LMFDB - Embedded newform 891.2.k.a.728.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] 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("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			728.19
Character	$\chi$	$=$	891.728
Dual form			891.2.k.a.809.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764034 - 2.35145i) q^{2} +(-3.32755 - 2.41761i) q^{4} +(-1.94468 + 0.631864i) q^{5} +(-0.637345 + 0.877230i) q^{7} +(-4.22672 + 3.07089i) q^{8} +5.05558i q^{10} +(-2.00182 + 2.64438i) q^{11} +(1.05744 + 0.343585i) q^{13} +(1.57581 + 2.16892i) q^{14} +(1.44968 + 4.46166i) q^{16} +(2.03372 + 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(7.99861 + 2.59891i) q^{20} +(4.68867 + 6.72757i) q^{22} +5.43823i q^{23} +(-0.662569 + 0.481384i) q^{25} +(1.61585 - 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(5.99406 + 4.35494i) q^{29} +(-0.366576 + 1.12820i) q^{31} +1.14997 q^{32} +16.2720 q^{34} +(0.685140 - 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(-16.7667 + 5.44783i) q^{38} +(6.27922 - 8.64261i) q^{40} +(-0.893490 + 0.649158i) q^{41} -5.11409i q^{43} +(13.0542 - 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(-2.52463 - 3.47485i) q^{47} +(1.79979 + 5.53920i) q^{49} +(0.625728 + 1.92579i) q^{50} +(-2.68805 - 3.69978i) q^{52} +(-10.3556 - 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} -5.66503i q^{56} +(14.8201 - 10.7674i) q^{58} +(-1.29661 + 1.78463i) q^{59} +(-5.51967 + 1.79345i) q^{61} +(2.37284 + 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} -2.27349 q^{65} -0.993479 q^{67} +(8.36487 - 25.7444i) q^{68} +(-4.43491 - 3.22215i) q^{70} +(-6.12170 + 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(1.93048 - 1.40258i) q^{74} +29.3277i q^{76} +(-1.04388 - 3.44144i) q^{77} +(5.79870 + 1.88411i) q^{79} +(-5.63833 - 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(0.677834 + 2.08616i) q^{83} +(-7.90987 - 10.8870i) q^{85} +(-12.0255 - 3.90734i) q^{86} +(0.340532 - 17.3244i) q^{88} +6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(13.1475 - 18.0960i) q^{92} +(-10.0998 + 3.28164i) q^{94} +(11.7953 + 8.56981i) q^{95} +(-2.94262 + 9.05644i) q^{97} +14.4003 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	0.764034	−	2.35145i	0.540253	−	1.66273i	−0.191763	−	0.981441i	$-0.561420\pi$
$2$	0.764034	−	2.35145i	0.540253	−	1.66273i	0.732016	−	0.681287i	$-0.238580\pi$
$3$		0			0
$3$		0			0
$4$	−3.32755	−	2.41761i	−1.66378	−	1.20880i
$5$	−1.94468	+	0.631864i	−0.869686	+	0.282578i	−0.709668	−	0.704536i	$-0.751155\pi$
$5$	−1.94468	+	0.631864i	−0.869686	+	0.282578i	−0.160018	+	0.987114i	$0.551155\pi$
$6$		0			0
$7$	−0.637345	+	0.877230i	−0.240894	+	0.331562i	−0.912296	−	0.409531i	$-0.865692\pi$
$7$	−0.637345	+	0.877230i	−0.240894	+	0.331562i	0.671402	+	0.741093i	$0.265692\pi$
$8$	−4.22672	+	3.07089i	−1.49437	+	1.08572i
$9$		0			0
$10$			5.05558i			1.59872i
$11$	−2.00182	+	2.64438i	−0.603571	+	0.797309i
$11$	−2.00182	+	2.64438i	−0.603571	+	0.797309i
$12$		0			0
$13$	1.05744	+	0.343585i	0.293282	+	0.0952932i	0.451963	−	0.892037i	$-0.350724\pi$
$13$	1.05744	+	0.343585i	0.293282	+	0.0952932i	−0.158680	+	0.987330i	$0.550724\pi$
$14$	1.57581	+	2.16892i	0.421154	+	0.579669i
$15$		0			0
$16$	1.44968	+	4.46166i	0.362421	+	1.11542i
$17$	2.03372	+	6.25916i	0.493251	+	1.51807i	0.819665	+	0.572843i	$0.194159\pi$
$17$	2.03372	+	6.25916i	0.493251	+	1.51807i	−0.326415	+	0.945227i	$0.605841\pi$
$18$		0			0
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.946221	−	0.323520i	$-0.895134\pi$
$19$	−4.19112	−	5.76858i	−0.961508	−	1.32340i	−0.0152869	−	0.999883i	$-0.504866\pi$
$20$	7.99861	+	2.59891i	1.78854	+	0.581133i
$21$		0			0
$22$	4.68867	+	6.72757i	0.999628	+	1.43432i
$23$			5.43823i			1.13395i	0.823735	+	0.566975i	$0.191886\pi$
$23$			5.43823i			1.13395i	−0.823735	+	0.566975i	$0.808114\pi$
$24$		0			0
$25$	−0.662569	+	0.481384i	−0.132514	+	0.0962769i
$26$	1.61585	−	2.22402i	0.316894	−	0.436166i
$27$		0			0
$28$	4.24160	−	1.37818i	0.801587	−	0.260451i
$29$	5.99406	+	4.35494i	1.11307	+	0.808692i	0.983144	−	0.182832i	$-0.0585265\pi$
$29$	5.99406	+	4.35494i	1.11307	+	0.808692i	0.129925	+	0.991524i	$0.458526\pi$
$30$		0			0
$31$	−0.366576	+	1.12820i	−0.0658390	+	0.202632i	−0.978564	−	0.205943i	$-0.933974\pi$
$31$	−0.366576	+	1.12820i	−0.0658390	+	0.202632i	0.912725	+	0.408574i	$0.133974\pi$
$32$	1.14997			0.203287
$33$		0			0
$34$	16.2720			2.79062
$35$	0.685140	−	2.10865i	0.115810	−	0.356426i
$36$		0			0
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	0.650114	−	0.759837i	$-0.274721\pi$
$37$	0.780793	+	0.567279i	0.128362	+	0.0932602i	−0.521752	+	0.853097i	$0.674721\pi$
$38$	−16.7667	+	5.44783i	−2.71992	+	0.883755i
$39$		0			0
$40$	6.27922	−	8.64261i	0.992832	−	1.36652i
$41$	−0.893490	+	0.649158i	−0.139540	+	0.101381i	−0.655365	−	0.755312i	$-0.727485\pi$
$41$	−0.893490	+	0.649158i	−0.139540	+	0.101381i	0.515826	+	0.856694i	$0.327485\pi$
$42$		0			0
$43$		−	5.11409i		−	0.779892i	−0.920838	−	0.389946i	$-0.872494\pi$
$43$		−	5.11409i		−	0.779892i	0.920838	−	0.389946i	$-0.127506\pi$
$44$	13.0542	−	3.95969i	1.96800	−	0.596945i
$45$		0			0
$46$	12.7877	+	4.15499i	1.88545	+	0.612620i
$47$	−2.52463	−	3.47485i	−0.368254	−	0.506859i	0.584171	−	0.811631i	$-0.301420\pi$
$47$	−2.52463	−	3.47485i	−0.368254	−	0.506859i	−0.952425	+	0.304772i	$0.901420\pi$
$48$		0			0
$49$	1.79979	+	5.53920i	0.257114	+	0.791314i
$50$	0.625728	+	1.92579i	0.0884913	+	0.272348i
$51$		0			0
$52$	−2.68805	−	3.69978i	−0.372765	−	0.513067i
$53$	−10.3556	−	3.36474i	−1.42245	−	0.462183i	−0.506072	−	0.862491i	$-0.668903\pi$
$53$	−10.3556	−	3.36474i	−1.42245	−	0.462183i	−0.916380	+	0.400308i	$0.868903\pi$
$54$		0			0
$55$	2.22200	−	6.40733i	0.299615	−	0.863965i
$56$		−	5.66503i		−	0.757021i
$57$		0			0
$58$	14.8201	−	10.7674i	1.94597	−	1.41383i
$59$	−1.29661	+	1.78463i	−0.168805	+	0.232340i	−0.885035	−	0.465524i	$-0.845866\pi$
$59$	−1.29661	+	1.78463i	−0.168805	+	0.232340i	0.716231	+	0.697864i	$0.245866\pi$
$60$		0			0
$61$	−5.51967	+	1.79345i	−0.706722	+	0.229628i	−0.640257	−	0.768161i	$-0.721172\pi$
$61$	−5.51967	+	1.79345i	−0.706722	+	0.229628i	−0.0664651	+	0.997789i	$0.521172\pi$
$62$	2.37284	+	1.72397i	0.301352	+	0.218945i
$63$		0			0
$64$	−2.02075	+	6.21923i	−0.252594	+	0.777404i
$65$	−2.27349			−0.281991
$66$		0			0
$67$	−0.993479			−0.121373			−0.0606864	−	0.998157i	$-0.519329\pi$
$67$	−0.993479			−0.121373			−0.0606864	+	0.998157i	$0.519329\pi$
$68$	8.36487	−	25.7444i	1.01439	−	3.12197i
$69$		0			0
$70$	−4.43491	−	3.22215i	−0.530073	−	0.385121i
$71$	−6.12170	+	1.98906i	−0.726512	+	0.236058i	−0.648844	−	0.760921i	$-0.724747\pi$
$71$	−6.12170	+	1.98906i	−0.726512	+	0.236058i	−0.0776676	+	0.996979i	$0.524747\pi$
$72$		0			0
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	−0.836523	−	0.547933i	$-0.815415\pi$
$73$	−0.486222	+	0.669227i	−0.0569080	+	0.0783271i	0.779615	+	0.626260i	$0.215415\pi$
$74$	1.93048	−	1.40258i	0.224414	−	0.163046i
$75$		0			0
$76$			29.3277i			3.36412i
$77$	−1.04388	−	3.44144i	−0.118961	−	0.392188i
$78$		0			0
$79$	5.79870	+	1.88411i	0.652405	+	0.211979i	0.616474	−	0.787375i	$-0.288560\pi$
$79$	5.79870	+	1.88411i	0.652405	+	0.211979i	0.0359307	+	0.999354i	$0.488560\pi$
$80$	−5.63833	−	7.76049i	−0.630384	−	0.867649i
$81$		0			0
