995	+	0.724314i
$406$	−20.6449	+	49.1123i	−1.02459	+	2.43740i
$407$	16.8389	+	18.7015i	0.834672	+	0.926997i
$408$	−0.0193399	−	0.0460077i	−0.000957466	−	0.00227772i
$409$	9.24719	−	19.6513i	0.457244	−	0.971693i	−0.534703	−	0.845040i	$-0.679576\pi$
$409$	9.24719	−	19.6513i	0.457244	−	0.971693i	0.991947	−	0.126653i	$-0.0404235\pi$
$410$	−11.9988	−	22.9516i	−0.592578	−	1.13350i
$411$	22.3355	−	3.77777i	1.10173	−	0.186344i
$412$	17.1595	−	2.16775i	0.845388	−	0.106797i
$413$	6.57551	+	44.5293i	0.323560	+	2.19114i
$414$	−1.50559	+	1.19331i	−0.0739955	+	0.0586481i
$415$	22.9972	−	4.88821i	1.12889	−	0.239953i
$416$	12.7073	−	18.2834i	0.623026	−	0.896417i
$417$	−7.29698	+	26.1348i	−0.357335	+	1.27983i
$418$	0.873686	−	41.7093i	0.0427334	−	2.04007i
$419$	−4.97888	+	33.7169i	−0.243234	+	1.64718i	0.426434	+	0.904519i	$0.359770\pi$
$419$	−4.97888	+	33.7169i	−0.243234	+	1.64718i	−0.669668	+	0.742661i	$0.733564\pi$
$420$	−25.4314	−	44.0485i	−1.24092	−	2.14934i
$421$	0.154994	−	0.268458i	0.00755395	−	0.0130838i	−0.862224	−	0.506528i	$-0.830929\pi$
$421$	0.154994	−	0.268458i	0.00755395	−	0.0130838i	0.869778	+	0.493444i	$0.164262\pi$
$422$	−0.274863	−	0.217854i	−0.0133801	−	0.0106050i
$423$	−4.62302	−	2.29489i	−0.224779	−	0.111581i
$424$	1.07989	+	5.66098i	0.0524441	+	0.274922i
$425$	−0.270649	+	0.327158i	−0.0131284	+	0.0158695i
$426$	32.8430	+	39.7003i	1.59125	+	1.92349i
$427$	2.42607	−	12.7179i	0.117406	−	0.615463i
$428$	10.9192	−	14.3855i	0.527801	−	0.695352i
$429$	−8.21887	−	17.4660i	−0.396811	−	0.843266i
$430$	0.0563305	−	0.0625614i	0.00271650	−	0.00301698i
$431$	−30.8591	−	10.7463i	−1.48643	−	0.517630i	−0.540317	−	0.841462i	$-0.681696\pi$
$431$	−30.8591	−	10.7463i	−1.48643	−	0.517630i	−0.946115	+	0.323831i	$0.895029\pi$
$432$	4.36604	+	15.6374i	0.210061	+	0.752355i
$433$	13.4354	−	3.44961i	0.645662	−	0.165778i	0.0883614	−	0.996088i	$-0.471837\pi$
$433$	13.4354	−	3.44961i	0.645662	−	0.165778i	0.557301	+	0.830311i	$0.311837\pi$
$434$	1.73047	+	5.32585i	0.0830653	+	0.255649i
$435$	60.5741	+	10.2453i	2.90431	+	0.491227i
$436$	2.00294	+	0.0839482i	0.0959236	+	0.00402039i
$437$	4.99828	+	2.22538i	0.239100	+	0.106454i
$438$	−20.1576	+	54.2021i	−0.963166	+	2.58987i
$439$	−16.1871	−	10.7547i	−0.772566	−	0.513292i	0.103997	−	0.994578i	$-0.466837\pi$
$439$	−16.1871	−	10.7547i	−0.772566	−	0.513292i	−0.876564	+	0.481286i	$0.840170\pi$
$440$	7.52994	+	0.632307i	0.358976	+	0.0301440i
$441$	−7.20196	+	4.36166i	−0.342951	+	0.207698i
$442$	0.0518566	−	0.221092i	0.00246657	−	0.0105163i
$443$	2.07629	+	5.58297i	0.0986474	+	0.265255i	0.977175	−	0.212437i	$-0.0681401\pi$
$443$	2.07629	+	5.58297i	0.0986474	+	0.265255i	−0.878527	+	0.477692i	$0.841473\pi$
$444$	−1.74880	+	27.7964i	−0.0829945	+	1.31916i
$445$	6.62302	−	20.3835i	0.313961	−	0.966273i
$446$	4.17025	−	7.97696i	0.197467	−	0.377720i
$447$	−15.0631	−	19.8449i	−0.712459	−	0.938631i
$448$	−17.5370	+	8.70544i	−0.828545	+	0.411293i
$449$	−8.50949	−	1.80875i	−0.401588	−	0.0853601i	0.00269011	−	0.999996i	$-0.499144\pi$
$449$	−8.50949	−	1.80875i	−0.401588	−	0.0853601i	−0.404278	+	0.914636i	$0.632477\pi$
$450$	−18.9053	+	17.7533i	−0.891206	+	0.836898i
$451$	−1.11929	+	10.6493i	−0.0527053	+	0.501458i
$452$	0.0116664			0.000548739
$453$	6.53236	+	24.5249i	0.306917	+	1.15228i
$454$	−23.1393			−1.08598
$455$	−4.54875	+	43.2785i	−0.213249	+	2.02893i
$456$	−6.32851	+	5.94287i	−0.296360	+	0.278300i
$457$	−24.2440	−	5.15322i	−1.13409	−	0.241057i	−0.397632	−	0.917545i	$-0.630168\pi$
$457$	−24.2440	−	5.15322i	−1.13409	−	0.241057i	−0.736454	+	0.676488i	$0.763501\pi$
$458$	−19.5277	+	9.69365i	−0.912471	+	0.452954i
$459$	0.0861328	+	0.113476i	0.00402033	+	0.00529659i
$460$	2.44184	−	4.67081i	0.113851	−	0.217778i
$461$	−1.28192	+	3.94534i	−0.0597049	+	0.183753i	−0.976461	−	0.215695i	$-0.930798\pi$
$461$	−1.28192	+	3.94534i	−0.0597049	+	0.183753i	0.916756	+	0.399448i	$0.130798\pi$
$462$	−2.88919	+	45.9224i	−0.134417	+	2.13650i
$463$	5.15508	+	13.8616i	0.239577	+	0.644203i	0.999986	−	0.00524119i	$-0.00166833\pi$
$463$	5.15508	+	13.8616i	0.239577	+	0.644203i	−0.760409	+	0.649444i	$0.775002\pi$
$464$	7.77647	−	33.1551i	0.361013	−	1.53919i
$465$	5.52358	−	3.34520i	0.256150	−	0.155130i
$466$	19.6746	+	1.65212i	0.911407	+	0.0765330i
$467$	−0.114620	−	0.0761535i	−0.00530399	−	0.00352396i	0.550737	−	0.834679i	$-0.314347\pi$
$467$	−0.114620	−	0.0761535i	−0.00530399	−	0.00352396i	−0.556041	+	0.831155i	$0.687680\pi$
$468$	2.20973	−	5.94179i	0.102145	−	0.274659i
$469$	0.0638463	+	0.0284262i	0.00294815	+	0.00131260i
$470$	30.9548	+	1.29739i	1.42784	+	0.0598442i
$471$	−32.9812	−	5.57835i	−1.51969	−	0.257037i
$472$	−2.28704	−	7.03878i	−0.105270	−	0.323986i
$473$	−0.0337132	+	0.00865607i	−0.00155013	+	0.000398006i
$474$	0.408345	+	1.46253i	0.0187559	+	0.0671761i
$475$	69.7511	+	24.2899i	3.20040	+	1.11450i
$476$	−0.165545	+	0.183856i	−0.00758772	+	0.00842702i
$477$	5.11288	+	10.8654i	0.234103	+	0.497494i
$478$	24.6748	−	32.5078i	1.12860	−	1.48687i
$479$	−5.76018	+	30.1959i	−0.263189	+	1.37969i	0.567693	+	0.823240i	$0.307836\pi$
$479$	−5.76018	+	30.1959i	−0.263189	+	1.37969i	−0.830883	+	0.556447i	$0.812164\pi$
$480$	39.0127	+	47.1582i	1.78068	+	2.15247i
$481$	15.1891	−	18.3605i	0.692564	−	0.837166i
$482$	−1.71742	−	9.00304i	−0.0782264	−	0.410077i
$483$	−5.40521	−	2.68317i	−0.245946	−	0.122088i
$484$	−1.49065	−	1.18147i	−0.0677567	−	0.0537033i
