LMFDB - Embedded newform 961.2.k.a.5.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(5,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(186)) chi = DirichletCharacter(H, H._module([88])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.k (of order $93$, degree $60$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4920$
Relative dimension:	$82$ over $\Q(\zeta_{93})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{93}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	961.5
Dual form			961.2.k.a.769.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41888 - 1.21807i) q^{2} +(0.0200290 + 0.236602i) q^{3} +(0.226677 + 1.47967i) q^{4} +(-2.57781 - 1.54693i) q^{5} +(0.259779 - 0.360107i) q^{6} +(2.63507 + 3.92569i) q^{7} +(-0.497621 + 0.798359i) q^{8} +(2.90173 - 0.494825i) q^{9} +(1.77334 + 5.33488i) q^{10} +(-1.12437 + 0.727476i) q^{11} +(-0.345552 + 0.0832683i) q^{12} +(-2.80913 + 3.38633i) q^{13} +(1.04292 - 8.77980i) q^{14} +(0.314376 - 0.640898i) q^{15} +(4.53508 - 1.42289i) q^{16} +(3.91973 - 0.532890i) q^{17} +(-4.71995 - 2.83242i) q^{18} +(-5.96077 - 5.86093i) q^{19} +(1.70461 - 4.16496i) q^{20} +(-0.876047 + 0.702089i) q^{21} +(2.48147 + 0.337357i) q^{22} +(-6.73036 - 3.73565i) q^{23} +(-0.198860 - 0.101748i) q^{24} +(1.89979 + 3.56331i) q^{25} +(8.11063 - 1.38309i) q^{26} +(0.353746 + 1.36625i) q^{27} +(-5.21141 + 4.78889i) q^{28} +(-6.12350 - 3.39882i) q^{29} +(-1.22672 + 0.526428i) q^{30} +(0.550583 - 5.54047i) q^{31} +(-6.43893 - 2.76316i) q^{32} +(-0.194642 - 0.251457i) q^{33} +(-6.21074 - 4.01841i) q^{34} +(-0.719938 - 14.1960i) q^{35} +(1.38993 + 4.18143i) q^{36} +(4.53433 + 0.773229i) q^{37} +(1.31860 + 15.5766i) q^{38} +(-0.857476 - 0.596821i) q^{39} +(2.51778 - 1.28823i) q^{40} +(-2.95134 - 0.0997360i) q^{41} +(2.09820 + 0.0709055i) q^{42} +(-1.81165 + 5.45010i) q^{43} +(-1.33129 - 1.49879i) q^{44} +(-8.24558 - 3.21321i) q^{45} +(4.99930 + 13.4985i) q^{46} +(4.73744 + 2.62949i) q^{47} +(0.427492 + 1.04451i) q^{48} +(-5.81601 + 14.2105i) q^{49} +(1.64478 - 7.37000i) q^{50} +(0.204591 + 0.916742i) q^{51} +(-5.64741 - 3.38898i) q^{52} +(-1.14461 - 0.537669i) q^{53} +(1.16226 - 2.36943i) q^{54} +(4.02377 - 0.135977i) q^{55} +(-4.44538 + 0.150224i) q^{56} +(1.26732 - 1.52772i) q^{57} +(4.54853 + 12.2814i) q^{58} +(-8.92487 - 1.52194i) q^{59} +(1.01958 + 0.319895i) q^{60} +(-1.84528 + 1.94124i) q^{61} +(-7.52991 + 7.19064i) q^{62} +(9.58879 + 10.0874i) q^{63} +(1.58392 + 3.22903i) q^{64} +(12.4798 - 4.38379i) q^{65} +(-0.0301180 + 0.593876i) q^{66} +(-2.17845 + 5.32271i) q^{67} +(1.67701 + 5.67911i) q^{68} +(0.749060 - 1.66724i) q^{69} +(-16.2702 + 21.0194i) q^{70} +(3.83036 - 3.76621i) q^{71} +(-1.04891 + 2.56286i) q^{72} +(-12.9591 - 9.68558i) q^{73} +(-5.49184 - 6.62027i) q^{74} +(-0.805033 + 0.520864i) q^{75} +(7.32106 - 10.1485i) q^{76} +(-5.81863 - 2.49697i) q^{77} +(0.489688 + 1.89129i) q^{78} +(0.949571 - 0.709703i) q^{79} +(-13.8917 - 3.34751i) q^{80} +(8.01560 - 2.81564i) q^{81} +(4.06613 + 3.73646i) q^{82} +(1.02617 - 5.45950i) q^{83} +(-1.23744 - 1.13711i) q^{84} +(-10.9287 - 4.68987i) q^{85} +(9.20913 - 5.52635i) q^{86} +(0.681520 - 1.51691i) q^{87} +(-0.0212780 - 1.25966i) q^{88} +(-7.94351 - 16.1940i) q^{89} +(7.78559 + 14.6029i) q^{90} +(-20.6960 - 2.10457i) q^{91} +(4.00191 - 10.8055i) q^{92} +(1.32191 + 0.0192987i) q^{93} +(-3.51897 - 9.50149i) q^{94} +(6.29929 + 24.3293i) q^{95} +(0.524803 - 1.57880i) q^{96} +(0.642176 - 4.19190i) q^{97} +(25.5617 - 13.0787i) q^{98} +(-2.90264 + 2.66730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) $ 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{44}{93}\right)$

Coefficient data

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

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

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

$2$	−1.41888	−	1.21807i	−1.00330	−	0.861307i	−0.0129551	−	0.999916i	$-0.504124\pi$
$2$	−1.41888	−	1.21807i	−1.00330	−	0.861307i	−0.990347	+	0.138609i	$0.955737\pi$
$3$	0.0200290	+	0.236602i	0.0115637	+	0.136602i	0.999874	−	0.0158516i	$-0.00504595\pi$
$3$	0.0200290	+	0.236602i	0.0115637	+	0.136602i	−0.988311	+	0.152454i	$0.951283\pi$
$4$	0.226677	+	1.47967i	0.113338	+	0.739834i
$5$	−2.57781	−	1.54693i	−1.15283	−	0.691809i	−0.195474	−	0.980709i	$-0.562624\pi$
$5$	−2.57781	−	1.54693i	−1.15283	−	0.691809i	−0.957359	+	0.288900i	$0.906710\pi$
$6$	0.259779	−	0.360107i	0.106054	−	0.147013i
$7$	2.63507	+	3.92569i	0.995962	+	1.48377i	0.870801	+	0.491635i	$0.163601\pi$
$7$	2.63507	+	3.92569i	0.995962	+	1.48377i	0.125161	+	0.992136i	$0.460055\pi$
$8$	−0.497621	+	0.798359i	−0.175936	+	0.282263i
$9$	2.90173	−	0.494825i	0.967243	−	0.164942i
$10$	1.77334	+	5.33488i	0.560780	+	1.68704i
$11$	−1.12437	+	0.727476i	−0.339010	+	0.219342i	−0.701541	−	0.712629i	$-0.747504\pi$
$11$	−1.12437	+	0.727476i	−0.339010	+	0.219342i	0.362531	+	0.931972i	$0.381913\pi$
$12$	−0.345552	+	0.0832683i	−0.0997522	+	0.0240375i
$13$	−2.80913	+	3.38633i	−0.779114	+	0.939200i	−0.999343	−	0.0362484i	$-0.988459\pi$
$13$	−2.80913	+	3.38633i	−0.779114	+	0.939200i	0.220229	+	0.975448i	$0.429319\pi$
$14$	1.04292	−	8.77980i	0.278731	−	2.34650i
$15$	0.314376	−	0.640898i	0.0811714	−	0.165479i
$16$	4.53508	−	1.42289i	1.13377	−	0.355723i
$17$	3.91973	−	0.532890i	0.950675	−	0.129245i	0.357138	−	0.934052i	$-0.383753\pi$
$17$	3.91973	−	0.532890i	0.950675	−	0.129245i	0.593537	+	0.804807i	$0.297731\pi$
$18$	−4.71995	−	2.83242i	−1.11250	−	0.667607i
$19$	−5.96077	−	5.86093i	−1.36749	−	1.34459i	−0.882681	−	0.469973i	$-0.844263\pi$
$19$	−5.96077	−	5.86093i	−1.36749	−	1.34459i	−0.484814	−	0.874617i	$-0.661113\pi$
$20$	1.70461	−	4.16496i	0.381163	−	0.931313i
$21$	−0.876047	+	0.702089i	−0.191169	+	0.153208i
$22$	2.48147	+	0.337357i	0.529050	+	0.0719247i
$23$	−6.73036	−	3.73565i	−1.40338	−	0.778938i	−0.412151	−	0.911116i	$-0.635222\pi$
$23$	−6.73036	−	3.73565i	−1.40338	−	0.778938i	−0.991226	+	0.132178i	$0.957803\pi$
$24$	−0.198860	−	0.101748i	−0.0405921	−	0.0207692i
$25$	1.89979	+	3.56331i	0.379959	+	0.712661i
$26$	8.11063	−	1.38309i	1.59063	−	0.271245i
$27$	0.353746	+	1.36625i	0.0680784	+	0.262934i
$28$	−5.21141	+	4.78889i	−0.984863	+	0.905014i
$29$	−6.12350	−	3.39882i	−1.13711	−	0.631145i	−0.199864	−	0.979824i	$-0.564050\pi$
$29$	−6.12350	−	3.39882i	−1.13711	−	0.631145i	−0.937242	+	0.348678i	$0.886631\pi$
$30$	−1.22672	+	0.526428i	−0.223968	+	0.0961122i
$31$	0.550583	−	5.54047i	0.0988876	−	0.995099i
$31$	0.550583	−	5.54047i	0.0988876	−	0.995099i
$32$	−6.43893	−	2.76316i	−1.13825	−	0.488462i
$33$	−0.194642	−	0.251457i	−0.0338828	−	0.0437730i
$34$	−6.21074	−	4.01841i	−1.06513	−	0.689151i
$35$	−0.719938	−	14.1960i	−0.121692	−	2.39956i
$36$	1.38993	+	4.18143i	0.231655	+	0.696905i
$37$	4.53433	+	0.773229i	0.745440	+	0.127118i	0.528342	−	0.849032i	$-0.322814\pi$
$37$	4.53433	+	0.773229i	0.745440	+	0.127118i	0.217098	+	0.976150i	$0.430341\pi$
$38$	1.31860	+	15.5766i	0.213906	+	2.52686i
$39$	−0.857476	−	0.596821i	−0.137306	−	0.0955679i
$40$	2.51778	−	1.28823i	0.398096	−	0.203688i
$41$	−2.95134	−	0.0997360i	−0.460923	−	0.0155761i	−0.197597	−	0.980283i	$-0.563314\pi$
$41$	−2.95134	−	0.0997360i	−0.460923	−	0.0155761i	−0.263325	+	0.964707i	$0.584819\pi$
$42$	2.09820	+	0.0709055i	0.323760	+	0.0109410i
$43$	−1.81165	+	5.45010i	−0.276273	+	0.831133i	0.714978	+	0.699147i	$0.246437\pi$
$43$	−1.81165	+	5.45010i	−0.276273	+	0.831133i	−0.991252	+	0.131986i	$0.957864\pi$
$44$	−1.33129	−	1.49879i	−0.200700	−	0.225951i
$45$	−8.24558	−	3.21321i	−1.22918	−	0.478997i
$46$	4.99930	+	13.4985i	0.737107	+	1.99025i
$47$	4.73744	+	2.62949i	0.691027	+	0.383551i	0.791316	−	0.611407i	$-0.209396\pi$
$47$	4.73744	+	2.62949i	0.691027	+	0.383551i	−0.100289	+	0.994958i	$0.531977\pi$
$48$	0.427492	+	1.04451i	0.0617031	+	0.150762i
$49$	−5.81601	+	14.2105i	−0.830858	+	2.03007i
$50$	1.64478	−	7.37000i	0.232606	−	1.04228i
$51$	0.204591	+	0.916742i	0.0286485	+	0.128370i
$52$	−5.64741	−	3.38898i	−0.783155	−	0.469967i
$53$	−1.14461	−	0.537669i	−0.157225	−	0.0738546i	0.344949	−	0.938621i	$-0.387896\pi$
$53$	−1.14461	−	0.537669i	−0.157225	−	0.0738546i	−0.502174	+	0.864767i	$0.667466\pi$
$54$	1.16226	−	2.36943i	0.158164	−	0.322439i
$55$	4.02377	−	0.135977i	0.542564	−	0.0183351i
$56$	−4.44538	+	0.150224i	−0.594038	+	0.0200746i
$57$	1.26732	−	1.52772i	0.167860	−	0.202351i
$58$	4.54853	+	12.2814i	0.597251	+	1.61263i
$59$	−8.92487	−	1.52194i	−1.16192	−	0.198139i	−0.445154	−	0.895454i	$-0.646851\pi$
$59$	−8.92487	−	1.52194i	−1.16192	−	0.198139i	−0.716765	+	0.697315i	$0.754378\pi$
$60$	1.01958	+	0.319895i	0.131627	+	0.0412982i
$61$	−1.84528	+	1.94124i	−0.236264	+	0.248550i	−0.832191	−	0.554489i	$-0.812914\pi$
$61$	−1.84528	+	1.94124i	−0.236264	+	0.248550i	0.595927	+	0.803039i	$0.296785\pi$
$62$	−7.52991	+	7.19064i	−0.956299	+	0.913212i
$63$	9.58879	+	10.0874i	1.20807	+	1.27089i
$64$	1.58392	+	3.22903i	0.197990	+	0.403629i
$65$	12.4798	−	4.38379i	1.54793	−	0.543743i
$66$	−0.0301180	+	0.593876i	−0.00370727	+	0.0731011i
$67$	−2.17845	+	5.32271i	−0.266140	+	0.650272i	−0.999565	−	0.0294985i	$-0.990609\pi$
$67$	−2.17845	+	5.32271i	−0.266140	+	0.650272i	0.733424	+	0.679771i	$0.237921\pi$
$68$	1.67701	+	5.67911i	0.203368	+	0.688693i
$69$	0.749060	−	1.66724i	0.0901762	−	0.200712i
$70$	−16.2702	+	21.0194i	−1.94466	+	2.51229i
$71$	3.83036	−	3.76621i	0.454581	−	0.446967i	−0.437247	−	0.899341i	$-0.644047\pi$
