LMFDB - Embedded newform 460.2.o.b.159.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			159.26
Character	$\chi$	$=$	460.159
Dual form			460.2.o.b.379.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.431771 + 1.34669i) q^{2} +(-0.448940 - 3.12245i) q^{3} +(-1.62715 - 1.16292i) q^{4} +(-2.15833 + 0.584474i) q^{5} +(4.39881 + 0.743600i) q^{6} +(-0.713367 - 0.618136i) q^{7} +(2.26865 - 1.68915i) q^{8} +(-6.66966 + 1.95839i) q^{9} +O(q^{10})$	\(q+(-0.431771 + 1.34669i) q^{2} +(-0.448940 - 3.12245i) q^{3} +(-1.62715 - 1.16292i) q^{4} +(-2.15833 + 0.584474i) q^{5} +(4.39881 + 0.743600i) q^{6} +(-0.713367 - 0.618136i) q^{7} +(2.26865 - 1.68915i) q^{8} +(-6.66966 + 1.95839i) q^{9} +(0.144800 - 3.15896i) q^{10} +(0.193099 - 0.124097i) q^{11} +(-2.90068 + 5.60277i) q^{12} +(-1.19446 + 1.03500i) q^{13} +(1.14045 - 0.693791i) q^{14} +(2.79395 + 6.47688i) q^{15} +(1.29522 + 3.78450i) q^{16} +(-0.523395 + 1.14607i) q^{17} +(0.242423 - 9.82754i) q^{18} +(1.95747 + 4.28626i) q^{19} +(4.19162 + 1.55895i) q^{20} +(-1.60984 + 2.50496i) q^{21} +(0.0837460 + 0.313626i) q^{22} +(4.74300 + 0.709905i) q^{23} +(-6.29276 - 6.32543i) q^{24} +(4.31678 - 2.52298i) q^{25} +(-0.878097 - 2.05545i) q^{26} +(5.17790 + 11.3380i) q^{27} +(0.441909 + 1.83539i) q^{28} +(-1.83115 + 4.00967i) q^{29} +(-9.92870 + 0.966056i) q^{30} +(-7.75952 - 1.11565i) q^{31} +(-5.65578 + 0.110222i) q^{32} +(-0.474178 - 0.547230i) q^{33} +(-1.31742 - 1.19969i) q^{34} +(1.90097 + 0.917198i) q^{35} +(13.1300 + 4.56972i) q^{36} +(-8.70861 + 2.55708i) q^{37} +(-6.61744 + 0.785421i) q^{38} +(3.76799 + 3.26498i) q^{39} +(-3.90924 + 4.97170i) q^{40} +(9.64819 + 2.83296i) q^{41} +(-2.67832 - 3.24952i) q^{42} +(-9.31394 + 1.33914i) q^{43} +(-0.458517 - 0.0226349i) q^{44} +(13.2507 - 8.12509i) q^{45} +(-3.00391 + 6.08083i) q^{46} -1.23269 q^{47} +(11.2354 - 5.74327i) q^{48} +(-0.869403 - 6.04683i) q^{49} +(1.53380 + 6.90271i) q^{50} +(3.81353 + 1.11975i) q^{51} +(3.14719 - 0.295041i) q^{52} +(-7.74330 + 8.93624i) q^{53} +(-17.5045 + 2.07760i) q^{54} +(-0.344240 + 0.380704i) q^{55} +(-2.66251 - 0.197354i) q^{56} +(12.5048 - 8.03637i) q^{57} +(-4.60914 - 4.19725i) q^{58} +(2.50331 - 2.16913i) q^{59} +(2.98595 - 13.7880i) q^{60} +(-9.64149 - 1.38624i) q^{61} +(4.85277 - 9.96796i) q^{62} +(5.96847 + 2.72571i) q^{63} +(2.29357 - 7.66417i) q^{64} +(1.97310 - 2.93201i) q^{65} +(0.941685 - 0.402292i) q^{66} +(2.05081 - 3.19112i) q^{67} +(2.18444 - 1.25616i) q^{68} +(0.0873179 - 15.1285i) q^{69} +(-2.05596 + 2.16399i) q^{70} +(4.79509 - 7.46131i) q^{71} +(-11.8231 + 15.7089i) q^{72} +(-4.43280 + 2.02439i) q^{73} +(0.316534 - 12.8319i) q^{74} +(-9.81584 - 12.3463i) q^{75} +(1.79950 - 9.25076i) q^{76} +(-0.214460 - 0.0308347i) q^{77} +(-6.02382 + 3.66459i) q^{78} +(1.04504 + 1.20603i) q^{79} +(-5.00745 - 7.41117i) q^{80} +(15.5346 - 9.98346i) q^{81} +(-7.98094 + 11.7699i) q^{82} +(0.146862 + 0.500168i) q^{83} +(5.53252 - 2.20382i) q^{84} +(0.459808 - 2.77952i) q^{85} +(2.21808 - 13.1212i) q^{86} +(13.3421 + 3.91758i) q^{87} +(0.228456 - 0.607707i) q^{88} +(-5.84562 + 0.840474i) q^{89} +(5.22071 + 21.3528i) q^{90} +1.49186 q^{91} +(-6.89199 - 6.67086i) q^{92} +24.7296i q^{93} +(0.532240 - 1.66005i) q^{94} +(-6.73007 - 8.10707i) q^{95} +(2.88327 + 17.6104i) q^{96} +(-11.0665 - 3.24940i) q^{97} +(8.51859 + 1.44003i) q^{98} +(-1.04488 + 1.20585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.431771	+	1.34669i	−0.305308	+	0.952254i
$2$	−0.431771	+	1.34669i	−0.305308	+	0.952254i
$3$	−0.448940	−	3.12245i	−0.259196	−	1.80275i	−0.538587	−	0.842570i	$-0.681042\pi$
$3$	−0.448940	−	3.12245i	−0.259196	−	1.80275i	0.279392	−	0.960177i	$-0.409867\pi$
$4$	−1.62715	−	1.16292i	−0.813574	−	0.581462i
$5$	−2.15833	+	0.584474i	−0.965235	+	0.261385i
$5$	−2.15833	+	0.584474i	−0.965235	+	0.261385i
$6$	4.39881	+	0.743600i	1.79581	+	0.303573i
$7$	−0.713367	−	0.618136i	−0.269628	−	0.233634i	0.509544	−	0.860445i	$-0.329814\pi$
$7$	−0.713367	−	0.618136i	−0.269628	−	0.233634i	−0.779171	+	0.626811i	$0.784360\pi$
$8$	2.26865	−	1.68915i	0.802090	−	0.597204i
$9$	−6.66966	+	1.95839i	−2.22322	+	0.652797i
$10$	0.144800	−	3.15896i	0.0457896	−	0.998951i
$11$	0.193099	−	0.124097i	0.0582216	−	0.0374167i	−0.511206	−	0.859458i	$-0.670801\pi$
$11$	0.193099	−	0.124097i	0.0582216	−	0.0374167i	0.569428	+	0.822041i	$0.307165\pi$
$12$	−2.90068	+	5.60277i	−0.837353	+	1.61738i
$13$	−1.19446	+	1.03500i	−0.331283	+	0.287058i	−0.804580	−	0.593845i	$-0.797609\pi$
$13$	−1.19446	+	1.03500i	−0.331283	+	0.287058i	0.473297	+	0.880903i	$0.343064\pi$
$14$	1.14045	−	0.693791i	0.304798	−	0.185424i
$15$	2.79395	+	6.47688i	0.721395	+	1.67232i
$16$	1.29522	+	3.78450i	0.323805	+	0.946124i
$17$	−0.523395	+	1.14607i	−0.126942	+	0.277964i	−0.962423	−	0.271556i	$-0.912462\pi$
$17$	−0.523395	+	1.14607i	−0.126942	+	0.277964i	0.835481	+	0.549520i	$0.185189\pi$
$18$	0.242423	−	9.82754i	0.0571398	−	2.31637i
$19$	1.95747	+	4.28626i	0.449074	+	0.983335i	0.989843	+	0.142164i	$0.0454061\pi$
$19$	1.95747	+	4.28626i	0.449074	+	0.983335i	−0.540769	+	0.841171i	$0.681867\pi$
$20$	4.19162	+	1.55895i	0.937275	+	0.348591i
$21$	−1.60984	+	2.50496i	−0.351296	+	0.546627i
$22$	0.0837460	+	0.313626i	0.0178547	+	0.0668654i
$23$	4.74300	+	0.709905i	0.988984	+	0.148025i
$23$	4.74300	+	0.709905i	0.988984	+	0.148025i
$24$	−6.29276	−	6.32543i	−1.28451	−	1.29117i
$25$	4.31678	−	2.52298i	0.863356	−	0.504595i
$26$	−0.878097	−	2.05545i	−0.172209	−	0.403107i
$27$	5.17790	+	11.3380i	0.996487	+	2.18200i
$28$	0.441909	+	1.83539i	0.0835129	+	0.346856i
$29$	−1.83115	+	4.00967i	−0.340037	+	0.744577i	−0.999977	−	0.00674123i	$-0.997854\pi$
$29$	−1.83115	+	4.00967i	−0.340037	+	0.744577i	0.659941	+	0.751318i	$0.270581\pi$
$30$	−9.92870	+	0.966056i	−1.81272	+	0.176377i
$31$	−7.75952	−	1.11565i	−1.39365	−	0.200377i	−0.595752	−	0.803169i	$-0.703146\pi$
$31$	−7.75952	−	1.11565i	−1.39365	−	0.200377i	−0.797899	+	0.602792i	$0.794055\pi$
$32$	−5.65578	+	0.110222i	−0.999810	+	0.0194847i
$33$	−0.474178	−	0.547230i	−0.0825437	−	0.0952605i
$34$	−1.31742	−	1.19969i	−0.225936	−	0.205746i
$35$	1.90097	+	0.917198i	0.321322	+	0.155035i
$36$	13.1300	+	4.56972i	2.18833	+	0.761620i
$37$	−8.70861	+	2.55708i	−1.43169	+	0.420381i	−0.903442	−	0.428711i	$-0.858968\pi$
$37$	−8.70861	+	2.55708i	−1.43169	+	0.420381i	−0.528245	+	0.849092i	$0.677150\pi$
$38$	−6.61744	+	0.785421i	−1.07349	+	0.127412i
$39$	3.76799	+	3.26498i	0.603361	+	0.522815i
$40$	−3.90924	+	4.97170i	−0.618105	+	0.786096i
$41$	9.64819	+	2.83296i	1.50679	+	0.442435i	0.927857	−	0.372937i	$-0.121649\pi$
$41$	9.64819	+	2.83296i	1.50679	+	0.442435i	0.578938	+	0.815372i	$0.303467\pi$
$42$	−2.67832	−	3.24952i	−0.413274	−	0.501412i
$43$	−9.31394	+	1.33914i	−1.42036	+	0.204217i	−0.809314	−	0.587376i	$-0.800161\pi$
$43$	−9.31394	+	1.33914i	−1.42036	+	0.204217i	−0.611049	+	0.791593i	$0.709252\pi$
$44$	−0.458517	−	0.0226349i	−0.0691240	−	0.00341234i
$45$	13.2507	−	8.12509i	1.97530	−	1.21122i
$46$	−3.00391	+	6.08083i	−0.442903	+	0.896570i
$47$	−1.23269			−0.179806			−0.0899031	−	0.995951i	$-0.528656\pi$
$47$	−1.23269			−0.179806			−0.0899031	+	0.995951i	$0.528656\pi$
$48$	11.2354	−	5.74327i	1.62169	−	0.828969i
$49$	−0.869403	−	6.04683i	−0.124200	−	0.863833i
$50$	1.53380	+	6.90271i	0.216913	+	0.976191i
$51$	3.81353	+	1.11975i	0.534001	+	0.156797i
$52$	3.14719	−	0.295041i	0.436437	−	0.0409148i
$53$	−7.74330	+	8.93624i	−1.06362	+	1.22749i	−0.0908177	+	0.995868i	$0.528948\pi$
$53$	−7.74330	+	8.93624i	−1.06362	+	1.22749i	−0.972806	+	0.231620i	$0.925597\pi$
$54$	−17.5045	+	2.07760i	−2.38206	+	0.282725i
$55$	−0.344240	+	0.380704i	−0.0464173	+	0.0513342i
$56$	−2.66251	−	0.197354i	−0.355792	−	0.0263726i
$57$	12.5048	−	8.03637i	1.65631	−	1.06444i
$58$	−4.60914	−	4.19725i	−0.605210	−	0.551127i
$59$	2.50331	−	2.16913i	0.325903	−	0.282397i	−0.476506	−	0.879171i	$-0.658097\pi$
$59$	2.50331	−	2.16913i	0.325903	−	0.282397i	0.802409	+	0.596775i	$0.203551\pi$
$60$	2.98595	−	13.7880i	0.385484	−	1.78002i
$61$	−9.64149	−	1.38624i	−1.23447	−	0.177490i	−0.505977	−	0.862547i	$-0.668868\pi$
$61$	−9.64149	−	1.38624i	−1.23447	−	0.177490i	−0.728489	+	0.685057i	$0.759777\pi$
$62$	4.85277	−	9.96796i	0.616302	−	1.26593i
$63$	5.96847	+	2.72571i	0.751957	+	0.343407i
$64$	2.29357	−	7.66417i	0.286696	−	0.958022i
$65$	1.97310	−	2.93201i	0.244733	−	0.363671i
$66$	0.941685	−	0.402292i	0.115913	−	0.0495187i
$67$	2.05081	−	3.19112i	0.250546	−	0.389858i	−0.693085	−	0.720856i	$-0.743749\pi$
$67$	2.05081	−	3.19112i	0.250546	−	0.389858i	0.943631	+	0.330998i	$0.107385\pi$
$68$	2.18444	−	1.25616i	0.264902	−	0.152332i
$69$	0.0873179	−	15.1285i	0.0105118	−	1.82125i
$70$	−2.05596	+	2.16399i	−0.245735	+	0.258647i
$71$	4.79509	−	7.46131i	0.569073	−	0.885494i	−0.430783	−	0.902455i	$-0.641763\pi$
$71$	4.79509	−	7.46131i	0.569073	−	0.885494i	0.999856	+	0.0169609i	$0.00539908\pi$
$72$	−11.8231	+	15.7089i	−1.39337	+	1.85132i
$73$	−4.43280	+	2.02439i	−0.518820	+	0.236937i	−0.657574	−	0.753390i	$-0.728417\pi$
$73$	−4.43280	+	2.02439i	−0.518820	+	0.236937i	0.138755	+	0.990327i	$0.455690\pi$
$74$	0.316534	−	12.8319i	0.0367963	−	1.49167i
$75$	−9.81584	−	12.3463i	−1.13344	−	1.42562i
$76$	1.79950	−	9.25076i	0.206417	−	1.06114i
$77$	−0.214460	−	0.0308347i	−0.0244400	−	0.00351393i
$78$	−6.02382	+	3.66459i	−0.682064	+	0.414933i