$485$	5.37156	−	9.30381i	0.243910	−	0.422464i
$486$	11.8774	+	20.5723i	0.538772	+	0.933180i
$487$	5.16439	−	34.9732i	0.234021	−	1.58479i	−0.475251	−	0.879850i	$-0.657643\pi$
$487$	5.16439	−	34.9732i	0.234021	−	1.58479i	0.709272	−	0.704935i	$-0.249024\pi$
$488$	−0.0445827	+	2.12836i	−0.00201816	+	0.0963461i
$489$	−2.89389	+	10.3647i	−0.130866	+	0.468710i
$490$	28.8450	−	41.5025i	1.30308	−	1.87489i
$491$	5.48102	−	1.16503i	0.247355	−	0.0525770i	−0.0825655	−	0.996586i	$-0.526311\pi$
$491$	5.48102	−	1.16503i	0.247355	−	0.0525770i	0.329921	+	0.944009i	$0.392978\pi$
$492$	−9.28751	+	7.36119i	−0.418713	+	0.331868i
$493$	−0.0436531	−	0.295618i	−0.00196604	−	0.0133140i
$494$	−39.1915	+	4.95104i	−1.76331	+	0.222758i
$495$	15.5246	−	2.62579i	0.697778	−	0.118020i
$496$	−1.65843	−	3.17228i	−0.0744656	−	0.142439i
$497$	−20.4483	+	43.4549i	−0.917234	+	1.94922i
$498$	−9.12194	−	21.7002i	−0.408764	−	0.972411i
$499$	4.38838	+	4.87379i	0.196451	+	0.218181i	0.833320	−	0.552791i	$-0.186437\pi$
$499$	4.38838	+	4.87379i	0.196451	+	0.218181i	−0.636869	+	0.770972i	$0.719771\pi$
$500$	14.6576	−	34.8690i	0.655506	−	1.55939i
$501$	−18.6953	+	6.51040i	−0.835245	+	0.290863i
$502$	10.5443	+	15.1712i	0.470613	+	0.677124i
$503$	−19.8336	−	18.6250i	−0.884337	−	0.830448i	0.102068	−	0.994777i	$-0.467454\pi$
$503$	−19.8336	−	18.6250i	−0.884337	−	0.830448i	−0.986405	+	0.164330i	$0.947454\pi$
$504$	2.15087	−	1.85658i	0.0958076	−	0.0826989i
$505$	69.2851	+	20.9184i	3.08315	+	0.930857i
$506$	−4.17828	+	2.29703i	−0.185747	+	0.102115i
$507$	7.13985	−	4.74370i	0.317092	−	0.210675i
$508$	−1.21508	−	5.18050i	−0.0539103	−	0.229848i
$509$	5.47447	+	5.59034i	0.242651	+	0.247788i	0.824974	−	0.565170i	$-0.191189\pi$
$509$	5.47447	+	5.59034i	0.242651	+	0.247788i	−0.582323	+	0.812958i	$0.697856\pi$
$510$	0.547016	+	0.300725i	0.0242223	+	0.0133163i
$511$	−53.7130	+	4.51041i	−2.37612	+	0.199529i
$512$	22.9918	−	16.7045i	1.01610	−	0.738243i
$513$	13.2786	−	20.9238i	0.586267	−	0.923808i
$514$	−46.4431	+	14.0220i	−2.04852	+	0.618484i
$515$	28.4598	−	29.0622i	1.25409	−	1.28063i
$516$	−0.0329502	−	0.0199554i	−0.00145055	−	0.000878485i
$517$	−10.3633	−	7.52935i	−0.455776	−	0.331141i
$518$	−52.8126	+	20.9100i	−2.32045	+	0.918732i
$519$	−7.91527	+	3.52411i	−0.347442	+	0.154691i
$520$	−0.449276	−	7.14104i	−0.0197021	−	0.313155i
$521$	−15.6457	−	4.01713i	−0.685449	−	0.175994i	−0.110124	−	0.993918i	$-0.535125\pi$
$521$	−15.6457	−	4.01713i	−0.685449	−	0.175994i	−0.575326	+	0.817924i	$0.695125\pi$
$522$	−0.382244	−	18.2481i	−0.0167304	−	0.798699i
$523$	17.1303	+	2.16406i	0.749057	+	0.0946279i	0.490588	−	0.871392i	$-0.336782\pi$
$523$	17.1303	+	2.16406i	0.749057	+	0.0946279i	0.258469	+	0.966020i	$0.416782\pi$
$524$	23.2678	−	0.975211i	1.01646	−	0.0426023i
$525$	−75.7424	−	29.9885i	−3.30567	−	1.30881i
$526$	−10.7429	−	16.9281i	−0.468414	−	0.738102i
$527$	−0.0237775	−	0.0205242i	−0.00103577	−	0.000894049i
$528$	−3.07449	−	29.2518i	−0.133800	−	1.27302i
$529$	2.33879	+	22.2521i	0.101687	+	0.967483i
$530$	−54.5665	−	47.1006i	−2.37022	−	2.04592i
$531$	−8.26311	−	13.0206i	−0.358588	−	0.565045i
$532$	40.0139	+	15.8426i	1.73482	+	0.686865i
$533$	10.1305	−	0.424592i	0.438799	−	0.0183911i
$534$	−21.2893	−	2.68947i	−0.921280	−	0.116385i
$535$	−0.889511	−	42.4648i	−0.0384569	−	1.83591i
$536$	−0.0111302	−	0.00285776i	−0.000480753	−	0.000123436i
$537$	−1.19525	−	18.9979i	−0.0515788	−	0.819821i
$538$	29.4431	−	13.1089i	1.26938	−	0.565166i
$539$	−19.4294	+	7.69266i	−0.836885	+	0.331346i
$540$	−19.3133	−	14.0319i	−0.831111	−	0.603838i
$541$	−18.2891	−	11.0763i	−0.786311	−	0.476207i	0.0669085	−	0.997759i	$-0.478686\pi$
$541$	−18.2891	−	11.0763i	−0.786311	−	0.476207i	−0.853219	+	0.521552i	$0.825353\pi$
$542$	39.6802	−	40.5201i	1.70441	−	1.74049i
$543$	12.6405	−	3.81639i	0.542455	−	0.163777i
$544$	0.159516	−	0.251358i	0.00683921	−	0.0107769i
$545$	3.81423	−	2.77120i	0.163384	−	0.118705i
$546$	43.4169	−	3.64582i	1.85807	−	0.156027i
$547$	20.7736	+	11.4204i	0.888215	+	0.488300i	0.859411	−	0.511285i	$-0.170830\pi$
$547$	20.7736	+	11.4204i	0.888215	+	0.488300i	0.0288035	+	0.999585i	$0.490830\pi$
$548$	12.9185	+	13.1919i	0.551851	+	0.563531i
$549$	1.01291	+	4.31855i	0.0432298	+	0.184311i
$550$	−53.6119	+	35.6197i	−2.28602	+	1.51883i
$551$	−45.5513	+	25.0420i	−1.94055	+	1.06683i
$552$	0.949867	+	0.286782i	0.0404290	+	0.0122062i
$553$	−1.07141	+	0.924820i	−0.0455612	+	0.0393273i
$554$	14.9132	+	14.0044i	0.633601	+	0.594991i
$555$	37.3822	+	53.7859i	1.58679	+	2.28309i
$556$	−20.8865	+	7.27346i	−0.885787	+	0.308464i
$557$	13.5482	−	32.2299i	0.574056	−	1.36563i	−0.332325	−	0.943165i	$-0.607833\pi$
$557$	13.5482	−	32.2299i	0.574056	−	1.36563i	0.906381	−	0.422460i	$-0.138833\pi$
$558$	−1.28376	−	1.42576i	−0.0543457	−	0.0603571i
$559$	0.0127718	+	0.0303830i	0.000540191	+	0.00128506i
$560$	−28.2327	+	59.9976i	−1.19305	+	2.53536i
$561$	−0.119573	−	0.228722i	−0.00504837	−	0.00965664i
$562$	13.6053	−	2.30117i	0.573907	−	0.0970690i
$563$	30.9504	−	3.90994i	1.30440	−	0.164784i	0.557756	−	0.830005i	$-0.311662\pi$
$563$	30.9504	−	3.90994i	1.30440	−	0.164784i	0.746647	+	0.665221i	$0.231662\pi$
$564$	−2.07102	−	14.0249i	−0.0872055	−	0.590554i
$565$	0.0215021	−	0.0170424i	0.000904601	−	0.000716978i
$566$	27.8003	−	5.90913i	1.16853	−	0.248379i
$567$	−23.6069	+	33.9659i	−0.991397	+	1.42643i
$568$	2.12353	−	7.60562i	0.0891013	−	0.319125i
