LMFDB - Embedded newform 693.2.cg.c.514.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(19,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("693.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.cg (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			514.11
Character	$\chi$	$=$	693.514
Dual form			693.2.cg.c.271.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.322290 - 0.723875i) q^{2} +(0.918138 + 1.01969i) q^{4} +(-1.19955 - 0.126078i) q^{5} +(2.32594 + 1.26095i) q^{7} +(2.54123 - 0.825697i) q^{8} +O(q^{10})$	\(q+(0.322290 - 0.723875i) q^{2} +(0.918138 + 1.01969i) q^{4} +(-1.19955 - 0.126078i) q^{5} +(2.32594 + 1.26095i) q^{7} +(2.54123 - 0.825697i) q^{8} +(-0.477866 + 0.827689i) q^{10} +(0.137461 + 3.31377i) q^{11} +(0.306792 - 0.222897i) q^{13} +(1.66240 - 1.27730i) q^{14} +(-0.0655419 + 0.623589i) q^{16} +(-0.981780 + 0.437117i) q^{17} +(-3.09598 + 3.43843i) q^{19} +(-0.972789 - 1.33893i) q^{20} +(2.44306 + 0.968491i) q^{22} +(-0.580792 - 1.00596i) q^{23} +(-3.46772 - 0.737086i) q^{25} +(-0.0624738 - 0.293916i) q^{26} +(0.849752 + 3.52948i) q^{28} +(6.27112 + 2.03761i) q^{29} +(5.71212 - 0.600367i) q^{31} +(5.05833 + 2.92043i) q^{32} +0.851564i q^{34} +(-2.63110 - 1.80582i) q^{35} +(10.3371 - 2.19723i) q^{37} +(1.49119 + 3.34927i) q^{38} +(-3.15243 + 0.670070i) q^{40} +(1.56301 + 4.81045i) q^{41} -10.6749i q^{43} +(-3.25283 + 3.18267i) q^{44} +(-0.915372 + 0.0962095i) q^{46} +(-8.59265 - 7.73686i) q^{47} +(3.82002 + 5.86579i) q^{49} +(-1.65117 + 2.27264i) q^{50} +(0.508964 + 0.108184i) q^{52} +(0.981621 + 9.33950i) q^{53} +(0.252901 - 3.99236i) q^{55} +(6.95192 + 1.28384i) q^{56} +(3.49609 - 3.88280i) q^{58} +(0.851375 - 0.766581i) q^{59} +(-0.00423519 + 0.0402952i) q^{61} +(1.40637 - 4.32835i) q^{62} +(2.72973 - 1.98326i) q^{64} +(-0.396113 + 0.228696i) q^{65} +(-1.03631 + 1.79495i) q^{67} +(-1.34714 - 0.599783i) q^{68} +(-2.15516 + 1.32259i) q^{70} +(1.06724 + 0.775393i) q^{71} +(-4.26853 - 4.74069i) q^{73} +(1.74104 - 8.19094i) q^{74} -6.34868 q^{76} +(-3.85877 + 7.88098i) q^{77} +(0.603644 - 1.35581i) q^{79} +(0.157241 - 0.739762i) q^{80} +(3.98590 + 0.418935i) q^{82} +(-11.5042 - 8.35828i) q^{83} +(1.23280 - 0.400562i) q^{85} +(-7.72726 - 3.44040i) q^{86} +(3.08549 + 8.30757i) q^{88} +(4.61647 - 2.66532i) q^{89} +(0.994641 - 0.131597i) q^{91} +(0.492526 - 1.51584i) q^{92} +(-8.36984 + 3.72649i) q^{94} +(4.14728 - 3.73423i) q^{95} +(-9.91056 - 13.6407i) q^{97} +(5.47725 - 0.874729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} - 12 q^{5} - 10 q^{7} + 40 q^{8}+O(q^{10}) $ 128 * q - 12 * q^4 - 12 * q^5 - 10 * q^7 + 40 * q^8	$ 128 q - 12 q^{4} - 12 q^{5} - 10 q^{7} + 40 q^{8} + 2 q^{11} - 12 q^{14} + 40 q^{16} + 60 q^{17} + 52 q^{22} + 24 q^{23} - 20 q^{25} - 24 q^{26} + 30 q^{28} - 40 q^{29} - 18 q^{31} + 80 q^{35} - 8 q^{37} + 24 q^{38} - 90 q^{40} + 82 q^{44} + 70 q^{46} + 24 q^{47} - 94 q^{49} - 4 q^{53} + 104 q^{56} - 32 q^{58} - 48 q^{59} + 30 q^{61} - 48 q^{64} - 40 q^{67} - 180 q^{68} + 146 q^{70} + 32 q^{71} + 90 q^{73} - 40 q^{74} + 50 q^{79} - 228 q^{80} + 168 q^{82} - 20 q^{85} - 146 q^{86} + 16 q^{88} + 48 q^{91} + 204 q^{92} - 10 q^{95}+O(q^{100}) $ 128 * q - 12 * q^4 - 12 * q^5 - 10 * q^7 + 40 * q^8 + 2 * q^11 - 12 * q^14 + 40 * q^16 + 60 * q^17 + 52 * q^22 + 24 * q^23 - 20 * q^25 - 24 * q^26 + 30 * q^28 - 40 * q^29 - 18 * q^31 + 80 * q^35 - 8 * q^37 + 24 * q^38 - 90 * q^40 + 82 * q^44 + 70 * q^46 + 24 * q^47 - 94 * q^49 - 4 * q^53 + 104 * q^56 - 32 * q^58 - 48 * q^59 + 30 * q^61 - 48 * q^64 - 40 * q^67 - 180 * q^68 + 146 * q^70 + 32 * q^71 + 90 * q^73 - 40 * q^74 + 50 * q^79 - 228 * q^80 + 168 * q^82 - 20 * q^85 - 146 * q^86 + 16 * q^88 + 48 * q^91 + 204 * q^92 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.322290	−	0.723875i	0.227893	−	0.511857i	−0.763017	−	0.646378i	$-0.776283\pi$
$2$	0.322290	−	0.723875i	0.227893	−	0.511857i	0.990911	+	0.134521i	$0.0429497\pi$
$3$		0			0
$3$		0			0
$4$	0.918138	+	1.01969i	0.459069	+	0.509847i
$5$	−1.19955	−	0.126078i	−0.536454	−	0.0563836i	−0.167572	−	0.985860i	$-0.553593\pi$
$5$	−1.19955	−	0.126078i	−0.536454	−	0.0563836i	−0.368882	+	0.929476i	$0.620259\pi$
$6$		0			0
$7$	2.32594	+	1.26095i	0.879124	+	0.476594i
$7$	2.32594	+	1.26095i	0.879124	+	0.476594i
$8$	2.54123	−	0.825697i	0.898461	−	0.291928i
$9$		0			0
$10$	−0.477866	+	0.827689i	−0.151115	+	0.261738i
$11$	0.137461	+	3.31377i	0.0414462	+	0.999141i
$11$	0.137461	+	3.31377i	0.0414462	+	0.999141i
$12$		0			0
$13$	0.306792	−	0.222897i	0.0850887	−	0.0618205i	−0.544428	−	0.838808i	$-0.683253\pi$
$13$	0.306792	−	0.222897i	0.0850887	−	0.0618205i	0.629516	+	0.776987i	$0.283253\pi$
$14$	1.66240	−	1.27730i	0.444294	−	0.341373i
$15$		0			0
$16$	−0.0655419	+	0.623589i	−0.0163855	+	0.155897i
$17$	−0.981780	+	0.437117i	−0.238117	+	0.106016i	−0.522326	−	0.852746i	$-0.674936\pi$
$17$	−0.981780	+	0.437117i	−0.238117	+	0.106016i	0.284209	+	0.958762i	$0.408269\pi$
$18$		0			0
$19$	−3.09598	+	3.43843i	−0.710266	+	0.788830i	−0.984975	−	0.172697i	$-0.944752\pi$
$19$	−3.09598	+	3.43843i	−0.710266	+	0.788830i	0.274709	+	0.961527i	$0.411418\pi$
$20$	−0.972789	−	1.33893i	−0.217522	−	0.299394i
$21$		0			0
$22$	2.44306	+	0.968491i	0.520862	+	0.206483i
$23$	−0.580792	−	1.00596i	−0.121103	−	0.209757i	0.799100	−	0.601199i	$-0.205310\pi$
$23$	−0.580792	−	1.00596i	−0.121103	−	0.209757i	−0.920203	+	0.391441i	$0.871977\pi$
$24$		0			0
$25$	−3.46772	−	0.737086i	−0.693544	−	0.147417i
$26$	−0.0624738	−	0.293916i	−0.0122521	−	0.0576417i
$27$		0			0
$28$	0.849752	+	3.52948i	0.160588	+	0.667008i
$29$	6.27112	+	2.03761i	1.16452	+	0.378375i	0.826594	−	0.562799i	$-0.190276\pi$
$29$	6.27112	+	2.03761i	1.16452	+	0.378375i	0.337923	+	0.941174i	$0.390276\pi$
$30$		0			0
$31$	5.71212	−	0.600367i	1.02593	−	0.107829i	0.423412	−	0.905937i	$-0.360832\pi$
$31$	5.71212	−	0.600367i	1.02593	−	0.107829i	0.602514	+	0.798108i	$0.294166\pi$
$32$	5.05833	+	2.92043i	0.894196	+	0.516264i
$33$		0			0
$34$			0.851564i			0.146042i
$35$	−2.63110	−	1.80582i	−0.444737	−	0.305239i
$36$		0			0
$37$	10.3371	−	2.19723i	1.69942	−	0.361222i	0.746718	−	0.665140i	$-0.231628\pi$
$37$	10.3371	−	2.19723i	1.69942	−	0.361222i	0.952698	+	0.303918i	$0.0982949\pi$
$38$	1.49119	+	3.34927i	0.241903	+	0.543323i
$39$		0			0
$40$	−3.15243	+	0.670070i	−0.498443	+	0.105947i
$41$	1.56301	+	4.81045i	0.244101	+	0.751266i	0.995783	+	0.0917399i	$0.0292428\pi$
$41$	1.56301	+	4.81045i	0.244101	+	0.751266i	−0.751682	+	0.659526i	$0.770757\pi$
$42$		0			0
$43$		−	10.6749i		−	1.62790i	−0.580934	−	0.813950i	$-0.697313\pi$
$43$		−	10.6749i		−	1.62790i	0.580934	−	0.813950i	$-0.302687\pi$
$44$	−3.25283	+	3.18267i	−0.490383	+	0.479806i
$45$		0			0
$46$	−0.915372	+	0.0962095i	−0.134964	+	0.0141853i
$47$	−8.59265	−	7.73686i	−1.25337	−	1.12854i	−0.986318	−	0.164854i	$-0.947285\pi$
$47$	−8.59265	−	7.73686i	−1.25337	−	1.12854i	−0.267050	−	0.963683i	$-0.586049\pi$
$48$		0			0
$49$	3.82002	+	5.86579i	0.545717	+	0.837970i
$50$	−1.65117	+	2.27264i	−0.233510	+	0.321400i
$51$		0			0
$52$	0.508964	+	0.108184i	0.0705806	+	0.0150024i
$53$	0.981621	+	9.33950i	0.134836	+	1.28288i	0.827437	+	0.561558i	$0.189798\pi$
$53$	0.981621	+	9.33950i	0.134836	+	1.28288i	−0.692601	+	0.721321i	$0.743535\pi$
$54$		0			0
$55$	0.252901	−	3.99236i	0.0341012	−	0.538330i
$56$	6.95192	+	1.28384i	0.928990	+	0.171561i
$57$		0			0
$58$	3.49609	−	3.88280i	0.459059	−	0.509837i
$59$	0.851375	−	0.766581i	0.110840	−	0.0998004i	−0.611848	−	0.790976i	$-0.709573\pi$
$59$	0.851375	−	0.766581i	0.110840	−	0.0998004i	0.722687	+	0.691175i	$0.242907\pi$
$60$		0			0
$61$	−0.00423519	+	0.0402952i	−0.000542261	+	0.00515927i	−0.994790	−	0.101948i	$-0.967492\pi$
$61$	−0.00423519	+	0.0402952i	−0.000542261	+	0.00515927i	0.994247	+	0.107108i	$0.0341590\pi$
$62$	1.40637	−	4.32835i	0.178609	−	0.549701i
$63$		0			0
$64$	2.72973	−	1.98326i	0.341216	−	0.247908i
$65$	−0.396113	+	0.228696i	−0.0491318	+	0.0283663i
$66$		0			0
