LMFDB - Embedded newform 656.2.bs.d.225.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			225.2
Character	$\chi$	$=$	656.225
Dual form			656.2.bs.d.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.55151 - 1.55151i) q^{3} +(1.49595 - 2.05900i) q^{5} +(1.01547 + 0.517405i) q^{7} -1.81438i q^{9} +O(q^{10})$	\(q+(1.55151 - 1.55151i) q^{3} +(1.49595 - 2.05900i) q^{5} +(1.01547 + 0.517405i) q^{7} -1.81438i q^{9} +(0.807883 - 5.10077i) q^{11} +(1.17315 + 2.30243i) q^{13} +(-0.873576 - 5.51554i) q^{15} +(-3.05576 - 0.483986i) q^{17} +(-3.74044 + 7.34102i) q^{19} +(2.37827 - 0.772746i) q^{21} +(1.17869 - 3.62763i) q^{23} +(-0.456519 - 1.40502i) q^{25} +(1.83950 + 1.83950i) q^{27} +(5.72573 - 0.906866i) q^{29} +(-3.65641 + 2.65654i) q^{31} +(-6.66047 - 9.16735i) q^{33} +(2.58442 - 1.31683i) q^{35} +(0.584132 + 0.424397i) q^{37} +(5.39241 + 1.75210i) q^{39} +(-5.78336 + 2.74822i) q^{41} +(-1.75698 - 0.570876i) q^{43} +(-3.73581 - 2.71423i) q^{45} +(3.15704 - 1.60859i) q^{47} +(-3.35104 - 4.61230i) q^{49} +(-5.49197 + 3.99015i) q^{51} +(-5.52741 + 0.875456i) q^{53} +(-9.29392 - 9.29392i) q^{55} +(5.58635 + 17.1930i) q^{57} +(-0.242763 + 0.747149i) q^{59} +(6.70623 - 2.17898i) q^{61} +(0.938773 - 1.84244i) q^{63} +(6.49567 + 1.02881i) q^{65} +(0.835907 + 5.27771i) q^{67} +(-3.79956 - 7.45706i) q^{69} +(-0.708805 + 4.47522i) q^{71} -0.149836i q^{73} +(-2.88820 - 1.47161i) q^{75} +(3.45954 - 4.76165i) q^{77} +(11.4389 - 11.4389i) q^{79} +11.1512 q^{81} -4.27258 q^{83} +(-5.56779 + 5.56779i) q^{85} +(7.47653 - 10.2906i) q^{87} +(-1.51781 - 0.773362i) q^{89} +2.94503i q^{91} +(-1.55132 + 9.79463i) q^{93} +(9.51963 + 18.6833i) q^{95} +(0.687542 + 4.34097i) q^{97} +(-9.25476 - 1.46581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.55151	−	1.55151i	0.895766	−	0.895766i	−0.0992919	−	0.995058i	$-0.531658\pi$
$3$	1.55151	−	1.55151i	0.895766	−	0.895766i	0.995058	+	0.0992919i	$0.0316578\pi$
$4$		0			0
$5$	1.49595	−	2.05900i	0.669008	−	0.920811i	−0.330729	−	0.943726i	$-0.607295\pi$
$5$	1.49595	−	2.05900i	0.669008	−	0.920811i	0.999737	+	0.0229146i	$0.00729460\pi$
$6$		0			0
$7$	1.01547	+	0.517405i	0.383810	+	0.195561i	0.635240	−	0.772314i	$-0.280901\pi$
$7$	1.01547	+	0.517405i	0.383810	+	0.195561i	−0.251431	+	0.967875i	$0.580901\pi$
$8$		0			0
$9$		−	1.81438i		−	0.604795i
$10$		0			0
$11$	0.807883	−	5.10077i	0.243586	−	1.53794i	−0.498057	−	0.867144i	$-0.665953\pi$
$11$	0.807883	−	5.10077i	0.243586	−	1.53794i	0.741642	−	0.670795i	$-0.234047\pi$
$12$		0			0
$13$	1.17315	+	2.30243i	0.325373	+	0.638580i	0.994520	−	0.104550i	$-0.0333403\pi$
$13$	1.17315	+	2.30243i	0.325373	+	0.638580i	−0.669147	+	0.743130i	$0.733340\pi$
$14$		0			0
$15$	−0.873576	−	5.51554i	−0.225556	−	1.42411i
$16$		0			0
$17$	−3.05576	−	0.483986i	−0.741132	−	0.117384i	−0.225559	−	0.974230i	$-0.572421\pi$
$17$	−3.05576	−	0.483986i	−0.741132	−	0.117384i	−0.515573	+	0.856846i	$0.672421\pi$
$18$		0			0
$19$	−3.74044	+	7.34102i	−0.858115	+	1.68415i	−0.137842	+	0.990454i	$0.544017\pi$
$19$	−3.74044	+	7.34102i	−0.858115	+	1.68415i	−0.720273	+	0.693691i	$0.755983\pi$
$20$		0			0
$21$	2.37827	−	0.772746i	0.518981	−	0.168627i
$22$		0			0
$23$	1.17869	−	3.62763i	0.245773	−	0.756413i	−0.749735	−	0.661738i	$-0.769819\pi$
$23$	1.17869	−	3.62763i	0.245773	−	0.756413i	0.995508	−	0.0946746i	$-0.0301811\pi$
$24$		0			0
$25$	−0.456519	−	1.40502i	−0.0913038	−	0.281004i
$26$		0			0
$27$	1.83950	+	1.83950i	0.354011	+	0.354011i
$28$		0			0
$29$	5.72573	−	0.906866i	1.06324	−	0.168401i	0.399780	−	0.916611i	$-0.369087\pi$
$29$	5.72573	−	0.906866i	1.06324	−	0.168401i	0.663461	+	0.748211i	$0.269087\pi$
$30$		0			0
$31$	−3.65641	+	2.65654i	−0.656711	+	0.477129i	−0.865551	−	0.500821i	$-0.833031\pi$
$31$	−3.65641	+	2.65654i	−0.656711	+	0.477129i	0.208840	+	0.977950i	$0.433031\pi$
$32$		0			0
$33$	−6.66047	−	9.16735i	−1.15944	−	1.59583i
$34$		0			0
$35$	2.58442	−	1.31683i	0.436847	−	0.222584i
$36$		0			0
$37$	0.584132	+	0.424397i	0.0960308	+	0.0697704i	0.634765	−	0.772706i	$-0.281097\pi$
$37$	0.584132	+	0.424397i	0.0960308	+	0.0697704i	−0.538734	+	0.842476i	$0.681097\pi$
$38$		0			0
$39$	5.39241	+	1.75210i	0.863476	+	0.280561i
$40$		0			0
$41$	−5.78336	+	2.74822i	−0.903210	+	0.429200i
$41$	−5.78336	+	2.74822i	−0.903210	+	0.429200i
$42$		0			0
$43$	−1.75698	−	0.570876i	−0.267936	−	0.0870578i	0.171968	−	0.985103i	$-0.444988\pi$
$43$	−1.75698	−	0.570876i	−0.267936	−	0.0870578i	−0.439904	+	0.898045i	$0.644988\pi$
$44$		0			0
$45$	−3.73581	−	2.71423i	−0.556902	−	0.404613i
$46$		0			0
$47$	3.15704	−	1.60859i	0.460502	−	0.234638i	−0.208319	−	0.978061i	$-0.566799\pi$
$47$	3.15704	−	1.60859i	0.460502	−	0.234638i	0.668821	+	0.743423i	$0.266799\pi$
$48$		0			0
$49$	−3.35104	−	4.61230i	−0.478719	−	0.658901i
$50$		0			0
$51$	−5.49197	+	3.99015i	−0.769029	+	0.558733i
$52$		0			0
$53$	−5.52741	+	0.875456i	−0.759249	+	0.120253i	−0.524042	−	0.851692i	$-0.675577\pi$
$53$	−5.52741	+	0.875456i	−0.759249	+	0.120253i	−0.235206	+	0.971945i	$0.575577\pi$
$54$		0			0
$55$	−9.29392	−	9.29392i	−1.25319	−	1.25319i
$56$		0			0
$57$	5.58635	+	17.1930i	0.739930	+	2.27727i
$58$		0			0
$59$	−0.242763	+	0.747149i	−0.0316051	+	0.0972705i	−0.965615	−	0.259977i	$-0.916285\pi$
$59$	−0.242763	+	0.747149i	−0.0316051	+	0.0972705i	0.934010	+	0.357248i	$0.116285\pi$
$60$		0			0
$61$	6.70623	−	2.17898i	0.858644	−	0.278990i	0.153582	−	0.988136i	$-0.450919\pi$
$61$	6.70623	−	2.17898i	0.858644	−	0.278990i	0.705062	+	0.709145i	$0.250919\pi$
$62$		0			0
$63$	0.938773	−	1.84244i	0.118274	−	0.232126i
$64$		0			0
$65$	6.49567	+	1.02881i	0.805689	+	0.127609i
$66$		0			0
$67$	0.835907	+	5.27771i	0.102122	+	0.644774i	0.984654	+	0.174521i	$0.0558376\pi$
$67$	0.835907	+	5.27771i	0.102122	+	0.644774i	−0.882531	+	0.470254i	$0.844162\pi$
$68$		0			0
$69$	−3.79956	−	7.45706i	−0.457414	−	0.897725i
$70$		0			0
$71$	−0.708805	+	4.47522i	−0.0841197	+	0.531111i	0.909260	+	0.416230i	$0.136649\pi$
$71$	−0.708805	+	4.47522i	−0.0841197	+	0.531111i	−0.993379	+	0.114881i	$0.963351\pi$
$72$		0			0
$73$		−	0.149836i		−	0.0175369i	−0.999962	−	0.00876846i	$-0.997209\pi$
$73$		−	0.149836i		−	0.0175369i	0.999962	−	0.00876846i	$-0.00279112\pi$
$74$		0			0
$75$	−2.88820	−	1.47161i	−0.333501	−	0.169927i
$76$		0			0
$77$	3.45954	−	4.76165i	0.394251	−	0.542641i
$78$		0			0
$79$	11.4389	−	11.4389i	1.28698	−	1.28698i	0.350367	−	0.936613i	$-0.386057\pi$
$79$	11.4389	−	11.4389i	1.28698	−	1.28698i	0.936613	−	0.350367i	$-0.113943\pi$
$80$		0			0
$81$	11.1512			1.23902
$82$		0			0
$83$	−4.27258			−0.468977			−0.234488	−	0.972119i	$-0.575341\pi$
$83$	−4.27258			−0.468977			−0.234488	+	0.972119i	$0.575341\pi$
$84$		0			0