$569$	−0.609039	+	29.0752i	−0.0255323	+	1.21890i	0.779783	+	0.626050i	$0.215329\pi$
$569$	−0.609039	+	29.0752i	−0.0255323	+	1.21890i	−0.805315	+	0.592847i	$0.798004\pi$
$570$	15.8625	−	107.421i	0.664408	−	4.49936i
$571$	−14.7839	−	25.6065i	−0.618688	−	1.07160i	−0.989725	−	0.142982i	$-0.954331\pi$
$571$	−14.7839	−	25.6065i	−0.618688	−	1.07160i	0.371037	−	0.928618i	$-0.379002\pi$
$572$	7.86681	−	13.6257i	0.328928	−	0.569720i
$573$	9.01886	+	7.14826i	0.376768	+	0.298623i
$574$	−21.6488	−	10.7466i	−0.903603	−	0.448552i
$575$	−1.58178	−	8.29197i	−0.0659647	−	0.345799i
$576$	4.27568	−	5.16840i	0.178153	−	0.215350i
$577$	−26.9199	−	32.5406i	−1.12069	−	1.35468i	−0.927632	−	0.373496i	$-0.878159\pi$
$577$	−26.9199	−	32.5406i	−1.12069	−	1.35468i	−0.193060	−	0.981187i	$-0.561841\pi$
$578$	−6.11312	+	32.0461i	−0.254272	+	1.33294i
$579$	−32.3129	+	42.5706i	−1.34288	+	1.76918i
$580$	21.3205	+	45.3084i	0.885286	+	1.88133i
$581$	14.6814	−	16.3054i	0.609089	−	0.676462i
$582$	−10.1579	−	3.53734i	−0.421057	−	0.146627i
$583$	8.01468	+	28.7053i	0.331934	+	1.18885i
$584$	8.58428	−	2.20407i	0.355220	−	0.0912050i
$585$	−4.60712	−	14.1792i	−0.190481	−	0.586240i
$586$	−41.9721	−	7.09905i	−1.73385	−	0.293259i
$587$	6.87136	+	0.287995i	0.283611	+	0.0118868i	0.183257	−	0.983065i	$-0.441336\pi$
$587$	6.87136	+	0.287995i	0.283611	+	0.0118868i	0.100354	+	0.994952i	$0.468002\pi$
$588$	−21.1279	−	9.40675i	−0.871300	−	0.387928i
$589$	−1.90456	+	5.12121i	−0.0784761	+	0.211016i
$590$	77.1037	+	51.2276i	3.17431	+	2.10901i
$591$	4.41342	+	0.370605i	0.181544	+	0.0152447i
$592$	31.0574	−	18.8091i	1.27645	−	0.773047i
$593$	−7.82922	+	33.3800i	−0.321507	+	1.37075i	0.530705	+	0.847557i	$0.321927\pi$
$593$	−7.82922	+	33.3800i	−0.321507	+	1.37075i	−0.852212	+	0.523197i	$0.824739\pi$
$594$	7.52789	+	20.2419i	0.308873	+	0.830535i
$595$	−0.0365341	+	0.580692i	−0.00149775	+	0.0238061i
$596$	6.27524	−	19.3132i	0.257044	−	0.791099i
$597$	5.08523	−	9.72715i	0.208125	−	0.398106i
$598$	2.72967	+	3.59621i	0.111625	+	0.147060i
$599$	−16.6476	+	8.26394i	−0.680203	+	0.337656i	−0.751438	−	0.659804i	$-0.770639\pi$
$599$	−16.6476	+	8.26394i	−0.680203	+	0.337656i	0.0712350	+	0.997460i	$0.477306\pi$
$600$	13.1017	+	2.78484i	0.534873	+	0.113691i
$601$	−10.1797	+	9.55934i	−0.415237	+	0.389933i	−0.863814	−	0.503811i	$-0.831931\pi$
$601$	−10.1797	+	9.55934i	−0.415237	+	0.389933i	0.448577	+	0.893744i	$0.351931\pi$
$602$	0.00821209	−	0.0781329i	0.000334700	−	0.00318446i
$603$	−0.0239439			−0.000975071
$604$	−13.3759	+	15.7806i	−0.544258	+	0.642103i
$605$	−4.47330			−0.181866
$606$	7.57433	−	72.0650i	0.307686	−	2.92744i
$607$	−28.8910	+	27.1305i	−1.17265	+	1.10119i	−0.179570	+	0.983745i	$0.557471\pi$
$607$	−28.8910	+	27.1305i	−1.17265	+	1.10119i	−0.993079	+	0.117446i	$0.962529\pi$
$608$	−50.6540	−	10.7668i	−2.05429	−	0.436653i
$609$	51.3531	−	25.4919i	2.08093	−	1.03298i
$610$	−16.0986	−	21.2091i	−0.651811	−	0.858730i
$611$	−5.61952	+	10.7492i	−0.227342	+	0.434864i
$612$	0.0261924	−	0.0806120i	0.00105877	−	0.00325855i
$613$	−2.45128	+	38.9620i	−0.0990064	+	1.57366i	0.564463	+	0.825458i	$0.309083\pi$
$613$	−2.45128	+	38.9620i	−0.0990064	+	1.57366i	−0.663470	+	0.748203i	$0.730917\pi$
$614$	−17.5927	−	47.3054i	−0.709985	−	1.90909i
$615$	−6.36437	+	27.1346i	−0.256636	+	1.09417i
$616$	6.03191	−	3.65306i	0.243033	−	0.147186i
$617$	−19.8818	−	1.66952i	−0.800411	−	0.0672124i	−0.323572	−	0.946203i	$-0.604884\pi$
$617$	−19.8818	−	1.66952i	−0.800411	−	0.0672124i	−0.476838	+	0.878991i	$0.658217\pi$
$618$	−33.9214	−	22.5373i	−1.36452	−	0.906584i
$619$	−5.01733	+	13.4912i	−0.201663	+	0.542256i	−0.998042	−	0.0625415i	$-0.980079\pi$
$619$	−5.01733	+	13.4912i	−0.201663	+	0.542256i	0.796379	+	0.604798i	$0.206746\pi$
$620$	4.80841	+	2.14084i	0.193110	+	0.0859782i
$621$	−2.82984	−	0.118605i	−0.113557	−	0.00475947i
$622$	57.4924	+	9.72411i	2.30523	+	0.389901i
$623$	−6.18077	−	19.0224i	−0.247627	−	0.762118i
$624$	−26.9760	+	6.92625i	−1.07990	+	0.277272i
$625$	−9.56830	−	34.2698i	−0.382732	−	1.37079i
$626$	−19.8414	−	6.90950i	−0.793021	−	0.276159i
$627$	−30.0409	+	33.3638i	−1.19972	+	1.33242i
$628$	−11.6085	−	24.6694i	−0.463230	−	0.984415i
$629$	0.192627	−	0.253777i	0.00768056	−	0.0101188i
$630$	−6.65929	+	34.9092i	−0.265313	+	1.39082i
$631$	25.3791	+	30.6781i	1.01033	+	1.22128i	0.975070	+	0.221897i	$0.0712250\pi$
$631$	25.3791	+	30.6781i	1.01033	+	1.22128i	0.0352569	+	0.999378i	$0.488775\pi$
$632$	0.148339	−	0.179311i	0.00590060	−	0.00713260i
$633$	0.0707247	+	0.370752i	0.00281105	+	0.0147361i
$634$	−19.9292	−	9.89296i	−0.791491	−	0.392900i
$635$	−9.80724	−	7.77312i	−0.389188	−	0.308467i
$636$	−16.4922	+	28.5653i	−0.653957	+	1.13269i
$637$	9.89358	+	17.1362i	0.391998	+	0.678961i
$638$	6.61752	−	44.8138i	0.261990	−	1.77419i
$639$	0.344580	−	16.4501i	0.0136314	−	0.650755i
$640$	5.10969	−	18.3009i	0.201978	−	0.723405i
$641$	−16.2111	+	23.3247i	−0.640300	+	0.921271i	−0.999930	−	0.0118237i	$-0.996236\pi$
$641$	−16.2111	+	23.3247i	−0.640300	+	0.921271i	0.359630	+	0.933095i	$0.382903\pi$
$642$	−41.5964	+	8.84159i	−1.64168	+	0.348950i
$643$	7.30075	−	5.78650i	0.287913	−	0.228197i	−0.466622	−	0.884457i	$-0.654529\pi$
$643$	7.30075	−	5.78650i	0.287913	−	0.228197i	0.754535	+	0.656260i	$0.227862\pi$
$644$	−0.718531	−	4.86588i	−0.0283141	−	0.191743i
$645$	−0.0898812	+	0.0113546i	−0.00353907	+	0.000447088i
