LMFDB - Embedded newform 968.2.q.b.89.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(89,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("968.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.q (of order $11$, degree $10$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$170$
Relative dimension:	$17$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.14
Character	$\chi$	$=$	968.89
Dual form			968.2.q.b.881.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00219 q^{3} +(-0.684988 - 1.49991i) q^{5} +(-0.643255 + 0.413395i) q^{7} +1.00878 q^{9} +(3.18405 - 0.928334i) q^{11} +(3.83417 + 1.12581i) q^{13} +(-1.37148 - 3.00312i) q^{15} +(1.46779 - 1.69392i) q^{17} +(-3.90850 - 4.51065i) q^{19} +(-1.28792 + 0.827697i) q^{21} +(6.30161 + 4.04980i) q^{23} +(1.49377 - 1.72390i) q^{25} -3.98681 q^{27} +(0.759925 + 0.877000i) q^{29} +(-1.05856 + 0.310822i) q^{31} +(6.37509 - 1.85871i) q^{33} +(1.06068 + 0.681657i) q^{35} +(7.58903 - 2.22834i) q^{37} +(7.67675 + 2.25410i) q^{39} +(1.60364 - 11.1535i) q^{41} +(1.90935 - 4.18089i) q^{43} +(-0.691003 - 1.51308i) q^{45} +(-1.22259 - 8.50330i) q^{47} +(-2.66502 + 5.83559i) q^{49} +(2.93879 - 3.39155i) q^{51} +(-11.2255 + 7.21418i) q^{53} +(-3.57346 - 4.13991i) q^{55} +(-7.82558 - 9.03120i) q^{57} +(2.05642 + 14.3027i) q^{59} +(0.268500 + 1.86746i) q^{61} +(-0.648904 + 0.417025i) q^{63} +(-0.937736 - 6.52209i) q^{65} +(1.04126 - 7.24214i) q^{67} +(12.6170 + 8.10848i) q^{69} +(8.61277 + 9.93966i) q^{71} +(-10.7306 - 6.89616i) q^{73} +(2.99082 - 3.45159i) q^{75} +(-1.66439 + 1.91343i) q^{77} +(6.19196 + 13.5585i) q^{79} -11.0087 q^{81} +(-12.6997 + 8.16162i) q^{83} +(-3.54615 - 1.04124i) q^{85} +(1.52152 + 1.75592i) q^{87} +(-2.81558 + 3.24936i) q^{89} +(-2.93176 + 0.860841i) q^{91} +(-2.11945 + 0.622326i) q^{93} +(-4.08831 + 8.95216i) q^{95} +(4.99956 - 10.9475i) q^{97} +(3.21201 - 0.936486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) $ 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.00219			1.15597			0.577984	−	0.816048i	$-0.303840\pi$
$3$	2.00219			1.15597			0.577984	+	0.816048i	$0.303840\pi$
$4$		0			0
$5$	−0.684988	−	1.49991i	−0.306336	−	0.670782i	0.692375	−	0.721538i	$-0.256564\pi$
$5$	−0.684988	−	1.49991i	−0.306336	−	0.670782i	−0.998711	+	0.0507556i	$0.983837\pi$
$6$		0			0
$7$	−0.643255	+	0.413395i	−0.243128	+	0.156249i	−0.656530	−	0.754300i	$-0.727977\pi$
$7$	−0.643255	+	0.413395i	−0.243128	+	0.156249i	0.413403	+	0.910548i	$0.364340\pi$
$8$		0			0
$9$	1.00878			0.336260
$10$		0			0
$11$	3.18405	−	0.928334i	0.960028	−	0.279903i
$11$	3.18405	−	0.928334i	0.960028	−	0.279903i
$12$		0			0
$13$	3.83417	+	1.12581i	1.06341	+	0.312245i	0.766222	−	0.642575i	$-0.222134\pi$
$13$	3.83417	+	1.12581i	1.06341	+	0.312245i	0.297185	+	0.954820i	$0.403952\pi$
$14$		0			0
$15$	−1.37148	−	3.00312i	−0.354114	−	0.775402i
$16$		0			0
$17$	1.46779	−	1.69392i	0.355991	−	0.410835i	−0.549302	−	0.835624i	$-0.685106\pi$
$17$	1.46779	−	1.69392i	0.355991	−	0.410835i	0.905292	+	0.424789i	$0.139652\pi$
$18$		0			0
$19$	−3.90850	−	4.51065i	−0.896672	−	1.03481i	−0.999196	−	0.0400837i	$-0.987238\pi$
$19$	−3.90850	−	4.51065i	−0.896672	−	1.03481i	0.102525	−	0.994730i	$-0.467308\pi$
$20$		0			0
$21$	−1.28792	+	0.827697i	−0.281048	+	0.180618i
$22$		0			0
$23$	6.30161	+	4.04980i	1.31398	+	0.844442i	0.994660	−	0.103206i	$-0.0329102\pi$
$23$	6.30161	+	4.04980i	1.31398	+	0.844442i	0.319317	+	0.947648i	$0.396547\pi$
$24$		0			0
$25$	1.49377	−	1.72390i	0.298754	−	0.344780i
$26$		0			0
$27$	−3.98681			−0.767261
$28$		0			0
$29$	0.759925	+	0.877000i	0.141114	+	0.162855i	0.821907	−	0.569621i	$-0.192910\pi$
$29$	0.759925	+	0.877000i	0.141114	+	0.162855i	−0.680793	+	0.732476i	$0.738365\pi$
$30$		0			0
$31$	−1.05856	+	0.310822i	−0.190123	+	0.0558253i	−0.375408	−	0.926860i	$-0.622497\pi$
$31$	−1.05856	+	0.310822i	−0.190123	+	0.0558253i	0.185285	+	0.982685i	$0.440679\pi$
$32$		0			0
$33$	6.37509	−	1.85871i	1.10976	−	0.323559i
$34$		0			0
$35$	1.06068	+	0.681657i	0.179288	+	0.115221i
$36$		0			0
$37$	7.58903	−	2.22834i	1.24763	−	0.366337i	0.409753	−	0.912197i	$-0.365615\pi$
$37$	7.58903	−	2.22834i	1.24763	−	0.366337i	0.837877	+	0.545860i	$0.183797\pi$
$38$		0			0
$39$	7.67675	+	2.25410i	1.22926	+	0.360944i
$40$		0			0
$41$	1.60364	−	11.1535i	0.250446	−	1.74189i	−0.345098	−	0.938567i	$-0.612154\pi$
$41$	1.60364	−	11.1535i	0.250446	−	1.74189i	0.595544	−	0.803323i	$-0.296937\pi$
$42$		0			0
$43$	1.90935	−	4.18089i	0.291173	−	0.637579i	−0.706355	−	0.707858i	$-0.749662\pi$
$43$	1.90935	−	4.18089i	0.291173	−	0.637579i	0.997527	+	0.0702787i	$0.0223889\pi$
$44$		0			0
$45$	−0.691003	−	1.51308i	−0.103009	−	0.225557i
$46$		0			0
$47$	−1.22259	−	8.50330i	−0.178333	−	1.24033i	−0.860619	−	0.509249i	$-0.829923\pi$
$47$	−1.22259	−	8.50330i	−0.178333	−	1.24033i	0.682286	−	0.731085i	$-0.260986\pi$
$48$		0			0
$49$	−2.66502	+	5.83559i	−0.380718	+	0.833655i
$50$		0			0
$51$	2.93879	−	3.39155i	0.411514	−	0.474912i
$52$		0			0
$53$	−11.2255	+	7.21418i	−1.54194	+	0.990944i	−0.554636	+	0.832093i	$0.687142\pi$
$53$	−11.2255	+	7.21418i	−1.54194	+	0.990944i	−0.987303	+	0.158850i	$0.949221\pi$
$54$		0			0
$55$	−3.57346	−	4.13991i	−0.481845	−	0.558225i
$56$		0			0
$57$	−7.82558	−	9.03120i	−1.03652	−	1.19621i
$58$		0			0
$59$	2.05642	+	14.3027i	0.267723	+	1.86205i	0.469921	+	0.882708i	$0.344282\pi$
$59$	2.05642	+	14.3027i	0.267723	+	1.86205i	−0.202199	+	0.979345i	$0.564809\pi$
$60$		0			0
$61$	0.268500	+	1.86746i	0.0343780	+	0.239104i	0.999764	−	0.0217210i	$-0.00691456\pi$
$61$	0.268500	+	1.86746i	0.0343780	+	0.239104i	−0.965386	+	0.260825i	$0.916005\pi$
$62$		0			0
$63$	−0.648904	+	0.417025i	−0.0817542	+	0.0525402i
$64$		0			0
$65$	−0.937736	−	6.52209i	−0.116312	−	0.808966i
$66$		0			0
$67$	1.04126	−	7.24214i	0.127211	−	0.884769i	−0.821856	−	0.569695i	$-0.807061\pi$
$67$	1.04126	−	7.24214i	0.127211	−	0.884769i	0.949067	−	0.315074i	$-0.102029\pi$
$68$		0			0
$69$	12.6170	+	8.10848i	1.51891	+	0.976147i
$70$		0			0
$71$	8.61277	+	9.93966i	1.02215	+	1.17962i	0.983600	+	0.180364i	$0.0577277\pi$
$71$	8.61277	+	9.93966i	1.02215	+	1.17962i	0.0385477	+	0.999257i	$0.487727\pi$
$72$		0			0
$73$	−10.7306	−	6.89616i	−1.25593	−	0.807134i	−0.268205	−	0.963362i	$-0.586430\pi$
$73$	−10.7306	−	6.89616i	−1.25593	−	0.807134i	−0.987721	+	0.156228i	$0.950067\pi$
$74$		0			0
$75$	2.99082	−	3.45159i	0.345350	−	0.398555i
$76$		0			0
$77$	−1.66439	+	1.91343i	−0.189675	+	0.218055i
$78$		0			0
$79$	6.19196	+	13.5585i	0.696649	+	1.52545i	0.843987	+	0.536363i	$0.180202\pi$
$79$	6.19196	+	13.5585i	0.696649	+	1.52545i	−0.147338	+	0.989086i	$0.547070\pi$
$80$		0			0
$81$	−11.0087			−1.22319
