LMFDB - Embedded newform 325.2.c.g.51.2

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			51.2
Root			$0.675970 - 0.675970i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.2.c.g.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08613i q^{2} +3.08613 q^{3} -2.35194 q^{4} -6.43807i q^{6} -1.35194i q^{7} +0.734191i q^{8} +6.52420 q^{9} +O(q^{10})$	\(q-2.08613i q^{2} +3.08613 q^{3} -2.35194 q^{4} -6.43807i q^{6} -1.35194i q^{7} +0.734191i q^{8} +6.52420 q^{9} +3.73419i q^{11} -7.25839 q^{12} +(-1.08613 + 3.43807i) q^{13} -2.82032 q^{14} -3.17226 q^{16} -2.70388 q^{17} -13.6103i q^{18} +0.438069i q^{19} -4.17226i q^{21} +7.79001 q^{22} -5.08613 q^{23} +2.26581i q^{24} +(7.17226 + 2.26581i) q^{26} +10.8761 q^{27} +3.17968i q^{28} -1.35194 q^{29} -6.43807i q^{31} +8.08613i q^{32} +11.5242i q^{33} +5.64064i q^{34} -15.3445 q^{36} -7.35194i q^{37} +0.913870 q^{38} +(-3.35194 + 10.6103i) q^{39} +6.87614i q^{41} -8.70388 q^{42} -0.209991 q^{43} -8.78259i q^{44} +10.6103i q^{46} +1.35194i q^{47} -9.79001 q^{48} +5.17226 q^{49} -8.34452 q^{51} +(2.55451 - 8.08613i) q^{52} +1.46838 q^{53} -22.6890i q^{54} +0.992582 q^{56} +1.35194i q^{57} +2.82032i q^{58} -2.26581i q^{59} +3.52420 q^{61} -13.4307 q^{62} -8.82032i q^{63} +10.5242 q^{64} +24.0410 q^{66} +11.5242i q^{67} +6.35936 q^{68} -15.6965 q^{69} +0.438069i q^{71} +4.79001i q^{72} +3.69646i q^{73} -15.3371 q^{74} -1.03031i q^{76} +5.04840 q^{77} +(22.1345 + 6.99258i) q^{78} +15.0484 q^{79} +13.9926 q^{81} +14.3445 q^{82} +0.475800i q^{83} +9.81290i q^{84} +0.438069i q^{86} -4.17226 q^{87} -2.74161 q^{88} -11.0484i q^{89} +(4.64806 + 1.46838i) q^{91} +11.9623 q^{92} -19.8687i q^{93} +2.82032 q^{94} +24.9549i q^{96} -3.29612i q^{97} -10.7900i q^{98} +24.3626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 - 10 * q^4 + 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$		−	2.08613i		−	1.47512i	−0.675283	−	0.737558i	$-0.735979\pi$
$2$		−	2.08613i		−	1.47512i	0.675283	−	0.737558i	$-0.264021\pi$
$3$	3.08613			1.78178			0.890889	−	0.454221i	$-0.150082\pi$
$3$	3.08613			1.78178			0.890889	+	0.454221i	$0.150082\pi$
$4$	−2.35194			−1.17597
$5$		0			0
$5$		0			0
$6$		−	6.43807i		−	2.62833i
$7$		−	1.35194i		−	0.510985i	−0.966811	−	0.255492i	$-0.917762\pi$
$7$		−	1.35194i		−	0.510985i	0.966811	−	0.255492i	$-0.0822376\pi$
$8$			0.734191i			0.259576i
$9$	6.52420			2.17473
$10$		0			0
$11$			3.73419i			1.12590i	0.826491	+	0.562950i	$0.190334\pi$
$11$			3.73419i			1.12590i	−0.826491	+	0.562950i	$0.809666\pi$
$12$	−7.25839			−2.09532
$13$	−1.08613	+	3.43807i	−0.301238	+	0.953549i
$13$	−1.08613	+	3.43807i	−0.301238	+	0.953549i
$14$	−2.82032			−0.753763
$15$		0			0
$16$	−3.17226			−0.793065
$17$	−2.70388			−0.655787			−0.327893	−	0.944715i	$-0.606339\pi$
$17$	−2.70388			−0.655787			−0.327893	+	0.944715i	$0.606339\pi$
$18$		−	13.6103i		−	3.20799i
$19$			0.438069i			0.100500i	0.998737	+	0.0502500i	$0.0160018\pi$
$19$			0.438069i			0.100500i	−0.998737	+	0.0502500i	$0.983998\pi$
$20$		0			0
$21$		−	4.17226i		−	0.910462i
$22$	7.79001			1.66084
$23$	−5.08613			−1.06053			−0.530266	−	0.847832i	$-0.677908\pi$
$23$	−5.08613			−1.06053			−0.530266	+	0.847832i	$0.677908\pi$
$24$			2.26581i			0.462506i
$25$		0			0
$26$	7.17226	+	2.26581i	1.40660	+	0.444362i
$27$	10.8761			2.09311
$28$			3.17968i			0.600903i
$29$	−1.35194			−0.251049			−0.125524	−	0.992091i	$-0.540061\pi$
$29$	−1.35194			−0.251049			−0.125524	+	0.992091i	$0.540061\pi$
$30$		0			0
$31$		−	6.43807i		−	1.15631i	−0.815926	−	0.578156i	$-0.803773\pi$
$31$		−	6.43807i		−	1.15631i	0.815926	−	0.578156i	$-0.196227\pi$
$32$			8.08613i			1.42944i
$33$			11.5242i			2.00611i
$34$			5.64064i			0.967362i
$35$		0			0
$36$	−15.3445			−2.55742
$37$		−	7.35194i		−	1.20865i	−0.796737	−	0.604326i	$-0.793443\pi$
$37$		−	7.35194i		−	1.20865i	0.796737	−	0.604326i	$-0.206557\pi$
$38$	0.913870			0.148249
$39$	−3.35194	+	10.6103i	−0.536740	+	1.69901i
$40$		0			0
$41$			6.87614i			1.07387i	0.843623	+	0.536936i	$0.180418\pi$
$41$			6.87614i			1.07387i	−0.843623	+	0.536936i	$0.819582\pi$
$42$	−8.70388			−1.34304
$43$	−0.209991			−0.0320234			−0.0160117	−	0.999872i	$-0.505097\pi$
$43$	−0.209991			−0.0320234			−0.0160117	+	0.999872i	$0.505097\pi$
$44$		−	8.78259i		−	1.32403i
$45$		0			0
$46$			10.6103i			1.56441i
$47$			1.35194i			0.197201i	0.995127	+	0.0986003i	$0.0314365\pi$
$47$			1.35194i			0.197201i	−0.995127	+	0.0986003i	$0.968563\pi$
$48$	−9.79001			−1.41307
$49$	5.17226			0.738894
$50$		0			0
$51$	−8.34452			−1.16847
$52$	2.55451	−	8.08613i	0.354247	−	1.12134i
$53$	1.46838			0.201698			0.100849	−	0.994902i	$-0.467844\pi$
$53$	1.46838			0.201698			0.100849	+	0.994902i	$0.467844\pi$
$54$		−	22.6890i		−	3.08759i
$55$		0			0
$56$	0.992582			0.132639
$57$			1.35194i			0.179069i
$58$			2.82032i			0.370326i
$59$		−	2.26581i		−	0.294983i	−0.989063	−	0.147492i	$-0.952880\pi$
$59$		−	2.26581i		−	0.294983i	0.989063	−	0.147492i	$-0.0471199\pi$
$60$		0			0
$61$	3.52420			0.451228			0.225614	−	0.974217i	$-0.427561\pi$
$61$	3.52420			0.451228			0.225614	+	0.974217i	$0.427561\pi$
$62$	−13.4307			−1.70569
$63$		−	8.82032i		−	1.11126i
$64$	10.5242			1.31552
$65$		0			0
$66$	24.0410			2.95924
$67$			11.5242i			1.40791i	0.710247	+	0.703953i	$0.248583\pi$
$67$			11.5242i			1.40791i	−0.710247	+	0.703953i	$0.751417\pi$
$68$	6.35936			0.771185
$69$	−15.6965			−1.88963
$70$		0			0
$71$			0.438069i			0.0519893i	0.999662	+	0.0259946i	$0.00827528\pi$
$71$			0.438069i			0.0519893i	−0.999662	+	0.0259946i	$0.991725\pi$
$72$			4.79001i			0.564508i
$73$			3.69646i			0.432638i	0.976323	+	0.216319i	$0.0694051\pi$
$73$			3.69646i			0.432638i	−0.976323	+	0.216319i	$0.930595\pi$
$74$	−15.3371			−1.78290
$75$		0			0
$76$		−	1.03031i		−	0.118185i
$77$	5.04840			0.575318
$78$	22.1345	+	6.99258i	2.50624	+	0.791754i
$79$	15.0484			1.69308			0.846539	−	0.532327i	$-0.178682\pi$
$79$	15.0484			1.69308			0.846539	+	0.532327i	$0.178682\pi$
$80$		0			0
$81$	13.9926			1.55473
$82$	14.3445			1.58409
$83$			0.475800i			0.0522259i	0.999659	+	0.0261129i	$0.00831295\pi$
$83$			0.475800i			0.0522259i	−0.999659	+	0.0261129i	$0.991687\pi$