$79$	1.04504	+	1.20603i	0.117576	+	0.135690i	0.811486	−	0.584372i	$-0.198659\pi$
$79$	1.04504	+	1.20603i	0.117576	+	0.135690i	−0.693910	+	0.720061i	$0.744114\pi$
$80$	−5.00745	−	7.41117i	−0.559850	−	0.828594i
$81$	15.5346	−	9.98346i	1.72606	−	1.10927i
$82$	−7.98094	+	11.7699i	−0.881347	+	1.29977i
$83$	0.146862	+	0.500168i	0.0161203	+	0.0549005i	0.967160	−	0.254167i	$-0.0818013\pi$
$83$	0.146862	+	0.500168i	0.0161203	+	0.0549005i	−0.951040	+	0.309068i	$0.899983\pi$
$84$	5.53252	−	2.20382i	0.603648	−	0.240456i
$85$	0.459808	−	2.77952i	0.0498732	−	0.301481i
$86$	2.21808	−	13.1212i	0.239182	−	1.41490i
$87$	13.3421	+	3.91758i	1.43042	+	0.420009i
$88$	0.228456	−	0.607707i	0.0243535	−	0.0647817i
$89$	−5.84562	+	0.840474i	−0.619635	+	0.0890900i	−0.444981	−	0.895540i	$-0.646790\pi$
$89$	−5.84562	+	0.840474i	−0.619635	+	0.0890900i	−0.174654	+	0.984630i	$0.555881\pi$
$90$	5.22071	+	21.3528i	0.550311	+	2.25078i
$91$	1.49186			0.156390
$92$	−6.89199	−	6.67086i	−0.718540	−	0.695486i
$93$			24.7296i			2.56434i
$94$	0.532240	−	1.66005i	0.0548963	−	0.171221i
$95$	−6.73007	−	8.10707i	−0.690491	−	0.831768i
$96$	2.88327	+	17.6104i	0.294273	+	1.79735i
$97$	−11.0665	−	3.24940i	−1.12363	−	0.329927i	−0.333428	−	0.942776i	$-0.608205\pi$
$97$	−11.0665	−	3.24940i	−1.12363	−	0.329927i	−0.790200	+	0.612849i	$0.790024\pi$
$98$	8.51859	+	1.44003i	0.860508	+	0.145465i
$99$	−1.04488	+	1.20585i	−0.105014	+	0.121193i
$100$	−9.95807	−	0.914832i	−0.995807	−	0.0914832i
$101$	−5.71537	+	1.67818i	−0.568700	+	0.166985i	−0.553427	−	0.832898i	$-0.686680\pi$
$101$	−5.71537	+	1.67818i	−0.568700	+	0.166985i	−0.0152735	+	0.999883i	$0.504862\pi$
$102$	−3.15454	+	4.65217i	−0.312346	+	0.460633i
$103$	−0.124887	−	0.194327i	−0.0123054	−	0.0191476i	0.835046	−	0.550180i	$-0.185441\pi$
$103$	−0.124887	−	0.194327i	−0.0123054	−	0.0191476i	−0.847352	+	0.531032i	$0.821804\pi$
$104$	−0.961537	+	4.36568i	−0.0942865	+	0.428090i
$105$	2.01048	−	6.34744i	0.196203	−	0.619447i
$106$	−8.69102	−	14.2862i	−0.844146	−	1.38760i
$107$	11.7724	+	1.69261i	1.13808	+	0.163631i	0.685486	−	0.728086i	$-0.259590\pi$
$107$	11.7724	+	1.69261i	1.13808	+	0.163631i	0.452593	+	0.891717i	$0.350499\pi$
$108$	4.76004	−	24.4701i	0.458035	−	2.35464i
$109$	14.8181	+	6.76719i	1.41931	+	0.648179i	0.969533	−	0.244959i	$-0.0787746\pi$
$109$	14.8181	+	6.76719i	1.41931	+	0.648179i	0.449781	+	0.893139i	$0.351502\pi$
$110$	−0.364058	−	0.627962i	−0.0347116	−	0.0598738i
$111$	11.8940	+	26.0442i	1.12893	+	2.47201i
$112$	1.41537	−	3.50036i	0.133740	−	0.330753i
$113$	7.61629	+	4.89469i	0.716480	+	0.460454i	0.847411	−	0.530938i	$-0.178160\pi$
$113$	7.61629	+	4.89469i	0.716480	+	0.460454i	−0.130931	+	0.991392i	$0.541796\pi$
$114$	5.42327	+	20.3100i	0.507936	+	1.90221i
$115$	−10.6519	+	1.23995i	−0.993293	+	0.115626i
$116$	7.64249	−	4.39483i	0.709588	−	0.408050i
$117$	5.93969	−	9.24234i	0.549125	−	0.854455i
$118$	1.84029	+	4.30775i	0.169413	+	0.396561i
$119$	1.08180	−	0.494043i	0.0991687	−	0.0452888i
$120$	17.2789	+	9.97440i	1.57734	+	0.910534i
$121$	−4.54768	+	9.95803i	−0.413425	+	0.905275i
$122$	6.02975	−	12.3856i	0.545908	−	1.12134i
$123$	4.51433	−	31.3978i	0.407043	−	2.83105i
$124$	11.3285	+	10.8391i	1.01733	+	0.973376i
$125$	−7.84243	+	7.96846i	−0.701448	+	0.712721i
$126$	−6.24770	+	6.86080i	−0.556589	+	0.611208i
$127$	−14.6783	+	9.43320i	−1.30249	+	0.837061i	−0.993481	−	0.113997i	$-0.963634\pi$
$127$	−14.6783	+	9.43320i	−1.30249	+	0.837061i	−0.309011	+	0.951058i	$0.599998\pi$
$128$	9.33097	+	6.39789i	0.824749	+	0.565499i
$129$	8.36281	+	28.4811i	0.736305	+	2.50762i
$130$	3.09658	+	3.92312i	0.271588	+	0.344080i
$131$	−12.9936	−	11.2590i	−1.13525	−	0.983703i	−0.135279	−	0.990808i	$-0.543193\pi$
$131$	−12.9936	−	11.2590i	−1.13525	−	0.983703i	−0.999975	+	0.00710438i	$0.997739\pi$
$132$	0.135170	+	1.44186i	0.0117651	+	0.125497i
$133$	1.25310	−	4.26766i	0.108657	−	0.370053i
$134$	3.41197	+	4.13964i	0.294749	+	0.357610i
$135$	−17.8024	−	21.4448i	−1.53219	−	1.84568i
$136$	0.748487	+	3.48414i	0.0641823	+	0.298762i
$137$	−3.20637			−0.273939			−0.136969	−	0.990575i	$-0.543736\pi$
$137$	−3.20637			−0.273939			−0.136969	+	0.990575i	$0.543736\pi$
$138$	20.3357	+	6.64963i	1.73109	+	0.566054i
$139$		−	14.0856i		−	1.19473i	−0.801970	−	0.597364i	$-0.796215\pi$
$139$		−	14.0856i		−	1.19473i	0.801970	−	0.597364i	$-0.203785\pi$
$140$	−2.02652	−	3.70310i	−0.171272	−	0.312969i
$141$	0.553404	+	3.84901i	0.0466050	+	0.324145i
$142$	7.97769	+	9.67908i	0.669473	+	0.812250i
$143$	−0.102208	+	0.348088i	−0.00854704	+	0.0291085i
$144$	−16.0502	−	22.7048i	−1.33752	−	1.89206i
$145$	1.60869	−	9.72445i	0.133594	−	0.807572i
$146$	−0.812273	−	6.84368i	−0.0672242	−	0.566387i
$147$	−18.4906	+	5.42934i	−1.52508	+	0.447804i
$148$	17.1439	+	5.96670i	1.40922	+	0.490460i
$149$	−2.14150	−	3.33225i	−0.175439	−	0.272988i	0.742387	−	0.669971i	$-0.233694\pi$
$149$	−2.14150	−	3.33225i	−0.175439	−	0.272988i	−0.917826	+	0.396983i	$0.870057\pi$
$150$	20.8648	−	7.88813i	1.70360	−	0.644063i
$151$	10.9413	−	9.48068i	0.890390	−	0.771527i	−0.0839828	−	0.996467i	$-0.526764\pi$
$151$	10.9413	−	9.48068i	0.890390	−	0.771527i	0.974373	+	0.224940i	$0.0722186\pi$
$152$	11.6809	+	6.41758i	0.947449	+	0.520535i
$153$	1.24641	−	8.66894i	0.100766	−	0.700843i
$154$	0.134122	−	0.275497i	0.0108079	−	0.0222002i
$155$	17.3997	−	2.12729i	1.39758	−	0.170868i
$156$	−2.33415	−	9.69449i	−0.186882	−	0.776180i
$157$	5.22894	+	11.4498i	0.417315	+	0.913792i	0.995217	+	0.0976860i	$0.0311441\pi$
$157$	5.22894	+	11.4498i	0.417315	+	0.913792i	−0.577903	+	0.816106i	$0.696129\pi$
$158$	−2.07537	+	0.886607i	−0.165108	+	0.0705347i
$159$	31.3792	+	20.1662i	2.48854	+	1.59929i
$160$	12.1426	−	3.54355i	0.959958	−	0.280142i
$161$	−2.94468	−	3.43824i	−0.232073	−	0.270971i
$162$	6.73725	+	25.2308i	0.529328	+	1.98232i
$163$	−12.0763	−	7.76096i	−0.945889	−	0.607886i	−0.0258299	−	0.999666i	$-0.508223\pi$
$163$	−12.0763	−	7.76096i	−0.945889	−	0.607886i	−0.920059	+	0.391781i	$0.871859\pi$
$164$	−12.4045	−	15.8298i	−0.968630	−	1.23610i
$165$	1.34327	+	0.903959i	0.104574	+	0.0703731i
$166$	−0.736982	−	0.0181797i	−0.0572009	−	0.00141102i
$167$	1.51664	−	3.32099i	0.117361	−	0.256986i	−0.841830	−	0.539742i	$-0.818522\pi$
$167$	1.51664	−	3.32099i	0.117361	−	0.256986i	0.959192	+	0.282757i	$0.0912489\pi$
$168$	0.579077	+	8.40214i	0.0446768	+	0.648239i
$169$	−1.49460	+	10.3951i	−0.114969	+	0.799626i
$170$	3.54462	+	1.81933i	0.271860	+	0.139537i
$171$	−21.4498	−	24.7544i	−1.64031	−	1.89302i
$172$	16.7125	+	8.65242i	1.27431	+	0.659741i
$173$	−2.85120	−	4.43655i	−0.216773	−	0.337305i	0.715788	−	0.698317i	$-0.246068\pi$
$173$	−2.85120	−	4.43655i	−0.216773	−	0.337305i	−0.932561	+	0.361013i	$0.882431\pi$
$174$	−11.0365	+	16.2761i	−0.836674	+	1.23389i
$175$	−4.63899	−	0.868551i	−0.350675	−	0.0656563i
$176$	0.719751	+	0.570050i	0.0542533	+	0.0429691i
$177$	−7.89684	−	6.84265i	−0.593563	−	0.514325i
$178$	1.39211	−	8.23514i	0.104343	−	0.617249i
$179$	−4.96807	+	16.9197i	−0.371331	+	1.26464i	0.535999	+	0.844219i	$0.319935\pi$
$179$	−4.96807	+	16.9197i	−0.371331	+	1.26464i	−0.907330	+	0.420419i	$0.861883\pi$
$180$	−31.0097	−	2.18883i	−2.31133	−	0.163146i
$181$	−9.14793	+	1.31527i	−0.679961	+	0.0977636i	−0.473637	−	0.880720i	$-0.657059\pi$
$181$	−9.14793	+	1.31527i	−0.679961	+	0.0977636i	−0.206324	+	0.978484i	$0.566150\pi$
$182$	−0.644142	+	2.00907i	−0.0477470	+	0.148923i
$183$			30.7274i			2.27144i
$184$	11.9593	−	6.40109i	0.881655	−	0.471895i
$185$	17.3015	−	10.6090i	1.27203	−	0.779988i
$186$	−33.3030	−	10.6775i	−2.44190	−	0.782913i
$187$	0.0411577	+	0.286258i	0.00300975	+	0.0209333i
$188$	2.00577	+	1.43352i	0.146286	+	0.104550i
$189$	3.31470	−	11.2888i	0.241109	−	0.821141i
$190$	13.8236	−	5.56292i	1.00287	−	0.403577i
$191$	−9.37639	+	10.8209i	−0.678451	+	0.782975i	−0.985674	−	0.168663i	$-0.946055\pi$
$191$	−9.37639	+	10.8209i	−0.678451	+	0.782975i	0.307222	+	0.951638i	$0.400600\pi$
$192$	−24.9607	−	3.72079i	−1.80138	−	0.268525i
$193$	−4.60086	−	15.6691i	−0.331177	−	1.12789i	−0.941858	−	0.336010i	$-0.890922\pi$
$193$	−4.60086	−	15.6691i	−0.331177	−	1.12789i	0.610681	−	0.791877i	$-0.290896\pi$
$194$	9.15412	−	13.5001i	0.657227	−	0.969250i
$195$	−10.0409	−	4.84462i	−0.719041	−	0.346930i
$196$	−5.61736	+	10.8501i	−0.401240	+	0.775010i
$197$	−13.5940	+	11.7793i	−0.968532	+	0.839238i	−0.987021	−	0.160591i	$-0.948660\pi$
$197$	−13.5940	+	11.7793i	−0.968532	+	0.839238i	0.0184888	+	0.999829i	$0.494114\pi$
$198$	−1.17276	−	1.92777i	−0.0833444	−	0.137001i
$199$	0.167076	−	1.16204i	0.0118437	−	0.0823748i	−0.983042	−	0.183379i	$-0.941296\pi$
$199$	0.167076	−	1.16204i	0.0118437	−	0.0823748i	0.994886	+	0.101004i	$0.0322055\pi$
$200$	5.53160	−	13.0154i	0.391143	−	0.920330i
$201$	−10.8848	−	4.97093i	−0.767755	−	0.350622i
$202$	0.207737	−	8.42142i	0.0146164	−	0.592529i
$203$	3.78481	−	1.72846i	0.265641	−	0.121314i
$204$	−4.90299	−	6.25685i	−0.343278	−	0.438067i
$205$	−22.4798	−	0.475359i	−1.57006	−	0.0332005i
$206$	0.315621	−	0.0842786i	0.0219904	−	0.00587197i
$207$	−33.0245	+	4.55381i	−2.29536	+	0.316512i
$208$	−5.46405	−	3.17987i	−0.378864	−	0.220484i
$209$	0.909899	+	0.584757i	0.0629390	+	0.0404485i
$210$	7.67997	+	5.44814i	0.529968	+	0.375957i
$211$	−1.98189	+	0.905100i	−0.136439	+	0.0623096i	−0.482465	−	0.875915i	$-0.660258\pi$
