LMFDB - Embedded newform 325.2.c.g.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(51,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("325.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.c (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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5089536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 16x^2 - 24*x + 18
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.4
Root			$-1.33641 + 1.33641i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.2.c.g.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.571993i q^{2} +0.428007 q^{3} +1.67282 q^{4} +0.244817i q^{6} +2.67282i q^{7} +2.10083i q^{8} -2.81681 q^{9} +5.10083i q^{11} +0.715980 q^{12} +(1.57199 - 3.24482i) q^{13} -1.52884 q^{14} +2.14399 q^{16} +5.34565 q^{17} -1.61120i q^{18} -6.24482i q^{19} +1.14399i q^{21} -2.91764 q^{22} -2.42801 q^{23} +0.899170i q^{24} +(1.85601 + 0.899170i) q^{26} -2.48963 q^{27} +4.47116i q^{28} +2.67282 q^{29} +0.244817i q^{31} +5.42801i q^{32} +2.18319i q^{33} +3.05767i q^{34} -4.71203 q^{36} -3.32718i q^{37} +3.57199 q^{38} +(0.672824 - 1.38880i) q^{39} -6.48963i q^{41} -0.654353 q^{42} -10.9176 q^{43} +8.53279i q^{44} -1.38880i q^{46} -2.67282i q^{47} +0.917641 q^{48} -0.143987 q^{49} +2.28797 q^{51} +(2.62967 - 5.42801i) q^{52} +4.20166 q^{53} -1.42405i q^{54} -5.61515 q^{56} -2.67282i q^{57} +1.52884i q^{58} -0.899170i q^{59} -5.81681 q^{61} -0.140034 q^{62} -7.52884i q^{63} +1.18319 q^{64} -1.24877 q^{66} +2.18319i q^{67} +8.94233 q^{68} -1.03920 q^{69} -6.24482i q^{71} -5.91764i q^{72} -10.9608i q^{73} +1.90312 q^{74} -10.4465i q^{76} -13.6336 q^{77} +(0.794386 + 0.384851i) q^{78} -3.63362 q^{79} +7.38485 q^{81} +3.71203 q^{82} +9.81681i q^{83} +1.91369i q^{84} -6.24482i q^{86} +1.14399 q^{87} -10.7160 q^{88} +7.63362i q^{89} +(8.67282 + 4.20166i) q^{91} -4.06163 q^{92} +0.104783i q^{93} +1.52884 q^{94} +2.32322i q^{96} -11.3456i q^{97} -0.0823593i q^{98} -14.3681i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 8 q^{14} + 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} + 14 q^{26} + 28 q^{27} - 4 q^{29} - 34 q^{36} + 20 q^{38} - 16 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48}+ \cdots - 8 q^{94}+O(q^{100}) $ 6 * q + 4 * q^3 - 10 * q^4 + 6 * q^9 + 8 * q^13 + 8 * q^14 + 10 * q^16 - 8 * q^17 + 24 * q^22 - 16 * q^23 + 14 * q^26 + 28 * q^27 - 4 * q^29 - 34 * q^36 + 20 * q^38 - 16 * q^39 - 44 * q^42 - 24 * q^43 - 36 * q^48 + 2 * q^49 + 8 * q^51 - 20 * q^52 - 12 * q^53 - 48 * q^56 - 12 * q^61 - 8 * q^62 + 30 * q^64 + 24 * q^66 + 88 * q^68 - 32 * q^69 + 20 * q^74 - 36 * q^77 + 52 * q^78 + 24 * q^79 + 30 * q^81 + 28 * q^82 + 4 * q^87 - 60 * q^88 + 32 * q^91 + 20 * q^92 - 8 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			0.571993i			0.404460i	0.979338	+	0.202230i	$0.0648189\pi$
$2$			0.571993i			0.404460i	−0.979338	+	0.202230i	$0.935181\pi$
$3$	0.428007			0.247110			0.123555	−	0.992338i	$-0.460570\pi$
$3$	0.428007			0.247110			0.123555	+	0.992338i	$0.460570\pi$
$4$	1.67282			0.836412
$5$		0			0
$5$		0			0
$6$			0.244817i			0.0999461i
$7$			2.67282i			1.01023i	0.863051	+	0.505116i	$0.168550\pi$
$7$			2.67282i			1.01023i	−0.863051	+	0.505116i	$0.831450\pi$
$8$			2.10083i			0.742756i
$9$	−2.81681			−0.938937
$10$		0			0
$11$			5.10083i			1.53796i	0.639274	+	0.768979i	$0.279235\pi$
$11$			5.10083i			1.53796i	−0.639274	+	0.768979i	$0.720765\pi$
$12$	0.715980			0.206686
$13$	1.57199	−	3.24482i	0.435992	−	0.899950i
$13$	1.57199	−	3.24482i	0.435992	−	0.899950i
$14$	−1.52884			−0.408599
$15$		0			0
$16$	2.14399			0.535997
$17$	5.34565			1.29651			0.648255	−	0.761423i	$-0.275499\pi$
$17$	5.34565			1.29651			0.648255	+	0.761423i	$0.275499\pi$
$18$		−	1.61120i		−	0.379763i
$19$		−	6.24482i		−	1.43266i	−0.697762	−	0.716330i	$-0.745821\pi$
$19$		−	6.24482i		−	1.43266i	0.697762	−	0.716330i	$-0.254179\pi$
$20$		0			0
$21$			1.14399i			0.249638i
$22$	−2.91764			−0.622043
$23$	−2.42801			−0.506274			−0.253137	−	0.967430i	$-0.581462\pi$
$23$	−2.42801			−0.506274			−0.253137	+	0.967430i	$0.581462\pi$
$24$			0.899170i			0.183542i
$25$		0			0
$26$	1.85601	+	0.899170i	0.363994	+	0.176342i
$27$	−2.48963			−0.479130
$28$			4.47116i			0.844970i
$29$	2.67282			0.496331			0.248165	−	0.968718i	$-0.420172\pi$
$29$	2.67282			0.496331			0.248165	+	0.968718i	$0.420172\pi$
$30$		0			0
$31$			0.244817i			0.0439704i	0.999758	+	0.0219852i	$0.00699867\pi$
$31$			0.244817i			0.0439704i	−0.999758	+	0.0219852i	$0.993001\pi$
$32$			5.42801i			0.959545i
$33$			2.18319i			0.380045i
$34$			3.05767i			0.524387i
$35$		0			0
$36$	−4.71203			−0.785338
$37$		−	3.32718i		−	0.546984i	−0.961874	−	0.273492i	$-0.911821\pi$
$37$		−	3.32718i		−	0.546984i	0.961874	−	0.273492i	$-0.0881788\pi$
$38$	3.57199			0.579454
$39$	0.672824	−	1.38880i	0.107738	−	0.222387i
$40$		0			0
$41$		−	6.48963i		−	1.01351i	−0.862090	−	0.506755i	$-0.830845\pi$
$41$		−	6.48963i		−	1.01351i	0.862090	−	0.506755i	$-0.169155\pi$
$42$	−0.654353			−0.100969
$43$	−10.9176			−1.66492			−0.832462	−	0.554082i	$-0.813070\pi$
$43$	−10.9176			−1.66492			−0.832462	+	0.554082i	$0.813070\pi$
$44$			8.53279i			1.28637i
$45$		0			0
$46$		−	1.38880i		−	0.204768i
$47$		−	2.67282i		−	0.389871i	−0.980816	−	0.194936i	$-0.937550\pi$
$47$		−	2.67282i		−	0.389871i	0.980816	−	0.194936i	$-0.0624498\pi$
$48$	0.917641			0.132450
$49$	−0.143987			−0.0205695
$50$		0			0
$51$	2.28797			0.320380
$52$	2.62967	−	5.42801i	0.364669	−	0.752729i
$53$	4.20166			0.577143			0.288571	−	0.957458i	$-0.406820\pi$
$53$	4.20166			0.577143			0.288571	+	0.957458i	$0.406820\pi$
$54$		−	1.42405i		−	0.193789i
$55$		0			0
$56$	−5.61515			−0.750356
$57$		−	2.67282i		−	0.354024i
$58$			1.52884i			0.200746i
$59$		−	0.899170i		−	0.117062i	−0.998286	−	0.0585310i	$-0.981358\pi$
$59$		−	0.899170i		−	0.117062i	0.998286	−	0.0585310i	$-0.0186416\pi$
$60$		0			0
$61$	−5.81681			−0.744766			−0.372383	−	0.928079i	$-0.621459\pi$
$61$	−5.81681			−0.744766			−0.372383	+	0.928079i	$0.621459\pi$
$62$	−0.140034			−0.0177843
$63$		−	7.52884i		−	0.948544i
$64$	1.18319			0.147899
$65$		0			0
$66$	−1.24877			−0.153713
$67$			2.18319i			0.266719i	0.991068	+	0.133360i	$0.0425765\pi$
$67$			2.18319i			0.266719i	−0.991068	+	0.133360i	$0.957423\pi$
$68$	8.94233			1.08442