$84$			9.81290i			1.07068i
$85$		0			0
$86$			0.438069i			0.0472382i
$87$	−4.17226			−0.447313
$88$	−2.74161			−0.292257
$89$		−	11.0484i		−	1.17113i	−0.810626	−	0.585564i	$-0.800873\pi$
$89$		−	11.0484i		−	1.17113i	0.810626	−	0.585564i	$-0.199127\pi$
$90$		0			0
$91$	4.64806	+	1.46838i	0.487249	+	0.153928i
$92$	11.9623			1.24715
$93$		−	19.8687i		−	2.06029i
$94$	2.82032			0.290894
$95$		0			0
$96$			24.9549i			2.54694i
$97$		−	3.29612i		−	0.334670i	−0.985900	−	0.167335i	$-0.946484\pi$
$97$		−	3.29612i		−	0.334670i	0.985900	−	0.167335i	$-0.0535162\pi$
$98$		−	10.7900i		−	1.08996i
$99$			24.3626i			2.44853i
$100$		0			0
$101$	−16.1723			−1.60920			−0.804600	−	0.593817i	$-0.797620\pi$
$101$	−16.1723			−1.60920			−0.804600	+	0.593817i	$0.797620\pi$
$102$			17.4078i			1.72362i
$103$	10.5545			1.03997			0.519983	−	0.854176i	$-0.325938\pi$
$103$	10.5545			1.03997			0.519983	+	0.854176i	$0.325938\pi$
$104$	−2.52420	−	0.797427i	−0.247518	−	0.0781942i
$105$		0			0
$106$		−	3.06324i		−	0.297528i
$107$	−13.4307			−1.29839			−0.649195	−	0.760622i	$-0.724894\pi$
$107$	−13.4307			−1.29839			−0.649195	+	0.760622i	$0.724894\pi$
$108$	−25.5800			−2.46144
$109$		−	11.6406i		−	1.11497i	−0.830187	−	0.557486i	$-0.811766\pi$
$109$		−	11.6406i		−	1.11497i	0.830187	−	0.557486i	$-0.188234\pi$
$110$		0			0
$111$		−	22.6890i		−	2.15355i
$112$			4.28870i			0.405244i
$113$	13.7523			1.29371			0.646853	−	0.762615i	$-0.276085\pi$
$113$	13.7523			1.29371			0.646853	+	0.762615i	$0.276085\pi$
$114$	2.82032			0.264147
$115$		0			0
$116$	3.17968			0.295226
$117$	−7.08613	+	22.4307i	−0.655113	+	2.07371i
$118$	−4.72677			−0.435135
$119$			3.65548i			0.335097i
$120$		0			0
$121$	−2.94418			−0.267653
$122$		−	7.35194i		−	0.665613i
$123$			21.2207i			1.91340i
$124$			15.1419i			1.35979i
$125$		0			0
$126$	−18.4003			−1.63923
$127$	−3.96227			−0.351595			−0.175797	−	0.984426i	$-0.556250\pi$
$127$	−3.96227			−0.351595			−0.175797	+	0.984426i	$0.556250\pi$
$128$		−	5.78259i		−	0.511114i
$129$	−0.648061			−0.0570586
$130$		0			0
$131$	−11.0484			−0.965303			−0.482652	−	0.875812i	$-0.660326\pi$
$131$	−11.0484			−0.965303			−0.482652	+	0.875812i	$0.660326\pi$
$132$		−	27.1042i		−	2.35912i
$133$	0.592243			0.0513540
$134$	24.0410			2.07682
$135$		0			0
$136$		−	1.98516i		−	0.170226i
$137$		−	12.5168i		−	1.06938i	−0.845048	−	0.534690i	$-0.820428\pi$
$137$		−	12.5168i		−	1.06938i	0.845048	−	0.534690i	$-0.179572\pi$
$138$			32.7449i			2.78743i
$139$	1.64064			0.139157			0.0695787	−	0.997576i	$-0.477834\pi$
$139$	1.64064			0.139157			0.0695787	+	0.997576i	$0.477834\pi$
$140$		0			0
$141$			4.17226i			0.351368i
$142$	0.913870			0.0766903
$143$	−12.8384	−	4.05582i	−1.07360	−	0.339165i
$144$	−20.6965			−1.72470
$145$		0			0
$146$	7.71130			0.638191
$147$	15.9623			1.31655
$148$			17.2913i			1.42134i
$149$			3.29612i			0.270029i	0.990844	+	0.135014i	$0.0431081\pi$
$149$			3.29612i			0.270029i	−0.990844	+	0.135014i	$0.956892\pi$
$150$		0			0
$151$		−	9.65873i		−	0.786016i	−0.919535	−	0.393008i	$-0.871434\pi$
$151$		−	9.65873i		−	0.786016i	0.919535	−	0.393008i	$-0.128566\pi$
$152$	−0.321627			−0.0260874
$153$	−17.6406			−1.42616
$154$		−	10.5316i		−	0.848662i
$155$		0			0
$156$	7.88356	−	24.9549i	0.631190	−	1.99799i
$157$	−11.5800			−0.924186			−0.462093	−	0.886831i	$-0.652901\pi$
$157$	−11.5800			−0.924186			−0.462093	+	0.886831i	$0.652901\pi$
$158$		−	31.3929i		−	2.49749i
$159$	4.53162			0.359381
$160$		0			0
$161$			6.87614i			0.541916i
$162$		−	29.1903i		−	2.29341i
$163$		−	18.9926i		−	1.48761i	−0.668395	−	0.743807i	$-0.733018\pi$
$163$		−	18.9926i		−	1.48761i	0.668395	−	0.743807i	$-0.266982\pi$
$164$		−	16.1723i		−	1.26284i
$165$		0			0
$166$	0.992582			0.0770393
$167$		−	16.9320i		−	1.31023i	−0.755527	−	0.655117i	$-0.772619\pi$
$167$		−	16.9320i		−	1.31023i	0.755527	−	0.655117i	$-0.227381\pi$
$168$	3.06324			0.236334
$169$	−10.6406	−	7.46838i	−0.818511	−	0.574491i
$170$		0			0
$171$			2.85805i			0.218561i
$172$	0.493887			0.0376585
$173$	−10.7645			−0.818410			−0.409205	−	0.912442i	$-0.634194\pi$
$173$	−10.7645			−0.818410			−0.409205	+	0.912442i	$0.634194\pi$
$174$			8.70388i			0.659839i
$175$		0			0
$176$		−	11.8458i		−	0.892913i
$177$		−	6.99258i		−	0.525595i
$178$	−23.0484			−1.72755
$179$	−18.5168			−1.38401			−0.692005	−	0.721893i	$-0.743272\pi$
$179$	−18.5168			−1.38401			−0.692005	+	0.721893i	$0.743272\pi$
$180$		0			0
$181$	12.2887			0.913412			0.456706	−	0.889618i	$-0.349029\pi$
$181$	12.2887			0.913412			0.456706	+	0.889618i	$0.349029\pi$
$182$	3.06324	−	9.69646i	0.227062	−	0.718749i
$183$	10.8761			0.803987
$184$		−	3.73419i		−	0.275288i
$185$		0			0
$186$	−41.4487			−3.03917
$187$		−	10.0968i		−	0.738351i
$188$		−	3.17968i		−	0.231902i
$189$		−	14.7039i		−	1.06955i
$190$		0			0
$191$	5.40776			0.391292			0.195646	−	0.980675i	$-0.437320\pi$
$191$	5.40776			0.391292			0.195646	+	0.980675i	$0.437320\pi$
$192$	32.4791			2.34397
$193$			19.1090i			1.37550i	0.725949	+	0.687749i	$0.241401\pi$
$193$			19.1090i			1.37550i	−0.725949	+	0.687749i	$0.758599\pi$
$194$	−6.87614			−0.493678
$195$		0			0
$196$	−12.1648			−0.868917
$197$			12.2839i			0.875191i	0.899172	+	0.437596i	$0.144170\pi$
$197$			12.2839i			0.875191i	−0.899172	+	0.437596i	$0.855830\pi$
$198$	50.8236			3.61187
$199$	−0.764504			−0.0541942			−0.0270971	−	0.999633i	$-0.508626\pi$
$199$	−0.764504			−0.0541942			−0.0270971	+	0.999633i	$0.508626\pi$
$200$		0			0
$201$			35.5652i			2.50857i
$202$			33.7374i			2.37376i
$203$			1.82774i			0.128282i
$204$	19.6258			1.37408
$205$		0			0
$206$		−	22.0181i		−	1.53407i
$207$	−33.1829			−2.30637
$208$	3.44549	−	10.9065i	0.238902	−	0.756226i
$209$	−1.63583			−0.113153
$210$		0			0
$211$	−7.92454			−0.545548			−0.272774	−	0.962078i	$-0.587941\pi$
$211$	−7.92454			−0.545548			−0.272774	+	0.962078i	$0.587941\pi$
$212$	−3.45355			−0.237190
$213$			1.35194i			0.0926333i
$214$			28.0181i			1.91528i
$215$		0			0
$216$			7.98516i			0.543322i
$217$	−8.70388			−0.590858
$218$	−24.2839			−1.64471
$219$			11.4078i			0.770865i
$220$		0			0
$221$	2.93676	−	9.29612i	0.197548	−	0.625325i
$222$	−47.3323			−3.17674
