LMFDB - Embedded newform 825.4.c.q.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not 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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 574x^{6} + 121601x^{4} + 11262916x^{2} + 384787456 $ x^8 + 574x^6 + 121601x^4 + 11262916*x^2 + 384787456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Root			$-12.6191i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.q.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56155i q^{2} +3.00000i q^{3} +5.56155 q^{4} +4.68466 q^{6} -16.7054i q^{7} -21.1771i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-1.56155i q^{2} +3.00000i q^{3} +5.56155 q^{4} +4.68466 q^{6} -16.7054i q^{7} -21.1771i q^{8} -9.00000 q^{9} -11.0000 q^{11} +16.6847i q^{12} +61.6896i q^{13} -26.0864 q^{14} +11.4233 q^{16} -81.9365i q^{17} +14.0540i q^{18} +66.0105 q^{19} +50.1163 q^{21} +17.1771i q^{22} -118.019i q^{23} +63.5312 q^{24} +96.3315 q^{26} -27.0000i q^{27} -92.9082i q^{28} -4.91776 q^{29} -286.654 q^{31} -187.255i q^{32} -33.0000i q^{33} -127.948 q^{34} -50.0540 q^{36} -271.441i q^{37} -103.079i q^{38} -185.069 q^{39} +117.544 q^{41} -78.2593i q^{42} +364.372i q^{43} -61.1771 q^{44} -184.294 q^{46} -465.470i q^{47} +34.2699i q^{48} +63.9280 q^{49} +245.810 q^{51} +343.090i q^{52} +600.056i q^{53} -42.1619 q^{54} -353.773 q^{56} +198.032i q^{57} +7.67935i q^{58} -647.656 q^{59} -190.684 q^{61} +447.625i q^{62} +150.349i q^{63} -201.022 q^{64} -51.5312 q^{66} -1086.95i q^{67} -455.694i q^{68} +354.058 q^{69} +811.734 q^{71} +190.594i q^{72} -1036.16i q^{73} -423.869 q^{74} +367.121 q^{76} +183.760i q^{77} +288.995i q^{78} -573.141 q^{79} +81.0000 q^{81} -183.551i q^{82} -510.318i q^{83} +278.725 q^{84} +568.986 q^{86} -14.7533i q^{87} +232.948i q^{88} +748.629 q^{89} +1030.55 q^{91} -656.371i q^{92} -859.962i q^{93} -726.856 q^{94} +561.764 q^{96} -96.0399i q^{97} -99.8270i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9	$ 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9} - 88 q^{11} + 6 q^{14} - 156 q^{16} - 236 q^{19} - 66 q^{21} - 36 q^{24} - 314 q^{26} - 502 q^{29} - 270 q^{31} - 578 q^{34} - 252 q^{36} - 150 q^{39} - 206 q^{41} - 308 q^{44} - 840 q^{46} - 2006 q^{49} + 510 q^{51} + 108 q^{54} + 154 q^{56} - 1902 q^{59} - 700 q^{61} - 3076 q^{64} + 132 q^{66} + 60 q^{69} + 3052 q^{71} - 2182 q^{74} - 792 q^{76} - 5134 q^{79} + 648 q^{81} - 282 q^{84} + 3674 q^{86} - 2106 q^{89} + 4300 q^{91} - 4418 q^{94} + 1476 q^{96} + 792 q^{99}+O(q^{100}) $ 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9 - 88 * q^11 + 6 * q^14 - 156 * q^16 - 236 * q^19 - 66 * q^21 - 36 * q^24 - 314 * q^26 - 502 * q^29 - 270 * q^31 - 578 * q^34 - 252 * q^36 - 150 * q^39 - 206 * q^41 - 308 * q^44 - 840 * q^46 - 2006 * q^49 + 510 * q^51 + 108 * q^54 + 154 * q^56 - 1902 * q^59 - 700 * q^61 - 3076 * q^64 + 132 * q^66 + 60 * q^69 + 3052 * q^71 - 2182 * q^74 - 792 * q^76 - 5134 * q^79 + 648 * q^81 - 282 * q^84 + 3674 * q^86 - 2106 * q^89 + 4300 * q^91 - 4418 * q^94 + 1476 * q^96 + 792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 1.56155i	− 0.552092i	−0.961144	−	0.276046i	$-0.910976\pi$
$2$	− 1.56155i	− 0.552092i	0.961144	−	0.276046i	$-0.0890243\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	5.56155	0.695194
$5$	0	0
$5$	0	0
$6$	4.68466	0.318751
$7$	− 16.7054i	− 0.902009i	−0.892522	−	0.451005i	$-0.851066\pi$
$7$	− 16.7054i	− 0.902009i	0.892522	−	0.451005i	$-0.148934\pi$
$8$	− 21.1771i	− 0.935904i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	16.6847i	0.401371i
$13$	61.6896i	1.31612i	0.752964	+	0.658062i	$0.228623\pi$
$13$	61.6896i	1.31612i	−0.752964	+	0.658062i	$0.771377\pi$
$14$	−26.0864	−0.497992
$15$	0	0
$16$	11.4233	0.178489
$17$	− 81.9365i	− 1.16897i	−0.811404	−	0.584486i	$-0.801296\pi$
$17$	− 81.9365i	− 1.16897i	0.811404	−	0.584486i	$-0.198704\pi$
$18$	14.0540i	0.184031i
$19$	66.0105	0.797045	0.398523	−	0.917159i	$-0.369523\pi$
$19$	66.0105	0.797045	0.398523	+	0.917159i	$0.369523\pi$
$20$	0	0
$21$	50.1163	0.520775
$22$	17.1771i	0.166462i
$23$	− 118.019i	− 1.06995i	−0.844869	−	0.534973i	$-0.820322\pi$
$23$	− 118.019i	− 1.06995i	0.844869	−	0.534973i	$-0.179678\pi$
$24$	63.5312	0.540344
$25$	0	0
$26$	96.3315	0.726622
$27$	− 27.0000i	− 0.192450i
$28$	− 92.9082i	− 0.627072i
$29$	−4.91776	−0.0314899	−0.0157449	−	0.999876i	$-0.505012\pi$
$29$	−4.91776	−0.0314899	−0.0157449	+	0.999876i	$0.505012\pi$
$30$	0	0
$31$	−286.654	−1.66079	−0.830396	−	0.557173i	$-0.811886\pi$
$31$	−286.654	−1.66079	−0.830396	+	0.557173i	$0.811886\pi$
$32$	− 187.255i	− 1.03445i
$33$	− 33.0000i	− 0.174078i
$34$	−127.948	−0.645380
$35$	0	0
$36$	−50.0540	−0.231731
$37$	− 271.441i	− 1.20607i	−0.797715	−	0.603035i	$-0.793958\pi$
$37$	− 271.441i	− 1.20607i	0.797715	−	0.603035i	$-0.206042\pi$
$38$	− 103.079i	− 0.440042i
$39$	−185.069	−0.759864
$40$	0	0
$41$	117.544	0.447737	0.223869	−	0.974619i	$-0.428131\pi$
$41$	117.544	0.447737	0.223869	+	0.974619i	$0.428131\pi$
$42$	− 78.2593i	− 0.287516i
$43$	364.372i	1.29224i	0.763237	+	0.646119i	$0.223609\pi$
$43$	364.372i	1.29224i	−0.763237	+	0.646119i	$0.776391\pi$
$44$	−61.1771	−0.209609
$45$	0	0
$46$	−184.294	−0.590709
$47$	− 465.470i	− 1.44459i	−0.691585	−	0.722296i	$-0.743087\pi$
$47$	− 465.470i	− 1.44459i	0.691585	−	0.722296i	$-0.256913\pi$
$48$	34.2699i	0.103051i
$49$	63.9280	0.186379
$50$	0	0
$51$	245.810	0.674906
$52$	343.090i	0.914961i
$53$	600.056i	1.55517i	0.628777	+	0.777586i	$0.283556\pi$
$53$	600.056i	1.55517i	−0.628777	+	0.777586i	$0.716444\pi$
$54$	−42.1619	−0.106250
$55$	0	0
$56$	−353.773	−0.844194
$57$	198.032i	0.460174i
$58$	7.67935i	0.0173853i