$82$		0			0
$83$	−12.6997	+	8.16162i	−1.39398	+	0.895854i	−0.999732	−	0.0231523i	$-0.992630\pi$
$83$	−12.6997	+	8.16162i	−1.39398	+	0.895854i	−0.394244	+	0.919006i	$0.628993\pi$
$84$		0			0
$85$	−3.54615	−	1.04124i	−0.384634	−	0.112939i
$86$		0			0
$87$	1.52152	+	1.75592i	0.163124	+	0.188255i
$88$		0			0
$89$	−2.81558	+	3.24936i	−0.298451	+	0.344431i	−0.885092	−	0.465416i	$-0.845905\pi$
$89$	−2.81558	+	3.24936i	−0.298451	+	0.344431i	0.586641	+	0.809847i	$0.300450\pi$
$90$		0			0
$91$	−2.93176	+	0.860841i	−0.307332	+	0.0902407i
$92$		0			0
$93$	−2.11945	+	0.622326i	−0.219776	+	0.0645322i
$94$		0			0
$95$	−4.08831	+	8.95216i	−0.419452	+	0.918472i
$96$		0			0
$97$	4.99956	−	10.9475i	0.507628	−	1.11155i	−0.466286	−	0.884634i	$-0.654408\pi$
$97$	4.99956	−	10.9475i	0.507628	−	1.11155i	0.973914	−	0.226917i	$-0.0728646\pi$
$98$		0			0
$99$	3.21201	−	0.936486i	0.322819	−	0.0941204i
$100$		0			0
$101$	−0.279069	−	1.94097i	−0.0277684	−	0.193133i	0.971215	−	0.238203i	$-0.0765583\pi$
$101$	−0.279069	−	1.94097i	−0.0277684	−	0.193133i	−0.998984	+	0.0450692i	$0.985649\pi$
$102$		0			0
$103$	−1.10436	+	7.68097i	−0.108816	+	0.756829i	0.860223	+	0.509918i	$0.170324\pi$
$103$	−1.10436	+	7.68097i	−0.108816	+	0.756829i	−0.969038	+	0.246910i	$0.920585\pi$
$104$		0			0
$105$	2.12369	+	1.36481i	0.207251	+	0.133192i
$106$		0			0
$107$	3.75118	+	8.21393i	0.362640	+	0.794071i	0.999729	+	0.0232806i	$0.00741113\pi$
$107$	3.75118	+	8.21393i	0.362640	+	0.794071i	−0.637089	+	0.770790i	$0.719862\pi$
$108$		0			0
$109$	−2.16407	−	0.635427i	−0.207280	−	0.0608629i	0.176444	−	0.984311i	$-0.443540\pi$
$109$	−2.16407	−	0.635427i	−0.207280	−	0.0608629i	−0.383724	+	0.923448i	$0.625359\pi$
$110$		0			0
$111$	15.1947	−	4.46157i	1.44222	−	0.423474i
$112$		0			0
$113$	−4.20500	+	9.20766i	−0.395573	+	0.866184i	0.602127	+	0.798400i	$0.294320\pi$
$113$	−4.20500	+	9.20766i	−0.395573	+	0.866184i	−0.997700	+	0.0677834i	$0.978407\pi$
$114$		0			0
$115$	1.75782	−	12.2259i	0.163918	−	1.14007i
$116$		0			0
$117$	3.86784	+	1.13570i	0.357582	+	0.104995i
$118$		0			0
$119$	−0.243905	+	1.69640i	−0.0223587	+	0.155508i
$120$		0			0
$121$	9.27639	−	5.91173i	0.843308	−	0.537430i
$122$		0			0
$123$	3.21079	−	22.3315i	0.289507	−	2.01357i
$124$		0			0
$125$	−11.5196	−	3.38245i	−1.03034	−	0.302536i
$126$		0			0
$127$	−0.488948	+	3.40071i	−0.0433872	+	0.301764i	0.956561	+	0.291534i	$0.0941656\pi$
$127$	−0.488948	+	3.40071i	−0.0433872	+	0.301764i	−0.999948	+	0.0102304i	$0.996743\pi$
$128$		0			0
$129$	3.82288	−	8.37095i	0.336586	−	0.737021i
$130$		0			0
$131$	−14.7445	+	4.32936i	−1.28823	+	0.378258i	−0.852929	−	0.522027i	$-0.825176\pi$
$131$	−14.7445	+	4.32936i	−1.28823	+	0.378258i	−0.435300	+	0.900285i	$0.643358\pi$
$132$		0			0
$133$	4.37885	+	1.28575i	0.379694	+	0.111488i
$134$		0			0
$135$	2.73091	+	5.97987i	0.235040	+	0.514665i
$136$		0			0
$137$	4.75666	+	3.05692i	0.406388	+	0.261170i	0.727827	−	0.685760i	$-0.240530\pi$
$137$	4.75666	+	3.05692i	0.406388	+	0.261170i	−0.321439	+	0.946930i	$0.604167\pi$
$138$		0			0
$139$	−0.385858	+	2.68370i	−0.0327280	+	0.227629i	−0.999620	−	0.0275566i	$-0.991227\pi$
$139$	−0.385858	+	2.68370i	−0.0327280	+	0.227629i	0.966892	+	0.255185i	$0.0821364\pi$
$140$		0			0
$141$	−2.44786	−	17.0253i	−0.206147	−	1.43379i
$142$		0			0
$143$	13.2533	+	0.0252601i	1.10830	+	0.00211235i
$144$		0			0
$145$	0.794885	−	1.74056i	0.0660116	−	0.144545i
$146$		0			0
$147$	−5.33589	+	11.6840i	−0.440097	+	0.963678i
$148$		0			0
$149$	7.15130	−	2.09981i	0.585858	−	0.172023i	0.0246468	−	0.999696i	$-0.492154\pi$
$149$	7.15130	−	2.09981i	0.585858	−	0.172023i	0.561211	+	0.827673i	$0.310336\pi$
$150$		0			0
$151$	0.981890	−	0.288309i	0.0799051	−	0.0234622i	−0.241536	−	0.970392i	$-0.577651\pi$
$151$	0.981890	−	0.288309i	0.0799051	−	0.0234622i	0.321441	+	0.946930i	$0.395833\pi$
$152$		0			0
$153$	1.48068	−	1.70879i	0.119706	−	0.138148i
$154$		0			0
$155$	1.19131	+	1.37484i	0.0956882	+	0.110430i
$156$		0			0
$157$	−7.01061	−	2.05850i	−0.559508	−	0.164286i	−0.0102622	−	0.999947i	$-0.503267\pi$
$157$	−7.01061	−	2.05850i	−0.559508	−	0.164286i	−0.549245	+	0.835661i	$0.685085\pi$
$158$		0			0
$159$	−22.4756	+	14.4442i	−1.78243	+	1.14550i
$160$		0			0
$161$	−5.72771			−0.451407
$162$		0			0
$163$	9.60103	+	21.0233i	0.752011	+	1.64667i	0.762718	+	0.646731i	$0.223864\pi$
$163$	9.60103	+	21.0233i	0.752011	+	1.64667i	−0.0107076	+	0.999943i	$0.503408\pi$
$164$		0			0
$165$	−7.15476	−	8.28890i	−0.556997	−	0.645290i
$166$		0			0
$167$	−2.48437	+	2.86711i	−0.192246	+	0.221864i	−0.843687	−	0.536836i	$-0.819619\pi$
$167$	−2.48437	+	2.86711i	−0.192246	+	0.221864i	0.651441	+	0.758700i	$0.274165\pi$
$168$		0			0
$169$	2.49710	+	1.60479i	0.192085	+	0.123445i
$170$		0			0
$171$	−3.94282	−	4.55026i	−0.301515	−	0.347967i
$172$		0			0
$173$	−12.8376	−	8.25025i	−0.976027	−	0.627255i	−0.0476382	−	0.998865i	$-0.515169\pi$
$173$	−12.8376	−	8.25025i	−0.976027	−	0.627255i	−0.928389	+	0.371610i	$0.878806\pi$
$174$		0			0
$175$	−0.248223	+	1.72643i	−0.0187639	+	0.130506i
$176$		0			0
$177$	4.11735	+	28.6368i	0.309479	+	2.15247i
$178$		0			0
$179$	17.0135	−	10.9339i	1.27165	−	0.817239i	0.281815	−	0.959469i	$-0.409063\pi$
$179$	17.0135	−	10.9339i	1.27165	−	0.817239i	0.989834	+	0.142229i	$0.0454271\pi$
$180$		0			0
$181$	0.691178	+	4.80725i	0.0513748	+	0.357320i	0.999252	+	0.0386825i	$0.0123161\pi$
$181$	0.691178	+	4.80725i	0.0513748	+	0.357320i	−0.947877	+	0.318637i	$0.896775\pi$
$182$		0			0
$183$	0.537590	+	3.73902i	0.0397398	+	0.276396i
$184$		0			0
$185$	−8.54072	−	9.85651i	−0.627926	−	0.724665i
$186$		0			0
$187$	3.10099	−	6.75612i	0.226767	−	0.494056i
$188$		0			0
$189$	2.56454	−	1.64813i	0.186542	−	0.119884i
$190$		0			0
$191$	−7.09126	+	8.18375i	−0.513106	+	0.592155i	−0.951891	−	0.306436i	$-0.900863\pi$
$191$	−7.09126	+	8.18375i	−0.513106	+	0.592155i	0.438786	+	0.898592i	$0.355409\pi$
$192$		0			0
$193$	1.07029	−	2.34360i	0.0770410	−	0.168696i	−0.867192	−	0.497973i	$-0.834078\pi$
$193$	1.07029	−	2.34360i	0.0770410	−	0.168696i	0.944233	+	0.329277i	$0.106805\pi$
$194$		0			0
$195$	−1.87753	−	13.0585i	−0.134453	−	0.935138i
$196$		0			0
$197$	−4.72752	−	10.3518i	−0.336822	−	0.737537i	0.663118	−	0.748515i	$-0.269233\pi$
$197$	−4.72752	−	10.3518i	−0.336822	−	0.737537i	−0.999940	+	0.0109782i	$0.996505\pi$
$198$		0			0
$199$	2.46932	−	5.40707i	0.175046	−	0.383297i	−0.801691	−	0.597739i	$-0.796066\pi$
$199$	2.46932	−	5.40707i	0.175046	−	0.383297i	0.976737	+	0.214442i	$0.0687933\pi$
$200$		0			0
$201$	2.08481	−	14.5002i	0.147051	−	1.02276i
$202$		0			0
$203$	−0.851373	−	0.249986i	−0.0597547	−	0.0175456i
$204$		0			0
