LMFDB - Embedded newform 1875.2.b.e.1249.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1249,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.b (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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 $ x^12 + 23x^10 + 199x^8 + 794x^6 + 1399x^4 + 783*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.9
Root			$2.02791i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.e.1249.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02791i q^{2} -1.00000i q^{3} -2.11242 q^{4} +2.02791 q^{6} -0.505614i q^{7} -0.227977i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.02791i q^{2} -1.00000i q^{3} -2.11242 q^{4} +2.02791 q^{6} -0.505614i q^{7} -0.227977i q^{8} -1.00000 q^{9} +0.687513 q^{11} +2.11242i q^{12} -5.78627i q^{13} +1.02534 q^{14} -3.76252 q^{16} +4.74333i q^{17} -2.02791i q^{18} -4.23709 q^{19} -0.505614 q^{21} +1.39422i q^{22} +8.36239i q^{23} -0.227977 q^{24} +11.7340 q^{26} +1.00000i q^{27} +1.06807i q^{28} -4.88758 q^{29} +2.68853 q^{31} -8.08601i q^{32} -0.687513i q^{33} -9.61905 q^{34} +2.11242 q^{36} +11.3806i q^{37} -8.59244i q^{38} -5.78627 q^{39} +0.144247 q^{41} -1.02534i q^{42} +5.94442i q^{43} -1.45232 q^{44} -16.9582 q^{46} +6.10650i q^{47} +3.76252i q^{48} +6.74435 q^{49} +4.74333 q^{51} +12.2230i q^{52} +10.8398i q^{53} -2.02791 q^{54} -0.115269 q^{56} +4.23709i q^{57} -9.91157i q^{58} +6.96817 q^{59} -3.98042 q^{61} +5.45211i q^{62} +0.505614i q^{63} +8.87266 q^{64} +1.39422 q^{66} +1.31351i q^{67} -10.0199i q^{68} +8.36239 q^{69} -3.79321 q^{71} +0.227977i q^{72} -10.9252i q^{73} -23.0787 q^{74} +8.95051 q^{76} -0.347616i q^{77} -11.7340i q^{78} +1.89869 q^{79} +1.00000 q^{81} +0.292519i q^{82} +2.51849i q^{83} +1.06807 q^{84} -12.0548 q^{86} +4.88758i q^{87} -0.156737i q^{88} -15.0809 q^{89} -2.92562 q^{91} -17.6649i q^{92} -2.68853i q^{93} -12.3834 q^{94} -8.08601 q^{96} -1.17394i q^{97} +13.6769i q^{98} -0.687513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times$.

$n$	$626$	$1252$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.02791i	1.43395i	0.697099	+	0.716975i	$0.254474\pi$
$2$	2.02791i	1.43395i	−0.697099	+	0.716975i	$0.745526\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−2.11242	−1.05621
$5$	0	0
$5$	0	0
$6$	2.02791	0.827891
$7$	− 0.505614i	− 0.191104i	−0.995424	−	0.0955521i	$-0.969538\pi$
$7$	− 0.505614i	− 0.191104i	0.995424	−	0.0955521i	$-0.0304617\pi$
$8$	− 0.227977i	− 0.0806021i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	0.687513	0.207293	0.103647	−	0.994614i	$-0.466949\pi$
$11$	0.687513	0.207293	0.103647	+	0.994614i	$0.466949\pi$
$12$	2.11242i	0.609803i
$13$	− 5.78627i	− 1.60482i	−0.596771	−	0.802412i	$-0.703550\pi$
$13$	− 5.78627i	− 1.60482i	0.596771	−	0.802412i	$-0.296450\pi$
$14$	1.02534	0.274034
$15$	0	0
$16$	−3.76252	−0.940631
$17$	4.74333i	1.15043i	0.818003	+	0.575214i	$0.195081\pi$
$17$	4.74333i	1.15043i	−0.818003	+	0.575214i	$0.804919\pi$
$18$	− 2.02791i	− 0.477983i
$19$	−4.23709	−0.972055	−0.486027	−	0.873944i	$-0.661554\pi$
$19$	−4.23709	−0.972055	−0.486027	+	0.873944i	$0.661554\pi$
$20$	0	0
$21$	−0.505614	−0.110334
$22$	1.39422i	0.297248i
$23$	8.36239i	1.74368i	0.489792	+	0.871839i	$0.337073\pi$
$23$	8.36239i	1.74368i	−0.489792	+	0.871839i	$0.662927\pi$
$24$	−0.227977	−0.0465357
$25$	0	0