$85$	−5.56779	+	5.56779i	−0.603912	+	0.603912i
$86$		0			0
$87$	7.47653	−	10.2906i	0.801568	−	1.10326i
$88$		0			0
$89$	−1.51781	−	0.773362i	−0.160887	−	0.0819762i	0.371693	−	0.928356i	$-0.378777\pi$
$89$	−1.51781	−	0.773362i	−0.160887	−	0.0819762i	−0.532580	+	0.846380i	$0.678777\pi$
$90$		0			0
$91$			2.94503i			0.308723i
$92$		0			0
$93$	−1.55132	+	9.79463i	−0.160864	+	1.01566i
$94$		0			0
$95$	9.51963	+	18.6833i	0.976694	+	1.91687i
$96$		0			0
$97$	0.687542	+	4.34097i	0.0698093	+	0.440758i	0.997693	+	0.0678885i	$0.0216262\pi$
$97$	0.687542	+	4.34097i	0.0698093	+	0.440758i	−0.927884	+	0.372870i	$0.878374\pi$
$98$		0			0
$99$	−9.25476	−	1.46581i	−0.930138	−	0.147319i
$100$		0			0
$101$	1.40554	−	2.75854i	0.139857	−	0.274485i	−0.810445	−	0.585815i	$-0.800775\pi$
$101$	1.40554	−	2.75854i	0.139857	−	0.274485i	0.950302	+	0.311330i	$0.100775\pi$
$102$		0			0
$103$	−2.80356	+	0.910931i	−0.276243	+	0.0897567i	−0.443862	−	0.896095i	$-0.646392\pi$
$103$	−2.80356	+	0.910931i	−0.276243	+	0.0897567i	0.167619	+	0.985852i	$0.446392\pi$
$104$		0			0
$105$	1.96669	−	6.05284i	0.191929	−	0.590696i
$106$		0			0
$107$	1.04654	+	3.22093i	0.101173	+	0.311379i	0.988813	−	0.149159i	$-0.0476565\pi$
$107$	1.04654	+	3.22093i	0.101173	+	0.311379i	−0.887640	+	0.460538i	$0.847656\pi$
$108$		0			0
$109$	9.65686	+	9.65686i	0.924960	+	0.924960i	0.997375	−	0.0724148i	$-0.0230705\pi$
$109$	9.65686	+	9.65686i	0.924960	+	0.924960i	−0.0724148	+	0.997375i	$0.523071\pi$
$110$		0			0
$111$	1.56475	−	0.247832i	0.148519	−	0.0235231i
$112$		0			0
$113$	−10.7162	+	7.78581i	−1.00810	+	0.732427i	−0.963810	−	0.266592i	$-0.914102\pi$
$113$	−10.7162	+	7.78581i	−1.00810	+	0.732427i	−0.0442897	+	0.999019i	$0.514102\pi$
$114$		0			0
$115$	−5.70602	−	7.85366i	−0.532089	−	0.732358i
$116$		0			0
$117$	4.17750	−	2.12854i	0.386210	−	0.196784i
$118$		0			0
$119$	−2.85261	−	2.07254i	−0.261498	−	0.189989i
$120$		0			0
$121$	−14.9036	−	4.84246i	−1.35487	−	0.440223i
$122$		0			0
$123$	−4.70906	+	13.2369i	−0.424602	+	1.19353i
$124$		0			0
$125$	8.52661	+	2.77046i	0.762643	+	0.247798i
$126$		0			0
$127$	10.9310	+	7.94181i	0.969966	+	0.704721i	0.955444	−	0.295173i	$-0.0953773\pi$
$127$	10.9310	+	7.94181i	0.969966	+	0.704721i	0.0145221	+	0.999895i	$0.495377\pi$
$128$		0			0
$129$	−3.61169	+	1.84025i	−0.317992	+	0.162025i
$130$		0			0
$131$	−6.01522	−	8.27923i	−0.525552	−	0.723360i	0.460893	−	0.887456i	$-0.347529\pi$
$131$	−6.01522	−	8.27923i	−0.525552	−	0.723360i	−0.986444	+	0.164096i	$0.947529\pi$
$132$		0			0
$133$	−7.59657	+	5.51923i	−0.658706	+	0.478578i
$134$		0			0
$135$	6.53931	−	1.03573i	0.562814	−	0.0891410i
$136$		0			0
$137$	4.05839	+	4.05839i	0.346731	+	0.346731i	0.858891	−	0.512159i	$-0.171154\pi$
$137$	4.05839	+	4.05839i	0.346731	+	0.346731i	−0.512159	+	0.858891i	$0.671154\pi$
$138$		0			0
$139$	4.98324	+	15.3368i	0.422673	+	1.30085i	0.905205	+	0.424975i	$0.139717\pi$
$139$	4.98324	+	15.3368i	0.422673	+	1.30085i	−0.482532	+	0.875878i	$0.660283\pi$
$140$		0			0
$141$	2.40244	−	7.39395i	0.202322	−	0.622683i
$142$		0			0
$143$	12.6919	−	4.12386i	1.06135	−	0.344855i
$144$		0			0
$145$	6.69816	−	13.1459i	0.556252	−	1.09171i
$146$		0			0
$147$	−12.3552	−	1.95688i	−1.01904	−	0.161400i
$148$		0			0
$149$	0.849406	+	5.36294i	0.0695860	+	0.439349i	0.997742	+	0.0671583i	$0.0213932\pi$
$149$	0.849406	+	5.36294i	0.0695860	+	0.439349i	−0.928156	+	0.372191i	$0.878607\pi$
$150$		0			0
$151$	−1.53796	−	3.01842i	−0.125158	−	0.245636i	0.819922	−	0.572475i	$-0.194017\pi$
$151$	−1.53796	−	3.01842i	−0.125158	−	0.245636i	−0.945080	+	0.326839i	$0.894017\pi$
$152$		0			0
$153$	−0.878136	+	5.54433i	−0.0709931	+	0.448233i
$154$		0			0
$155$			11.5026i			0.923910i
$156$		0			0
$157$	−9.01316	−	4.59244i	−0.719329	−	0.366516i	0.0556954	−	0.998448i	$-0.482262\pi$
$157$	−9.01316	−	4.59244i	−0.719329	−	0.366516i	−0.775024	+	0.631931i	$0.782262\pi$
$158$		0			0
$159$	−7.21757	+	9.93413i	−0.572391	+	0.787828i
$160$		0			0
$161$	3.07387	−	3.07387i	0.242255	−	0.242255i
$162$		0			0
$163$	−18.7430			−1.46807			−0.734033	−	0.679113i	$-0.762365\pi$
$163$	−18.7430			−1.46807			−0.734033	+	0.679113i	$0.762365\pi$
$164$		0			0
$165$	−28.8393			−2.24513
$166$		0			0
$167$	−2.16228	+	2.16228i	−0.167322	+	0.167322i	−0.785801	−	0.618479i	$-0.787749\pi$
$167$	−2.16228	+	2.16228i	−0.167322	+	0.167322i	0.618479	+	0.785801i	$0.287749\pi$
$168$		0			0
$169$	3.71629	−	5.11503i	0.285868	−	0.393464i
$170$		0			0
$171$	13.3194	+	6.78659i	1.01856	+	0.518983i
$172$		0			0
$173$			10.5897i			0.805117i	0.915394	+	0.402558i	$0.131879\pi$
$173$			10.5897i			0.805117i	−0.915394	+	0.402558i	$0.868121\pi$
$174$		0			0
$175$	0.263386	−	1.66296i	0.0199101	−	0.125708i
$176$		0			0
$177$	0.782560	+	1.53586i	0.0588208	+	0.115442i
$178$		0			0
$179$	0.298749	+	1.88623i	0.0223295	+	0.140983i	0.996334	−	0.0855440i	$-0.0272628\pi$
$179$	0.298749	+	1.88623i	0.0223295	+	0.140983i	−0.974005	+	0.226527i	$0.927263\pi$
$180$		0			0
$181$	−5.82173	−	0.922071i	−0.432726	−	0.0685370i	−0.0637279	−	0.997967i	$-0.520299\pi$
$181$	−5.82173	−	0.922071i	−0.432726	−	0.0685370i	−0.368998	+	0.929430i	$0.620299\pi$
$182$		0			0
$183$	7.02407	−	13.7855i	0.519234	−	1.01905i
$184$		0			0
$185$	1.74766	−	0.567850i	0.128491	−	0.0417492i
$186$		0			0
$187$	−4.93740	+	15.1957i	−0.361058	+	1.11122i
$188$		0			0
$189$	0.916180	+	2.81971i	0.0666423	+	0.205104i
$190$		0			0
$191$	2.23597	+	2.23597i	0.161789	+	0.161789i	0.783359	−	0.621570i	$-0.213505\pi$
$191$	2.23597	+	2.23597i	0.161789	+	0.161789i	−0.621570	+	0.783359i	$0.713505\pi$
$192$		0			0
$193$	15.5972	−	2.47036i	1.12271	−	0.177820i	0.432645	−	0.901565i	$-0.357580\pi$
$193$	15.5972	−	2.47036i	1.12271	−	0.177820i	0.690068	+	0.723744i	$0.257580\pi$
$194$		0			0
$195$	11.6743	−	8.48190i	0.836016	−	0.607401i
$196$		0			0
$197$	2.67161	+	3.67715i	0.190344	+	0.261986i	0.893514	−	0.449036i	$-0.148233\pi$
$197$	2.67161	+	3.67715i	0.190344	+	0.261986i	−0.703170	+	0.711022i	$0.748233\pi$
$198$		0			0
$199$	−8.00456	+	4.07852i	−0.567428	+	0.289119i	−0.714074	−	0.700070i	$-0.753152\pi$
$199$	−8.00456	+	4.07852i	−0.567428	+	0.289119i	0.146646	+	0.989189i	$0.453152\pi$
$200$		0			0
$201$	9.48535	+	6.89151i	0.669045	+	0.486090i
$202$		0			0
$203$	6.28350	+	2.04163i	0.441015	+	0.143294i
$204$		0			0
$205$	−2.99304	+	16.0191i	−0.209043	+	1.11882i
$206$		0			0
$207$	−6.58192	−	2.13859i	−0.457475	−	0.148643i
$208$		0			0
$209$	34.4230	+	25.0098i	2.38109	+	1.72996i
$210$		0			0
$211$	−5.75578	+	2.93272i	−0.396245	+	0.201897i	−0.640747	−	0.767752i	$-0.721375\pi$
$211$	−5.75578	+	2.93272i	−0.396245	+	0.201897i	0.244503	+	0.969649i	$0.421375\pi$
$212$		0			0
$213$	5.84364	+	8.04308i	0.400399	+	0.551103i
