LMFDB - Embedded newform 357.2.bh.a.100.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(25,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 16, 15]))

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

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

chi := DirichletCharacter("357.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			100.23
Character	$\chi$	$=$	357.100
Dual form			357.2.bh.a.25.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47406 - 0.662922i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(3.94945 - 2.28022i) q^{4} +(-0.293850 + 2.23202i) q^{5} +(-0.980180 + 2.36636i) q^{6} +(-1.00447 + 2.44766i) q^{7} +(4.63730 - 4.63730i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.752649 + 5.71694i) q^{10} +(4.26117 - 0.560994i) q^{11} +(-0.595256 + 4.52142i) q^{12} -3.57889i q^{13} +(-0.862510 + 6.72154i) q^{14} +(-1.59189 - 1.59189i) q^{15} +(3.83834 - 6.64821i) q^{16} +(-2.55091 - 3.23927i) q^{17} +(-1.28067 - 2.21818i) q^{18} +(-2.17700 + 0.583325i) q^{19} +(3.92893 + 9.48528i) q^{20} +(-1.33038 - 2.28694i) q^{21} +(10.1705 - 4.21276i) q^{22} +(-3.68136 - 4.79764i) q^{23} +(0.856007 + 6.50202i) q^{24} +(-0.0659185 - 0.0176628i) q^{25} +(-2.37252 - 8.85438i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.61409 + 11.9573i) q^{28} +(-7.92686 + 3.28341i) q^{29} +(-4.99374 - 2.88314i) q^{30} +(1.67311 - 2.18045i) q^{31} +(1.69431 - 6.32325i) q^{32} +(-2.14897 + 3.72213i) q^{33} +(-8.45848 - 6.32309i) q^{34} +(-5.16805 - 2.96124i) q^{35} +(-3.22471 - 3.22471i) q^{36} +(-1.05721 - 0.139184i) q^{37} +(-4.99932 + 2.88636i) q^{38} +(2.83932 + 2.17869i) q^{39} +(8.98785 + 11.7132i) q^{40} +(-0.180713 - 0.0748539i) q^{41} +(-4.80749 - 4.77609i) q^{42} +(2.78924 - 2.78924i) q^{43} +(15.5501 - 11.9320i) q^{44} +(2.23202 - 0.293850i) q^{45} +(-12.2884 - 9.42920i) q^{46} +(3.50473 + 2.02346i) q^{47} +(2.93774 + 7.09234i) q^{48} +(-4.98208 - 4.91720i) q^{49} -0.174795 q^{50} +(4.12278 - 0.0518318i) q^{51} +(-8.16064 - 14.1346i) q^{52} +(-3.22868 + 12.0496i) q^{53} +(2.53942 + 0.334321i) q^{54} +9.67586i q^{55} +(6.69250 + 16.0085i) q^{56} +(0.862489 - 2.08223i) q^{57} +(-17.4349 + 13.3782i) q^{58} +(11.3861 + 3.05089i) q^{59} +(-9.91696 - 2.65724i) q^{60} +(6.67594 - 5.12263i) q^{61} +(2.69392 - 6.50370i) q^{62} +(2.62423 + 0.336742i) q^{63} -1.41392i q^{64} +(7.98814 + 1.05166i) q^{65} +(-2.84920 + 10.6334i) q^{66} +(-2.73113 - 4.73046i) q^{67} +(-17.4609 - 6.97670i) q^{68} +6.04730 q^{69} +(-14.7491 - 3.90026i) q^{70} +(4.02229 + 9.71066i) q^{71} +(-5.67950 - 3.27906i) q^{72} +(4.22558 + 3.24240i) q^{73} +(-2.70786 + 0.356497i) q^{74} +(0.0541415 - 0.0415442i) q^{75} +(-7.26784 + 7.26784i) q^{76} +(-2.90710 + 10.9934i) q^{77} +(8.46896 + 3.50796i) q^{78} +(-9.24119 - 12.0434i) q^{79} +(13.7110 + 10.5208i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-0.496718 - 0.0653942i) q^{82} +(-11.9612 - 11.9612i) q^{83} +(-10.4690 - 5.99861i) q^{84} +(7.97968 - 4.74181i) q^{85} +(5.05169 - 8.74978i) q^{86} +(2.22066 - 8.28761i) q^{87} +(17.1588 - 22.3618i) q^{88} +(-9.71538 - 5.60918i) q^{89} +(5.32734 - 2.20666i) q^{90} +(8.75990 + 3.59489i) q^{91} +(-25.4790 - 10.5538i) q^{92} +(0.711336 + 2.65474i) q^{93} +(10.0123 + 2.68279i) q^{94} +(-0.662278 - 5.03050i) q^{95} +(3.98514 + 5.19354i) q^{96} +(-2.30575 + 0.955073i) q^{97} +(-15.5857 - 8.86272i) q^{98} +(-1.64475 - 3.97078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	2.47406	−	0.662922i	1.74942	−	0.468757i	0.764921	−	0.644124i	$-0.222778\pi$
$2$	2.47406	−	0.662922i	1.74942	−	0.468757i	0.984503	+	0.175368i	$0.0561114\pi$
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$4$	3.94945	−	2.28022i	1.97473	−	1.14011i
$5$	−0.293850	+	2.23202i	−0.131414	+	0.998188i	0.790954	+	0.611876i	$0.209585\pi$
$5$	−0.293850	+	2.23202i	−0.131414	+	0.998188i	−0.922368	+	0.386312i	$0.873749\pi$
$6$	−0.980180	+	2.36636i	−0.400157	+	0.966064i
$7$	−1.00447	+	2.44766i	−0.379654	+	0.925129i
$7$	−1.00447	+	2.44766i	−0.379654	+	0.925129i
$8$	4.63730	−	4.63730i	1.63953	−	1.63953i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	0.752649	+	5.71694i	0.238009	+	1.80786i
$11$	4.26117	−	0.560994i	1.28479	−	0.169146i	0.542975	−	0.839749i	$-0.317298\pi$
$11$	4.26117	−	0.560994i	1.28479	−	0.169146i	0.741817	+	0.670602i	$0.233964\pi$
$12$	−0.595256	+	4.52142i	−0.171836	+	1.30522i
$13$		−	3.57889i		−	0.992605i	−0.868150	−	0.496303i	$-0.834691\pi$
$13$		−	3.57889i		−	0.992605i	0.868150	−	0.496303i	$-0.165309\pi$
$14$	−0.862510	+	6.72154i	−0.230515	+	1.79641i
$15$	−1.59189	−	1.59189i	−0.411025	−	0.411025i
$16$	3.83834	−	6.64821i	0.959586	−	1.66205i
$17$	−2.55091	−	3.23927i	−0.618687	−	0.785638i
$17$	−2.55091	−	3.23927i	−0.618687	−	0.785638i
$18$	−1.28067	−	2.21818i	−0.301856	−	0.522830i
$19$	−2.17700	+	0.583325i	−0.499437	+	0.133824i	−0.499739	−	0.866176i	$-0.666571\pi$
$19$	−2.17700	+	0.583325i	−0.499437	+	0.133824i	0.000301470		1.00000i	$0.499904\pi$
$20$	3.92893	+	9.48528i	0.878536	+	2.12097i
$21$	−1.33038	−	2.28694i	−0.290312	−	0.499051i
$22$	10.1705	−	4.21276i	2.16836	−	0.898163i
$23$	−3.68136	−	4.79764i	−0.767617	−	1.00038i	−0.999617	−	0.0276623i	$-0.991194\pi$
$23$	−3.68136	−	4.79764i	−0.767617	−	1.00038i	0.232000	−	0.972716i	$-0.425473\pi$
$24$	0.856007	+	6.50202i	0.174732	+	1.32722i
$25$	−0.0659185	−	0.0176628i	−0.0131837	−	0.00353256i
$26$	−2.37252	−	8.85438i	−0.465290	−	1.73649i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	1.61409	+	11.9573i	0.305034	+	2.25972i
$29$	−7.92686	+	3.28341i	−1.47198	+	0.609714i	−0.967310	−	0.253598i	$-0.918386\pi$
$29$	−7.92686	+	3.28341i	−1.47198	+	0.609714i	−0.504670	+	0.863312i	$0.668386\pi$
$30$	−4.99374	−	2.88314i	−0.911727	−	0.526386i
$31$	1.67311	−	2.18045i	0.300500	−	0.391620i	−0.618559	−	0.785738i	$-0.712283\pi$
$31$	1.67311	−	2.18045i	0.300500	−	0.391620i	0.919060	+	0.394118i	$0.128950\pi$
$32$	1.69431	−	6.32325i	0.299515	−	1.11780i
$33$	−2.14897	+	3.72213i	−0.374088	+	0.647939i
$34$	−8.45848	−	6.32309i	−1.45062	−	1.08440i
$35$	−5.16805	−	2.96124i	−0.873560	−	0.500541i
$36$	−3.22471	−	3.22471i	−0.537452	−	0.537452i
$37$	−1.05721	−	0.139184i	−0.173804	−	0.0228817i	0.0431219	−	0.999070i	$-0.486270\pi$
$37$	−1.05721	−	0.139184i	−0.173804	−	0.0228817i	−0.216926	+	0.976188i	$0.569603\pi$
$38$	−4.99932	+	2.88636i	−0.810997	+	0.468229i
$39$	2.83932	+	2.17869i	0.454656	+	0.348870i
$40$	8.98785	+	11.7132i	1.42110	+	1.85202i
$41$	−0.180713	−	0.0748539i	−0.0282227	−	0.0116902i	0.368527	−	0.929617i	$-0.379862\pi$
$41$	−0.180713	−	0.0748539i	−0.0282227	−	0.0116902i	−0.396750	+	0.917927i	$0.629862\pi$
$42$	−4.80749	−	4.77609i	−0.741812	−	0.736967i
$43$	2.78924	−	2.78924i	0.425354	−	0.425354i	−0.461688	−	0.887042i	$-0.652756\pi$
$43$	2.78924	−	2.78924i	0.425354	−	0.425354i	0.887042	+	0.461688i	$0.152756\pi$
$44$	15.5501	−	11.9320i	2.34427	−	1.79882i
$45$	2.23202	−	0.293850i	0.332729	−	0.0438046i
$46$	−12.2884	−	9.42920i	−1.81182	−	1.39026i
$47$	3.50473	+	2.02346i	0.511217	+	0.295152i	0.733334	−	0.679869i	$-0.237963\pi$
$47$	3.50473	+	2.02346i	0.511217	+	0.295152i	−0.222116	+	0.975020i	$0.571297\pi$
$48$	2.93774	+	7.09234i	0.424026	+	1.02369i
$49$	−4.98208	−	4.91720i	−0.711726	−	0.702457i
$50$	−0.174795			−0.0247198
$51$	4.12278	−	0.0518318i	0.577305	−	0.00725790i
$52$	−8.16064	−	14.1346i	−1.13168	−	1.96012i
$53$	−3.22868	+	12.0496i	−0.443493	+	1.65514i	0.276391	+	0.961045i	$0.410861\pi$
$53$	−3.22868	+	12.0496i	−0.443493	+	1.65514i	−0.719884	+	0.694094i	$0.755805\pi$
$54$	2.53942	+	0.334321i	0.345572	+	0.0454954i
$55$			9.67586i			1.30469i
$56$	6.69250	+	16.0085i	0.894323	+	2.13923i
$57$	0.862489	−	2.08223i	0.114240	−	0.275799i
$58$	−17.4349	+	13.3782i	−2.28931	+	1.75665i
$59$	11.3861	+	3.05089i	1.48234	+	0.397193i	0.907144	−	0.420821i	$-0.138258\pi$
$59$	11.3861	+	3.05089i	1.48234	+	0.397193i	0.575199	+	0.818014i	$0.304925\pi$
$60$	−9.91696	−	2.65724i	−1.28027	−	0.343048i
$61$	6.67594	−	5.12263i	0.854766	−	0.655885i	−0.0854954	−	0.996339i	$-0.527247\pi$
$61$	6.67594	−	5.12263i	0.854766	−	0.655885i	0.940261	+	0.340454i	$0.110581\pi$
$62$	2.69392	−	6.50370i	0.342128	−	0.825970i
$63$	2.62423	+	0.336742i	0.330622	+	0.0424256i
$64$		−	1.41392i		−	0.176740i
$65$	7.98814	+	1.05166i	0.990807	+	0.130442i
$66$	−2.84920	+	10.6334i	−0.350713	+	1.30888i
$67$	−2.73113	−	4.73046i	−0.333661	−	0.577917i	0.649566	−	0.760305i	$-0.274951\pi$
$67$	−2.73113	−	4.73046i	−0.333661	−	0.577917i	−0.983227	+	0.182388i	$0.941617\pi$
$68$	−17.4609	−	6.97670i	−2.11745	−	0.846050i
$69$	6.04730			0.728009
$70$	−14.7491	−	3.90026i	−1.76286	−	0.466171i
$71$	4.02229	+	9.71066i	0.477358	+	1.15244i	0.960844	+	0.277091i	$0.0893705\pi$
$71$	4.02229	+	9.71066i	0.477358	+	1.15244i	−0.483486	+	0.875352i	$0.660629\pi$
$72$	−5.67950	−	3.27906i	−0.669336	−	0.386441i
$73$	4.22558	+	3.24240i	0.494567	+	0.379495i	0.825718	−	0.564083i	$-0.190770\pi$
$73$	4.22558	+	3.24240i	0.494567	+	0.379495i	−0.331151	+	0.943578i	$0.607437\pi$
$74$	−2.70786	+	0.356497i	−0.314782	+	0.0414419i
$75$	0.0541415	−	0.0415442i	0.00625172	−	0.00479711i
$76$	−7.26784	+	7.26784i	−0.833678	+	0.833678i
$77$	−2.90710	+	10.9934i	−0.331295	+	1.25282i
