LMFDB - Embedded newform 361.3.b.c.360.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(360,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("361.360");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.b (of order $2$, degree $1$, 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:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			360.9
Root			$1.89323i$ of defining polynomial
Character	$\chi$	$=$	361.360
Dual form			361.3.b.c.360.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89323i q^{2} +1.94309i q^{3} +0.415663 q^{4} -2.79304 q^{5} -3.67872 q^{6} +2.41591 q^{7} +8.35989i q^{8} +5.22441 q^{9} +O(q^{10})$	\(q+1.89323i q^{2} +1.94309i q^{3} +0.415663 q^{4} -2.79304 q^{5} -3.67872 q^{6} +2.41591 q^{7} +8.35989i q^{8} +5.22441 q^{9} -5.28787i q^{10} +19.2072 q^{11} +0.807671i q^{12} +14.5166i q^{13} +4.57389i q^{14} -5.42712i q^{15} -14.1646 q^{16} -17.1573 q^{17} +9.89103i q^{18} -1.16096 q^{20} +4.69433i q^{21} +36.3637i q^{22} -7.62897 q^{23} -16.2440 q^{24} -17.1990 q^{25} -27.4834 q^{26} +27.6393i q^{27} +1.00421 q^{28} -8.23762i q^{29} +10.2748 q^{30} -6.00256i q^{31} +6.62269i q^{32} +37.3213i q^{33} -32.4828i q^{34} -6.74773 q^{35} +2.17159 q^{36} -59.5153i q^{37} -28.2071 q^{39} -23.3495i q^{40} +30.8898i q^{41} -8.88747 q^{42} +24.5734 q^{43} +7.98373 q^{44} -14.5920 q^{45} -14.4434i q^{46} +73.1731 q^{47} -27.5230i q^{48} -43.1634 q^{49} -32.5617i q^{50} -33.3381i q^{51} +6.03403i q^{52} +28.0298i q^{53} -52.3276 q^{54} -53.6464 q^{55} +20.1968i q^{56} +15.5957 q^{58} +9.21508i q^{59} -2.25585i q^{60} -61.6552 q^{61} +11.3643 q^{62} +12.6217 q^{63} -69.1966 q^{64} -40.5455i q^{65} -70.6580 q^{66} +12.0480i q^{67} -7.13165 q^{68} -14.8238i q^{69} -12.7750i q^{70} +38.4590i q^{71} +43.6754i q^{72} +50.8244 q^{73} +112.676 q^{74} -33.4191i q^{75} +46.4029 q^{77} -53.4026i q^{78} -107.466i q^{79} +39.5621 q^{80} -6.68592 q^{81} -58.4816 q^{82} +71.2672 q^{83} +1.95126i q^{84} +47.9209 q^{85} +46.5232i q^{86} +16.0064 q^{87} +160.570i q^{88} +8.10667i q^{89} -27.6260i q^{90} +35.0709i q^{91} -3.17108 q^{92} +11.6635 q^{93} +138.534i q^{94} -12.8685 q^{96} +119.119i q^{97} -81.7184i q^{98} +100.346 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 24 q^{6} - 12 q^{7} + 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 - 24 * q^6 - 12 * q^7 + 18 * q^9	$ 12 q + 6 q^{5} - 24 q^{6} - 12 q^{7} + 18 q^{9} + 36 q^{11} - 96 q^{16} - 66 q^{17} - 90 q^{20} + 120 q^{23} + 36 q^{24} - 66 q^{25} - 42 q^{26} + 210 q^{28} - 48 q^{30} - 270 q^{35} + 144 q^{36} - 108 q^{39} + 234 q^{42} + 102 q^{43} - 42 q^{44} + 6 q^{45} + 228 q^{47} + 48 q^{49} + 288 q^{54} - 66 q^{55} - 132 q^{58} + 102 q^{61} - 438 q^{62} + 42 q^{63} - 54 q^{64} - 276 q^{66} + 60 q^{68} + 36 q^{73} - 78 q^{74} + 246 q^{77} - 468 q^{80} + 204 q^{81} + 96 q^{82} + 312 q^{83} - 210 q^{85} - 138 q^{87} + 480 q^{92} - 240 q^{93} + 558 q^{96} - 318 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 - 24 * q^6 - 12 * q^7 + 18 * q^9 + 36 * q^11 - 96 * q^16 - 66 * q^17 - 90 * q^20 + 120 * q^23 + 36 * q^24 - 66 * q^25 - 42 * q^26 + 210 * q^28 - 48 * q^30 - 270 * q^35 + 144 * q^36 - 108 * q^39 + 234 * q^42 + 102 * q^43 - 42 * q^44 + 6 * q^45 + 228 * q^47 + 48 * q^49 + 288 * q^54 - 66 * q^55 - 132 * q^58 + 102 * q^61 - 438 * q^62 + 42 * q^63 - 54 * q^64 - 276 * q^66 + 60 * q^68 + 36 * q^73 - 78 * q^74 + 246 * q^77 - 468 * q^80 + 204 * q^81 + 96 * q^82 + 312 * q^83 - 210 * q^85 - 138 * q^87 + 480 * q^92 - 240 * q^93 + 558 * q^96 - 318 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	1.89323i	0.946617i	0.880897	+	0.473309i	$0.156940\pi$
$2$	1.89323i	0.946617i	−0.880897	+	0.473309i	$0.843060\pi$
$3$	1.94309i	0.647696i	0.946109	+	0.323848i	$0.104977\pi$
$3$	1.94309i	0.647696i	−0.946109	+	0.323848i	$0.895023\pi$
$4$	0.415663	0.103916
$5$	−2.79304	−0.558607	−0.279304	−	0.960203i	$-0.590104\pi$
$5$	−2.79304	−0.558607	−0.279304	+	0.960203i	$0.590104\pi$
$6$	−3.67872	−0.613120
$7$	2.41591	0.345130	0.172565	−	0.984998i	$-0.444794\pi$
$7$	2.41591	0.345130	0.172565	+	0.984998i	$0.444794\pi$
$8$	8.35989i	1.04499i
$9$	5.22441	0.580490
$10$	− 5.28787i	− 0.528787i
$11$	19.2072	1.74611	0.873055	−	0.487622i	$-0.162136\pi$
$11$	19.2072	1.74611	0.873055	+	0.487622i	$0.162136\pi$
$12$	0.807671i	0.0673059i
$13$	14.5166i	1.11666i	0.829618	+	0.558332i	$0.188558\pi$
$13$	14.5166i	1.11666i	−0.829618	+	0.558332i	$0.811442\pi$
$14$	4.57389i	0.326706i
$15$	− 5.42712i	− 0.361808i
$16$	−14.1646	−0.885286
$17$	−17.1573	−1.00925	−0.504626	−	0.863338i	$-0.668370\pi$
$17$	−17.1573	−1.00925	−0.504626	+	0.863338i	$0.668370\pi$
$18$	9.89103i	0.549501i
$19$	0	0
$19$	0	0
$20$	−1.16096	−0.0580481
$21$	4.69433i	0.223540i
$22$	36.3637i	1.65290i
$23$	−7.62897	−0.331694	−0.165847	−	0.986151i	$-0.553036\pi$
$23$	−7.62897	−0.331694	−0.165847	+	0.986151i	$0.553036\pi$
$24$	−16.2440	−0.676833
$25$	−17.1990	−0.687958
$26$	−27.4834	−1.05705
$27$	27.6393i	1.02368i
$28$	1.00421	0.0358645
$29$	− 8.23762i	− 0.284056i	−0.989863	−	0.142028i	$-0.954638\pi$
$29$	− 8.23762i	− 0.284056i	0.989863	−	0.142028i	$-0.0453623\pi$
$30$	10.2748	0.342493
$31$	− 6.00256i	− 0.193631i	−0.995302	−	0.0968155i	$-0.969134\pi$
$31$	− 6.00256i	− 0.193631i	0.995302	−	0.0968155i	$-0.0308657\pi$
$32$	6.62269i	0.206959i
$33$	37.3213i	1.13095i
$34$	− 32.4828i	− 0.955375i
$35$	−6.74773	−0.192792
$36$	2.17159	0.0603221
$37$	− 59.5153i	− 1.60852i	−0.594277	−	0.804260i	$-0.702562\pi$
$37$	− 59.5153i	− 1.60852i	0.594277	−	0.804260i	$-0.297438\pi$
$38$	0	0
$39$	−28.2071	−0.723259
$40$	− 23.3495i	− 0.583736i
$41$	30.8898i	0.753410i	0.926333	+	0.376705i	$0.122943\pi$
$41$	30.8898i	0.753410i	−0.926333	+	0.376705i	$0.877057\pi$
$42$	−8.88747	−0.211606
$43$	24.5734	0.571474	0.285737	−	0.958308i	$-0.407762\pi$
$43$	24.5734	0.571474	0.285737	+	0.958308i	$0.407762\pi$
$44$	7.98373	0.181448
$45$	−14.5920	−0.324266
$46$	− 14.4434i	− 0.313987i
$47$	73.1731	1.55687	0.778437	−	0.627722i	$-0.216013\pi$
$47$	73.1731	1.55687	0.778437	+	0.627722i	$0.216013\pi$
$48$	− 27.5230i	− 0.573396i
$49$	−43.1634	−0.880885
$50$	− 32.5617i	− 0.651233i
$51$	− 33.3381i	− 0.653689i
$52$	6.03403i	0.116039i
$53$	28.0298i	0.528864i	0.964404	+	0.264432i	$0.0851844\pi$
