LMFDB - Embedded newform 912.2.bb.h.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (of order $6$, degree $2$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 $ x^8 - 2x^7 - 30x^5 - 5x^4 + 114x^3 + 300x^2 + 116x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$-1.27736 + 1.04884i$ of defining polynomial
Character	$\chi$	$=$	912.31
Dual form			912.2.bb.h.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.912850 - 1.58110i) q^{5} -4.99333i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.912850 - 1.58110i) q^{5} -4.99333i q^{7} +(-0.500000 + 0.866025i) q^{9} +3.82973i q^{11} +(1.00771 + 0.581803i) q^{13} +(0.912850 - 1.58110i) q^{15} +(-3.73720 - 6.47303i) q^{17} +(-3.22949 + 2.92752i) q^{19} +(4.32435 - 2.49667i) q^{21} +(-2.24626 - 1.29688i) q^{23} +(0.833411 - 1.44351i) q^{25} -1.00000 q^{27} +(-6.63328 - 3.82973i) q^{29} -0.158876 q^{31} +(-3.31664 + 1.91486i) q^{33} +(-7.89497 + 4.55816i) q^{35} -8.25462i q^{37} +1.16361i q^{39} +(-1.07038 + 0.617985i) q^{41} +(1.90245 - 1.09838i) q^{43} +1.82570 q^{45} +(-0.0858062 - 0.0495402i) q^{47} -17.9334 q^{49} +(3.73720 - 6.47303i) q^{51} +(2.82435 + 1.63064i) q^{53} +(6.05519 - 3.49597i) q^{55} +(-4.15005 - 1.33306i) q^{57} +(5.14234 + 8.90680i) q^{59} +(5.64100 - 9.77049i) q^{61} +(4.32435 + 2.49667i) q^{63} -2.12439i q^{65} +(6.97575 - 12.0824i) q^{67} -2.59376i q^{69} +(1.91151 + 3.31082i) q^{71} +(-2.32570 - 4.02823i) q^{73} +1.66682 q^{75} +19.1231 q^{77} +(4.74626 + 8.22077i) q^{79} +(-0.500000 - 0.866025i) q^{81} -2.83193i q^{83} +(-6.82301 + 11.8178i) q^{85} -7.65946i q^{87} +(11.9102 + 6.87633i) q^{89} +(2.90514 - 5.03185i) q^{91} +(-0.0794381 - 0.137591i) q^{93} +(7.57675 + 2.43377i) q^{95} +(8.50771 - 4.91193i) q^{97} +(-3.31664 - 1.91486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9	$ 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9} + 2 q^{15} + 4 q^{17} + 6 q^{21} + 6 q^{23} - 12 q^{25} - 8 q^{27} - 12 q^{29} - 28 q^{31} - 6 q^{33} + 18 q^{35} - 12 q^{41} - 18 q^{43} + 4 q^{45} + 12 q^{47} - 24 q^{49} - 4 q^{51} - 6 q^{53} + 12 q^{55} + 6 q^{57} + 10 q^{59} - 4 q^{61} + 6 q^{63} + 6 q^{67} - 8 q^{71} - 8 q^{73} - 24 q^{75} + 28 q^{77} + 14 q^{79} - 4 q^{81} - 8 q^{85} + 54 q^{89} + 26 q^{91} - 14 q^{93} + 38 q^{95} + 60 q^{97} - 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9 + 2 * q^15 + 4 * q^17 + 6 * q^21 + 6 * q^23 - 12 * q^25 - 8 * q^27 - 12 * q^29 - 28 * q^31 - 6 * q^33 + 18 * q^35 - 12 * q^41 - 18 * q^43 + 4 * q^45 + 12 * q^47 - 24 * q^49 - 4 * q^51 - 6 * q^53 + 12 * q^55 + 6 * q^57 + 10 * q^59 - 4 * q^61 + 6 * q^63 + 6 * q^67 - 8 * q^71 - 8 * q^73 - 24 * q^75 + 28 * q^77 + 14 * q^79 - 4 * q^81 - 8 * q^85 + 54 * q^89 + 26 * q^91 - 14 * q^93 + 38 * q^95 + 60 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.912850	−	1.58110i	−0.408239	−	0.707090i	0.586454	−	0.809983i	$-0.300524\pi$
$5$	−0.912850	−	1.58110i	−0.408239	−	0.707090i	−0.994692	+	0.102892i	$0.967190\pi$
$6$		0			0
$7$		−	4.99333i		−	1.88730i	−0.330941	−	0.943652i	$-0.607366\pi$
$7$		−	4.99333i		−	1.88730i	0.330941	−	0.943652i	$-0.392634\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			3.82973i			1.15471i	0.816494	+	0.577353i	$0.195914\pi$
$11$			3.82973i			1.15471i	−0.816494	+	0.577353i	$0.804086\pi$
$12$		0			0
$13$	1.00771	+	0.581803i	0.279489	+	0.161363i	0.633192	−	0.773995i	$-0.281744\pi$
$13$	1.00771	+	0.581803i	0.279489	+	0.161363i	−0.353703	+	0.935358i	$0.615078\pi$
$14$		0			0
$15$	0.912850	−	1.58110i	0.235697	−	0.408239i
$16$		0			0
$17$	−3.73720	−	6.47303i	−0.906405	−	1.56994i	−0.819020	−	0.573765i	$-0.805482\pi$
$17$	−3.73720	−	6.47303i	−0.906405	−	1.56994i	−0.0873854	−	0.996175i	$-0.527851\pi$
$18$		0			0
$19$	−3.22949	+	2.92752i	−0.740896	+	0.671619i
$19$	−3.22949	+	2.92752i	−0.740896	+	0.671619i
$20$		0			0
$21$	4.32435	−	2.49667i	0.943652	−	0.544817i
$22$		0			0
$23$	−2.24626	−	1.29688i	−0.468378	−	0.270418i	0.247183	−	0.968969i	$-0.420495\pi$
$23$	−2.24626	−	1.29688i	−0.468378	−	0.270418i	−0.715560	+	0.698551i	$0.753829\pi$
$24$		0			0
$25$	0.833411	−	1.44351i	0.166682	−	0.288702i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−6.63328	−	3.82973i	−1.23177	−	0.711163i	−0.264371	−	0.964421i	$-0.585164\pi$
$29$	−6.63328	−	3.82973i	−1.23177	−	0.711163i	−0.967399	+	0.253258i	$0.918498\pi$
$30$		0			0
$31$	−0.158876			−0.0285350			−0.0142675	−	0.999898i	$-0.504542\pi$
$31$	−0.158876			−0.0285350			−0.0142675	+	0.999898i	$0.504542\pi$
$32$		0			0
$33$	−3.31664	+	1.91486i	−0.577353	+	0.333335i
$34$		0			0
$35$	−7.89497	+	4.55816i	−1.33449	+	0.770470i
$36$		0			0
$37$		−	8.25462i		−	1.35705i	−0.734577	−	0.678525i	$-0.762619\pi$
$37$		−	8.25462i		−	1.35705i	0.734577	−	0.678525i	$-0.237381\pi$
$38$		0			0
$39$			1.16361i			0.186326i
$40$		0			0
$41$	−1.07038	+	0.617985i	−0.167166	+	0.0965130i	−0.581249	−	0.813726i	$-0.697436\pi$
$41$	−1.07038	+	0.617985i	−0.167166	+	0.0965130i	0.414083	+	0.910239i	$0.364102\pi$
$42$		0			0
$43$	1.90245	−	1.09838i	0.290121	−	0.167501i	−0.347876	−	0.937541i	$-0.613097\pi$
$43$	1.90245	−	1.09838i	0.290121	−	0.167501i	0.637996	+	0.770039i	$0.279764\pi$
$44$		0			0
$45$	1.82570			0.272159
$46$		0			0
$47$	−0.0858062	−	0.0495402i	−0.0125161	−	0.00722618i	0.493729	−	0.869616i	$-0.335634\pi$
$47$	−0.0858062	−	0.0495402i	−0.0125161	−	0.00722618i	−0.506245	+	0.862390i	$0.668967\pi$
$48$		0			0
$49$	−17.9334			−2.56191
$50$		0			0
$51$	3.73720	−	6.47303i	0.523313	−	0.906405i
$52$		0			0
$53$	2.82435	+	1.63064i	0.387955	+	0.223986i	0.681274	−	0.732029i	$-0.261426\pi$
$53$	2.82435	+	1.63064i	0.387955	+	0.223986i	−0.293319	+	0.956015i	$0.594760\pi$
$54$		0			0
$55$	6.05519	−	3.49597i	0.816482	−	0.471396i
$56$		0			0
$57$	−4.15005	−	1.33306i	−0.549688	−	0.176568i
$58$		0			0
$59$	5.14234	+	8.90680i	0.669476	+	1.15957i	0.978051	+	0.208366i	$0.0668146\pi$
$59$	5.14234	+	8.90680i	0.669476	+	1.15957i	−0.308575	+	0.951200i	$0.599852\pi$
$60$		0			0
$61$	5.64100	−	9.77049i	0.722256	−	1.25098i	−0.237838	−	0.971305i	$-0.576439\pi$
$61$	5.64100	−	9.77049i	0.722256	−	1.25098i	0.960094	−	0.279679i	$-0.0902279\pi$
$62$		0			0
$63$	4.32435	+	2.49667i	0.544817	+	0.314551i
$64$		0			0
$65$		−	2.12439i		−	0.263499i
$66$		0			0
$67$	6.97575	−	12.0824i	0.852224	−	1.47610i	−0.0269729	−	0.999636i	$-0.508587\pi$
$67$	6.97575	−	12.0824i	0.852224	−	1.47610i	0.879197	−	0.476459i	$-0.158080\pi$
$68$		0			0
$69$		−	2.59376i		−	0.312252i
$70$		0			0
$71$	1.91151	+	3.31082i	0.226854	+	0.392923i	0.956874	−	0.290503i	$-0.0938227\pi$