$78$	8.46896	+	3.50796i	0.958920	+	0.397198i
$79$	−9.24119	−	12.0434i	−1.03972	−	1.35498i	−0.932671	−	0.360729i	$-0.882528\pi$
$79$	−9.24119	−	12.0434i	−1.03972	−	1.35498i	−0.107044	−	0.994254i	$-0.534139\pi$
$80$	13.7110	+	10.5208i	1.53294	+	1.17626i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−0.496718	−	0.0653942i	−0.0548533	−	0.00722158i
$83$	−11.9612	−	11.9612i	−1.31291	−	1.31291i	−0.919263	−	0.393644i	$-0.871214\pi$
$83$	−11.9612	−	11.9612i	−1.31291	−	1.31291i	−0.393644	−	0.919263i	$-0.628786\pi$
$84$	−10.4690	−	5.99861i	−1.14226	−	0.654502i
$85$	7.97968	−	4.74181i	0.865518	−	0.514322i
$86$	5.05169	−	8.74978i	0.544737	−	0.943513i
$87$	2.22066	−	8.28761i	0.238080	−	0.888525i
$88$	17.1588	−	22.3618i	1.82914	−	2.38378i
$89$	−9.71538	−	5.60918i	−1.02983	−	0.594572i	−0.112893	−	0.993607i	$-0.536012\pi$
$89$	−9.71538	−	5.60918i	−1.02983	−	0.594572i	−0.916936	+	0.399035i	$0.869345\pi$
$90$	5.32734	−	2.20666i	0.561551	−	0.232602i
$91$	8.75990	+	3.59489i	0.918287	+	0.376846i
$92$	−25.4790	−	10.5538i	−2.65637	−	1.10031i
$93$	0.711336	+	2.65474i	0.0737621	+	0.275284i
$94$	10.0123	+	2.68279i	1.03269	+	0.276709i
$95$	−0.662278	−	5.03050i	−0.0679483	−	0.516119i
$96$	3.98514	+	5.19354i	0.406732	+	0.530063i
$97$	−2.30575	+	0.955073i	−0.234113	+	0.0969730i	−0.496656	−	0.867947i	$-0.665439\pi$
$97$	−2.30575	+	0.955073i	−0.234113	+	0.0969730i	0.262543	+	0.964920i	$0.415439\pi$
$98$	−15.5857	−	8.86272i	−1.57439	−	0.895270i
$99$	−1.64475	−	3.97078i	−0.165304	−	0.399079i
$100$	−0.300617	+	0.0805500i	−0.0300617	+	0.00805500i
$101$	6.29970	+	10.9114i	0.626844	+	1.08573i	0.988181	+	0.153290i	$0.0489870\pi$
$101$	6.29970	+	10.9114i	0.626844	+	1.08573i	−0.361337	+	0.932435i	$0.617680\pi$
$102$	10.1656	−	2.86132i	1.00655	−	0.283313i
$103$	0.212783	−	0.368550i	0.0209661	−	0.0363144i	−0.855352	−	0.518047i	$-0.826659\pi$
$103$	0.212783	−	0.368550i	0.0209661	−	0.0363144i	0.876318	+	0.481733i	$0.159992\pi$
$104$	−16.5964	−	16.5964i	−1.62741	−	1.62741i
$105$	5.49542	−	2.29740i	0.536298	−	0.224204i
$106$			31.9518i			3.10343i
$107$	0.463861	−	3.52337i	0.0448431	−	0.340617i	−0.954286	−	0.298895i	$-0.903382\pi$
$107$	0.463861	−	3.52337i	0.0448431	−	0.340617i	0.999129	−	0.0417227i	$-0.0132846\pi$
$108$	4.52142	−	0.595256i	0.435074	−	0.0572785i
$109$	0.0713670	+	0.542086i	0.00683572	+	0.0519224i	0.994523	−	0.104520i	$-0.0333307\pi$
$109$	0.0713670	+	0.542086i	0.00683572	+	0.0519224i	−0.987687	+	0.156443i	$0.949997\pi$
$110$	6.41434	+	23.9386i	0.611583	+	2.28246i
$111$	0.754009	−	0.754009i	0.0715674	−	0.0715674i
$112$	12.4171	+	16.0729i	1.17330	+	1.51875i
$113$	−6.04112	+	14.5846i	−0.568301	+	1.37200i	0.334686	+	0.942330i	$0.391370\pi$
$113$	−6.04112	+	14.5846i	−0.568301	+	1.37200i	−0.902986	+	0.429669i	$0.858630\pi$
$114$	0.753491	−	5.72333i	0.0705709	−	0.536039i
$115$	11.7902	−	6.80707i	1.09944	−	0.634762i
$116$	−23.8198	+	31.0426i	−2.21162	+	2.88224i
$117$	−3.45694	+	0.926285i	−0.319594	+	0.0856350i
$118$	30.1924			2.77943
$119$	10.4909	−	2.99001i	0.961703	−	0.274094i
$120$	−14.7642			−1.34778
$121$	7.21771	−	1.93398i	0.656155	−	0.175816i
$122$	13.1208	−	17.0993i	1.18790	−	1.54810i
$123$	0.169397	−	0.0978014i	0.0152740	−	0.00881845i
$124$	1.63600	−	12.4266i	0.146917	−	1.11594i
$125$	−4.24884	+	10.2576i	−0.380027	+	0.917467i
$126$	6.71574	−	0.906542i	0.598286	−	0.0807612i
$127$	6.17358	−	6.17358i	0.547816	−	0.547816i	−0.377992	−	0.925809i	$-0.623385\pi$
$127$	6.17358	−	6.17358i	0.547816	−	0.547816i	0.925809	+	0.377992i	$0.123385\pi$
$128$	2.45130	+	9.14839i	0.216667	+	0.808611i
$129$	0.514870	+	3.91083i	0.0453318	+	0.344329i
$130$	20.4603	−	2.69365i	1.79449	−	0.236249i
$131$	−0.470162	+	3.57123i	−0.0410782	+	0.312020i	0.958554	+	0.284910i	$0.0919638\pi$
$131$	−0.470162	+	3.57123i	−0.0410782	+	0.312020i	−0.999632	+	0.0271100i	$0.991370\pi$
$132$			19.6005i			1.70600i
$133$	0.758948	−	5.91448i	0.0658091	−	0.512851i
$134$	−9.89290	−	9.89290i	−0.854616	−	0.854616i
$135$	−1.12564	+	1.94966i	−0.0968795	+	0.167800i
$136$	−26.8508	−	3.19212i	−2.30243	−	0.273722i
$137$	1.77301	+	3.07094i	0.151478	+	0.262368i	0.931771	−	0.363046i	$-0.118263\pi$
$137$	1.77301	+	3.07094i	0.151478	+	0.262368i	−0.780293	+	0.625414i	$0.784930\pi$
$138$	14.9614	−	4.00889i	1.27360	−	0.341259i
$139$	4.54762	+	10.9789i	0.385724	+	0.931220i	0.990835	+	0.135079i	$0.0431288\pi$
$139$	4.54762	+	10.9789i	0.385724	+	0.931220i	−0.605111	+	0.796141i	$0.706871\pi$
$140$	−27.1632	+	0.0890107i	−2.29571	+	0.00752277i
$141$	−3.73886	+	1.54869i	−0.314869	+	0.130423i
$142$	16.3888	+	21.3583i	1.37532	+	1.79235i
$143$	−2.00774	−	15.2503i	−0.167895	−	1.27529i
$144$	−7.41511	−	1.98687i	−0.617926	−	0.165573i
$145$	−4.99932	−	18.6577i	−0.415171	−	1.54944i
$146$	12.6038	+	5.22067i	1.04310	+	0.432065i
$147$	6.93398	−	0.959147i	0.571905	−	0.0791091i
$148$	−4.49276	+	1.86096i	−0.369302	+	0.152970i
$149$	7.26642	+	4.19527i	0.595288	+	0.343690i	0.767186	−	0.641425i	$-0.221656\pi$
$149$	7.26642	+	4.19527i	0.595288	+	0.343690i	−0.171897	+	0.985115i	$0.554990\pi$
$150$	0.106409	−	0.138674i	0.00868823	−	0.0113227i
$151$	−1.94412	+	7.25554i	−0.158210	+	0.590448i	0.840599	+	0.541658i	$0.182203\pi$
$151$	−1.94412	+	7.25554i	−0.158210	+	0.590448i	−0.998809	+	0.0487899i	$0.984464\pi$
$152$	−7.39033	+	12.8004i	−0.599435	+	1.03825i
$153$	−2.46867	+	3.30237i	−0.199580	+	0.266981i
$154$	0.0954408	+	29.1255i	0.00769084	+	2.34700i
$155$	4.37514	+	4.37514i	0.351420	+	0.351420i
$156$	16.1817	+	2.13036i	1.29557	+	0.170565i
$157$	1.77183	−	1.02296i	0.141407	−	0.0816414i	−0.427627	−	0.903955i	$-0.640650\pi$
$157$	1.77183	−	1.02296i	0.141407	−	0.0816414i	0.569034	+	0.822314i	$0.307317\pi$
$158$	−30.8471	−	23.6698i	−2.45406	−	1.88307i
$159$	−7.59409	−	9.89681i	−0.602251	−	0.784868i
$160$	13.6157	+	5.63982i	1.07642	+	0.445867i
$161$	15.4408	−	4.19163i	1.21691	−	0.330347i
$162$	−1.81114	+	1.81114i	−0.142296	+	0.142296i
$163$	16.0278	−	12.2985i	1.25539	−	0.963296i	0.255398	−	0.966836i	$-0.417794\pi$
$163$	16.0278	−	12.2985i	1.25539	−	0.963296i	0.999994	+	0.00354056i	$0.00112700\pi$
$164$	−0.884402	+	0.116434i	−0.0690602	+	0.00909195i
$165$	−7.67637	−	5.89029i	−0.597605	−	0.458558i
$166$	−37.5219	−	21.6633i	−2.91227	−	1.68140i
$167$	6.79407	+	16.4023i	0.525741	+	1.26925i	0.934290	+	0.356514i	$0.116035\pi$
$167$	6.79407	+	16.4023i	0.525741	+	1.26925i	−0.408549	+	0.912736i	$0.633965\pi$
$168$	−16.7746	−	4.43587i	−1.29419	−	0.342235i
$169$	0.191553			0.0147349
$170$	16.5988	−	17.0214i	1.27307	−	1.30548i
$171$	1.12690	+	1.95184i	0.0861759	+	0.149261i
$172$	4.65589	−	17.3760i	0.355008	−	1.32491i
$173$	−20.2354	−	2.66404i	−1.53847	−	0.202543i	−0.686887	−	0.726765i	$-0.741023\pi$
$173$	−20.2354	−	2.66404i	−1.53847	−	0.202543i	−0.851582	+	0.524221i	$0.824356\pi$
$174$		−	21.9762i		−	1.66601i
$175$	0.109446	−	0.143604i	0.00827331	−	0.0108555i
$176$	12.6262	−	30.4825i	0.951739	−	2.29770i
$177$	−9.35185	+	7.17593i	−0.702928	+	0.539376i
$178$	−27.7549	−	7.43690i	−2.08032	−	0.557419i
$179$	7.72798	+	2.07071i	0.577617	+	0.154772i	0.535787	−	0.844353i	$-0.320015\pi$
$179$	7.72798	+	2.07071i	0.577617	+	0.154772i	0.0418291	+	0.999125i	$0.486682\pi$
$180$	8.14520	−	6.25003i	0.607107	−	0.465850i
$181$	−0.661601	+	1.59725i	−0.0491764	+	0.118722i	−0.946559	−	0.322532i	$-0.895466\pi$
$181$	−0.661601	+	1.59725i	−0.0491764	+	0.118722i	0.897382	+	0.441254i	$0.145466\pi$
$182$	24.0556	+	3.08683i	1.78312	+	0.228811i
$183$			8.41483i			0.622042i
$184$	−39.3197	−	5.17653i	−2.89868	−	0.381619i
$185$	0.621322	−	2.31880i	0.0456805	−	0.170482i
$186$	3.51977	+	6.09643i	0.258082	+	0.447012i
$187$	−12.6871	−	12.3720i	−0.927771	−	0.904733i
$188$	18.4557			1.34602
$189$	−1.86469	+	1.87695i	−0.135636	+	0.136528i
$190$	−4.97335	−	12.0067i	−0.360805	−	0.871059i
$191$	8.03933	+	4.64151i	0.581705	+	0.335848i	0.761811	−	0.647800i	$-0.224311\pi$
$191$	8.03933	+	4.64151i	0.581705	+	0.335848i	−0.180105	+	0.983647i	$0.557644\pi$
$192$	1.12174	+	0.860739i	0.0809544	+	0.0621185i
$193$	12.4758	−	1.64247i	0.898026	−	0.118227i	0.332640	−	0.943054i	$-0.392061\pi$
$193$	12.4758	−	1.64247i	0.898026	−	0.118227i	0.565386	+	0.824827i	$0.308727\pi$
$194$	−5.07142	+	3.89144i	−0.364107	+	0.279389i
$195$	−5.69721	+	5.69721i	−0.407985	+	0.407985i
$196$	−30.8888	−	8.06003i	−2.20634	−	0.575716i
$197$	−17.0013	−	7.04219i	−1.21130	−	0.501735i	−0.316663	−	0.948538i	$-0.602563\pi$
$197$	−17.0013	−	7.04219i	−1.21130	−	0.501735i	−0.894632	+	0.446803i	$0.852563\pi$
$198$	−6.70153	−	8.73361i	−0.476257	−	0.620670i
$199$	−18.7901	−	14.4181i	−1.33199	−	1.02207i	−0.996801	−	0.0799228i	$-0.974533\pi$
$199$	−18.7901	−	14.4181i	−1.33199	−	1.02207i	−0.335191	−	0.942150i	$-0.608801\pi$
$200$	−0.387591	+	0.223776i	−0.0274068	+	0.0158233i
$201$	5.41553	+	0.712968i	0.381982	+	0.0502889i
$202$	22.8193	+	22.8193i	1.60556	+	1.60556i
$203$	−0.0743863	−	22.7003i	−0.00522089	−	1.59325i
$204$	16.1645	−	9.60554i	1.13174	−	0.672522i
$205$	0.220178	−	0.381359i	0.0153779	−	0.0266353i
$206$	0.282117	−	1.05287i	0.0196560	−	0.0733572i
$207$	−3.68136	+	4.79764i	−0.255872	+	0.333459i
$208$	−23.7932	−	13.7370i	−1.64976	−	0.952490i
$209$	−8.94932	+	3.70693i	−0.619038	+	0.256414i