$214$		0			0
$215$	−3.80378	+	2.76361i	−0.259415	+	0.188476i
$216$		0			0
$217$	−5.08747	+	0.805776i	−0.345360	+	0.0546996i
$218$		0			0
$219$	−0.232472	−	0.232472i	−0.0157090	−	0.0157090i
$220$		0			0
$221$	−2.47052	−	7.60348i	−0.166185	−	0.511465i
$222$		0			0
$223$	1.26478	−	3.89258i	0.0846956	−	0.260666i	−0.899736	−	0.436435i	$-0.856241\pi$
$223$	1.26478	−	3.89258i	0.0846956	−	0.260666i	0.984432	+	0.175768i	$0.0562410\pi$
$224$		0			0
$225$	−2.54925	+	0.828302i	−0.169950	+	0.0552201i
$226$		0			0
$227$	0.260675	−	0.511604i	0.0173016	−	0.0339564i	−0.882194	−	0.470886i	$-0.843934\pi$
$227$	0.260675	−	0.511604i	0.0173016	−	0.0339564i	0.899496	+	0.436930i	$0.143934\pi$
$228$		0			0
$229$	−23.7418	−	3.76033i	−1.56890	−	0.248490i	−0.689399	−	0.724382i	$-0.742125\pi$
$229$	−23.7418	−	3.76033i	−1.56890	−	0.248490i	−0.879504	+	0.475892i	$0.842125\pi$
$230$		0			0
$231$	−2.02024	−	12.7553i	−0.132922	−	0.839236i
$232$		0			0
$233$	−5.63580	−	11.0609i	−0.369213	−	0.724622i	0.629410	−	0.777073i	$-0.283297\pi$
$233$	−5.63580	−	11.0609i	−0.369213	−	0.724622i	−0.998623	+	0.0524514i	$0.983297\pi$
$234$		0			0
$235$	1.41069	−	8.90672i	0.0920230	−	0.581010i
$236$		0			0
$237$		−	35.4953i		−	2.30567i
$238$		0			0
$239$	6.04489	+	3.08002i	0.391011	+	0.199230i	0.638433	−	0.769678i	$-0.279583\pi$
$239$	6.04489	+	3.08002i	0.391011	+	0.199230i	−0.247421	+	0.968908i	$0.579583\pi$
$240$		0			0
$241$	−11.2730	+	15.5159i	−0.726155	+	0.999467i	0.273142	+	0.961974i	$0.411937\pi$
$241$	−11.2730	+	15.5159i	−0.726155	+	0.999467i	−0.999297	+	0.0374932i	$0.988063\pi$
$242$		0			0
$243$	11.7827	−	11.7827i	0.755859	−	0.755859i
$244$		0			0
$245$	−14.5097			−0.926990
$246$		0			0
$247$	−21.2903			−1.35467
$248$		0			0
$249$	−6.62896	+	6.62896i	−0.420093	+	0.420093i
$250$		0			0
$251$	−1.10805	+	1.52510i	−0.0699397	+	0.0962637i	−0.842554	−	0.538612i	$-0.818949\pi$
$251$	−1.10805	+	1.52510i	−0.0699397	+	0.0962637i	0.772614	+	0.634876i	$0.218949\pi$
$252$		0			0
$253$	−17.5515	−	8.94292i	−1.10345	−	0.562236i
$254$		0			0
$255$			17.2770i			1.08193i
$256$		0			0
$257$	4.37877	−	27.6464i	0.273140	−	1.72454i	−0.345116	−	0.938560i	$-0.612160\pi$
$257$	4.37877	−	27.6464i	0.273140	−	1.72454i	0.618256	−	0.785977i	$-0.287840\pi$
$258$		0			0
$259$	0.373581	+	0.733194i	0.0232132	+	0.0455584i
$260$		0			0
$261$	−1.64540	−	10.3887i	−0.101848	−	0.643043i
$262$		0			0
$263$	−4.08854	−	0.647561i	−0.252110	−	0.0399303i	0.0291002	−	0.999576i	$-0.490736\pi$
$263$	−4.08854	−	0.647561i	−0.252110	−	0.0399303i	−0.281210	+	0.959646i	$0.590736\pi$
$264$		0			0
$265$	−6.46616	+	12.6906i	−0.397213	+	0.779575i
$266$		0			0
$267$	−3.55478	+	1.15502i	−0.217549	+	0.0706860i
$268$		0			0
$269$	−9.19596	+	28.3022i	−0.560687	+	1.72562i	0.119742	+	0.992805i	$0.461793\pi$
$269$	−9.19596	+	28.3022i	−0.560687	+	1.72562i	−0.680430	+	0.732813i	$0.738207\pi$
$270$		0			0
$271$	−7.16633	−	22.0557i	−0.435324	−	1.33979i	−0.892754	−	0.450544i	$-0.851230\pi$
$271$	−7.16633	−	22.0557i	−0.435324	−	1.33979i	0.457431	−	0.889245i	$-0.348770\pi$
$272$		0			0
$273$	4.56926	+	4.56926i	0.276544	+	0.276544i
$274$		0			0
$275$	−7.53551	+	1.19351i	−0.454408	+	0.0719712i
$276$		0			0
$277$	20.0368	−	14.5576i	1.20389	−	0.874680i	0.209231	−	0.977866i	$-0.432904\pi$
$277$	20.0368	−	14.5576i	1.20389	−	0.874680i	0.994662	+	0.103187i	$0.0329039\pi$
$278$		0			0
$279$	4.81998	+	6.63414i	0.288565	+	0.397176i
$280$		0			0
$281$	−0.189482	+	0.0965459i	−0.0113035	+	0.00575945i	−0.459633	−	0.888109i	$-0.652019\pi$
$281$	−0.189482	+	0.0965459i	−0.0113035	+	0.00575945i	0.448330	+	0.893868i	$0.352019\pi$
$282$		0			0
$283$	−8.92649	−	6.48547i	−0.530625	−	0.385521i	0.289967	−	0.957037i	$-0.406356\pi$
$283$	−8.92649	−	6.48547i	−0.530625	−	0.385521i	−0.820591	+	0.571515i	$0.806356\pi$
$284$		0			0
$285$	43.7573	+	14.2176i	2.59196	+	0.842178i
$286$		0			0
$287$	−7.29475	−	0.201622i	−0.430595	−	0.0119014i
$288$		0			0
$289$	−7.06450	−	2.29540i	−0.415559	−	0.135023i
$290$		0			0
$291$	7.80180	+	5.66834i	0.457349	+	0.332284i
$292$		0			0
$293$	6.77986	−	3.45451i	0.396083	−	0.201815i	−0.244593	−	0.969626i	$-0.578654\pi$
$293$	6.77986	−	3.45451i	0.396083	−	0.201815i	0.640676	+	0.767811i	$0.278654\pi$
$294$		0			0
$295$	1.17521	+	1.61754i	0.0684237	+	0.0941771i
$296$		0			0
$297$	10.8689	−	7.89675i	0.630680	−	0.458216i
$298$		0			0
$299$	9.73515	−	1.54190i	0.562998	−	0.0891702i
$300$		0			0
$301$	−1.48877	−	1.48877i	−0.0858115	−	0.0858115i
$302$		0			0
$303$	−2.09919	−	6.46063i	−0.120595	−	0.371153i
$304$		0			0
$305$	5.54565	−	17.0677i	0.317543	−	0.977296i
$306$		0			0
$307$	29.8761	−	9.70732i	1.70512	−	0.554026i	0.715608	−	0.698502i	$-0.246150\pi$
$307$	29.8761	−	9.70732i	1.70512	−	0.554026i	0.989508	+	0.144476i	$0.0461497\pi$
$308$		0			0
$309$	−2.93643	+	5.76308i	−0.167048	+	0.327850i
$310$		0			0
$311$	−14.5714	−	2.30789i	−0.826270	−	0.130868i	−0.271043	−	0.962567i	$-0.587369\pi$
$311$	−14.5714	−	2.30789i	−0.826270	−	0.130868i	−0.555227	+	0.831699i	$0.687369\pi$
$312$		0			0
$313$	−2.59799	−	16.4031i	−0.146847	−	0.927155i	−0.945561	−	0.325445i	$-0.894486\pi$
$313$	−2.59799	−	16.4031i	−0.146847	−	0.927155i	0.798714	−	0.601711i	$-0.205514\pi$
$314$		0			0
$315$	−2.38923	−	4.68913i	−0.134618	−	0.264203i
$316$		0			0
$317$	5.09527	−	32.1703i	0.286179	−	1.80686i	−0.256085	−	0.966654i	$-0.582433\pi$
$317$	5.09527	−	32.1703i	0.286179	−	1.80686i	0.542264	−	0.840208i	$-0.317567\pi$
$318$		0			0
$319$		−	29.9383i		−	1.67622i
$320$		0			0
$321$	6.62105	+	3.37359i	0.369551	+	0.188296i
$322$		0			0
$323$	14.9828	−	20.6221i	0.833667	−	1.14744i
$324$		0			0
$325$	2.69940	−	2.69940i	0.149736	−	0.149736i
$326$		0			0
$327$	29.9655			1.65710
$328$		0			0
$329$	4.03816			0.222631
$330$		0			0
$331$	1.33145	−	1.33145i	0.0731829	−	0.0731829i	−0.669568	−	0.742751i	$-0.733521\pi$
$331$	1.33145	−	1.33145i	0.0731829	−	0.0731829i	0.742751	+	0.669568i	$0.233521\pi$
$332$		0			0
$333$	0.770020	−	1.05984i	0.0421968	−	0.0580789i
$334$		0			0
$335$	12.1173	+	6.17405i	0.662036	+	0.337324i
$336$		0			0
$337$			29.3757i			1.60020i	0.599870	+	0.800098i	$0.295219\pi$
$337$			29.3757i			1.60020i	−0.599870	+	0.800098i	$0.704781\pi$
$338$		0			0
$339$	−4.54661	+	28.7062i	−0.246938	+	1.55910i
$340$		0			0
$341$	10.5964	+	20.7967i	0.573830	+	1.12620i
$342$		0			0
$343$	−2.26443	−	14.2970i	−0.122268	−	0.771968i
$344$		0			0
$345$	−21.0380	−	3.33209i	−1.13265	−	0.179394i
$346$		0			0
$347$	12.7217	−	24.9677i	0.682936	−	1.34034i	−0.245700	−	0.969346i	$-0.579018\pi$
$347$	12.7217	−	24.9677i	0.682936	−	1.34034i	0.928636	−	0.370992i	$-0.120982\pi$
$348$		0			0