$211$	−1.98189	+	0.905100i	−0.136439	+	0.0623096i	0.346026	+	0.938225i	$0.387531\pi$
$212$	22.9917	−	5.53572i	1.57907	−	0.380195i
$213$	−25.4503	−	11.6227i	−1.74382	−	0.796378i
$214$	−7.36239	+	15.1229i	−0.503283	+	1.03378i
$215$	19.3199	−	8.33407i	1.31760	−	0.568379i
$216$	30.8984	+	16.9758i	2.10237	+	1.15506i
$217$	4.84576	+	5.59231i	0.328952	+	0.379631i
$218$	−15.5113	+	17.0335i	−1.05056	+	1.15365i
$219$	8.31112	+	12.9324i	0.561613	+	0.873887i
$220$	1.00286	−	0.219137i	0.0676128	−	0.0147742i
$221$	−0.561019	−	1.91065i	−0.0377382	−	0.128525i
$222$	−40.2090	+	4.77239i	−2.69865	+	0.320302i
$223$	−10.0923	+	11.6471i	−0.675828	+	0.779947i	−0.985276	−	0.170969i	$-0.945310\pi$
$223$	−10.0923	+	11.6471i	−0.675828	+	0.779947i	0.309448	+	0.950916i	$0.399856\pi$
$224$	4.10278	+	3.41741i	0.274129	+	0.228336i
$225$	−23.8505	+	25.2813i	−1.59003	+	1.68542i
$226$	−9.88013	+	8.14340i	−0.657216	+	0.541691i
$227$	11.3290	−	1.62886i	0.751932	−	0.108112i	0.244317	−	0.969695i	$-0.421436\pi$
$227$	11.3290	−	1.62886i	0.751932	−	0.108112i	0.507615	+	0.861584i	$0.330527\pi$
$228$	−29.6929	−	1.46581i	−1.96646	−	0.0970754i
$229$		−	2.57413i		−	0.170103i	−0.996377	−	0.0850515i	$-0.972895\pi$
$229$		−	2.57413i		−	0.170103i	0.996377	−	0.0850515i	$-0.0271055\pi$
$230$	2.92935	−	14.8802i	0.193155	−	0.981168i
$231$			0.683483i			0.0449698i
$232$	2.61867	+	12.1896i	0.171924	+	0.800288i
$233$	26.7236	−	3.84227i	1.75072	−	0.251715i	0.808926	−	0.587910i	$-0.200049\pi$
$233$	26.7236	−	3.84227i	1.75072	−	0.251715i	0.941792	+	0.336195i	$0.109140\pi$
$234$	9.88198	+	11.9895i	0.646005	+	0.783778i
$235$	2.66055	−	0.720475i	0.173555	−	0.0469986i
$236$	−6.59579	+	0.618338i	−0.429350	+	0.0402504i
$237$	3.29662	−	3.80451i	0.214139	−	0.247129i
$238$	0.198231	+	1.67017i	0.0128494	+	0.108261i
$239$	−0.443587	−	1.51072i	−0.0286933	−	0.0977203i	0.943901	−	0.330227i	$-0.107125\pi$
$239$	−0.443587	−	1.51072i	−0.0286933	−	0.0977203i	−0.972595	+	0.232507i	$0.925307\pi$
$240$	−20.8930	+	18.9627i	−1.34863	+	1.22404i
$241$	2.81858	+	4.38580i	0.181561	+	0.282514i	0.920090	−	0.391708i	$-0.128116\pi$
$241$	2.81858	+	4.38580i	0.181561	+	0.282514i	−0.738529	+	0.674222i	$0.764479\pi$
$242$	−11.4468	−	10.4239i	−0.735829	−	0.670074i
$243$	−13.6596	−	15.7640i	−0.876264	−	1.01126i
$244$	14.0760	+	13.4679i	0.901126	+	0.862196i
$245$	5.41068	+	12.5429i	0.345675	+	0.801338i
$246$	40.3340	+	19.6361i	2.57160	+	1.25195i
$247$	−6.77441	−	3.09377i	−0.431045	−	0.196852i
$248$	−19.4881	+	10.5759i	−1.23750	+	0.671573i
$249$	1.49582	−	0.683116i	0.0947935	−	0.0432907i
$250$	−7.34491	−	14.0019i	−0.464533	−	0.885556i
$251$	−25.4055	−	16.3271i	−1.60358	−	1.03056i	−0.965434	−	0.260648i	$-0.916064\pi$
$251$	−25.4055	−	16.3271i	−1.60358	−	1.03056i	−0.638150	−	0.769912i	$-0.720300\pi$
$252$	−6.54179	−	11.3760i	−0.412094	−	0.716621i
$253$	1.00397	−	0.451511i	0.0631188	−	0.0283863i
$254$	−6.36591	−	23.8402i	−0.399433	−	1.49586i
$255$	−8.88533	−	0.187890i	−0.556421	−	0.0117661i
$256$	−12.6448	+	9.80350i	−0.790301	+	0.612719i
$257$	11.3244	−	5.17166i	0.706394	−	0.322599i	−0.0296244	−	0.999561i	$-0.509431\pi$
$257$	11.3244	−	5.17166i	0.706394	−	0.322599i	0.736018	+	0.676962i	$0.236704\pi$
$258$	−41.9661	−	1.03521i	−2.61269	−	0.0644493i
$259$	7.79306	+	3.55897i	0.484237	+	0.221144i
$260$	−6.62023	+	2.47625i	−0.410569	+	0.153570i
$261$	4.36069	−	30.3292i	0.269920	−	1.87733i
$262$	20.7726	−	12.6370i	1.28334	−	0.780717i
$263$	0.00609133	−	0.00527817i	0.000375608	−	0.000325466i	−0.654673	−	0.755912i	$-0.727194\pi$
$263$	0.00609133	−	0.00527817i	0.000375608	−	0.000325466i	0.655049	+	0.755587i	$0.272648\pi$
$264$	−2.00010	−	0.440519i	−0.123097	−	0.0271121i
$265$	11.4896	−	23.8131i	0.705800	−	1.46283i
$266$	5.20616	+	3.53019i	0.319210	+	0.216450i
$267$	5.24867	+	17.8753i	0.321214	+	1.09395i
$268$	−7.04800	+	2.80749i	−0.430525	+	0.171495i
$269$	3.06085	−	3.53241i	0.186624	−	0.215375i	−0.654726	−	0.755866i	$-0.727216\pi$
$269$	3.06085	−	3.53241i	0.186624	−	0.215375i	0.841350	+	0.540491i	$0.181762\pi$
$270$	36.5661	−	14.7150i	2.22534	−	0.895529i
$271$	6.16540	−	20.9974i	0.374521	−	1.27550i	−0.529608	−	0.848243i	$-0.677661\pi$
$271$	6.16540	−	20.9974i	0.374521	−	1.27550i	0.904129	−	0.427260i	$-0.140521\pi$
$272$	−5.01523	−	0.496368i	−0.304093	−	0.0300968i
$273$	−0.669757	−	4.65826i	−0.0405355	−	0.281931i
$274$	1.38442	−	4.31799i	0.0836358	−	0.260859i
$275$	0.520472	−	1.02289i	0.0313857	−	0.0616823i
$276$	−17.7353	+	24.5147i	−1.06754	+	1.47561i
$277$		−	1.15243i		−	0.0692426i	−0.999401	−	0.0346213i	$-0.988978\pi$
$277$		−	1.15243i		−	0.0692426i	0.999401	−	0.0346213i	$-0.0110225\pi$
$278$	18.9690	+	6.08177i	1.13768	+	0.364760i
$279$	53.9382	−	7.75515i	3.22920	−	0.464289i
$280$	5.86192	−	1.13021i	0.350316	−	0.0675429i
$281$	1.05115	−	3.57988i	0.0627063	−	0.213558i	−0.922180	−	0.386762i	$-0.873594\pi$
$281$	1.05115	−	3.57988i	0.0627063	−	0.213558i	0.984886	+	0.173204i	$0.0554118\pi$
$282$	−5.42237	−	0.916627i	−0.322897	−	0.0545844i
$283$	−8.40986	−	7.28719i	−0.499915	−	0.433178i	0.368049	−	0.929806i	$-0.380026\pi$
$283$	−8.40986	−	7.28719i	−0.499915	−	0.433178i	−0.867963	+	0.496628i	$0.834571\pi$
$284$	−16.4793	+	6.56433i	−0.977864	+	0.389521i
$285$	−22.2925	+	24.6539i	−1.32050	+	1.46037i
$286$	−0.424636	−	0.287936i	−0.0251092	−	0.0170260i
$287$	−5.13155	−	7.98484i	−0.302906	−	0.471330i
$288$	37.5063	−	11.8114i	2.21008	−	0.695991i
$289$	10.0931	+	11.6480i	0.593711	+	0.685179i
$290$	12.4012	+	6.36514i	0.728225	+	0.373774i
$291$	−5.17792	+	36.0132i	−0.303535	+	2.11113i
$292$	9.56703	+	1.86102i	0.559868	+	0.108908i
$293$	7.79845	−	17.0762i	0.455590	−	0.997604i	−0.532880	−	0.846191i	$-0.678890\pi$
$293$	7.79845	−	17.0762i	0.455590	−	0.997604i	0.988471	−	0.151413i	$-0.0483824\pi$
$294$	0.672082	−	27.2454i	0.0391966	−	1.58898i
$295$	−4.13517	+	6.14482i	−0.240759	+	0.357766i
$296$	−15.4375	+	20.5112i	−0.897288	+	1.19219i
$297$	2.40687	+	1.54680i	0.139661	+	0.0897544i
$298$	5.41214	−	1.44518i	0.313517	−	0.0837167i
$299$	−6.40007	+	4.06107i	−0.370126	+	0.234858i
$300$	1.61406	+	31.5043i	0.0931878	+	1.81890i
$301$	7.47204	+	4.80199i	0.430681	+	0.276782i
$302$	8.04341	+	18.8280i	0.462846	+	1.08343i
$303$	7.80590	+	17.0925i	0.448437	+	0.981941i
$304$	−13.6860	+	12.9597i	−0.784945	+	0.743288i
$305$	21.6197	−	2.64324i	1.23794	−	0.151352i
$306$	11.1362	+	5.42152i	0.636615	+	0.309928i
$307$	1.22940	−	8.55068i	0.0701657	−	0.488013i	−0.924191	−	0.381929i	$-0.875260\pi$
$307$	1.22940	−	8.55068i	0.0701657	−	0.488013i	0.994357	−	0.106084i	$-0.0338312\pi$
$308$	0.313099	+	0.299573i	0.0178405	+	0.0170697i
$309$	−0.550710	+	0.477193i	−0.0313288	+	0.0271466i
$310$	−4.64787	+	24.3505i	−0.263981	+	1.38301i
$311$	−2.51168	−	3.90826i	−0.142425	−	0.221617i	0.762712	−	0.646739i	$-0.223868\pi$
$311$	−2.51168	−	3.90826i	−0.142425	−	0.221617i	−0.905136	+	0.425122i	$0.860231\pi$
$312$	14.0633	+	1.04242i	0.796177	+	0.0590155i
$313$	26.9175	−	7.90370i	1.52147	−	0.446744i	0.589042	−	0.808102i	$-0.299505\pi$
$313$	26.9175	−	7.90370i	1.52147	−	0.446744i	0.932427	+	0.361359i	$0.117687\pi$
$314$	−17.6770	+	2.09808i	−0.997571	+	0.118401i
$315$	−14.4750	−	2.39457i	−0.815576	−	0.134919i
$316$	−0.297900	−	3.17769i	−0.0167582	−	0.178759i
$317$	−4.49433	+	15.3063i	−0.252427	+	0.859686i	0.731610	+	0.681723i	$0.238769\pi$
$317$	−4.49433	+	15.3063i	−0.252427	+	0.859686i	−0.984037	+	0.177963i	$0.943049\pi$
$318$	−40.7063	+	33.5509i	−2.28270	+	1.88144i
$319$	0.143995	+	1.00150i	0.00806215	+	0.0560735i
$320$	−0.470768	+	17.8823i	−0.0263167	+	0.999654i
$321$		−	37.5185i		−	2.09408i
$322$	5.90168	−	2.48104i	0.328888	−	0.138263i
$323$	−5.93690			−0.330338
$324$	−36.8870	−	1.82095i	−2.04928	−	0.101164i
$325$	−2.54493	+	7.48147i	−0.141167	+	0.414998i
$326$	15.6658	−	12.9121i	0.867649	−	0.715133i
$327$	14.4778	−	49.3068i	0.800623	−	2.72667i
$328$	26.6737	−	9.87020i	1.47281	−	0.544991i
$329$	0.879360	+	0.761970i	0.0484807	+	0.0420088i
$330$	−1.79734	+	1.41867i	−0.0989403	+	0.0780952i
$331$	4.19805	+	14.2973i	0.230746	+	0.785848i	0.990723	+	0.135898i	$0.0433920\pi$
$331$	4.19805	+	14.2973i	0.230746	+	0.785848i	−0.759977	+	0.649950i	$0.774790\pi$
$332$	0.342690	−	0.984636i	0.0188075	−	0.0540389i
$333$	53.0757	−	34.1097i	2.90853	−	1.86920i
$334$	3.81749	+	3.47635i	0.208884	+	0.190218i
$335$	−2.56120	+	8.08614i	−0.139933	+	0.441793i
$336$	−11.5651	−	2.84796i	−0.630928	−	0.155369i
$337$	−1.37899	+	9.59112i	−0.0751186	+	0.522462i	0.917168	+	0.398500i	$0.130469\pi$
$337$	−1.37899	+	9.59112i	−0.0751186	+	0.522462i	−0.992287	+	0.123962i	$0.960440\pi$
$338$	−13.3537	−	6.50108i	−0.726346	−	0.353612i
$339$	11.8642	−	25.9789i	0.644373	−	1.41098i
$340$	−3.98054	+	3.98797i	−0.215875	+	0.216278i
$341$	−1.63681	+	0.747504i	−0.0886380	+	0.0404796i
$342$	42.5979	−	18.1980i	2.30343	−	0.984036i
$343$	−6.68982	+	10.4096i	−0.361216	+	0.562063i
$344$	−18.8681	+	18.7707i	−1.01730	+	1.01205i
$345$	8.65374	+	32.7033i	0.465902	+	1.76069i
$346$	7.20572	−	1.92411i	0.387382	−	0.103441i
$347$	−14.0539	−	9.03191i	−0.754455	−	0.484859i	0.106012	−	0.994365i	$-0.466192\pi$
$347$	−14.0539	−	9.03191i	−0.754455	−	0.484859i	−0.860467	+	0.509506i	$0.829828\pi$
$348$	−17.1537	−	21.8903i	−0.919532	−	1.17344i
$349$	2.76175	+	6.04739i	0.147833	+	0.323709i	0.969033	−	0.246931i	$-0.0794222\pi$