$205$	−17.8278	+	5.23472i	−1.24515	+	0.365609i
$206$		0			0
$207$	6.35695	+	4.08536i	0.441838	+	0.283952i
$208$		0			0
$209$	−16.6323	−	10.7338i	−1.15048	−	0.742469i
$210$		0			0
$211$	1.90261	−	0.558655i	0.130981	−	0.0384594i	−0.215585	−	0.976485i	$-0.569166\pi$
$211$	1.90261	−	0.558655i	0.130981	−	0.0384594i	0.346566	+	0.938026i	$0.387348\pi$
$212$		0			0
$213$	17.2444	+	19.9011i	1.18157	+	1.36360i
$214$		0			0
$215$	−7.57885			−0.516874
$216$		0			0
$217$	0.552434	−	0.637542i	0.0375016	−	0.0432792i
$218$		0			0
$219$	−21.4848	−	13.8074i	−1.45181	−	0.933021i
$220$		0			0
$221$	7.53478	−	4.84231i	0.506844	−	0.325729i
$222$		0			0
$223$	16.3074	+	18.8197i	1.09202	+	1.26026i	0.963255	+	0.268587i	$0.0865568\pi$
$223$	16.3074	+	18.8197i	1.09202	+	1.26026i	0.128768	+	0.991675i	$0.458898\pi$
$224$		0			0
$225$	1.50689	−	1.73904i	0.100459	−	0.115936i
$226$		0			0
$227$	−3.40604	−	7.45819i	−0.226067	−	0.495017i	0.762278	−	0.647250i	$-0.224081\pi$
$227$	−3.40604	−	7.45819i	−0.226067	−	0.495017i	−0.988345	+	0.152233i	$0.951354\pi$
$228$		0			0
$229$	−2.08101	−	0.611039i	−0.137517	−	0.0403786i	0.212250	−	0.977215i	$-0.431921\pi$
$229$	−2.08101	−	0.611039i	−0.137517	−	0.0403786i	−0.349767	+	0.936837i	$0.613739\pi$
$230$		0			0
$231$	−3.33243	+	3.83105i	−0.219258	+	0.252065i
$232$		0			0
$233$	−10.3776			−0.679857			−0.339929	−	0.940451i	$-0.610403\pi$
$233$	−10.3776			−0.679857			−0.339929	+	0.940451i	$0.610403\pi$
$234$		0			0
$235$	−11.9168	+	7.65844i	−0.777364	+	0.499582i
$236$		0			0
$237$	12.3975	+	27.1467i	0.805304	+	1.76337i
$238$		0			0
$239$	−22.6126			−1.46269			−0.731344	−	0.682008i	$-0.761107\pi$
$239$	−22.6126			−1.46269			−0.731344	+	0.682008i	$0.761107\pi$
$240$		0			0
$241$	6.21087			0.400077			0.200039	−	0.979788i	$-0.435893\pi$
$241$	6.21087			0.400077			0.200039	+	0.979788i	$0.435893\pi$
$242$		0			0
$243$	−10.0811			−0.646705
$244$		0			0
$245$	10.5784			0.675828
$246$		0			0
$247$	−9.90770	−	21.6948i	−0.630412	−	1.38041i
$248$		0			0
$249$	−25.4273	+	16.3411i	−1.61139	+	1.03558i
$250$		0			0
$251$	3.49075			0.220334			0.110167	−	0.993913i	$-0.464861\pi$
$251$	3.49075			0.220334			0.110167	+	0.993913i	$0.464861\pi$
$252$		0			0
$253$	23.8242	+	7.04478i	1.49782	+	0.442901i
$254$		0			0
$255$	−7.10007	−	2.08477i	−0.444624	−	0.130553i
$256$		0			0
$257$	12.0172	+	26.3140i	0.749613	+	1.64142i	0.767059	+	0.641576i	$0.221719\pi$
$257$	12.0172	+	26.3140i	0.749613	+	1.64142i	−0.0174459	+	0.999848i	$0.505553\pi$
$258$		0			0
$259$	−3.96050	+	4.57066i	−0.246094	+	0.284007i
$260$		0			0
$261$	0.766598	+	0.884701i	0.0474512	+	0.0547616i
$262$		0			0
$263$	−15.0880	+	9.69644i	−0.930364	+	0.597908i	−0.915647	−	0.401983i	$-0.868321\pi$
$263$	−15.0880	+	9.69644i	−0.930364	+	0.597908i	−0.0147166	+	0.999892i	$0.504685\pi$
$264$		0			0
$265$	18.5100	+	11.8956i	1.13706	+	0.730743i
$266$		0			0
$267$	−5.63734	+	6.50584i	−0.345000	+	0.398151i
$268$		0			0
$269$	−1.85154			−0.112890			−0.0564451	−	0.998406i	$-0.517977\pi$
$269$	−1.85154			−0.112890			−0.0564451	+	0.998406i	$0.517977\pi$
$270$		0			0
$271$	−0.243331	−	0.280819i	−0.0147813	−	0.0170585i	0.748311	−	0.663348i	$-0.230865\pi$
$271$	−0.243331	−	0.280819i	−0.0147813	−	0.0170585i	−0.763092	+	0.646290i	$0.776320\pi$
$272$		0			0
$273$	−5.86994	+	1.72357i	−0.355265	+	0.104315i
$274$		0			0
$275$	3.15588	−	6.87571i	0.190307	−	0.414621i
$276$		0			0
$277$	−27.6344	−	17.7596i	−1.66039	−	1.06707i	−0.917564	−	0.397588i	$-0.869847\pi$
$277$	−27.6344	−	17.7596i	−1.66039	−	1.06707i	−0.742829	−	0.669481i	$-0.766516\pi$
$278$		0			0
$279$	−1.06786	+	0.313551i	−0.0639310	+	0.0187718i
$280$		0			0
$281$	13.3679	+	3.92517i	0.797463	+	0.234156i	0.654985	−	0.755642i	$-0.272675\pi$
$281$	13.3679	+	3.92517i	0.797463	+	0.234156i	0.142478	+	0.989798i	$0.454493\pi$
$282$		0			0
$283$	2.39987	−	16.6915i	0.142658	−	0.992206i	−0.785192	−	0.619252i	$-0.787436\pi$
$283$	2.39987	−	16.6915i	0.142658	−	0.992206i	0.927850	−	0.372954i	$-0.121655\pi$
$284$		0			0
$285$	−8.18560	+	17.9240i	−0.484873	+	1.06172i
$286$		0			0
$287$	3.57927	+	7.83751i	0.211278	+	0.462633i
$288$		0			0
$289$	1.70440	+	11.8543i	0.100259	+	0.697315i
$290$		0			0
$291$	10.0101	−	21.9190i	0.586802	−	1.28492i
$292$		0			0
$293$	−21.3670	+	24.6588i	−1.24827	+	1.44058i	−0.395360	+	0.918526i	$0.629380\pi$
$293$	−21.3670	+	24.6588i	−1.24827	+	1.44058i	−0.852912	+	0.522055i	$0.825165\pi$
$294$		0			0
$295$	20.0442	−	12.8816i	1.16702	−	0.749997i
$296$		0			0
$297$	−12.6942	+	3.70109i	−0.736593	+	0.214759i
$298$		0			0
$299$	19.6021	+	22.6221i	1.13362	+	1.30827i
$300$		0			0
$301$	0.500161	+	3.47869i	0.0288288	+	0.200509i
$302$		0			0
$303$	−0.558750	−	3.88619i	−0.0320994	−	0.223256i
$304$		0			0
$305$	2.61711	−	1.68192i	0.149855	−	0.0963062i
$306$		0			0
$307$	0.263771	+	1.83457i	0.0150542	+	0.104704i	0.995963	−	0.0897635i	$-0.0286111\pi$
$307$	0.263771	+	1.83457i	0.0150542	+	0.104704i	−0.980909	+	0.194468i	$0.937702\pi$
$308$		0			0
$309$	−2.21114	+	15.3788i	−0.125787	+	0.874869i
$310$		0			0
$311$	−12.3695	−	7.94942i	−0.701412	−	0.450770i	0.140714	−	0.990050i	$-0.455060\pi$
$311$	−12.3695	−	7.94942i	−0.701412	−	0.450770i	−0.842127	+	0.539280i	$0.818696\pi$
$312$		0			0
$313$	−14.6266	−	16.8800i	−0.826745	−	0.954114i	0.172779	−	0.984961i	$-0.444725\pi$
$313$	−14.6266	−	16.8800i	−0.826745	−	0.954114i	−0.999524	+	0.0308463i	$0.990180\pi$
$314$		0			0
$315$	1.06999	+	0.687643i	0.0602873	+	0.0387443i
$316$		0			0
$317$	5.98473	−	6.90675i	0.336136	−	0.387922i	−0.562368	−	0.826887i	$-0.690110\pi$
$317$	5.98473	−	6.90675i	0.336136	−	0.387922i	0.898504	+	0.438966i	$0.144655\pi$
$318$		0			0
$319$	3.23379	+	2.08695i	0.181057	+	0.116847i
$320$		0			0
$321$	7.51059	+	16.4459i	0.419200	+	0.917920i
$322$		0			0
$323$	−13.3775			−0.744345
$324$		0			0
$325$	7.66816	−	4.92802i	0.425353	−	0.273358i
$326$		0			0
$327$	−4.33288	−	1.27225i	−0.239609	−	0.0703555i
$328$		0			0
$329$	4.30166	+	4.96438i	0.237158	+	0.273695i
$330$		0			0
$331$	−7.42978	+	8.57442i	−0.408377	+	0.471293i	−0.922261	−	0.386567i	$-0.873661\pi$
$331$	−7.42978	+	8.57442i	−0.408377	+	0.471293i	0.513884	+	0.857860i	$0.328206\pi$
$332$		0			0
$333$	7.65567	−	2.24791i	0.419528	−	0.123185i
$334$		0			0
$335$	−11.5758	+	3.39898i	−0.632456	+	0.185706i
$336$		0			0
$337$	5.81846	−	12.7406i	0.316952	−	0.694027i	−0.682364	−	0.731012i	$-0.739048\pi$
$337$	5.81846	−	12.7406i	0.316952	−	0.694027i	0.999316	+	0.0369852i	$0.0117754\pi$
$338$		0			0
$339$	−8.41922	+	18.4355i	−0.457269	+	1.00128i
$340$		0			0
$341$	−3.08197	+	1.97237i	−0.166898	+	0.106810i
$342$		0			0
$343$	−1.45985	−	10.1535i	−0.0788245	−	0.548236i
$344$		0			0
