LMFDB - Embedded newform 845.2.d.e.844.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(844,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.844"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.14
Character	$\chi$	$=$	845.844
Dual form			845.2.d.e.844.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.887876 q^{2} +1.26907i q^{3} -1.21168 q^{4} +(1.79562 + 1.33257i) q^{5} -1.12678i q^{6} -2.28128 q^{7} +2.85157 q^{8} +1.38947 q^{9} +(-1.59429 - 1.18316i) q^{10} +3.13829i q^{11} -1.53770i q^{12} +2.02549 q^{14} +(-1.69112 + 2.27877i) q^{15} -0.108488 q^{16} +1.72423i q^{17} -1.23367 q^{18} +4.27007i q^{19} +(-2.17571 - 1.61464i) q^{20} -2.89510i q^{21} -2.78641i q^{22} -8.63424i q^{23} +3.61884i q^{24} +(1.44852 + 4.78558i) q^{25} +5.57053i q^{27} +2.76417 q^{28} +7.94250 q^{29} +(1.50151 - 2.02326i) q^{30} +4.17039i q^{31} -5.60682 q^{32} -3.98270 q^{33} -1.53090i q^{34} +(-4.09631 - 3.03996i) q^{35} -1.68358 q^{36} -8.80437 q^{37} -3.79129i q^{38} +(5.12034 + 3.79991i) q^{40} +2.94700i q^{41} +2.57049i q^{42} +0.153762i q^{43} -3.80259i q^{44} +(2.49496 + 1.85156i) q^{45} +7.66614i q^{46} -6.54786 q^{47} -0.137679i q^{48} -1.79577 q^{49} +(-1.28610 - 4.24900i) q^{50} -2.18817 q^{51} -1.93126i q^{53} -4.94594i q^{54} +(-4.18199 + 5.63518i) q^{55} -6.50522 q^{56} -5.41901 q^{57} -7.05195 q^{58} +5.51115i q^{59} +(2.04909 - 2.76113i) q^{60} -9.90052 q^{61} -3.70279i q^{62} -3.16976 q^{63} +5.19513 q^{64} +3.53615 q^{66} -6.45526 q^{67} -2.08921i q^{68} +10.9574 q^{69} +(3.63702 + 2.69911i) q^{70} -4.74432i q^{71} +3.96216 q^{72} +13.1891 q^{73} +7.81719 q^{74} +(-6.07323 + 1.83827i) q^{75} -5.17394i q^{76} -7.15931i q^{77} -13.4510 q^{79} +(-0.194804 - 0.144568i) q^{80} -2.90099 q^{81} -2.61657i q^{82} -6.32511 q^{83} +3.50792i q^{84} +(-2.29766 + 3.09607i) q^{85} -0.136522i q^{86} +10.0796i q^{87} +8.94905i q^{88} +15.7373i q^{89} +(-2.21521 - 1.64396i) q^{90} +10.4619i q^{92} -5.29250 q^{93} +5.81368 q^{94} +(-5.69016 + 7.66743i) q^{95} -7.11543i q^{96} +12.0815 q^{97} +1.59442 q^{98} +4.36055i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 32 q^{4} - 36 q^{9} - 26 q^{10} - 8 q^{14} - 24 q^{16} + 16 q^{25} + 40 q^{29} - 62 q^{30} + 20 q^{35} - 64 q^{36} + 6 q^{40} + 88 q^{49} + 80 q^{51} - 40 q^{55} + 40 q^{56} + 16 q^{61} - 136 q^{64}+ \cdots - 82 q^{95}+O(q^{100}) $ 36 * q + 32 * q^4 - 36 * q^9 - 26 * q^10 - 8 * q^14 - 24 * q^16 + 16 * q^25 + 40 * q^29 - 62 * q^30 + 20 * q^35 - 64 * q^36 + 6 * q^40 + 88 * q^49 + 80 * q^51 - 40 * q^55 + 40 * q^56 + 16 * q^61 - 136 * q^64 + 16 * q^66 + 60 * q^69 - 60 * q^74 - 26 * q^75 - 32 * q^79 - 60 * q^81 + 140 * q^90 + 256 * q^94 - 82 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.887876			−0.627823			−0.313912	−	0.949452i	$-0.601640\pi$
$2$	−0.887876			−0.627823			−0.313912	+	0.949452i	$0.601640\pi$
$3$			1.26907i			0.732697i	0.930478	+	0.366348i	$0.119392\pi$
$3$			1.26907i			0.732697i	−0.930478	+	0.366348i	$0.880608\pi$
$4$	−1.21168			−0.605838
$5$	1.79562	+	1.33257i	0.803027	+	0.595943i
$5$	1.79562	+	1.33257i	0.803027	+	0.595943i
$6$		−	1.12678i		−	0.460004i
$7$	−2.28128			−0.862242			−0.431121	−	0.902294i	$-0.641882\pi$
$7$	−2.28128			−0.862242			−0.431121	+	0.902294i	$0.641882\pi$
$8$	2.85157			1.00818
$9$	1.38947			0.463155
$10$	−1.59429	−	1.18316i	−0.504159	−	0.374147i
$11$			3.13829i			0.946230i	0.881001	+	0.473115i	$0.156870\pi$
$11$			3.13829i			0.946230i	−0.881001	+	0.473115i	$0.843130\pi$
$12$		−	1.53770i		−	0.443896i
$13$		0			0
$13$		0			0
$14$	2.02549			0.541335
$15$	−1.69112	+	2.27877i	−0.436646	+	0.588375i
$16$	−0.108488			−0.0271220
$17$			1.72423i			0.418187i	0.977896	+	0.209094i	$0.0670513\pi$
$17$			1.72423i			0.418187i	−0.977896	+	0.209094i	$0.932949\pi$
$18$	−1.23367			−0.290780
$19$			4.27007i			0.979621i	0.871829	+	0.489810i	$0.162934\pi$
$19$			4.27007i			0.979621i	−0.871829	+	0.489810i	$0.837066\pi$
$20$	−2.17571	−	1.61464i	−0.486504	−	0.361045i
$21$		−	2.89510i		−	0.631762i
$22$		−	2.78641i		−	0.594065i
$23$		−	8.63424i		−	1.80036i	−0.435514	−	0.900182i	$-0.643433\pi$
$23$		−	8.63424i		−	1.80036i	0.435514	−	0.900182i	$-0.356567\pi$
$24$			3.61884i			0.738692i
$25$	1.44852	+	4.78558i	0.289704	+	0.957116i
$26$		0			0
$27$			5.57053i			1.07205i
$28$	2.76417			0.522379
$29$	7.94250			1.47488			0.737442	−	0.675410i	$-0.236033\pi$
$29$	7.94250			1.47488			0.737442	+	0.675410i	$0.236033\pi$
$30$	1.50151	−	2.02326i	0.274136	−	0.369395i
$31$			4.17039i			0.749024i	0.927222	+	0.374512i	$0.122190\pi$
$31$			4.17039i			0.749024i	−0.927222	+	0.374512i	$0.877810\pi$
$32$	−5.60682			−0.991154
$33$	−3.98270			−0.693300
$34$		−	1.53090i		−	0.262548i
$35$	−4.09631	−	3.03996i	−0.692403	−	0.513847i
$36$	−1.68358			−0.280597
$37$	−8.80437			−1.44743			−0.723715	−	0.690099i	$-0.757567\pi$
$37$	−8.80437			−1.44743			−0.723715	+	0.690099i	$0.757567\pi$
$38$		−	3.79129i		−	0.615028i
$39$		0			0
$40$	5.12034	+	3.79991i	0.809597	+	0.600819i
$41$			2.94700i			0.460244i	0.973162	+	0.230122i	$0.0739125\pi$
$41$			2.94700i			0.460244i	−0.973162	+	0.230122i	$0.926088\pi$
$42$			2.57049i			0.396635i
$43$			0.153762i			0.0234486i	0.999931	+	0.0117243i	$0.00373204\pi$
$43$			0.153762i			0.0234486i	−0.999931	+	0.0117243i	$0.996268\pi$
$44$		−	3.80259i		−	0.573262i
$45$	2.49496	+	1.85156i	0.371926	+	0.276014i
$46$			7.66614i			1.13031i
$47$	−6.54786			−0.955103			−0.477552	−	0.878604i	$-0.658476\pi$
$47$	−6.54786			−0.955103			−0.477552	+	0.878604i	$0.658476\pi$
$48$		−	0.137679i		−	0.0198722i
$49$	−1.79577			−0.256539
$50$	−1.28610	−	4.24900i	−0.181883	−	0.600900i
$51$	−2.18817			−0.306404
$52$		0			0
$53$		−	1.93126i		−	0.265279i	−0.991164	−	0.132640i	$-0.957655\pi$
$53$		−	1.93126i		−	0.265279i	0.991164	−	0.132640i	$-0.0423453\pi$
$54$		−	4.94594i		−	0.673057i
$55$	−4.18199	+	5.63518i	−0.563899	+	0.759848i
$56$	−6.50522			−0.869297
$57$	−5.41901			−0.717765
$58$	−7.05195			−0.925967
$59$			5.51115i			0.717490i	0.933436	+	0.358745i	$0.116795\pi$
$59$			5.51115i			0.717490i	−0.933436	+	0.358745i	$0.883205\pi$
$60$	2.04909	−	2.76113i	0.264537	−	0.356460i
$61$	−9.90052			−1.26763			−0.633816	−	0.773484i	$-0.718512\pi$
$61$	−9.90052			−1.26763			−0.633816	+	0.773484i	$0.718512\pi$
$62$		−	3.70279i		−	0.470254i
$63$	−3.16976			−0.399352
$64$	5.19513			0.649392
$65$		0			0
$66$	3.53615			0.435270
$67$	−6.45526			−0.788635			−0.394318	−	0.918974i	$-0.629019\pi$
$67$	−6.45526			−0.788635			−0.394318	+	0.918974i	$0.629019\pi$
$68$		−	2.08921i		−	0.253354i
$69$	10.9574			1.31912
$70$	3.63702	+	2.69911i	0.434707	+	0.322605i
$71$		−	4.74432i		−	0.563047i	−0.959554	−	0.281524i	$-0.909160\pi$
$71$		−	4.74432i		−	0.563047i	0.959554	−	0.281524i	$-0.0908398\pi$
$72$	3.96216			0.466945
$73$	13.1891			1.54367			0.771834	−	0.635824i	$-0.219340\pi$
$73$	13.1891			1.54367			0.771834	+	0.635824i	$0.219340\pi$
$74$	7.81719			0.908730