$223$			4.28870i			0.287193i	0.989636	+	0.143596i	$0.0458667\pi$
$223$			4.28870i			0.287193i	−0.989636	+	0.143596i	$0.954133\pi$
$224$	10.9320			0.730422
$225$		0			0
$226$		−	28.6890i		−	1.90837i
$227$			25.5094i			1.69312i	0.532297	+	0.846558i	$0.321329\pi$
$227$			25.5094i			1.69312i	−0.532297	+	0.846558i	$0.678671\pi$
$228$		−	3.17968i		−	0.210579i
$229$			25.1090i			1.65925i	0.558320	+	0.829626i	$0.311446\pi$
$229$			25.1090i			1.65925i	−0.558320	+	0.829626i	$0.688554\pi$
$230$		0			0
$231$	15.5800			1.02509
$232$		−	0.992582i		−	0.0651662i
$233$	15.2961			1.00208			0.501041	−	0.865423i	$-0.332951\pi$
$233$	15.2961			1.00208			0.501041	+	0.865423i	$0.332951\pi$
$234$	46.7933	+	14.7826i	3.05897	+	0.966368i
$235$		0			0
$236$			5.32905i			0.346891i
$237$	46.4413			3.01669
$238$	7.62581			0.494308
$239$		−	13.6736i		−	0.884469i	−0.896899	−	0.442235i	$-0.854186\pi$
$239$		−	13.6736i		−	0.884469i	0.896899	−	0.442235i	$-0.145814\pi$
$240$		0			0
$241$			12.5168i			0.806277i	0.915139	+	0.403138i	$0.132081\pi$
$241$			12.5168i			0.806277i	−0.915139	+	0.403138i	$0.867919\pi$
$242$			6.14195i			0.394819i
$243$	10.5545			0.677072
$244$	−8.28870			−0.530630
$245$		0			0
$246$	44.2691			2.82249
$247$	−1.50611	−	0.475800i	−0.0958317	−	0.0302745i
$248$	4.72677			0.300150
$249$			1.46838i			0.0930549i
$250$		0			0
$251$	14.6284			0.923337			0.461669	−	0.887052i	$-0.347251\pi$
$251$	14.6284			0.923337			0.461669	+	0.887052i	$0.347251\pi$
$252$			20.7449i			1.30680i
$253$		−	18.9926i		−	1.19405i
$254$			8.26581i			0.518643i
$255$		0			0
$256$	8.98516			0.561573
$257$	28.0968			1.75263			0.876315	−	0.481738i	$-0.159994\pi$
$257$	28.0968			1.75263			0.876315	+	0.481738i	$0.159994\pi$
$258$			1.35194i			0.0841681i
$259$	−9.93937			−0.617603
$260$		0			0
$261$	−8.82032			−0.545964
$262$			23.0484i			1.42393i
$263$	−15.7752			−0.972739			−0.486369	−	0.873753i	$-0.661679\pi$
$263$	−15.7752			−0.972739			−0.486369	+	0.873753i	$0.661679\pi$
$264$	−8.46096			−0.520736
$265$		0			0
$266$		−	1.23550i		−	0.0757531i
$267$		−	34.0968i		−	2.08669i
$268$		−	27.1042i		−	1.65565i
$269$	−4.17226			−0.254387			−0.127194	−	0.991878i	$-0.540597\pi$
$269$	−4.17226			−0.254387			−0.127194	+	0.991878i	$0.540597\pi$
$270$		0			0
$271$			6.07871i			0.369255i	0.982809	+	0.184628i	$0.0591079\pi$
$271$			6.07871i			0.369255i	−0.982809	+	0.184628i	$0.940892\pi$
$272$	8.57741			0.520082
$273$	14.3445	+	4.53162i	0.868170	+	0.274266i
$274$	−26.1116			−1.57746
$275$		0			0
$276$	36.9171			2.22215
$277$	−26.1574			−1.57165			−0.785824	−	0.618451i	$-0.787761\pi$
$277$	−26.1574			−1.57165			−0.785824	+	0.618451i	$0.787761\pi$
$278$		−	3.42259i		−	0.205274i
$279$		−	42.0032i		−	2.51467i
$280$		0			0
$281$			6.64325i			0.396303i	0.980171	+	0.198152i	$0.0634938\pi$
$281$			6.64325i			0.396303i	−0.980171	+	0.198152i	$0.936506\pi$
$282$	8.70388			0.518308
$283$	17.5423			1.04278			0.521390	−	0.853318i	$-0.325414\pi$
$283$	17.5423			1.04278			0.521390	+	0.853318i	$0.325414\pi$
$284$		−	1.03031i		−	0.0611378i
$285$		0			0
$286$	−8.46096	+	26.7826i	−0.500307	+	1.58369i
$287$	9.29612			0.548733
$288$			52.7555i			3.10865i
$289$	−9.68904			−0.569944
$290$		0			0
$291$		−	10.1723i		−	0.596308i
$292$		−	8.69385i		−	0.508769i
$293$			13.9442i			0.814628i	0.913288	+	0.407314i	$0.133535\pi$
$293$			13.9442i			0.814628i	−0.913288	+	0.407314i	$0.866465\pi$
$294$		−	33.2994i		−	1.94206i
$295$		0			0
$296$	5.39773			0.313737
$297$			40.6136i			2.35664i
$298$	6.87614			0.398324
$299$	5.52420	−	17.4865i	0.319473	−	1.01127i
$300$		0			0
$301$			0.283896i			0.0163635i
$302$	−20.1494			−1.15947
$303$	−49.9097			−2.86724
$304$		−	1.38967i		−	0.0797031i
$305$		0			0
$306$			36.8007i			2.10375i
$307$		−	28.2132i		−	1.61021i	−0.593129	−	0.805107i	$-0.702108\pi$
$307$		−	28.2132i		−	1.61021i	0.593129	−	0.805107i	$-0.297892\pi$
$308$	−11.8735			−0.676557
$309$	32.5726			1.85299
$310$		0			0
$311$	−7.23550			−0.410287			−0.205144	−	0.978732i	$-0.565766\pi$
$311$	−7.23550			−0.410287			−0.205144	+	0.978732i	$0.565766\pi$
$312$	−7.79001	−	2.46096i	−0.441022	−	0.139325i
$313$	21.7523			1.22951			0.614756	−	0.788718i	$-0.289255\pi$
$313$	21.7523			1.22951			0.614756	+	0.788718i	$0.289255\pi$
$314$			24.1574i			1.36328i
$315$		0			0
$316$	−35.3929			−1.99101
$317$			14.7449i			0.828154i	0.910242	+	0.414077i	$0.135896\pi$
$317$			14.7449i			0.828154i	−0.910242	+	0.414077i	$0.864104\pi$
$318$		−	9.45355i		−	0.530128i
$319$		−	5.04840i		−	0.282656i
$320$		0			0
$321$	−41.4487			−2.31344
$322$	14.3445			0.799389
$323$		−	1.18449i		−	0.0659066i
$324$	−32.9097			−1.82832
$325$		0			0
$326$	−39.6210			−2.19440
$327$		−	35.9245i		−	1.98663i
$328$	−5.04840			−0.278751
$329$	1.82774			0.100767
$330$		0			0
$331$		−	34.0181i		−	1.86980i	−0.354907	−	0.934902i	$-0.615488\pi$
$331$		−	34.0181i		−	1.86980i	0.354907	−	0.934902i	$-0.384512\pi$
$332$		−	1.11905i		−	0.0614160i
$333$		−	47.9655i		−	2.62849i
$334$	−35.3223			−1.93275
$335$		0			0
$336$			13.2355i			0.722056i
$337$	15.3929			0.838506			0.419253	−	0.907869i	$-0.362292\pi$
$337$	15.3929			0.838506			0.419253	+	0.907869i	$0.362292\pi$
$338$	−15.5800	+	22.1978i	−0.847441	+	1.20740i
$339$	42.4413			2.30510
$340$		0			0
$341$	24.0410			1.30189
$342$	5.96227			0.322403
$343$		−	16.4562i		−	0.888549i
$344$		−	0.154174i		−	0.00831249i
$345$		0			0
$346$			22.4562i			1.20725i
$347$	2.89903			0.155628			0.0778141	−	0.996968i	$-0.475206\pi$
$347$	2.89903			0.155628			0.0778141	+	0.996968i	$0.475206\pi$
$348$	9.81290			0.526027
$349$		−	18.2839i		−	0.978714i	−0.872083	−	0.489357i	$-0.837231\pi$
$349$		−	18.2839i		−	0.978714i	0.872083	−	0.489357i	$-0.162769\pi$
$350$		0			0
$351$	−11.8129	+	37.3929i	−0.630526	+	1.99589i
$352$	−30.1952			−1.60941
$353$			21.1042i			1.12326i	0.827387	+	0.561632i	$0.189826\pi$
$353$			21.1042i			1.12326i	−0.827387	+	0.561632i	$0.810174\pi$
$354$	−14.5874			−0.775313
$355$		0			0
$356$			25.9852i			1.37721i
$357$			11.2813i			0.597069i
$358$			38.6284i			2.04158i
$359$		−	34.5349i		−	1.82268i	−0.411654	−	0.911340i	$-0.635049\pi$
$359$		−	34.5349i		−	1.82268i	0.411654	−	0.911340i	$-0.364951\pi$