$82$	0.843809	+	2.59698i	0.0931831	+	0.286788i
$83$	0.677834	+	2.08616i	0.0744020	+	0.228986i	0.981341	−	0.192277i	$-0.0615871\pi$
$83$	0.677834	+	2.08616i	0.0744020	+	0.228986i	−0.906939	+	0.421262i	$0.861587\pi$
$84$		0			0
$85$	−7.90987	−	10.8870i	−0.857946	−	1.18086i
$86$	−12.0255	−	3.90734i	−1.29675	−	0.421339i
$87$		0			0
$88$	0.340532	−	17.3244i	0.0363009	−	1.84679i
$89$			6.19738i			0.656921i	0.944518	+	0.328460i	$0.106530\pi$
$89$			6.19738i			0.656921i	−0.944518	+	0.328460i	$0.893470\pi$
$90$		0			0
$91$	−0.975360	+	0.708641i	−0.102246	+	0.0742857i
$92$	13.1475	−	18.0960i	1.37072	−	1.88664i
$93$		0			0
$94$	−10.0998	+	3.28164i	−1.04172	+	0.338475i
$95$	11.7953	+	8.56981i	1.21017	+	0.879244i
$96$		0			0
$97$	−2.94262	+	9.05644i	−0.298777	+	0.919542i	0.683149	+	0.730279i	$0.260610\pi$
$97$	−2.94262	+	9.05644i	−0.298777	+	0.919542i	−0.981926	+	0.189263i	$0.939390\pi$
$98$	14.4003			1.45465
$99$		0			0
$100$	3.36853			0.336853
$101$	−1.10067	+	3.38753i	−0.109521	+	0.337072i	−0.990765	−	0.135591i	$-0.956707\pi$
$101$	−1.10067	+	3.38753i	−0.109521	+	0.337072i	0.881244	+	0.472662i	$0.156707\pi$
$102$		0			0
$103$	−4.26145	−	3.09612i	−0.419893	−	0.305070i	0.357702	−	0.933836i	$-0.383560\pi$
$103$	−4.26145	−	3.09612i	−0.419893	−	0.305070i	−0.777595	+	0.628766i	$0.783560\pi$
$104$	−5.52464	+	1.79506i	−0.541735	+	0.176020i
$105$		0			0
$106$	−15.8241	+	21.7800i	−1.53697	+	2.11546i
$107$	−8.88743	+	6.45709i	−0.859180	+	0.624231i	−0.927662	−	0.373422i	$-0.878185\pi$
$107$	−8.88743	+	6.45709i	−0.859180	+	0.624231i	0.0684817	+	0.997652i	$0.478185\pi$
$108$		0			0
$109$			2.65252i			0.254065i	0.991899	+	0.127033i	$0.0405453\pi$
$109$			2.65252i			0.254065i	−0.991899	+	0.127033i	$0.959455\pi$
$110$	−13.3689	−	10.1204i	−1.27467	−	0.964938i
$111$		0			0
$112$	−4.83785	−	1.57191i	−0.457134	−	0.148532i
$113$	−5.44759	−	7.49796i	−0.512466	−	0.705349i	0.471867	−	0.881670i	$-0.343580\pi$
$113$	−5.44759	−	7.49796i	−0.512466	−	0.705349i	−0.984333	+	0.176321i	$0.943580\pi$
$114$		0			0
$115$	−3.43622	−	10.5756i	−0.320429	−	0.986180i
$116$	−9.41701	−	28.9826i	−0.874347	−	2.69096i
$117$		0			0
$118$	3.20583	+	4.41245i	0.295121	+	0.406199i
$119$	−6.78691	−	2.20520i	−0.622155	−	0.202150i
$120$		0			0
$121$	−2.98545	−	10.5871i	−0.271404	−	0.962465i
$122$			14.3495i			1.29914i
$123$		0			0
$124$	3.94736	−	2.86792i	0.354483	−	0.257547i
$125$	6.99369	−	9.62600i	0.625535	−	0.860975i
$126$		0			0
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.754182	−	0.656666i	$-0.771966\pi$
$127$	−11.0254	+	3.58238i	−0.978349	+	0.317885i	−0.224167	+	0.974551i	$0.571966\pi$
$128$	14.9410	+	10.8553i	1.32061	+	0.959480i
$129$		0			0
$130$	−1.73702	+	5.34600i	−0.152347	+	0.468875i
$131$	10.3610			0.905247			0.452624	−	0.891702i	$-0.350488\pi$
$131$	10.3610			0.905247			0.452624	+	0.891702i	$0.350488\pi$
$132$		0			0
$133$	7.73156			0.670411
$134$	−0.759051	+	2.33612i	−0.0655720	+	0.201810i
$135$		0			0
$136$	−27.8172	−	20.2104i	−2.38531	−	1.73303i
$137$	0.278975	−	0.0906444i	0.0238344	−	0.00774428i	−0.297076	−	0.954854i	$-0.596011\pi$
$137$	0.278975	−	0.0906444i	0.0238344	−	0.00774428i	0.320910	+	0.947110i	$0.396011\pi$
$138$		0			0
$139$	1.22469	−	1.68564i	0.103876	−	0.142974i	−0.753914	−	0.656973i	$-0.771837\pi$
$139$	1.22469	−	1.68564i	0.103876	−	0.142974i	0.857791	+	0.513999i	$0.171837\pi$
$140$	−7.37772	+	5.36023i	−0.623531	+	0.453022i
$141$		0			0
$142$			15.9146i			1.33552i
$143$	−3.02538	+	2.10849i	−0.252995	+	0.176321i
$144$		0			0
$145$	−14.4082	−	4.68152i	−1.19654	−	0.388779i
$146$	1.20217	+	1.65464i	0.0994921	+	0.136939i
$147$		0			0
$148$	−1.22667	−	3.77530i	−0.100832	−	0.310328i
$149$	−5.17593	−	15.9299i	−0.424028	−	1.30503i	−0.903921	−	0.427698i	$-0.859325\pi$
$149$	−5.17593	−	15.9299i	−0.424028	−	1.30503i	0.479893	−	0.877327i	$-0.340675\pi$
$150$		0			0
$151$	5.69569	+	7.83945i	0.463509	+	0.637965i	0.975232	−	0.221185i	$-0.0709926\pi$
$151$	5.69569	+	7.83945i	0.463509	+	0.637965i	−0.511723	+	0.859150i	$0.670993\pi$
$152$	35.4294	+	11.5117i	2.87370	+	0.933723i
$153$		0			0
$154$	−8.88994	−	0.174742i	−0.716371	−	0.0140811i
$155$		−	2.42562i		−	0.194830i
$156$		0			0
$157$	−2.38672	+	1.73405i	−0.190481	+	0.138393i	−0.678939	−	0.734195i	$-0.737560\pi$
$157$	−2.38672	+	1.73405i	−0.190481	+	0.138393i	0.488458	+	0.872588i	$0.337560\pi$
$158$	8.86081	−	12.1959i	0.704928	−	0.970250i
$159$		0			0
$160$	−2.23631	+	0.726622i	−0.176796	+	0.0574445i
$161$	−4.77058	−	3.46603i	−0.375975	−	0.273162i
$162$		0			0
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	−0.209493	−	0.977810i	$-0.567181\pi$
$163$	6.82701	−	21.0114i	0.534733	−	1.64574i	0.744226	−	0.667928i	$-0.232819\pi$
$164$	4.54254			0.354713
$165$		0			0
$166$	5.42340			0.420937
$167$	−3.60147	+	11.0842i	−0.278690	+	0.857720i	0.709529	+	0.704676i	$0.248908\pi$
$167$	−3.60147	+	11.0842i	−0.278690	+	0.857720i	−0.988219	+	0.153044i	$0.951092\pi$
$168$		0			0
$169$	−9.51708	−	6.91457i	−0.732083	−	0.531890i
$170$	−31.6437	+	10.2817i	−2.42696	+	0.788567i
$171$		0			0
$172$	−12.3639	+	17.0174i	−0.942736	+	1.29756i
$173$	−9.73716	+	7.07446i	−0.740303	+	0.537862i	−0.892806	−	0.450441i	$-0.851267\pi$
$173$	−9.73716	+	7.07446i	−0.740303	+	0.537862i	0.152503	+	0.988303i	$0.451267\pi$
$174$		0			0
$175$		−	0.888034i		−	0.0671290i
$176$	−14.7003	−	5.09793i	−1.10808	−	0.384271i
$177$		0			0
$178$	14.5728	+	4.73501i	1.09228	+	0.354904i
$179$	−1.69252	−	2.32955i	−0.126505	−	0.174119i	0.741067	−	0.671431i	$-0.234320\pi$
$179$	−1.69252	−	2.32955i	−0.126505	−	0.174119i	−0.867571	+	0.497313i	$0.834320\pi$
$180$		0			0
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	0.737021	+	0.675870i	$0.236232\pi$
$181$	7.23838	+	22.2775i	0.538025	+	1.65587i	−0.198996	+	0.980000i	$0.563768\pi$
$182$	0.921128	+	2.83494i	0.0682785	+	0.210140i
$183$		0			0
$184$	−16.7002	−	22.9859i	−1.23116	−	1.69454i
$185$	−1.87683	−	0.609820i	−0.137988	−	0.0448349i
$186$		0			0
$187$	−20.6227	−	7.15177i	−1.50808	−	0.522989i
$188$			17.6663i			1.28845i
$189$		0			0
$190$	29.1635	−	21.1885i	2.11574	−	1.53718i
$191$	−0.482161	+	0.663637i	−0.0348879	+	0.0480191i	−0.826105	−	0.563517i	$-0.809448\pi$
$191$	−0.482161	+	0.663637i	−0.0348879	+	0.0480191i	0.791217	+	0.611536i	$0.209448\pi$
$192$		0			0
$193$	13.5417	−	4.39995i	0.974750	−	0.316715i	0.222018	−	0.975043i	$-0.428736\pi$
$193$	13.5417	−	4.39995i	0.974750	−	0.316715i	0.752732	+	0.658327i	$0.228736\pi$
$194$	19.0475	+	13.8388i	1.36753	+	0.993571i
$195$		0			0
$196$	7.40270	−	22.7832i	0.528764	−	1.62737i
$197$	13.4127			0.955618			0.477809	−	0.878464i	$-0.341431\pi$
$197$	13.4127			0.955618			0.477809	+	0.878464i	$0.341431\pi$
$198$		0			0
$199$	21.2586			1.50698			0.753489	−	0.657460i	$-0.228369\pi$
$199$	21.2586			1.50698			0.753489	+	0.657460i	$0.228369\pi$
$200$	1.32221	−	4.06936i	0.0934947	−	0.287747i
$201$		0			0
$202$	7.12466	+	5.17637i	0.501289	+	0.364208i
$203$	−7.64057	+	2.48257i	−0.536263	+	0.174242i
$204$		0			0
$205$	1.32737	−	1.82697i	0.0927075	−	0.127601i
$206$	−10.5363	+	7.65505i	−0.734097	+	0.533353i
$207$		0			0
$208$			5.21605i			0.361668i
$209$	23.6441	+	0.464754i	1.63550	+	0.0321477i
$210$		0			0
$211$	−14.2042	−	4.61522i	−0.977856	−	0.317725i	−0.223873	−	0.974618i	$-0.571870\pi$
$211$	−14.2042	−	4.61522i	−0.977856	−	0.317725i	−0.753983	+	0.656894i	$0.771870\pi$