$349$	19.4391	−	6.31615i	1.04055	−	0.338096i	0.261598	−	0.965177i	$-0.415751\pi$
$349$	19.4391	−	6.31615i	1.04055	−	0.338096i	0.778954	+	0.627081i	$0.215751\pi$
$350$		0			0
$351$	−2.07732	+	6.39332i	−0.110879	+	0.341250i
$352$		0			0
$353$	−8.94631	−	27.5339i	−0.476164	−	1.46548i	−0.844381	−	0.535743i	$-0.820032\pi$
$353$	−8.94631	−	27.5339i	−0.476164	−	1.46548i	0.368217	−	0.929740i	$-0.379968\pi$
$354$		0			0
$355$	8.15412	+	8.15412i	0.432776	+	0.432776i
$356$		0			0
$357$	−7.64143	+	1.21028i	−0.404427	+	0.0640550i
$358$		0			0
$359$	−17.5745	+	12.7687i	−0.927549	+	0.673904i	−0.945391	−	0.325937i	$-0.894320\pi$
$359$	−17.5745	+	12.7687i	−0.927549	+	0.673904i	0.0178425	+	0.999841i	$0.494320\pi$
$360$		0			0
$361$	−28.7318	−	39.5459i	−1.51220	−	2.08136i
$362$		0			0
$363$	−30.6362	+	15.6099i	−1.60798	+	0.819308i
$364$		0			0
$365$	−0.308511	−	0.224146i	−0.0161482	−	0.0117324i
$366$		0			0
$367$	−16.4047	−	5.33020i	−0.856316	−	0.278234i	−0.152227	−	0.988346i	$-0.548645\pi$
$367$	−16.4047	−	5.33020i	−0.856316	−	0.278234i	−0.704089	+	0.710112i	$0.748645\pi$
$368$		0			0
$369$	4.98633	+	10.4932i	0.259578	+	0.546257i
$370$		0			0
$371$	−6.06586	−	1.97092i	−0.314924	−	0.102325i
$372$		0			0
$373$	−13.7898	−	10.0189i	−0.714007	−	0.518756i	0.170457	−	0.985365i	$-0.445476\pi$
$373$	−13.7898	−	10.0189i	−0.714007	−	0.518756i	−0.884464	+	0.466609i	$0.845476\pi$
$374$		0			0
$375$	17.5276	−	8.93074i	0.905119	−	0.461181i
$376$		0			0
$377$	8.80513	+	12.1192i	0.453487	+	0.624171i
$378$		0			0
$379$	29.9726	−	21.7764i	1.53959	−	1.11858i	0.588995	−	0.808137i	$-0.299524\pi$
$379$	29.9726	−	21.7764i	1.53959	−	1.11858i	0.950593	−	0.310439i	$-0.100476\pi$
$380$		0			0
$381$	29.2813	−	4.63771i	1.50013	−	0.237597i
$382$		0			0
$383$	23.8870	+	23.8870i	1.22057	+	1.22057i	0.967430	+	0.253137i	$0.0814624\pi$
$383$	23.8870	+	23.8870i	1.22057	+	1.22057i	0.253137	+	0.967430i	$0.418538\pi$
$384$		0			0
$385$	−4.62893	−	14.2464i	−0.235912	−	0.726062i
$386$		0			0
$387$	−1.03579	+	3.18783i	−0.0526521	+	0.162046i
$388$		0			0
$389$	−8.46056	+	2.74900i	−0.428967	+	0.139380i	−0.515540	−	0.856866i	$-0.672409\pi$
$389$	−8.46056	+	2.74900i	−0.428967	+	0.139380i	0.0865726	+	0.996246i	$0.472409\pi$
$390$		0			0
$391$	−5.35751	+	10.5147i	−0.270941	+	0.531752i
$392$		0			0
$393$	−22.1780	−	3.51265i	−1.11873	−	0.177190i
$394$		0			0
$395$	−6.44066	−	40.6647i	−0.324065	−	2.04606i
$396$		0			0
$397$	3.80671	+	7.47109i	0.191053	+	0.374963i	0.966585	−	0.256345i	$-0.0825183\pi$
$397$	3.80671	+	7.47109i	0.191053	+	0.374963i	−0.775532	+	0.631308i	$0.782518\pi$
$398$		0			0
$399$	−3.22302	+	20.3493i	−0.161353	+	1.01874i
$400$		0			0
$401$		−	24.8940i		−	1.24315i	−0.783356	−	0.621573i	$-0.786494\pi$
$401$		−	24.8940i		−	1.24315i	0.783356	−	0.621573i	$-0.213506\pi$
$402$		0			0
$403$	−10.4060	−	5.30213i	−0.518361	−	0.264118i
$404$		0			0
$405$	16.6816	−	22.9602i	0.828914	−	1.14090i
$406$		0			0
$407$	2.63666	−	2.63666i	0.130694	−	0.130694i
$408$		0			0
$409$	−8.75194			−0.432756			−0.216378	−	0.976310i	$-0.569424\pi$
$409$	−8.75194			−0.432756			−0.216378	+	0.976310i	$0.569424\pi$
$410$		0			0
$411$	12.5933			0.621181
$412$		0			0
$413$	−0.633096	+	0.633096i	−0.0311526	+	0.0311526i
$414$		0			0
$415$	−6.39156	+	8.79722i	−0.313749	+	0.431839i
$416$		0			0
$417$	31.5269	+	16.0637i	1.54388	+	0.786645i
$418$		0			0
$419$			24.9286i			1.21784i	0.793232	+	0.608920i	$0.208397\pi$
$419$			24.9286i			1.21784i	−0.793232	+	0.608920i	$0.791603\pi$
$420$		0			0
$421$	−1.70359	+	10.7560i	−0.0830279	+	0.524217i	0.910761	+	0.412934i	$0.135496\pi$
$421$	−1.70359	+	10.7560i	−0.0830279	+	0.524217i	−0.993789	+	0.111283i	$0.964504\pi$
$422$		0			0
$423$	−2.91861	−	5.72809i	−0.141908	−	0.278509i
$424$		0			0
$425$	0.715005	+	4.51436i	0.0346828	+	0.218979i
$426$		0			0
$427$	7.93736	+	1.25715i	0.384116	+	0.0608380i
$428$		0			0
$429$	13.2935	−	26.0899i	0.641816	−	1.25963i
$430$		0			0
$431$	18.5078	−	6.01355i	0.891490	−	0.289663i	0.172770	−	0.984962i	$-0.444728\pi$
$431$	18.5078	−	6.01355i	0.891490	−	0.289663i	0.718720	+	0.695300i	$0.244728\pi$
$432$		0			0
$433$	−1.43880	+	4.42816i	−0.0691441	+	0.212804i	−0.979658	−	0.200675i	$-0.935686\pi$
$433$	−1.43880	+	4.42816i	−0.0691441	+	0.212804i	0.910514	+	0.413479i	$0.135686\pi$
$434$		0			0
$435$	−10.0037	−	30.7883i	−0.479642	−	1.47618i
$436$		0			0
$437$	22.2217	+	22.2217i	1.06301	+	1.06301i
$438$		0			0
$439$	−12.3177	+	1.95093i	−0.587891	+	0.0931127i	−0.443291	−	0.896378i	$-0.646189\pi$
$439$	−12.3177	+	1.95093i	−0.587891	+	0.0931127i	−0.144599	+	0.989490i	$0.546189\pi$
$440$		0			0
$441$	−8.36849	+	6.08007i	−0.398500	+	0.289527i
$442$		0			0
$443$	−8.10317	−	11.1531i	−0.384993	−	0.529897i	0.571906	−	0.820319i	$-0.306204\pi$
$443$	−8.10317	−	11.1531i	−0.384993	−	0.529897i	−0.956899	+	0.290422i	$0.906204\pi$
$444$		0			0
$445$	−3.86291	+	1.96825i	−0.183120	+	0.0933041i
$446$		0			0
$447$	9.63853	+	7.00280i	0.455887	+	0.331221i
$448$		0			0
$449$	−5.07254	−	1.64817i	−0.239388	−	0.0777819i	0.186866	−	0.982385i	$-0.440167\pi$
$449$	−5.07254	−	1.64817i	−0.239388	−	0.0777819i	−0.426254	+	0.904604i	$0.640167\pi$
$450$		0			0
$451$	9.34576	+	31.7198i	0.440075	+	1.49363i
$452$		0			0
$453$	−7.06929	−	2.29695i	−0.332144	−	0.107920i
$454$		0			0
$455$	6.06381	+	4.40562i	0.284276	+	0.206539i
$456$		0			0
$457$	−9.05273	+	4.61259i	−0.423469	+	0.215768i	−0.652720	−	0.757599i	$-0.726372\pi$
$457$	−9.05273	+	4.61259i	−0.423469	+	0.215768i	0.229251	+	0.973367i	$0.426372\pi$
$458$		0			0
$459$	−4.73078	−	6.51136i	−0.220814	−	0.303924i
$460$		0			0
$461$	−24.0238	+	17.4543i	−1.11890	+	0.812927i	−0.984042	−	0.177938i	$-0.943057\pi$
$461$	−24.0238	+	17.4543i	−1.11890	+	0.812927i	−0.134856	+	0.990865i	$0.543057\pi$
$462$		0			0
$463$	−37.9429	+	6.00956i	−1.76336	+	0.279288i	−0.952185	−	0.305521i	$-0.901169\pi$
$463$	−37.9429	+	6.00956i	−1.76336	+	0.279288i	−0.811171	+	0.584809i	$0.801169\pi$
$464$		0			0
$465$	17.8464	+	17.8464i	0.827607	+	0.827607i
$466$		0			0
$467$	−0.851187	−	2.61968i	−0.0393882	−	0.121224i	0.929429	−	0.369001i	$-0.120300\pi$
$467$	−0.851187	−	2.61968i	−0.0393882	−	0.121224i	−0.968817	+	0.247777i	$0.920300\pi$
$468$		0			0
$469$	−1.88188	+	5.79183i	−0.0868971	+	0.267442i
$470$		0			0
$471$	−21.1093	+	6.85882i	−0.972664	+	0.316038i
$472$		0			0
$473$	−4.33134	+	8.50073i	−0.199155	+	0.390864i
$474$		0			0
$475$	12.0219	+	1.90408i	0.551601	+	0.0873651i
$476$		0			0
$477$	1.58841	+	10.0289i	0.0727285	+	0.459190i
$478$		0			0
$479$	−16.3580	−	32.1043i	−0.747415	−	1.46688i	−0.879628	−	0.475663i	$-0.842208\pi$
$479$	−16.3580	−	32.1043i	−0.747415	−	1.46688i	0.132213	−	0.991221i	$-0.457792\pi$
$480$		0			0