$67$	−1.03631	+	1.79495i	−0.126606	+	0.219288i	−0.922359	−	0.386333i	$-0.873742\pi$
$67$	−1.03631	+	1.79495i	−0.126606	+	0.219288i	0.795754	+	0.605620i	$0.207075\pi$
$68$	−1.34714	−	0.599783i	−0.163364	−	0.0727344i
$69$		0			0
$70$	−2.15516	+	1.32259i	−0.257591	+	0.158080i
$71$	1.06724	+	0.775393i	0.126658	+	0.0920222i	0.649310	−	0.760523i	$-0.275058\pi$
$71$	1.06724	+	0.775393i	0.126658	+	0.0920222i	−0.522653	+	0.852546i	$0.675058\pi$
$72$		0			0
$73$	−4.26853	−	4.74069i	−0.499594	−	0.554855i	0.439622	−	0.898183i	$-0.355113\pi$
$73$	−4.26853	−	4.74069i	−0.499594	−	0.554855i	−0.939216	+	0.343328i	$0.888446\pi$
$74$	1.74104	−	8.19094i	0.202392	−	0.952178i
$75$		0			0
$76$	−6.34868			−0.728244
$77$	−3.85877	+	7.88098i	−0.439748	+	0.898121i
$78$		0			0
$79$	0.603644	−	1.35581i	0.0679152	−	0.152540i	−0.876398	−	0.481587i	$-0.840061\pi$
$79$	0.603644	−	1.35581i	0.0679152	−	0.152540i	0.944314	+	0.329047i	$0.106727\pi$
$80$	0.157241	−	0.739762i	0.0175801	−	0.0827079i
$81$		0			0
$82$	3.98590	+	0.418935i	0.440169	+	0.0462636i
$83$	−11.5042	−	8.35828i	−1.26275	−	0.917440i	−0.263859	−	0.964561i	$-0.584995\pi$
$83$	−11.5042	−	8.35828i	−1.26275	−	0.917440i	−0.998889	+	0.0471213i	$0.984995\pi$
$84$		0			0
$85$	1.23280	−	0.400562i	0.133716	−	0.0434471i
$86$	−7.72726	−	3.44040i	−0.833252	−	0.370988i
$87$		0			0
$88$	3.08549	+	8.30757i	0.328915	+	0.885590i
$89$	4.61647	−	2.66532i	0.489345	−	0.282524i	−0.234958	−	0.972006i	$-0.575495\pi$
$89$	4.61647	−	2.66532i	0.489345	−	0.282524i	0.724303	+	0.689482i	$0.242162\pi$
$90$		0			0
$91$	0.994641	−	0.131597i	0.104267	−	0.0137952i
$92$	0.492526	−	1.51584i	0.0513494	−	0.158037i
$93$		0			0
$94$	−8.36984	+	3.72649i	−0.863283	+	0.384358i
$95$	4.14728	−	3.73423i	0.425502	−	0.383124i
$96$		0			0
$97$	−9.91056	−	13.6407i	−1.00626	−	1.38500i	−0.921401	−	0.388612i	$-0.872955\pi$
$97$	−9.91056	−	13.6407i	−1.00626	−	1.38500i	−0.0848633	−	0.996393i	$-0.527045\pi$
$98$	5.47725	−	0.874729i	0.553286	−	0.0883610i
$99$		0			0
$100$	−2.43224	−	4.21276i	−0.243224	−	0.421276i
$101$	−1.40495	−	13.3672i	−0.139798	−	1.33009i	−0.809352	−	0.587324i	$-0.800182\pi$
$101$	−1.40495	−	13.3672i	−0.139798	−	1.33009i	0.669554	−	0.742763i	$-0.266485\pi$
$102$		0			0
$103$	2.59900	+	12.2273i	0.256087	+	1.20479i	0.898687	+	0.438591i	$0.144522\pi$
$103$	2.59900	+	12.2273i	0.256087	+	1.20479i	−0.642600	+	0.766202i	$0.722144\pi$
$104$	0.595583	−	0.819750i	0.0584018	−	0.0803831i
$105$		0			0
$106$	7.07699	+	2.29945i	0.687378	+	0.223343i
$107$	1.22845	+	1.10610i	0.118759	+	0.106931i	0.726371	−	0.687303i	$-0.241206\pi$
$107$	1.22845	+	1.10610i	0.118759	+	0.106931i	−0.607612	+	0.794234i	$0.707872\pi$
$108$		0			0
$109$	−11.1675	−	6.44757i	−1.06965	−	0.617566i	−0.141568	−	0.989929i	$-0.545214\pi$
$109$	−11.1675	−	6.44757i	−1.06965	−	0.617566i	−0.928087	+	0.372363i	$0.878548\pi$
$110$	−2.80846	−	1.46977i	−0.267776	−	0.140137i
$111$		0			0
$112$	−0.938761	+	1.36779i	−0.0887046	+	0.129244i
$113$	−3.02558	−	9.31178i	−0.284623	−	0.875979i	−0.986511	−	0.163692i	$-0.947660\pi$
$113$	−3.02558	−	9.31178i	−0.284623	−	0.875979i	0.701889	−	0.712287i	$-0.252340\pi$
$114$		0			0
$115$	0.569858	+	1.27992i	0.0531396	+	0.119353i
$116$	3.68001	+	8.26543i	0.341680	+	0.767426i
$117$		0			0
$118$	−0.280519	−	0.863350i	−0.0258239	−	0.0794778i
$119$	−2.83475	−	0.221266i	−0.259861	−	0.0202835i
$120$		0			0
$121$	−10.9622	+	0.911032i	−0.996564	+	0.0828211i
$122$	0.0278037	+	0.0160525i	0.00251723	+	0.00145332i
$123$		0			0
$124$	5.85670	+	5.27340i	0.525947	+	0.473565i
$125$	9.80237	+	3.18498i	0.876751	+	0.284874i
$126$		0			0
$127$	3.87165	−	5.32886i	0.343553	−	0.472860i	−0.601922	−	0.798555i	$-0.705598\pi$
$127$	3.87165	−	5.32886i	0.343553	−	0.472860i	0.945475	+	0.325695i	$0.105598\pi$
$128$	1.87290	+	8.81128i	0.165542	+	0.778815i
$129$		0			0
$130$	0.0378841	+	0.360443i	0.00332265	+	0.0316129i
$131$	−0.317831	−	0.550499i	−0.0277690	−	0.0480973i	0.851807	−	0.523856i	$-0.175507\pi$
$131$	−0.317831	−	0.550499i	−0.0277690	−	0.0480973i	−0.879576	+	0.475759i	$0.842174\pi$
$132$		0			0
$133$	−11.5367	+	4.09372i	−1.00036	+	0.354971i
$134$	0.965323	+	1.32865i	0.0833912	+	0.114778i
$135$		0			0
$136$	−2.13401	+	1.92147i	−0.182990	+	0.164765i
$137$	1.56922	−	0.698661i	0.134067	−	0.0596906i	−0.338607	−	0.940928i	$-0.609956\pi$
$137$	1.56922	−	0.698661i	0.134067	−	0.0596906i	0.472674	+	0.881237i	$0.343289\pi$
$138$		0			0
$139$	−0.214074	+	0.658851i	−0.0181575	+	0.0558830i	−0.959725	−	0.280942i	$-0.909353\pi$
$139$	−0.214074	+	0.658851i	−0.0181575	+	0.0558830i	0.941567	+	0.336825i	$0.109353\pi$
$140$	−0.574330	−	4.34091i	−0.0485398	−	0.366874i
$141$		0			0
$142$	0.905247	−	0.522644i	0.0759666	−	0.0438593i
$143$	0.780803	+	0.985998i	0.0652940	+	0.0824533i
$144$		0			0
$145$	−7.26561	−	3.23486i	−0.603376	−	0.268640i
$146$	−4.80737	+	1.56201i	−0.397861	+	0.129273i
$147$		0			0
$148$	11.7314	+	8.52338i	0.964317	+	0.700617i
$149$	−0.407224	−	0.0428010i	−0.0333611	−	0.00350639i	0.0878332	−	0.996135i	$-0.472006\pi$
$149$	−0.407224	−	0.0428010i	−0.0333611	−	0.00350639i	−0.121194	+	0.992629i	$0.538672\pi$
$150$		0			0
$151$	−2.51404	+	11.8277i	−0.204590	+	0.962521i	0.749269	+	0.662266i	$0.230405\pi$
$151$	−2.51404	+	11.8277i	−0.204590	+	0.962521i	−0.953859	+	0.300255i	$0.902928\pi$
$152$	−5.02850	+	11.2942i	−0.407865	+	0.916080i
$153$		0			0
$154$	4.46120	+	5.33323i	0.359494	+	0.429764i
$155$	−6.92765			−0.556442
$156$		0			0
$157$	0.540933	−	2.54489i	0.0431712	−	0.203104i	−0.951276	−	0.308340i	$-0.900226\pi$
$157$	0.540933	−	2.54489i	0.0431712	−	0.203104i	0.994447	+	0.105236i	$0.0335598\pi$
$158$	−0.786885	−	0.873925i	−0.0626012	−	0.0695257i
$159$		0			0
$160$	−5.69951	−	4.14094i	−0.450586	−	0.327370i
$161$	−0.0824230	−	3.07215i	−0.00649584	−	0.242120i
$162$		0			0
$163$	−4.57477	−	2.03682i	−0.358324	−	0.159536i	0.219676	−	0.975573i	$-0.429500\pi$
$163$	−4.57477	−	2.03682i	−0.358324	−	0.159536i	−0.578000	+	0.816037i	$0.696167\pi$
$164$	−3.47013	+	6.01044i	−0.270972	+	0.469337i
$165$		0			0
$166$	−9.75802	+	5.63380i	−0.757369	+	0.437267i
$167$	−5.11356	+	3.71522i	−0.395699	+	0.287492i	−0.767787	−	0.640705i	$-0.778642\pi$
$167$	−5.11356	+	3.71522i	−0.395699	+	0.287492i	0.372088	+	0.928198i	$0.378642\pi$
$168$		0			0
$169$	−3.97278	+	12.2270i	−0.305599	+	0.940536i
$170$	0.107363	−	1.02149i	0.00823438	−	0.0783448i
$171$		0			0
$172$	10.8851	−	9.80099i	0.829981	−	0.747318i
$173$	12.9782	−	14.4138i	0.986718	−	1.09586i	−0.00867360	−	0.999962i	$-0.502761\pi$
$173$	12.9782	−	14.4138i	0.986718	−	1.09586i	0.995391	−	0.0958984i	$-0.0305724\pi$
$174$		0			0
$175$	−7.13629	−	6.08704i	−0.539452	−	0.460137i
$176$	−2.07544	−	0.131472i	−0.156443	−	0.00991004i
$177$		0			0
$178$	−0.441517	−	4.20075i	−0.0330931	−	0.314860i
$179$	5.29058	+	1.12455i	0.395437	+	0.0840526i	0.401338	−	0.915930i	$-0.368545\pi$
$179$	5.29058	+	1.12455i	0.395437	+	0.0840526i	−0.00590160	+	0.999983i	$0.501879\pi$
$180$		0			0
$181$	9.73127	−	13.3939i	0.723320	−	0.995564i	−0.276087	−	0.961133i	$-0.589038\pi$
$181$	9.73127	−	13.3939i	0.723320	−	0.995564i	0.999407	−	0.0344317i	$-0.0109621\pi$
$182$	0.225303	−	0.762408i	0.0167005	−	0.0565134i
$183$		0			0
$184$	−2.30654	−	2.07682i	−0.170041	−	0.153105i
$185$	−12.6769	+	1.33240i	−0.932026	+	0.0979599i
$186$		0			0
$187$	−1.58346	−	3.19331i	−0.115794	−	0.233518i
$188$		−	15.8654i		−	1.15710i
$189$		0			0
$190$	−1.36649	−	4.20562i	−0.0991354	−	0.305107i
$191$	−16.1190	+	3.42620i	−1.16633	+	0.247911i	−0.750085	−	0.661341i	$-0.769987\pi$
$191$	−16.1190	+	3.42620i	−1.16633	+	0.247911i	−0.416245	+	0.909253i	$0.636654\pi$
$192$		0			0
$193$	−6.19830	−	13.9216i	−0.446163	−	1.00210i	−0.986963	−	0.160948i	$-0.948545\pi$
$193$	−6.19830	−	13.9216i	−0.446163	−	1.00210i	0.540800	−	0.841151i	$-0.318122\pi$
$194$	−13.0682	+	2.77774i	−0.938245	+	0.199430i
$195$		0			0
$196$	−2.47402	+	9.28085i	−0.176715	+	0.662918i
$197$			12.8617i			0.916358i	0.888860	+	0.458179i	$0.151498\pi$