$69$	−1.03920			−0.125105
$70$		0			0
$71$		−	6.24482i		−	0.741123i	−0.928808	−	0.370562i	$-0.879165\pi$
$71$		−	6.24482i		−	0.741123i	0.928808	−	0.370562i	$-0.120835\pi$
$72$		−	5.91764i		−	0.697401i
$73$		−	10.9608i		−	1.28286i	−0.767180	−	0.641432i	$-0.778341\pi$
$73$		−	10.9608i		−	1.28286i	0.767180	−	0.641432i	$-0.221659\pi$
$74$	1.90312			0.221233
$75$		0			0
$76$		−	10.4465i		−	1.19829i
$77$	−13.6336			−1.55370
$78$	0.794386	+	0.384851i	0.0899465	+	0.0435758i
$79$	−3.63362			−0.408814			−0.204407	−	0.978886i	$-0.565527\pi$
$79$	−3.63362			−0.408814			−0.204407	+	0.978886i	$0.565527\pi$
$80$		0			0
$81$	7.38485			0.820539
$82$	3.71203			0.409925
$83$			9.81681i			1.07753i	0.842455	+	0.538767i	$0.181110\pi$
$83$			9.81681i			1.07753i	−0.842455	+	0.538767i	$0.818890\pi$
$84$			1.91369i			0.208800i
$85$		0			0
$86$		−	6.24482i		−	0.673396i
$87$	1.14399			0.122648
$88$	−10.7160			−1.14233
$89$			7.63362i			0.809162i	0.914502	+	0.404581i	$0.132583\pi$
$89$			7.63362i			0.809162i	−0.914502	+	0.404581i	$0.867417\pi$
$90$		0			0
$91$	8.67282	+	4.20166i	0.909159	+	0.440454i
$92$	−4.06163			−0.423454
$93$			0.104783i			0.0108655i
$94$	1.52884			0.157688
$95$		0			0
$96$			2.32322i			0.237113i
$97$		−	11.3456i		−	1.15198i	−0.817458	−	0.575988i	$-0.804617\pi$
$97$		−	11.3456i		−	1.15198i	0.817458	−	0.575988i	$-0.195383\pi$
$98$		−	0.0823593i		−	0.00831955i
$99$		−	14.3681i		−	1.44405i
$100$		0			0
$101$	−10.8560			−1.08021			−0.540107	−	0.841596i	$-0.681616\pi$
$101$	−10.8560			−1.08021			−0.540107	+	0.841596i	$0.681616\pi$
$102$			1.30871i			0.129581i
$103$	10.6297			1.04737			0.523686	−	0.851911i	$-0.324556\pi$
$103$	10.6297			1.04737			0.523686	+	0.851911i	$0.324556\pi$
$104$	6.81681	+	3.30249i	0.668443	+	0.323836i
$105$		0			0
$106$			2.40332i			0.233431i
$107$	−0.140034			−0.0135376			−0.00676878	−	0.999977i	$-0.502155\pi$
$107$	−0.140034			−0.0135376			−0.00676878	+	0.999977i	$0.502155\pi$
$108$	−4.16472			−0.400750
$109$		−	9.05767i		−	0.867568i	−0.901017	−	0.433784i	$-0.857178\pi$
$109$		−	9.05767i		−	0.867568i	0.901017	−	0.433784i	$-0.142822\pi$
$110$		0			0
$111$		−	1.42405i		−	0.135165i
$112$			5.73050i			0.541481i
$113$	−12.9793			−1.22099			−0.610493	−	0.792021i	$-0.709029\pi$
$113$	−12.9793			−1.22099			−0.610493	+	0.792021i	$0.709029\pi$
$114$	1.52884			0.143189
$115$		0			0
$116$	4.47116			0.415137
$117$	−4.42801	+	9.14003i	−0.409369	+	0.844996i
$118$	0.514319			0.0473469
$119$			14.2880i			1.30978i
$120$		0			0
$121$	−15.0185			−1.36532
$122$		−	3.32718i		−	0.301228i
$123$		−	2.77761i		−	0.250448i
$124$			0.409536i			0.0367774i
$125$		0			0
$126$	4.30644			0.383649
$127$	12.0616			1.07030			0.535148	−	0.844758i	$-0.320256\pi$
$127$	12.0616			1.07030			0.535148	+	0.844758i	$0.320256\pi$
$128$			11.5328i			1.01936i
$129$	−4.67282			−0.411419
$130$		0			0
$131$	7.63362			0.666953			0.333476	−	0.942758i	$-0.391778\pi$
$131$	7.63362			0.666953			0.333476	+	0.942758i	$0.391778\pi$
$132$			3.65209i			0.317874i
$133$	16.6913			1.44732
$134$	−1.24877			−0.107877
$135$		0			0
$136$			11.2303i			0.962990i
$137$			3.43196i			0.293212i	0.989195	+	0.146606i	$0.0468350\pi$
$137$			3.43196i			0.293212i	−0.989195	+	0.146606i	$0.953165\pi$
$138$		−	0.594417i		−	0.0506002i
$139$	−0.942326			−0.0799270			−0.0399635	−	0.999201i	$-0.512724\pi$
$139$	−0.942326			−0.0799270			−0.0399635	+	0.999201i	$0.512724\pi$
$140$		0			0
$141$		−	1.14399i		−	0.0963410i
$142$	3.57199			0.299755
$143$	16.5513	+	8.01847i	1.38409	+	0.670538i
$144$	−6.03920			−0.503267
$145$		0			0
$146$	6.26950			0.518868
$147$	−0.0616272			−0.00508293
$148$		−	5.56578i		−	0.457504i
$149$			11.3456i			0.929472i	0.885449	+	0.464736i	$0.153851\pi$
$149$			11.3456i			0.929472i	−0.885449	+	0.464736i	$0.846149\pi$
$150$		0			0
$151$			21.0224i			1.71078i	0.517984	+	0.855390i	$0.326683\pi$
$151$			21.0224i			1.71078i	−0.517984	+	0.855390i	$0.673317\pi$
$152$	13.1193			1.06412
$153$	−15.0577			−1.21734
$154$		−	7.79834i		−	0.628408i
$155$		0			0
$156$	1.12552	−	2.32322i	0.0901134	−	0.186007i
$157$	9.83528			0.784941			0.392470	−	0.919765i	$-0.371621\pi$
$157$	9.83528			0.784941			0.392470	+	0.919765i	$0.371621\pi$
$158$		−	2.07841i		−	0.165349i
$159$	1.79834			0.142618
$160$		0			0
$161$		−	6.48963i		−	0.511455i
$162$			4.22408i			0.331875i
$163$		−	12.3849i		−	0.970056i	−0.874499	−	0.485028i	$-0.838809\pi$
$163$		−	12.3849i		−	0.970056i	0.874499	−	0.485028i	$-0.161191\pi$
$164$		−	10.8560i		−	0.847712i
$165$		0			0
$166$	−5.61515			−0.435820
$167$			8.50811i			0.658377i	0.944264	+	0.329188i	$0.106775\pi$
$167$			8.50811i			0.658377i	−0.944264	+	0.329188i	$0.893225\pi$
$168$	−2.40332			−0.185420
$169$	−8.05767	−	10.2017i	−0.619821	−	0.784743i
$170$		0			0
$171$			17.5905i			1.34518i
$172$	−18.2633			−1.39256
$173$	−21.5473			−1.63821			−0.819106	−	0.573643i	$-0.805530\pi$
$173$	−21.5473			−1.63821			−0.819106	+	0.573643i	$0.805530\pi$
$174$			0.654353i			0.0496063i
$175$		0			0
$176$			10.9361i			0.824340i
$177$		−	0.384851i		−	0.0289271i
$178$	−4.36638			−0.327274
$179$	−2.56804			−0.191944			−0.0959722	−	0.995384i	$-0.530596\pi$
$179$	−2.56804			−0.191944			−0.0959722	+	0.995384i	$0.530596\pi$
$180$		0			0
$181$	13.7305			1.02058			0.510290	−	0.860002i	$-0.329538\pi$
$181$	13.7305			1.02058			0.510290	+	0.860002i	$0.329538\pi$
$182$	−2.40332	+	4.96080i	−0.178146	+	0.367719i
$183$	−2.48963			−0.184039
$184$		−	5.10083i		−	0.376038i
$185$		0			0
$186$	−0.0599353			−0.00439467
$187$			27.2672i			1.99398i
$188$		−	4.47116i		−	0.326093i
$189$		−	6.65435i		−	0.484033i
$190$		0			0
$191$	−10.6913			−0.773595			−0.386797	−	0.922165i	$-0.626419\pi$
$191$	−10.6913			−0.773595			−0.386797	+	0.922165i	$0.626419\pi$
$192$	0.506413			0.0365472
$193$			19.2593i			1.38632i	0.720785	+	0.693159i	$0.243781\pi$
$193$			19.2593i			1.38632i	−0.720785	+	0.693159i	$0.756219\pi$
$194$	6.48963			0.465929
$195$		0			0
$196$	−0.240864			−0.0172046
$197$		−	17.1809i		−	1.22409i	−0.790823	−	0.612045i	$-0.790347\pi$
$197$		−	17.1809i		−	1.22409i	0.790823	−	0.612045i	$-0.209653\pi$
$198$	8.21844			0.584059
$199$	−11.5473			−0.818567			−0.409283	−	0.912407i	$-0.634221\pi$
$199$	−11.5473			−0.818567			−0.409283	+	0.912407i	$0.634221\pi$
$200$		0			0
$201$			0.934420i			0.0659089i
$202$		−	6.20957i		−	0.436904i