$210$	12.0730	−	9.32695i	0.833116	−	0.643621i
$211$	21.6037	+	8.94855i	1.48726	+	0.616043i	0.970719	−	0.240219i	$-0.0772192\pi$
$211$	21.6037	+	8.94855i	1.48726	+	0.616043i	0.516541	+	0.856262i	$0.327219\pi$
$212$	14.7242	+	54.9514i	1.01126	+	3.77408i
$213$	−10.1526	−	2.72038i	−0.695645	−	0.186397i
$214$	−1.18810	−	9.02454i	−0.0812171	−	0.616905i
$215$	5.40600	+	7.04524i	0.368686	+	0.480481i
$216$	6.05892	−	2.50969i	0.412257	−	0.170763i
$217$	3.65640	+	6.28541i	0.248212	+	0.426681i
$218$	0.535927	+	1.29384i	0.0362976	+	0.0876301i
$219$	−5.14474	+	1.37853i	−0.347650	+	0.0931524i
$220$	22.0631	+	38.2143i	1.48749	+	2.57641i
$221$	−11.5930	+	9.12942i	−0.779828	+	0.614112i
$222$	1.36561	−	2.36531i	0.0916540	−	0.158749i
$223$	1.67456	+	1.67456i	0.112137	+	0.112137i	0.760949	−	0.648812i	$-0.224734\pi$
$223$	1.67456	+	1.67456i	0.112137	+	0.112137i	−0.648812	+	0.760949i	$0.724734\pi$
$224$	13.7753	+	10.4986i	0.920400	+	0.701468i
$225$			0.0682438i			0.00454959i
$226$	−5.27766	+	40.0878i	−0.351065	+	2.66660i
$227$	5.31427	−	0.699637i	0.352720	−	0.0464365i	0.0479157	−	0.998851i	$-0.484742\pi$
$227$	5.31427	−	0.699637i	0.352720	−	0.0464365i	0.304805	+	0.952415i	$0.401409\pi$
$228$	−1.34158	−	10.1903i	−0.0888486	−	0.674872i
$229$	5.83046	+	21.7596i	0.385288	+	1.43791i	0.837713	+	0.546111i	$0.183892\pi$
$229$	5.83046	+	21.7596i	0.385288	+	1.43791i	−0.452426	+	0.891802i	$0.649441\pi$
$230$	24.6571	−	24.6571i	1.62584	−	1.62584i
$231$	−6.95193	−	8.99872i	−0.457403	−	0.592072i
$232$	−21.5330	+	51.9853i	−1.41371	+	3.41300i
$233$	−0.210949	+	1.60232i	−0.0138198	+	0.104971i	−0.996965	−	0.0778574i	$-0.975192\pi$
$233$	−0.210949	+	1.60232i	−0.0138198	+	0.104971i	0.983145	+	0.182829i	$0.0585254\pi$
$234$	−7.93862	+	4.58337i	−0.518964	+	0.299624i
$235$	−5.54626	+	7.22802i	−0.361798	+	0.471504i
$236$	51.9255	−	13.9134i	3.38006	−	0.905685i
$237$	15.1803			0.986067
$238$	23.9731	−	14.3521i	1.55394	−	0.930312i
$239$	7.39035			0.478042			0.239021	−	0.971014i	$-0.423173\pi$
$239$	7.39035			0.478042			0.239021	+	0.971014i	$0.423173\pi$
$240$	−16.6935	+	4.47300i	−1.07756	+	0.288731i
$241$	−4.39548	+	5.72830i	−0.283138	+	0.368992i	−0.913172	−	0.407575i	$-0.866374\pi$
$241$	−4.39548	+	5.72830i	−0.283138	+	0.368992i	0.630034	+	0.776568i	$0.283041\pi$
$242$	16.5750	−	9.56955i	1.06548	−	0.615154i
$243$	0.130526	−	0.991445i	0.00837326	−	0.0636012i
$244$	14.6856	−	35.4541i	0.940148	−	2.26972i
$245$	12.4393	−	9.67516i	0.794715	−	0.618123i
$246$	0.354263	−	0.354263i	0.0225870	−	0.0225870i
$247$	2.08765	+	7.79123i	0.132834	+	0.495744i
$248$	−2.35264	−	17.8701i	−0.149393	−	1.13475i
$249$	16.7709	−	2.20793i	1.06281	−	0.139922i
$250$	−3.71188	+	28.1946i	−0.234760	+	1.78318i
$251$		−	1.79656i		−	0.113398i	−0.998391	−	0.0566990i	$-0.981942\pi$
$251$		−	1.79656i		−	0.113398i	0.998391	−	0.0566990i	$-0.0180575\pi$
$252$	11.1321	−	4.65388i	0.701258	−	0.293167i
$253$	−18.3784	−	18.3784i	−1.15544	−	1.15544i
$254$	11.1812	−	19.3664i	0.701570	−	1.21516i
$255$	−1.09579	+	9.21734i	−0.0686211	+	0.577212i
$256$	13.5433	+	23.4576i	0.846453	+	1.46610i
$257$	−0.451681	+	0.121028i	−0.0281751	+	0.00754949i	−0.272879	−	0.962048i	$-0.587976\pi$
$257$	−0.451681	+	0.121028i	−0.0281751	+	0.00754949i	0.244704	+	0.969598i	$0.421309\pi$
$258$	3.86639	+	9.33430i	0.240711	+	0.581128i
$259$	1.40261	−	2.44788i	0.0871538	−	0.152104i
$260$	33.9468	−	14.0612i	2.10529	−	0.872039i
$261$	5.22315	+	6.80695i	0.323305	+	0.421339i
$262$	1.20424	+	9.14712i	0.0743983	+	0.565111i
$263$	−28.1152	−	7.53344i	−1.73366	−	0.464532i	−0.752636	−	0.658436i	$-0.771218\pi$
$263$	−28.1152	−	7.53344i	−1.73366	−	0.464532i	−0.981020	+	0.193904i	$0.937885\pi$
$264$	7.29519	+	27.2260i	0.448988	+	1.67565i
$265$	−25.9461	−	10.7472i	−1.59386	−	0.660198i
$266$	−2.04316	−	15.1359i	−0.125274	−	0.928042i
$267$	10.3644	−	4.29308i	0.634292	−	0.262732i
$268$	−21.5729	−	12.4551i	−1.31778	−	0.760819i
$269$	−6.87311	+	8.95721i	−0.419061	+	0.546131i	−0.954409	−	0.298500i	$-0.903514\pi$
$269$	−6.87311	+	8.95721i	−0.419061	+	0.546131i	0.535349	+	0.844631i	$0.320180\pi$
$270$	−1.49242	+	5.56979i	−0.0908258	+	0.338967i
$271$	3.50335	−	6.06799i	0.212814	−	0.368604i	−0.739780	−	0.672848i	$-0.765071\pi$
$271$	3.50335	−	6.06799i	0.212814	−	0.368604i	0.952594	+	0.304244i	$0.0984040\pi$
$272$	−31.3266	+	4.52555i	−1.89945	+	0.274402i
$273$	−8.18471	+	4.76127i	−0.495361	+	0.288165i
$274$	6.42232	+	6.42232i	0.387986	+	0.387986i
$275$	−0.290799	−	0.0382844i	−0.0175358	−	0.00230864i
$276$	23.8835	−	13.7892i	1.43762	−	0.830009i
$277$	−9.82665	−	7.54026i	−0.590426	−	0.453050i	0.269833	−	0.962907i	$-0.413032\pi$
$277$	−9.82665	−	7.54026i	−0.590426	−	0.453050i	−0.860259	+	0.509857i	$0.829698\pi$
$278$	18.5292	+	24.1478i	1.11131	+	1.44829i
$279$	−2.53918	−	1.05176i	−0.152017	−	0.0629675i
$280$	−37.6979	+	10.2336i	−2.25288	+	0.611577i
$281$	7.39026	−	7.39026i	0.440866	−	0.440866i	−0.451437	−	0.892303i	$-0.649088\pi$
$281$	7.39026	−	7.39026i	0.440866	−	0.440866i	0.892303	+	0.451437i	$0.149088\pi$
$282$	−8.22350	+	6.31012i	−0.489703	+	0.375762i
$283$	6.54493	−	0.861656i	0.389055	−	0.0512201i	0.0665386	−	0.997784i	$-0.478804\pi$
$283$	6.54493	−	0.861656i	0.389055	−	0.0512201i	0.322517	+	0.946564i	$0.395471\pi$
$284$	38.0283	+	29.1801i	2.25656	+	1.73152i
$285$	4.39414	+	2.53696i	0.260286	+	0.150276i
$286$	−15.0770	−	36.3991i	−0.891522	−	2.15232i
$287$	0.364738	−	0.367136i	0.0215298	−	0.0216714i
$288$	−6.54631			−0.385745
$289$	−3.98571	+	16.5262i	−0.234454	+	0.972127i
$290$	−24.7372	−	42.8461i	−1.45262	−	2.51601i
$291$	0.645941	−	2.41069i	0.0378658	−	0.141317i
$292$	24.0821	+	3.17047i	1.40930	+	0.185538i
$293$		−	22.2873i		−	1.30204i	−0.759062	−	0.651019i	$-0.774342\pi$
$293$		−	22.2873i		−	1.30204i	0.759062	−	0.651019i	$-0.225658\pi$
$294$	16.5192	−	6.96967i	0.963421	−	0.406480i
$295$	−10.1555	+	24.5174i	−0.591273	+	1.42746i
$296$	−5.54802	+	4.25715i	−0.322472	+	0.247442i
$297$	4.15149	+	1.11239i	0.240894	+	0.0645474i
$298$	20.7587	+	5.56227i	1.20252	+	0.322214i
$299$	−17.1702	+	13.1752i	−0.992980	+	0.761941i
$300$	0.119099	−	0.287531i	0.00687620	−	0.0166006i
$301$	4.02540	+	9.62880i	0.232020	+	0.554995i
$302$			19.2394i			1.10711i
$303$	−12.4916	−	1.64455i	−0.717625	−	0.0944771i
$304$	−4.47800	+	16.7121i	−0.256831	+	0.958506i
$305$	9.47206	+	16.4061i	0.542368	+	0.939409i
$306$	−3.91841	+	9.80680i	−0.224001	+	0.560618i
$307$	7.32407			0.418007			0.209003	−	0.977915i	$-0.432978\pi$
$307$	7.32407			0.418007			0.209003	+	0.977915i	$0.432978\pi$
$308$	13.5859	+	50.0467i	0.774129	+	2.85168i
$309$	0.162857	+	0.393171i	0.00926460	+	0.0223667i
$310$	13.7247	+	7.92399i	0.779513	+	0.450052i
$311$	17.4391	+	13.3815i	0.988882	+	0.758796i	0.970516	−	0.241035i	$-0.0774870\pi$
$311$	17.4391	+	13.3815i	0.988882	+	0.758796i	0.0183658	+	0.999831i	$0.494154\pi$
$312$	23.2700	−	3.06356i	1.31741	−	0.173440i
$313$	−21.0770	+	16.1730i	−1.19134	+	0.914150i	−0.997757	−	0.0669333i	$-0.978679\pi$
$313$	−21.0770	+	16.1730i	−1.19134	+	0.914150i	−0.193586	+	0.981083i	$0.562012\pi$
$314$	3.70546	−	3.70546i	0.209111	−	0.209111i
$315$	−1.52275	+	5.75838i	−0.0857971	+	0.324448i
$316$	−63.9591	−	26.4927i	−3.59798	−	1.49033i
$317$	−17.0134	−	22.1724i	−0.955571	−	1.24532i	−0.969417	−	0.245420i	$-0.921074\pi$
$317$	−17.0134	−	22.1724i	−0.955571	−	1.24532i	0.0138464	−	0.999904i	$-0.495592\pi$
$318$	−25.3490	−	19.4510i	−1.42150	−	1.09076i
$319$	−31.9357	+	18.4381i	−1.78806	+	1.03234i
$320$	3.15589	+	0.415481i	0.176420	+	0.0232261i
$321$	2.51290	+	2.51290i	0.140256	+	0.140256i
$322$	35.4228	−	20.6064i	1.97403	−	1.14835i
$323$	7.44287	+	5.56387i	0.414132	+	0.309582i
$324$	−2.28022	+	3.94945i	−0.126679	+	0.219414i
$325$	−0.0632132	+	0.235915i	−0.00350644	+	0.0130862i
$326$	31.5007	−	41.0525i	1.74466	−	2.27369i
$327$	−0.473511	−	0.273382i	−0.0261852	−	0.0151181i
$328$	−1.18514	+	0.490902i	−0.0654385	+	0.0271055i
$329$	−8.47313	+	6.54589i	−0.467139	+	0.360886i
$330$	−22.8966	−	9.48408i	−1.26042	−	0.522082i
$331$	−8.26614	−	30.8496i	−0.454348	−	1.69565i	−0.689998	−	0.723812i	$-0.742388\pi$
$331$	−8.26614	−	30.8496i	−0.454348	−	1.69565i	0.235650	−	0.971838i	$-0.424278\pi$
$332$	−74.5140	−	19.9660i	−4.08949	−	1.09578i
$333$	0.139184	+	1.05721i	0.00762723	+	0.0579346i
$334$	27.6824	+	36.0764i	1.51471	+	1.97401i
$335$	11.3610	−	4.70588i	0.620718	−	0.257110i
$336$	−20.3105	+	0.0665551i	−1.10803	+	0.00363088i
$337$	−6.42887	−	15.5207i	−0.350203	−	0.845465i	−0.996594	−	0.0824587i	$-0.973723\pi$
$337$	−6.42887	−	15.5207i	−0.350203	−	0.845465i	0.646392	−	0.763006i	$-0.276277\pi$
$338$	0.473914	−	0.126985i	0.0257775	−	0.00690707i
$339$	−7.89310	−	13.6713i	−0.428695	−	0.742521i
$340$	20.7030	−	36.9230i	1.12278	−	2.00243i
$341$	5.90622	−	10.2299i	0.319840	−	0.553978i
$342$	4.08193	+	4.08193i	0.220725	+	0.220725i
$343$	17.0400	−	7.25526i	0.920073	−	0.391747i
$344$		−	25.8690i		−	1.39476i
$345$	−1.77700	+	13.4977i	−0.0956706	+	0.726690i
$346$	−51.8296	+	6.82350i	−2.78638	+	0.366834i
$347$	0.787995	+	5.98542i	0.0423018	+	0.321314i	0.999492	+	0.0318559i	$0.0101418\pi$
$347$	0.787995	+	5.98542i	0.0423018	+	0.321314i	−0.957191	+	0.289458i	$0.906525\pi$