$26$	11.7340	2.30124
$27$	1.00000i	0.192450i
$28$	1.06807i	0.201846i
$29$	−4.88758	−0.907601	−0.453800	−	0.891103i	$-0.649932\pi$
$29$	−4.88758	−0.907601	−0.453800	+	0.891103i	$0.649932\pi$
$30$	0	0
$31$	2.68853	0.482875	0.241437	−	0.970416i	$-0.422381\pi$
$31$	2.68853	0.482875	0.241437	+	0.970416i	$0.422381\pi$
$32$	− 8.08601i	− 1.42942i
$33$	− 0.687513i	− 0.119681i
$34$	−9.61905	−1.64965
$35$	0	0
$36$	2.11242	0.352070
$37$	11.3806i	1.87095i	0.353390	+	0.935476i	$0.385029\pi$
$37$	11.3806i	1.87095i	−0.353390	+	0.935476i	$0.614971\pi$
$38$	− 8.59244i	− 1.39388i
$39$	−5.78627	−0.926545
$40$	0	0
$41$	0.144247	0.0225275	0.0112638	−	0.999937i	$-0.496415\pi$
$41$	0.144247	0.0225275	0.0112638	+	0.999937i	$0.496415\pi$
$42$	− 1.02534i	− 0.158213i
$43$	5.94442i	0.906516i	0.891379	+	0.453258i	$0.149738\pi$
$43$	5.94442i	0.906516i	−0.891379	+	0.453258i	$0.850262\pi$
$44$	−1.45232	−0.218945
$45$	0	0
$46$	−16.9582	−2.50035
$47$	6.10650i	0.890725i	0.895350	+	0.445362i	$0.146925\pi$
$47$	6.10650i	0.890725i	−0.895350	+	0.445362i	$0.853075\pi$
$48$	3.76252i	0.543073i
$49$	6.74435	0.963479
$50$	0	0
$51$	4.74333	0.664200
$52$	12.2230i	1.69503i
$53$	10.8398i	1.48896i	0.667643	+	0.744481i	$0.267303\pi$
$53$	10.8398i	1.48896i	−0.667643	+	0.744481i	$0.732697\pi$
$54$	−2.02791	−0.275964
$55$	0	0
$56$	−0.115269	−0.0154034
$57$	4.23709i	0.561216i
$58$	− 9.91157i	− 1.30145i
$59$	6.96817	0.907179	0.453589	−	0.891211i	$-0.350143\pi$
$59$	6.96817	0.907179	0.453589	+	0.891211i	$0.350143\pi$
$60$	0	0
$61$	−3.98042	−0.509641	−0.254820	−	0.966988i	$-0.582016\pi$
$61$	−3.98042	−0.509641	−0.254820	+	0.966988i	$0.582016\pi$
$62$	5.45211i	0.692418i
$63$	0.505614i	0.0637014i
$64$	8.87266	1.10908
$65$	0	0
$66$	1.39422	0.171616
$67$	1.31351i	0.160470i	0.996776	+	0.0802352i	$0.0255672\pi$
$67$	1.31351i	0.160470i	−0.996776	+	0.0802352i	$0.974433\pi$
$68$	− 10.0199i	− 1.21509i
$69$	8.36239	1.00671
$70$	0	0
$71$	−3.79321	−0.450172	−0.225086	−	0.974339i	$-0.572266\pi$
$71$	−3.79321	−0.450172	−0.225086	+	0.974339i	$0.572266\pi$
$72$	0.227977i	0.0268674i
$73$	− 10.9252i	− 1.27870i	−0.768915	−	0.639351i	$-0.779203\pi$
$73$	− 10.9252i	− 1.27870i	0.768915	−	0.639351i	$-0.220797\pi$
$74$	−23.0787	−2.68285
$75$	0	0
$76$	8.95051	1.02669
$77$	− 0.347616i	− 0.0396146i
$78$	− 11.7340i	− 1.32862i
$79$	1.89869	0.213620	0.106810	−	0.994279i	$-0.465936\pi$
$79$	1.89869	0.213620	0.106810	+	0.994279i	$0.465936\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.292519i	0.0323033i
$83$	2.51849i	0.276441i	0.990402	+	0.138220i	$0.0441382\pi$
$83$	2.51849i	0.276441i	−0.990402	+	0.138220i	$0.955862\pi$
$84$	1.06807	0.116536
$85$	0	0
$86$	−12.0548	−1.29990
$87$	4.88758i	0.524004i
$88$	− 0.156737i	− 0.0167083i
$89$	−15.0809	−1.59858	−0.799289	−	0.600947i	$-0.794790\pi$
$89$	−15.0809	−1.59858	−0.799289	+	0.600947i	$0.794790\pi$
$90$	0	0
$91$	−2.92562	−0.306689
$92$	− 17.6649i	− 1.84169i
$93$	− 2.68853i	− 0.278788i
$94$	−12.3834	−1.27725
$95$	0	0
$96$	−8.08601	−0.825275
$97$	− 1.17394i	− 0.119195i	−0.998222	−	0.0595977i	$-0.981018\pi$
$97$	− 1.17394i	− 0.119195i	0.998222	−	0.0595977i	$-0.0189818\pi$
$98$	13.6769i	1.38158i
$99$	−0.687513	−0.0690977
$100$	0	0
$101$	7.23262	0.719672	0.359836	−	0.933016i	$-0.382833\pi$
$101$	7.23262	0.719672	0.359836	+	0.933016i	$0.382833\pi$
$102$	9.61905i	0.952428i