$59$	−647.656	−1.42911	−0.714556	−	0.699578i	$-0.753371\pi$
$59$	−647.656	−1.42911	−0.714556	+	0.699578i	$0.753371\pi$
$60$	0	0
$61$	−190.684	−0.400239	−0.200119	−	0.979772i	$-0.564133\pi$
$61$	−190.684	−0.400239	−0.200119	+	0.979772i	$0.564133\pi$
$62$	447.625i	0.916911i
$63$	150.349i	0.300670i
$64$	−201.022	−0.392621
$65$	0	0
$66$	−51.5312	−0.0961069
$67$	− 1086.95i	− 1.98197i	−0.133957	−	0.990987i	$-0.542768\pi$
$67$	− 1086.95i	− 1.98197i	0.133957	−	0.990987i	$-0.457232\pi$
$68$	− 455.694i	− 0.812662i
$69$	354.058	0.617734
$70$	0	0
$71$	811.734	1.35683	0.678416	−	0.734678i	$-0.262667\pi$
$71$	811.734	1.35683	0.678416	+	0.734678i	$0.262667\pi$
$72$	190.594i	0.311968i
$73$	− 1036.16i	− 1.66127i	−0.556816	−	0.830636i	$-0.687977\pi$
$73$	− 1036.16i	− 1.66127i	0.556816	−	0.830636i	$-0.312023\pi$
$74$	−423.869	−0.665862
$75$	0	0
$76$	367.121	0.554101
$77$	183.760i	0.271966i
$78$	288.995i	0.419515i
$79$	−573.141	−0.816246	−0.408123	−	0.912927i	$-0.633816\pi$
$79$	−573.141	−0.816246	−0.408123	+	0.912927i	$0.633816\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 183.551i	− 0.247192i
$83$	− 510.318i	− 0.674876i	−0.941348	−	0.337438i	$-0.890440\pi$
$83$	− 510.318i	− 0.674876i	0.941348	−	0.337438i	$-0.109560\pi$
$84$	278.725	0.362040
$85$	0	0
$86$	568.986	0.713434
$87$	− 14.7533i	− 0.0181807i
$88$	232.948i	0.282186i
$89$	748.629	0.891624	0.445812	−	0.895127i	$-0.352915\pi$
$89$	748.629	0.891624	0.445812	+	0.895127i	$0.352915\pi$
$90$	0	0
$91$	1030.55	1.18716
$92$	− 656.371i	− 0.743820i
$93$	− 859.962i	− 0.958859i
$94$	−726.856	−0.797548
$95$	0	0
$96$	561.764	0.597238
$97$	− 96.0399i	− 0.100530i	−0.998736	−	0.0502648i	$-0.983993\pi$
$97$	− 96.0399i	− 0.100530i	0.998736	−	0.0502648i	$-0.0160065\pi$
$98$	− 99.8270i	− 0.102898i
$99$	99.0000	0.100504
$100$	0	0
$101$	74.1075	0.0730096	0.0365048	−	0.999333i	$-0.488378\pi$
$101$	74.1075	0.0730096	0.0365048	+	0.999333i	$0.488378\pi$
$102$	− 383.845i	− 0.372611i
$103$	185.421i	0.177380i	0.996059	+	0.0886898i	$0.0282680\pi$
$103$	185.421i	0.177380i	−0.996059	+	0.0886898i	$0.971732\pi$
$104$	1306.41	1.23176
$105$	0	0
$106$	937.020	0.858598
$107$	− 1817.88i	− 1.64244i	−0.570611	−	0.821221i	$-0.693293\pi$
$107$	− 1817.88i	− 1.64244i	0.570611	−	0.821221i	$-0.306707\pi$
$108$	− 150.162i	− 0.133790i
$109$	−1264.64	−1.11129	−0.555645	−	0.831420i	$-0.687529\pi$
$109$	−1264.64	−1.11129	−0.555645	+	0.831420i	$0.687529\pi$
$110$	0	0
$111$	814.323	0.696325
$112$	− 190.831i	− 0.160999i
$113$	− 1237.95i	− 1.03059i	−0.857013	−	0.515295i	$-0.827682\pi$
$113$	− 1237.95i	− 1.03059i	0.857013	−	0.515295i	$-0.172318\pi$
$114$	309.237	0.254059
$115$	0	0
$116$	−27.3504	−0.0218916
$117$	− 555.206i	− 0.438708i
$118$	1011.35i	0.789002i
$119$	−1368.79	−1.05442
$120$	0	0
$121$	121.000	0.0909091
$122$	297.763i	0.220969i
$123$	352.631i	0.258501i
$124$	−1594.24	−1.15457
$125$	0	0
$126$	234.778	0.165997
$127$	1931.43i	1.34950i	0.738046	+	0.674750i	$0.235749\pi$
$127$	1931.43i	1.34950i	−0.738046	+	0.674750i	$0.764251\pi$
$128$	− 1184.13i	− 0.817683i
$129$	−1093.12	−0.746073
$130$	0	0
$131$	249.355	0.166307	0.0831537	−	0.996537i	$-0.473501\pi$
$131$	249.355	0.166307	0.0831537	+	0.996537i	$0.473501\pi$
$132$	− 183.531i	− 0.121018i
$133$	− 1102.74i	− 0.718942i
$134$	−1697.33	−1.09423
$135$	0	0
$136$	−1735.18	−1.09404
$137$	− 207.235i	− 0.129235i	−0.997910	−	0.0646177i	$-0.979417\pi$
$137$	− 207.235i	− 0.129235i	0.997910	−	0.0646177i	$-0.0205828\pi$
$138$	− 552.881i	− 0.341046i
$139$	−1511.95	−0.922601	−0.461301	−	0.887244i	$-0.652617\pi$
$139$	−1511.95	−0.922601	−0.461301	+	0.887244i	$0.652617\pi$
$140$	0	0
$141$	1396.41	0.834035
$142$	− 1267.57i	− 0.749096i
$143$	− 678.585i	− 0.396826i
$144$	−102.810	−0.0594963
$145$	0	0
$146$	−1618.01	−0.917176
$147$	191.784i	0.107606i
$148$	− 1509.63i	− 0.838453i
$149$	1837.89	1.01051	0.505254	−	0.862971i	$-0.331399\pi$
$149$	1837.89	1.01051	0.505254	+	0.862971i	$0.331399\pi$
$150$	0	0
$151$	−460.761	−0.248319	−0.124160	−	0.992262i	$-0.539623\pi$
$151$	−460.761	−0.248319	−0.124160	+	0.992262i	$0.539623\pi$
$152$	− 1397.91i	− 0.745957i
$153$	737.429i	0.389657i
$154$	286.951	0.150150
$155$	0	0
$156$	−1029.27	−0.528253
$157$	2078.08i	1.05636i	0.849132	+	0.528180i	$0.177125\pi$
$157$	2078.08i	1.05636i	−0.849132	+	0.528180i	$0.822875\pi$
$158$	894.990i	0.450643i
$159$	−1800.17	−0.897879
$160$	0	0
$161$	−1971.57	−0.965101
$162$	− 126.486i	− 0.0613436i
$163$	1373.25i	0.659885i	0.944001	+	0.329943i	$0.107029\pi$
$163$	1373.25i	0.659885i	−0.944001	+	0.329943i	$0.892971\pi$
$164$	653.725	0.311264
$165$	0	0
$166$	−796.889	−0.372594
$167$	1622.31i	0.751727i	0.926675	+	0.375864i	$0.122654\pi$
$167$	1622.31i	0.751727i	−0.926675	+	0.375864i	$0.877346\pi$
$168$	− 1061.32i	− 0.487396i
$169$	−1608.60	−0.732182
$170$	0	0
$171$	−594.095	−0.265682
$172$	2026.47i	0.898356i
$173$	− 1325.62i	− 0.582572i	−0.956636	−	0.291286i	$-0.905917\pi$
$173$	− 1325.62i	− 0.582572i	0.956636	−	0.291286i	$-0.0940831\pi$
$174$	−23.0380	−0.0100374
$175$	0	0
$176$	−125.656	−0.0538164
$177$	− 1942.97i	− 0.825098i
$178$	− 1169.02i	− 0.492259i
$179$	918.136	0.383378	0.191689	−	0.981456i	$-0.438603\pi$
$179$	918.136	0.383378	0.191689	+	0.981456i	$0.438603\pi$
$180$	0	0
$181$	3387.30	1.39103	0.695513	−	0.718514i	$-0.255177\pi$
$181$	3387.30	1.39103	0.695513	+	0.718514i	$0.255177\pi$
$182$	− 1609.26i	− 0.655420i
$183$	− 572.052i	− 0.231078i
$184$	−2499.31	−1.00137
$185$	0	0
$186$	−1342.88	−0.529379
$187$	901.302i	0.352458i
$188$	− 2588.74i	− 1.00427i
$189$	−451.047	−0.173592
$190$	0	0
$191$	−2126.29	−0.805513	−0.402756	−	0.915307i	$-0.631948\pi$
$191$	−2126.29	−0.805513	−0.402756	+	0.915307i	$0.631948\pi$