$349$	2.76175	+	6.04739i	0.147833	+	0.323709i	−0.821200	+	0.570641i	$0.806695\pi$
$350$	3.17265	−	5.87227i	0.169585	−	0.313886i
$351$	−17.9197	−	8.18365i	−0.956482	−	0.436811i
$352$	−1.07845	+	0.723151i	−0.0574815	+	0.0385441i
$353$	−11.9257	−	1.71466i	−0.634743	−	0.0912623i	−0.182571	−	0.983193i	$-0.558442\pi$
$353$	−11.9257	−	1.71466i	−0.634743	−	0.0912623i	−0.452173	+	0.891930i	$0.649351\pi$
$354$	12.6246	−	7.68014i	0.670988	−	0.408195i
$355$	−5.98845	+	18.9066i	−0.317834	+	1.00346i
$356$	10.4891	+	5.43044i	0.555921	+	0.287813i
$357$	−2.02829	−	3.15608i	−0.107348	−	0.167037i
$358$	−20.6405	−	13.9959i	−1.09089	−	0.739706i
$359$	−33.8889	+	9.95067i	−1.78859	+	0.525176i	−0.996375	−	0.0850710i	$-0.972888\pi$
$359$	−33.8889	+	9.95067i	−1.78859	+	0.525176i	−0.792211	+	0.610247i	$0.791070\pi$
$360$	16.3368	−	40.8154i	0.861024	−	2.15116i
$361$	−2.09798	+	2.42120i	−0.110420	+	0.127432i
$362$	2.17855	−	12.8873i	0.114502	−	0.677343i
$363$	33.1351	+	9.72933i	1.73914	+	0.510658i
$364$	−2.42748	−	1.73492i	−0.127234	−	0.0909345i
$365$	8.38424	−	6.96016i	0.438851	−	0.364311i
$366$	−41.3803	−	13.2672i	−2.16298	−	0.693488i
$367$			34.5882i			1.80549i	0.430178	+	0.902744i	$0.358451\pi$
$367$			34.5882i			1.80549i	−0.430178	+	0.902744i	$0.641549\pi$
$368$	3.45659	+	18.8693i	0.180187	+	0.983632i
$369$	−69.8982			−3.63876
$370$	6.81671	+	27.8804i	0.354384	+	1.44943i
$371$	11.0476	−	1.58841i	0.573565	−	0.0824661i
$372$	28.7586	−	40.2386i	1.49106	−	2.08628i
$373$	35.5888	+	10.4498i	1.84272	+	0.541071i	0.999996	+	0.00272102i	$0.000866129\pi$
$373$	35.5888	+	10.4498i	1.84272	+	0.541071i	0.842722	+	0.538350i	$0.180952\pi$
$374$	−0.403272	−	0.0681713i	−0.0208527	−	0.00352505i
$375$	28.4019	+	20.9102i	1.46667	+	1.07980i
$376$	−2.79654	+	2.08219i	−0.144221	+	0.107381i
$377$	−1.96279	−	6.68463i	−0.101089	−	0.344276i
$378$	13.7714	+	9.33806i	0.708322	+	0.480298i
$379$	−15.1672	+	9.74735i	−0.779085	+	0.500688i	−0.868730	−	0.495286i	$-0.835063\pi$
$379$	−15.1672	+	9.74735i	−0.779085	+	0.500688i	0.0896446	+	0.995974i	$0.471427\pi$
$380$	1.52291	+	21.0180i	0.0781238	+	1.07820i
$381$	36.0444	+	41.5974i	1.84661	+	2.13110i
$382$	−10.5240	−	17.2992i	−0.538454	−	0.885106i
$383$	32.4693	+	4.66838i	1.65910	+	0.238543i	0.907191	−	0.420720i	$-0.138222\pi$
$383$	32.4693	+	4.66838i	1.65910	+	0.238543i	0.751913	+	0.659263i	$0.229132\pi$
$384$	15.7880	−	32.0077i	0.805680	−	1.63339i
$385$	0.480897	−	0.0587947i	0.0245088	−	0.00299646i
$386$	23.0879	+	0.569528i	1.17515	+	0.0289882i
$387$	59.4983	−	27.1720i	3.02447	−	1.38123i
$388$	14.2279	+	18.1567i	0.722315	+	0.921767i
$389$	10.8384	−	16.8649i	0.549530	−	0.855086i	−0.449745	−	0.893157i	$-0.648485\pi$
$389$	10.8384	−	16.8649i	0.549530	−	0.855086i	0.999275	+	0.0380713i	$0.0121214\pi$
$390$	10.8595	−	11.4302i	0.549895	−	0.578789i
$391$	−3.29606	+	5.06427i	−0.166689	+	0.256111i
$392$	−12.1864	−	12.2496i	−0.615504	−	0.618699i
$393$	−29.3223	+	45.6264i	−1.47911	+	2.30155i
$394$	−9.99352	−	23.3928i	−0.503466	−	1.17851i
$395$	−2.96043	−	1.99223i	−0.148955	−	0.100240i
$396$	3.10248	−	0.746987i	0.155905	−	0.0375375i
$397$	−6.30273	−	2.87836i	−0.316325	−	0.144461i	0.250925	−	0.968007i	$-0.419265\pi$
$397$	−6.30273	−	2.87836i	−0.316325	−	0.144461i	−0.567250	+	0.823546i	$0.691993\pi$
$398$	1.49277	+	0.726735i	0.0748257	+	0.0364279i
$399$	−13.8881	−	1.99681i	−0.695276	−	0.0999655i
$400$	15.1394	+	13.0690i	0.756968	+	0.653452i
$401$	−6.59396	+	5.71370i	−0.329287	+	0.285329i	−0.803775	−	0.594933i	$-0.797179\pi$
$401$	−6.59396	+	5.71370i	−0.329287	+	0.285329i	0.474488	+	0.880262i	$0.342633\pi$
$402$	11.3940	−	12.5122i	0.568283	−	0.624050i
$403$	10.4231	−	6.69853i	0.519213	−	0.333678i
$404$	11.2513	+	3.91588i	0.559775	+	0.194822i
$405$	−27.6937	+	30.6272i	−1.37611	+	1.52188i
$406$	0.693534	+	5.84326i	0.0344195	+	0.289996i
$407$	−1.36430	+	1.57449i	−0.0676258	+	0.0780443i
$408$	10.5430	−	3.90128i	0.521957	−	0.193142i
$409$	−22.0365	−	6.47051i	−1.08964	−	0.319946i	−0.312910	−	0.949783i	$-0.601304\pi$
$409$	−22.0365	−	6.47051i	−1.08964	−	0.319946i	−0.776728	+	0.629837i	$0.783122\pi$
$410$	10.3463	−	30.0680i	0.510966	−	1.48496i
$411$	1.43947	+	10.0117i	0.0710038	+	0.493842i
$412$	−0.0227789	+	0.461433i	−0.00112223	+	0.0227332i
$413$	−3.12660			−0.153850
$414$	8.12643	−	46.4399i	0.399392	−	2.28240i
$415$	−0.609313	−	0.993690i	−0.0299100	−	0.0487783i
$416$	6.64151	−	5.98541i	0.325627	−	0.293459i
$417$	−43.9817	+	6.32361i	−2.15379	+	0.309669i
$418$	−1.18035	+	0.972871i	−0.0577330	+	0.0475847i
$419$	32.4993	+	9.54265i	1.58769	+	0.466189i	0.952088	−	0.305825i	$-0.0989323\pi$
$419$	32.4993	+	9.54265i	1.58769	+	0.466189i	0.635606	+	0.772014i	$0.280750\pi$
$420$	−10.6529	+	7.99018i	−0.519810	+	0.389881i
$421$	−7.82352	−	6.77912i	−0.381295	−	0.330394i	0.443034	−	0.896505i	$-0.353902\pi$
$421$	−7.82352	−	6.77912i	−0.381295	−	0.330394i	−0.824329	+	0.566111i	$0.808447\pi$
$422$	−0.363165	−	3.05979i	−0.0176786	−	0.148948i
$423$	8.22162	−	2.41409i	0.399749	−	0.117377i
$424$	−2.47223	+	33.3528i	−0.120062	+	1.61976i
$425$	0.632138	+	6.26787i	0.0306632	+	0.304036i
$426$	26.6409	−	29.2553i	1.29076	−	1.41742i
$427$	6.02104	+	6.94865i	0.291379	+	0.336269i
$428$	−17.1870	−	16.4445i	−0.830766	−	0.794875i
$429$	1.13277	+	0.162868i	0.0546907	+	0.00786333i
$430$	2.88165	+	29.6163i	0.138965	+	1.42822i
$431$	−4.47810	+	9.80566i	−0.215702	+	0.472322i	−0.986292	−	0.165009i	$-0.947235\pi$
$431$	−4.47810	+	9.80566i	−0.215702	+	0.472322i	0.770590	+	0.637332i	$0.219962\pi$
$432$	−36.2022	+	34.2810i	−1.74178	+	1.64934i
$433$	−13.3673	−	29.2702i	−0.642389	−	1.40664i	−0.898060	−	0.439873i	$-0.855024\pi$
$433$	−13.3673	−	29.2702i	−0.642389	−	1.40664i	0.255671	−	0.966764i	$-0.417704\pi$
$434$	−9.62336	+	4.11114i	−0.461936	+	0.197341i
$435$	−31.0863	−	0.657353i	−1.49047	−	0.0315177i
$436$	−16.2415	−	28.2435i	−0.777826	−	1.35262i
$437$	6.24144	+	21.7193i	0.298568	+	1.03898i
$438$	−21.0044	+	5.60868i	−1.00363	+	0.267993i
$439$	16.9324	−	26.3473i	0.808138	−	1.25749i	−0.154849	−	0.987938i	$-0.549489\pi$
$439$	16.9324	−	26.3473i	0.808138	−	1.25749i	0.962987	−	0.269549i	$-0.0868747\pi$
$440$	−0.137896	+	1.44516i	−0.00657393	+	0.0688952i
$441$	17.6407	+	38.6277i	0.840033	+	1.83941i
$442$	2.81529	+	0.0694469i	0.133910	+	0.00330325i
$443$	−7.46031	+	16.3358i	−0.354450	+	0.776137i	0.645474	+	0.763783i	$0.276660\pi$
$443$	−7.46031	+	16.3358i	−0.354450	+	0.776137i	−0.999924	+	0.0123548i	$0.996067\pi$
$444$	10.9341	−	56.2096i	0.518912	−	2.66759i
$445$	12.1256	−	5.23063i	0.574806	−	0.247956i
$446$	−11.3275	−	18.6200i	−0.536372	−	0.881684i
$447$	−9.44336	+	8.18272i	−0.446656	+	0.387029i
$448$	−6.37366	+	4.04963i	−0.301127	+	0.191327i
$449$	−5.22387	+	3.35718i	−0.246529	+	0.158435i	−0.658070	−	0.752956i	$-0.728627\pi$
$449$	−5.22387	+	3.35718i	−0.246529	+	0.158435i	0.411541	+	0.911391i	$0.364991\pi$
$450$	−23.7482	−	43.0350i	−1.11950	−	2.02869i
$451$	2.21462	−	0.650272i	0.104282	−	0.0306201i
$452$	−6.70068	−	16.8216i	−0.315173	−	0.791219i
$453$	−34.5149	−	29.9074i	−1.62165	−	1.40517i
$454$	−2.69796	+	15.9599i	−0.126621	+	0.749037i
$455$	−3.21993	+	0.871954i	−0.150953	+	0.0408778i
$456$	14.7945	−	39.3542i	0.692817	−	1.84293i
$457$	5.47454	+	38.0763i	0.256088	+	1.78113i	0.560060	+	0.828452i	$0.310778\pi$
$457$	5.47454	+	38.0763i	0.256088	+	1.78113i	−0.303972	+	0.952681i	$0.598313\pi$
$458$	3.46655	+	1.11143i	0.161981	+	0.0519338i
$459$	−15.7043			−0.733014
$460$	18.7741	+	10.3697i	0.875349	+	0.483492i
$461$	−24.9770			−1.16330			−0.581648	−	0.813441i	$-0.697592\pi$
$461$	−24.9770			−1.16330			−0.581648	+	0.813441i	$0.697592\pi$
$462$	−0.920439	−	0.295108i	−0.0428227	−	0.0137297i
$463$	−5.75399	−	40.0199i	−0.267410	−	1.85988i	−0.472760	−	0.881191i	$-0.656742\pi$
$463$	−5.75399	−	40.0199i	−0.267410	−	1.85988i	0.205349	−	0.978689i	$-0.434167\pi$
$464$	−17.5463	−	1.73660i	−0.814567	−	0.0806196i
$465$	−14.4538	−	53.3746i	−0.670278	−	2.47519i
$466$	−6.36412	+	37.6473i	−0.294812	+	1.74398i
$467$	−13.7383	−	11.9043i	−0.635735	−	0.550867i	0.276253	−	0.961085i	$-0.410907\pi$
$467$	−13.7383	−	11.9043i	−0.635735	−	0.550867i	−0.911988	+	0.410218i	$0.865453\pi$
$468$	−20.4129	+	8.13125i	−0.943586	+	0.375867i
$469$	−3.43553	+	1.00876i	−0.158638	+	0.0465803i
$470$	−0.178493	+	3.89402i	−0.00823326	+	0.179618i
$471$	33.4039	−	21.4674i	1.53917	−	0.989164i
$472$	2.01516	−	9.14947i	0.0927554	−	0.421138i
$473$	−1.63233	+	1.41442i	−0.0750547	+	0.0650352i
$474$	3.70010	+	6.08221i	0.169951	+	0.279365i
$475$	19.2641	+	13.5642i	0.883897	+	0.622368i
$476$	−2.33479	−	0.454173i	−0.107015	−	0.0208170i
$477$	34.1445	−	74.7661i	1.56337	−	3.42331i
$478$	2.22600	+	0.0549104i	0.101815	+	0.00251154i
$479$	−1.82409	−	3.99420i	−0.0833448	−	0.182500i	0.863371	−	0.504569i	$-0.168349\pi$
$479$	−1.82409	−	3.99420i	−0.0833448	−	0.182500i	−0.946716	+	0.322070i	$0.895621\pi$
$480$	−16.5159	−	36.3239i	−0.753843	−	1.65795i
$481$	7.75549	−	12.0678i	0.353620	−	0.550243i
$482$	−7.12329	+	1.90209i	−0.324457	+	0.0866380i
$483$	−9.41375	+	10.7382i	−0.428340	+	0.488604i
$484$	18.9802	−	10.9146i	0.862735	−	0.496117i
$485$	25.7843	+	0.545235i	1.17080	+	0.0247579i
$486$	27.1271	−	11.5888i	1.23051	−	0.525678i
$487$	−11.7789	−	25.7922i	−0.533752	−	1.16875i	−0.963965	−	0.266027i	$-0.914289\pi$
$487$	−11.7789	−	25.7922i	−0.533752	−	1.16875i	0.430213	−	0.902727i	$-0.358438\pi$