$197$			12.8617i			0.916358i	−0.888860	+	0.458179i	$0.848502\pi$
$198$		0			0
$199$	−13.9041	−	8.02753i	−0.985634	−	0.569056i	−0.0816679	−	0.996660i	$-0.526025\pi$
$199$	−13.9041	−	8.02753i	−0.985634	−	0.569056i	−0.903966	+	0.427603i	$0.859358\pi$
$200$	−9.42089	+	0.990175i	−0.666157	+	0.0700160i
$201$		0			0
$202$	−10.1290	−	3.29111i	−0.712673	−	0.231561i
$203$	12.0169	+	12.6469i	0.843424	+	0.887640i
$204$		0			0
$205$	−1.26841	−	5.96742i	−0.0885899	−	0.416783i
$206$	9.68867	+	2.05939i	0.675042	+	0.143485i
$207$		0			0
$208$	0.118889	+	0.205921i	0.00824344	+	0.0142781i
$209$	−11.8198	−	9.78672i	−0.817590	−	0.676962i
$210$		0			0
$211$	−9.08915	−	12.5101i	−0.625723	−	0.861233i	0.372031	−	0.928220i	$-0.378661\pi$
$211$	−9.08915	−	12.5101i	−0.625723	−	0.861233i	−0.997754	+	0.0669869i	$0.978661\pi$
$212$	−8.62218	+	9.57590i	−0.592173	+	0.657675i
$213$		0			0
$214$	1.19660	−	0.532760i	0.0817977	−	0.0364187i
$215$	−1.34586	+	12.8050i	−0.0917869	+	0.873294i
$216$		0			0
$217$	14.0431	+	5.80626i	0.953307	+	0.394155i
$218$	−8.26641	+	6.00590i	−0.559872	+	0.406771i
$219$		0			0
$220$	4.30319	−	3.40766i	0.290121	−	0.229744i
$221$	−0.203770	+	0.352940i	−0.0137070	+	0.0237413i
$222$		0			0
$223$	−6.04220	+	1.96323i	−0.404615	+	0.131468i	−0.504252	−	0.863556i	$-0.668232\pi$
$223$	−6.04220	+	1.96323i	−0.404615	+	0.131468i	0.0996370	+	0.995024i	$0.468232\pi$
$224$	8.08288	+	13.1711i	0.540060	+	0.880028i
$225$		0			0
$226$	−7.71567	−	0.810950i	−0.513239	−	0.0539436i
$227$	−1.74589	−	1.93900i	−0.115879	−	0.128696i	0.682414	−	0.730966i	$-0.260930\pi$
$227$	−1.74589	−	1.93900i	−0.115879	−	0.128696i	−0.798293	+	0.602269i	$0.794263\pi$
$228$		0			0
$229$	−4.44423	+	9.98191i	−0.293683	+	0.659623i	−0.998774	−	0.0494932i	$-0.984239\pi$
$229$	−4.44423	+	9.98191i	−0.293683	+	0.659623i	0.705091	+	0.709117i	$0.250906\pi$
$230$	1.11016			0.0732020
$231$		0			0
$232$	17.6188			1.15673
$233$	5.76928	−	12.9580i	0.377958	−	0.848908i	−0.619973	−	0.784623i	$-0.712857\pi$
$233$	5.76928	−	12.9580i	0.377958	−	0.848908i	0.997932	−	0.0642851i	$-0.0204767\pi$
$234$		0			0
$235$	9.33186	+	10.3641i	0.608743	+	0.676078i
$236$	1.56336	+	0.164316i	0.101766	+	0.0106960i
$237$		0			0
$238$	−1.07378	+	1.98069i	−0.0696027	+	0.128389i
$239$	26.8225	−	8.71515i	1.73500	−	0.563736i	0.740844	−	0.671677i	$-0.234426\pi$
$239$	26.8225	−	8.71515i	1.73500	−	0.563736i	0.994157	+	0.107940i	$0.0344255\pi$
$240$		0			0
$241$	0.0638441	−	0.110581i	0.00411256	−	0.00712316i	−0.863962	−	0.503557i	$-0.832024\pi$
$241$	0.0638441	−	0.110581i	0.00411256	−	0.00712316i	0.868074	+	0.496434i	$0.165358\pi$
$242$	−2.87353	+	8.22888i	−0.184718	+	0.528972i
$243$		0			0
$244$	−0.0449773	+	0.0326779i	−0.00287938	+	0.00209199i
$245$	−3.84275	−	7.51791i	−0.245504	−	0.480302i
$246$		0			0
$247$	−0.183403	+	1.74497i	−0.0116697	+	0.111030i
$248$	14.0201	−	6.24215i	0.890277	−	0.396377i
$249$		0			0
$250$	5.46473	−	6.06920i	0.345620	−	0.383850i
$251$	4.86452	+	6.69544i	0.307046	+	0.422613i	0.934457	−	0.356076i	$-0.115885\pi$
$251$	4.86452	+	6.69544i	0.307046	+	0.422613i	−0.627411	+	0.778688i	$0.715885\pi$
$252$		0			0
$253$	3.25369	−	2.06289i	0.204558	−	0.129693i
$254$	−2.60964	−	4.52002i	−0.163743	−	0.283611i
$255$		0			0
$256$	13.5827	+	2.88709i	0.848917	+	0.180443i
$257$	5.73472	+	26.9797i	0.357722	+	1.68295i	0.677553	+	0.735474i	$0.263041\pi$
$257$	5.73472	+	26.9797i	0.357722	+	1.68295i	−0.319831	+	0.947475i	$0.603626\pi$
$258$		0			0
$259$	26.8142	+	7.92399i	1.66615	+	0.492373i
$260$	−0.596887	−	0.193940i	−0.0370174	−	0.0120277i
$261$		0			0
$262$	−0.500926	+	0.0526494i	−0.0309473	+	0.00325269i
$263$	−20.6969	−	11.9493i	−1.27622	−	0.736828i	−0.300071	−	0.953917i	$-0.597010\pi$
$263$	−20.6969	−	11.9493i	−1.27622	−	0.736828i	−0.976152	+	0.217089i	$0.930344\pi$
$264$		0			0
$265$		−	11.3269i		−	0.695808i
$266$	−0.754834	+	9.67052i	−0.0462818	+	0.592938i
$267$		0			0
$268$	−2.78177	+	0.591285i	−0.169924	+	0.0361185i
$269$	7.52166	+	16.8939i	0.458604	+	1.03004i	0.983834	+	0.179081i	$0.0573125\pi$
$269$	7.52166	+	16.8939i	0.458604	+	1.03004i	−0.525230	+	0.850960i	$0.676021\pi$
$270$		0			0
$271$	−25.0691	+	5.32859i	−1.52284	+	0.323689i	−0.891931	−	0.452171i	$-0.850650\pi$
$271$	−25.0691	+	5.32859i	−1.52284	+	0.323689i	−0.630905	+	0.775860i	$0.717316\pi$
$272$	−0.208234	−	0.640877i	−0.0126260	−	0.0388589i
$273$		0			0
$274$		−	1.36109i		−	0.0822263i
$275$	1.96586	−	11.5926i	0.118546	−	0.699058i
$276$		0			0
$277$	5.84910	−	0.614765i	0.351438	−	0.0369377i	0.0728353	−	0.997344i	$-0.476795\pi$
$277$	5.84910	−	0.614765i	0.351438	−	0.0369377i	0.278603	+	0.960406i	$0.410129\pi$
$278$	0.407932	+	0.367304i	0.0244661	+	0.0220294i
$279$		0			0
$280$	−8.17730	−	2.41651i	−0.488687	−	0.144414i
$281$	16.7454	−	23.0480i	0.998944	−	1.37493i	0.0729737	−	0.997334i	$-0.476751\pi$
$281$	16.7454	−	23.0480i	0.998944	−	1.37493i	0.925971	−	0.377595i	$-0.123249\pi$
$282$		0			0
$283$	16.0034	+	3.40162i	0.951301	+	0.202205i	0.657325	−	0.753607i	$-0.271688\pi$
$283$	16.0034	+	3.40162i	0.951301	+	0.202205i	0.293976	+	0.955813i	$0.405021\pi$
$284$	0.189206	+	1.80017i	0.0112273	+	0.106821i
$285$		0			0
$286$	0.965384	−	0.247426i	0.0570843	−	0.0146306i
$287$	−2.43026	+	13.1597i	−0.143454	+	0.776792i
$288$		0			0
$289$	−10.6024	+	11.7752i	−0.623671	+	0.692656i
$290$	−4.68326	+	4.21683i	−0.275011	+	0.247621i
$291$		0			0
$292$	0.914954	−	8.70520i	0.0535436	−	0.509434i
$293$	7.57791	−	23.3224i	0.442706	−	1.36251i	−0.442273	−	0.896880i	$-0.645828\pi$
$293$	7.57791	−	23.3224i	0.442706	−	1.36251i	0.884980	−	0.465630i	$-0.154172\pi$
$294$		0			0
$295$	−1.11791	+	0.812212i	−0.0650874	+	0.0472888i
$296$	24.4549	−	14.1190i	1.42141	−	0.820651i
$297$		0			0
$298$	−0.162227	+	0.280985i	−0.00939755	+	0.0162770i
$299$	−0.402408	−	0.179163i	−0.0232718	−	0.0103613i
$300$		0			0
$301$	13.4605	−	24.8291i	0.775848	−	1.43113i
$302$	7.75148	+	5.63178i	0.446048	+	0.324073i
$303$		0			0
$304$	−1.94125	−	2.15598i	−0.111338	−	0.123654i
$305$	0.0101606	−	0.0478020i	0.000581796	−	0.00273714i
$306$		0			0
$307$	26.1242			1.49099			0.745494	−	0.666512i	$-0.232214\pi$
$307$	26.1242			1.49099			0.745494	+	0.666512i	$0.232214\pi$
$308$	−11.5791	+	3.30105i	−0.659779	+	0.188095i
$309$		0			0
$310$	−2.23271	+	5.01475i	−0.126809	+	0.284819i
$311$	4.19880	−	19.7538i	0.238092	−	1.12013i	−0.682888	−	0.730523i	$-0.739276\pi$
$311$	4.19880	−	19.7538i	0.238092	−	1.12013i	0.920980	−	0.389611i	$-0.127391\pi$
$312$		0			0
$313$	14.5486	+	1.52912i	0.822337	+	0.0864311i	0.506345	−	0.862331i	$-0.330996\pi$
$313$	14.5486	+	1.52912i	0.822337	+	0.0864311i	0.315992	+	0.948762i	$0.397663\pi$
$314$	−1.66784	−	1.21176i	−0.0941219	−	0.0683836i
$315$		0			0
$316$	1.93674	−	0.629284i	0.108950	−	0.0354000i
$317$	15.9238	+	7.08973i	0.894369	+	0.398199i	0.801859	−	0.597513i	$-0.203844\pi$
$317$	15.9238	+	7.08973i	0.894369	+	0.398199i	0.0925099	+	0.995712i	$0.470511\pi$
$318$		0			0
$319$	−5.89014	+	21.0612i	−0.329785	+	1.17920i
$320$	−3.52448	+	2.03486i	−0.197025	+	0.113752i
$321$		0			0
$322$	−2.25042	−	0.930460i	−0.125411	−	0.0518525i
$323$	1.53657	−	4.72909i	0.0854972	−	0.263133i
$324$		0			0
$325$	−1.22816	+	0.546813i	−0.0681261	+	0.0303317i
$326$	−2.94880	+	2.65511i	−0.163319	+	0.147053i
$327$		0			0
$328$	7.94394	+	10.9339i	0.438631	+	0.603723i
$329$	−10.2302	−	28.8304i	−0.564011	−	1.58947i
$330$		0			0
$331$	10.7196	+	18.5669i	0.589203	+	1.02053i	0.994337	+	0.106272i	$0.0338914\pi$
$331$	10.7196	+	18.5669i	0.589203	+	1.02053i	−0.405135	+	0.914257i	$0.632775\pi$
$332$	−2.03953	−	19.4048i	−0.111934	−	1.06498i
$333$		0			0
$334$	1.04131	+	4.89896i	0.0569777	+	0.268059i
$335$	1.46941	−	2.02247i	0.0802824	−	0.110499i
$336$		0			0
$337$	28.5884	+	9.28892i	1.55731	+	0.506000i	0.956087	−	0.293083i	$-0.0946813\pi$
$337$	28.5884	+	9.28892i	1.55731	+	0.506000i	0.601221	+	0.799083i	$0.294681\pi$
$338$	7.57040	+	6.81642i	0.411776	+	0.370765i
$339$		0			0
$340$	1.54033	+	0.889312i	0.0835363	+	0.0482297i