$360$		0			0
$361$	18.8081			0.989900
$362$		−	25.6358i		−	1.34739i
$363$	−9.08613			−0.476898
$364$	−10.9320	−	3.45355i	−0.572990	−	0.181015i
$365$		0			0
$366$		−	22.6890i		−	1.18598i
$367$	−1.60291			−0.0836713			−0.0418356	−	0.999125i	$-0.513321\pi$
$367$	−1.60291			−0.0836713			−0.0418356	+	0.999125i	$0.513321\pi$
$368$	16.1345			0.841070
$369$			44.8613i			2.33539i
$370$		0			0
$371$		−	1.98516i		−	0.103065i
$372$			46.7300i			2.42284i
$373$	−19.5800			−1.01381			−0.506907	−	0.862000i	$-0.669211\pi$
$373$	−19.5800			−1.01381			−0.506907	+	0.862000i	$0.669211\pi$
$374$	−21.0632			−1.08915
$375$		0			0
$376$	−0.992582			−0.0511885
$377$	1.46838	−	4.64806i	0.0756255	−	0.239387i
$378$	−30.6742			−1.57771
$379$			6.36261i			0.326825i	0.986558	+	0.163413i	$0.0522502\pi$
$379$			6.36261i			0.326825i	−0.986558	+	0.163413i	$0.947750\pi$
$380$		0			0
$381$	−12.2281			−0.626463
$382$		−	11.2813i		−	0.577201i
$383$		−	15.9804i		−	0.816558i	−0.912857	−	0.408279i	$-0.866129\pi$
$383$		−	15.9804i		−	0.816558i	0.912857	−	0.408279i	$-0.133871\pi$
$384$		−	17.8458i		−	0.910691i
$385$		0			0
$386$	39.8639			2.02902
$387$	−1.37003			−0.0696423
$388$			7.75228i			0.393562i
$389$	21.5046			1.09032			0.545162	−	0.838331i	$-0.316468\pi$
$389$	21.5046			1.09032			0.545162	+	0.838331i	$0.316468\pi$
$390$		0			0
$391$	13.7523			0.695483
$392$			3.79743i			0.191799i
$393$	−34.0968			−1.71996
$394$	25.6258			1.29101
$395$		0			0
$396$		−	57.2994i		−	2.87940i
$397$			15.4636i			0.776095i	0.921639	+	0.388047i	$0.126850\pi$
$397$			15.4636i			0.776095i	−0.921639	+	0.388047i	$0.873150\pi$
$398$			1.59485i			0.0799428i
$399$	1.82774			0.0915014
$400$		0			0
$401$			25.7523i			1.28601i	0.765863	+	0.643004i	$0.222312\pi$
$401$			25.7523i			1.28601i	−0.765863	+	0.643004i	$0.777688\pi$
$402$	74.1936			3.70044
$403$	22.1345	+	6.99258i	1.10260	+	0.348325i
$404$	38.0362			1.89237
$405$		0			0
$406$	3.81290			0.189231
$407$	27.4535			1.36082
$408$		−	6.12647i		−	0.303306i
$409$			10.5316i			0.520755i	0.965507	+	0.260377i	$0.0838470\pi$
$409$			10.5316i			0.520755i	−0.965507	+	0.260377i	$0.916153\pi$
$410$		0			0
$411$		−	38.6284i		−	1.90540i
$412$	−24.8236			−1.22297
$413$	−3.06324			−0.150732
$414$			69.2239i			3.40217i
$415$		0			0
$416$	−27.8007	−	8.78259i	−1.36304	−	0.430602i
$417$	5.06324			0.247948
$418$			3.41256i			0.166914i
$419$	7.46838			0.364854			0.182427	−	0.983219i	$-0.441605\pi$
$419$	7.46838			0.364854			0.182427	+	0.983219i	$0.441605\pi$
$420$		0			0
$421$		−	35.4897i		−	1.72966i	−0.502062	−	0.864832i	$-0.667425\pi$
$421$		−	35.4897i		−	1.72966i	0.502062	−	0.864832i	$-0.332575\pi$
$422$			16.5316i			0.804747i
$423$			8.82032i			0.428859i
$424$			1.07807i			0.0523558i
$425$		0			0
$426$	2.82032			0.136645
$427$		−	4.76450i		−	0.230570i
$428$	31.5881			1.52687
$429$	−39.6210	−	12.5168i	−1.91292	−	0.604316i
$430$		0			0
$431$			0.154174i			0.00742629i	0.999993	+	0.00371315i	$0.00118193\pi$
$431$			0.154174i			0.00742629i	−0.999993	+	0.00371315i	$0.998818\pi$
$432$	−34.5019			−1.65998
$433$	5.65548			0.271785			0.135892	−	0.990724i	$-0.456610\pi$
$433$	5.65548			0.271785			0.135892	+	0.990724i	$0.456610\pi$
$434$			18.1574i			0.871584i
$435$		0			0
$436$			27.3781i			1.31117i
$437$		−	2.22808i		−	0.106583i
$438$	23.7981			1.13712
$439$	−26.9729			−1.28735			−0.643674	−	0.765300i	$-0.722591\pi$
$439$	−26.9729			−1.28735			−0.643674	+	0.765300i	$0.722591\pi$
$440$		0			0
$441$	33.7449			1.60690
$442$	−19.3929	−	6.12647i	−0.922427	−	0.291407i
$443$	−29.3700			−1.39541			−0.697706	−	0.716384i	$-0.745796\pi$
$443$	−29.3700			−1.39541			−0.697706	+	0.716384i	$0.745796\pi$
$444$			53.3632i			2.53251i
$445$		0			0
$446$	8.94679			0.423643
$447$			10.1723i			0.481131i
$448$		−	14.2281i		−	0.672214i
$449$			31.6768i			1.49492i	0.664306	+	0.747461i	$0.268727\pi$
$449$			31.6768i			1.49492i	−0.664306	+	0.747461i	$0.731273\pi$
$450$		0			0
$451$	−25.6768			−1.20907
$452$	−32.3445			−1.52136
$453$		−	29.8081i		−	1.40051i
$454$	53.2159			2.49754
$455$		0			0
$456$	−0.992582			−0.0464819
$457$			21.1696i			0.990274i	0.868815	+	0.495137i	$0.164882\pi$
$457$			21.1696i			0.990274i	−0.868815	+	0.495137i	$0.835118\pi$
$458$	52.3807			2.44759
$459$	−29.4078			−1.37264
$460$		0			0
$461$			35.2058i			1.63970i	0.572579	+	0.819849i	$0.305943\pi$
$461$			35.2058i			1.63970i	−0.572579	+	0.819849i	$0.694057\pi$
$462$		−	32.5019i		−	1.51213i
$463$			1.35194i			0.0628299i	0.999506	+	0.0314150i	$0.0100013\pi$
$463$			1.35194i			0.0628299i	−0.999506	+	0.0314150i	$0.989999\pi$
$464$	4.28870			0.199098
$465$		0			0
$466$		−	31.9097i		−	1.47819i
$467$	−31.6635			−1.46521			−0.732607	−	0.680652i	$-0.761697\pi$
$467$	−31.6635			−1.46521			−0.732607	+	0.680652i	$0.761697\pi$
$468$	16.6661	−	52.7555i	0.770393	−	2.43863i
$469$	15.5800			0.719418
$470$		0			0
$471$	−35.7374			−1.64669
$472$	1.66354			0.0765705
$473$		−	0.784148i		−	0.0360552i
$474$		−	96.8826i		−	4.44997i
$475$		0			0
$476$		−	8.59746i		−	0.394064i
$477$	9.58002			0.438639
$478$	−28.5248			−1.30470
$479$			13.3142i			0.608342i	0.952617	+	0.304171i	$0.0983794\pi$
$479$			13.3142i			0.608342i	−0.952617	+	0.304171i	$0.901621\pi$
$480$		0			0
$481$	25.2765	+	7.98516i	1.15251	+	0.364092i
$482$	26.1116			1.18935
$483$			21.2207i			0.965573i
$484$	6.92454			0.314752
$485$		0			0
$486$		−	22.0181i		−	0.998761i
$487$			8.89578i			0.403106i	0.979478	+	0.201553i	$0.0645989\pi$
$487$			8.89578i			0.403106i	−0.979478	+	0.201553i	$0.935401\pi$
$488$			2.58744i			0.117128i
$489$		−	58.6136i		−	2.65060i
$490$		0			0
$491$	9.52901			0.430038			0.215019	−	0.976610i	$-0.431019\pi$
$491$	9.52901			0.430038			0.215019	+	0.976610i	$0.431019\pi$
$492$		−	49.9097i		−	2.25010i
$493$	3.65548			0.164635
$494$	−0.992582	+	3.14195i	−0.0446584	+	0.141363i
$495$		0			0
$496$			20.4232i			0.917030i
$497$	0.592243			0.0265657
$498$	3.06324			0.137267
$499$			25.4716i			1.14027i	0.821552	+	0.570133i	$0.193109\pi$
$499$			25.4716i			1.14027i	−0.821552	+	0.570133i	$0.806891\pi$
$500$		0			0
$501$		−	52.2542i		−	2.33455i
$502$		−	30.5168i		−	1.36203i
$503$	32.6661			1.45651			0.728256	−	0.685305i	$-0.240331\pi$