$53$	28.0298i	0.528864i	−0.964404	+	0.264432i	$0.914816\pi$
$54$	−52.3276	−0.969030
$55$	−53.6464	−0.975389
$56$	20.1968i	0.360656i
$57$	0	0
$58$	15.5957	0.268892
$59$	9.21508i	0.156188i	0.996946	+	0.0780939i	$0.0248834\pi$
$59$	9.21508i	0.156188i	−0.996946	+	0.0780939i	$0.975117\pi$
$60$	− 2.25585i	− 0.0375975i
$61$	−61.6552	−1.01074	−0.505371	−	0.862902i	$-0.668644\pi$
$61$	−61.6552	−1.01074	−0.505371	+	0.862902i	$0.668644\pi$
$62$	11.3643	0.183294
$63$	12.6217	0.200345
$64$	−69.1966	−1.08120
$65$	− 40.5455i	− 0.623776i
$66$	−70.6580	−1.07058
$67$	12.0480i	0.179821i	0.995950	+	0.0899103i	$0.0286580\pi$
$67$	12.0480i	0.179821i	−0.995950	+	0.0899103i	$0.971342\pi$
$68$	−7.13165	−0.104877
$69$	− 14.8238i	− 0.214837i
$70$	− 12.7750i	− 0.182500i
$71$	38.4590i	0.541676i	0.962625	+	0.270838i	$0.0873007\pi$
$71$	38.4590i	0.541676i	−0.962625	+	0.270838i	$0.912699\pi$
$72$	43.6754i	0.606603i
$73$	50.8244	0.696225	0.348112	−	0.937453i	$-0.386823\pi$
$73$	50.8244	0.696225	0.348112	+	0.937453i	$0.386823\pi$
$74$	112.676	1.52265
$75$	− 33.4191i	− 0.445588i
$76$	0	0
$77$	46.4029	0.602635
$78$	− 53.4026i	− 0.684649i
$79$	− 107.466i	− 1.36033i	−0.733058	−	0.680166i	$-0.761908\pi$
$79$	− 107.466i	− 1.36033i	0.733058	−	0.680166i	$-0.238092\pi$
$80$	39.5621	0.494527
$81$	−6.68592	−0.0825422
$82$	−58.4816	−0.713191
$83$	71.2672	0.858641	0.429321	−	0.903152i	$-0.358753\pi$
$83$	71.2672	0.858641	0.429321	+	0.903152i	$0.358753\pi$
$84$	1.95126i	0.0232293i
$85$	47.9209	0.563775
$86$	46.5232i	0.540967i
$87$	16.0064	0.183982
$88$	160.570i	1.82466i
$89$	8.10667i	0.0910862i	0.998962	+	0.0455431i	$0.0145018\pi$
$89$	8.10667i	0.0910862i	−0.998962	+	0.0455431i	$0.985498\pi$
$90$	− 27.6260i	− 0.306955i
$91$	35.0709i	0.385394i
$92$	−3.17108	−0.0344683
$93$	11.6635	0.125414
$94$	138.534i	1.47376i
$95$	0	0
$96$	−12.8685	−0.134047
$97$	119.119i	1.22803i	0.789293	+	0.614017i	$0.210447\pi$
$97$	119.119i	1.22803i	−0.789293	+	0.614017i	$0.789553\pi$
$98$	− 81.7184i	− 0.833861i
$99$	100.346	1.01360
$100$	−7.14898	−0.0714898
$101$	131.407	1.30106	0.650529	−	0.759481i	$-0.274547\pi$
$101$	131.407	1.30106	0.650529	+	0.759481i	$0.274547\pi$
$102$	63.1169	0.618793
$103$	13.2134i	0.128285i	0.997941	+	0.0641427i	$0.0204313\pi$
$103$	13.2134i	0.128285i	−0.997941	+	0.0641427i	$0.979569\pi$
$104$	−121.357	−1.16690
$105$	− 13.1114i	− 0.124871i
$106$	−53.0670	−0.500632
$107$	− 109.544i	− 1.02378i	−0.859051	−	0.511890i	$-0.828945\pi$
$107$	− 109.544i	− 1.02378i	0.859051	−	0.511890i	$-0.171055\pi$
$108$	11.4886i	0.106376i
$109$	− 206.100i	− 1.89083i	−0.325869	−	0.945415i	$-0.605657\pi$
$109$	− 206.100i	− 1.89083i	0.325869	−	0.945415i	$-0.394343\pi$
$110$	− 101.565i	− 0.923320i
$111$	115.643	1.04183
$112$	−34.2204	−0.305539
$113$	18.3671i	0.162541i	0.996692	+	0.0812705i	$0.0258978\pi$
$113$	18.3671i	0.162541i	−0.996692	+	0.0812705i	$0.974102\pi$
$114$	0	0
$115$	21.3080	0.185287
$116$	− 3.42407i	− 0.0295179i
$117$	75.8408i	0.648212i
$118$	−17.4463	−0.147850
$119$	−41.4505	−0.348323
$120$	45.3701	0.378084
$121$	247.917	2.04890
$122$	− 116.728i	− 0.956786i
$123$	−60.0216	−0.487981
$124$	− 2.49504i	− 0.0201213i
$125$	117.863	0.942905
$126$	23.8959i	0.189650i
$127$	− 11.3308i	− 0.0892188i	−0.999005	−	0.0446094i	$-0.985796\pi$
$127$	− 11.3308i	− 0.0892188i	0.999005	−	0.0446094i	$-0.0142043\pi$
$128$	− 104.515i	− 0.816520i
$129$	47.7483i	0.370142i
$130$	76.7620	0.590477
$131$	11.2242	0.0856809	0.0428404	−	0.999082i	$-0.486359\pi$
$131$	11.2242	0.0856809	0.0428404	+	0.999082i	$0.486359\pi$
$132$	15.5131i	0.117523i
$133$	0	0
$134$	−22.8097	−0.170221
$135$	− 77.1975i	− 0.571833i
$136$	− 143.433i	− 1.05465i
$137$	161.739	1.18058	0.590288	−	0.807193i	$-0.299014\pi$
$137$	161.739	1.18058	0.590288	+	0.807193i	$0.299014\pi$
$138$	28.0648	0.203368
$139$	−192.057	−1.38171	−0.690853	−	0.722996i	$-0.742765\pi$
$139$	−192.057	−1.38171	−0.690853	+	0.722996i	$0.742765\pi$
$140$	−2.80478	−0.0200342
$141$	142.182i	1.00838i
$142$	−72.8118	−0.512759
$143$	278.824i	1.94982i
$144$	−74.0015	−0.513899
$145$	23.0079i	0.158676i
$146$	96.2225i	0.659058i
$147$	− 83.8702i	− 0.570546i
$148$	− 24.7383i	− 0.167151i
$149$	140.566	0.943395	0.471698	−	0.881760i	$-0.343641\pi$
$149$	140.566	0.943395	0.471698	+	0.881760i	$0.343641\pi$
$150$	63.2702	0.421801
$151$	− 101.605i	− 0.672880i	−0.941705	−	0.336440i	$-0.890777\pi$
$151$	− 101.605i	− 0.672880i	0.941705	−	0.336440i	$-0.109223\pi$
$152$	0	0
$153$	−89.6366	−0.585860
$154$	87.8516i	0.570465i
$155$	16.7654i	0.108164i
$156$	−11.7247	−0.0751581
$157$	167.351	1.06593	0.532966	−	0.846137i	$-0.321078\pi$
$157$	167.351	1.06593	0.532966	+	0.846137i	$0.321078\pi$
$158$	203.459	1.28771
$159$	−54.4644	−0.342543
$160$	− 18.4974i	− 0.115609i
$161$	−18.4309	−0.114478
$162$	− 12.6580i	− 0.0781359i
$163$	−33.8390	−0.207601	−0.103801	−	0.994598i	$-0.533100\pi$
$163$	−33.8390	−0.207601	−0.103801	+	0.994598i	$0.533100\pi$
$164$	12.8398i	0.0782912i
$165$	− 104.240i	− 0.631756i
$166$	134.926i	0.812805i
$167$	48.2777i	0.289088i	0.989498	+	0.144544i	$0.0461716\pi$
$167$	48.2777i	0.289088i	−0.989498	+	0.144544i	$0.953828\pi$
$168$	−39.2441	−0.233596
$169$	−41.7325	−0.246938
$170$	90.7255i	0.533679i
$171$	0	0
$172$	10.2143	0.0593852
$173$	51.7204i	0.298962i	0.988765	+	0.149481i	$0.0477602\pi$
$173$	51.7204i	0.298962i	−0.988765	+	0.149481i	$0.952240\pi$
$174$	30.3039i	0.174160i
$175$	−41.5512	−0.237435
$176$	−272.062	−1.54581
$177$	−17.9057	−0.101162
$178$	−15.3478	−0.0862237
$179$	− 232.001i	− 1.29610i	−0.761600	−	0.648048i	$-0.775586\pi$
$179$	− 232.001i	− 1.29610i	0.761600	−	0.648048i	$-0.224414\pi$
$180$	−6.06534	−0.0336963
$181$	− 270.398i	− 1.49391i	−0.664874	−	0.746956i	$-0.731515\pi$
$181$	− 270.398i	− 1.49391i	0.664874	−	0.746956i	$-0.268485\pi$
$182$	−66.3974	−0.364821
$183$	− 119.802i	− 0.654654i
$184$	− 63.7773i	− 0.346616i
$185$	166.228i	0.898531i
$186$	22.0818i	0.118719i
$187$	−329.543	−1.76226
$188$	30.4154	0.161784
$189$	66.7741i	0.353302i
$190$	0	0
$191$	81.4552	0.426467	0.213233	−	0.977001i	$-0.431601\pi$
$191$	81.4552	0.426467	0.213233	+	0.977001i	$0.431601\pi$
$192$	− 134.455i	− 0.700287i
$193$	29.8306i	0.154562i	0.997009	+	0.0772812i	$0.0246239\pi$
