LMFDB - Embedded newform 920.2.bv.a.217.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.15
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959355 + 0.208695i) q^{3} +(0.726866 + 2.11463i) q^{5} +(-0.0753241 + 0.0411301i) q^{7} +(-1.85209 + 0.845820i) q^{9} +O(q^{10})$	\(q+(-0.959355 + 0.208695i) q^{3} +(0.726866 + 2.11463i) q^{5} +(-0.0753241 + 0.0411301i) q^{7} +(-1.85209 + 0.845820i) q^{9} +(4.51994 + 3.91655i) q^{11} +(0.877281 - 1.60662i) q^{13} +(-1.13863 - 1.87699i) q^{15} +(-3.86341 - 2.89211i) q^{17} +(-0.144686 + 1.00631i) q^{19} +(0.0636789 - 0.0551781i) q^{21} +(3.88395 + 2.81335i) q^{23} +(-3.94333 + 3.07411i) q^{25} +(3.95818 - 2.96306i) q^{27} +(-8.38734 + 1.20592i) q^{29} +(-7.17751 + 4.61271i) q^{31} +(-5.15358 - 2.81407i) q^{33} +(-0.141726 - 0.129387i) q^{35} +(2.39284 + 0.892482i) q^{37} +(-0.506330 + 1.72440i) q^{39} +(0.746664 - 1.63497i) q^{41} +(-0.299608 - 1.37727i) q^{43} +(-3.13482 - 3.30169i) q^{45} +(3.73416 + 3.73416i) q^{47} +(-3.78050 + 5.88258i) q^{49} +(4.30995 + 1.96829i) q^{51} +(3.64573 + 6.67665i) q^{53} +(-4.99666 + 12.4048i) q^{55} +(-0.0712072 - 0.995606i) q^{57} +(2.26731 + 7.72176i) q^{59} +(-6.29683 - 9.79806i) q^{61} +(0.104718 - 0.139887i) q^{63} +(4.03508 + 0.687328i) q^{65} +(-10.8925 - 0.779044i) q^{67} +(-4.31322 - 1.88844i) q^{69} +(-0.0606133 - 0.0699515i) q^{71} +(0.676454 + 0.903637i) q^{73} +(3.14150 - 3.77211i) q^{75} +(-0.501548 - 0.109105i) q^{77} +(2.40156 - 0.705161i) q^{79} +(0.821130 - 0.947634i) q^{81} +(-3.35451 + 8.99379i) q^{83} +(3.30757 - 10.2719i) q^{85} +(7.79477 - 2.90730i) q^{87} +(-3.69732 - 2.37612i) q^{89} +0.157100i q^{91} +(5.92313 - 5.92313i) q^{93} +(-2.23315 + 0.425497i) q^{95} +(4.13052 + 11.0743i) q^{97} +(-11.6840 - 3.43074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.959355	+	0.208695i	−0.553884	+	0.120490i	−0.480791	−	0.876835i	$-0.659650\pi$
$3$	−0.959355	+	0.208695i	−0.553884	+	0.120490i	−0.0730925	+	0.997325i	$0.523287\pi$
$4$		0			0
$5$	0.726866	+	2.11463i	0.325064	+	0.945692i
$5$	0.726866	+	2.11463i	0.325064	+	0.945692i
$6$		0			0
$7$	−0.0753241	+	0.0411301i	−0.0284698	+	0.0155457i	−0.493421	−	0.869791i	$-0.664254\pi$
$7$	−0.0753241	+	0.0411301i	−0.0284698	+	0.0155457i	0.464951	+	0.885336i	$0.346072\pi$
$8$		0			0
$9$	−1.85209	+	0.845820i	−0.617363	+	0.281940i
$10$		0			0
$11$	4.51994	+	3.91655i	1.36281	+	1.18088i	0.964640	+	0.263572i	$0.0849008\pi$
$11$	4.51994	+	3.91655i	1.36281	+	1.18088i	0.398172	+	0.917311i	$0.369645\pi$
$12$		0			0
$13$	0.877281	−	1.60662i	0.243314	−	0.445596i	−0.727273	−	0.686349i	$-0.759212\pi$
$13$	0.877281	−	1.60662i	0.243314	−	0.445596i	0.970587	+	0.240752i	$0.0773942\pi$
$14$		0			0
$15$	−1.13863	−	1.87699i	−0.293994	−	0.484636i
$16$		0			0
$17$	−3.86341	−	2.89211i	−0.937015	−	0.701440i	0.0174239	−	0.999848i	$-0.494454\pi$
$17$	−3.86341	−	2.89211i	−0.937015	−	0.701440i	−0.954438	+	0.298408i	$0.903544\pi$
$18$		0			0
$19$	−0.144686	+	1.00631i	−0.0331932	+	0.230864i	−0.999664	−	0.0259118i	$-0.991751\pi$
$19$	−0.144686	+	1.00631i	−0.0331932	+	0.230864i	0.966471	+	0.256776i	$0.0826602\pi$
$20$		0			0
$21$	0.0636789	−	0.0551781i	0.0138959	−	0.0120408i
$22$		0			0
$23$	3.88395	+	2.81335i	0.809860	+	0.586623i
$23$	3.88395	+	2.81335i	0.809860	+	0.586623i
$24$		0			0
$25$	−3.94333	+	3.07411i	−0.788666	+	0.614822i
$26$		0			0
$27$	3.95818	−	2.96306i	0.761753	−	0.570241i
$28$		0			0
$29$	−8.38734	+	1.20592i	−1.55749	+	0.223933i	−0.866592	−	0.499018i	$-0.833694\pi$
$29$	−8.38734	+	1.20592i	−1.55749	+	0.223933i	−0.690899	+	0.722951i	$0.742785\pi$
$30$		0			0
$31$	−7.17751	+	4.61271i	−1.28912	+	0.828467i	−0.991983	−	0.126369i	$-0.959668\pi$
$31$	−7.17751	+	4.61271i	−1.28912	+	0.828467i	−0.297136	+	0.954835i	$0.596031\pi$
$32$		0			0
$33$	−5.15358	−	2.81407i	−0.897124	−	0.489867i
$34$		0			0
$35$	−0.141726	−	0.129387i	−0.0239560	−	0.0218703i
$36$		0			0
$37$	2.39284	+	0.892482i	0.393380	+	0.146723i	0.538367	−	0.842710i	$-0.319041\pi$
$37$	2.39284	+	0.892482i	0.393380	+	0.146723i	−0.144987	+	0.989434i	$0.546314\pi$
$38$		0			0
$39$	−0.506330	+	1.72440i	−0.0810777	+	0.276125i
$40$		0			0
$41$	0.746664	−	1.63497i	0.116609	−	0.255339i	−0.842323	−	0.538972i	$-0.818813\pi$
$41$	0.746664	−	1.63497i	0.116609	−	0.255339i	0.958933	+	0.283634i	$0.0915400\pi$
$42$		0			0
$43$	−0.299608	−	1.37727i	−0.0456898	−	0.210032i	0.948642	−	0.316350i	$-0.102458\pi$
$43$	−0.299608	−	1.37727i	−0.0456898	−	0.210032i	−0.994332	+	0.106318i	$0.966094\pi$
$44$		0			0
$45$	−3.13482	−	3.30169i	−0.467311	−	0.492186i
$46$		0			0
$47$	3.73416	+	3.73416i	0.544683	+	0.544683i	0.924898	−	0.380215i	$-0.124150\pi$
$47$	3.73416	+	3.73416i	0.544683	+	0.544683i	−0.380215	+	0.924898i	$0.624150\pi$
$48$		0			0
$49$	−3.78050	+	5.88258i	−0.540072	+	0.840368i
$50$		0			0
$51$	4.30995	+	1.96829i	0.603514	+	0.275615i
$52$		0			0
$53$	3.64573	+	6.67665i	0.500779	+	0.917109i	0.998753	+	0.0499169i	$0.0158957\pi$
$53$	3.64573	+	6.67665i	0.500779	+	0.917109i	−0.497974	+	0.867192i	$0.665923\pi$
$54$		0			0
$55$	−4.99666	+	12.4048i	−0.673750	+	1.67266i
$56$		0			0
$57$	−0.0712072	−	0.995606i	−0.00943162	−	0.131871i
$58$		0			0
$59$	2.26731	+	7.72176i	0.295179	+	1.00529i	0.964887	+	0.262664i	$0.0846009\pi$
$59$	2.26731	+	7.72176i	0.295179	+	1.00529i	−0.669708	+	0.742624i	$0.733581\pi$
$60$		0			0
$61$	−6.29683	−	9.79806i	−0.806227	−	1.25451i	−0.963699	−	0.266990i	$-0.913971\pi$
$61$	−6.29683	−	9.79806i	−0.806227	−	1.25451i	0.157472	−	0.987523i	$-0.449665\pi$
$62$		0			0
$63$	0.104718	−	0.139887i	0.0131933	−	0.0176241i
$64$		0			0
$65$	4.03508	+	0.687328i	0.500490	+	0.0852526i
$66$		0			0
$67$	−10.8925	−	0.779044i	−1.33073	−	0.0951754i	−0.612215	−	0.790691i	$-0.709721\pi$
$67$	−10.8925	−	0.779044i	−1.33073	−	0.0951754i	−0.718511	+	0.695516i	$0.755176\pi$
$68$		0			0
$69$	−4.31322	−	1.88844i	−0.519250	−	0.227341i
$70$		0			0
$71$	−0.0606133	−	0.0699515i	−0.00719348	−	0.00830171i	0.752141	−	0.659002i	$-0.229021\pi$
$71$	−0.0606133	−	0.0699515i	−0.00719348	−	0.00830171i	−0.759335	+	0.650700i	$0.774476\pi$
$72$		0			0
$73$	0.676454	+	0.903637i	0.0791730	+	0.105763i	0.838379	−	0.545087i	$-0.183504\pi$
$73$	0.676454	+	0.903637i	0.0791730	+	0.105763i	−0.759206	+	0.650850i	$0.774413\pi$
$74$		0			0
$75$	3.14150	−	3.77211i	0.362749	−	0.435566i
$76$		0			0
$77$	−0.501548	−	0.109105i	−0.0571567	−	0.0124337i
$78$		0			0
$79$	2.40156	−	0.705161i	0.270196	−	0.0793368i	−0.143828	−	0.989603i	$-0.545941\pi$
$79$	2.40156	−	0.705161i	0.270196	−	0.0793368i	0.414024	+	0.910266i	$0.364123\pi$
$80$		0			0
$81$	0.821130	−	0.947634i	0.0912366	−	0.105293i
$82$		0			0
$83$	−3.35451	+	8.99379i	−0.368205	+	0.987197i	0.612286	+	0.790636i	$0.290250\pi$
$83$	−3.35451	+	8.99379i	−0.368205	+	0.987197i	−0.980492	+	0.196561i	$0.937023\pi$
$84$		0			0