$71$	3.83036	−	3.76621i	0.454581	−	0.446967i	0.891828	+	0.452374i	$0.149423\pi$
$72$	−1.04891	+	2.56286i	−0.123616	+	0.302036i
$73$	−12.9591	−	9.68558i	−1.51675	−	1.13361i	−0.951064	−	0.308993i	$-0.900008\pi$
$73$	−12.9591	−	9.68558i	−1.51675	−	1.13361i	−0.565689	−	0.824619i	$-0.691390\pi$
$74$	−5.49184	−	6.62027i	−0.638414	−	0.769590i
$75$	−0.805033	+	0.520864i	−0.0929572	+	0.0601441i
$76$	7.32106	−	10.1485i	0.839784	−	1.16411i
$77$	−5.81863	−	2.49697i	−0.663095	−	0.284556i
$78$	0.489688	+	1.89129i	0.0554463	+	0.214146i
$79$	0.949571	−	0.709703i	0.106835	−	0.0798478i	−0.543913	−	0.839142i	$-0.683058\pi$
$79$	0.949571	−	0.709703i	0.106835	−	0.0798478i	0.650748	+	0.759294i	$0.274456\pi$
$80$	−13.8917	−	3.34751i	−1.55314	−	0.374263i
$81$	8.01560	−	2.81564i	0.890622	−	0.312849i
$82$	4.06613	+	3.73646i	0.449029	+	0.412623i
$83$	1.02617	−	5.45950i	0.112637	−	0.599258i	−0.879683	−	0.475561i	$-0.842245\pi$
$83$	1.02617	−	5.45950i	0.112637	−	0.599258i	0.992320	−	0.123697i	$-0.0394752\pi$
$84$	−1.23744	−	1.13711i	−0.135016	−	0.124069i
$85$	−10.9287	−	4.68987i	−1.18538	−	0.508687i
$86$	9.20913	−	5.52635i	0.993046	−	0.595922i
$87$	0.681520	−	1.51691i	0.0730666	−	0.162629i
$88$	−0.0212780	−	1.25966i	−0.00226824	−	0.134280i
$89$	−7.94351	−	16.1940i	−0.842011	−	1.71656i	−0.684467	−	0.729044i	$-0.739965\pi$
$89$	−7.94351	−	16.1940i	−0.842011	−	1.71656i	−0.157544	−	0.987512i	$-0.550358\pi$
$90$	7.78559	+	14.6029i	0.820673	+	1.53928i
$91$	−20.6960	−	2.10457i	−2.16953	−	0.220619i
$92$	4.00191	−	10.8055i	0.417228	−	1.12655i
$93$	1.32191	+	0.0192987i	0.137076	+	0.00200119i
$94$	−3.51897	−	9.50149i	−0.362954	−	0.980004i
$95$	6.29929	+	24.3293i	0.646294	+	2.49613i
$96$	0.524803	−	1.57880i	0.0535625	−	0.161136i
$97$	0.642176	−	4.19190i	0.0652030	−	0.425623i	−0.932686	−	0.360688i	$-0.882542\pi$
$97$	0.642176	−	4.19190i	0.0652030	−	0.425623i	0.997890	−	0.0649348i	$-0.0206839\pi$
$98$	25.5617	−	13.0787i	2.58212	−	1.32115i
$99$	−2.90264	+	2.66730i	−0.291726	+	0.268074i
$100$	−4.84187	+	3.61878i	−0.484187	+	0.361878i
$101$	−3.38403	−	2.90509i	−0.336723	−	0.289067i	0.466773	−	0.884377i	$-0.345416\pi$
$101$	−3.38403	−	2.90509i	−0.336723	−	0.289067i	−0.803496	+	0.595310i	$0.797029\pi$
$102$	0.826367	−	1.54996i	0.0818225	−	0.153469i
$103$	4.98986	+	4.58530i	0.491665	+	0.451803i	0.883636	−	0.468175i	$-0.155088\pi$
$103$	4.98986	+	4.58530i	0.491665	+	0.451803i	−0.391971	+	0.919978i	$0.628207\pi$
$104$	−1.30563	−	3.92781i	−0.128027	−	0.385153i
$105$	3.34437	−	0.454669i	0.326377	−	0.0443712i
$106$	0.969152	+	2.15711i	0.0941323	+	0.209517i
$107$	0.377150	+	0.454644i	0.0364605	+	0.0439521i	0.787568	−	0.616228i	$-0.211340\pi$
$107$	0.377150	+	0.454644i	0.0364605	+	0.0439521i	−0.751107	+	0.660180i	$0.770480\pi$
$108$	−1.94141	+	0.833123i	−0.186812	+	0.0801673i
$109$	−9.72775	+	15.6067i	−0.931749	+	1.49485i	−0.0639409	+	0.997954i	$0.520367\pi$
$109$	−9.72775	+	15.6067i	−0.931749	+	1.49485i	−0.867808	+	0.496899i	$0.834472\pi$
$110$	−5.87488	−	4.70830i	−0.560148	−	0.448919i
$111$	−0.0921291	+	1.08832i	−0.00874451	+	0.103299i
$112$	17.5361	+	14.0539i	1.65700	+	1.32797i
$113$	−9.67869	−	1.31582i	−0.910494	−	0.123782i	−0.335595	−	0.942006i	$-0.608937\pi$
$113$	−9.67869	−	1.31582i	−0.910494	−	0.123782i	−0.574899	+	0.818224i	$0.694959\pi$
$114$	−3.65905	+	0.623968i	−0.342701	+	0.0584400i
$115$	11.5708	+	20.0412i	1.07898	+	1.86885i
$116$	3.64107	−	9.83118i	0.338065	−	0.912802i
$117$	−6.47571	+	11.2163i	−0.598679	+	1.03694i
$118$	10.8095	+	13.0306i	0.995097	+	1.19956i
$119$	12.4207	+	13.9835i	1.13861	+	1.28186i
$120$	0.355227	+	0.569909i	0.0324276	+	0.0520253i
$121$	−3.77304	+	8.39793i	−0.343004	+	0.763448i
$122$	4.98281	−	0.506702i	0.451122	−	0.0458746i
$123$	−0.0355147	−	0.700291i	−0.00320225	−	0.0631431i
$124$	8.32286	−	0.441217i	0.747415	−	0.0396225i
$125$	−0.146465	+	2.88805i	−0.0131003	+	0.258315i
$126$	−1.31820	−	25.9927i	−0.117434	−	2.31561i
$127$	−9.25991	−	13.7953i	−0.821684	−	1.22413i	−0.971880	−	0.235478i	$-0.924334\pi$
$127$	−9.25991	−	13.7953i	−0.821684	−	1.22413i	0.150195	−	0.988656i	$-0.452010\pi$
$128$	−1.82673	+	7.05524i	−0.161461	+	0.623601i
$129$	−1.32579	−	0.319478i	−0.116729	−	0.0281285i
$130$	−23.0472	−	8.98125i	−2.02137	−	0.787708i
$131$	17.1505	−	2.33162i	1.49845	−	0.203715i	0.661063	−	0.750331i	$-0.270106\pi$
$131$	17.1505	−	2.33162i	1.49845	−	0.203715i	0.837384	+	0.546616i	$0.184084\pi$
$132$	0.327952	−	0.345005i	0.0285445	−	0.0300288i
$133$	7.30117	−	38.8441i	0.633092	−	3.36821i
$134$	9.57441	−	4.89879i	0.827103	−	0.423191i
$135$	1.20160	−	4.06915i	0.103417	−	0.350217i
$136$	−1.52510	+	3.39453i	−0.130777	+	0.291079i
$137$	−13.1832	+	3.65202i	−1.12631	+	0.312013i	−0.779798	−	0.626031i	$-0.784678\pi$
$137$	−13.1832	+	3.65202i	−1.12631	+	0.312013i	−0.346516	+	0.938044i	$0.612635\pi$
$138$	−3.09364	+	1.45321i	−0.263348	+	0.123705i
$139$	−3.54713	+	9.57755i	−0.300864	+	0.812357i	0.694789	+	0.719214i	$0.255498\pi$
$139$	−3.54713	+	9.57755i	−0.300864	+	0.812357i	−0.995653	+	0.0931430i	$0.970309\pi$
$140$	20.8421	−	4.28316i	1.76148	−	0.361993i
$141$	−0.527257	+	1.17355i	−0.0444030	+	0.0988310i
$142$	−10.0224	+	0.678154i	−0.841057	+	0.0569094i
$143$	0.695024	−	5.85106i	0.0581208	−	0.489290i
$144$	12.4555	−	6.37292i	1.03796	−	0.531077i
$145$	10.5275	+	18.2342i	0.874261	+	1.51427i
$146$	6.58979	+	29.5279i	0.545375	+	2.44374i
$147$	−3.47872	−	1.09146i	−0.286920	−	0.0900217i
$148$	−0.116294	+	6.88458i	−0.00955927	+	0.565909i
$149$	−2.67639	+	0.644935i	−0.219258	+	0.0528351i	−0.342401	−	0.939554i	$-0.611240\pi$
$149$	−2.67639	+	0.644935i	−0.219258	+	0.0528351i	0.123143	+	0.992389i	$0.460703\pi$
$150$	1.77670	+	0.241543i	0.145067	+	0.0197219i
$151$	−0.281579	−	0.363770i	−0.0229145	−	0.0296032i	0.779180	−	0.626800i	$-0.215636\pi$
$151$	−0.281579	−	0.363770i	−0.0229145	−	0.0296032i	−0.802094	+	0.597197i	$0.796281\pi$
$152$	7.64534	−	1.84231i	0.620119	−	0.149431i
$153$	11.1103	−	3.48589i	0.898216	−	0.281817i
$154$	5.21447	+	10.6304i	0.420194	+	0.856624i
$155$	−9.99003	+	13.4306i	−0.802419	+	1.07877i
$156$	0.688727	−	1.40406i	0.0551423	−	0.112415i
$157$	3.66905	−	23.9503i	0.292822	−	1.91144i	−0.105914	−	0.994375i	$-0.533777\pi$
$157$	3.66905	−	23.9503i	0.292822	−	1.91144i	0.398736	−	0.917066i	$-0.369449\pi$
$158$	−2.21180	−	0.149659i	−0.175961	−	0.0119063i
$159$	0.104288	−	0.281586i	0.00827058	−	0.0223312i
$160$	12.3239	+	17.0835i	0.974292	+	1.35057i
$161$	−3.06993	−	36.2650i	−0.241945	−	2.85808i
$162$	−14.8029	−	5.76851i	−1.16302	−	0.453217i
$163$	−6.76599	−	7.11782i	−0.529953	−	0.557511i	0.404068	−	0.914729i	$-0.367596\pi$
$163$	−6.76599	−	7.11782i	−0.529953	−	0.557511i	−0.934021	+	0.357219i	$0.883725\pi$
$164$	−0.521425	−	4.38961i	−0.0407164	−	0.342771i
$165$	0.112764	+	0.949306i	0.00877869	+	0.0739034i
$166$	−8.10608	+	6.49644i	−0.629154	+	0.504222i
$167$	9.51654	+	14.1776i	0.736412	+	1.09710i	0.991491	+	0.130177i	$0.0415546\pi$
$167$	9.51654	+	14.1776i	0.736412	+	1.09710i	−0.255079	+	0.966920i	$0.582101\pi$
$168$	−0.124580	−	1.04877i	−0.00961153	−	0.0809147i
$169$	−1.17458	−	6.24905i	−0.0903521	−	0.480696i
$170$	9.79393	+	19.9663i	0.751160	+	1.53134i
$171$	−20.1967	−	14.0573i	−1.54448	−	1.07499i
$172$	−8.47500	−	1.44522i	−0.646212	−	0.110197i
$173$	2.76615	+	12.3947i	0.210307	+	0.942353i	0.959876	+	0.280426i	$0.0904759\pi$
$173$	2.76615	+	12.3947i	0.210307	+	0.942353i	−0.749569	+	0.661926i	$0.769739\pi$
$174$	−2.81470	+	1.32217i	−0.213382	+	0.100234i
$175$	−8.98235	+	16.8475i	−0.679002	+	1.27355i
$176$	−4.06398	+	4.89902i	−0.306334	+	0.369277i
$177$	0.181337	−	2.14212i	0.0136301	−	0.161012i
$178$	−8.45447	+	32.6531i	−0.633690	+	2.44745i
$179$	−3.22785	−	6.05425i	−0.241261	−	0.452516i	0.732288	−	0.680995i	$-0.238453\pi$
$179$	−3.22785	−	6.05425i	−0.241261	−	0.452516i	−0.973549	+	0.228479i	$0.926625\pi$
$180$	2.88540	−	12.9291i	0.215065	−	0.963676i
$181$	6.55068	−	4.23835i	0.486908	−	0.315034i	−0.276429	−	0.961034i	$-0.589151\pi$
$181$	6.55068	−	4.23835i	0.486908	−	0.315034i	0.763337	+	0.646001i	$0.223560\pi$
$182$	26.8016	+	28.1953i	1.98667	+	2.08997i
$183$	−0.496259	−	0.397716i	−0.0366845	−	0.0294000i
$184$	6.33156	−	3.51430i	0.466769	−	0.259078i
$185$	−10.4925	−	9.00754i	−0.771426	−	0.662248i
$186$	−1.85213	−	1.63757i	−0.135805	−	0.120072i
$187$	−4.01956	+	3.45068i	−0.293939	+	0.252339i
$188$	−2.81691	+	7.60588i	−0.205444	+	0.554716i
$189$	−4.43132	+	4.98885i	−0.322331	+	0.362886i
$190$	20.6969	−	42.1934i	1.50151	−	3.06103i
$191$	−1.20834	+	14.2740i	−0.0874321	+	1.03283i	0.808457	+	0.588555i	$0.200303\pi$
$191$	−1.20834	+	14.2740i	−0.0874321	+	1.03283i	−0.895889	+	0.444278i	$0.853460\pi$
$192$	−0.732271	+	0.439432i	−0.0528471	+	0.0317133i
$193$	−7.24747	−	8.73663i	−0.521685	−	0.628876i	0.441647	−	0.897189i	$-0.354394\pi$
$193$	−7.24747	−	8.73663i	−0.521685	−	0.628876i	−0.963332	+	0.268312i	$0.913534\pi$
$194$	−6.01721	+	5.16560i	−0.432010	+	0.370869i
$195$	1.28717	+	2.86495i	0.0921763	+	0.205163i
$196$	−22.3452	−	5.38456i	−1.59608	−	0.384612i
$197$	−12.8542	+	0.869769i	−0.915825	+	0.0619685i	−0.517892	−	0.855446i	$-0.673283\pi$
$197$	−12.8542	+	0.869769i	−0.915825	+	0.0619685i	−0.397933	+	0.917415i	$0.630272\pi$
$198$	7.36748	−	0.248972i	0.523584	−	0.0176937i
$199$	21.3380	+	0.721083i	1.51261	+	0.0511163i	0.778384	−	0.627789i	$-0.216040\pi$
$199$	21.3380	+	0.721083i	1.51261	+	0.0511163i	0.734226	+	0.678905i	$0.237545\pi$
$200$	−3.79017	−	0.256459i	−0.268006	−	0.0181344i