$348$	−10.1272	−	37.7951i	−0.542873	−	2.02603i
$349$	15.1062	−	15.1062i	0.808614	−	0.808614i	−0.175810	−	0.984424i	$-0.556254\pi$
$349$	15.1062	−	15.1062i	0.808614	−	0.808614i	0.984424	+	0.175810i	$0.0562544\pi$
$350$	0.175577	−	0.427839i	0.00938496	−	0.0228690i
$351$	1.36958	−	3.30646i	0.0731029	−	0.176486i
$352$	3.67244	−	27.8950i	0.195742	−	1.48681i
$353$	9.74058	−	5.62373i	0.518439	−	0.299321i	−0.217857	−	0.975981i	$-0.569907\pi$
$353$	9.74058	−	5.62373i	0.518439	−	0.299321i	0.736296	+	0.676660i	$0.236573\pi$
$354$	−18.3799	+	23.9532i	−0.976883	+	1.27310i
$355$	−22.8563	+	6.12433i	−1.21309	+	0.325046i
$356$	−51.1606			−2.71151
$357$	−4.01434	+	10.1432i	−0.212461	+	0.536837i
$358$	20.4922			1.08305
$359$	−21.9716	+	5.88727i	−1.15962	+	0.310718i	−0.786813	−	0.617192i	$-0.788270\pi$
$359$	−21.9716	+	5.88727i	−1.15962	+	0.310718i	−0.372804	+	0.927910i	$0.621604\pi$
$360$	8.98785	−	11.7132i	0.473701	−	0.617339i
$361$	−12.0554	+	6.96021i	−0.634496	+	0.366327i
$362$	−0.577990	+	4.39027i	−0.0303785	+	0.230747i
$363$	−2.85953	+	6.90352i	−0.150087	+	0.362341i
$364$	42.7939	−	5.77665i	2.24301	−	0.302779i
$365$	−8.47879	+	8.47879i	−0.443800	+	0.443800i
$366$	5.57838	+	20.8188i	0.291587	+	1.08822i
$367$	0.0558029	+	0.423865i	0.00291289	+	0.0221256i	0.992840	−	0.119455i	$-0.0381148\pi$
$367$	0.0558029	+	0.423865i	0.00291289	+	0.0221256i	−0.989927	+	0.141581i	$0.954781\pi$
$368$	−46.0261	+	6.05945i	−2.39927	+	0.315871i
$369$	−0.0255313	+	0.193929i	−0.00132911	+	0.0100956i
$370$		−	6.14875i		−	0.319658i
$371$	−26.2502	−	20.0062i	−1.36284	−	1.03867i
$372$	8.86278	+	8.86278i	0.459514	+	0.459514i
$373$	3.01600	−	5.22387i	0.156163	−	0.270482i	−0.777319	−	0.629106i	$-0.783421\pi$
$373$	3.01600	−	5.22387i	0.156163	−	0.270482i	0.933482	+	0.358625i	$0.116754\pi$
$374$	−39.5903	−	22.1986i	−2.04717	−	1.14786i
$375$	−5.55137	−	9.61526i	−0.286672	−	0.496530i
$376$	25.6358	−	6.86910i	1.32207	−	0.354247i
$377$	11.7510	+	28.3693i	0.605205	+	1.46110i
$378$	−3.36908	+	5.87983i	−0.173287	+	0.302426i
$379$	25.7144	−	10.6513i	1.32086	−	0.547119i	0.392827	−	0.919612i	$-0.371497\pi$
$379$	25.7144	−	10.6513i	1.32086	−	0.547119i	0.928035	+	0.372493i	$0.121497\pi$
$380$	−14.0863	−	18.3576i	−0.722611	−	0.941725i
$381$	1.13959	+	8.65606i	0.0583831	+	0.443463i
$382$	22.9667	+	6.15392i	1.17508	+	0.314862i
$383$	−0.545657	−	2.03642i	−0.0278818	−	0.104056i	0.950583	−	0.310471i	$-0.100487\pi$
$383$	−0.545657	−	2.03642i	−0.0278818	−	0.104056i	−0.978464	+	0.206415i	$0.933820\pi$
$384$	−8.75016	−	3.62444i	−0.446530	−	0.184959i
$385$	−23.6832	−	9.71911i	−1.20701	−	0.495332i
$386$	29.7770	−	12.3340i	1.51561	−	0.627785i
$387$	−3.41610	−	1.97229i	−0.173650	−	0.100257i
$388$	−6.92868	+	9.02963i	−0.351750	+	0.458410i
$389$	1.77556	−	6.62648i	0.0900245	−	0.335976i	−0.906194	−	0.422863i	$-0.861025\pi$
$389$	1.77556	−	6.62648i	0.0900245	−	0.335976i	0.996218	+	0.0868868i	$0.0276919\pi$
$390$	−10.3184	+	17.8720i	−0.522494	+	0.904985i
$391$	−6.15003	+	24.1633i	−0.311020	+	1.22199i
$392$	−45.9059	+	0.300859i	−2.31860	+	0.0151957i
$393$	−2.54703	−	2.54703i	−0.128481	−	0.128481i
$394$	−46.7308	−	6.15222i	−2.35426	−	0.309944i
$395$	29.5965	−	17.0875i	1.48916	−	0.859767i
$396$	−15.5501	−	11.9320i	−0.781423	−	0.599607i
$397$	−16.8954	−	22.0185i	−0.847956	−	1.10508i	−0.993285	−	0.115694i	$-0.963091\pi$
$397$	−16.8954	−	22.0185i	−0.847956	−	1.10508i	0.145329	−	0.989383i	$-0.453576\pi$
$398$	−56.0458	−	23.2149i	−2.80932	−	1.16366i
$399$	4.23026	+	4.20262i	0.211778	+	0.210394i
$400$	−0.370444	+	0.370444i	−0.0185222	+	0.0185222i
$401$	−11.8107	+	9.06269i	−0.589800	+	0.452569i	−0.860042	−	0.510223i	$-0.829563\pi$
$401$	−11.8107	+	9.06269i	−0.589800	+	0.452569i	0.270242	+	0.962792i	$0.412896\pi$
$402$	13.8710	−	1.82615i	0.691822	−	0.0910801i
$403$	−7.80357	−	5.98789i	−0.388724	−	0.298278i
$404$	49.7607	+	28.7294i	2.47569	+	1.42934i
$405$	−0.861526	−	2.07991i	−0.0428096	−	0.103351i
$406$	−15.2326	−	56.1127i	−0.755981	−	2.78482i
$407$	−4.58302			−0.227172
$408$	18.8782	−	19.3589i	0.934610	−	0.958409i
$409$	−0.870273	−	1.50736i	−0.0430322	−	0.0745340i	0.843707	−	0.536804i	$-0.180368\pi$
$409$	−0.870273	−	1.50736i	−0.0430322	−	0.0745340i	−0.886739	+	0.462270i	$0.847035\pi$
$410$	0.291922	−	1.08947i	0.0144170	−	0.0538049i
$411$	−3.51568	−	0.462848i	−0.173416	−	0.0228306i
$412$		−	1.94076i		−	0.0956145i
$413$	−18.9045	+	24.8047i	−0.930231	+	1.22056i
$414$	−5.92744	+	14.3101i	−0.291318	+	0.703304i
$415$	30.2123	−	23.1827i	1.48306	−	1.13799i
$416$	−22.6302	−	6.06375i	−1.10954	−	0.297300i
$417$	−11.4786	−	3.07568i	−0.562108	−	0.150616i
$418$	−19.6837	+	15.1039i	−0.962763	+	0.738754i
$419$	14.3497	−	34.6432i	0.701029	−	1.69243i	−0.0202564	−	0.999795i	$-0.506448\pi$
$419$	14.3497	−	34.6432i	0.701029	−	1.69243i	0.721285	−	0.692638i	$-0.243552\pi$
$420$	16.4653	−	21.6042i	0.803425	−	1.05418i
$421$			16.7153i			0.814655i	0.913282	+	0.407328i	$0.133539\pi$
$421$			16.7153i			0.814655i	−0.913282	+	0.407328i	$0.866461\pi$
$422$	59.3810	+	7.81766i	2.89062	+	0.380558i
$423$	1.04742	−	3.90902i	0.0509272	−	0.190063i
$424$	40.9052	+	70.8499i	1.98653	+	3.44077i
$425$	0.110938	+	0.258584i	0.00538126	+	0.0125432i
$426$	−26.9215			−1.30435
$427$	5.83267	+	21.4859i	0.282263	+	1.03978i
$428$	−6.20206	−	14.9731i	−0.299788	−	0.723752i
$429$	13.3211	+	7.69093i	0.643148	+	0.371322i
$430$	18.0452	+	13.8466i	0.870217	+	0.667741i
$431$	5.79358	−	0.762739i	0.279067	−	0.0367398i	0.0103063	−	0.999947i	$-0.496719\pi$
$431$	5.79358	−	0.762739i	0.279067	−	0.0367398i	0.268760	+	0.963207i	$0.413386\pi$
$432$	6.09033	−	4.67327i	0.293021	−	0.224843i
$433$	−21.0480	+	21.0480i	−1.01150	+	1.01150i	−0.0115671	+	0.999933i	$0.503682\pi$
$433$	−21.0480	+	21.0480i	−1.01150	+	1.01150i	−0.999933	+	0.0115671i	$0.996318\pi$
$434$	13.2129	+	13.1266i	0.634238	+	0.630095i
$435$	17.8455	+	7.39186i	0.855628	+	0.354413i
$436$	1.51793	+	1.97821i	0.0726959	+	0.0947391i
$437$	10.8129	+	8.29703i	0.517251	+	0.396901i
$438$	−11.8145	+	6.82113i	−0.564521	+	0.325926i
$439$	14.3123	+	1.88424i	0.683087	+	0.0899301i	0.464080	−	0.885793i	$-0.346385\pi$
$439$	14.3123	+	1.88424i	0.683087	+	0.0899301i	0.219007	+	0.975723i	$0.429718\pi$
$440$	44.8698	+	44.8698i	2.13908	+	2.13908i
$441$	−3.46020	+	6.08499i	−0.164771	+	0.289761i
$442$	−22.6296	+	30.2720i	−1.07638	+	1.43989i
$443$	−2.18103	+	3.77766i	−0.103624	+	0.179482i	−0.913175	−	0.407567i	$-0.866377\pi$
$443$	−2.18103	+	3.77766i	−0.103624	+	0.179482i	0.809551	+	0.587049i	$0.199711\pi$
$444$	1.25862	−	4.69723i	0.0597314	−	0.222920i
$445$	15.3746	−	20.0366i	0.728828	−	0.949827i
$446$	5.25306	+	3.03286i	0.248740	+	0.143610i
$447$	−7.75185	+	3.21092i	−0.366650	+	0.151871i
$448$	3.46079	+	1.42024i	0.163507	+	0.0671000i
$449$	−8.93281	−	3.70009i	−0.421566	−	0.174618i	0.161808	−	0.986822i	$-0.448268\pi$
$449$	−8.93281	−	3.70009i	−0.421566	−	0.174618i	−0.583373	+	0.812204i	$0.698268\pi$
$450$	0.0452403	+	0.168839i	0.00213265	+	0.00795916i
$451$	−0.812044	−	0.217587i	−0.0382377	−	0.0102457i
$452$	9.39684	+	71.3760i	0.441990	+	3.35725i
$453$	−4.57271	−	5.95927i	−0.214844	−	0.279991i
$454$	12.6840	−	5.25389i	0.595290	−	0.246577i
$455$	−10.5979	+	18.4959i	−0.496839	+	0.867101i
$456$	−5.65632	−	13.6556i	−0.264881	−	0.639480i
$457$	−9.33529	+	2.50138i	−0.436687	+	0.117010i	−0.470463	−	0.882420i	$-0.655913\pi$
$457$	−9.33529	+	2.50138i	−0.436687	+	0.117010i	0.0337767	+	0.999429i	$0.489247\pi$
$458$	28.8498	+	49.9693i	1.34806	+	2.33491i
$459$	−1.11712	−	3.96888i	−0.0521427	−	0.185252i
$460$	31.0432	−	53.7684i	1.44740	−	2.50696i
$461$	3.39342	+	3.39342i	0.158047	+	0.158047i	0.781701	−	0.623653i	$-0.214352\pi$
$461$	3.39342	+	3.39342i	0.158047	+	0.158047i	−0.623653	+	0.781701i	$0.714352\pi$
$462$	−23.1649	−	17.6548i	−1.07773	−	0.821374i
$463$			22.6765i			1.05386i	0.849907	+	0.526932i	$0.176658\pi$
$463$			22.6765i			1.05386i	−0.849907	+	0.526932i	$0.823342\pi$
$464$	−8.59720	+	65.3022i	−0.399115	+	3.03158i
$465$	−6.13445	+	0.807616i	−0.284479	+	0.0374523i
$466$	0.540312	+	4.10408i	0.0250295	+	0.190118i
$467$	−4.38639	−	16.3702i	−0.202978	−	0.757524i	−0.990056	−	0.140671i	$-0.955074\pi$
$467$	−4.38639	−	16.3702i	−0.202978	−	0.757524i	0.787078	−	0.616853i	$-0.211593\pi$
$468$	−11.5409	+	11.5409i	−0.533478	+	0.533478i
$469$	14.3219	−	1.93328i	0.661323	−	0.0892704i
$470$	−8.93015	+	21.5593i	−0.411917	+	0.994456i
$471$	−0.267047	+	2.02843i	−0.0123049	+	0.0934649i
$472$	66.9486	−	38.6528i	3.08156	−	1.77914i
$473$	10.3207	−	13.4502i	0.474545	−	0.618439i
$474$	37.5570	−	10.0634i	1.72505	−	0.462226i
$475$	0.153807			0.00705717
$476$	34.6156	−	35.7305i	1.58660	−	1.63771i
$477$	12.4747			0.571175
$478$	18.2842	−	4.89923i	0.836299	−	0.224086i
$479$	−12.7966	+	16.6769i	−0.584692	+	0.761986i	−0.988230	−	0.152977i	$-0.951114\pi$
$479$	−12.7966	+	16.6769i	−0.584692	+	0.761986i	0.403537	+	0.914963i	$0.367781\pi$
$480$	−12.7631	+	7.36878i	−0.582553	+	0.336337i
$481$	−0.498124	+	3.78363i	−0.0227125	+	0.172519i
$482$	−7.07726	+	17.0860i	−0.322360	+	0.778247i
$483$	−6.07433	+	14.8017i	−0.276392	+	0.673502i
$484$	24.0961	−	24.0961i	1.09528	−	1.09528i
$485$	−1.45419	−	5.42712i	−0.0660315	−	0.246433i