$71$	1.91151	+	3.31082i	0.226854	+	0.392923i	−0.730020	+	0.683426i	$0.760489\pi$
$72$		0			0
$73$	−2.32570	−	4.02823i	−0.272202	−	0.471469i	0.697223	−	0.716854i	$-0.254419\pi$
$73$	−2.32570	−	4.02823i	−0.272202	−	0.471469i	−0.969426	+	0.245386i	$0.921085\pi$
$74$		0			0
$75$	1.66682			0.192468
$76$		0			0
$77$	19.1231			2.17928
$78$		0			0
$79$	4.74626	+	8.22077i	0.533996	+	0.924908i	0.999211	+	0.0397107i	$0.0126436\pi$
$79$	4.74626	+	8.22077i	0.533996	+	0.924908i	−0.465215	+	0.885198i	$0.654023\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	2.83193i		−	0.310844i	−0.987848	−	0.155422i	$-0.950326\pi$
$83$		−	2.83193i		−	0.310844i	0.987848	−	0.155422i	$-0.0496738\pi$
$84$		0			0
$85$	−6.82301	+	11.8178i	−0.740059	+	1.28182i
$86$		0			0
$87$		−	7.65946i		−	0.821180i
$88$		0			0
$89$	11.9102	+	6.87633i	1.26247	+	0.728890i	0.973553	−	0.228463i	$-0.0733699\pi$
$89$	11.9102	+	6.87633i	1.26247	+	0.728890i	0.288922	+	0.957353i	$0.406703\pi$
$90$		0			0
$91$	2.90514	−	5.03185i	0.304541	−	0.527481i
$92$		0			0
$93$	−0.0794381	−	0.137591i	−0.00823735	−	0.0142675i
$94$		0			0
$95$	7.57675	+	2.43377i	0.777358	+	0.249699i
$96$		0			0
$97$	8.50771	−	4.91193i	0.863827	−	0.498731i	−0.00146478	−	0.999999i	$-0.500466\pi$
$97$	8.50771	−	4.91193i	0.863827	−	0.498731i	0.865292	+	0.501268i	$0.167133\pi$
$98$		0			0
$99$	−3.31664	−	1.91486i	−0.333335	−	0.192451i
$100$		0			0
$101$	−7.57833	+	13.1260i	−0.754072	+	1.30609i	0.191763	+	0.981441i	$0.438580\pi$
$101$	−7.57833	+	13.1260i	−0.754072	+	1.30609i	−0.945834	+	0.324649i	$0.894754\pi$
$102$		0			0
$103$	−10.6487			−1.04925			−0.524624	−	0.851334i	$-0.675794\pi$
$103$	−10.6487			−1.04925			−0.524624	+	0.851334i	$0.675794\pi$
$104$		0			0
$105$	−7.89497	−	4.55816i	−0.770470	−	0.444831i
$106$		0			0
$107$	−11.3336			−1.09566			−0.547832	−	0.836588i	$-0.684547\pi$
$107$	−11.3336			−1.09566			−0.547832	+	0.836588i	$0.684547\pi$
$108$		0			0
$109$	6.14100	−	3.54551i	0.588201	−	0.339598i	−0.176185	−	0.984357i	$-0.556376\pi$
$109$	6.14100	−	3.54551i	0.588201	−	0.339598i	0.764386	+	0.644759i	$0.223042\pi$
$110$		0			0
$111$	7.14871	−	4.12731i	0.678525	−	0.391747i
$112$		0			0
$113$		−	13.6536i		−	1.28442i	−0.766528	−	0.642211i	$-0.778017\pi$
$113$		−	13.6536i		−	1.28442i	0.766528	−	0.642211i	$-0.221983\pi$
$114$		0			0
$115$			4.73542i			0.441580i
$116$		0			0
$117$	−1.00771	+	0.581803i	−0.0931630	+	0.0537877i
$118$		0			0
$119$	−32.3220	+	18.6611i	−2.96295	+	1.71066i
$120$		0			0
$121$	−3.66682			−0.333348
$122$		0			0
$123$	−1.07038	−	0.617985i	−0.0965130	−	0.0557218i
$124$		0			0
$125$	−12.1716			−1.08866
$126$		0			0
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$		0			0
$129$	1.90245	+	1.09838i	0.167501	+	0.0967069i
$130$		0			0
$131$	−11.2116	+	6.47303i	−0.979563	+	0.565551i	−0.902138	−	0.431447i	$-0.858003\pi$
$131$	−11.2116	+	6.47303i	−0.979563	+	0.565551i	−0.0774250	+	0.996998i	$0.524670\pi$
$132$		0			0
$133$	14.6181	+	16.1259i	1.26755	+	1.39830i
$134$		0			0
$135$	0.912850	+	1.58110i	0.0785656	+	0.136080i
$136$		0			0
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	7.26916	+	4.19685i	0.616562	+	0.355972i	0.775529	−	0.631311i	$-0.217483\pi$
$139$	7.26916	+	4.19685i	0.616562	+	0.355972i	−0.158967	+	0.987284i	$0.550816\pi$
$140$		0			0
$141$		−	0.0990805i		−	0.00834408i
$142$		0			0
$143$	−2.22815	+	3.85927i	−0.186327	+	0.322728i
$144$		0			0
$145$			13.9839i			1.16130i
$146$		0			0
$147$	−8.96670	−	15.5308i	−0.739561	−	1.28096i
$148$		0			0
$149$	2.63463	+	4.56331i	0.215837	+	0.373841i	0.953531	−	0.301294i	$-0.0974186\pi$
$149$	2.63463	+	4.56331i	0.215837	+	0.373841i	−0.737694	+	0.675135i	$0.764085\pi$
$150$		0			0
$151$	−4.34860			−0.353884			−0.176942	−	0.984221i	$-0.556621\pi$
$151$	−4.34860			−0.353884			−0.176942	+	0.984221i	$0.556621\pi$
$152$		0			0
$153$	7.47441			0.604270
$154$		0			0
$155$	0.145030	+	0.251199i	0.0116491	+	0.0201768i
$156$		0			0
$157$	3.97441	+	6.88388i	0.317192	+	0.549393i	0.979901	−	0.199484i	$-0.0639266\pi$
$157$	3.97441	+	6.88388i	0.317192	+	0.549393i	−0.662709	+	0.748877i	$0.730593\pi$
$158$		0			0
$159$			3.26128i			0.258637i
$160$		0			0
$161$	−6.47575	+	11.2163i	−0.510361	+	0.883971i
$162$		0			0
$163$			6.13022i			0.480156i	0.970754	+	0.240078i	$0.0771731\pi$
$163$			6.13022i			0.480156i	−0.970754	+	0.240078i	$0.922827\pi$
$164$		0			0
$165$	6.05519	+	3.49597i	0.471396	+	0.272161i
$166$		0			0
$167$	11.2463	−	19.4791i	0.870262	−	1.50734i	0.00853590	−	0.999964i	$-0.497283\pi$
$167$	11.2463	−	19.4791i	0.870262	−	1.50734i	0.861726	−	0.507374i	$-0.169384\pi$
$168$		0			0
$169$	−5.82301	−	10.0858i	−0.447924	−	0.775827i
$170$		0			0
$171$	−0.920562	−	4.26058i	−0.0703971	−	0.325815i
$172$		0			0
$173$	13.2666	−	7.65946i	1.00864	−	0.582338i	0.0978458	−	0.995202i	$-0.468805\pi$
$173$	13.2666	−	7.65946i	1.00864	−	0.582338i	0.910793	+	0.412864i	$0.135471\pi$
$174$		0			0
$175$	−7.20793	−	4.16150i	−0.544869	−	0.314580i
$176$		0			0
$177$	−5.14234	+	8.90680i	−0.386522	+	0.669476i
$178$		0			0
$179$	20.2793			1.51575			0.757873	−	0.652402i	$-0.226239\pi$
$179$	20.2793			1.51575			0.757873	+	0.652402i	$0.226239\pi$
$180$		0			0
$181$	11.6181	+	6.70771i	0.863566	+	0.498580i	0.865205	−	0.501419i	$-0.167188\pi$
$181$	11.6181	+	6.70771i	0.863566	+	0.498580i	−0.00163872	+	0.999999i	$0.500522\pi$
$182$		0			0
$183$	11.2820			0.833989
$184$		0			0
$185$	−13.0514	+	7.53523i	−0.959557	+	0.554001i
$186$		0			0
$187$	24.7899	−	14.3125i	1.81282	−	1.04663i
$188$		0			0
$189$			4.99333i			0.363212i
$190$		0			0
$191$		−	15.6389i		−	1.13159i	−0.824546	−	0.565795i	$-0.808569\pi$
$191$		−	15.6389i		−	1.13159i	0.824546	−	0.565795i	$-0.191431\pi$
$192$		0			0
$193$	−16.9773	+	9.80187i	−1.22206	+	0.705554i	−0.965356	−	0.260937i	$-0.915968\pi$
$193$	−16.9773	+	9.80187i	−1.22206	+	0.705554i	−0.256699	+	0.966491i	$0.582635\pi$
$194$		0			0
$195$	1.83978	−	1.06220i	0.131749	−	0.0760655i
$196$		0			0
$197$	−4.17430			−0.297407			−0.148703	−	0.988882i	$-0.547510\pi$
$197$	−4.17430			−0.297407			−0.148703	+	0.988882i	$0.547510\pi$
$198$		0			0
$199$	19.4899	+	11.2525i	1.38160	+	0.797670i	0.992349	−	0.123460i	$-0.0393992\pi$
$199$	19.4899	+	11.2525i	1.38160	+	0.797670i	0.389255	+	0.921130i	$0.372733\pi$
$200$		0			0
$201$	13.9515			0.984063
$202$		0			0
$203$	−19.1231	+	33.1222i	−1.34218	+	2.32472i
$204$		0			0
$205$	1.95419	+	1.12825i	0.136487	+	0.0788007i
$206$		0			0
$207$	2.24626	−	1.29688i	0.156126	−	0.0901393i