$75$	−6.07323	+	1.83827i	−0.701276	+	0.212265i
$76$		−	5.17394i		−	0.593492i
$77$		−	7.15931i		−	0.815879i
$78$		0			0
$79$	−13.4510			−1.51335			−0.756676	−	0.653791i	$-0.773178\pi$
$79$	−13.4510			−1.51335			−0.756676	+	0.653791i	$0.773178\pi$
$80$	−0.194804	−	0.144568i	−0.0217797	−	0.0161632i
$81$	−2.90099			−0.322332
$82$		−	2.61657i		−	0.288952i
$83$	−6.32511			−0.694271			−0.347136	−	0.937815i	$-0.612846\pi$
$83$	−6.32511			−0.694271			−0.347136	+	0.937815i	$0.612846\pi$
$84$			3.50792i			0.382745i
$85$	−2.29766	+	3.09607i	−0.249216	+	0.335816i
$86$		−	0.136522i		−	0.0147215i
$87$			10.0796i			1.08064i
$88$			8.94905i			0.953972i
$89$			15.7373i			1.66815i	0.551649	+	0.834077i	$0.313999\pi$
$89$			15.7373i			1.66815i	−0.551649	+	0.834077i	$0.686001\pi$
$90$	−2.21521	−	1.64396i	−0.233504	−	0.173288i
$91$		0			0
$92$			10.4619i			1.09073i
$93$	−5.29250			−0.548807
$94$	5.81368			0.599636
$95$	−5.69016	+	7.66743i	−0.583798	+	0.786661i
$96$		−	7.11543i		−	0.726216i
$97$	12.0815			1.22669			0.613345	−	0.789815i	$-0.289823\pi$
$97$	12.0815			1.22669			0.613345	+	0.789815i	$0.289823\pi$
$98$	1.59442			0.161061
$99$			4.36055i			0.438251i
$100$	−1.75513	−	5.79858i	−0.175513	−	0.579858i
$101$	−3.79100			−0.377218			−0.188609	−	0.982052i	$-0.560398\pi$
$101$	−3.79100			−0.377218			−0.188609	+	0.982052i	$0.560398\pi$
$102$	1.94282			0.192368
$103$			14.6259i			1.44113i	0.693388	+	0.720564i	$0.256117\pi$
$103$			14.6259i			1.44113i	−0.693388	+	0.720564i	$0.743883\pi$
$104$		0			0
$105$	3.85792	−	5.19850i	0.376494	−	0.507322i
$106$			1.71472i			0.166548i
$107$		−	4.19100i		−	0.405159i	−0.979266	−	0.202580i	$-0.935067\pi$
$107$		−	4.19100i		−	0.405159i	0.979266	−	0.202580i	$-0.0649325\pi$
$108$		−	6.74968i		−	0.649488i
$109$		−	16.1460i		−	1.54650i	−0.634099	−	0.773252i	$-0.718629\pi$
$109$		−	16.1460i		−	1.54650i	0.634099	−	0.773252i	$-0.281371\pi$
$110$	3.71309	−	5.00334i	0.354029	−	0.477050i
$111$		−	11.1733i		−	1.06053i
$112$	0.247491			0.0233857
$113$			3.51935i			0.331072i	0.986204	+	0.165536i	$0.0529355\pi$
$113$			3.51935i			0.331072i	−0.986204	+	0.165536i	$0.947065\pi$
$114$	4.81141			0.450629
$115$	11.5057	−	15.5038i	1.07291	−	1.44574i
$116$	−9.62373			−0.893541
$117$		0			0
$118$		−	4.89322i		−	0.450457i
$119$		−	3.93345i		−	0.360579i
$120$	−4.82235	+	6.49806i	−0.440218	+	0.593189i
$121$	1.15114			0.104649
$122$	8.79043			0.795848
$123$	−3.73994			−0.337219
$124$		−	5.05316i		−	0.453787i
$125$	−3.77613	+	10.5233i	−0.337747	+	0.941237i
$126$	2.81435			0.250722
$127$			2.42242i			0.214955i	0.994208	+	0.107478i	$0.0342774\pi$
$127$			2.42242i			0.214955i	−0.994208	+	0.107478i	$0.965723\pi$
$128$	6.60100			0.583451
$129$	−0.195135			−0.0171807
$130$		0			0
$131$	−5.00647			−0.437418			−0.218709	−	0.975790i	$-0.570184\pi$
$131$	−5.00647			−0.437418			−0.218709	+	0.975790i	$0.570184\pi$
$132$	4.82575			0.420027
$133$		−	9.74121i		−	0.844670i
$134$	5.73147			0.495124
$135$	−7.42312	+	10.0026i	−0.638880	+	0.860884i
$136$			4.91676i			0.421609i
$137$	12.8154			1.09489			0.547447	−	0.836840i	$-0.315600\pi$
$137$	12.8154			1.09489			0.547447	+	0.836840i	$0.315600\pi$
$138$	−9.72885			−0.828175
$139$	15.5289			1.31714			0.658571	−	0.752519i	$-0.271161\pi$
$139$	15.5289			1.31714			0.658571	+	0.752519i	$0.271161\pi$
$140$	4.96340	+	3.68345i	0.419484	+	0.311308i
$141$		−	8.30968i		−	0.699801i
$142$			4.21237i			0.353494i
$143$		0			0
$144$	−0.150740			−0.0125617
$145$	14.2617	+	10.5839i	1.18437	+	0.878947i
$146$	−11.7103			−0.969151
$147$		−	2.27896i		−	0.187965i
$148$	10.6681			0.876908
$149$			0.0413812i			0.00339008i	0.999999	+	0.00169504i	$0.000539549\pi$
$149$			0.0413812i			0.00339008i	−0.999999	+	0.00169504i	$0.999460\pi$
$150$	5.39227	−	1.63215i	0.440277	−	0.133265i
$151$			6.01321i			0.489348i	0.969605	+	0.244674i	$0.0786809\pi$
$151$			6.01321i			0.489348i	−0.969605	+	0.244674i	$0.921319\pi$
$152$			12.1764i			0.987636i
$153$			2.39576i			0.193686i
$154$			6.35658i			0.512228i
$155$	−5.55733	+	7.48844i	−0.446375	+	0.601486i
$156$		0			0
$157$		−	22.7846i		−	1.81841i	−0.416348	−	0.909205i	$-0.636690\pi$
$157$		−	22.7846i		−	1.81841i	0.416348	−	0.909205i	$-0.363310\pi$
$158$	11.9428			0.950117
$159$	2.45090			0.194369
$160$	−10.0677	−	7.47147i	−0.795923	−	0.590672i
$161$			19.6971i			1.55235i
$162$	2.57572			0.202367
$163$	−1.52126			−0.119154			−0.0595772	−	0.998224i	$-0.518975\pi$
$163$	−1.52126			−0.119154			−0.0595772	+	0.998224i	$0.518975\pi$
$164$		−	3.57081i		−	0.278833i
$165$	−7.15143	−	5.30723i	−0.556738	−	0.413167i
$166$	5.61592			0.435880
$167$	0.0491982			0.00380707			0.00190353	−	0.999998i	$-0.499394\pi$
$167$	0.0491982			0.00380707			0.00190353	+	0.999998i	$0.499394\pi$
$168$		−	8.25557i		−	0.636931i
$169$		0			0
$170$	2.04003	−	2.74892i	0.156463	−	0.210833i
$171$			5.93311i			0.453717i
$172$		−	0.186310i		−	0.0142060i
$173$			9.00465i			0.684611i	0.939589	+	0.342305i	$0.111208\pi$
$173$			9.00465i			0.684611i	−0.939589	+	0.342305i	$0.888792\pi$
$174$		−	8.94941i		−	0.678453i
$175$	−3.30447	−	10.9172i	−0.249795	−	0.825266i
$176$		−	0.340467i		−	0.0256637i
$177$	−6.99402			−0.525703
$178$		−	13.9728i		−	1.04731i
$179$	22.8604			1.70866			0.854332	−	0.519727i	$-0.173966\pi$
$179$	22.8604			1.70866			0.854332	+	0.519727i	$0.173966\pi$
$180$	−3.02308	−	2.24349i	−0.225327	−	0.167220i
$181$	17.7138			1.31666			0.658328	−	0.752731i	$-0.271264\pi$
$181$	17.7138			1.31666			0.658328	+	0.752731i	$0.271264\pi$
$182$		0			0
$183$		−	12.5644i		−	0.928789i
$184$		−	24.6211i		−	1.81509i
$185$	−15.8093	−	11.7324i	−1.16232	−	0.862586i
$186$	4.69909			0.344554
$187$	−5.41113			−0.395701
$188$	7.93388			0.578638
$189$		−	12.7079i		−	0.924366i
$190$	5.05216	−	6.80772i	0.366522	−	0.493884i
$191$	9.73516			0.704411			0.352206	−	0.935923i	$-0.385432\pi$
$191$	9.73516			0.704411			0.352206	+	0.935923i	$0.385432\pi$
$192$			6.59298i			0.475807i
$193$	10.0009			0.719883			0.359942	−	0.932975i	$-0.382797\pi$
$193$	10.0009			0.719883			0.359942	+	0.932975i	$0.382797\pi$
$194$	−10.7269			−0.770145
$195$		0			0
$196$	2.17590			0.155421
$197$	−5.99999			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−5.99999			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		−	3.87162i		−	0.275144i
$199$	5.81284			0.412061			0.206031	−	0.978546i	$-0.433945\pi$
$199$	5.81284			0.412061			0.206031	+	0.978546i	$0.433945\pi$
$200$	4.13055	+	13.6464i	0.292074	+	0.964948i
$201$		−	8.19216i		−	0.577831i
$202$	3.36593			0.236826
$203$	−18.1190			−1.27171
$204$	2.65135			0.185632
$205$	−3.92708	+	5.29169i	−0.274279	+	0.369588i
$206$		−	12.9859i		−	0.904774i
$207$		−	11.9970i		−	0.833848i
$208$		0			0
$209$	−13.4007			−0.926946
$210$	−3.42535	+	4.61562i	−0.236372	+	0.318508i
$211$	8.71262			0.599801			0.299901	−	0.953970i	$-0.403046\pi$
$211$	8.71262			0.599801			0.299901	+	0.953970i	$0.403046\pi$
$212$			2.34006i			0.160716i