$85$	3.30757	−	10.2719i	0.358756	−	1.11414i
$86$		0			0
$87$	7.79477	−	2.90730i	0.835687	−	0.311695i
$88$		0			0
$89$	−3.69732	−	2.37612i	−0.391915	−	0.251869i	0.329811	−	0.944047i	$-0.393015\pi$
$89$	−3.69732	−	2.37612i	−0.391915	−	0.251869i	−0.721727	+	0.692178i	$0.756651\pi$
$90$		0			0
$91$			0.157100i			0.0164685i
$92$		0			0
$93$	5.92313	−	5.92313i	0.614200	−	0.614200i
$94$		0			0
$95$	−2.23315	+	0.425497i	−0.229116	+	0.0436551i
$96$		0			0
$97$	4.13052	+	11.0743i	0.419390	+	1.12443i	0.959221	+	0.282656i	$0.0912154\pi$
$97$	4.13052	+	11.0743i	0.419390	+	1.12443i	−0.539831	+	0.841773i	$0.681512\pi$
$98$		0			0
$99$	−11.6840	−	3.43074i	−1.17429	−	0.344802i
$100$		0			0
$101$	0.677707	+	1.48397i	0.0674344	+	0.147661i	0.940348	−	0.340214i	$-0.110500\pi$
$101$	0.677707	+	1.48397i	0.0674344	+	0.147661i	−0.872914	+	0.487875i	$0.837772\pi$
$102$		0			0
$103$	−3.50695	+	0.250822i	−0.345550	+	0.0247142i	−0.243036	−	0.970017i	$-0.578143\pi$
$103$	−3.50695	+	0.250822i	−0.345550	+	0.0247142i	−0.102514	+	0.994732i	$0.532689\pi$
$104$		0			0
$105$	0.162967	+	0.0945503i	0.0159040	+	0.00922717i
$106$		0			0
$107$	1.51031	−	6.94277i	0.146007	−	0.671183i	−0.844708	−	0.535227i	$-0.820226\pi$
$107$	1.51031	−	6.94277i	0.146007	−	0.671183i	0.990715	−	0.135955i	$-0.0434104\pi$
$108$		0			0
$109$	1.32991	+	9.24970i	0.127382	+	0.885961i	0.948855	+	0.315713i	$0.102244\pi$
$109$	1.32991	+	9.24970i	0.127382	+	0.885961i	−0.821473	+	0.570248i	$0.806847\pi$
$110$		0			0
$111$	−2.48183	−	0.356834i	−0.235565	−	0.0338692i
$112$		0			0
$113$	−0.0943829	+	1.31965i	−0.00887880	+	0.124142i	−0.999958	−	0.00913001i	$-0.997094\pi$
$113$	−0.0943829	+	1.31965i	−0.00887880	+	0.124142i	0.991080	+	0.133272i	$0.0425483\pi$
$114$		0			0
$115$	−3.12608	+	10.2581i	−0.291508	+	0.956568i
$116$		0			0
$117$	−0.265890	+	3.71763i	−0.0245815	+	0.343695i
$118$		0			0
$119$	0.409961	+	0.0589435i	0.0375810	+	0.00540334i
$120$		0			0
$121$	3.52502	+	24.5170i	0.320456	+	2.22882i
$122$		0			0
$123$	−0.375107	+	1.72434i	−0.0338222	+	0.155478i
$124$		0			0
$125$	−9.36688	−	6.10423i	−0.837799	−	0.545979i
$126$		0			0
$127$	21.3967	−	1.53032i	1.89865	−	0.135794i	0.927432	−	0.373993i	$-0.122012\pi$
$127$	21.3967	−	1.53032i	1.89865	−	0.135794i	0.971216	+	0.238199i	$0.0765570\pi$
$128$		0			0
$129$	0.574860	+	1.25877i	0.0506136	+	0.110828i
$130$		0			0
$131$	4.14347	+	1.21663i	0.362017	+	0.106298i	0.457682	−	0.889116i	$-0.348680\pi$
$131$	4.14347	+	1.21663i	0.362017	+	0.106298i	−0.0956656	+	0.995414i	$0.530498\pi$
$132$		0			0
$133$	−0.0304914	−	0.0817506i	−0.00264394	−	0.00708868i
$134$		0			0
$135$	9.14285	+	6.21635i	0.786891	+	0.535019i
$136$		0			0
$137$	10.0988	−	10.0988i	0.862799	−	0.862799i	−0.128864	−	0.991662i	$-0.541133\pi$
$137$	10.0988	−	10.0988i	0.862799	−	0.862799i	0.991662	+	0.128864i	$0.0411329\pi$
$138$		0			0
$139$		−	6.25614i		−	0.530639i	−0.964161	−	0.265320i	$-0.914523\pi$
$139$		−	6.25614i		−	0.530639i	0.964161	−	0.265320i	$-0.0854775\pi$
$140$		0			0
$141$	−4.36168	−	2.80308i	−0.367320	−	0.236062i
$142$		0			0
$143$	10.2577	−	3.82591i	0.857788	−	0.319939i
$144$		0			0
$145$	−8.64655	−	16.8596i	−0.718057	−	1.40011i
$146$		0			0
$147$	2.39918	−	6.43245i	0.197881	−	0.530540i
$148$		0			0
$149$	11.8635	−	13.6913i	0.971899	−	1.12163i	−0.0206498	−	0.999787i	$-0.506574\pi$
$149$	11.8635	−	13.6913i	0.971899	−	1.12163i	0.992549	−	0.121845i	$-0.0388810\pi$
$150$		0			0
$151$	1.51177	−	0.443895i	0.123026	−	0.0361237i	−0.219640	−	0.975581i	$-0.570488\pi$
$151$	1.51177	−	0.443895i	0.123026	−	0.0361237i	0.342666	+	0.939457i	$0.388670\pi$
$152$		0			0
$153$	9.60158	+	2.08870i	0.776242	+	0.168861i
$154$		0			0
$155$	−14.9713	−	11.8250i	−1.20252	−	0.949805i
$156$		0			0
$157$	−14.6887	−	19.6218i	−1.17229	−	1.56599i	−0.752830	−	0.658215i	$-0.771312\pi$
$157$	−14.6887	−	19.6218i	−1.17229	−	1.56599i	−0.419456	−	0.907776i	$-0.637779\pi$
$158$		0			0
$159$	−4.89093	−	5.64443i	−0.387876	−	0.447633i
$160$		0			0
$161$	−0.408268	−	0.0521656i	−0.0321761	−	0.00411123i
$162$		0			0
$163$	24.9032	+	1.78111i	1.95057	+	0.139507i	0.990240	−	0.139370i	$-0.0445078\pi$
$163$	24.9032	+	1.78111i	1.95057	+	0.139507i	0.960327	+	0.278878i	$0.0899623\pi$
$164$		0			0
$165$	2.20475	−	12.9434i	0.171640	−	1.00764i
$166$		0			0
$167$	8.43074	−	11.2621i	0.652390	−	0.871491i	−0.345364	−	0.938469i	$-0.612245\pi$
$167$	8.43074	−	11.2621i	0.652390	−	0.871491i	0.997754	+	0.0669775i	$0.0213356\pi$
$168$		0			0
$169$	5.21672	+	8.11738i	0.401286	+	0.624414i
$170$		0			0
$171$	−0.583189	−	1.98616i	−0.0445976	−	0.151885i
$172$		0			0
$173$	−1.29763	−	18.1432i	−0.0986569	−	1.37940i	−0.769899	−	0.638165i	$-0.779694\pi$
$173$	−1.29763	−	18.1432i	−0.0986569	−	1.37940i	0.671242	−	0.741238i	$-0.265761\pi$
$174$		0			0
$175$	0.170590	−	0.393744i	0.0128954	−	0.0297643i
$176$		0			0
$177$	−3.78665	−	6.93473i	−0.284622	−	0.521246i
$178$		0			0
$179$	−2.56518	−	1.17148i	−0.191731	−	0.0875605i	0.317236	−	0.948347i	$-0.397245\pi$
$179$	−2.56518	−	1.17148i	−0.191731	−	0.0875605i	−0.508967	+	0.860786i	$0.669972\pi$
$180$		0			0
$181$	−13.5089	+	21.0203i	−1.00411	+	1.56243i	−0.189943	+	0.981795i	$0.560830\pi$
$181$	−13.5089	+	21.0203i	−1.00411	+	1.56243i	−0.814167	+	0.580630i	$0.802806\pi$
$182$		0			0
$183$	8.08570	+	8.08570i	0.597712	+	0.597712i
$184$		0			0
$185$	−0.147998	+	5.70868i	−0.0108810	+	0.419711i
$186$		0			0
$187$	−6.13527	−	28.2034i	−0.448655	−	2.06244i
$188$		0			0
$189$	−0.176276	+	0.385990i	−0.0128222	+	0.0280767i
$190$		0			0
$191$	1.73901	−	5.92252i	0.125830	−	0.428539i	−0.872347	−	0.488887i	$-0.837403\pi$
$191$	1.73901	−	5.92252i	0.125830	−	0.428539i	0.998177	+	0.0603484i	$0.0192212\pi$
$192$		0			0
$193$	1.38436	+	0.516341i	0.0996487	+	0.0371671i	0.398794	−	0.917040i	$-0.369429\pi$
$193$	1.38436	+	0.516341i	0.0996487	+	0.0371671i	−0.299145	+	0.954208i	$0.596702\pi$
$194$		0			0
$195$	−4.01451	+	0.182708i	−0.287485	+	0.0130840i
$196$		0			0
$197$	−9.03107	−	4.93134i	−0.643437	−	0.351343i	0.124173	−	0.992261i	$-0.460372\pi$
$197$	−9.03107	−	4.93134i	−0.643437	−	0.351343i	−0.767610	+	0.640917i	$0.778554\pi$
$198$		0			0
$199$	12.6020	−	8.09881i	0.893331	−	0.574109i	−0.0114743	−	0.999934i	$-0.503652\pi$
$199$	12.6020	−	8.09881i	0.893331	−	0.574109i	0.904806	+	0.425825i	$0.140016\pi$
$200$		0			0
$201$	10.6123	−	1.52582i	0.748535	−	0.107623i
$202$		0			0
$203$	0.582170	−	0.435807i	0.0408603	−	0.0305877i
$204$		0			0
$205$	4.00008	+	0.390518i	0.279377	+	0.0272749i
$206$		0			0
$207$	−9.57301	−	1.92544i	−0.665370	−	0.133827i
$208$		0			0
$209$	−4.59524	+	3.98180i	−0.317860	+	0.275427i
$210$		0			0
$211$	−1.00059	+	6.95925i	−0.0688834	+	0.479095i	0.925956	+	0.377632i	$0.123261\pi$
$211$	−1.00059	+	6.95925i	−0.0688834	+	0.479095i	−0.994839	+	0.101463i	$0.967648\pi$
$212$		0			0