$646$	−0.520777	+	0.0880828i	−0.0204897	+	0.00346557i
$647$	11.8349	+	22.6380i	0.465276	+	0.889991i	0.999016	+	0.0443428i	$0.0141194\pi$
$647$	11.8349	+	22.6380i	0.465276	+	0.889991i	−0.533740	+	0.845649i	$0.679214\pi$
$648$	2.89579	−	6.15387i	0.113757	−	0.241747i
$649$	−14.8317	−	35.2832i	−0.582194	−	1.38498i
$650$	40.7822	+	45.2932i	1.59961	+	1.77654i
$651$	2.33532	−	5.55550i	0.0915283	−	0.217737i
$652$	−8.28334	+	2.88456i	−0.324401	+	0.112968i
$653$	−18.0940	−	26.0338i	−0.708071	−	1.01878i	−0.998091	−	0.0617602i	$-0.980329\pi$
$653$	−18.0940	−	26.0338i	−0.708071	−	1.01878i	0.290020	−	0.957021i	$-0.406338\pi$
$654$	−3.44101	−	3.23132i	−0.134554	−	0.126355i
$655$	41.4601	−	35.7874i	1.61998	−	1.39833i
$656$	14.7903	+	4.46546i	0.577465	+	0.174347i
$657$	16.1827	−	8.89651i	0.631347	−	0.347086i
$658$	24.0824	−	16.0003i	0.938830	−	0.623757i
$659$	−6.52654	−	27.8260i	−0.254238	−	1.08395i	−0.935896	−	0.352277i	$-0.885407\pi$
$659$	−6.52654	−	27.8260i	−0.254238	−	1.08395i	0.681658	−	0.731671i	$-0.261259\pi$
$660$	30.2594	+	30.8999i	1.17785	+	1.20278i
$661$	23.7251	+	13.0430i	0.922800	+	0.507313i	0.870967	−	0.491342i	$-0.163494\pi$
$661$	23.7251	+	13.0430i	0.922800	+	0.507313i	0.0518331	+	0.998656i	$0.483494\pi$
$662$	16.0287	−	1.34597i	0.622973	−	0.0523125i
$663$	−0.197712	+	0.143646i	−0.00767851	+	0.00557876i
$664$	−1.93305	+	3.04600i	−0.0750170	+	0.118208i
$665$	96.8923	−	29.2535i	3.75732	−	1.13440i
$666$	13.6156	−	13.9038i	0.527595	−	0.538762i
$667$	5.08169	+	3.07758i	0.196764	+	0.119164i
$668$	−13.0541	−	9.48435i	−0.505078	−	0.366961i
$669$	−9.00652	+	3.56593i	−0.348212	+	0.137867i
$670$	0.131304	−	0.0584602i	0.00507271	−	0.00225851i
$671$	0.691263	+	10.9873i	0.0266859	+	0.424160i
$672$	55.3224	+	14.2044i	2.13411	+	0.547945i
$673$	0.841823	+	40.1882i	0.0324499	+	1.54914i	0.648365	+	0.761329i	$0.275453\pi$
$673$	0.841823	+	40.1882i	0.0324499	+	1.54914i	−0.615916	+	0.787812i	$0.711214\pi$
$674$	14.3995	+	1.81908i	0.554648	+	0.0700684i
$675$	−38.2012	+	1.60111i	−1.47037	+	0.0616266i
$676$	6.49628	+	2.57206i	0.249857	+	0.0989254i
$677$	−15.1106	−	23.8104i	−0.580746	−	0.915110i	−0.999974	−	0.00722857i	$-0.997699\pi$
$677$	−15.1106	−	23.8104i	−0.580746	−	0.915110i	0.419228	−	0.907881i	$-0.362301\pi$
$678$	−0.0207948	−	0.0179496i	−0.000798620	−	0.000689350i
$679$	−1.04798	−	9.97083i	−0.0402176	−	0.382645i
$680$	−0.0100000	−	0.0951437i	−0.000383483	−	0.00364859i
$681$	18.8503	+	16.2711i	0.722344	+	0.623511i
$682$	−2.55140	−	4.02036i	−0.0976980	−	0.153947i
$683$	19.8908	+	7.87532i	0.761099	+	0.301341i	0.716428	−	0.697661i	$-0.245776\pi$
$683$	19.8908	+	7.87532i	0.761099	+	0.301341i	0.0446715	+	0.999002i	$0.485776\pi$
$684$	−14.7313	+	0.617424i	−0.563265	+	0.0236078i
$685$	43.0809	+	5.44238i	1.64604	+	0.207943i
$686$	0.0517534	+	2.47068i	0.00197595	+	0.0943310i
$687$	22.7245	+	5.83466i	0.866994	+	0.222606i
$688$	0.00315333	+	0.0501207i	0.000120219	+	0.00191083i
$689$	25.7807	−	11.4783i	0.982168	−	0.437289i
$690$	−11.5389	+	4.56857i	−0.439278	+	0.173923i
$691$	−28.7020	−	20.8532i	−1.09188	−	0.793294i	−0.112161	−	0.993690i	$-0.535777\pi$
$691$	−28.7020	−	20.8532i	−1.09188	−	0.793294i	−0.979715	+	0.200396i	$0.935777\pi$
$692$	−6.04071	−	3.65839i	−0.229633	−	0.139071i
$693$	10.2807	−	10.4983i	0.390530	−	0.398796i
$694$	11.5310	−	3.48141i	0.437710	−	0.132152i
$695$	−27.8706	+	43.9170i	−1.05719	+	1.66587i
$696$	−7.62637	+	5.54088i	−0.289077	+	0.210027i
$697$	0.135092	−	0.0113440i	0.00511699	−	0.000429686i
$698$	−20.1546	−	11.0801i	−0.762862	−	0.419387i
$699$	−14.8660	−	15.1807i	−0.562284	−	0.574186i
$700$	−15.1623	−	64.6447i	−0.573080	−	2.44334i
$701$	21.1784	−	14.0709i	0.799895	−	0.531449i	−0.0854724	−	0.996341i	$-0.527240\pi$
$701$	21.1784	−	14.0709i	0.799895	−	0.531449i	0.885368	+	0.464891i	$0.153907\pi$
$702$	17.9200	−	9.85162i	0.676348	−	0.371826i
$703$	−53.0562	−	16.0186i	−2.00105	−	0.604153i
$704$	12.6023	−	10.8781i	0.474969	−	0.409982i
$705$	−24.3048	−	22.8237i	−0.915372	−	0.859592i
$706$	18.2599	+	26.2726i	0.687222	+	0.988783i
$707$	63.7844	−	22.2121i	2.39886	−	0.835371i
$708$	16.4148	−	39.0492i	0.616905	−	1.46756i
$709$	24.0901	+	26.7548i	0.904724	+	1.00480i	0.999956	+	0.00934276i	$0.00297394\pi$
$709$	24.0901	+	26.7548i	0.904724	+	1.00480i	−0.0952323	+	0.995455i	$0.530359\pi$
$710$	38.2740	+	91.0503i	1.43640	+	3.41706i
$711$	0.206461	−	0.438752i	0.00774290	−	0.0164545i
$712$	1.52363	+	2.91444i	0.0571006	+	0.109223i
$713$	0.615730	−	0.104143i	0.0230593	−	0.00390019i
$714$	0.577953	−	0.0730125i	0.0216294	−	0.00273242i
$715$	−5.40541	−	36.6054i	−0.202151	−	1.36896i
$716$	12.1594	−	9.63741i	0.454418	−	0.360167i
$717$	−42.9600	+	9.13143i	−1.60437	+	0.341020i
$718$	−16.1442	+	23.2284i	−0.602495	+	0.866877i
$719$	−0.630719	+	2.25898i	−0.0235219	+	0.0842459i	−0.974002	−	0.226540i	$-0.927259\pi$
$719$	−0.630719	+	2.25898i	−0.0235219	+	0.0842459i	0.950480	+	0.310785i	$0.100592\pi$
$720$	0.475756	−	22.7124i	0.0177304	−	0.846439i
$721$	5.54535	−	37.5531i	0.206520	−	1.39855i
$722$	27.7056	+	47.9875i	1.03110	+	1.78591i
$723$	−4.93168	+	8.54192i	−0.183411	+	0.317677i
$724$	8.43441	+	6.68503i	0.313462	+	0.248447i
$725$	71.8359	+	35.6596i	2.66792	+	1.32437i
$726$	0.839231	+	4.39941i	0.0311468	+	0.163277i
$727$	0.347862	−	0.420493i	0.0129015	−	0.0155952i	−0.764023	−	0.645189i	$-0.776779\pi$
$727$	0.347862	−	0.420493i	0.0129015	−	0.0155952i	0.776925	+	0.629594i	$0.216779\pi$