$481$	−0.291872	+	1.84281i	−0.0133082	+	0.0840247i
$482$		0			0
$483$		−	9.53831i		−	0.434008i
$484$		0			0
$485$	9.96656	+	5.07822i	0.452558	+	0.230590i
$486$		0			0
$487$	8.99982	−	12.3872i	0.407821	−	0.561317i	−0.554865	−	0.831941i	$-0.687230\pi$
$487$	8.99982	−	12.3872i	0.407821	−	0.561317i	0.962685	+	0.270624i	$0.0872300\pi$
$488$		0			0
$489$	−29.0800	+	29.0800i	−1.31505	+	1.31505i
$490$		0			0
$491$	−8.39830			−0.379010			−0.189505	−	0.981880i	$-0.560688\pi$
$491$	−8.39830			−0.379010			−0.189505	+	0.981880i	$0.560688\pi$
$492$		0			0
$493$	−17.9354			−0.807769
$494$		0			0
$495$	−16.8627	+	16.8627i	−0.757924	+	0.757924i
$496$		0			0
$497$	−3.03527	+	4.17769i	−0.136150	+	0.187395i
$498$		0			0
$499$	−6.86475	−	3.49776i	−0.307308	−	0.156581i	0.293535	−	0.955948i	$-0.405168\pi$
$499$	−6.86475	−	3.49776i	−0.307308	−	0.156581i	−0.600843	+	0.799367i	$0.705168\pi$
$500$		0			0
$501$			6.70961i			0.299763i
$502$		0			0
$503$	−2.90709	+	18.3546i	−0.129621	+	0.818392i	0.834126	+	0.551574i	$0.185972\pi$
$503$	−2.90709	+	18.3546i	−0.129621	+	0.818392i	−0.963747	+	0.266818i	$0.914028\pi$
$504$		0			0
$505$	−3.57720	−	7.02064i	−0.159183	−	0.312414i
$506$		0			0
$507$	−2.17017	−	13.7019i	−0.0963806	−	0.608523i
$508$		0			0
$509$	−17.4808	−	2.76869i	−0.774823	−	0.122720i	−0.243513	−	0.969898i	$-0.578300\pi$
$509$	−17.4808	−	2.76869i	−0.774823	−	0.122720i	−0.531310	+	0.847178i	$0.678300\pi$
$510$		0			0
$511$	0.0775257	−	0.152153i	0.00342954	−	0.00673085i
$512$		0			0
$513$	−20.3843	+	6.62326i	−0.899989	+	0.292424i
$514$		0			0
$515$	−2.31837	+	7.13522i	−0.102160	+	0.314415i
$516$		0			0
$517$	−5.65455	−	17.4029i	−0.248687	−	0.765379i
$518$		0			0
$519$	16.4300	+	16.4300i	0.721196	+	0.721196i
$520$		0			0
$521$	−25.2617	+	4.00106i	−1.10673	+	0.175289i	−0.682944	−	0.730471i	$-0.739301\pi$
$521$	−25.2617	+	4.00106i	−1.10673	+	0.175289i	−0.423790	+	0.905760i	$0.639301\pi$
$522$		0			0
$523$	−21.3827	+	15.5354i	−0.934998	+	0.679316i	−0.947211	−	0.320609i	$-0.896112\pi$
$523$	−21.3827	+	15.5354i	−0.934998	+	0.679316i	0.0122132	+	0.999925i	$0.496112\pi$
$524$		0			0
$525$	−2.17145	−	2.98875i	−0.0947699	−	0.130440i
$526$		0			0
$527$	12.4589	−	6.34811i	0.542717	−	0.276528i
$528$		0			0
$529$	6.83700	+	4.96737i	0.297261	+	0.215973i
$530$		0			0
$531$	1.35562	+	0.440466i	0.0588287	+	0.0191146i
$532$		0			0
$533$	−13.1123	−	10.0917i	−0.567958	−	0.437122i
$534$		0			0
$535$	8.19747	+	2.66352i	0.354407	+	0.115154i
$536$		0			0
$537$	3.39001	+	2.46299i	0.146290	+	0.106286i
$538$		0			0
$539$	−26.2335	+	13.3667i	−1.12996	+	0.575743i
$540$		0			0
$541$	11.1474	+	15.3431i	0.479266	+	0.659653i	0.978364	−	0.206893i	$-0.0663351\pi$
$541$	11.1474	+	15.3431i	0.479266	+	0.659653i	−0.499098	+	0.866546i	$0.666335\pi$
$542$		0			0
$543$	−10.4631	+	7.60188i	−0.449014	+	0.326228i
$544$		0			0
$545$	34.3296	−	5.43728i	1.47052	−	0.232907i
$546$		0			0
$547$	−11.0744	−	11.0744i	−0.473506	−	0.473506i	0.429541	−	0.903047i	$-0.358675\pi$
$547$	−11.0744	−	11.0744i	−0.473506	−	0.473506i	−0.903047	+	0.429541i	$0.858675\pi$
$548$		0			0
$549$	−3.95352	−	12.1677i	−0.168732	−	0.519304i
$550$		0			0
$551$	−14.7594	+	45.4247i	−0.628771	+	1.93516i
$552$		0			0
$553$	17.5344	−	5.69727i	0.745638	−	0.242273i
$554$		0			0
$555$	1.83050	−	3.59255i	0.0777002	−	0.152495i
$556$		0			0
$557$	30.3636	+	4.80913i	1.28655	+	0.203769i	0.761981	−	0.647600i	$-0.224227\pi$
$557$	30.3636	+	4.80913i	1.28655	+	0.203769i	0.524567	+	0.851369i	$0.324227\pi$
$558$		0			0
$559$	−0.746789	−	4.71504i	−0.0315858	−	0.199425i
$560$		0			0
$561$	15.9160	+	31.2368i	0.671973	+	1.31882i
$562$		0			0
$563$	3.47564	−	21.9443i	0.146481	−	0.924844i	−0.799510	−	0.600652i	$-0.794908\pi$
$563$	3.47564	−	21.9443i	0.146481	−	0.924844i	0.945991	−	0.324192i	$-0.105092\pi$
$564$		0			0
$565$			33.7119i			1.41827i
$566$		0			0
$567$	11.3236	+	5.76967i	0.475547	+	0.242303i
$568$		0			0
$569$	2.76582	−	3.80682i	0.115949	−	0.159590i	−0.747098	−	0.664714i	$-0.768553\pi$
$569$	2.76582	−	3.80682i	0.115949	−	0.159590i	0.863047	+	0.505124i	$0.168553\pi$
$570$		0			0
$571$	−9.49358	+	9.49358i	−0.397294	+	0.397294i	−0.877278	−	0.479983i	$-0.840643\pi$
$571$	−9.49358	+	9.49358i	−0.397294	+	0.397294i	0.479983	+	0.877278i	$0.340643\pi$
$572$		0			0
$573$	6.93828			0.289851
$574$		0			0
$575$	−5.63499			−0.234995
$576$		0			0
$577$	−11.7501	+	11.7501i	−0.489162	+	0.489162i	−0.908042	−	0.418880i	$-0.862423\pi$
$577$	−11.7501	+	11.7501i	−0.489162	+	0.489162i	0.418880	+	0.908042i	$0.362423\pi$
$578$		0			0
$579$	20.3665	−	28.0321i	0.846403	−	1.16497i
$580$		0			0
$581$	−4.33866	−	2.21066i	−0.179998	−	0.0917135i
$582$		0			0
$583$			28.9013i			1.19697i
$584$		0			0
$585$	1.86666	−	11.7856i	0.0771770	−	0.487276i
$586$		0			0
$587$	11.9109	+	23.3764i	0.491615	+	0.964849i	0.994913	+	0.100736i	$0.0321197\pi$
$587$	11.9109	+	23.3764i	0.491615	+	0.964849i	−0.503298	+	0.864113i	$0.667880\pi$
$588$		0			0
$589$	−5.82513	−	36.7784i	−0.240020	−	1.51543i
$590$		0			0
$591$	9.85018	+	1.56012i	0.405182	+	0.0641746i
$592$		0			0
$593$	1.10491	−	2.16850i	0.0453730	−	0.0890496i	−0.867207	−	0.497948i	$-0.834087\pi$
$593$	1.10491	−	2.16850i	0.0453730	−	0.0890496i	0.912580	+	0.408898i	$0.134087\pi$
$594$		0			0
$595$	−8.53470	+	2.77309i	−0.349889	+	0.113686i
$596$		0			0
$597$	−6.09129	+	18.7471i	−0.249300	+	0.767266i
$598$		0			0
$599$	−5.18017	−	15.9429i	−0.211656	−	0.651410i	−0.999374	−	0.0353745i	$-0.988738\pi$
$599$	−5.18017	−	15.9429i	−0.211656	−	0.651410i	0.787718	−	0.616036i	$-0.211262\pi$
$600$		0			0
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	0.509256	−	0.860615i	$-0.329921\pi$
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	−0.860615	+	0.509256i	$0.829921\pi$
$602$		0			0
$603$	9.57579	−	1.51666i	0.389956	−	0.0617630i
$604$		0			0
$605$	−32.2656	+	23.4423i	−1.31178	+	0.953065i
$606$		0			0
$607$	−2.60922	−	3.59129i	−0.105905	−	0.145766i	0.752775	−	0.658278i	$-0.228715\pi$
$607$	−2.60922	−	3.59129i	−0.105905	−	0.145766i	−0.858680	+	0.512512i	$0.828715\pi$
$608$		0			0
$609$	12.9165	−	6.58131i	0.523405	−	0.266688i
$610$		0			0
$611$	7.40736	+	5.38176i	0.299670	+	0.217723i
$612$		0			0
$613$	45.1753	+	14.6783i	1.82461	+	0.592852i	0.999616	+	0.0277136i	$0.00882263\pi$
$613$	45.1753	+	14.6783i	1.82461	+	0.592852i	0.824996	+	0.565139i	$0.191177\pi$
$614$		0			0
$615$	20.2101	+	29.4976i	0.814951	+	1.18946i
$616$		0			0
$617$	−35.6237	−	11.5748i	−1.43416	−	0.465985i	−0.514086	−	0.857739i	$-0.671869\pi$
$617$	−35.6237	−	11.5748i	−1.43416	−	0.465985i	−0.920070	+	0.391753i	$0.871869\pi$
$618$		0			0
$619$	12.2778	+	8.92032i	0.493485	+	0.358538i	0.806523	−	0.591203i	$-0.201347\pi$