$213$	0.0727482	+	0.0544586i	0.00498462	+	0.00373144i
$214$		0			0
$215$	2.69465	−	1.63465i	0.183774	−	0.111482i
$216$		0			0
$217$	0.350919	−	0.642660i	0.0238219	−	0.0436266i
$218$		0			0
$219$	−0.837544	−	0.725736i	−0.0565960	−	0.0490407i
$220$		0			0
$221$	−8.03582	+	3.66984i	−0.540548	+	0.246860i
$222$		0			0
$223$	−7.36564	+	4.02194i	−0.493240	+	0.269329i	−0.706560	−	0.707653i	$-0.749754\pi$
$223$	−7.36564	+	4.02194i	−0.493240	+	0.269329i	0.213320	+	0.976982i	$0.431572\pi$
$224$		0			0
$225$	4.70325	−	9.02887i	0.313550	−	0.601925i
$226$		0			0
$227$	17.0691	−	3.71315i	1.13291	−	0.246450i	0.393253	−	0.919430i	$-0.371349\pi$
$227$	17.0691	−	3.71315i	1.13291	−	0.246450i	0.739661	+	0.672980i	$0.234986\pi$
$228$		0			0
$229$	26.2812			1.73671			0.868357	−	0.495940i	$-0.165176\pi$
$229$	26.2812			1.73671			0.868357	+	0.495940i	$0.165176\pi$
$230$		0			0
$231$	0.503932			0.0331563
$232$		0			0
$233$	3.79423	−	0.825384i	0.248568	−	0.0540727i	−0.0865548	−	0.996247i	$-0.527586\pi$
$233$	3.79423	−	0.825384i	0.248568	−	0.0540727i	0.335123	+	0.942174i	$0.391222\pi$
$234$		0			0
$235$	−5.18213	+	10.6106i	−0.338045	+	0.692159i
$236$		0			0
$237$	−2.15678	+	1.17769i	−0.140098	+	0.0764993i
$238$		0			0
$239$	−22.2765	+	10.1733i	−1.44094	+	0.658057i	−0.974066	−	0.226264i	$-0.927349\pi$
$239$	−22.2765	+	10.1733i	−1.44094	+	0.658057i	−0.466879	+	0.884321i	$0.654621\pi$
$240$		0			0
$241$	12.1955	+	10.5675i	0.785581	+	0.680710i	0.952256	−	0.305302i	$-0.0987574\pi$
$241$	12.1955	+	10.5675i	0.785581	+	0.680710i	−0.166674	+	0.986012i	$0.553303\pi$
$242$		0			0
$243$	−7.69876	+	14.0992i	−0.493876	+	0.904466i
$244$		0			0
$245$	−15.1874	−	3.71852i	−0.970288	−	0.237568i
$246$		0			0
$247$	1.48983	+	1.11527i	0.0947958	+	0.0709632i
$248$		0			0
$249$	1.34121	−	9.32830i	0.0849955	−	0.591157i
$250$		0			0
$251$	23.2979	−	20.1877i	1.47055	−	1.27424i	0.583873	−	0.811845i	$-0.301536\pi$
$251$	23.2979	−	20.1877i	1.47055	−	1.27424i	0.886675	−	0.462393i	$-0.153009\pi$
$252$		0			0
$253$	6.53661	+	27.9278i	0.410953	+	1.75581i
$254$		0			0
$255$	−1.02945	+	10.5446i	−0.0644665	+	0.660331i
$256$		0			0
$257$	0.920490	−	0.689070i	0.0574186	−	0.0429830i	−0.570183	−	0.821518i	$-0.693128\pi$
$257$	0.920490	−	0.689070i	0.0574186	−	0.0429830i	0.627601	+	0.778535i	$0.284037\pi$
$258$		0			0
$259$	−0.216946	+	0.0311921i	−0.0134804	+	0.00193819i
$260$		0			0
$261$	14.5141	−	9.32765i	0.898401	−	0.577367i
$262$		0			0
$263$	5.69744	+	3.11104i	0.351319	+	0.191835i	0.645212	−	0.764004i	$-0.276769\pi$
$263$	5.69744	+	3.11104i	0.351319	+	0.191835i	−0.293893	+	0.955838i	$0.594951\pi$
$264$		0			0
$265$	−11.4687	+	12.5624i	−0.704517	+	0.771702i
$266$		0			0
$267$	4.04293	+	1.50793i	0.247423	+	0.0922841i
$268$		0			0
$269$	−1.79168	+	6.10191i	−0.109241	+	0.372040i	−0.995909	−	0.0903671i	$-0.971196\pi$
$269$	−1.79168	+	6.10191i	−0.109241	+	0.372040i	0.886668	+	0.462407i	$0.153014\pi$
$270$		0			0
$271$	−5.92270	+	12.9689i	−0.359778	+	0.787804i	0.640032	+	0.768348i	$0.278921\pi$
$271$	−5.92270	+	12.9689i	−0.359778	+	0.787804i	−0.999811	+	0.0194566i	$0.993806\pi$
$272$		0			0
$273$	−0.0327859	−	0.150715i	−0.00198430	−	0.00912166i
$274$		0			0
$275$	−29.8635	−	1.54947i	−1.80084	−	0.0934365i
$276$		0			0
$277$	−18.5188	−	18.5188i	−1.11269	−	1.11269i	−0.992786	−	0.119904i	$-0.961741\pi$
$277$	−18.5188	−	18.5188i	−1.11269	−	1.11269i	−0.119904	−	0.992786i	$-0.538259\pi$
$278$		0			0
$279$	9.39187	−	14.6140i	0.562276	−	0.874919i
$280$		0			0
$281$	20.6671	+	9.43833i	1.23289	+	0.563044i	0.921922	−	0.387375i	$-0.126618\pi$
$281$	20.6671	+	9.43833i	1.23289	+	0.563044i	0.310972	+	0.950419i	$0.399346\pi$
$282$		0			0
$283$	−1.02916	−	1.88477i	−0.0611774	−	0.112038i	0.845301	−	0.534291i	$-0.179421\pi$
$283$	−1.02916	−	1.88477i	−0.0611774	−	0.112038i	−0.906478	+	0.422253i	$0.861239\pi$
$284$		0			0
$285$	2.05358	−	0.874249i	0.121644	−	0.0517861i
$286$		0			0
$287$	0.0110045	+	0.153863i	0.000649574	+	0.00908223i
$288$		0			0
$289$	1.77217	+	6.03545i	0.104245	+	0.355027i
$290$		0			0
$291$	−6.27379	−	9.76220i	−0.367776	−	0.572270i
$292$		0			0
$293$	8.09751	−	10.8170i	0.473062	−	0.631937i	−0.499017	−	0.866592i	$-0.666305\pi$
$293$	8.09751	−	10.8170i	0.473062	−	0.631937i	0.972079	+	0.234656i	$0.0753963\pi$
$294$		0			0
$295$	−14.6806	+	10.4072i	−0.854740	+	0.605932i
$296$		0			0
$297$	29.4957	+	2.10957i	1.71151	+	0.122410i
$298$		0			0
$299$	7.92730	−	3.77194i	0.458447	−	0.218137i
$300$		0			0
$301$	0.0792151	+	0.0914191i	0.00456588	+	0.00526931i
$302$		0			0
$303$	−0.959859	−	1.28222i	−0.0551424	−	0.0736617i
$304$		0			0
$305$	16.1423	−	20.4374i	0.924308	−	1.17024i
$306$		0			0
$307$	24.1241	+	5.24789i	1.37684	+	0.299513i	0.839273	−	0.543710i	$-0.182981\pi$
$307$	24.1241	+	5.24789i	1.37684	+	0.299513i	0.537565	+	0.843223i	$0.319344\pi$
$308$		0			0
$309$	3.31206	−	0.972509i	0.188417	−	0.0553241i
$310$		0			0
$311$	−7.77861	+	8.97699i	−0.441084	+	0.509038i	−0.932144	−	0.362087i	$-0.882064\pi$
$311$	−7.77861	+	8.97699i	−0.441084	+	0.509038i	0.491060	+	0.871126i	$0.336610\pi$
$312$		0			0
$313$	−5.74811	+	15.4113i	−0.324902	+	0.871097i	0.667110	+	0.744959i	$0.267531\pi$
$313$	−5.74811	+	15.4113i	−0.324902	+	0.871097i	−0.992013	+	0.126138i	$0.959742\pi$
$314$		0			0
$315$	0.371926	+	0.119761i	0.0209557	+	0.00674778i
$316$		0			0
$317$	2.12983	−	0.794386i	0.119623	−	0.0446172i	−0.288940	−	0.957347i	$-0.593303\pi$
$317$	2.12983	−	0.794386i	0.119623	−	0.0446172i	0.408563	+	0.912730i	$0.366030\pi$
$318$		0			0
$319$	−42.6333	−	27.3988i	−2.38701	−	1.53404i
$320$		0			0
$321$			6.97577i			0.389349i
$322$		0			0
$323$	3.46935	−	3.46935i	0.193040	−	0.193040i
$324$		0			0
$325$	1.47951	+	9.03229i	0.0820687	+	0.501022i
$326$		0			0
$327$	−3.20622	−	8.59620i	−0.177304	−	0.475371i
$328$		0			0
$329$	−0.434858	−	0.127686i	−0.0239745	−	0.00703955i
$330$		0			0
$331$	12.4982	+	27.3672i	0.686961	+	1.50423i	0.855095	+	0.518471i	$0.173498\pi$
$331$	12.4982	+	27.3672i	0.686961	+	1.50423i	−0.168135	+	0.985764i	$0.553774\pi$
$332$		0			0
$333$	−5.18662	+	0.370955i	−0.284225	+	0.0203282i
$334$		0			0
$335$	−6.26997	−	23.5998i	−0.342565	−	1.28939i
$336$		0			0
$337$	−4.67150	+	21.4746i	−0.254473	+	1.16979i	0.655523	+	0.755176i	$0.272448\pi$
$337$	−4.67150	+	21.4746i	−0.254473	+	1.16979i	−0.909996	+	0.414618i	$0.863915\pi$
$338$		0			0
$339$	−0.184857	−	1.28571i	−0.0100400	−	0.0698299i
$340$		0			0
$341$	−50.5078	−	7.26192i	−2.73515	−	0.393255i
$342$		0			0
$343$	0.0856695	−	1.19782i	0.00462572	−	0.0646760i
$344$		0			0
$345$	0.858214	−	10.4935i	0.0462047	−	0.564951i
$346$		0			0
$347$	−1.42737	+	19.9572i	−0.0766250	+	1.07136i	0.803090	+	0.595857i	$0.203188\pi$
$347$	−1.42737	+	19.9572i	−0.0766250	+	1.07136i	−0.879715	+	0.475501i	$0.842267\pi$
$348$		0			0