$212$	26.3242	+	36.2322i	1.80795	+	2.48844i
$213$		0			0
$214$	8.39326	+	25.8318i	0.573752	+	1.76583i
$215$	3.23141	+	9.94525i	0.220380	+	0.678261i
$216$		0			0
$217$	−0.756060	−	1.04063i	−0.0513247	−	0.0706424i
$218$	6.23727	+	2.02661i	0.422441	+	0.137259i
$219$		0			0
$220$	−22.8843	+	15.9488i	−1.54286	+	1.07527i
$221$			7.31747i			0.492226i
$222$		0			0
$223$	20.2832	−	14.7366i	1.35826	−	0.986835i	0.359709	−	0.933064i	$-0.382876\pi$
$223$	20.2832	−	14.7366i	1.35826	−	0.986835i	0.998553	−	0.0537709i	$-0.0171241\pi$
$224$	−0.732925	+	1.00879i	−0.0489706	+	0.0674023i
$225$		0			0
$226$	−21.7932	+	7.08105i	−1.44966	+	0.471025i
$227$	2.36227	+	1.71629i	0.156789	+	0.113914i	0.663414	−	0.748253i	$-0.269107\pi$
$227$	2.36227	+	1.71629i	0.156789	+	0.113914i	−0.506625	+	0.862167i	$0.669107\pi$
$228$		0			0
$229$	−1.03485	+	3.18494i	−0.0683848	+	0.210467i	−0.979409	−	0.201886i	$-0.935293\pi$
$229$	−1.03485	+	3.18494i	−0.0683848	+	0.210467i	0.911024	+	0.412353i	$0.135293\pi$
$230$	−27.4934			−1.81286
$231$		0			0
$232$	−38.7088			−2.54136
$233$	−3.74639	+	11.5302i	−0.245434	+	0.755369i	0.750131	+	0.661290i	$0.229991\pi$
$233$	−3.74639	+	11.5302i	−0.245434	+	0.755369i	−0.995565	+	0.0940790i	$0.970009\pi$
$234$		0			0
$235$	7.10521	+	5.16224i	0.463493	+	0.336747i
$236$	8.62909	−	2.80376i	0.561706	−	0.182509i
$237$		0			0
$238$	−10.3709	+	14.2743i	−0.672243	+	0.925263i
$239$	5.49803	−	3.99455i	0.355638	−	0.258386i	−0.395592	−	0.918426i	$-0.629461\pi$
$239$	5.49803	−	3.99455i	0.355638	−	0.258386i	0.751230	+	0.660040i	$0.229461\pi$
$240$		0			0
$241$		−	3.26017i		−	0.210006i	−0.994472	−	0.105003i	$-0.966515\pi$
$241$		−	3.26017i		−	0.210006i	0.994472	−	0.105003i	$-0.0334852\pi$
$242$	−27.1761	−	1.06877i	−1.74695	−	0.0687032i
$243$		0			0
$244$	22.7029	+	7.37661i	1.45340	+	0.472239i
$245$	−7.00004	−	9.63473i	−0.447216	−	0.615540i
$246$		0			0
$247$	−2.44988	−	7.53996i	−0.155882	−	0.479756i
$248$	−1.91518	−	5.89432i	−0.121614	−	0.374290i
$249$		0			0
$250$	−17.2917	−	23.7999i	−1.09362	−	1.50524i
$251$	11.6389	+	3.78172i	0.734643	+	0.238700i	0.652360	−	0.757909i	$-0.273779\pi$
$251$	11.6389	+	3.78172i	0.734643	+	0.238700i	0.0822830	+	0.996609i	$0.473779\pi$
$252$		0			0
$253$	−14.3807	−	10.8864i	−0.904109	−	0.684419i
$254$			28.6628i			1.79847i
$255$		0			0
$256$	26.3603	−	19.1519i	1.64752	−	1.19699i
$257$	−9.35196	+	12.8719i	−0.583359	+	0.802925i	−0.994059	−	0.108846i	$-0.965285\pi$
$257$	−9.35196	+	12.8719i	−0.583359	+	0.802925i	0.410699	+	0.911771i	$0.365285\pi$
$258$		0			0
$259$	−0.995270	+	0.323383i	−0.0618430	+	0.0200940i
$260$	7.56514	+	5.49640i	0.469170	+	0.340872i
$261$		0			0
$262$	7.91617	−	24.3635i	0.489063	−	1.50518i
$263$	−11.9141			−0.734658			−0.367329	−	0.930091i	$-0.619728\pi$
$263$	−11.9141			−0.734658			−0.367329	+	0.930091i	$0.619728\pi$
$264$		0			0
$265$	22.2644			1.36769
$266$	5.90717	−	18.1804i	0.362192	−	1.11471i
$267$		0			0
$268$	3.30585	+	2.40184i	0.201937	+	0.146716i
$269$	24.0428	−	7.81198i	1.46592	−	0.476305i	0.536045	−	0.844190i	$-0.319918\pi$
$269$	24.0428	−	7.81198i	1.46592	−	0.476305i	0.929872	+	0.367884i	$0.119918\pi$
$270$		0			0
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	−0.643317	−	0.765600i	$-0.722442\pi$
$271$	4.66877	−	6.42601i	0.283608	−	0.390352i	0.926925	+	0.375248i	$0.122442\pi$
$272$	−24.9780	+	18.1476i	−1.51451	+	1.10036i
$273$		0			0
$274$		−	0.725252i		−	0.0438141i
$275$	0.0533809	−	2.71572i	0.00321899	−	0.163764i
$276$		0			0
$277$	−9.12562	−	2.96509i	−0.548305	−	0.178155i	0.0217470	−	0.999764i	$-0.493077\pi$
$277$	−9.12562	−	2.96509i	−0.548305	−	0.178155i	−0.570053	+	0.821608i	$0.693077\pi$
$278$	−3.02799	−	4.16767i	−0.181607	−	0.249960i
$279$		0			0
$280$	3.57953	+	11.0167i	0.213918	+	0.658371i
$281$	−5.60759	−	17.2584i	−0.334521	−	1.02955i	−0.966958	−	0.254937i	$-0.917945\pi$
$281$	−5.60759	−	17.2584i	−0.334521	−	1.02955i	0.632437	−	0.774612i	$-0.282055\pi$
$282$		0			0
$283$	11.4039	+	15.6961i	0.677891	+	0.933037i	0.999906	−	0.0136978i	$-0.00436028\pi$
$283$	11.4039	+	15.6961i	0.677891	+	0.933037i	−0.322015	+	0.946734i	$0.604360\pi$
$284$	25.1790	+	8.18116i	1.49410	+	0.485463i
$285$		0			0
$286$	2.64652	+	8.72499i	0.156492	+	0.515920i
$287$		−	1.19753i		−	0.0706882i
$288$		0			0
$289$	−21.2878	+	15.4665i	−1.25222	+	0.909792i
$290$	−22.0167	+	30.3035i	−1.29287	+	1.77948i
$291$		0			0
$292$	3.23586	−	1.05139i	0.189364	−	0.0615282i
$293$	−12.4449	−	9.04177i	−0.727041	−	0.528226i	0.161585	−	0.986859i	$-0.448339\pi$
$293$	−12.4449	−	9.04177i	−0.727041	−	0.528226i	−0.888626	+	0.458633i	$0.848339\pi$
$294$		0			0
$295$	1.39385	−	4.28982i	0.0811529	−	0.249763i
$296$	−5.04225			−0.293075
$297$		0			0
$298$	−41.4129			−2.39899
$299$	−1.86849	+	5.75063i	−0.108058	+	0.332567i
$300$		0			0
$301$	4.48624	+	3.25944i	0.258582	+	0.187871i
$302$	22.7858	−	7.40355i	1.31117	−	0.426027i
$303$		0			0
$304$	19.6617	−	27.0620i	1.12767	−	1.55211i
$305$	9.60077	−	6.97537i	0.549738	−	0.399408i
$306$		0			0
$307$			5.86988i			0.335012i	0.985871	+	0.167506i	$0.0535713\pi$
$307$			5.86988i			0.335012i	−0.985871	+	0.167506i	$0.946429\pi$
$308$	−4.84649	+	13.9752i	−0.276154	+	0.796314i
$309$		0			0
$310$	−5.70373	−	1.85325i	−0.323950	−	0.105258i
$311$	−15.5469	−	21.3984i	−0.881581	−	1.21339i	−0.975980	−	0.217858i	$-0.930093\pi$
$311$	−15.5469	−	21.3984i	−0.881581	−	1.21339i	0.0943993	−	0.995534i	$-0.469907\pi$
$312$		0			0
$313$	2.39743	+	7.37853i	0.135511	+	0.417059i	0.995669	−	0.0929680i	$-0.0296354\pi$
$313$	2.39743	+	7.37853i	0.135511	+	0.417059i	−0.860158	+	0.510027i	$0.829635\pi$
$314$	2.25401	+	6.93714i	0.127201	+	0.391485i
$315$		0			0
$316$	−14.7404	−	20.2885i	−0.829214	−	1.14132i
$317$	5.86805	+	1.90665i	0.329583	+	0.107088i	0.469134	−	0.883127i	$-0.344566\pi$
$317$	5.86805	+	1.90665i	0.329583	+	0.107088i	−0.139552	+	0.990215i	$0.544566\pi$
$318$		0			0
$319$	−23.5151	+	7.13275i	−1.31659	+	0.399357i
$320$		−	13.3712i		−	0.747475i
$321$		0			0
$322$	−11.7951	+	8.56964i	−0.657315	+	0.477567i
$323$	27.5829	−	37.9646i	1.53475	−	2.11241i
$324$		0			0
$325$	−0.866026	+	0.281389i	−0.0480385	+	0.0156086i
$326$	−44.1912	−	32.1068i	−2.44752	−	1.77823i
$327$		0			0
$328$	1.78304	−	5.48762i	0.0984517	−	0.303003i
$329$	4.65730			0.256765
$330$		0			0
$331$	−16.8929			−0.928516			−0.464258	−	0.885700i	$-0.653679\pi$
$331$	−16.8929			−0.928516			−0.464258	+	0.885700i	$0.653679\pi$
$332$	2.78799	−	8.58054i	0.153011	−	0.470918i
$333$		0			0
$334$	23.3123	+	16.9374i	1.27559	+	0.926772i
$335$	1.93199	−	0.627743i	0.105556	−	0.0342973i
$336$		0			0
$337$	−17.7335	+	24.4080i	−0.966003	+	1.32959i	−0.0219622	+	0.999759i	$0.506991\pi$
$337$	−17.7335	+	24.4080i	−0.966003	+	1.32959i	−0.944040	+	0.329830i	$0.893009\pi$
$338$	−23.5306	+	17.0960i	−1.27990	+	0.929901i
$339$		0			0
$340$			55.3500i			3.00178i
$341$	−2.24958	−	3.22782i	−0.121822	−	0.174797i
$342$		0			0
$343$	−13.2250	−	4.29705i	−0.714081	−	0.232019i
$344$	15.7048	+	21.6158i	0.846748	+	1.16545i
$345$		0			0
$346$	9.19575	+	28.3016i	0.494367	+	1.52150i
$347$	5.48573	+	16.8833i	0.294489	+	0.906345i	0.983392	+	0.181492i	$0.0580926\pi$
$347$	5.48573	+	16.8833i	0.294489	+	0.906345i	−0.688903	+	0.724854i	$0.741907\pi$
$348$		0			0
$349$	5.48431	+	7.54851i	0.293568	+	0.404062i	0.930169	−	0.367131i	$-0.119660\pi$