$213$	6.02087			0.412543
$214$			3.72109i			0.254368i
$215$	−0.204899	+	0.276099i	−0.0139740	+	0.0188298i
$216$			15.8848i			1.08082i
$217$		−	9.51381i		−	0.645839i
$218$			14.3356i			0.970930i
$219$			16.7379i			1.13104i
$220$	5.06722	−	6.82802i	0.341632	−	0.460345i
$221$		0			0
$222$			9.92055i			0.665824i
$223$	−0.0454220			−0.00304168			−0.00152084	−	0.999999i	$-0.500484\pi$
$223$	−0.0454220			−0.00304168			−0.00152084	+	0.999999i	$0.500484\pi$
$224$	12.7907			0.854615
$225$	2.01267	+	6.64940i	0.134178	+	0.443294i
$226$		−	3.12474i		−	0.207855i
$227$	−6.42258			−0.426281			−0.213141	−	0.977022i	$-0.568369\pi$
$227$	−6.42258			−0.426281			−0.213141	+	0.977022i	$0.568369\pi$
$228$	6.56608			0.434849
$229$		−	7.27972i		−	0.481057i	−0.970642	−	0.240529i	$-0.922679\pi$
$229$		−	7.27972i		−	0.481057i	0.970642	−	0.240529i	$-0.0773208\pi$
$230$	−10.2157	+	13.7655i	−0.673600	+	0.907669i
$231$	9.08565			0.597792
$232$	22.6486			1.48695
$233$		−	4.56107i		−	0.298806i	−0.988776	−	0.149403i	$-0.952265\pi$
$233$		−	4.56107i		−	0.298806i	0.988776	−	0.149403i	$-0.0477351\pi$
$234$		0			0
$235$	−11.7575	−	8.72547i	−0.766973	−	0.569187i
$236$		−	6.67773i		−	0.434683i
$237$		−	17.0702i		−	1.10883i
$238$			3.49241i			0.226380i
$239$		−	16.9338i		−	1.09536i	−0.836688	−	0.547680i	$-0.815511\pi$
$239$		−	16.9338i		−	1.09536i	0.836688	−	0.547680i	$-0.184489\pi$
$240$	0.183466	−	0.247219i	0.0118427	−	0.0159579i
$241$		−	6.13059i		−	0.394906i	−0.980312	−	0.197453i	$-0.936733\pi$
$241$		−	6.13059i		−	0.394906i	0.980312	−	0.197453i	$-0.0632670\pi$
$242$	−1.02207			−0.0657010
$243$			13.0300i			0.835878i
$244$	11.9962			0.767979
$245$	−3.22453	−	2.39299i	−0.206008	−	0.152883i
$246$	3.32060			0.211714
$247$		0			0
$248$			11.8922i			0.755152i
$249$		−	8.02700i		−	0.508690i
$250$	3.35273	−	9.34343i	0.212046	−	0.590930i
$251$	−11.5843			−0.731192			−0.365596	−	0.930774i	$-0.619135\pi$
$251$	−11.5843			−0.731192			−0.365596	+	0.930774i	$0.619135\pi$
$252$	3.84072			0.241943
$253$	27.0967			1.70356
$254$		−	2.15081i		−	0.134954i
$255$	−3.92912	−	2.91588i	−0.246051	−	0.182600i
$256$	−16.2511			−1.01570
$257$			12.4669i			0.777665i	0.921309	+	0.388832i	$0.127121\pi$
$257$			12.4669i			0.777665i	−0.921309	+	0.388832i	$0.872879\pi$
$258$	0.173256			0.0107864
$259$	20.0852			1.24803
$260$		0			0
$261$	11.0358			0.683101
$262$	4.44513			0.274621
$263$			28.3288i			1.74683i	0.486975	+	0.873416i	$0.338100\pi$
$263$			28.3288i			1.74683i	−0.486975	+	0.873416i	$0.661900\pi$
$264$	−11.3570			−0.698972
$265$	2.57354	−	3.46781i	0.158091	−	0.213026i
$266$			8.64898i			0.530303i
$267$	−19.9717			−1.22225
$268$	7.82168			0.477785
$269$	12.1886			0.743154			0.371577	−	0.928402i	$-0.378817\pi$
$269$	12.1886			0.743154			0.371577	+	0.928402i	$0.378817\pi$
$270$	6.59081	−	8.88104i	0.401104	−	0.540483i
$271$		−	17.6547i		−	1.07245i	−0.844076	−	0.536224i	$-0.819850\pi$
$271$		−	17.6547i		−	1.07245i	0.844076	−	0.536224i	$-0.180150\pi$
$272$		−	0.187058i		−	0.0113421i
$273$		0			0
$274$	−11.3785			−0.687400
$275$	−15.0185	+	4.54587i	−0.905652	+	0.274126i
$276$	−13.2769			−0.799174
$277$			11.7250i			0.704489i	0.935908	+	0.352245i	$0.114581\pi$
$277$			11.7250i			0.704489i	−0.935908	+	0.352245i	$0.885419\pi$
$278$	−13.7877			−0.826932
$279$			5.79461i			0.346914i
$280$	−11.6809	−	8.66866i	−0.698069	−	0.518051i
$281$		−	20.2642i		−	1.20886i	−0.796659	−	0.604430i	$-0.793401\pi$
$281$		−	20.2642i		−	1.20886i	0.796659	−	0.604430i	$-0.206599\pi$
$282$			7.37796i			0.439351i
$283$		−	8.24330i		−	0.490013i	−0.969521	−	0.245007i	$-0.921210\pi$
$283$		−	8.24330i		−	0.490013i	0.969521	−	0.245007i	$-0.0787901\pi$
$284$			5.74858i			0.341116i
$285$	−9.73049	−	7.22120i	−0.576384	−	0.427747i
$286$		0			0
$287$		−	6.72292i		−	0.396841i
$288$	−7.79048			−0.459059
$289$	14.0270			0.825119
$290$	−12.6626	−	9.39721i	−0.743576	−	0.551823i
$291$			15.3322i			0.898792i
$292$	−15.9809			−0.935213
$293$	21.3215			1.24562			0.622808	−	0.782375i	$-0.285992\pi$
$293$	21.3215			1.24562			0.622808	+	0.782375i	$0.285992\pi$
$294$			2.02343i			0.118009i
$295$	−7.34399	+	9.89594i	−0.427583	+	0.576164i
$296$	−25.1063			−1.45927
$297$	−17.4819			−1.01441
$298$		−	0.0367414i		−	0.00212837i
$299$		0			0
$300$	7.35879	−	2.22739i	0.424860	−	0.128598i
$301$		−	0.350775i		−	0.0202183i
$302$		−	5.33898i		−	0.307224i
$303$		−	4.81103i		−	0.276387i
$304$		−	0.463251i		−	0.0265693i
$305$	−17.7776	−	13.1931i	−1.01794	−	0.755436i
$306$		−	2.12714i		−	0.121600i
$307$	8.38560			0.478591			0.239296	−	0.970947i	$-0.423083\pi$
$307$	8.38560			0.478591			0.239296	+	0.970947i	$0.423083\pi$
$308$			8.67476i			0.494291i
$309$	−18.5612			−1.05591
$310$	4.93422	−	6.64881i	0.280245	−	0.377627i
$311$	2.82308			0.160082			0.0800412	−	0.996792i	$-0.474495\pi$
$311$	2.82308			0.160082			0.0800412	+	0.996792i	$0.474495\pi$
$312$		0			0
$313$			19.1965i			1.08505i	0.840040	+	0.542525i	$0.182532\pi$
$313$			19.1965i			1.08505i	−0.840040	+	0.542525i	$0.817468\pi$
$314$			20.2299i			1.14164i
$315$	−5.69169	−	4.22392i	−0.320690	−	0.237991i
$316$	16.2982			0.916846
$317$	−5.76453			−0.323768			−0.161884	−	0.986810i	$-0.551757\pi$
$317$	−5.76453			−0.323768			−0.161884	+	0.986810i	$0.551757\pi$
$318$	−2.17610			−0.122029
$319$			24.9259i			1.39558i
$320$	9.32850	+	6.92288i	0.521479	+	0.387001i
$321$	5.31867			0.296859
$322$		−	17.4886i		−	0.974600i
$323$	−7.36258			−0.409665
$324$	3.51506			0.195281
$325$		0			0
$326$	1.35069			0.0748079
$327$	20.4903			1.13312
$328$			8.40357i			0.464010i
$329$	14.9375			0.823530
$330$	6.34958	+	4.71216i	0.349533	+	0.259396i
$331$		−	4.06009i		−	0.223163i	−0.993755	−	0.111581i	$-0.964408\pi$
$331$		−	4.06009i		−	0.223163i	0.993755	−	0.111581i	$-0.0355915\pi$
$332$	7.66399			0.420616
$333$	−12.2334			−0.670385
$334$	−0.0436819			−0.00239017
$335$	−11.5912	−	8.60208i	−0.633295	−	0.469982i
$336$			0.314083i			0.0171346i
$337$			24.8339i			1.35279i	0.736539	+	0.676395i	$0.236459\pi$
$337$			24.8339i			1.35279i	−0.736539	+	0.676395i	$0.763541\pi$
$338$		0			0
$339$	−4.46629			−0.242576
$340$	2.78402	−	3.75143i	0.150984	−	0.203450i
$341$	−13.0879			−0.708749
$342$		−	5.26787i		−	0.284854i
$343$	20.0656			1.08344
$344$			0.438465i			0.0236404i
$345$	19.6754	+	14.6015i	1.05929	+	0.786121i
$346$		−	7.99501i		−	0.429815i
$347$		−	29.1599i		−	1.56538i	−0.622409	−	0.782692i	$-0.713846\pi$
$347$		−	29.1599i		−	1.56538i	0.622409	−	0.782692i	$-0.286154\pi$
$348$		−	12.2132i		−	0.654695i
$349$			7.29040i			0.390246i	0.980779	+	0.195123i	$0.0625107\pi$
$349$			7.29040i			0.390246i	−0.980779	+	0.195123i	$0.937489\pi$
$350$	2.93396	+	9.69315i	0.156827	+	0.518121i
$351$		0			0
$352$		−	17.5958i		−	0.937860i
$353$	−13.9534			−0.742665			−0.371333	−	0.928500i	$-0.621099\pi$
$353$	−13.9534			−0.742665			−0.371333	+	0.928500i	$0.621099\pi$
$354$	6.20982			0.330048
$355$	6.32214	−	8.51901i	0.335544	−	0.452142i