$349$	9.37199	+	1.34749i	0.501671	+	0.0721294i	0.388505	−	0.921447i	$-0.372992\pi$
$349$	9.37199	+	1.34749i	0.501671	+	0.0721294i	0.113166	+	0.993576i	$0.463901\pi$
$350$		0			0
$351$	−1.28807	−	8.95874i	−0.0687522	−	0.478182i
$352$		0			0
$353$	1.40724	−	6.46899i	0.0748999	−	0.344309i	−0.924412	−	0.381395i	$-0.875444\pi$
$353$	1.40724	−	6.46899i	0.0748999	−	0.344309i	0.999312	+	0.0370856i	$0.0118074\pi$
$354$		0			0
$355$	0.103864	−	0.179020i	0.00551252	−	0.00950140i
$356$		0			0
$357$	−0.405599	+	0.0290090i	−0.0214666	+	0.00153532i
$358$		0			0
$359$	2.36992	+	5.18939i	0.125079	+	0.273886i	0.961804	−	0.273738i	$-0.0882600\pi$
$359$	2.36992	+	5.18939i	0.125079	+	0.273886i	−0.836725	+	0.547623i	$0.815533\pi$
$360$		0			0
$361$	17.2386	+	5.06172i	0.907297	+	0.266406i
$362$		0			0
$363$	−8.49832	−	22.7849i	−0.446046	−	1.19590i
$364$		0			0
$365$	−1.41917	+	2.08727i	−0.0742826	+	0.109253i
$366$		0			0
$367$	−4.04017	+	4.04017i	−0.210895	+	0.210895i	−0.804648	−	0.593753i	$-0.797646\pi$
$367$	−4.04017	+	4.04017i	−0.210895	+	0.210895i	0.593753	+	0.804648i	$0.297646\pi$
$368$		0			0
$369$			3.65965i			0.190514i
$370$		0			0
$371$	−0.549223	−	0.352964i	−0.0285142	−	0.0183250i
$372$		0			0
$373$	−19.9421	+	7.43801i	−1.03256	+	0.385125i	−0.807905	−	0.589313i	$-0.799399\pi$
$373$	−19.9421	+	7.43801i	−1.03256	+	0.385125i	−0.224656	+	0.974438i	$0.572126\pi$
$374$		0			0
$375$	10.2601	+	3.90130i	0.529828	+	0.201462i
$376$		0			0
$377$	−5.42061	+	14.5332i	−0.279175	+	0.748498i
$378$		0			0
$379$	−7.06163	+	8.14956i	−0.362732	+	0.418615i	−0.907553	−	0.419938i	$-0.862052\pi$
$379$	−7.06163	+	8.14956i	−0.362732	+	0.418615i	0.544821	+	0.838552i	$0.316597\pi$
$380$		0			0
$381$	−20.2076	+	5.93349i	−1.03527	+	0.303982i
$382$		0			0
$383$	−6.41929	−	1.39643i	−0.328010	−	0.0713543i	0.0455447	−	0.998962i	$-0.485498\pi$
$383$	−6.41929	−	1.39643i	−0.328010	−	0.0713543i	−0.373555	+	0.927608i	$0.621861\pi$
$384$		0			0
$385$	−0.133841	−	1.13989i	−0.00682118	−	0.0580944i
$386$		0			0
$387$	1.71983	+	2.29742i	0.0874237	+	0.116784i
$388$		0			0
$389$	8.02540	+	9.26180i	0.406904	+	0.469592i	0.921803	−	0.387659i	$-0.126716\pi$
$389$	8.02540	+	9.26180i	0.406904	+	0.469592i	−0.514899	+	0.857251i	$0.672171\pi$
$390$		0			0
$391$	−6.86878	−	22.1019i	−0.347369	−	1.11774i
$392$		0			0
$393$	−4.22896	−	0.302461i	−0.213323	−	0.0152572i
$394$		0			0
$395$	3.23677	+	4.56585i	0.162859	+	0.229733i
$396$		0			0
$397$	19.4170	−	25.9381i	0.974511	−	1.30179i	0.0212085	−	0.999775i	$-0.493249\pi$
$397$	19.4170	−	25.9381i	0.974511	−	1.30179i	0.953302	−	0.302019i	$-0.0976605\pi$
$398$		0			0
$399$	0.0463130	+	0.0720644i	0.00231855	+	0.00360773i
$400$		0			0
$401$	0.158422	+	0.539535i	0.00791121	+	0.0269431i	0.963354	−	0.268233i	$-0.0864398\pi$
$401$	0.158422	+	0.539535i	0.00791121	+	0.0269431i	−0.955443	+	0.295176i	$0.904622\pi$
$402$		0			0
$403$	1.11417	+	15.5782i	0.0555009	+	0.776004i
$404$		0			0
$405$	2.60075	+	1.04758i	0.129232	+	0.0520548i
$406$		0			0
$407$	7.32002	+	13.4056i	0.362840	+	0.664492i
$408$		0			0
$409$	−7.37995	−	3.37031i	−0.364915	−	0.166651i	0.224515	−	0.974471i	$-0.427920\pi$
$409$	−7.37995	−	3.37031i	−0.364915	−	0.166651i	−0.589430	+	0.807820i	$0.700648\pi$
$410$		0			0
$411$	−7.58076	+	11.7959i	−0.373931	+	0.581849i
$412$		0			0
$413$	−0.488380	−	0.488380i	−0.0240316	−	0.0240316i
$414$		0			0
$415$	−21.4568	−	0.556270i	−1.05327	−	0.0273062i
$416$		0			0
$417$	1.30562	+	6.00186i	0.0639367	+	0.293912i
$418$		0			0
$419$	−4.85328	+	10.6272i	−0.237098	+	0.519173i	−0.990355	−	0.138554i	$-0.955755\pi$
$419$	−4.85328	+	10.6272i	−0.237098	+	0.519173i	0.753256	+	0.657727i	$0.228482\pi$
$420$		0			0
$421$	−4.63666	+	15.7910i	−0.225977	+	0.769607i	0.765961	+	0.642887i	$0.222263\pi$
$421$	−4.63666	+	15.7910i	−0.225977	+	0.769607i	−0.991938	+	0.126721i	$0.959555\pi$
$422$		0			0
$423$	−10.0744	−	3.75756i	−0.489835	−	0.182699i
$424$		0			0
$425$	24.1254	−	0.471982i	1.17025	−	0.0228945i
$426$		0			0
$427$	0.877299	+	0.479041i	0.0424555	+	0.0231824i
$428$		0			0
$429$	−9.04228	+	5.81112i	−0.436566	+	0.280564i
$430$		0			0
$431$	19.6283	−	2.82212i	0.945460	−	0.135937i	0.347695	−	0.937608i	$-0.386965\pi$
$431$	19.6283	−	2.82212i	0.945460	−	0.135937i	0.597765	+	0.801671i	$0.296055\pi$
$432$		0			0
$433$	13.2516	−	9.91999i	0.636829	−	0.476724i	−0.231419	−	0.972854i	$-0.574337\pi$
$433$	13.2516	−	9.91999i	0.636829	−	0.476724i	0.868248	+	0.496130i	$0.165246\pi$
$434$		0			0
$435$	11.8136	+	14.3698i	0.566420	+	0.688981i
$436$		0			0
$437$	−3.39306	+	3.50142i	−0.162312	+	0.167496i
$438$		0			0
$439$	−2.67063	+	2.31412i	−0.127462	+	0.110447i	−0.716259	−	0.697834i	$-0.754147\pi$
$439$	−2.67063	+	2.31412i	−0.127462	+	0.110447i	0.588797	+	0.808281i	$0.299602\pi$
$440$		0			0
$441$	2.02622	−	14.0927i	0.0964868	−	0.671080i
$442$		0			0
$443$	−16.7714	−	12.5549i	−0.796834	−	0.596502i	0.121371	−	0.992607i	$-0.461271\pi$
$443$	−16.7714	−	12.5549i	−0.796834	−	0.596502i	−0.918205	+	0.396105i	$0.870362\pi$
$444$		0			0
$445$	2.33717	−	9.54560i	0.110792	−	0.452505i
$446$		0			0
$447$	−8.52405	+	15.6106i	−0.403174	+	0.738358i
$448$		0			0
$449$	19.6607	+	17.0361i	0.927848	+	0.803985i	0.980881	−	0.194608i	$-0.0623435\pi$
$449$	19.6607	+	17.0361i	0.927848	+	0.803985i	−0.0530334	+	0.998593i	$0.516889\pi$
$450$		0			0
$451$	9.77829	−	4.46560i	0.460442	−	0.210277i
$452$		0			0
$453$	−1.35768	+	0.741351i	−0.0637895	+	0.0348317i
$454$		0			0
$455$	−0.332208	+	0.114191i	−0.0155742	+	0.00535334i
$456$		0			0
$457$	−13.5242	+	2.94201i	−0.632635	+	0.137621i	−0.517437	−	0.855721i	$-0.673114\pi$
$457$	−13.5242	+	2.94201i	−0.632635	+	0.137621i	−0.115198	+	0.993343i	$0.536750\pi$
$458$		0			0
$459$	−23.8616			−1.11376
$460$		0			0
$461$	−19.3209			−0.899866			−0.449933	−	0.893062i	$-0.648552\pi$
$461$	−19.3209			−0.899866			−0.449933	+	0.893062i	$0.648552\pi$
$462$		0			0
$463$	−16.4576	+	3.58012i	−0.764848	+	0.166382i	−0.578034	−	0.816013i	$-0.696180\pi$
$463$	−16.4576	+	3.58012i	−0.764848	+	0.166382i	−0.186814	+	0.982395i	$0.559816\pi$
$464$		0			0
$465$	16.8306	+	8.21991i	0.780499	+	0.381189i
$466$		0			0
$467$	−20.1753	+	11.0165i	−0.933600	+	0.509784i	−0.872644	−	0.488356i	$-0.837597\pi$
$467$	−20.1753	+	11.0165i	−0.933600	+	0.509784i	−0.0609560	+	0.998140i	$0.519415\pi$
$468$		0			0
$469$	0.852507	−	0.389327i	0.0393651	−	0.0179774i
$470$		0			0
$471$	18.1866	+	15.7588i	0.837996	+	0.726128i
$472$		0			0
$473$	4.03995	−	7.39862i	0.185757	−	0.340189i
$474$		0			0
$475$	−2.52297	−	4.41301i	−0.115762	−	0.202483i
$476$		0			0
$477$	−12.3995	−	9.28212i	−0.567732	−	0.424999i
$478$		0			0
$479$	2.54443	−	17.6969i	0.116258	−	0.808590i	−0.845360	−	0.534197i	$-0.820614\pi$
$479$	2.54443	−	17.6969i	0.116258	−	0.808590i	0.961618	−	0.274393i	$-0.0884770\pi$
$480$		0			0