$349$	5.48431	+	7.54851i	0.293568	+	0.404062i	−0.636601	+	0.771194i	$0.719660\pi$
$350$	−2.08817	−	0.678487i	−0.111617	−	0.0362667i
$351$		0			0
$352$	−2.30202	+	3.04094i	−0.122698	+	0.162083i
$353$			14.6080i			0.777505i	0.921342	+	0.388752i	$0.127094\pi$
$353$			14.6080i			0.777505i	−0.921342	+	0.388752i	$0.872906\pi$
$354$		0			0
$355$	10.6479	−	7.73616i	0.565132	−	0.410593i
$356$	14.9828	−	20.6221i	0.794089	−	1.09297i
$357$		0			0
$358$	−6.77097	+	2.20002i	−0.357857	+	0.116275i
$359$	−13.4671	−	9.78443i	−0.710767	−	0.516402i	0.172654	−	0.984983i	$-0.444766\pi$
$359$	−13.4671	−	9.78443i	−0.710767	−	0.516402i	−0.883421	+	0.468580i	$0.844766\pi$
$360$		0			0
$361$	−9.83971	+	30.2835i	−0.517880	+	1.59387i
$362$	57.9148			3.04393
$363$		0			0
$364$	4.95878			0.259911
$365$	0.522684	−	1.60866i	0.0273586	−	0.0842010i
$366$		0			0
$367$	−23.8902	−	17.3572i	−1.24706	−	0.906040i	−0.249009	−	0.968501i	$-0.580105\pi$
$367$	−23.8902	−	17.3572i	−1.24706	−	0.906040i	−0.998047	+	0.0624615i	$0.980105\pi$
$368$	−24.2636	+	7.88371i	−1.26483	+	0.410967i
$369$		0			0
$370$	−2.86793	+	3.94736i	−0.149096	+	0.205214i
$371$	9.55175	−	6.93976i	0.495902	−	0.360294i
$372$		0			0
$373$		−	6.98351i		−	0.361593i	−0.983521	−	0.180796i	$-0.942133\pi$
$373$		−	6.98351i		−	0.361593i	0.983521	−	0.180796i	$-0.0578675\pi$
$374$	−32.5735	+	43.0292i	−1.68434	+	2.22499i
$375$		0			0
$376$	21.3418	+	6.93437i	1.10062	+	0.357613i
$377$	4.84209	+	6.66457i	0.249381	+	0.343243i
$378$		0			0
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	−0.779353	−	0.626585i	$-0.784452\pi$
$379$	−10.0677	−	30.9850i	−0.517140	−	1.59159i	0.262213	−	0.965010i	$-0.415548\pi$
$380$	−18.5311	−	57.0330i	−0.950627	−	2.92573i
$381$		0			0
$382$	1.19213	+	1.64082i	0.0609944	+	0.0839517i
$383$	23.3292	+	7.58013i	1.19207	+	0.387326i	0.836837	−	0.547452i	$-0.184402\pi$
$383$	23.3292	+	7.58013i	1.19207	+	0.387326i	0.355231	+	0.934779i	$0.384402\pi$
$384$		0			0
$385$	4.20452	+	6.03289i	0.214282	+	0.307465i
$386$		−	35.2043i		−	1.79185i
$387$		0			0
$388$	31.6866	−	23.0217i	1.60864	−	1.16875i
$389$	16.1015	−	22.1618i	0.816377	−	1.12365i	−0.173931	−	0.984758i	$-0.555647\pi$
$389$	16.1015	−	22.1618i	0.816377	−	1.12365i	0.990308	−	0.138889i	$-0.0443530\pi$
$390$		0			0
$391$	−34.0388	+	11.0599i	−1.72141	+	0.559321i
$392$	−24.6175	−	17.8857i	−1.24337	−	0.903363i
$393$		0			0
$394$	10.2478	−	31.5394i	0.516276	−	1.58893i
$395$	−12.4671			−0.627288
$396$		0			0
$397$	20.5147			1.02960			0.514801	−	0.857310i	$-0.327866\pi$
$397$	20.5147			1.02960			0.514801	+	0.857310i	$0.327866\pi$
$398$	16.2422	−	49.9885i	0.814150	−	2.50570i
$399$		0			0
$400$	−3.10829	−	2.25830i	−0.155414	−	0.112915i
$401$	−9.51397	+	3.09128i	−0.475105	+	0.154371i	−0.536775	−	0.843726i	$-0.680357\pi$
$401$	−9.51397	+	3.09128i	−0.475105	+	0.154371i	0.0616697	+	0.998097i	$0.480357\pi$
$402$		0			0
$403$	−0.775267	+	1.06706i	−0.0386188	+	0.0531542i
$404$	11.8523	−	8.61117i	0.589672	−	0.428422i
$405$		0			0
$406$			19.8632i			0.985795i
$407$	−3.06311	+	0.929120i	−0.151833	+	0.0460548i
$408$		0			0
$409$	7.73588	+	2.51354i	0.382515	+	0.124287i	0.493961	−	0.869484i	$-0.335548\pi$
$409$	7.73588	+	2.51354i	0.382515	+	0.124287i	−0.111447	+	0.993770i	$0.535548\pi$
$410$	−3.28187	−	4.51711i	−0.162080	−	0.223084i
$411$		0			0
$412$	6.69498	+	20.6050i	0.329838	+	1.01514i
$413$	−0.739146	−	2.27486i	−0.0363710	−	0.111938i
$414$		0			0
$415$	−2.63634	−	3.62861i	−0.129413	−	0.178121i
$416$	1.21603	+	0.395110i	0.0596205	+	0.0193719i
$417$		0			0
$418$	19.1578	−	55.2430i	0.937037	−	2.70202i
$419$		−	26.2133i		−	1.28060i	−0.768123	−	0.640302i	$-0.778809\pi$
$419$		−	26.2133i		−	1.28060i	0.768123	−	0.640302i	$-0.221191\pi$
$420$		0			0
$421$	30.3039	−	22.0170i	1.47692	−	1.07305i	0.498387	−	0.866955i	$-0.333926\pi$
$421$	30.3039	−	22.0170i	1.47692	−	1.07305i	0.978533	−	0.206091i	$-0.0660741\pi$
$422$	−21.7049	+	29.8743i	−1.05658	+	1.45426i
$423$		0			0
$424$	54.1031	−	17.5791i	2.62748	−	0.853719i
$425$	−4.36054	−	3.16812i	−0.211517	−	0.153676i
$426$		0			0
$427$	1.94467	−	5.98507i	0.0941091	−	0.289638i
$428$	45.1841			2.18406
$429$		0			0
$430$	25.8547			1.24682
$431$	−7.37759	+	22.7059i	−0.355366	+	1.09370i	0.600431	+	0.799677i	$0.294996\pi$
$431$	−7.37759	+	22.7059i	−0.355366	+	1.09370i	−0.955797	+	0.294027i	$0.905004\pi$
$432$		0			0
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	0.921050	−	0.389445i	$-0.127333\pi$
$433$	17.3812	+	12.6282i	0.835286	+	0.606871i	−0.0857640	+	0.996315i	$0.527333\pi$
$434$	−3.02464	+	0.982766i	−0.145187	+	0.0471743i
$435$		0			0
$436$	6.41275	−	8.82639i	0.307115	−	0.422707i
$437$	31.3709	−	22.7923i	1.50067	−	1.09030i
$438$		0			0
$439$		−	10.3312i		−	0.493081i	−0.969132	−	0.246541i	$-0.920706\pi$
$439$		−	10.3312i		−	0.493081i	0.969132	−	0.246541i	$-0.0792939\pi$
$440$	10.2844	+	33.9056i	0.490292	+	1.61638i
$441$		0			0
$442$	17.2067	+	5.59079i	0.818439	+	0.265927i
$443$	18.6529	+	25.6735i	0.886224	+	1.21978i	0.974658	+	0.223701i	$0.0718140\pi$
$443$	18.6529	+	25.6735i	0.886224	+	1.21978i	−0.0884334	+	0.996082i	$0.528186\pi$
$444$		0			0
$445$	−3.91590	−	12.0519i	−0.185631	−	0.571315i
$446$	−19.1554	−	58.9542i	−0.907034	−	2.79156i
$447$		0			0
$448$	−4.16779	−	5.73647i	−0.196909	−	0.271023i
$449$	−8.43287	−	2.74001i	−0.397972	−	0.129309i	0.103192	−	0.994661i	$-0.467094\pi$
$449$	−8.43287	−	2.74001i	−0.397972	−	0.129309i	−0.501163	+	0.865353i	$0.667094\pi$
$450$		0			0
$451$	0.0719854	−	3.66222i	0.00338966	−	0.172447i
$452$			38.1200i			1.79301i
$453$		0			0
$454$	5.84062	−	4.24346i	0.274114	−	0.199155i
$455$	1.44900	−	1.99437i	0.0679300	−	0.0934976i
$456$		0			0
$457$	15.9850	−	5.19384i	0.747746	−	0.242957i	0.0897350	−	0.995966i	$-0.471398\pi$
$457$	15.9850	−	5.19384i	0.747746	−	0.242957i	0.658011	+	0.753008i	$0.271398\pi$
$458$	6.69858	+	4.86681i	0.313004	+	0.227411i
$459$		0			0
$460$	−14.1335	+	43.4983i	−0.658976	+	2.02812i
$461$	9.96568			0.464148			0.232074	−	0.972698i	$-0.425449\pi$
$461$	9.96568			0.464148			0.232074	+	0.972698i	$0.425449\pi$
$462$		0			0
$463$	35.2721			1.63923			0.819616	−	0.572913i	$-0.194187\pi$
$463$	35.2721			1.63923			0.819616	+	0.572913i	$0.194187\pi$
$464$	−10.7408	+	33.0567i	−0.498629	+	1.53462i
$465$		0			0
$466$	24.2504	+	17.6189i	1.12338	+	0.816181i
$467$	3.77750	−	1.22739i	0.174802	−	0.0567966i	−0.220308	−	0.975430i	$-0.570706\pi$
$467$	3.77750	−	1.22739i	0.174802	−	0.0567966i	0.395110	+	0.918634i	$0.370706\pi$
$468$		0			0
$469$	0.633189	−	0.871510i	0.0292379	−	0.0402426i
$470$	17.5674	−	12.7635i	0.810323	−	0.588734i
$471$		0			0
$472$		−	11.5249i		−	0.530477i
$473$	13.5236	+	10.2375i	0.621815	+	0.470720i
$474$		0			0
$475$	5.55381	+	1.80454i	0.254826	+	0.0827980i
$476$	17.2525	+	23.7460i	0.790766	+	1.08840i
$477$		0			0
$478$	−5.19232	−	15.9803i	−0.237491	−	0.730923i
$479$	−10.4431	−	32.1406i	−0.477158	−	1.46854i	−0.843025	−	0.537874i	$-0.819227\pi$
$479$	−10.4431	−	32.1406i	−0.477158	−	1.46854i	0.365867	−	0.930667i	$-0.380773\pi$
$480$		0			0
$481$	0.630737	+	0.868135i	0.0287591	+	0.0395835i
$482$	−7.66614	−	2.49088i	−0.349183	−	0.113457i
$483$		0			0
$484$	−15.6613	+	42.4468i	−0.711876	+	1.92940i
$485$		−	19.4712i		−	0.884141i
$486$		0			0