$208$		0			0
$209$	−11.2116	−	12.3681i	−0.775523	−	0.855518i
$210$		0			0
$211$	−9.53573	−	16.5164i	−0.656467	−	1.13703i	−0.981524	−	0.191340i	$-0.938717\pi$
$211$	−9.53573	−	16.5164i	−0.656467	−	1.13703i	0.325057	−	0.945694i	$-0.394617\pi$
$212$		0			0
$213$	−1.91151	+	3.31082i	−0.130974	+	0.226854i
$214$		0			0
$215$	−3.47330	−	2.00531i	−0.236877	−	0.136761i
$216$		0			0
$217$			0.793322i			0.0538542i
$218$		0			0
$219$	2.32570	−	4.02823i	0.157156	−	0.272202i
$220$		0			0
$221$		−	8.69727i		−	0.585041i
$222$		0			0
$223$	−6.92056	−	11.9868i	−0.463435	−	0.802693i	0.535694	−	0.844412i	$-0.320050\pi$
$223$	−6.92056	−	11.9868i	−0.463435	−	0.802693i	−0.999129	+	0.0417189i	$0.986717\pi$
$224$		0			0
$225$	0.833411	+	1.44351i	0.0555608	+	0.0962341i
$226$		0			0
$227$	−5.53833			−0.367592			−0.183796	−	0.982964i	$-0.558839\pi$
$227$	−5.53833			−0.367592			−0.183796	+	0.982964i	$0.558839\pi$
$228$		0			0
$229$	−1.31822			−0.0871105			−0.0435552	−	0.999051i	$-0.513868\pi$
$229$	−1.31822			−0.0871105			−0.0435552	+	0.999051i	$0.513868\pi$
$230$		0			0
$231$	9.56156	+	16.5611i	0.629104	+	1.08964i
$232$		0			0
$233$	2.56290	+	4.43908i	0.167901	+	0.290814i	0.937682	−	0.347495i	$-0.112968\pi$
$233$	2.56290	+	4.43908i	0.167901	+	0.290814i	−0.769780	+	0.638309i	$0.779634\pi$
$234$		0			0
$235$			0.180891i			0.0118000i
$236$		0			0
$237$	−4.74626	+	8.22077i	−0.308303	+	0.533996i
$238$		0			0
$239$			5.42569i			0.350958i	0.984483	+	0.175479i	$0.0561475\pi$
$239$			5.42569i			0.350958i	−0.984483	+	0.175479i	$0.943853\pi$
$240$		0			0
$241$	26.4153	+	15.2509i	1.70156	+	0.982395i	0.944187	+	0.329410i	$0.106850\pi$
$241$	26.4153	+	15.2509i	1.70156	+	0.982395i	0.757371	+	0.652985i	$0.226484\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	16.3705	+	28.3545i	1.04587	+	1.81150i
$246$		0			0
$247$	−4.95764	+	1.07117i	−0.315447	+	0.0681570i
$248$		0			0
$249$	2.45252	−	1.41596i	0.155422	−	0.0897331i
$250$		0			0
$251$	20.2974	+	11.7187i	1.28116	+	0.739679i	0.977061	−	0.212961i	$-0.0683106\pi$
$251$	20.2974	+	11.7187i	1.28116	+	0.739679i	0.304101	+	0.952640i	$0.401644\pi$
$252$		0			0
$253$	4.96670	−	8.60257i	0.312254	−	0.540839i
$254$		0			0
$255$	−13.6460			−0.854547
$256$		0			0
$257$	9.45764	+	5.46037i	0.589951	+	0.340609i	0.765078	−	0.643937i	$-0.222700\pi$
$257$	9.45764	+	5.46037i	0.589951	+	0.340609i	−0.175127	+	0.984546i	$0.556034\pi$
$258$		0			0
$259$	−41.2181			−2.56117
$260$		0			0
$261$	6.63328	−	3.82973i	0.410590	−	0.237054i
$262$		0			0
$263$	−12.1962	+	7.04147i	−0.752049	+	0.434196i	−0.826434	−	0.563034i	$-0.809634\pi$
$263$	−12.1962	+	7.04147i	−0.752049	+	0.434196i	0.0743847	+	0.997230i	$0.476301\pi$
$264$		0			0
$265$		−	5.95412i		−	0.365759i
$266$		0			0
$267$			13.7527i			0.841650i
$268$		0			0
$269$	18.4576	−	10.6565i	1.12538	−	0.649740i	0.182613	−	0.983185i	$-0.441545\pi$
$269$	18.4576	−	10.6565i	1.12538	−	0.649740i	0.942769	+	0.333445i	$0.108211\pi$
$270$		0			0
$271$	−1.21053	+	0.698898i	−0.0735343	+	0.0424551i	−0.536316	−	0.844017i	$-0.680185\pi$
$271$	−1.21053	+	0.698898i	−0.0735343	+	0.0424551i	0.462782	+	0.886472i	$0.346851\pi$
$272$		0			0
$273$	5.81027			0.351654
$274$		0			0
$275$	5.52826	+	3.19174i	0.333366	+	0.192469i
$276$		0			0
$277$	−0.703049			−0.0422421			−0.0211211	−	0.999777i	$-0.506724\pi$
$277$	−0.703049			−0.0422421			−0.0211211	+	0.999777i	$0.506724\pi$
$278$		0			0
$279$	0.0794381	−	0.137591i	0.00475583	−	0.00823735i
$280$		0			0
$281$	−2.56694	−	1.48202i	−0.153131	−	0.0884100i	0.421477	−	0.906839i	$-0.361512\pi$
$281$	−2.56694	−	1.48202i	−0.153131	−	0.0884100i	−0.574607	+	0.818429i	$0.694845\pi$
$282$		0			0
$283$	11.2974	−	6.52257i	0.671562	−	0.387726i	−0.125106	−	0.992143i	$-0.539927\pi$
$283$	11.2974	−	6.52257i	0.671562	−	0.387726i	0.796668	+	0.604417i	$0.206594\pi$
$284$		0			0
$285$	1.68067	+	7.77854i	0.0995542	+	0.460761i
$286$		0			0
$287$	3.08581	+	5.34477i	0.182149	+	0.315492i
$288$		0			0
$289$	−19.4334	+	33.6596i	−1.14314	+	1.97998i
$290$		0			0
$291$	8.50771	+	4.91193i	0.498731	+	0.287942i
$292$		0			0
$293$			7.92036i			0.462713i	0.972869	+	0.231356i	$0.0743163\pi$
$293$			7.92036i			0.462713i	−0.972869	+	0.231356i	$0.925684\pi$
$294$		0			0
$295$	9.38837	−	16.2611i	0.546612	−	0.946760i
$296$		0			0
$297$		−	3.82973i		−	0.222223i
$298$		0			0
$299$	−1.50906	−	2.61376i	−0.0872710	−	0.151158i
$300$		0			0
$301$	−5.48458	−	9.49956i	−0.316126	−	0.547546i
$302$		0			0
$303$	−15.1567			−0.870727
$304$		0			0
$305$	−20.5975			−1.17941
$306$		0			0
$307$	5.22949	+	9.05775i	0.298463	+	0.516953i	0.975784	−	0.218734i	$-0.0701928\pi$
$307$	5.22949	+	9.05775i	0.298463	+	0.516953i	−0.677322	+	0.735687i	$0.736859\pi$
$308$		0			0
$309$	−5.32435	−	9.22205i	−0.302892	−	0.524624i
$310$		0			0
$311$		−	21.9806i		−	1.24640i	−0.782061	−	0.623202i	$-0.785831\pi$
$311$		−	21.9806i		−	1.24640i	0.782061	−	0.623202i	$-0.214169\pi$
$312$		0			0
$313$	14.4438	−	25.0174i	0.816411	−	1.41407i	−0.0918985	−	0.995768i	$-0.529294\pi$
$313$	14.4438	−	25.0174i	0.816411	−	1.41407i	0.908310	−	0.418298i	$-0.137373\pi$
$314$		0			0
$315$		−	9.11633i		−	0.513647i
$316$		0			0
$317$	0.511979	+	0.295591i	0.0287556	+	0.0166021i	0.514309	−	0.857605i	$-0.328048\pi$
$317$	0.511979	+	0.295591i	0.0287556	+	0.0166021i	−0.485553	+	0.874207i	$0.661382\pi$
$318$		0			0
$319$	14.6668	−	25.4037i	0.821184	−	1.42233i
$320$		0			0
$321$	−5.66682	−	9.81523i	−0.316291	−	0.547832i
$322$		0			0
$323$	31.0192	+	9.96385i	1.72595	+	0.554403i
$324$		0			0
$325$	1.67968	−	0.969763i	0.0931718	−	0.0537927i
$326$		0			0
$327$	6.14100	+	3.54551i	0.339598	+	0.196067i
$328$		0			0
$329$	−0.247371	+	0.428459i	−0.0136380	+	0.0236217i
$330$		0			0
$331$	−11.4254			−0.627999			−0.314000	−	0.949423i	$-0.601669\pi$
$331$	−11.4254			−0.627999			−0.314000	+	0.949423i	$0.601669\pi$
$332$		0			0
$333$	7.14871	+	4.12731i	0.391747	+	0.226175i
$334$		0			0
$335$	−25.4713			−1.39164
$336$		0			0
$337$	−6.78176	+	3.91545i	−0.369426	+	0.213288i	−0.673208	−	0.739453i	$-0.735084\pi$
$337$	−6.78176	+	3.91545i	−0.369426	+	0.213288i	0.303782	+	0.952742i	$0.401751\pi$
$338$		0			0
$339$	11.8244	−	6.82679i	0.642211	−	0.370781i
$340$		0			0
$341$		−	0.608453i		−	0.0329496i
$342$		0			0
$343$			54.5941i			2.94780i
$344$		0			0
$345$	−4.10100	+	2.36771i	−0.220790	+	0.127473i
$346$		0			0
$347$	−10.3475	+	5.97413i	−0.555482	+	0.320708i	−0.751330	−	0.659926i	$-0.770587\pi$
$347$	−10.3475	+	5.97413i	−0.555482	+	0.320708i	0.195848	+	0.980634i	$0.437254\pi$