$341$	2.77468	+	18.8461i	0.150257	+	1.02058i
$342$		0			0
$343$	1.48868	+	18.4603i	0.0803810	+	0.996764i
$344$	−8.81419	−	27.1273i	−0.475229	−	1.46261i
$345$		0			0
$346$	−6.25103	−	14.0400i	−0.336057	−	0.754797i
$347$	−0.346151	−	0.777468i	−0.0185824	−	0.0417367i	0.904016	−	0.427499i	$-0.140605\pi$
$347$	−0.346151	−	0.777468i	−0.0185824	−	0.0417367i	−0.922598	+	0.385762i	$0.873939\pi$
$348$		0			0
$349$	−8.71538	−	26.8232i	−0.466524	−	1.43581i	−0.857056	−	0.515223i	$-0.827709\pi$
$349$	−8.71538	−	26.8232i	−0.466524	−	1.43581i	0.390533	−	0.920589i	$-0.372291\pi$
$350$	−6.70620	+	3.20399i	−0.358462	+	0.171260i
$351$		0			0
$352$	−8.98232	+	17.1636i	−0.478759	+	0.914824i
$353$	−12.0480	−	6.95591i	−0.641250	−	0.370226i	0.143846	−	0.989600i	$-0.454053\pi$
$353$	−12.0480	−	6.95591i	−0.641250	−	0.370226i	−0.785096	+	0.619374i	$0.787386\pi$
$354$		0			0
$355$	−1.18244	−	1.06468i	−0.0627575	−	0.0565071i
$356$	6.95637	+	2.26026i	0.368687	+	0.119794i
$357$		0			0
$358$	2.51913	−	3.46729i	0.133140	−	0.183252i
$359$	0.562103	+	2.64448i	0.0296666	+	0.139571i	0.990488	−	0.137597i	$-0.0439378\pi$
$359$	0.562103	+	2.64448i	0.0296666	+	0.139571i	−0.960822	+	0.277167i	$0.910604\pi$
$360$		0			0
$361$	−0.251692	−	2.39469i	−0.0132470	−	0.126036i
$362$	−6.55925	−	11.3610i	−0.344746	−	0.597118i
$363$		0			0
$364$	1.04741	+	0.893406i	0.0548990	+	0.0468272i
$365$	4.52262	+	6.22485i	0.236725	+	0.325823i
$366$		0			0
$367$	−22.9739	+	20.6858i	−1.19923	+	1.07979i	−0.204330	+	0.978902i	$0.565501\pi$
$367$	−22.9739	+	20.6858i	−1.19923	+	1.07979i	−0.994898	+	0.100887i	$0.967832\pi$
$368$	0.665372	−	0.296243i	0.0346849	−	0.0154427i
$369$		0			0
$370$	−3.12115	+	9.60592i	−0.162261	+	0.499388i
$371$	−9.49343	+	22.9609i	−0.492875	+	1.19207i
$372$		0			0
$373$	−10.9674	+	6.33202i	−0.567870	+	0.327860i	−0.756298	−	0.654227i	$-0.772994\pi$
$373$	−10.9674	+	6.33202i	−0.567870	+	0.327860i	0.188428	+	0.982087i	$0.439661\pi$
$374$	−2.82189	+	0.117057i	−0.145917	+	0.00605288i
$375$		0			0
$376$	−28.2242	−	12.5662i	−1.45555	−	0.648054i
$377$	2.37810	−	0.772692i	0.122479	−	0.0397957i
$378$		0			0
$379$	7.23647	+	5.25760i	0.371713	+	0.270065i	0.757921	−	0.652347i	$-0.226215\pi$
$379$	7.23647	+	5.25760i	0.371713	+	0.270065i	−0.386208	+	0.922412i	$0.626215\pi$
$380$	7.61555	+	0.800427i	0.390669	+	0.0410610i
$381$		0			0
$382$	−2.71485	+	12.7724i	−0.138904	+	0.653491i
$383$	−2.77158	+	6.22506i	−0.141621	+	0.318086i	−0.970405	−	0.241483i	$-0.922366\pi$
$383$	−2.77158	+	6.22506i	−0.141621	+	0.318086i	0.828784	+	0.559568i	$0.189033\pi$
$384$		0			0
$385$	5.62240	−	8.96711i	0.286544	−	0.457006i
$386$	−12.0751			−0.614609
$387$		0			0
$388$	4.81011	−	22.6298i	0.244196	−	1.14885i
$389$	−13.8039	−	15.3308i	−0.699885	−	0.777301i	0.283473	−	0.958980i	$-0.408513\pi$
$389$	−13.8039	−	15.3308i	−0.699885	−	0.777301i	−0.983358	+	0.181679i	$0.941847\pi$
$390$		0			0
$391$	1.00993	+	0.733759i	0.0510745	+	0.0371078i
$392$	14.5509	+	11.7522i	0.734932	+	0.593574i
$393$		0			0
$394$	9.31026	+	4.14519i	0.469044	+	0.208832i
$395$	−0.895036	+	1.55025i	−0.0450342	+	0.0780015i
$396$		0			0
$397$	17.0455	−	9.84124i	0.855490	−	0.493918i	−0.00700915	−	0.999975i	$-0.502231\pi$
$397$	17.0455	−	9.84124i	0.855490	−	0.493918i	0.862500	+	0.506058i	$0.168898\pi$
$398$	−10.2921	+	7.47762i	−0.515895	+	0.374819i
$399$		0			0
$400$	0.686920	−	2.11412i	0.0343460	−	0.105706i
$401$	0.642989	−	6.11764i	0.0321094	−	0.305500i	−0.966667	−	0.256038i	$-0.917583\pi$
$401$	0.642989	−	6.11764i	0.0321094	−	0.305500i	0.998776	−	0.0494619i	$-0.0157506\pi$
$402$		0			0
$403$	1.61861	−	1.45740i	0.0806286	−	0.0725983i
$404$	12.3405	−	13.7056i	0.613965	−	0.681877i
$405$		0			0
$406$	13.0277	−	4.62278i	0.646555	−	0.229425i
$407$	8.70208	+	33.9529i	0.431346	+	1.68299i
$408$		0			0
$409$	1.74512	+	16.6037i	0.0862907	+	0.821001i	0.948995	+	0.315292i	$0.102102\pi$
$409$	1.74512	+	16.6037i	0.0862907	+	0.821001i	−0.862704	+	0.505709i	$0.831231\pi$
$410$	−4.72846	−	1.00507i	−0.233522	−	0.0496367i
$411$		0			0
$412$	−10.0819	+	13.8765i	−0.496699	+	0.683648i
$413$	2.94687	−	0.709484i	0.145006	−	0.0349114i
$414$		0			0
$415$	12.7460	+	11.4766i	0.625678	+	0.563363i
$416$	2.20281	−	0.231525i	0.108002	−	0.0113514i
$417$		0			0
$418$	−10.8937	+	5.40187i	−0.532831	+	0.264214i
$419$			30.3688i			1.48361i	0.670615	+	0.741806i	$0.266030\pi$
$419$			30.3688i			1.48361i	−0.670615	+	0.741806i	$0.733970\pi$
$420$		0			0
$421$	−8.54671	−	26.3041i	−0.416541	−	1.28198i	−0.910865	−	0.412705i	$-0.864584\pi$
$421$	−8.54671	−	26.3041i	−0.416541	−	1.28198i	0.494324	−	0.869278i	$-0.335416\pi$
$422$	−11.9851	+	2.54751i	−0.583426	+	0.124011i
$423$		0			0
$424$	10.2061	+	22.9233i	0.495653	+	1.11325i
$425$	3.72673	−	0.792141i	0.180773	−	0.0384245i
$426$		0			0
$427$	−0.0606610	+	0.0883839i	−0.00293559	+	0.00427720i
$428$			2.26820i			0.109638i
$429$		0			0
$430$	8.83546	+	5.10116i	0.426084	+	0.246000i
$431$	−12.5063	+	1.31446i	−0.602406	+	0.0633154i	−0.400822	−	0.916156i	$-0.631276\pi$
$431$	−12.5063	+	1.31446i	−0.602406	+	0.0633154i	−0.201584	+	0.979471i	$0.564609\pi$
$432$		0			0
$433$	12.1688	+	3.95390i	0.584797	+	0.190012i	0.586449	−	0.809986i	$-0.300526\pi$
$433$	12.1688	+	3.95390i	0.584797	+	0.190012i	−0.00165129	+	0.999999i	$0.500526\pi$
$434$	8.72895	−	8.29413i	0.419003	−	0.398131i
$435$		0			0
$436$	−3.67877	−	17.3072i	−0.176181	−	0.828866i
$437$	5.25704	+	1.11742i	0.251478	+	0.0534534i
$438$		0			0
$439$	2.70288	+	4.68152i	0.129001	+	0.223437i	0.923290	−	0.384104i	$-0.125490\pi$
$439$	2.70288	+	4.68152i	0.129001	+	0.223437i	−0.794289	+	0.607541i	$0.792156\pi$
$440$	−2.65380	−	10.3543i	−0.126515	−	0.493624i
$441$		0			0
$442$	0.189811	+	0.261253i	0.00902840	+	0.0124265i
$443$	16.7504	−	18.6032i	0.795837	−	0.883866i	−0.199542	−	0.979889i	$-0.563946\pi$
$443$	16.7504	−	18.6032i	0.795837	−	0.883866i	0.995379	+	0.0960230i	$0.0306122\pi$
$444$		0			0
$445$	−5.87372	+	2.61515i	−0.278441	+	0.123970i
$446$	−0.526207	+	5.00652i	−0.0249166	+	0.237066i
$447$		0			0
$448$	8.84998	−	1.17091i	0.418122	−	0.0553203i
$449$	13.1899	−	9.58302i	0.622470	−	0.452251i	−0.231314	−	0.972879i	$-0.574302\pi$
$449$	13.1899	−	9.58302i	0.622470	−	0.452251i	0.853783	+	0.520629i	$0.174302\pi$
$450$		0			0
$451$	−15.7259	+	5.84071i	−0.740503	+	0.275028i
$452$	6.71728	−	11.6347i	0.315954	−	0.547249i
$453$		0			0
$454$	−1.96628	+	0.638882i	−0.0922819	+	0.0299842i
$455$	−1.20971	+	0.0324554i	−0.0567121	+	0.00152153i
$456$		0			0
$457$	9.77389	+	1.02728i	0.457203	+	0.0480540i	0.330331	−	0.943865i	$-0.392840\pi$
$457$	9.77389	+	1.02728i	0.457203	+	0.0480540i	0.126872	+	0.991919i	$0.459506\pi$
$458$	5.79332	+	6.43414i	0.270704	+	0.300647i
$459$		0			0
$460$	−0.781922	+	1.75623i	−0.0364573	+	0.0818845i
$461$	−17.1955			−0.800875			−0.400438	−	0.916324i	$-0.631142\pi$
$461$	−17.1955			−0.800875			−0.400438	+	0.916324i	$0.631142\pi$
$462$		0			0
$463$	7.06449			0.328315			0.164157	−	0.986434i	$-0.447510\pi$
$463$	7.06449			0.328315			0.164157	+	0.986434i	$0.447510\pi$
$464$	−1.68165	+	3.77705i	−0.0780688	+	0.175345i
$465$		0			0
$466$	−7.52060	−	8.35247i	−0.348385	−	0.386921i
$467$	19.1282	+	2.01046i	0.885149	+	0.0930329i	0.536182	−	0.844102i	$-0.319866\pi$
$467$	19.1282	+	2.01046i	0.885149	+	0.0930329i	0.348967	+	0.937135i	$0.386533\pi$
$468$		0			0
$469$	−4.67374	+	2.86820i	−0.215813	+	0.132441i
$470$	10.5099	−	3.41486i	0.484783	−	0.157516i
$471$		0			0
$472$	1.53058	−	2.65104i	0.0704506	−	0.122024i
$473$	35.3741	−	1.46738i	1.62650	−	0.0674703i
$474$		0			0
$475$	13.2704	−	9.64151i	0.608888	−	0.442383i
$476$	−2.37706	−	3.09373i	−0.108952	−	0.141801i
$477$		0			0
$478$	2.33593	−	22.2249i	0.106843	−	1.01654i
$479$	−32.3167	+	14.3883i	−1.47659	+	0.657419i	−0.977845	−	0.209332i	$-0.932871\pi$
$479$	−32.3167	+	14.3883i	−1.47659	+	0.657419i	−0.498742	+	0.866751i	$0.666204\pi$
$480$		0			0
$481$	2.68159	−	2.97821i	0.122270	−	0.135795i
$482$	−0.0594706	−	0.0818543i	−0.00270881	−	0.00372836i