$503$	32.6661			1.45651			0.728256	+	0.685305i	$0.240331\pi$
$504$	6.47580			0.288455
$505$		0			0
$506$	−39.6210			−1.76137
$507$	−32.8384	−	23.0484i	−1.45840	−	1.02362i
$508$	9.31902			0.413464
$509$		−	8.41998i		−	0.373209i	−0.982435	−	0.186605i	$-0.940252\pi$
$509$		−	8.41998i		−	0.373209i	0.982435	−	0.186605i	$-0.0597483\pi$
$510$		0			0
$511$	4.99739			0.221071
$512$		−	30.3094i		−	1.33950i
$513$			4.76450i			0.210358i
$514$		−	58.6136i		−	2.58533i
$515$		0			0
$516$	1.52420			0.0670991
$517$	−5.04840			−0.222028
$518$			20.7348i			0.911036i
$519$	−33.2207			−1.45823
$520$		0			0
$521$	27.3371			1.19766			0.598830	−	0.800876i	$-0.295632\pi$
$521$	27.3371			1.19766			0.598830	+	0.800876i	$0.295632\pi$
$522$			18.4003i			0.805361i
$523$	7.77517			0.339985			0.169992	−	0.985445i	$-0.445626\pi$
$523$	7.77517			0.339985			0.169992	+	0.985445i	$0.445626\pi$
$524$	25.9852			1.13517
$525$		0			0
$526$			32.9091i			1.43490i
$527$			17.4078i			0.758294i
$528$		−	36.5578i		−	1.59097i
$529$	2.86872			0.124727
$530$		0			0
$531$		−	14.7826i		−	0.641510i
$532$	−1.39292			−0.0603907
$533$	−23.6406	−	7.46838i	−1.02399	−	0.323492i
$534$	−71.1304			−3.07811
$535$		0			0
$536$	−8.46096			−0.365458
$537$	−57.1452			−2.46600
$538$			8.70388i			0.375251i
$539$			19.3142i			0.831922i
$540$		0			0
$541$			2.77934i			0.119493i	0.998214	+	0.0597466i	$0.0190293\pi$
$541$			2.77934i			0.119493i	−0.998214	+	0.0597466i	$0.980971\pi$
$542$	12.6810			0.544695
$543$	37.9245			1.62750
$544$		−	21.8639i		−	0.937408i
$545$		0			0
$546$	9.45355	−	29.9245i	0.404574	−	1.28065i
$547$	38.4184			1.64265			0.821327	−	0.570458i	$-0.193234\pi$
$547$	38.4184			1.64265			0.821327	+	0.570458i	$0.193234\pi$
$548$			29.4387i			1.25756i
$549$	22.9926			0.981299
$550$		0			0
$551$		−	0.592243i		−	0.0252304i
$552$		−	11.5242i		−	0.490503i
$553$		−	20.3445i		−	0.865137i
$554$			54.5678i			2.31836i
$555$		0			0
$556$	−3.85869			−0.163645
$557$			7.11905i			0.301644i	0.988561	+	0.150822i	$0.0481920\pi$
$557$			7.11905i			0.301644i	−0.988561	+	0.150822i	$0.951808\pi$
$558$	−87.6242			−3.70943
$559$	0.228078	−	0.721965i	0.00964667	−	0.0305359i
$560$		0			0
$561$		−	31.1600i		−	1.31558i
$562$	13.8587			0.584594
$563$	32.8236			1.38335			0.691674	−	0.722210i	$-0.256873\pi$
$563$	32.8236			1.38335			0.691674	+	0.722210i	$0.256873\pi$
$564$		−	9.81290i		−	0.413198i
$565$		0			0
$566$		−	36.5955i		−	1.53822i
$567$		−	18.9171i		−	0.794444i
$568$	−0.321627			−0.0134952
$569$	−15.4126			−0.646128			−0.323064	−	0.946377i	$-0.604713\pi$
$569$	−15.4126			−0.646128			−0.323064	+	0.946377i	$0.604713\pi$
$570$		0			0
$571$	−31.5142			−1.31883			−0.659413	−	0.751780i	$-0.729195\pi$
$571$	−31.5142			−1.31883			−0.659413	+	0.751780i	$0.729195\pi$
$572$	30.1952	+	9.53904i	1.26252	+	0.398847i
$573$	16.6890			0.697195
$574$		−	19.3929i		−	0.809445i
$575$		0			0
$576$	68.6620			2.86092
$577$		−	44.3855i		−	1.84779i	−0.382643	−	0.923896i	$-0.624986\pi$
$577$		−	44.3855i		−	1.84779i	0.382643	−	0.923896i	$-0.375014\pi$
$578$			20.2126i			0.840733i
$579$			58.9729i			2.45083i
$580$		0			0
$581$	0.643253			0.0266866
$582$	−21.2207			−0.879625
$583$			5.48322i			0.227092i
$584$	−2.71391			−0.112302
$585$		0			0
$586$	29.0894			1.20167
$587$		−	13.3519i		−	0.551094i	−0.961288	−	0.275547i	$-0.911141\pi$
$587$		−	13.3519i		−	0.551094i	0.961288	−	0.275547i	$-0.0888589\pi$
$588$	−37.5423			−1.54822
$589$	2.82032			0.116209
$590$		0			0
$591$			37.9097i			1.55940i
$592$			23.3223i			0.958539i
$593$			37.3929i			1.53554i	0.640724	+	0.767772i	$0.278634\pi$
$593$			37.3929i			1.53554i	−0.640724	+	0.767772i	$0.721366\pi$
$594$	84.7252			3.47632
$595$		0			0
$596$		−	7.75228i		−	0.317546i
$597$	−2.35936			−0.0965621
$598$	−36.4791	−	11.5242i	−1.49174	−	0.471260i
$599$	13.8277			0.564986			0.282493	−	0.959269i	$-0.408839\pi$
$599$	13.8277			0.564986			0.282493	+	0.959269i	$0.408839\pi$
$600$		0			0
$601$	6.34452			0.258798			0.129399	−	0.991593i	$-0.458695\pi$
$601$	6.34452			0.258798			0.129399	+	0.991593i	$0.458695\pi$
$602$	0.592243			0.0241380
$603$			75.1862i			3.06182i
$604$			22.7167i			0.924331i
$605$		0			0
$606$			104.118i			4.22951i
$607$	16.2462			0.659411			0.329706	−	0.944084i	$-0.393050\pi$
$607$	16.2462			0.659411			0.329706	+	0.944084i	$0.393050\pi$
$608$	−3.54229			−0.143659
$609$			5.64064i			0.228570i
$610$		0			0
$611$	−4.64806	−	1.46838i	−0.188040	−	0.0594044i
$612$	41.4897			1.67712
$613$			22.6890i			0.916402i	0.888849	+	0.458201i	$0.151506\pi$
$613$			22.6890i			0.916402i	−0.888849	+	0.458201i	$0.848494\pi$
$614$	−58.8565			−2.37525
$615$		0			0
$616$			3.70649i			0.149339i
$617$		−	9.01223i		−	0.362819i	−0.983408	−	0.181409i	$-0.941934\pi$
$617$		−	9.01223i		−	0.362819i	0.983408	−	0.181409i	$-0.0580659\pi$
$618$		−	67.9507i		−	2.73338i
$619$		−	3.45030i		−	0.138679i	−0.997593	−	0.0693395i	$-0.977911\pi$
$619$		−	3.45030i		−	0.138679i	0.997593	−	0.0693395i	$-0.0220892\pi$
$620$		0			0
$621$	−55.3175			−2.21981
$622$			15.0942i			0.605222i
$623$	−14.9368			−0.598429
$624$	10.6332	−	33.6587i	0.425670	−	1.34743i
$625$		0			0
$626$		−	45.3781i		−	1.81367i
$627$	−5.04840			−0.201614
$628$	27.2355			1.08681
$629$			19.8787i			0.792618i
$630$		0			0
$631$			24.9549i			0.993437i	0.867912	+	0.496718i	$0.165462\pi$
$631$			24.9549i			0.993437i	−0.867912	+	0.496718i	$0.834538\pi$
$632$			11.0484i			0.439482i
$633$	−24.4562			−0.972045
$634$	30.7597			1.22162
$635$		0			0
$636$	−10.6581			−0.422621
$637$	−5.61775	+	17.7826i	−0.222583	+	0.704572i
$638$	−10.5316			−0.416951
$639$			2.85805i			0.113063i
$640$		0			0
$641$	−41.1304			−1.62455			−0.812276	−	0.583274i	$-0.801772\pi$
$641$	−41.1304			−1.62455			−0.812276	+	0.583274i	$0.801772\pi$
$642$			86.4675i			3.41260i
$643$		−	7.22547i		−	0.284945i	−0.989799	−	0.142472i	$-0.954495\pi$
$643$		−	7.22547i		−	0.284945i	0.989799	−	0.142472i	$-0.0455052\pi$
$644$		−	16.1723i		−	0.637276i
$645$		0			0
$646$	−2.47099			−0.0972199
$647$	−8.45771			−0.332507			−0.166254	−	0.986083i	$-0.553167\pi$
$647$	−8.45771			−0.332507			−0.166254	+	0.986083i	$0.553167\pi$
$648$			10.2732i			0.403570i