$192$	− 603.065i	− 0.226680i
$193$	− 2214.54i	− 0.825937i	−0.910745	−	0.412968i	$-0.864492\pi$
$193$	− 2214.54i	− 0.825937i	0.910745	−	0.412968i	$-0.135508\pi$
$194$	−149.971	−0.0555017
$195$	0	0
$196$	355.539	0.129570
$197$	− 3975.19i	− 1.43767i	−0.695181	−	0.718834i	$-0.744676\pi$
$197$	− 3975.19i	− 1.43767i	0.695181	−	0.718834i	$-0.255324\pi$
$198$	− 154.594i	− 0.0554874i
$199$	2260.57	0.805266	0.402633	−	0.915362i	$-0.368095\pi$
$199$	2260.57	0.805266	0.402633	+	0.915362i	$0.368095\pi$
$200$	0	0
$201$	3260.85	1.14429
$202$	− 115.723i	− 0.0403080i
$203$	82.1534i	0.0284041i
$204$	1367.08	0.469191
$205$	0	0
$206$	289.545	0.0979299
$207$	1062.18i	0.356649i
$208$	704.698i	0.234914i
$209$	−726.116	−0.240318
$210$	0	0
$211$	−628.529	−0.205070	−0.102535	−	0.994729i	$-0.532695\pi$
$211$	−628.529	−0.205070	−0.102535	+	0.994729i	$0.532695\pi$
$212$	3337.24i	1.08115i
$213$	2435.20i	0.783367i
$214$	−2838.72	−0.906779
$215$	0	0
$216$	−571.781	−0.180115
$217$	4788.68i	1.49805i
$218$	1974.80i	0.613534i
$219$	3108.47	0.959136
$220$	0	0
$221$	5054.63	1.53851
$222$	− 1271.61i	− 0.384436i
$223$	− 2625.65i	− 0.788459i	−0.919012	−	0.394229i	$-0.871012\pi$
$223$	− 2625.65i	− 0.788459i	0.919012	−	0.394229i	$-0.128988\pi$
$224$	−3128.17	−0.933080
$225$	0	0
$226$	−1933.13	−0.568980
$227$	− 1803.50i	− 0.527324i	−0.964615	−	0.263662i	$-0.915070\pi$
$227$	− 1803.50i	− 0.527324i	0.964615	−	0.263662i	$-0.0849304\pi$
$228$	1101.36i	0.319910i
$229$	4627.26	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$229$	4627.26	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$230$	0	0
$231$	−551.280	−0.157020
$232$	104.144i	0.0294715i
$233$	− 1123.04i	− 0.315762i	−0.987458	−	0.157881i	$-0.949534\pi$
$233$	− 1123.04i	− 0.315762i	0.987458	−	0.157881i	$-0.0504663\pi$
$234$	−866.984	−0.242207
$235$	0	0
$236$	−3601.97	−0.993510
$237$	− 1719.42i	− 0.471260i
$238$	2137.43i	0.582139i
$239$	−4319.87	−1.16916	−0.584579	−	0.811337i	$-0.698740\pi$
$239$	−4319.87	−1.16916	−0.584579	+	0.811337i	$0.698740\pi$
$240$	0	0
$241$	−6737.26	−1.80077	−0.900384	−	0.435096i	$-0.856714\pi$
$241$	−6737.26	−1.80077	−0.900384	+	0.435096i	$0.856714\pi$
$242$	− 188.948i	− 0.0501902i
$243$	243.000i	0.0641500i
$244$	−1060.50	−0.278244
$245$	0	0
$246$	550.652	0.142717
$247$	4072.16i	1.04901i
$248$	6070.49i	1.55434i
$249$	1530.95	0.389640
$250$	0	0
$251$	5686.46	1.42999	0.714993	−	0.699132i	$-0.246430\pi$
$251$	5686.46	1.42999	0.714993	+	0.699132i	$0.246430\pi$
$252$	836.174i	0.209024i
$253$	1298.21i	0.322601i
$254$	3016.03	0.745049
$255$	0	0
$256$	−3457.26	−0.844057
$257$	− 6856.63i	− 1.66422i	−0.554610	−	0.832110i	$-0.687133\pi$
$257$	− 6856.63i	− 1.66422i	0.554610	−	0.832110i	$-0.312867\pi$
$258$	1706.96i	0.411901i
$259$	−4534.54	−1.08789
$260$	0	0
$261$	44.2599	0.0104966
$262$	− 389.381i	− 0.0918170i
$263$	− 460.002i	− 0.107852i	−0.998545	−	0.0539258i	$-0.982827\pi$
$263$	− 460.002i	− 0.107852i	0.998545	−	0.0539258i	$-0.0171734\pi$
$264$	−698.844	−0.162920
$265$	0	0
$266$	−1721.98	−0.396922
$267$	2245.89i	0.514779i
$268$	− 6045.14i	− 1.37786i
$269$	1066.11	0.241642	0.120821	−	0.992674i	$-0.461447\pi$
$269$	1066.11	0.241642	0.120821	+	0.992674i	$0.461447\pi$
$270$	0	0
$271$	4887.89	1.09564	0.547819	−	0.836597i	$-0.315458\pi$
$271$	4887.89	1.09564	0.547819	+	0.836597i	$0.315458\pi$
$272$	− 935.985i	− 0.208649i
$273$	3091.66i	0.685405i
$274$	−323.608	−0.0713499
$275$	0	0
$276$	1969.11	0.429445
$277$	2913.91i	0.632058i	0.948750	+	0.316029i	$0.102350\pi$
$277$	2913.91i	0.632058i	−0.948750	+	0.316029i	$0.897650\pi$
$278$	2360.98i	0.509361i
$279$	2579.89	0.553597
$280$	0	0
$281$	−2461.01	−0.522462	−0.261231	−	0.965276i	$-0.584128\pi$
$281$	−2461.01	−0.522462	−0.261231	+	0.965276i	$0.584128\pi$
$282$	− 2180.57i	− 0.460464i
$283$	2432.41i	0.510926i	0.966819	+	0.255463i	$0.0822278\pi$
$283$	2432.41i	0.510926i	−0.966819	+	0.255463i	$0.917772\pi$
$284$	4514.50	0.943262
$285$	0	0
$286$	−1059.65	−0.219085
$287$	− 1963.62i	− 0.403863i
$288$	1685.29i	0.344815i
$289$	−1800.59	−0.366495
$290$	0	0
$291$	288.120	0.0580408
$292$	− 5762.64i	− 1.15491i
$293$	5099.64i	1.01681i	0.861119	+	0.508403i	$0.169764\pi$
$293$	5099.64i	1.01681i	−0.861119	+	0.508403i	$0.830236\pi$
$294$	299.481	0.0594084
$295$	0	0
$296$	−5748.33	−1.12877
$297$	297.000i	0.0580259i
$298$	− 2869.96i	− 0.557894i
$299$	7280.57	1.40818
$300$	0	0
$301$	6087.00	1.16561
$302$	719.503i	0.137095i
$303$	222.322i	0.0421521i
$304$	754.058	0.142264
$305$	0	0
$306$	1151.53	0.215127
$307$	5697.12i	1.05913i	0.848270	+	0.529563i	$0.177644\pi$
$307$	5697.12i	1.05913i	−0.848270	+	0.529563i	$0.822356\pi$
$308$	1021.99i	0.189069i
$309$	−556.264	−0.102410
$310$	0	0
$311$	−1043.49	−0.190260	−0.0951298	−	0.995465i	$-0.530327\pi$
$311$	−1043.49	−0.190260	−0.0951298	+	0.995465i	$0.530327\pi$
$312$	3919.22i	0.711160i
$313$	6924.21i	1.25041i	0.780459	+	0.625207i	$0.214986\pi$
$313$	6924.21i	1.25041i	−0.780459	+	0.625207i	$0.785014\pi$
$314$	3245.03	0.583208
$315$	0	0
$316$	−3187.55	−0.567449
$317$	3834.49i	0.679390i	0.940536	+	0.339695i	$0.110324\pi$
$317$	3834.49i	0.679390i	−0.940536	+	0.339695i	$0.889676\pi$
$318$	2811.06i	0.495712i
$319$	54.0954	0.00949455
$320$	0	0
$321$	5453.64	0.948264
$322$	3078.71i	0.532825i
$323$	− 5408.67i	− 0.931723i
$324$	450.486	0.0772438
$325$	0	0
$326$	2144.40	0.364318
$327$	− 3793.92i	− 0.641603i
$328$	− 2489.23i	− 0.419039i
$329$	−7775.89	−1.30303
$330$	0	0
$331$	−1312.42	−0.217937	−0.108969	−	0.994045i	$-0.534755\pi$
$331$	−1312.42	−0.217937	−0.108969	+	0.994045i	$0.534755\pi$
$332$	− 2838.16i	− 0.469170i
$333$	2442.97i	0.402024i
$334$	2533.33	0.415023
$335$	0	0
$336$	572.494	0.0929526