$203$			7.14399i			0.501410i
$204$	3.82738			0.267970
$205$		0			0
$206$			6.08010i			0.423621i
$207$	6.83923			0.475360
$208$	3.37033	−	6.95684i	0.233691	−	0.482370i
$209$	31.8538			2.20337
$210$		0			0
$211$	24.1233			1.66071			0.830357	−	0.557232i	$-0.188137\pi$
$211$	24.1233			1.66071			0.830357	+	0.557232i	$0.188137\pi$
$212$	7.02864			0.482729
$213$		−	2.67282i		−	0.183139i
$214$		−	0.0800983i		−	0.00547541i
$215$		0			0
$216$		−	5.23030i		−	0.355877i
$217$	−0.654353			−0.0444203
$218$	5.18093			0.350897
$219$		−	4.69129i		−	0.317008i
$220$		0			0
$221$	8.40332	−	17.3456i	0.565269	−	1.16679i
$222$	0.814549			0.0546690
$223$			5.73050i			0.383743i	0.981420	+	0.191871i	$0.0614556\pi$
$223$			5.73050i			0.383743i	−0.981420	+	0.191871i	$0.938544\pi$
$224$	−14.5081			−0.969364
$225$		0			0
$226$		−	7.42405i		−	0.493841i
$227$			2.95289i			0.195990i	0.995187	+	0.0979951i	$0.0312430\pi$
$227$			2.95289i			0.195990i	−0.995187	+	0.0979951i	$0.968757\pi$
$228$		−	4.47116i		−	0.296110i
$229$			25.2593i			1.66918i	0.550869	+	0.834592i	$0.314297\pi$
$229$			25.2593i			1.66918i	−0.550869	+	0.834592i	$0.685703\pi$
$230$		0			0
$231$	−5.83528			−0.383933
$232$			5.61515i			0.368653i
$233$	23.3456			1.52942			0.764712	−	0.644372i	$-0.222881\pi$
$233$	23.3456			1.52942			0.764712	+	0.644372i	$0.222881\pi$
$234$	−5.22804	−	2.53279i	−0.341768	−	0.165574i
$235$		0			0
$236$		−	1.50415i		−	0.0979120i
$237$	−1.55521			−0.101022
$238$	−8.17262			−0.529753
$239$			3.79213i			0.245292i	0.992450	+	0.122646i	$0.0391380\pi$
$239$			3.79213i			0.245292i	−0.992450	+	0.122646i	$0.960862\pi$
$240$		0			0
$241$		−	3.43196i		−	0.221072i	−0.993872	−	0.110536i	$-0.964743\pi$
$241$		−	3.43196i		−	0.221072i	0.993872	−	0.110536i	$-0.0352567\pi$
$242$		−	8.59046i		−	0.552216i
$243$	10.6297			0.681893
$244$	−9.73050			−0.622931
$245$		0			0
$246$	1.58877			0.101296
$247$	−20.2633	−	9.81681i	−1.28932	−	0.624629i
$248$	−0.514319			−0.0326593
$249$			4.20166i			0.266269i
$250$		0			0
$251$	−25.4689			−1.60758			−0.803791	−	0.594911i	$-0.797187\pi$
$251$	−25.4689			−1.60758			−0.803791	+	0.594911i	$0.797187\pi$
$252$		−	12.5944i		−	0.793374i
$253$		−	12.3849i		−	0.778629i
$254$			6.89917i			0.432892i
$255$		0			0
$256$	−4.23030			−0.264394
$257$	−9.26724			−0.578075			−0.289037	−	0.957318i	$-0.593335\pi$
$257$	−9.26724			−0.578075			−0.289037	+	0.957318i	$0.593335\pi$
$258$		−	2.67282i		−	0.166403i
$259$	8.89296			0.552581
$260$		0			0
$261$	−7.52884			−0.466023
$262$			4.36638i			0.269756i
$263$	8.14794			0.502423			0.251212	−	0.967932i	$-0.419171\pi$
$263$	8.14794			0.502423			0.251212	+	0.967932i	$0.419171\pi$
$264$	−4.58651			−0.282280
$265$		0			0
$266$			9.54731i			0.585383i
$267$			3.26724i			0.199952i
$268$			3.65209i			0.223087i
$269$	1.14399			0.0697501			0.0348750	−	0.999392i	$-0.488897\pi$
$269$	1.14399			0.0697501			0.0348750	+	0.999392i	$0.488897\pi$
$270$		0			0
$271$		−	3.18714i		−	0.193605i	−0.995304	−	0.0968026i	$-0.969138\pi$
$271$		−	3.18714i		−	0.193605i	0.995304	−	0.0968026i	$-0.0308615\pi$
$272$	11.4610			0.694925
$273$	3.71203	+	1.79834i	0.224662	+	0.108840i
$274$	−1.96306			−0.118593
$275$		0			0
$276$	−1.73840			−0.104640
$277$	−7.62571			−0.458185			−0.229092	−	0.973405i	$-0.573576\pi$
$277$	−7.62571			−0.458185			−0.229092	+	0.973405i	$0.573576\pi$
$278$		−	0.539004i		−	0.0323273i
$279$		−	0.689603i		−	0.0412854i
$280$		0			0
$281$		−	20.2386i		−	1.20733i	−0.797237	−	0.603667i	$-0.793706\pi$
$281$		−	20.2386i		−	1.20733i	0.797237	−	0.603667i	$-0.206294\pi$
$282$	0.654353			0.0389661
$283$	−19.8969			−1.18275			−0.591374	−	0.806397i	$-0.701414\pi$
$283$	−19.8969			−1.18275			−0.591374	+	0.806397i	$0.701414\pi$
$284$		−	10.4465i		−	0.619884i
$285$		0			0
$286$	−4.58651	+	9.46721i	−0.271206	+	0.559808i
$287$	17.3456			1.02388
$288$		−	15.2897i		−	0.900952i
$289$	11.5759			0.680938
$290$		0			0
$291$		−	4.85601i		−	0.284665i
$292$		−	18.3355i		−	1.07300i
$293$			26.0185i			1.52002i	0.649914	+	0.760008i	$0.274805\pi$
$293$			26.0185i			1.52002i	−0.649914	+	0.760008i	$0.725195\pi$
$294$		−	0.0352503i		−	0.00205584i
$295$		0			0
$296$	6.98983			0.406276
$297$		−	12.6992i		−	0.736882i
$298$	−6.48963			−0.375934
$299$	−3.81681	+	7.87844i	−0.220732	+	0.455622i
$300$		0			0
$301$		−	29.1809i		−	1.68196i
$302$	−12.0247			−0.691943
$303$	−4.64645			−0.266931
$304$		−	13.3888i		−	0.767901i
$305$		0			0
$306$		−	8.61289i		−	0.492366i
$307$			2.39276i			0.136562i	0.997666	+	0.0682809i	$0.0217514\pi$
$307$			2.39276i			0.136562i	−0.997666	+	0.0682809i	$0.978249\pi$
$308$	−22.8066			−1.29953
$309$	4.54957			0.258816
$310$		0			0
$311$	3.54731			0.201149			0.100575	−	0.994930i	$-0.467932\pi$
$311$	3.54731			0.201149			0.100575	+	0.994930i	$0.467932\pi$
$312$	2.91764	+	1.41349i	0.165179	+	0.0800230i
$313$	−4.97927			−0.281445			−0.140722	−	0.990049i	$-0.544943\pi$
$313$	−4.97927			−0.281445			−0.140722	+	0.990049i	$0.544943\pi$
$314$			5.62571i			0.317477i
$315$		0			0
$316$	−6.07841			−0.341937
$317$		−	18.5944i		−	1.04437i	−0.852833	−	0.522183i	$-0.825118\pi$
$317$		−	18.5944i		−	1.04437i	0.852833	−	0.522183i	$-0.174882\pi$
$318$			1.02864i			0.0576831i
$319$			13.6336i			0.763336i
$320$		0			0
$321$	−0.0599353			−0.00334526
$322$	3.71203			0.206863
$323$		−	33.3826i		−	1.85746i
$324$	12.3536			0.686309
$325$		0			0
$326$	7.08405			0.392349
$327$		−	3.87675i		−	0.214385i
$328$	13.6336			0.752791
$329$	7.14399			0.393861
$330$		0			0
$331$		−	5.91990i		−	0.325387i	−0.986677	−	0.162694i	$-0.947982\pi$
$331$		−	5.91990i		−	0.325387i	0.986677	−	0.162694i	$-0.0520182\pi$
$332$			16.4218i			0.901263i
$333$			9.37202i			0.513584i
$334$	−4.86658			−0.266287
$335$		0			0
$336$			2.45269i			0.133805i
$337$	−13.9216			−0.758358			−0.379179	−	0.925323i	$-0.623793\pi$
$337$	−13.9216			−0.758358			−0.379179	+	0.925323i	$0.623793\pi$
$338$	5.83528	−	4.60894i	0.317397	−	0.250693i
$339$	−5.55521			−0.301718
$340$		0			0
$341$	−1.24877			−0.0676247
$342$	−10.0616			−0.544070
$343$			18.3249i			0.989452i
$344$		−	22.9361i		−	1.23663i
$345$		0			0
$346$		−	12.3249i		−	0.662592i
$347$	−7.65831			−0.411119			−0.205560	−	0.978645i	$-0.565901\pi$
$347$	−7.65831			−0.411119			−0.205560	+	0.978645i	$0.565901\pi$
$348$	1.91369			0.102584