$201$	−1.30299	−	0.408817i	−0.0919061	−	0.0288357i
$202$	1.26293	+	8.24397i	0.0888594	+	0.580044i
$203$	−2.79313	−	32.9951i	−0.196039	−	2.31580i
$204$	−1.31010	+	0.510531i	−0.0917252	+	0.0357443i
$205$	7.45373	+	4.82263i	0.520591	+	0.336827i
$206$	−1.49480	−	12.5840i	−0.104148	−	0.876769i
$207$	−21.3782	−	7.50951i	−1.48589	−	0.521947i
$208$	−7.92127	+	19.3544i	−0.549241	+	1.34199i
$209$	10.9658	+	2.25353i	0.758520	+	0.155880i
$210$	−5.29909	−	3.42856i	−0.365672	−	0.236593i
$211$	−3.19290	−	2.55888i	−0.219808	−	0.176161i	0.509236	−	0.860627i	$-0.329928\pi$
$211$	−3.19290	−	2.55888i	−0.219808	−	0.176161i	−0.729045	+	0.684466i	$0.760035\pi$
$212$	0.536115	−	1.81552i	0.0368205	−	0.124691i
$213$	0.967810	+	0.830837i	0.0663132	+	0.0569280i
$214$	0.0186568	−	1.10448i	0.00127535	−	0.0755009i
$215$	13.1010	−	11.2469i	0.893482	−	0.767029i
$216$	−1.26679	−	0.397457i	−0.0861940	−	0.0270435i
$217$	23.2010	−	12.4381i	1.57499	−	0.844354i
$218$	32.8126	−	10.2950i	2.22235	−	0.697268i
$219$	2.03207	−	3.26015i	0.137314	−	0.220300i
$220$	1.11329	+	5.92301i	0.0750583	+	0.399329i
$221$	−9.20651	+	14.7705i	−0.619297	+	0.993570i
$222$	1.45637	−	1.43198i	0.0977452	−	0.0961080i
$223$	−3.71437	−	2.40323i	−0.248732	−	0.160932i	0.412863	−	0.910793i	$-0.364529\pi$
$223$	−3.71437	−	2.40323i	−0.248732	−	0.160932i	−0.661595	+	0.749861i	$0.730120\pi$
$224$	−6.11969	−	32.5583i	−0.408889	−	2.17540i
$225$	7.27590	+	9.39969i	0.485060	+	0.626646i
$226$	12.1302	+	13.6563i	0.806886	+	0.908406i
$227$	−4.71129	+	7.01882i	−0.312699	+	0.465856i	−0.953303	−	0.302016i	$-0.902340\pi$
$227$	−4.71129	+	7.01882i	−0.312699	+	0.465856i	0.640603	+	0.767872i	$0.278684\pi$
$228$	2.54778	+	1.52891i	0.168731	+	0.101255i
$229$	6.72630	−	11.6503i	0.444486	−	0.769873i	−0.553530	−	0.832829i	$-0.686720\pi$
$229$	6.72630	−	11.6503i	0.444486	−	0.769873i	0.998016	+	0.0629562i	$0.0200528\pi$
$230$	7.99402	−	42.5302i	0.527110	−	2.80436i
$231$	0.474246	−	1.42671i	0.0312031	−	0.0938706i
$232$	5.76066	−	3.19743i	0.378206	−	0.209922i
$233$	5.11968	−	6.61408i	0.335401	−	0.433303i	−0.592818	−	0.805337i	$-0.701985\pi$
$233$	5.11968	−	6.61408i	0.335401	−	0.433303i	0.928219	+	0.372034i	$0.121339\pi$
$234$	22.8505	−	8.02668i	1.49378	−	0.524721i
$235$	−8.14459	−	14.1068i	−0.531294	−	0.920229i
$236$	0.228899	−	13.5508i	0.0149001	−	0.882084i
$237$	0.186936	+	0.210456i	0.0121428	+	0.0136706i
$238$	−0.590713	−	34.9702i	−0.0382903	−	2.26678i
$239$	−4.99771	+	6.02460i	−0.323275	+	0.389699i	−0.906216	−	0.422816i	$-0.861042\pi$
$239$	−4.99771	+	6.02460i	−0.323275	+	0.389699i	0.582941	+	0.812515i	$0.301902\pi$
$240$	0.513791	−	3.35385i	0.0331651	−	0.216490i
$241$	−21.3120	−	1.44205i	−1.37282	−	0.0928909i	−0.637418	−	0.770518i	$-0.719998\pi$
$241$	−21.3120	−	1.44205i	−1.37282	−	0.0928909i	−0.735406	+	0.677627i	$0.763008\pi$
$242$	15.5828	−	7.31985i	1.00170	−	0.470538i
$243$	2.56187	+	5.70213i	0.164344	+	0.365792i
$244$	−3.29067	−	2.29037i	−0.210663	−	0.146626i
$245$	36.9753	−	27.6351i	2.36226	−	1.76554i
$246$	−0.802613	+	1.03689i	−0.0511727	+	0.0661097i
$247$	36.5917	−	3.72101i	2.32827	−	0.236762i
$248$	4.14931	+	3.19662i	0.263481	+	0.202986i
$249$	1.31228	+	0.133446i	0.0831624	+	0.00845679i
$250$	3.72567	−	3.91941i	0.235632	−	0.247885i
$251$	−3.83296	−	1.96115i	−0.241934	−	0.123787i	0.330303	−	0.943875i	$-0.392849\pi$
$251$	−3.83296	−	1.96115i	−0.241934	−	0.123787i	−0.572237	+	0.820088i	$0.693924\pi$
$252$	−12.7524	+	16.4748i	−0.803328	+	1.03781i
$253$	10.2850	−	0.695926i	0.646612	−	0.0437525i
$254$	−3.66492	+	30.8532i	−0.229958	+	1.93590i
$255$	0.890740	−	2.67968i	0.0557803	−	0.167808i
$256$	17.0896	−	11.8947i	1.06810	−	0.743419i
$257$	−1.04078	−	0.624569i	−0.0649223	−	0.0389595i	0.481725	−	0.876322i	$-0.340010\pi$
$257$	−1.04078	−	0.624569i	−0.0649223	−	0.0389595i	−0.546648	+	0.837363i	$0.684096\pi$
$258$	1.49199	+	2.06821i	0.0928875	+	0.128761i
$259$	8.91282	+	19.8379i	0.553816	+	1.23267i
$260$	9.31544	+	17.4723i	0.577719	+	1.08359i
$261$	−19.4506	−	6.83240i	−1.20396	−	0.422915i
$262$	−27.1746	−	17.5822i	−1.67886	−	1.08623i
$263$	2.66705	−	10.3007i	0.164457	−	0.635171i	−0.832273	−	0.554366i	$-0.812961\pi$
$263$	2.66705	−	10.3007i	0.164457	−	0.635171i	0.996730	−	0.0808046i	$-0.0257490\pi$
$264$	0.297611	−	0.0302641i	0.0183167	−	0.00186262i
$265$	2.11886	+	3.15665i	0.130160	+	0.193911i
$266$	−57.6744	+	46.2219i	−3.53625	+	2.83405i
$267$	3.67242	−	2.20380i	0.224748	−	0.134870i
$268$	−8.36964	−	2.01685i	−0.511257	−	0.123199i
$269$	−2.59362	+	1.01071i	−0.158136	+	0.0616238i	−0.440852	−	0.897580i	$-0.645324\pi$
$269$	−2.59362	+	1.01071i	−0.158136	+	0.0616238i	0.282716	+	0.959204i	$0.408765\pi$
$270$	−6.66145	+	4.31001i	−0.405403	+	0.262299i
$271$	5.17255	+	0.525997i	0.314210	+	0.0319521i	0.257004	−	0.966410i	$-0.417265\pi$
$271$	5.17255	+	0.525997i	0.314210	+	0.0319521i	0.0572062	+	0.998362i	$0.481781\pi$
$272$	17.0181	−	7.99406i	1.03187	−	0.484711i
$273$	0.0834265	−	4.93885i	0.00504920	−	0.298913i
$274$	23.1538	+	10.8763i	1.39877	+	0.657058i
$275$	−4.72829	−	2.62441i	−0.285126	−	0.158258i
$276$	2.63675	+	0.730436i	0.158714	+	0.0439671i
$277$	−2.36192	+	4.81511i	−0.141914	+	0.289312i	−0.957031	−	0.289984i	$-0.906350\pi$
$277$	−2.36192	+	4.81511i	−0.141914	+	0.289312i	0.815117	+	0.579296i	$0.196673\pi$
$278$	16.6991	−	9.26876i	1.00155	−	0.555903i
$279$	−1.14392	−	16.3494i	−0.0684848	−	0.978813i
$280$	11.6917	+	6.48944i	0.698715	+	0.387818i
$281$	−14.5923	+	10.1566i	−0.870507	+	0.605890i	−0.919579	−	0.392905i	$-0.871470\pi$
$281$	−14.5923	+	10.1566i	−0.870507	+	0.605890i	0.0490726	+	0.998795i	$0.484373\pi$
$282$	2.17759	−	1.02290i	0.129673	−	0.0609127i
$283$	9.57953	−	10.0777i	0.569444	−	0.599054i	−0.375284	−	0.926910i	$-0.622455\pi$
$283$	9.57953	−	10.0777i	0.569444	−	0.599054i	0.944728	+	0.327855i	$0.106326\pi$
$284$	6.44099	+	4.81395i	0.382202	+	0.285656i
$285$	−5.63018	+	1.97771i	−0.333503	+	0.117150i
$286$	−8.11317	+	7.45539i	−0.479742	+	0.440846i
$287$	−7.38546	−	11.8489i	−0.435950	−	0.699417i
$288$	−20.0513	−	4.83181i	−1.18153	−	0.284717i
$289$	−1.30266	+	0.360864i	−0.0766269	+	0.0212273i
$290$	7.27322	−	38.6954i	0.427098	−	2.27227i
$291$	1.00467	+	0.0679803i	0.0588950	+	0.00398508i
$292$	11.3939	−	21.3707i	0.666777	−	1.25063i
$293$	−13.0585	+	11.9997i	−0.762885	+	0.701033i	−0.960202	−	0.279307i	$-0.909895\pi$
$293$	−13.0585	+	11.9997i	−0.762885	+	0.701033i	0.197317	+	0.980340i	$0.436777\pi$
$294$	3.60643	+	5.78598i	0.210331	+	0.337445i
$295$	20.6523	+	17.7294i	1.20242	+	1.03225i
$296$	−2.87369	+	3.23525i	−0.167030	+	0.188045i
$297$	−1.39165	−	1.27882i	−0.0807519	−	0.0742048i
$298$	4.58306	+	2.34494i	0.265490	+	0.135839i
$299$	31.5567	−	12.2973i	1.82497	−	0.711170i
$300$	−0.953187	−	1.07311i	−0.0550323	−	0.0619562i
$301$	−26.1692	+	7.24944i	−1.50837	+	0.417851i
$302$	−0.0435701	+	0.859130i	−0.00250718	+	0.0494374i
$303$	0.619571	−	0.858852i	0.0355934	−	0.0493398i
$304$	−35.3721	−	18.0983i	−2.02873	−	1.03801i
$305$	7.75975	−	2.14962i	0.444322	−	0.123087i
$306$	−20.0103	−	8.58710i	−1.14391	−	0.490892i
$307$	−4.71977	−	11.5320i	−0.269371	−	0.658167i	0.730318	−	0.683108i	$-0.239372\pi$
$307$	−4.71977	−	11.5320i	−0.269371	−	0.658167i	−0.999689	+	0.0249408i	$0.992060\pi$
$308$	2.37574	−	9.17564i	0.135370	−	0.522831i
$309$	−0.984948	+	1.27245i	−0.0560317	+	0.0723870i
$310$	30.5341	−	6.88787i	1.73422	−	0.391205i
$311$	14.1821	+	18.3217i	0.804192	+	1.03893i	0.998319	+	0.0579545i	$0.0184578\pi$
$311$	14.1821	+	18.3217i	0.804192	+	1.03893i	−0.194127	+	0.980976i	$0.562187\pi$
$312$	0.903176	−	0.387583i	0.0511323	−	0.0219426i
$313$	6.15884	−	27.5969i	0.348118	−	1.55987i	−0.412678	−	0.910877i	$-0.635407\pi$
$313$	6.15884	−	27.5969i	0.348118	−	1.55987i	0.760797	−	0.648990i	$-0.224808\pi$
$314$	−34.3791	+	29.5135i	−1.94013	+	1.66554i
$315$	−9.11358	−	40.8366i	−0.513492	−	2.30088i
$316$	1.26537	+	1.24418i	0.0711826	+	0.0699904i
$317$	9.48569	−	2.28579i	0.532770	−	0.128383i	0.0410844	−	0.999156i	$-0.486919\pi$
$317$	9.48569	−	2.28579i	0.532770	−	0.128383i	0.491685	+	0.870773i	$0.336381\pi$
$318$	−0.490965	+	0.272508i	−0.0275319	+	0.0152815i
$319$	9.35763	−	0.633176i	0.523927	−	0.0354511i
$320$	0.912054	−	10.7741i	0.0509853	−	0.602288i
$321$	−0.100016	+	0.0983405i	−0.00558233	+	0.00548883i
$322$	−39.8175	+	55.1952i	−2.21894	+	3.07591i
$323$	−26.4879	−	19.7969i	−1.47382	−	1.10153i
$324$	5.98316	+	11.2222i	0.332398	+	0.623455i
$325$	−17.4033	−	3.57647i	−0.965362	−	0.198387i
$326$	0.930141	+	18.3408i	0.0515157	+	1.01580i
$327$	−3.88741	−	1.98901i	−0.214975	−	0.109993i
$328$	1.54828	−	2.30660i	0.0854892	−	0.127361i
$329$	2.16090	+	25.5266i	0.119134	+	1.40733i
$330$	0.996324	−	1.48431i	0.0548458	−	0.0817086i
$331$	10.4161	−	19.5367i	0.572519	−	1.07383i	−0.414013	−	0.910271i	$-0.635873\pi$
$331$	10.4161	−	19.5367i	0.572519	−	1.07383i	0.986533	−	0.163563i	$-0.0522987\pi$
$332$	8.31085	+	0.280852i	0.456117	+	0.0154138i
$333$	13.5400			0.741989
$334$	3.76649	−	31.7082i	0.206093	−	1.73500i
$335$	13.8495	−	10.3510i	0.756679	−	0.565537i
$336$	−2.97395	+	4.43055i	−0.162242	+	0.241706i
$337$	3.39765	+	1.06602i	0.185082	+	0.0580697i	0.390493	−	0.920606i	$-0.372305\pi$
$337$	3.39765	+	1.06602i	0.185082	+	0.0580697i	−0.205411	+	0.978676i	$0.565853\pi$
$338$	−5.94521	+	10.2974i	−0.323377	+	0.560105i
$339$	0.117472	−	2.31635i	0.00638020	−	0.125807i
$340$	4.46216	−	17.2339i	0.241995	−	0.934639i
$341$	3.41151	+	6.63007i	0.184743	+	0.359038i