$345$	3.51951	−	24.4787i	0.189484	−	1.31789i
$346$		0			0
$347$	−4.93809	−	3.17352i	−0.265091	−	0.170363i	0.401343	−	0.915928i	$-0.368544\pi$
$347$	−4.93809	−	3.17352i	−0.265091	−	0.170363i	−0.666433	+	0.745564i	$0.732180\pi$
$348$		0			0
$349$	3.70800	+	8.11940i	0.198485	+	0.434621i	0.982535	−	0.186076i	$-0.0595770\pi$
$349$	3.70800	+	8.11940i	0.198485	+	0.434621i	−0.784051	+	0.620697i	$0.786850\pi$
$350$		0			0
$351$	−15.2861	−	4.48840i	−0.815911	−	0.239573i
$352$		0			0
$353$	−14.1484	+	4.15434i	−0.753042	+	0.221113i	−0.635655	−	0.771973i	$-0.719270\pi$
$353$	−14.1484	+	4.15434i	−0.753042	+	0.221113i	−0.117387	+	0.993086i	$0.537452\pi$
$354$		0			0
$355$	9.00900	−	19.7270i	0.478148	−	1.04700i
$356$		0			0
$357$	−0.488345	+	3.39652i	−0.0258460	+	0.179763i
$358$		0			0
$359$	−6.74039	−	1.97916i	−0.355744	−	0.104456i	0.0989770	−	0.995090i	$-0.468443\pi$
$359$	−6.74039	−	1.97916i	−0.355744	−	0.104456i	−0.454721	+	0.890634i	$0.650261\pi$
$360$		0			0
$361$	−2.36561	+	16.4532i	−0.124506	+	0.865956i
$362$		0			0
$363$	18.5731	−	11.8364i	0.974837	−	0.621252i
$364$		0			0
$365$	−2.99329	+	20.8188i	−0.156676	+	1.08971i
$366$		0			0
$367$	−2.77968	−	0.816188i	−0.145098	−	0.0426047i	0.208377	−	0.978049i	$-0.433182\pi$
$367$	−2.77968	−	0.816188i	−0.145098	−	0.0426047i	−0.353475	+	0.935444i	$0.615000\pi$
$368$		0			0
$369$	1.61772	−	11.2515i	0.0842150	−	0.585728i
$370$		0			0
$371$	4.23854	−	9.28112i	0.220054	−	0.481852i
$372$		0			0
$373$	26.3922	−	7.74944i	1.36654	−	0.401251i	0.485473	−	0.874252i	$-0.338647\pi$
$373$	26.3922	−	7.74944i	1.36654	−	0.401251i	0.881062	+	0.473001i	$0.156829\pi$
$374$		0			0
$375$	−23.0644	−	6.77233i	−1.19104	−	0.349721i
$376$		0			0
$377$	1.92634	+	4.21810i	0.0992116	+	0.217243i
$378$		0			0
$379$	−17.7584	−	11.4126i	−0.912185	−	0.586226i	−0.00180505	−	0.999998i	$-0.500575\pi$
$379$	−17.7584	−	11.4126i	−0.912185	−	0.586226i	−0.910380	+	0.413772i	$0.864211\pi$
$380$		0			0
$381$	−0.978970	+	6.80888i	−0.0501541	+	0.348830i
$382$		0			0
$383$	4.85332	+	33.7556i	0.247993	+	1.72483i	0.609782	+	0.792570i	$0.291257\pi$
$383$	4.85332	+	33.7556i	0.247993	+	1.72483i	−0.361789	+	0.932260i	$0.617834\pi$
$384$		0			0
$385$	4.01007	+	1.18577i	0.204372	+	0.0604323i
$386$		0			0
$387$	1.92611	−	4.21760i	0.0979099	−	0.214393i
$388$		0			0
$389$	8.95356	−	19.6056i	0.453964	−	0.994042i	−0.534858	−	0.844942i	$-0.679635\pi$
$389$	8.95356	−	19.6056i	0.453964	−	0.994042i	0.988822	−	0.149100i	$-0.0476377\pi$
$390$		0			0
$391$	16.1094	−	4.73016i	0.814690	−	0.239214i
$392$		0			0
$393$	−29.5213	+	8.66823i	−1.48915	+	0.437254i
$394$		0			0
$395$	16.0952	−	18.5748i	0.809835	−	0.934600i
$396$		0			0
$397$	4.20672	+	4.85481i	0.211129	+	0.243656i	0.851430	−	0.524468i	$-0.175736\pi$
$397$	4.20672	+	4.85481i	0.211129	+	0.243656i	−0.640301	+	0.768124i	$0.721190\pi$
$398$		0			0
$399$	8.76730	+	2.57431i	0.438914	+	0.128877i
$400$		0			0
$401$	0.693940	−	0.445968i	0.0346537	−	0.0222706i	−0.523199	−	0.852210i	$-0.675262\pi$
$401$	0.693940	−	0.445968i	0.0346537	−	0.0222706i	0.557853	+	0.829940i	$0.311625\pi$
$402$		0			0
$403$	−4.40863			−0.219610
$404$		0			0
$405$	7.54083	+	16.5121i	0.374707	+	0.820493i
$406$		0			0
$407$	22.0952	−	14.1403i	1.09522	−	0.700909i
$408$		0			0
$409$	6.98532	−	8.06149i	0.345402	−	0.398615i	−0.556294	−	0.830985i	$-0.687777\pi$
$409$	6.98532	−	8.06149i	0.345402	−	0.398615i	0.901696	+	0.432370i	$0.142323\pi$
$410$		0			0
$411$	9.52375	+	6.12054i	0.469772	+	0.301904i
$412$		0			0
$413$	−7.23547	−	8.35018i	−0.356034	−	0.410885i
$414$		0			0
$415$	20.9409	+	13.4579i	1.02795	+	0.660622i
$416$		0			0
$417$	−0.772563	+	5.37329i	−0.0378326	+	0.263131i
$418$		0			0
$419$	−5.58141	−	38.8196i	−0.272670	−	1.89646i	−0.420246	−	0.907410i	$-0.638056\pi$
$419$	−5.58141	−	38.8196i	−0.272670	−	1.89646i	0.147576	−	0.989051i	$-0.452853\pi$
$420$		0			0
$421$	16.3911	−	10.5339i	0.798852	−	0.513391i	−0.0763887	−	0.997078i	$-0.524339\pi$
$421$	16.3911	−	10.5339i	0.798852	−	0.513391i	0.875241	+	0.483687i	$0.160703\pi$
$422$		0			0
$423$	−1.23333	−	8.57797i	−0.0599664	−	0.417075i
$424$		0			0
$425$	−0.727610	−	5.06064i	−0.0352943	−	0.245477i
$426$		0			0
$427$	−0.944714	−	1.09026i	−0.0457179	−	0.0527613i
$428$		0			0
$429$	26.5357	+	0.0505756i	1.28116	+	0.00244181i
$430$		0			0
$431$	−0.379929	+	0.244166i	−0.0183005	+	0.0117610i	−0.549759	−	0.835323i	$-0.685280\pi$
$431$	−0.379929	+	0.244166i	−0.0183005	+	0.0117610i	0.531459	+	0.847084i	$0.321644\pi$
$432$		0			0
$433$	11.8852	−	13.7162i	0.571164	−	0.659159i	−0.394517	−	0.918889i	$-0.629088\pi$
$433$	11.8852	−	13.7162i	0.571164	−	0.659159i	0.965681	+	0.259730i	$0.0836335\pi$
$434$		0			0
$435$	1.59151	−	3.48493i	0.0763073	−	0.167090i
$436$		0			0
$437$	−6.36262	−	44.2530i	−0.304366	−	2.11691i
$438$		0			0
$439$	−6.97541	−	15.2740i	−0.332918	−	0.728989i	0.666952	−	0.745101i	$-0.267599\pi$
$439$	−6.97541	−	15.2740i	−0.332918	−	0.728989i	−0.999870	+	0.0161116i	$0.994871\pi$
$440$		0			0
$441$	−2.68842	+	5.88683i	−0.128020	+	0.280325i
$442$		0			0
$443$	0.187784	−	1.30607i	0.00892188	−	0.0620530i	−0.984874	−	0.173271i	$-0.944566\pi$
$443$	0.187784	−	1.30607i	0.00892188	−	0.0620530i	0.993796	+	0.111218i	$0.0354753\pi$
$444$		0			0
$445$	6.80240	+	1.99736i	0.322465	+	0.0946841i
$446$		0			0
$447$	14.3183	−	4.20423i	0.677232	−	0.198853i
$448$		0			0
$449$	17.3582	+	11.1554i	0.819184	+	0.526458i	0.881824	−	0.471579i	$-0.156316\pi$
$449$	17.3582	+	11.1554i	0.819184	+	0.526458i	−0.0626400	+	0.998036i	$0.519952\pi$
$450$		0			0
$451$	−5.24814	−	37.0022i	−0.247125	−	1.74236i
$452$		0			0
$453$	1.96593	−	0.577250i	0.0923677	−	0.0271216i
$454$		0			0
$455$	3.29941	+	3.80772i	0.154679	+	0.178509i
$456$		0			0
$457$	25.5140			1.19349			0.596747	−	0.802429i	$-0.296460\pi$
$457$	25.5140			1.19349			0.596747	+	0.802429i	$0.296460\pi$
$458$		0			0
$459$	−5.85178	+	6.75332i	−0.273138	+	0.315218i
$460$		0			0
$461$	−16.6032	−	10.6702i	−0.773286	−	0.496961i	0.0935131	−	0.995618i	$-0.470190\pi$
$461$	−16.6032	−	10.6702i	−0.773286	−	0.496961i	−0.866799	+	0.498657i	$0.833827\pi$
$462$		0			0
$463$	−0.739531	+	0.475268i	−0.0343689	+	0.0220876i	−0.557712	−	0.830034i	$-0.688321\pi$
$463$	−0.739531	+	0.475268i	−0.0343689	+	0.0220876i	0.523344	+	0.852122i	$0.324684\pi$
$464$		0			0
$465$	2.38523	+	2.75270i	0.110612	+	0.127654i
$466$		0			0
$467$	18.5541	−	21.4126i	0.858582	−	0.990857i	−0.141417	−	0.989950i	$-0.545166\pi$
$467$	18.5541	−	21.4126i	0.858582	−	0.990857i	1.00000		0.000906594i	$-0.000288578\pi$
$468$		0			0
$469$	2.32407	+	5.08900i	0.107316	+	0.234988i
$470$		0			0
$471$	−14.0366	−	4.12152i	−0.646772	−	0.189910i
$472$		0			0