$349$			11.1809i			0.598501i	0.954175	+	0.299251i	$0.0967367\pi$
$349$			11.1809i			0.598501i	−0.954175	+	0.299251i	$0.903263\pi$
$350$		0			0
$351$	−3.91369	+	8.07841i	−0.208897	+	0.431193i
$352$	−27.6873			−1.47574
$353$		−	9.65209i		−	0.513729i	−0.966447	−	0.256864i	$-0.917311\pi$
$353$		−	9.65209i		−	0.513729i	0.966447	−	0.256864i	$-0.0826894\pi$
$354$	0.220132			0.0116999
$355$		0			0
$356$			12.7697i			0.676793i
$357$			6.11535i			0.323659i
$358$		−	1.46890i		−	0.0776339i
$359$			9.51206i			0.502027i	0.967984	+	0.251014i	$0.0807639\pi$
$359$			9.51206i			0.502027i	−0.967984	+	0.251014i	$0.919236\pi$
$360$		0			0
$361$	−19.9977			−1.05251
$362$			7.85375i			0.412784i
$363$	−6.42801			−0.337383
$364$	14.5081	+	7.02864i	0.760431	+	0.368401i
$365$		0			0
$366$		−	1.42405i		−	0.0744365i
$367$	17.0040			0.887599			0.443800	−	0.896126i	$-0.353630\pi$
$367$	17.0040			0.887599			0.443800	+	0.896126i	$0.353630\pi$
$368$	−5.20561			−0.271361
$369$			18.2801i			0.951622i
$370$		0			0
$371$			11.2303i			0.583048i
$372$			0.175284i			0.00908805i
$373$	1.83528			0.0950273			0.0475136	−	0.998871i	$-0.484870\pi$
$373$	1.83528			0.0950273			0.0475136	+	0.998871i	$0.484870\pi$
$374$	−15.5967			−0.806485
$375$		0			0
$376$	5.61515			0.289579
$377$	4.20166	−	8.67282i	0.216397	−	0.446673i
$378$	3.80624			0.195772
$379$		−	32.3681i		−	1.66264i	−0.555797	−	0.831318i	$-0.687587\pi$
$379$		−	32.3681i		−	1.66264i	0.555797	−	0.831318i	$-0.312413\pi$
$380$		0			0
$381$	5.16246			0.264481
$382$		−	6.11535i		−	0.312888i
$383$			28.1417i			1.43798i	0.695023	+	0.718988i	$0.255394\pi$
$383$			28.1417i			1.43798i	−0.695023	+	0.718988i	$0.744606\pi$
$384$			4.93611i			0.251895i
$385$		0			0
$386$	−11.0162			−0.560710
$387$	30.7529			1.56326
$388$		−	18.9793i		−	0.963526i
$389$	−31.9585			−1.62036			−0.810181	−	0.586180i	$-0.800631\pi$
$389$	−31.9585			−1.62036			−0.810181	+	0.586180i	$0.800631\pi$
$390$		0			0
$391$	−12.9793			−0.656390
$392$		−	0.302491i		−	0.0152781i
$393$	3.26724			0.164811
$394$	9.82738			0.495096
$395$		0			0
$396$		−	24.0353i		−	1.20782i
$397$		−	12.7098i		−	0.637885i	−0.947774	−	0.318942i	$-0.896672\pi$
$397$		−	12.7098i		−	0.637885i	0.947774	−	0.318942i	$-0.103328\pi$
$398$		−	6.60498i		−	0.331078i
$399$	7.14399			0.357647
$400$		0			0
$401$		−	0.979268i		−	0.0489023i	−0.999701	−	0.0244512i	$-0.992216\pi$
$401$		−	0.979268i		−	0.0489023i	0.999701	−	0.0244512i	$-0.00778382\pi$
$402$	−0.534482			−0.0266575
$403$	0.794386	+	0.384851i	0.0395712	+	0.0191708i
$404$	−18.1602			−0.903504
$405$		0			0
$406$	−4.08631			−0.202800
$407$	16.9714			0.841239
$408$			4.80664i			0.237964i
$409$			7.79834i			0.385603i	0.981238	+	0.192802i	$0.0617574\pi$
$409$			7.79834i			0.385603i	−0.981238	+	0.192802i	$0.938243\pi$
$410$		0			0
$411$			1.46890i			0.0724556i
$412$	17.7816			0.876035
$413$	2.40332			0.118260
$414$			3.91200i			0.192264i
$415$		0			0
$416$	17.6129	+	8.53279i	0.863543	+	0.418354i
$417$	−0.403322			−0.0197508
$418$			18.2201i			0.891176i
$419$	10.2017			0.498384			0.249192	−	0.968454i	$-0.419835\pi$
$419$	10.2017			0.498384			0.249192	+	0.968454i	$0.419835\pi$
$420$		0			0
$421$			31.1888i			1.52005i	0.649893	+	0.760025i	$0.274814\pi$
$421$			31.1888i			1.52005i	−0.649893	+	0.760025i	$0.725186\pi$
$422$			13.7983i			0.671693i
$423$			7.52884i			0.366065i
$424$			8.82698i			0.428676i
$425$		0			0
$426$	1.52884			0.0740724
$427$		−	15.5473i		−	0.752387i
$428$	−0.234252			−0.0113230
$429$	7.08405	+	3.43196i	0.342021	+	0.165697i
$430$		0			0
$431$			22.9361i			1.10479i	0.833581	+	0.552397i	$0.186287\pi$
$431$			22.9361i			1.10479i	−0.833581	+	0.552397i	$0.813713\pi$
$432$	−5.33774			−0.256812
$433$	16.2880			0.782750			0.391375	−	0.920231i	$-0.372000\pi$
$433$	16.2880			0.782750			0.391375	+	0.920231i	$0.372000\pi$
$434$		−	0.374285i		−	0.0179663i
$435$		0			0
$436$		−	15.1519i		−	0.725644i
$437$			15.1625i			0.725319i
$438$	2.68339			0.128217
$439$	23.7569			1.13385			0.566927	−	0.823768i	$-0.308132\pi$
$439$	23.7569			1.13385			0.566927	+	0.823768i	$0.308132\pi$
$440$		0			0
$441$	0.405583			0.0193135
$442$	9.92159	+	4.80664i	0.471922	+	0.228629i
$443$	2.75292			0.130795			0.0653976	−	0.997859i	$-0.479168\pi$
$443$	2.75292			0.130795			0.0653976	+	0.997859i	$0.479168\pi$
$444$		−	2.38219i		−	0.113054i
$445$		0			0
$446$	−3.27781			−0.155209
$447$			4.85601i			0.229682i
$448$			3.16246i			0.149412i
$449$		−	27.1025i		−	1.27905i	−0.768772	−	0.639524i	$-0.779132\pi$
$449$		−	27.1025i		−	1.27905i	0.768772	−	0.639524i	$-0.220868\pi$
$450$		0			0
$451$	33.1025			1.55874
$452$	−21.7120			−1.02125
$453$			8.99774i			0.422751i
$454$	−1.68903			−0.0792703
$455$		0			0
$456$	5.61515			0.262953
$457$			40.1523i			1.87824i	0.343583	+	0.939122i	$0.388359\pi$
$457$			40.1523i			1.87824i	−0.343583	+	0.939122i	$0.611641\pi$
$458$	−14.4482			−0.675119
$459$	−13.3087			−0.621197
$460$		0			0
$461$		−	2.00791i		−	0.0935175i	−0.998906	−	0.0467587i	$-0.985111\pi$
$461$		−	2.00791i		−	0.0935175i	0.998906	−	0.0467587i	$-0.0148892\pi$
$462$		−	3.33774i		−	0.155286i
$463$		−	2.67282i		−	0.124217i	−0.998069	−	0.0621083i	$-0.980218\pi$
$463$		−	2.67282i		−	0.124217i	0.998069	−	0.0621083i	$-0.0197824\pi$
$464$	5.73050			0.266032
$465$		0			0
$466$			13.3536i			0.618591i
$467$	−31.8890			−1.47565			−0.737824	−	0.674994i	$-0.764146\pi$
$467$	−31.8890			−1.47565			−0.737824	+	0.674994i	$0.764146\pi$
$468$	−7.40727	+	15.2897i	−0.342401	+	0.706765i
$469$	−5.83528			−0.269448
$470$		0			0
$471$	4.20957			0.193967
$472$	1.88900			0.0869484
$473$		−	55.6890i		−	2.56058i
$474$		−	0.889572i		−	0.0408594i
$475$		0			0
$476$			23.9013i			1.09551i
$477$	−11.8353			−0.541900
$478$	−2.16907			−0.0992110
$479$		−	6.73445i		−	0.307705i	−0.988094	−	0.153852i	$-0.950832\pi$
$479$		−	6.73445i		−	0.307705i	0.988094	−	0.153852i	$-0.0491680\pi$
$480$		0			0
$481$	−10.7961	−	5.23030i	−0.492259	−	0.238481i
$482$	1.96306			0.0894148
$483$		−	2.77761i		−	0.126385i
$484$	−25.1233			−1.14197
$485$		0			0
$486$			6.08010i			0.275799i
$487$			39.6521i			1.79681i	0.439170	+	0.898404i	$0.355273\pi$
$487$			39.6521i			1.79681i	−0.439170	+	0.898404i	$0.644727\pi$
$488$		−	12.2201i		−	0.553179i
$489$		−	5.30080i		−	0.239710i
$490$		0			0
$491$	31.0946			1.40328			0.701640	−	0.712531i	$-0.252451\pi$