$481$	3.53307	−	3.06142i	0.161094	−	0.139589i
$482$		0			0
$483$	0.402561	−	0.0351582i	0.0183172	−	0.00159975i
$484$		0			0
$485$	−20.4158	+	16.7841i	−0.927034	+	0.762126i
$486$		0			0
$487$	−20.7035	+	15.4985i	−0.938166	+	0.702303i	−0.954703	−	0.297561i	$-0.903827\pi$
$487$	−20.7035	+	15.4985i	−0.938166	+	0.702303i	0.0165365	+	0.999863i	$0.494736\pi$
$488$		0			0
$489$	−24.2627	+	3.48845i	−1.09720	+	0.157753i
$490$		0			0
$491$	17.6668	−	11.3538i	0.797292	−	0.512389i	−0.0774389	−	0.996997i	$-0.524674\pi$
$491$	17.6668	−	11.3538i	0.797292	−	0.512389i	0.874731	+	0.484608i	$0.161038\pi$
$492$		0			0
$493$	35.8914	+	19.5982i	1.61647	+	0.882658i
$494$		0			0
$495$	−1.23797	−	27.2011i	−0.0556427	−	1.22260i
$496$		0			0
$497$	0.00744276	+	0.00277600i	0.000333853	+	0.000124521i
$498$		0			0
$499$	5.39794	−	18.3837i	0.241645	−	0.822967i	−0.745958	−	0.665993i	$-0.768008\pi$
$499$	5.39794	−	18.3837i	0.241645	−	0.822967i	0.987603	−	0.156974i	$-0.0501738\pi$
$500$		0			0
$501$	−5.73772	+	12.5638i	−0.256342	+	0.561311i
$502$		0			0
$503$	−2.71184	−	12.4661i	−0.120915	−	0.555837i	−0.997248	−	0.0741320i	$-0.976381\pi$
$503$	−2.71184	−	12.4661i	−0.120915	−	0.555837i	0.876334	−	0.481705i	$-0.159982\pi$
$504$		0			0
$505$	−2.64545	+	2.51175i	−0.117721	+	0.111771i
$506$		0			0
$507$	−6.69874	−	6.69874i	−0.297502	−	0.297502i
$508$		0			0
$509$	20.9054	−	32.5294i	0.926614	−	1.44184i	0.0297387	−	0.999558i	$-0.490532\pi$
$509$	20.9054	−	32.5294i	0.926614	−	1.44184i	0.896876	−	0.442283i	$-0.145831\pi$
$510$		0			0
$511$	−0.0881200	−	0.0402431i	−0.00389820	−	0.00178025i
$512$		0			0
$513$	2.40907	+	4.41189i	0.106363	+	0.194790i
$514$		0			0
$515$	−3.07948	−	7.23359i	−0.135698	−	0.318750i
$516$		0			0
$517$	2.25315	+	31.5031i	0.0990934	+	1.38551i
$518$		0			0
$519$	5.03128	+	17.1350i	0.220849	+	0.752142i
$520$		0			0
$521$	17.4062	+	27.0846i	0.762581	+	1.18660i	0.977699	+	0.210011i	$0.0673500\pi$
$521$	17.4062	+	27.0846i	0.762581	+	1.18660i	−0.215118	+	0.976588i	$0.569014\pi$
$522$		0			0
$523$	−0.471594	+	0.629976i	−0.0206214	+	0.0275469i	−0.810733	−	0.585416i	$-0.800931\pi$
$523$	−0.471594	+	0.629976i	−0.0206214	+	0.0275469i	0.790112	+	0.612962i	$0.210022\pi$
$524$		0			0
$525$	−0.0814836	+	0.413341i	−0.00355624	+	0.0180397i
$526$		0			0
$527$	41.0701	+	2.93739i	1.78904	+	0.127955i
$528$		0			0
$529$	7.17016	+	21.8538i	0.311746	+	0.950165i
$530$		0			0
$531$	−10.7305	−	12.3836i	−0.465664	−	0.537404i
$532$		0			0
$533$	−1.97174	−	2.63393i	−0.0854054	−	0.114088i
$534$		0			0
$535$	15.7792	−	1.85272i	0.682193	−	0.0801001i
$536$		0			0
$537$	2.70540	+	0.588524i	0.116747	+	0.0253967i
$538$		0			0
$539$	−40.1270	+	11.7824i	−1.72839	+	0.507502i
$540$		0			0
$541$	24.9608	−	28.8063i	1.07315	−	1.23848i	0.103334	−	0.994647i	$-0.467049\pi$
$541$	24.9608	−	28.8063i	1.07315	−	1.23848i	0.969817	−	0.243835i	$-0.0784055\pi$
$542$		0			0
$543$	8.57302	−	22.9851i	0.367903	−	0.986387i
$544$		0			0
$545$	−18.5930	+	9.53556i	−0.796439	+	0.408458i
$546$		0			0
$547$	−4.23160	+	1.57831i	−0.180930	+	0.0674835i	−0.438297	−	0.898830i	$-0.644418\pi$
$547$	−4.23160	+	1.57831i	−0.180930	+	0.0674835i	0.257366	+	0.966314i	$0.417145\pi$
$548$		0			0
$549$	19.9497	+	12.8209i	0.851432	+	0.547182i
$550$		0			0
$551$		−	8.61477i		−	0.367002i
$552$		0			0
$553$	−0.151892	+	0.151892i	−0.00645910	+	0.00645910i
$554$		0			0
$555$	−1.04939	−	5.50754i	−0.0445441	−	0.233782i
$556$		0			0
$557$	1.54274	+	4.13625i	0.0653681	+	0.175259i	0.965527	−	0.260303i	$-0.0838225\pi$
$557$	1.54274	+	4.13625i	0.0653681	+	0.175259i	−0.900159	+	0.435562i	$0.856550\pi$
$558$		0			0
$559$	−2.47560	−	0.726901i	−0.104707	−	0.0307446i
$560$		0			0
$561$	11.7718	+	25.7766i	0.497006	+	1.08829i
$562$		0			0
$563$	−15.5662	+	1.11332i	−0.656039	+	0.0469208i	−0.395391	−	0.918513i	$-0.629391\pi$
$563$	−15.5662	+	1.11332i	−0.656039	+	0.0469208i	−0.260648	+	0.965434i	$0.583936\pi$
$564$		0			0
$565$	−2.85917	+	0.759621i	−0.120286	+	0.0319575i
$566$		0			0
$567$	−0.0228746	+	0.105153i	−0.000960643	+	0.00441600i
$568$		0			0
$569$	3.40986	+	23.7161i	0.142949	+	0.994229i	0.927409	+	0.374050i	$0.122031\pi$
$569$	3.40986	+	23.7161i	0.142949	+	0.994229i	−0.784460	+	0.620179i	$0.787060\pi$
$570$		0			0
$571$	−31.9394	−	4.59219i	−1.33662	−	0.192177i	−0.563332	−	0.826230i	$-0.690481\pi$
$571$	−31.9394	−	4.59219i	−1.33662	−	0.192177i	−0.773290	+	0.634053i	$0.781390\pi$
$572$		0			0
$573$	−0.432327	+	6.04472i	−0.0180607	+	0.252522i
$574$		0			0
$575$	−23.9642	+	0.845730i	−0.999378	+	0.0352694i
$576$		0			0
$577$	−1.17685	+	16.4546i	−0.0489931	+	0.685013i	0.912307	+	0.409508i	$0.134300\pi$
$577$	−1.17685	+	16.4546i	−0.0489931	+	0.685013i	−0.961300	+	0.275505i	$0.911155\pi$
$578$		0			0
$579$	−1.43585	−	0.206445i	−0.0596721	−	0.00857955i
$580$		0			0
$581$	−0.117240	−	0.815421i	−0.00486393	−	0.0338293i
$582$		0			0
$583$	−9.67096	+	44.4567i	−0.400530	+	1.84121i
$584$		0			0
$585$	−8.05467	+	2.13996i	−0.333020	+	0.0884763i
$586$		0			0
$587$	33.3480	−	2.38510i	1.37642	−	0.0984435i	0.636572	−	0.771217i	$-0.280352\pi$
$587$	33.3480	−	2.38510i	1.37642	−	0.0984435i	0.739848	+	0.672774i	$0.234897\pi$
$588$		0			0
$589$	−3.60334	−	7.89022i	−0.148473	−	0.325111i
$590$		0			0
$591$	9.69315	+	2.84616i	0.398723	+	0.117076i
$592$		0			0
$593$	−9.02200	−	24.1889i	−0.370489	−	0.993320i	−0.979728	−	0.200333i	$-0.935798\pi$
$593$	−9.02200	−	24.1889i	−0.370489	−	0.993320i	0.609239	−	0.792987i	$-0.291475\pi$
$594$		0			0
$595$	0.173343	+	0.909760i	0.00710637	+	0.0372965i
$596$		0			0
$597$	−10.3996	+	10.3996i	−0.425627	+	0.425627i
$598$		0			0
$599$			25.5587i			1.04430i	0.852853	+	0.522151i	$0.174870\pi$
$599$			25.5587i			1.04430i	−0.852853	+	0.522151i	$0.825130\pi$
$600$		0			0
$601$	−38.5241	−	24.7579i	−1.57143	−	1.00990i	−0.978898	−	0.204352i	$-0.934491\pi$
$601$	−38.5241	−	24.7579i	−1.57143	−	1.00990i	−0.592534	−	0.805546i	$-0.701872\pi$
$602$		0			0
$603$	20.8327	−	7.77020i	0.848374	−	0.316427i
$604$		0			0
$605$	−49.2823	+	25.2747i	−2.00361	+	1.02756i
$606$		0			0
$607$	0.525263	−	1.40828i	0.0213198	−	0.0571605i	−0.925854	−	0.377882i	$-0.876653\pi$
$607$	0.525263	−	1.40828i	0.0213198	−	0.0571605i	0.947174	+	0.320721i	$0.103925\pi$
$608$		0			0
$609$	−0.467557	+	0.539589i	−0.0189464	+	0.0218653i
$610$		0			0
$611$	9.27528	−	2.72347i	0.375238	−	0.110180i
$612$		0			0
$613$	−3.51094	−	0.763758i	−0.141805	−	0.0308479i	0.141102	−	0.989995i	$-0.454935\pi$
$613$	−3.51094	−	0.763758i	−0.141805	−	0.0308479i	−0.282908	+	0.959147i	$0.591299\pi$
$614$		0			0
$615$	−3.91899	+	0.460150i	−0.158029	+	0.0185550i
$616$		0			0
$617$	−5.10930	−	6.82523i	−0.205693	−	0.274773i	0.685818	−	0.727773i	$-0.259445\pi$
$617$	−5.10930	−	6.82523i	−0.205693	−	0.274773i	−0.891511	+	0.453000i	$0.850354\pi$
$618$		0			0