$348$		0			0
$349$	−14.2053			−0.760394			−0.380197	−	0.924905i	$-0.624144\pi$
$349$	−14.2053			−0.760394			−0.380197	+	0.924905i	$0.624144\pi$
$350$		0			0
$351$	−1.00771	−	0.581803i	−0.0537877	−	0.0310543i
$352$		0			0
$353$	18.9153			1.00676			0.503379	−	0.864066i	$-0.332090\pi$
$353$	18.9153			1.00676			0.503379	+	0.864066i	$0.332090\pi$
$354$		0			0
$355$	3.48983	−	6.04457i	0.185221	−	0.320812i
$356$		0			0
$357$	−32.3220	−	18.6611i	−1.71066	−	0.987651i
$358$		0			0
$359$	14.6338	−	8.44880i	0.772340	−	0.445911i	−0.0613687	−	0.998115i	$-0.519547\pi$
$359$	14.6338	−	8.44880i	0.772340	−	0.445911i	0.833709	+	0.552204i	$0.186213\pi$
$360$		0			0
$361$	1.85924	−	18.9088i	0.0978546	−	0.995201i
$362$		0			0
$363$	−1.83341	−	3.17556i	−0.0962291	−	0.166674i
$364$		0			0
$365$	−4.24603	+	7.35433i	−0.222247	+	0.384943i
$366$		0			0
$367$	20.7617	+	11.9868i	1.08375	+	0.625704i	0.931906	−	0.362700i	$-0.118145\pi$
$367$	20.7617	+	11.9868i	1.08375	+	0.625704i	0.151845	+	0.988404i	$0.451478\pi$
$368$		0			0
$369$		−	1.23597i		−	0.0643420i
$370$		0			0
$371$	8.14234	−	14.1029i	0.422729	−	0.732189i
$372$		0			0
$373$		−	2.10166i		−	0.108820i	−0.998519	−	0.0544098i	$-0.982672\pi$
$373$		−	2.10166i		−	0.108820i	0.998519	−	0.0544098i	$-0.0173277\pi$
$374$		0			0
$375$	−6.08581	−	10.5409i	−0.314270	−	0.544331i
$376$		0			0
$377$	−4.45630	−	7.71853i	−0.229511	−	0.397525i
$378$		0			0
$379$	−0.923156			−0.0474193			−0.0237097	−	0.999719i	$-0.507548\pi$
$379$	−0.923156			−0.0474193			−0.0237097	+	0.999719i	$0.507548\pi$
$380$		0			0
$381$	−2.00000			−0.102463
$382$		0			0
$383$	−14.1951	−	24.5866i	−0.725335	−	1.25632i	−0.958836	−	0.283960i	$-0.908352\pi$
$383$	−14.1951	−	24.5866i	−0.725335	−	1.25632i	0.233502	−	0.972356i	$-0.424982\pi$
$384$		0			0
$385$	−17.4565	−	30.2356i	−0.889667	−	1.54095i
$386$		0			0
$387$			2.19676i			0.111668i
$388$		0			0
$389$	4.94370	−	8.56274i	0.250655	−	0.434148i	−0.713051	−	0.701112i	$-0.752687\pi$
$389$	4.94370	−	8.56274i	0.250655	−	0.434148i	0.963706	+	0.266964i	$0.0860205\pi$
$390$		0			0
$391$			19.3868i			0.980433i
$392$		0			0
$393$	−11.2116	−	6.47303i	−0.565551	−	0.326521i
$394$		0			0
$395$	8.66524	−	15.0086i	0.435996	−	0.755167i
$396$		0			0
$397$	6.83072	+	11.8312i	0.342824	+	0.593789i	0.984956	−	0.172805i	$-0.0552832\pi$
$397$	6.83072	+	11.8312i	0.342824	+	0.593789i	−0.642132	+	0.766594i	$0.721950\pi$
$398$		0			0
$399$	−6.65642	+	20.7226i	−0.333238	+	1.03743i
$400$		0			0
$401$	−30.6538	+	17.6980i	−1.53078	+	0.883796i	−0.531453	+	0.847088i	$0.678354\pi$
$401$	−30.6538	+	17.6980i	−1.53078	+	0.883796i	−0.999326	+	0.0367080i	$0.988313\pi$
$402$		0			0
$403$	−0.160102	−	0.0924347i	−0.00797522	−	0.00460450i
$404$		0			0
$405$	−0.912850	+	1.58110i	−0.0453599	+	0.0785656i
$406$		0			0
$407$	31.6130			1.56700
$408$		0			0
$409$	15.1410	+	8.74166i	0.748674	+	0.432247i	0.825215	−	0.564819i	$-0.191054\pi$
$409$	15.1410	+	8.74166i	0.748674	+	0.432247i	−0.0765405	+	0.997066i	$0.524387\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$		0			0
$413$	44.4746	−	25.6774i	2.18845	−	1.26350i
$414$		0			0
$415$	−4.47757	+	2.58512i	−0.219795	+	0.126899i
$416$		0			0
$417$			8.39371i			0.411042i
$418$		0			0
$419$		−	20.5655i		−	1.00469i	−0.864667	−	0.502345i	$-0.832471\pi$
$419$		−	20.5655i		−	1.00469i	0.864667	−	0.502345i	$-0.167529\pi$
$420$		0			0
$421$	2.03108	−	1.17265i	0.0989890	−	0.0571513i	−0.449688	−	0.893186i	$-0.648465\pi$
$421$	2.03108	−	1.17265i	0.0989890	−	0.0571513i	0.548677	+	0.836034i	$0.315132\pi$
$422$		0			0
$423$	0.0858062	−	0.0495402i	0.00417204	−	0.00240873i
$424$		0			0
$425$	−12.4585			−0.604327
$426$		0			0
$427$	−48.7873	−	28.1674i	−2.36099	−	1.36312i
$428$		0			0
$429$	−4.45630			−0.215152
$430$		0			0
$431$	5.21161	−	9.02678i	0.251035	−	0.434805i	−0.712776	−	0.701391i	$-0.752563\pi$
$431$	5.21161	−	9.02678i	0.251035	−	0.434805i	0.963811	+	0.266587i	$0.0858959\pi$
$432$		0			0
$433$	−2.68680	−	1.55123i	−0.129120	−	0.0745472i	0.434049	−	0.900889i	$-0.357084\pi$
$433$	−2.68680	−	1.55123i	−0.129120	−	0.0745472i	−0.563168	+	0.826342i	$0.690418\pi$
$434$		0			0
$435$	−12.1104	+	6.99193i	−0.580648	+	0.335237i
$436$		0			0
$437$	11.0509	−	2.38772i	0.528637	−	0.114220i
$438$		0			0
$439$	5.30624	+	9.19068i	0.253253	+	0.438647i	0.964420	−	0.264376i	$-0.0851661\pi$
$439$	5.30624	+	9.19068i	0.253253	+	0.438647i	−0.711166	+	0.703024i	$0.751833\pi$
$440$		0			0
$441$	8.96670	−	15.5308i	0.426986	−	0.739561i
$442$		0			0
$443$	16.8438	+	9.72478i	0.800274	+	0.462038i	0.843567	−	0.537024i	$-0.180452\pi$
$443$	16.8438	+	9.72478i	0.800274	+	0.462038i	−0.0432932	+	0.999062i	$0.513785\pi$
$444$		0			0
$445$		−	25.1082i		−	1.19024i
$446$		0			0
$447$	−2.63463	+	4.56331i	−0.124614	+	0.215837i
$448$		0			0
$449$		−	10.3750i		−	0.489628i	−0.969570	−	0.244814i	$-0.921273\pi$
$449$		−	10.3750i		−	0.489628i	0.969570	−	0.244814i	$-0.0787269\pi$
$450$		0			0
$451$	−2.36672	−	4.09927i	−0.111444	−	0.193027i
$452$		0			0
$453$	−2.17430	−	3.76600i	−0.102158	−	0.176942i
$454$		0			0
$455$	−10.6078			−0.497302
$456$		0			0
$457$	−23.9483			−1.12026			−0.560128	−	0.828406i	$-0.689248\pi$
$457$	−23.9483			−1.12026			−0.560128	+	0.828406i	$0.689248\pi$
$458$		0			0
$459$	3.73720	+	6.47303i	0.174438	+	0.302135i
$460$		0			0
$461$	−16.1090	−	27.9017i	−0.750273	−	1.29951i	−0.947690	−	0.319191i	$-0.896589\pi$
$461$	−16.1090	−	27.9017i	−0.750273	−	1.29951i	0.197418	−	0.980319i	$-0.436744\pi$
$462$		0			0
$463$		−	14.0506i		−	0.652986i	−0.945200	−	0.326493i	$-0.894133\pi$
$463$		−	14.0506i		−	0.652986i	0.945200	−	0.326493i	$-0.105867\pi$
$464$		0			0
$465$	−0.145030	+	0.251199i	−0.00672561	+	0.0116491i
$466$		0			0
$467$			27.3890i			1.26741i	0.773574	+	0.633706i	$0.218467\pi$
$467$			27.3890i			1.26741i	−0.773574	+	0.633706i	$0.781533\pi$
$468$		0			0
$469$	−60.3313	−	34.8323i	−2.78584	−	1.60840i
$470$		0			0
$471$	−3.97441	+	6.88388i	−0.183131	+	0.317192i
$472$		0			0
$473$	4.20649	+	7.28586i	0.193415	+	0.335004i
$474$		0			0
$475$	1.53441	+	7.10164i	0.0704037	+	0.325845i
$476$		0			0
$477$	−2.82435	+	1.63064i	−0.129318	+	0.0746620i
$478$		0			0
$479$	−19.8140	−	11.4396i	−0.905327	−	0.522691i	−0.0264023	−	0.999651i	$-0.508405\pi$
$479$	−19.8140	−	11.4396i	−0.905327	−	0.522691i	−0.878925	+	0.476961i	$0.841738\pi$
$480$		0			0
$481$	4.80256	−	8.31828i	0.218978	−	0.379281i
$482$		0			0
$483$	−12.9515			−0.589314
$484$		0			0
$485$	−15.5325	−	8.96771i	−0.705296	−	0.407203i