$728$	−4.25632	−	5.14501i	−0.157750	−	0.190687i
$729$	−1.50310	+	7.87952i	−0.0556703	+	0.291834i
$730$	−67.0215	+	88.2976i	−2.48058	+	3.26804i
$731$	0.000187627	0	0.000398728i	6.93964e−6	0	1.47475e-5i
$732$	−8.15276	+	9.05455i	−0.301335	+	0.334666i
$733$	40.8777	+	14.2351i	1.50985	+	0.525786i	0.952513	−	0.304499i	$-0.0984891\pi$
$733$	40.8777	+	14.2351i	1.50985	+	0.525786i	0.557339	+	0.830285i	$0.311822\pi$
$734$	−7.50664	−	26.8857i	−0.277075	−	0.992371i
$735$	−52.6821	+	13.5265i	−1.94321	+	0.498931i
$736$	1.82896	+	5.62897i	0.0674165	+	0.207487i
$737$	−0.0585938	−	0.00991041i	−0.00215833	−	0.000365055i
$738$	8.27320	+	0.346750i	0.304541	+	0.0127640i
$739$	−13.9722	−	6.22083i	−0.513976	−	0.228837i	0.133323	−	0.991073i	$-0.457435\pi$
$739$	−13.9722	−	6.22083i	−0.513976	−	0.228837i	−0.647300	+	0.762236i	$0.724102\pi$
$740$	−18.6097	+	50.0401i	−0.684108	+	1.83951i
$741$	35.4086	+	23.5254i	1.30077	+	0.864227i
$742$	−67.0338	−	5.62899i	−2.46089	−	0.206647i
$743$	2.60608	−	1.57830i	0.0956077	−	0.0579021i	−0.469414	−	0.882978i	$-0.655535\pi$
$743$	2.60608	−	1.57830i	0.0956077	−	0.0579021i	0.565021	+	0.825076i	$0.308868\pi$
$744$	−0.226267	+	0.964693i	−0.00829534	+	0.0353674i
$745$	−16.6472	−	44.7629i	−0.609905	−	1.63998i
$746$	0.645011	−	10.2522i	0.0236155	−	0.375358i
$747$	−2.32289	+	7.14913i	−0.0849903	+	0.261573i
$748$	0.0974617	−	0.186427i	0.00356355	−	0.00681645i
$749$	−23.9651	−	31.5728i	−0.875664	−	1.15364i
$750$	−79.7752	+	39.6007i	−2.91298	+	1.44601i
$751$	−43.5492	−	9.25668i	−1.58913	−	0.337781i	−0.673310	−	0.739360i	$-0.735128\pi$
$751$	−43.5492	−	9.25668i	−1.58913	−	0.337781i	−0.915824	+	0.401579i	$0.868461\pi$
$752$	−13.4729	+	12.6519i	−0.491305	+	0.461366i
$753$	2.07829	−	19.7736i	0.0757372	−	0.720591i
$754$	−42.8941			−1.56211
$755$	−1.60047	+	48.6247i	−0.0582472	+	1.76963i
$756$	−22.2784			−0.810259
$757$	−2.80236	+	26.6627i	−0.101854	+	0.969072i	0.817577	+	0.575819i	$0.195317\pi$
$757$	−2.80236	+	26.6627i	−0.101854	+	0.969072i	−0.919430	+	0.393253i	$0.871350\pi$
$758$	4.25336	−	3.99417i	0.154489	−	0.145075i
$759$	5.01903	+	1.06683i	0.182179	+	0.0387234i
$760$	−14.9060	+	7.39943i	−0.540699	+	0.268405i
$761$	11.1667	+	14.7116i	0.404793	+	0.533294i	0.952969	−	0.303068i	$-0.0980111\pi$
$761$	11.1667	+	14.7116i	0.404793	+	0.533294i	−0.548176	+	0.836363i	$0.684678\pi$
$762$	−5.80478	+	11.1035i	−0.210285	+	0.402238i
$763$	1.35962	−	4.18449i	0.0492217	−	0.151489i
$764$	−0.588981	+	9.36158i	−0.0213086	+	0.338690i
$765$	−0.0694842	−	0.186837i	−0.00251221	−	0.00675512i
$766$	−4.65309	+	19.8386i	−0.168123	+	0.716797i
$767$	−30.9994	+	18.7739i	−1.11933	+	0.677887i
$768$	−40.7695	−	3.42351i	−1.47114	−	0.123535i
$769$	18.9306	+	12.5774i	0.682653	+	0.453554i	0.846118	−	0.532995i	$-0.178934\pi$
$769$	18.9306	+	12.5774i	0.682653	+	0.453554i	−0.163465	+	0.986549i	$0.552267\pi$
$770$	−30.7451	+	82.6712i	−1.10798	+	2.97926i
$771$	47.6945	+	21.2350i	1.71768	+	0.764759i
$772$	−43.5239	−	1.82419i	−1.56646	−	0.0656542i
$773$	13.1785	+	2.22898i	0.473999	+	0.0801710i	0.398879	−	0.917004i	$-0.369399\pi$
$773$	13.1785	+	2.22898i	0.473999	+	0.0801710i	0.0751201	+	0.997174i	$0.476066\pi$
$774$	0.00831747	+	0.0255985i	0.000298965	+	0.000920120i
$775$	8.16523	−	2.09647i	0.293304	−	0.0753076i
$776$	0.443304	+	1.58774i	0.0159137	+	0.0569964i
$777$	57.7269	+	20.1026i	2.07094	+	0.721178i
$778$	15.2936	−	16.9852i	0.548301	−	0.608950i
$779$	−10.0408	−	21.3379i	−0.359750	−	0.764508i
$780$	24.7594	−	32.6194i	0.886530	−	1.16796i
$781$	7.65193	−	40.1128i	0.273808	−	1.43535i
$782$	0.0384785	+	0.0465125i	0.00137599	+	0.00166328i
$783$	17.1524	−	20.7337i	0.612977	−	0.740962i
$784$	5.64963	+	29.6164i	0.201773	+	1.05773i
$785$	−57.4329	−	28.5099i	−2.04987	−	1.01756i
$786$	−42.9744	−	34.0611i	−1.53285	−	1.21492i
$787$	10.3957	−	18.0059i	0.370567	−	0.641841i	−0.619086	−	0.785324i	$-0.712497\pi$
$787$	10.3957	−	18.0059i	0.370567	−	0.641841i	0.989653	+	0.143482i	$0.0458299\pi$
$788$	1.80498	+	3.12631i	0.0642997	+	0.111370i
$789$	−3.15190	+	21.3446i	−0.112211	+	0.759888i
$790$	−0.0609583	+	2.91012i	−0.00216880	+	0.103537i
$791$	0.00688564	−	0.0246616i	0.000244825	−	0.000876866i
$792$	−1.37883	+	1.98388i	−0.0489947	+	0.0704941i
$793$	10.1966	−	2.16735i	0.362092	−	0.0769650i
$794$	24.1564	−	19.1461i	0.857279	−	0.679471i
$795$	11.3320	+	76.7403i	0.401905	+	2.72170i
$796$	8.87595	−	1.12129i	0.314600	−	0.0397432i
$797$	24.2545	−	4.10235i	0.859139	−	0.145313i	0.279460	−	0.960157i	$-0.409845\pi$
$797$	24.2545	−	4.10235i	0.859139	−	0.145313i	0.579679	+	0.814845i	$0.303178\pi$
$798$	−46.9481	−	89.8034i	−1.66194	−	3.17901i
$799$	−0.0690513	+	0.146742i	−0.00244286	+	0.00519134i
$800$	30.9619	+	73.6555i	1.09467	+	2.60411i
$801$	4.58522	+	5.09240i	0.162011	+	0.179931i
$802$	4.30882	−	10.2503i	0.152150	−	0.361950i
$803$	43.2834	−	15.0729i	1.52744	−	0.531911i
$804$	−0.0375353	−	0.0540062i	−0.00132377	−	0.00190465i
$805$	−8.43246	−	7.91861i	−0.297205	−	0.279094i
$806$	−3.41310	+	2.94611i	−0.120221	+	0.103772i
$807$	−33.2036	−	10.0248i	−1.16882	−	0.352888i
$808$	−9.73167	+	5.35003i	−0.342359	+	0.188213i
$809$	12.3131	−	8.18078i	0.432904	−	0.287621i	−0.317927	−	0.948115i	$-0.602987\pi$
$809$	12.3131	−	8.18078i	0.432904	−	0.287621i	0.750831	+	0.660494i	$0.229653\pi$
$810$	19.4252	+	82.8197i	0.682532	+	2.90999i