$473$	2.19820	−	15.0847i	0.101073	−	0.693595i
$474$		0			0
$475$	−13.6143			−0.624668
$476$		0			0
$477$	−11.3241	+	7.27753i	−0.518493	+	0.333215i
$478$		0			0
$479$	10.6109	+	23.2347i	0.484826	+	1.06162i	0.981108	+	0.193459i	$0.0619708\pi$
$479$	10.6109	+	23.2347i	0.484826	+	1.06162i	−0.496282	+	0.868161i	$0.665302\pi$
$480$		0			0
$481$	31.6063			1.44112
$482$		0			0
$483$	−11.4680			−0.521812
$484$		0			0
$485$	−19.8450			−0.901113
$486$		0			0
$487$	23.2428			1.05323			0.526615	−	0.850104i	$-0.323461\pi$
$487$	23.2428			1.05323			0.526615	+	0.850104i	$0.323461\pi$
$488$		0			0
$489$	19.2231	+	42.0928i	0.869300	+	1.90350i
$490$		0			0
$491$	1.10627	−	0.710959i	0.0499255	−	0.0320851i	−0.515440	−	0.856926i	$-0.672372\pi$
$491$	1.10627	−	0.710959i	0.0499255	−	0.0320851i	0.565365	+	0.824841i	$0.308735\pi$
$492$		0			0
$493$	2.60097			0.117142
$494$		0			0
$495$	−3.60484	−	4.17626i	−0.162025	−	0.187709i
$496$		0			0
$497$	−9.64922	−	2.83327i	−0.432827	−	0.127089i
$498$		0			0
$499$	−6.36648	−	13.9406i	−0.285003	−	0.624069i	0.711937	−	0.702243i	$-0.247818\pi$
$499$	−6.36648	−	13.9406i	−0.285003	−	0.624069i	−0.996940	+	0.0781746i	$0.975091\pi$
$500$		0			0
$501$	−4.97419	+	5.74052i	−0.222230	+	0.256467i
$502$		0			0
$503$	18.2559	+	21.0685i	0.813992	+	0.939396i	0.999061	−	0.0433291i	$-0.0137964\pi$
$503$	18.2559	+	21.0685i	0.813992	+	0.939396i	−0.185069	+	0.982725i	$0.559251\pi$
$504$		0			0
$505$	−2.72013	+	1.74812i	−0.121044	+	0.0777903i
$506$		0			0
$507$	4.99968	+	3.21310i	0.222044	+	0.142699i
$508$		0			0
$509$	−1.40960	+	1.62676i	−0.0624794	+	0.0721051i	−0.786129	−	0.618063i	$-0.787918\pi$
$509$	−1.40960	+	1.62676i	−0.0624794	+	0.0721051i	0.723649	+	0.690168i	$0.242463\pi$
$510$		0			0
$511$	9.75338			0.431464
$512$		0			0
$513$	15.5824	+	17.9831i	0.687981	+	0.793973i
$514$		0			0
$515$	12.2773	−	3.60493i	0.541001	−	0.158852i
$516$		0			0
$517$	−11.7867	−	25.9400i	−0.518378	−	1.14084i
$518$		0			0
$519$	−25.7034	−	16.5186i	−1.12826	−	0.725086i
$520$		0			0
$521$	−11.6410	+	3.41812i	−0.510004	+	0.149751i	−0.526602	−	0.850112i	$-0.676534\pi$
$521$	−11.6410	+	3.41812i	−0.510004	+	0.149751i	0.0165989	+	0.999862i	$0.494716\pi$
$522$		0			0
$523$	15.0460	+	4.41790i	0.657914	+	0.193181i	0.593615	−	0.804750i	$-0.297700\pi$
$523$	15.0460	+	4.41790i	0.657914	+	0.193181i	0.0642998	+	0.997931i	$0.479519\pi$
$524$		0			0
$525$	−0.496990	+	3.45664i	−0.0216904	+	0.150860i
$526$		0			0
$527$	−1.02724	+	2.24934i	−0.0447472	+	0.0979826i
$528$		0			0
$529$	13.7549	+	30.1190i	0.598038	+	1.30952i
$530$		0			0
$531$	2.07447	+	14.4283i	0.0900245	+	0.626134i
$532$		0			0
$533$	18.7054	−	40.9591i	0.810221	−	1.77414i
$534$		0			0
$535$	9.75069	−	11.2529i	0.421559	−	0.486505i
$536$		0			0
$537$	34.0643	−	21.8918i	1.46998	−	0.944702i
$538$		0			0
$539$	−3.06820	+	21.0549i	−0.132157	+	0.906897i
$540$		0			0
$541$	−21.9677	−	25.3521i	−0.944465	−	1.08997i	−0.995824	−	0.0912903i	$-0.970901\pi$
$541$	−21.9677	−	25.3521i	−0.944465	−	1.08997i	0.0513595	−	0.998680i	$-0.483645\pi$
$542$		0			0
$543$	1.38387	+	9.62504i	0.0593876	+	0.413050i
$544$		0			0
$545$	0.529273	+	3.68117i	0.0226716	+	0.157684i
$546$		0			0
$547$	26.8216	−	17.2372i	1.14681	−	0.737008i	0.177806	−	0.984065i	$-0.443100\pi$
$547$	26.8216	−	17.2372i	1.14681	−	0.737008i	0.969001	+	0.247057i	$0.0794635\pi$
$548$		0			0
$549$	0.270858	+	1.88386i	0.0115599	+	0.0804012i
$550$		0			0
$551$	0.985674	−	6.85551i	0.0419911	−	0.292055i
$552$		0			0
$553$	−9.58802	−	6.16185i	−0.407724	−	0.262028i
$554$		0			0
$555$	−17.1002	−	19.7346i	−0.725862	−	0.837689i
$556$		0			0
$557$	10.3405	+	6.64541i	0.438140	+	0.281575i	0.741058	−	0.671441i	$-0.234325\pi$
$557$	10.3405	+	6.64541i	0.438140	+	0.281575i	−0.302918	+	0.953017i	$0.597961\pi$
$558$		0			0
$559$	12.0277	−	13.8807i	0.508716	−	0.587090i
$560$		0			0
$561$	6.20879	−	13.5271i	0.262135	−	0.571113i
$562$		0			0
$563$	−7.34296	−	16.0788i	−0.309469	−	0.677643i	0.689440	−	0.724343i	$-0.257857\pi$
$563$	−7.34296	−	16.0788i	−0.309469	−	0.677643i	−0.998909	+	0.0467003i	$0.985129\pi$
$564$		0			0
$565$	16.6911			0.702199
$566$		0			0
$567$	7.08141	−	4.55095i	0.297391	−	0.191122i
$568$		0			0
$569$	31.9483	+	9.38087i	1.33934	+	0.393267i	0.871435	−	0.490510i	$-0.163190\pi$
$569$	31.9483	+	9.38087i	1.33934	+	0.393267i	0.467908	+	0.883777i	$0.345008\pi$
$570$		0			0
$571$	11.8230	+	13.6444i	0.494775	+	0.571001i	0.947135	−	0.320834i	$-0.103963\pi$
$571$	11.8230	+	13.6444i	0.494775	+	0.571001i	−0.452360	+	0.891835i	$0.649418\pi$
$572$		0			0
$573$	−14.1981	+	16.3855i	−0.593133	+	0.684512i
$574$		0			0
$575$	16.3946	−	4.81389i	0.683702	−	0.200753i
$576$		0			0
$577$	−21.9938	+	6.45797i	−0.915616	+	0.268849i	−0.705403	−	0.708807i	$-0.749234\pi$
$577$	−21.9938	+	6.45797i	−0.915616	+	0.268849i	−0.210213	+	0.977656i	$0.567416\pi$
$578$		0			0
$579$	2.14292	−	4.69235i	0.0890569	−	0.195007i
$580$		0			0
$581$	4.79519	−	10.5000i	0.198938	−	0.435614i
$582$		0			0
$583$	−29.0454	+	33.3913i	−1.20294	+	1.38293i
$584$		0			0
$585$	−0.945970	−	6.57936i	−0.0391110	−	0.272023i
$586$		0			0
$587$	−5.40574	+	37.5978i	−0.223119	+	1.55183i	0.503018	+	0.864276i	$0.332223\pi$
$587$	−5.40574	+	37.5978i	−0.223119	+	1.55183i	−0.726137	+	0.687550i	$0.758686\pi$
$588$		0			0
$589$	5.53940	+	3.55996i	0.228247	+	0.146685i
$590$		0			0
$591$	−9.46541	−	20.7264i	−0.389355	−	0.852568i
$592$		0			0
$593$	45.4620	+	13.3489i	1.86690	+	0.548172i	0.998644	+	0.0520589i	$0.0165784\pi$
$593$	45.4620	+	13.3489i	1.86690	+	0.548172i	0.868258	+	0.496113i	$0.165240\pi$
$594$		0			0
$595$	2.71152	−	0.796175i	0.111162	−	0.0326400i
$596$		0			0
$597$	4.94407	−	10.8260i	0.202347	−	0.443078i
$598$		0			0
$599$	1.67706	−	11.6642i	0.0685229	−	0.476587i	−0.926448	−	0.376423i	$-0.877154\pi$
$599$	1.67706	−	11.6642i	0.0685229	−	0.476587i	0.994971	−	0.100164i	$-0.0319369\pi$
$600$		0			0
$601$	−5.81322	−	1.70691i	−0.237126	−	0.0696265i	0.161010	−	0.986953i	$-0.448525\pi$
$601$	−5.81322	−	1.70691i	−0.237126	−	0.0696265i	−0.398136	+	0.917326i	$0.630343\pi$
$602$		0			0
$603$	1.05041	−	7.30574i	0.0427759	−	0.297513i
$604$		0			0
$605$	−15.2213	−	9.86433i	−0.618834	−	0.401042i
$606$		0			0
$607$	−6.81512	+	47.4002i	−0.276617	+	1.92391i	0.0948976	+	0.995487i	$0.469748\pi$
$607$	−6.81512	+	47.4002i	−0.276617	+	1.92391i	−0.371515	+	0.928427i	$0.621161\pi$
$608$		0			0
$609$	−1.70461	−	0.500520i	−0.0690745	−	0.0202821i
$610$		0			0
$611$	4.88552	−	33.9795i	0.197647	−	1.37466i
$612$		0			0
$613$	13.2532	−	29.0204i	0.535291	−	1.17212i	−0.428028	−	0.903766i	$-0.640791\pi$
$613$	13.2532	−	29.0204i	0.535291	−	1.17212i	0.963319	−	0.268359i	$-0.0864813\pi$