$356$		−	19.0685i		−	1.01063i
$357$	4.99181			0.264195
$358$	−20.2972			−1.07274
$359$			16.2637i			0.858366i	0.903218	+	0.429183i	$0.141198\pi$
$359$			16.2637i			0.858366i	−0.903218	+	0.429183i	$0.858802\pi$
$360$	7.11454	+	5.27985i	0.374969	+	0.278273i
$361$	0.766527			0.0403435
$362$	−15.7276			−0.826627
$363$			1.46087i			0.0766759i
$364$		0			0
$365$	23.6827	+	17.5754i	1.23961	+	0.919939i
$366$			11.1557i			0.583115i
$367$			34.4480i			1.79817i	0.437774	+	0.899085i	$0.355767\pi$
$367$			34.4480i			1.79817i	−0.437774	+	0.899085i	$0.644233\pi$
$368$			0.936712i			0.0488295i
$369$			4.09475i			0.213164i
$370$	14.0367	+	10.4169i	0.729734	+	0.541551i
$371$			4.40574i			0.228735i
$372$	6.41280			0.332488
$373$		−	23.2179i		−	1.20218i	−0.799183	−	0.601088i	$-0.794734\pi$
$373$		−	23.2179i		−	1.20218i	0.799183	−	0.601088i	$-0.205266\pi$
$374$	4.80442			0.248430
$375$	−13.3548	−	4.79216i	−0.689641	−	0.247466i
$376$	−18.6717			−0.962918
$377$		0			0
$378$			11.2831i			0.580338i
$379$		−	12.2666i		−	0.630094i	−0.949076	−	0.315047i	$-0.897980\pi$
$379$		−	12.2666i		−	0.630094i	0.949076	−	0.315047i	$-0.102020\pi$
$380$	6.89463	−	9.29044i	0.353687	−	0.476590i
$381$	−3.07422			−0.157497
$382$	−8.64361			−0.442246
$383$	−1.88332			−0.0962329			−0.0481165	−	0.998842i	$-0.515322\pi$
$383$	−1.88332			−0.0962329			−0.0481165	+	0.998842i	$0.515322\pi$
$384$			8.37712i			0.427493i
$385$	9.54027	−	12.8554i	0.486217	−	0.655173i
$386$	−8.87959			−0.451959
$387$			0.213648i			0.0108603i
$388$	−14.6389			−0.743176
$389$	−20.0438			−1.01626			−0.508131	−	0.861280i	$-0.669663\pi$
$389$	−20.0438			−1.01626			−0.508131	+	0.861280i	$0.669663\pi$
$390$		0			0
$391$	14.8874			0.752889
$392$	−5.12078			−0.258638
$393$		−	6.35356i		−	0.320494i
$394$	5.32725			0.268383
$395$	−24.1528	−	17.9243i	−1.21526	−	0.901871i
$396$		−	5.28357i		−	0.265509i
$397$	−20.6134			−1.03456			−0.517279	−	0.855817i	$-0.673055\pi$
$397$	−20.6134			−1.03456			−0.517279	+	0.855817i	$0.673055\pi$
$398$	−5.16108			−0.258702
$399$	12.3623			0.618887
$400$	−0.157147	−	0.519178i	−0.00785734	−	0.0259589i
$401$			35.8148i			1.78851i	0.447560	+	0.894254i	$0.352293\pi$
$401$			35.8148i			1.78851i	−0.447560	+	0.894254i	$0.647707\pi$
$402$			7.27362i			0.362775i
$403$		0			0
$404$	4.59346			0.228533
$405$	−5.20907	−	3.86576i	−0.258841	−	0.192091i
$406$	16.0875			0.798407
$407$		−	27.6307i		−	1.36960i
$408$	−6.23971			−0.308912
$409$			0.221949i			0.0109747i	0.999985	+	0.00548733i	$0.00174668\pi$
$409$			0.221949i			0.0109747i	−0.999985	+	0.00548733i	$0.998253\pi$
$410$	3.48676	−	4.69837i	0.172199	−	0.232036i
$411$			16.2636i			0.802226i
$412$		−	17.7218i		−	0.873091i
$413$		−	12.5725i		−	0.618650i
$414$			10.6518i			0.523509i
$415$	−11.3575	−	8.42865i	−0.557518	−	0.413746i
$416$		0			0
$417$			19.7072i			0.965065i
$418$	11.8982			0.581958
$419$	−0.680369			−0.0332382			−0.0166191	−	0.999862i	$-0.505290\pi$
$419$	−0.680369			−0.0332382			−0.0166191	+	0.999862i	$0.505290\pi$
$420$	−4.67455	+	6.29890i	−0.228094	+	0.307355i
$421$		−	2.01932i		−	0.0984155i	−0.998789	−	0.0492078i	$-0.984330\pi$
$421$		−	2.01932i		−	0.0984155i	0.998789	−	0.0492078i	$-0.0156696\pi$
$422$	−7.73572			−0.376569
$423$	−9.09803			−0.442361
$424$		−	5.50712i		−	0.267450i
$425$	−8.25145	+	2.49758i	−0.400254	+	0.121150i
$426$	−5.34578			−0.259004
$427$	22.5858			1.09300
$428$			5.07814i			0.245461i
$429$		0			0
$430$	0.181925	−	0.245142i	0.00877321	−	0.0118218i
$431$			6.85397i			0.330144i	0.986281	+	0.165072i	$0.0527857\pi$
$431$			6.85397i			0.330144i	−0.986281	+	0.165072i	$0.947214\pi$
$432$		−	0.604336i		−	0.0290761i
$433$		−	0.520934i		−	0.0250345i	−0.999922	−	0.0125172i	$-0.996016\pi$
$433$		−	0.520934i		−	0.0250345i	0.999922	−	0.0125172i	$-0.00398447\pi$
$434$			8.44708i			0.405473i
$435$	−13.4317	+	18.0991i	−0.644002	+	0.867785i
$436$			19.5637i			0.936931i
$437$	36.8688			1.76367
$438$		−	14.8612i		−	0.710094i
$439$	−27.5889			−1.31675			−0.658374	−	0.752691i	$-0.728756\pi$
$439$	−27.5889			−1.31675			−0.658374	+	0.752691i	$0.728756\pi$
$440$	−11.9252	+	16.0691i	−0.568513	+	0.766065i
$441$	−2.49517			−0.118818
$442$		0			0
$443$			7.20684i			0.342408i	0.985236	+	0.171204i	$0.0547656\pi$
$443$			7.20684i			0.342408i	−0.985236	+	0.171204i	$0.945234\pi$
$444$			13.5385i			0.642508i
$445$	−20.9711	+	28.2583i	−0.994124	+	1.33957i
$446$	0.0403291			0.00190964
$447$	−0.0525156			−0.00248390
$448$	−11.8515			−0.559933
$449$			0.135634i			0.00640098i	0.999995	+	0.00320049i	$0.00101875\pi$
$449$			0.135634i			0.00640098i	−0.999995	+	0.00320049i	$0.998981\pi$
$450$	−1.78700	−	5.90385i	−0.0842399	−	0.278310i
$451$	−9.24853			−0.435496
$452$		−	4.26431i		−	0.200576i
$453$	−7.63117			−0.358544
$454$	5.70245			0.267629
$455$		0			0
$456$	−15.4527			−0.723638
$457$	−0.308011			−0.0144081			−0.00720406	−	0.999974i	$-0.502293\pi$
$457$	−0.308011			−0.0144081			−0.00720406	+	0.999974i	$0.502293\pi$
$458$			6.46349i			0.302019i
$459$	−9.60488			−0.448317
$460$	−13.9412	+	18.7856i	−0.650012	+	0.875884i
$461$			28.6721i			1.33539i	0.744434	+	0.667696i	$0.232719\pi$
$461$			28.6721i			1.33539i	−0.744434	+	0.667696i	$0.767281\pi$
$462$	−8.06693			−0.375308
$463$	16.1023			0.748339			0.374169	−	0.927360i	$-0.377928\pi$
$463$	16.1023			0.748339			0.374169	+	0.927360i	$0.377928\pi$
$464$	−0.861666			−0.0400018
$465$	−9.50334	−	7.05263i	−0.440707	−	0.327058i
$466$			4.04967i			0.187597i
$467$		−	3.47589i		−	0.160845i	−0.996761	−	0.0804224i	$-0.974373\pi$
$467$		−	3.47589i		−	0.160845i	0.996761	−	0.0804224i	$-0.0256269\pi$
$468$		0			0
$469$	14.7262			0.679994
$470$	10.4392	+	7.74714i	0.481524	+	0.357349i
$471$	28.9152			1.33234
$472$			15.7154i			0.723361i
$473$	−0.482551			−0.0221877
$474$			15.1562i			0.696148i
$475$	−20.4348	+	6.18527i	−0.937611	+	0.283800i
$476$			4.76606i			0.218452i
$477$		−	2.68342i		−	0.122865i
$478$			15.0352i			0.687692i
$479$		−	14.4576i		−	0.660587i	−0.943878	−	0.330293i	$-0.892852\pi$
$479$		−	14.4576i		−	0.660587i	0.943878	−	0.330293i	$-0.107148\pi$
$480$	9.48181	−	12.7766i	0.432783	−	0.583171i
$481$		0			0
$482$			5.44320i			0.247931i
$483$	−24.9970			−1.13740
$484$	−1.39481			−0.0634003
$485$	21.6938	+	16.0994i	0.985065	+	0.731038i
$486$		−	11.5691i		−	0.524783i
$487$	−2.91278			−0.131991			−0.0659954	−	0.997820i	$-0.521022\pi$
$487$	−2.91278			−0.131991			−0.0659954	+	0.997820i	$0.521022\pi$
$488$	−28.2320			−1.27800
$489$		−	1.93058i		−	0.0873040i
$490$	2.86298	+	2.12468i	0.129336	+	0.0959833i
$491$	7.60764			0.343328			0.171664	−	0.985156i	$-0.445086\pi$
$491$	7.60764			0.343328			0.171664	+	0.985156i	$0.445086\pi$
$492$	4.53160			0.204300
$493$			13.6947i			0.616778i
$494$		0			0
$495$	−5.81073	+	7.82990i	−0.261173	+	0.351928i
$496$		−	0.452437i		−	0.0203150i
$497$			10.8231i			0.485483i
$498$			7.12698i			0.319368i
$499$			4.07246i			0.182309i	0.995837	+	0.0911543i	$0.0290556\pi$