$337$	8762.01i	1.41631i	0.706056	+	0.708156i	$0.250473\pi$
$337$	8762.01i	1.41631i	−0.706056	+	0.708156i	$0.749527\pi$
$338$	2511.92i	0.404232i
$339$	3713.85	0.595011
$340$	0	0
$341$	3153.19	0.500748
$342$	927.711i	0.146681i
$343$	− 6797.91i	− 1.07013i
$344$	7716.33	1.20941
$345$	0	0
$346$	−2070.02	−0.321633
$347$	11149.5i	1.72489i	0.506154	+	0.862443i	$0.331067\pi$
$347$	11149.5i	1.72489i	−0.506154	+	0.862443i	$0.668933\pi$
$348$	− 82.0512i	− 0.0126391i
$349$	10850.8	1.66427	0.832137	−	0.554570i	$-0.187117\pi$
$349$	10850.8	1.66427	0.832137	+	0.554570i	$0.187117\pi$
$350$	0	0
$351$	1665.62	0.253288
$352$	2059.80i	0.311897i
$353$	1462.13i	0.220457i	0.993906	+	0.110229i	$0.0351583\pi$
$353$	1462.13i	0.220457i	−0.993906	+	0.110229i	$0.964842\pi$
$354$	−3034.05	−0.455530
$355$	0	0
$356$	4163.54	0.619852
$357$	− 4106.36i	− 0.608772i
$358$	− 1433.72i	− 0.211660i
$359$	−4074.45	−0.599001	−0.299500	−	0.954096i	$-0.596820\pi$
$359$	−4074.45	−0.599001	−0.299500	+	0.954096i	$0.596820\pi$
$360$	0	0
$361$	−2501.61	−0.364719
$362$	− 5289.44i	− 0.767975i
$363$	363.000i	0.0524864i
$364$	5731.47	0.825304
$365$	0	0
$366$	−893.289	−0.127576
$367$	2856.24i	0.406252i	0.979153	+	0.203126i	$0.0651101\pi$
$367$	2856.24i	0.406252i	−0.979153	+	0.203126i	$0.934890\pi$
$368$	− 1348.17i	− 0.190974i
$369$	−1057.89	−0.149246
$370$	0	0
$371$	10024.2	1.40278
$372$	− 4782.72i	− 0.666593i
$373$	10600.9i	1.47156i	0.677218	+	0.735782i	$0.263185\pi$
$373$	10600.9i	1.47156i	−0.677218	+	0.735782i	$0.736815\pi$
$374$	1407.43	0.194589
$375$	0	0
$376$	−9857.30	−1.35200
$377$	− 303.375i	− 0.0414445i
$378$	704.334i	0.0958387i
$379$	−9442.90	−1.27981	−0.639907	−	0.768453i	$-0.721027\pi$
$379$	−9442.90	−1.27981	−0.639907	+	0.768453i	$0.721027\pi$
$380$	0	0
$381$	−5794.29	−0.779135
$382$	3320.31i	0.444717i
$383$	10175.8i	1.35760i	0.734324	+	0.678799i	$0.237499\pi$
$383$	10175.8i	1.35760i	−0.734324	+	0.678799i	$0.762501\pi$
$384$	3552.39	0.472090
$385$	0	0
$386$	−3458.11	−0.455993
$387$	− 3279.35i	− 0.430746i
$388$	− 534.131i	− 0.0698876i
$389$	9563.21	1.24646	0.623231	−	0.782038i	$-0.285820\pi$
$389$	9563.21	1.24646	0.623231	+	0.782038i	$0.285820\pi$
$390$	0	0
$391$	−9670.10	−1.25074
$392$	− 1353.81i	− 0.174433i
$393$	748.065i	0.0960176i
$394$	−6207.47	−0.793726
$395$	0	0
$396$	550.594	0.0698696
$397$	9487.62i	1.19942i	0.800217	+	0.599710i	$0.204718\pi$
$397$	9487.62i	1.19942i	−0.800217	+	0.599710i	$0.795282\pi$
$398$	− 3530.01i	− 0.444581i
$399$	3308.21	0.415081
$400$	0	0
$401$	−6157.50	−0.766810	−0.383405	−	0.923580i	$-0.625249\pi$
$401$	−6157.50	−0.766810	−0.383405	+	0.923580i	$0.625249\pi$
$402$	− 5092.00i	− 0.631756i
$403$	− 17683.6i	− 2.18581i
$404$	412.153	0.0507558
$405$	0	0
$406$	128.287	0.0156817
$407$	2985.85i	0.363644i
$408$	− 5205.53i	− 0.631647i
$409$	8819.17	1.06621	0.533105	−	0.846049i	$-0.321025\pi$
$409$	8819.17	1.06621	0.533105	+	0.846049i	$0.321025\pi$
$410$	0	0
$411$	621.704	0.0746141
$412$	1031.23i	0.123313i
$413$	10819.4i	1.28907i
$414$	1658.64	0.196903
$415$	0	0
$416$	11551.7	1.36146
$417$	− 4535.84i	− 0.532664i
$418$	1133.87i	0.132678i
$419$	16313.0	1.90201	0.951004	−	0.309180i	$-0.100054\pi$
$419$	16313.0	1.90201	0.951004	+	0.309180i	$0.100054\pi$
$420$	0	0
$421$	2449.66	0.283585	0.141792	−	0.989896i	$-0.454713\pi$
$421$	2449.66	0.283585	0.141792	+	0.989896i	$0.454713\pi$
$422$	981.482i	0.113218i
$423$	4189.23i	0.481530i
$424$	12707.4	1.45549
$425$	0	0
$426$	3802.70	0.432491
$427$	3185.46i	0.361019i
$428$	− 10110.2i	− 1.14182i
$429$	2035.76	0.229108
$430$	0	0
$431$	7674.65	0.857714	0.428857	−	0.903372i	$-0.358916\pi$
$431$	7674.65	0.857714	0.428857	+	0.903372i	$0.358916\pi$
$432$	− 308.429i	− 0.0343502i
$433$	3969.44i	0.440553i	0.975438	+	0.220276i	$0.0706959\pi$
$433$	3969.44i	0.440553i	−0.975438	+	0.220276i	$0.929304\pi$
$434$	7477.78	0.827062
$435$	0	0
$436$	−7033.36	−0.772562
$437$	− 7790.53i	− 0.852795i
$438$	− 4854.04i	− 0.529532i
$439$	15154.3	1.64756	0.823778	−	0.566913i	$-0.191862\pi$
$439$	15154.3	1.64756	0.823778	+	0.566913i	$0.191862\pi$
$440$	0	0
$441$	−575.352	−0.0621263
$442$	− 7893.07i	− 0.849400i
$443$	11681.4i	1.25282i	0.779492	+	0.626412i	$0.215477\pi$
$443$	11681.4i	1.25282i	−0.779492	+	0.626412i	$0.784523\pi$
$444$	4528.90	0.484081
$445$	0	0
$446$	−4100.09	−0.435302
$447$	5513.67i	0.583417i
$448$	3358.16i	0.354148i
$449$	5001.77	0.525719	0.262860	−	0.964834i	$-0.415334\pi$
$449$	5001.77	0.525719	0.262860	+	0.964834i	$0.415334\pi$
$450$	0	0
$451$	−1292.98	−0.134998
$452$	− 6884.93i	− 0.716460i
$453$	− 1382.28i	− 0.143367i
$454$	−2816.26	−0.291132
$455$	0	0
$456$	4193.73	0.430679
$457$	2426.79i	0.248404i	0.992257	+	0.124202i	$0.0396370\pi$
$457$	2426.79i	0.248404i	−0.992257	+	0.124202i	$0.960363\pi$
$458$	− 7225.71i	− 0.737195i
$459$	−2212.29	−0.224969
$460$	0	0
$461$	−7723.17	−0.780269	−0.390134	−	0.920758i	$-0.627571\pi$
$461$	−7723.17	−0.780269	−0.390134	+	0.920758i	$0.627571\pi$
$462$	860.852i	0.0866894i
$463$	− 2498.90i	− 0.250829i	−0.992104	−	0.125414i	$-0.959974\pi$
$463$	− 2498.90i	− 0.250829i	0.992104	−	0.125414i	$-0.0400260\pi$
$464$	−56.1770	−0.00562059
$465$	0	0
$466$	−1753.68	−0.174330
$467$	1849.41i	0.183256i	0.995793	+	0.0916282i	$0.0292071\pi$
$467$	1849.41i	0.183256i	−0.995793	+	0.0916282i	$0.970793\pi$
$468$	− 3087.81i	− 0.304987i
$469$	−18158.0	−1.78776
$470$	0	0
$471$	−6234.23	−0.609890
$472$	13715.5i	1.33751i
$473$	− 4008.09i	− 0.389624i
$474$	−2684.97	−0.260179
$475$	0	0
$476$	−7612.58	−0.733029
$477$	− 5400.51i	− 0.518390i
$478$	6745.70i	0.645484i
$479$	−18825.7	−1.79576	−0.897879	−	0.440242i	$-0.854893\pi$
$479$	−18825.7	−1.79576	−0.897879	+	0.440242i	$0.854893\pi$