$193$	29.8306i	0.154562i	−0.997009	+	0.0772812i	$0.975376\pi$
$194$	−225.521	−1.16248
$195$	78.7834	0.404017
$196$	−17.9414	−0.0915379
$197$	−180.038	−0.913900	−0.456950	−	0.889492i	$-0.651058\pi$
$197$	−180.038	−0.913900	−0.456950	+	0.889492i	$0.651058\pi$
$198$	189.979i	0.959490i
$199$	110.128	0.553405	0.276702	−	0.960956i	$-0.410758\pi$
$199$	110.128	0.553405	0.276702	+	0.960956i	$0.410758\pi$
$200$	− 143.781i	− 0.718906i
$201$	−23.4103	−0.116469
$202$	248.784i	1.23160i
$203$	− 19.9014i	− 0.0980362i
$204$	− 13.8574i	− 0.0679286i
$205$	− 86.2763i	− 0.420860i
$206$	−25.0161	−0.121437
$207$	−39.8568	−0.192545
$208$	− 205.622i	− 0.988566i
$209$	0	0
$210$	24.8230	0.118205
$211$	− 153.910i	− 0.729432i	−0.931119	−	0.364716i	$-0.881166\pi$
$211$	− 153.910i	− 0.729432i	0.931119	−	0.364716i	$-0.118834\pi$
$212$	11.6510i	0.0549573i
$213$	−74.7292	−0.350841
$214$	207.393	0.969128
$215$	−68.6343	−0.319229
$216$	−231.061	−1.06973
$217$	− 14.5017i	− 0.0668279i
$218$	390.197	1.78989
$219$	98.7563i	0.450942i
$220$	−22.2988	−0.101358
$221$	− 249.066i	− 1.12699i
$222$	218.940i	0.986217i
$223$	155.632i	0.697901i	0.937141	+	0.348950i	$0.113462\pi$
$223$	155.632i	0.697901i	−0.937141	+	0.348950i	$0.886538\pi$
$224$	15.9998i	0.0714279i
$225$	−89.8543	−0.399353
$226$	−34.7733	−0.153864
$227$	− 67.0830i	− 0.295520i	−0.989023	−	0.147760i	$-0.952794\pi$
$227$	− 67.0830i	− 0.295520i	0.989023	−	0.147760i	$-0.0472063\pi$
$228$	0	0
$229$	69.2740	0.302506	0.151253	−	0.988495i	$-0.451669\pi$
$229$	69.2740	0.302506	0.151253	+	0.988495i	$0.451669\pi$
$230$	40.3410i	0.175396i
$231$	90.1650i	0.390325i
$232$	68.8655	0.296834
$233$	−163.212	−0.700482	−0.350241	−	0.936660i	$-0.613900\pi$
$233$	−163.212	−0.700482	−0.350241	+	0.936660i	$0.613900\pi$
$234$	−143.584	−0.613608
$235$	−204.375	−0.869681
$236$	3.83037i	0.0162304i
$237$	208.816	0.881082
$238$	− 78.4755i	− 0.329729i
$239$	305.632	1.27879	0.639397	−	0.768877i	$-0.279184\pi$
$239$	305.632	1.27879	0.639397	+	0.768877i	$0.279184\pi$
$240$	76.8728i	0.320303i
$241$	− 240.050i	− 0.996057i	−0.867161	−	0.498028i	$-0.834058\pi$
$241$	− 240.050i	− 0.996057i	0.867161	−	0.498028i	$-0.165942\pi$
$242$	469.365i	1.93952i
$243$	235.762i	0.970215i
$244$	−25.6278	−0.105032
$245$	120.557	0.492069
$246$	− 113.635i	− 0.461931i
$247$	0	0
$248$	50.1807	0.202342
$249$	138.479i	0.556139i
$250$	223.143i	0.892570i
$251$	−319.370	−1.27239	−0.636196	−	0.771528i	$-0.719493\pi$
$251$	−319.370	−1.27239	−0.636196	+	0.771528i	$0.719493\pi$
$252$	5.24638	0.0208190
$253$	−146.531	−0.579174
$254$	21.4518	0.0844561
$255$	93.1145i	0.365155i
$256$	−78.9157	−0.308265
$257$	− 115.132i	− 0.447985i	−0.974591	−	0.223992i	$-0.928091\pi$
$257$	− 115.132i	− 0.447985i	0.974591	−	0.223992i	$-0.0719090\pi$
$258$	−90.3987	−0.350382
$259$	− 143.784i	− 0.555149i
$260$	− 16.8533i	− 0.0648202i
$261$	− 43.0367i	− 0.164891i
$262$	21.2500i	0.0811070i
$263$	−22.7199	−0.0863876	−0.0431938	−	0.999067i	$-0.513753\pi$
$263$	−22.7199	−0.0863876	−0.0431938	+	0.999067i	$0.513753\pi$
$264$	−312.002	−1.18183
$265$	− 78.2882i	− 0.295427i
$266$	0	0
$267$	−15.7520	−0.0589962
$268$	5.00791i	0.0186862i
$269$	277.819i	1.03278i	0.856352	+	0.516392i	$0.172725\pi$
$269$	277.819i	1.03278i	−0.856352	+	0.516392i	$0.827275\pi$
$270$	146.153	0.541307
$271$	3.38373	0.0124861	0.00624304	−	0.999981i	$-0.498013\pi$
$271$	3.38373	0.0124861	0.00624304	+	0.999981i	$0.498013\pi$
$272$	243.026	0.893476
$273$	−68.1459	−0.249619
$274$	306.210i	1.11755i
$275$	−330.344	−1.20125
$276$	− 6.16169i	− 0.0223250i
$277$	−135.770	−0.490143	−0.245072	−	0.969505i	$-0.578811\pi$
$277$	−135.770	−0.490143	−0.245072	+	0.969505i	$0.578811\pi$
$278$	− 363.609i	− 1.30795i
$279$	− 31.3598i	− 0.112401i
$280$	− 56.4102i	− 0.201465i
$281$	− 493.227i	− 1.75526i	−0.479341	−	0.877629i	$-0.659124\pi$
$281$	− 493.227i	− 1.75526i	0.479341	−	0.877629i	$-0.340876\pi$
$282$	−269.184	−0.954552
$283$	−374.667	−1.32391	−0.661955	−	0.749543i	$-0.730273\pi$
$283$	−374.667	−1.32391	−0.661955	+	0.749543i	$0.730273\pi$
$284$	15.9860i	0.0562887i
$285$	0	0
$286$	−527.879	−1.84573
$287$	74.6270i	0.260025i
$288$	34.5996i	0.120138i
$289$	5.37231	0.0185893
$290$	−43.5594	−0.150205
$291$	−231.459	−0.795393
$292$	21.1258	0.0723488
$293$	− 73.3812i	− 0.250448i	−0.992129	−	0.125224i	$-0.960035\pi$
$293$	− 73.3812i	− 0.250448i	0.992129	−	0.125224i	$-0.0399649\pi$
$294$	158.786	0.540089
$295$	− 25.7380i	− 0.0872476i
$296$	497.541	1.68088
$297$	530.873i	1.78745i
$298$	266.124i	0.893034i
$299$	− 110.747i	− 0.370391i
$300$	− 13.8911i	− 0.0463036i
$301$	59.3672	0.197233
$302$	192.362	0.636960
$303$	255.335i	0.842691i
$304$	0	0
$305$	172.205	0.564607
$306$	− 169.703i	− 0.554585i
$307$	92.4331i	0.301085i	0.988604	+	0.150543i	$0.0481020\pi$
$307$	92.4331i	0.301085i	−0.988604	+	0.150543i	$0.951898\pi$
$308$	19.2880	0.0626234
$309$	−25.6748	−0.0830900
$310$	−31.7408	−0.102390
$311$	199.231	0.640614	0.320307	−	0.947314i	$-0.396214\pi$
$311$	199.231	0.640614	0.320307	+	0.947314i	$0.396214\pi$
$312$	− 235.808i	− 0.755795i
$313$	30.5976	0.0977559	0.0488780	−	0.998805i	$-0.484435\pi$
$313$	30.5976	0.0977559	0.0488780	+	0.998805i	$0.484435\pi$
$314$	316.835i	1.00903i
$315$	−35.2529	−0.111914
$316$	− 44.6698i	− 0.141360i
$317$	569.906i	1.79781i	0.438144	+	0.898905i	$0.355636\pi$
$317$	569.906i	1.79781i	−0.438144	+	0.898905i	$0.644364\pi$
$318$	− 103.114i	− 0.324257i
$319$	− 158.222i	− 0.495992i
$320$	193.269	0.603964
$321$	212.855	0.663099
$322$	− 34.8940i	− 0.108367i
$323$	0	0
$324$	−2.77909	−0.00857744
$325$	− 249.671i	− 0.768218i
$326$	− 64.0651i	− 0.196519i
$327$	400.472	1.22468
$328$	−258.235	−0.787302
$329$	176.780	0.537325
$330$	197.350	0.598031
$331$	442.268i	1.33616i	0.744090	+	0.668079i	$0.232883\pi$
$331$	442.268i	1.33616i	−0.744090	+	0.668079i	$0.767117\pi$
$332$	29.6232	0.0892264
$333$	− 310.932i	− 0.933729i
$334$	−91.4011	−0.273656
$335$	− 33.6504i	− 0.100449i
$336$	− 66.4932i	− 0.197896i
$337$	− 442.246i	− 1.31230i	−0.754630	−	0.656151i	$-0.772184\pi$
$337$	− 442.246i	− 1.31230i	0.754630	−	0.656151i	$-0.227816\pi$
$338$	− 79.0094i	− 0.233756i
$339$	−35.6890	−0.105277
$340$	19.9190	0.0585852