$499$			4.07246i			0.182309i	−0.995837	+	0.0911543i	$0.970944\pi$
$500$	4.57545	−	12.7509i	0.204620	−	0.570237i
$501$			0.0624358i			0.00278943i
$502$	10.2854			0.459059
$503$			34.0821i			1.51965i	0.650130	+	0.759823i	$0.274714\pi$
$503$			34.0821i			1.51965i	−0.650130	+	0.759823i	$0.725286\pi$
$504$	−9.03879			−0.402620
$505$	−6.80720	−	5.05177i	−0.302916	−	0.224801i
$506$	−24.0586			−1.06953
$507$		0			0
$508$		−	2.93519i		−	0.130228i
$509$		−	1.30664i		−	0.0579159i	−0.999581	−	0.0289579i	$-0.990781\pi$
$509$		−	1.30664i		−	0.0579159i	0.999581	−	0.0289579i	$-0.00921889\pi$
$510$	3.48857	+	2.58894i	0.154476	+	0.114640i
$511$	−30.0880			−1.33102
$512$	1.22700			0.0542260
$513$	−23.7865			−1.05020
$514$		−	11.0691i		−	0.488236i
$515$	−19.4900	+	26.2625i	−0.858831	+	1.15726i
$516$	0.236441			0.0104087
$517$		−	20.5491i		−	0.903747i
$518$	−17.8332			−0.783545
$519$	−11.4275			−0.501612
$520$		0			0
$521$	−0.550102			−0.0241004			−0.0120502	−	0.999927i	$-0.503836\pi$
$521$	−0.550102			−0.0241004			−0.0120502	+	0.999927i	$0.503836\pi$
$522$	−9.79845			−0.428866
$523$		−	17.0531i		−	0.745679i	−0.927896	−	0.372840i	$-0.878384\pi$
$523$		−	17.0531i		−	0.745679i	0.927896	−	0.372840i	$-0.121616\pi$
$524$	6.06622			0.265004
$525$	13.8547	−	4.19360i	0.604670	−	0.183024i
$526$		−	25.1525i		−	1.09670i
$527$	−7.19071			−0.313232
$528$	0.432076			0.0188037
$529$	−51.5501			−2.24131
$530$	−2.28498	+	3.07899i	−0.0992533	+	0.133743i
$531$			7.65755i			0.332309i
$532$			11.8032i			0.511733i
$533$		0			0
$534$	17.7324			0.767357
$535$	5.58480	−	7.52546i	0.241452	−	0.325354i
$536$	−18.4076			−0.795088
$537$			29.0114i			1.25193i
$538$	−10.8220			−0.466569
$539$		−	5.63566i		−	0.242745i
$540$	8.99442	−	12.1199i	0.387058	−	0.521556i
$541$		−	30.1330i		−	1.29552i	−0.761845	−	0.647759i	$-0.775706\pi$
$541$		−	30.1330i		−	1.29552i	0.761845	−	0.647759i	$-0.224294\pi$
$542$			15.6752i			0.673307i
$543$			22.4800i			0.964709i
$544$		−	9.66744i		−	0.414488i
$545$	21.5156	−	28.9921i	0.921628	−	1.24188i
$546$		0			0
$547$		−	5.36791i		−	0.229515i	−0.993394	−	0.114758i	$-0.963391\pi$
$547$		−	5.36791i		−	0.229515i	0.993394	−	0.114758i	$-0.0366091\pi$
$548$	−15.5281			−0.663329
$549$	−13.7564			−0.587110
$550$	13.3346	−	4.03617i	0.568589	−	0.172103i
$551$			33.9150i			1.44483i
$552$	31.2459			1.32991
$553$	30.6854			1.30487
$554$		−	10.4104i		−	0.442294i
$555$	14.8893	−	20.0631i	0.632014	−	0.851632i
$556$	−18.8160			−0.797974
$557$	7.05530			0.298943			0.149471	−	0.988766i	$-0.452243\pi$
$557$	7.05530			0.298943			0.149471	+	0.988766i	$0.452243\pi$
$558$		−	5.14490i		−	0.217801i
$559$		0			0
$560$	0.444401	+	0.329799i	0.0187794	+	0.0139366i
$561$		−	6.86710i		−	0.289929i
$562$			17.9921i			0.758950i
$563$		−	31.6656i		−	1.33455i	−0.744814	−	0.667273i	$-0.767462\pi$
$563$		−	31.6656i		−	1.33455i	0.744814	−	0.667273i	$-0.232538\pi$
$564$			10.0686i			0.423966i
$565$	−4.68977	+	6.31942i	−0.197300	+	0.265860i
$566$			7.31903i			0.307642i
$567$	6.61795			0.277928
$568$		−	13.5288i		−	0.567655i
$569$	13.5818			0.569380			0.284690	−	0.958620i	$-0.408109\pi$
$569$	13.5818			0.569380			0.284690	+	0.958620i	$0.408109\pi$
$570$	8.63947	+	6.41153i	0.361867	+	0.268549i
$571$	34.7338			1.45356			0.726782	−	0.686868i	$-0.241015\pi$
$571$	34.7338			1.45356			0.726782	+	0.686868i	$0.241015\pi$
$572$		0			0
$573$			12.3546i			0.516120i
$574$			5.96912i			0.249146i
$575$	41.3199	−	12.5069i	1.72316	−	0.521572i
$576$	7.21846			0.300769
$577$	43.8511			1.82555			0.912773	−	0.408467i	$-0.133937\pi$
$577$	43.8511			1.82555			0.912773	+	0.408467i	$0.133937\pi$
$578$	−12.4543			−0.518029
$579$			12.6919i			0.527456i
$580$	−17.2806	−	12.8243i	−0.717538	−	0.532500i
$581$	14.4293			0.598630
$582$		−	13.6131i		−	0.564283i
$583$	6.06085			0.251015
$584$	37.6097			1.55630
$585$		0			0
$586$	−18.9308			−0.782026
$587$	−4.11991			−0.170047			−0.0850235	−	0.996379i	$-0.527097\pi$
$587$	−4.11991			−0.170047			−0.0850235	+	0.996379i	$0.527097\pi$
$588$			2.76136i			0.113877i
$589$	−17.8078			−0.733759
$590$	6.52055	−	8.78637i	0.268447	−	0.361729i
$591$		−	7.61440i		−	0.313215i
$592$	0.955169			0.0392572
$593$	2.16800			0.0890292			0.0445146	−	0.999009i	$-0.485826\pi$
$593$	2.16800			0.0890292			0.0445146	+	0.999009i	$0.485826\pi$
$594$	15.5218			0.636867
$595$	5.24159	−	7.06299i	0.214884	−	0.289554i
$596$		−	0.0501407i		−	0.00205384i
$597$			7.37689i			0.301916i
$598$		0			0
$599$	37.1445			1.51768			0.758841	−	0.651276i	$-0.225766\pi$
$599$	37.1445			1.51768			0.758841	+	0.651276i	$0.225766\pi$
$600$	−17.3182	+	5.24195i	−0.707014	+	0.214002i
$601$	−1.11320			−0.0454085			−0.0227043	−	0.999742i	$-0.507228\pi$
$601$	−1.11320			−0.0454085			−0.0227043	+	0.999742i	$0.507228\pi$
$602$			0.311445i			0.0126935i
$603$	−8.96936			−0.365261
$604$		−	7.28606i		−	0.296466i
$605$	2.06701	+	1.53397i	0.0840359	+	0.0623648i
$606$			4.27160i			0.173522i
$607$			8.21780i			0.333550i	0.985995	+	0.166775i	$0.0533354\pi$
$607$			8.21780i			0.333550i	−0.985995	+	0.166775i	$0.946665\pi$
$608$		−	23.9415i		−	0.970955i
$609$		−	22.9943i		−	0.931776i
$610$	15.7843	+	11.7139i	0.639087	+	0.474280i
$611$		0			0
$612$		−	2.90289i		−	0.117342i
$613$	28.6108			1.15558			0.577790	−	0.816185i	$-0.303915\pi$
$613$	28.6108			1.15558			0.577790	+	0.816185i	$0.303915\pi$
$614$	−7.44537			−0.300471
$615$	−6.71552	−	4.98373i	−0.270796	−	0.200963i
$616$		−	20.4153i		−	0.822555i
$617$	0.844622			0.0340032			0.0170016	−	0.999855i	$-0.494588\pi$
$617$	0.844622			0.0340032			0.0170016	+	0.999855i	$0.494588\pi$
$618$	16.4801			0.662925
$619$		−	9.06143i		−	0.364210i	−0.983279	−	0.182105i	$-0.941709\pi$
$619$		−	9.06143i		−	0.364210i	0.983279	−	0.182105i	$-0.0582910\pi$
$620$	6.73368	−	9.07356i	0.270431	−	0.364403i
$621$	48.0973			1.93008
$622$	−2.50655			−0.100503
$623$		−	35.9012i		−	1.43835i
$624$		0			0
$625$	−20.8036	+	13.8640i	−0.832144	+	0.554560i
$626$		−	17.0441i		−	0.681219i
$627$		−	17.0064i		−	0.679171i
$628$			27.6076i			1.10166i
$629$		−	15.1808i		−	0.605297i
$630$	5.05351	+	3.75032i	0.201337	+	0.149416i
$631$		−	14.1174i		−	0.562003i	−0.959707	−	0.281002i	$-0.909333\pi$
$631$		−	14.1174i		−	0.562003i	0.959707	−	0.281002i	$-0.0906667\pi$
$632$	−38.3564			−1.52573
$633$			11.0569i			0.439472i
$634$	5.11819			0.203269
$635$	−3.22805	+	4.34976i	−0.128101	+	0.172615i
$636$	−2.96970			−0.117756
$637$		0			0
$638$		−	22.1311i		−	0.876177i
$639$		−	6.59208i		−	0.260778i
$640$	11.8529	+	8.79629i	0.468527	+	0.347704i
$641$	9.19011			0.362988			0.181494	−	0.983392i	$-0.441907\pi$
$641$	9.19011			0.362988			0.181494	+	0.983392i	$0.441907\pi$
$642$	−4.72232			−0.186375
$643$	4.14150			0.163325			0.0816624	−	0.996660i	$-0.473977\pi$
$643$	4.14150			0.163325			0.0816624	+	0.996660i	$0.473977\pi$
$644$		−	23.8665i		−	0.940472i
$645$	−0.350389	−	0.260031i	−0.0137965	−	0.0102387i