$486$	−0.334321	−	2.53942i	−0.0151651	−	0.115191i
$487$	0.587725	−	0.0773754i	0.0266324	−	0.00350622i	−0.117198	−	0.993109i	$-0.537391\pi$
$487$	0.587725	−	0.0773754i	0.0266324	−	0.00350622i	0.143831	+	0.989602i	$0.454058\pi$
$488$	7.20316	−	54.7134i	0.326072	−	2.47676i
$489$			20.2026i			0.913591i
$490$	24.3616	−	32.1832i	1.10054	−	1.45389i
$491$	−5.24517	−	5.24517i	−0.236711	−	0.236711i	0.578776	−	0.815487i	$-0.303531\pi$
$491$	−5.24517	−	5.24517i	−0.236711	−	0.236711i	−0.815487	+	0.578776i	$0.803531\pi$
$492$	0.446017	−	0.772524i	0.0201080	−	0.0348281i
$493$	30.8565	+	17.3015i	1.38971	+	0.779221i
$494$	10.3300	+	17.8920i	0.464767	+	0.805000i
$495$	9.34616	−	2.50430i	0.420079	−	0.112560i
$496$	−8.07406	−	19.4925i	−0.362536	−	0.875240i
$497$	−27.8087	+	0.0911257i	−1.24739	+	0.00408754i
$498$	40.0285	−	16.5804i	1.79372	−	0.742984i
$499$	−6.34424	−	8.26798i	−0.284007	−	0.370126i	0.629463	−	0.777030i	$-0.283275\pi$
$499$	−6.34424	−	8.26798i	−0.284007	−	0.370126i	−0.913471	+	0.406905i	$0.866608\pi$
$500$	6.60898	+	50.2002i	0.295562	+	2.24502i
$501$	−17.1488	−	4.59501i	−0.766152	−	0.205290i
$502$	−1.19098	−	4.44480i	−0.0531561	−	0.198381i
$503$	−8.42978	−	3.49173i	−0.375865	−	0.155688i	0.186750	−	0.982408i	$-0.440205\pi$
$503$	−8.42978	−	3.49173i	−0.375865	−	0.155688i	−0.562615	+	0.826719i	$0.690205\pi$
$504$	13.7309	−	10.6078i	0.611624	−	0.472508i
$505$	−26.2056	+	10.8547i	−1.16613	+	0.483029i
$506$	−57.6526	−	33.2858i	−2.56297	−	1.47973i
$507$	−0.116610	+	0.151970i	−0.00517885	+	0.00674920i
$508$	10.3051	−	38.4593i	0.457217	−	1.70636i
$509$	−1.46363	+	2.53509i	−0.0648744	+	0.112366i	−0.896638	−	0.442764i	$-0.853998\pi$
$509$	−1.46363	+	2.53509i	−0.0648744	+	0.112366i	0.831764	+	0.555130i	$0.187331\pi$
$510$	3.39933	+	23.5307i	0.150525	+	1.04196i
$511$	−12.1808	+	7.08589i	−0.538846	+	0.313461i
$512$	35.6632	+	35.6632i	1.57611	+	1.57611i
$513$	−2.23451	−	0.294179i	−0.0986561	−	0.0129883i
$514$	−1.03725	+	0.598859i	−0.0457513	+	0.0264145i
$515$	0.760084	+	0.583233i	0.0334933	+	0.0257003i
$516$	10.9510	+	14.2716i	0.482090	+	0.628273i
$517$	16.0694	+	6.65617i	0.706732	+	0.292738i
$518$	1.84738	−	6.98601i	0.0811693	−	0.306948i
$519$	14.4321	−	14.4321i	0.633497	−	0.633497i
$520$	41.9202	−	32.1665i	1.83832	−	1.41059i
$521$	31.5436	−	4.15280i	1.38195	−	0.181937i	0.597371	−	0.801965i	$-0.296212\pi$
$521$	31.5436	−	4.15280i	1.38195	−	0.181937i	0.784580	+	0.620027i	$0.212878\pi$
$522$	17.4349	+	13.3782i	0.763103	+	0.585550i
$523$	15.4086	+	8.89614i	0.673769	+	0.389001i	0.797503	−	0.603314i	$-0.206154\pi$
$523$	15.4086	+	8.89614i	0.673769	+	0.389001i	−0.123734	+	0.992315i	$0.539487\pi$
$524$	6.28631	+	15.1765i	0.274619	+	0.662988i
$525$	0.0473026	+	0.174250i	0.00206446	+	0.00760488i
$526$	−74.5527			−3.25065
$527$	−11.3310	+	0.142454i	−0.493587	+	0.00620540i
$528$	16.4970	+	28.5736i	0.717939	+	1.24351i
$529$	−3.51213	+	13.1074i	−0.152701	+	0.569889i
$530$	−71.3169	−	9.38904i	−3.09781	−	0.407834i
$531$		−	11.7877i		−	0.511545i
$532$	−10.4889	−	25.0895i	−0.454750	−	1.08777i
$533$	−0.267894	+	0.646753i	−0.0116038	+	0.0280140i
$534$	22.7962	−	17.4921i	0.986488	−	0.756959i
$535$	7.72792	+	2.07069i	0.334107	+	0.0895238i
$536$	−34.6016	−	9.27147i	−1.49456	−	0.400466i
$537$	−6.34730	+	4.87045i	−0.273906	+	0.210176i
$538$	−11.0665	+	26.7170i	−0.477113	+	1.15185i
$539$	−23.9880	−	18.1581i	−1.03324	−	0.782126i
$540$			10.2668i			0.441813i
$541$	11.8092	+	1.55471i	0.507717	+	0.0668422i	0.380034	−	0.924973i	$-0.375912\pi$
$541$	11.8092	+	1.55471i	0.507717	+	0.0668422i	0.127684	+	0.991815i	$0.459246\pi$
$542$	4.64490	−	17.3350i	0.199516	−	0.744602i
$543$	−0.864423	−	1.49722i	−0.0370960	−	0.0642521i
$544$	−24.8047	+	10.6417i	−1.06349	+	0.456260i
$545$	−1.23092			−0.0527267
$546$	−17.0931	+	17.2055i	−0.731517	+	0.736327i
$547$	−12.0786	−	29.1603i	−0.516443	−	1.24680i	−0.940075	−	0.340969i	$-0.889245\pi$
$547$	−12.0786	−	29.1603i	−0.516443	−	1.24680i	0.423632	−	0.905834i	$-0.360755\pi$
$548$	14.0048	+	8.08568i	0.598256	+	0.345403i
$549$	−6.67594	−	5.12263i	−0.284922	−	0.218628i
$550$	−0.744833	+	0.0980591i	−0.0317598	+	0.00418125i
$551$	15.3414	−	11.7719i	0.653568	−	0.501500i
$552$	28.0431	−	28.0431i	1.19359	−	1.19359i
$553$	38.7605	−	10.5221i	1.64827	−	0.447445i
$554$	−29.3103	−	12.1407i	−1.24528	−	0.515810i
$555$	1.46139	+	1.90453i	0.0620327	+	0.0808426i
$556$	42.9949	+	32.9912i	1.82339	+	1.39914i
$557$	28.6066	−	16.5160i	1.21210	−	0.699807i	0.248884	−	0.968533i	$-0.419936\pi$
$557$	28.6066	−	16.5160i	1.21210	−	0.699807i	0.963217	+	0.268726i	$0.0866027\pi$
$558$	−6.97933	−	0.918846i	−0.295458	−	0.0388978i
$559$	−9.98236	−	9.98236i	−0.422209	−	0.422209i
$560$	−39.5237	+	22.9920i	−1.67018	+	0.971591i
$561$	17.5388	−	2.53372i	0.740489	−	0.106974i
$562$	13.3848	−	23.1831i	0.564603	−	0.977921i
$563$	10.3131	−	38.4889i	0.434644	−	1.62211i	−0.307272	−	0.951622i	$-0.599416\pi$
$563$	10.3131	−	38.4889i	0.434644	−	1.62211i	0.741916	−	0.670493i	$-0.233917\pi$
$564$	−11.2351	+	14.6419i	−0.473083	+	0.616534i
$565$	−30.7778	−	17.7696i	−1.29483	−	0.747571i
$566$	15.6213	−	6.47056i	0.656613	−	0.271978i
$567$	−0.353934	−	2.62197i	−0.0148638	−	0.110112i
$568$	63.6838	+	26.3787i	2.67211	+	1.10682i
$569$	−9.30502	−	34.7268i	−0.390087	−	1.45582i	−0.829990	−	0.557779i	$-0.811654\pi$
$569$	−9.30502	−	34.7268i	−0.390087	−	1.45582i	0.439903	−	0.898045i	$-0.355013\pi$
$570$	12.5532	+	3.36361i	0.525794	+	0.140886i
$571$	−2.25751	−	17.1475i	−0.0944737	−	0.717599i	−0.971480	−	0.237121i	$-0.923796\pi$
$571$	−2.25751	−	17.1475i	−0.0944737	−	0.717599i	0.877007	−	0.480478i	$-0.159537\pi$
$572$	−42.7034	−	55.6521i	−1.78552	−	2.32693i
$573$	−8.57639	+	3.55246i	−0.358284	+	0.148406i
$574$	0.659001	−	1.15011i	0.0275062	−	0.0480047i
$575$	0.157930	+	0.381277i	0.00658613	+	0.0159003i
$576$	−1.36574	+	0.365949i	−0.0569059	+	0.0152479i
$577$	−0.931953	−	1.61419i	−0.0387977	−	0.0671996i	0.845975	−	0.533223i	$-0.179019\pi$
$577$	−0.931953	−	1.61419i	−0.0387977	−	0.0671996i	−0.884772	+	0.466024i	$0.845686\pi$
$578$	1.09467	+	43.5289i	0.0455322	+	1.81056i
$579$	−6.29171	+	10.8976i	−0.261475	+	0.452887i
$580$	−62.2882	−	62.2882i	−2.58638	−	2.58638i
$581$	41.2915	−	17.2622i	1.71306	−	0.716158i
$582$		−	6.39239i		−	0.264973i
$583$	−6.99821	+	53.1567i	−0.289836	+	2.20153i
$584$	34.6313	−	4.55929i	1.43305	−	0.188665i
$585$	−1.05166	−	7.98814i	−0.0434807	−	0.330269i
$586$	−14.7747	−	55.1401i	−0.610339	−	2.27782i
$587$	−0.759095	+	0.759095i	−0.0313312	+	0.0313312i	−0.722599	−	0.691268i	$-0.757053\pi$
$587$	−0.759095	+	0.759095i	−0.0313312	+	0.0313312i	0.691268	+	0.722599i	$0.257053\pi$
$588$	25.1983	−	19.5991i	1.03916	−	0.808252i
$589$	−2.37046	+	5.72279i	−0.0976730	+	0.235804i
$590$	−8.87204	+	67.3898i	−0.365256	+	2.77440i
$591$	15.9367	−	9.20106i	0.655549	−	0.378481i
$592$	−4.98325	+	6.49430i	−0.204810	+	0.266914i
$593$	−3.03053	+	0.812029i	−0.124449	+	0.0333461i	−0.320506	−	0.947246i	$-0.603853\pi$
$593$	−3.03053	+	0.812029i	−0.124449	+	0.0333461i	0.196057	+	0.980593i	$0.437186\pi$
$594$	11.0085			0.451683
$595$	3.59099	+	24.2946i	0.147216	+	0.995980i
$596$	38.2645			1.56738
$597$	22.8773	−	6.12996i	0.936306	−	0.250883i
$598$	−33.7461	+	43.9787i	−1.37998	+	1.79842i
$599$	−20.2653	+	11.7002i	−0.828019	+	0.478057i	−0.853174	−	0.521626i	$-0.825326\pi$
$599$	−20.2653	+	11.7002i	−0.828019	+	0.478057i	0.0251546	+	0.999684i	$0.491992\pi$
$600$	0.0584172	−	0.443723i	0.00238487	−	0.0181149i
$601$	2.30574	−	5.56656i	0.0940532	−	0.227065i	−0.869851	−	0.493315i	$-0.835785\pi$
$601$	2.30574	−	5.56656i	0.0940532	−	0.227065i	0.963904	+	0.266251i	$0.0857849\pi$
$602$	16.3422	+	21.1537i	0.666059	+	0.862161i
$603$	−3.86240	+	3.86240i	−0.157289	+	0.157289i
$604$	8.86602	+	33.0884i	0.360753	+	1.34635i
$605$	2.19574	+	16.6783i	0.0892697	+	0.678071i
$606$	−31.9952	+	4.21225i	−1.29972	+	0.171111i
$607$	−3.40199	+	25.8407i	−0.138082	+	1.04884i	0.772355	+	0.635192i	$0.219079\pi$
$607$	−3.40199	+	25.8407i	−0.138082	+	1.04884i	−0.910437	+	0.413648i	$0.864254\pi$
$608$			14.7540i			0.598355i
$609$	18.0547	+	13.7601i	0.731612	+	0.557586i
$610$	34.3104	+	34.3104i	1.38919	+	1.38919i
$611$	7.24173	−	12.5430i	0.292969	−	0.507437i
$612$	−2.21976	+	18.6717i	−0.0897283	+	0.754757i
$613$	9.97071	+	17.2698i	0.402713	+	0.697520i	0.994052	−	0.108903i	$-0.0347338\pi$
$613$	9.97071	+	17.2698i	0.402713	+	0.697520i	−0.591339	+	0.806423i	$0.701400\pi$
$614$	18.1202	−	4.85529i	0.731271	−	0.195944i
$615$	0.168517	+	0.406836i	0.00679526	+	0.0164052i
$616$	37.4986	+	64.4608i	1.51086	+	2.59720i
$617$	25.5359	−	10.5773i	1.02804	−	0.425827i	0.196034	−	0.980597i	$-0.437194\pi$
$617$	25.5359	−	10.5773i	1.02804	−	0.425827i	0.832004	+	0.554770i	$0.187194\pi$
$618$	0.663559	+	0.864767i	0.0266923	+	0.0347860i
$619$	−5.88241	−	44.6814i	−0.236434	−	1.79590i	−0.538518	−	0.842614i	$-0.681016\pi$
$619$	−5.88241	−	44.6814i	−0.236434	−	1.79590i	0.302084	−	0.953281i	$-0.402318\pi$
$620$	27.2557	+	7.30314i	1.09462	+	0.293301i
$621$	−1.56516	−	5.84124i	−0.0628075	−	0.234401i
$622$	52.0163	+	21.5459i	2.08566	+	0.863911i
$623$	23.4882	−	18.1457i	0.941034	−	0.726992i
$624$	25.3827	−	10.5139i	1.01612	−	0.420891i