$486$		0			0
$487$	−3.11288			−0.141058			−0.0705291	−	0.997510i	$-0.522469\pi$
$487$	−3.11288			−0.141058			−0.0705291	+	0.997510i	$0.522469\pi$
$488$		0			0
$489$	−5.30893	+	3.06511i	−0.240078	+	0.138609i
$490$		0			0
$491$	−1.41361	+	0.816146i	−0.0637952	+	0.0368322i	−0.531558	−	0.847022i	$-0.678393\pi$
$491$	−1.41361	+	0.816146i	−0.0637952	+	0.0368322i	0.467763	+	0.883854i	$0.345060\pi$
$492$		0			0
$493$			57.2499i			2.57841i
$494$		0			0
$495$			6.99193i			0.314264i
$496$		0			0
$497$	16.5321	−	9.54479i	0.741564	−	0.428142i
$498$		0			0
$499$	−1.97260	+	1.13888i	−0.0883055	+	0.0509832i	−0.543503	−	0.839408i	$-0.682902\pi$
$499$	−1.97260	+	1.13888i	−0.0883055	+	0.0509832i	0.455197	+	0.890391i	$0.349569\pi$
$500$		0			0
$501$	22.4925			1.00489
$502$		0			0
$503$	−30.0411	−	17.3442i	−1.33947	−	0.773341i	−0.352738	−	0.935722i	$-0.614749\pi$
$503$	−30.0411	−	17.3442i	−1.33947	−	0.773341i	−0.986728	+	0.162381i	$0.948083\pi$
$504$		0			0
$505$	27.6715			1.23137
$506$		0			0
$507$	5.82301	−	10.0858i	0.258609	−	0.447924i
$508$		0			0
$509$	−36.8310	−	21.2644i	−1.63251	−	0.942528i	−0.983317	−	0.181902i	$-0.941775\pi$
$509$	−36.8310	−	21.2644i	−1.63251	−	0.942528i	−0.649190	−	0.760626i	$-0.724892\pi$
$510$		0			0
$511$	−20.1143	+	11.6130i	−0.889804	+	0.513729i
$512$		0			0
$513$	3.22949	−	2.92752i	0.142586	−	0.129253i
$514$		0			0
$515$	9.72067	+	16.8367i	0.428344	+	0.741913i
$516$		0			0
$517$	0.189726	−	0.328614i	0.00834412	−	0.0144524i
$518$		0			0
$519$	13.2666	+	7.65946i	0.582338	+	0.336213i
$520$		0			0
$521$			33.0231i			1.44677i	0.690445	+	0.723385i	$0.257415\pi$
$521$			33.0231i			1.44677i	−0.690445	+	0.723385i	$0.742585\pi$
$522$		0			0
$523$	−13.2604	+	22.9677i	−0.579838	+	1.00431i	0.415659	+	0.909521i	$0.363551\pi$
$523$	−13.2604	+	22.9677i	−0.579838	+	1.00431i	−0.995497	+	0.0947890i	$0.969782\pi$
$524$		0			0
$525$		−	8.32300i		−	0.363246i
$526$		0			0
$527$	0.593753	+	1.02841i	0.0258643	+	0.0447982i
$528$		0			0
$529$	−8.13621	−	14.0923i	−0.353748	−	0.612710i
$530$		0			0
$531$	−10.2847			−0.446317
$532$		0			0
$533$	−1.43818			−0.0622946
$534$		0			0
$535$	10.3459	+	17.9196i	0.447293	+	0.774734i
$536$		0			0
$537$	10.1397	+	17.5624i	0.437558	+	0.757873i
$538$		0			0
$539$		−	68.6800i		−	2.95826i
$540$		0			0
$541$	17.4488	−	30.2222i	0.750183	−	1.29936i	−0.197550	−	0.980293i	$-0.563299\pi$
$541$	17.4488	−	30.2222i	0.750183	−	1.29936i	0.947734	−	0.319063i	$-0.103368\pi$
$542$		0			0
$543$			13.4154i			0.575711i
$544$		0			0
$545$	−11.2116	−	6.47303i	−0.480253	−	0.277274i
$546$		0			0
$547$	−5.20524	+	9.01575i	−0.222560	+	0.385486i	−0.955585	−	0.294717i	$-0.904775\pi$
$547$	−5.20524	+	9.01575i	−0.222560	+	0.385486i	0.733024	+	0.680202i	$0.238108\pi$
$548$		0			0
$549$	5.64100	+	9.77049i	0.240752	+	0.416995i
$550$		0			0
$551$	32.6338	−	7.05100i	1.39024	−	0.300383i
$552$		0			0
$553$	41.0490	−	23.6997i	1.74558	−	1.00781i
$554$		0			0
$555$	−13.0514	−	7.53523i	−0.554001	−	0.319852i
$556$		0			0
$557$	7.49252	−	12.9774i	0.317468	−	0.549871i	−0.662491	−	0.749070i	$-0.730501\pi$
$557$	7.49252	−	12.9774i	0.317468	−	0.549871i	0.979959	+	0.199199i	$0.0638339\pi$
$558$		0			0
$559$	2.55616			0.108114
$560$		0			0
$561$	24.7899	+	14.3125i	1.04663	+	0.604273i
$562$		0			0
$563$	17.8614			0.752769			0.376384	−	0.926464i	$-0.377167\pi$
$563$	17.8614			0.752769			0.376384	+	0.926464i	$0.377167\pi$
$564$		0			0
$565$	−21.5877	+	12.4637i	−0.908202	+	0.524351i
$566$		0			0
$567$	−4.32435	+	2.49667i	−0.181606	+	0.104850i
$568$		0			0
$569$		−	33.5325i		−	1.40576i	−0.711311	−	0.702878i	$-0.751898\pi$
$569$		−	33.5325i		−	1.40576i	0.711311	−	0.702878i	$-0.248102\pi$
$570$		0			0
$571$			15.6638i			0.655510i	0.944763	+	0.327755i	$0.106292\pi$
$571$			15.6638i			0.655510i	−0.944763	+	0.327755i	$0.893708\pi$
$572$		0			0
$573$	13.5437	−	7.81945i	0.565795	−	0.326662i
$574$		0			0
$575$	−3.74412	+	2.16167i	−0.156141	+	0.0901478i
$576$		0			0
$577$	31.8972			1.32790			0.663948	−	0.747779i	$-0.268880\pi$
$577$	31.8972			1.32790			0.663948	+	0.747779i	$0.268880\pi$
$578$		0			0
$579$	−16.9773	−	9.80187i	−0.705554	−	0.407352i
$580$		0			0
$581$	−14.1408			−0.586658
$582$		0			0
$583$	−6.24492	+	10.8165i	−0.258638	+	0.447974i
$584$		0			0
$585$	1.83978	+	1.06220i	0.0760655	+	0.0439164i
$586$		0			0
$587$	−14.5826	+	8.41927i	−0.601888	+	0.347500i	−0.769784	−	0.638304i	$-0.779636\pi$
$587$	−14.5826	+	8.41927i	−0.601888	+	0.347500i	0.167896	+	0.985805i	$0.446303\pi$
$588$		0			0
$589$	0.513089	−	0.465113i	0.0211415	−	0.0191647i
$590$		0			0
$591$	−2.08715	−	3.61505i	−0.0858539	−	0.148703i
$592$		0			0
$593$	−10.9256	+	18.9237i	−0.448660	+	0.777102i	−0.998299	−	0.0583003i	$-0.981432\pi$
$593$	−10.9256	+	18.9237i	−0.448660	+	0.777102i	0.549639	+	0.835402i	$0.314765\pi$
$594$		0			0
$595$	59.0102	+	34.0696i	2.41918	+	1.39672i
$596$		0			0
$597$			22.5050i			0.921070i
$598$		0			0
$599$	20.7180	−	35.8846i	0.846514	−	1.46620i	−0.0377863	−	0.999286i	$-0.512031\pi$
$599$	20.7180	−	35.8846i	0.846514	−	1.46620i	0.884300	−	0.466919i	$-0.154636\pi$
$600$		0			0
$601$			0.432352i			0.0176360i	0.999961	+	0.00881799i	$0.00280689\pi$
$601$			0.432352i			0.0176360i	−0.999961	+	0.00881799i	$0.997193\pi$
$602$		0			0
$603$	6.97575	+	12.0824i	0.284075	+	0.492032i
$604$		0			0
$605$	3.34726	+	5.79762i	0.136085	+	0.235707i
$606$		0			0
$607$	−39.9948			−1.62334			−0.811670	−	0.584117i	$-0.801441\pi$
$607$	−39.9948			−1.62334			−0.811670	+	0.584117i	$0.801441\pi$
$608$		0			0
$609$	−38.2462			−1.54982
$610$		0			0
$611$	−0.0576453	−	0.0998446i	−0.00233208	−	0.00403928i
$612$		0			0
$613$	−2.49229	−	4.31677i	−0.100663	−	0.174353i	0.811295	−	0.584637i	$-0.198763\pi$
$613$	−2.49229	−	4.31677i	−0.100663	−	0.174353i	−0.911958	+	0.410284i	$0.865430\pi$
$614$		0			0
$615$			2.25651i			0.0909912i
$616$		0			0
$617$	22.9139	−	39.6881i	0.922480	−	1.59778i	0.126916	−	0.991913i	$-0.459492\pi$
$617$	22.9139	−	39.6881i	0.922480	−	1.59778i	0.795564	−	0.605869i	$-0.207175\pi$
$618$		0			0
$619$		−	21.8455i		−	0.878043i	−0.898476	−	0.439022i	$-0.855325\pi$
$619$		−	21.8455i		−	0.878043i	0.898476	−	0.439022i	$-0.144675\pi$
$620$		0			0
$621$	2.24626	+	1.29688i	0.0901393	+	0.0520420i
$622$		0			0
$623$	34.3358	−	59.4714i	1.37564	−	2.38267i
$624$		0			0
$625$	6.94379	+	12.0270i	0.277752	+	0.481080i
$626$		0			0
$627$	5.10526	−	15.8936i	0.203885	−	0.634728i
$628$		0			0
$629$	−53.4324	+	30.8492i	−2.13049	+	1.23004i
$630$		0			0