$342$	11.5339	+	44.5467i	0.623684	+	2.40881i
$343$	−38.6926	+	7.95154i	−2.08921	+	0.429343i
$344$	−3.44963	−	4.15843i	−0.185991	−	0.224208i
$345$	−4.51004	+	3.13908i	−0.242812	+	0.169002i
$346$	11.1728	−	20.9560i	0.600654	−	1.12660i
$347$	2.59607	−	7.80994i	0.139364	−	0.419260i	−0.855821	−	0.517272i	$-0.826947\pi$
$347$	2.59607	−	7.80994i	0.139364	−	0.419260i	0.995185	+	0.0980125i	$0.0312485\pi$
$348$	2.39900	+	0.664575i	0.128600	+	0.0356249i
$349$	−2.55460	−	5.20790i	−0.136744	−	0.278773i	0.818546	−	0.574441i	$-0.194780\pi$
$349$	−2.55460	−	5.20790i	−0.136744	−	0.278773i	−0.955291	+	0.295668i	$0.904458\pi$
$350$	33.2664	−	12.9636i	1.77817	−	0.692932i
$351$	−5.62029	−	2.64007i	−0.299989	−	0.140917i
$352$	9.24985	−	1.57735i	0.493019	−	0.0840733i
$353$	0.652221	+	1.59360i	0.0347142	+	0.0848188i	0.941872	−	0.335972i	$-0.109065\pi$
$353$	0.652221	+	1.59360i	0.0347142	+	0.0848188i	−0.907158	+	0.420790i	$0.861753\pi$
$354$	−2.86655	+	2.81854i	−0.152356	+	0.149804i
$355$	−15.7000	+	3.78327i	−0.833271	+	0.200795i
$356$	22.1611	−	15.4245i	1.17453	−	0.817499i
$357$	−3.05974	+	3.21884i	−0.161938	+	0.170359i
$358$	−2.79457	+	12.5220i	−0.147697	+	0.661810i
$359$	11.1970	+	5.25969i	0.590957	+	0.277596i	0.697353	−	0.716728i	$-0.254361\pi$
$359$	11.1970	+	5.25969i	0.590957	+	0.277596i	−0.106396	+	0.994324i	$0.533931\pi$
$360$	6.66847	−	4.98397i	0.351459	−	0.262678i
$361$	0.859360	+	50.8741i	0.0452295	+	2.67758i
$362$	−14.4573	−	1.96547i	−0.759857	−	0.103303i
$363$	−2.06253	−	0.724506i	−0.108255	−	0.0380267i
$364$	−1.57722	−	31.1002i	−0.0826689	−	1.63009i
$365$	18.4233	+	45.0145i	0.964321	+	2.35617i
$366$	0.219687	+	1.16879i	0.0114832	+	0.0610937i
$367$	3.11412	+	26.2162i	0.162556	+	1.36847i	0.800934	+	0.598752i	$0.204337\pi$
$367$	3.11412	+	26.2162i	0.162556	+	1.36847i	−0.638379	+	0.769722i	$0.720395\pi$
$368$	−35.8382	−	7.36493i	−1.86819	−	0.383924i
$369$	−8.61336	+	1.17099i	−0.448393	+	0.0609594i
$370$	3.91585	+	25.5613i	0.203575	+	1.32887i
$371$	−0.905408	−	5.91019i	−0.0470064	−	0.306842i
$372$	0.271091	+	1.96037i	0.0140554	+	0.101640i
$373$	−2.51195	+	16.3972i	−0.130064	+	0.849014i	0.827640	+	0.561259i	$0.189683\pi$
$373$	−2.51195	+	16.3972i	−0.130064	+	0.849014i	−0.957704	+	0.287754i	$0.907091\pi$
$374$	9.90646			0.512251
$375$	−0.686252	+	0.0231908i	−0.0354379	+	0.00119757i
$376$	−4.45673	+	2.47369i	−0.229838	+	0.127571i
$377$	28.7113	−	11.1885i	1.47871	−	0.576236i
$378$	12.3643	−	1.68094i	0.635951	−	0.0864580i
$379$	−18.5959	−	18.2845i	−0.955208	−	0.939209i	0.0429982	−	0.999075i	$-0.486309\pi$
$379$	−18.5959	−	18.2845i	−0.955208	−	0.939209i	−0.998206	+	0.0598659i	$0.980933\pi$
$380$	−34.5714	+	14.8357i	−1.77347	+	0.761057i
$381$	3.07852	−	2.46722i	0.157718	−	0.126399i
$382$	19.1013	−	18.7813i	0.977307	−	0.960937i
$383$	21.2296	+	9.97236i	1.08478	+	0.509564i	0.882763	−	0.469819i	$-0.155681\pi$
$383$	21.2296	+	9.97236i	1.08478	+	0.509564i	0.202016	+	0.979382i	$0.435251\pi$
$384$	−1.70587	−	0.290898i	−0.0870522	−	0.0148448i
$385$	11.1367	+	15.4377i	0.567579	+	0.786780i
$386$	−0.358517	+	21.2242i	−0.0182480	+	1.08028i
$387$	−2.56006	+	16.7112i	−0.130135	+	0.849477i
$388$	6.34818			0.322280
$389$	−32.4552	+	1.09677i	−1.64554	+	0.0556086i	−0.841946	−	0.539563i	$-0.818590\pi$
$389$	−32.4552	+	1.09677i	−1.64554	+	0.0556086i	−0.803599	+	0.595171i	$0.797084\pi$
$390$	1.66337	−	5.63290i	0.0842279	−	0.285233i
$391$	−28.3719	−	11.0562i	−1.43483	−	0.559137i
$392$	−8.45092	−	11.7147i	−0.426836	−	0.591682i
$393$	0.895173	+	4.01114i	0.0451555	+	0.202335i
$394$	19.2981	+	14.4232i	0.972223	+	0.726633i
$395$	−3.54568	+	0.360560i	−0.178402	+	0.0181418i
$396$	−4.60468	−	3.69032i	−0.231394	−	0.185446i
$397$	−3.33124	−	0.922825i	−0.167190	−	0.0463152i	0.182366	−	0.983231i	$-0.441625\pi$
$397$	−3.33124	−	0.922825i	−0.167190	−	0.0463152i	−0.349556	+	0.936916i	$0.613668\pi$
$398$	−29.3978	−	27.0143i	−1.47358	−	1.35411i
$399$	9.33682	+	0.949461i	0.467425	+	0.0475325i
$400$	13.6859	+	13.4567i	0.684296	+	0.672834i
$401$	−1.06302	−	2.87023i	−0.0530844	−	0.143332i	0.908467	−	0.417956i	$-0.137253\pi$
$401$	−1.06302	−	2.87023i	−0.0530844	−	0.143332i	−0.961552	+	0.274623i	$0.911447\pi$
$402$	1.35083	+	2.16720i	0.0673732	+	0.108090i
$403$	17.2152	+	17.4284i	0.857552	+	0.868170i
$404$	3.53149	−	5.66575i	0.175698	−	0.281881i
$405$	−25.0183	−	5.14139i	−1.24317	−	0.255478i
$406$	−36.2273	+	50.2184i	−1.79793	+	2.49230i
$407$	−5.66077	+	2.42923i	−0.280594	+	0.120412i
$408$	−0.833698	−	0.292853i	−0.0412742	−	0.0144984i
$409$	12.9917	+	19.3549i	0.642400	+	0.957040i	0.999734	+	0.0230630i	$0.00734182\pi$
$409$	12.9917	+	19.3549i	0.642400	+	0.957040i	−0.357334	+	0.933977i	$0.616314\pi$
$410$	−4.70167	−	15.9219i	−0.232199	−	0.786328i
$411$	−1.12812	−	3.04601i	−0.0556460	−	0.150249i
$412$	−5.65363	+	8.42271i	−0.278534	+	0.414957i
$413$	−17.5430	−	39.0467i	−0.863234	−	1.92136i
$414$	21.1860	+	36.6953i	1.04124	+	1.80347i
$415$	−11.0907	+	12.4861i	−0.544423	+	0.612921i
$416$	27.4448	−	14.0423i	1.34559	−	0.688478i
$417$	−2.33711	−	0.647429i	−0.114449	−	0.0317047i
$418$	−12.8142	−	16.5546i	−0.626764	−	0.809713i
$419$	3.80877	+	4.00682i	0.186070	+	0.195746i	0.811189	−	0.584783i	$-0.198821\pi$
$419$	3.80877	+	4.00682i	0.186070	+	0.195746i	−0.625119	+	0.780529i	$0.714950\pi$
$420$	1.43085	+	4.84549i	0.0698183	+	0.236436i
$421$	17.3923	+	2.36450i	0.847651	+	0.115239i	0.545592	−	0.838051i	$-0.316305\pi$
$421$	17.3923	+	2.36450i	0.847651	+	0.115239i	0.302059	+	0.953289i	$0.402326\pi$
$422$	1.41345	+	7.51994i	0.0688059	+	0.366065i
$423$	15.0479	+	5.28588i	0.731655	+	0.257008i
$424$	0.998836	−	0.646256i	0.0485078	−	0.0313850i
$425$	9.34553	+	12.9548i	0.453325	+	0.628401i
$426$	−0.361190	−	2.35772i	−0.0174997	−	0.114232i
$427$	−12.4831	−	2.12872i	−0.604101	−	0.103016i
$428$	−0.587231	+	0.661114i	−0.0283849	+	0.0319562i
$429$	1.39829	+	0.0472531i	0.0675102	+	0.00228140i
$430$	−32.2883			−1.55708
$431$	−2.19039	+	18.4398i	−0.105508	+	0.888215i	0.835421	+	0.549610i	$0.185224\pi$
$431$	−2.19039	+	18.4398i	−0.105508	+	0.888215i	−0.940929	+	0.338605i	$0.890045\pi$
$432$	3.54829	+	5.69270i	0.170717	+	0.273890i
$433$	22.0163	+	15.3238i	1.05803	+	0.736413i	0.965791	−	0.259323i	$-0.0834996\pi$
$433$	22.0163	+	15.3238i	1.05803	+	0.736413i	0.0922430	+	0.995737i	$0.470596\pi$
$434$	−48.0700	−	10.6123i	−2.30744	−	0.509405i
$435$	−4.10338	+	2.85604i	−0.196742	+	0.136936i
$436$	−25.2978	−	10.8561i	−1.21155	−	0.519915i
$437$	18.2237	+	61.7136i	0.871759	+	2.95216i
$438$	−6.85436	+	2.15057i	−0.327514	+	0.102758i
$439$	−1.33942	−	2.31994i	−0.0639268	−	0.110724i	0.832291	−	0.554340i	$-0.187029\pi$
$439$	−1.33942	−	2.31994i	−0.0639268	−	0.110724i	−0.896217	+	0.443615i	$0.853696\pi$
$440$	−1.89375	+	3.28007i	−0.0902811	+	0.156371i
$441$	−9.84477	+	44.1130i	−0.468799	+	2.10062i
$442$	31.0545	−	9.74340i	1.47711	−	0.463446i
$443$	−2.16699	+	7.33838i	−0.102957	+	0.348657i	−0.994561	−	0.104159i	$-0.966785\pi$
$443$	−2.16699	+	7.33838i	−0.102957	+	0.348657i	0.891604	+	0.452816i	$0.149581\pi$
$444$	−1.63123	+	0.110376i	−0.0774149	+	0.00523821i
$445$	−4.57405	+	54.0330i	−0.216831	+	2.56141i
$446$	2.34295	+	7.93427i	0.110942	+	0.375699i
$447$	−0.206198	−	0.620321i	−0.00975283	−	0.0293402i
$448$	−8.50246	+	14.7267i	−0.401704	+	0.695771i
$449$	7.99923	+	0.813442i	0.377507	+	0.0383887i	0.288084	−	0.957605i	$-0.406982\pi$
$449$	7.99923	+	0.813442i	0.377507	+	0.0383887i	0.0894228	+	0.995994i	$0.471498\pi$
$450$	1.12584	−	22.1996i	0.0530725	−	1.04650i
$451$	3.39095	−	2.03489i	0.159674	−	0.0958193i
$452$	−0.246951	−	14.6195i	−0.0116156	−	0.687643i
$453$	0.0804288	−	0.0739079i	0.00377887	−	0.00347250i
$454$	15.2342	−	4.22020i	0.714976	−	0.198064i
$455$	50.0946	+	37.4404i	2.34847	+	1.75523i
$456$	0.589023	+	1.77200i	0.0275835	+	0.0829815i
$457$	−9.85975	+	2.02623i	−0.461219	+	0.0947830i	−0.426250	−	0.904605i	$-0.640166\pi$
$457$	−9.85975	+	2.02623i	−0.461219	+	0.0947830i	−0.0349694	+	0.999388i	$0.511133\pi$
$458$	−23.7347	+	8.33730i	−1.10905	+	0.389576i
$459$	2.11465	+	5.16682i	0.0987034	+	0.241166i
$460$	−27.0315	+	21.6638i	−1.26035	+	1.01008i
$461$	−5.76322	+	0.586062i	−0.268420	+	0.0272956i	−0.234454	−	0.972127i	$-0.575330\pi$
$461$	−5.76322	+	0.586062i	−0.268420	+	0.0272956i	−0.0339664	+	0.999423i	$0.510814\pi$
$462$	−2.41074	+	1.44667i	−0.112158	+	0.0673051i
$463$	12.6118	+	13.2676i	0.586119	+	0.616597i	0.949014	−	0.315233i	$-0.102083\pi$
$463$	12.6118	+	13.2676i	0.586119	+	0.616597i	−0.362895	+	0.931830i	$0.618212\pi$
$464$	−32.6068	−	6.70086i	−1.51373	−	0.311080i
$465$	−3.37779	−	2.09466i	−0.156641	−	0.0971374i
$466$	−15.3207	+	3.14847i	−0.709716	+	0.145850i
$467$	24.3721	+	16.9635i	1.12781	+	0.784977i	0.978994	−	0.203889i	$-0.0653581\pi$
$467$	24.3721	+	16.9635i	1.12781	+	0.784977i	0.148813	+	0.988865i	$0.452455\pi$
$468$	−18.0642	−	7.03943i	−0.835018	−	0.325398i
$469$	−26.6357	+	5.47377i	−1.22992	+	0.252755i
$470$	−5.62692	+	29.9367i	−0.259550	+	1.38088i
$471$	5.74017	+	0.388403i	0.264493	+	0.0178967i
$472$	5.65625	−	6.36790i	0.260350	−	0.293107i
$473$	−1.92786	−	7.44585i	−0.0886433	−	0.342361i
$474$	−0.00889042	−	0.526313i	−0.000408351	−	0.0241744i
$475$	9.56006	−	32.3746i	0.438646	−	1.48545i
$476$	−17.8754	+	21.5483i	−0.819316	+	0.987663i
$477$	−3.58741	−	0.993789i	−0.164256	−	0.0455025i
$478$	14.4296	−	2.46064i	0.659992	−	0.112547i
$479$	−12.7584	−	12.5447i	−0.582947	−	0.573183i	0.348387	−	0.937351i	$-0.386730\pi$