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	−0.264725	−	0.964324i	$-0.585281\pi$
$487$	12.5920	−	9.14862i	0.570598	−	0.414563i	0.835322	+	0.549761i	$0.185281\pi$
$488$	17.8226	−	24.5308i	0.806793	−	1.11046i
$489$		0			0
$490$	−28.0039	+	9.09901i	−1.26509	+	0.411051i
$491$	−6.75097	−	4.90487i	−0.304667	−	0.221353i	0.424938	−	0.905223i	$-0.360296\pi$
$491$	−6.75097	−	4.90487i	−0.304667	−	0.221353i	−0.729605	+	0.683869i	$0.760296\pi$
$492$		0			0
$493$	−15.0680	+	46.3745i	−0.678628	+	2.08860i
$494$	−19.6016			−0.881920
$495$		0			0
$496$	−5.56509			−0.249880
$497$	2.15677	−	6.63786i	0.0967444	−	0.297749i
$498$		0			0
$499$	0.147503	+	0.107167i	0.00660315	+	0.00479747i	0.591082	−	0.806612i	$-0.298701\pi$
$499$	0.147503	+	0.107167i	0.00660315	+	0.00479747i	−0.584479	+	0.811409i	$0.698701\pi$
$500$	−46.5438	+	15.1230i	−2.08150	+	0.676321i
$501$		0			0
$502$	17.7851	−	24.4791i	0.793787	−	1.09255i
$503$	11.2333	−	8.16148i	0.500869	−	0.363902i	−0.308480	−	0.951231i	$-0.599820\pi$
$503$	11.2333	−	8.16148i	0.500869	−	0.363902i	0.809349	+	0.587328i	$0.199820\pi$
$504$		0			0
$505$		−	7.28312i		−	0.324095i
$506$	−36.5861	+	25.4981i	−1.62645	+	1.13353i
$507$		0			0
$508$	45.3485	+	14.7346i	2.01201	+	0.653743i
$509$	15.0933	+	20.7742i	0.668999	+	0.920798i	0.999737	−	0.0229245i	$-0.00729773\pi$
$509$	15.0933	+	20.7742i	0.668999	+	0.920798i	−0.330738	+	0.943723i	$0.607298\pi$
$510$		0			0
$511$	−0.277175	−	0.853058i	−0.0122615	−	0.0377371i
$512$	−13.4807	−	41.4893i	−0.595768	−	1.83359i
$513$		0			0
$514$	23.1224	+	31.8252i	1.01988	+	1.40375i
$515$	10.2435	+	3.32830i	0.451381	+	0.146663i
$516$		0			0
$517$	14.2426	+	0.279957i	0.626391	+	0.0123125i
$518$			2.58741i			0.113684i
$519$		0			0
$520$	9.60940	−	6.98164i	0.421400	−	0.306165i
$521$	−23.3218	+	32.0997i	−1.02175	+	1.40631i	−0.110774	+	0.993846i	$0.535333\pi$
$521$	−23.3218	+	32.0997i	−1.02175	+	1.40631i	−0.910972	+	0.412468i	$0.864667\pi$
$522$		0			0
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	−0.222431	−	0.974949i	$-0.571399\pi$
$523$	3.90330	−	1.26826i	0.170679	−	0.0554571i	0.393110	+	0.919491i	$0.371399\pi$
$524$	−34.4769	−	25.0489i	−1.50613	−	1.09427i
$525$		0			0
$526$	−9.10281	+	28.0156i	−0.396901	+	1.22154i
$527$	−7.80713			−0.340084
$528$		0			0
$529$	−6.57437			−0.285842
$530$	17.0107	−	52.3536i	0.738899	−	2.27410i
$531$		0			0
$532$	−25.7272	−	18.6919i	−1.11541	−	0.810396i
$533$	−1.16786	+	0.379460i	−0.0505855	+	0.0164362i
$534$		0			0
$535$	13.2032	−	18.1726i	0.570823	−	0.785670i
$536$	4.19916	−	3.05087i	0.181376	−	0.131777i
$537$		0			0
$538$		−	62.5042i		−	2.69475i
$539$	−18.2506	−	6.32913i	−0.786108	−	0.272615i
$540$		0			0
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.768627	−	0.639697i	$-0.220940\pi$
$541$	23.5956	+	7.66668i	1.01445	+	0.329616i	0.245828	+	0.969314i	$0.420940\pi$
$542$	−11.5434	−	15.8881i	−0.495830	−	0.682452i
$543$		0			0
$544$	2.33871	+	7.19782i	0.100272	+	0.308604i
$545$	−1.67603	−	5.15829i	−0.0717932	−	0.220957i
$546$		0			0
$547$	22.9973	+	31.6531i	0.983295	+	1.35339i	0.935035	+	0.354555i	$0.115368\pi$
$547$	22.9973	+	31.6531i	0.983295	+	1.35339i	0.0482600	+	0.998835i	$0.484632\pi$
$548$	−1.14745	−	0.372828i	−0.0490165	−	0.0159264i
$549$		0			0
$550$	−6.34512	−	2.20043i	−0.270557	−	0.0938265i
$551$		−	52.8293i		−	2.25060i
$552$		0			0
$553$	−5.34858	+	3.88597i	−0.227445	+	0.165248i
$554$	−13.9446	+	19.1930i	−0.592448	+	0.815434i
$555$		0			0
$556$	−8.15041	+	2.64823i	−0.345654	+	0.112310i
$557$	−4.19799	−	3.05002i	−0.177874	−	0.129233i	0.495285	−	0.868730i	$-0.335063\pi$
$557$	−4.19799	−	3.05002i	−0.177874	−	0.129233i	−0.673160	+	0.739497i	$0.735063\pi$
$558$		0			0
$559$	1.75712	−	5.40787i	0.0743184	−	0.228728i
$560$	10.4013			0.439535
$561$		0			0
$562$	−44.8667			−1.89259
$563$	2.48886	−	7.65992i	0.104893	−	0.322827i	−0.884812	−	0.465947i	$-0.845714\pi$
$563$	2.48886	−	7.65992i	0.104893	−	0.322827i	0.989705	+	0.143120i	$0.0457136\pi$
$564$		0			0
$565$	15.3315	+	11.1390i	0.645000	+	0.468620i
$566$	45.6216	−	14.8234i	1.91762	−	0.623072i
$567$		0			0
$568$	19.7665	−	27.2063i	0.829385	−	1.14155i
$569$	−24.5721	+	17.8527i	−1.03012	+	0.748424i	−0.968332	−	0.249666i	$-0.919679\pi$
$569$	−24.5721	+	17.8527i	−1.03012	+	0.748424i	−0.0617850	+	0.998089i	$0.519679\pi$
$570$		0			0
$571$		−	38.6722i		−	1.61838i	−0.587547	−	0.809190i	$-0.699906\pi$
$571$		−	38.6722i		−	1.61838i	0.587547	−	0.809190i	$-0.300094\pi$
$572$	15.1646	+	0.298079i	0.634064	+	0.0124633i
$573$		0			0
$574$	−2.81595	−	0.914956i	−0.117535	−	0.0381895i
$575$	−2.61788	−	3.60320i	−0.109173	−	0.150264i
$576$		0			0
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	0.999346	+	0.0361598i	$0.0115125\pi$
$577$	5.09511	+	15.6811i	0.212112	+	0.652815i	−0.787234	+	0.616655i	$0.788487\pi$
$578$	20.1041	+	61.8741i	0.836220	+	2.57362i
$579$		0			0
$580$	36.6261	+	50.4115i	1.52081	+	2.09322i
$581$	−2.26206	−	0.734987i	−0.0938459	−	0.0304924i
$582$		0			0
$583$	29.6277	−	20.6485i	1.22705	−	0.855175i
$584$		−	4.32178i		−	0.178836i
$585$		0			0
$586$	−30.7697	+	22.3555i	−1.27108	+	0.923496i
$587$	−26.5994	+	36.6109i	−1.09787	+	1.51109i	−0.259702	+	0.965689i	$0.583624\pi$
$587$	−26.5994	+	36.6109i	−1.09787	+	1.51109i	−0.838172	+	0.545406i	$0.816376\pi$
$588$		0			0
$589$	8.04450	−	2.61382i	0.331468	−	0.107700i
$590$	−9.02237	−	6.55513i	−0.371445	−	0.269871i
$591$		0			0
$592$	−1.39911	+	4.30601i	−0.0575030	+	0.176976i
$593$	4.03343			0.165633			0.0828166	−	0.996565i	$-0.473608\pi$
$593$	4.03343			0.165633			0.0828166	+	0.996565i	$0.473608\pi$
$594$		0			0
$595$	14.5917			0.598203
$596$	−21.2890	+	65.5208i	−0.872032	+	2.68384i
$597$		0			0
$598$	12.0947	+	8.78735i	0.494591	+	0.359341i
$599$	−5.89513	+	1.91544i	−0.240868	+	0.0782629i	−0.426964	−	0.904269i	$-0.640417\pi$
$599$	−5.89513	+	1.91544i	−0.240868	+	0.0782629i	0.186095	+	0.982532i	$0.440417\pi$
$600$		0			0
$601$	−27.9940	+	38.5304i	−1.14190	+	1.57169i	−0.378709	+	0.925516i	$0.623632\pi$
$601$	−27.9940	+	38.5304i	−1.14190	+	1.57169i	−0.763190	+	0.646174i	$0.776368\pi$
$602$	11.0921	−	8.05885i	0.452079	−	0.328454i
$603$		0			0
$604$		−	39.8561i		−	1.62172i
$605$	12.4954	+	18.7021i	0.508008	+	0.760350i
$606$		0			0
$607$	−7.89536	−	2.56536i	−0.320463	−	0.104125i	0.144368	−	0.989524i	$-0.453885\pi$
$607$	−7.89536	−	2.56536i	−0.320463	−	0.104125i	−0.464831	+	0.885399i	$0.653885\pi$
$608$	−4.81964	−	6.63367i	−0.195462	−	0.269031i
$609$		0			0
$610$	−9.06694	−	27.9052i	−0.367110	−	1.12985i
$611$	−1.47575	−	4.54188i	−0.0597023	−	0.183745i
$612$		0			0
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	0.459702	−	0.888073i	$-0.347956\pi$
$613$	−13.0470	−	17.9576i	−0.526962	−	0.725301i	−0.986664	+	0.162773i	$0.947956\pi$
$614$	13.8028	+	4.48479i	0.557034	+	0.180991i
$615$		0			0
$616$	14.9805	+	11.3404i	0.603580	+	0.456916i
$617$			3.04777i			0.122698i	0.998116	+	0.0613492i	$0.0195403\pi$
$617$			3.04777i			0.122698i	−0.998116	+	0.0613492i	$0.980460\pi$
$618$		0			0
$619$	−20.0091	+	14.5375i	−0.804234	+	0.584310i	−0.912153	−	0.409850i	$-0.865581\pi$
$619$	−20.0091	+	14.5375i	−0.804234	+	0.584310i	0.107919	+	0.994160i	$0.465581\pi$
$620$	−5.86420	+	8.07137i	−0.235512	+	0.324154i
$621$		0			0
$622$	−62.1957	+	20.2086i	−2.49382	+	0.810291i
$623$	−5.43653	−	3.94987i	−0.217810	−	0.158248i
$624$		0			0