$619$	−8.67549	−	10.0120i	−0.348697	−	0.402418i	0.554124	−	0.832434i	$-0.313053\pi$
$619$	−8.67549	−	10.0120i	−0.348697	−	0.402418i	−0.902821	+	0.430016i	$0.858508\pi$
$620$		0			0
$621$	23.7095	−	0.372637i	0.951430	−	0.0149534i
$622$		0			0
$623$	0.376228	+	0.0269083i	0.0150732	+	0.00107806i
$624$		0			0
$625$	6.09972	−	24.2445i	0.243989	−	0.969778i
$626$		0			0
$627$	3.57749	−	4.77896i	0.142871	−	0.190853i
$628$		0			0
$629$	−6.66335	−	10.3684i	−0.265685	−	0.413414i
$630$		0			0
$631$	5.16919	+	17.6046i	0.205782	+	0.700830i	0.996108	+	0.0881428i	$0.0280932\pi$
$631$	5.16919	+	17.6046i	0.205782	+	0.700830i	−0.790326	+	0.612687i	$0.790089\pi$
$632$		0			0
$633$	−0.492440	−	6.88521i	−0.0195727	−	0.273662i
$634$		0			0
$635$	18.7886	+	44.1337i	0.745602	+	1.75139i
$636$		0			0
$637$	6.13451	+	11.2345i	0.243058	+	0.445128i
$638$		0			0
$639$	0.171428	+	0.0782884i	0.00678157	+	0.00309704i
$640$		0			0
$641$	−22.0432	+	34.2999i	−0.870655	+	1.35477i	0.0635318	+	0.997980i	$0.479764\pi$
$641$	−22.0432	+	34.2999i	−0.870655	+	1.35477i	−0.934186	+	0.356785i	$0.883873\pi$
$642$		0			0
$643$	33.2225	+	33.2225i	1.31017	+	1.31017i	0.921288	+	0.388882i	$0.127138\pi$
$643$	33.2225	+	33.2225i	1.31017	+	1.31017i	0.388882	+	0.921288i	$0.372862\pi$
$644$		0			0
$645$	−2.24398	+	2.13057i	−0.0883568	+	0.0838912i
$646$		0			0
$647$	−6.14507	−	28.2484i	−0.241588	−	1.11056i	−0.924834	−	0.380372i	$-0.875796\pi$
$647$	−6.14507	−	28.2484i	−0.241588	−	1.11056i	0.683246	−	0.730188i	$-0.260568\pi$
$648$		0			0
$649$	−19.9945	+	43.7819i	−0.784854	+	1.71859i
$650$		0			0
$651$	−0.202536	+	0.689774i	−0.00793800	+	0.0270344i
$652$		0			0
$653$	−16.3271	−	6.08968i	−0.638928	−	0.238308i	0.00905956	−	0.999959i	$-0.497116\pi$
$653$	−16.3271	−	6.08968i	−0.638928	−	0.238308i	−0.647987	+	0.761651i	$0.724389\pi$
$654$		0			0
$655$	0.439019	+	9.64624i	0.0171539	+	0.376910i
$656$		0			0
$657$	−2.01717	−	1.10146i	−0.0786972	−	0.0429719i
$658$		0			0
$659$	22.2863	−	14.3225i	0.868151	−	0.557927i	−0.0290354	−	0.999578i	$-0.509244\pi$
$659$	22.2863	−	14.3225i	0.868151	−	0.557927i	0.897187	+	0.441651i	$0.145607\pi$
$660$		0			0
$661$	35.0532	−	5.03989i	1.36341	−	0.196029i	0.578522	−	0.815666i	$-0.303630\pi$
$661$	35.0532	−	5.03989i	1.36341	−	0.196029i	0.784888	+	0.619638i	$0.212720\pi$
$662$		0			0
$663$	6.94333	−	5.19771i	0.269657	−	0.201862i
$664$		0			0
$665$	0.150709	−	0.123900i	0.00584425	−	0.00480463i
$666$		0			0
$667$	−35.9687	−	18.9128i	−1.39271	−	0.732306i
$668$		0			0
$669$	6.22690	−	5.39564i	0.240746	−	0.208607i
$670$		0			0
$671$	9.91329	−	68.9485i	0.382698	−	2.66173i
$672$		0			0
$673$	−6.79439	−	5.08622i	−0.261904	−	0.196059i	0.460253	−	0.887788i	$-0.347759\pi$
$673$	−6.79439	−	5.08622i	−0.261904	−	0.196059i	−0.722158	+	0.691728i	$0.756850\pi$
$674$		0			0
$675$	−6.49967	+	23.8522i	−0.250172	+	0.918072i
$676$		0			0
$677$	7.04654	−	12.9048i	0.270821	−	0.495971i	−0.706506	−	0.707707i	$-0.749730\pi$
$677$	7.04654	−	12.9048i	0.270821	−	0.495971i	0.977327	+	0.211736i	$0.0679117\pi$
$678$		0			0
$679$	−0.766616	−	0.664277i	−0.0294200	−	0.0254926i
$680$		0			0
$681$	−15.6004	+	7.12446i	−0.597808	+	0.273010i
$682$		0			0
$683$	29.9081	−	16.3310i	1.14440	−	0.624890i	0.208803	−	0.977958i	$-0.433043\pi$
$683$	29.9081	−	16.3310i	1.14440	−	0.624890i	0.935598	+	0.353068i	$0.114862\pi$
$684$		0			0
$685$	28.6957	+	14.0148i	1.09641	+	0.535477i
$686$		0			0
$687$	−25.2130	+	5.48476i	−0.961937	+	0.209257i
$688$		0			0
$689$	13.9252			0.530507
$690$		0			0
$691$	−21.0326			−0.800116			−0.400058	−	0.916490i	$-0.631010\pi$
$691$	−21.0326			−0.800116			−0.400058	+	0.916490i	$0.631010\pi$
$692$		0			0
$693$	1.02119	−	0.222147i	0.0387920	−	0.00843868i
$694$		0			0
$695$	13.2294	−	4.54738i	0.501821	−	0.172492i
$696$		0			0
$697$	−7.61318	+	4.15711i	−0.288370	+	0.157462i
$698$		0			0
$699$	−3.46776	+	1.58367i	−0.131163	+	0.0599000i
$700$		0			0
$701$	−28.0708	−	24.3235i	−1.06022	−	0.918685i	−0.0633690	−	0.997990i	$-0.520185\pi$
$701$	−28.0708	−	24.3235i	−1.06022	−	0.918685i	−0.996850	+	0.0793048i	$0.974730\pi$
$702$		0			0
$703$	−1.24433	+	2.27881i	−0.0469306	+	0.0859470i
$704$		0			0
$705$	2.75713	−	11.2608i	0.103839	−	0.424107i
$706$		0			0
$707$	−0.112084	−	0.0839047i	−0.00421534	−	0.00315556i
$708$		0			0
$709$	3.79435	−	26.3903i	0.142500	−	0.991107i	−0.785589	−	0.618748i	$-0.787640\pi$
$709$	3.79435	−	26.3903i	0.142500	−	0.991107i	0.928089	−	0.372359i	$-0.121451\pi$
$710$		0			0
$711$	−3.85146	+	3.33731i	−0.144441	+	0.125159i
$712$		0			0
$713$	−40.8543	−	2.27730i	−1.53000	−	0.0852855i
$714$		0			0
$715$	15.5463	+	18.9102i	0.581400	+	0.707203i
$716$		0			0
$717$	19.2479	−	14.4088i	0.718826	−	0.538107i
$718$		0			0
$719$	13.4285	−	1.93073i	0.500799	−	0.0720041i	0.112714	−	0.993627i	$-0.464046\pi$
$719$	13.4285	−	1.93073i	0.500799	−	0.0720041i	0.388085	+	0.921623i	$0.373137\pi$
$720$		0			0
$721$	0.253842	−	0.163134i	0.00945355	−	0.00607543i
$722$		0			0
$723$	−13.9052	−	7.59280i	−0.517139	−	0.282379i
$724$		0			0
$725$	29.3670	−	30.5389i	1.09066	−	1.13419i
$726$		0			0
$727$	−3.97935	−	1.48422i	−0.147586	−	0.0550467i	0.274586	−	0.961563i	$-0.411459\pi$
$727$	−3.97935	−	1.48422i	−0.147586	−	0.0550467i	−0.422172	+	0.906516i	$0.638732\pi$
$728$		0			0
$729$	3.38361	−	11.5235i	0.125319	−	0.426797i
$730$		0			0
$731$	−2.82573	+	6.18748i	−0.104513	+	0.228852i
$732$		0			0
$733$	−6.51021	−	29.9270i	−0.240460	−	1.10538i	−0.926053	−	0.377393i	$-0.876821\pi$
$733$	−6.51021	−	29.9270i	−0.240460	−	1.10538i	0.685593	−	0.727985i	$-0.259543\pi$
$734$		0			0
$735$	15.3461	+	0.397850i	0.566051	+	0.0146749i
$736$		0			0
$737$	−46.1820	−	46.1820i	−1.70114	−	1.70114i
$738$		0			0
$739$	−15.4307	+	24.0106i	−0.567627	+	0.883244i	−0.999828	−	0.0185327i	$-0.994101\pi$
$739$	−15.4307	+	24.0106i	−0.567627	+	0.883244i	0.432202	+	0.901777i	$0.357737\pi$
$740$		0			0
$741$	−1.66203	−	0.759024i	−0.0610562	−	0.0278834i
$742$		0			0
$743$	4.22788	+	7.74278i	0.155106	+	0.284055i	0.943664	−	0.330905i	$-0.107354\pi$
$743$	4.22788	+	7.74278i	0.155106	+	0.284055i	−0.788558	+	0.614960i	$0.789172\pi$
$744$		0			0
$745$	37.5752	+	15.1353i	1.37665	+	0.554515i
$746$		0			0
$747$	−1.39428	−	19.4946i	−0.0510141	−	0.713270i
$748$		0			0
$749$	0.171794	+	0.585077i	0.00627722	+	0.0213782i
$750$		0			0
$751$	−14.2174	−	22.1227i	−0.518801	−	0.807270i	0.478696	−	0.877981i	$-0.341110\pi$
$751$	−14.2174	−	22.1227i	−0.518801	−	0.807270i	−0.997497	+	0.0707107i	$0.977473\pi$
$752$		0			0
$753$	−18.1378	+	24.2293i	−0.660980	+	0.882966i
$754$		0			0
$755$	2.03753	+	2.87418i	0.0741532	+	0.104602i
$756$		0			0
$757$	−19.1770	−	1.37157i	−0.697001	−	0.0498505i	−0.281657	−	0.959515i	$-0.590884\pi$
$757$	−19.1770	−	1.37157i	−0.697001	−	0.0498505i	−0.415344	+	0.909665i	$0.636339\pi$
$758$		0			0