$480$	0	0
$481$	16745.1	1.58734
$482$	10520.6i	0.994190i
$483$	− 5914.70i	− 0.557202i
$484$	672.948	0.0631995
$485$	0	0
$486$	379.457	0.0354167
$487$	− 2913.82i	− 0.271125i	−0.990769	−	0.135562i	$-0.956716\pi$
$487$	− 2913.82i	− 0.271125i	0.990769	−	0.135562i	$-0.0432842\pi$
$488$	4038.13i	0.374585i
$489$	−4119.75	−0.380985
$490$	0	0
$491$	9021.20	0.829167	0.414583	−	0.910011i	$-0.363927\pi$
$491$	9021.20	0.829167	0.414583	+	0.910011i	$0.363927\pi$
$492$	1961.18i	0.179709i
$493$	402.944i	0.0368108i
$494$	6358.90	0.579150
$495$	0	0
$496$	−3274.53	−0.296433
$497$	− 13560.4i	− 1.22388i
$498$	− 2390.67i	− 0.215117i
$499$	−17329.5	−1.55466	−0.777330	−	0.629093i	$-0.783426\pi$
$499$	−17329.5	−1.55466	−0.777330	+	0.629093i	$0.783426\pi$
$500$	0	0
$501$	−4866.94	−0.434010
$502$	− 8879.71i	− 0.789484i
$503$	57.6061i	0.00510642i	0.999997	+	0.00255321i	$0.000812713\pi$
$503$	57.6061i	0.00510642i	−0.999997	+	0.00255321i	$0.999187\pi$
$504$	3183.95	0.281398
$505$	0	0
$506$	2027.23	0.178105
$507$	− 4825.81i	− 0.422725i
$508$	10741.7i	0.938165i
$509$	17785.2	1.54875	0.774376	−	0.632726i	$-0.218064\pi$
$509$	17785.2	1.54875	0.774376	+	0.632726i	$0.218064\pi$
$510$	0	0
$511$	−17309.4	−1.49848
$512$	− 4074.36i	− 0.351686i
$513$	− 1782.28i	− 0.153391i
$514$	−10707.0	−0.918803
$515$	0	0
$516$	−6079.42	−0.518666
$517$	5120.17i	0.435561i
$518$	7080.93i	0.600614i
$519$	3976.86	0.336348
$520$	0	0
$521$	12041.2	1.01254	0.506271	−	0.862374i	$-0.331024\pi$
$521$	12041.2	1.01254	0.506271	+	0.862374i	$0.331024\pi$
$522$	− 69.1141i	− 0.00579510i
$523$	5046.68i	0.421943i	0.977492	+	0.210971i	$0.0676627\pi$
$523$	5046.68i	0.421943i	−0.977492	+	0.210971i	$0.932337\pi$
$524$	1386.80	0.115616
$525$	0	0
$526$	−718.318	−0.0595440
$527$	23487.4i	1.94142i
$528$	− 376.969i	− 0.0310709i
$529$	−1761.59	−0.144785
$530$	0	0
$531$	5828.90	0.476371
$532$	− 6132.92i	− 0.499804i
$533$	7251.22i	0.589278i
$534$	3507.07	0.284206
$535$	0	0
$536$	−23018.5	−1.85494
$537$	2754.41i	0.221344i
$538$	− 1664.78i	− 0.133408i
$539$	−703.208	−0.0561954
$540$	0	0
$541$	2501.98	0.198833	0.0994165	−	0.995046i	$-0.468302\pi$
$541$	2501.98	0.198833	0.0994165	+	0.995046i	$0.468302\pi$
$542$	− 7632.69i	− 0.604894i
$543$	10161.9i	0.803109i
$544$	−15343.0	−1.20924
$545$	0	0
$546$	4827.78	0.378407
$547$	5594.27i	0.437283i	0.975805	+	0.218642i	$0.0701625\pi$
$547$	5594.27i	0.437283i	−0.975805	+	0.218642i	$0.929837\pi$
$548$	− 1152.55i	− 0.0898437i
$549$	1716.16	0.133413
$550$	0	0
$551$	−324.624	−0.0250988
$552$	− 7497.92i	− 0.578139i
$553$	9574.58i	0.736261i
$554$	4550.23	0.348954
$555$	0	0
$556$	−8408.77	−0.641387
$557$	16121.6i	1.22638i	0.789935	+	0.613190i	$0.210114\pi$
$557$	16121.6i	1.22638i	−0.789935	+	0.613190i	$0.789886\pi$
$558$	− 4028.63i	− 0.305637i
$559$	−22477.9	−1.70074
$560$	0	0
$561$	−2703.90	−0.203492
$562$	3843.00i	0.288447i
$563$	7135.68i	0.534162i	0.963674	+	0.267081i	$0.0860591\pi$
$563$	7135.68i	0.534162i	−0.963674	+	0.267081i	$0.913941\pi$
$564$	7766.21	0.579816
$565$	0	0
$566$	3798.34	0.282078
$567$	− 1353.14i	− 0.100223i
$568$	− 17190.2i	− 1.26986i
$569$	−22953.1	−1.69112	−0.845559	−	0.533882i	$-0.820733\pi$
$569$	−22953.1	−1.69112	−0.845559	+	0.533882i	$0.820733\pi$
$570$	0	0
$571$	−4405.10	−0.322851	−0.161425	−	0.986885i	$-0.551609\pi$
$571$	−4405.10	−0.322851	−0.161425	+	0.986885i	$0.551609\pi$
$572$	− 3773.99i	− 0.275871i
$573$	− 6378.87i	− 0.465063i
$574$	−3066.29	−0.222970
$575$	0	0
$576$	1809.20	0.130874
$577$	14535.4i	1.04873i	0.851493	+	0.524365i	$0.175697\pi$
$577$	14535.4i	1.04873i	−0.851493	+	0.524365i	$0.824303\pi$
$578$	2811.72i	0.202339i
$579$	6643.61	0.476855
$580$	0	0
$581$	−8525.10	−0.608744
$582$	− 449.914i	− 0.0320439i
$583$	− 6600.62i	− 0.468902i
$584$	−21942.8	−1.55479
$585$	0	0
$586$	7963.36	0.561371
$587$	− 4466.29i	− 0.314043i	−0.987595	−	0.157022i	$-0.949811\pi$
$587$	− 4466.29i	− 0.314043i	0.987595	−	0.157022i	$-0.0501893\pi$
$588$	1066.62i	0.0748070i
$589$	−18922.2	−1.32373
$590$	0	0
$591$	11925.6	0.830039
$592$	− 3100.75i	− 0.215270i
$593$	2458.37i	0.170242i	0.996371	+	0.0851208i	$0.0271276\pi$
$593$	2458.37i	0.170242i	−0.996371	+	0.0851208i	$0.972872\pi$
$594$	463.781	0.0320356
$595$	0	0
$596$	10221.5	0.702499
$597$	6781.72i	0.464920i
$598$	− 11369.0i	− 0.777446i
$599$	−10918.0	−0.744736	−0.372368	−	0.928085i	$-0.621454\pi$
$599$	−10918.0	−0.744736	−0.372368	+	0.928085i	$0.621454\pi$
$600$	0	0
$601$	−11119.6	−0.754708	−0.377354	−	0.926069i	$-0.623166\pi$
$601$	−11119.6	−0.754708	−0.377354	+	0.926069i	$0.623166\pi$
$602$	− 9505.17i	− 0.643524i
$603$	9782.56i	0.660658i
$604$	−2562.55	−0.172630
$605$	0	0
$606$	347.168	0.0232718
$607$	− 3857.04i	− 0.257912i	−0.991650	−	0.128956i	$-0.958837\pi$
$607$	− 3857.04i	− 0.257912i	0.991650	−	0.128956i	$-0.0411626\pi$
$608$	− 12360.8i	− 0.824500i
$609$	−246.460	−0.0163991
$610$	0	0
$611$	28714.6	1.90126
$612$	4101.25i	0.270887i
$613$	− 968.805i	− 0.0638331i	−0.999491	−	0.0319165i	$-0.989839\pi$
$613$	− 968.805i	− 0.0638331i	0.999491	−	0.0319165i	$-0.0101611\pi$
$614$	8896.36	0.584736
$615$	0	0
$616$	3891.50	0.254534
$617$	10122.0i	0.660446i	0.943903	+	0.330223i	$0.107124\pi$
$617$	10122.0i	0.660446i	−0.943903	+	0.330223i	$0.892876\pi$
$618$	868.635i	0.0565399i
$619$	22675.2	1.47237	0.736183	−	0.676783i	$-0.236626\pi$
$619$	22675.2	1.47237	0.736183	+	0.676783i	$0.236626\pi$
$620$	0	0
$621$	−3186.53	−0.205911
$622$	1629.46i	0.105041i
$623$	− 12506.2i	− 0.804253i
$624$	−2114.09	−0.135627
$625$	0	0
$626$	10812.5	0.690344
$627$	− 2178.35i	− 0.138748i
$628$	11557.3i	0.734375i
$629$	−22240.9	−1.40986
$630$	0	0
$631$	13483.2	0.850644	0.425322	−	0.905042i	$-0.360161\pi$