$625$	−6.25276	+	19.2440i	−0.250111	+	0.769761i
$626$	19.1820			0.766666
$627$		0			0
$628$	12.1342			0.484207
$629$	−1.96277	+	6.04080i	−0.0782609	+	0.240862i
$630$		0			0
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	0.232119	−	0.972687i	$-0.425434\pi$
$631$	−15.6052	−	11.3378i	−0.621233	−	0.451352i	−0.853352	+	0.521335i	$0.825434\pi$
$632$	−30.2954	+	9.84358i	−1.20509	+	0.391556i
$633$		0			0
$634$	8.96678	−	12.3417i	0.356116	−	0.490152i
$635$	19.1773	−	13.9331i	0.761029	−	0.552920i
$636$		0			0
$637$			6.47578i			0.256580i
$638$	−1.19400	+	60.7443i	−0.0472711	+	2.40489i
$639$		0			0
$640$	−35.9145	−	11.6693i	−1.41964	−	0.461270i
$641$	−0.165428	−	0.227692i	−0.00653402	−	0.00899330i	0.805737	−	0.592273i	$-0.201769\pi$
$641$	−0.165428	−	0.227692i	−0.00653402	−	0.00899330i	−0.812272	+	0.583280i	$0.801769\pi$
$642$		0			0
$643$	3.78679	+	11.6545i	0.149336	+	0.459610i	0.997543	−	0.0700554i	$-0.0223176\pi$
$643$	3.78679	+	11.6545i	0.149336	+	0.459610i	−0.848207	+	0.529665i	$0.822318\pi$
$644$	7.49486	+	23.0668i	0.295339	+	0.908959i
$645$		0			0
$646$	−68.1977	−	93.8661i	−2.68320	−	3.69311i
$647$	12.4773	+	4.05411i	0.490532	+	0.159383i	0.543830	−	0.839195i	$-0.316974\pi$
$647$	12.4773	+	4.05411i	0.490532	+	0.159383i	−0.0532987	+	0.998579i	$0.516974\pi$
$648$		0			0
$649$	−2.12366	−	7.00125i	−0.0833610	−	0.274823i
$650$			2.25141i			0.0883076i
$651$		0			0
$652$	−73.5145	+	53.4114i	−2.87905	+	2.09175i
$653$	−4.11053	+	5.65766i	−0.160858	+	0.221401i	−0.881836	−	0.471556i	$-0.843693\pi$
$653$	−4.11053	+	5.65766i	−0.160858	+	0.221401i	0.720979	+	0.692957i	$0.243693\pi$
$654$		0			0
$655$	−20.1489	+	6.54676i	−0.787281	+	0.255803i
$656$	−4.19160	−	3.04538i	−0.163655	−	0.118902i
$657$		0			0
$658$	3.55833	−	10.9514i	0.138718	−	0.426931i
$659$	9.18342			0.357735			0.178868	−	0.983873i	$-0.442757\pi$
$659$	9.18342			0.357735			0.178868	+	0.983873i	$0.442757\pi$
$660$		0			0
$661$	−13.7010			−0.532908			−0.266454	−	0.963848i	$-0.585852\pi$
$661$	−13.7010			−0.532908			−0.266454	+	0.963848i	$0.585852\pi$
$662$	−12.9067	+	39.7228i	−0.501634	+	1.54387i
$663$		0			0
$664$	−9.27139	−	6.73606i	−0.359800	−	0.261410i
$665$	−15.0354	+	4.88529i	−0.583047	+	0.189444i
$666$		0			0
$667$	−23.6832	+	32.5971i	−0.917016	+	1.26216i
$668$	38.7813	−	28.1763i	1.50049	−	1.09017i
$669$		0			0
$670$		−	5.02261i		−	0.194040i
$671$	6.30683	−	18.1863i	0.243472	−	0.702073i
$672$		0			0
$673$	−17.1709	−	5.57916i	−0.661889	−	0.215061i	−0.0412401	−	0.999149i	$-0.513131\pi$
$673$	−17.1709	−	5.57916i	−0.661889	−	0.215061i	−0.620649	+	0.784088i	$0.713131\pi$
$674$	43.8453	+	60.3479i	1.68886	+	2.32451i
$675$		0			0
$676$	14.9519	+	46.0171i	0.575072	+	1.76989i
$677$	8.16370	+	25.1253i	0.313756	+	0.965643i	0.976263	+	0.216587i	$0.0694925\pi$
$677$	8.16370	+	25.1253i	0.313756	+	0.965643i	−0.662507	+	0.749056i	$0.730507\pi$
$678$		0			0
$679$	−6.06912	−	8.35343i	−0.232912	−	0.320575i
$680$	66.8657	+	21.7260i	2.56418	+	0.833153i
$681$		0			0
$682$	−9.30883	+	2.82361i	−0.356454	+	0.108122i
$683$			19.4399i			0.743848i	0.928263	+	0.371924i	$0.121302\pi$
$683$			19.4399i			0.743848i	−0.928263	+	0.371924i	$0.878698\pi$
$684$		0			0
$685$	−0.485241	+	0.352548i	−0.0185401	+	0.0134702i
$686$	−20.2086	+	27.8148i	−0.771569	+	1.06197i
$687$		0			0
$688$	22.8174	−	7.41381i	0.869903	−	0.282649i
$689$	−9.79441	−	7.11606i	−0.373137	−	0.271100i
$690$		0			0
$691$	−8.38512	+	25.8068i	−0.318985	+	0.981735i	0.655098	+	0.755544i	$0.272627\pi$
$691$	−8.38512	+	25.8068i	−0.318985	+	0.981735i	−0.974083	+	0.226191i	$0.927373\pi$
$692$	49.5042			1.88187
$693$		0			0
$694$	43.8917			1.66611
$695$	−1.31653	+	4.05185i	−0.0499387	+	0.153695i
$696$		0			0
$697$	−5.88030	−	4.27228i	−0.222732	−	0.161824i
$698$	21.9402	−	7.12879i	0.830447	−	0.269829i
$699$		0			0
$700$	−2.14692	+	2.95498i	−0.0811458	+	0.111688i
$701$	−39.8170	+	28.9287i	−1.50387	+	1.09262i	−0.535058	+	0.844815i	$0.679710\pi$
$701$	−39.8170	+	28.9287i	−1.50387	+	1.09262i	−0.968809	+	0.247808i	$0.920290\pi$
$702$		0			0
$703$		−	6.88160i		−	0.259545i
$704$	−12.4008	−	17.7934i	−0.467373	−	0.670614i
$705$		0			0
$706$	34.3500	+	11.1610i	1.29278	+	0.420049i
$707$	−2.27013	−	3.12457i	−0.0853771	−	0.117512i
$708$		0			0
$709$	−7.72893	−	23.7872i	−0.290266	−	0.893347i	−0.984771	−	0.173858i	$-0.944376\pi$
$709$	−7.72893	−	23.7872i	−0.290266	−	0.893347i	0.694505	−	0.719488i	$-0.255624\pi$
$710$	−10.0559	−	30.9487i	−0.377390	−	1.16149i
$711$		0			0
$712$	−19.0315	−	26.1946i	−0.713235	−	0.981684i
$713$	−6.13544	−	1.99352i	−0.229774	−	0.0746581i
$714$		0			0
$715$	4.55111	−	6.01195i	0.170202	−	0.224834i
$716$			11.8435i			0.442614i
$717$		0			0
$718$	−33.2970	+	24.1917i	−1.24263	+	0.902824i
$719$	2.83956	−	3.90832i	0.105898	−	0.145756i	−0.752779	−	0.658273i	$-0.771287\pi$
$719$	2.83956	−	3.90832i	0.105898	−	0.145756i	0.858677	+	0.512518i	$0.171287\pi$
$720$		0			0
$721$	5.43203	−	1.76497i	0.202299	−	0.0657310i
$722$	63.6924	+	46.2752i	2.37039	+	1.72219i
$723$		0			0
$724$	29.7721	−	91.6290i	1.10647	−	3.40536i
$725$	−6.06788			−0.225355
$726$		0			0
$727$	53.3287			1.97785			0.988926	−	0.148412i	$-0.0474162\pi$
$727$	53.3287			1.97785			0.988926	+	0.148412i	$0.0474162\pi$
$728$	1.94642	−	5.99045i	0.0721390	−	0.222021i
$729$		0			0
$730$	−3.38333	−	2.45814i	−0.125223	−	0.0909797i
$731$	32.0099	−	10.4007i	1.18393	−	0.384682i
$732$		0			0
$733$	−23.5368	+	32.3956i	−0.869352	+	1.19656i	0.109906	+	0.993942i	$0.464945\pi$
$733$	−23.5368	+	32.3956i	−0.869352	+	1.19656i	−0.979258	+	0.202618i	$0.935055\pi$
$734$	−59.0676	+	42.9151i	−2.18022	+	1.58403i
$735$		0			0
$736$			6.25378i			0.230517i
$737$	1.98876	−	2.62713i	0.0732570	−	0.0967716i
$738$		0			0
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	0.194841	−	0.980835i	$-0.437581\pi$
$739$	−6.09069	−	1.97899i	−0.224050	−	0.0727982i	−0.418891	+	0.908037i	$0.637581\pi$
$740$	4.77096	+	6.56666i	0.175384	+	0.241395i
$741$		0			0
$742$	−9.02065	−	27.7627i	−0.331159	−	1.01920i
$743$	5.82650	+	17.9321i	0.213754	+	0.657866i	0.999240	+	0.0389869i	$0.0124131\pi$
$743$	5.82650	+	17.9321i	0.213754	+	0.657866i	−0.785486	+	0.618879i	$0.787587\pi$
$744$		0			0
$745$	20.1310	+	27.7080i	0.737543	+	1.01514i
$746$	−16.4214	−	5.33564i	−0.601230	−	0.195352i
$747$		0			0
$748$	51.3330	+	73.6555i	1.87692	+	2.69311i
$749$		−	11.9117i		−	0.435245i
$750$		0			0
$751$	−15.6486	+	11.3694i	−0.571025	+	0.414874i	−0.835478	−	0.549525i	$-0.814809\pi$
$751$	−15.6486	+	11.3694i	−0.571025	+	0.414874i	0.264452	+	0.964399i	$0.414809\pi$
$752$	11.8437	−	16.3015i	0.431895	−	0.594453i
$753$		0			0
$754$	19.3710	−	6.29400i	0.705448	−	0.229214i
$755$	−16.0297	−	11.6463i	−0.583382	−	0.423852i
$756$		0			0
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	−0.998373	−	0.0570248i	$-0.981839\pi$
$757$	−4.32387	+	13.3075i	−0.157154	+	0.483670i	0.841219	+	0.540695i	$0.181839\pi$
$758$	−80.5519			−2.92578
$759$		0			0
$760$	−76.1725			−2.76307
$761$	−6.52539	+	20.0831i	−0.236545	+	0.728011i	0.760368	+	0.649493i	$0.225019\pi$
$761$	−6.52539	+	20.0831i	−0.236545	+	0.728011i	−0.996913	+	0.0785180i	$0.974981\pi$
$762$		0			0
$763$	−2.32687	−	1.69057i	−0.0842383	−	0.0612027i
$764$	3.20883	−	1.04261i	0.116091	−	0.0377204i
$765$		0			0
$766$	35.6486	−	49.0661i	1.28804	−	1.77283i