$341$	− 115.292i	− 0.338101i
$342$	0	0
$343$	−222.659	−0.649150
$344$	205.431i	0.597182i
$345$	41.4033i	0.120010i
$346$	−97.9188	−0.283002
$347$	3.50563	0.0101027	0.00505134	−	0.999987i	$-0.498392\pi$
$347$	3.50563	0.0101027	0.00505134	+	0.999987i	$0.498392\pi$
$348$	6.65328	0.0191186
$349$	88.3547	0.253165	0.126583	−	0.991956i	$-0.459599\pi$
$349$	88.3547	0.253165	0.126583	+	0.991956i	$0.459599\pi$
$350$	− 78.6661i	− 0.224760i
$351$	−401.229	−1.14310
$352$	127.203i	0.361373i
$353$	−125.885	−0.356614	−0.178307	−	0.983975i	$-0.557062\pi$
$353$	−125.885	−0.356614	−0.178307	+	0.983975i	$0.557062\pi$
$354$	− 33.8997i	− 0.0957619i
$355$	− 107.417i	− 0.302584i
$356$	3.36965i	0.00946530i
$357$	− 80.5420i	− 0.225608i
$358$	439.232	1.22691
$359$	−60.1877	−0.167654	−0.0838268	−	0.996480i	$-0.526714\pi$
$359$	−60.1877	−0.167654	−0.0838268	+	0.996480i	$0.526714\pi$
$360$	− 121.987i	− 0.338853i
$361$	0	0
$362$	511.927	1.41416
$363$	481.724i	1.32706i
$364$	14.5777i	0.0400486i
$365$	−141.954	−0.388916
$366$	226.813	0.619706
$367$	153.381	0.417931	0.208965	−	0.977923i	$-0.432990\pi$
$367$	153.381	0.417931	0.208965	+	0.977923i	$0.432990\pi$
$368$	108.061	0.293644
$369$	161.381i	0.437347i
$370$	−314.709	−0.850565
$371$	67.7175i	0.182527i
$372$	4.84809	0.0130325
$373$	266.421i	0.714265i	0.934054	+	0.357132i	$0.116245\pi$
$373$	266.421i	0.714265i	−0.934054	+	0.357132i	$0.883755\pi$
$374$	− 623.903i	− 1.66819i
$375$	229.019i	0.610716i
$376$	611.719i	1.62691i
$377$	119.582	0.317195
$378$	−126.419	−0.334442
$379$	670.093i	1.76806i	0.467435	+	0.884028i	$0.345178\pi$
$379$	670.093i	1.76806i	−0.467435	+	0.884028i	$0.654822\pi$
$380$	0	0
$381$	22.0167	0.0577867
$382$	154.214i	0.403701i
$383$	− 689.895i	− 1.80129i	−0.434553	−	0.900646i	$-0.643094\pi$
$383$	− 689.895i	− 1.80129i	0.434553	−	0.900646i	$-0.356906\pi$
$384$	203.081	0.528857
$385$	−129.605	−0.336636
$386$	−56.4762	−0.146311
$387$	128.381	0.331735
$388$	49.5136i	0.127612i
$389$	225.830	0.580539	0.290270	−	0.956945i	$-0.406255\pi$
$389$	225.830	0.580539	0.290270	+	0.956945i	$0.406255\pi$
$390$	149.155i	0.382450i
$391$	130.892	0.334763
$392$	− 360.841i	− 0.920512i
$393$	21.8096i	0.0554952i
$394$	− 340.855i	− 0.865113i
$395$	300.157i	0.759891i
$396$	41.7103	0.105329
$397$	604.586	1.52289	0.761444	−	0.648231i	$-0.224491\pi$
$397$	604.586	1.52289	0.761444	+	0.648231i	$0.224491\pi$
$398$	208.497i	0.523862i
$399$	0	0
$400$	243.616	0.609039
$401$	− 324.176i	− 0.808418i	−0.914667	−	0.404209i	$-0.867547\pi$
$401$	− 324.176i	− 0.808418i	0.914667	−	0.404209i	$-0.132453\pi$
$402$	− 44.3212i	− 0.110252i
$403$	87.1369	0.216221
$404$	54.6210	0.135201
$405$	18.6740	0.0461086
$406$	37.6779	0.0928028
$407$	− 1143.12i	− 2.80865i
$408$	278.703	0.683095
$409$	261.437i	0.639210i	0.947551	+	0.319605i	$0.103550\pi$
$409$	261.437i	0.639210i	−0.947551	+	0.319605i	$0.896450\pi$
$410$	163.341	0.398393
$411$	314.273i	0.764655i
$412$	5.49233i	0.0133309i
$413$	22.2628i	0.0539052i
$414$	− 75.4583i	− 0.182266i
$415$	−199.052	−0.479643
$416$	−96.1391	−0.231104
$417$	− 373.184i	− 0.894925i
$418$	0	0
$419$	−242.808	−0.579495	−0.289747	−	0.957103i	$-0.593571\pi$
$419$	−242.808	−0.579495	−0.289747	+	0.957103i	$0.593571\pi$
$420$	− 5.44994i	− 0.0129761i
$421$	− 555.794i	− 1.32017i	−0.751189	−	0.660087i	$-0.770519\pi$
$421$	− 555.794i	− 1.32017i	0.751189	−	0.660087i	$-0.229481\pi$
$422$	291.388	0.690493
$423$	382.286	0.903750
$424$	−234.326	−0.552655
$425$	295.087	0.694323
$426$	− 141.480i	− 0.332112i
$427$	−148.954	−0.348838
$428$	− 45.5336i	− 0.106387i
$429$	−541.779	−1.26289
$430$	− 129.941i	− 0.302188i
$431$	6.40432i	0.0148592i	0.999972	+	0.00742961i	$0.00236494\pi$
$431$	6.40432i	0.0148592i	−0.999972	+	0.00742961i	$0.997635\pi$
$432$	− 391.499i	− 0.906247i
$433$	57.2666i	0.132255i	0.997811	+	0.0661277i	$0.0210645\pi$
$433$	57.2666i	0.132255i	−0.997811	+	0.0661277i	$0.978936\pi$
$434$	27.4550	0.0632605
$435$	−44.7065	−0.102774
$436$	− 85.6684i	− 0.196487i
$437$	0	0
$438$	−186.969	−0.426870
$439$	− 523.561i	− 1.19262i	−0.802753	−	0.596311i	$-0.796632\pi$
$439$	− 523.561i	− 1.19262i	0.802753	−	0.596311i	$-0.203368\pi$
$440$	− 448.478i	− 1.01927i
$441$	−225.503	−0.511345
$442$	471.540	1.06683
$443$	434.530	0.980880	0.490440	−	0.871475i	$-0.336836\pi$
$443$	434.530	0.980880	0.490440	+	0.871475i	$0.336836\pi$
$444$	48.0687	0.108263
$445$	− 22.6422i	− 0.0508814i
$446$	−294.648	−0.660645
$447$	273.132i	0.611033i
$448$	−167.173	−0.373154
$449$	314.402i	0.700227i	0.936707	+	0.350114i	$0.113857\pi$
$449$	314.402i	0.700227i	−0.936707	+	0.350114i	$0.886143\pi$
$450$	− 170.115i	− 0.378034i
$451$	593.307i	1.31554i
$452$	7.63455i	0.0168906i
$453$	197.427	0.435822
$454$	127.004	0.279744
$455$	− 97.9543i	− 0.215284i
$456$	0	0
$457$	525.189	1.14921	0.574606	−	0.818431i	$-0.305155\pi$
$457$	525.189	1.14921	0.574606	+	0.818431i	$0.305155\pi$
$458$	131.152i	0.286358i
$459$	− 474.215i	− 1.03315i
$460$	8.85694	0.0192542
$461$	−609.602	−1.32235	−0.661174	−	0.750233i	$-0.729941\pi$
$461$	−609.602	−1.32235	−0.661174	+	0.750233i	$0.729941\pi$
$462$	−170.703	−0.369488
$463$	−763.440	−1.64890	−0.824449	−	0.565936i	$-0.808515\pi$
$463$	−763.440	−1.64890	−0.824449	+	0.565936i	$0.808515\pi$
$464$	116.682i	0.251470i
$465$	−32.5766	−0.0700572
$466$	− 308.999i	− 0.663089i
$467$	−448.623	−0.960649	−0.480324	−	0.877091i	$-0.659481\pi$
$467$	−448.623	−0.960649	−0.480324	+	0.877091i	$0.659481\pi$
$468$	31.5242i	0.0673595i
$469$	29.1069i	0.0620616i
$470$	− 386.930i	− 0.823255i
$471$	325.178i	0.690400i
$472$	−77.0370	−0.163214
$473$	471.986	0.997857
$474$	395.338i	0.834047i
$475$	0	0
$476$	−17.2294	−0.0361963
$477$	146.439i	0.307000i
$478$	578.632i	1.21053i
$479$	−696.664	−1.45441	−0.727207	−	0.686418i	$-0.759182\pi$
$479$	−696.664	−1.45441	−0.727207	+	0.686418i	$0.759182\pi$
$480$	35.9421	0.0748794
$481$	863.961	1.79618
$482$	454.470	0.942885
$483$	− 35.8129i	− 0.0741468i
$484$	103.050	0.212913
$485$	− 332.705i	− 0.685989i
$486$	−446.353	−0.918422
$487$	− 19.4275i	− 0.0398921i	−0.999801	−	0.0199461i	$-0.993651\pi$
$487$	− 19.4275i	− 0.0398921i	0.999801	−	0.0199461i	$-0.00634945\pi$
$488$	− 515.431i	− 1.05621i
$489$	− 65.7522i	− 0.134462i
$490$	228.242i	0.465801i