$103$	18.4207i	1.81505i	0.420000	+	0.907524i	$0.362030\pi$
$103$	18.4207i	1.81505i	−0.420000	+	0.907524i	$0.637970\pi$
$104$	−1.31914	−0.129352
$105$	0	0
$106$	−21.9822	−2.13510
$107$	− 17.5572i	− 1.69732i	−0.528937	−	0.848661i	$-0.677409\pi$
$107$	− 17.5572i	− 1.69732i	0.528937	−	0.848661i	$-0.322591\pi$
$108$	− 2.11242i	− 0.203268i
$109$	−11.4098	−1.09286	−0.546429	−	0.837506i	$-0.684013\pi$
$109$	−11.4098	−1.09286	−0.546429	+	0.837506i	$0.684013\pi$
$110$	0	0
$111$	11.3806	1.08019
$112$	1.90238i	0.179758i
$113$	9.64827i	0.907632i	0.891095	+	0.453816i	$0.149938\pi$
$113$	9.64827i	0.907632i	−0.891095	+	0.453816i	$0.850062\pi$
$114$	−8.59244	−0.804755
$115$	0	0
$116$	10.3246	0.958617
$117$	5.78627i	0.534941i
$118$	14.1308i	1.30085i
$119$	2.39830	0.219852
$120$	0	0
$121$	−10.5273	−0.957030
$122$	− 8.07194i	− 0.730799i
$123$	− 0.144247i	− 0.0130063i
$124$	−5.67931	−0.510017
$125$	0	0
$126$	−1.02534	−0.0913446
$127$	− 4.32804i	− 0.384051i	−0.981390	−	0.192026i	$-0.938494\pi$
$127$	− 4.32804i	− 0.384051i	0.981390	−	0.192026i	$-0.0615057\pi$
$128$	1.82094i	0.160950i
$129$	5.94442	0.523377
$130$	0	0
$131$	−10.1642	−0.888047	−0.444023	−	0.896015i	$-0.646449\pi$
$131$	−10.1642	−0.888047	−0.444023	+	0.896015i	$0.646449\pi$
$132$	1.45232i	0.126408i
$133$	2.14233i	0.185764i
$134$	−2.66368	−0.230106
$135$	0	0
$136$	1.08137	0.0927269
$137$	− 5.57509i	− 0.476312i	−0.971227	−	0.238156i	$-0.923457\pi$
$137$	− 5.57509i	− 0.476312i	0.971227	−	0.238156i	$-0.0765430\pi$
$138$	16.9582i	1.44358i
$139$	−9.24097	−0.783809	−0.391904	−	0.920006i	$-0.628184\pi$
$139$	−9.24097	−0.783809	−0.391904	+	0.920006i	$0.628184\pi$
$140$	0	0
$141$	6.10650	0.514260
$142$	− 7.69230i	− 0.645523i
$143$	− 3.97814i	− 0.332669i
$144$	3.76252	0.313544
$145$	0	0
$146$	22.1554	1.83359
$147$	− 6.74435i	− 0.556265i
$148$	− 24.0405i	− 1.97612i
$149$	9.91157	0.811988	0.405994	−	0.913876i	$-0.366925\pi$
$149$	9.91157	0.811988	0.405994	+	0.913876i	$0.366925\pi$
$150$	0	0
$151$	−21.8846	−1.78094	−0.890471	−	0.455041i	$-0.849625\pi$
$151$	−21.8846	−1.78094	−0.890471	+	0.455041i	$0.849625\pi$
$152$	0.965960i	0.0783497i
$153$	− 4.74333i	− 0.383476i
$154$	0.704935	0.0568053
$155$	0	0
$156$	12.2230	0.978626
$157$	− 4.47331i	− 0.357009i	−0.983939	−	0.178504i	$-0.942874\pi$
$157$	− 4.47331i	− 0.357009i	0.983939	−	0.178504i	$-0.0571259\pi$
$158$	3.85038i	0.306320i
$159$	10.8398	0.859653
$160$	0	0
$161$	4.22814	0.333224
$162$	2.02791i	0.159328i
$163$	14.2898i	1.11927i	0.828740	+	0.559634i	$0.189058\pi$
$163$	14.2898i	1.11927i	−0.828740	+	0.559634i	$0.810942\pi$
$164$	−0.304709	−0.0237938
$165$	0	0
$166$	−5.10728	−0.396402
$167$	0.473306i	0.0366255i	0.999832	+	0.0183128i	$0.00582946\pi$
$167$	0.473306i	0.0366255i	−0.999832	+	0.0183128i	$0.994171\pi$
$168$	0.115269i	0.00889316i
$169$	−20.4810	−1.57546
$170$	0	0
$171$	4.23709	0.324018
$172$	− 12.5571i	− 0.957471i
$173$	2.14939i	0.163415i	0.996656	+	0.0817074i	$0.0260373\pi$
$173$	2.14939i	0.163415i	−0.996656	+	0.0817074i	$0.973963\pi$
$174$	−9.91157	−0.751394
$175$	0	0
$176$	−2.58678	−0.194986
$177$	− 6.96817i	− 0.523760i
$178$	− 30.5828i	− 2.29228i
$179$	1.35831	0.101525	0.0507623	−	0.998711i	$-0.483835\pi$
$179$	1.35831	0.101525	0.0507623	+	0.998711i	$0.483835\pi$
$180$	0	0
$181$	3.37725	0.251029	0.125515	−	0.992092i	$-0.459942\pi$