$483$		0			0
$484$	−10.9938	−	10.3417i	−0.499718	−	0.470075i
$485$	10.1684	+	17.6122i	0.461723	+	0.799728i
$486$		0			0
$487$	−27.9722	−	5.94568i	−1.26754	−	0.269424i	−0.475405	−	0.879767i	$-0.657698\pi$
$487$	−27.9722	−	5.94568i	−1.26754	−	0.269424i	−0.792137	+	0.610343i	$0.791032\pi$
$488$	0.0225090	+	0.105896i	0.00101893	+	0.00479371i
$489$		0			0
$490$	−6.68050	+	0.358721i	−0.301794	+	0.0162054i
$491$	−24.0555	−	7.81611i	−1.08561	−	0.352736i	−0.289062	−	0.957310i	$-0.593343\pi$
$491$	−24.0555	−	7.81611i	−1.08561	−	0.352736i	−0.796549	+	0.604574i	$0.793343\pi$
$492$		0			0
$493$	−7.04753	+	0.740726i	−0.317405	+	0.0333606i
$494$	1.20403	+	0.695146i	0.0541718	+	0.0312761i
$495$		0			0
$496$			3.60136i			0.161706i
$497$	1.50460	+	3.14925i	0.0674906	+	0.141263i
$498$		0			0
$499$	14.9133	−	3.16992i	0.667611	−	0.141905i	0.138375	−	0.990380i	$-0.455812\pi$
$499$	14.9133	−	3.16992i	0.667611	−	0.141905i	0.529236	+	0.848475i	$0.322479\pi$
$500$	5.75221	+	12.9197i	0.257247	+	0.577786i
$501$		0			0
$502$	6.41445	−	1.36343i	0.286291	−	0.0608530i
$503$	4.26343	+	13.1215i	0.190097	+	0.585058i	0.999999	−	0.00150720i	$-0.000479756\pi$
$503$	4.26343	+	13.1215i	0.190097	+	0.585058i	−0.809902	+	0.586565i	$0.800480\pi$
$504$		0			0
$505$			16.2117i			0.721413i
$506$	−0.444645	−	3.02011i	−0.0197669	−	0.134260i
$507$		0			0
$508$	8.98852	−	0.944731i	0.398801	−	0.0419157i
$509$	31.6038	+	28.4562i	1.40082	+	1.26130i	0.924051	+	0.382269i	$0.124857\pi$
$509$	31.6038	+	28.4562i	1.40082	+	1.26130i	0.476765	+	0.879031i	$0.341809\pi$
$510$		0			0
$511$	−3.95060	−	16.4090i	−0.174764	−	0.725890i
$512$	−4.12225	+	5.67379i	−0.182179	+	0.250749i
$513$		0			0
$514$	21.3782	+	4.54407i	0.942951	+	0.200430i
$515$	−1.57603	−	14.9949i	−0.0694482	−	0.660755i
$516$		0			0
$517$	24.4571	−	29.5376i	1.07562	−	1.29906i
$518$	14.3779	−	16.8563i	0.631729	−	0.740623i
$519$		0			0
$520$	−0.817783	+	0.908240i	−0.0358622	+	0.0398290i
$521$	−27.8746	+	25.0984i	−1.22121	+	1.09958i	−0.229203	+	0.973379i	$0.573612\pi$
$521$	−27.8746	+	25.0984i	−1.22121	+	1.09958i	−0.992005	+	0.126202i	$0.959721\pi$
$522$		0			0
$523$	1.45841	−	13.8758i	0.0637716	−	0.606746i	−0.915235	−	0.402920i	$-0.867995\pi$
$523$	1.45841	−	13.8758i	0.0637716	−	0.606746i	0.979007	−	0.203827i	$-0.0653379\pi$
$524$	0.269529	−	0.829524i	0.0117744	−	0.0362379i
$525$		0			0
$526$	−15.3202	+	11.1308i	−0.667993	+	0.485325i
$527$	−5.34561	+	3.08629i	−0.232858	+	0.134441i
$528$		0			0
$529$	10.8254	−	18.7501i	0.470668	−	0.815221i
$530$	−8.19928	−	3.65055i	−0.356154	−	0.158570i
$531$		0			0
$532$	−14.7667	−	8.00537i	−0.640216	−	0.347077i
$533$	1.55175	+	1.12741i	0.0672139	+	0.0488337i
$534$		0			0
$535$	−1.33413	−	1.48170i	−0.0576796	−	0.0640597i
$536$	−1.15143	+	5.41706i	−0.0497342	+	0.233981i
$537$		0			0
$538$	14.6532			0.631746
$539$	−18.9128	+	13.4650i	−0.814632	+	0.579978i
$540$		0			0
$541$	5.00723	−	11.2464i	0.215278	−	0.483522i	−0.773336	−	0.633996i	$-0.781414\pi$
$541$	5.00723	−	11.2464i	0.215278	−	0.483522i	0.988614	+	0.150475i	$0.0480802\pi$
$542$	−4.22227	+	19.8642i	−0.181362	+	0.853241i
$543$		0			0
$544$	−6.24274	−	0.656139i	−0.267655	−	0.0281317i
$545$	12.5831	+	9.14215i	0.539000	+	0.391607i
$546$		0			0
$547$	−14.4580	+	4.69769i	−0.618179	+	0.200859i	−0.601332	−	0.798999i	$-0.705363\pi$
$547$	−14.4580	+	4.69769i	−0.618179	+	0.200859i	−0.0168475	+	0.999858i	$0.505363\pi$
$548$	2.15318	+	0.958657i	0.0919792	+	0.0409518i
$549$		0			0
$550$	−7.75798	−	5.15920i	−0.330801	−	0.219989i
$551$	−26.4214	+	15.2544i	−1.12559	+	0.649860i
$552$		0			0
$553$	3.11364	−	2.39236i	0.132406	−	0.101734i
$554$	1.44009	−	4.43215i	0.0611836	−	0.188304i
$555$		0			0
$556$	−0.868376	+	0.386626i	−0.0368274	+	0.0163966i
$557$	−14.8449	+	13.3664i	−0.628998	+	0.566352i	−0.920756	−	0.390140i	$-0.872427\pi$
$557$	−14.8449	+	13.3664i	−0.628998	+	0.566352i	0.291758	+	0.956492i	$0.405760\pi$
$558$		0			0
$559$	−2.37940	−	3.27496i	−0.100638	−	0.138516i
$560$	1.29854	−	1.52237i	0.0548732	−	0.0643319i
$561$		0			0
$562$	−11.2870	−	19.5497i	−0.476114	−	0.824653i
$563$	−1.76886	−	16.8296i	−0.0745485	−	0.709282i	−0.966416	−	0.256984i	$-0.917271\pi$
$563$	−1.76886	−	16.8296i	−0.0745485	−	0.709282i	0.891867	−	0.452298i	$-0.149396\pi$
$564$		0			0
$565$	2.45532	+	11.5514i	0.103296	+	0.485970i
$566$	7.62007	−	10.4881i	0.320295	−	0.440849i
$567$		0			0
$568$	3.35234	+	1.08924i	0.140661	+	0.0457035i
$569$	−9.77003	−	8.79697i	−0.409581	−	0.368788i	0.438432	−	0.898765i	$-0.355534\pi$
$569$	−9.77003	−	8.79697i	−0.409581	−	0.368788i	−0.848012	+	0.529976i	$0.822201\pi$
$570$		0			0
$571$	3.84826	+	2.22180i	0.161045	+	0.0929793i	0.578356	−	0.815784i	$-0.303694\pi$
$571$	3.84826	+	2.22180i	0.161045	+	0.0929793i	−0.417312	+	0.908763i	$0.637028\pi$
$572$	−0.288533	+	1.70146i	−0.0120642	+	0.0711417i
$573$		0			0
$574$	8.74272	+	6.00044i	0.364914	+	0.250453i
$575$	1.27254	+	3.91648i	0.0530687	+	0.163329i
$576$		0			0
$577$	15.8013	+	35.4903i	0.657816	+	1.47748i	0.866336	+	0.499462i	$0.166469\pi$
$577$	15.8013	+	35.4903i	0.657816	+	1.47748i	−0.208520	+	0.978018i	$0.566864\pi$
$578$	5.10669	+	11.4698i	0.212410	+	0.477082i
$579$		0			0
$580$	−3.37226	−	10.3787i	−0.140025	−	0.430954i
$581$	−16.2187	−	33.9471i	−0.672865	−	1.40836i
$582$		0			0
$583$	−30.8141	+	4.53669i	−1.27619	+	0.187891i
$584$	−14.7617	−	8.52267i	−0.610844	−	0.352671i
$585$		0			0
$586$	−14.4402	−	13.0020i	−0.596520	−	0.537109i
$587$	31.4703	+	10.2253i	1.29892	+	0.422044i	0.875205	−	0.483753i	$-0.160727\pi$
$587$	31.4703	+	10.2253i	1.29892	+	0.422044i	0.423713	+	0.905797i	$0.360727\pi$
$588$		0			0
$589$	−15.6203	+	21.4994i	−0.643621	+	0.885869i
$590$	0.227647	+	1.07100i	0.00937209	+	0.0440922i
$591$		0			0
$592$	0.692652	+	6.59015i	0.0284678	+	0.270853i
$593$	−9.41234	−	16.3027i	−0.386519	−	0.669470i	0.605460	−	0.795876i	$-0.292989\pi$
$593$	−9.41234	−	16.3027i	−0.386519	−	0.669470i	−0.991979	+	0.126406i	$0.959656\pi$
$594$		0			0
$595$	3.37252	+	0.622818i	0.138260	+	0.0255330i
$596$	−0.330244	−	0.454542i	−0.0135273	−	0.0186188i
$597$		0			0
$598$	−0.259384	+	0.233550i	−0.0106070	+	0.00955058i
$599$	0.597011	−	0.265807i	0.0243932	−	0.0108606i	−0.394504	−	0.918894i	$-0.629083\pi$
$599$	0.597011	−	0.265807i	0.0243932	−	0.0108606i	0.418897	+	0.908034i	$0.362417\pi$
$600$		0			0
$601$	−8.79714	+	27.0748i	−0.358843	+	1.10440i	0.594905	+	0.803796i	$0.297190\pi$
$601$	−8.79714	+	27.0748i	−0.358843	+	1.10440i	−0.953748	+	0.300608i	$0.902810\pi$
$602$	−13.6350	−	17.7458i	−0.555721	−	0.723267i
$603$		0			0
$604$	−14.3688	+	8.29585i	−0.584660	+	0.337553i
$605$	13.2646	+	0.289262i	0.539281	+	0.0117602i
$606$		0			0
$607$	11.9564	+	5.32333i	0.485295	+	0.216067i	0.634774	−	0.772698i	$-0.281093\pi$
$607$	11.9564	+	5.32333i	0.485295	+	0.216067i	−0.149479	+	0.988765i	$0.547760\pi$
$608$	−25.7022	+	8.35115i	−1.04236	+	0.338684i
$609$		0			0
$610$	−0.0313280	−	0.0227611i	−0.00126843	−	0.000921571i
$611$	−4.36068	−	0.458326i	−0.176414	−	0.0185419i
$612$		0			0
$613$	7.30620	−	34.3730i	0.295095	−	1.38831i	−0.541598	−	0.840638i	$-0.682180\pi$
$613$	7.30620	−	34.3730i	0.295095	−	1.38831i	0.836692	−	0.547673i	$-0.184486\pi$
$614$	8.41957	−	18.9107i	0.339786	−	0.763172i
$615$		0			0
$616$	−3.29874	+	23.2136i	−0.132910	+	0.935302i
$617$	−42.0432			−1.69260			−0.846298	−	0.532709i	$-0.821174\pi$
$617$	−42.0432			−1.69260			−0.846298	+	0.532709i	$0.821174\pi$
$618$		0			0
$619$	−1.59168	+	7.48825i	−0.0639749	+	0.300978i	−0.998489	−	0.0549472i	$-0.982501\pi$
$619$	−1.59168	+	7.48825i	−0.0639749	+	0.300978i	0.934514	+	0.355925i	$0.115834\pi$
$620$	−6.36053	−	7.06409i	−0.255445	−	0.283701i
$621$		0			0
$622$	−12.9460	−	9.40584i	−0.519089	−	0.377140i
$623$	14.0985	−	0.378249i	0.564844	−	0.0151542i
$624$		0			0
$625$	4.83660	+	2.15339i	0.193464	+	0.0861356i
$626$	5.79576	−	10.0386i	0.231645	−	0.401221i
$627$		0			0
$628$	3.09166	−	1.78497i	0.123371	−	0.0712282i
$629$	−9.18836	+	6.67574i	−0.366364	+	0.266179i