$491$	662.349	1.34898	0.674489	−	0.738285i	$-0.264364\pi$
$491$	662.349	1.34898	0.674489	+	0.738285i	$0.264364\pi$
$492$	−24.9488	−0.0507089
$493$	141.335i	0.286684i
$494$	0	0
$495$	−280.271	−0.566203
$496$	85.0237i	0.171419i
$497$	92.9135i	0.186949i
$498$	−262.172	−0.526450
$499$	−133.603	−0.267742	−0.133871	−	0.990999i	$-0.542741\pi$
$499$	−133.603	−0.267742	−0.133871	+	0.990999i	$0.542741\pi$
$500$	48.9914	0.0979828
$501$	−93.8079	−0.187241
$502$	− 604.643i	− 1.20447i
$503$	−324.746	−0.645618	−0.322809	−	0.946464i	$-0.604627\pi$
$503$	−324.746	−0.645618	−0.322809	+	0.946464i	$0.604627\pi$
$504$	105.516i	0.209357i
$505$	−367.024	−0.726780
$506$	− 277.418i	− 0.548257i
$507$	− 81.0899i	− 0.159941i
$508$	− 4.70979i	− 0.00927125i
$509$	− 488.553i	− 0.959828i	−0.877315	−	0.479914i	$-0.840668\pi$
$509$	− 488.553i	− 0.959828i	0.877315	−	0.479914i	$-0.159332\pi$
$510$	−176.288	−0.345662
$511$	122.787	0.240288
$512$	− 567.464i	− 1.10833i
$513$	0	0
$514$	217.972	0.424070
$515$	− 36.9055i	− 0.0716612i
$516$	19.8472i	0.0384636i
$517$	1405.45	2.71847
$518$	272.216	0.525514
$519$	−100.497	−0.193636
$520$	338.955	0.651837
$521$	623.213i	1.19619i	0.801427	+	0.598093i	$0.204075\pi$
$521$	623.213i	1.19619i	−0.801427	+	0.598093i	$0.795925\pi$
$522$	81.4785	0.156089
$523$	657.309i	1.25680i	0.777888	+	0.628402i	$0.216291\pi$
$523$	657.309i	1.25680i	−0.777888	+	0.628402i	$0.783709\pi$
$524$	4.66549	0.00890360
$525$	− 80.7376i	− 0.153786i
$526$	− 43.0142i	− 0.0817760i
$527$	102.988i	0.195422i
$528$	− 528.640i	− 1.00121i
$529$	−470.799	−0.889979
$530$	148.218	0.279656
$531$	48.1433i	0.0906654i
$532$	0	0
$533$	−448.416	−0.841305
$534$	− 29.8222i	− 0.0558468i
$535$	305.962i	0.571891i
$536$	−100.720	−0.187910
$537$	450.799	0.839476
$538$	−525.976	−0.977651
$539$	−829.048	−1.53812
$540$	− 32.0882i	− 0.0594225i
$541$	89.3979	0.165246	0.0826228	−	0.996581i	$-0.473670\pi$
$541$	89.3979	0.165246	0.0826228	+	0.996581i	$0.473670\pi$
$542$	6.40619i	0.0118195i
$543$	525.407	0.967601
$544$	− 113.627i	− 0.208874i
$545$	575.646i	1.05623i
$546$	− 129.016i	− 0.236293i
$547$	700.813i	1.28119i	0.767878	+	0.640597i	$0.221313\pi$
$547$	700.813i	1.28119i	−0.767878	+	0.640597i	$0.778687\pi$
$548$	67.2289	0.122681
$549$	−322.112	−0.586725
$550$	− 625.418i	− 1.13712i
$551$	0	0
$552$	123.925	0.224502
$553$	− 259.629i	− 0.469492i
$554$	− 257.044i	− 0.463978i
$555$	−322.996	−0.581975
$556$	−79.8311	−0.143581
$557$	−210.656	−0.378198	−0.189099	−	0.981958i	$-0.560557\pi$
$557$	−210.656	−0.378198	−0.189099	+	0.981958i	$0.560557\pi$
$558$	59.3715	0.106401
$559$	356.723i	0.638144i
$560$	95.5787	0.170676
$561$	− 640.332i	− 1.14141i
$562$	933.795	1.66156
$563$	533.304i	0.947255i	0.880725	+	0.473627i	$0.157056\pi$
$563$	533.304i	0.947255i	−0.880725	+	0.473627i	$0.842944\pi$
$564$	59.0998i	0.104787i
$565$	− 51.3001i	− 0.0907966i
$566$	− 709.332i	− 1.25324i
$567$	−16.1526	−0.0284878
$568$	−321.513	−0.566043
$569$	610.046i	1.07214i	0.844174	+	0.536068i	$0.180091\pi$
$569$	610.046i	1.07214i	−0.844174	+	0.536068i	$0.819909\pi$
$570$	0	0
$571$	−678.976	−1.18910	−0.594550	−	0.804059i	$-0.702670\pi$
$571$	−678.976	−1.18910	−0.594550	+	0.804059i	$0.702670\pi$
$572$	115.897i	0.202617i
$573$	158.275i	0.276221i
$574$	−141.286	−0.246144
$575$	131.210	0.228192
$576$	−361.511	−0.627623
$577$	727.338	1.26055	0.630276	−	0.776371i	$-0.282942\pi$
$577$	727.338	1.26055	0.630276	+	0.776371i	$0.282942\pi$
$578$	10.1710i	0.0175969i
$579$	−57.9634	−0.100110
$580$	9.56356i	0.0164889i
$581$	172.175	0.296343
$582$	− 438.207i	− 0.752933i
$583$	538.374i	0.923454i
$584$	424.886i	0.727545i
$585$	− 211.826i	− 0.362096i
$586$	138.928	0.237078
$587$	−979.801	−1.66917	−0.834584	−	0.550881i	$-0.814292\pi$
$587$	−979.801	−1.66917	−0.834584	+	0.550881i	$0.814292\pi$
$588$	− 34.8618i	− 0.0592888i
$589$	0	0
$590$	48.7282	0.0825901
$591$	− 349.830i	− 0.591930i
$592$	843.008i	1.42400i
$593$	−348.562	−0.587794	−0.293897	−	0.955837i	$-0.594952\pi$
$593$	−348.562	−0.587794	−0.293897	+	0.955837i	$0.594952\pi$
$594$	−1005.07	−1.69203
$595$	115.773	0.194576
$596$	58.4281	0.0980337
$597$	213.988i	0.358438i
$598$	209.670	0.350618
$599$	423.312i	0.706697i	0.935492	+	0.353349i	$0.114957\pi$
$599$	423.312i	0.706697i	−0.935492	+	0.353349i	$0.885043\pi$
$600$	279.380	0.465633
$601$	− 504.663i	− 0.839705i	−0.907592	−	0.419853i	$-0.862082\pi$
$601$	− 504.663i	− 0.839705i	0.907592	−	0.419853i	$-0.137918\pi$
$602$	112.396i	0.186704i
$603$	62.9436i	0.104384i
$604$	− 42.2334i	− 0.0699229i
$605$	−692.440	−1.14453
$606$	−483.410	−0.797705
$607$	− 73.0072i	− 0.120275i	−0.998190	−	0.0601377i	$-0.980846\pi$
$607$	− 73.0072i	− 0.120275i	0.998190	−	0.0601377i	$-0.0191540\pi$
$608$	0	0
$609$	38.6701	0.0634977
$610$	326.025i	0.534467i
$611$	1062.23i	1.73851i
$612$	−37.2587	−0.0608802
$613$	−1027.16	−1.67564	−0.837818	−	0.545950i	$-0.816169\pi$
$613$	−1027.16	−1.67564	−0.837818	+	0.545950i	$0.816169\pi$
$614$	−174.998	−0.285012
$615$	167.642	0.272589
$616$	387.923i	0.629745i
$617$	424.167	0.687467	0.343733	−	0.939067i	$-0.388308\pi$
$617$	424.167	0.687467	0.343733	+	0.939067i	$0.388308\pi$
$618$	− 48.6084i	− 0.0786544i
$619$	328.703	0.531023	0.265512	−	0.964108i	$-0.414459\pi$
$619$	328.703	0.531023	0.265512	+	0.964108i	$0.414459\pi$
$620$	6.96875i	0.0112399i
$621$	− 210.859i	− 0.339548i
$622$	377.191i	0.606416i
$623$	19.5850i	0.0314366i
$624$	399.541	0.640291
$625$	100.778	0.161245
$626$	57.9284i	0.0925375i
$627$	0	0
$628$	69.5618	0.110767
$629$	1021.12i	1.62340i
$630$	− 66.7420i	− 0.105940i
$631$	117.779	0.186655	0.0933275	−	0.995635i	$-0.470250\pi$
$631$	117.779	0.186655	0.0933275	+	0.995635i	$0.470250\pi$
$632$	898.405	1.42153
$633$	299.061	0.472450
$634$	−1078.97	−1.70184
$635$	31.6473i	0.0498383i
$636$	−22.6388	−0.0355957
$637$	− 626.587i	− 0.983652i
$638$	299.551	0.469515
$639$	200.925i	0.314437i
$640$	291.913i	0.456114i
$641$	74.4129i	0.116089i	0.998314	+	0.0580444i	$0.0184865\pi$
$641$	74.4129i	0.116089i	−0.998314	+	0.0580444i	$0.981514\pi$
$642$	402.984i	0.627701i
$643$	−492.966	−0.766665	−0.383333	−	0.923610i	$-0.625224\pi$
$643$	−492.966	−0.766665	−0.383333	+	0.923610i	$0.625224\pi$
$644$	−7.66106	−0.0118960