$649$	8.46096			0.332122
$650$		0			0
$651$	−26.8613			−1.05278
$652$			44.6694i			1.74939i
$653$	16.3807			0.641026			0.320513	−	0.947244i	$-0.396145\pi$
$653$	16.3807			0.641026			0.320513	+	0.947244i	$0.396145\pi$
$654$	−74.9433			−2.93051
$655$		0			0
$656$		−	21.8129i		−	0.851651i
$657$			24.1164i			0.940872i
$658$		−	3.81290i		−	0.148642i
$659$	−0.308348			−0.0120115			−0.00600576	−	0.999982i	$-0.501912\pi$
$659$	−0.308348			−0.0120115			−0.00600576	+	0.999982i	$0.501912\pi$
$660$		0			0
$661$			32.7858i			1.27522i	0.770359	+	0.637611i	$0.220077\pi$
$661$			32.7858i			1.27522i	−0.770359	+	0.637611i	$0.779923\pi$
$662$	−70.9662			−2.75818
$663$	9.06324	−	28.6890i	0.351987	−	1.11419i
$664$	−0.349328			−0.0135566
$665$		0			0
$666$	−100.062			−3.87734
$667$	6.87614			0.266245
$668$			39.8229i			1.54080i
$669$			13.2355i			0.511714i
$670$		0			0
$671$			13.1600i			0.508037i
$672$	33.7374			1.30145
$673$	−21.7523			−0.838489			−0.419244	−	0.907873i	$-0.637705\pi$
$673$	−21.7523			−0.838489			−0.419244	+	0.907873i	$0.637705\pi$
$674$		−	32.1116i		−	1.23689i
$675$		0			0
$676$	25.0261	+	17.5652i	0.962544	+	0.675584i
$677$	14.4200			0.554205			0.277102	−	0.960840i	$-0.410626\pi$
$677$	14.4200			0.554205			0.277102	+	0.960840i	$0.410626\pi$
$678$		−	88.5381i		−	3.40029i
$679$	−4.45616			−0.171012
$680$		0			0
$681$			78.7252i			3.01676i
$682$		−	50.1526i		−	1.92044i
$683$		−	39.1797i		−	1.49917i	−0.661909	−	0.749584i	$-0.730253\pi$
$683$		−	39.1797i		−	1.49917i	0.661909	−	0.749584i	$-0.269747\pi$
$684$		−	6.72197i		−	0.257021i
$685$		0			0
$686$	−34.3297			−1.31071
$687$			77.4897i			2.95642i
$688$	0.666147			0.0253966
$689$	−1.59485	+	5.04840i	−0.0607591	+	0.192329i
$690$		0			0
$691$		−	5.56193i		−	0.211586i	−0.994388	−	0.105793i	$-0.966262\pi$
$691$		−	5.56193i		−	0.211586i	0.994388	−	0.105793i	$-0.0337381\pi$
$692$	25.3175			0.962425
$693$	32.9368			1.25116
$694$		−	6.04776i		−	0.229570i
$695$		0			0
$696$		−	3.06324i		−	0.116112i
$697$		−	18.5922i		−	0.704231i
$698$	−38.1426			−1.44372
$699$	47.2058			1.78549
$700$		0			0
$701$	9.58002			0.361832			0.180916	−	0.983499i	$-0.442094\pi$
$701$	9.58002			0.361832			0.180916	+	0.983499i	$0.442094\pi$
$702$	78.0065	+	24.6433i	2.94417	+	0.930100i
$703$	3.22066			0.121469
$704$			39.2994i			1.48115i
$705$		0			0
$706$	44.0261			1.65695
$707$			21.8639i			0.822277i
$708$			16.4461i			0.618083i
$709$		−	12.1574i		−	0.456582i	−0.973593	−	0.228291i	$-0.926686\pi$
$709$		−	12.1574i		−	0.456582i	0.973593	−	0.228291i	$-0.0733137\pi$
$710$		0			0
$711$	98.1788			3.68199
$712$	8.11164			0.303996
$713$			32.7449i			1.22630i
$714$	23.5342			0.880746
$715$		0			0
$716$	43.5503			1.62755
$717$		−	42.1984i		−	1.57593i
$718$	−72.0442			−2.68867
$719$	−21.1452			−0.788583			−0.394291	−	0.918985i	$-0.629010\pi$
$719$	−21.1452			−0.788583			−0.394291	+	0.918985i	$0.629010\pi$
$720$		0			0
$721$		−	14.2691i		−	0.531408i
$722$		−	39.2361i		−	1.46022i
$723$			38.6284i			1.43661i
$724$	−28.9023			−1.07414
$725$		0			0
$726$			18.9549i			0.703480i
$727$	−9.72938			−0.360843			−0.180421	−	0.983589i	$-0.557746\pi$
$727$	−9.72938			−0.360843			−0.180421	+	0.983589i	$0.557746\pi$
$728$	−1.07807	+	3.41256i	−0.0399560	+	0.126478i
$729$	−9.40515			−0.348339
$730$		0			0
$731$	0.567791			0.0210005
$732$	−25.5800			−0.945465
$733$			4.40515i			0.162708i	0.996685	+	0.0813539i	$0.0259244\pi$
$733$			4.40515i			0.162708i	−0.996685	+	0.0813539i	$0.974076\pi$
$734$			3.34388i			0.123425i
$735$		0			0
$736$		−	41.1271i		−	1.51597i
$737$	−43.0336			−1.58516
$738$	93.5865			3.44497
$739$			12.4891i			0.459418i	0.973259	+	0.229709i	$0.0737775\pi$
$739$			12.4891i			0.459418i	−0.973259	+	0.229709i	$0.926223\pi$
$740$		0			0
$741$	−4.64806	−	1.46838i	−0.170751	−	0.0539424i
$742$	−4.14131			−0.152032
$743$		−	23.7571i		−	0.871563i	−0.900053	−	0.435781i	$-0.856472\pi$
$743$		−	23.7571i		−	0.871563i	0.900053	−	0.435781i	$-0.143528\pi$
$744$	14.5874			0.534801
$745$		0			0
$746$			40.8465i			1.49550i
$747$			3.10422i			0.113577i
$748$			23.7471i			0.868278i
$749$			18.1574i			0.663458i
$750$		0			0
$751$	32.1574			1.17344			0.586721	−	0.809789i	$-0.300419\pi$
$751$	32.1574			1.17344			0.586721	+	0.809789i	$0.300419\pi$
$752$		−	4.28870i		−	0.156393i
$753$	45.1452			1.64518
$754$	−9.69646	−	3.06324i	−0.353124	−	0.111556i
$755$		0			0
$756$			34.5826i			1.25776i
$757$	36.1723			1.31470			0.657352	−	0.753584i	$-0.271677\pi$
$757$	36.1723			1.31470			0.657352	+	0.753584i	$0.271677\pi$
$758$	13.2732			0.482105
$759$		−	58.6136i		−	2.12754i
$760$		0			0
$761$		−	33.8639i		−	1.22757i	−0.789475	−	0.613783i	$-0.789647\pi$
$761$		−	33.8639i		−	1.22757i	0.789475	−	0.613783i	$-0.210353\pi$
$762$			25.5094i			0.924107i
$763$	−15.7374			−0.569734
$764$	−12.7187			−0.460147
$765$		0			0
$766$	−33.3371			−1.20452
$767$	7.79001	+	2.46096i	0.281281	+	0.0888602i
$768$	27.7294			1.00060
$769$		−	21.8639i		−	0.788433i	−0.919018	−	0.394216i	$-0.871016\pi$
$769$		−	21.8639i		−	0.788433i	0.919018	−	0.394216i	$-0.128984\pi$
$770$		0			0
$771$	86.7104			3.12280
$772$		−	44.9433i		−	1.61754i
$773$			22.1378i			0.796241i	0.917333	+	0.398120i	$0.130337\pi$
$773$			22.1378i			0.796241i	−0.917333	+	0.398120i	$0.869663\pi$
$774$			2.85805i			0.102731i
$775$		0			0
$776$	2.41998			0.0868723
$777$	−30.6742			−1.10043
$778$		−	44.8613i		−	1.60836i
$779$	−3.01223			−0.107924
$780$		0			0
$781$	−1.63583			−0.0585348
$782$		−	28.6890i		−	1.02592i
$783$	−14.7039			−0.525474
$784$	−16.4078			−0.585991
$785$		0			0
$786$			71.1304i			2.53714i
$787$			15.2616i			0.544019i	0.962295	+	0.272009i	$0.0876882\pi$
$787$			15.2616i			0.544019i	−0.962295	+	0.272009i	$0.912312\pi$
$788$		−	28.8910i		−	1.02920i
$789$	−48.6842			−1.73320
$790$		0			0
$791$		−	18.5922i		−	0.661064i
$792$	−17.8868			−0.635580
$793$	−3.82774	+	12.1164i	−0.135927	+	0.430267i
$794$	32.2590			1.14483
$795$		0			0
$796$	1.79807			0.0637308
$797$	9.22066			0.326613			0.163306	−	0.986575i	$-0.447784\pi$
$797$	9.22066			0.326613			0.163306	+	0.986575i	$0.447784\pi$
$798$		−	3.81290i		−	0.134975i
$799$		−	3.65548i		−	0.129322i