$767$	−1.98427	+	1.44166i	−0.0716478	+	0.0520552i
$768$		0			0
$769$			42.3583i			1.52748i	0.645524	+	0.763740i	$0.276639\pi$
$769$			42.3583i			1.52748i	−0.645524	+	0.763740i	$0.723361\pi$
$770$	17.3985	−	5.27741i	0.626997	−	0.190185i
$771$		0			0
$772$	−55.6979	−	18.0974i	−2.00461	−	0.651338i
$773$	9.77676	+	13.4566i	0.351646	+	0.483999i	0.947797	−	0.318873i	$-0.103304\pi$
$773$	9.77676	+	13.4566i	0.351646	+	0.483999i	−0.596152	+	0.802872i	$0.703304\pi$
$774$		0			0
$775$	−0.300218	−	0.923977i	−0.0107842	−	0.0331902i
$776$	−15.3737	−	47.3155i	−0.551885	−	1.69853i
$777$		0			0
$778$	−39.8103	−	54.7942i	−1.42727	−	1.96447i
$779$	7.48944	+	2.43347i	0.268337	+	0.0871880i
$780$		0			0
$781$	6.99470	−	20.1698i	0.250290	−	0.721732i
$782$			88.4907i			3.16442i
$783$		0			0
$784$	−22.1049	+	16.0602i	−0.789461	+	0.573577i
$785$	3.54571	−	4.88026i	0.126552	−	0.174184i
$786$		0			0
$787$	36.0163	−	11.7024i	1.28384	−	0.417145i	0.413910	−	0.910318i	$-0.364163\pi$
$787$	36.0163	−	11.7024i	1.28384	−	0.417145i	0.869932	+	0.493172i	$0.164163\pi$
$788$	−44.6316	−	32.4268i	−1.58993	−	1.15516i
$789$		0			0
$790$	−9.52529	+	29.3158i	−0.338894	+	1.04301i
$791$	10.0494			0.357317
$792$		0			0
$793$	−6.45295			−0.229151
$794$	15.6739	−	48.2393i	0.556246	−	1.71195i
$795$		0			0
$796$	−70.7389	−	51.3948i	−2.50728	−	1.82164i
$797$	28.6234	−	9.30032i	1.01389	−	0.329434i	0.245490	−	0.969399i	$-0.421051\pi$
$797$	28.6234	−	9.30032i	1.01389	−	0.329434i	0.768404	+	0.639965i	$0.221051\pi$
$798$		0			0
$799$	16.6152	−	22.8689i	0.587805	−	0.809044i
$800$	−0.761931	+	0.553576i	−0.0269383	+	0.0195719i
$801$		0			0
$802$			24.7335i			0.873370i
$803$	−0.796361	−	2.62543i	−0.0281030	−	0.0926493i
$804$		0			0
$805$	11.4673	+	3.72595i	0.404169	+	0.131323i
$806$	1.91682	+	2.63828i	0.0675171	+	0.0929294i
$807$		0			0
$808$	−5.75049	−	17.6982i	−0.202302	−	0.622620i
$809$	−13.7550	−	42.3334i	−0.483599	−	1.48836i	−0.834000	−	0.551765i	$-0.813955\pi$
$809$	−13.7550	−	42.3334i	−0.483599	−	1.48836i	0.350401	−	0.936600i	$-0.386045\pi$
$810$		0			0
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	0.994814	−	0.101710i	$-0.0324314\pi$
$811$	16.8211	+	23.1522i	0.590667	+	0.812984i	−0.404147	+	0.914694i	$0.632431\pi$
$812$	31.4263	+	10.2110i	1.10285	+	0.358336i
$813$		0			0
$814$	−0.155532	+	7.91263i	−0.00545141	+	0.277338i
$815$			45.1741i			1.58238i
$816$		0			0
$817$	−29.5010	+	21.4338i	−1.03211	+	0.749872i
$818$	11.8209	−	16.2701i	0.413309	−	0.568872i
$819$		0			0
$820$	−8.83378	+	2.87027i	−0.308489	+	0.100234i
$821$	−5.03027	−	3.65470i	−0.175558	−	0.127550i	0.496536	−	0.868016i	$-0.334605\pi$
$821$	−5.03027	−	3.65470i	−0.175558	−	0.127550i	−0.672094	+	0.740466i	$0.734605\pi$
$822$		0			0
$823$	−9.85099	+	30.3182i	−0.343384	+	1.05683i	0.619059	+	0.785344i	$0.287514\pi$
$823$	−9.85099	+	30.3182i	−0.343384	+	1.05683i	−0.962443	+	0.271483i	$0.912486\pi$
$824$	27.5198			0.958698
$825$		0			0
$826$	−5.91395			−0.205773
$827$	3.59606	−	11.0675i	0.125047	−	0.384856i	−0.868862	−	0.495054i	$-0.835148\pi$
$827$	3.59606	−	11.0675i	0.125047	−	0.384856i	0.993910	+	0.110198i	$0.0351484\pi$
$828$		0			0
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.987385	−	0.158340i	$-0.0506141\pi$
$829$	32.8784	+	23.8875i	1.14191	+	0.829649i	0.154529	+	0.987988i	$0.450614\pi$
$830$	−10.5468	+	3.42685i	−0.366083	+	0.118948i
$831$		0			0
$832$	−4.27367	+	5.88220i	−0.148163	+	0.203928i
$833$	−31.0104	+	22.5304i	−1.07445	+	0.780632i
$834$		0			0
$835$		−	23.8308i		−	0.824699i
$836$	−77.5535	−	58.7088i	−2.68225	−	2.03049i
$837$		0			0
$838$	−61.6394	−	20.0278i	−2.12930	−	0.691850i
$839$	1.18034	+	1.62460i	0.0407499	+	0.0560875i	0.828906	−	0.559388i	$-0.188964\pi$
$839$	1.18034	+	1.62460i	0.0407499	+	0.0560875i	−0.788156	+	0.615476i	$0.788964\pi$
$840$		0			0
$841$	8.00175	+	24.6269i	0.275923	+	0.849202i
$842$	−28.6189	−	88.0799i	−0.986272	−	3.03543i
$843$		0			0
$844$	36.1074	+	49.6975i	1.24287	+	1.71066i
$845$	22.8767	+	7.43309i	0.786983	+	0.255706i
$846$		0			0
$847$	11.1901	+	4.12872i	0.384497	+	0.141865i
$848$		−	51.0811i		−	1.75413i
$849$		0			0
$850$	−10.7813	+	7.83307i	−0.369795	+	0.268672i
$851$	−3.08500	+	4.24613i	−0.105752	+	0.145556i
$852$		0			0
$853$	9.44425	−	3.06862i	0.323365	−	0.105068i	−0.142836	−	0.989746i	$-0.545622\pi$
$853$	9.44425	−	3.06862i	0.323365	−	0.105068i	0.466201	+	0.884679i	$0.345622\pi$
$854$	−12.5878	−	9.14560i	−0.430747	−	0.312956i
$855$		0			0
$856$	17.7356	−	54.5847i	0.606192	−	1.86567i
$857$	−36.7570			−1.25559			−0.627797	−	0.778377i	$-0.716043\pi$
$857$	−36.7570			−1.25559			−0.627797	+	0.778377i	$0.716043\pi$
$858$		0			0
$859$	33.2013			1.13281			0.566407	−	0.824126i	$-0.308333\pi$
$859$	33.2013			1.13281			0.566407	+	0.824126i	$0.308333\pi$
$860$	13.2910	−	40.9056i	0.453221	−	1.39487i
$861$		0			0
$862$	47.7551	+	34.6961i	1.62655	+	1.18175i
$863$	−0.486372	+	0.158032i	−0.0165563	+	0.00537947i	−0.317283	−	0.948331i	$-0.602771\pi$
$863$	−0.486372	+	0.158032i	−0.0165563	+	0.00537947i	0.300727	+	0.953710i	$0.402771\pi$
$864$		0			0
$865$	14.4655	−	19.9101i	0.491843	−	0.676964i
$866$	42.9743	−	31.2227i	1.46033	−	1.06099i
$867$		0			0
$868$			5.29060i			0.179575i
$869$	−16.5902	+	11.5623i	−0.562786	+	0.392224i
$870$		0			0
$871$	−1.05055	−	0.341344i	−0.0355965	−	0.0115660i
$872$	−8.14560	−	11.2115i	−0.275845	−	0.379668i
$873$		0			0
$874$	−29.6266	−	91.1812i	−1.00213	−	3.08425i
$875$	3.98682	+	12.2702i	0.134779	+	0.414807i
$876$		0			0
$877$	21.1042	+	29.0475i	0.712639	+	0.980863i	0.999736	+	0.0229615i	$0.00730952\pi$
$877$	21.1042	+	29.0475i	0.712639	+	0.980863i	−0.287098	+	0.957901i	$0.592690\pi$
$878$	−24.2933	−	7.89338i	−0.819860	−	0.266389i
$879$		0			0
$880$	31.8086	+	0.625236i	1.07227	+	0.0210767i
$881$		−	6.31663i		−	0.212813i	−0.994323	−	0.106406i	$-0.966066\pi$
$881$		−	6.31663i		−	0.212813i	0.994323	−	0.106406i	$-0.0339345\pi$
$882$		0			0
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	−0.877084	−	0.480337i	$-0.840514\pi$
$883$	−20.5419	+	14.9246i	−0.691290	+	0.502252i	0.185794	+	0.982589i	$0.440514\pi$
$884$	17.6908	−	24.3493i	0.595005	−	0.818954i
$885$		0			0
$886$	74.6214	−	24.2460i	2.50695	−	0.814559i
$887$	−31.0922	−	22.5898i	−1.04398	−	0.758493i	−0.0729179	−	0.997338i	$-0.523231\pi$
$887$	−31.0922	−	22.5898i	−1.04398	−	0.758493i	−0.971058	+	0.238845i	$0.923231\pi$
$888$		0			0
$889$	3.88443	−	11.9551i	0.130280	−	0.400960i
$890$	−31.3314			−1.05023
$891$		0			0
$892$	−103.121			−3.45274
$893$	−9.46394	+	29.1270i	−0.316699	+	0.974698i
$894$		0			0
$895$	4.76336	+	3.46078i	0.159221	+	0.115681i
$896$	−19.0452	+	6.18815i	−0.636254	+	0.206731i
$897$		0			0
$898$	−12.8860	+	17.7360i	−0.430011	+	0.591859i
$899$	−7.11054	+	5.16611i	−0.237150	+	0.172299i
$900$		0			0
$901$		−	71.6604i		−	2.38735i
$902$	−8.55654	−	2.96733i	−0.284902	−	0.0988012i
$903$		0			0
$904$	46.0509	+	14.9628i	1.53163	+	0.497657i
$905$	−28.1526	−	38.7488i	−0.935825	−	1.28805i
$906$		0			0
$907$	−8.07919	−	24.8652i	−0.268265	−	0.825635i	−0.990923	−	0.134430i	$-0.957080\pi$
$907$	−8.07919	−	24.8652i	−0.268265	−	0.825635i	0.722658	−	0.691206i	$-0.242920\pi$
$908$	−3.71125	−	11.4221i	−0.123162	−	0.379055i
$909$		0			0
$910$	−3.58259	−	4.93101i	−0.118762	−	0.163461i
$911$	31.7533	+	10.3173i	1.05203	+	0.341827i	0.783467	−	0.621434i	$-0.213450\pi$