$625$	−21.9421	−	12.6683i	−0.877684	−	0.506731i
$626$	−41.4244	+	53.9853i	−1.65565	+	2.15769i
$627$	2.50710	−	9.35661i	0.100124	−	0.373667i
$628$	4.66516	−	8.08030i	0.186160	−	0.322439i
$629$	2.24599	+	3.77962i	0.0895533	+	0.150703i
$630$	0.0499922	+	15.2560i	0.00199174	+	0.607815i
$631$	10.3855	+	10.3855i	0.413439	+	0.413439i	0.882935	−	0.469496i	$-0.155564\pi$
$631$	10.3855	+	10.3855i	0.413439	+	0.413439i	−0.469496	+	0.882935i	$0.655564\pi$
$632$	−98.7027	−	12.9945i	−3.92618	−	0.516892i
$633$	−20.2509	+	11.6918i	−0.804899	+	0.464709i
$634$	−56.7908	−	43.5771i	−2.25545	−	1.73067i
$635$	11.9654	+	15.5936i	0.474833	+	0.618814i
$636$	−52.5594	−	21.7708i	−2.08411	−	0.863269i
$637$	−17.5981	+	17.8303i	−0.697263	+	0.706463i
$638$	−66.7879	+	66.7879i	−2.64416	+	2.64416i
$639$	8.33874	−	6.39854i	0.329875	−	0.253122i
$640$	−21.1397	+	2.78309i	−0.835619	+	0.110011i
$641$	−7.27252	−	5.58040i	−0.287247	−	0.220413i	0.455079	−	0.890451i	$-0.349611\pi$
$641$	−7.27252	−	5.58040i	−0.287247	−	0.220413i	−0.742326	+	0.670038i	$0.766278\pi$
$642$	7.88292	+	4.55121i	0.311114	+	0.179622i
$643$	5.64972	+	13.6396i	0.222803	+	0.537894i	0.995269	−	0.0971627i	$-0.0309767\pi$
$643$	5.64972	+	13.6396i	0.222803	+	0.537894i	−0.772465	+	0.635057i	$0.780977\pi$
$644$	51.4249	−	51.7631i	2.02643	−	2.03975i
$645$	−8.88033			−0.349662
$646$	22.1025	+	8.83130i	0.869612	+	0.347463i
$647$	−0.0652966	−	0.113097i	−0.00256707	−	0.00444630i	0.864739	−	0.502222i	$-0.167484\pi$
$647$	−0.0652966	−	0.113097i	−0.00256707	−	0.00444630i	−0.867306	+	0.497775i	$0.834150\pi$
$648$	−1.69737	+	6.33466i	−0.0666789	+	0.248849i
$649$	50.2296	+	6.61286i	1.97169	+	0.259577i
$650$			0.625573i			0.0245370i
$651$	−7.21242	−	0.925500i	−0.282677	−	0.0362732i
$652$	35.2575	−	85.1192i	1.38079	−	3.33353i
$653$	10.5187	−	8.07126i	0.411627	−	0.315853i	−0.382106	−	0.924118i	$-0.624801\pi$
$653$	10.5187	−	8.07126i	0.411627	−	0.315853i	0.793734	+	0.608266i	$0.208134\pi$
$654$	−1.35273	−	0.362462i	−0.0528958	−	0.0141734i
$655$	−7.83289	−	2.09882i	−0.306056	−	0.0820076i
$656$	−1.19128	+	0.914105i	−0.0465119	+	0.0356898i
$657$	2.03826	−	4.92079i	0.0795201	−	0.191978i
$658$	−16.6236	+	21.8119i	−0.648056	+	0.850318i
$659$			26.6394i			1.03772i	0.854858	+	0.518861i	$0.173644\pi$
$659$			26.6394i			1.03772i	−0.854858	+	0.518861i	$0.826356\pi$
$660$	−43.7486	−	5.75961i	−1.70291	−	0.224193i
$661$	6.17731	−	23.0540i	0.240269	−	0.896698i	−0.735433	−	0.677598i	$-0.763021\pi$
$661$	6.17731	−	23.0540i	0.240269	−	0.896698i	0.975702	−	0.219100i	$-0.0703122\pi$
$662$	−40.9018	−	70.8440i	−1.58969	−	2.75343i
$663$	−0.185500	−	14.7550i	−0.00720423	−	0.573036i
$664$	−110.935			−4.30511
$665$	12.9782	+	3.43196i	0.503273	+	0.133086i
$666$	1.04520	+	2.52332i	0.0405005	+	0.0977768i
$667$	44.9343	+	25.9428i	1.73986	+	1.00451i
$668$	64.2337	+	49.2883i	2.48528	+	1.90702i
$669$	−2.34792	+	0.309110i	−0.0907760	+	0.0119509i
$670$	24.9881	−	19.1741i	0.965376	−	0.740759i
$671$	25.5736	−	25.5736i	0.987256	−	0.987256i
$672$	−16.7150	+	4.53752i	−0.644794	+	0.175039i
$673$	−20.5511	−	8.51255i	−0.792187	−	0.328134i	−0.0503644	−	0.998731i	$-0.516038\pi$
$673$	−20.5511	−	8.51255i	−0.792187	−	0.328134i	−0.741822	+	0.670596i	$0.766038\pi$
$674$	−26.1944	−	34.1372i	−1.00897	−	1.31492i
$675$	−0.0541415	−	0.0415442i	−0.00208391	−	0.00159904i
$676$	0.756531	−	0.436783i	0.0290973	−	0.0167994i
$677$	45.7077	+	6.01753i	1.75669	+	0.231272i	0.938887	−	0.344227i	$-0.111859\pi$
$677$	45.7077	+	6.01753i	1.75669	+	0.231272i	0.817802	+	0.575499i	$0.195192\pi$
$678$	−28.5910	−	28.5910i	−1.09803	−	1.09803i
$679$	−0.0216373	−	6.60304i	−0.000830365	−	0.253401i
$680$	15.0150	−	58.9933i	0.575798	−	2.26229i
$681$	−2.68006	+	4.64201i	−0.102700	+	0.177882i
$682$	7.83072	−	29.2247i	0.299854	−	1.11907i
$683$	−15.6349	+	20.3758i	−0.598252	+	0.779658i	−0.990099	−	0.140373i	$-0.955170\pi$
$683$	−15.6349	+	20.3758i	−0.598252	+	0.779658i	0.391846	+	0.920031i	$0.371836\pi$
$684$	8.90125	+	5.13914i	0.340348	+	0.196500i
$685$	−7.37538	+	3.05498i	−0.281799	+	0.116725i
$686$	37.3483	−	29.2461i	1.42596	−	1.11662i
$687$	−20.8124	−	8.62077i	−0.794042	−	0.328903i
$688$	−7.83737	−	29.2495i	−0.298797	−	1.11513i
$689$	43.1242	+	11.5551i	1.64290	+	0.440214i
$690$	4.55150	+	34.5720i	0.173272	+	1.31614i
$691$	−7.85023	−	10.2306i	−0.298637	−	0.389191i	0.619799	−	0.784760i	$-0.287214\pi$
$691$	−7.85023	−	10.2306i	−0.298637	−	0.389191i	−0.918436	+	0.395569i	$0.870547\pi$
$692$	−85.9933	+	35.6196i	−3.26897	+	1.35405i
$693$	11.3712	−	0.0372621i	0.431957	−	0.00141547i
$694$	5.91741	+	14.2859i	0.224622	+	0.542285i
$695$	−25.8414	+	6.92420i	−0.980222	+	0.262650i
$696$	−28.1343	−	48.7300i	−1.06643	−	1.84710i
$697$	0.218512	+	0.776325i	0.00827672	+	0.0294054i
$698$	27.3593	−	47.3878i	1.03557	−	1.79365i
$699$	−1.14279	−	1.14279i	−0.0432242	−	0.0432242i
$700$	0.104801	−	0.816718i	0.00396112	−	0.0308690i
$701$			33.6476i			1.27085i	0.772161	+	0.635427i	$0.219176\pi$
$701$			33.6476i			1.27085i	−0.772161	+	0.635427i	$0.780824\pi$
$702$	1.19650	−	9.08831i	0.0451589	−	0.343016i
$703$	2.38273	−	0.313692i	0.0898662	−	0.0118311i
$704$	−0.793200	−	6.02495i	−0.0298949	−	0.227074i
$705$	−2.35803	−	8.80028i	−0.0888085	−	0.331438i
$706$	20.3707	−	20.3707i	0.766661	−	0.766661i
$707$	−33.0353	+	4.45935i	−1.24242	+	0.167711i
$708$	−20.5720	+	49.6652i	−0.773143	+	1.86653i
$709$	1.45813	−	11.0756i	0.0547613	−	0.415953i	−0.942005	−	0.335599i	$-0.891061\pi$
$709$	1.45813	−	11.0756i	0.0547613	−	0.415953i	0.996766	−	0.0803546i	$-0.0256053\pi$
$710$	−52.4879	+	30.3039i	−1.96984	+	1.13729i
$711$	−9.24119	+	12.0434i	−0.346572	+	0.451661i
$712$	−71.0645	+	19.0417i	−2.66326	+	0.713617i
$713$	−16.6203			−0.622437
$714$	−3.20755	+	27.7561i	−0.120040	+	1.03875i
$715$	34.6288			1.29504
$716$	35.2430	−	9.44332i	1.31709	−	0.352913i
$717$	−4.49896	+	5.86316i	−0.168017	+	0.218964i
$718$	−50.4562	+	29.1309i	−1.88301	+	1.08716i
$719$	2.49752	−	18.9706i	0.0931419	−	0.707483i	−0.879620	−	0.475677i	$-0.842203\pi$
$719$	2.49752	−	18.9706i	0.0931419	−	0.707483i	0.972762	−	0.231806i	$-0.0744635\pi$
$720$	6.61367	−	15.9668i	0.246477	−	0.595048i
$721$	0.688352	+	0.891018i	0.0256356	+	0.0331832i
$722$	−25.2118	+	25.2118i	−0.938285	+	0.938285i
$723$	−1.86877	−	6.97434i	−0.0695003	−	0.259378i
$724$	1.02911	+	7.81684i	0.0382464	+	0.290511i
$725$	0.580520	−	0.0764270i	0.0215600	−	0.00283843i
$726$	−2.49815	+	18.9754i	−0.0927152	+	0.704242i
$727$			26.6025i			0.986634i	0.869850	+	0.493317i	$0.164216\pi$
$727$			26.6025i			0.986634i	−0.869850	+	0.493317i	$0.835784\pi$
$728$	57.2928	−	23.9517i	2.12341	−	0.887710i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−15.3562	+	26.5978i	−0.568360	+	0.984428i
$731$	−16.1502	−	1.91999i	−0.597336	−	0.0710135i
$732$	19.1876	+	33.2340i	0.709196	+	1.22836i
$733$	−10.7314	+	2.87546i	−0.396373	+	0.106208i	−0.451499	−	0.892272i	$-0.649111\pi$
$733$	−10.7314	+	2.87546i	−0.396373	+	0.106208i	0.0551264	+	0.998479i	$0.482444\pi$
$734$	0.419049	+	1.01167i	0.0154674	+	0.0373416i
$735$	0.103279	+	15.7586i	0.00380951	+	0.581264i
$736$	−36.5741	+	15.1495i	−1.34814	+	0.558417i
$737$	−14.2916	−	18.6251i	−0.526437	−	0.686066i
$738$	0.0653942	+	0.496718i	0.00240719	+	0.0182844i
$739$	37.5265	+	10.0552i	1.38043	+	0.369886i	0.871279	−	0.490789i	$-0.163291\pi$
$739$	37.5265	+	10.0552i	1.38043	+	0.369886i	0.509155	+	0.860675i	$0.329958\pi$
$740$	−2.83350	−	10.5748i	−0.104161	−	0.388736i
$741$	−7.45208	−	3.08675i	−0.273759	−	0.113395i
$742$	−78.2071	−	32.0946i	−2.87107	−	1.17823i
$743$	−4.99243	+	2.06793i	−0.183155	+	0.0758651i	−0.472376	−	0.881397i	$-0.656604\pi$
$743$	−4.99243	+	2.06793i	−0.183155	+	0.0758651i	0.289222	+	0.957262i	$0.406604\pi$
$744$	15.6095	+	9.01215i	0.572272	+	0.330401i
$745$	−11.4992	+	14.9860i	−0.421296	+	0.549044i
$746$	3.99875	−	14.9235i	0.146405	−	0.546389i
$747$	−8.45781	+	14.6494i	−0.309455	+	0.535992i
$748$	−78.3180	−	19.9335i	−2.86359	−	0.728840i
$749$	8.15809	+	4.67450i	0.298090	+	0.170802i
$750$	−20.1086	−	20.1086i	−0.734262	−	0.734262i
$751$	35.0594	+	4.61566i	1.27934	+	0.168428i	0.739393	−	0.673274i	$-0.235113\pi$
$751$	35.0594	+	4.61566i	1.27934	+	0.168428i	0.539942	+	0.841702i	$0.318446\pi$
$752$	26.9047	−	15.5335i	0.981114	−	0.566447i
$753$	1.42531	+	1.09368i	0.0519412	+	0.0398559i
$754$	47.8792	+	62.3974i	1.74366	+	2.27238i
$755$	−15.6232	−	6.47135i	−0.568587	−	0.235516i
$756$	−3.08464	+	11.6648i	−0.112187	+	0.424245i
$757$	30.8014	−	30.8014i	1.11950	−	1.11950i	0.127682	−	0.991815i	$-0.459246\pi$
$757$	30.8014	−	30.8014i	1.11950	−	1.11950i	0.991815	−	0.127682i	$-0.0407537\pi$
$758$	56.5581	−	43.3986i	2.05428	−	1.57631i
$759$	25.7686	−	3.39250i	0.935341	−	0.123140i
$760$	−26.3991	−	20.2568i	−0.957596	−	0.734790i
$761$	20.9201	+	12.0782i	0.758353	+	0.437835i	0.828704	−	0.559687i	$-0.189079\pi$
$761$	20.9201	+	12.0782i	0.758353	+	0.437835i	−0.0703510	+	0.997522i	$0.522412\pi$
$762$	8.55771	+	20.6601i	0.310013	+	0.748438i
$763$	−1.39853	−	0.369827i	−0.0506301	−	0.0133886i
$764$	42.3346			1.53161
$765$	−6.64553	−	6.48051i	−0.240270	−	0.234303i
$766$	−2.69997	−	4.67649i	−0.0975541	−	0.168969i