$645$	− 133.363i	− 0.206764i
$646$	0	0
$647$	989.083	1.52872	0.764361	−	0.644789i	$-0.223055\pi$
$647$	989.083	1.52872	0.764361	+	0.644789i	$0.223055\pi$
$648$	− 55.8935i	− 0.0862554i
$649$	176.996i	0.272721i
$650$	472.685	0.727208
$651$	28.1780	0.0432842
$652$	−14.0656	−0.0215731
$653$	−159.020	−0.243522	−0.121761	−	0.992559i	$-0.538854\pi$
$653$	−159.020	−0.243522	−0.121761	+	0.992559i	$0.538854\pi$
$654$	758.186i	1.15931i
$655$	−31.3496	−0.0478619
$656$	− 437.541i	− 0.666983i
$657$	265.527	0.404151
$658$	334.686i	0.508641i
$659$	744.335i	1.12949i	0.825265	+	0.564746i	$0.191026\pi$
$659$	744.335i	1.12949i	−0.825265	+	0.564746i	$0.808974\pi$
$660$	− 43.3286i	− 0.0656494i
$661$	− 766.535i	− 1.15966i	−0.814738	−	0.579830i	$-0.803119\pi$
$661$	− 766.535i	− 1.15966i	0.814738	−	0.579830i	$-0.196881\pi$
$662$	−837.318	−1.26483
$663$	483.957	0.729950
$664$	595.786i	0.897268i
$665$	0	0
$666$	588.667	0.883884
$667$	62.8445i	0.0942196i
$668$	20.0673i	0.0300408i
$669$	−302.407	−0.452028
$670$	63.7082	0.0950868
$671$	−1184.23	−1.76487
$672$	−31.0891	−0.0462636
$673$	802.654i	1.19265i	0.802743	+	0.596326i	$0.203373\pi$
$673$	802.654i	1.19265i	−0.802743	+	0.596326i	$0.796627\pi$
$674$	837.275	1.24225
$675$	− 475.367i	− 0.704247i
$676$	−17.3467	−0.0256607
$677$	499.851i	0.738333i	0.929363	+	0.369166i	$0.120357\pi$
$677$	499.851i	0.738333i	−0.929363	+	0.369166i	$0.879643\pi$
$678$	− 67.5676i	− 0.0996573i
$679$	287.782i	0.423832i
$680$	400.613i	0.589137i
$681$	130.348	0.191407
$682$	218.276	0.320052
$683$	52.2603i	0.0765159i	0.999268	+	0.0382579i	$0.0121808\pi$
$683$	52.2603i	0.0765159i	−0.999268	+	0.0382579i	$0.987819\pi$
$684$	0	0
$685$	−451.742	−0.659478
$686$	− 421.545i	− 0.614497i
$687$	134.605i	0.195932i
$688$	−348.071	−0.505918
$689$	−406.898	−0.590563
$690$	−78.3861	−0.113603
$691$	−260.166	−0.376507	−0.188253	−	0.982120i	$-0.560283\pi$
$691$	−260.166	−0.376507	−0.188253	+	0.982120i	$0.560283\pi$
$692$	21.4983i	0.0310669i
$693$	242.428	0.349824
$694$	6.63698i	0.00956336i
$695$	536.422	0.771830
$696$	133.812i	0.192258i
$697$	− 529.985i	− 0.760380i
$698$	167.276i	0.239651i
$699$	− 317.136i	− 0.453700i
$700$	−17.2713	−0.0246733
$701$	480.052	0.684810	0.342405	−	0.939552i	$-0.388759\pi$
$701$	480.052	0.684810	0.342405	+	0.939552i	$0.388759\pi$
$702$	− 759.621i	− 1.08208i
$703$	0	0
$704$	−1329.07	−1.88789
$705$	− 397.119i	− 0.563289i
$706$	− 238.329i	− 0.337577i
$707$	317.468	0.449035
$708$	−7.44275	−0.0105124
$709$	425.773	0.600526	0.300263	−	0.953856i	$-0.402926\pi$
$709$	425.773	0.600526	0.300263	+	0.953856i	$0.402926\pi$
$710$	203.366	0.286431
$711$	− 561.447i	− 0.789658i
$712$	−67.7708	−0.0951837
$713$	45.7933i	0.0642263i
$714$	152.485	0.213564
$715$	− 778.765i	− 1.08918i
$716$	− 96.4344i	− 0.134685i
$717$	593.870i	0.828270i
$718$	− 113.949i	− 0.158704i
$719$	562.073	0.781743	0.390871	−	0.920445i	$-0.372174\pi$
$719$	562.073	0.781743	0.390871	+	0.920445i	$0.372174\pi$
$720$	206.689	0.287068
$721$	31.9224i	0.0442752i
$722$	0	0
$723$	466.438	0.645142
$724$	− 112.395i	− 0.155241i
$725$	141.678i	0.195418i
$726$	−912.017	−1.25622
$727$	265.792	0.365601	0.182800	−	0.983150i	$-0.441484\pi$
$727$	265.792	0.365601	0.182800	+	0.983150i	$0.441484\pi$
$728$	−293.189	−0.402732
$729$	−518.280	−0.710947
$730$	− 268.753i	− 0.368155i
$731$	−421.613	−0.576761
$732$	− 49.7971i	− 0.0680289i
$733$	−708.910	−0.967135	−0.483567	−	0.875307i	$-0.660659\pi$
$733$	−708.910	−0.967135	−0.483567	+	0.875307i	$0.660659\pi$
$734$	290.385i	0.395620i
$735$	234.253i	0.318711i
$736$	− 50.5243i	− 0.0686471i
$737$	231.408i	0.313987i
$738$	−305.532	−0.414000
$739$	−621.986	−0.841659	−0.420829	−	0.907140i	$-0.638261\pi$
$739$	−621.986	−0.841659	−0.420829	+	0.907140i	$0.638261\pi$
$740$	69.0950i	0.0933716i
$741$	0	0
$742$	−128.205	−0.172783
$743$	− 509.023i	− 0.685091i	−0.939501	−	0.342546i	$-0.888711\pi$
$743$	− 509.023i	− 0.685091i	0.939501	−	0.342546i	$-0.111289\pi$
$744$	97.5056i	0.131056i
$745$	−392.605	−0.526987
$746$	−504.397	−0.676135
$747$	372.329	0.498432
$748$	−136.979	−0.183127
$749$	− 264.650i	− 0.353338i
$750$	−433.586	−0.578114
$751$	543.075i	0.723136i	0.932346	+	0.361568i	$0.117758\pi$
$751$	543.075i	0.723136i	−0.932346	+	0.361568i	$0.882242\pi$
$752$	−1036.47	−1.37828
$753$	− 620.565i	− 0.824123i
$754$	226.397i	0.300262i
$755$	283.786i	0.375876i
$756$	27.7555i	0.0367137i
$757$	−615.712	−0.813358	−0.406679	−	0.913571i	$-0.633313\pi$
$757$	−615.712	−0.813358	−0.406679	+	0.913571i	$0.633313\pi$
$758$	−1268.64	−1.67367
$759$	− 284.723i	− 0.375129i
$760$	0	0
$761$	841.391	1.10564	0.552819	−	0.833301i	$-0.313552\pi$
$761$	841.391	1.10564	0.552819	+	0.833301i	$0.313552\pi$
$762$	41.6828i	0.0547019i
$763$	− 497.921i	− 0.652583i
$764$	33.8579	0.0443167
$765$	250.358	0.327266
$766$	1306.13	1.70513
$767$	−133.772	−0.174409
$768$	− 153.340i	− 0.199662i
$769$	782.700	1.01782	0.508908	−	0.860821i	$-0.330049\pi$
$769$	782.700	1.01782	0.508908	+	0.860821i	$0.330049\pi$
$770$	− 245.373i	− 0.318666i
$771$	223.712	0.290158
$772$	12.3995i	0.0160615i
$773$	− 964.938i	− 1.24830i	−0.781304	−	0.624151i	$-0.785445\pi$
$773$	− 964.938i	− 1.24830i	0.781304	−	0.624151i	$-0.214555\pi$
$774$	243.056i	0.314026i
$775$	103.238i	0.133210i
$776$	−995.824	−1.28328
$777$	279.384	0.359568
$778$	427.549i	0.549548i
$779$	0	0
$780$	32.7474	0.0419838
$781$	738.689i	0.945825i
$782$	247.810i	0.316892i
$783$	227.682	0.290781
$784$	611.391	0.779835
$785$	−467.418	−0.595437
$786$	−41.2907	−0.0525327
$787$	− 1343.25i	− 1.70680i	−0.521253	−	0.853402i	$-0.674535\pi$
$787$	− 1343.25i	− 1.70680i	0.521253	−	0.853402i	$-0.325465\pi$
$788$	−74.8353	−0.0949687
$789$	− 44.1469i	− 0.0559529i
$790$	−568.267	−0.719326
$791$	44.3734i	0.0560979i
$792$	838.883i	1.05920i
$793$	− 895.026i	− 1.12866i
$794$	1144.62i	1.44159i
$795$	152.121	0.191347
$796$	45.7760	0.0575075
$797$	− 1393.79i	− 1.74880i	−0.485209	−	0.874398i	$-0.661257\pi$
$797$	− 1393.79i	− 1.74880i	0.485209	−	0.874398i	$-0.338743\pi$
$798$	0	0
$799$	−1255.45	−1.57128
$800$	− 113.903i	− 0.142379i
$801$	42.3525i	0.0528746i
$802$	613.741	0.765263
$803$	976.195	1.21568
$804$	−9.73080	−0.0121030
$805$	51.4782	0.0639481
$806$	164.971i	0.204678i