$181$	3.37725	0.251029	0.125515	+	0.992092i	$0.459942\pi$
$182$	− 5.93290i	− 0.439776i
$183$	3.98042i	0.294241i
$184$	1.90643	0.140544
$185$	0	0
$186$	5.45211	0.399768
$187$	3.26110i	0.238476i
$188$	− 12.8995i	− 0.940792i
$189$	0.505614	0.0367780
$190$	0	0
$191$	21.8942	1.58421	0.792103	−	0.610388i	$-0.208986\pi$
$191$	21.8942	1.58421	0.792103	+	0.610388i	$0.208986\pi$
$192$	− 8.87266i	− 0.640329i
$193$	20.3890i	1.46763i	0.679347	+	0.733817i	$0.262263\pi$
$193$	20.3890i	1.46763i	−0.679347	+	0.733817i	$0.737737\pi$
$194$	2.38064	0.170920
$195$	0	0
$196$	−14.2469	−1.01764
$197$	− 24.9688i	− 1.77895i	−0.456980	−	0.889477i	$-0.651069\pi$
$197$	− 24.9688i	− 1.77895i	0.456980	−	0.889477i	$-0.348931\pi$
$198$	− 1.39422i	− 0.0990826i
$199$	10.2138	0.724038	0.362019	−	0.932171i	$-0.382087\pi$
$199$	10.2138	0.724038	0.362019	+	0.932171i	$0.382087\pi$
$200$	0	0
$201$	1.31351	0.0926477
$202$	14.6671i	1.03197i
$203$	2.47123i	0.173446i
$204$	−10.0199	−0.701534
$205$	0	0
$206$	−37.3556	−2.60269
$207$	− 8.36239i	− 0.581226i
$208$	21.7710i	1.50955i
$209$	−2.91305	−0.201500
$210$	0	0
$211$	5.46907	0.376507	0.188253	−	0.982121i	$-0.439717\pi$
$211$	5.46907	0.376507	0.188253	+	0.982121i	$0.439717\pi$
$212$	− 22.8982i	− 1.57266i
$213$	3.79321i	0.259907i
$214$	35.6045	2.43387
$215$	0	0
$216$	0.227977	0.0155119
$217$	− 1.35936i	− 0.0922794i
$218$	− 23.1380i	− 1.56710i
$219$	−10.9252	−0.738259
$220$	0	0
$221$	27.4462	1.84623
$222$	23.0787i	1.54894i
$223$	− 22.8887i	− 1.53274i	−0.642399	−	0.766370i	$-0.722061\pi$
$223$	− 22.8887i	− 1.53274i	0.642399	−	0.766370i	$-0.277939\pi$
$224$	−4.08840	−0.273168
$225$	0	0
$226$	−19.5658	−1.30150
$227$	− 12.9219i	− 0.857659i	−0.903386	−	0.428829i	$-0.858926\pi$
$227$	− 12.9219i	− 0.857659i	0.903386	−	0.428829i	$-0.141074\pi$
$228$	− 8.95051i	− 0.592762i
$229$	−14.5252	−0.959850	−0.479925	−	0.877309i	$-0.659336\pi$
$229$	−14.5252	−0.959850	−0.479925	+	0.877309i	$0.659336\pi$
$230$	0	0
$231$	−0.347616	−0.0228715
$232$	1.11426i	0.0731545i
$233$	9.94748i	0.651681i	0.945425	+	0.325841i	$0.105647\pi$
$233$	9.94748i	0.651681i	−0.945425	+	0.325841i	$0.894353\pi$
$234$	−11.7340	−0.767078
$235$	0	0
$236$	−14.7197	−0.958171
$237$	− 1.89869i	− 0.123333i
$238$	4.86353i	0.315256i
$239$	−1.58509	−0.102531	−0.0512656	−	0.998685i	$-0.516326\pi$
$239$	−1.58509	−0.102531	−0.0512656	+	0.998685i	$0.516326\pi$
$240$	0	0
$241$	23.7485	1.52978	0.764889	−	0.644163i	$-0.222794\pi$
$241$	23.7485	1.52978	0.764889	+	0.644163i	$0.222794\pi$
$242$	− 21.3485i	− 1.37233i
$243$	− 1.00000i	− 0.0641500i
$244$	8.40832	0.538288
$245$	0	0
$246$	0.292519	0.0186503
$247$	24.5170i	1.55998i
$248$	− 0.612924i	− 0.0389207i
$249$	2.51849	0.159603
$250$	0	0
$251$	20.2887	1.28061	0.640307	−	0.768119i	$-0.278807\pi$
$251$	20.2887	1.28061	0.640307	+	0.768119i	$0.278807\pi$
$252$	− 1.06807i	− 0.0672821i
$253$	5.74925i	0.361452i
$254$	8.77687	0.550710
$255$	0	0
$256$	14.0526	0.878289
$257$	21.8997i	1.36607i	0.730387	+	0.683033i	$0.239340\pi$
$257$	21.8997i	1.36607i	−0.730387	+	0.683033i	$0.760660\pi$
$258$	12.0548i	0.750496i
$259$	5.75417	0.357547
$260$	0	0
$261$	4.88758	0.302534
$262$	− 20.6120i	− 1.27341i
$263$	− 4.76922i	− 0.294083i	−0.989130	−	0.147041i	$-0.953025\pi$
$263$	− 4.76922i	− 0.294083i	0.989130	−	0.147041i	$-0.0469750\pi$
$264$	−0.156737	−0.00964652
$265$	0	0