$619$	12.2778	+	8.92032i	0.493485	+	0.358538i	−0.313038	+	0.949741i	$0.601347\pi$
$620$		0			0
$621$	8.84121	−	4.50482i	0.354785	−	0.180772i
$622$		0			0
$623$	−1.14114	−	1.57064i	−0.0457188	−	0.0629265i
$624$		0			0
$625$	24.4357	−	17.7535i	0.977427	−	0.710142i
$626$		0			0
$627$	92.2107	−	14.6047i	3.68254	−	0.583257i
$628$		0			0
$629$	−1.57957	−	1.57957i	−0.0629816	−	0.0629816i
$630$		0			0
$631$	1.82817	+	5.62652i	0.0727782	+	0.223988i	0.980829	−	0.194873i	$-0.0624294\pi$
$631$	1.82817	+	5.62652i	0.0727782	+	0.223988i	−0.908050	+	0.418861i	$0.862429\pi$
$632$		0			0
$633$	−4.38002	+	13.4803i	−0.174090	+	0.535795i
$634$		0			0
$635$	32.7043	−	10.6263i	1.29783	−	0.421691i
$636$		0			0
$637$	6.68826	−	13.1264i	0.264999	−	0.520089i
$638$		0			0
$639$	8.11977	+	1.28604i	0.321213	+	0.0508751i
$640$		0			0
$641$	−5.46005	−	34.4734i	−0.215659	−	1.36162i	−0.823391	−	0.567475i	$-0.807920\pi$
$641$	−5.46005	−	34.4734i	−0.215659	−	1.36162i	0.607732	−	0.794143i	$-0.292080\pi$
$642$		0			0
$643$	14.6680	+	28.7876i	0.578451	+	1.13527i	0.976016	+	0.217700i	$0.0698553\pi$
$643$	14.6680	+	28.7876i	0.578451	+	1.13527i	−0.397565	+	0.917574i	$0.630145\pi$
$644$		0			0
$645$	−1.61384	+	10.1894i	−0.0635448	+	0.401206i
$646$		0			0
$647$			0.686839i			0.0270024i	0.999909	+	0.0135012i	$0.00429770\pi$
$647$			0.686839i			0.0270024i	−0.999909	+	0.0135012i	$0.995702\pi$
$648$		0			0
$649$	3.61491	+	1.84189i	0.141898	+	0.0723004i
$650$		0			0
$651$	−6.64310	+	9.14344i	−0.260364	+	0.358360i
$652$		0			0
$653$	33.7065	−	33.7065i	1.31904	−	1.31904i	0.404500	−	0.914538i	$-0.367446\pi$
$653$	33.7065	−	33.7065i	1.31904	−	1.31904i	0.914538	−	0.404500i	$-0.132554\pi$
$654$		0			0
$655$	−26.0454			−1.01768
$656$		0			0
$657$	−0.271859			−0.0106062
$658$		0			0
$659$	−31.4326	+	31.4326i	−1.22444	+	1.22444i	−0.258404	+	0.966037i	$0.583197\pi$
$659$	−31.4326	+	31.4326i	−1.22444	+	1.22444i	−0.966037	+	0.258404i	$0.916803\pi$
$660$		0			0
$661$	−14.1153	+	19.4280i	−0.549020	+	0.755662i	−0.989879	−	0.141915i	$-0.954674\pi$
$661$	−14.1153	+	19.4280i	−0.549020	+	0.755662i	0.440859	+	0.897577i	$0.354674\pi$
$662$		0			0
$663$	−15.6299	−	7.96385i	−0.607017	−	0.309290i
$664$		0			0
$665$			23.8978i			0.926716i
$666$		0			0
$667$	3.45907	−	21.8397i	0.133936	−	0.845638i
$668$		0			0
$669$	−4.07707	−	8.00170i	−0.157629	−	0.309364i
$670$		0			0
$671$	−5.69666	−	35.9673i	−0.219917	−	1.38850i
$672$		0			0
$673$	15.1756	+	2.40357i	0.584975	+	0.0926510i	0.441906	−	0.897062i	$-0.354303\pi$
$673$	15.1756	+	2.40357i	0.584975	+	0.0926510i	0.143070	+	0.989713i	$0.454303\pi$
$674$		0			0
$675$	1.74477	−	3.42430i	0.0671561	−	0.131801i
$676$		0			0
$677$	−30.7055	+	9.97682i	−1.18011	+	0.383440i	−0.832407	−	0.554165i	$-0.813038\pi$
$677$	−30.7055	+	9.97682i	−1.18011	+	0.383440i	−0.347701	+	0.937605i	$0.613038\pi$
$678$		0			0
$679$	−1.54787	+	4.76384i	−0.0594016	+	0.182819i
$680$		0			0
$681$	−0.389319	−	1.19820i	−0.0149187	−	0.0459152i
$682$		0			0
$683$	−11.8785	−	11.8785i	−0.454518	−	0.454518i	0.442333	−	0.896851i	$-0.354151\pi$
$683$	−11.8785	−	11.8785i	−0.454518	−	0.454518i	−0.896851	+	0.442333i	$0.854151\pi$
$684$		0			0
$685$	14.4273	−	2.28507i	0.551240	−	0.0873079i
$686$		0			0
$687$	−42.6699	+	31.0015i	−1.62796	+	1.18278i
$688$		0			0
$689$	−8.50015	−	11.6995i	−0.323830	−	0.445714i
$690$		0			0
$691$	23.1214	−	11.7810i	0.879581	−	0.448169i	0.0449572	−	0.998989i	$-0.485685\pi$
$691$	23.1214	−	11.7810i	0.879581	−	0.448169i	0.834624	+	0.550820i	$0.185685\pi$
$692$		0			0
$693$	−8.63947	−	6.27694i	−0.328186	−	0.238441i
$694$		0			0
$695$	39.0332	+	12.6826i	1.48061	+	0.481080i
$696$		0			0
$697$	19.0027	−	5.59885i	0.719778	−	0.212072i
$698$		0			0
$699$	−25.9051	−	8.41708i	−0.979821	−	0.318363i
$700$		0			0
$701$	22.0790	+	16.0413i	0.833911	+	0.605872i	0.920663	−	0.390358i	$-0.127649\pi$
$701$	22.0790	+	16.0413i	0.833911	+	0.605872i	−0.0867523	+	0.996230i	$0.527649\pi$
$702$		0			0
$703$	−5.30042	+	2.70070i	−0.199909	+	0.101859i
$704$		0			0
$705$	−11.6302	−	16.0076i	−0.438018	−	0.602880i
$706$		0			0
$707$	2.85456	−	2.07396i	0.107357	−	0.0779994i
$708$		0			0
$709$	−44.8571	+	7.10466i	−1.68464	+	0.266821i	−0.924012	−	0.382364i	$-0.875110\pi$
$709$	−44.8571	+	7.10466i	−1.68464	+	0.266821i	−0.760631	+	0.649185i	$0.775110\pi$
$710$		0			0
$711$	−20.7546	−	20.7546i	−0.778359	−	0.778359i
$712$		0			0
$713$	5.32717	+	16.3953i	0.199504	+	0.614010i
$714$		0			0
$715$	10.4955	−	32.3018i	0.392509	−	1.20802i
$716$		0			0
$717$	14.1574	−	4.60002i	0.528719	−	0.171791i
$718$		0			0
$719$	12.6131	−	24.7546i	0.470390	−	0.923192i	−0.526922	−	0.849914i	$-0.676654\pi$
$719$	12.6131	−	24.7546i	0.470390	−	0.923192i	0.997312	−	0.0732784i	$-0.0233462\pi$
$720$		0			0
$721$	−3.31824	−	0.525557i	−0.123578	−	0.0195728i
$722$		0			0
$723$	6.58297	+	41.5633i	0.244823	+	1.54575i
$724$		0			0
$725$	−3.88807	−	7.63077i	−0.144399	−	0.283400i
$726$		0			0
$727$	2.75993	−	17.4255i	0.102360	−	0.646276i	−0.882153	−	0.470963i	$-0.843906\pi$
$727$	2.75993	−	17.4255i	0.102360	−	0.646276i	0.984513	−	0.175313i	$-0.0560936\pi$
$728$		0			0
$729$		−	3.10848i		−	0.115129i
$730$		0			0
$731$	5.09261	+	2.59481i	0.188357	+	0.0959726i
$732$		0			0
$733$	−5.53747	+	7.62168i	−0.204531	+	0.281513i	−0.898944	−	0.438064i	$-0.855664\pi$
$733$	−5.53747	+	7.62168i	−0.204531	+	0.281513i	0.694413	+	0.719577i	$0.255664\pi$
$734$		0			0
$735$	−22.5120	+	22.5120i	−0.830367	+	0.830367i
$736$		0			0
$737$	27.5957			1.01650
$738$		0			0
$739$	−0.347492			−0.0127827			−0.00639135	−	0.999980i	$-0.502034\pi$
$739$	−0.347492			−0.0127827			−0.00639135	+	0.999980i	$0.502034\pi$
$740$		0			0
$741$	−33.0322	+	33.0322i	−1.21347	+	1.21347i
$742$		0			0
$743$	−4.23794	+	5.83302i	−0.155475	+	0.213993i	−0.879648	−	0.475626i	$-0.842222\pi$
$743$	−4.23794	+	5.83302i	−0.155475	+	0.213993i	0.724173	+	0.689618i	$0.242222\pi$
$744$		0			0
$745$	12.3129	+	6.27375i	0.451111	+	0.229853i
$746$		0			0
$747$			7.75210i			0.283635i
$748$		0			0
$749$	−0.603799	+	3.81223i	−0.0220623	+	0.139296i
$750$		0			0
$751$	−8.85526	−	17.3794i	−0.323133	−	0.634184i	0.671107	−	0.741361i	$-0.265819\pi$
$751$	−8.85526	−	17.3794i	−0.323133	−	0.634184i	−0.994240	+	0.107176i	$0.965819\pi$
$752$		0			0
$753$	0.647060	+	4.08538i	0.0235802	+	0.148879i
$754$		0			0
$755$	−8.51564	−	1.34874i	−0.309916	−	0.0490858i
$756$		0			0
$757$	−7.98828	+	15.6779i	−0.290339	+	0.569823i	−0.989396	−	0.145244i	$-0.953603\pi$
$757$	−7.98828	+	15.6779i	−0.290339	+	0.569823i	0.699057	+	0.715066i	$0.253603\pi$
$758$		0			0
$759$	−41.1064	+	13.3563i	−1.49207	+	0.484802i
$760$		0			0
$761$	7.86010	−	24.1909i	0.284928	−	0.876919i	−0.701492	−	0.712678i	$-0.747482\pi$