$800$		0			0
$801$		−	72.0820i		−	2.54689i
$802$	53.7226			1.89701
$803$	−13.8033			−0.487107
$804$		−	83.6471i		−	2.95001i
$805$		0			0
$806$	14.5874	−	46.1755i	0.513821	−	1.62646i
$807$	−12.8761			−0.453262
$808$		−	11.8735i		−	0.417709i
$809$	0.167453			0.00588733			0.00294366	−	0.999996i	$-0.499063\pi$
$809$	0.167453			0.00588733			0.00294366	+	0.999996i	$0.499063\pi$
$810$		0			0
$811$		−	36.0032i		−	1.26425i	−0.774868	−	0.632123i	$-0.782184\pi$
$811$		−	36.0032i		−	1.26425i	0.774868	−	0.632123i	$-0.217816\pi$
$812$		−	4.29873i		−	0.150856i
$813$			18.7597i			0.657931i
$814$		−	57.2717i		−	2.00737i
$815$		0			0
$816$	26.4710			0.926670
$817$		−	0.0919908i		−	0.00321835i
$818$	21.9703			0.768174
$819$	30.3249	+	9.58002i	1.05964	+	0.334753i
$820$		0			0
$821$		−	5.04840i		−	0.176190i	−0.996112	−	0.0880952i	$-0.971922\pi$
$821$		−	5.04840i		−	0.176190i	0.996112	−	0.0880952i	$-0.0280780\pi$
$822$	−80.5839			−2.81069
$823$	−11.3094			−0.394221			−0.197110	−	0.980381i	$-0.563156\pi$
$823$	−11.3094			−0.394221			−0.197110	+	0.980381i	$0.563156\pi$
$824$			7.74903i			0.269950i
$825$		0			0
$826$			6.39031i			0.222347i
$827$			43.8687i			1.52546i	0.646714	+	0.762732i	$0.276143\pi$
$827$			43.8687i			1.52546i	−0.646714	+	0.762732i	$0.723857\pi$
$828$	78.0442			2.71222
$829$	44.4461			1.54368			0.771839	−	0.635818i	$-0.219337\pi$
$829$	44.4461			1.54368			0.771839	+	0.635818i	$0.219337\pi$
$830$		0			0
$831$	−80.7252			−2.80033
$832$	−11.4307	+	36.1829i	−0.396287	+	1.25442i
$833$	−13.9852			−0.484557
$834$		−	10.5626i		−	0.365752i
$835$		0			0
$836$	3.84738			0.133065
$837$		−	70.0213i		−	2.42029i
$838$		−	15.5800i		−	0.538203i
$839$		−	1.44068i		−	0.0497378i	−0.999691	−	0.0248689i	$-0.992083\pi$
$839$		−	1.44068i		−	0.0497378i	0.999691	−	0.0248689i	$-0.00791683\pi$
$840$		0			0
$841$	−27.1723			−0.936974
$842$	−74.0362			−2.55146
$843$			20.5019i			0.706124i
$844$	18.6380			0.641548
$845$		0			0
$846$	18.4003			0.632617
$847$			3.98036i			0.136767i
$848$	−4.65809			−0.159959
$849$	54.1378			1.85800
$850$		0			0
$851$			37.3929i			1.28181i
$852$		−	3.17968i		−	0.108934i
$853$		−	0.992582i		−	0.0339853i	−0.999856	−	0.0169927i	$-0.994591\pi$
$853$		−	0.992582i		−	0.0339853i	0.999856	−	0.0169927i	$-0.00540920\pi$
$854$	−9.93937			−0.340118
$855$		0			0
$856$		−	9.86066i		−	0.337031i
$857$	−10.6071			−0.362331			−0.181165	−	0.983453i	$-0.557987\pi$
$857$	−10.6071			−0.362331			−0.181165	+	0.983453i	$0.557987\pi$
$858$	−26.1116	+	82.6546i	−0.891437	+	2.82178i
$859$	−40.9123			−1.39591			−0.697955	−	0.716142i	$-0.745906\pi$
$859$	−40.9123			−1.39591			−0.697955	+	0.716142i	$0.745906\pi$
$860$		0			0
$861$	28.6890			0.977720
$862$	0.321627			0.0109546
$863$		−	48.2494i		−	1.64243i	−0.570619	−	0.821215i	$-0.693297\pi$
$863$		−	48.2494i		−	1.64243i	0.570619	−	0.821215i	$-0.306703\pi$
$864$			87.9459i			2.99198i
$865$		0			0
$866$		−	11.7981i		−	0.400915i
$867$	−29.9016			−1.01551
$868$	20.4710			0.694831
$869$			56.1936i			1.90624i
$870$		0			0
$871$	−39.6210	−	12.5168i	−1.34251	−	0.424115i
$872$	8.54645			0.289419
$873$		−	21.5046i		−	0.727819i
$874$	−4.64806			−0.157223
$875$		0			0
$876$		−	26.8304i		−	0.906514i
$877$		−	4.81551i		−	0.162608i	−0.996689	−	0.0813042i	$-0.974091\pi$
$877$		−	4.81551i		−	0.162608i	0.996689	−	0.0813042i	$-0.0259085\pi$
$878$			56.2691i			1.89899i
$879$			43.0336i			1.45149i
$880$		0			0
$881$	−21.6210			−0.728430			−0.364215	−	0.931315i	$-0.618663\pi$
$881$	−21.6210			−0.728430			−0.364215	+	0.931315i	$0.618663\pi$
$882$		−	70.3962i		−	2.37036i
$883$	−21.1616			−0.712144			−0.356072	−	0.934458i	$-0.615884\pi$
$883$	−21.1616			−0.712144			−0.356072	+	0.934458i	$0.615884\pi$
$884$	−6.90709	+	21.8639i	−0.232311	+	0.735363i
$885$		0			0
$886$			61.2697i			2.05840i
$887$	9.10097			0.305581			0.152790	−	0.988259i	$-0.451174\pi$
$887$	9.10097			0.305581			0.152790	+	0.988259i	$0.451174\pi$
$888$	16.6581			0.559009
$889$			5.35675i			0.179660i
$890$		0			0
$891$			52.2510i			1.75047i
$892$		−	10.0868i		−	0.337730i
$893$	−0.592243			−0.0198187
$894$	21.2207			0.709725
$895$		0			0
$896$	−7.81771			−0.261171
$897$	17.0484	−	53.9655i	0.569229	−	1.80186i
$898$	66.0820			2.20518
$899$			8.70388i			0.290291i
$900$		0			0
$901$	−3.97033			−0.132271
$902$			53.5652i			1.78353i
$903$			0.876139i			0.0291561i
$904$			10.0968i			0.335815i
$905$		0			0
$906$	−62.1836			−2.06591
$907$	43.2436			1.43588			0.717939	−	0.696106i	$-0.245086\pi$
$907$	43.2436			1.43588			0.717939	+	0.696106i	$0.245086\pi$
$908$		−	59.9965i		−	1.99105i
$909$	−105.511			−3.49958
$910$		0			0
$911$	23.2058			0.768843			0.384422	−	0.923158i	$-0.374401\pi$
$911$	23.2058			0.768843			0.384422	+	0.923158i	$0.374401\pi$
$912$		−	4.28870i		−	0.142013i
$913$	−1.77673			−0.0588012
$914$	44.1626			1.46077
$915$		0			0
$916$		−	59.0549i		−	1.95123i
$917$			14.9368i			0.493255i
$918$			61.3484i			2.02480i
$919$	0.419983			0.0138540			0.00692698	−	0.999976i	$-0.497795\pi$
$919$	0.419983			0.0138540			0.00692698	+	0.999976i	$0.497795\pi$
$920$		0			0
$921$		−	87.0697i		−	2.86905i
$922$	73.4439			2.41875
$923$	−1.50611	−	0.475800i	−0.0495743	−	0.0156612i
$924$	−36.6433			−1.20547
$925$		0			0
$926$	2.82032			0.0926815
$927$	68.8597			2.26165
$928$		−	10.9320i		−	0.358859i
$929$		−	39.2207i		−	1.28679i	−0.765535	−	0.643394i	$-0.777526\pi$
$929$		−	39.2207i		−	1.28679i	0.765535	−	0.643394i	$-0.222474\pi$
$930$		0			0
$931$			2.26581i			0.0742589i
$932$	−35.9755			−1.17842
$933$	−22.3297			−0.731041
$934$			66.0543i			2.16136i
$935$		0			0
$936$	−16.4684	−	5.20257i	−0.538286	−	0.170051i
$937$	22.5774			0.737572			0.368786	−	0.929514i	$-0.379774\pi$
$937$	22.5774			0.737572			0.368786	+	0.929514i	$0.379774\pi$
$938$		−	32.5019i		−	1.06123i
$939$	67.1304			2.19072
$940$		0			0
$941$		−	18.0510i		−	0.588446i	−0.955737	−	0.294223i	$-0.904939\pi$
$941$		−	18.0510i		−	0.588446i	0.955737	−	0.294223i	$-0.0950609\pi$
$942$			74.5530i			2.42907i
$943$		−	34.9729i		−	1.13888i
$944$			7.18774i			0.233941i
$945$		0			0
$946$	−1.63583			−0.0531856
$947$			24.5578i			0.798020i	0.916947	+	0.399010i	$0.130646\pi$