$646$	6.53706			0.257197
$647$		−	4.86077i		−	0.191097i	−0.995425	−	0.0955483i	$-0.969540\pi$
$647$		−	4.86077i		−	0.191097i	0.995425	−	0.0955483i	$-0.0304604\pi$
$648$	−8.27236			−0.324969
$649$	−17.2956			−0.678911
$650$		0			0
$651$	12.0737			0.473204
$652$	1.84328			0.0721883
$653$		−	42.8456i		−	1.67668i	−0.545148	−	0.838340i	$-0.683527\pi$
$653$		−	42.8456i		−	1.67668i	0.545148	−	0.838340i	$-0.316473\pi$
$654$	−18.1929			−0.711398
$655$	−8.98973	−	6.67147i	−0.351258	−	0.260676i
$656$		−	0.319714i		−	0.0124827i
$657$	18.3258			0.714958
$658$	−13.2626			−0.517031
$659$	−0.355635			−0.0138536			−0.00692678	−	0.999976i	$-0.502205\pi$
$659$	−0.355635			−0.0138536			−0.00692678	+	0.999976i	$0.502205\pi$
$660$	8.66522	+	6.43064i	0.337293	+	0.250312i
$661$			12.9399i			0.503303i	0.967818	+	0.251651i	$0.0809736\pi$
$661$			12.9399i			0.503303i	−0.967818	+	0.251651i	$0.919026\pi$
$662$			3.60485i			0.140107i
$663$		0			0
$664$	−18.0365			−0.699952
$665$	12.9808	−	17.4915i	0.503375	−	0.678292i
$666$	10.8617			0.420883
$667$		−	68.5774i		−	2.65533i
$668$	−0.0596123			−0.00230647
$669$		−	0.0576436i		−	0.00222863i
$670$	10.2916	+	7.63758i	0.397597	+	0.295065i
$671$		−	31.0707i		−	1.19947i
$672$			16.2323i			0.626174i
$673$		−	27.5011i		−	1.06009i	−0.847970	−	0.530045i	$-0.822175\pi$
$673$		−	27.5011i		−	1.06009i	0.847970	−	0.530045i	$-0.177825\pi$
$674$		−	22.0494i		−	0.849312i
$675$	−26.6582	+	8.06902i	−1.02608	+	0.310577i
$676$		0			0
$677$		−	12.6270i		−	0.485297i	−0.970114	−	0.242648i	$-0.921984\pi$
$677$		−	12.6270i		−	0.485297i	0.970114	−	0.242648i	$-0.0780161\pi$
$678$	3.96551			0.152295
$679$	−27.5613			−1.05770
$680$	−6.55193	+	8.82865i	−0.251255	+	0.338563i
$681$		−	8.15069i		−	0.312335i
$682$	11.6204			0.444969
$683$	−29.0442			−1.11135			−0.555673	−	0.831401i	$-0.687539\pi$
$683$	−29.0442			−1.11135			−0.555673	+	0.831401i	$0.687539\pi$
$684$		−	7.18901i		−	0.274879i
$685$	23.0116	+	17.0774i	0.879230	+	0.652495i
$686$	−17.8158			−0.680209
$687$	9.23846			0.352469
$688$		−	0.0166814i		−	0.000635972i
$689$		0			0
$690$	−17.4693	−	12.9644i	−0.665046	−	0.493545i
$691$			5.54360i			0.210889i	0.994425	+	0.105444i	$0.0336265\pi$
$691$			5.54360i			0.210889i	−0.994425	+	0.105444i	$0.966374\pi$
$692$		−	10.9107i		−	0.414763i
$693$		−	9.94762i		−	0.377879i
$694$			25.8904i			0.982785i
$695$	27.8840	+	20.6933i	1.05770	+	0.784941i
$696$			28.7426i			1.08949i
$697$	−5.08130			−0.192468
$698$		−	6.47297i		−	0.245006i
$699$	5.78831			0.218934
$700$	4.00395	+	13.2282i	0.151335	+	0.499977i
$701$	7.14386			0.269820			0.134910	−	0.990858i	$-0.456925\pi$
$701$	7.14386			0.269820			0.134910	+	0.990858i	$0.456925\pi$
$702$		0			0
$703$		−	37.5953i		−	1.41793i
$704$			16.3038i			0.614474i
$705$	11.0732	−	14.9210i	0.417042	−	0.561959i
$706$	12.3889			0.466262
$707$	8.64831			0.325253
$708$	8.47449			0.318491
$709$		−	33.2696i		−	1.24947i	−0.780838	−	0.624733i	$-0.785208\pi$
$709$		−	33.2696i		−	1.24947i	0.780838	−	0.624733i	$-0.214792\pi$
$710$	−5.61327	+	7.56382i	−0.210662	+	0.283865i
$711$	−18.6897			−0.700917
$712$			44.8761i			1.68180i
$713$	36.0081			1.34851
$714$	−4.43211			−0.165868
$715$		0			0
$716$	−27.6994			−1.03517
$717$	21.4902			0.802567
$718$		−	14.4402i		−	0.538902i
$719$	2.93123			0.109317			0.0546583	−	0.998505i	$-0.482593\pi$
$719$	2.93123			0.109317			0.0546583	+	0.998505i	$0.482593\pi$
$720$	−0.270673	−	0.200872i	−0.0100874	−	0.00748606i
$721$		−	33.3656i		−	1.24260i
$722$	−0.680581			−0.0253286
$723$	7.78013			0.289346
$724$	−21.4634			−0.797680
$725$	11.5048	+	38.0095i	0.427279	+	1.41164i
$726$		−	1.29707i		−	0.0481389i
$727$		−	14.9385i		−	0.554039i	−0.960864	−	0.277019i	$-0.910653\pi$
$727$		−	14.9385i		−	0.554039i	0.960864	−	0.277019i	$-0.0893466\pi$
$728$		0			0
$729$	−25.2390			−0.934777
$730$	−21.0273	−	15.6048i	−0.778254	−	0.577559i
$731$	−0.265122			−0.00980589
$732$			15.2240i			0.562696i
$733$	9.64485			0.356241			0.178120	−	0.984009i	$-0.442998\pi$
$733$	9.64485			0.356241			0.178120	+	0.984009i	$0.442998\pi$
$734$		−	30.5855i		−	1.12893i
$735$	3.03687	−	4.09215i	0.112017	−	0.150941i
$736$			48.4106i			1.78444i
$737$		−	20.2585i		−	0.746230i
$738$		−	3.63563i		−	0.133830i
$739$		−	38.6006i		−	1.41995i	−0.704229	−	0.709973i	$-0.748707\pi$
$739$		−	38.6006i		−	1.41995i	0.704229	−	0.709973i	$-0.251293\pi$
$740$	19.1558	+	14.2159i	0.704181	+	0.522588i
$741$		0			0
$742$		−	3.91175i		−	0.143605i
$743$	43.3909			1.59186			0.795928	−	0.605391i	$-0.206983\pi$
$743$	43.3909			1.59186			0.795928	+	0.605391i	$0.206983\pi$
$744$	−15.0919			−0.553298
$745$	−0.0551434	+	0.0743051i	−0.00202030	+	0.00272233i
$746$			20.6146i			0.754754i
$747$	−8.78853			−0.321555
$748$	6.55654			0.239731
$749$			9.56084i			0.349345i
$750$	11.8574	+	4.25485i	0.432973	+	0.155365i
$751$	34.8770			1.27268			0.636341	−	0.771408i	$-0.280447\pi$
$751$	34.8770			1.27268			0.636341	+	0.771408i	$0.280447\pi$
$752$	0.710364			0.0259043
$753$		−	14.7012i		−	0.535742i
$754$		0			0
$755$	−8.01302	+	10.7974i	−0.291624	+	0.392959i
$756$			15.3979i			0.560016i
$757$		−	11.6518i		−	0.423493i	−0.977325	−	0.211746i	$-0.932085\pi$
$757$		−	11.6518i		−	0.423493i	0.977325	−	0.211746i	$-0.0679151\pi$
$758$			10.8912i			0.395588i
$759$			34.3876i			1.24819i
$760$	−16.2259	+	21.8642i	−0.588575	+	0.793098i
$761$		−	49.0684i		−	1.77873i	−0.457200	−	0.889364i	$-0.651148\pi$
$761$		−	49.0684i		−	1.77873i	0.457200	−	0.889364i	$-0.348852\pi$
$762$	2.72952			0.0988803
$763$			36.8334i			1.33346i
$764$	−11.7959			−0.426759
$765$	−3.19252	+	4.30188i	−0.115426	+	0.155535i
$766$	1.67215			0.0604172
$767$		0			0
$768$		−	20.6238i		−	0.744197i
$769$			40.1202i			1.44677i	0.690444	+	0.723386i	$0.257415\pi$
$769$			40.1202i			1.44677i	−0.690444	+	0.723386i	$0.742585\pi$
$770$	−8.47058	+	11.4140i	−0.305259	+	0.411332i
$771$	−15.8214			−0.569792
$772$	−12.1179			−0.436133
$773$	11.6461			0.418883			0.209441	−	0.977821i	$-0.432835\pi$
$773$	11.6461			0.418883			0.209441	+	0.977821i	$0.432835\pi$
$774$		−	0.189693i		−	0.00681836i
$775$	−19.9577	+	6.04088i	−0.716903	+	0.216995i
$776$	34.4512			1.23673
$777$			25.4895i			0.914431i
$778$	17.7964			0.638032
$779$	−12.5839			−0.450864
$780$		0			0
$781$	14.8891			0.532772
$782$	−13.2182			−0.472681
$783$			44.2439i			1.58115i
$784$	0.194820			0.00695786
$785$	30.3621	−	40.9126i	1.08367	−	1.46023i
$786$			5.64117i			0.201214i
$787$	25.5641			0.911262			0.455631	−	0.890169i	$-0.349414\pi$
$787$	25.5641			0.911262			0.455631	+	0.890169i	$0.349414\pi$
$788$	7.27005			0.258985
$789$	−35.9512			−1.27990
$790$	21.4447	+	15.9146i	0.762969	+	0.566216i
$791$		−	8.02860i		−	0.285464i
$792$			12.4344i			0.441837i
$793$		0			0
$794$	18.3022			0.649519
$795$	4.40089	+	3.26600i	0.156084	+	0.115833i
$796$	−7.04328			−0.249642
$797$			45.7347i			1.62001i	0.586425	+	0.810003i	$0.300535\pi$