$807$	−539.827	−0.668930
$808$	1098.55i	1.35959i
$809$	−1301.02	−1.60819	−0.804095	−	0.594501i	$-0.797349\pi$
$809$	−1301.02	−1.60819	−0.804095	+	0.594501i	$0.797349\pi$
$810$	35.3543i	0.0436472i
$811$	− 1476.90i	− 1.82108i	−0.413421	−	0.910540i	$-0.635666\pi$
$811$	− 1476.90i	− 1.82108i	0.413421	−	0.910540i	$-0.364334\pi$
$812$	− 8.27226i	− 0.0101875i
$813$	6.57489i	0.00808719i
$814$	2164.20	2.65872
$815$	94.5135	0.115967
$816$	472.220i	0.578701i
$817$	0	0
$818$	−494.961	−0.605087
$819$	183.225i	0.223718i
$820$	− 35.8619i	− 0.0437340i
$821$	−118.948	−0.144882	−0.0724409	−	0.997373i	$-0.523079\pi$
$821$	−118.948	−0.144882	−0.0724409	+	0.997373i	$0.523079\pi$
$822$	−594.992	−0.723835
$823$	−1049.87	−1.27566	−0.637829	−	0.770178i	$-0.720167\pi$
$823$	−1049.87	−1.27566	−0.637829	+	0.770178i	$0.720167\pi$
$824$	−110.463	−0.134056
$825$	− 641.887i	− 0.778045i
$826$	−42.1488	−0.0510275
$827$	− 366.879i	− 0.443627i	−0.975089	−	0.221813i	$-0.928802\pi$
$827$	− 366.879i	− 0.443627i	0.975089	−	0.221813i	$-0.0711976\pi$
$828$	−16.5670	−0.0200085
$829$	− 335.857i	− 0.405136i	−0.979268	−	0.202568i	$-0.935071\pi$
$829$	− 335.857i	− 0.405136i	0.979268	−	0.202568i	$-0.0649287\pi$
$830$	− 376.852i	− 0.454038i
$831$	− 263.812i	− 0.317464i
$832$	− 1004.50i	− 1.20733i
$833$	740.566	0.889035
$834$	706.524	0.847152
$835$	− 134.841i	− 0.161487i
$836$	0	0
$837$	165.906	0.198216
$838$	− 459.693i	− 0.548560i
$839$	− 1054.94i	− 1.25738i	−0.777655	−	0.628691i	$-0.783591\pi$
$839$	− 1054.94i	− 1.25738i	0.777655	−	0.628691i	$-0.216409\pi$
$840$	109.610	0.130488
$841$	773.142	0.919312
$842$	1052.25	1.24970
$843$	958.384	1.13687
$844$	− 63.9748i	− 0.0757995i
$845$	116.560	0.137941
$846$	723.757i	0.855505i
$847$	598.945	0.707137
$848$	− 397.030i	− 0.468196i
$849$	− 728.011i	− 0.857492i
$850$	558.669i	0.657258i
$851$	454.040i	0.533537i
$852$	−31.0622	−0.0364580
$853$	536.855	0.629372	0.314686	−	0.949196i	$-0.398101\pi$
$853$	536.855	0.629372	0.314686	+	0.949196i	$0.398101\pi$
$854$	− 282.004i	− 0.330216i
$855$	0	0
$856$	915.780	1.06984
$857$	− 1248.19i	− 1.45646i	−0.685331	−	0.728232i	$-0.740342\pi$
$857$	− 1248.19i	− 1.45646i	0.685331	−	0.728232i	$-0.259658\pi$
$858$	− 1025.72i	− 1.19547i
$859$	−506.289	−0.589394	−0.294697	−	0.955591i	$-0.595219\pi$
$859$	−506.289	−0.589394	−0.294697	+	0.955591i	$0.595219\pi$
$860$	−28.5288	−0.0331730
$861$	−145.007	−0.168417
$862$	−12.1249	−0.0140660
$863$	1273.02i	1.47511i	0.675286	+	0.737556i	$0.264020\pi$
$863$	1273.02i	1.47511i	−0.675286	+	0.737556i	$0.735980\pi$
$864$	−183.046	−0.211859
$865$	− 144.457i	− 0.167002i
$866$	−108.419	−0.125195
$867$	10.4389i	0.0120402i
$868$	− 6.02781i	− 0.00694448i
$869$	− 2064.13i	− 2.37529i
$870$	− 84.6399i	− 0.0972872i
$871$	−174.896	−0.200799
$872$	1722.98	1.97589
$873$	622.328i	0.712861i
$874$	0	0
$875$	284.747	0.325425
$876$	41.0494i	0.0468600i
$877$	− 307.824i	− 0.350997i	−0.984480	−	0.175499i	$-0.943846\pi$
$877$	− 307.824i	− 0.350997i	0.984480	−	0.175499i	$-0.0561537\pi$
$878$	991.224	1.12896
$879$	142.586	0.162214
$880$	759.878	0.863498
$881$	234.546	0.266227	0.133113	−	0.991101i	$-0.457503\pi$
$881$	234.546	0.266227	0.133113	+	0.991101i	$0.457503\pi$
$882$	− 426.930i	− 0.484048i
$883$	−275.426	−0.311921	−0.155960	−	0.987763i	$-0.549847\pi$
$883$	−275.426	−0.311921	−0.155960	+	0.987763i	$0.549847\pi$
$884$	− 103.528i	− 0.117113i
$885$	50.0113	0.0565100
$886$	822.667i	0.928518i
$887$	337.311i	0.380283i	0.981757	+	0.190142i	$0.0608948\pi$
$887$	337.311i	0.380283i	−0.981757	+	0.190142i	$0.939105\pi$
$888$	966.766i	1.08870i
$889$	− 27.3742i	− 0.0307921i
$890$	42.8670	0.0481652
$891$	−128.418	−0.144128
$892$	64.6905i	0.0725230i
$893$	0	0
$894$	−517.103	−0.578415
$895$	647.987i	0.724008i
$896$	− 252.498i	− 0.281806i
$897$	215.191	0.239901
$898$	−595.237	−0.662847
$899$	−49.4468	−0.0550020
$900$	−37.3492	−0.0414991
$901$	− 480.915i	− 0.533757i
$902$	−1123.27	−1.24531
$903$	115.356i	0.127747i
$904$	−153.547	−0.169853
$905$	755.231i	0.834509i
$906$	373.776i	0.412557i
$907$	− 255.540i	− 0.281742i	−0.990028	−	0.140871i	$-0.955010\pi$
$907$	− 255.540i	− 0.281742i	0.990028	−	0.140871i	$-0.0449903\pi$
$908$	− 27.8839i	− 0.0307092i
$909$	686.523	0.755251
$910$	185.450	0.203792
$911$	598.961i	0.657477i	0.944421	+	0.328738i	$0.106623\pi$
$911$	598.961i	0.657477i	−0.944421	+	0.328738i	$0.893377\pi$
$912$	0	0
$913$	1368.84	1.49928
$914$	994.307i	1.08786i
$915$	334.610i	0.365694i
$916$	28.7946	0.0314352
$917$	27.1167	0.0295711
$918$	897.800	0.977996
$919$	1449.69	1.57746	0.788730	−	0.614740i	$-0.210739\pi$
$919$	1449.69	1.57746	0.788730	+	0.614740i	$0.210739\pi$
$920$	178.132i	0.193622i
$921$	−179.606	−0.195012
$922$	− 1154.12i	− 1.25176i
$923$	−558.295	−0.604869
$924$	37.4783i	0.0405609i
$925$	1023.60i	1.10659i
$926$	− 1445.37i	− 1.56087i
$927$	69.0322i	0.0744684i
$928$	54.5552	0.0587879
$929$	−1770.96	−1.90630	−0.953152	−	0.302491i	$-0.902182\pi$
$929$	−1770.96	−1.90630	−0.953152	+	0.302491i	$0.902182\pi$
$930$	− 61.6751i	− 0.0663173i
$931$	0	0
$932$	−67.8414	−0.0727912
$933$	387.124i	0.414923i
$934$	− 849.348i	− 0.909367i
$935$	920.426	0.984413
$936$	−634.020	−0.677372
$937$	−647.635	−0.691179	−0.345589	−	0.938386i	$-0.612321\pi$
$937$	−647.635	−0.691179	−0.345589	+	0.938386i	$0.612321\pi$
$938$	−55.1061	−0.0587485
$939$	59.4539i	0.0633162i
$940$	−84.9513	−0.0903737
$941$	1355.19i	1.44016i	0.693892	+	0.720079i	$0.255894\pi$
$941$	1355.19i	1.44016i	−0.693892	+	0.720079i	$0.744106\pi$
$942$	−615.639	−0.653544
$943$	− 235.657i	− 0.249902i
$944$	− 130.528i	− 0.138271i
$945$	− 186.502i	− 0.197357i
$946$	893.580i	0.944588i
$947$	−318.095	−0.335898	−0.167949	−	0.985796i	$-0.553714\pi$
$947$	−318.095	−0.335898	−0.167949	+	0.985796i	$0.553714\pi$
$948$	86.7973	0.0915583
$949$	737.799i	0.777449i
$950$	0	0
$951$	−1107.38	−1.16443
$952$	− 346.521i	− 0.363993i
$953$	918.053i	0.963330i	0.876356	+	0.481665i	$0.159968\pi$
$953$	918.053i	0.963330i	−0.876356	+	0.481665i	$0.840032\pi$
$954$	−277.243	−0.290611
$955$	−227.507	−0.238227
$956$	127.040	0.132887
$957$	307.439	0.321252
$958$	− 1318.95i	− 1.37677i
$959$	390.747	0.407453
$960$	375.538i	0.391185i
$961$	924.969	0.962507
$962$	1635.68i	1.70029i