$614$		0			0
$615$	−35.6947	+	10.4809i	−1.43935	+	0.422632i
$616$		0			0
$617$	−0.107906	−	0.0316839i	−0.00434411	−	0.00127555i	0.279560	−	0.960128i	$-0.409811\pi$
$617$	−0.107906	−	0.0316839i	−0.00434411	−	0.00127555i	−0.283904	+	0.958853i	$0.591630\pi$
$618$		0			0
$619$	−7.18346	−	15.7296i	−0.288728	−	0.632225i	0.708574	−	0.705636i	$-0.249339\pi$
$619$	−7.18346	−	15.7296i	−0.288728	−	0.632225i	−0.997302	+	0.0734111i	$0.976611\pi$
$620$		0			0
$621$	−25.1233	−	16.1458i	−1.00816	−	0.647907i
$622$		0			0
$623$	0.467871	−	3.25412i	0.0187449	−	0.130373i
$624$		0			0
$625$	1.19425	+	8.30616i	0.0477698	+	0.332246i
$626$		0			0
$627$	−33.3010	−	21.4911i	−1.32991	−	0.858270i
$628$		0			0
$629$	7.36446	−	16.1259i	0.293640	−	0.642982i
$630$		0			0
$631$	0.106118	−	0.232366i	0.00422449	−	0.00925034i	−0.907508	−	0.420035i	$-0.862018\pi$
$631$	0.106118	−	0.232366i	0.00422449	−	0.00925034i	0.911732	+	0.410784i	$0.134745\pi$
$632$		0			0
$633$	3.80938	−	1.11854i	0.151409	−	0.0444578i
$634$		0			0
$635$	5.43570	−	1.59607i	0.215709	−	0.0633379i
$636$		0			0
$637$	−16.7879	+	19.3743i	−0.665162	+	0.767638i
$638$		0			0
$639$	8.68840	+	10.0269i	0.343708	+	0.396660i
$640$		0			0
$641$	−29.8779	−	8.77296i	−1.18011	−	0.346511i	−0.367892	−	0.929868i	$-0.619921\pi$
$641$	−29.8779	−	8.77296i	−1.18011	−	0.346511i	−0.812216	+	0.583357i	$0.801739\pi$
$642$		0			0
$643$	−7.60665	+	4.88850i	−0.299977	+	0.192783i	−0.681967	−	0.731383i	$-0.738875\pi$
$643$	−7.60665	+	4.88850i	−0.299977	+	0.192783i	0.381990	+	0.924166i	$0.375239\pi$
$644$		0			0
$645$	−15.1743			−0.597489
$646$		0			0
$647$	15.4113	+	33.7461i	0.605883	+	1.32670i	0.925355	+	0.379102i	$0.123767\pi$
$647$	15.4113	+	33.7461i	0.605883	+	1.32670i	−0.319472	+	0.947596i	$0.603506\pi$
$648$		0			0
$649$	19.8254	+	43.6315i	0.778216	+	1.71269i
$650$		0			0
$651$	1.10608	−	1.27648i	0.0433507	−	0.0500293i
$652$		0			0
$653$	18.6956	+	12.0150i	0.731617	+	0.470182i	0.852661	−	0.522465i	$-0.174988\pi$
$653$	18.6956	+	12.0150i	0.731617	+	0.470182i	−0.121043	+	0.992647i	$0.538624\pi$
$654$		0			0
$655$	16.5934	+	19.1499i	0.648360	+	0.748247i
$656$		0			0
$657$	−10.8249	−	6.95671i	−0.422318	−	0.271407i
$658$		0			0
$659$	−4.48738	+	31.2104i	−0.174803	+	1.21578i	0.693760	+	0.720206i	$0.255953\pi$
$659$	−4.48738	+	31.2104i	−0.174803	+	1.21578i	−0.868563	+	0.495578i	$0.834956\pi$
$660$		0			0
$661$	0.594846	+	4.13724i	0.0231368	+	0.160920i	0.998114	−	0.0613838i	$-0.0195514\pi$
$661$	0.594846	+	4.13724i	0.0231368	+	0.160920i	−0.974977	+	0.222304i	$0.928642\pi$
$662$		0			0
$663$	15.0861	−	9.69524i	0.585895	−	0.376532i
$664$		0			0
$665$	−1.07095	−	7.44861i	−0.0415296	−	0.288845i
$666$		0			0
$667$	1.23708	+	8.60406i	0.0478998	+	0.333150i
$668$		0			0
$669$	32.6506	+	37.6807i	1.26234	+	1.45682i
$670$		0			0
$671$	2.58855	+	5.69684i	0.0999298	+	0.219924i
$672$		0			0
$673$	−28.9820	+	18.6256i	−1.11717	+	0.717964i	−0.962845	−	0.270056i	$-0.912958\pi$
$673$	−28.9820	+	18.6256i	−1.11717	+	0.717964i	−0.154329	+	0.988020i	$0.549322\pi$
$674$		0			0
$675$	−5.95537	+	6.87286i	−0.229222	+	0.264537i
$676$		0			0
$677$	−8.85117	+	19.3814i	−0.340178	+	0.744887i	−0.999979	−	0.00655451i	$-0.997914\pi$
$677$	−8.85117	+	19.3814i	−0.340178	+	0.744887i	0.659800	+	0.751441i	$0.270641\pi$
$678$		0			0
$679$	1.30965	+	9.10884i	0.0502599	+	0.349565i
$680$		0			0
$681$	−6.81955	−	14.9327i	−0.261326	−	0.572224i
$682$		0			0
$683$	−10.4937	+	22.9780i	−0.401530	+	0.879227i	0.595583	+	0.803294i	$0.296921\pi$
$683$	−10.4937	+	22.9780i	−0.401530	+	0.879227i	−0.997113	+	0.0759338i	$0.975806\pi$
$684$		0			0
$685$	1.32686	−	9.22853i	0.0506968	−	0.352604i
$686$		0			0
$687$	−4.16658	−	1.22342i	−0.158965	−	0.0466763i
$688$		0			0
$689$	−51.1622	+	15.0226i	−1.94913	+	0.572315i
$690$		0			0
$691$	23.0260	+	14.7979i	0.875952	+	0.562940i	0.899568	−	0.436781i	$-0.143882\pi$
$691$	23.0260	+	14.7979i	0.875952	+	0.562940i	−0.0236162	+	0.999721i	$0.507518\pi$
$692$		0			0
$693$	−1.67901	+	1.93023i	−0.0637802	+	0.0733234i
$694$		0			0
$695$	4.28963	−	1.25955i	0.162715	−	0.0477774i
$696$		0			0
$697$	−16.5394	−	19.0874i	−0.626473	−	0.722988i
$698$		0			0
$699$	−20.7779			−0.785893
$700$		0			0
$701$	3.56122	−	4.10987i	0.134506	−	0.155228i	−0.684501	−	0.729012i	$-0.739980\pi$
$701$	3.56122	−	4.10987i	0.134506	−	0.155228i	0.819006	+	0.573784i	$0.194525\pi$
$702$		0			0
$703$	−39.7130	−	25.5220i	−1.49780	−	0.962580i
$704$		0			0
$705$	−23.8597	+	15.3337i	−0.898607	+	0.577500i
$706$		0			0
$707$	0.981899	+	1.13317i	0.0369281	+	0.0426173i
$708$		0			0
$709$	20.5492	−	23.7151i	0.771743	−	0.890639i	−0.224742	−	0.974418i	$-0.572154\pi$
$709$	20.5492	−	23.7151i	0.771743	−	0.890639i	0.996484	+	0.0837798i	$0.0266992\pi$
$710$		0			0
$711$	6.24633	+	13.6775i	0.234256	+	0.512948i
$712$		0			0
$713$	−7.92941	−	2.32829i	−0.296959	−	0.0871950i
$714$		0			0
$715$	−9.04048	−	19.8962i	−0.338095	−	0.744074i
$716$		0			0
$717$	−45.2749			−1.69082
$718$		0			0
$719$	−36.8583	+	23.6874i	−1.37458	+	0.883390i	−0.999057	−	0.0434218i	$-0.986174\pi$
$719$	−36.8583	+	23.6874i	−1.37458	+	0.883390i	−0.375525	+	0.926812i	$0.622538\pi$
$720$		0			0
$721$	−2.46489	−	5.39737i	−0.0917975	−	0.201008i
$722$		0			0
$723$	12.4354			0.462476
$724$		0			0
$725$	2.64701			0.0983076
$726$		0			0
$727$	22.8562			0.847689			0.423844	−	0.905735i	$-0.360680\pi$
$727$	22.8562			0.847689			0.423844	+	0.905735i	$0.360680\pi$
$728$		0			0
$729$	12.8417			0.475619
$730$		0			0
$731$	−4.27956	−	9.37093i	−0.158285	−	0.346596i
$732$		0			0
$733$	26.3851	−	16.9566i	0.974554	−	0.626308i	0.0465652	−	0.998915i	$-0.485172\pi$
$733$	26.3851	−	16.9566i	0.974554	−	0.626308i	0.927989	+	0.372607i	$0.121536\pi$
$734$		0			0
$735$	21.1800			0.781236
$736$		0			0
$737$	−3.40769	−	24.0260i	−0.125524	−	0.885010i
$738$		0			0
$739$	13.3109	+	3.90843i	0.489649	+	0.143774i	0.517231	−	0.855846i	$-0.326963\pi$
$739$	13.3109	+	3.90843i	0.489649	+	0.143774i	−0.0275825	+	0.999620i	$0.508781\pi$
$740$		0			0
$741$	−19.8371	−	43.4373i	−0.728736	−	1.59571i
$742$		0			0
$743$	29.7277	−	34.3076i	1.09060	−	1.25862i	0.126824	−	0.991925i	$-0.459522\pi$
$743$	29.7277	−	34.3076i	1.09060	−	1.25862i	0.963780	−	0.266699i	$-0.0859329\pi$
$744$		0			0
$745$	−8.04810	−	9.28800i	−0.294859	−	0.340286i
$746$		0			0
$747$	−12.8112	+	8.23328i	−0.468739	+	0.301240i
$748$		0			0
$749$	−5.80857	−	3.73294i	−0.212240	−	0.136399i
$750$		0			0
$751$	7.06928	−	8.15839i	0.257962	−	0.297704i	−0.611965	−	0.790885i	$-0.709621\pi$
$751$	7.06928	−	8.15839i	0.257962	−	0.297704i	0.869927	+	0.493181i	$0.164166\pi$
$752$		0			0
$753$	6.98915			0.254699
$754$		0			0
$755$	−1.10502	−	1.27526i	−0.0402158	−	0.0464116i