$630$		0			0
$631$	−3.16160	+	9.73041i	−0.125861	+	0.387362i	−0.994057	−	0.108861i	$-0.965280\pi$
$631$	−3.16160	+	9.73041i	−0.125861	+	0.387362i	0.868196	+	0.496222i	$0.165280\pi$
$632$	0.414515	−	3.94385i	0.0164885	−	0.156878i
$633$		0			0
$634$	10.2641	−	9.24188i	0.407641	−	0.367042i
$635$	−5.31607	+	5.90410i	−0.210962	+	0.234297i
$636$		0			0
$637$	2.47942	+	0.948104i	0.0982380	+	0.0375652i
$638$	13.3473	+	11.0515i	0.528425	+	0.437534i
$639$		0			0
$640$	−1.13572	−	10.8057i	−0.0448934	−	0.427132i
$641$	−18.9023	−	4.01781i	−0.746597	−	0.158694i	−0.181123	−	0.983460i	$-0.557973\pi$
$641$	−18.9023	−	4.01781i	−0.746597	−	0.158694i	−0.565474	+	0.824766i	$0.691307\pi$
$642$		0			0
$643$	−29.0184	+	39.9405i	−1.14438	+	1.57510i	−0.387053	+	0.922058i	$0.626507\pi$
$643$	−29.0184	+	39.9405i	−1.14438	+	1.57510i	−0.757323	+	0.653040i	$0.773493\pi$
$644$	3.05699	−	2.90471i	0.120462	−	0.114461i
$645$		0			0
$646$	−2.92804	−	2.63642i	−0.115202	−	0.103729i
$647$	21.7691	−	2.28803i	0.855832	−	0.0899516i	0.333558	−	0.942729i	$-0.391751\pi$
$647$	21.7691	−	2.28803i	0.855832	−	0.0899516i	0.522274	+	0.852778i	$0.325084\pi$
$648$		0			0
$649$	2.65731	+	2.71589i	0.104309	+	0.106608i
$650$			1.06527i			0.0417832i
$651$		0			0
$652$	−2.12333	−	6.53495i	−0.0831562	−	0.255928i
$653$	−27.5714	+	5.86049i	−1.07895	+	0.229339i	−0.712908	−	0.701258i	$-0.752622\pi$
$653$	−27.5714	+	5.86049i	−1.07895	+	0.229339i	−0.366046	+	0.930597i	$0.619289\pi$
$654$		0			0
$655$	0.311847	+	0.700421i	0.0121849	+	0.0273677i
$656$	−3.10219	+	0.659390i	−0.121120	+	0.0257449i
$657$		0			0
$658$	−24.1667	−	1.88633i	−0.942115	−	0.0735369i
$659$			4.61974i			0.179960i	0.995944	+	0.0899798i	$0.0286802\pi$
$659$			4.61974i			0.179960i	−0.995944	+	0.0899798i	$0.971320\pi$
$660$		0			0
$661$	−36.7567	−	21.2215i	−1.42967	−	0.825421i	−0.432577	−	0.901597i	$-0.642396\pi$
$661$	−36.7567	−	21.2215i	−1.42967	−	0.825421i	−0.997094	+	0.0761754i	$0.975729\pi$
$662$	16.8949	−	1.77573i	0.656640	−	0.0690156i
$663$		0			0
$664$	−36.1362	−	11.7414i	−1.40236	−	0.455653i
$665$	14.3550	−	3.45609i	0.556663	−	0.134022i
$666$		0			0
$667$	−1.59246	−	7.49192i	−0.0616602	−	0.290088i
$668$	−8.48335	−	1.80319i	−0.328231	−	0.0697676i
$669$		0			0
$670$	−0.990438	−	1.71549i	−0.0382639	−	0.0662751i
$671$	−0.134111	−	0.00849545i	−0.00517731	−	0.000327963i
$672$		0			0
$673$	−8.25702	−	11.3648i	−0.318285	−	0.438081i	0.619658	−	0.784872i	$-0.287271\pi$
$673$	−8.25702	−	11.3648i	−0.318285	−	0.438081i	−0.937943	+	0.346791i	$0.887271\pi$
$674$	15.9378	−	17.7007i	0.613899	−	0.681804i
$675$		0			0
$676$	−16.1153	+	7.17501i	−0.619821	+	0.275962i
$677$	4.37766	−	41.6506i	0.168247	−	1.60076i	−0.506184	−	0.862425i	$-0.668944\pi$
$677$	4.37766	−	41.6506i	0.168247	−	1.60076i	0.674431	−	0.738338i	$-0.264389\pi$
$678$		0			0
$679$	−5.85115	−	44.2242i	−0.224546	−	1.69717i
$680$	2.80210	−	2.03584i	0.107456	−	0.0780710i
$681$		0			0
$682$	14.5365	+	4.06540i	0.556631	+	0.155672i
$683$	8.82101	−	15.2784i	0.337526	−	0.584613i	−0.646440	−	0.762965i	$-0.723743\pi$
$683$	8.82101	−	15.2784i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570764\pi$
$684$		0			0
$685$	−1.97044	+	0.640234i	−0.0752866	+	0.0244621i
$686$	13.8427	+	4.87196i	0.528519	+	0.186012i
$687$		0			0
$688$	6.65673	+	0.699650i	0.253785	+	0.0266739i
$689$	2.38290	+	2.64648i	0.0907813	+	0.100823i
$690$		0			0
$691$	−12.7588	+	28.6568i	−0.485369	+	1.09016i	0.490428	+	0.871482i	$0.336840\pi$
$691$	−12.7588	+	28.6568i	−0.485369	+	1.09016i	−0.975798	+	0.218676i	$0.929826\pi$
$692$	26.6135			1.01169
$693$		0			0
$694$	−0.674350			−0.0255980
$695$	0.339858	−	0.763334i	0.0128916	−	0.0289549i
$696$		0			0
$697$	−3.63726	−	4.03958i	−0.137771	−	0.153010i
$698$	−22.2255	−	2.33599i	−0.841247	−	0.0884187i
$699$		0			0
$700$	−0.345171	−	12.8656i	−0.0130462	−	0.486273i
$701$	2.16439	−	0.703254i	0.0817480	−	0.0265615i	−0.267857	−	0.963459i	$-0.586316\pi$
$701$	2.16439	−	0.703254i	0.0817480	−	0.0265615i	0.349605	+	0.936897i	$0.386316\pi$
$702$		0			0
$703$	−24.4486	+	42.3461i	−0.922095	+	1.59711i
$704$	6.94732	+	8.77308i	0.261837	+	0.330648i
$705$		0			0
$706$	−8.91815	+	6.47941i	−0.335639	+	0.243856i
$707$	13.5875	−	32.8629i	0.511012	−	1.23594i
$708$		0			0
$709$	1.38713	−	13.1976i	0.0520946	−	0.495647i	−0.937102	−	0.349055i	$-0.886503\pi$
$709$	1.38713	−	13.1976i	0.0520946	−	0.495647i	0.989197	−	0.146593i	$-0.0468306\pi$
$710$	−1.15178	+	0.512806i	−0.0432256	+	0.0192453i
$711$		0			0
$712$	9.53079	−	10.5850i	0.357181	−	0.396690i
$713$	−3.92149	−	5.39747i	−0.146861	−	0.202137i
$714$		0			0
$715$	−0.812298	−	1.28119i	−0.0303782	−	0.0479139i
$716$	3.71079	+	6.42727i	0.138679	+	0.240198i
$717$		0			0
$718$	2.09544	+	0.445398i	0.0782009	+	0.0166221i
$719$	−2.21660	−	10.4283i	−0.0826651	−	0.388909i	0.917292	−	0.398216i	$-0.130371\pi$
$719$	−2.21660	−	10.4283i	−0.0826651	−	0.388909i	−0.999957	+	0.00930760i	$0.997037\pi$
$720$		0			0
$721$	−9.37290	+	31.7172i	−0.349065	+	1.18121i
$722$	−1.81457	−	0.589591i	−0.0675314	−	0.0219423i
$723$		0			0
$724$	22.5924	−	2.37456i	0.839639	−	0.0882497i
$725$	−20.2446	−	11.6882i	−0.751865	−	0.434089i
$726$		0			0
$727$			53.7153i			1.99219i	0.0882861	+	0.996095i	$0.471861\pi$
$727$			53.7153i			1.99219i	−0.0882861	+	0.996095i	$0.528139\pi$
$728$	2.41896	−	1.15569i	0.0896525	−	0.0428328i
$729$		0			0
$730$	5.96360	−	1.26760i	0.220723	−	0.0469161i
$731$	4.66616	+	10.4804i	0.172584	+	0.387630i
$732$		0			0
$733$	20.0701	−	4.26602i	0.741304	−	0.157569i	0.178246	−	0.983986i	$-0.442958\pi$
$733$	20.0701	−	4.26602i	0.741304	−	0.157569i	0.563059	+	0.826417i	$0.309624\pi$
$734$	7.56967	+	23.2970i	0.279401	+	0.859909i
$735$		0			0
$736$		−	6.78465i		−	0.250085i
$737$	−6.09050	−	3.18737i	−0.224346	−	0.117408i
$738$		0			0
$739$	−29.8685	+	3.13931i	−1.09873	+	0.115481i	−0.636499	−	0.771277i	$-0.719618\pi$
$739$	−29.8685	+	3.13931i	−1.09873	+	0.115481i	−0.462232	+	0.886759i	$0.652951\pi$
$740$	−12.9978	−	11.7033i	−0.477809	−	0.430221i
$741$		0			0
$742$	13.5612	+	14.2721i	0.497847	+	0.523946i
$743$	−7.92631	+	10.9096i	−0.290788	+	0.400236i	−0.929270	−	0.369401i	$-0.879563\pi$
$743$	−7.92631	+	10.9096i	−0.290788	+	0.400236i	0.638482	+	0.769637i	$0.279563\pi$
$744$		0			0
$745$	0.483089	+	0.102684i	0.0176990	+	0.00376204i
$746$	1.04891	+	9.97976i	0.0384035	+	0.365385i
$747$		0			0
$748$	1.80237	−	4.54655i	0.0659011	−	0.166238i
$749$	1.46257	+	4.12175i	0.0534411	+	0.150605i
$750$		0			0
$751$	21.5746	−	23.9610i	0.787267	−	0.874348i	−0.207318	−	0.978274i	$-0.566474\pi$
$751$	21.5746	−	23.9610i	0.787267	−	0.874348i	0.994585	+	0.103925i	$0.0331403\pi$
$752$	5.38780	−	4.85120i	0.196473	−	0.176905i
$753$		0			0
$754$	0.207106	−	1.97048i	0.00754234	−	0.0717606i
$755$	4.50692	−	13.8709i	0.164024	−	0.504813i
$756$		0			0
$757$	−4.15237	+	3.01687i	−0.150920	+	0.109650i	−0.660683	−	0.750665i	$-0.729733\pi$
$757$	−4.15237	+	3.01687i	−0.150920	+	0.109650i	0.509763	+	0.860315i	$0.329733\pi$
$758$	6.13809	−	3.54383i	0.222945	−	0.128718i
$759$		0			0
$760$	7.45587	−	12.9139i	0.270453	−	0.468438i
$761$	−33.6560	−	14.9846i	−1.22003	−	0.543191i	−0.307242	−	0.951631i	$-0.599406\pi$
$761$	−33.6560	−	14.9846i	−1.22003	−	0.543191i	−0.912785	+	0.408440i	$0.866073\pi$
$762$		0			0
$763$	−17.8450	−	29.0784i	−0.646031	−	1.05271i
$764$	−18.2931	−	13.2907i	−0.661822	−	0.480842i
$765$		0			0
$766$	3.61291	+	4.01255i	0.130540	+	0.144979i
$767$	0.0903258	−	0.424950i	0.00326148	−	0.0153440i
$768$		0			0
$769$	24.8757			0.897040			0.448520	−	0.893773i	$-0.351951\pi$
$769$	24.8757			0.897040			0.448520	+	0.893773i	$0.351951\pi$
$770$	−4.67902	−	6.95992i	−0.168620	−	0.250818i
$771$		0			0
$772$	8.50490	−	19.1023i	0.306098	−	0.687508i
$773$	−8.76079	+	41.2163i	−0.315104	+	1.48245i	0.480696	+	0.876887i	$0.340384\pi$
$773$	−8.76079	+	41.2163i	−0.315104	+	1.48245i	−0.795800	+	0.605560i	$0.792949\pi$
$774$		0			0
$775$	−20.2505	−	2.12842i	−0.727420	−	0.0764550i
$776$	−36.4481	−	26.4811i	−1.30841	−	0.950617i