$767$	10.9188	−	40.7496i	0.394255	−	1.47138i
$768$	−26.8548	−	3.53550i	−0.969038	−	0.127576i
$769$		−	24.6967i		−	0.890585i	−0.895385	−	0.445292i	$-0.853100\pi$
$769$		−	24.6967i		−	0.890585i	0.895385	−	0.445292i	$-0.146900\pi$
$770$	−65.0367	−	8.34552i	−2.34376	−	0.300752i
$771$	0.178948	−	0.432020i	0.00644467	−	0.0155588i
$772$	45.5273	−	34.9343i	1.63856	−	1.25731i
$773$	9.82449	+	2.63246i	0.353362	+	0.0946831i	0.431134	−	0.902288i	$-0.358114\pi$
$773$	9.82449	+	2.63246i	0.353362	+	0.0946831i	−0.0777714	+	0.996971i	$0.524780\pi$
$774$	−9.75911	−	2.61495i	−0.350784	−	0.0939923i
$775$	−0.148802	+	0.114180i	−0.00534512	+	0.00410146i
$776$	−6.26349	+	15.1214i	−0.224846	+	0.542827i
$777$	1.08818	+	2.60294i	0.0390382	+	0.0933798i
$778$		−	17.5714i		−	0.629964i
$779$	0.437077	+	0.0575422i	0.0156599	+	0.00206166i
$780$	−9.50997	+	35.4917i	−0.340512	+	1.27081i
$781$	22.5873	+	39.1223i	0.808237	+	1.39991i
$782$	0.802830	+	63.8584i	0.0287092	+	2.28357i
$783$	−8.57997			−0.306623
$784$	−51.8135	+	14.2480i	−1.85048	+	0.508857i
$785$	1.76262	+	4.25534i	0.0629106	+	0.151880i
$786$	−7.99000	−	4.61303i	−0.284994	−	0.164541i
$787$	−16.8624	−	12.9390i	−0.601079	−	0.461224i	0.262850	−	0.964837i	$-0.415337\pi$
$787$	−16.8624	−	12.9390i	−0.601079	−	0.461224i	−0.863930	+	0.503612i	$0.832004\pi$
$788$	−83.2037	+	10.9540i	−2.96401	+	0.390219i
$789$	23.0921	−	17.7192i	0.822101	−	0.630821i
$790$	61.8957	−	61.8957i	2.20215	−	2.20215i
$791$	−29.6299	−	29.4364i	−1.05352	−	1.04664i
$792$	−26.0409	−	10.7865i	−0.925323	−	0.383281i
$793$	−18.3333	−	23.8924i	−0.651035	−	0.848445i
$794$	−56.3968	−	43.2748i	−2.00145	−	1.53576i
$795$	24.3214	−	14.0420i	0.862590	−	0.498017i
$796$	−107.087	−	14.0983i	−3.79559	−	0.499699i
$797$	18.1038	+	18.1038i	0.641270	+	0.641270i	0.950868	−	0.309598i	$-0.100194\pi$
$797$	18.1038	+	18.1038i	0.641270	+	0.641270i	−0.309598	+	0.950868i	$0.600194\pi$
$798$	13.2519	+	7.59320i	0.469113	+	0.268797i
$799$	−2.38573	−	16.5144i	−0.0844012	−	0.584238i
$800$	−0.223373	+	0.386893i	−0.00789742	+	0.0136787i
$801$	−2.90352	+	10.8361i	−0.102591	+	0.382875i
$802$	−23.2126	+	30.2512i	−0.819665	+	1.06821i
$803$	19.8249	+	11.4459i	0.699606	+	0.403918i
$804$	23.0141	−	9.53275i	0.811644	−	0.336194i
$805$	4.81850	+	35.6959i	0.169830	+	1.25811i
$806$	−23.2760	−	9.64124i	−0.819862	−	0.339598i
$807$	−2.92215	−	10.9056i	−0.102864	−	0.383896i
$808$	79.8130	+	21.3858i	2.80781	+	0.752351i
$809$	−1.61626	−	12.2767i	−0.0568246	−	0.431625i	−0.996084	−	0.0884163i	$-0.971819\pi$
$809$	−1.61626	−	12.2767i	−0.0568246	−	0.431625i	0.939259	−	0.343209i	$-0.111514\pi$
$810$	−3.51028	−	4.57469i	−0.123339	−	0.160738i
$811$	−15.7423	+	6.52066i	−0.552786	+	0.228972i	−0.641550	−	0.767081i	$-0.721708\pi$
$811$	−15.7423	+	6.52066i	−0.552786	+	0.228972i	0.0887639	+	0.996053i	$0.471708\pi$
$812$	−52.0555	−	89.4843i	−1.82679	−	3.14028i
$813$	2.68135	+	6.47335i	0.0940391	+	0.227030i
$814$	−11.3387	+	3.03819i	−0.397420	+	0.106488i
$815$	22.7408	+	39.3882i	0.796574	+	1.37971i
$816$	15.4801	−	27.6080i	0.541911	−	0.966475i
$817$	−4.44513	+	7.69919i	−0.155515	+	0.269360i
$818$	−3.15237	−	3.15237i	−0.110220	−	0.110220i
$819$	1.20516	−	9.39184i	0.0421118	−	0.328178i
$820$		−	2.00821i		−	0.0701299i
$821$	5.18710	−	39.3999i	0.181031	−	1.37507i	−0.623810	−	0.781576i	$-0.714416\pi$
$821$	5.18710	−	39.3999i	0.181031	−	1.37507i	0.804841	−	0.593491i	$-0.202251\pi$
$822$	−9.00482	+	1.18551i	−0.314079	+	0.0413493i
$823$	−1.61369	−	12.2572i	−0.0562498	−	0.427260i	−0.996280	−	0.0861699i	$-0.972537\pi$
$823$	−1.61369	−	12.2572i	−0.0562498	−	0.427260i	0.940031	−	0.341090i	$-0.110796\pi$
$824$	−0.722341	−	2.69581i	−0.0251639	−	0.0939131i
$825$	0.207400	−	0.207400i	0.00722075	−	0.00722075i
$826$	−30.3273	+	73.9006i	−1.05522	+	2.57133i
$827$	6.56727	−	15.8548i	0.228366	−	0.551325i	−0.767612	−	0.640914i	$-0.778555\pi$
$827$	6.56727	−	15.8548i	0.228366	−	0.551325i	0.995979	+	0.0895890i	$0.0285554\pi$
$828$	−3.59969	+	27.3424i	−0.125098	+	0.950213i
$829$	11.4581	−	6.61534i	0.397956	−	0.229760i	−0.287646	−	0.957737i	$-0.592873\pi$
$829$	11.4581	−	6.61534i	0.397956	−	0.229760i	0.685602	+	0.727977i	$0.259539\pi$
$830$	59.3786	−	77.3837i	2.06106	−	2.68603i
$831$	11.9642	−	3.20579i	0.415033	−	0.111208i
$832$	−5.06026			−0.175433
$833$	−3.21930	+	28.6816i	−0.111542	+	0.993760i
$834$	−30.4376			−1.05397
$835$	−38.6067	+	10.3446i	−1.33604	+	0.357991i
$836$	−26.8923	+	35.0467i	−0.930090	+	1.21212i
$837$	2.38018	−	1.37420i	0.0822710	−	0.0474992i
$838$	12.5362	−	95.2222i	0.433057	−	3.28939i
$839$	−12.9308	+	31.2178i	−0.446422	+	1.07776i	0.527230	+	0.849722i	$0.323230\pi$
$839$	−12.9308	+	31.2178i	−0.446422	+	1.07776i	−0.973653	+	0.228036i	$0.926770\pi$
$840$	14.8301	−	36.1376i	0.511689	−	1.24687i
$841$	31.5482	−	31.5482i	1.08787	−	1.08787i
$842$	11.0810	+	41.3547i	0.381875	+	1.42518i
$843$	1.36418	+	10.3620i	0.0469850	+	0.356886i
$844$	105.727	−	13.9193i	3.63929	−	0.479121i
$845$	−0.0562881	+	0.427550i	−0.00193637	+	0.0147082i
$846$		−	10.3655i		−	0.356373i
$847$	−2.51625	+	19.6091i	−0.0864593	+	0.673777i
$848$	67.7154	+	67.7154i	2.32536	+	2.32536i
$849$	−3.30070	+	5.71698i	−0.113280	+	0.196206i
$850$	0.445887	+	0.566209i	0.0152938	+	0.0194208i
$851$	3.22421	+	5.58449i	0.110524	+	0.191434i
$852$	−46.3003	+	12.4061i	−1.58622	+	0.425027i
$853$	−19.4113	−	46.8631i	−0.664631	−	1.60456i	−0.790464	−	0.612509i	$-0.790160\pi$
$853$	−19.4113	−	46.8631i	−0.664631	−	1.60456i	0.125833	−	0.992051i	$-0.459840\pi$
$854$	28.6739	+	49.2909i	0.981200	+	1.68670i
$855$	−4.68768	+	1.94170i	−0.160315	+	0.0664048i
$856$	−14.1879	−	18.4900i	−0.484931	−	0.631975i
$857$	0.847735	+	6.43918i	0.0289581	+	0.219958i	0.999805	−	0.0197415i	$-0.00628431\pi$
$857$	0.847735	+	6.43918i	0.0289581	+	0.219958i	−0.970847	+	0.239700i	$0.922951\pi$
$858$	38.0556	+	10.1970i	1.29920	+	0.348119i
$859$	0.993821	+	3.70899i	0.0339087	+	0.126549i	0.980806	−	0.194989i	$-0.0624670\pi$
$859$	0.993821	+	3.70899i	0.0339087	+	0.126549i	−0.946897	+	0.321538i	$0.895800\pi$
$860$	37.4154	+	15.4980i	1.27585	+	0.528476i
$861$	0.0692304	+	0.512865i	0.00235937	+	0.0174784i
$862$	13.8280	−	5.72775i	0.470984	−	0.195088i
$863$	35.0237	+	20.2210i	1.19222	+	0.688329i	0.958810	−	0.284049i	$-0.0916778\pi$
$863$	35.0237	+	20.2210i	1.19222	+	0.688329i	0.233411	+	0.972378i	$0.425011\pi$
$864$	3.98514	−	5.19354i	0.135577	−	0.176688i
$865$	11.8924	−	44.3829i	0.404352	−	1.50906i
$866$	−38.1207	+	66.0270i	−1.29540	+	2.24369i
$867$	−10.6847	−	13.2226i	−0.362873	−	0.449062i
$868$	28.7729	+	16.4865i	0.976614	+	0.559590i
$869$	−46.1346	−	46.1346i	−1.56501	−	1.56501i
$870$	49.0512	+	6.45771i	1.66299	+	0.218937i
$871$	−16.9298	+	9.77441i	−0.573644	+	0.331193i
$872$	2.84476	+	2.18286i	0.0963359	+	0.0739211i
$873$	1.51930	+	1.97999i	0.0514206	+	0.0670126i
$874$	32.2520	+	13.3592i	1.09094	+	0.451883i
$875$	−20.8393	−	20.7032i	−0.704496	−	0.699894i
$876$	−17.1756	+	17.1756i	−0.580309	+	0.580309i
$877$	−26.2212	+	20.1202i	−0.885427	+	0.679412i	−0.947877	−	0.318636i	$-0.896775\pi$
$877$	−26.2212	+	20.1202i	−0.885427	+	0.679412i	0.0624503	+	0.998048i	$0.480109\pi$
$878$	36.6585	−	4.82618i	1.23716	−	0.162876i
$879$	17.6817	+	13.5676i	0.596389	+	0.457625i
$880$	64.3271	+	37.1393i	2.16847	+	1.25196i
$881$	7.24355	+	17.4875i	0.244041	+	0.589168i	0.997677	−	0.0681247i	$-0.0217016\pi$
$881$	7.24355	+	17.4875i	0.244041	+	0.589168i	−0.753635	+	0.657293i	$0.771702\pi$
$882$	−4.52686	+	17.3485i	−0.152427	+	0.584153i
$883$	−48.1977			−1.62198			−0.810990	−	0.585060i	$-0.801071\pi$
$883$	−48.1977			−1.62198			−0.810990	+	0.585060i	$0.801071\pi$
$884$	−24.9688	+	62.4907i	−0.839793	+	2.10179i
$885$	−13.2687	−	22.9821i	−0.446024	−	0.772536i
$886$	−2.89171	+	10.7920i	−0.0971489	+	0.362565i
$887$	3.02972	+	0.398871i	0.101728	+	0.0133928i	0.181218	−	0.983443i	$-0.441996\pi$
$887$	3.02972	+	0.398871i	0.101728	+	0.0133928i	−0.0794902	+	0.996836i	$0.525329\pi$
$888$		−	6.99313i		−	0.234674i
$889$	8.90964	+	21.3120i	0.298820	+	0.714781i
$890$	24.7551	−	59.7640i	0.829792	−	2.00329i
$891$	−3.40979	+	2.61642i	−0.114232	+	0.0876534i
$892$	10.4319	+	2.79523i	0.349287	+	0.0935913i
$893$	−8.81012	−	2.36066i	−0.294819	−	0.0789966i
$894$	−17.0499	+	13.0829i	−0.570235	+	0.437557i
$895$	−6.89272	+	16.6405i	−0.230398	+	0.556231i
$896$	−24.8544	−	3.18932i	−0.830327	−	0.106548i
$897$		−	21.6426i		−	0.722626i
$898$	−24.5532	−	3.23249i	−0.819350	−	0.107870i
$899$	−6.10324	+	22.7776i	−0.203554	+	0.759676i
$900$	0.155611	+	0.269526i	0.00518702	+	0.00898419i
$901$	47.2679	−	20.2789i	1.57472	−	0.675587i
$902$	−2.15329			−0.0716966
$903$	−10.0895	−	2.66808i	−0.335759	−	0.0887882i
$904$	39.6184	+	95.6474i	1.31769	+	3.18118i
$905$	−3.37067	−	1.94606i	−0.112045	−	0.0646891i
$906$	−15.2637	−	11.7122i	−0.507102	−	0.389113i
$907$	−12.3762	+	1.62936i	−0.410946	+	0.0541021i	−0.333165	−	0.942868i	$-0.608117\pi$
$907$	−12.3762	+	1.62936i	−0.410946	+	0.0541021i	−0.0777807	+	0.996970i	$0.524783\pi$
$908$	19.3931	−	14.8809i	0.643583	−	0.493839i
$909$	8.90913	−	8.90913i	0.295497	−	0.295497i
$910$	−13.9586	+	52.7855i	−0.462723	+	1.74982i
$911$	13.9902	+	5.79492i	0.463515	+	0.191994i	0.602205	−	0.798342i	$-0.294289\pi$