$761$	7.86010	−	24.1909i	0.284928	−	0.876919i	0.986420	−	0.164242i	$-0.0525177\pi$
$762$		0			0
$763$	4.80970	+	14.8027i	0.174123	+	0.535895i
$764$		0			0
$765$	10.1021	+	10.1021i	0.365243	+	0.365243i
$766$		0			0
$767$	−2.00506	+	0.317570i	−0.0723984	+	0.0114668i
$768$		0			0
$769$	−10.8491	+	7.88236i	−0.391230	+	0.284245i	−0.765959	−	0.642889i	$-0.777736\pi$
$769$	−10.8491	+	7.88236i	−0.391230	+	0.284245i	0.374729	+	0.927134i	$0.377736\pi$
$770$		0			0
$771$	−36.1001	−	49.6875i	−1.30011	−	1.78945i
$772$		0			0
$773$	33.8688	−	17.2570i	1.21817	−	0.620691i	0.277737	−	0.960657i	$-0.410416\pi$
$773$	33.8688	−	17.2570i	1.21817	−	0.620691i	0.940438	+	0.339966i	$0.110416\pi$
$774$		0			0
$775$	5.40172	+	3.92458i	0.194035	+	0.140975i
$776$		0			0
$777$	1.71718	+	0.557944i	0.0616033	+	0.0200161i
$778$		0			0
$779$	1.45757	−	52.7353i	0.0522228	−	1.88944i
$780$		0			0
$781$	22.2544	+	7.23090i	0.796326	+	0.258742i
$782$		0			0
$783$	12.2006	+	8.86428i	0.436015	+	0.316784i
$784$		0			0
$785$	−22.9390	+	11.6880i	−0.818729	+	0.417163i
$786$		0			0
$787$	28.9010	+	39.7788i	1.03021	+	1.41796i	0.904791	+	0.425856i	$0.140027\pi$
$787$	28.9010	+	39.7788i	1.03021	+	1.41796i	0.125417	+	0.992104i	$0.459973\pi$
$788$		0			0
$789$	−7.34812	+	5.33872i	−0.261600	+	0.190063i
$790$		0			0
$791$	−14.9104	+	2.36157i	−0.530152	+	0.0839679i
$792$		0			0
$793$	12.8844	+	12.8844i	0.457537	+	0.457537i
$794$		0			0
$795$	9.65723	+	29.7219i	0.342507	+	1.05413i
$796$		0			0
$797$	1.66232	−	5.11611i	0.0588825	−	0.181222i	−0.917289	−	0.398222i	$-0.869627\pi$
$797$	1.66232	−	5.11611i	0.0588825	−	0.181222i	0.976172	+	0.217000i	$0.0696273\pi$
$798$		0			0
$799$	−10.4257	+	3.38752i	−0.368836	+	0.119842i
$800$		0			0
$801$	−1.40318	+	2.75389i	−0.0495788	+	0.0973038i
$802$		0			0
$803$	−0.764277	−	0.121050i	−0.0269707	−	0.00427175i
$804$		0			0
$805$	−1.73074	−	10.9274i	−0.0610005	−	0.385142i
$806$		0			0
$807$	29.6437	+	58.1789i	1.04351	+	2.04800i
$808$		0			0
$809$	−4.90251	+	30.9532i	−0.172363	+	1.08826i	0.738107	+	0.674683i	$0.235720\pi$
$809$	−4.90251	+	30.9532i	−0.172363	+	1.08826i	−0.910470	+	0.413574i	$0.864280\pi$
$810$		0			0
$811$			18.8699i			0.662610i	0.943524	+	0.331305i	$0.107489\pi$
$811$			18.8699i			0.662610i	−0.943524	+	0.331305i	$0.892511\pi$
$812$		0			0
$813$	−45.3384	−	23.1011i	−1.59009	−	0.810189i
$814$		0			0
$815$	−28.0386	+	38.5918i	−0.982149	+	1.35181i
$816$		0			0
$817$	10.7627	−	10.7627i	0.376538	−	0.376538i
$818$		0			0
$819$	5.34342			0.186714
$820$		0			0
$821$	1.59911			0.0558094			0.0279047	−	0.999611i	$-0.491117\pi$
$821$	1.59911			0.0558094			0.0279047	+	0.999611i	$0.491117\pi$
$822$		0			0
$823$	18.3789	−	18.3789i	0.640647	−	0.640647i	−0.310068	−	0.950715i	$-0.600352\pi$
$823$	18.3789	−	18.3789i	0.640647	−	0.640647i	0.950715	+	0.310068i	$0.100352\pi$
$824$		0			0
$825$	−9.83969	+	13.5432i	−0.342574	+	0.471513i
$826$		0			0
$827$	−7.57401	−	3.85915i	−0.263374	−	0.134196i	0.317318	−	0.948319i	$-0.397218\pi$
$827$	−7.57401	−	3.85915i	−0.263374	−	0.134196i	−0.580692	+	0.814124i	$0.697218\pi$
$828$		0			0
$829$		−	0.285264i		−	0.00990764i	−0.999988	−	0.00495382i	$-0.998423\pi$
$829$		−	0.285264i		−	0.00990764i	0.999988	−	0.00495382i	$-0.00157686\pi$
$830$		0			0
$831$	8.50106	−	53.6736i	0.294898	−	1.86192i
$832$		0			0
$833$	8.00769	+	15.7160i	0.277450	+	0.544526i
$834$		0			0
$835$	1.21747	+	7.68678i	0.0421322	+	0.266012i
$836$		0			0
$837$	−11.6127	−	1.83926i	−0.401392	−	0.0635743i
$838$		0			0
$839$	5.30778	−	10.4171i	0.183245	−	0.359638i	−0.781050	−	0.624468i	$-0.785316\pi$
$839$	5.30778	−	10.4171i	0.183245	−	0.359638i	0.964295	+	0.264830i	$0.0853157\pi$
$840$		0			0
$841$	4.38091	−	1.42344i	0.151066	−	0.0490843i
$842$		0			0
$843$	−0.144192	+	0.443776i	−0.00496622	+	0.0152845i
$844$		0			0
$845$	−4.97246	−	15.3036i	−0.171058	−	0.526461i
$846$		0			0
$847$	−12.6285	−	12.6285i	−0.433921	−	0.433921i
$848$		0			0
$849$	−23.9119	+	3.78727i	−0.820653	+	0.129979i
$850$		0			0
$851$	2.22807	−	1.61878i	0.0763771	−	0.0554912i
$852$		0			0
$853$	−14.3175	−	19.7064i	−0.490223	−	0.674734i	0.490206	−	0.871607i	$-0.336921\pi$
$853$	−14.3175	−	19.7064i	−0.490223	−	0.674734i	−0.980429	+	0.196873i	$0.936921\pi$
$854$		0			0
$855$	33.8987	−	17.2723i	1.15931	−	0.590699i
$856$		0			0
$857$	−4.13061	−	3.00106i	−0.141099	−	0.102514i	0.514997	−	0.857192i	$-0.327793\pi$
$857$	−4.13061	−	3.00106i	−0.141099	−	0.102514i	−0.656096	+	0.754678i	$0.727793\pi$
$858$		0			0
$859$	−0.384709	−	0.125000i	−0.0131261	−	0.00426493i	0.302447	−	0.953166i	$-0.402197\pi$
$859$	−0.384709	−	0.125000i	−0.0131261	−	0.00426493i	−0.315573	+	0.948901i	$0.602197\pi$
$860$		0			0
$861$	−11.6307	+	11.0051i	−0.396374	+	0.375052i
$862$		0			0
$863$	−36.1033	−	11.7307i	−1.22897	−	0.399316i	−0.378629	−	0.925549i	$-0.623604\pi$
$863$	−36.1033	−	11.7307i	−1.22897	−	0.399316i	−0.850341	+	0.526232i	$0.823604\pi$
$864$		0			0
$865$	21.8041	+	15.8416i	0.741360	+	0.538630i
$866$		0			0
$867$	−14.5220	+	7.39933i	−0.493193	+	0.251294i
$868$		0			0
$869$	−49.1060	−	67.5886i	−1.66581	−	2.29279i
$870$		0			0
$871$	−11.1709	+	8.11615i	−0.378512	+	0.275005i
$872$		0			0
$873$	7.87618	−	1.24747i	0.266568	−	0.0422203i
$874$		0			0
$875$	7.22503	+	7.22503i	0.244250	+	0.244250i
$876$		0			0
$877$	11.4052	+	35.1015i	0.385125	+	1.18529i	0.936389	+	0.350963i	$0.114146\pi$
$877$	11.4052	+	35.1015i	0.385125	+	1.18529i	−0.551264	+	0.834331i	$0.685854\pi$
$878$		0			0
$879$	5.15932	−	15.8788i	0.174020	−	0.535577i
$880$		0			0
$881$	−10.6200	+	3.45065i	−0.357798	+	0.116255i	−0.482399	−	0.875951i	$-0.660235\pi$
$881$	−10.6200	+	3.45065i	−0.357798	+	0.116255i	0.124602	+	0.992207i	$0.460235\pi$
$882$		0			0
$883$	10.6504	−	20.9026i	0.358415	−	0.703429i	−0.639444	−	0.768838i	$-0.720835\pi$
$883$	10.6504	−	20.9026i	0.358415	−	0.703429i	0.997859	+	0.0654092i	$0.0208353\pi$
$884$		0			0
$885$	4.33300	+	0.686280i	0.145652	+	0.0230691i
$886$		0			0
$887$	−4.35893	−	27.5212i	−0.146358	−	0.924071i	−0.946135	−	0.323773i	$-0.895049\pi$
$887$	−4.35893	−	27.5212i	−0.146358	−	0.924071i	0.799776	−	0.600298i	$-0.204951\pi$
$888$		0			0
$889$	6.99088	+	13.7204i	0.234467	+	0.460166i
$890$		0			0
$891$	9.00883	−	56.8795i	0.301807	−	1.90554i
$892$		0			0
$893$			29.1928i			0.976899i
$894$		0			0
$895$	4.33064	+	2.20657i	0.144757	+	0.0737576i
$896$		0			0
$897$	12.7119	−	17.4965i	0.424439	−	0.584190i
$898$		0			0
$899$	−18.5265	+	18.5265i	−0.617893	+	0.617893i
$900$		0			0
$901$	17.3142			0.576819
$902$		0			0
$903$	−4.61970			−0.153734
$904$		0			0
$905$	−10.6075	+	10.6075i	−0.352607	+	0.352607i
$906$		0			0
$907$	−22.2821	+	30.6687i	−0.739865	+	1.01834i	0.258761	+	0.965941i	$0.416686\pi$