$911$	31.7533	+	10.3173i	1.05203	+	0.341827i	0.268568	+	0.963261i	$0.413450\pi$
$912$		0			0
$913$	−6.87349	−	2.38366i	−0.227479	−	0.0788877i
$914$		−	41.5562i		−	1.37456i
$915$		0			0
$916$	11.1435	−	8.09620i	0.368190	−	0.267506i
$917$	−6.60355	+	9.08901i	−0.218069	+	0.300146i
$918$		0			0
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	−0.584937	−	0.811079i	$-0.698881\pi$
$919$	−17.6258	+	5.72696i	−0.581420	+	0.188915i	0.00351649	+	0.999994i	$0.498881\pi$
$920$	47.0005	+	34.1479i	1.54956	+	1.12582i
$921$		0			0
$922$	7.61411	−	23.4338i	0.250757	−	0.771752i
$923$	−7.15677			−0.235568
$924$		0			0
$925$	−0.790409			−0.0259885
$926$	26.9490	−	82.9406i	0.885600	−	2.72560i
$927$		0			0
$928$	6.89296	+	5.00803i	0.226273	+	0.164397i
$929$	−32.0788	+	10.4230i	−1.05247	+	0.341969i	−0.783638	−	0.621218i	$-0.786638\pi$
$929$	−32.0788	+	10.4230i	−1.05247	+	0.341969i	−0.268834	+	0.963187i	$0.586638\pi$
$930$		0			0
$931$	24.4102	−	33.5977i	0.800010	−	1.10112i
$932$	40.3418	−	29.3101i	1.32144	−	0.960083i
$933$		0			0
$934$		−	9.82039i		−	0.321333i
$935$	44.6235	+	0.877128i	1.45934	+	0.0286852i
$936$		0			0
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	0.214054	−	0.976822i	$-0.431333\pi$
$937$	−5.72211	−	1.85923i	−0.186933	−	0.0607383i	−0.400988	+	0.916083i	$0.631333\pi$
$938$	−1.56554	−	2.15478i	−0.0511166	−	0.0703560i
$939$		0			0
$940$	−11.1627	−	34.3552i	−0.364087	−	1.12054i
$941$	13.4367	+	41.3540i	0.438025	+	1.34810i	0.889955	+	0.456048i	$0.150735\pi$
$941$	13.4367	+	41.3540i	0.438025	+	1.34810i	−0.451931	+	0.892053i	$0.649265\pi$
$942$		0			0
$943$	−3.53027	−	4.85900i	−0.114961	−	0.158231i
$944$	−9.84211	−	3.19790i	−0.320334	−	0.104083i
$945$		0			0
$946$	34.4054	−	23.9783i	1.11862	−	0.779601i
$947$		−	6.00319i		−	0.195077i	−0.995232	−	0.0975387i	$-0.968903\pi$
$947$		−	6.00319i		−	0.195077i	0.995232	−	0.0975387i	$-0.0310970\pi$
$948$		0			0
$949$	−0.744089	+	0.540612i	−0.0241542	+	0.0175490i
$950$	8.48659	−	11.6808i	0.275341	−	0.378975i
$951$		0			0
$952$	35.4583	−	11.5211i	1.14921	−	0.373401i
$953$	4.38241	+	3.18400i	0.141960	+	0.103140i	0.656499	−	0.754327i	$-0.272037\pi$
$953$	4.38241	+	3.18400i	0.141960	+	0.103140i	−0.514539	+	0.857467i	$0.672037\pi$
$954$		0			0
$955$	0.518319	−	1.59522i	0.0167724	−	0.0516201i
$956$	−27.9522			−0.904040
$957$		0			0
$958$	−83.5560			−2.69957
$959$	−0.0982873	+	0.302497i	−0.00317386	+	0.00976814i
$960$		0			0
$961$	23.9411	+	17.3942i	0.772292	+	0.561103i
$962$	2.52328	−	0.819864i	0.0813539	−	0.0264335i
$963$		0			0
$964$	−7.88182	+	10.8484i	−0.253856	+	0.349403i
$965$	−23.5540	+	17.1130i	−0.758229	+	0.550886i
$966$		0			0
$967$		−	34.8895i		−	1.12197i	−0.827826	−	0.560985i	$-0.810423\pi$
$967$		−	34.8895i		−	1.12197i	0.827826	−	0.560985i	$-0.189577\pi$
$968$	45.1306	+	35.5808i	1.45055	+	1.14361i
$969$		0			0
$970$	−45.7856	−	14.8766i	−1.47009	−	0.477660i
$971$	−25.4555	−	35.0365i	−0.816907	−	1.12438i	−0.990221	−	0.139509i	$-0.955447\pi$
$971$	−25.4555	−	35.0365i	−0.816907	−	1.12438i	0.173314	−	0.984867i	$-0.444553\pi$
$972$		0			0
$973$	0.698143	+	2.14866i	0.0223814	+	0.0688830i
$974$	−11.8918	−	36.5993i	−0.381039	−	1.17272i
$975$		0			0
$976$	−16.0035	−	22.0270i	−0.512261	−	0.705067i
$977$	30.8598	+	10.0270i	0.987293	+	0.320791i	0.757777	−	0.652514i	$-0.226286\pi$
$977$	30.8598	+	10.0270i	0.987293	+	0.320791i	0.229516	+	0.973305i	$0.426286\pi$
$978$		0			0
$979$	−16.3882	−	12.4060i	−0.523769	−	0.396498i
$980$			48.9834i			1.56472i
$981$		0			0
$982$	−16.6915	+	12.1271i	−0.532648	+	0.386991i
$983$	10.5024	−	14.4554i	0.334975	−	0.461054i	−0.607990	−	0.793945i	$-0.708024\pi$
$983$	10.5024	−	14.4554i	0.334975	−	0.461054i	0.942965	+	0.332891i	$0.108024\pi$
$984$		0			0
$985$	−26.0835	+	8.47503i	−0.831088	+	0.270037i
$986$	97.5350	+	70.8634i	3.10615	+	2.25675i
$987$		0			0
$988$	−10.0766	+	31.0124i	−0.320578	+	0.986637i
$989$	27.8116			0.884358
$990$		0			0
$991$	21.5914			0.685875			0.342937	−	0.939358i	$-0.388578\pi$
$991$	21.5914			0.685875			0.342937	+	0.939358i	$0.388578\pi$
$992$	−0.421550	+	1.29740i	−0.0133842	+	0.0411924i
$993$		0			0
$994$	−13.9608	−	10.1431i	−0.442809	−	0.321719i
$995$	−41.3410	+	13.4325i	−1.31060	+	0.425839i
$996$		0			0
$997$	14.0600	−	19.3519i	0.445283	−	0.612880i	−0.526093	−	0.850427i	$-0.676344\pi$
$997$	14.0600	−	19.3519i	0.445283	−	0.612880i	0.971376	+	0.237547i	$0.0763435\pi$
$998$	0.364697	−	0.264968i	0.0115443	−	0.00838740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.728.19		80
3.2	odd	2	inner	891.2.k.a.728.2		80
9.2	odd	6		297.2.t.a.233.9		80
9.4	even	3		297.2.t.a.35.9		80
9.5	odd	6		99.2.p.a.2.2	✓	80
9.7	even	3		99.2.p.a.68.2	yes	80
11.6	odd	10	inner	891.2.k.a.809.2		80
33.17	even	10	inner	891.2.k.a.809.19		80
99.50	even	30		99.2.p.a.83.2	yes	80
99.61	odd	30		99.2.p.a.50.2	yes	80
99.83	even	30		297.2.t.a.17.9		80
99.94	odd	30		297.2.t.a.116.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.2	✓	80	9.5	odd	6
99.2.p.a.50.2	yes	80	99.61	odd	30
99.2.p.a.68.2	yes	80	9.7	even	3
99.2.p.a.83.2	yes	80	99.50	even	30
297.2.t.a.17.9		80	99.83	even	30
297.2.t.a.35.9		80	9.4	even	3
297.2.t.a.116.9		80	99.94	odd	30
297.2.t.a.233.9		80	9.2	odd	6
891.2.k.a.728.2		80	3.2	odd	2	inner
891.2.k.a.728.19		80	1.1	even	1	trivial
891.2.k.a.809.2		80	11.6	odd	10	inner
891.2.k.a.809.19		80	33.17	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764034 - 2.35145i) q^{2} +(-3.32755 - 2.41761i) q^{4} +(-1.94468 + 0.631864i) q^{5} +(-0.637345 + 0.877230i) q^{7} +(-4.22672 + 3.07089i) q^{8} +5.05558i q^{10} +(-2.00182 + 2.64438i) q^{11} +(1.05744 + 0.343585i) q^{13} +(1.57581 + 2.16892i) q^{14} +(1.44968 + 4.46166i) q^{16} +(2.03372 + 6.25916i) q^{17} +(-4.19112 - 5.76858i) q^{19} +(7.99861 + 2.59891i) q^{20} +(4.68867 + 6.72757i) q^{22} +5.43823i q^{23} +(-0.662569 + 0.481384i) q^{25} +(1.61585 - 2.22402i) q^{26} +(4.24160 - 1.37818i) q^{28} +(5.99406 + 4.35494i) q^{29} +(-0.366576 + 1.12820i) q^{31} +1.14997 q^{32} +16.2720 q^{34} +(0.685140 - 2.10865i) q^{35} +(0.780793 + 0.567279i) q^{37} +(-16.7667 + 5.44783i) q^{38} +(6.27922 - 8.64261i) q^{40} +(-0.893490 + 0.649158i) q^{41} -5.11409i q^{43} +(13.0542 - 3.95969i) q^{44} +(12.7877 + 4.15499i) q^{46} +(-2.52463 - 3.47485i) q^{47} +(1.79979 + 5.53920i) q^{49} +(0.625728 + 1.92579i) q^{50} +(-2.68805 - 3.69978i) q^{52} +(-10.3556 - 3.36474i) q^{53} +(2.22200 - 6.40733i) q^{55} -5.66503i q^{56} +(14.8201 - 10.7674i) q^{58} +(-1.29661 + 1.78463i) q^{59} +(-5.51967 + 1.79345i) q^{61} +(2.37284 + 1.72397i) q^{62} +(-2.02075 + 6.21923i) q^{64} -2.27349 q^{65} -0.993479 q^{67} +(8.36487 - 25.7444i) q^{68} +(-4.43491 - 3.22215i) q^{70} +(-6.12170 + 1.98906i) q^{71} +(-0.486222 + 0.669227i) q^{73} +(1.93048 - 1.40258i) q^{74} +29.3277i q^{76} +(-1.04388 - 3.44144i) q^{77} +(5.79870 + 1.88411i) q^{79} +(-5.63833 - 7.76049i) q^{80} +(0.843809 + 2.59698i) q^{82} +(0.677834 + 2.08616i) q^{83} +(-7.90987 - 10.8870i) q^{85} +(-12.0255 - 3.90734i) q^{86} +(0.340532 - 17.3244i) q^{88} +6.19738i q^{89} +(-0.975360 + 0.708641i) q^{91} +(13.1475 - 18.0960i) q^{92} +(-10.0998 + 3.28164i) q^{94} +(11.7953 + 8.56981i) q^{95} +(-2.94262 + 9.05644i) q^{97} +14.4003 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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