$479$	−12.7584	−	12.5447i	−0.582947	−	0.573183i	−0.931333	+	0.364168i	$0.881353\pi$
$480$	−3.79515	+	3.25803i	−0.173224	+	0.148708i
$481$	−15.3560	+	13.1827i	−0.700172	+	0.601078i
$482$	28.4827	+	28.0056i	1.29735	+	1.27562i
$483$	8.51888	−	1.45270i	0.387622	−	0.0661003i
$484$	−13.2814	−	3.67923i	−0.603700	−	0.167238i
$485$	−8.13999	+	9.81253i	−0.369618	+	0.445564i
$486$	3.31061	−	11.2112i	0.150172	−	0.508550i
$487$	−0.144061	−	8.52839i	−0.00652801	−	0.386458i	−0.984272	−	0.176658i	$-0.943471\pi$
$487$	−0.144061	−	8.52839i	−0.00652801	−	0.386458i	0.977744	−	0.209800i	$-0.0672813\pi$
$488$	−0.631552	−	2.43920i	−0.0285890	−	0.110417i
$489$	1.54857	−	1.74341i	0.0700288	−	0.0788396i
$490$	−86.1251	−	5.82758i	−3.89073	−	0.263263i
$491$	3.22227	−	17.1433i	0.145419	−	0.773666i	−0.830749	−	0.556648i	$-0.812087\pi$
$491$	3.22227	−	17.1433i	0.145419	−	0.773666i	0.976168	−	0.217018i	$-0.0696331\pi$
$492$	1.02815	−	0.211290i	0.0463524	−	0.00952567i
$493$	−25.8137	−	10.0593i	−1.16259	−	0.453049i
$494$	−56.4518	−	39.2916i	−2.53989	−	1.76781i
$495$	11.6086	−	2.38563i	0.521768	−	0.107226i
$496$	−5.38655	−	25.9099i	−0.241863	−	1.16339i
$497$	24.8782	+	5.11261i	1.11594	+	0.229332i
$498$	−1.69943	−	1.78779i	−0.0761531	−	0.0801130i
$499$	21.2526	−	12.7536i	0.951398	−	0.570929i	0.0475901	−	0.998867i	$-0.484846\pi$
$499$	21.2526	−	12.7536i	0.951398	−	0.570929i	0.903808	+	0.427938i	$0.140760\pi$
$500$	−4.30656	+	0.437934i	−0.192595	+	0.0195850i
$501$	−3.16384	+	2.53559i	−0.141350	+	0.113282i
$502$	3.04970	+	7.45146i	0.136115	+	0.332575i
$503$	−8.51826	+	2.99221i	−0.379810	+	0.133416i	−0.514540	−	0.857467i	$-0.672037\pi$
$503$	−8.51826	+	2.99221i	−0.379810	+	0.133416i	0.134730	+	0.990882i	$0.456983\pi$
$504$	−12.8249	+	2.63559i	−0.571268	+	0.117399i
$505$	4.22941	+	12.7236i	0.188206	+	0.566194i
$506$	−15.4409	−	11.5404i	−0.686432	−	0.513035i
$507$	1.45501	−	0.403069i	0.0646193	−	0.0179009i
$508$	18.3134	−	16.8287i	0.812528	−	0.746651i
$509$	−0.165468	−	9.79571i	−0.00733424	−	0.434187i	−0.979672	−	0.200607i	$-0.935709\pi$
$509$	−0.165468	−	9.79571i	−0.00733424	−	0.434187i	0.972338	−	0.233580i	$-0.0750441\pi$
$510$	−4.52790	+	2.71717i	−0.200499	+	0.120318i
$511$	3.87435	−	76.3958i	0.171391	−	3.37955i
$512$	−24.2358	−	2.46454i	−1.07108	−	0.108918i
$513$	5.89889	−	10.2172i	0.260442	−	0.451099i
$514$	0.715981	+	2.15394i	0.0315806	+	0.0950062i
$515$	−5.76977	−	19.5390i	−0.254247	−	0.860991i
$516$	0.172196	−	2.03415i	0.00758051	−	0.0895482i
$517$	−7.23952	+	0.489856i	−0.318394	+	0.0215438i
$518$	11.5177	−	39.0041i	0.506060	−	1.71374i
$519$	−2.87721	+	0.902730i	−0.126295	+	0.0396254i
$520$	−2.71039	+	12.1449i	−0.118859	+	0.532588i
$521$	12.8066	−	22.1816i	0.561066	−	0.971794i	−0.436338	−	0.899783i	$-0.643725\pi$
$521$	12.8066	−	22.1816i	0.561066	−	0.971794i	0.997404	−	0.0720113i	$-0.0229418\pi$
$522$	19.2758	+	33.3866i	0.843677	+	1.46129i
$523$	−4.34278	+	1.36256i	−0.189897	+	0.0595805i	−0.392826	−	0.919613i	$-0.628502\pi$
$523$	−4.34278	+	1.36256i	−0.189897	+	0.0595805i	0.202929	+	0.979193i	$0.434954\pi$
$524$	7.33764	+	24.8485i	0.320546	+	1.08551i
$525$	−4.16607	−	1.78780i	−0.181822	−	0.0780260i
$526$	−16.3313	+	11.3669i	−0.712077	+	0.495620i
$527$	−0.794328	−	22.0106i	−0.0346015	−	0.958796i
$528$	−1.24051	−	0.863423i	−0.0539864	−	0.0375757i
$529$	19.1765	+	30.7658i	0.833759	+	1.33764i
$530$	0.838610	−	7.05984i	0.0364269	−	0.306660i
$531$	−26.6507			−1.15654
$532$	59.1313	+	1.99825i	2.56367	+	0.0866351i
$533$	8.62846	−	9.71406i	0.373740	−	0.420763i
$534$	−7.89512	−	1.34633i	−0.341655	−	0.0582616i
$535$	−0.268919	−	1.75541i	−0.0116264	−	0.0758931i
$536$	−3.16539	−	4.38788i	−0.136724	−	0.189528i
$537$	1.36780	−	0.884976i	0.0590247	−	0.0381895i
$538$	4.91116	+	1.72514i	0.211735	+	0.0743761i
$539$	−3.79847	−	20.2088i	−0.163612	−	0.870457i
$540$	6.29336	+	0.855587i	0.270823	+	0.0368186i
$541$	−1.44868	−	4.90587i	−0.0622836	−	0.210920i	0.922102	−	0.386948i	$-0.126471\pi$
$541$	−1.44868	−	4.90587i	−0.0622836	−	0.210920i	−0.984385	+	0.176028i	$0.943675\pi$
$542$	−6.69855	−	7.04687i	−0.287727	−	0.302689i
$543$	1.13400	+	1.46501i	0.0486648	+	0.0628697i
$544$	−26.7113	−	7.39961i	−1.14524	−	0.317256i
$545$	49.2188	−	25.1831i	2.10830	−	1.07872i
$546$	−6.13425	+	6.90603i	−0.262521	+	0.295551i
$547$	11.4695	+	19.8657i	0.490400	+	0.849397i	0.999939	−	0.0110504i	$-0.00351752\pi$
$547$	11.4695	+	19.8657i	0.490400	+	0.849397i	−0.509539	+	0.860447i	$0.670184\pi$
$548$	−8.39209	−	18.6789i	−0.358492	−	0.797922i
$549$	−4.39394	+	6.54603i	−0.187529	+	0.279378i
$550$	3.51216	+	9.48313i	0.149759	+	0.404362i
$551$	16.5805	+	56.1491i	0.706355	+	2.39203i
$552$	0.958305	+	1.42767i	0.0407882	+	0.0607657i
$553$	5.28826	+	1.85761i	0.224880	+	0.0789934i
$554$	9.21644	−	3.95509i	0.391569	−	0.168036i
$555$	1.92105	−	2.66296i	0.0815438	−	0.113036i
$556$	−14.9756	−	3.07757i	−0.635108	−	0.130518i
$557$	−7.20930	+	11.5663i	−0.305468	+	0.490078i	−0.965232	−	0.261395i	$-0.915818\pi$
$557$	−7.20930	+	11.5663i	−0.305468	+	0.490078i	0.659764	+	0.751473i	$0.270656\pi$
$558$	−18.2917	+	24.5913i	−0.774347	+	1.04103i
$559$	−13.3667	−	21.4449i	−0.565352	−	0.907023i
$560$	−23.4643	−	63.3555i	−0.991547	−	2.67726i
$561$	−0.896944	−	0.881921i	−0.0378690	−	0.0372347i
$562$	33.0763	+	3.36353i	1.39524	+	0.141882i
$563$	−21.9837	−	20.2014i	−0.926504	−	0.851387i	0.0626851	−	0.998033i	$-0.480034\pi$
$563$	−21.9837	−	20.2014i	−0.926504	−	0.851387i	−0.989189	+	0.146647i	$0.953152\pi$
$564$	−1.85598	−	0.514147i	−0.0781510	−	0.0216495i
$565$	22.9143	+	18.3642i	0.964014	+	0.772588i
$566$	−25.8675	+	2.63047i	−1.08729	+	0.110567i
$567$	32.1750	+	24.0474i	1.35122	+	1.00989i
$568$	1.10072	+	4.93215i	0.0461851	+	0.206948i
$569$	−14.6944	−	20.3694i	−0.616020	−	0.853930i	0.381496	−	0.924370i	$-0.375409\pi$
$569$	−14.6944	−	20.3694i	−0.616020	−	0.853930i	−0.997516	+	0.0704404i	$0.977560\pi$
$570$	10.3976	+	4.05182i	0.435506	+	0.169712i
$571$	6.69763	−	22.6811i	0.280287	−	0.949176i	−0.693260	−	0.720688i	$-0.743826\pi$
$571$	6.69763	−	22.6811i	0.280287	−	0.949176i	0.973547	−	0.228488i	$-0.0733781\pi$
$572$	8.81517	−	0.297895i	0.368581	−	0.0124556i
$573$	−3.40146			−0.142098
$574$	−3.95367	+	25.8082i	−0.165023	+	1.07721i
$575$	0.524988	−	31.0793i	0.0218935	−	1.29610i
$576$	6.19391	+	8.58603i	0.258079	+	0.357751i
$577$	−35.3353	−	6.02564i	−1.47103	−	0.250851i	−0.623592	−	0.781750i	$-0.714327\pi$
$577$	−35.3353	−	6.02564i	−1.47103	−	0.250851i	−0.847435	+	0.530900i	$0.821854\pi$
$578$	2.28788	+	1.07471i	0.0951632	+	0.0447019i
$579$	1.92194	−	1.88975i	0.0798732	−	0.0785354i
$580$	−24.5942	+	19.7105i	−1.02122	+	0.818432i
$581$	24.1363	−	10.3577i	1.00134	−	0.429710i
$582$	−1.34271	−	1.32022i	−0.0556571	−	0.0547249i
$583$	1.67811	−	0.228140i	0.0695001	−	0.00944858i
$584$	14.1813	−	5.52630i	0.586827	−	0.228680i
$585$	34.0439	−	18.8959i	1.40754	−	0.781250i
$586$	33.1450	−	1.12008i	1.36921	−	0.0462702i
$587$	−11.8448			−0.488888			−0.244444	−	0.969663i	$-0.578605\pi$
$587$	−11.8448			−0.488888			−0.244444	+	0.969663i	$0.578605\pi$
$588$	0.826446	−	5.39475i	0.0340821	−	0.222476i
$589$	−35.7543	+	29.7986i	−1.47323	+	1.22783i
$590$	−7.70751	−	50.3120i	−0.317313	−	2.07131i
$591$	−0.463246	−	3.02391i	−0.0190554	−	0.124387i
$592$	21.6638	−	2.94521i	0.890377	−	0.121047i
$593$	43.4637	+	8.93201i	1.78484	+	0.366794i	0.975405	−	0.220418i	$-0.0707422\pi$
$593$	43.4637	+	8.93201i	1.78484	+	0.366794i	0.809433	+	0.587212i	$0.199774\pi$
$594$	0.416895	+	3.50963i	0.0171054	+	0.144002i
$595$	−10.3869	−	55.2607i	−0.425820	−	2.26547i
$596$	−1.56096	−	3.81397i	−0.0639396	−	0.156226i
$597$	0.256769	+	5.06305i	0.0105088	+	0.207217i
$598$	−59.7542	−	20.9898i	−2.44353	−	0.858339i
$599$	−5.49156	−	0.746581i	−0.224379	−	0.0305045i	0.0216557	−	0.999765i	$-0.493106\pi$
$599$	−5.49156	−	0.746581i	−0.224379	−	0.0305045i	−0.246035	+	0.969261i	$0.579128\pi$
$600$	−0.0152348	−	0.901898i	−0.000621957	−	0.0368198i
$601$	−18.5808	+	13.8872i	−0.757926	+	0.566469i	−0.906387	−	0.422449i	$-0.861170\pi$
$601$	−18.5808	+	13.8872i	−0.757926	+	0.566469i	0.148460	+	0.988918i	$0.452568\pi$
$602$	45.9614	+	21.5899i	1.87325	+	0.879938i
$603$	−3.68747	+	16.5230i	−0.150165	+	0.672869i
$604$	0.474431	−	0.499101i	0.0193043	−	0.0203081i
$605$	22.7172	−	15.8116i	0.923586	−	0.642835i
$606$	−1.92524	+	0.463930i	−0.0782076	+	0.0188459i
$607$	−9.75224	+	9.58889i	−0.395831	+	0.389201i	−0.871478	−	0.490435i	$-0.836838\pi$
$607$	−9.75224	+	9.58889i	−0.395831	+	0.389201i	0.475647	+	0.879636i	$0.342214\pi$
$608$	22.1863	+	54.2087i	0.899772	+	2.19845i
$609$	7.75076	−	1.32172i	0.314076	−	0.0535587i
$610$	−13.6286	−	6.40188i	−0.551805	−	0.259204i
$611$	−22.2125	+	8.65595i	−0.898620	+	0.350182i
$612$	7.67640	+	15.6494i	0.310300	+	0.632590i
$613$	40.4644	+	11.2095i	1.63434	+	0.452747i	0.958685	−	0.284470i	$-0.0918176\pi$
$613$	40.4644	+	11.2095i	1.63434	+	0.452747i	0.675656	+	0.737217i	$0.263861\pi$
$614$	−7.35002	+	22.1116i	−0.296623	+	0.892352i
$615$	−0.991751	+	1.86016i	−0.0399913	+	0.0750088i
$616$	4.88895	−	3.40281i	0.196982	−	0.137103i
$617$	9.03549	+	10.8920i	0.363755	+	0.438497i	0.919640	−	0.392763i	$-0.128481\pi$
$617$	9.03549	+	10.8920i	0.363755	+	0.438497i	−0.555885	+	0.831259i	$0.687620\pi$
$618$	2.94746	−	0.605718i	0.118564	−	0.0243656i
$619$	0.991416	+	3.82907i	0.0398484	+	0.153903i	0.984938	−	0.172908i	$-0.0553162\pi$
$619$	0.991416	+	3.82907i	0.0398484	+	0.153903i	−0.945090	+	0.326811i	$0.894026\pi$