$631$	23.0531	+	13.3097i	0.917728	+	0.529851i	0.882910	−	0.469543i	$-0.155581\pi$
$631$	23.0531	+	13.3097i	0.917728	+	0.529851i	0.0348185	+	0.999394i	$0.488915\pi$
$632$		0			0
$633$	9.53573	−	16.5164i	0.379011	−	0.656467i
$634$		0			0
$635$	3.65140			0.144901
$636$		0			0
$637$	−18.0717	−	10.4337i	−0.716027	−	0.413398i
$638$		0			0
$639$	−3.82301			−0.151236
$640$		0			0
$641$	4.42167	−	2.55285i	0.174646	−	0.100832i	−0.410129	−	0.912028i	$-0.634516\pi$
$641$	4.42167	−	2.55285i	0.174646	−	0.100832i	0.584775	+	0.811196i	$0.301183\pi$
$642$		0			0
$643$	0.870748	−	0.502727i	0.0343389	−	0.0198256i	−0.482732	−	0.875768i	$-0.660356\pi$
$643$	0.870748	−	0.502727i	0.0343389	−	0.0198256i	0.517071	+	0.855942i	$0.327022\pi$
$644$		0			0
$645$		−	4.01062i		−	0.157918i
$646$		0			0
$647$			25.7740i			1.01328i	0.862158	+	0.506640i	$0.169113\pi$
$647$			25.7740i			1.01328i	−0.862158	+	0.506640i	$0.830887\pi$
$648$		0			0
$649$	−34.1106	+	19.6938i	−1.33896	+	0.773048i
$650$		0			0
$651$	−0.687037	+	0.396661i	−0.0269271	+	0.0155464i
$652$		0			0
$653$	−14.9359			−0.584487			−0.292243	−	0.956344i	$-0.594402\pi$
$653$	−14.9359			−0.584487			−0.292243	+	0.956344i	$0.594402\pi$
$654$		0			0
$655$	20.4690	+	11.8178i	0.799791	+	0.461760i
$656$		0			0
$657$	4.65140			0.181468
$658$		0			0
$659$	−4.04738	+	7.01027i	−0.157664	+	0.273082i	−0.934026	−	0.357206i	$-0.883730\pi$
$659$	−4.04738	+	7.01027i	−0.157664	+	0.273082i	0.776362	+	0.630287i	$0.217063\pi$
$660$		0			0
$661$	15.2208	+	8.78771i	0.592019	+	0.341802i	0.765895	−	0.642965i	$-0.222296\pi$
$661$	15.2208	+	8.78771i	0.592019	+	0.341802i	−0.173876	+	0.984767i	$0.555629\pi$
$662$		0			0
$663$	7.53205	−	4.34863i	0.292521	−	0.168887i
$664$		0			0
$665$	12.1526	−	37.8332i	0.471259	−	1.46711i
$666$		0			0
$667$	9.93339	+	17.2051i	0.384623	+	0.666186i
$668$		0			0
$669$	6.92056	−	11.9868i	0.267564	−	0.463435i
$670$		0			0
$671$	37.4183	+	21.6035i	1.44452	+	0.833993i
$672$		0			0
$673$			5.53985i			0.213546i	0.994283	+	0.106773i	$0.0340518\pi$
$673$			5.53985i			0.213546i	−0.994283	+	0.106773i	$0.965948\pi$
$674$		0			0
$675$	−0.833411	+	1.44351i	−0.0320780	+	0.0555608i
$676$		0			0
$677$			13.7230i			0.527416i	0.964603	+	0.263708i	$0.0849456\pi$
$677$			13.7230i			0.527416i	−0.964603	+	0.263708i	$0.915054\pi$
$678$		0			0
$679$	−24.5269	−	42.4819i	−0.941256	−	1.63030i
$680$		0			0
$681$	−2.76916	−	4.79633i	−0.106115	−	0.183796i
$682$		0			0
$683$	−23.1589			−0.886150			−0.443075	−	0.896485i	$-0.646112\pi$
$683$	−23.1589			−0.886150			−0.443075	+	0.896485i	$0.646112\pi$
$684$		0			0
$685$	10.9542			0.418538
$686$		0			0
$687$	−0.659111	−	1.14161i	−0.0251466	−	0.0435552i
$688$		0			0
$689$	1.89742	+	3.28644i	0.0722861	+	0.125203i
$690$		0			0
$691$		−	45.8007i		−	1.74234i	−0.490980	−	0.871171i	$-0.663361\pi$
$691$		−	45.8007i		−	1.74234i	0.490980	−	0.871171i	$-0.336639\pi$
$692$		0			0
$693$	−9.56156	+	16.5611i	−0.363214	+	0.629104i
$694$		0			0
$695$		−	15.3244i		−	0.581287i
$696$		0			0
$697$	8.00047	+	4.61907i	0.303039	+	0.174960i
$698$		0			0
$699$	−2.56290	+	4.43908i	−0.0969379	+	0.167901i
$700$		0			0
$701$	3.61274	+	6.25745i	0.136451	+	0.236341i	0.926151	−	0.377153i	$-0.123097\pi$
$701$	3.61274	+	6.25745i	0.136451	+	0.236341i	−0.789700	+	0.613494i	$0.789764\pi$
$702$		0			0
$703$	24.1656	+	26.6582i	0.911422	+	1.00543i
$704$		0			0
$705$	−0.156656	+	0.0904455i	−0.00590002	+	0.00340638i
$706$		0			0
$707$	65.5428	+	37.8411i	2.46499	+	1.42316i
$708$		0			0
$709$	−16.9076	+	29.2848i	−0.634977	+	1.09981i	0.351543	+	0.936172i	$0.385657\pi$
$709$	−16.9076	+	29.2848i	−0.634977	+	1.09981i	−0.986520	+	0.163641i	$0.947676\pi$
$710$		0			0
$711$	−9.49252			−0.355997
$712$		0			0
$713$	0.356877	+	0.206043i	0.0133652	+	0.00771638i
$714$		0			0
$715$	8.13585			0.304264
$716$		0			0
$717$	−4.69878	+	2.71284i	−0.175479	+	0.101313i
$718$		0			0
$719$	23.4424	−	13.5345i	0.874256	−	0.504752i	0.00549567	−	0.999985i	$-0.498251\pi$
$719$	23.4424	−	13.5345i	0.874256	−	0.504752i	0.868760	+	0.495233i	$0.164917\pi$
$720$		0			0
$721$			53.1726i			1.98025i
$722$		0			0
$723$			30.5017i			1.13437i
$724$		0			0
$725$	−11.0565	+	6.38348i	−0.410629	+	0.237076i
$726$		0			0
$727$	−12.1279	+	7.00206i	−0.449800	+	0.259692i	−0.707746	−	0.706467i	$-0.750288\pi$
$727$	−12.1279	+	7.00206i	−0.449800	+	0.259692i	0.257946	+	0.966159i	$0.416954\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−14.2197	−	8.20974i	−0.525934	−	0.303648i
$732$		0			0
$733$	8.34907			0.308380			0.154190	−	0.988041i	$-0.450723\pi$
$733$	8.34907			0.308380			0.154190	+	0.988041i	$0.450723\pi$
$734$		0			0
$735$	−16.3705	+	28.3545i	−0.603835	+	1.04587i
$736$		0			0
$737$	46.2722	+	26.7152i	1.70446	+	0.984069i
$738$		0			0
$739$	−25.9427	+	14.9780i	−0.954317	+	0.550975i	−0.894419	−	0.447229i	$-0.852411\pi$
$739$	−25.9427	+	14.9780i	−0.954317	+	0.550975i	−0.0598977	+	0.998205i	$0.519077\pi$
$740$		0			0
$741$	−3.40648	−	3.75786i	−0.125140	−	0.138048i
$742$		0			0
$743$	−23.6386	−	40.9433i	−0.867218	−	1.50206i	−0.864828	−	0.502068i	$-0.832573\pi$
$743$	−23.6386	−	40.9433i	−0.867218	−	1.50206i	−0.00238915	−	0.999997i	$-0.500760\pi$
$744$		0			0
$745$	4.81004	−	8.33123i	0.176226	−	0.305233i
$746$		0			0
$747$	2.45252	+	1.41596i	0.0897331	+	0.0518074i
$748$		0			0
$749$			56.5927i			2.06785i
$750$		0			0
$751$	16.5114	−	28.5986i	0.602509	−	1.04358i	−0.389931	−	0.920844i	$-0.627501\pi$
$751$	16.5114	−	28.5986i	0.602509	−	1.04358i	0.992440	−	0.122732i	$-0.0391657\pi$
$752$		0			0
$753$			23.4374i			0.854108i
$754$		0			0
$755$	3.96962	+	6.87558i	0.144469	+	0.250228i
$756$		0			0
$757$	−10.8643	−	18.8175i	−0.394868	−	0.683932i	0.598216	−	0.801335i	$-0.295876\pi$
$757$	−10.8643	−	18.8175i	−0.394868	−	0.683932i	−0.993084	+	0.117403i	$0.962543\pi$
$758$		0			0
$759$	9.93339			0.360559
$760$		0			0
$761$	28.1510			1.02047			0.510236	−	0.860034i	$-0.329558\pi$
$761$	28.1510			1.02047			0.510236	+	0.860034i	$0.329558\pi$
$762$		0			0
$763$	−17.7039	−	30.6641i	−0.640924	−	1.11011i
$764$		0			0
$765$	−6.82301	−	11.8178i	−0.246686	−	0.427273i
$766$		0			0
$767$			11.9673i			0.432115i
$768$		0			0
$769$	8.81822	−	15.2736i	0.317993	−	0.550780i	−0.662076	−	0.749437i	$-0.730324\pi$
$769$	8.81822	−	15.2736i	0.317993	−	0.550780i	0.980069	+	0.198656i	$0.0636578\pi$
$770$		0			0
$771$			10.9207i			0.393301i
$772$		0			0
$773$	−22.9759	−	13.2651i	−0.826385	−	0.477114i	0.0262280	−	0.999656i	$-0.491650\pi$