$777$		0			0
$778$	−15.5464	+	5.05133i	−0.557366	+	0.181099i
$779$	−21.3794	−	9.51874i	−0.765998	−	0.341044i
$780$		0			0
$781$	−2.42277	+	3.64317i	−0.0866937	+	0.130363i
$782$	0.856640	−	0.494581i	0.0306334	−	0.0176862i
$783$		0			0
$784$	−3.90821	+	1.99767i	−0.139579	+	0.0713452i
$785$	−0.969729	+	2.98452i	−0.0346111	+	0.106522i
$786$		0			0
$787$	−23.5548	+	10.4873i	−0.839637	+	0.373831i	−0.781063	−	0.624452i	$-0.785322\pi$
$787$	−23.5548	+	10.4873i	−0.839637	+	0.373831i	−0.0585744	+	0.998283i	$0.518655\pi$
$788$	−13.1150	+	11.8088i	−0.467203	+	0.420671i
$789$		0			0
$790$	0.833724	+	1.14752i	0.0296626	+	0.0408270i
$791$	4.70435	−	25.4738i	0.167267	−	0.905743i
$792$		0			0
$793$	0.00768236	+	0.0133062i	0.000272809	+	0.000472518i
$794$	−1.63022	−	15.5106i	−0.0578545	−	0.550449i
$795$		0			0
$796$	−4.58023	−	21.5483i	−0.162342	−	0.763759i
$797$	19.4251	−	26.7364i	0.688074	−	0.947052i	−0.311922	−	0.950108i	$-0.600973\pi$
$797$	19.4251	−	26.7364i	0.688074	−	0.947052i	0.999995	+	0.00305568i	$0.000972656\pi$
$798$		0			0
$799$	11.8180	+	3.83990i	0.418091	+	0.135846i
$800$	−15.3883	−	13.8557i	−0.544057	−	0.489872i
$801$		0			0
$802$	−4.22117	−	2.43709i	−0.149055	−	0.0860568i
$803$	15.1228	−	14.7966i	0.533672	−	0.522161i
$804$		0			0
$805$	−0.288459	+	3.69559i	−0.0101669	+	0.130252i
$806$	−0.533315	−	1.64138i	−0.0187852	−	0.0578150i
$807$		0			0
$808$	−14.6076	−	32.8091i	−0.513892	−	1.15422i
$809$	12.4975	+	28.0698i	0.439387	+	0.986880i	0.988512	+	0.151140i	$0.0482944\pi$
$809$	12.4975	+	28.0698i	0.439387	+	0.986880i	−0.549125	+	0.835740i	$0.685039\pi$
$810$		0			0
$811$	0.119626	+	0.368171i	0.00420064	+	0.0129282i	0.953135	−	0.302546i	$-0.0978365\pi$
$811$	0.119626	+	0.368171i	0.00420064	+	0.0129282i	−0.948934	+	0.315474i	$0.897837\pi$
$812$	−1.86280	+	23.8652i	−0.0653715	+	0.837505i
$813$		0			0
$814$	27.3823	+	4.64347i	0.959748	+	0.162754i
$815$	5.23086	+	3.02004i	0.183229	+	0.105787i
$816$		0			0
$817$	36.7048	+	33.0491i	1.28414	+	1.15624i
$818$	12.5814	+	4.08796i	0.439900	+	0.142932i
$819$		0			0
$820$	4.92037	−	6.77231i	0.171827	−	0.236499i
$821$	7.43901	+	34.9978i	0.259623	+	1.22143i	0.893879	+	0.448308i	$0.147973\pi$
$821$	7.43901	+	34.9978i	0.259623	+	1.22143i	−0.634256	+	0.773123i	$0.718693\pi$
$822$		0			0
$823$	−2.72759	−	25.9513i	−0.0950779	−	0.904606i	−0.933257	−	0.359210i	$-0.883046\pi$
$823$	−2.72759	−	25.9513i	−0.0950779	−	0.904606i	0.838179	−	0.545396i	$-0.183621\pi$
$824$	16.7007	+	28.9265i	0.581797	+	1.00770i
$825$		0			0
$826$	0.436168	−	2.36182i	0.0151762	−	0.0821783i
$827$	19.9761	+	27.4948i	0.694638	+	0.956087i	0.999993	+	0.00384841i	$0.00122499\pi$
$827$	19.9761	+	27.4948i	0.694638	+	0.956087i	−0.305355	+	0.952239i	$0.598775\pi$
$828$		0			0
$829$	34.2228	−	30.8143i	1.18861	−	1.07023i	0.192569	−	0.981283i	$-0.438318\pi$
$829$	34.2228	−	30.8143i	1.18861	−	1.07023i	0.996037	−	0.0889421i	$-0.0283486\pi$
$830$	12.4155	−	5.52774i	0.430949	−	0.191871i
$831$		0			0
$832$	0.395394	−	1.21690i	0.0137078	−	0.0421883i
$833$	−6.31445	−	4.08912i	−0.218783	−	0.141680i
$834$		0			0
$835$	6.60237	−	3.81188i	0.228484	−	0.131916i
$836$	−0.872699	−	21.0381i	−0.0301829	−	0.727618i
$837$		0			0
$838$	21.9832	+	9.78754i	0.759396	+	0.338105i
$839$	40.3881	−	13.1229i	1.39435	−	0.453052i	0.486991	−	0.873407i	$-0.338094\pi$
$839$	40.3881	−	13.1229i	1.39435	−	0.453052i	0.907360	+	0.420355i	$0.138094\pi$
$840$		0			0
$841$	11.7136	+	8.51040i	0.403916	+	0.293462i
$842$	−21.7954	−	2.29079i	−0.751118	−	0.0789457i
$843$		0			0
$844$	4.41144	−	20.7542i	0.151848	−	0.714388i
$845$	6.30709	−	14.1660i	0.216970	−	0.487324i
$846$		0			0
$847$	−26.6462	−	11.7038i	−0.915575	−	0.402146i
$848$	−5.88835			−0.202207
$849$		0			0
$850$	0.627676	−	2.95298i	0.0215291	−	0.101287i
$851$	−8.21405	−	9.12263i	−0.281574	−	0.312720i
$852$		0			0
$853$	19.3198	+	14.0367i	0.661498	+	0.480606i	0.867168	−	0.498015i	$-0.165938\pi$
$853$	19.3198	+	14.0367i	0.661498	+	0.480606i	−0.205671	+	0.978621i	$0.565938\pi$
$854$	0.0444285	+	0.0723962i	0.00152031	+	0.00247735i
$855$		0			0
$856$	4.03509	+	1.79654i	0.137916	+	0.0614044i
$857$	−8.68578	+	15.0442i	−0.296700	+	0.513900i	−0.975379	−	0.220535i	$-0.929220\pi$
$857$	−8.68578	+	15.0442i	−0.296700	+	0.513900i	0.678679	+	0.734435i	$0.262553\pi$
$858$		0			0
$859$	13.4299	−	7.75377i	0.458223	−	0.264555i	−0.253074	−	0.967447i	$-0.581441\pi$
$859$	13.4299	−	7.75377i	0.458223	−	0.264555i	0.711297	+	0.702892i	$0.248108\pi$
$860$	−14.2929	+	10.3844i	−0.487383	+	0.354105i
$861$		0			0
$862$	−3.07914	+	9.47661i	−0.104876	+	0.322775i
$863$	−3.96600	+	37.7339i	−0.135004	+	1.28448i	0.691842	+	0.722049i	$0.256800\pi$
$863$	−3.96600	+	37.7339i	−0.135004	+	1.28448i	−0.826846	+	0.562429i	$0.809867\pi$
$864$		0			0
$865$	−17.3853	+	15.6538i	−0.591117	+	0.532244i
$866$	6.78402	−	7.53442i	0.230530	−	0.256030i
$867$		0			0
$868$	6.97286	+	19.6506i	0.236674	+	0.666985i
$869$	4.57581	+	1.81397i	0.155224	+	0.0615347i
$870$		0			0
$871$	0.0821563	+	0.781665i	0.00278376	+	0.0264857i
$872$	−33.7030	−	7.16380i	−1.14133	−	0.242597i
$873$		0			0
$874$	2.50316	−	3.44531i	0.0846707	−	0.116539i
$875$	18.7837	+	19.7684i	0.635003	+	0.668293i
$876$		0			0
$877$	23.0062	+	20.7149i	0.776865	+	0.699493i	0.958883	−	0.283803i	$-0.0915960\pi$
$877$	23.0062	+	20.7149i	0.776865	+	0.699493i	−0.182017	+	0.983295i	$0.558263\pi$
$878$	4.25995	−	0.447738i	0.143766	−	0.0151104i
$879$		0			0
$880$	2.47302	+	0.419373i	0.0833655	+	0.0141371i
$881$		−	4.42680i		−	0.149143i	−0.997216	−	0.0745714i	$-0.976241\pi$
$881$		−	4.42680i		−	0.149143i	0.997216	−	0.0745714i	$-0.0237589\pi$
$882$		0			0
$883$	9.24944	+	28.4669i	0.311269	+	0.957986i	0.977263	+	0.212030i	$0.0680073\pi$
$883$	9.24944	+	28.4669i	0.311269	+	0.957986i	−0.665995	+	0.745956i	$0.731993\pi$
$884$	−0.546980	+	0.116264i	−0.0183969	+	0.00391039i
$885$		0			0
$886$	−8.06792	−	18.1208i	−0.271047	−	0.608781i
$887$	−10.0196	+	2.12973i	−0.336425	+	0.0715092i	−0.373027	−	0.927821i	$-0.621680\pi$
$887$	−10.0196	+	2.12973i	−0.336425	+	0.0715092i	0.0366020	+	0.999330i	$0.488347\pi$
$888$		0			0
$889$	15.7246	−	7.51268i	0.527388	−	0.251967i
$890$			5.09467i			0.170774i
$891$		0			0
$892$	−7.54946	−	4.35868i	−0.252775	−	0.145940i
$893$	53.2053	−	5.59210i	1.78045	−	0.187133i
$894$		0			0
$895$	−6.20453	−	2.01597i	−0.207394	−	0.0673865i
$896$	−6.75433	+	22.8562i	−0.225646	+	0.763571i
$897$		0			0
$898$	−2.68594	−	12.6363i	−0.0896309	−	0.421680i
$899$	37.0447	+	7.87408i	1.23551	+	0.262615i
$900$		0			0
$901$	−5.04619	−	8.74025i	−0.168113	−	0.291180i
$902$	−0.840349	+	13.2660i	−0.0279806	+	0.441708i
$903$		0			0
$904$	−15.3774	−	21.1652i	−0.511445	−	0.703944i
$905$	−13.3618	+	14.8398i	−0.444161	+	0.493291i
$906$		0			0
$907$	11.6482	−	5.18611i	0.386772	−	0.172202i	−0.204133	−	0.978943i	$-0.565438\pi$
$907$	11.6482	−	5.18611i	0.386772	−	0.172202i	0.590905	+	0.806741i	$0.298771\pi$
$908$	0.374228	−	3.56054i	0.0124192	−	0.118161i
$909$		0			0
$910$	−0.366384	+	0.886139i	−0.0121455	+	0.0293752i
$911$	−30.1979	+	21.9400i	−1.00050	+	0.726906i	−0.962195	−	0.272360i	$-0.912196\pi$
$911$	−30.1979	+	21.9400i	−1.00050	+	0.726906i	−0.0383045	+	0.999266i	$0.512196\pi$
$912$		0			0
$913$	26.1161	−	39.2712i	0.864316	−	1.29969i
$914$	3.89364	−	6.74399i	0.128790	−	0.223071i
$915$		0			0
$916$	−14.2589	+	4.63301i	−0.471128	+	0.153079i
$917$	−0.0451049	−	1.68120i	−0.00148950	−	0.0555180i
$918$		0			0
$919$	10.7924	+	1.13433i	0.356009	+	0.0374181i	0.280845	−	0.959753i	$-0.409385\pi$
$919$	10.7924	+	1.13433i	0.356009	+	0.0374181i	0.0751641	+	0.997171i	$0.476052\pi$
$920$	2.50497	+	2.78205i	0.0825864	+	0.0917215i
$921$		0			0
$922$	−5.54194	+	12.4474i	−0.182514	+	0.409933i
$923$	0.500252			0.0164660
$924$		0			0
$925$	−37.4659			−1.23187
$926$	2.27681	−	5.11380i	0.0748207	−	0.168050i
$927$		0			0
$928$	25.7707	+	28.6213i	0.845965	+	0.939539i
$929$	−3.30645	−	0.347522i	−0.108481	−	0.0114018i	0.0501323	−	0.998743i	$-0.484036\pi$