$488$	−24.2148	+	13.1410i	−1.09615	+	0.594865i
$489$	−18.8117	+	41.1918i	−0.850694	+	1.86276i
$490$	−19.2276	+	1.87083i	−0.868614	+	0.0845156i
$491$	23.4303	+	3.36876i	1.05739	+	0.152030i	0.649010	−	0.760780i	$-0.275183\pi$
$491$	23.4303	+	3.36876i	1.05739	+	0.152030i	0.408384	+	0.912810i	$0.366093\pi$
$492$	−43.8587	+	45.8391i	−1.97730	+	2.06659i
$493$	−3.63696	−	4.19728i	−0.163801	−	0.189036i
$494$	7.09134	−	7.78723i	0.319055	−	0.350364i
$495$	1.55040	−	3.21333i	0.0696852	−	0.144428i
$496$	−5.82810	−	30.8109i	−0.261689	−	1.38345i
$497$	−8.03277	+	2.35863i	−0.360319	+	0.105799i
$498$	0.274096	+	2.30935i	0.0122825	+	0.103484i
$499$	−25.2281	−	21.8602i	−1.12936	−	0.978599i	−0.129448	−	0.991586i	$-0.541320\pi$
$499$	−25.2281	−	21.8602i	−1.12936	−	0.978599i	−0.999916	+	0.0129872i	$0.995866\pi$
$500$	22.0275	−	3.84572i	0.985099	−	0.171986i
$501$	−11.0505	−	3.24472i	−0.493699	−	0.144963i
$502$	32.9570	−	27.1638i	1.47094	−	1.21238i
$503$	18.1825	−	2.61425i	0.810718	−	0.116564i	0.275526	−	0.961294i	$-0.411148\pi$
$503$	18.1825	−	2.61425i	0.810718	−	0.116564i	0.535193	+	0.844730i	$0.320239\pi$
$504$	18.1445	−	3.89794i	0.808221	−	0.173628i
$505$	11.3548	−	6.96255i	0.505282	−	0.309830i
$506$	0.174562	+	1.54698i	0.00776023	+	0.0687717i
$507$	33.1293			1.47132
$508$	34.8539	+	1.72058i	1.54639	+	0.0763385i
$509$	−1.49540	−	10.4007i	−0.0662823	−	0.461004i	−0.995750	−	0.0920996i	$-0.970642\pi$
$509$	−1.49540	−	10.4007i	−0.0662823	−	0.461004i	0.929467	−	0.368904i	$-0.120267\pi$
$510$	4.08946	−	11.8847i	0.181084	−	0.526262i
$511$	4.41356	+	1.29594i	0.195244	+	0.0573289i
$512$	−7.74260	−	21.2615i	−0.342178	−	0.939635i
$513$	−38.4621	+	44.3876i	−1.69814	+	1.95976i
$514$	2.07509	+	17.4834i	0.0915284	+	0.771158i
$515$	0.383126	+	0.346430i	0.0168825	+	0.0152655i
$516$	19.5138	−	56.0683i	0.859049	−	2.46827i
$517$	−0.238031	+	0.152973i	−0.0104686	+	0.00672776i
$518$	−8.15765	+	8.95818i	−0.358427	+	0.393600i
$519$	−12.5729	+	10.8945i	−0.551889	+	0.478214i
$520$	−0.476310	−	9.98457i	−0.0208876	−	0.437852i
$521$	−5.36974	−	0.772052i	−0.235252	−	0.0338242i	0.0236801	−	0.999720i	$-0.492462\pi$
$521$	−5.36974	−	0.772052i	−0.235252	−	0.0338242i	−0.258933	+	0.965895i	$0.583371\pi$
$522$	38.9613	+	18.9678i	1.70529	+	0.830197i
$523$	−4.30229	−	1.96479i	−0.188126	−	0.0859143i	0.319125	−	0.947713i	$-0.396611\pi$
$523$	−4.30229	−	1.96479i	−0.188126	−	0.0859143i	−0.507251	+	0.861798i	$0.669338\pi$
$524$	8.04911	+	33.4306i	0.351627	+	1.46042i
$525$	−0.629374	+	14.8749i	−0.0274682	+	0.649196i
$526$	0.00447800	+	0.0104821i	0.000195250	+	0.000457041i
$527$	5.33991	−	8.30906i	0.232610	−	0.361948i
$528$	1.45683	−	2.50331i	0.0634002	−	0.108942i
$529$	21.9921	+	6.73415i	0.956177	+	0.292789i
$530$	27.1080	+	25.7547i	1.17750	+	1.11871i
$531$	−12.4482	+	19.3698i	−0.540208	+	0.840579i
$532$	−7.00194	+	5.48686i	−0.303572	+	0.237885i
$533$	−14.4565	+	6.60206i	−0.626180	+	0.285967i
$534$	−26.3388	−	0.649718i	−1.13979	−	0.0281161i
$535$	−26.3980	+	3.22743i	−1.14128	+	0.139534i
$536$	−0.737699	−	10.7037i	−0.0318637	−	0.462328i
$537$	55.0613	+	7.91662i	2.37607	+	0.341627i
$538$	3.43548	+	5.64721i	0.148114	+	0.243469i
$539$	−0.918277	−	1.05975i	−0.0395530	−	0.0456466i
$540$	4.02841	+	55.5968i	0.173355	+	2.39250i
$541$	−4.86739	+	3.12808i	−0.209266	+	0.134487i	−0.641076	−	0.767478i	$-0.721511\pi$
$541$	−4.86739	+	3.12808i	−0.209266	+	0.134487i	0.431810	+	0.901965i	$0.357875\pi$
$542$	25.6150	+	17.3690i	1.10026	+	0.746061i
$543$	8.21376	+	27.9735i	0.352486	+	1.20046i
$544$	2.83388	−	6.53964i	0.121502	−	0.280385i
$545$	−35.9376	−	5.94505i	−1.53940	−	0.254658i
$546$	6.56241	+	1.10935i	0.280845	+	0.0474757i
$547$	−8.25999	−	2.42535i	−0.353172	−	0.103701i	0.100334	−	0.994954i	$-0.468009\pi$
$547$	−8.25999	−	2.42535i	−0.353172	−	0.103701i	−0.453506	+	0.891253i	$0.649827\pi$
$548$	5.21724	+	3.72876i	0.222869	+	0.159285i
$549$	67.0203	−	9.63606i	2.86036	−	0.411257i
$550$	1.15278	+	1.14257i	0.0491549	+	0.0487192i
$551$	−20.7709			−0.884870
$552$	−25.3561	−	34.4687i	−1.07923	−	1.46709i
$553$		−	1.50632i		−	0.0640552i
$554$	1.55196	+	0.497584i	0.0659365	+	0.0211403i
$555$	−40.8933	−	49.2603i	−1.73583	−	2.09098i
$556$	−16.3805	+	22.9194i	−0.694689	+	0.972000i
$557$	10.7564	+	3.15838i	0.455765	+	0.133825i	0.501554	−	0.865126i	$-0.332762\pi$
$557$	10.7564	+	3.15838i	0.455765	+	0.133825i	−0.0457888	+	0.998951i	$0.514580\pi$
$558$	−12.8452	+	75.9865i	−0.543780	+	3.21677i
$559$	9.73910	−	11.2395i	0.411920	−	0.475381i
$560$	−1.00896	+	8.38217i	−0.0426365	+	0.354211i
$561$	0.875349	−	0.257026i	0.0369573	−	0.0108516i
$562$	4.36714	+	2.96126i	0.184217	+	0.124913i
$563$	16.9891	+	26.4356i	0.716007	+	1.11413i	0.988390	+	0.151939i	$0.0485518\pi$
$563$	16.9891	+	26.4356i	0.716007	+	1.11413i	−0.272383	+	0.962189i	$0.587812\pi$
$564$	3.57563	−	6.90647i	0.150561	−	0.290815i
$565$	−19.2993	−	6.11284i	−0.811927	−	0.257169i
$566$	13.4447	−	8.17908i	0.565124	−	0.343792i
$567$	−17.2530	−	2.48061i	−0.724558	−	0.104176i
$568$	−1.72485	−	25.0267i	−0.0723730	−	1.05010i
$569$	−13.1412	−	6.00139i	−0.550908	−	0.251591i	0.120456	−	0.992719i	$-0.461564\pi$
$569$	−13.1412	−	6.00139i	−0.550908	−	0.251591i	−0.671364	+	0.741127i	$0.734291\pi$
$570$	−23.5759	−	40.6660i	−0.987485	−	1.70331i
$571$	−4.22247	−	9.24592i	−0.176705	−	0.386930i	0.800468	−	0.599375i	$-0.204584\pi$
$571$	−4.22247	−	9.24592i	−0.176705	−	0.386930i	−0.977173	+	0.212446i	$0.931857\pi$
$572$	0.571106	−	0.447530i	0.0238791	−	0.0187122i
$573$	37.9972	+	24.4193i	1.58736	+	1.02013i
$574$	12.9688	−	3.46298i	0.541306	−	0.144542i
$575$	22.2656	−	8.90196i	0.928538	−	0.371238i
$576$	−0.287884	+	55.6091i	−0.0119952	+	2.31705i
$577$	−2.76638	+	4.30458i	−0.115166	+	0.179202i	−0.894051	−	0.447965i	$-0.852149\pi$
$577$	−2.76638	+	4.30458i	−0.115166	+	0.179202i	0.778885	+	0.627166i	$0.215785\pi$
$578$	−20.0442	+	8.56297i	−0.833729	+	0.356173i
$579$	−46.8605	+	21.4005i	−1.94745	+	0.889372i
$580$	−13.9264	+	13.9523i	−0.578261	+	0.579339i
$581$	0.204405	−	0.447584i	0.00848014	−	0.0185689i
$582$	−46.2630	−	22.5225i	−1.91766	−	0.933589i
$583$	−0.386261	+	2.68650i	−0.0159973	+	0.111264i
$584$	−6.63698	+	12.0803i	−0.274640	+	0.499886i
$585$	−7.41791	+	23.4196i	−0.306693	+	0.968282i
$586$	19.6292	+	17.8751i	0.810876	+	0.738414i
$587$	−9.50340	+	6.10747i	−0.392247	+	0.252082i	−0.721867	−	0.692032i	$-0.756716\pi$
$587$	−9.50340	+	6.10747i	−0.392247	+	0.252082i	0.329620	+	0.944114i	$0.393079\pi$
$588$	36.4009	+	12.6688i	1.50115	+	0.522454i
$589$	−10.4070	−	35.4432i	−0.428815	−	1.46041i
$590$	−6.48973	−	8.22195i	−0.267178	−	0.338492i
$591$	42.8831	+	37.1584i	1.76397	+	1.52849i
$592$	−20.9568	−	29.6457i	−0.861320	−	1.21843i
$593$	3.89173	−	13.2540i	0.159814	−	0.544278i	−0.840184	−	0.542302i	$-0.817553\pi$
$593$	3.89173	−	13.2540i	0.159814	−	0.544278i	0.999998	−	0.00197570i	$-0.000628886\pi$
$594$	−3.12227	+	2.57344i	−0.128108	+	0.105590i
$595$	−2.04613	+	1.69859i	−0.0838833	+	0.0696356i
$596$	−0.390603	+	7.91246i	−0.0159997	+	0.324107i
$597$	−3.70342			−0.151571
$598$	−2.70564	−	10.3724i	−0.110642	−	0.424157i
$599$			9.84606i			0.402299i	0.979561	+	0.201149i	$0.0644677\pi$
$599$			9.84606i			0.402299i	−0.979561	+	0.201149i	$0.935532\pi$
$600$	−43.1234	−	11.4290i	−1.76050	−	0.466586i
$601$	−2.92235	−	20.3254i	−0.119205	−	0.829091i	−0.958434	−	0.285313i	$-0.907902\pi$
$601$	−2.92235	−	20.3254i	−0.119205	−	0.829091i	0.839229	−	0.543778i	$-0.183007\pi$
$602$	−9.69300	+	7.98916i	−0.395057	+	0.325614i
$603$	−7.42875	+	25.3000i	−0.302522	+	1.03030i
$604$	−28.8284	+	2.70259i	−1.17301	+	0.109967i
$605$	3.99519	−	24.1507i	0.162427	−	0.981866i
$606$	−26.3887	+	3.13206i	−1.07197	+	0.127231i
$607$	0.988346	−	0.290205i	0.0401157	−	0.0117790i	−0.261613	−	0.965173i	$-0.584254\pi$
$607$	0.988346	−	0.290205i	0.0401157	−	0.0117790i	0.301729	+	0.953394i	$0.402436\pi$
$608$	−11.5435	−	24.0264i	−0.468149	−	0.974399i
$609$	−7.09619	−	11.0419i	−0.287552	−	0.447440i
$610$	−5.77515	+	30.2564i	−0.233829	+	1.22504i
$611$	1.47240	−	1.27584i	0.0595668	−	0.0516149i
$612$	−12.1094	+	12.6562i	−0.489494	+	0.511596i
$613$	−1.64063	+	11.4108i	−0.0662644	+	0.460879i	0.929491	+	0.368844i	$0.120246\pi$
$613$	−1.64063	+	11.4108i	−0.0662644	+	0.460879i	−0.995756	+	0.0920350i	$0.970663\pi$
$614$	10.9843	+	5.34756i	0.443290	+	0.215810i
$615$	8.60780	+	70.4054i	0.347100	+	2.83902i
$616$	−0.538619	+	0.292301i	−0.0217016	+	0.0117771i
$617$	4.87169	+	10.6675i	0.196127	+	0.429458i	0.981988	−	0.188946i	$-0.0605070\pi$
$617$	4.87169	+	10.6675i	0.196127	+	0.429458i	−0.785861	+	0.618403i	$0.787780\pi$
$618$	−0.404851	−	0.947675i	−0.0162855	−	0.0381211i
$619$	11.8802	+	7.63492i	0.477504	+	0.306873i	0.757163	−	0.653226i	$-0.226585\pi$
$619$	11.8802	+	7.63492i	0.477504	+	0.306873i	−0.279659	+	0.960100i	$0.590221\pi$
$620$	−30.7857	−	16.7731i	−1.23638	−	0.673622i
$621$	16.5099	+	57.4520i	0.662518	+	2.30547i
$622$	6.34768	−	1.69499i	0.254519	−	0.0679628i
$623$	4.68960	+	3.01383i	0.187885	+	0.120746i
$624$	−7.47594	+	18.4888i	−0.299277	+	0.740144i
$625$	12.2692	−	21.7823i	0.490768	−	0.871290i
$626$	−0.978376	+	39.6622i	−0.0391038	+	1.58522i
$627$	1.41738	−	3.10363i	0.0566048	−	0.123947i
$628$	4.80696	−	24.7113i	0.191819	−	0.986090i
$629$	1.62744	−	11.3191i	0.0648902	−	0.451321i
$630$	9.47464	−	18.4595i	0.377479	−	0.735443i