$907$	−22.2821	+	30.6687i	−0.739865	+	1.01834i	−0.998626	+	0.0523958i	$0.983314\pi$
$908$		0			0
$909$	−5.00505	−	2.55020i	−0.166007	−	0.0845848i
$910$		0			0
$911$			23.3777i			0.774537i	0.921967	+	0.387269i	$0.126581\pi$
$911$			23.3777i			0.774537i	−0.921967	+	0.387269i	$0.873419\pi$
$912$		0			0
$913$	−3.45174	+	21.7934i	−0.114236	+	0.721258i
$914$		0			0
$915$	−17.8767	−	35.0850i	−0.590985	−	1.15987i
$916$		0			0
$917$	−1.82452	−	11.5196i	−0.0602510	−	0.380410i
$918$		0			0
$919$	−19.4344	−	3.07810i	−0.641080	−	0.101537i	−0.172573	−	0.984997i	$-0.555208\pi$
$919$	−19.4344	−	3.07810i	−0.641080	−	0.101537i	−0.468507	+	0.883460i	$0.655208\pi$
$920$		0			0
$921$	31.2921	−	61.4141i	1.03111	−	2.02366i
$922$		0			0
$923$	−11.1354	+	3.61812i	−0.366527	+	0.119092i
$924$		0			0
$925$	0.329619	−	1.01446i	0.0108378	−	0.0333554i
$926$		0			0
$927$	1.65278	+	5.08673i	0.0542844	+	0.167070i
$928$		0			0
$929$	5.06327	+	5.06327i	0.166120	+	0.166120i	0.785272	−	0.619151i	$-0.212523\pi$
$929$	5.06327	+	5.06327i	0.166120	+	0.166120i	−0.619151	+	0.785272i	$0.712523\pi$
$930$		0			0
$931$	46.3933	−	7.34798i	1.52048	−	0.240820i
$932$		0			0
$933$	−26.1885	+	19.0271i	−0.857373	+	0.622918i
$934$		0			0
$935$	23.9019	+	32.8981i	0.781676	+	1.07588i
$936$		0			0
$937$	38.9861	−	19.8644i	1.27362	−	0.648942i	0.319280	−	0.947660i	$-0.396559\pi$
$937$	38.9861	−	19.8644i	1.27362	−	0.648942i	0.954341	+	0.298718i	$0.0965590\pi$
$938$		0			0
$939$	−29.4804	−	21.4187i	−0.962055	−	0.698974i
$940$		0			0
$941$	−24.9275	−	8.09943i	−0.812613	−	0.264034i	−0.126909	−	0.991914i	$-0.540506\pi$
$941$	−24.9275	−	8.09943i	−0.812613	−	0.264034i	−0.685704	+	0.727881i	$0.740506\pi$
$942$		0			0
$943$	3.15274	+	24.2192i	0.102667	+	0.788685i
$944$		0			0
$945$	7.17633	+	2.33173i	0.233446	+	0.0758513i
$946$		0			0
$947$	−26.7046	−	19.4020i	−0.867781	−	0.630480i	0.0622093	−	0.998063i	$-0.480185\pi$
$947$	−26.7046	−	19.4020i	−0.867781	−	0.630480i	−0.929991	+	0.367583i	$0.880185\pi$
$948$		0			0
$949$	0.344986	−	0.175779i	0.0111987	−	0.00570604i
$950$		0			0
$951$	−42.0072	−	57.8180i	−1.36218	−	1.87488i
$952$		0			0
$953$	−2.15205	+	1.56356i	−0.0697119	+	0.0506486i	−0.622095	−	0.782941i	$-0.713718\pi$
$953$	−2.15205	+	1.56356i	−0.0697119	+	0.0506486i	0.552384	+	0.833590i	$0.313718\pi$
$954$		0			0
$955$	7.94876	−	1.25896i	0.257216	−	0.0407390i
$956$		0			0
$957$	−46.4496	−	46.4496i	−1.50150	−	1.50150i
$958$		0			0
$959$	2.02132	+	6.22098i	0.0652718	+	0.200886i
$960$		0			0
$961$	−3.26738	+	10.0559i	−0.105399	+	0.324385i
$962$		0			0
$963$	5.84401	−	1.89884i	0.188321	−	0.0611891i
$964$		0			0
$965$	18.2462	−	35.8102i	0.587366	−	1.15277i
$966$		0			0
$967$	−12.8463	−	2.03466i	−0.413110	−	0.0654303i	−0.0535799	−	0.998564i	$-0.517063\pi$
$967$	−12.8463	−	2.03466i	−0.413110	−	0.0654303i	−0.359531	+	0.933133i	$0.617063\pi$
$968$		0			0
$969$	−8.74940	−	55.2415i	−0.281071	−	1.77461i
$970$		0			0
$971$	3.29747	+	6.47166i	0.105821	+	0.207685i	0.937845	−	0.347054i	$-0.112818\pi$
$971$	3.29747	+	6.47166i	0.105821	+	0.207685i	−0.832024	+	0.554739i	$0.812818\pi$
$972$		0			0
$973$	−2.87505	+	18.1524i	−0.0921700	+	0.581939i
$974$		0			0
$975$		−	8.37632i		−	0.268257i
$976$		0			0
$977$	26.7289	+	13.6190i	0.855132	+	0.435711i	0.825870	−	0.563860i	$-0.190684\pi$
$977$	26.7289	+	13.6190i	0.855132	+	0.435711i	0.0292617	+	0.999572i	$0.490684\pi$
$978$		0			0
$979$	−5.17095	+	7.11720i	−0.165264	+	0.227467i
$980$		0			0
$981$	17.5213	−	17.5213i	0.559411	−	0.559411i
$982$		0			0
$983$	47.8093			1.52488			0.762439	−	0.647060i	$-0.224002\pi$
$983$	47.8093			1.52488			0.762439	+	0.647060i	$0.224002\pi$
$984$		0			0
$985$	11.5678			0.368582
$986$		0			0
$987$	6.26526	−	6.26526i	0.199426	−	0.199426i
$988$		0			0
$989$	−4.14185	+	5.70077i	−0.131703	+	0.181274i
$990$		0			0
$991$	37.8416	+	19.2812i	1.20208	+	0.612489i	0.936183	−	0.351513i	$-0.114333\pi$
$991$	37.8416	+	19.2812i	1.20208	+	0.612489i	0.265894	+	0.964002i	$0.414333\pi$
$992$		0			0
$993$		−	4.13151i		−	0.131110i
$994$		0			0
$995$	−3.57673	+	22.5826i	−0.113390	+	0.715917i
$996$		0			0
$997$	−19.2309	−	37.7427i	−0.609048	−	1.19532i	−0.965351	−	0.260954i	$-0.915963\pi$
$997$	−19.2309	−	37.7427i	−0.609048	−	1.19532i	0.356303	−	0.934370i	$-0.384037\pi$
$998$		0			0
$999$	0.293833	+	1.85519i	0.00929646	+	0.0586955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.225.2		24
4.3	odd	2		41.2.g.a.20.3	✓	24
12.11	even	2		369.2.u.a.307.1		24
41.39	even	20	inner	656.2.bs.d.449.2		24
164.11	even	40		1681.2.a.m.1.15		24
164.39	odd	20		41.2.g.a.39.3	yes	24
164.71	even	40		1681.2.a.m.1.16		24
492.203	even	20		369.2.u.a.244.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.3	✓	24	4.3	odd	2
41.2.g.a.39.3	yes	24	164.39	odd	20
369.2.u.a.244.1		24	492.203	even	20
369.2.u.a.307.1		24	12.11	even	2
656.2.bs.d.225.2		24	1.1	even	1	trivial
656.2.bs.d.449.2		24	41.39	even	20	inner
1681.2.a.m.1.15		24	164.11	even	40
1681.2.a.m.1.16		24	164.71	even	40

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.55151 - 1.55151i) q^{3} +(1.49595 - 2.05900i) q^{5} +(1.01547 + 0.517405i) q^{7} -1.81438i q^{9} +O(q^{10})\)	\(q+(1.55151 - 1.55151i) q^{3} +(1.49595 - 2.05900i) q^{5} +(1.01547 + 0.517405i) q^{7} -1.81438i q^{9} +(0.807883 - 5.10077i) q^{11} +(1.17315 + 2.30243i) q^{13} +(-0.873576 - 5.51554i) q^{15} +(-3.05576 - 0.483986i) q^{17} +(-3.74044 + 7.34102i) q^{19} +(2.37827 - 0.772746i) q^{21} +(1.17869 - 3.62763i) q^{23} +(-0.456519 - 1.40502i) q^{25} +(1.83950 + 1.83950i) q^{27} +(5.72573 - 0.906866i) q^{29} +(-3.65641 + 2.65654i) q^{31} +(-6.66047 - 9.16735i) q^{33} +(2.58442 - 1.31683i) q^{35} +(0.584132 + 0.424397i) q^{37} +(5.39241 + 1.75210i) q^{39} +(-5.78336 + 2.74822i) q^{41} +(-1.75698 - 0.570876i) q^{43} +(-3.73581 - 2.71423i) q^{45} +(3.15704 - 1.60859i) q^{47} +(-3.35104 - 4.61230i) q^{49} +(-5.49197 + 3.99015i) q^{51} +(-5.52741 + 0.875456i) q^{53} +(-9.29392 - 9.29392i) q^{55} +(5.58635 + 17.1930i) q^{57} +(-0.242763 + 0.747149i) q^{59} +(6.70623 - 2.17898i) q^{61} +(0.938773 - 1.84244i) q^{63} +(6.49567 + 1.02881i) q^{65} +(0.835907 + 5.27771i) q^{67} +(-3.79956 - 7.45706i) q^{69} +(-0.708805 + 4.47522i) q^{71} -0.149836i q^{73} +(-2.88820 - 1.47161i) q^{75} +(3.45954 - 4.76165i) q^{77} +(11.4389 - 11.4389i) q^{79} +11.1512 q^{81} -4.27258 q^{83} +(-5.56779 + 5.56779i) q^{85} +(7.47653 - 10.2906i) q^{87} +(-1.51781 - 0.773362i) q^{89} +2.94503i q^{91} +(-1.55132 + 9.79463i) q^{93} +(9.51963 + 18.6833i) q^{95} +(0.687542 + 4.34097i) q^{97} +(-9.25476 - 1.46581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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