$756$		0			0
$757$	−39.3259	+	11.5471i	−1.42932	+	0.419688i	−0.902648	−	0.430379i	$-0.858380\pi$
$757$	−39.3259	+	11.5471i	−1.42932	+	0.419688i	−0.526676	+	0.850066i	$0.676562\pi$
$758$		0			0
$759$	47.7007	+	14.1050i	1.73143	+	0.511979i
$760$		0			0
$761$	−42.9674	−	27.6135i	−1.55757	−	1.00099i	−0.983230	−	0.182371i	$-0.941623\pi$
$761$	−42.9674	−	27.6135i	−1.55757	−	1.00099i	−0.574339	−	0.818618i	$-0.694741\pi$
$762$		0			0
$763$	1.65473	−	0.485873i	0.0599053	−	0.0175898i
$764$		0			0
$765$	−3.57728	−	1.05039i	−0.129337	−	0.0379768i
$766$		0			0
$767$	−8.21752	+	57.1541i	−0.296717	+	2.06372i
$768$		0			0
$769$	2.63803	−	5.77649i	0.0951300	−	0.208306i	−0.856085	−	0.516836i	$-0.827110\pi$
$769$	2.63803	−	5.77649i	0.0951300	−	0.208306i	0.951215	+	0.308530i	$0.0998371\pi$
$770$		0			0
$771$	24.0608	+	52.6858i	0.866528	+	1.89743i
$772$		0			0
$773$	−6.46785	−	44.9849i	−0.232633	−	1.61799i	−0.686641	−	0.726997i	$-0.740915\pi$
$773$	−6.46785	−	44.9849i	−0.232633	−	1.61799i	0.454008	−	0.890998i	$-0.349994\pi$
$774$		0			0
$775$	−1.04542	+	2.28915i	−0.0375526	+	0.0822288i
$776$		0			0
$777$	−7.92969	+	9.15135i	−0.284476	+	0.328303i
$778$		0			0
$779$	−56.5775	+	36.3602i	−2.02710	+	1.30274i
$780$		0			0
$781$	36.6508	+	23.6529i	1.31147	+	0.846367i
$782$		0			0
$783$	−3.02967	−	3.49643i	−0.108272	−	0.124952i
$784$		0			0
$785$	1.71461	+	11.9254i	0.0611970	+	0.425634i
$786$		0			0
$787$	−6.50983	−	45.2769i	−0.232050	−	1.61395i	−0.689210	−	0.724561i	$-0.742042\pi$
$787$	−6.50983	−	45.2769i	−0.232050	−	1.61395i	0.457160	−	0.889384i	$-0.348867\pi$
$788$		0			0
$789$	−30.2090	+	19.4142i	−1.07547	+	0.691163i
$790$		0			0
$791$	−1.10151	−	7.66120i	−0.0391653	−	0.272401i
$792$		0			0
$793$	−1.07294	+	7.46244i	−0.0381011	+	0.264999i
$794$		0			0
$795$	37.0605	+	23.8174i	1.31440	+	0.844715i
$796$		0			0
$797$	3.92130	+	4.52542i	0.138899	+	0.160299i	0.820937	−	0.571018i	$-0.193452\pi$
$797$	3.92130	+	4.52542i	0.138899	+	0.160299i	−0.682038	+	0.731317i	$0.738906\pi$
$798$		0			0
$799$	−16.1984	−	10.4101i	−0.573058	−	0.368282i
$800$		0			0
$801$	−2.84031	+	3.27789i	−0.100357	+	0.115819i
$802$		0			0
$803$	−40.5688	−	11.9961i	−1.43164	−	0.423334i
$804$		0			0
$805$	3.92341	+	8.59108i	0.138282	+	0.302796i
$806$		0			0
$807$	−3.70713			−0.130497
$808$		0			0
$809$	32.2175	−	20.7049i	1.13271	−	0.727946i	0.166583	−	0.986027i	$-0.446726\pi$
$809$	32.2175	−	20.7049i	1.13271	−	0.727946i	0.966123	+	0.258081i	$0.0830901\pi$
$810$		0			0
$811$	−21.9175	−	6.43555i	−0.769627	−	0.225983i	−0.126732	−	0.991937i	$-0.540449\pi$
$811$	−21.9175	−	6.43555i	−0.769627	−	0.225983i	−0.642895	+	0.765954i	$0.722267\pi$
$812$		0			0
$813$	−0.487196	−	0.562254i	−0.0170867	−	0.0197191i
$814$		0			0
$815$	24.9566	−	28.8014i	0.874191	−	1.00887i
$816$		0			0
$817$	−26.3212	+	7.72861i	−0.920863	+	0.270390i
$818$		0			0
$819$	−2.95750	+	0.868400i	−0.103343	+	0.0303444i
$820$		0			0
$821$	−9.18228	+	20.1064i	−0.320464	+	0.701718i	−0.999475	−	0.0324104i	$-0.989682\pi$
$821$	−9.18228	+	20.1064i	−0.320464	+	0.701718i	0.679011	+	0.734128i	$0.262409\pi$
$822$		0			0
$823$	8.55644	−	18.7360i	0.298259	−	0.653096i	−0.699868	−	0.714272i	$-0.746758\pi$
$823$	8.55644	−	18.7360i	0.298259	−	0.653096i	0.998127	+	0.0611765i	$0.0194852\pi$
$824$		0			0
$825$	6.31869	−	13.7665i	0.219989	−	0.479288i
$826$		0			0
$827$	−4.32064	−	30.0507i	−0.150243	−	1.04497i	−0.915811	−	0.401610i	$-0.868451\pi$
$827$	−4.32064	−	30.0507i	−0.150243	−	1.04497i	0.765567	−	0.643356i	$-0.222458\pi$
$828$		0			0
$829$	2.65822	−	18.4883i	0.0923238	−	0.642126i	−0.890142	−	0.455683i	$-0.849395\pi$
$829$	2.65822	−	18.4883i	0.0923238	−	0.642126i	0.982466	−	0.186443i	$-0.0596959\pi$
$830$		0			0
$831$	−55.3295	−	35.5581i	−1.91936	−	1.23350i
$832$		0			0
$833$	5.97331	+	13.0797i	0.206963	+	0.453186i
$834$		0			0
$835$	6.00219	+	1.76240i	0.207714	+	0.0609904i
$836$		0			0
$837$	4.22028	−	1.23919i	0.145874	−	0.0428326i
$838$		0			0
$839$	−12.7208	+	27.8547i	−0.439171	+	0.961651i	0.552578	+	0.833461i	$0.313644\pi$
$839$	−12.7208	+	27.8547i	−0.439171	+	0.961651i	−0.991750	+	0.128190i	$0.959083\pi$
$840$		0			0
$841$	3.93549	−	27.3719i	0.135706	−	0.943859i
$842$		0			0
$843$	26.7652	+	7.85896i	0.921841	+	0.270677i
$844$		0			0
$845$	0.696563	−	4.84470i	0.0239625	−	0.166663i
$846$		0			0
$847$	−3.52321	+	7.63757i	−0.121059	+	0.262430i
$848$		0			0
$849$	4.80501	−	33.4196i	0.164908	−	1.14696i
$850$		0			0
$851$	56.8475	+	16.6919i	1.94871	+	0.572192i
$852$		0			0
$853$	−6.15333	+	42.7974i	−0.210686	+	1.46535i	0.560188	+	0.828366i	$0.310729\pi$
$853$	−6.15333	+	42.7974i	−0.210686	+	1.46535i	−0.770874	+	0.636988i	$0.780180\pi$
$854$		0			0
$855$	−4.12421	+	9.03077i	−0.141045	+	0.308846i
$856$		0			0
$857$	−36.3115	+	10.6620i	−1.24038	+	0.364207i	−0.835157	−	0.550012i	$-0.814623\pi$
$857$	−36.3115	+	10.6620i	−1.24038	+	0.364207i	−0.405219	+	0.914219i	$0.632805\pi$
$858$		0			0
$859$	−4.54687	−	1.33508i	−0.155137	−	0.0455524i	0.203242	−	0.979129i	$-0.434852\pi$
$859$	−4.54687	−	1.33508i	−0.155137	−	0.0455524i	−0.358379	+	0.933576i	$0.616670\pi$
$860$		0			0
$861$	7.16639	+	15.6922i	0.244230	+	0.534789i
$862$		0			0
$863$	−6.52636	−	4.19423i	−0.222160	−	0.142773i	0.424827	−	0.905274i	$-0.360335\pi$
$863$	−6.52636	−	4.19423i	−0.222160	−	0.142773i	−0.646987	+	0.762501i	$0.723971\pi$
$864$		0			0
$865$	−3.58104	+	24.9067i	−0.121759	+	0.846852i
$866$		0			0
$867$	3.41254	+	23.7347i	0.115896	+	0.806073i
$868$		0			0
$869$	32.3023	+	37.4228i	1.09578	+	1.26948i
$870$		0			0
$871$	12.1457	−	26.5953i	0.411541	−	0.901149i
$872$		0			0
$873$	5.04346	−	11.0436i	0.170695	−	0.373771i
$874$		0			0
$875$	8.80832	−	2.58636i	0.297776	−	0.0874348i
$876$		0			0
$877$	6.05196	−	1.77702i	0.204360	−	0.0600056i	−0.177950	−	0.984039i	$-0.556947\pi$
$877$	6.05196	−	1.77702i	0.204360	−	0.0600056i	0.382311	+	0.924034i	$0.375128\pi$
$878$		0			0
$879$	−42.7808	+	49.3717i	−1.44296	+	1.66527i
$880$		0			0
$881$	22.0010	+	25.3906i	0.741234	+	0.855430i	0.993688	−	0.112179i	$-0.0357831\pi$
$881$	22.0010	+	25.3906i	0.741234	+	0.855430i	−0.252454	+	0.967609i	$0.581238\pi$
$882$		0			0
$883$	−52.9507	−	15.5477i	−1.78193	−	0.523222i	−0.786406	−	0.617710i	$-0.788060\pi$
$883$	−52.9507	−	15.5477i	−1.78193	−	0.523222i	−0.995526	+	0.0944880i	$0.969879\pi$
$884$		0			0
$885$	40.1324	−	25.7915i	1.34904	−	0.866972i
$886$		0			0
$887$	−1.85493			−0.0622824			−0.0311412	−	0.999515i	$-0.509914\pi$
$887$	−1.85493			−0.0622824			−0.0311412	+	0.999515i	$0.509914\pi$
$888$		0			0
$889$	−1.09132	−	2.38965i	−0.0366017	−	0.0801464i
$890$		0			0
$891$	−35.0523	+	10.2198i	−1.17430	+	0.342375i