$631$	15.7491	+	18.1754i	0.626962	+	0.723552i	0.977013	−	0.213178i	$-0.0683814\pi$
$631$	15.7491	+	18.1754i	0.626962	+	0.723552i	−0.350052	+	0.936730i	$0.613836\pi$
$632$	4.40799	+	0.970856i	0.175340	+	0.0386186i
$633$	3.71588	+	5.78202i	0.147693	+	0.229815i
$634$	−18.6723	−	12.6613i	−0.741572	−	0.502844i
$635$	26.1673	−	28.9391i	1.03842	−	1.14841i
$636$	−27.6069	−	69.3051i	−1.09468	−	2.74812i
$637$	7.29696	+	6.32285i	0.289116	+	0.250521i
$638$	−1.41089	−	0.238505i	−0.0558576	−	0.00944249i
$639$	−17.3695	+	59.1551i	−0.687127	+	2.34014i
$640$	−23.8787	−	8.35506i	−0.943889	−	0.330263i
$641$	18.8637	−	2.71219i	0.745071	−	0.107125i	0.240685	−	0.970603i	$-0.422628\pi$
$641$	18.8637	−	2.71219i	0.745071	−	0.107125i	0.504386	+	0.863478i	$0.331719\pi$
$642$	50.5258	+	16.1994i	1.99410	+	0.639340i
$643$		−	20.9784i		−	0.827306i	−0.910435	−	0.413653i	$-0.864253\pi$
$643$		−	20.9784i		−	0.827306i	0.910435	−	0.413653i	$-0.135747\pi$
$644$	0.793020	+	9.01897i	0.0312494	+	0.355397i
$645$	−34.6962	−	56.5838i	−1.36616	−	2.22799i
$646$	2.56338	−	7.99517i	0.100855	−	0.314566i
$647$	0.735207	+	5.11348i	0.0289040	+	0.201032i	0.999157	−	0.0410634i	$-0.0130746\pi$
$647$	0.735207	+	5.11348i	0.0289040	+	0.201032i	−0.970253	+	0.242095i	$0.922165\pi$
$648$	18.3790	−	48.8892i	0.721996	−	1.92055i
$649$	0.214204	−	0.729512i	0.00840824	−	0.0286359i
$650$	−8.97640	−	6.65751i	−0.352083	−	0.261129i
$651$	15.2862	−	17.6413i	0.599115	−	0.691415i
$652$	10.6245	+	26.6720i	0.416088	+	1.04456i
$653$	7.13313	+	24.2932i	0.279141	+	0.950667i	0.973048	+	0.230602i	$0.0740696\pi$
$653$	7.13313	+	24.2932i	0.279141	+	0.950667i	−0.693907	+	0.720065i	$0.744112\pi$
$654$	60.1499	+	40.7863i	2.35205	+	1.59487i
$655$	34.6250	+	16.7062i	1.35291	+	0.652767i
$656$	1.77517	+	40.1829i	0.0693088	+	1.56888i
$657$	25.6007	−	22.1831i	0.998779	−	0.865447i
$658$	−1.40582	+	0.855229i	−0.0548046	+	0.0333403i
$659$	0.588131	−	4.09054i	0.0229103	−	0.159345i	−0.975155	−	0.221525i	$-0.928896\pi$
$659$	0.588131	−	4.09054i	0.0229103	−	0.159345i	0.998065	+	0.0621807i	$0.0198055\pi$
$660$	−1.13447	−	3.03300i	−0.0441592	−	0.118059i
$661$	−6.73505	−	3.07579i	−0.261963	−	0.119635i	0.280104	−	0.959970i	$-0.409631\pi$
$661$	−6.73505	−	3.07579i	−0.261963	−	0.119635i	−0.542067	+	0.840335i	$0.682358\pi$
$662$	−21.0666	−	0.519665i	−0.818775	−	0.0201974i
$663$	−5.71406	+	2.60952i	−0.221916	+	0.101345i
$664$	1.17804	+	0.886634i	0.0457167	+	0.0344081i
$665$	−0.210264	+	9.94342i	−0.00815370	+	0.385589i
$666$	23.0186	+	86.2042i	0.891954	+	3.34034i
$667$	−11.5316	+	17.7179i	−0.446507	+	0.686040i
$668$	−6.32985	+	3.63999i	−0.244909	+	0.140836i
$669$	40.8983	+	26.2837i	1.58122	+	1.01619i
$670$	−9.78367	−	6.94050i	−0.377976	−	0.268135i
$671$	−2.03379	+	0.928802i	−0.0785137	+	0.0358560i
$672$	8.82880	−	14.3449i	0.340578	−	0.553368i
$673$	12.0346	+	5.49600i	0.463898	+	0.211855i	0.633632	−	0.773635i	$-0.281563\pi$
$673$	12.0346	+	5.49600i	0.463898	+	0.211855i	−0.169734	+	0.985490i	$0.554291\pi$
$674$	−12.3209	−	5.99825i	−0.474582	−	0.231044i
$675$	50.9574	+	35.8800i	1.96135	+	1.38102i
$676$	14.5207	−	15.1763i	0.558488	−	0.583705i
$677$	−4.77810	−	5.51422i	−0.183637	−	0.211929i	0.656465	−	0.754356i	$-0.272051\pi$
$677$	−4.77810	−	5.51422i	−0.183637	−	0.211929i	−0.840103	+	0.542427i	$0.817505\pi$
$678$	29.8629	+	27.1943i	1.14688	+	1.04439i
$679$	5.88587	+	9.15860i	0.225879	+	0.351475i
$680$	−3.65187	−	7.08245i	−0.140043	−	0.271599i
$681$	−10.1721	−	34.6430i	−0.389795	−	1.32752i
$682$	−0.299931	−	2.52702i	−0.0114850	−	0.0967646i
$683$	1.08656	−	1.25396i	0.0415762	−	0.0479814i	−0.734581	−	0.678521i	$-0.762621\pi$
$683$	1.08656	−	1.25396i	0.0415762	−	0.0479814i	0.776157	+	0.630540i	$0.217167\pi$
$684$	6.11454	+	65.2236i	0.233795	+	2.49389i
$685$	6.92041	−	1.87404i	0.264415	−	0.0716034i
$686$	−11.1300	−	13.5037i	−0.424945	−	0.515572i
$687$	−8.03758	+	1.15563i	−0.306653	+	0.0440900i
$688$	−17.1316	−	33.5141i	−0.653135	−	1.27771i
$689$		−	18.6883i		−	0.711968i
$690$	−47.7776	−	2.46643i	−1.81886	−	0.0938954i
$691$		−	16.2308i		−	0.617449i	−0.951151	−	0.308725i	$-0.900098\pi$
$691$		−	16.2308i		−	0.617449i	0.951151	−	0.308725i	$-0.0999022\pi$
$692$	−0.520049	+	10.5346i	−0.0197693	+	0.400467i
$693$	1.49076	−	0.214339i	0.0566293	−	0.00814206i
$694$	18.2313	−	15.0266i	0.692049	−	0.570401i
$695$	8.23269	+	30.4015i	0.312284	+	1.15319i
$696$	36.8859	−	13.6491i	1.39816	−	0.517367i
$697$	−8.29660	+	9.57479i	−0.314256	+	0.362671i
$698$	−9.33640	+	1.10813i	−0.353388	+	0.0419435i
$699$	−23.9946	−	81.7180i	−0.907558	−	3.09086i
$700$	6.53827	+	6.80805i	0.247123	+	0.257320i
$701$	−2.37339	−	3.69306i	−0.0896416	−	0.139485i	0.793537	−	0.608522i	$-0.208237\pi$
$701$	−2.37339	−	3.69306i	−0.0896416	−	0.139485i	−0.883178	+	0.469037i	$0.844601\pi$
$702$	18.7580	−	20.5988i	0.707976	−	0.777451i
$703$	−28.0071	−	32.3220i	−1.05631	−	1.21905i
$704$	−0.508217	−	1.76457i	−0.0191542	−	0.0665048i
$705$	−3.44407	−	7.98399i	−0.129711	−	0.300694i
$706$	7.45831	−	15.3199i	0.280697	−	0.576573i
$707$	5.11450	+	2.33571i	0.192351	+	0.0878436i
$708$	4.89185	+	20.3174i	0.183847	+	0.763576i
$709$	24.8624	−	11.3543i	0.933727	−	0.426419i	0.110336	−	0.993894i	$-0.464807\pi$
$709$	24.8624	−	11.3543i	0.933727	−	0.426419i	0.823390	+	0.567476i	$0.192080\pi$
$710$	−22.8757	−	16.2279i	−0.858508	−	0.609022i
$711$	−9.33192	−	5.99726i	−0.349974	−	0.224915i
$712$	−11.8420	+	11.7809i	−0.443798	+	0.441506i
$713$	−36.0114	−	10.8000i	−1.34864	−	0.404465i
$714$	5.12602	−	1.36877i	0.191836	−	0.0512250i
$715$	0.0171500	−	0.811026i	0.000641373	−	0.0303306i
$716$	27.7601	−	21.7534i	1.03744	−	0.812961i
$717$	−4.51800	+	2.06330i	−0.168728	+	0.0770554i
$718$	1.23176	−	49.9342i	0.0459691	−	1.86353i
$719$	38.6587	+	17.6548i	1.44173	+	0.658414i	0.974225	−	0.225579i	$-0.0724274\pi$
$719$	38.6587	+	17.6548i	1.44173	+	0.658414i	0.467500	+	0.883993i	$0.345155\pi$
$720$	47.9119	+	39.6235i	1.78557	+	1.47668i
$721$	−0.0310308	+	0.215824i	−0.00115565	+	0.00803769i
$722$	−2.35476	−	3.87073i	−0.0876350	−	0.144054i
$723$	12.4291	−	10.7698i	0.462242	−	0.400535i
$724$	16.4146	+	8.49820i	0.610044	+	0.315833i
$725$	2.21160	+	21.9288i	0.0821369	+	0.814416i
$726$	−27.4092	+	40.4218i	−1.01725	+	1.50019i
$727$	−7.21986	−	24.5886i	−0.267770	−	0.911940i	−0.978111	−	0.208083i	$-0.933278\pi$
$727$	−7.21986	−	24.5886i	−0.267770	−	0.911940i	0.710341	−	0.703857i	$-0.248541\pi$
$728$	3.38451	−	2.51997i	0.125438	−	0.0933964i
$729$	−6.81206	+	7.86154i	−0.252299	+	0.291168i
$730$	5.75310	+	14.2962i	0.212932	+	0.529125i
$731$	3.34011	−	11.3754i	0.123539	−	0.420734i
$732$	35.7336	−	49.9980i	1.32075	−	1.84798i
$733$	−4.83473	−	33.6263i	−0.178575	−	1.24202i	−0.860063	−	0.510187i	$-0.829576\pi$
$733$	−4.83473	−	33.6263i	−0.178575	−	1.24202i	0.681488	−	0.731829i	$-0.261333\pi$
$734$	−46.5796	−	14.9342i	−1.71928	−	0.551230i
$735$	36.7356	−	22.5256i	1.35501	−	0.830869i
$736$	−26.9036	−	3.49228i	−0.991680	−	0.128727i
$737$		−	0.870703i		−	0.0320728i
$738$	30.1800	−	94.1312i	1.11094	−	3.46502i
$739$	15.7100	−	2.25876i	0.577903	−	0.0830899i	0.152835	−	0.988252i	$-0.451160\pi$
$739$	15.7100	−	2.25876i	0.577903	−	0.0830899i	0.425067	+	0.905162i	$0.360250\pi$
$740$	−40.4895	−	2.85797i	−1.48843	−	0.105061i
$741$	−6.61883	+	22.5417i	−0.243149	+	0.828089i
$742$	−2.63095	+	15.5636i	−0.0965853	+	0.571357i
$743$	−18.4774	−	16.0107i	−0.677869	−	0.587377i	0.246377	−	0.969174i	$-0.420760\pi$
$743$	−18.4774	−	16.0107i	−0.677869	−	0.587377i	−0.924246	+	0.381797i	$0.875305\pi$
$744$	41.7718	+	56.1028i	1.53143	+	2.05683i
$745$	6.56968	+	5.94043i	0.240695	+	0.217641i
$746$	−29.4389	+	43.4151i	−1.07783	+	1.58954i
$747$	−1.95905	−	3.04834i	−0.0716778	−	0.111533i
$748$	0.265927	−	0.513647i	0.00972324	−	0.0187808i
$749$	−7.35176	−	8.48439i	−0.268628	−	0.310013i
$750$	−40.4227	+	29.2201i	−1.47603	+	1.06697i
$751$	5.56873	−	38.7314i	0.203206	−	1.41333i	−0.591487	−	0.806315i	$-0.701459\pi$
$751$	5.56873	−	38.7314i	0.203206	−	1.41333i	0.794692	−	0.607012i	$-0.207632\pi$
$752$	−1.59660	−	4.66511i	−0.0582221	−	0.170119i
$753$	−39.5751	+	86.6574i	−1.44220	+	3.15797i
$754$	9.84960	+	0.242968i	0.358701	+	0.00884836i
$755$	−18.0737	+	26.8573i	−0.657770	+	0.977439i
$756$	−18.5215	+	14.5138i	−0.673622	+	0.527863i
$757$	15.1805	+	9.75592i	0.551745	+	0.354585i	0.786617	−	0.617441i	$-0.211831\pi$
$757$	15.1805	+	9.75592i	0.551745	+	0.354585i	−0.234872	+	0.972026i	$0.575467\pi$
$758$	−6.57791	−	24.6341i	−0.238921	−	0.894751i
$759$	−1.86054	−	2.93213i	−0.0675334	−	0.106430i
$760$	−28.9622	−	7.02406i	−1.05057	−	0.254789i
$761$	−28.5344	−	18.3380i	−1.03437	−	0.664751i	−0.0907839	−	0.995871i	$-0.528937\pi$
$761$	−28.5344	−	18.3380i	−1.03437	−	0.664751i	−0.943589	+	0.331120i	$0.892574\pi$
$762$	−71.5818	+	30.5800i	−2.59313	+	1.10780i
$763$	−6.38769	−	13.9871i	−0.231250	−	0.506367i
$764$	27.8407	−	6.70322i	1.00724	−	0.242514i
$765$	2.37661	+	19.4389i	0.0859267	+	0.702816i
$766$	−20.3062	+	41.7104i	−0.733691	+	1.50706i
$767$	−0.745041	+	5.18188i	−0.0269019	+	0.187107i
$768$	36.2877	+	35.0816i	1.30942	+	1.26590i
$769$	−4.36070	+	3.77857i	−0.157251	+	0.136259i	−0.729933	−	0.683519i	$-0.760449\pi$
$769$	−4.36070	+	3.77857i	−0.157251	+	0.136259i	0.572682	+	0.819778i	$0.305903\pi$
$770$	−0.128459	+	0.673005i	−0.00462935	+	0.0242534i
$771$	−21.2322	−	33.0379i	−0.764659	−	1.18983i