$773$	−22.9759	−	13.2651i	−0.826385	−	0.477114i	−0.852613	+	0.522542i	$0.824984\pi$
$774$		0			0
$775$	−0.132409	+	0.229340i	−0.00475628	+	0.00823812i
$776$		0			0
$777$	−20.6090	−	35.6959i	−0.739345	−	1.28058i
$778$		0			0
$779$	1.64762	−	5.12934i	0.0590323	−	0.183778i
$780$		0			0
$781$	−12.6796	+	7.32055i	−0.453710	+	0.261950i
$782$		0			0
$783$	6.63328	+	3.82973i	0.237054	+	0.136863i
$784$		0			0
$785$	7.25607	−	12.5679i	0.258980	−	0.448567i
$786$		0			0
$787$	−51.8183			−1.84712			−0.923561	−	0.383451i	$-0.874736\pi$
$787$	−51.8183			−1.84712			−0.923561	+	0.383451i	$0.874736\pi$
$788$		0			0
$789$	−12.1962	−	7.04147i	−0.434196	−	0.250683i
$790$		0			0
$791$	−68.1769			−2.42409
$792$		0			0
$793$	11.3690	−	6.56390i	0.403725	−	0.233091i
$794$		0			0
$795$	5.15642	−	2.97706i	0.182879	−	0.105585i
$796$		0			0
$797$		−	22.0033i		−	0.779397i	−0.920942	−	0.389699i	$-0.872579\pi$
$797$		−	22.0033i		−	0.779397i	0.920942	−	0.389699i	$-0.127421\pi$
$798$		0			0
$799$			0.740568i			0.0261994i
$800$		0			0
$801$	−11.9102	+	6.87633i	−0.420825	+	0.242963i
$802$		0			0
$803$	15.4270	−	8.90680i	0.544408	−	0.314314i
$804$		0			0
$805$	23.6456			0.833396
$806$		0			0
$807$	18.4576	+	10.6565i	0.649740	+	0.375127i
$808$		0			0
$809$	19.1593			0.673607			0.336803	−	0.941575i	$-0.390654\pi$
$809$	19.1593			0.673607			0.336803	+	0.941575i	$0.390654\pi$
$810$		0			0
$811$	−15.1412	+	26.2254i	−0.531681	+	0.920898i	0.467636	+	0.883921i	$0.345106\pi$
$811$	−15.1412	+	26.2254i	−0.531681	+	0.920898i	−0.999316	+	0.0369764i	$0.988227\pi$
$812$		0			0
$813$	−1.21053	−	0.698898i	−0.0424551	−	0.0245114i
$814$		0			0
$815$	9.69251	−	5.59597i	0.339514	−	0.196018i
$816$		0			0
$817$	−2.92841	+	9.11667i	−0.102452	+	0.318952i
$818$		0			0
$819$	2.90514	+	5.03185i	0.101514	+	0.175827i
$820$		0			0
$821$	1.78947	−	3.09946i	0.0624530	−	0.108172i	−0.833108	−	0.553110i	$-0.813441\pi$
$821$	1.78947	−	3.09946i	0.0624530	−	0.108172i	0.895561	+	0.444938i	$0.146774\pi$
$822$		0			0
$823$	−25.7052	−	14.8409i	−0.896028	−	0.517322i	−0.0201184	−	0.999798i	$-0.506404\pi$
$823$	−25.7052	−	14.8409i	−0.896028	−	0.517322i	−0.875909	+	0.482476i	$0.839738\pi$
$824$		0			0
$825$			6.38348i			0.222244i
$826$		0			0
$827$	−6.31822	+	10.9435i	−0.219706	+	0.380542i	−0.954718	−	0.297512i	$-0.903843\pi$
$827$	−6.31822	+	10.9435i	−0.219706	+	0.380542i	0.735012	+	0.678054i	$0.237176\pi$
$828$		0			0
$829$			33.3267i			1.15748i	0.815511	+	0.578742i	$0.196456\pi$
$829$			33.3267i			1.15748i	−0.815511	+	0.578742i	$0.803544\pi$
$830$		0			0
$831$	−0.351525	−	0.608859i	−0.0121943	−	0.0211211i
$832$		0			0
$833$	67.0208	+	116.083i	2.32213	+	4.02205i
$834$		0			0
$835$	−41.0646			−1.42110
$836$		0			0
$837$	0.158876			0.00549157
$838$		0			0
$839$	−9.97450	−	17.2763i	−0.344358	−	0.596446i	0.640879	−	0.767642i	$-0.278570\pi$
$839$	−9.97450	−	17.2763i	−0.344358	−	0.596446i	−0.985237	+	0.171196i	$0.945237\pi$
$840$		0			0
$841$	14.8336	+	25.6926i	0.511505	+	0.885953i
$842$		0			0
$843$		−	2.96404i		−	0.102087i
$844$		0			0
$845$	−10.6311	+	18.4135i	−0.365720	+	0.633445i
$846$		0			0
$847$			18.3097i			0.629128i
$848$		0			0
$849$	11.2974	+	6.52257i	0.387726	+	0.223854i
$850$		0			0
$851$	−10.7052	+	18.5420i	−0.366971	+	0.635613i
$852$		0			0
$853$	1.95630	+	3.38840i	0.0669823	+	0.116017i	0.897572	−	0.440869i	$-0.145330\pi$
$853$	1.95630	+	3.38840i	0.0669823	+	0.116017i	−0.830589	+	0.556885i	$0.811996\pi$
$854$		0			0
$855$	−5.89608	+	5.34477i	−0.201642	+	0.182787i
$856$		0			0
$857$	4.83862	−	2.79358i	0.165284	−	0.0954269i	−0.415076	−	0.909787i	$-0.636245\pi$
$857$	4.83862	−	2.79358i	0.165284	−	0.0954269i	0.580360	+	0.814360i	$0.302912\pi$
$858$		0			0
$859$	28.4810	+	16.4435i	0.971760	+	0.561046i	0.899772	−	0.436360i	$-0.143733\pi$
$859$	28.4810	+	16.4435i	0.971760	+	0.561046i	0.0719873	+	0.997406i	$0.477066\pi$
$860$		0			0
$861$	−3.08581	+	5.34477i	−0.105164	+	0.182149i
$862$		0			0
$863$	−8.80712			−0.299798			−0.149899	−	0.988701i	$-0.547895\pi$
$863$	−8.80712			−0.299798			−0.149899	+	0.988701i	$0.547895\pi$
$864$		0			0
$865$	−24.2208	−	13.9839i	−0.823531	−	0.475466i
$866$		0			0
$867$	−38.8668			−1.31999
$868$		0			0
$869$	−31.4833	+	18.1769i	−1.06800	+	0.616609i
$870$		0			0
$871$	14.0591	−	8.11703i	0.476375	−	0.275035i
$872$		0			0
$873$			9.82386i			0.332487i
$874$		0			0
$875$			60.7769i			2.05464i
$876$		0			0
$877$	20.2586	−	11.6963i	0.684085	−	0.394957i	−0.117307	−	0.993096i	$-0.537426\pi$
$877$	20.2586	−	11.6963i	0.684085	−	0.394957i	0.801392	+	0.598139i	$0.204093\pi$
$878$		0			0
$879$	−6.85924	+	3.96018i	−0.231356	+	0.133574i
$880$		0			0
$881$	−2.94396			−0.0991845			−0.0495922	−	0.998770i	$-0.515792\pi$
$881$	−2.94396			−0.0991845			−0.0495922	+	0.998770i	$0.515792\pi$
$882$		0			0
$883$	−4.80013	−	2.77136i	−0.161537	−	0.0932636i	0.417052	−	0.908883i	$-0.363063\pi$
$883$	−4.80013	−	2.77136i	−0.161537	−	0.0932636i	−0.578589	+	0.815619i	$0.696397\pi$
$884$		0			0
$885$	18.7767			0.631173
$886$		0			0
$887$	−6.76020	+	11.7090i	−0.226985	+	0.393150i	−0.956913	−	0.290374i	$-0.906220\pi$
$887$	−6.76020	+	11.7090i	−0.226985	+	0.393150i	0.729928	+	0.683524i	$0.239554\pi$
$888$		0			0
$889$	8.64871	+	4.99333i	0.290068	+	0.167471i
$890$		0			0
$891$	3.31664	−	1.91486i	0.111112	−	0.0641504i
$892$		0			0
$893$	0.422140	−	0.0912097i	0.0141264	−	0.00305222i
$894$		0			0
$895$	−18.5120	−	32.0636i	−0.618786	−	1.07177i
$896$		0			0
$897$	1.50906	−	2.61376i	0.0503859	−	0.0872710i
$898$		0			0
$899$	1.05387	+	0.608453i	0.0351486	+	0.0202930i
$900$		0			0
$901$		−	24.3762i		−	0.812088i
$902$		0			0
$903$	5.48458	−	9.49956i	0.182515	−	0.316126i
$904$		0			0
$905$		−	24.4925i		−	0.814159i
$906$		0			0
$907$	−1.63328	−	2.82893i	−0.0542323	−	0.0939332i	0.837635	−	0.546231i	$-0.183938\pi$
$907$	−1.63328	−	2.82893i	−0.0542323	−	0.0939332i	−0.891867	+	0.452298i	$0.850604\pi$
$908$		0			0
$909$	−7.57833	−	13.1260i	−0.251357	−	0.435364i
$910$		0			0
$911$	42.3199			1.40212			0.701061	−	0.713101i	$-0.252710\pi$
$911$	42.3199			1.40212			0.701061	+	0.713101i	$0.252710\pi$
$912$		0			0
$913$	10.8455			0.358934
$914$		0			0
$915$	−10.2988	−	17.8380i	−0.340467	−	0.589705i
$916$		0			0
$917$	32.3220	+	55.9833i	1.06737	+	1.84873i
$918$		0			0
$919$			0.647260i			0.0213511i	0.999943	+	0.0106756i	$0.00339820\pi$
$919$			0.647260i			0.0213511i	−0.999943	+	0.0106756i	$0.996602\pi$
$920$		0			0
$921$	−5.22949	+	9.05775i	−0.172318	+	0.298463i
$922$		0			0
$923$			4.44848i			0.146423i
$924$		0			0