$963$	− 572.305i	− 0.594294i
$964$	− 99.7799i	− 0.103506i
$965$	− 83.3178i	− 0.0863397i
$966$	67.8022	0.0701886
$967$	392.392	0.405783	0.202891	−	0.979201i	$-0.434966\pi$
$967$	392.392	0.405783	0.202891	+	0.979201i	$0.434966\pi$
$968$	2072.56i	2.14107i
$969$	0	0
$970$	629.888	0.649369
$971$	471.065i	0.485134i	0.970135	+	0.242567i	$0.0779894\pi$
$971$	471.065i	0.485134i	−0.970135	+	0.242567i	$0.922011\pi$
$972$	97.9977i	0.100821i
$973$	−463.993	−0.476868
$974$	36.7808	0.0377626
$975$	485.133	0.497572
$976$	873.320	0.894795
$977$	197.318i	0.201963i	0.994888	+	0.100982i	$0.0321983\pi$
$977$	197.318i	0.201963i	−0.994888	+	0.100982i	$0.967802\pi$
$978$	124.484	0.127285
$979$	155.706i	0.159046i
$980$	50.1111	0.0511337
$981$	− 1076.75i	− 1.09761i
$982$	1253.98i	1.27697i
$983$	− 768.932i	− 0.782230i	−0.920342	−	0.391115i	$-0.872090\pi$
$983$	− 768.932i	− 0.782230i	0.920342	−	0.391115i	$-0.127910\pi$
$984$	− 501.774i	− 0.509933i
$985$	502.853	0.510511
$986$	−267.580	−0.271380
$987$	343.499i	0.348023i
$988$	0	0
$989$	−187.470	−0.189555
$990$	− 530.618i	− 0.535978i
$991$	− 1745.22i	− 1.76107i	−0.473982	−	0.880534i	$-0.657184\pi$
$991$	− 1745.22i	− 1.76107i	0.473982	−	0.880534i	$-0.342816\pi$
$992$	39.7531	0.0400737
$993$	−859.367	−0.865425
$994$	−175.907	−0.176969
$995$	−307.590	−0.309136
$996$	57.5605i	0.0577916i
$997$	−1233.15	−1.23686	−0.618430	−	0.785840i	$-0.712231\pi$
$997$	−1233.15	−1.23686	−0.618430	+	0.785840i	$0.712231\pi$
$998$	− 252.942i	− 0.253449i
$999$	1644.96	1.64661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.b.c.360.9		12
19.2	odd	18		361.3.f.g.262.1		12
19.3	odd	18		361.3.f.b.333.2		12
19.4	even	9		361.3.f.c.307.1		12
19.5	even	9		361.3.f.e.127.2		12
19.6	even	9		361.3.f.b.116.2		12
19.7	even	3		361.3.d.d.293.2		12
19.8	odd	6		361.3.d.d.69.2		12
19.9	even	9		361.3.f.g.299.1		12
19.10	odd	18		19.3.f.a.14.2	✓	12
19.11	even	3		361.3.d.f.69.5		12
19.12	odd	6		361.3.d.f.293.5		12
19.13	odd	18		361.3.f.f.116.1		12
19.14	odd	18		361.3.f.c.127.1		12
19.15	odd	18		361.3.f.e.307.2		12
19.16	even	9		361.3.f.f.333.1		12
19.17	even	9		19.3.f.a.15.2	yes	12
19.18	odd	2	inner	361.3.b.c.360.4		12
57.17	odd	18		171.3.ba.b.91.1		12
57.29	even	18		171.3.ba.b.109.1		12
76.55	odd	18		304.3.z.a.129.2		12
76.67	even	18		304.3.z.a.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.2	✓	12	19.10	odd	18
19.3.f.a.15.2	yes	12	19.17	even	9
171.3.ba.b.91.1		12	57.17	odd	18
171.3.ba.b.109.1		12	57.29	even	18
304.3.z.a.33.2		12	76.67	even	18
304.3.z.a.129.2		12	76.55	odd	18
361.3.b.c.360.4		12	19.18	odd	2	inner
361.3.b.c.360.9		12	1.1	even	1	trivial
361.3.d.d.69.2		12	19.8	odd	6
361.3.d.d.293.2		12	19.7	even	3
361.3.d.f.69.5		12	19.11	even	3
361.3.d.f.293.5		12	19.12	odd	6
361.3.f.b.116.2		12	19.6	even	9
361.3.f.b.333.2		12	19.3	odd	18
361.3.f.c.127.1		12	19.14	odd	18
361.3.f.c.307.1		12	19.4	even	9
361.3.f.e.127.2		12	19.5	even	9
361.3.f.e.307.2		12	19.15	odd	18
361.3.f.f.116.1		12	19.13	odd	18
361.3.f.f.333.1		12	19.16	even	9
361.3.f.g.262.1		12	19.2	odd	18
361.3.f.g.299.1		12	19.9	even	9

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.89323i q^{2} +1.94309i q^{3} +0.415663 q^{4} -2.79304 q^{5} -3.67872 q^{6} +2.41591 q^{7} +8.35989i q^{8} +5.22441 q^{9} +O(q^{10})\)	\(q+1.89323i q^{2} +1.94309i q^{3} +0.415663 q^{4} -2.79304 q^{5} -3.67872 q^{6} +2.41591 q^{7} +8.35989i q^{8} +5.22441 q^{9} -5.28787i q^{10} +19.2072 q^{11} +0.807671i q^{12} +14.5166i q^{13} +4.57389i q^{14} -5.42712i q^{15} -14.1646 q^{16} -17.1573 q^{17} +9.89103i q^{18} -1.16096 q^{20} +4.69433i q^{21} +36.3637i q^{22} -7.62897 q^{23} -16.2440 q^{24} -17.1990 q^{25} -27.4834 q^{26} +27.6393i q^{27} +1.00421 q^{28} -8.23762i q^{29} +10.2748 q^{30} -6.00256i q^{31} +6.62269i q^{32} +37.3213i q^{33} -32.4828i q^{34} -6.74773 q^{35} +2.17159 q^{36} -59.5153i q^{37} -28.2071 q^{39} -23.3495i q^{40} +30.8898i q^{41} -8.88747 q^{42} +24.5734 q^{43} +7.98373 q^{44} -14.5920 q^{45} -14.4434i q^{46} +73.1731 q^{47} -27.5230i q^{48} -43.1634 q^{49} -32.5617i q^{50} -33.3381i q^{51} +6.03403i q^{52} +28.0298i q^{53} -52.3276 q^{54} -53.6464 q^{55} +20.1968i q^{56} +15.5957 q^{58} +9.21508i q^{59} -2.25585i q^{60} -61.6552 q^{61} +11.3643 q^{62} +12.6217 q^{63} -69.1966 q^{64} -40.5455i q^{65} -70.6580 q^{66} +12.0480i q^{67} -7.13165 q^{68} -14.8238i q^{69} -12.7750i q^{70} +38.4590i q^{71} +43.6754i q^{72} +50.8244 q^{73} +112.676 q^{74} -33.4191i q^{75} +46.4029 q^{77} -53.4026i q^{78} -107.466i q^{79} +39.5621 q^{80} -6.68592 q^{81} -58.4816 q^{82} +71.2672 q^{83} +1.95126i q^{84} +47.9209 q^{85} +46.5232i q^{86} +16.0064 q^{87} +160.570i q^{88} +8.10667i q^{89} -27.6260i q^{90} +35.0709i q^{91} -3.17108 q^{92} +11.6635 q^{93} +138.534i q^{94} -12.8685 q^{96} +119.119i q^{97} -81.7184i q^{98} +100.346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 24 q^{6} - 12 q^{7} + 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 - 24 * q^6 - 12 * q^7 + 18 * q^9	\( 12 q + 6 q^{5} - 24 q^{6} - 12 q^{7} + 18 q^{9} + 36 q^{11} - 96 q^{16} - 66 q^{17} - 90 q^{20} + 120 q^{23} + 36 q^{24} - 66 q^{25} - 42 q^{26} + 210 q^{28} - 48 q^{30} - 270 q^{35} + 144 q^{36} - 108 q^{39} + 234 q^{42} + 102 q^{43} - 42 q^{44} + 6 q^{45} + 228 q^{47} + 48 q^{49} + 288 q^{54} - 66 q^{55} - 132 q^{58} + 102 q^{61} - 438 q^{62} + 42 q^{63} - 54 q^{64} - 276 q^{66} + 60 q^{68} + 36 q^{73} - 78 q^{74} + 246 q^{77} - 468 q^{80} + 204 q^{81} + 96 q^{82} + 312 q^{83} - 210 q^{85} - 138 q^{87} + 480 q^{92} - 240 q^{93} + 558 q^{96} - 318 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 - 24 * q^6 - 12 * q^7 + 18 * q^9 + 36 * q^11 - 96 * q^16 - 66 * q^17 - 90 * q^20 + 120 * q^23 + 36 * q^24 - 66 * q^25 - 42 * q^26 + 210 * q^28 - 48 * q^30 - 270 * q^35 + 144 * q^36 - 108 * q^39 + 234 * q^42 + 102 * q^43 - 42 * q^44 + 6 * q^45 + 228 * q^47 + 48 * q^49 + 288 * q^54 - 66 * q^55 - 132 * q^58 + 102 * q^61 - 438 * q^62 + 42 * q^63 - 54 * q^64 - 276 * q^66 + 60 * q^68 + 36 * q^73 - 78 * q^74 + 246 * q^77 - 468 * q^80 + 204 * q^81 + 96 * q^82 + 312 * q^83 - 210 * q^85 - 138 * q^87 + 480 * q^92 - 240 * q^93 + 558 * q^96 - 318 * q^99

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