$266$	−4.34446	−0.266376
$267$	15.0809i	0.922939i
$268$	− 2.77468i	− 0.169490i
$269$	12.0532	0.734899	0.367450	−	0.930043i	$-0.380231\pi$
$269$	12.0532	0.734899	0.367450	+	0.930043i	$0.380231\pi$
$270$	0	0
$271$	27.5843	1.67562	0.837812	−	0.545959i	$-0.183834\pi$
$271$	27.5843	1.67562	0.837812	+	0.545959i	$0.183834\pi$
$272$	− 17.8469i	− 1.08213i
$273$	2.92562i	0.177067i
$274$	11.3058	0.683008
$275$	0	0
$276$	−17.6649	−1.06330
$277$	− 28.9858i	− 1.74159i	−0.491646	−	0.870795i	$-0.663605\pi$
$277$	− 28.9858i	− 1.74159i	0.491646	−	0.870795i	$-0.336395\pi$
$278$	− 18.7399i	− 1.12394i
$279$	−2.68853	−0.160958
$280$	0	0
$281$	5.93418	0.354003	0.177002	−	0.984211i	$-0.443360\pi$
$281$	5.93418	0.354003	0.177002	+	0.984211i	$0.443360\pi$
$282$	12.3834i	0.737423i
$283$	− 15.2381i	− 0.905812i	−0.891558	−	0.452906i	$-0.850387\pi$
$283$	− 15.2381i	− 0.905812i	0.891558	−	0.452906i	$-0.149613\pi$
$284$	8.01286	0.475476
$285$	0	0
$286$	8.06731	0.477030
$287$	− 0.0729331i	− 0.00430511i
$288$	8.08601i	0.476473i
$289$	−5.49921	−0.323483
$290$	0	0
$291$	−1.17394	−0.0688175
$292$	23.0787i	1.35058i
$293$	1.73298i	0.101242i	0.998718	+	0.0506208i	$0.0161200\pi$
$293$	1.73298i	0.101242i	−0.998718	+	0.0506208i	$0.983880\pi$
$294$	13.6769	0.797656
$295$	0	0
$296$	2.59451	0.150803
$297$	0.687513i	0.0398936i
$298$	20.0998i	1.16435i
$299$	48.3871	2.79830
$300$	0	0
$301$	3.00558	0.173239
$302$	− 44.3800i	− 2.55378i
$303$	− 7.23262i	− 0.415503i
$304$	15.9421	0.914344
$305$	0	0
$306$	9.61905	0.549885
$307$	− 11.6087i	− 0.662541i	−0.943536	−	0.331271i	$-0.892523\pi$
$307$	− 11.6087i	− 0.662541i	0.943536	−	0.331271i	$-0.107477\pi$
$308$	0.734312i	0.0418413i
$309$	18.4207	1.04792
$310$	0	0
$311$	6.60870	0.374745	0.187372	−	0.982289i	$-0.440003\pi$
$311$	6.60870	0.374745	0.187372	+	0.982289i	$0.440003\pi$
$312$	1.31914i	0.0746815i
$313$	12.5410i	0.708860i	0.935082	+	0.354430i	$0.115325\pi$
$313$	12.5410i	0.708860i	−0.935082	+	0.354430i	$0.884675\pi$
$314$	9.07146	0.511932
$315$	0	0
$316$	−4.01084	−0.225627
$317$	11.7318i	0.658925i	0.944169	+	0.329463i	$0.106868\pi$
$317$	11.7318i	0.658925i	−0.944169	+	0.329463i	$0.893132\pi$
$318$	21.9822i	1.23270i
$319$	−3.36028	−0.188139
$320$	0	0
$321$	−17.5572	−0.979949
$322$	8.57429i	0.477827i
$323$	− 20.0979i	− 1.11828i
$324$	−2.11242	−0.117357
$325$	0	0
$326$	−28.9785	−1.60497
$327$	11.4098i	0.630962i
$328$	− 0.0328849i	− 0.00181577i
$329$	3.08753	0.170221
$330$	0	0
$331$	8.16236	0.448644	0.224322	−	0.974515i	$-0.427983\pi$
$331$	8.16236	0.448644	0.224322	+	0.974515i	$0.427983\pi$
$332$	− 5.32012i	− 0.291979i
$333$	− 11.3806i	− 0.623651i
$334$	−0.959822	−0.0525191
$335$	0	0
$336$	1.90238	0.103784
$337$	11.1478i	0.607259i	0.952790	+	0.303629i	$0.0981985\pi$
$337$	11.1478i	0.607259i	−0.952790	+	0.303629i	$0.901802\pi$
$338$	− 41.5336i	− 2.25913i
$339$	9.64827	0.524022
$340$	0	0
$341$	1.84840	0.100097
$342$	8.59244i	0.464626i
$343$	− 6.94934i	− 0.375229i
$344$	1.35519	0.0730671
$345$	0	0
$346$	−4.35876	−0.234329
$347$	10.2954i	0.552687i	0.961059	+	0.276343i	$0.0891227\pi$
$347$	10.2954i	0.552687i	−0.961059	+	0.276343i	$0.910877\pi$
$348$	− 10.3246i	− 0.553458i
$349$	−20.8288	−1.11494	−0.557471	−	0.830196i	$-0.688228\pi$
$349$	−20.8288	−1.11494	−0.557471	+	0.830196i	$0.688228\pi$
$350$	0	0
$351$	5.78627	0.308848
$352$	− 5.55924i	− 0.296308i