$811$	−22.3528	−	22.8259i	−0.784913	−	0.801527i	0.199033	−	0.979993i	$-0.436220\pi$
$811$	−22.3528	−	22.8259i	−0.784913	−	0.801527i	−0.983946	+	0.178466i	$0.942887\pi$
$812$	40.9502	+	22.5126i	1.43707	+	0.790036i
$813$	−60.8181	+	5.10704i	−2.13299	+	0.179112i
$814$	39.0740	−	28.3889i	1.36954	−	0.995032i
$815$	−11.0531	+	17.4169i	−0.387174	+	0.610088i
$816$	−0.356487	+	0.107630i	−0.0124795	+	0.00376779i
$817$	0.0536326	−	0.0547678i	0.00187637	−	0.00191608i
$818$	−35.6537	−	21.5926i	−1.24660	−	0.754969i
$819$	−11.2562	−	8.17810i	−0.393323	−	0.285766i
$820$	−21.1219	+	8.36275i	−0.737608	+	0.292040i
$821$	−8.10466	+	3.60843i	−0.282855	+	0.125935i	−0.543260	−	0.839564i	$-0.682810\pi$
$821$	−8.10466	+	3.60843i	−0.282855	+	0.125935i	0.260406	+	0.965499i	$0.416144\pi$
$822$	−2.72988	−	43.3902i	−0.0952155	−	1.51341i
$823$	−31.1633	−	8.00137i	−1.08628	−	0.278910i	−0.337232	−	0.941422i	$-0.609491\pi$
$823$	−31.1633	−	8.00137i	−1.08628	−	0.278910i	−0.749052	+	0.662512i	$0.769491\pi$
$824$	0.130713	+	6.24016i	0.00455359	+	0.217386i
$825$	68.7216	+	8.68156i	2.39258	+	0.302253i
$826$	86.3131	−	3.61759i	3.00322	−	0.125872i
$827$	36.0393	+	14.2690i	1.25321	+	0.496181i	0.898573	−	0.438823i	$-0.144605\pi$
$827$	36.0393	+	14.2690i	1.25321	+	0.496181i	0.354636	+	0.935004i	$0.384605\pi$
$828$	0.902941	+	1.42281i	0.0313794	+	0.0494460i
$829$	−35.6683	−	30.7881i	−1.23881	−	1.06931i	−0.995039	−	0.0994814i	$-0.968282\pi$
$829$	−35.6683	−	30.7881i	−1.23881	−	1.06931i	−0.243773	−	0.969832i	$-0.578385\pi$
$830$	−4.71665	−	44.8759i	−0.163717	−	1.55767i
$831$	−2.30129	−	21.8953i	−0.0798307	−	0.759538i
$832$	−11.9331	−	10.3004i	−0.413706	−	0.357101i
$833$	0.141760	+	0.223378i	0.00491170	+	0.00773960i
$834$	48.4202	+	19.1709i	1.67666	+	0.663835i
$835$	−37.9147	+	1.58910i	−1.31209	+	0.0549930i
$836$	−36.3049	−	4.58638i	−1.25563	−	0.158623i
$837$	−0.0592354	−	2.82787i	−0.00204748	−	0.0977455i
$838$	63.3574	+	16.2674i	2.18864	+	0.561948i
$839$	−0.373251	−	5.93265i	−0.0128861	−	0.204818i	−0.999202	−	0.0399499i	$-0.987280\pi$
$839$	−0.373251	−	5.93265i	−0.0128861	−	0.204818i	0.986316	−	0.164868i	$-0.0527198\pi$
$840$	16.7679	−	7.46555i	0.578547	−	0.257586i
$841$	−25.5160	+	10.1025i	−0.879863	+	0.348362i
$842$	−0.481317	−	0.349697i	−0.0165873	−	0.0120514i
$843$	−12.7016	−	7.69238i	−0.437468	−	0.264940i
$844$	−0.215246	+	0.219802i	−0.00740908	+	0.00756590i
$845$	15.7305	−	4.74932i	0.541146	−	0.163382i
$846$	−5.30774	+	8.36366i	−0.182484	+	0.287549i
$847$	−3.37732	+	2.45377i	−0.116046	+	0.0843125i
$848$	42.8499	−	3.59821i	1.47147	−	0.123563i
$849$	−26.8025	−	14.7348i	−0.919858	−	0.505696i
$850$	0.570157	+	0.582226i	0.0195562	+	0.0199702i
$851$	1.44642	+	6.16685i	0.0495827	+	0.211397i
$852$	37.6438	−	25.0105i	1.28965	−	0.856845i
$853$	−19.5836	+	10.7661i	−0.670528	+	0.368626i	−0.780366	−	0.625324i	$-0.784967\pi$
$853$	−19.5836	+	10.7661i	−0.670528	+	0.368626i	0.109837	+	0.993950i	$0.464967\pi$
$854$	−23.7883	−	7.18210i	−0.814018	−	0.245766i
$855$	−26.2491	+	22.6576i	−0.897701	+	0.774875i
$856$	4.75096	+	4.46145i	0.162385	+	0.152489i
$857$	−25.2948	−	36.3944i	−0.864053	−	1.24321i	−0.968584	−	0.248687i	$-0.920001\pi$
$857$	−25.2948	−	36.3944i	−0.864053	−	1.24321i	0.104531	−	0.994522i	$-0.466666\pi$
$858$	−34.9865	+	12.1836i	−1.19442	+	0.415941i
$859$	−8.99178	+	21.3906i	−0.306795	+	0.729837i	0.693164	+	0.720780i	$0.256216\pi$
$859$	−8.99178	+	21.3906i	−0.306795	+	0.729837i	−0.999959	+	0.00905714i	$0.997117\pi$
$860$	−0.0494105	−	0.0548759i	−0.00168488	−	0.00187125i
$861$	10.0793	+	23.9776i	0.343500	+	0.817155i
$862$	−26.7025	+	56.7456i	−0.909489	+	1.93276i
$863$	6.50659	+	12.4460i	0.221487	+	0.423665i	0.971257	−	0.238033i	$-0.0765026\pi$
$863$	6.50659	+	12.4460i	0.221487	+	0.423665i	−0.749770	+	0.661698i	$0.769836\pi$
$864$	26.4324	−	4.47071i	0.899250	−	0.152097i
$865$	−16.4778	+	2.08163i	−0.560262	+	0.0707775i
$866$	−3.88902	−	26.3364i	−0.132154	−	0.894948i
$867$	27.5142	−	21.8075i	0.934432	−	0.740621i
$868$	4.80465	−	1.02126i	0.163081	−	0.0346639i
$869$	0.686837	−	0.988229i	0.0232994	−	0.0335234i
$870$	31.7076	−	113.564i	1.07499	−	3.85017i
$871$	−0.00117843	+	0.0562579i	−3.99297e−5	+	0.00190623i
$872$	−0.105681	+	0.715672i	−0.00357882	+	0.0242357i
$873$	1.71742	+	2.97466i	0.0581258	+	0.100677i
$874$	5.25035	−	9.09388i	0.177596	−	0.307605i
$875$	−65.0587	−	51.5649i	−2.19939	−	1.74321i
$876$	45.4349	+	22.5541i	1.53510	+	0.762031i
$877$	1.89677	+	9.94323i	0.0640494	+	0.335759i	0.999860	−	0.0167450i	$-0.00533034\pi$
$877$	1.89677	+	9.94323i	0.0640494	+	0.335759i	−0.935810	+	0.352504i	$0.885330\pi$
$878$	−23.7750	+	28.7391i	−0.802368	+	0.969896i
$879$	29.2004	+	35.2972i	0.984904	+	1.19054i
$880$	10.5649	−	55.3832i	0.356143	−	1.86697i
$881$	20.1400	−	26.5335i	0.678535	−	0.893937i	−0.320034	−	0.947406i	$-0.603694\pi$
$881$	20.1400	−	26.5335i	0.678535	−	0.893937i	0.998570	+	0.0534686i	$0.0170277\pi$
$882$	6.88038	+	14.6216i	0.231674	+	0.492333i
$883$	24.6435	−	27.3694i	0.829321	−	0.921055i	−0.168588	−	0.985687i	$-0.553921\pi$
$883$	24.6435	−	27.3694i	0.829321	−	0.921055i	0.997909	+	0.0646320i	$0.0205874\pi$
$884$	−0.188115	−	0.0655084i	−0.00632698	−	0.00220329i
$885$	−26.7897	−	95.9500i	−0.900527	−	3.22532i
$886$	11.0729	−	2.84303i	0.372000	−	0.0955134i
$887$	4.83826	+	14.8906i	0.162453	+	0.499978i	0.998840	−	0.0481615i	$-0.0153362\pi$
$887$	4.83826	+	14.8906i	0.162453	+	0.499978i	−0.836387	+	0.548140i	$0.815336\pi$