$797$			45.7347i			1.62001i	−0.586425	+	0.810003i	$0.699465\pi$
$798$	−10.9761			−0.388551
$799$		−	11.2900i		−	0.399412i
$800$	−8.12157	−	26.8319i	−0.287141	−	0.948650i
$801$			21.8665i			0.772614i
$802$		−	31.7991i		−	1.12287i
$803$			41.3912i			1.46067i
$804$			9.92625i			0.350072i
$805$	−26.2477	+	35.3685i	−0.925112	+	1.24658i
$806$		0			0
$807$			15.4682i			0.544506i
$808$	−10.8103			−0.380305
$809$	−31.4562			−1.10594			−0.552970	−	0.833201i	$-0.686506\pi$
$809$	−31.4562			−1.10594			−0.552970	+	0.833201i	$0.686506\pi$
$810$	4.62501	+	3.43232i	0.162506	+	0.120599i
$811$		−	38.0128i		−	1.33481i	−0.744694	−	0.667406i	$-0.767405\pi$
$811$		−	38.0128i		−	1.33481i	0.744694	−	0.667406i	$-0.232595\pi$
$812$	21.9544			0.770449
$813$	22.4050			0.785779
$814$			24.5326i			0.859868i
$815$	−2.73161	−	2.02719i	−0.0956842	−	0.0710092i
$816$	0.237390			0.00831031
$817$	−0.656576			−0.0229707
$818$		−	0.197063i		−	0.00689015i
$819$		0			0
$820$	4.75835	−	6.41182i	0.166169	−	0.223910i
$821$		−	55.7593i		−	1.94601i	−0.230778	−	0.973006i	$-0.574127\pi$
$821$		−	55.7593i		−	1.94601i	0.230778	−	0.973006i	$-0.425873\pi$
$822$		−	14.4401i		−	0.503656i
$823$			30.7203i			1.07084i	0.844586	+	0.535420i	$0.179847\pi$
$823$			30.7203i			1.07084i	−0.844586	+	0.535420i	$0.820153\pi$
$824$			41.7067i			1.45292i
$825$	−5.76902	−	19.0596i	−0.200851	−	0.663568i
$826$			11.1628i			0.388403i
$827$	−37.7024			−1.31104			−0.655520	−	0.755177i	$-0.727551\pi$
$827$	−37.7024			−1.31104			−0.655520	+	0.755177i	$0.727551\pi$
$828$			14.5365i			0.505177i
$829$	−13.8208			−0.480015			−0.240008	−	0.970771i	$-0.577150\pi$
$829$	−13.8208			−0.480015			−0.240008	+	0.970771i	$0.577150\pi$
$830$	10.0841	+	7.48360i	0.350023	+	0.259759i
$831$	−14.8799			−0.516177
$832$		0			0
$833$		−	3.09633i		−	0.107281i
$834$		−	17.4975i		−	0.605890i
$835$	0.0883413	+	0.0655600i	0.00305718	+	0.00226880i
$836$	16.2373			0.561579
$837$	−23.2313			−0.802990
$838$	0.604083			0.0208677
$839$			16.0902i			0.555495i	0.960654	+	0.277747i	$0.0895879\pi$
$839$			16.0902i			0.555495i	−0.960654	+	0.277747i	$0.910412\pi$
$840$	11.0011	−	14.8239i	0.379575	−	0.511473i
$841$	34.0833			1.17528
$842$			1.79290i			0.0617875i
$843$	25.7166			0.885727
$844$	−10.5569			−0.363382
$845$		0			0
$846$	8.07792			0.277725
$847$	−2.62607			−0.0902327
$848$			0.209519i			0.00719490i
$849$	10.4613			0.359031
$850$	7.32626	−	2.21754i	0.251289	−	0.0760610i
$851$			76.0191i			2.60590i
$852$	−7.29534			−0.249934
$853$	48.9861			1.67725			0.838625	−	0.544709i	$-0.183360\pi$
$853$	48.9861			1.67725			0.838625	+	0.544709i	$0.183360\pi$
$854$	−20.0534			−0.686213
$855$	−7.90629	+	10.6536i	−0.270389	+	0.364346i
$856$		−	11.9509i		−	0.408475i
$857$		−	8.57696i		−	0.292983i	−0.989212	−	0.146492i	$-0.953202\pi$
$857$		−	8.57696i		−	0.292983i	0.989212	−	0.146492i	$-0.0467982\pi$
$858$		0			0
$859$	17.9983			0.614095			0.307048	−	0.951694i	$-0.400659\pi$
$859$	17.9983			0.614095			0.307048	+	0.951694i	$0.400659\pi$
$860$	0.248271	−	0.334543i	0.00846599	−	0.0114078i
$861$	8.53184			0.290764
$862$		−	6.08548i		−	0.207272i
$863$	−2.18400			−0.0743444			−0.0371722	−	0.999309i	$-0.511835\pi$
$863$	−2.18400			−0.0743444			−0.0371722	+	0.999309i	$0.511835\pi$
$864$		−	31.2329i		−	1.06257i
$865$	−11.9993	+	16.1689i	−0.407989	+	0.549761i
$866$			0.462525i			0.0157172i
$867$			17.8013i			0.604562i
$868$			11.5277i			0.391274i
$869$		−	42.2130i		−	1.43198i
$870$	11.9257	−	16.0698i	0.404319	−	0.544816i
$871$		0			0
$872$		−	46.0414i		−	1.55916i
$873$	16.7868			0.568148
$874$	−32.7349			−1.10727
$875$	8.61440	−	24.0067i	0.291220	−	0.811574i
$876$		−	20.2809i		−	0.685228i
$877$	−27.9605			−0.944158			−0.472079	−	0.881556i	$-0.656496\pi$
$877$	−27.9605			−0.944158			−0.472079	+	0.881556i	$0.656496\pi$
$878$	24.4956			0.826685
$879$			27.0584i			0.912658i
$880$	0.453696	−	0.611350i	0.0152941	−	0.0206086i
$881$	3.38544			0.114058			0.0570292	−	0.998373i	$-0.481837\pi$
$881$	3.38544			0.114058			0.0570292	+	0.998373i	$0.481837\pi$
$882$	2.21540			0.0745964
$883$			9.67005i			0.325423i	0.986674	+	0.162712i	$0.0520240\pi$
$883$			9.67005i			0.325423i	−0.986674	+	0.162712i	$0.947976\pi$
$884$		0			0
$885$	−12.5586	−	9.32002i	−0.422153	−	0.313289i
$886$		−	6.39878i		−	0.214971i
$887$			10.1393i			0.340445i	0.985406	+	0.170223i	$0.0544486\pi$
$887$			10.1393i			0.340445i	−0.985406	+	0.170223i	$0.945551\pi$
$888$		−	31.8616i		−	1.06920i
$889$		−	5.52622i		−	0.185343i
$890$	18.6197	−	25.0899i	0.624134	−	0.841014i
$891$		−	9.10413i		−	0.305000i
$892$	0.0550368			0.00184277
$893$		−	27.9598i		−	0.935639i
$894$	0.0466273			0.00155945
$895$	41.0486	+	30.4630i	1.37210	+	1.01827i
$896$	−15.0587			−0.503076
$897$		0			0
$898$		−	0.120427i		−	0.00401869i
$899$			33.1233i			1.10472i
$900$	−2.43870	−	8.05693i	−0.0812900	−	0.268564i
$901$	3.32994			0.110936
$902$	8.21155			0.273415
$903$	0.445157			0.0148139
$904$			10.0357i			0.333781i
$905$	31.8073	+	23.6048i	1.05731	+	0.784652i
$906$	6.77553			0.225102
$907$			48.7631i			1.61915i	0.587014	+	0.809577i	$0.300303\pi$
$907$			48.7631i			1.61915i	−0.587014	+	0.809577i	$0.699697\pi$
$908$	7.78208			0.258258
$909$	−5.26746			−0.174711
$910$		0			0
$911$	−53.5943			−1.77566			−0.887829	−	0.460174i	$-0.847787\pi$
$911$	−53.5943			−1.77566			−0.887829	+	0.460174i	$0.847787\pi$
$912$	0.587897			0.0194672
$913$		−	19.8500i		−	0.656940i
$914$	0.273475			0.00904575
$915$	16.7430	−	22.5610i	0.553506	−	0.745843i
$916$			8.82066i			0.291443i
$917$	11.4212			0.377160
$918$	8.52794			0.281464
$919$	28.2142			0.930701			0.465350	−	0.885127i	$-0.345928\pi$
$919$	28.2142			0.930701			0.465350	+	0.885127i	$0.345928\pi$
$920$	32.8094	−	44.2103i	1.08169	−	1.45757i
$921$			10.6419i			0.350662i
$922$		−	25.4572i		−	0.838390i
$923$		0			0
$924$	−11.0089			−0.362165
$925$	−12.7533	−	42.1341i	−0.419326	−	1.38536i
$926$	−14.2969			−0.469824
$927$			20.3221i			0.667466i
$928$	−44.5321			−1.46184
$929$			2.90575i			0.0953346i	0.998863	+	0.0476673i	$0.0151787\pi$
$929$			2.90575i			0.0953346i	−0.998863	+	0.0476673i	$0.984821\pi$
$930$	8.43779	+	6.26186i	0.276686	+	0.205334i
$931$		−	7.66808i		−	0.251311i
$932$			5.52654i			0.181028i
$933$			3.58269i			0.117292i
$934$			3.08616i			0.100982i
$935$	−9.71635	−	7.21071i	−0.317759	−	0.235815i
$936$		0			0
$937$			44.6821i			1.45970i	0.683607	+	0.729850i	$0.260410\pi$
$937$			44.6821i			1.45970i	−0.683607	+	0.729850i	$0.739590\pi$
$938$	−13.0751			−0.426916
$939$	−24.3616			−0.795012
$940$	14.2463	+	10.5724i	0.464662	+	0.344835i
$941$			5.09938i			0.166235i	0.996540	+	0.0831175i	$0.0264877\pi$
$941$			5.09938i			0.166235i	−0.996540	+	0.0831175i	$0.973512\pi$
$942$	−25.6731			−0.836476
$943$	25.4451			0.828606
$944$		−	0.597894i		−	0.0194598i
$945$	16.9342	−	22.8186i	0.550869	−	0.742290i
$946$	0.428446			0.0139300
$947$	6.85210			0.222663			0.111332	−	0.993783i	$-0.464488\pi$