$491$	31.0946			1.40328			0.701640	+	0.712531i	$0.252451\pi$
$492$		−	4.64645i		−	0.209478i
$493$	14.2880			0.643498
$494$	5.61515	−	11.5905i	0.252638	−	0.521480i
$495$		0			0
$496$			0.524884i			0.0235680i
$497$	16.6913			0.748707
$498$	−2.40332			−0.107695
$499$		−	13.1087i		−	0.586828i	−0.955986	−	0.293414i	$-0.905209\pi$
$499$		−	13.1087i		−	0.586828i	0.955986	−	0.293414i	$-0.0947914\pi$
$500$		0			0
$501$			3.64153i			0.162691i
$502$		−	14.5680i		−	0.650203i
$503$	8.59273			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$503$	8.59273			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$504$	15.8168			0.704537
$505$		0			0
$506$	7.08405			0.314924
$507$	−3.44874	−	4.36638i	−0.153164	−	0.193918i
$508$	20.1770			0.895209
$509$		−	29.8353i		−	1.32243i	−0.750198	−	0.661213i	$-0.770042\pi$
$509$		−	29.8353i		−	1.32243i	0.750198	−	0.661213i	$-0.229958\pi$
$510$		0			0
$511$	29.2963			1.29599
$512$			20.6459i			0.912428i
$513$			15.5473i			0.686430i
$514$		−	5.30080i		−	0.233808i
$515$		0			0
$516$	−7.81681			−0.344116
$517$	13.6336			0.599606
$518$			5.08671i			0.223497i
$519$	−9.22239			−0.404818
$520$		0			0
$521$	10.0969			0.442352			0.221176	−	0.975234i	$-0.429010\pi$
$521$	10.0969			0.442352			0.221176	+	0.975234i	$0.429010\pi$
$522$		−	4.30644i		−	0.188488i
$523$	−16.1479			−0.706100			−0.353050	−	0.935604i	$-0.614855\pi$
$523$	−16.1479			−0.706100			−0.353050	+	0.935604i	$0.614855\pi$
$524$	12.7697			0.557847
$525$		0			0
$526$			4.66057i			0.203210i
$527$			1.30871i			0.0570081i
$528$			4.68073i			0.203703i
$529$	−17.1048			−0.743686
$530$		0			0
$531$			2.53279i			0.109914i
$532$	27.9216			1.21055
$533$	−21.0577	−	10.2017i	−0.912109	−	0.441883i
$534$	−1.86884			−0.0808726
$535$		0			0
$536$	−4.58651			−0.198107
$537$	−1.09914			−0.0474313
$538$			0.654353i			0.0282111i
$539$		−	0.734451i		−	0.0316350i
$540$		0			0
$541$			26.7776i			1.15126i	0.817711	+	0.575630i	$0.195243\pi$
$541$			26.7776i			1.15126i	−0.817711	+	0.575630i	$0.804757\pi$
$542$	1.82302			0.0783056
$543$	5.87675			0.252195
$544$			29.0162i			1.24406i
$545$		0			0
$546$	−1.02864	+	2.12325i	−0.0440216	+	0.0908669i
$547$	−12.3865			−0.529610			−0.264805	−	0.964302i	$-0.585308\pi$
$547$	−12.3865			−0.529610			−0.264805	+	0.964302i	$0.585308\pi$
$548$			5.74106i			0.245246i
$549$	16.3849			0.699288
$550$		0			0
$551$		−	16.6913i		−	0.711073i
$552$		−	2.18319i		−	0.0929227i
$553$		−	9.71203i		−	0.412997i
$554$		−	4.36186i		−	0.185318i
$555$		0			0
$556$	−1.57634			−0.0668519
$557$		−	10.4218i		−	0.441586i	−0.975321	−	0.220793i	$-0.929136\pi$
$557$		−	10.4218i		−	0.441586i	0.975321	−	0.220793i	$-0.0708644\pi$
$558$	0.394448			0.0166983
$559$	−17.1625	+	35.4257i	−0.725895	+	1.49835i
$560$		0			0
$561$			11.6706i			0.492732i
$562$	11.5763			0.488319
$563$	−9.78156			−0.412244			−0.206122	−	0.978526i	$-0.566084\pi$
$563$	−9.78156			−0.412244			−0.206122	+	0.978526i	$0.566084\pi$
$564$		−	1.91369i		−	0.0805808i
$565$		0			0
$566$		−	11.3809i		−	0.478375i
$567$			19.7384i			0.828935i
$568$	13.1193			0.550474
$569$	−30.2201			−1.26689			−0.633447	−	0.773786i	$-0.718361\pi$
$569$	−30.2201			−1.26689			−0.633447	+	0.773786i	$0.718361\pi$
$570$		0			0
$571$	−39.8643			−1.66827			−0.834135	−	0.551561i	$-0.814033\pi$
$571$	−39.8643			−1.66827			−0.834135	+	0.551561i	$0.814033\pi$
$572$	27.6873	+	13.4135i	1.15767	+	0.560846i
$573$	−4.57595			−0.191163
$574$			9.92159i			0.414119i
$575$		0			0
$576$	−3.33282			−0.138868
$577$		−	8.46326i		−	0.352330i	−0.984361	−	0.176165i	$-0.943631\pi$
$577$		−	8.46326i		−	0.352330i	0.984361	−	0.176165i	$-0.0563692\pi$
$578$			6.62136i			0.275412i
$579$			8.24313i			0.342573i
$580$		0			0
$581$	−26.2386			−1.08856
$582$	2.77761			0.115136
$583$			21.4320i			0.887621i
$584$	23.0268			0.952855
$585$		0			0
$586$	−14.8824			−0.614786
$587$		−	9.32718i		−	0.384974i	−0.981300	−	0.192487i	$-0.938345\pi$
$587$		−	9.32718i		−	0.384974i	0.981300	−	0.192487i	$-0.0616553\pi$
$588$	−0.103091			−0.00425142
$589$	1.52884			0.0629946
$590$		0			0
$591$		−	7.35355i		−	0.302485i
$592$		−	7.13342i		−	0.293182i
$593$			8.07841i			0.331740i	0.986148	+	0.165870i	$0.0530433\pi$
$593$			8.07841i			0.331740i	−0.986148	+	0.165870i	$0.946957\pi$
$594$	7.26386			0.298040
$595$		0			0
$596$			18.9793i			0.777421i
$597$	−4.94233			−0.202276
$598$	−4.50641	−	2.18319i	−0.184281	−	0.0892773i
$599$	19.1440			0.782202			0.391101	−	0.920348i	$-0.372094\pi$
$599$	19.1440			0.782202			0.391101	+	0.920348i	$0.372094\pi$
$600$		0			0
$601$	−4.28797			−0.174910			−0.0874550	−	0.996168i	$-0.527873\pi$
$601$	−4.28797			−0.174910			−0.0874550	+	0.996168i	$0.527873\pi$
$602$	16.6913			0.680286
$603$		−	6.14963i		−	0.250432i
$604$			35.1668i			1.43092i
$605$		0			0
$606$		−	2.65774i		−	0.107963i
$607$	−29.2426			−1.18692			−0.593459	−	0.804864i	$-0.702238\pi$
$607$	−29.2426			−1.18692			−0.593459	+	0.804864i	$0.702238\pi$
$608$	33.8969			1.37470
$609$			3.05767i			0.123903i
$610$		0			0
$611$	−8.67282	−	4.20166i	−0.350865	−	0.169981i
$612$	−25.1888			−1.01820
$613$			1.42405i			0.0575170i	0.999586	+	0.0287585i	$0.00915538\pi$
$613$			1.42405i			0.0575170i	−0.999586	+	0.0287585i	$0.990845\pi$
$614$	−1.36864			−0.0552338
$615$		0			0
$616$		−	28.6419i		−	1.15402i
$617$		−	46.5266i		−	1.87309i	−0.350548	−	0.936545i	$-0.614005\pi$
$617$		−	46.5266i		−	1.87309i	0.350548	−	0.936545i	$-0.385995\pi$
$618$			2.60232i			0.104681i
$619$		−	34.2818i		−	1.37790i	−0.724809	−	0.688950i	$-0.758072\pi$
$619$		−	34.2818i		−	1.37790i	0.724809	−	0.688950i	$-0.241928\pi$
$620$		0			0
$621$	6.04485			0.242571
$622$			2.02904i			0.0813569i
$623$	−20.4033			−0.817442
$624$	1.44252	−	2.97758i	0.0577472	−	0.119198i
$625$		0			0
$626$		−	2.84811i		−	0.113833i
$627$	13.6336			0.544474
$628$	16.4527			0.656534
$629$		−	17.7859i		−	0.709171i
$630$		0			0
$631$			2.32322i			0.0924861i	0.998930	+	0.0462430i	$0.0147249\pi$
$631$			2.32322i			0.0924861i	−0.998930	+	0.0462430i	$0.985275\pi$
$632$		−	7.63362i		−	0.303649i
$633$	10.3249			0.410379
$634$	10.6359			0.422405
$635$		0			0
$636$	3.00830			0.119287
$637$	−0.226346	+	0.467210i	−0.00896815	+	0.0185115i
$638$	−7.79834			−0.308739
$639$			17.5905i			0.695868i
$640$		0			0
$641$	28.1312			1.11111			0.555557	−	0.831478i	$-0.312505\pi$