$759$	−12.0993	−	25.4285i	−0.439177	−	0.922997i
$760$		0			0
$761$	−10.8926	−	12.5708i	−0.394857	−	0.455690i	0.523157	−	0.852236i	$-0.324754\pi$
$761$	−10.8926	−	12.5708i	−0.394857	−	0.455690i	−0.918015	+	0.396546i	$0.870209\pi$
$762$		0			0
$763$	−0.480615	−	0.642027i	−0.0173994	−	0.0232429i
$764$		0			0
$765$	2.56224	+	21.8220i	0.0926381	+	0.788977i
$766$		0			0
$767$	14.3950	+	3.13144i	0.519774	+	0.113070i
$768$		0			0
$769$	40.1936	−	11.8019i	1.44942	−	0.425587i	0.540068	−	0.841621i	$-0.318398\pi$
$769$	40.1936	−	11.8019i	1.44942	−	0.425587i	0.909349	+	0.416034i	$0.136580\pi$
$770$		0			0
$771$	−0.739271	+	0.853164i	−0.0266242	+	0.0307260i
$772$		0			0
$773$	14.8860	−	39.9110i	0.535414	−	1.43550i	−0.334547	−	0.942379i	$-0.608583\pi$
$773$	14.8860	−	39.9110i	0.535414	−	1.43550i	0.869961	−	0.493121i	$-0.164144\pi$
$774$		0			0
$775$	14.1233	−	40.2539i	0.507326	−	1.44596i
$776$		0			0
$777$	0.201619	−	0.0751999i	0.00723303	−	0.00269778i
$778$		0			0
$779$	1.53726	+	0.987934i	0.0550779	+	0.0353964i
$780$		0			0
$781$		−	0.553571i		−	0.0198083i
$782$		0			0
$783$	−29.6255	+	29.6255i	−1.05873	+	1.05873i
$784$		0			0
$785$	30.8162	−	45.3236i	1.09988	−	1.61767i
$786$		0			0
$787$	10.5458	+	28.2743i	0.375916	+	1.00787i	0.977847	+	0.209321i	$0.0671254\pi$
$787$	10.5458	+	28.2743i	0.375916	+	1.00787i	−0.601931	+	0.798548i	$0.705602\pi$
$788$		0			0
$789$	−6.11512	−	1.79556i	−0.217704	−	0.0639237i
$790$		0			0
$791$	−0.0471678	−	0.103283i	−0.00167709	−	0.00367233i
$792$		0			0
$793$	−21.2659	+	1.52096i	−0.755173	+	0.0540110i
$794$		0			0
$795$	8.38084	−	14.4453i	0.297238	−	0.512321i
$796$		0			0
$797$	3.26568	−	15.0121i	0.115676	−	0.531755i	−0.882441	−	0.470423i	$-0.844101\pi$
$797$	3.26568	−	15.0121i	0.115676	−	0.531755i	0.998117	−	0.0613322i	$-0.0195349\pi$
$798$		0			0
$799$	−3.62698	−	25.2262i	−0.128313	−	0.892438i
$800$		0			0
$801$	8.85754	+	1.27352i	0.312966	+	0.0449977i
$802$		0			0
$803$	−0.481607	+	6.73375i	−0.0169955	+	0.237629i
$804$		0			0
$805$	−0.186446	−	0.901255i	−0.00657134	−	0.0317651i
$806$		0			0
$807$	0.445422	−	6.22781i	0.0156796	−	0.219229i
$808$		0			0
$809$	42.3911	+	6.09492i	1.49039	+	0.214286i	0.838864	−	0.544340i	$-0.183220\pi$
$809$	42.3911	+	6.09492i	1.49039	+	0.214286i	0.651526	+	0.758626i	$0.274129\pi$
$810$		0			0
$811$	−5.92318	−	41.1966i	−0.207991	−	1.44661i	−0.779700	−	0.626153i	$-0.784628\pi$
$811$	−5.92318	−	41.1966i	−0.207991	−	1.44661i	0.571709	−	0.820457i	$-0.306281\pi$
$812$		0			0
$813$	2.97542	−	13.6778i	0.104353	−	0.479702i
$814$		0			0
$815$	14.3349	+	53.9557i	0.502129	+	1.88998i
$816$		0			0
$817$	1.42932	−	0.102227i	0.0500055	−	0.00357647i
$818$		0			0
$819$	−0.132878	−	0.290963i	−0.00464315	−	0.0101671i
$820$		0			0
$821$	−29.9386	−	8.79077i	−1.04486	−	0.306800i	−0.286124	−	0.958193i	$-0.592367\pi$
$821$	−29.9386	−	8.79077i	−1.04486	−	0.306800i	−0.758741	+	0.651393i	$0.774185\pi$
$822$		0			0
$823$	11.0856	+	29.7216i	0.386419	+	1.03603i	0.973937	+	0.226819i	$0.0728325\pi$
$823$	11.0856	+	29.7216i	0.386419	+	1.03603i	−0.587518	+	0.809211i	$0.699895\pi$
$824$		0			0
$825$	28.9730	−	4.74586i	1.00871	−	0.165230i
$826$		0			0
$827$	0.160110	−	0.160110i	0.00556758	−	0.00556758i	−0.704318	−	0.709885i	$-0.748747\pi$
$827$	0.160110	−	0.160110i	0.00556758	−	0.00556758i	0.709885	+	0.704318i	$0.248747\pi$
$828$		0			0
$829$		−	26.2820i		−	0.912812i	−0.889772	−	0.456406i	$-0.849136\pi$
$829$		−	26.2820i		−	0.912812i	0.889772	−	0.456406i	$-0.150864\pi$
$830$		0			0
$831$	21.6309	+	13.9013i	0.750368	+	0.482232i
$832$		0			0
$833$	31.6187	−	11.7932i	1.09552	−	0.408609i
$834$		0			0
$835$	29.9433	+	9.64183i	1.03623	+	0.333669i
$836$		0			0
$837$	−14.7422	+	39.5253i	−0.509565	+	1.36620i
$838$		0			0
$839$	−17.9006	+	20.6584i	−0.617998	+	0.713208i	−0.975326	−	0.220771i	$-0.929143\pi$
$839$	−17.9006	+	20.6584i	−0.617998	+	0.713208i	0.357328	+	0.933979i	$0.383688\pi$
$840$		0			0
$841$	41.0680	−	12.0587i	1.41614	−	0.415816i
$842$		0			0
$843$	−21.7968	−	4.74160i	−0.750721	−	0.163309i
$844$		0			0
$845$	−13.3734	+	16.9317i	−0.460059	+	0.582468i
$846$		0			0
$847$	−1.27391	−	1.70174i	−0.0437720	−	0.0584725i
$848$		0			0
$849$	1.38067	+	1.59338i	0.0473846	+	0.0546848i
$850$		0			0
$851$	6.78280	+	10.1982i	0.232511	+	0.349591i
$852$		0			0
$853$	15.2873	+	1.09337i	0.523426	+	0.0374361i	0.330553	−	0.943788i	$-0.392765\pi$
$853$	15.2873	+	1.09337i	0.523426	+	0.0374361i	0.192873	+	0.981224i	$0.438219\pi$
$854$		0			0
$855$	3.77609	−	2.67690i	0.129140	−	0.0915481i
$856$		0			0
$857$	3.82167	−	5.10515i	0.130546	−	0.174389i	−0.730506	−	0.682907i	$-0.760716\pi$
$857$	3.82167	−	5.10515i	0.130546	−	0.174389i	0.861051	+	0.508518i	$0.169806\pi$
$858$		0			0
$859$	−0.791301	−	1.23129i	−0.0269988	−	0.0420110i	0.827492	−	0.561478i	$-0.189767\pi$
$859$	−0.791301	−	1.23129i	−0.0269988	−	0.0420110i	−0.854491	+	0.519467i	$0.826131\pi$
$860$		0			0
$861$	−0.0426676	−	0.145312i	−0.00145411	−	0.00495223i
$862$		0			0
$863$	−0.213169	−	2.98049i	−0.00725636	−	0.101457i	0.992533	−	0.121975i	$-0.0389229\pi$
$863$	−0.213169	−	2.98049i	−0.00725636	−	0.101457i	−0.999789	+	0.0205183i	$0.993468\pi$
$864$		0			0
$865$	37.4230	−	15.9317i	1.27242	−	0.541694i
$866$		0			0
$867$	−2.95971	−	5.42030i	−0.100517	−	0.184083i
$868$		0			0
$869$	13.6167	+	6.21853i	0.461914	+	0.210949i
$870$		0			0
$871$	−10.8074	+	16.8166i	−0.366194	+	0.569809i
$872$		0			0
$873$	−17.0170	−	17.0170i	−0.575938	−	0.575938i
$874$		0			0
$875$	0.956619	+	0.0745350i	0.0323396	+	0.00251974i
$876$		0			0
$877$	7.52931	+	34.6117i	0.254247	+	1.16875i	0.910271	+	0.414014i	$0.135873\pi$
$877$	7.52931	+	34.6117i	0.254247	+	1.16875i	−0.656024	+	0.754740i	$0.727763\pi$
$878$		0			0
$879$	−5.51093	+	12.0673i	−0.185879	+	0.407019i
$880$		0			0
$881$	−2.93678	+	10.0018i	−0.0989427	+	0.336968i	−0.994056	−	0.108871i	$-0.965276\pi$
$881$	−2.93678	+	10.0018i	−0.0989427	+	0.336968i	0.895113	+	0.445839i	$0.147095\pi$
$882$		0			0
$883$	31.0196	+	11.5697i	1.04389	+	0.389351i	0.812164	−	0.583429i	$-0.198289\pi$
$883$	31.0196	+	11.5697i	1.04389	+	0.389351i	0.231728	+	0.972781i	$0.425562\pi$
$884$		0			0
$885$	11.9120	−	13.0480i	0.400418	−	0.438603i
$886$		0			0
$887$	44.8088	+	24.4675i	1.50453	+	0.821537i	0.999144	−	0.0413554i	$-0.0131676\pi$
$887$	44.8088	+	24.4675i	1.50453	+	0.821537i	0.505388	+	0.862892i	$0.331349\pi$
$888$		0			0
$889$	−1.54874	+	0.995317i	−0.0519432	+	0.0333819i
$890$		0			0
$891$	7.42291	−	1.06725i	0.248677	−	0.0357543i
$892$		0			0
$893$	−4.29801	+	3.21745i	−0.143827	+	0.107668i
$894$		0			0
$895$	0.612703	−	6.27593i	0.0204804	−	0.209781i
$896$		0			0
$897$	−6.81791	+	5.27301i	−0.227643	+	0.176061i
$898$		0			0
$899$	54.6377	−	47.3439i	1.82227	−	1.57901i
$900$		0			0
$901$	5.22469	−	36.3385i	0.174060	−	1.21061i
$902$		0			0