$947$	6.85210			0.222663			0.111332	+	0.993783i	$0.464488\pi$
$948$			20.6835i			0.671770i
$949$		0			0
$950$	18.1435	−	5.49175i	0.588654	−	0.178176i
$951$		−	7.31558i		−	0.237224i
$952$		−	11.2165i		−	0.363529i
$953$		−	31.9155i		−	1.03385i	−0.856032	−	0.516923i	$-0.827077\pi$
$953$		−	31.9155i		−	1.03385i	0.856032	−	0.516923i	$-0.172923\pi$
$954$			2.38254i			0.0771377i
$955$	17.4807	+	12.9728i	0.565661	+	0.419789i
$956$			20.5183i			0.663611i
$957$	−31.6326			−1.02254
$958$			12.8366i			0.414732i
$959$	−29.2355			−0.944064
$960$	−8.78560	+	11.8385i	−0.283554	+	0.382086i
$961$	13.6079			0.438964
$962$		0			0
$963$		−	5.82325i		−	0.187652i
$964$			7.42829i			0.239249i
$965$	17.9579	+	13.3269i	0.578086	+	0.429010i
$966$	22.1942			0.714087
$967$	−15.8568			−0.509920			−0.254960	−	0.966952i	$-0.582062\pi$
$967$	−15.8568			−0.509920			−0.254960	+	0.966952i	$0.582062\pi$
$968$	3.28255			0.105505
$969$		−	9.34361i		−	0.300160i
$970$	−19.2614	−	14.2943i	−0.618447	−	0.458962i
$971$	18.3168			0.587813			0.293907	−	0.955834i	$-0.405045\pi$
$971$	18.3168			0.587813			0.293907	+	0.955834i	$0.405045\pi$
$972$		−	15.7882i		−	0.506407i
$973$	−35.4256			−1.13569
$974$	2.58619			0.0828669
$975$		0			0
$976$	1.07409			0.0343807
$977$	13.5382			0.433127			0.216563	−	0.976269i	$-0.430515\pi$
$977$	13.5382			0.433127			0.216563	+	0.976269i	$0.430515\pi$
$978$			1.71412i			0.0548115i
$979$	−49.3883			−1.57846
$980$	3.90709	+	2.89953i	0.124807	+	0.0926222i
$981$		−	22.4343i		−	0.716271i
$982$	−6.75464			−0.215549
$983$	−34.5313			−1.10138			−0.550688	−	0.834711i	$-0.685635\pi$
$983$	−34.5313			−1.10138			−0.550688	+	0.834711i	$0.685635\pi$
$984$	−10.6647			−0.339978
$985$	−10.7737	−	7.99541i	−0.343279	−	0.254755i
$986$		−	12.1592i		−	0.387227i
$987$			18.9567i			0.603398i
$988$		0			0
$989$	1.32762			0.0422159
$990$	5.15921	−	6.95198i	0.163970	−	0.220948i
$991$	43.5272			1.38269			0.691343	−	0.722526i	$-0.257019\pi$
$991$	43.5272			1.38269			0.691343	+	0.722526i	$0.257019\pi$
$992$		−	23.3826i		−	0.742398i
$993$	5.15253			0.163510
$994$		−	9.60958i		−	0.304797i
$995$	10.4377	+	7.74601i	0.330896	+	0.245565i
$996$			9.72612i			0.308184i
$997$			45.3802i			1.43720i	0.695422	+	0.718602i	$0.255218\pi$
$997$			45.3802i			1.43720i	−0.695422	+	0.718602i	$0.744782\pi$
$998$		−	3.61584i		−	0.114457i
$999$		−	49.0450i		−	1.55172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.e.844.14		36
5.4	even	2	inner	845.2.d.e.844.23		36
13.2	odd	12		845.2.n.h.529.7		36
13.3	even	3		845.2.l.g.654.23		72
13.4	even	6		845.2.l.g.699.14		72
13.5	odd	4		845.2.b.h.339.12	yes	18
13.6	odd	12		845.2.n.h.484.12		36
13.7	odd	12		845.2.n.i.484.7		36
13.8	odd	4		845.2.b.g.339.7	✓	18
13.9	even	3		845.2.l.g.699.24		72
13.10	even	6		845.2.l.g.654.13		72
13.11	odd	12		845.2.n.i.529.12		36
13.12	even	2	inner	845.2.d.e.844.24		36
65.4	even	6		845.2.l.g.699.23		72
65.8	even	4		4225.2.a.ca.1.7		18
65.9	even	6		845.2.l.g.699.13		72
65.18	even	4		4225.2.a.cb.1.12		18
65.19	odd	12		845.2.n.h.484.7		36
65.24	odd	12		845.2.n.i.529.7		36
65.29	even	6		845.2.l.g.654.14		72
65.34	odd	4		845.2.b.g.339.12	yes	18
65.44	odd	4		845.2.b.h.339.7	yes	18
65.47	even	4		4225.2.a.ca.1.12		18
65.49	even	6		845.2.l.g.654.24		72
65.54	odd	12		845.2.n.h.529.12		36
65.57	even	4		4225.2.a.cb.1.7		18
65.59	odd	12		845.2.n.i.484.12		36
65.64	even	2	inner	845.2.d.e.844.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.b.g.339.7	✓	18	13.8	odd	4
845.2.b.g.339.12	yes	18	65.34	odd	4
845.2.b.h.339.7	yes	18	65.44	odd	4
845.2.b.h.339.12	yes	18	13.5	odd	4
845.2.d.e.844.13		36	65.64	even	2	inner
845.2.d.e.844.14		36	1.1	even	1	trivial
845.2.d.e.844.23		36	5.4	even	2	inner
845.2.d.e.844.24		36	13.12	even	2	inner
845.2.l.g.654.13		72	13.10	even	6
845.2.l.g.654.14		72	65.29	even	6
845.2.l.g.654.23		72	13.3	even	3
845.2.l.g.654.24		72	65.49	even	6
845.2.l.g.699.13		72	65.9	even	6
845.2.l.g.699.14		72	13.4	even	6
845.2.l.g.699.23		72	65.4	even	6
845.2.l.g.699.24		72	13.9	even	3
845.2.n.h.484.7		36	65.19	odd	12
845.2.n.h.484.12		36	13.6	odd	12
845.2.n.h.529.7		36	13.2	odd	12
845.2.n.h.529.12		36	65.54	odd	12
845.2.n.i.484.7		36	13.7	odd	12
845.2.n.i.484.12		36	65.59	odd	12
845.2.n.i.529.7		36	65.24	odd	12
845.2.n.i.529.12		36	13.11	odd	12
4225.2.a.ca.1.7		18	65.8	even	4
4225.2.a.ca.1.12		18	65.47	even	4
4225.2.a.cb.1.7		18	65.57	even	4
4225.2.a.cb.1.12		18	65.18	even	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.887876 q^{2} +1.26907i q^{3} -1.21168 q^{4} +(1.79562 + 1.33257i) q^{5} -1.12678i q^{6} -2.28128 q^{7} +2.85157 q^{8} +1.38947 q^{9} +(-1.59429 - 1.18316i) q^{10} +3.13829i q^{11} -1.53770i q^{12} +2.02549 q^{14} +(-1.69112 + 2.27877i) q^{15} -0.108488 q^{16} +1.72423i q^{17} -1.23367 q^{18} +4.27007i q^{19} +(-2.17571 - 1.61464i) q^{20} -2.89510i q^{21} -2.78641i q^{22} -8.63424i q^{23} +3.61884i q^{24} +(1.44852 + 4.78558i) q^{25} +5.57053i q^{27} +2.76417 q^{28} +7.94250 q^{29} +(1.50151 - 2.02326i) q^{30} +4.17039i q^{31} -5.60682 q^{32} -3.98270 q^{33} -1.53090i q^{34} +(-4.09631 - 3.03996i) q^{35} -1.68358 q^{36} -8.80437 q^{37} -3.79129i q^{38} +(5.12034 + 3.79991i) q^{40} +2.94700i q^{41} +2.57049i q^{42} +0.153762i q^{43} -3.80259i q^{44} +(2.49496 + 1.85156i) q^{45} +7.66614i q^{46} -6.54786 q^{47} -0.137679i q^{48} -1.79577 q^{49} +(-1.28610 - 4.24900i) q^{50} -2.18817 q^{51} -1.93126i q^{53} -4.94594i q^{54} +(-4.18199 + 5.63518i) q^{55} -6.50522 q^{56} -5.41901 q^{57} -7.05195 q^{58} +5.51115i q^{59} +(2.04909 - 2.76113i) q^{60} -9.90052 q^{61} -3.70279i q^{62} -3.16976 q^{63} +5.19513 q^{64} +3.53615 q^{66} -6.45526 q^{67} -2.08921i q^{68} +10.9574 q^{69} +(3.63702 + 2.69911i) q^{70} -4.74432i q^{71} +3.96216 q^{72} +13.1891 q^{73} +7.81719 q^{74} +(-6.07323 + 1.83827i) q^{75} -5.17394i q^{76} -7.15931i q^{77} -13.4510 q^{79} +(-0.194804 - 0.144568i) q^{80} -2.90099 q^{81} -2.61657i q^{82} -6.32511 q^{83} +3.50792i q^{84} +(-2.29766 + 3.09607i) q^{85} -0.136522i q^{86} +10.0796i q^{87} +8.94905i q^{88} +15.7373i q^{89} +(-2.21521 - 1.64396i) q^{90} +10.4619i q^{92} -5.29250 q^{93} +5.81368 q^{94} +(-5.69016 + 7.66743i) q^{95} -7.11543i q^{96} +12.0815 q^{97} +1.59442 q^{98} +4.36055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 32 q^{4} - 36 q^{9} - 26 q^{10} - 8 q^{14} - 24 q^{16} + 16 q^{25} + 40 q^{29} - 62 q^{30} + 20 q^{35} - 64 q^{36} + 6 q^{40} + 88 q^{49} + 80 q^{51} - 40 q^{55} + 40 q^{56} + 16 q^{61} - 136 q^{64}+ \cdots - 82 q^{95}+O(q^{100}) \) 36 * q + 32 * q^4 - 36 * q^9 - 26 * q^10 - 8 * q^14 - 24 * q^16 + 16 * q^25 + 40 * q^29 - 62 * q^30 + 20 * q^35 - 64 * q^36 + 6 * q^40 + 88 * q^49 + 80 * q^51 - 40 * q^55 + 40 * q^56 + 16 * q^61 - 136 * q^64 + 16 * q^66 + 60 * q^69 - 60 * q^74 - 26 * q^75 - 32 * q^79 - 60 * q^81 + 140 * q^90 + 256 * q^94 - 82 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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