$641$	28.1312			1.11111			0.555557	+	0.831478i	$0.312505\pi$
$642$		−	0.0342826i		−	0.00135303i
$643$		−	14.1338i		−	0.557383i	−0.960381	−	0.278692i	$-0.910099\pi$
$643$		−	14.1338i		−	0.557383i	0.960381	−	0.278692i	$-0.0899008\pi$
$644$		−	10.8560i		−	0.427787i
$645$		0			0
$646$	19.0946			0.751268
$647$	−45.8969			−1.80439			−0.902197	−	0.431325i	$-0.858046\pi$
$647$	−45.8969			−1.80439			−0.902197	+	0.431325i	$0.858046\pi$
$648$			15.5143i			0.609460i
$649$	4.58651			0.180036
$650$		0			0
$651$	−0.280067			−0.0109767
$652$		−	20.7177i		−	0.811367i
$653$	−50.4482			−1.97419			−0.987095	−	0.160137i	$-0.948806\pi$
$653$	−50.4482			−1.97419			−0.987095	+	0.160137i	$0.948806\pi$
$654$	2.21747			0.0867100
$655$		0			0
$656$		−	13.9137i		−	0.543238i
$657$			30.8745i			1.20453i
$658$			4.08631i			0.159301i
$659$	−45.8722			−1.78693			−0.893464	−	0.449135i	$-0.851732\pi$
$659$	−45.8722			−1.78693			−0.893464	+	0.449135i	$0.851732\pi$
$660$		0			0
$661$		−	25.8432i		−	1.00518i	−0.864524	−	0.502592i	$-0.832380\pi$
$661$		−	25.8432i		−	1.00518i	0.864524	−	0.502592i	$-0.167620\pi$
$662$	3.38614			0.131606
$663$	3.59668	−	7.42405i	0.139683	−	0.288326i
$664$	−20.6235			−0.800345
$665$		0			0
$666$	−5.36073			−0.207724
$667$	−6.48963			−0.251280
$668$			14.2326i			0.550674i
$669$			2.45269i			0.0948265i
$670$		0			0
$671$		−	29.6706i		−	1.14542i
$672$	−6.20957			−0.239539
$673$	4.97927			0.191937			0.0959683	−	0.995384i	$-0.469405\pi$
$673$	4.97927			0.191937			0.0959683	+	0.995384i	$0.469405\pi$
$674$		−	7.96306i		−	0.306726i
$675$		0			0
$676$	−13.4791	−	17.0656i	−0.518426	−	0.656368i
$677$	35.8353			1.37726			0.688631	−	0.725112i	$-0.258212\pi$
$677$	35.8353			1.37726			0.688631	+	0.725112i	$0.258212\pi$
$678$		−	3.17755i		−	0.122033i
$679$	30.3249			1.16376
$680$		0			0
$681$			1.26386i			0.0484311i
$682$		−	0.714288i		−	0.0273515i
$683$		−	40.4712i		−	1.54859i	−0.632827	−	0.774293i	$-0.718106\pi$
$683$		−	40.4712i		−	1.54859i	0.632827	−	0.774293i	$-0.281894\pi$
$684$			29.4257i			1.12512i
$685$		0			0
$686$	−10.4817			−0.400194
$687$			10.8112i			0.412472i
$688$	−23.4073			−0.892394
$689$	6.60498	−	13.6336i	0.251630	−	0.519400i
$690$		0			0
$691$		−	12.2448i		−	0.465815i	−0.972499	−	0.232907i	$-0.925176\pi$
$691$		−	12.2448i		−	0.465815i	0.972499	−	0.232907i	$-0.0748239\pi$
$692$	−36.0448			−1.37022
$693$	38.4033			1.45882
$694$		−	4.38050i		−	0.166281i
$695$		0			0
$696$			2.40332i			0.0910977i
$697$		−	34.6913i		−	1.31403i
$698$	−6.39542			−0.242070
$699$	9.99209			0.377936
$700$		0			0
$701$	−11.8353			−0.447012			−0.223506	−	0.974703i	$-0.571750\pi$
$701$	−11.8353			−0.447012			−0.223506	+	0.974703i	$0.571750\pi$
$702$	−4.62079	−	2.23860i	−0.174401	−	0.0844906i
$703$	−20.7776			−0.783642
$704$			6.03525i			0.227462i
$705$		0			0
$706$	5.52093			0.207783
$707$		−	29.0162i		−	1.09127i
$708$		−	0.643787i		−	0.0241950i
$709$			6.37429i			0.239391i	0.992811	+	0.119696i	$0.0381919\pi$
$709$			6.37429i			0.239391i	−0.992811	+	0.119696i	$0.961808\pi$
$710$		0			0
$711$	10.2352			0.383851
$712$	−16.0369			−0.601010
$713$		−	0.594417i		−	0.0222611i
$714$	−3.49794			−0.130907
$715$		0			0
$716$	−4.29588			−0.160545
$717$			1.62306i			0.0606141i
$718$	−5.44083			−0.203050
$719$	34.9009			1.30158			0.650791	−	0.759257i	$-0.274437\pi$
$719$	34.9009			1.30158			0.650791	+	0.759257i	$0.274437\pi$
$720$		0			0
$721$			28.4112i			1.05809i
$722$		−	11.4386i		−	0.425700i
$723$		−	1.46890i		−	0.0546290i
$724$	22.9687			0.853625
$725$		0			0
$726$		−	3.67678i		−	0.136458i
$727$	19.8106			0.734734			0.367367	−	0.930076i	$-0.380259\pi$
$727$	19.8106			0.734734			0.367367	+	0.930076i	$0.380259\pi$
$728$	−8.82698	+	18.2201i	−0.327150	+	0.675283i
$729$	−17.6050			−0.652036
$730$		0			0
$731$	−58.3619			−2.15859
$732$	−4.16472			−0.153932
$733$			12.6050i			0.465576i	0.972528	+	0.232788i	$0.0747848\pi$
$733$			12.6050i			0.465576i	−0.972528	+	0.232788i	$0.925215\pi$
$734$			9.72615i			0.358999i
$735$		0			0
$736$		−	13.1792i		−	0.485793i
$737$	−11.1361			−0.410203
$738$	−10.4561			−0.384893
$739$		−	37.1747i		−	1.36749i	−0.729719	−	0.683747i	$-0.760349\pi$
$739$		−	37.1747i		−	1.36749i	0.729719	−	0.683747i	$-0.239651\pi$
$740$		0			0
$741$	−8.67282	−	4.20166i	−0.318604	−	0.154352i
$742$	−6.42366			−0.235820
$743$		−	27.9322i		−	1.02473i	−0.858767	−	0.512366i	$-0.828769\pi$
$743$		−	27.9322i		−	1.02473i	0.858767	−	0.512366i	$-0.171231\pi$
$744$	−0.220132			−0.00807043
$745$		0			0
$746$			1.04977i			0.0384348i
$747$		−	27.6521i		−	1.01174i
$748$			45.6133i			1.66779i
$749$		−	0.374285i		−	0.0136761i
$750$		0			0
$751$	13.6257			0.497209			0.248605	−	0.968605i	$-0.420028\pi$
$751$	13.6257			0.497209			0.248605	+	0.968605i	$0.420028\pi$
$752$		−	5.73050i		−	0.208970i
$753$	−10.9009			−0.397249
$754$	4.96080	+	2.40332i	0.180662	+	0.0875238i
$755$		0			0
$756$		−	11.1316i		−	0.404851i
$757$	30.8560			1.12148			0.560740	−	0.827992i	$-0.310517\pi$
$757$	30.8560			1.12148			0.560740	+	0.827992i	$0.310517\pi$
$758$	18.5143			0.672470
$759$		−	5.30080i		−	0.192407i
$760$		0			0
$761$			17.0162i			0.616837i	0.951251	+	0.308419i	$0.0997997\pi$
$761$			17.0162i			0.616837i	−0.951251	+	0.308419i	$0.900200\pi$
$762$			2.95289i			0.106972i
$763$	24.2096			0.876445
$764$	−17.8847			−0.647044
$765$		0			0
$766$	−16.0969			−0.581604
$767$	−2.91764	−	1.41349i	−0.105350	−	0.0510381i
$768$	−1.81060			−0.0653343
$769$			29.0162i			1.04635i	0.852225	+	0.523176i	$0.175253\pi$
$769$			29.0162i			1.04635i	−0.852225	+	0.523176i	$0.824747\pi$
$770$		0			0
$771$	−3.96644			−0.142848
$772$			32.2175i			1.15953i
$773$		−	40.5160i		−	1.45726i	−0.684908	−	0.728630i	$-0.740158\pi$
$773$		−	40.5160i		−	1.45726i	0.684908	−	0.728630i	$-0.259842\pi$
$774$			17.5905i			0.632276i
$775$		0			0
$776$	23.8353			0.855637
$777$	3.80624			0.136548
$778$		−	18.2801i		−	0.655372i
$779$	−40.5266			−1.45202
$780$		0			0
$781$	31.8538			1.13982
$782$		−	7.42405i		−	0.265484i
$783$	−6.65435			−0.237807
$784$	−0.308705			−0.0110252
$785$		0			0
$786$			1.86884i			0.0666593i
$787$		−	34.0264i		−	1.21291i	−0.795118	−	0.606455i	$-0.792591\pi$
$787$		−	34.0264i		−	1.21291i	0.795118	−	0.606455i	$-0.207409\pi$
$788$		−	28.7407i		−	1.02384i
$789$	3.48737			0.124154
$790$		0			0
$791$		−	34.6913i		−	1.23348i
$792$	30.1849			1.07257