$947$			24.5578i			0.798020i	−0.916947	+	0.399010i	$0.869354\pi$
$948$	−109.227			−3.54753
$949$	−12.7087	−	4.01484i	−0.412541	−	0.130327i
$950$		0			0
$951$			45.5046i			1.47559i
$952$	−2.68382			−0.0869831
$953$	34.9219			1.13123			0.565616	−	0.824669i	$-0.308638\pi$
$953$	34.9219			1.13123			0.565616	+	0.824669i	$0.308638\pi$
$954$		−	19.9852i		−	0.647044i
$955$		0			0
$956$			32.1594i			1.04011i
$957$		−	15.5800i		−	0.503630i
$958$	27.7752			0.897375
$959$	−16.9219			−0.546438
$960$		0			0
$961$	−10.4487			−0.337056
$962$	16.6581	−	52.7300i	0.537078	−	1.70008i
$963$	−87.6242			−2.82365
$964$		−	29.4387i		−	0.948157i
$965$		0			0
$966$	44.2691			1.42433
$967$			5.16484i			0.166090i	0.996546	+	0.0830451i	$0.0264645\pi$
$967$			5.16484i			0.166090i	−0.996546	+	0.0830451i	$0.973535\pi$
$968$		−	2.16159i		−	0.0694762i
$969$		−	3.65548i		−	0.117431i
$970$		0			0
$971$	14.2935			0.458701			0.229350	−	0.973344i	$-0.426340\pi$
$971$	14.2935			0.458701			0.229350	+	0.973344i	$0.426340\pi$
$972$	−24.8236			−0.796216
$973$		−	2.21805i		−	0.0711074i
$974$	18.5578			0.594629
$975$		0			0
$976$	−11.1797			−0.357853
$977$			0.424790i			0.0135902i	0.999977	+	0.00679512i	$0.00216297\pi$
$977$			0.424790i			0.0135902i	−0.999977	+	0.00679512i	$0.997837\pi$
$978$	−122.276			−3.90994
$979$	41.2568			1.31857
$980$		0			0
$981$		−	75.9459i		−	2.42477i
$982$		−	19.8787i		−	0.634356i
$983$		−	17.8081i		−	0.567990i	−0.958826	−	0.283995i	$-0.908340\pi$
$983$		−	17.8081i		−	0.567990i	0.958826	−	0.283995i	$-0.0916599\pi$
$984$	−15.5800			−0.496673
$985$		0			0
$986$		−	7.62581i		−	0.242855i
$987$	5.64064			0.179544
$988$	3.54229	+	1.11905i	0.112695	+	0.0356018i
$989$	1.06804			0.0339618
$990$		0			0
$991$	−34.7497			−1.10386			−0.551930	−	0.833891i	$-0.686108\pi$
$991$	−34.7497			−1.10386			−0.551930	+	0.833891i	$0.686108\pi$
$992$	52.0591			1.65288
$993$		−	104.984i		−	3.33157i
$994$		−	1.23550i		−	0.0391876i
$995$		0			0
$996$		−	3.45355i		−	0.109430i
$997$	−48.0213			−1.52085			−0.760425	−	0.649425i	$-0.775010\pi$
$997$	−48.0213			−1.52085			−0.760425	+	0.649425i	$0.775010\pi$
$998$	53.1371			1.68203
$999$		−	79.9607i		−	2.52984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.c.g.51.2		6
5.2	odd	4		325.2.d.e.324.5		6
5.3	odd	4		325.2.d.f.324.2		6
5.4	even	2		65.2.c.a.51.5	yes	6
13.5	odd	4		4225.2.a.be.1.1		3
13.8	odd	4		4225.2.a.bc.1.3		3
13.12	even	2	inner	325.2.c.g.51.5		6
15.14	odd	2		585.2.b.g.181.2		6
20.19	odd	2		1040.2.k.d.961.6		6
65.4	even	6		845.2.m.h.361.2		12
65.9	even	6		845.2.m.h.361.5		12
65.12	odd	4		325.2.d.f.324.1		6
65.19	odd	12		845.2.e.k.146.1		6
65.24	odd	12		845.2.e.i.191.3		6
65.29	even	6		845.2.m.h.316.2		12
65.34	odd	4		845.2.a.k.1.1		3
65.38	odd	4		325.2.d.e.324.6		6
65.44	odd	4		845.2.a.i.1.3		3
65.49	even	6		845.2.m.h.316.5		12
65.54	odd	12		845.2.e.k.191.1		6
65.59	odd	12		845.2.e.i.146.3		6
65.64	even	2		65.2.c.a.51.2	✓	6
195.44	even	4		7605.2.a.cc.1.1		3
195.164	even	4		7605.2.a.bs.1.3		3
195.194	odd	2		585.2.b.g.181.5		6
260.259	odd	2		1040.2.k.d.961.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.2	✓	6	65.64	even	2
65.2.c.a.51.5	yes	6	5.4	even	2
325.2.c.g.51.2		6	1.1	even	1	trivial
325.2.c.g.51.5		6	13.12	even	2	inner
325.2.d.e.324.5		6	5.2	odd	4
325.2.d.e.324.6		6	65.38	odd	4
325.2.d.f.324.1		6	65.12	odd	4
325.2.d.f.324.2		6	5.3	odd	4
585.2.b.g.181.2		6	15.14	odd	2
585.2.b.g.181.5		6	195.194	odd	2
845.2.a.i.1.3		3	65.44	odd	4
845.2.a.k.1.1		3	65.34	odd	4
845.2.e.i.146.3		6	65.59	odd	12
845.2.e.i.191.3		6	65.24	odd	12
845.2.e.k.146.1		6	65.19	odd	12
845.2.e.k.191.1		6	65.54	odd	12
845.2.m.h.316.2		12	65.29	even	6
845.2.m.h.316.5		12	65.49	even	6
845.2.m.h.361.2		12	65.4	even	6
845.2.m.h.361.5		12	65.9	even	6
1040.2.k.d.961.5		6	260.259	odd	2
1040.2.k.d.961.6		6	20.19	odd	2
4225.2.a.bc.1.3		3	13.8	odd	4
4225.2.a.be.1.1		3	13.5	odd	4
7605.2.a.bs.1.3		3	195.164	even	4
7605.2.a.cc.1.1		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)

\(f(q)\)	\(=\)	\(q-2.08613i q^{2} +3.08613 q^{3} -2.35194 q^{4} -6.43807i q^{6} -1.35194i q^{7} +0.734191i q^{8} +6.52420 q^{9} +O(q^{10})\)	\(q-2.08613i q^{2} +3.08613 q^{3} -2.35194 q^{4} -6.43807i q^{6} -1.35194i q^{7} +0.734191i q^{8} +6.52420 q^{9} +3.73419i q^{11} -7.25839 q^{12} +(-1.08613 + 3.43807i) q^{13} -2.82032 q^{14} -3.17226 q^{16} -2.70388 q^{17} -13.6103i q^{18} +0.438069i q^{19} -4.17226i q^{21} +7.79001 q^{22} -5.08613 q^{23} +2.26581i q^{24} +(7.17226 + 2.26581i) q^{26} +10.8761 q^{27} +3.17968i q^{28} -1.35194 q^{29} -6.43807i q^{31} +8.08613i q^{32} +11.5242i q^{33} +5.64064i q^{34} -15.3445 q^{36} -7.35194i q^{37} +0.913870 q^{38} +(-3.35194 + 10.6103i) q^{39} +6.87614i q^{41} -8.70388 q^{42} -0.209991 q^{43} -8.78259i q^{44} +10.6103i q^{46} +1.35194i q^{47} -9.79001 q^{48} +5.17226 q^{49} -8.34452 q^{51} +(2.55451 - 8.08613i) q^{52} +1.46838 q^{53} -22.6890i q^{54} +0.992582 q^{56} +1.35194i q^{57} +2.82032i q^{58} -2.26581i q^{59} +3.52420 q^{61} -13.4307 q^{62} -8.82032i q^{63} +10.5242 q^{64} +24.0410 q^{66} +11.5242i q^{67} +6.35936 q^{68} -15.6965 q^{69} +0.438069i q^{71} +4.79001i q^{72} +3.69646i q^{73} -15.3371 q^{74} -1.03031i q^{76} +5.04840 q^{77} +(22.1345 + 6.99258i) q^{78} +15.0484 q^{79} +13.9926 q^{81} +14.3445 q^{82} +0.475800i q^{83} +9.81290i q^{84} +0.438069i q^{86} -4.17226 q^{87} -2.74161 q^{88} -11.0484i q^{89} +(4.64806 + 1.46838i) q^{91} +11.9623 q^{92} -19.8687i q^{93} +2.82032 q^{94} +24.9549i q^{96} -3.29612i q^{97} -10.7900i q^{98} +24.3626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 - 10 * q^4 + 6 * q^9	\( 6 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 8 q^{14} + 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} + 14 q^{26} + 28 q^{27} - 4 q^{29} - 34 q^{36} + 20 q^{38} - 16 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48} + 2 q^{49} + 8 q^{51} - 20 q^{52} - 12 q^{53} - 48 q^{56} - 12 q^{61} - 8 q^{62} + 30 q^{64} + 24 q^{66} + 88 q^{68} - 32 q^{69} + 20 q^{74} - 36 q^{77} + 52 q^{78} + 24 q^{79} + 30 q^{81} + 28 q^{82} + 4 q^{87} - 60 q^{88} + 32 q^{91} + 20 q^{92} - 8 q^{94}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more