$903$	−0.0950741	−	0.0711716i	−0.00316387	−	0.00236844i
$904$		0			0
$905$	−54.2693	−	13.2874i	−1.80397	−	0.441690i
$906$		0			0
$907$	−24.6614	+	45.1640i	−0.818869	+	1.49965i	0.0467285	+	0.998908i	$0.485120\pi$
$907$	−24.6614	+	45.1640i	−0.818869	+	1.49965i	−0.865598	+	0.500740i	$0.833061\pi$
$908$		0			0
$909$	−2.51035	−	2.17523i	−0.0832630	−	0.0721478i
$910$		0			0
$911$	−22.0819	+	10.0845i	−0.731607	+	0.334114i	−0.746148	−	0.665781i	$-0.768099\pi$
$911$	−22.0819	+	10.0845i	−0.731607	+	0.334114i	0.0145406	+	0.999894i	$0.495371\pi$
$912$		0			0
$913$	−50.3868	+	27.5133i	−1.66756	+	0.910556i
$914$		0			0
$915$	−11.2211	+	22.9755i	−0.370957	+	0.759547i
$916$		0			0
$917$	−0.362143	+	0.0787795i	−0.0119590	+	0.00260153i
$918$		0			0
$919$	6.88301			0.227050			0.113525	−	0.993535i	$-0.463786\pi$
$919$	6.88301			0.227050			0.113525	+	0.993535i	$0.463786\pi$
$920$		0			0
$921$	−24.2388			−0.798696
$922$		0			0
$923$	−0.165560	+	0.0360155i	−0.00544949	+	0.00118546i
$924$		0			0
$925$	−12.1793	+	3.83649i	−0.400454	+	0.126143i
$926$		0			0
$927$	6.28303	−	3.43079i	0.206362	−	0.112682i
$928$		0			0
$929$	−17.4798	+	7.98276i	−0.573494	+	0.261906i	−0.680982	−	0.732301i	$-0.738447\pi$
$929$	−17.4798	+	7.98276i	−0.573494	+	0.261906i	0.107488	+	0.994206i	$0.465719\pi$
$930$		0			0
$931$	−5.37273	−	4.65550i	−0.176084	−	0.152578i
$932$		0			0
$933$	5.58899	−	10.2355i	0.182975	−	0.335094i
$934$		0			0
$935$	55.1802	−	33.4739i	1.80459	−	1.09471i
$936$		0			0
$937$	−37.0511	−	27.7361i	−1.21041	−	0.906099i	−0.212928	−	0.977068i	$-0.568300\pi$
$937$	−37.0511	−	27.7361i	−1.21041	−	0.906099i	−0.997479	+	0.0709687i	$0.977391\pi$
$938$		0			0
$939$	2.29822	−	15.9845i	0.0749996	−	0.521634i
$940$		0			0
$941$	−12.0695	+	10.4583i	−0.393453	+	0.340929i	−0.829012	−	0.559231i	$-0.811096\pi$
$941$	−12.0695	+	10.4583i	−0.393453	+	0.340929i	0.435558	+	0.900160i	$0.356551\pi$
$942$		0			0
$943$	7.49973	−	4.24951i	0.244225	−	0.138383i
$944$		0			0
$945$	−0.944356	−	0.0921952i	−0.0307199	−	0.00299911i
$946$		0			0
$947$	38.4746	−	28.8017i	1.25026	−	0.935929i	0.250771	−	0.968046i	$-0.419316\pi$
$947$	38.4746	−	28.8017i	1.25026	−	0.935929i	0.999484	+	0.0321169i	$0.0102249\pi$
$948$		0			0
$949$	2.04524	−	0.294061i	0.0663914	−	0.00954564i
$950$		0			0
$951$	−1.87748	+	1.20658i	−0.0608814	+	0.0391261i
$952$		0			0
$953$	16.1742	+	8.83177i	0.523933	+	0.286089i	0.719370	−	0.694627i	$-0.244431\pi$
$953$	16.1742	+	8.83177i	0.523933	+	0.286089i	−0.195437	+	0.980716i	$0.562612\pi$
$954$		0			0
$955$	13.7880	−	0.627517i	0.446168	−	0.0203060i
$956$		0			0
$957$	46.6184	+	17.3878i	1.50696	+	0.562067i
$958$		0			0
$959$	−0.345319	+	1.17605i	−0.0111509	+	0.0379766i
$960$		0			0
$961$	17.3618	−	38.0169i	0.560056	−	1.22635i
$962$		0			0
$963$	3.07511	+	14.1361i	0.0990941	+	0.455528i
$964$		0			0
$965$	−0.0856237	+	3.30273i	−0.00275632	+	0.106319i
$966$		0			0
$967$	−16.1186	−	16.1186i	−0.518339	−	0.518339i	0.398730	−	0.917069i	$-0.369451\pi$
$967$	−16.1186	−	16.1186i	−0.518339	−	0.518339i	−0.917069	+	0.398730i	$0.869451\pi$
$968$		0			0
$969$	−2.60430	+	4.05237i	−0.0836622	+	0.130181i
$970$		0			0
$971$	24.8546	+	11.3507i	0.797623	+	0.364262i	0.772172	−	0.635414i	$-0.219170\pi$
$971$	24.8546	+	11.3507i	0.797623	+	0.364262i	0.0254514	+	0.999676i	$0.491898\pi$
$972$		0			0
$973$	0.257316	+	0.471239i	0.00824916	+	0.0151072i
$974$		0			0
$975$	−3.30437	−	8.35641i	−0.105825	−	0.267619i
$976$		0			0
$977$	2.29542	+	32.0942i	0.0734371	+	1.02678i	0.891902	+	0.452229i	$0.149371\pi$
$977$	2.29542	+	32.0942i	0.0734371	+	1.02678i	−0.818465	+	0.574556i	$0.805175\pi$
$978$		0			0
$979$	−7.40545	−	25.2207i	−0.236679	−	0.806056i
$980$		0			0
$981$	−10.2867	−	16.0064i	−0.328429	−	0.511045i
$982$		0			0
$983$	−4.69846	+	6.27641i	−0.149858	+	0.200186i	−0.869188	−	0.494482i	$-0.835358\pi$
$983$	−4.69846	+	6.27641i	−0.149858	+	0.200186i	0.719330	+	0.694668i	$0.244449\pi$
$984$		0			0
$985$	3.86358	−	22.6818i	0.123104	−	0.722703i
$986$		0			0
$987$	0.443831	+	0.0317434i	0.0141273	+	0.00101040i
$988$		0			0
$989$	2.71109	−	6.19217i	0.0862076	−	0.196900i
$990$		0			0
$991$	−9.15858	−	10.5696i	−0.290932	−	0.335753i	0.591402	−	0.806377i	$-0.298575\pi$
$991$	−9.15858	−	10.5696i	−0.290932	−	0.335753i	−0.882334	+	0.470623i	$0.844029\pi$
$992$		0			0
$993$	−17.7015	−	23.6465i	−0.561742	−	0.750399i
$994$		0			0
$995$	26.2859	+	20.7618i	0.833320	+	0.658194i
$996$		0			0
$997$	−42.0814	−	9.15425i	−1.33273	−	0.289918i	−0.510896	−	0.859643i	$-0.670686\pi$
$997$	−42.0814	−	9.15425i	−1.33273	−	0.289918i	−0.821836	+	0.569724i	$0.807050\pi$
$998$		0			0
$999$	12.1158	−	3.55751i	0.383326	−	0.112555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.15	yes	720
5.3	odd	4	inner	920.2.bv.a.33.15	✓	720
23.7	odd	22	inner	920.2.bv.a.697.15	yes	720
115.53	even	44	inner	920.2.bv.a.513.15	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.15	✓	720	5.3	odd	4	inner
920.2.bv.a.217.15	yes	720	1.1	even	1	trivial
920.2.bv.a.513.15	yes	720	115.53	even	44	inner
920.2.bv.a.697.15	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959355 + 0.208695i) q^{3} +(0.726866 + 2.11463i) q^{5} +(-0.0753241 + 0.0411301i) q^{7} +(-1.85209 + 0.845820i) q^{9} +O(q^{10})\)	\(q+(-0.959355 + 0.208695i) q^{3} +(0.726866 + 2.11463i) q^{5} +(-0.0753241 + 0.0411301i) q^{7} +(-1.85209 + 0.845820i) q^{9} +(4.51994 + 3.91655i) q^{11} +(0.877281 - 1.60662i) q^{13} +(-1.13863 - 1.87699i) q^{15} +(-3.86341 - 2.89211i) q^{17} +(-0.144686 + 1.00631i) q^{19} +(0.0636789 - 0.0551781i) q^{21} +(3.88395 + 2.81335i) q^{23} +(-3.94333 + 3.07411i) q^{25} +(3.95818 - 2.96306i) q^{27} +(-8.38734 + 1.20592i) q^{29} +(-7.17751 + 4.61271i) q^{31} +(-5.15358 - 2.81407i) q^{33} +(-0.141726 - 0.129387i) q^{35} +(2.39284 + 0.892482i) q^{37} +(-0.506330 + 1.72440i) q^{39} +(0.746664 - 1.63497i) q^{41} +(-0.299608 - 1.37727i) q^{43} +(-3.13482 - 3.30169i) q^{45} +(3.73416 + 3.73416i) q^{47} +(-3.78050 + 5.88258i) q^{49} +(4.30995 + 1.96829i) q^{51} +(3.64573 + 6.67665i) q^{53} +(-4.99666 + 12.4048i) q^{55} +(-0.0712072 - 0.995606i) q^{57} +(2.26731 + 7.72176i) q^{59} +(-6.29683 - 9.79806i) q^{61} +(0.104718 - 0.139887i) q^{63} +(4.03508 + 0.687328i) q^{65} +(-10.8925 - 0.779044i) q^{67} +(-4.31322 - 1.88844i) q^{69} +(-0.0606133 - 0.0699515i) q^{71} +(0.676454 + 0.903637i) q^{73} +(3.14150 - 3.77211i) q^{75} +(-0.501548 - 0.109105i) q^{77} +(2.40156 - 0.705161i) q^{79} +(0.821130 - 0.947634i) q^{81} +(-3.35451 + 8.99379i) q^{83} +(3.30757 - 10.2719i) q^{85} +(7.79477 - 2.90730i) q^{87} +(-3.69732 - 2.37612i) q^{89} +0.157100i q^{91} +(5.92313 - 5.92313i) q^{93} +(-2.23315 + 0.425497i) q^{95} +(4.13052 + 11.0743i) q^{97} +(-11.6840 - 3.43074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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