$911$	13.9902	+	5.79492i	0.463515	+	0.191994i	−0.138690	+	0.990336i	$0.544289\pi$
$912$	−10.5326	−	13.7263i	−0.348769	−	0.454524i
$913$	−57.6787	−	44.2584i	−1.90889	−	1.46474i
$914$	−21.4378	+	12.3771i	−0.709101	+	0.409400i
$915$	−18.7820	−	2.47270i	−0.620915	−	0.0817450i
$916$	72.6436	+	72.6436i	2.40021	+	2.40021i
$917$	−8.26890	−	4.73799i	−0.273063	−	0.156462i
$918$	−5.39488	−	9.07869i	−0.178058	−	0.299641i
$919$	−21.0113	+	36.3926i	−0.693099	+	1.20048i	0.277718	+	0.960662i	$0.410422\pi$
$919$	−21.0113	+	36.3926i	−0.693099	+	1.20048i	−0.970817	+	0.239820i	$0.922912\pi$
$920$	23.1082	−	86.2410i	0.761855	−	2.84328i
$921$	−4.45861	+	5.81058i	−0.146916	+	0.191465i
$922$	10.6451	+	6.14595i	0.350578	+	0.202406i
$923$	34.7534	−	14.3953i	1.14392	−	0.473828i
$924$	−47.9753	−	19.6881i	−1.57827	−	0.647691i
$925$	0.0672311	+	0.0278480i	0.00221054	+	0.000915638i
$926$	15.0327	+	56.1029i	0.494006	+	1.84366i
$927$	−0.411065	−	0.110144i	−0.0135011	−	0.00361762i
$928$	7.33128	+	55.6866i	0.240661	+	1.82800i
$929$	31.1140	+	40.5485i	1.02082	+	1.33035i	0.942785	+	0.333402i	$0.108197\pi$
$929$	31.1140	+	40.5485i	1.02082	+	1.33035i	0.0780312	+	0.996951i	$0.475137\pi$
$930$	−14.6416	+	6.06476i	−0.480117	+	0.198871i
$931$	13.7143	+	7.79857i	0.449468	+	0.255588i
$932$	2.82050	+	6.80929i	0.0923886	+	0.223046i
$933$	−21.2325	+	5.68924i	−0.695122	+	0.186257i
$934$	−21.7044	−	37.5931i	−0.710189	−	1.23008i
$935$	31.3427	−	24.6822i	1.02502	−	0.807196i
$936$	−11.7354	+	20.3263i	−0.383584	+	0.664386i
$937$	9.66343	+	9.66343i	0.315690	+	0.315690i	0.847109	−	0.531419i	$-0.178341\pi$
$937$	9.66343	+	9.66343i	0.315690	+	0.315690i	−0.531419	+	0.847109i	$0.678341\pi$
$938$	34.1516	−	14.2773i	1.11509	−	0.466172i
$939$		−	26.5670i		−	0.866981i
$940$	−5.42321	+	41.1934i	−0.176886	+	1.34358i
$941$	20.9952	−	2.76407i	0.684425	−	0.0901062i	0.219708	−	0.975566i	$-0.429490\pi$
$941$	20.9952	−	2.76407i	0.684425	−	0.0901062i	0.464717	+	0.885459i	$0.346156\pi$
$942$	0.683997	+	5.19548i	0.0222858	+	0.169278i
$943$	0.306149	+	1.14256i	0.00996958	+	0.0372070i
$944$	63.9867	−	63.9867i	2.08259	−	2.08259i
$945$	−3.64144	−	4.71356i	−0.118456	−	0.153332i
$946$	16.6175	−	40.1183i	0.540283	−	1.30436i
$947$	2.54260	−	19.3130i	0.0826234	−	0.627587i	−0.899165	−	0.437610i	$-0.855825\pi$
$947$	2.54260	−	19.3130i	0.0826234	−	0.627587i	0.981788	−	0.189977i	$-0.0608415\pi$
$948$	59.9539	−	34.6144i	1.94721	−	1.12422i
$949$	11.6042	−	15.1229i	0.376688	−	0.490910i
$950$	0.380529	−	0.101962i	0.0123460	−	0.00330810i
$951$	27.9476			0.906265
$952$	34.7840	−	62.5152i	1.12736	−	2.02613i
$953$	−15.2901			−0.495294			−0.247647	−	0.968850i	$-0.579657\pi$
$953$	−15.2901			−0.495294			−0.247647	+	0.968850i	$0.579657\pi$
$954$	30.8630	−	8.26973i	0.999228	−	0.267742i
$955$	−12.7223	+	16.5800i	−0.411683	+	0.536516i
$956$	29.1878	−	16.8516i	0.944002	−	0.545020i
$957$	4.81331	−	36.5607i	0.155592	−	1.18184i
$958$	−20.6041	+	49.7427i	−0.665689	+	1.60711i
$959$	−9.29754	+	1.25505i	−0.300233	+	0.0405278i
$960$	−2.25081	+	2.25081i	−0.0726445	+	0.0726445i
$961$	6.06836	+	22.6474i	0.195754	+	0.730562i
$962$	1.27586	+	9.69113i	0.0411354	+	0.312455i
$963$	−3.52337	+	0.463861i	−0.113539	+	0.0149477i
$964$	−4.29797	+	32.6463i	−0.138428	+	1.05147i
$965$			28.3288i			0.911935i
$966$	−5.21585	+	40.6472i	−0.167817	+	1.30780i
$967$	18.2416	+	18.2416i	0.586610	+	0.586610i	0.936712	−	0.350102i	$-0.113853\pi$
$967$	18.2416	+	18.2416i	0.586610	+	0.586610i	−0.350102	+	0.936712i	$0.613853\pi$
$968$	24.5022	−	42.4391i	0.787531	−	1.36404i
$969$	−8.94505	+	2.51776i	−0.287356	+	0.0808820i
$970$	−7.19552	−	12.4630i	−0.231034	−	0.400163i
$971$	−14.5621	+	3.90190i	−0.467319	+	0.125218i	−0.484792	−	0.874630i	$-0.661105\pi$
$971$	−14.5621	+	3.90190i	−0.467319	+	0.125218i	0.0174726	+	0.999847i	$0.494438\pi$
$972$	−1.74520	−	4.21329i	−0.0559774	−	0.135141i
$973$	−31.4406	+	0.103027i	−1.00794	+	0.00330290i
$974$	1.40277	−	0.581047i	0.0449477	−	0.0186180i
$975$	−0.148682	−	0.193766i	−0.00476164	−	0.00620549i
$976$	−8.43174	−	64.0454i	−0.269893	−	2.05004i
$977$	−35.9499	−	9.63275i	−1.15014	−	0.308179i	−0.367118	−	0.930174i	$-0.619656\pi$
$977$	−35.9499	−	9.63275i	−1.15014	−	0.308179i	−0.783021	+	0.621995i	$0.786322\pi$
$978$	13.3927	+	49.9823i	0.428252	+	1.59826i
$979$	−44.5457	−	18.4514i	−1.42369	−	0.589710i
$980$	27.0668	−	66.5758i	0.864617	−	2.12669i
$981$	0.505144	−	0.209237i	0.0161280	−	0.00668044i
$982$	−16.4540	−	9.49972i	−0.525068	−	0.303148i
$983$	−14.4836	+	18.8753i	−0.461954	+	0.602030i	−0.965007	−	0.262226i	$-0.915543\pi$
$983$	−14.4836	+	18.8753i	−0.461954	+	0.602030i	0.503053	+	0.864256i	$0.332210\pi$
$984$	0.332010	−	1.23908i	0.0105841	−	0.0395004i
$985$	20.7141	−	35.8779i	0.660007	−	1.14317i
$986$	87.8105	+	22.3495i	2.79646	+	0.711753i
$987$	−0.0350858	−	10.7071i	−0.00111679	−	0.340810i
$988$	26.0108	+	26.0108i	0.827513	+	0.827513i
$989$	−23.6499	−	3.11357i	−0.752024	−	0.0990059i
$990$	21.4628	−	12.3916i	0.682133	−	0.393829i
$991$	45.9595	+	35.2660i	1.45995	+	1.12026i	0.968397	+	0.249415i	$0.0802384\pi$
$991$	45.9595	+	35.2660i	1.45995	+	1.12026i	0.491556	+	0.870846i	$0.336428\pi$
$992$	−10.9527	−	14.2739i	−0.347750	−	0.453196i
$993$	29.5068	+	12.2221i	0.936369	+	0.387857i
$994$	−68.7399	+	18.6604i	−2.18030	+	0.591873i
$995$	37.7029	−	37.7029i	1.19526	−	1.19526i
$996$	61.2013	−	46.9614i	1.93924	−	1.48803i
$997$	−27.0087	+	3.55576i	−0.855373	+	0.112612i	−0.545443	−	0.838148i	$-0.683639\pi$
$997$	−27.0087	+	3.55576i	−0.855373	+	0.112612i	−0.309929	+	0.950760i	$0.600305\pi$
$998$	−21.1771	−	16.2497i	−0.670348	−	0.514376i
$999$	−0.923469	−	0.533165i	−0.0292173	−	0.0168686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.100.23	yes	192
7.4	even	3	inner	357.2.bh.a.151.2	yes	192
17.8	even	8	inner	357.2.bh.a.331.2	yes	192
119.25	even	24	inner	357.2.bh.a.25.23	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.23	✓	192	119.25	even	24	inner
357.2.bh.a.100.23	yes	192	1.1	even	1	trivial
357.2.bh.a.151.2	yes	192	7.4	even	3	inner
357.2.bh.a.331.2	yes	192	17.8	even	8	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47406 - 0.662922i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(3.94945 - 2.28022i) q^{4} +(-0.293850 + 2.23202i) q^{5} +(-0.980180 + 2.36636i) q^{6} +(-1.00447 + 2.44766i) q^{7} +(4.63730 - 4.63730i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.752649 + 5.71694i) q^{10} +(4.26117 - 0.560994i) q^{11} +(-0.595256 + 4.52142i) q^{12} -3.57889i q^{13} +(-0.862510 + 6.72154i) q^{14} +(-1.59189 - 1.59189i) q^{15} +(3.83834 - 6.64821i) q^{16} +(-2.55091 - 3.23927i) q^{17} +(-1.28067 - 2.21818i) q^{18} +(-2.17700 + 0.583325i) q^{19} +(3.92893 + 9.48528i) q^{20} +(-1.33038 - 2.28694i) q^{21} +(10.1705 - 4.21276i) q^{22} +(-3.68136 - 4.79764i) q^{23} +(0.856007 + 6.50202i) q^{24} +(-0.0659185 - 0.0176628i) q^{25} +(-2.37252 - 8.85438i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.61409 + 11.9573i) q^{28} +(-7.92686 + 3.28341i) q^{29} +(-4.99374 - 2.88314i) q^{30} +(1.67311 - 2.18045i) q^{31} +(1.69431 - 6.32325i) q^{32} +(-2.14897 + 3.72213i) q^{33} +(-8.45848 - 6.32309i) q^{34} +(-5.16805 - 2.96124i) q^{35} +(-3.22471 - 3.22471i) q^{36} +(-1.05721 - 0.139184i) q^{37} +(-4.99932 + 2.88636i) q^{38} +(2.83932 + 2.17869i) q^{39} +(8.98785 + 11.7132i) q^{40} +(-0.180713 - 0.0748539i) q^{41} +(-4.80749 - 4.77609i) q^{42} +(2.78924 - 2.78924i) q^{43} +(15.5501 - 11.9320i) q^{44} +(2.23202 - 0.293850i) q^{45} +(-12.2884 - 9.42920i) q^{46} +(3.50473 + 2.02346i) q^{47} +(2.93774 + 7.09234i) q^{48} +(-4.98208 - 4.91720i) q^{49} -0.174795 q^{50} +(4.12278 - 0.0518318i) q^{51} +(-8.16064 - 14.1346i) q^{52} +(-3.22868 + 12.0496i) q^{53} +(2.53942 + 0.334321i) q^{54} +9.67586i q^{55} +(6.69250 + 16.0085i) q^{56} +(0.862489 - 2.08223i) q^{57} +(-17.4349 + 13.3782i) q^{58} +(11.3861 + 3.05089i) q^{59} +(-9.91696 - 2.65724i) q^{60} +(6.67594 - 5.12263i) q^{61} +(2.69392 - 6.50370i) q^{62} +(2.62423 + 0.336742i) q^{63} -1.41392i q^{64} +(7.98814 + 1.05166i) q^{65} +(-2.84920 + 10.6334i) q^{66} +(-2.73113 - 4.73046i) q^{67} +(-17.4609 - 6.97670i) q^{68} +6.04730 q^{69} +(-14.7491 - 3.90026i) q^{70} +(4.02229 + 9.71066i) q^{71} +(-5.67950 - 3.27906i) q^{72} +(4.22558 + 3.24240i) q^{73} +(-2.70786 + 0.356497i) q^{74} +(0.0541415 - 0.0415442i) q^{75} +(-7.26784 + 7.26784i) q^{76} +(-2.90710 + 10.9934i) q^{77} +(8.46896 + 3.50796i) q^{78} +(-9.24119 - 12.0434i) q^{79} +(13.7110 + 10.5208i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-0.496718 - 0.0653942i) q^{82} +(-11.9612 - 11.9612i) q^{83} +(-10.4690 - 5.99861i) q^{84} +(7.97968 - 4.74181i) q^{85} +(5.05169 - 8.74978i) q^{86} +(2.22066 - 8.28761i) q^{87} +(17.1588 - 22.3618i) q^{88} +(-9.71538 - 5.60918i) q^{89} +(5.32734 - 2.20666i) q^{90} +(8.75990 + 3.59489i) q^{91} +(-25.4790 - 10.5538i) q^{92} +(0.711336 + 2.65474i) q^{93} +(10.0123 + 2.68279i) q^{94} +(-0.662278 - 5.03050i) q^{95} +(3.98514 + 5.19354i) q^{96} +(-2.30575 + 0.955073i) q^{97} +(-15.5857 - 8.86272i) q^{98} +(-1.64475 - 3.97078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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