$772$	−10.7357	+	30.8464i	−0.386386	+	1.11019i
$773$	−6.18765	+	1.81686i	−0.222554	+	0.0653478i	−0.391109	−	0.920345i	$-0.627908\pi$
$773$	−6.18765	+	1.81686i	−0.222554	+	0.0653478i	0.168554	+	0.985692i	$0.446090\pi$
$774$	10.9026	+	91.8578i	0.391885	+	3.30176i
$775$	−36.3109	+	14.7611i	−1.30433	+	0.530233i
$776$	−30.5947	+	11.3211i	−1.09828	+	0.406404i
$777$	7.61409	−	25.9312i	0.273154	−	0.930277i
$778$	18.0321	+	21.8778i	0.646482	+	0.784357i
$779$	6.74322	+	46.9001i	0.241601	+	1.68037i
$780$	10.7040	+	19.5597i	0.383266	+	0.700348i
$781$		−	2.03583i		−	0.0728478i
$782$	−5.39686	−	6.62538i	−0.192991	−	0.236923i
$783$	−54.9432			−1.96351
$784$	21.7581	−	11.1222i	0.777077	−	0.397222i
$785$	−17.9779	−	21.6562i	−0.641658	−	0.772944i
$786$	−48.7841	−	59.1882i	−1.74007	−	2.11117i
$787$	−1.66549	+	5.67215i	−0.0593684	+	0.202190i	−0.983836	−	0.179069i	$-0.942691\pi$
$787$	−1.66549	+	5.67215i	−0.0593684	+	0.202190i	0.924468	+	0.381260i	$0.124510\pi$
$788$	35.8178	−	3.35783i	1.27596	−	0.119618i
$789$	−0.0192155	−	0.0166503i	−0.000684088	−	0.000592766i
$790$	3.96114	−	3.12659i	0.140931	−	0.111239i
$791$	−2.40763	−	8.19962i	−0.0856053	−	0.291545i
$792$	−0.333601	+	4.50060i	−0.0118540	+	0.159922i
$793$	12.9511	−	8.32318i	0.459908	−	0.295565i
$794$	6.59760	−	7.24503i	0.234140	−	0.257117i
$795$	−79.5134	−	25.1850i	−2.82005	−	0.893220i
$796$	−1.62322	+	1.69651i	−0.0575335	+	0.0601313i
$797$	−2.78223	+	19.3508i	−0.0985516	+	0.685441i	0.879319	+	0.476233i	$0.157998\pi$
$797$	−2.78223	+	19.3508i	−0.0985516	+	0.685441i	−0.977871	+	0.209209i	$0.932911\pi$
$798$	8.68557	−	17.8408i	0.307466	−	0.631558i
$799$	0.645183	−	1.41275i	0.0228249	−	0.0499797i
$800$	−24.1367	+	14.7452i	−0.853360	+	0.521321i
$801$	37.3424	−	17.0537i	1.31943	−	0.602562i
$802$	−4.84750	−	11.3470i	−0.171171	−	0.400678i
$803$	−0.604748	+	0.941006i	−0.0213411	+	0.0332074i
$804$	11.9304	+	20.7466i	0.420752	+	0.731677i
$805$	8.36516	+	5.69977i	0.294833	+	0.200891i
$806$	4.52045	+	16.9289i	0.159226	+	0.596297i
$807$	−12.4039	−	7.97152i	−0.436639	−	0.280611i
$808$	−10.1315	+	13.4613i	−0.356424	+	0.473567i
$809$	4.04395	+	8.85501i	0.142178	+	0.311326i	0.967303	−	0.253624i	$-0.0816227\pi$
$809$	4.04395	+	8.85501i	0.142178	+	0.311326i	−0.825125	+	0.564950i	$0.808895\pi$
$810$	−29.2880	−	50.5187i	−1.02907	−	1.77505i
$811$	−7.26762	−	3.31901i	−0.255200	−	0.116546i	0.283707	−	0.958911i	$-0.408436\pi$
$811$	−7.26762	−	3.31901i	−0.255200	−	0.116546i	−0.538908	+	0.842365i	$0.681163\pi$
$812$	−8.16851	−	1.58898i	−0.286658	−	0.0557621i
$813$	−68.3313	−	9.82456i	−2.39648	−	0.344562i
$814$	−1.53128	−	2.51711i	−0.0536713	−	0.0882245i
$815$	30.6007	+	9.69245i	1.07190	+	0.339512i
$816$	0.701652	+	15.8826i	0.0245627	+	0.556003i
$817$	−23.9717	−	37.3007i	−0.838663	−	1.30498i
$818$	18.2285	−	26.8826i	0.637345	−	0.939929i
$819$	−9.95021	+	2.92165i	−0.347688	+	0.102091i
$820$	36.0251	+	26.9157i	1.25805	+	0.939939i
$821$	6.74438	−	7.78343i	0.235380	−	0.271644i	−0.625754	−	0.780020i	$-0.715209\pi$
$821$	6.74438	−	7.78343i	0.235380	−	0.271644i	0.861135	+	0.508377i	$0.169754\pi$
$822$	−14.1042	−	2.38426i	−0.491941	−	0.0831605i
$823$	−34.4591	−	10.1181i	−1.20117	−	0.352695i	−0.380869	−	0.924629i	$-0.624375\pi$
$823$	−34.4591	−	10.1181i	−1.20117	−	0.352695i	−0.820299	+	0.571934i	$0.806193\pi$
$824$	−0.611572	−	0.229909i	−0.0213051	−	0.00800927i
$825$	−3.42757	−	1.16593i	−0.119333	−	0.0405926i
$826$	1.34998	−	4.21056i	0.0469717	−	0.146504i
$827$			13.8307i			0.480942i	0.970656	+	0.240471i	$0.0773019\pi$
$827$			13.8307i			0.480942i	−0.970656	+	0.240471i	$0.922698\pi$
$828$	59.0314	+	30.9952i	2.05148	+	1.07716i
$829$	10.9290			0.379579			0.189789	−	0.981825i	$-0.439219\pi$
$829$	10.9290			0.379579			0.189789	+	0.981825i	$0.439219\pi$
$830$	1.60128	−	0.391509i	0.0555811	−	0.0135895i
$831$	−3.59839	+	0.517371i	−0.124827	+	0.0179474i
$832$	5.19288	+	11.5284i	0.180031	+	0.399675i
$833$	7.38516	+	2.16848i	0.255881	+	0.0751334i
$834$	10.4741	−	61.9601i	0.362688	−	2.14550i
$835$	−1.33239	+	8.05422i	−0.0461092	+	0.278728i
$836$	−0.800513	−	2.00963i	−0.0276863	−	0.0695044i
$837$	−27.5287	−	93.7543i	−0.951533	−	3.24062i
$838$	−26.8832	+	39.6462i	−0.928666	+	1.36956i
$839$	−8.62816	+	5.54498i	−0.297877	+	0.191434i	−0.681039	−	0.732247i	$-0.738472\pi$
$839$	−8.62816	+	5.54498i	−0.297877	+	0.191434i	0.383162	+	0.923681i	$0.374835\pi$
$840$	−6.16067	−	17.7961i	−0.212563	−	0.614025i
$841$	6.26665	+	7.23210i	0.216091	+	0.249383i
$842$	12.5073	−	7.60882i	0.431031	−	0.262217i
$843$	−11.6499	−	1.67500i	−0.401244	−	0.0576902i
$844$	4.27739	+	0.832058i	0.147234	+	0.0286406i
$845$	−2.84986	−	23.3097i	−0.0980380	−	0.801878i
$846$	−0.298833	+	12.1143i	−0.0102741	+	0.416498i
$847$	9.39958	−	4.29265i	0.322973	−	0.147497i
$848$	−43.8484	−	17.7301i	−1.50576	−	0.608854i
$849$	−18.9783	+	29.5309i	−0.651335	+	1.01350i
$850$	−8.71381	−	1.85499i	−0.298881	−	0.0636256i
$851$	−43.1202	+	5.94594i	−1.47814	+	0.203824i
$852$	27.8950	+	48.5086i	0.955666	+	1.66188i
$853$	−14.1963	+	22.0898i	−0.486071	+	0.756342i	−0.994497	−	0.104764i	$-0.966591\pi$
$853$	−14.1963	+	22.0898i	−0.486071	+	0.756342i	0.508426	+	0.861106i	$0.330228\pi$
$854$	−11.9574	+	5.10825i	−0.409174	+	0.174801i
$855$	60.7641	+	40.8914i	2.07809	+	1.39845i
$856$	29.5665	−	16.0453i	1.01056	−	0.548418i
$857$	−3.38355	−	1.54521i	−0.115580	−	0.0527835i	0.356786	−	0.934186i	$-0.383873\pi$
$857$	−3.38355	−	1.54521i	−0.115580	−	0.0527835i	−0.472366	+	0.881403i	$0.656600\pi$
$858$	−0.708430	+	1.45517i	−0.0241854	+	0.0496787i
$859$	−28.4225	−	4.08655i	−0.969765	−	0.139431i	−0.360813	−	0.932638i	$-0.617501\pi$
$859$	−28.4225	−	4.08655i	−0.969765	−	0.139431i	−0.608952	+	0.793207i	$0.708410\pi$
$860$	−41.1282	−	8.90677i	−1.40246	−	0.303718i
$861$	−22.6285	+	19.6077i	−0.771177	+	0.668229i
$862$	−11.2717	−	10.2644i	−0.383915	−	0.349607i
$863$	−25.0022	+	16.0679i	−0.851084	+	0.546958i	−0.891913	−	0.452208i	$-0.850637\pi$
$863$	−25.0022	+	16.0679i	−0.851084	+	0.546958i	0.0408287	+	0.999166i	$0.487000\pi$
$864$	−30.5348	−	63.5546i	−1.03881	−	2.16217i
$865$	8.74688	+	7.90909i	0.297403	+	0.268917i
$866$	45.1895	−	5.36352i	1.53560	−	0.182260i
$867$	31.8392	−	36.7444i	1.08132	−	1.24791i
$868$	−1.38134	−	14.7348i	−0.0468859	−	0.500130i
$869$	0.351461	+	0.103198i	0.0119225	+	0.00350076i
$870$	14.3074	−	41.5798i	0.485067	−	1.40969i
$871$	0.853218	+	5.93426i	0.0289102	+	0.201075i
$872$	45.0479	−	9.67751i	1.52551	−	0.327722i
$873$	80.1731			2.71345
$874$	−31.9441	−	0.972501i	−1.08052	−	0.0328953i
$875$	10.5201	−	0.836750i	0.355645	−	0.0282873i
$876$	1.51592	−	30.7080i	0.0512182	−	1.03753i
$877$	1.78638	−	0.256843i	0.0603218	−	0.00867296i	−0.112088	−	0.993698i	$-0.535754\pi$
$877$	1.78638	−	0.256843i	0.0603218	−	0.00867296i	0.172410	+	0.985025i	$0.444845\pi$
$878$	28.1707	+	34.1787i	0.950716	+	1.15347i
$879$	−56.8207	−	16.6841i	−1.91651	−	0.562739i
$880$	−1.88664	−	0.809680i	−0.0635986	−	0.0272943i
$881$	44.5428	+	38.5966i	1.50069	+	1.30035i	0.828533	+	0.559941i	$0.189176\pi$
$881$	44.5428	+	38.5966i	1.50069	+	1.30035i	0.672154	+	0.740412i	$0.265369\pi$
$882$	−59.6363	+	7.07821i	−2.00806	+	0.238336i
$883$	42.9498	−	12.6112i	1.44538	−	0.424401i	0.537367	−	0.843349i	$-0.319419\pi$
$883$	42.9498	−	12.6112i	1.44538	−	0.424401i	0.908010	+	0.418948i	$0.137601\pi$
$884$	−1.30908	+	3.76134i	−0.0440293	+	0.126508i
$885$	21.0433	+	10.1532i	0.707364	+	0.341296i
$886$	−18.7781	−	17.1001i	−0.630863	−	0.574487i
$887$	33.4427	+	38.5949i	1.12289	+	1.29589i	0.950453	+	0.310870i	$0.100620\pi$
$887$	33.4427	+	38.5949i	1.12289	+	1.29589i	0.172442	+	0.985020i	$0.444834\pi$
$888$	70.9759	+	38.9946i	2.38179	+	1.30857i
$889$	16.3021	+	2.34388i	0.546753	+	0.0786113i
$890$	1.80858	+	18.5878i	0.0606237	+	0.623064i
$891$	1.76079	−	3.85560i	0.0589887	−	0.129167i
$892$	29.9663	−	7.21501i	1.00335	−	0.241576i
$893$	−2.41295	−	5.28363i	−0.0807463	−	0.176810i
$894$	−6.94221	−	16.2503i	−0.232182	−	0.543493i
$895$	0.833620	−	39.4220i	0.0278649	−	1.31773i
$896$	−2.70164	−	10.3319i	−0.0902554	−	0.345163i
$897$	15.5537	+	18.1607i	0.519324	+	0.606368i
$898$	−2.26556	−	8.48446i	−0.0756027	−	0.283130i
$899$	18.6823	−	29.0702i	0.623088	−	0.969544i
$900$	68.2085	−	13.4001i	2.27362	−	0.446672i
$901$	−6.18880	−	13.5516i	−0.206179	−	0.451469i
$902$	−0.0804953	+	3.26318i	−0.00268020	+	0.108652i
$903$	11.6395	−	25.4869i	0.387337	−	0.848150i
$904$	25.5466	−	1.76068i	0.849666	−	0.0585592i
$905$	18.9755	−	8.18553i	0.630768	−	0.272096i
$906$	55.1785	−	33.5678i	1.83318	−	1.11522i
$907$	−29.6809	+	25.7186i	−0.985537	+	0.853973i	−0.989282	−	0.146020i	$-0.953354\pi$
$907$	−29.6809	+	25.7186i	−0.985537	+	0.853973i	0.00374442	+	0.999993i	$0.498808\pi$
$908$	−20.3282	−	10.5244i	−0.674615	−	0.349263i
$909$	34.8330	−	22.3858i	1.15534	−	0.742491i
$910$	0.216021	−	4.71273i	0.00716102	−	0.156226i
$911$	−33.2270	+	9.75631i	−1.10086	+	0.323241i	−0.781193	−	0.624289i	$-0.785389\pi$
$911$	−33.2270	+	9.75631i	−1.10086	+	0.323241i	−0.319665	+	0.947531i	$0.603570\pi$
$912$	46.6101	+	36.9157i	1.54342	+	1.22240i
$913$	0.0904285	+	0.0783567i	0.00299275	+	0.00259323i
$914$	−53.6407	−	9.06772i	−1.77428	−	0.299934i
$915$	−17.9594	−	66.3199i	−0.593718	−	2.19247i
$916$	−2.99351	+	4.18848i	−0.0989084	+	0.138391i
$917$	2.30960	+	16.0636i	0.0762696	+	0.530467i