$925$	−11.9156	−	6.87949i	−0.391784	−	0.226196i
$926$		0			0
$927$	5.32435	−	9.22205i	0.174875	−	0.302892i
$928$		0			0
$929$	6.07173	+	10.5165i	0.199207	+	0.345036i	0.948271	−	0.317461i	$-0.102830\pi$
$929$	6.07173	+	10.5165i	0.199207	+	0.345036i	−0.749065	+	0.662497i	$0.769497\pi$
$930$		0			0
$931$	57.9157	−	52.5004i	1.89811	−	1.72063i
$932$		0			0
$933$	19.0357	−	10.9903i	0.623202	−	0.359806i
$934$		0			0
$935$	−45.2590	−	26.1303i	−1.48013	−	0.854552i
$936$		0			0
$937$	−15.6537	+	27.1131i	−0.511385	+	0.885745i	0.488528	+	0.872548i	$0.337534\pi$
$937$	−15.6537	+	27.1131i	−0.511385	+	0.885745i	−0.999913	+	0.0131968i	$0.995799\pi$
$938$		0			0
$939$	28.8876			0.942711
$940$		0			0
$941$	27.8310	+	16.0683i	0.907266	+	0.523810i	0.879550	−	0.475806i	$-0.157844\pi$
$941$	27.8310	+	16.0683i	0.907266	+	0.523810i	0.0277152	+	0.999616i	$0.491177\pi$
$942$		0			0
$943$	3.20581			0.104395
$944$		0			0
$945$	7.89497	−	4.55816i	0.256823	−	0.148277i
$946$		0			0
$947$	51.2522	−	29.5905i	1.66547	−	0.961562i	0.695442	−	0.718582i	$-0.255208\pi$
$947$	51.2522	−	29.5905i	1.66547	−	0.961562i	0.970031	−	0.242980i	$-0.0781249\pi$
$948$		0			0
$949$		−	5.41239i		−	0.175694i
$950$		0			0
$951$			0.591183i			0.0191704i
$952$		0			0
$953$	27.1853	−	15.6954i	0.880617	−	0.508425i	0.00975528	−	0.999952i	$-0.496895\pi$
$953$	27.1853	−	15.6954i	0.880617	−	0.508425i	0.870862	+	0.491528i	$0.163561\pi$
$954$		0			0
$955$	−24.7267	+	14.2760i	−0.800137	+	0.461959i
$956$		0			0
$957$	29.3336			0.948222
$958$		0			0
$959$	25.9461	+	14.9800i	0.837844	+	0.483730i
$960$		0			0
$961$	−30.9748			−0.999186
$962$		0			0
$963$	5.66682	−	9.81523i	0.182611	−	0.316291i
$964$		0			0
$965$	30.9955	+	17.8953i	0.997780	+	0.576069i
$966$		0			0
$967$	7.65177	−	4.41775i	0.246064	−	0.142065i	−0.371896	−	0.928274i	$-0.621292\pi$
$967$	7.65177	−	4.41775i	0.246064	−	0.142065i	0.617961	+	0.786209i	$0.287959\pi$
$968$		0			0
$969$	6.88066	+	31.8453i	0.221039	+	1.02302i
$970$		0			0
$971$	−12.4040	−	21.4844i	−0.398064	−	0.689467i	0.595423	−	0.803412i	$-0.296985\pi$
$971$	−12.4040	−	21.4844i	−0.398064	−	0.689467i	−0.993487	+	0.113945i	$0.963651\pi$
$972$		0			0
$973$	20.9563	−	36.2974i	0.671828	−	1.16364i
$974$		0			0
$975$	1.67968	+	0.969763i	0.0537927	+	0.0310573i
$976$		0			0
$977$		−	40.2360i		−	1.28726i	−0.765336	−	0.643631i	$-0.777427\pi$
$977$		−	40.2360i		−	1.28726i	0.765336	−	0.643631i	$-0.222573\pi$
$978$		0			0
$979$	−26.3345	+	45.6127i	−0.841654	+	1.45779i
$980$		0			0
$981$			7.09101i			0.226399i
$982$		0			0
$983$	−3.20942	−	5.55887i	−0.102365	−	0.177301i	0.810294	−	0.586024i	$-0.199307\pi$
$983$	−3.20942	−	5.55887i	−0.102365	−	0.177301i	−0.912658	+	0.408723i	$0.865974\pi$
$984$		0			0
$985$	3.81051	+	6.59999i	0.121413	+	0.210293i
$986$		0			0
$987$	−0.494742			−0.0157478
$988$		0			0
$989$	−5.69786			−0.181181
$990$		0			0
$991$	24.9947	+	43.2921i	0.793983	+	1.37522i	0.923483	+	0.383640i	$0.125330\pi$
$991$	24.9947	+	43.2921i	0.793983	+	1.37522i	−0.129499	+	0.991580i	$0.541337\pi$
$992$		0			0
$993$	−5.71272	−	9.89473i	−0.181288	−	0.314000i
$994$		0			0
$995$		−	41.0874i		−	1.30256i
$996$		0			0
$997$	−20.6258	+	35.7249i	−0.653226	+	1.13142i	0.329110	+	0.944292i	$0.393251\pi$
$997$	−20.6258	+	35.7249i	−0.653226	+	1.13142i	−0.982335	+	0.187129i	$0.940082\pi$
$998$		0			0
$999$			8.25462i			0.261165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.h.31.2	yes	8
3.2	odd	2		2736.2.bm.r.1855.3		8
4.3	odd	2		912.2.bb.g.31.2	✓	8
12.11	even	2		2736.2.bm.s.1855.3		8
19.8	odd	6		912.2.bb.g.559.2	yes	8
57.8	even	6		2736.2.bm.s.559.3		8
76.27	even	6	inner	912.2.bb.h.559.2	yes	8
228.179	odd	6		2736.2.bm.r.559.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.g.31.2	✓	8	4.3	odd	2
912.2.bb.g.559.2	yes	8	19.8	odd	6
912.2.bb.h.31.2	yes	8	1.1	even	1	trivial
912.2.bb.h.559.2	yes	8	76.27	even	6	inner
2736.2.bm.r.559.3		8	228.179	odd	6
2736.2.bm.r.1855.3		8	3.2	odd	2
2736.2.bm.s.559.3		8	57.8	even	6
2736.2.bm.s.1855.3		8	12.11	even	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.912850 - 1.58110i) q^{5} -4.99333i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.912850 - 1.58110i) q^{5} -4.99333i q^{7} +(-0.500000 + 0.866025i) q^{9} +3.82973i q^{11} +(1.00771 + 0.581803i) q^{13} +(0.912850 - 1.58110i) q^{15} +(-3.73720 - 6.47303i) q^{17} +(-3.22949 + 2.92752i) q^{19} +(4.32435 - 2.49667i) q^{21} +(-2.24626 - 1.29688i) q^{23} +(0.833411 - 1.44351i) q^{25} -1.00000 q^{27} +(-6.63328 - 3.82973i) q^{29} -0.158876 q^{31} +(-3.31664 + 1.91486i) q^{33} +(-7.89497 + 4.55816i) q^{35} -8.25462i q^{37} +1.16361i q^{39} +(-1.07038 + 0.617985i) q^{41} +(1.90245 - 1.09838i) q^{43} +1.82570 q^{45} +(-0.0858062 - 0.0495402i) q^{47} -17.9334 q^{49} +(3.73720 - 6.47303i) q^{51} +(2.82435 + 1.63064i) q^{53} +(6.05519 - 3.49597i) q^{55} +(-4.15005 - 1.33306i) q^{57} +(5.14234 + 8.90680i) q^{59} +(5.64100 - 9.77049i) q^{61} +(4.32435 + 2.49667i) q^{63} -2.12439i q^{65} +(6.97575 - 12.0824i) q^{67} -2.59376i q^{69} +(1.91151 + 3.31082i) q^{71} +(-2.32570 - 4.02823i) q^{73} +1.66682 q^{75} +19.1231 q^{77} +(4.74626 + 8.22077i) q^{79} +(-0.500000 - 0.866025i) q^{81} -2.83193i q^{83} +(-6.82301 + 11.8178i) q^{85} -7.65946i q^{87} +(11.9102 + 6.87633i) q^{89} +(2.90514 - 5.03185i) q^{91} +(-0.0794381 - 0.137591i) q^{93} +(7.57675 + 2.43377i) q^{95} +(8.50771 - 4.91193i) q^{97} +(-3.31664 - 1.91486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9	\( 8 q + 4 q^{3} - 2 q^{5} - 4 q^{9} + 2 q^{15} + 4 q^{17} + 6 q^{21} + 6 q^{23} - 12 q^{25} - 8 q^{27} - 12 q^{29} - 28 q^{31} - 6 q^{33} + 18 q^{35} - 12 q^{41} - 18 q^{43} + 4 q^{45} + 12 q^{47} - 24 q^{49} - 4 q^{51} - 6 q^{53} + 12 q^{55} + 6 q^{57} + 10 q^{59} - 4 q^{61} + 6 q^{63} + 6 q^{67} - 8 q^{71} - 8 q^{73} - 24 q^{75} + 28 q^{77} + 14 q^{79} - 4 q^{81} - 8 q^{85} + 54 q^{89} + 26 q^{91} - 14 q^{93} + 38 q^{95} + 60 q^{97} - 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 2 * q^5 - 4 * q^9 + 2 * q^15 + 4 * q^17 + 6 * q^21 + 6 * q^23 - 12 * q^25 - 8 * q^27 - 12 * q^29 - 28 * q^31 - 6 * q^33 + 18 * q^35 - 12 * q^41 - 18 * q^43 + 4 * q^45 + 12 * q^47 - 24 * q^49 - 4 * q^51 - 6 * q^53 + 12 * q^55 + 6 * q^57 + 10 * q^59 - 4 * q^61 + 6 * q^63 + 6 * q^67 - 8 * q^71 - 8 * q^73 - 24 * q^75 + 28 * q^77 + 14 * q^79 - 4 * q^81 - 8 * q^85 + 54 * q^89 + 26 * q^91 - 14 * q^93 + 38 * q^95 + 60 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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