$631$	13483.2	0.850644	0.425322	+	0.905042i	$0.360161\pi$
$632$	12137.5i	0.763927i
$633$	− 1885.59i	− 0.118397i
$634$	5987.76	0.375086
$635$	0	0
$636$	−10011.7	−0.624200
$637$	3943.69i	0.245298i
$638$	− 84.4728i	− 0.00524187i
$639$	−7305.60	−0.452277
$640$	0	0
$641$	−1716.86	−0.105791	−0.0528954	−	0.998600i	$-0.516845\pi$
$641$	−1716.86	−0.105791	−0.0528954	+	0.998600i	$0.516845\pi$
$642$	− 8516.15i	− 0.523529i
$643$	− 27479.9i	− 1.68538i	−0.538399	−	0.842690i	$-0.680970\pi$
$643$	− 27479.9i	− 1.68538i	0.538399	−	0.842690i	$-0.319030\pi$
$644$	−10965.0	−0.670933
$645$	0	0
$646$	−8445.93	−0.514397
$647$	− 19128.7i	− 1.16233i	−0.813787	−	0.581163i	$-0.802598\pi$
$647$	− 19128.7i	− 1.16233i	0.813787	−	0.581163i	$-0.197402\pi$
$648$	− 1715.34i	− 0.103989i
$649$	7124.21	0.430893
$650$	0	0
$651$	−14366.0	−0.864900
$652$	7637.41i	0.458748i
$653$	− 27431.5i	− 1.64392i	−0.569548	−	0.821958i	$-0.692882\pi$
$653$	− 27431.5i	− 1.64392i	0.569548	−	0.821958i	$-0.307118\pi$
$654$	−5924.41	−0.354224
$655$	0	0
$656$	1342.74	0.0799162
$657$	9325.40i	0.553757i
$658$	12142.5i	0.719395i
$659$	12343.4	0.729638	0.364819	−	0.931078i	$-0.381131\pi$
$659$	12343.4	0.729638	0.364819	+	0.931078i	$0.381131\pi$
$660$	0	0
$661$	−10421.4	−0.613228	−0.306614	−	0.951834i	$-0.599196\pi$
$661$	−10421.4	−0.613228	−0.306614	+	0.951834i	$0.599196\pi$
$662$	2049.42i	0.120322i
$663$	15163.9i	0.888260i
$664$	−10807.1	−0.631619
$665$	0	0
$666$	3814.82	0.221954
$667$	580.392i	0.0336924i
$668$	9022.58i	0.522596i
$669$	7876.94	0.455217
$670$	0	0
$671$	2097.52	0.120677
$672$	− 9384.52i	− 0.538714i
$673$	16002.5i	0.916571i	0.888805	+	0.458286i	$0.151536\pi$
$673$	16002.5i	0.916571i	−0.888805	+	0.458286i	$0.848464\pi$
$674$	13682.3	0.781935
$675$	0	0
$676$	−8946.33	−0.509008
$677$	− 8198.64i	− 0.465435i	−0.972544	−	0.232717i	$-0.925238\pi$
$677$	− 8198.64i	− 0.465435i	0.972544	−	0.232717i	$-0.0747617\pi$
$678$	− 5799.38i	− 0.328501i
$679$	−1604.39	−0.0906787
$680$	0	0
$681$	5410.51	0.304451
$682$	− 4923.88i	− 0.276459i
$683$	− 19992.1i	− 1.12003i	−0.828484	−	0.560013i	$-0.810796\pi$
$683$	− 19992.1i	− 1.12003i	0.828484	−	0.560013i	$-0.189204\pi$
$684$	−3304.09	−0.184700
$685$	0	0
$686$	−10615.3	−0.590808
$687$	13881.8i	0.770921i
$688$	4162.33i	0.230650i
$689$	−37017.2	−2.04680
$690$	0	0
$691$	21429.4	1.17976	0.589878	−	0.807492i	$-0.299176\pi$
$691$	21429.4	1.17976	0.589878	+	0.807492i	$0.299176\pi$
$692$	− 7372.50i	− 0.405001i
$693$	− 1653.84i	− 0.0906554i
$694$	17410.5	0.952297
$695$	0	0
$696$	−312.432	−0.0170154
$697$	− 9631.11i	− 0.523392i
$698$	− 16944.1i	− 0.918833i
$699$	3369.11	0.182306
$700$	0	0
$701$	−624.394	−0.0336420	−0.0168210	−	0.999859i	$-0.505355\pi$
$701$	−624.394	−0.0336420	−0.0168210	+	0.999859i	$0.505355\pi$
$702$	− 2600.95i	− 0.139838i
$703$	− 17918.0i	− 0.961293i
$704$	2211.24	0.118380
$705$	0	0
$706$	2283.19	0.121713
$707$	− 1238.00i	− 0.0658553i
$708$	− 10805.9i	− 0.573603i
$709$	12385.4	0.656055	0.328028	−	0.944668i	$-0.393616\pi$
$709$	12385.4	0.656055	0.328028	+	0.944668i	$0.393616\pi$
$710$	0	0
$711$	5158.27	0.272082
$712$	− 15853.8i	− 0.834474i
$713$	33830.7i	1.77696i
$714$	−6412.29	−0.336098
$715$	0	0
$716$	5106.26	0.266522
$717$	− 12959.6i	− 0.675014i
$718$	6362.47i	0.330704i
$719$	−10006.7	−0.519035	−0.259517	−	0.965738i	$-0.583564\pi$
$719$	−10006.7	−0.519035	−0.259517	+	0.965738i	$0.583564\pi$
$720$	0	0
$721$	3097.54	0.159998
$722$	3906.39i	0.201359i
$723$	− 20211.8i	− 1.03967i
$724$	18838.6	0.967033
$725$	0	0
$726$	566.844	0.0289773
$727$	− 6629.20i	− 0.338189i	−0.985600	−	0.169094i	$-0.945916\pi$
$727$	− 6629.20i	− 0.338189i	0.985600	−	0.169094i	$-0.0540843\pi$
$728$	− 21824.1i	− 1.11106i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	29855.4	1.51059
$732$	− 3181.50i	− 0.160644i
$733$	− 17972.1i	− 0.905612i	−0.891609	−	0.452806i	$-0.850423\pi$
$733$	− 17972.1i	− 0.905612i	0.891609	−	0.452806i	$-0.149577\pi$
$734$	4460.17	0.224289
$735$	0	0
$736$	−22099.7	−1.10680
$737$	11956.5i	0.597588i
$738$	1651.96i	0.0823974i
$739$	−11351.7	−0.565062	−0.282531	−	0.959258i	$-0.591174\pi$
$739$	−11351.7	−0.565062	−0.282531	+	0.959258i	$0.591174\pi$
$740$	0	0
$741$	−12216.5	−0.605646
$742$	− 15653.3i	− 0.774464i
$743$	18059.6i	0.891714i	0.895104	+	0.445857i	$0.147101\pi$
$743$	18059.6i	0.891714i	−0.895104	+	0.445857i	$0.852899\pi$
$744$	−18211.5	−0.897400
$745$	0	0
$746$	16553.9	0.812440
$747$	4592.86i	0.224959i
$748$	5012.64i	0.245027i
$749$	−30368.5	−1.48150
$750$	0	0
$751$	−13399.7	−0.651081	−0.325541	−	0.945528i	$-0.605546\pi$
$751$	−13399.7	−0.651081	−0.325541	+	0.945528i	$0.605546\pi$
$752$	− 5317.20i	− 0.257844i
$753$	17059.4i	0.825603i
$754$	−473.736	−0.0228812
$755$	0	0
$756$	−2508.52	−0.120680
$757$	− 27996.6i	− 1.34419i	−0.740465	−	0.672095i	$-0.765395\pi$
$757$	− 27996.6i	− 1.34419i	0.740465	−	0.672095i	$-0.234605\pi$
$758$	14745.6i	0.706575i
$759$	−3894.64	−0.186254
$760$	0	0
$761$	22755.4	1.08395	0.541974	−	0.840396i	$-0.317677\pi$
$761$	22755.4	1.08395	0.541974	+	0.840396i	$0.317677\pi$
$762$	9048.08i	0.430154i
$763$	21126.4i	1.00239i
$764$	−11825.5	−0.559988
$765$	0	0
$766$	15890.1	0.749519
$767$	− 39953.6i	− 1.88089i
$768$	− 10371.8i	− 0.487317i
$769$	−1902.40	−0.0892097	−0.0446049	−	0.999005i	$-0.514203\pi$
$769$	−1902.40	−0.0892097	−0.0446049	+	0.999005i	$0.514203\pi$
$770$	0	0
$771$	20569.9	0.960838
$772$	− 12316.3i	− 0.574186i
$773$	18296.5i	0.851333i	0.904880	+	0.425666i	$0.139960\pi$
$773$	18296.5i	0.851333i	−0.904880	+	0.425666i	$0.860040\pi$
$774$	−5120.87	−0.237811
$775$	0	0
$776$	−2033.85	−0.0940861
$777$	− 13603.6i	− 0.628092i
$778$	− 14933.5i	− 0.688162i