$793$	−9.14399	+	18.8745i	−0.324712	+	0.670253i
$794$	7.26990			0.257999
$795$		0			0
$796$	−19.3166			−0.684659
$797$	−14.7776			−0.523450			−0.261725	−	0.965143i	$-0.584291\pi$
$797$	−14.7776			−0.523450			−0.261725	+	0.965143i	$0.584291\pi$
$798$			4.08631i			0.144654i
$799$		−	14.2880i		−	0.505472i
$800$		0			0
$801$		−	21.5025i		−	0.759752i
$802$	0.560135			0.0197790
$803$	55.9092			1.97299
$804$			1.56312i			0.0551270i
$805$		0			0
$806$	−0.220132	+	0.454384i	−0.00775382	+	0.0160050i
$807$	0.489634			0.0172359
$808$		−	22.8066i		−	0.802335i
$809$	−36.0554			−1.26764			−0.633820	−	0.773480i	$-0.718514\pi$
$809$	−36.0554			−1.26764			−0.633820	+	0.773480i	$0.718514\pi$
$810$		0			0
$811$			5.31040i			0.186473i	0.995644	+	0.0932366i	$0.0297213\pi$
$811$			5.31040i			0.186473i	−0.995644	+	0.0932366i	$0.970279\pi$
$812$			11.9506i			0.419385i
$813$		−	1.36412i		−	0.0478417i
$814$			9.70750i			0.340248i
$815$		0			0
$816$	4.90538			0.171723
$817$			68.1787i			2.38527i
$818$	−4.46060			−0.155961
$819$	−24.4297	−	11.8353i	−0.853643	−	0.413558i
$820$		0			0
$821$			13.6336i			0.475817i	0.971288	+	0.237908i	$0.0764618\pi$
$821$			13.6336i			0.475817i	−0.971288	+	0.237908i	$0.923538\pi$
$822$	−0.840202			−0.0293054
$823$	39.6459			1.38197			0.690984	−	0.722870i	$-0.257177\pi$
$823$	39.6459			1.38197			0.690984	+	0.722870i	$0.257177\pi$
$824$			22.3311i			0.777942i
$825$		0			0
$826$			1.37468i			0.0478314i
$827$			23.8952i			0.830918i	0.909612	+	0.415459i	$0.136379\pi$
$827$			23.8952i			0.830918i	−0.909612	+	0.415459i	$0.863621\pi$
$828$	11.4408			0.397596
$829$	27.3562			0.950121			0.475060	−	0.879953i	$-0.342426\pi$
$829$	27.3562			0.950121			0.475060	+	0.879953i	$0.342426\pi$
$830$		0			0
$831$	−3.26386			−0.113222
$832$	1.85997	−	3.83923i	0.0644827	−	0.133101i
$833$	−0.769701			−0.0266686
$834$		−	0.230697i		−	0.00798839i
$835$		0			0
$836$	53.2857			1.84292
$837$		−	0.609505i		−	0.0210676i
$838$			5.83528i			0.201576i
$839$			29.5411i			1.01987i	0.860212	+	0.509936i	$0.170331\pi$
$839$			29.5411i			1.01987i	−0.860212	+	0.509936i	$0.829669\pi$
$840$		0			0
$841$	−21.8560			−0.753656
$842$	−17.8398			−0.614800
$843$		−	8.66226i		−	0.298344i
$844$	40.3540			1.38904
$845$		0			0
$846$	−4.30644			−0.148059
$847$		−	40.1417i		−	1.37929i
$848$	9.00830			0.309346
$849$	−8.51601			−0.292269
$850$		0			0
$851$			8.07841i			0.276924i
$852$		−	4.47116i		−	0.153180i
$853$			5.61515i			0.192259i	0.995369	+	0.0961295i	$0.0306463\pi$
$853$			5.61515i			0.192259i	−0.995369	+	0.0961295i	$0.969354\pi$
$854$	8.89296			0.304311
$855$		0			0
$856$		−	0.294187i		−	0.0100551i
$857$	−39.9216			−1.36370			−0.681848	−	0.731494i	$-0.738823\pi$
$857$	−39.9216			−1.36370			−0.681848	+	0.731494i	$0.738823\pi$
$858$	−1.96306	+	4.05203i	−0.0670177	+	0.138334i
$859$	28.6498			0.977520			0.488760	−	0.872418i	$-0.337449\pi$
$859$	28.6498			0.977520			0.488760	+	0.872418i	$0.337449\pi$
$860$		0			0
$861$	7.42405			0.253011
$862$	−13.1193			−0.446845
$863$			38.5530i			1.31236i	0.754605	+	0.656179i	$0.227828\pi$
$863$			38.5530i			1.31236i	−0.754605	+	0.656179i	$0.772172\pi$
$864$		−	13.5137i		−	0.459747i
$865$		0			0
$866$			9.31661i			0.316591i
$867$	4.95458			0.168266
$868$	−1.09462			−0.0371537
$869$		−	18.5345i		−	0.628739i
$870$		0			0
$871$	7.08405	+	3.43196i	0.240034	+	0.116288i
$872$	19.0286			0.644391
$873$			31.9585i			1.08163i
$874$	−8.67282			−0.293363
$875$		0			0
$876$		−	7.84771i		−	0.265150i
$877$			27.3826i			0.924644i	0.886712	+	0.462322i	$0.152984\pi$
$877$			27.3826i			0.924644i	−0.886712	+	0.462322i	$0.847016\pi$
$878$			13.5888i			0.458599i
$879$			11.1361i			0.375611i
$880$		0			0
$881$	25.0841			0.845103			0.422552	−	0.906339i	$-0.361135\pi$
$881$	25.0841			0.845103			0.422552	+	0.906339i	$0.361135\pi$
$882$			0.231991i			0.00781153i
$883$	−50.5513			−1.70119			−0.850593	−	0.525825i	$-0.823757\pi$
$883$	−50.5513			−1.70119			−0.850593	+	0.525825i	$0.823757\pi$
$884$	14.0573	−	29.0162i	0.472797	−	0.975921i
$885$		0			0
$886$			1.57465i			0.0529015i
$887$	19.6583			0.660061			0.330031	−	0.943970i	$-0.392941\pi$
$887$	19.6583			0.660061			0.330031	+	0.943970i	$0.392941\pi$
$888$	2.99170			0.100395
$889$			32.2386i			1.08125i
$890$		0			0
$891$			37.6689i			1.26195i
$892$			9.58611i			0.320967i
$893$	−16.6913			−0.558553
$894$	−2.77761			−0.0928971
$895$		0			0
$896$	−30.8251			−1.02979
$897$	−1.63362	+	3.37202i	−0.0545450	+	0.112589i
$898$	15.5025			0.517324
$899$			0.654353i			0.0218239i
$900$		0			0
$901$	22.4606			0.748271
$902$			18.9344i			0.630447i
$903$		−	12.4896i		−	0.415629i
$904$		−	27.2672i		−	0.906895i
$905$		0			0
$906$	−5.14665			−0.170986
$907$	22.0537			0.732282			0.366141	−	0.930559i	$-0.380679\pi$
$907$	22.0537			0.732282			0.366141	+	0.930559i	$0.380679\pi$
$908$			4.93967i			0.163929i
$909$	30.5793			1.01425
$910$		0			0
$911$	−14.0079			−0.464103			−0.232051	−	0.972704i	$-0.574544\pi$
$911$	−14.0079			−0.464103			−0.232051	+	0.972704i	$0.574544\pi$
$912$		−	5.73050i		−	0.189756i
$913$	−50.0739			−1.65720
$914$	−22.9668			−0.759676
$915$		0			0
$916$			42.2544i			1.39613i
$917$			20.4033i			0.673777i
$918$		−	7.61249i		−	0.251250i
$919$	21.8353			0.720279			0.360140	−	0.932898i	$-0.382729\pi$
$919$	21.8353			0.720279			0.360140	+	0.932898i	$0.382729\pi$
$920$		0			0
$921$			1.02412i			0.0337458i
$922$	1.14851			0.0378241
$923$	−20.2633	−	9.81681i	−0.666974	−	0.323124i
$924$	−9.76140			−0.321126
$925$		0			0
$926$	1.52884			0.0502407
$927$	−29.9418			−0.983416
$928$			14.5081i			0.476252i
$929$		−	15.2224i		−	0.499431i	−0.968319	−	0.249715i	$-0.919663\pi$
$929$		−	15.2224i		−	0.499431i	0.968319	−	0.249715i	$-0.0803370\pi$
$930$		0			0
$931$			0.899170i			0.0294691i
$932$	39.0532			1.27923
$933$	1.51827			0.0497060
$934$		−	18.2403i		−	0.596841i
$935$		0			0
$936$	−19.2017	−	9.30249i	−0.627626	−	0.304061i
$937$	25.4610			0.831774			0.415887	−	0.909416i	$-0.363471\pi$
$937$	25.4610			0.831774			0.415887	+	0.909416i	$0.363471\pi$
$938$		−	3.33774i		−	0.108981i
$939$	−2.13116			−0.0695478
$940$		0			0
$941$			24.9299i			0.812691i	0.913719	+	0.406346i	$0.133197\pi$
$941$			24.9299i			0.812691i	−0.913719	+	0.406346i	$0.866803\pi$
$942$			2.40784i			0.0784518i
$943$			15.7569i			0.513114i
$944$		−	1.92781i		−	0.0627448i