$620$	−22.1373	−	11.7375i	−0.889056	−	0.471390i
$621$	2.72299	−	10.5168i	0.109270	−	0.422025i
$622$	2.19447	−	43.2712i	0.0879902	−	1.73502i
$623$	42.6407	−	73.8559i	1.70837	−	2.95898i
$624$	−4.73794	−	1.48654i	−0.189669	−	0.0595091i
$625$	16.0979	−	23.9824i	0.643915	−	0.959296i
$626$	−42.3536	+	31.6548i	−1.69279	+	1.26518i
$627$	−0.313555	+	2.63966i	−0.0125222	+	0.105418i
$628$	36.2701			1.44734
$629$	18.1854	+	0.614548i	0.725101	+	0.0245036i
$630$	−36.8108	+	69.0434i	−1.46658	+	2.75075i
$631$	3.86227	−	5.75396i	0.153755	−	0.229062i	−0.745480	−	0.666528i	$-0.767780\pi$
$631$	3.86227	−	5.75396i	0.153755	−	0.229062i	0.899235	+	0.437466i	$0.144124\pi$
$632$	0.0940714	+	1.11126i	0.00374196	+	0.0442036i
$633$	0.541485	−	0.806698i	0.0215221	−	0.0320634i
$634$	−16.2433	−	8.31099i	−0.645106	−	0.330071i
$635$	2.52994	+	49.8861i	0.100398	+	1.97967i
$636$	0.440293	+	0.0904826i	0.0174588	+	0.00358787i
$637$	−31.7836	−	59.6142i	−1.25931	−	2.36200i
$638$	−14.0486	−	10.4999i	−0.556191	−	0.415694i
$639$	9.25107	−	12.8239i	0.365967	−	0.507305i
$640$	15.6229	−	15.3613i	0.617550	−	0.607207i
$641$	−1.05277	+	12.4363i	−0.0415819	+	0.491205i	0.944903	+	0.327351i	$0.106156\pi$
$641$	−1.05277	+	12.4363i	−0.0415819	+	0.491205i	−0.986485	+	0.163854i	$0.947607\pi$
$642$	0.261696	−	0.0177074i	0.0103283	−	0.000698857i
$643$	−20.6865	+	11.4819i	−0.815795	+	0.452803i	−0.837153	−	0.546969i	$-0.815782\pi$
$643$	−20.6865	+	11.4819i	−0.815795	+	0.452803i	0.0213582	+	0.999772i	$0.493201\pi$
$644$	52.9643	−	12.7629i	2.08708	−	0.502929i
$645$	2.92343	+	2.87446i	0.115110	+	0.113182i
$646$	13.4692	+	60.3536i	0.529939	+	2.37458i
$647$	21.2984	−	18.2841i	0.837326	−	0.718821i	−0.124578	−	0.992210i	$-0.539758\pi$
$647$	21.2984	−	18.2841i	0.837326	−	0.718821i	0.961904	+	0.273389i	$0.0881447\pi$
$648$	−1.74084	+	7.80045i	−0.0683867	+	0.306431i
$649$	11.1420	−	4.78141i	0.437362	−	0.187687i
$650$	20.3369	+	26.2731i	0.797678	+	1.03051i
$651$	3.40757	+	5.24028i	0.133553	+	0.205383i
$652$	8.99831	−	11.6249i	0.352401	−	0.455264i
$653$	−4.90431	+	18.9416i	−0.191920	+	0.741240i	0.798363	+	0.602176i	$0.205700\pi$
$653$	−4.90431	+	18.9416i	−0.191920	+	0.741240i	−0.990283	+	0.139064i	$0.955591\pi$
$654$	3.09303	+	7.55733i	0.120947	+	0.295515i
$655$	−47.8176	−	20.5202i	−1.86839	−	0.801789i
$656$	−13.5265	+	3.74713i	−0.528121	+	0.146301i
$657$	−42.3966	−	21.6924i	−1.65405	−	0.846302i
$658$	28.0272	−	38.8514i	1.09261	−	1.51459i
$659$	−1.79353	+	35.3654i	−0.0698661	+	1.37764i	0.688227	+	0.725495i	$0.258389\pi$
$659$	−1.79353	+	35.3654i	−0.0698661	+	1.37764i	−0.758093	+	0.652146i	$0.773869\pi$
$660$	−1.37910	+	0.382039i	−0.0536812	+	0.0148709i
$661$	−23.3535	−	26.2918i	−0.908347	−	1.02263i	−0.999641	−	0.0268078i	$-0.991466\pi$
$661$	−23.3535	−	26.2918i	−0.908347	−	1.02263i	0.0912936	−	0.995824i	$-0.470900\pi$
$662$	−38.5763	+	15.0328i	−1.49931	+	0.584265i
$663$	−3.67912	−	1.88244i	−0.142885	−	0.0731079i
$664$	3.84800	+	3.53601i	0.149331	+	0.137224i
$665$	−78.9102	+	88.8384i	−3.06001	+	3.44501i
$666$	−19.2117	−	16.4927i	−0.744439	−	0.639080i
$667$	28.5166	+	45.7506i	1.10417	+	1.77147i
$668$	−18.8210	+	17.2950i	−0.728206	+	0.669166i
$669$	0.494213	−	0.926960i	0.0191074	−	0.0358383i
$670$	−32.2591	−	2.18279i	−1.24628	−	0.0843284i
$671$	0.662574	−	3.52506i	0.0255784	−	0.136084i
$672$	7.58079	−	2.10004i	0.292435	−	0.0810108i
$673$	−46.0226	−	11.0902i	−1.77404	−	0.427494i	−0.791140	−	0.611635i	$-0.790512\pi$
$673$	−46.0226	−	11.0902i	−1.77404	−	0.427494i	−0.982900	+	0.184141i	$0.941050\pi$
$674$	−3.52238	−	5.65113i	−0.135677	−	0.217673i
$675$	−4.19631	+	3.85609i	−0.161516	+	0.148421i
$676$	8.98027	−	3.15450i	0.345395	−	0.121327i
$677$	4.14163	+	3.09542i	0.159176	+	0.118967i	0.675288	−	0.737554i	$-0.264019\pi$
$677$	4.14163	+	3.09542i	0.159176	+	0.118967i	−0.516113	+	0.856521i	$0.672621\pi$
$678$	−2.98816	+	3.14354i	−0.114759	+	0.120727i
$679$	18.1483	−	8.52496i	0.696467	−	0.327158i
$680$	9.18254	−	6.39124i	0.352134	−	0.245093i
$681$	−1.75503	−	0.974120i	−0.0672528	−	0.0373283i
$682$	3.23537	−	13.5628i	0.123889	−	0.519345i
$683$	2.47002	−	1.37097i	0.0945126	−	0.0524588i	−0.437336	−	0.899298i	$-0.644078\pi$
$683$	2.47002	−	1.37097i	0.0945126	−	0.0524588i	0.531849	+	0.846839i	$0.321497\pi$
$684$	16.2220	−	33.0708i	0.620264	−	1.26450i
$685$	39.6332	+	10.9792i	1.51430	+	0.419495i
$686$	64.5859	+	35.8481i	2.46590	+	1.36869i
$687$	2.89120	+	1.35811i	0.110306	+	0.0518152i
$688$	−0.461055	+	27.2944i	−0.0175775	+	1.04059i
$689$	5.03610	−	2.36565i	0.191860	−	0.0901242i
$690$	10.2228	+	1.03956i	0.389177	+	0.0395754i
$691$	42.2683	−	27.3480i	1.60796	−	1.04037i	0.647459	−	0.762101i	$-0.275832\pi$
$691$	42.2683	−	27.3480i	1.60796	−	1.04037i	0.960504	−	0.278266i	$-0.0897595\pi$
$692$	−17.7130	+	6.90257i	−0.673348	+	0.262396i
$693$	−18.1197	−	4.36633i	−0.688309	−	0.165863i
$694$	−13.1966	+	7.91920i	−0.500936	+	0.300609i
$695$	23.9596	−	19.2019i	0.908841	−	0.728371i
$696$	0.871898	+	1.29894i	0.0330492	+	0.0492363i
$697$	−11.6216	+	1.18180i	−0.440201	+	0.0447640i
$698$	−2.71892	+	10.5011i	−0.102913	+	0.397472i
$699$	1.66744	+	1.07885i	0.0630686	+	0.0408059i
$700$	−26.9649	−	9.47194i	−1.01918	−	0.358006i
$701$	20.3245	+	38.1212i	0.767646	+	1.43982i	0.894110	+	0.447848i	$0.147809\pi$
$701$	20.3245	+	38.1212i	0.767646	+	1.43982i	−0.126464	+	0.991971i	$0.540363\pi$
$702$	4.75874	+	10.5919i	0.179607	+	0.399764i
$703$	−22.4963	−	31.1845i	−0.848464	−	1.17614i
$704$	−4.12995	−	2.47836i	−0.155653	−	0.0934068i
$705$	3.17458	−	2.20957i	0.119561	−	0.0832172i
$706$	1.01569	−	3.05559i	0.0382262	−	0.114999i
$707$	2.48735	−	20.9397i	0.0935464	−	0.787520i
$708$	3.21073	−	0.217251i	0.120667	−	0.00816481i
$709$	23.1299	−	29.8813i	0.868660	−	1.12222i	−0.122881	−	0.992421i	$-0.539213\pi$
$709$	23.1299	−	29.8813i	0.868660	−	1.12222i	0.991541	−	0.129795i	$-0.0414319\pi$
$710$	26.8848	+	13.7557i	1.00897	+	0.516244i
$711$	2.40422	−	2.52924i	0.0901653	−	0.0948538i
$712$	16.8814	+	1.71668i	0.632659	+	0.0643351i
$713$	−24.4029	+	35.2326i	−0.913897	+	1.31947i
$714$	8.26219	−	0.840182i	0.309205	−	0.0314430i
$715$	−10.8428	+	14.0078i	−0.405499	+	0.523861i
$716$	8.22660	−	6.14850i	0.307442	−	0.229780i
$717$	−1.52553	−	1.06180i	−0.0569719	−	0.0396536i
$718$	−9.48061	−	21.1017i	−0.353813	−	0.787507i
$719$	−19.1401	+	8.99084i	−0.713804	+	0.335302i	−0.747620	−	0.664126i	$-0.768804\pi$
$719$	−19.1401	+	8.99084i	−0.713804	+	0.335302i	0.0338167	+	0.999428i	$0.489234\pi$
$720$	−41.9664	−	2.83962i	−1.56400	−	0.105826i
$721$	−4.85185	+	31.6712i	−0.180692	+	1.17950i
$722$	60.7490	−	73.2312i	2.26084	−	2.72538i
$723$	−0.0856643	−	5.07133i	−0.00318589	−	0.188605i
$724$	7.75623	+	8.73209i	0.288258	+	0.324526i
$725$	0.477651	−	28.2770i	0.0177395	−	1.05018i
$726$	2.04400	+	3.54030i	0.0758598	+	0.131393i
$727$	5.98854	−	2.10359i	0.222103	−	0.0780180i	−0.218063	−	0.975935i	$-0.569974\pi$
$727$	5.98854	−	2.10359i	0.222103	−	0.0780180i	0.440165	+	0.897917i	$0.354920\pi$
$728$	11.9789	−	15.4755i	0.443969	−	0.573561i
$729$	20.9869	−	11.6487i	0.777291	−	0.431432i
$730$	28.6904	−	86.3113i	1.06188	−	3.19452i
$731$	−4.19686	+	22.3284i	−0.155226	+	0.825844i
$732$	0.475997	−	0.824451i	0.0175934	−	0.0304726i
$733$	12.1842	+	7.31168i	0.450034	+	0.270063i	0.721539	−	0.692374i	$-0.243435\pi$
$733$	12.1842	+	7.31168i	0.450034	+	0.270063i	−0.271504	+	0.962437i	$0.587521\pi$
$734$	27.5146	−	40.9909i	1.01558	−	1.51300i
$735$	7.27908	+	8.19491i	0.268493	+	0.302274i
$736$	33.0141	+	42.6507i	1.21691	+	1.57212i
$737$	−1.42276	−	7.56946i	−0.0524081	−	0.278825i
$738$	13.6477	+	8.83018i	0.502379	+	0.325044i
$739$	−36.4951	+	35.8838i	−1.34249	+	1.32001i	−0.434709	+	0.900571i	$0.643149\pi$
$739$	−36.4951	+	35.8838i	−1.34249	+	1.32001i	−0.907785	+	0.419437i	$0.862228\pi$
$740$	10.9498	−	17.5673i	0.402521	−	0.645785i
$741$	1.61329	+	8.58313i	0.0592658	+	0.315309i
$742$	−5.91436	+	9.48872i	−0.217123	+	0.348342i
$743$	14.2595	−	4.47396i	0.523132	−	0.164134i	−0.0263287	−	0.999653i	$-0.508382\pi$
$743$	14.2595	−	4.47396i	0.523132	−	0.164134i	0.549461	+	0.835520i	$0.314833\pi$
$744$	−0.673219	+	1.04576i	−0.0246814	+	0.0383394i
$745$	7.89690	+	2.47767i	0.289320	+	0.0907747i
$746$	23.5371	−	20.2059i	0.861755	−	0.739792i
$747$	0.276178	−	16.3498i	0.0101048	−	0.598207i
$748$	−6.01699	−	5.16542i	−0.220003	−	0.188866i
$749$	−0.790975	+	2.67859i	−0.0289016	+	0.0978737i
$750$	1.00196	+	0.802999i	0.0365864	+	0.0293214i
$751$	−0.704360	−	0.455727i	−0.0257025	−	0.0166297i	0.530307	−	0.847806i	$-0.322077\pi$
$751$	−0.704360	−	0.455727i	−0.0257025	−	0.0166297i	−0.556009	+	0.831176i	$0.687668\pi$
$752$	25.2262	+	5.18411i	0.919904	+	0.189045i
$753$	0.387241	−	0.946164i	0.0141119	−	0.0344801i
$754$	−54.3663	−	19.0973i	−1.97991	−	0.695481i
$755$	0.163130	+	1.37331i	0.00593692	+	0.0499800i
$756$	−8.38632	−	5.42602i	−0.305007	−	0.197342i
$757$	27.6435	−	10.7724i	1.00472	−	0.391528i	0.196560	−	0.980492i	$-0.437023\pi$
$757$	27.6435	−	10.7724i	1.00472	−	0.391528i	0.808159	+	0.588964i	$0.200464\pi$
$758$	4.11367	+	48.5947i	0.149415	+	1.76504i
$759$	0.370655	+	2.41951i	0.0134539	+	0.0878227i
$760$	−22.5582	−	7.07767i	−0.818271	−	0.256734i
$761$	−15.2415	−	1.03130i	−0.552503	−	0.0373847i	−0.211381	−	0.977404i	$-0.567796\pi$
$761$	−15.2415	−	1.03130i	−0.552503	−	0.0373847i	−0.341122	+	0.940019i	$0.610807\pi$
$762$	−7.37331	−	0.249170i	−0.267107	−	0.00902646i