$779$	7759.12	0.356867
$780$	0	0
$781$	−8929.07	−0.409100
$782$	15100.4i	0.690522i
$783$	132.780i	0.00606023i
$784$	730.268	0.0332666
$785$	0	0
$786$	1168.14	0.0530106
$787$	− 38853.5i	− 1.75982i	−0.475142	−	0.879909i	$-0.657603\pi$
$787$	− 38853.5i	− 1.75982i	0.475142	−	0.879909i	$-0.342397\pi$
$788$	− 22108.2i	− 0.999459i
$789$	1380.01	0.0622681
$790$	0	0
$791$	−20680.5	−0.929601
$792$	− 2096.53i	− 0.0940619i
$793$	− 11763.2i	− 0.526764i
$794$	14815.4	0.662191
$795$	0	0
$796$	12572.3	0.559816
$797$	9707.15i	0.431424i	0.976457	+	0.215712i	$0.0692072\pi$
$797$	9707.15i	0.431424i	−0.976457	+	0.215712i	$0.930793\pi$
$798$	− 5165.94i	− 0.229163i
$799$	−38139.0	−1.68869
$800$	0	0
$801$	−6737.66	−0.297208
$802$	9615.26i	0.423350i
$803$	11397.7i	0.500892i
$804$	18135.4	0.795506
$805$	0	0
$806$	−27613.8	−1.20677
$807$	3198.32i	0.139512i
$808$	− 1569.38i	− 0.0683299i
$809$	9284.08	0.403475	0.201737	−	0.979440i	$-0.435341\pi$
$809$	9284.08	0.403475	0.201737	+	0.979440i	$0.435341\pi$
$810$	0	0
$811$	13296.4	0.575709	0.287855	−	0.957674i	$-0.407058\pi$
$811$	13296.4	0.575709	0.287855	+	0.957674i	$0.407058\pi$
$812$	456.901i	0.0197464i
$813$	14663.7i	0.632567i
$814$	4662.56	0.200765
$815$	0	0
$816$	2807.95	0.120463
$817$	24052.4i	1.02997i
$818$	− 13771.6i	− 0.588646i
$819$	−9274.97	−0.395719
$820$	0	0
$821$	996.492	0.0423603	0.0211801	−	0.999776i	$-0.493258\pi$
$821$	996.492	0.0423603	0.0211801	+	0.999776i	$0.493258\pi$
$822$	− 970.823i	− 0.0411939i
$823$	− 28608.2i	− 1.21169i	−0.795584	−	0.605843i	$-0.792836\pi$
$823$	− 28608.2i	− 1.21169i	0.795584	−	0.605843i	$-0.207164\pi$
$824$	3926.68	0.166010
$825$	0	0
$826$	16895.0	0.711687
$827$	− 29873.5i	− 1.25611i	−0.778170	−	0.628054i	$-0.783852\pi$
$827$	− 29873.5i	− 1.25611i	0.778170	−	0.628054i	$-0.216148\pi$
$828$	5907.34i	0.247940i
$829$	−17313.2	−0.725345	−0.362673	−	0.931917i	$-0.618136\pi$
$829$	−17313.2	−0.725345	−0.362673	+	0.931917i	$0.618136\pi$
$830$	0	0
$831$	−8741.74	−0.364919
$832$	− 12400.9i	− 0.516737i
$833$	− 5238.04i	− 0.217872i
$834$	−7082.95	−0.294080
$835$	0	0
$836$	−4038.33	−0.167068
$837$	7739.66i	0.319620i
$838$	− 25473.6i	− 1.05008i
$839$	−19574.6	−0.805471	−0.402736	−	0.915316i	$-0.631941\pi$
$839$	−19574.6	−0.805471	−0.402736	+	0.915316i	$0.631941\pi$
$840$	0	0
$841$	−24364.8	−0.999008
$842$	− 3825.27i	− 0.156565i
$843$	− 7383.04i	− 0.301644i
$844$	−3495.60	−0.142563
$845$	0	0
$846$	6541.70	0.265849
$847$	− 2021.36i	− 0.0820009i
$848$	6854.62i	0.277581i
$849$	−7297.24	−0.294983
$850$	0	0
$851$	−32035.3	−1.29043
$852$	13543.5i	0.544592i
$853$	− 31871.9i	− 1.27933i	−0.768652	−	0.639667i	$-0.779072\pi$
$853$	− 31871.9i	− 1.27933i	0.768652	−	0.639667i	$-0.220928\pi$
$854$	4974.26	0.199316
$855$	0	0
$856$	−38497.4	−1.53717
$857$	31147.5i	1.24152i	0.784002	+	0.620758i	$0.213175\pi$
$857$	31147.5i	1.24152i	−0.784002	+	0.620758i	$0.786825\pi$
$858$	− 3178.94i	− 0.126489i
$859$	48143.6	1.91227	0.956134	−	0.292929i	$-0.0946300\pi$
$859$	48143.6	1.91227	0.956134	+	0.292929i	$0.0946300\pi$
$860$	0	0
$861$	5890.86	0.233171
$862$	− 11984.4i	− 0.473538i
$863$	− 34119.1i	− 1.34580i	−0.739733	−	0.672901i	$-0.765048\pi$
$863$	− 34119.1i	− 1.34580i	0.739733	−	0.672901i	$-0.234952\pi$
$864$	−5055.88	−0.199079
$865$	0	0
$866$	6198.50	0.243226
$867$	− 5401.77i	− 0.211596i
$868$	26632.5i	1.04144i
$869$	6304.55	0.246107
$870$	0	0
$871$	67053.6	2.60852
$872$	26781.4i	1.04006i
$873$	864.359i	0.0335099i
$874$	−12165.3	−0.470822
$875$	0	0
$876$	17287.9	0.666786
$877$	34221.4i	1.31764i	0.752299	+	0.658822i	$0.228945\pi$
$877$	34221.4i	1.31764i	−0.752299	+	0.658822i	$0.771055\pi$
$878$	− 23664.3i	− 0.909603i
$879$	−15298.9	−0.587054
$880$	0	0
$881$	1531.02	0.0585488	0.0292744	−	0.999571i	$-0.490680\pi$
$881$	1531.02	0.0585488	0.0292744	+	0.999571i	$0.490680\pi$
$882$	898.443i	0.0342995i
$883$	− 7551.43i	− 0.287798i	−0.989592	−	0.143899i	$-0.954036\pi$
$883$	− 7551.43i	− 0.287798i	0.989592	−	0.143899i	$-0.0459641\pi$
$884$	28111.6	1.06956
$885$	0	0
$886$	18241.2	0.691674
$887$	− 1919.81i	− 0.0726730i	−0.999340	−	0.0363365i	$-0.988431\pi$
$887$	− 1919.81i	− 0.0726730i	0.999340	−	0.0363365i	$-0.0115688\pi$
$888$	− 17245.0i	− 0.651693i
$889$	32265.4	1.21726
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 14602.7i	− 0.548132i
$893$	− 30725.9i	− 1.15140i
$894$	8609.88	0.322100
$895$	0	0
$896$	−19781.4	−0.737558
$897$	21841.7i	0.813014i
$898$	− 7810.52i	− 0.290246i
$899$	1409.70	0.0522981
$900$	0	0
$901$	49166.5	1.81795
$902$	2019.06i	0.0745313i
$903$	18261.0i	0.672965i
$904$	−26216.2	−0.964532
$905$	0	0
$906$	−2158.51	−0.0791519
$907$	− 18531.4i	− 0.678417i	−0.940711	−	0.339208i	$-0.889841\pi$
$907$	− 18531.4i	− 0.678417i	0.940711	−	0.339208i	$-0.110159\pi$
$908$	− 10030.3i	− 0.366593i
$909$	−666.967	−0.0243365
$910$	0	0
$911$	13534.8	0.492237	0.246119	−	0.969240i	$-0.420845\pi$
$911$	13534.8	0.492237	0.246119	+	0.969240i	$0.420845\pi$
$912$	2262.17i	0.0821360i
$913$	5613.50i	0.203483i
$914$	3789.56	0.137142
$915$	0	0
$916$	25734.7	0.928275
$917$	− 4165.59i	− 0.150011i
$918$	3454.60i	0.124204i
$919$	30810.2	1.10591	0.552956	−	0.833210i	$-0.313500\pi$
$919$	30810.2	1.10591	0.552956	+	0.833210i	$0.313500\pi$
$920$	0	0
$921$	−17091.4	−0.611487
$922$	12060.1i	0.430780i
$923$	50075.5i	1.78576i
$924$	−3065.97	−0.109159
$925$	0	0
$926$	−3902.16	−0.138481
$927$	− 1668.79i	− 0.0591265i
$928$	920.874i	0.0325746i
$929$	3111.95	0.109903	0.0549515	−	0.998489i	$-0.482500\pi$
$929$	3111.95	0.109903	0.0549515	+	0.998489i	$0.482500\pi$
$930$	0	0
$931$	4219.92	0.148553
$932$	− 6245.83i	− 0.219516i
$933$	− 3130.46i	− 0.109846i
$934$	2887.96	0.101174
$935$	0	0