$918$	6.78066	−	21.1488i	0.223795	−	0.698015i
$919$	−2.49391			−0.0822664			−0.0411332	−	0.999154i	$-0.513097\pi$
$919$	−2.49391			−0.0822664			−0.0411332	+	0.999154i	$0.513097\pi$
$920$	−22.0710	+	20.8056i	−0.727658	+	0.685940i
$921$	−27.2510			−0.897951
$922$	10.7844	−	33.6363i	0.355164	−	1.10775i
$923$	1.99495	+	13.8752i	0.0656645	+	0.456707i
$924$	0.794838	−	1.11213i	0.0261482	−	0.0365863i
$925$	−31.1417	+	33.0100i	−1.02393	+	1.08536i
$926$	56.3787	+	9.53058i	1.85272	+	0.313194i
$927$	1.21352	+	1.05152i	0.0398572	+	0.0345365i
$928$	9.91465	−	22.8796i	0.325464	−	0.751061i
$929$	−11.7613	+	3.45342i	−0.385875	+	0.113303i	−0.468915	−	0.883243i	$-0.655355\pi$
$929$	−11.7613	+	3.45342i	−0.385875	+	0.113303i	0.0830405	+	0.996546i	$0.473537\pi$
$930$	78.1197	+	3.58083i	2.56165	+	0.117420i
$931$	24.2165	−	15.5630i	0.793663	−	0.510056i
$932$	−47.9514	−	24.8255i	−1.57070	−	0.813187i
$933$	−11.0757	+	9.59718i	−0.362603	+	0.314198i
$934$	21.9633	−	13.3613i	0.718660	−	0.437196i
$935$	−0.256142	−	0.593784i	−0.00837675	−	0.0194188i
$936$	−2.13657	−	31.0007i	−0.0698361	−	1.01329i
$937$	1.40109	−	3.06796i	0.0457716	−	0.100226i	−0.885365	−	0.464897i	$-0.846091\pi$
$937$	1.40109	−	3.06796i	0.0457716	−	0.100226i	0.931136	+	0.364671i	$0.118819\pi$
$938$	0.124872	−	5.06215i	0.00407721	−	0.165285i
$939$	−36.7633	−	80.5003i	−1.19972	−	2.62703i
$940$	−5.16697	−	1.92170i	−0.168528	−	0.0626789i
$941$	2.62244	−	4.08060i	0.0854891	−	0.133024i	−0.795876	−	0.605460i	$-0.792989\pi$
$941$	2.62244	−	4.08060i	0.0854891	−	0.133024i	0.881365	+	0.472437i	$0.156625\pi$
$942$	14.4871	+	54.2536i	0.472014	+	1.76768i
$943$	43.7502	+	20.2860i	1.42470	+	0.660605i
$944$	11.4514	+	6.66427i	0.372712	+	0.216904i
$945$	−0.556191	+	26.3024i	−0.0180929	+	0.855616i
$946$	−1.20000	−	2.80895i	−0.0390152	−	0.0913269i
$947$	−9.22284	−	20.1952i	−0.299702	−	0.656256i	0.698537	−	0.715574i	$-0.253835\pi$
$947$	−9.22284	−	20.1952i	−0.299702	−	0.656256i	−0.998239	+	0.0593179i	$0.981107\pi$
$948$	−9.78844	+	2.35677i	−0.317914	+	0.0765444i
$949$	3.19954	−	7.00601i	0.103861	−	0.227425i
$950$	−26.5844	+	20.0861i	−0.862513	+	0.651680i
$951$	49.8108	+	7.16171i	1.61522	+	0.232234i
$952$	1.61972	−	2.94814i	0.0524956	−	0.0955496i
$953$	−29.9683	−	34.5852i	−0.970767	−	1.12032i	−0.992705	−	0.120566i	$-0.961529\pi$
$953$	−29.9683	−	34.5852i	−0.970767	−	1.12032i	0.0219382	−	0.999759i	$-0.493016\pi$
$954$	85.9442	+	78.2640i	2.78255	+	2.53389i
$955$	13.9128	−	28.8354i	0.450207	−	0.933091i
$956$	−1.03507	+	2.97402i	−0.0334765	+	0.0961867i
$957$	3.06250	−	0.899232i	0.0989967	−	0.0290680i
$958$	6.16654	−	0.731904i	0.199232	−	0.0236468i
$959$	2.28732	+	1.98197i	0.0738614	+	0.0640013i
$960$	56.0481	−	6.55816i	1.80894	−	0.211664i
$961$	29.2211	+	8.58010i	0.942618	+	0.276778i
$962$	12.9030	+	15.6548i	0.416008	+	0.504729i
$963$	−81.8326	+	11.7657i	−2.63702	+	0.379146i
$964$	0.514099	−	10.4141i	0.0165580	−	0.335417i
$965$	19.0884	+	31.1300i	0.614476	+	1.00211i
$966$	−10.3964	−	17.3138i	−0.334499	−	0.557064i
$967$	−0.737688			−0.0237224			−0.0118612	−	0.999930i	$-0.503776\pi$
$967$	−0.737688			−0.0237224			−0.0118612	+	0.999930i	$0.503776\pi$
$968$	6.50346	+	30.2730i	0.209029	+	0.973011i
$969$	2.66532	+	18.5377i	0.0856223	+	0.595516i
$970$	−11.8672	+	34.4880i	−0.381032	+	1.10734i
$971$	11.1596	+	3.27674i	0.358128	+	0.105156i	0.455847	−	0.890058i	$-0.349337\pi$
$971$	11.1596	+	3.27674i	0.358128	+	0.105156i	−0.0977192	+	0.995214i	$0.531155\pi$
$972$	3.89384	+	41.5354i	0.124895	+	1.33225i
$973$	−8.70685	+	10.0482i	−0.279129	+	0.322132i
$974$	39.8198	−	4.72620i	1.27591	−	0.151437i
$975$	24.5030	+	4.58766i	0.784725	+	0.146923i
$976$	−7.24163	−	38.2837i	−0.231799	−	1.22543i
$977$	−17.6039	+	11.3133i	−0.563198	+	0.361945i	−0.791051	−	0.611750i	$-0.790466\pi$
$977$	−17.6039	+	11.3133i	−0.563198	+	0.361945i	0.227853	+	0.973695i	$0.426829\pi$
$978$	−47.3503	−	43.1189i	−1.51410	−	1.37879i
$979$	−1.02448	+	0.887721i	−0.0327427	+	0.0283717i
$980$	5.78249	−	26.7014i	0.184715	−	0.852944i
$981$	−112.084	−	16.1153i	−3.57858	−	0.514522i
$982$	−14.6532	+	30.0988i	−0.467602	+	0.960491i
$983$	−11.2543	−	5.13965i	−0.358955	−	0.163929i	0.227771	−	0.973715i	$-0.426856\pi$
$983$	−11.2543	−	5.13965i	−0.358955	−	0.163929i	−0.586726	+	0.809785i	$0.699584\pi$
$984$	−42.7941	−	78.8561i	−1.36423	−	2.51384i
$985$	22.4557	−	33.3689i	0.715497	−	1.06322i
$986$	7.22277	−	3.08560i	0.230020	−	0.0982655i
$987$	1.98443	−	3.08784i	0.0631652	−	0.0982869i
$988$	7.42515	+	12.9121i	0.236225	+	0.410790i
$989$	−45.1267	−	0.260460i	−1.43495	−	0.00828215i
$990$	3.65794	+	3.47533i	0.116257	+	0.110453i
$991$	−19.3883	+	30.1687i	−0.615888	+	0.958341i	0.383506	+	0.923538i	$0.374717\pi$
$991$	−19.3883	+	30.1687i	−0.615888	+	0.958341i	−0.999394	+	0.0348024i	$0.988920\pi$
$992$	44.0091	+	5.45460i	1.39729	+	0.173184i
$993$	42.7578	−	19.5268i	1.35688	−	0.619665i
$994$	0.291968	−	11.8360i	0.00926068	−	0.375416i
$995$	0.318576	+	2.60572i	0.0100996	+	0.0826068i
$996$	−3.22832	−	0.627988i	−0.102293	−	0.0198986i
$997$	−7.98231	−	1.14768i	−0.252802	−	0.0363475i	0.0147485	−	0.999891i	$-0.495305\pi$
$997$	−7.98231	−	1.14768i	−0.252802	−	0.0363475i	−0.267551	+	0.963544i	$0.586214\pi$
$998$	40.3317	−	24.5358i	1.27668	−	0.776666i
$999$	−74.0845	−	85.4981i	−2.34393	−	2.70504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.159.26	yes	640
4.3	odd	2	inner	460.2.o.b.159.13	✓	640
5.4	even	2	inner	460.2.o.b.159.39	yes	640
20.19	odd	2	inner	460.2.o.b.159.52	yes	640
23.11	odd	22	inner	460.2.o.b.379.52	yes	640
92.11	even	22	inner	460.2.o.b.379.39	yes	640
115.34	odd	22	inner	460.2.o.b.379.13	yes	640
460.379	even	22	inner	460.2.o.b.379.26	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.159.13	✓	640	4.3	odd	2	inner
460.2.o.b.159.26	yes	640	1.1	even	1	trivial
460.2.o.b.159.39	yes	640	5.4	even	2	inner
460.2.o.b.159.52	yes	640	20.19	odd	2	inner
460.2.o.b.379.13	yes	640	115.34	odd	22	inner
460.2.o.b.379.26	yes	640	460.379	even	22	inner
460.2.o.b.379.39	yes	640	92.11	even	22	inner
460.2.o.b.379.52	yes	640	23.11	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.431771 + 1.34669i) q^{2} +(-0.448940 - 3.12245i) q^{3} +(-1.62715 - 1.16292i) q^{4} +(-2.15833 + 0.584474i) q^{5} +(4.39881 + 0.743600i) q^{6} +(-0.713367 - 0.618136i) q^{7} +(2.26865 - 1.68915i) q^{8} +(-6.66966 + 1.95839i) q^{9} +O(q^{10})\)	\(q+(-0.431771 + 1.34669i) q^{2} +(-0.448940 - 3.12245i) q^{3} +(-1.62715 - 1.16292i) q^{4} +(-2.15833 + 0.584474i) q^{5} +(4.39881 + 0.743600i) q^{6} +(-0.713367 - 0.618136i) q^{7} +(2.26865 - 1.68915i) q^{8} +(-6.66966 + 1.95839i) q^{9} +(0.144800 - 3.15896i) q^{10} +(0.193099 - 0.124097i) q^{11} +(-2.90068 + 5.60277i) q^{12} +(-1.19446 + 1.03500i) q^{13} +(1.14045 - 0.693791i) q^{14} +(2.79395 + 6.47688i) q^{15} +(1.29522 + 3.78450i) q^{16} +(-0.523395 + 1.14607i) q^{17} +(0.242423 - 9.82754i) q^{18} +(1.95747 + 4.28626i) q^{19} +(4.19162 + 1.55895i) q^{20} +(-1.60984 + 2.50496i) q^{21} +(0.0837460 + 0.313626i) q^{22} +(4.74300 + 0.709905i) q^{23} +(-6.29276 - 6.32543i) q^{24} +(4.31678 - 2.52298i) q^{25} +(-0.878097 - 2.05545i) q^{26} +(5.17790 + 11.3380i) q^{27} +(0.441909 + 1.83539i) q^{28} +(-1.83115 + 4.00967i) q^{29} +(-9.92870 + 0.966056i) q^{30} +(-7.75952 - 1.11565i) q^{31} +(-5.65578 + 0.110222i) q^{32} +(-0.474178 - 0.547230i) q^{33} +(-1.31742 - 1.19969i) q^{34} +(1.90097 + 0.917198i) q^{35} +(13.1300 + 4.56972i) q^{36} +(-8.70861 + 2.55708i) q^{37} +(-6.61744 + 0.785421i) q^{38} +(3.76799 + 3.26498i) q^{39} +(-3.90924 + 4.97170i) q^{40} +(9.64819 + 2.83296i) q^{41} +(-2.67832 - 3.24952i) q^{42} +(-9.31394 + 1.33914i) q^{43} +(-0.458517 - 0.0226349i) q^{44} +(13.2507 - 8.12509i) q^{45} +(-3.00391 + 6.08083i) q^{46} -1.23269 q^{47} +(11.2354 - 5.74327i) q^{48} +(-0.869403 - 6.04683i) q^{49} +(1.53380 + 6.90271i) q^{50} +(3.81353 + 1.11975i) q^{51} +(3.14719 - 0.295041i) q^{52} +(-7.74330 + 8.93624i) q^{53} +(-17.5045 + 2.07760i) q^{54} +(-0.344240 + 0.380704i) q^{55} +(-2.66251 - 0.197354i) q^{56} +(12.5048 - 8.03637i) q^{57} +(-4.60914 - 4.19725i) q^{58} +(2.50331 - 2.16913i) q^{59} +(2.98595 - 13.7880i) q^{60} +(-9.64149 - 1.38624i) q^{61} +(4.85277 - 9.96796i) q^{62} +(5.96847 + 2.72571i) q^{63} +(2.29357 - 7.66417i) q^{64} +(1.97310 - 2.93201i) q^{65} +(0.941685 - 0.402292i) q^{66} +(2.05081 - 3.19112i) q^{67} +(2.18444 - 1.25616i) q^{68} +(0.0873179 - 15.1285i) q^{69} +(-2.05596 + 2.16399i) q^{70} +(4.79509 - 7.46131i) q^{71} +(-11.8231 + 15.7089i) q^{72} +(-4.43280 + 2.02439i) q^{73} +(0.316534 - 12.8319i) q^{74} +(-9.81584 - 12.3463i) q^{75} +(1.79950 - 9.25076i) q^{76} +(-0.214460 - 0.0308347i) q^{77} +(-6.02382 + 3.66459i) q^{78} +(1.04504 + 1.20603i) q^{79} +(-5.00745 - 7.41117i) q^{80} +(15.5346 - 9.98346i) q^{81} +(-7.98094 + 11.7699i) q^{82} +(0.146862 + 0.500168i) q^{83} +(5.53252 - 2.20382i) q^{84} +(0.459808 - 2.77952i) q^{85} +(2.21808 - 13.1212i) q^{86} +(13.3421 + 3.91758i) q^{87} +(0.228456 - 0.607707i) q^{88} +(-5.84562 + 0.840474i) q^{89} +(5.22071 + 21.3528i) q^{90} +1.49186 q^{91} +(-6.89199 - 6.67086i) q^{92} +24.7296i q^{93} +(0.532240 - 1.66005i) q^{94} +(-6.73007 - 8.10707i) q^{95} +(2.88327 + 17.6104i) q^{96} +(-11.0665 - 3.24940i) q^{97} +(8.51859 + 1.44003i) q^{98} +(-1.04488 + 1.20585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more