$929$	−3.30645	−	0.347522i	−0.108481	−	0.0114018i	−0.158613	+	0.987341i	$0.550702\pi$
$930$		0			0
$931$	−31.9958	−	5.02549i	−1.04862	−	0.164704i
$932$	18.5102	−	6.01433i	0.606322	−	0.197006i
$933$		0			0
$934$	7.62015	−	13.1985i	0.249339	−	0.431868i
$935$	1.49684	+	4.03017i	0.0489517	+	0.131801i
$936$		0			0
$937$	15.5011	−	11.2622i	0.506398	−	0.367920i	−0.305058	−	0.952334i	$-0.598676\pi$
$937$	15.5011	−	11.2622i	0.506398	−	0.367920i	0.811455	+	0.584414i	$0.198676\pi$
$938$	0.569922	+	4.30759i	0.0186086	+	0.140648i
$939$		0			0
$940$	−2.00027	+	19.0313i	−0.0652416	+	0.620732i
$941$	12.9258	−	5.75492i	0.421368	−	0.187605i	−0.185088	−	0.982722i	$-0.559257\pi$
$941$	12.9258	−	5.75492i	0.421368	−	0.187605i	0.606456	+	0.795117i	$0.292590\pi$
$942$		0			0
$943$	3.93134	−	4.36619i	0.128022	−	0.142183i
$944$	0.422231	+	0.581151i	0.0137425	+	0.0189149i
$945$		0			0
$946$	10.3385	−	26.0793i	0.336134	−	0.847912i
$947$	29.4803	+	51.0614i	0.957982	+	1.65927i	0.727391	+	0.686223i	$0.240733\pi$
$947$	29.4803	+	51.0614i	0.957982	+	1.65927i	0.230591	+	0.973051i	$0.425934\pi$
$948$		0			0
$949$	−2.36624	−	0.502959i	−0.0768113	−	0.0163267i
$950$	−2.70233	−	12.7135i	−0.0876752	−	0.412479i
$951$		0			0
$952$	−7.38645	+	1.77835i	−0.239396	+	0.0576367i
$953$	−32.7290	−	10.6343i	−1.06020	−	0.344478i	−0.273534	−	0.961862i	$-0.588192\pi$
$953$	−32.7290	−	10.6343i	−1.06020	−	0.344478i	−0.786662	+	0.617384i	$0.788192\pi$
$954$		0			0
$955$	19.7675	−	2.07765i	0.639661	−	0.0672310i
$956$	33.5135	+	19.3490i	1.08390	+	0.625793i
$957$		0			0
$958$			28.0304i			0.905622i
$959$	4.53089	+	0.353659i	0.146310	+	0.0114202i
$960$		0			0
$961$	1.94524	−	0.413474i	0.0627497	−	0.0133379i
$962$	−1.29160	−	2.90098i	−0.0416429	−	0.0935315i
$963$		0			0
$964$	0.171377	−	0.0364272i	0.00551967	−	0.00117324i
$965$	5.67995	+	17.4811i	0.182844	+	0.562737i
$966$		0			0
$967$		−	18.5798i		−	0.597485i	−0.954334	−	0.298742i	$-0.903433\pi$
$967$		−	18.5798i		−	0.597485i	0.954334	−	0.298742i	$-0.0965671\pi$
$968$	−27.1053	+	11.3666i	−0.871197	+	0.365336i
$969$		0			0
$970$	16.0262	−	1.68442i	0.514570	−	0.0540835i
$971$	19.2202	+	17.3059i	0.616805	+	0.555374i	0.917193	−	0.398443i	$-0.130449\pi$
$971$	19.2202	+	17.3059i	0.616805	+	0.555374i	−0.300388	+	0.953817i	$0.597116\pi$
$972$		0			0
$973$	−1.32870	+	1.26251i	−0.0425962	+	0.0404743i
$974$	−13.3191	+	18.3321i	−0.426771	+	0.587400i
$975$		0			0
$976$	−0.0248501	−	0.00528204i	−0.000795431	−	0.000169074i
$977$	−1.29215	−	12.2940i	−0.0413396	−	0.393320i	−0.995554	−	0.0941957i	$-0.969972\pi$
$977$	−1.29215	−	12.2940i	−0.0413396	−	0.393320i	0.954214	−	0.299125i	$-0.0966946\pi$
$978$		0			0
$979$	9.46687	+	14.9316i	0.302562	+	0.477215i
$980$	4.13781	−	10.8209i	0.132177	−	0.345661i
$981$		0			0
$982$	−13.4107	+	14.8941i	−0.427954	+	0.475291i
$983$	12.1444	−	10.9348i	0.387345	−	0.348767i	−0.452335	−	0.891848i	$-0.649409\pi$
$983$	12.1444	−	10.9348i	0.387345	−	0.348767i	0.839680	+	0.543081i	$0.182742\pi$
$984$		0			0
$985$	1.62157	−	15.4282i	0.0516676	−	0.491584i
$986$	−1.73515	+	5.34026i	−0.0552586	+	0.170068i
$987$		0			0
$988$	−1.94772	+	1.41510i	−0.0619653	+	0.0450204i
$989$	−10.7385	+	6.19987i	−0.341464	+	0.197144i
$990$		0			0
$991$	1.00540	−	1.74141i	0.0319376	−	0.0553176i	−0.849615	−	0.527404i	$-0.823166\pi$
$991$	1.00540	−	1.74141i	0.0319376	−	0.0553176i	0.881552	+	0.472086i	$0.156499\pi$
$992$	30.6471	+	13.6450i	0.973047	+	0.433228i
$993$		0			0
$994$	2.76458	−	0.0741711i	0.0876871	−	0.00235256i
$995$	15.6665	+	11.3824i	0.496662	+	0.360846i
$996$		0			0
$997$	17.4647	+	19.3965i	0.553111	+	0.614292i	0.953258	−	0.302159i	$-0.0977073\pi$
$997$	17.4647	+	19.3965i	0.553111	+	0.614292i	−0.400146	+	0.916451i	$0.631041\pi$
$998$	2.51178	−	11.8170i	0.0795089	−	0.374060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.cg.c.514.11		128
3.2	odd	2		231.2.ba.a.52.6	yes	128
7.5	odd	6	inner	693.2.cg.c.19.6		128
11.7	odd	10	inner	693.2.cg.c.73.6		128
21.5	even	6		231.2.ba.a.19.11	✓	128
33.29	even	10		231.2.ba.a.73.11	yes	128
77.40	even	30	inner	693.2.cg.c.271.11		128
231.194	odd	30		231.2.ba.a.40.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.11	✓	128	21.5	even	6
231.2.ba.a.40.6	yes	128	231.194	odd	30
231.2.ba.a.52.6	yes	128	3.2	odd	2
231.2.ba.a.73.11	yes	128	33.29	even	10
693.2.cg.c.19.6		128	7.5	odd	6	inner
693.2.cg.c.73.6		128	11.7	odd	10	inner
693.2.cg.c.271.11		128	77.40	even	30	inner
693.2.cg.c.514.11		128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.cg (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.322290 - 0.723875i) q^{2} +(0.918138 + 1.01969i) q^{4} +(-1.19955 - 0.126078i) q^{5} +(2.32594 + 1.26095i) q^{7} +(2.54123 - 0.825697i) q^{8} +O(q^{10})\)	\(q+(0.322290 - 0.723875i) q^{2} +(0.918138 + 1.01969i) q^{4} +(-1.19955 - 0.126078i) q^{5} +(2.32594 + 1.26095i) q^{7} +(2.54123 - 0.825697i) q^{8} +(-0.477866 + 0.827689i) q^{10} +(0.137461 + 3.31377i) q^{11} +(0.306792 - 0.222897i) q^{13} +(1.66240 - 1.27730i) q^{14} +(-0.0655419 + 0.623589i) q^{16} +(-0.981780 + 0.437117i) q^{17} +(-3.09598 + 3.43843i) q^{19} +(-0.972789 - 1.33893i) q^{20} +(2.44306 + 0.968491i) q^{22} +(-0.580792 - 1.00596i) q^{23} +(-3.46772 - 0.737086i) q^{25} +(-0.0624738 - 0.293916i) q^{26} +(0.849752 + 3.52948i) q^{28} +(6.27112 + 2.03761i) q^{29} +(5.71212 - 0.600367i) q^{31} +(5.05833 + 2.92043i) q^{32} +0.851564i q^{34} +(-2.63110 - 1.80582i) q^{35} +(10.3371 - 2.19723i) q^{37} +(1.49119 + 3.34927i) q^{38} +(-3.15243 + 0.670070i) q^{40} +(1.56301 + 4.81045i) q^{41} -10.6749i q^{43} +(-3.25283 + 3.18267i) q^{44} +(-0.915372 + 0.0962095i) q^{46} +(-8.59265 - 7.73686i) q^{47} +(3.82002 + 5.86579i) q^{49} +(-1.65117 + 2.27264i) q^{50} +(0.508964 + 0.108184i) q^{52} +(0.981621 + 9.33950i) q^{53} +(0.252901 - 3.99236i) q^{55} +(6.95192 + 1.28384i) q^{56} +(3.49609 - 3.88280i) q^{58} +(0.851375 - 0.766581i) q^{59} +(-0.00423519 + 0.0402952i) q^{61} +(1.40637 - 4.32835i) q^{62} +(2.72973 - 1.98326i) q^{64} +(-0.396113 + 0.228696i) q^{65} +(-1.03631 + 1.79495i) q^{67} +(-1.34714 - 0.599783i) q^{68} +(-2.15516 + 1.32259i) q^{70} +(1.06724 + 0.775393i) q^{71} +(-4.26853 - 4.74069i) q^{73} +(1.74104 - 8.19094i) q^{74} -6.34868 q^{76} +(-3.85877 + 7.88098i) q^{77} +(0.603644 - 1.35581i) q^{79} +(0.157241 - 0.739762i) q^{80} +(3.98590 + 0.418935i) q^{82} +(-11.5042 - 8.35828i) q^{83} +(1.23280 - 0.400562i) q^{85} +(-7.72726 - 3.44040i) q^{86} +(3.08549 + 8.30757i) q^{88} +(4.61647 - 2.66532i) q^{89} +(0.994641 - 0.131597i) q^{91} +(0.492526 - 1.51584i) q^{92} +(-8.36984 + 3.72649i) q^{94} +(4.14728 - 3.73423i) q^{95} +(-9.91056 - 13.6407i) q^{97} +(5.47725 - 0.874729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} - 12 q^{5} - 10 q^{7} + 40 q^{8}+O(q^{10}) \) 128 * q - 12 * q^4 - 12 * q^5 - 10 * q^7 + 40 * q^8	\( 128 q - 12 q^{4} - 12 q^{5} - 10 q^{7} + 40 q^{8} + 2 q^{11} - 12 q^{14} + 40 q^{16} + 60 q^{17} + 52 q^{22} + 24 q^{23} - 20 q^{25} - 24 q^{26} + 30 q^{28} - 40 q^{29} - 18 q^{31} + 80 q^{35} - 8 q^{37} + 24 q^{38} - 90 q^{40} + 82 q^{44} + 70 q^{46} + 24 q^{47} - 94 q^{49} - 4 q^{53} + 104 q^{56} - 32 q^{58} - 48 q^{59} + 30 q^{61} - 48 q^{64} - 40 q^{67} - 180 q^{68} + 146 q^{70} + 32 q^{71} + 90 q^{73} - 40 q^{74} + 50 q^{79} - 228 q^{80} + 168 q^{82} - 20 q^{85} - 146 q^{86} + 16 q^{88} + 48 q^{91} + 204 q^{92} - 10 q^{95}+O(q^{100}) \) 128 * q - 12 * q^4 - 12 * q^5 - 10 * q^7 + 40 * q^8 + 2 * q^11 - 12 * q^14 + 40 * q^16 + 60 * q^17 + 52 * q^22 + 24 * q^23 - 20 * q^25 - 24 * q^26 + 30 * q^28 - 40 * q^29 - 18 * q^31 + 80 * q^35 - 8 * q^37 + 24 * q^38 - 90 * q^40 + 82 * q^44 + 70 * q^46 + 24 * q^47 - 94 * q^49 - 4 * q^53 + 104 * q^56 - 32 * q^58 - 48 * q^59 + 30 * q^61 - 48 * q^64 - 40 * q^67 - 180 * q^68 + 146 * q^70 + 32 * q^71 + 90 * q^73 - 40 * q^74 + 50 * q^79 - 228 * q^80 + 168 * q^82 - 20 * q^85 - 146 * q^86 + 16 * q^88 + 48 * q^91 + 204 * q^92 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more