$936$	−11757.6	−0.410588
$937$	− 17155.6i	− 0.598132i	−0.954232	−	0.299066i	$-0.903325\pi$
$937$	− 17155.6i	− 0.598132i	0.954232	−	0.299066i	$-0.0966751\pi$
$938$	28354.7i	0.987008i
$939$	−20772.6	−0.721927
$940$	0	0
$941$	−16060.8	−0.556394	−0.278197	−	0.960524i	$-0.589737\pi$
$941$	−16060.8	−0.556394	−0.278197	+	0.960524i	$0.589737\pi$
$942$	9735.08i	0.336715i
$943$	− 13872.4i	− 0.479055i
$944$	−7398.36	−0.255081
$945$	0	0
$946$	−6258.85	−0.215108
$947$	− 32056.9i	− 1.10001i	−0.835162	−	0.550005i	$-0.814626\pi$
$947$	− 32056.9i	− 1.10001i	0.835162	−	0.550005i	$-0.185374\pi$
$948$	− 9562.66i	− 0.327617i
$949$	63920.0	2.18644
$950$	0	0
$951$	−11503.5	−0.392246
$952$	28986.9i	0.986839i
$953$	39746.9i	1.35103i	0.737348	+	0.675513i	$0.236078\pi$
$953$	39746.9i	1.35103i	−0.737348	+	0.675513i	$0.763922\pi$
$954$	−8433.18	−0.286199
$955$	0	0
$956$	−24025.2	−0.812792
$957$	162.286i	0.00548168i
$958$	29397.3i	0.991424i
$959$	−3461.95	−0.116572
$960$	0	0
$961$	52379.5	1.75823
$962$	− 26148.3i	− 0.876357i
$963$	16360.9i	0.547481i
$964$	−37469.6	−1.25188
$965$	0	0
$966$	−9236.12	−0.307627
$967$	− 11278.6i	− 0.375073i	−0.982258	−	0.187536i	$-0.939950\pi$
$967$	− 11278.6i	− 0.375073i	0.982258	−	0.187536i	$-0.0600503\pi$
$968$	− 2562.43i	− 0.0850821i
$969$	16226.0	0.537931
$970$	0	0
$971$	−29310.7	−0.968718	−0.484359	−	0.874869i	$-0.660947\pi$
$971$	−29310.7	−0.968718	−0.484359	+	0.874869i	$0.660947\pi$
$972$	1351.46i	0.0445967i
$973$	25257.7i	0.832195i
$974$	−4550.09	−0.149686
$975$	0	0
$976$	−2178.24	−0.0714382
$977$	− 36592.1i	− 1.19825i	−0.800657	−	0.599123i	$-0.795516\pi$
$977$	− 36592.1i	− 1.19825i	0.800657	−	0.599123i	$-0.204484\pi$
$978$	6433.21i	0.210339i
$979$	−8234.92	−0.268835
$980$	0	0
$981$	11381.8	0.370430
$982$	− 14087.1i	− 0.457777i
$983$	11341.2i	0.367983i	0.982928	+	0.183992i	$0.0589019\pi$
$983$	11341.2i	0.367983i	−0.982928	+	0.183992i	$0.941098\pi$
$984$	7467.69	0.241932
$985$	0	0
$986$	629.219	0.0203229
$987$	− 23327.7i	− 0.752307i
$988$	22647.5i	0.729266i
$989$	43003.0	1.38262
$990$	0	0
$991$	43462.8	1.39318	0.696591	−	0.717469i	$-0.254699\pi$
$991$	43462.8	1.39318	0.696591	+	0.717469i	$0.254699\pi$
$992$	53677.3i	1.71800i
$993$	− 3937.27i	− 0.125826i
$994$	−21175.2	−0.675692
$995$	0	0
$996$	8514.49	0.270875
$997$	− 39682.4i	− 1.26054i	−0.776378	−	0.630268i	$-0.782945\pi$
$997$	− 39682.4i	− 1.26054i	0.776378	−	0.630268i	$-0.217055\pi$
$998$	27060.9i	0.858316i
$999$	−7328.90	−0.232108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.q.199.3		8
5.2	odd	4		825.4.a.u.1.4	✓	4
5.3	odd	4		825.4.a.v.1.1	yes	4
5.4	even	2	inner	825.4.c.q.199.6		8
15.2	even	4		2475.4.a.bd.1.2		4
15.8	even	4		2475.4.a.bb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.u.1.4	✓	4	5.2	odd	4
825.4.a.v.1.1	yes	4	5.3	odd	4
825.4.c.q.199.3		8	1.1	even	1	trivial
825.4.c.q.199.6		8	5.4	even	2	inner
2475.4.a.bb.1.3		4	15.8	even	4
2475.4.a.bd.1.2		4	15.2	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.56155i q^{2} +3.00000i q^{3} +5.56155 q^{4} +4.68466 q^{6} -16.7054i q^{7} -21.1771i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-1.56155i q^{2} +3.00000i q^{3} +5.56155 q^{4} +4.68466 q^{6} -16.7054i q^{7} -21.1771i q^{8} -9.00000 q^{9} -11.0000 q^{11} +16.6847i q^{12} +61.6896i q^{13} -26.0864 q^{14} +11.4233 q^{16} -81.9365i q^{17} +14.0540i q^{18} +66.0105 q^{19} +50.1163 q^{21} +17.1771i q^{22} -118.019i q^{23} +63.5312 q^{24} +96.3315 q^{26} -27.0000i q^{27} -92.9082i q^{28} -4.91776 q^{29} -286.654 q^{31} -187.255i q^{32} -33.0000i q^{33} -127.948 q^{34} -50.0540 q^{36} -271.441i q^{37} -103.079i q^{38} -185.069 q^{39} +117.544 q^{41} -78.2593i q^{42} +364.372i q^{43} -61.1771 q^{44} -184.294 q^{46} -465.470i q^{47} +34.2699i q^{48} +63.9280 q^{49} +245.810 q^{51} +343.090i q^{52} +600.056i q^{53} -42.1619 q^{54} -353.773 q^{56} +198.032i q^{57} +7.67935i q^{58} -647.656 q^{59} -190.684 q^{61} +447.625i q^{62} +150.349i q^{63} -201.022 q^{64} -51.5312 q^{66} -1086.95i q^{67} -455.694i q^{68} +354.058 q^{69} +811.734 q^{71} +190.594i q^{72} -1036.16i q^{73} -423.869 q^{74} +367.121 q^{76} +183.760i q^{77} +288.995i q^{78} -573.141 q^{79} +81.0000 q^{81} -183.551i q^{82} -510.318i q^{83} +278.725 q^{84} +568.986 q^{86} -14.7533i q^{87} +232.948i q^{88} +748.629 q^{89} +1030.55 q^{91} -656.371i q^{92} -859.962i q^{93} -726.856 q^{94} +561.764 q^{96} -96.0399i q^{97} -99.8270i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9	\( 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9} - 88 q^{11} + 6 q^{14} - 156 q^{16} - 236 q^{19} - 66 q^{21} - 36 q^{24} - 314 q^{26} - 502 q^{29} - 270 q^{31} - 578 q^{34} - 252 q^{36} - 150 q^{39} - 206 q^{41} - 308 q^{44} - 840 q^{46} - 2006 q^{49} + 510 q^{51} + 108 q^{54} + 154 q^{56} - 1902 q^{59} - 700 q^{61} - 3076 q^{64} + 132 q^{66} + 60 q^{69} + 3052 q^{71} - 2182 q^{74} - 792 q^{76} - 5134 q^{79} + 648 q^{81} - 282 q^{84} + 3674 q^{86} - 2106 q^{89} + 4300 q^{91} - 4418 q^{94} + 1476 q^{96} + 792 q^{99}+O(q^{100}) \) 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9 - 88 * q^11 + 6 * q^14 - 156 * q^16 - 236 * q^19 - 66 * q^21 - 36 * q^24 - 314 * q^26 - 502 * q^29 - 270 * q^31 - 578 * q^34 - 252 * q^36 - 150 * q^39 - 206 * q^41 - 308 * q^44 - 840 * q^46 - 2006 * q^49 + 510 * q^51 + 108 * q^54 + 154 * q^56 - 1902 * q^59 - 700 * q^61 - 3076 * q^64 + 132 * q^66 + 60 * q^69 + 3052 * q^71 - 2182 * q^74 - 792 * q^76 - 5134 * q^79 + 648 * q^81 - 282 * q^84 + 3674 * q^86 - 2106 * q^89 + 4300 * q^91 - 4418 * q^94 + 1476 * q^96 + 792 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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