$353$	27.6165i	1.46988i	0.678133	+	0.734939i	$0.262789\pi$
$353$	27.6165i	1.46988i	−0.678133	+	0.734939i	$0.737211\pi$
$354$	14.1308	0.751045
$355$	0	0
$356$	31.8573	1.68843
$357$	− 2.39830i	− 0.126931i
$358$	2.75452i	0.145581i
$359$	−19.2421	−1.01556	−0.507781	−	0.861486i	$-0.669534\pi$
$359$	−19.2421	−1.01556	−0.507781	+	0.861486i	$0.669534\pi$
$360$	0	0
$361$	−1.04708	−0.0551095
$362$	6.84877i	0.359963i
$363$	10.5273i	0.552541i
$364$	6.18014	0.323927
$365$	0	0
$366$	−8.07194	−0.421927
$367$	− 8.23097i	− 0.429653i	−0.976652	−	0.214826i	$-0.931081\pi$
$367$	− 8.23097i	− 0.429653i	0.976652	−	0.214826i	$-0.0689186\pi$
$368$	− 31.4637i	− 1.64016i
$369$	−0.144247	−0.00750918
$370$	0	0
$371$	5.48076	0.284547
$372$	5.67931i	0.294459i
$373$	29.1863i	1.51121i	0.655027	+	0.755606i	$0.272657\pi$
$373$	29.1863i	1.51121i	−0.655027	+	0.755606i	$0.727343\pi$
$374$	−6.61323	−0.341962
$375$	0	0
$376$	1.39214	0.0717943
$377$	28.2809i	1.45654i
$378$	1.02534i	0.0527378i
$379$	4.34734	0.223308	0.111654	−	0.993747i	$-0.464385\pi$
$379$	4.34734	0.223308	0.111654	+	0.993747i	$0.464385\pi$
$380$	0	0
$381$	−4.32804	−0.221732
$382$	44.3994i	2.27167i
$383$	− 22.6224i	− 1.15595i	−0.816054	−	0.577976i	$-0.803843\pi$
$383$	− 22.6224i	− 1.15595i	0.816054	−	0.577976i	$-0.196157\pi$
$384$	1.82094	0.0929243
$385$	0	0
$386$	−41.3471	−2.10451
$387$	− 5.94442i	− 0.302172i
$388$	2.47985i	0.125895i
$389$	−11.2860	−0.572221	−0.286111	−	0.958197i	$-0.592362\pi$
$389$	−11.2860	−0.572221	−0.286111	+	0.958197i	$0.592362\pi$
$390$	0	0
$391$	−39.6656	−2.00598
$392$	− 1.53756i	− 0.0776585i
$393$	10.1642i	0.512714i
$394$	50.6345	2.55093
$395$	0	0
$396$	1.45232	0.0729817
$397$	9.06606i	0.455013i	0.973777	+	0.227506i	$0.0730572\pi$
$397$	9.06606i	0.455013i	−0.973777	+	0.227506i	$0.926943\pi$
$398$	20.7127i	1.03823i
$399$	2.14233	0.107251
$400$	0	0
$401$	−11.9700	−0.597752	−0.298876	−	0.954292i	$-0.596612\pi$
$401$	−11.9700	−0.597752	−0.298876	+	0.954292i	$0.596612\pi$
$402$	2.66368i	0.132852i
$403$	− 15.5566i	− 0.774929i
$404$	−15.2783	−0.760125
$405$	0	0
$406$	−5.01143	−0.248713
$407$	7.82428i	0.387835i
$408$	− 1.08137i	− 0.0535359i
$409$	23.1228	1.14335	0.571673	−	0.820481i	$-0.306294\pi$
$409$	23.1228	1.14335	0.571673	+	0.820481i	$0.306294\pi$
$410$	0	0
$411$	−5.57509	−0.274999
$412$	− 38.9123i	− 1.91707i
$413$	− 3.52321i	− 0.173366i
$414$	16.9582	0.833449
$415$	0	0
$416$	−46.7879	−2.29396
$417$	9.24097i	0.452532i
$418$	− 5.90741i	− 0.288941i
$419$	32.8579	1.60521	0.802606	−	0.596509i	$-0.203446\pi$
$419$	32.8579	1.60521	0.802606	+	0.596509i	$0.203446\pi$
$420$	0	0
$421$	8.70039	0.424031	0.212016	−	0.977266i	$-0.431997\pi$
$421$	8.70039	0.424031	0.212016	+	0.977266i	$0.431997\pi$
$422$	11.0908i	0.539891i
$423$	− 6.10650i	− 0.296908i
$424$	2.47123	0.120014
$425$	0	0
$426$	−7.69230	−0.372693
$427$	2.01256i	0.0973945i
$428$	37.0883i	1.79273i
$429$	−3.97814	−0.192066
$430$	0	0
$431$	5.70635	0.274865	0.137432	−	0.990511i	$-0.456115\pi$
$431$	5.70635	0.274865	0.137432	+	0.990511i	$0.456115\pi$
$432$	− 3.76252i	− 0.181024i
$433$	− 18.2221i	− 0.875700i	−0.899048	−	0.437850i	$-0.855740\pi$
$433$	− 18.2221i	− 0.875700i	0.899048	−	0.437850i	$-0.144260\pi$
$434$	2.75666	0.132324
$435$	0	0
$436$	24.1022	1.15429
$437$	− 35.4322i	− 1.69495i
$438$	− 22.1554i	− 1.05863i