$763$	−86.9004	+	2.93666i	−3.14601	+	0.106314i
$764$	−21.3947	+	1.44765i	−0.774034	+	0.0523743i
$765$	−34.0327	−	8.20094i	−1.23046	−	0.296506i
$766$	−17.9752	−	40.0087i	−0.649471	−	1.44557i
$767$	30.2249	−	25.9473i	1.09136	−	0.936901i
$768$	3.15660	+	3.80519i	0.113904	+	0.137308i
$769$	−6.18789	+	3.71332i	−0.223141	+	0.133906i	−0.621751	−	0.783215i	$-0.713579\pi$
$769$	−6.18789	+	3.71332i	−0.223141	+	0.133906i	0.398610	+	0.917120i	$0.369493\pi$
$770$	3.00260	−	35.4697i	0.108206	−	1.27824i
$771$	0.126928	−	0.258761i	0.00457121	−	0.00931904i
$772$	11.2845	−	12.7042i	0.406137	−	0.457236i
$773$	−4.24199	+	11.4537i	−0.152574	+	0.411962i	−0.991137	−	0.132842i	$-0.957590\pi$
$773$	−4.24199	+	11.4537i	−0.152574	+	0.411962i	0.838563	+	0.544804i	$0.183396\pi$
$774$	23.9878	−	20.5929i	0.862225	−	0.740196i
$775$	20.7884	−	8.56386i	0.746741	−	0.307623i
$776$	3.02708	+	2.59866i	0.108666	+	0.0932866i
$777$	−4.51517	+	2.50612i	−0.161981	+	0.0899066i
$778$	47.3861	+	37.9766i	1.69887	+	1.36153i
$779$	17.0077	+	17.8921i	0.609366	+	0.641052i
$780$	−3.94740	+	2.55400i	−0.141340	+	0.0914480i
$781$	−1.56691	+	7.02110i	−0.0560685	+	0.251235i
$782$	26.7892	+	50.2465i	0.957979	+	1.79681i
$783$	2.47747	−	9.56854i	0.0885374	−	0.341952i
$784$	−6.15607	+	72.7214i	−0.219859	+	2.59719i
$785$	−46.5076	+	56.0636i	−1.65993	+	2.00099i
$786$	3.61571	−	6.78172i	0.128968	−	0.241896i
$787$	15.8003	−	7.42200i	0.563219	−	0.264566i	−0.122456	−	0.992474i	$-0.539077\pi$
$787$	15.8003	−	7.42200i	0.563219	−	0.264566i	0.685675	+	0.727908i	$0.259507\pi$
$788$	−4.20072	−	18.8228i	−0.149644	−	0.670534i
$789$	2.49059	+	0.424714i	0.0886674	+	0.0151202i
$790$	5.47009	+	3.80730i	0.194617	+	0.135458i
$791$	−20.3385	−	41.4628i	−0.723153	−	1.47425i
$792$	−0.685052	−	3.64466i	−0.0243423	−	0.129507i
$793$	−1.39003	−	11.7019i	−0.0493613	−	0.415548i
$794$	3.60258	+	5.36707i	0.127851	+	0.190470i
$795$	−0.704430	+	0.564550i	−0.0249835	+	0.0200225i
$796$	3.76986	+	31.7366i	0.133619	+	1.12487i
$797$	−3.04092	−	25.6000i	−0.107715	−	0.906799i	−0.937325	−	0.348456i	$-0.886706\pi$
$797$	−3.04092	−	25.6000i	−0.107715	−	0.906799i	0.829610	−	0.558343i	$-0.188563\pi$
$798$	−12.0913	−	12.7201i	−0.428029	−	0.450286i
$799$	19.9707	+	7.78238i	0.706514	+	0.275321i
$800$	−2.38664	−	28.1933i	−0.0843805	−	0.996783i
$801$	−31.0631	−	43.0598i	−1.09756	−	1.52144i
$802$	−1.98785	+	5.36735i	−0.0701933	+	0.189528i
$803$	21.6169	+	1.46269i	0.762843	+	0.0516171i
$804$	0.309555	−	2.02067i	0.0109172	−	0.0712634i
$805$	−48.1858	+	98.2334i	−1.69833	+	3.46227i
$806$	−3.19738	−	45.6982i	−0.112623	−	1.60965i
$807$	−0.291082	−	0.593412i	−0.0102466	−	0.0208891i
$808$	4.00327	−	1.25603i	0.140834	−	0.0441871i
$809$	−19.3832	+	4.67080i	−0.681476	+	0.164217i	−0.560144	−	0.828395i	$-0.689254\pi$
$809$	−19.3832	+	4.67080i	−0.681476	+	0.164217i	−0.121332	+	0.992612i	$0.538717\pi$
$810$	29.2355	+	37.7691i	1.02723	+	1.32707i
$811$	38.0308	+	5.17032i	1.33544	+	0.181554i	0.767254	−	0.641344i	$-0.221623\pi$
$811$	38.0308	+	5.17032i	1.33544	+	0.181554i	0.568189	+	0.822898i	$0.307644\pi$
$812$	48.1886	−	11.6121i	1.69109	−	0.407505i
$813$	−0.0208508	+	1.23437i	−0.000731271	+	0.0432913i
$814$	10.9909	+	3.44843i	0.385232	+	0.120867i
$815$	6.43068	+	28.8149i	0.225257	+	1.00934i
$816$	2.23226	+	3.86639i	0.0781448	+	0.135351i
$817$	42.7415	−	21.8689i	1.49534	−	0.765096i
$818$	5.14192	−	43.2873i	0.179783	−	1.51350i
$819$	−61.0955	+	4.13397i	−2.13485	+	0.144453i
$820$	−5.44630	+	12.1222i	−0.190193	+	0.423326i
$821$	−43.6175	+	8.96363i	−1.52226	+	0.312833i	−0.887840	−	0.460153i	$-0.847795\pi$
$821$	−43.6175	+	8.96363i	−1.52226	+	0.312833i	−0.634423	+	0.772986i	$0.718762\pi$
$822$	−2.10959	+	5.69607i	−0.0735805	+	0.198673i
$823$	21.3327	−	10.0208i	0.743612	−	0.349304i	−0.0158334	−	0.999875i	$-0.505040\pi$
$823$	21.3327	−	10.0208i	0.743612	−	0.349304i	0.759446	+	0.650571i	$0.225470\pi$
$824$	−6.14377	+	1.70196i	−0.214028	+	0.0592905i
$825$	0.526238	−	1.17128i	0.0183212	−	0.0407789i
$826$	−22.6702	+	76.7713i	−0.788797	+	2.67122i
$827$	31.5729	−	16.1544i	1.09790	−	0.561744i	0.190358	−	0.981715i	$-0.439035\pi$
$827$	31.5729	−	16.1544i	1.09790	−	0.561744i	0.907538	+	0.419971i	$0.137960\pi$
$828$	6.26564	−	33.3348i	0.217746	−	1.15847i
$829$	20.2452	−	21.2979i	0.703144	−	0.739707i	−0.271752	−	0.962367i	$-0.587603\pi$
$829$	20.2452	−	21.2979i	0.703144	−	0.739707i	0.974896	+	0.222660i	$0.0714741\pi$
$830$	30.9455	−	4.20706i	1.07413	−	0.146029i
$831$	−1.18657	−	0.462393i	−0.0411617	−	0.0160403i
$832$	−15.3840	−	3.70712i	−0.533345	−	0.128521i
$833$	−15.2246	+	58.8007i	−0.527500	+	2.03732i
$834$	2.52747	+	3.76539i	0.0875192	+	0.130385i
$835$	−2.60005	−	51.2687i	−0.0899786	−	1.77423i
$836$	−0.848781	+	16.7365i	−0.0293557	+	0.578845i
$837$	7.76442	−	1.20769i	0.268378	−	0.0417438i
$838$	−0.523603	−	10.3246i	−0.0180876	−	0.356656i
$839$	−26.5252	+	2.69735i	−0.915751	+	0.0931228i	−0.547692	−	0.836680i	$-0.684494\pi$
$839$	−26.5252	+	2.69735i	−0.915751	+	0.0931228i	−0.368059	+	0.929803i	$0.619977\pi$
$840$	−1.30124	+	2.89626i	−0.0448970	+	0.0999305i
$841$	10.6054	+	17.0147i	0.365702	+	0.586714i
$842$	−21.7976	−	24.5401i	−0.751194	−	0.845707i
$843$	−2.69533	−	3.24915i	−0.0928322	−	0.111907i
$844$	3.06254	−	5.30447i	0.105417	−	0.182587i
$845$	−6.63902	+	17.9259i	−0.228389	+	0.616669i
$846$	−14.9127	−	25.8295i	−0.512708	−	0.888036i
$847$	−42.9099	+	7.31732i	−1.47440	+	0.251426i
$848$	−5.95596	−	0.809716i	−0.204528	−	0.0278058i
$849$	2.57626	+	2.06469i	0.0884170	+	0.0708599i
$850$	2.51968	−	29.7649i	0.0864244	−	1.02093i
$851$	−27.6292	−	22.1428i	−0.947116	−	0.759046i
$852$	−1.00998	+	1.62037i	−0.0346014	+	0.0555129i
$853$	−23.8957	+	10.2545i	−0.818174	+	0.351106i	−0.762212	−	0.647327i	$-0.775887\pi$
$853$	−23.8957	+	10.2545i	−0.818174	+	0.351106i	−0.0559613	+	0.998433i	$0.517822\pi$
$854$	15.1192	+	18.2258i	0.517368	+	0.623672i
$855$	30.3176	+	67.4800i	1.03684	+	2.30777i
$856$	−0.550647	+	0.0748609i	−0.0188207	+	0.00255869i
$857$	−14.7435	−	44.3538i	−0.503627	−	1.51510i	−0.823320	−	0.567577i	$-0.807881\pi$
$857$	−14.7435	−	44.3538i	−0.503627	−	1.51510i	0.319693	−	0.947521i	$-0.396420\pi$
$858$	−1.92646	−	1.77027i	−0.0657681	−	0.0604359i
$859$	−21.2356	+	39.8301i	−0.724550	+	1.35899i	0.200709	+	0.979651i	$0.435675\pi$
$859$	−21.2356	+	39.8301i	−0.724550	+	1.35899i	−0.925259	+	0.379336i	$0.876153\pi$
$860$	19.6113	+	16.8357i	0.668740	+	0.574094i
$861$	2.65554	−	1.98473i	0.0905006	−	0.0676395i
$862$	25.5689	−	23.4959i	0.870882	−	0.800274i
$863$	−33.4183	+	17.0986i	−1.13757	+	0.582044i	−0.919188	−	0.393819i	$-0.871154\pi$
$863$	−33.4183	+	17.0986i	−1.13757	+	0.582044i	−0.218384	+	0.975863i	$0.570078\pi$
$864$	1.49742	−	9.77462i	0.0509432	−	0.332539i
$865$	12.0432	−	36.2303i	0.409479	−	1.23187i
$866$	−12.5731	−	48.5600i	−0.427250	−	1.65014i
$867$	−0.111472	−	0.300983i	−0.00378579	−	0.0102219i
$868$	23.6634	+	31.5103i	0.803188	+	1.06953i
$869$	−0.551375	+	1.48876i	−0.0187041	+	0.0505026i
$870$	9.30108	+	0.945827i	0.315336	+	0.0320665i
$871$	−11.9049	−	22.3292i	−0.403382	−	0.756595i
$872$	−7.61904	−	15.5325i	−0.258013	−	0.525996i
$873$	−0.210837	−	12.4815i	−0.00713574	−	0.422436i
$874$	49.3142	−	109.762i	1.66808	−	3.71276i
$875$	−11.7235	+	7.03524i	−0.396328	+	0.237834i
$876$	5.28456	+	2.26778i	0.178549	+	0.0766212i
$877$	−13.6866	−	12.5769i	−0.462162	−	0.424692i	0.411362	−	0.911472i	$-0.365053\pi$
$877$	−13.6866	−	12.5769i	−0.462162	−	0.424692i	−0.873525	+	0.486780i	$0.838171\pi$
$878$	−0.925373	+	4.92322i	−0.0312298	+	0.166151i
$879$	−3.10071	−	2.84932i	−0.104584	−	0.0961050i
$880$	18.0546	−	6.34205i	0.608621	−	0.213790i
$881$	−18.7001	−	4.50620i	−0.630022	−	0.151818i	−0.0933837	−	0.995630i	$-0.529768\pi$
$881$	−18.7001	−	4.50620i	−0.630022	−	0.151818i	−0.536638	+	0.843812i	$0.680306\pi$
$882$	67.7013	−	50.5995i	2.27962	−	1.70377i
$883$	11.2193	+	43.3316i	0.377560	+	1.45822i	0.825623	+	0.564222i	$0.190824\pi$
$883$	11.2193	+	43.3316i	0.377560	+	1.45822i	−0.448063	+	0.894002i	$0.647886\pi$
$884$	−23.9423	−	10.2744i	−0.805267	−	0.345567i
$885$	−3.78117	+	5.24147i	−0.127103	+	0.176190i
$886$	12.0134	−	7.77276i	0.403597	−	0.261131i
$887$	8.92417	+	10.7578i	0.299644	+	0.361213i	0.897983	−	0.440031i	$-0.145032\pi$
$887$	8.92417	+	10.7578i	0.299644	+	0.361213i	−0.598339	+	0.801243i	$0.704172\pi$
$888$	−0.823023	−	0.615122i	−0.0276189	−	0.0206421i
$889$	29.7556	−	72.7031i	0.997970	−	2.43838i
$890$	72.3062	−	71.0951i	2.42371	−	2.38311i
$891$	−6.96418	+	8.99697i	−0.233309	+	0.301410i
$892$	2.71402	−	6.04078i	0.0908721	−	0.202260i
$893$	−12.8275	−	43.4397i	−0.429257	−	1.45365i
$894$	−0.463024	+	1.13133i	−0.0154858	+	0.0378372i
$895$	−1.04471	+	20.6000i	−0.0349209	+	0.688582i
$896$	−32.5102	+	11.4199i	−1.08609	+	0.381511i
$897$	3.54161	+	7.22006i	0.118251	+	0.241071i
$898$	−10.3591	−	10.8978i	−0.345689	−	0.363665i
$899$	−22.2026	+	32.0558i	−0.740498	+	1.06912i
$900$	−12.2591	+	12.8966i	−0.408638	+	0.429887i
$901$	−4.77309	−	1.49757i	−0.159015	−	0.0498912i
$902$	−7.29001	−	1.24315i	−0.242731	−	0.0413923i
$903$	−2.23937	−	6.04649i	−0.0745216	−	0.201214i
$904$	5.86682	−	7.07229i	0.195127	−	0.235221i
$905$	−23.4429	+	0.792214i	−0.779267	+	0.0263341i
$906$	−0.204144	+	0.00689873i	−0.00678224	+	0.000229195i
$907$	12.8378	−	26.1716i	0.426272	−	0.869014i	−0.572521	−	0.819890i	$-0.694034\pi$
$907$	12.8378	−	26.1716i	0.426272	−	0.869014i	0.998793	−	0.0491239i	$-0.0156429\pi$