$888$	−9.90992	−	1.67614i	−0.332555	−	0.0562475i
$889$	−11.6683	−	0.489045i	−0.391341	−	0.0164020i
$890$	−37.5778	−	16.7307i	−1.25961	−	0.560815i
$891$	12.2598	−	32.9657i	0.410720	−	1.10439i
$892$	−6.57633	−	4.36930i	−0.220192	−	0.146295i
$893$	28.1119	+	2.36062i	0.940729	+	0.0789952i
$894$	−40.9002	+	24.7701i	−1.36791	+	0.828435i
$895$	8.33236	−	35.5252i	0.278520	−	1.18748i
$896$	−6.18089	−	16.6199i	−0.206489	−	0.555233i
$897$	0.305079	−	4.84909i	0.0101863	−	0.161906i
$898$	−5.15952	+	15.8794i	−0.172176	+	0.529902i
$899$	−2.74870	+	5.25779i	−0.0916744	+	0.175357i
$900$	13.7537	+	18.1198i	0.458455	+	0.603993i
$901$	0.337971	−	0.167770i	0.0112595	−	0.00558924i
$902$	20.1021	+	4.27283i	0.669326	+	0.142270i
$903$	−0.0616315	+	0.0578758i	−0.00205097	+	0.00192599i
$904$	−0.000440066		0.00418695i	−1.46364e−5		0.000139256i
$905$	25.3109			0.841364
$906$	48.1217	−	7.54839i	1.59874	−	0.250778i
$907$	−40.5854			−1.34762			−0.673808	−	0.738906i	$-0.735343\pi$
$907$	−40.5854			−1.34762			−0.673808	+	0.738906i	$0.735343\pi$
$908$	−2.12159	+	20.1855i	−0.0704073	+	0.669880i
$909$	−16.8682	+	15.8403i	−0.559482	+	0.525388i
$910$	81.6940	+	17.3646i	2.70813	+	0.575631i
$911$	42.5191	−	21.1067i	1.40872	−	0.699296i	0.429685	−	0.902979i	$-0.358624\pi$
$911$	42.5191	−	21.1067i	1.40872	−	0.699296i	0.979037	+	0.203683i	$0.0652912\pi$
$912$	39.1636	+	51.5961i	1.29684	+	1.70852i
$913$	−8.64346	+	16.5334i	−0.286057	+	0.547176i
$914$	−14.6998	+	45.2412i	−0.486225	+	1.49645i
$915$	−1.79923	+	28.5980i	−0.0594808	+	0.945421i
$916$	6.66579	+	17.9238i	0.220244	+	0.592218i
$917$	11.6715	−	49.7616i	0.385427	−	1.64327i
$918$	0.233873	−	0.141639i	0.00771896	−	0.00467477i
$919$	4.99962	+	0.419830i	0.164922	+	0.0138489i	0.165852	−	0.986151i	$-0.446963\pi$
$919$	4.99962	+	0.419830i	0.164922	+	0.0138489i	−0.000929734		1.00000i	$0.500296\pi$
$920$	1.58420	+	1.05254i	0.0522297	+	0.0347013i
$921$	−18.9325	+	50.9079i	−0.623846	+	1.67747i
$922$	7.27338	+	3.23832i	0.239536	+	0.106648i
$923$	−38.6336	−	1.61923i	−1.27164	−	0.0532976i
$924$	39.7954	+	6.73089i	1.30917	+	0.221430i
$925$	26.4235	+	81.3232i	0.868800	+	2.67389i
$926$	27.4921	−	7.05877i	0.903447	−	0.231966i
$927$	3.49737	+	12.5262i	0.114869	+	0.411413i
$928$	−53.1033	−	18.4925i	−1.74320	−	0.607047i
$929$	34.9521	−	38.8182i	1.14674	−	1.27359i	0.190279	−	0.981730i	$-0.439061\pi$
$929$	34.9521	−	38.8182i	1.14674	−	1.27359i	0.956462	−	0.291855i	$-0.0942726\pi$
$930$	−5.27694	−	11.2141i	−0.173038	−	0.367724i
$931$	27.8244	−	36.6573i	0.911909	−	1.20140i
$932$	3.24514	−	17.0116i	0.106298	−	0.557233i
$933$	−39.9980	−	48.3492i	−1.30947	−	1.58288i
$934$	−0.168350	+	0.203501i	−0.00550859	+	0.00665874i
$935$	−0.0927046	−	0.485975i	−0.00303177	−	0.0158931i
$936$	2.04910	+	1.01718i	0.0669770	+	0.0332477i
$937$	−15.6767	−	12.4252i	−0.512134	−	0.405913i	0.330988	−	0.943635i	$-0.392618\pi$
$937$	−15.6767	−	12.4252i	−0.512134	−	0.405913i	−0.843122	+	0.537723i	$0.819285\pi$
$938$	0.0670662	−	0.116162i	0.00218979	−	0.00379283i
$939$	11.3050	+	19.5808i	0.368925	+	0.638997i
$940$	3.96995	−	26.8844i	0.129485	−	0.876873i
$941$	0.239731	−	11.4446i	0.00781501	−	0.373085i	−0.978316	−	0.207117i	$-0.933592\pi$
$941$	0.239731	−	11.4446i	0.00781501	−	0.373085i	0.986131	−	0.165968i	$-0.0530748\pi$
$942$	−17.2640	+	61.8328i	−0.562492	+	2.01462i
$943$	−1.53821	+	2.21320i	−0.0500911	+	0.0720717i
$944$	−54.0154	+	11.4813i	−1.75805	+	0.373685i
$945$	−41.0612	+	32.5447i	−1.33572	+	1.05868i
$946$	0.00975867	+	0.0660856i	0.000317282	+	0.00214863i
$947$	−12.8128	+	1.61863i	−0.416360	+	0.0525985i	−0.330723	−	0.943728i	$-0.607293\pi$
$947$	−12.8128	+	1.61863i	−0.416360	+	0.0525985i	−0.0856370	+	0.996326i	$0.527293\pi$
$948$	1.31327	−	0.222124i	0.0426532	−	0.00721424i
$949$	−20.1065	−	38.4602i	−0.652685	−	1.24847i
$950$	60.3558	−	128.263i	1.95820	−	4.16139i
$951$	9.27867	+	22.0731i	0.300881	+	0.715769i
$952$	−0.0597397	−	0.0663477i	−0.00193618	−	0.00215034i
$953$	−11.3987	+	27.1164i	−0.369239	+	0.878386i	0.625899	+	0.779904i	$0.284732\pi$
$953$	−11.3987	+	27.1164i	−0.369239	+	0.878386i	−0.995139	+	0.0984821i	$0.968601\pi$
$954$	21.7648	−	7.57930i	0.704661	−	0.245389i
$955$	12.5900	+	18.1146i	0.407402	+	0.586175i
$956$	−26.0958	−	24.5056i	−0.843997	−	0.792566i
$957$	−36.9031	+	31.8539i	−1.19291	+	1.02969i
$958$	56.4801	+	17.0523i	1.82479	+	0.550936i
$959$	35.5112	−	19.5224i	1.14672	−	0.630413i
$960$	36.0916	−	23.9792i	1.16485	−	0.773926i
$961$	−6.93647	−	29.5738i	−0.223757	−	0.953993i
$962$	−31.9979	−	32.6752i	−1.03165	−	1.05349i
$963$	11.9003	+	6.54222i	0.383481	+	0.210820i
$964$	−8.01125	+	0.672723i	−0.258025	+	0.0216670i
$965$	−82.8833	+	60.2182i	−2.66811	+	1.93849i
$966$	−6.20579	+	9.77876i	−0.199668	+	0.314626i
$967$	−14.5304	+	4.38698i	−0.467266	+	0.141076i	−0.513925	−	0.857835i	$-0.671809\pi$
$967$	−14.5304	+	4.38698i	−0.467266	+	0.141076i	0.0466594	+	0.998911i	$0.485142\pi$
$968$	0.480248	−	0.490414i	0.0154358	−	0.0157625i
$969$	0.486185	+	0.294444i	0.0156185	+	0.00945892i
$970$	−16.6808	−	12.1193i	−0.535587	−	0.389127i
$971$	37.0507	−	14.6694i	1.18901	−	0.470764i	0.311468	−	0.950257i	$-0.399179\pi$
$971$	37.0507	−	14.6694i	1.18901	−	0.470764i	0.877546	+	0.479493i	$0.159179\pi$
$972$	19.0353	−	8.47504i	0.610556	−	0.271837i
$973$	3.04791	+	48.4451i	0.0977115	+	1.55308i
$974$	−65.7180	−	16.8735i	−2.10574	−	0.540662i