$439$	−13.2419	−0.632002	−0.316001	−	0.948759i	$-0.602340\pi$
$439$	−13.2419	−0.632002	−0.316001	+	0.948759i	$0.602340\pi$
$440$	0	0
$441$	−6.74435	−0.321160
$442$	55.6585i	2.64740i
$443$	26.3276i	1.25086i	0.780279	+	0.625431i	$0.215077\pi$
$443$	26.3276i	1.25086i	−0.780279	+	0.625431i	$0.784923\pi$
$444$	−24.0405	−1.14091
$445$	0	0
$446$	46.4162	2.19787
$447$	− 9.91157i	− 0.468801i
$448$	− 4.48614i	− 0.211950i
$449$	−22.2932	−1.05208	−0.526040	−	0.850460i	$-0.676324\pi$
$449$	−22.2932	−1.05208	−0.526040	+	0.850460i	$0.676324\pi$
$450$	0	0
$451$	0.0991714	0.00466980
$452$	− 20.3812i	− 0.958650i
$453$	21.8846i	1.02823i
$454$	26.2045	1.22984
$455$	0	0
$456$	0.965960	0.0452352
$457$	17.3159i	0.810002i	0.914316	+	0.405001i	$0.132729\pi$
$457$	17.3159i	0.810002i	−0.914316	+	0.405001i	$0.867271\pi$
$458$	− 29.4557i	− 1.37638i
$459$	−4.74333	−0.221400
$460$	0	0
$461$	−16.2204	−0.755460	−0.377730	−	0.925916i	$-0.623295\pi$
$461$	−16.2204	−0.755460	−0.377730	+	0.925916i	$0.623295\pi$
$462$	− 0.704935i	− 0.0327965i
$463$	− 20.1061i	− 0.934412i	−0.884149	−	0.467206i	$-0.845261\pi$
$463$	− 20.1061i	− 0.934412i	0.884149	−	0.467206i	$-0.154739\pi$
$464$	18.3896	0.853717
$465$	0	0
$466$	−20.1726	−0.934478
$467$	− 32.4922i	− 1.50356i	−0.659414	−	0.751780i	$-0.729195\pi$
$467$	− 32.4922i	− 1.50356i	0.659414	−	0.751780i	$-0.270805\pi$
$468$	− 12.2230i	− 0.565010i
$469$	0.664128	0.0306666
$470$	0	0
$471$	−4.47331	−0.206119
$472$	− 1.58858i	− 0.0731205i
$473$	4.08687i	0.187914i
$474$	3.85038	0.176854
$475$	0	0
$476$	−5.06621	−0.232209
$477$	− 10.8398i	− 0.496321i
$478$	− 3.21443i	− 0.147025i
$479$	8.99966	0.411205	0.205603	−	0.978636i	$-0.434085\pi$
$479$	8.99966	0.411205	0.205603	+	0.978636i	$0.434085\pi$
$480$	0	0
$481$	65.8510	3.00255
$482$	48.1599i	2.19362i
$483$	− 4.22814i	− 0.192387i
$484$	22.2381	1.01082
$485$	0	0
$486$	2.02791	0.0919879
$487$	40.1153i	1.81780i	0.417018	+	0.908898i	$0.363075\pi$
$487$	40.1153i	1.81780i	−0.417018	+	0.908898i	$0.636925\pi$
$488$	0.907446i	0.0410781i
$489$	14.2898	0.646209
$490$	0	0
$491$	−35.7772	−1.61460	−0.807302	−	0.590138i	$-0.799073\pi$
$491$	−35.7772	−1.61460	−0.807302	+	0.590138i	$0.799073\pi$
$492$	0.304709i	0.0137374i
$493$	− 23.1834i	− 1.04413i
$494$	−49.7182	−2.23693
$495$	0	0
$496$	−10.1157	−0.454207
$497$	1.91790i	0.0860297i
$498$	5.10728i	0.228863i
$499$	−14.9592	−0.669665	−0.334832	−	0.942278i	$-0.608680\pi$
$499$	−14.9592	−0.669665	−0.334832	+	0.942278i	$0.608680\pi$
$500$	0	0
$501$	0.473306	0.0211458
$502$	41.1437i	1.83633i
$503$	33.8165i	1.50780i	0.656988	+	0.753901i	$0.271830\pi$
$503$	33.8165i	1.50780i	−0.656988	+	0.753901i	$0.728170\pi$
$504$	0.115269	0.00513447
$505$	0	0
$506$	−11.6590	−0.518304
$507$	20.4810i	0.909592i
$508$	9.14263i	0.405639i
$509$	−4.54546	−0.201474	−0.100737	−	0.994913i	$-0.532120\pi$
$509$	−4.54546	−0.201474	−0.100737	+	0.994913i	$0.532120\pi$
$510$	0	0
$511$	−5.52395	−0.244365
$512$	32.1393i	1.42037i
$513$	− 4.23709i	− 0.187072i
$514$	−44.4107	−1.95887
$515$	0	0
$516$	−12.5571	−0.552796
$517$	4.19830i	0.184641i
$518$	11.6689i	0.512704i
$519$	2.14939	0.0943476
$520$	0	0
$521$	−27.5808	−1.20834	−0.604169	−	0.796857i	$-0.706495\pi$
$521$	−27.5808	−1.20834	−0.604169	+	0.796857i	$0.706495\pi$
$522$	9.91157i	0.433818i
$523$	8.22959i	0.359855i	0.983680	+	0.179927i	$0.0575863\pi$