$908$	−11.4535	−	5.38014i	−0.380096	−	0.178546i
$909$	−11.2570	−	6.75529i	−0.373372	−	0.224059i
$910$	−25.4734	−	114.142i	−0.844434	−	3.78379i
$911$	4.54978	−	20.3869i	0.150741	−	0.675448i	−0.840326	−	0.542081i	$-0.817636\pi$
$911$	4.54978	−	20.3869i	0.150741	−	0.675448i	0.991067	−	0.133366i	$-0.0425787\pi$
$912$	3.57362	−	8.73158i	0.118334	−	0.289132i
$913$	2.81786	+	6.88500i	0.0932575	+	0.227860i
$914$	16.4579	+	9.13489i	0.544380	+	0.302155i
$915$	0.664023	+	1.79292i	0.0219519	+	0.0592720i
$916$	18.7633	+	7.31184i	0.619955	+	0.241590i
$917$	54.3460	+	61.1836i	1.79466	+	2.02046i
$918$	3.29311	−	9.90691i	0.108689	−	0.326977i
$919$	21.0860	+	0.712570i	0.695564	+	0.0235055i	0.379445	−	0.925214i	$-0.376115\pi$
$919$	21.0860	+	0.712570i	0.695564	+	0.0235055i	0.316119	+	0.948720i	$0.397620\pi$
$920$	−21.7580	−	0.735276i	−0.717339	−	0.0242413i
$921$	2.63396	−	1.34768i	0.0867920	−	0.0444076i
$922$	8.89121	+	6.18846i	0.292816	+	0.203806i
$923$	1.99363	+	23.5507i	0.0656211	+	0.775180i
$924$	2.21856	+	0.378325i	0.0729851	+	0.0124460i
$925$	5.85905	+	17.6262i	0.192644	+	0.579546i
$926$	−1.73378	−	34.1872i	−0.0569755	−	1.12346i
$927$	16.7481	+	10.8362i	0.550081	+	0.355907i
$928$	30.0373	+	38.8050i	0.986022	+	1.27384i
$929$	−40.3945	−	17.3346i	−1.32530	−	0.568731i	−0.389424	−	0.921059i	$-0.627326\pi$
$929$	−40.3945	−	17.3346i	−1.32530	−	0.568731i	−0.935877	+	0.352328i	$0.885390\pi$
$930$	2.24125	+	7.08647i	0.0734934	+	0.232374i
$931$	117.955	−	50.6184i	3.86581	−	1.65895i
$932$	10.9472	+	6.07616i	0.358586	+	0.199031i
$933$	−4.05090	+	3.72247i	−0.132621	+	0.121868i
$934$	−13.9184	−	53.7562i	−0.455425	−	1.75896i
$935$	15.6996	−	2.67722i	0.513433	−	0.0875544i
$936$	−5.73215	−	10.7514i	−0.187361	−	0.351420i
$937$	45.1681	+	23.1105i	1.47558	+	0.754987i	0.992690	−	0.120694i	$-0.0385121\pi$
$937$	45.1681	+	23.1105i	1.47558	+	0.754987i	0.482889	+	0.875681i	$0.339587\pi$
$938$	44.4604	+	24.6775i	1.45168	+	0.805750i
$939$	6.65282	+	0.904455i	0.217107	+	0.0295158i
$940$	19.0272	−	15.2490i	0.620600	−	0.497367i
$941$	6.19749	−	15.1426i	0.202032	−	0.493635i	−0.790952	−	0.611878i	$-0.790414\pi$
$941$	6.19749	−	15.1426i	0.202032	−	0.493635i	0.992985	+	0.118243i	$0.0377262\pi$
$942$	−7.67152	−	7.54303i	−0.249952	−	0.245765i
$943$	19.4910	+	11.6965i	0.634715	+	0.380889i
$944$	−42.6406	+	5.79701i	−1.38783	+	0.188677i
$945$	19.1405	−	6.00538i	0.622641	−	0.195355i
$946$	−6.33417	+	12.9131i	−0.205941	+	0.419840i
$947$	−1.29074	+	10.8661i	−0.0419435	+	0.353102i	0.956226	+	0.292628i	$0.0945299\pi$
$947$	−1.29074	+	10.8661i	−0.0419435	+	0.353102i	−0.998170	+	0.0604734i	$0.980739\pi$
$948$	−0.269030	+	0.324308i	−0.00873769	+	0.0105330i
$949$	69.2026	−	16.6759i	2.24641	−	0.541322i
$950$	−52.9992	+	34.2910i	−1.71952	+	1.11255i
$951$	0.730810	+	2.19855i	0.0236981	+	0.0712928i
$952$	−17.3446	+	2.95774i	−0.562143	+	0.0958608i
$953$	11.1090	−	17.8227i	0.359856	−	0.577335i	−0.618112	−	0.786090i	$-0.712102\pi$
$953$	11.1090	−	17.8227i	0.359856	−	0.577335i	0.977968	+	0.208755i	$0.0669410\pi$
$954$	3.87961	+	5.77979i	0.125607	+	0.187128i
$955$	25.1958	−	34.9266i	0.815317	−	1.13020i
$956$	−10.0473	−	6.02931i	−0.324952	−	0.195002i
$957$	0.337234	+	2.20135i	0.0109012	+	0.0711596i
$958$	2.82234	+	33.3401i	0.0911855	+	1.07717i
$959$	−49.0752	−	42.1297i	−1.58472	−	1.36044i
$960$	2.56743			0.0828634
$961$	−30.3937	−	6.10098i	−0.980442	−	0.196806i
$962$	37.8457			1.22020
$963$	1.31936	+	1.13263i	0.0425157	+	0.0364985i
$964$	−2.69716	−	31.8615i	−0.0868698	−	1.02619i
$965$	5.16766	+	33.7327i	0.166353	+	1.08590i
$966$	−13.8568	−	8.31538i	−0.445835	−	0.267543i
$967$	−1.92879	+	2.67370i	−0.0620257	+	0.0859804i	−0.840871	−	0.541236i	$-0.817956\pi$
$967$	−1.92879	+	2.67370i	−0.0620257	+	0.0859804i	0.778845	+	0.627217i	$0.215806\pi$
$968$	−4.82702	−	7.19123i	−0.155146	−	0.231135i
$969$	4.15345	−	6.66359i	0.133428	−	0.214065i
$970$	23.5021	−	4.00775i	0.754606	−	0.128681i
$971$	−8.02652	−	24.1468i	−0.257583	−	0.774906i	−0.995037	−	0.0995085i	$-0.968273\pi$
$971$	−8.02652	−	24.1468i	−0.257583	−	0.774906i	0.737453	−	0.675398i	$-0.236028\pi$
$972$	−7.85654	+	5.08325i	−0.251999	+	0.163045i
$973$	−46.9454	+	11.3125i	−1.50500	+	0.362663i
$974$	−10.1838	+	12.2763i	−0.326309	+	0.393357i
$975$	0.497628	−	4.18929i	0.0159369	−	0.134165i
$976$	−5.60634	+	11.4293i	−0.179455	+	0.365843i
$977$	−14.4701	+	4.54003i	−0.462940	+	0.145248i	−0.521890	−	0.853013i	$-0.674773\pi$
$977$	−14.4701	+	4.54003i	−0.462940	+	0.145248i	0.0589505	+	0.998261i	$0.481225\pi$
$978$	−4.32084	+	0.587421i	−0.138165	+	0.0187836i
$979$	20.7121	+	12.4292i	0.661963	+	0.397241i
$980$	49.2721	+	48.4468i	1.57394	+	1.54758i
$981$	−20.5047	+	50.1000i	−0.654665	+	1.59957i
$982$	−25.4538	+	20.3994i	−0.812263	+	0.650971i
$983$	18.6621	+	2.53712i	0.595227	+	0.0809216i	0.426105	−	0.904674i	$-0.359885\pi$
$983$	18.6621	+	2.53712i	0.595227	+	0.0809216i	0.169122	+	0.985595i	$0.445907\pi$
$984$	0.576756	+	0.320126i	0.0183863	+	0.0102052i
$985$	34.4812	+	17.6425i	1.09866	+	0.562136i
$986$	24.3737	+	45.7159i	0.776216	+	1.45589i
$987$	−5.99636	+	1.02255i	−0.190866	+	0.0325480i
$988$	13.8003	+	53.3000i	0.439047	+	1.69570i
$989$	32.5527	−	29.9135i	1.03512	−	0.951193i
$990$	−19.3771	−	10.7552i	−0.615845	−	0.341822i
$991$	19.7554	−	8.47771i	0.627551	−	0.269303i	−0.0568799	−	0.998381i	$-0.518115\pi$
$991$	19.7554	−	8.47771i	0.627551	−	0.269303i	0.684431	+	0.729078i	$0.260051\pi$
$992$	−18.8544	+	34.1534i	−0.598627	+	1.08437i
$993$	4.83104	+	2.07316i	0.153308	+	0.0657898i
$994$	−29.0718	−	37.5577i	−0.922102	−	1.19126i
$995$	−53.8899	−	34.8672i	−1.70842	−	1.10536i
$996$	0.100008	+	1.97199i	0.00316887	+	0.0624848i
$997$	17.0045	+	51.1559i	0.538538	+	1.62012i	0.763537	+	0.645764i	$0.223461\pi$
$997$	17.0045	+	51.1559i	0.538538	+	1.62012i	−0.224999	+	0.974359i	$0.572238\pi$
$998$	−45.6898	−	7.79137i	−1.44628	−	0.246631i
$999$	0.547580	+	6.46855i	0.0173247	+	0.204656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.k.a.5.17	✓	4920
961.769	even	93	inner	961.2.k.a.769.17	yes	4920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.k.a.5.17	✓	4920	1.1	even	1	trivial
961.2.k.a.769.17	yes	4920	961.769	even	93	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.k (of order \(93\), degree \(60\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41888 - 1.21807i) q^{2} +(0.0200290 + 0.236602i) q^{3} +(0.226677 + 1.47967i) q^{4} +(-2.57781 - 1.54693i) q^{5} +(0.259779 - 0.360107i) q^{6} +(2.63507 + 3.92569i) q^{7} +(-0.497621 + 0.798359i) q^{8} +(2.90173 - 0.494825i) q^{9} +(1.77334 + 5.33488i) q^{10} +(-1.12437 + 0.727476i) q^{11} +(-0.345552 + 0.0832683i) q^{12} +(-2.80913 + 3.38633i) q^{13} +(1.04292 - 8.77980i) q^{14} +(0.314376 - 0.640898i) q^{15} +(4.53508 - 1.42289i) q^{16} +(3.91973 - 0.532890i) q^{17} +(-4.71995 - 2.83242i) q^{18} +(-5.96077 - 5.86093i) q^{19} +(1.70461 - 4.16496i) q^{20} +(-0.876047 + 0.702089i) q^{21} +(2.48147 + 0.337357i) q^{22} +(-6.73036 - 3.73565i) q^{23} +(-0.198860 - 0.101748i) q^{24} +(1.89979 + 3.56331i) q^{25} +(8.11063 - 1.38309i) q^{26} +(0.353746 + 1.36625i) q^{27} +(-5.21141 + 4.78889i) q^{28} +(-6.12350 - 3.39882i) q^{29} +(-1.22672 + 0.526428i) q^{30} +(0.550583 - 5.54047i) q^{31} +(-6.43893 - 2.76316i) q^{32} +(-0.194642 - 0.251457i) q^{33} +(-6.21074 - 4.01841i) q^{34} +(-0.719938 - 14.1960i) q^{35} +(1.38993 + 4.18143i) q^{36} +(4.53433 + 0.773229i) q^{37} +(1.31860 + 15.5766i) q^{38} +(-0.857476 - 0.596821i) q^{39} +(2.51778 - 1.28823i) q^{40} +(-2.95134 - 0.0997360i) q^{41} +(2.09820 + 0.0709055i) q^{42} +(-1.81165 + 5.45010i) q^{43} +(-1.33129 - 1.49879i) q^{44} +(-8.24558 - 3.21321i) q^{45} +(4.99930 + 13.4985i) q^{46} +(4.73744 + 2.62949i) q^{47} +(0.427492 + 1.04451i) q^{48} +(-5.81601 + 14.2105i) q^{49} +(1.64478 - 7.37000i) q^{50} +(0.204591 + 0.916742i) q^{51} +(-5.64741 - 3.38898i) q^{52} +(-1.14461 - 0.537669i) q^{53} +(1.16226 - 2.36943i) q^{54} +(4.02377 - 0.135977i) q^{55} +(-4.44538 + 0.150224i) q^{56} +(1.26732 - 1.52772i) q^{57} +(4.54853 + 12.2814i) q^{58} +(-8.92487 - 1.52194i) q^{59} +(1.01958 + 0.319895i) q^{60} +(-1.84528 + 1.94124i) q^{61} +(-7.52991 + 7.19064i) q^{62} +(9.58879 + 10.0874i) q^{63} +(1.58392 + 3.22903i) q^{64} +(12.4798 - 4.38379i) q^{65} +(-0.0301180 + 0.593876i) q^{66} +(-2.17845 + 5.32271i) q^{67} +(1.67701 + 5.67911i) q^{68} +(0.749060 - 1.66724i) q^{69} +(-16.2702 + 21.0194i) q^{70} +(3.83036 - 3.76621i) q^{71} +(-1.04891 + 2.56286i) q^{72} +(-12.9591 - 9.68558i) q^{73} +(-5.49184 - 6.62027i) q^{74} +(-0.805033 + 0.520864i) q^{75} +(7.32106 - 10.1485i) q^{76} +(-5.81863 - 2.49697i) q^{77} +(0.489688 + 1.89129i) q^{78} +(0.949571 - 0.709703i) q^{79} +(-13.8917 - 3.34751i) q^{80} +(8.01560 - 2.81564i) q^{81} +(4.06613 + 3.73646i) q^{82} +(1.02617 - 5.45950i) q^{83} +(-1.23744 - 1.13711i) q^{84} +(-10.9287 - 4.68987i) q^{85} +(9.20913 - 5.52635i) q^{86} +(0.681520 - 1.51691i) q^{87} +(-0.0212780 - 1.25966i) q^{88} +(-7.94351 - 16.1940i) q^{89} +(7.78559 + 14.6029i) q^{90} +(-20.6960 - 2.10457i) q^{91} +(4.00191 - 10.8055i) q^{92} +(1.32191 + 0.0192987i) q^{93} +(-3.51897 - 9.50149i) q^{94} +(6.29929 + 24.3293i) q^{95} +(0.524803 - 1.57880i) q^{96} +(0.642176 - 4.19190i) q^{97} +(25.5617 - 13.0787i) q^{98} +(-2.90264 + 2.66730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) \) 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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