$975$	−1.37360	−	65.5750i	−0.0439904	−	2.10008i
$976$	15.7588	+	1.99080i	0.504427	+	0.0637240i
$977$	38.4676	−	1.61227i	1.23069	−	0.0515812i	0.582353	−	0.812936i	$-0.302132\pi$
$977$	38.4676	−	1.61227i	1.23069	−	0.0515812i	0.648336	+	0.761355i	$0.275465\pi$
$978$	19.2029	+	7.60295i	0.614040	+	0.243115i
$979$	9.11288	+	14.3596i	0.291249	+	0.458935i
$980$	−33.5599	−	28.9681i	−1.07203	−	0.925353i
$981$	0.157565	+	1.49913i	0.00503067	+	0.0478636i
$982$	−1.12414	−	10.6955i	−0.0358727	−	0.341306i
$983$	17.5070	+	15.1117i	0.558388	+	0.481988i	0.886549	−	0.462634i	$-0.153096\pi$
$983$	17.5070	+	15.1117i	0.558388	+	0.481988i	−0.328161	+	0.944622i	$0.606429\pi$
$984$	−2.29153	−	3.61087i	−0.0730513	−	0.115110i
$985$	7.89370	+	3.12534i	0.251514	+	0.0995815i
$986$	−0.573011	+	0.0240163i	−0.0182484	+	0.000764834i
$987$	−30.8697	−	3.89975i	−0.982593	−	0.124130i
$988$	0.725659	+	34.6426i	0.0230863	+	1.10213i
$989$	−0.00848573	−	0.00217877i	−0.000269831	−	6.92807e-5i
$990$	−1.89744	−	30.1589i	−0.0603045	−	0.958512i
$991$	26.8515	−	11.9551i	0.852966	−	0.379765i	0.0667897	−	0.997767i	$-0.478724\pi$
$991$	26.8515	−	11.9551i	0.852966	−	0.379765i	0.786176	+	0.618002i	$0.212058\pi$
$992$	−5.49558	+	2.17585i	−0.174485	+	0.0690834i
$993$	−14.0041	−	10.1746i	−0.444407	−	0.322881i
$994$	78.8411	+	47.7479i	2.50069	+	1.51447i
$995$	14.7212	−	15.0328i	0.466692	−	0.476571i
$996$	−19.7665	+	5.96787i	−0.626327	+	0.189099i
$997$	−12.8459	+	20.2419i	−0.406834	+	0.641068i	−0.984537	−	0.175179i	$-0.943949\pi$
$997$	−12.8459	+	20.2419i	−0.406834	+	0.641068i	0.577702	+	0.816247i	$0.303949\pi$
$998$	10.1831	−	7.39844i	0.322340	−	0.234193i
$999$	28.5894	−	2.40072i	0.904530	−	0.0759555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.k.a.90.10	✓	480
151.99	even	75	inner	151.2.k.a.99.10	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.k.a.90.10	✓	480	1.1	even	1	trivial
151.2.k.a.99.10	yes	480	151.99	even	75	inner

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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.k (of order \(75\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.200615 - 1.90872i) q^{2} +(-1.50561 + 1.41386i) q^{3} +(-1.64668 - 0.350012i) q^{4} +(-3.54627 + 1.76038i) q^{5} +(2.39661 + 3.15742i) q^{6} +(-1.71178 + 3.27434i) q^{7} +(0.187730 - 0.577774i) q^{8} +(0.0794829 - 1.26334i) q^{9} +O(q^{10})\)	\(q+(0.200615 - 1.90872i) q^{2} +(-1.50561 + 1.41386i) q^{3} +(-1.64668 - 0.350012i) q^{4} +(-3.54627 + 1.76038i) q^{5} +(2.39661 + 3.15742i) q^{6} +(-1.71178 + 3.27434i) q^{7} +(0.187730 - 0.577774i) q^{8} +(0.0794829 - 1.26334i) q^{9} +(2.64865 + 7.12200i) q^{10} +(0.717405 - 3.05867i) q^{11} +(2.97411 - 1.80119i) q^{12} +(-2.96441 - 0.248928i) q^{13} +(5.90639 + 3.92420i) q^{14} +(2.85035 - 7.66437i) q^{15} +(-4.14099 - 1.84369i) q^{16} +(-0.0397401 - 0.00166560i) q^{17} +(-2.39543 - 0.405156i) q^{18} +(2.13806 + 6.58029i) q^{19} +(6.45571 - 1.65755i) q^{20} +(-2.05218 - 7.35008i) q^{21} +(-5.69423 - 1.98294i) q^{22} +(0.529130 - 0.587659i) q^{23} +(0.534243 + 1.13532i) q^{24} +(6.45409 - 8.50295i) q^{25} +(-1.06984 + 5.60829i) q^{26} +(-2.28307 - 2.75976i) q^{27} +(3.96481 - 4.79263i) q^{28} +(1.40777 + 7.37979i) q^{29} +(-14.0573 - 6.97811i) q^{30} +(0.618885 + 0.490522i) q^{31} +(-3.74232 + 6.48189i) q^{32} +(3.24440 + 5.61946i) q^{33} +(-0.0111516 + 0.0755186i) q^{34} +(0.306352 - 14.6251i) q^{35} +(-0.573068 + 2.05250i) q^{36} +(-4.57150 + 6.57753i) q^{37} +(12.9889 - 2.76087i) q^{38} +(4.81518 - 3.81646i) q^{39} +(0.351363 + 2.37942i) q^{40} +(-3.38149 + 0.427182i) q^{41} +(-14.4410 + 2.44251i) q^{42} +(-0.00513286 - 0.00981826i) q^{43} +(-2.25190 + 4.78554i) q^{44} +(1.94210 + 4.62008i) q^{45} +(-1.01553 - 1.12786i) q^{46} +(1.58003 - 3.75875i) q^{47} +(8.84141 - 3.07890i) q^{48} +(-3.79611 - 5.46188i) q^{49} +(-14.9350 - 14.0249i) q^{50} +(0.0621878 - 0.0536791i) q^{51} +(4.79429 + 1.44748i) q^{52} +(-8.31300 + 4.57011i) q^{53} +(-5.72563 + 3.80410i) q^{54} +(2.84032 + 12.1098i) q^{55} +(1.57048 + 1.60372i) q^{56} +(-12.5227 - 6.88440i) q^{57} +(14.3684 - 1.20655i) q^{58} +(9.85592 - 7.16074i) q^{59} +(-7.37623 + 11.6231i) q^{60} +(-3.35463 + 1.01282i) q^{61} +(1.06043 - 1.08287i) q^{62} +(4.00056 + 2.42283i) q^{63} +(4.28701 + 3.11469i) q^{64} +(10.9508 - 4.33573i) q^{65} +(11.3769 - 5.06530i) q^{66} +(-0.00118771 - 0.0188781i) q^{67} +(0.0648561 + 0.0166522i) q^{68} +(0.0342043 + 1.63290i) q^{69} +(-27.8538 - 3.51875i) q^{70} +(12.9868 - 0.544308i) q^{71} +(-0.715007 - 0.283091i) q^{72} +(7.81699 + 12.3176i) q^{73} +(11.6376 + 10.0453i) q^{74} +(2.30465 + 21.9273i) q^{75} +(-1.21752 - 11.5839i) q^{76} +(8.78709 + 7.58481i) q^{77} +(-6.31857 - 9.95647i) q^{78} +(0.356166 + 0.141016i) q^{79} +(17.9307 - 0.751518i) q^{80} +(11.1069 + 1.40313i) q^{81} +(0.136994 + 6.54003i) q^{82} +(-5.75181 - 1.47681i) q^{83} +(0.806660 + 12.8215i) q^{84} +(0.143861 - 0.0640511i) q^{85} +(-0.0197700 + 0.00782751i) q^{86} +(-12.5535 - 9.12067i) q^{87} +(-1.63254 - 0.988703i) q^{88} +(-3.78755 + 3.86772i) q^{89} +(9.20807 - 2.78008i) q^{90} +(5.88950 - 9.28036i) q^{91} +(-1.07699 + 0.782481i) q^{92} +(-1.62533 + 0.136482i) q^{93} +(-6.85744 - 3.76991i) q^{94} +(-19.1660 - 19.5717i) q^{95} +(-3.53001 - 15.0503i) q^{96} +(-2.26011 + 1.50162i) q^{97} +(-11.1868 + 6.14997i) q^{98} +(-3.80713 - 1.14944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more