$892$		0			0
$893$	−33.5769	+	38.7498i	−1.12361	+	1.29671i
$894$		0			0
$895$	−28.0540	−	18.0292i	−0.937741	−	0.602650i
$896$		0			0
$897$	39.2473	+	45.2937i	1.31043	+	1.51231i
$898$		0			0
$899$	−1.07702	−	0.692158i	−0.0359206	−	0.0230848i
$900$		0			0
$901$	−4.25640	+	29.6039i	−0.141801	+	0.986249i
$902$		0			0
$903$	1.00142	+	6.96502i	0.0333251	+	0.231781i
$904$		0			0
$905$	6.73701	−	4.32961i	0.223946	−	0.143921i
$906$		0			0
$907$	4.90720	+	34.1303i	0.162941	+	1.13328i	0.893053	+	0.449952i	$0.148559\pi$
$907$	4.90720	+	34.1303i	0.162941	+	1.13328i	−0.730112	+	0.683328i	$0.760532\pi$
$908$		0			0
$909$	−0.281519	−	1.95801i	−0.00933741	−	0.0649431i
$910$		0			0
$911$	13.8742	+	16.0117i	0.459672	+	0.530490i	0.937510	−	0.347958i	$-0.113125\pi$
$911$	13.8742	+	16.0117i	0.459672	+	0.530490i	−0.477838	+	0.878448i	$0.658579\pi$
$912$		0			0
$913$	−32.8599	+	37.7766i	−1.08750	+	1.25022i
$914$		0			0
$915$	5.23997	−	3.36752i	0.173228	−	0.111327i
$916$		0			0
$917$	7.69471	−	8.88017i	0.254102	−	0.293249i
$918$		0			0
$919$	12.8813	−	28.2060i	0.424914	−	0.930431i	−0.569211	−	0.822191i	$-0.692751\pi$
$919$	12.8813	−	28.2060i	0.424914	−	0.930431i	0.994125	−	0.108240i	$-0.0345214\pi$
$920$		0			0
$921$	0.528121	+	3.67316i	0.0174022	+	0.121035i
$922$		0			0
$923$	21.8326	+	47.8067i	0.718629	+	1.57358i
$924$		0			0
$925$	7.49482	−	16.4114i	0.246428	−	0.539603i
$926$		0			0
$927$	−1.11405	+	7.74842i	−0.0365904	+	0.254492i
$928$		0			0
$929$	13.9231	+	4.08819i	0.456802	+	0.134129i	0.502035	−	0.864847i	$-0.332585\pi$
$929$	13.9231	+	4.08819i	0.456802	+	0.134129i	−0.0452329	+	0.998976i	$0.514403\pi$
$930$		0			0
$931$	36.7385	−	10.7874i	1.20406	−	0.353543i
$932$		0			0
$933$	−24.7662	−	15.9163i	−0.810810	−	0.521076i
$934$		0			0
$935$	−12.2577	−	0.0233625i	−0.400871	−	0.000764037i
$936$		0			0
$937$	35.4580	−	10.4114i	1.15836	−	0.340126i	0.354566	−	0.935031i	$-0.384629\pi$
$937$	35.4580	−	10.4114i	1.15836	−	0.340126i	0.803796	+	0.594906i	$0.202811\pi$
$938$		0			0
$939$	−29.2853	−	33.7970i	−0.955690	−	1.10292i
$940$		0			0
$941$	0.184388			0.00601087			0.00300544	−	0.999995i	$-0.499043\pi$
$941$	0.184388			0.00601087			0.00300544	+	0.999995i	$0.499043\pi$
$942$		0			0
$943$	55.2751	−	63.7908i	1.80000	−	2.07732i
$944$		0			0
$945$	−4.22872	−	2.71764i	−0.137560	−	0.0884047i
$946$		0			0
$947$	−21.2553	+	13.6600i	−0.690704	+	0.443889i	−0.838336	−	0.545154i	$-0.816471\pi$
$947$	−21.2553	+	13.6600i	−0.690704	+	0.443889i	0.147632	+	0.989042i	$0.452835\pi$
$948$		0			0
$949$	−33.3793	−	38.5217i	−1.08354	−	1.25047i
$950$		0			0
$951$	11.9826	−	13.8287i	0.388562	−	0.448425i
$952$		0			0
$953$	−12.6069	−	27.6053i	−0.408378	−	0.894222i	−0.996352	−	0.0853424i	$-0.972802\pi$
$953$	−12.6069	−	27.6053i	−0.408378	−	0.894222i	0.587974	−	0.808880i	$-0.299926\pi$
$954$		0			0
$955$	17.1324	+	5.03051i	0.554390	+	0.162784i
$956$		0			0
$957$	6.47468	+	4.17848i	0.209297	+	0.135071i
$958$		0			0
$959$	−4.32346			−0.139612
$960$		0			0
$961$	−25.0549	+	16.1018i	−0.808223	+	0.519413i
$962$		0			0
$963$	3.78412	+	8.28606i	0.121941	+	0.267015i
$964$		0			0
$965$	−4.24834			−0.136759
$966$		0			0
$967$	19.7423			0.634870			0.317435	−	0.948280i	$-0.397178\pi$
$967$	19.7423			0.634870			0.317435	+	0.948280i	$0.397178\pi$
$968$		0			0
$969$	−26.7844			−0.860438
$970$		0			0
$971$	5.28846			0.169715			0.0848574	−	0.996393i	$-0.472957\pi$
$971$	5.28846			0.169715			0.0848574	+	0.996393i	$0.472957\pi$
$972$		0			0
$973$	−0.861224	−	1.88582i	−0.0276096	−	0.0604565i
$974$		0			0
$975$	15.3531	−	9.86686i	0.491694	−	0.315992i
$976$		0			0
$977$	−13.4012			−0.428742			−0.214371	−	0.976752i	$-0.568770\pi$
$977$	−13.4012			−0.428742			−0.214371	+	0.976752i	$0.568770\pi$
$978$		0			0
$979$	−5.94848	+	12.9599i	−0.190114	+	0.414201i
$980$		0			0
$981$	−2.18307	−	0.641007i	−0.0697000	−	0.0204658i
$982$		0			0
$983$	2.41216	+	5.28189i	0.0769359	+	0.168466i	0.944192	−	0.329397i	$-0.106845\pi$
$983$	2.41216	+	5.28189i	0.0769359	+	0.168466i	−0.867256	+	0.497863i	$0.834118\pi$
$984$		0			0
$985$	−12.2885	+	14.1817i	−0.391546	+	0.451868i
$986$		0			0
$987$	8.61276	+	9.93966i	0.274147	+	0.316383i
$988$		0			0
$989$	28.9637	−	18.6139i	0.920993	−	0.591886i
$990$		0			0
$991$	−47.1846	−	30.3237i	−1.49887	−	0.963264i	−0.995042	−	0.0994591i	$-0.968289\pi$
$991$	−47.1846	−	30.3237i	−1.49887	−	0.963264i	−0.503826	−	0.863805i	$-0.668075\pi$
$992$		0			0
$993$	−14.8759	+	17.1676i	−0.472071	+	0.544799i
$994$		0			0
$995$	−9.80159			−0.310731
$996$		0			0
$997$	16.4523	+	18.9869i	0.521048	+	0.601322i	0.953893	−	0.300147i	$-0.0970356\pi$
$997$	16.4523	+	18.9869i	0.521048	+	0.601322i	−0.432845	+	0.901468i	$0.642490\pi$
$998$		0			0
$999$	−30.2560	+	8.88397i	−0.957258	+	0.281076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.q.b.89.14	✓	170
121.34	even	11	inner	968.2.q.b.881.14	yes	170

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.q.b.89.14	✓	170	1.1	even	1	trivial
968.2.q.b.881.14	yes	170	121.34	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+2.00219 q^{3} +(-0.684988 - 1.49991i) q^{5} +(-0.643255 + 0.413395i) q^{7} +1.00878 q^{9} +(3.18405 - 0.928334i) q^{11} +(3.83417 + 1.12581i) q^{13} +(-1.37148 - 3.00312i) q^{15} +(1.46779 - 1.69392i) q^{17} +(-3.90850 - 4.51065i) q^{19} +(-1.28792 + 0.827697i) q^{21} +(6.30161 + 4.04980i) q^{23} +(1.49377 - 1.72390i) q^{25} -3.98681 q^{27} +(0.759925 + 0.877000i) q^{29} +(-1.05856 + 0.310822i) q^{31} +(6.37509 - 1.85871i) q^{33} +(1.06068 + 0.681657i) q^{35} +(7.58903 - 2.22834i) q^{37} +(7.67675 + 2.25410i) q^{39} +(1.60364 - 11.1535i) q^{41} +(1.90935 - 4.18089i) q^{43} +(-0.691003 - 1.51308i) q^{45} +(-1.22259 - 8.50330i) q^{47} +(-2.66502 + 5.83559i) q^{49} +(2.93879 - 3.39155i) q^{51} +(-11.2255 + 7.21418i) q^{53} +(-3.57346 - 4.13991i) q^{55} +(-7.82558 - 9.03120i) q^{57} +(2.05642 + 14.3027i) q^{59} +(0.268500 + 1.86746i) q^{61} +(-0.648904 + 0.417025i) q^{63} +(-0.937736 - 6.52209i) q^{65} +(1.04126 - 7.24214i) q^{67} +(12.6170 + 8.10848i) q^{69} +(8.61277 + 9.93966i) q^{71} +(-10.7306 - 6.89616i) q^{73} +(2.99082 - 3.45159i) q^{75} +(-1.66439 + 1.91343i) q^{77} +(6.19196 + 13.5585i) q^{79} -11.0087 q^{81} +(-12.6997 + 8.16162i) q^{83} +(-3.54615 - 1.04124i) q^{85} +(1.52152 + 1.75592i) q^{87} +(-2.81558 + 3.24936i) q^{89} +(-2.93176 + 0.860841i) q^{91} +(-2.11945 + 0.622326i) q^{93} +(-4.08831 + 8.95216i) q^{95} +(4.99956 - 10.9475i) q^{97} +(3.21201 - 0.936486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) \) 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Introduction

L-functions

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