$945$		0			0
$946$	31.8538			1.03565
$947$		−	16.6807i		−	0.542051i	−0.962572	−	0.271025i	$-0.912637\pi$
$947$		−	16.6807i		−	0.542051i	0.962572	−	0.271025i	$-0.0873628\pi$
$948$	−2.60160			−0.0844960
$949$	−35.5658	−	17.2303i	−1.15451	−	0.559319i
$950$		0			0
$951$		−	7.95854i		−	0.258073i
$952$	−30.0166			−0.972844
$953$	27.1730			0.880221			0.440110	−	0.897944i	$-0.354939\pi$
$953$	27.1730			0.880221			0.440110	+	0.897944i	$0.354939\pi$
$954$		−	6.76970i		−	0.219177i
$955$		0			0
$956$			6.34356i			0.205165i
$957$			5.83528i			0.188628i
$958$	3.85206			0.124454
$959$	−9.17302			−0.296212
$960$		0			0
$961$	30.9401			0.998067
$962$	2.99170	−	6.17528i	0.0964561	−	0.199099i
$963$	0.394448			0.0127109
$964$		−	5.74106i		−	0.184907i
$965$		0			0
$966$	1.58877			0.0511179
$967$		−	6.75914i		−	0.217359i	−0.994077	−	0.108680i	$-0.965338\pi$
$967$		−	6.75914i		−	0.217359i	0.994077	−	0.108680i	$-0.0346622\pi$
$968$		−	31.5513i		−	1.01410i
$969$		−	14.2880i		−	0.458996i
$970$		0			0
$971$	46.6419			1.49681			0.748405	−	0.663242i	$-0.230820\pi$
$971$	46.6419			1.49681			0.748405	+	0.663242i	$0.230820\pi$
$972$	17.7816			0.570344
$973$		−	2.51867i		−	0.0807449i
$974$	−22.6807			−0.726737
$975$		0			0
$976$	−12.4712			−0.399192
$977$			52.7467i			1.68752i	0.536723	+	0.843758i	$0.319662\pi$
$977$			52.7467i			1.68752i	−0.536723	+	0.843758i	$0.680338\pi$
$978$	3.03202			0.0969534
$979$	−38.9378			−1.24446
$980$		0			0
$981$			25.5137i			0.814591i
$982$			17.7859i			0.567571i
$983$			20.9977i			0.669724i	0.942267	+	0.334862i	$0.108690\pi$
$983$			20.9977i			0.669724i	−0.942267	+	0.334862i	$0.891310\pi$
$984$	5.83528			0.186022
$985$		0			0
$986$			8.17262i			0.260269i
$987$	3.05767			0.0973268
$988$	−33.8969	−	16.4218i	−1.07840	−	0.522447i
$989$	26.5081			0.842909
$990$		0			0
$991$	−32.3170			−1.02658			−0.513292	−	0.858214i	$-0.671574\pi$
$991$	−32.3170			−1.02658			−0.513292	+	0.858214i	$0.671574\pi$
$992$	−1.32887			−0.0421916
$993$		−	2.53376i		−	0.0804064i
$994$			9.54731i			0.302822i
$995$		0			0
$996$			7.02864i			0.222711i
$997$	21.3905			0.677444			0.338722	−	0.940887i	$-0.390005\pi$
$997$	21.3905			0.677444			0.338722	+	0.940887i	$0.390005\pi$
$998$	7.49811			0.237348
$999$			8.28345i			0.262077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.c.g.51.4		6
5.2	odd	4		325.2.d.e.324.3		6
5.3	odd	4		325.2.d.f.324.4		6
5.4	even	2		65.2.c.a.51.3	✓	6
13.5	odd	4		4225.2.a.be.1.2		3
13.8	odd	4		4225.2.a.bc.1.2		3
13.12	even	2	inner	325.2.c.g.51.3		6
15.14	odd	2		585.2.b.g.181.4		6
20.19	odd	2		1040.2.k.d.961.4		6
65.4	even	6		845.2.m.h.361.4		12
65.9	even	6		845.2.m.h.361.3		12
65.12	odd	4		325.2.d.f.324.3		6
65.19	odd	12		845.2.e.k.146.2		6
65.24	odd	12		845.2.e.i.191.2		6
65.29	even	6		845.2.m.h.316.4		12
65.34	odd	4		845.2.a.k.1.2		3
65.38	odd	4		325.2.d.e.324.4		6
65.44	odd	4		845.2.a.i.1.2		3
65.49	even	6		845.2.m.h.316.3		12
65.54	odd	12		845.2.e.k.191.2		6
65.59	odd	12		845.2.e.i.146.2		6
65.64	even	2		65.2.c.a.51.4	yes	6
195.44	even	4		7605.2.a.cc.1.2		3
195.164	even	4		7605.2.a.bs.1.2		3
195.194	odd	2		585.2.b.g.181.3		6
260.259	odd	2		1040.2.k.d.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.3	✓	6	5.4	even	2
65.2.c.a.51.4	yes	6	65.64	even	2
325.2.c.g.51.3		6	13.12	even	2	inner
325.2.c.g.51.4		6	1.1	even	1	trivial
325.2.d.e.324.3		6	5.2	odd	4
325.2.d.e.324.4		6	65.38	odd	4
325.2.d.f.324.3		6	65.12	odd	4
325.2.d.f.324.4		6	5.3	odd	4
585.2.b.g.181.3		6	195.194	odd	2
585.2.b.g.181.4		6	15.14	odd	2
845.2.a.i.1.2		3	65.44	odd	4
845.2.a.k.1.2		3	65.34	odd	4
845.2.e.i.146.2		6	65.59	odd	12
845.2.e.i.191.2		6	65.24	odd	12
845.2.e.k.146.2		6	65.19	odd	12
845.2.e.k.191.2		6	65.54	odd	12
845.2.m.h.316.3		12	65.49	even	6
845.2.m.h.316.4		12	65.29	even	6
845.2.m.h.361.3		12	65.9	even	6
845.2.m.h.361.4		12	65.4	even	6
1040.2.k.d.961.3		6	260.259	odd	2
1040.2.k.d.961.4		6	20.19	odd	2
4225.2.a.bc.1.2		3	13.8	odd	4
4225.2.a.be.1.2		3	13.5	odd	4
7605.2.a.bs.1.2		3	195.164	even	4
7605.2.a.cc.1.2		3	195.44	even	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.571993i q^{2} +0.428007 q^{3} +1.67282 q^{4} +0.244817i q^{6} +2.67282i q^{7} +2.10083i q^{8} -2.81681 q^{9} +5.10083i q^{11} +0.715980 q^{12} +(1.57199 - 3.24482i) q^{13} -1.52884 q^{14} +2.14399 q^{16} +5.34565 q^{17} -1.61120i q^{18} -6.24482i q^{19} +1.14399i q^{21} -2.91764 q^{22} -2.42801 q^{23} +0.899170i q^{24} +(1.85601 + 0.899170i) q^{26} -2.48963 q^{27} +4.47116i q^{28} +2.67282 q^{29} +0.244817i q^{31} +5.42801i q^{32} +2.18319i q^{33} +3.05767i q^{34} -4.71203 q^{36} -3.32718i q^{37} +3.57199 q^{38} +(0.672824 - 1.38880i) q^{39} -6.48963i q^{41} -0.654353 q^{42} -10.9176 q^{43} +8.53279i q^{44} -1.38880i q^{46} -2.67282i q^{47} +0.917641 q^{48} -0.143987 q^{49} +2.28797 q^{51} +(2.62967 - 5.42801i) q^{52} +4.20166 q^{53} -1.42405i q^{54} -5.61515 q^{56} -2.67282i q^{57} +1.52884i q^{58} -0.899170i q^{59} -5.81681 q^{61} -0.140034 q^{62} -7.52884i q^{63} +1.18319 q^{64} -1.24877 q^{66} +2.18319i q^{67} +8.94233 q^{68} -1.03920 q^{69} -6.24482i q^{71} -5.91764i q^{72} -10.9608i q^{73} +1.90312 q^{74} -10.4465i q^{76} -13.6336 q^{77} +(0.794386 + 0.384851i) q^{78} -3.63362 q^{79} +7.38485 q^{81} +3.71203 q^{82} +9.81681i q^{83} +1.91369i q^{84} -6.24482i q^{86} +1.14399 q^{87} -10.7160 q^{88} +7.63362i q^{89} +(8.67282 + 4.20166i) q^{91} -4.06163 q^{92} +0.104783i q^{93} +1.52884 q^{94} +2.32322i q^{96} -11.3456i q^{97} -0.0823593i q^{98} -14.3681i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 8 q^{14} + 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} + 14 q^{26} + 28 q^{27} - 4 q^{29} - 34 q^{36} + 20 q^{38} - 16 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48}+ \cdots - 8 q^{94}+O(q^{100}) \) 6 * q + 4 * q^3 - 10 * q^4 + 6 * q^9 + 8 * q^13 + 8 * q^14 + 10 * q^16 - 8 * q^17 + 24 * q^22 - 16 * q^23 + 14 * q^26 + 28 * q^27 - 4 * q^29 - 34 * q^36 + 20 * q^38 - 16 * q^39 - 44 * q^42 - 24 * q^43 - 36 * q^48 + 2 * q^49 + 8 * q^51 - 20 * q^52 - 12 * q^53 - 48 * q^56 - 12 * q^61 - 8 * q^62 + 30 * q^64 + 24 * q^66 + 88 * q^68 - 32 * q^69 + 20 * q^74 - 36 * q^77 + 52 * q^78 + 24 * q^79 + 30 * q^81 + 28 * q^82 + 4 * q^87 - 60 * q^88 + 32 * q^91 + 20 * q^92 - 8 * q^94

Introduction

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