$523$	8.22959i	0.359855i	−0.983680	+	0.179927i	$0.942414\pi$
$524$	21.4710	0.937964
$525$	0	0
$526$	9.67155	0.421700
$527$	12.7526i	0.555513i
$528$	2.58678i	0.112575i
$529$	−46.9295	−2.04041
$530$	0	0
$531$	−6.96817	−0.302393
$532$	− 4.52550i	− 0.196206i
$533$	− 0.834650i	− 0.0361527i
$534$	−30.5828	−1.32345
$535$	0	0
$536$	0.299450	0.0129343
$537$	− 1.35831i	− 0.0586152i
$538$	24.4429i	1.05381i
$539$	4.63683	0.199723
$540$	0	0
$541$	17.8165	0.765993	0.382996	−	0.923750i	$-0.374892\pi$
$541$	17.8165	0.765993	0.382996	+	0.923750i	$0.374892\pi$
$542$	55.9384i	2.40276i
$543$	− 3.37725i	− 0.144932i
$544$	38.3547	1.64444
$545$	0	0
$546$	−5.93290	−0.253905
$547$	− 9.56762i	− 0.409082i	−0.978858	−	0.204541i	$-0.934430\pi$
$547$	− 9.56762i	− 0.409082i	0.978858	−	0.204541i	$-0.0655701\pi$
$548$	11.7769i	0.503086i
$549$	3.98042	0.169880
$550$	0	0
$551$	20.7091	0.882238
$552$	− 1.90643i	− 0.0811432i
$553$	− 0.960007i	− 0.0408236i
$554$	58.7807	2.49735
$555$	0	0
$556$	19.5208	0.827866
$557$	− 20.5472i	− 0.870613i	−0.900282	−	0.435306i	$-0.856640\pi$
$557$	− 20.5472i	− 0.870613i	0.900282	−	0.435306i	$-0.143360\pi$
$558$	− 5.45211i	− 0.230806i
$559$	34.3961	1.45480
$560$	0	0
$561$	3.26110	0.137684
$562$	12.0340i	0.507623i
$563$	− 18.7411i	− 0.789842i	−0.918715	−	0.394921i	$-0.870772\pi$
$563$	− 18.7411i	− 0.789842i	0.918715	−	0.394921i	$-0.129228\pi$
$564$	−12.8995	−0.543167
$565$	0	0
$566$	30.9015	1.29889
$567$	− 0.505614i	− 0.0212338i
$568$	0.864766i	0.0362848i
$569$	−4.66977	−0.195767	−0.0978834	−	0.995198i	$-0.531207\pi$
$569$	−4.66977	−0.195767	−0.0978834	+	0.995198i	$0.531207\pi$
$570$	0	0
$571$	14.9699	0.626471	0.313235	−	0.949676i	$-0.398587\pi$
$571$	14.9699	0.626471	0.313235	+	0.949676i	$0.398587\pi$
$572$	8.40350i	0.351368i
$573$	− 21.8942i	− 0.914641i
$574$	0.147902	0.00617330
$575$	0	0
$576$	−8.87266	−0.369694
$577$	− 15.6712i	− 0.652400i	−0.945301	−	0.326200i	$-0.894232\pi$
$577$	− 15.6712i	− 0.652400i	0.945301	−	0.326200i	$-0.105768\pi$
$578$	− 11.1519i	− 0.463858i
$579$	20.3890	0.847339
$580$	0	0
$581$	1.27339	0.0528290
$582$	− 2.38064i	− 0.0986808i
$583$	7.45251i	0.308652i
$584$	−2.49070	−0.103066
$585$	0	0
$586$	−3.51432	−0.145175
$587$	− 30.0310i	− 1.23951i	−0.784794	−	0.619756i	$-0.787231\pi$
$587$	− 30.0310i	− 1.23951i	0.784794	−	0.619756i	$-0.212769\pi$
$588$	14.2469i	0.587533i
$589$	−11.3916	−0.469381
$590$	0	0
$591$	−24.9688	−1.02708
$592$	− 42.8196i	− 1.75987i
$593$	26.2392i	1.07751i	0.842461	+	0.538757i	$0.181106\pi$
$593$	26.2392i	1.07751i	−0.842461	+	0.538757i	$0.818894\pi$
$594$	−1.39422	−0.0572053
$595$	0	0
$596$	−20.9374	−0.857630
$597$	− 10.2138i	− 0.418024i
$598$	98.1246i	4.01261i
$599$	15.5681	0.636095	0.318048	−	0.948075i	$-0.396973\pi$
$599$	15.5681	0.636095	0.318048	+	0.948075i	$0.396973\pi$
$600$	0	0
$601$	−6.27437	−0.255937	−0.127969	−	0.991778i	$-0.540846\pi$
$601$	−6.27437	−0.255937	−0.127969	+	0.991778i	$0.540846\pi$
$602$	6.09505i	0.248416i
$603$	− 1.31351i	− 0.0534902i
$604$	46.2294	1.88105
$605$	0	0
$606$	14.6671	0.595810
$607$	8.47616i	0.344037i	0.985094	+	0.172018i	$0.0550289\pi$
$607$	8.47616i	0.344037i	−0.985094	+	0.172018i	$0.944971\pi$
$608$	34.2611i	1.38947i
$609$	2.47123	0.100139
$610$	0	0
$611$	35.3339	1.42946
$612$	10.0199i	0.405031i
$613$	− 6.60744i	− 0.266872i	−0.991057	−	0.133436i	$-0.957399\pi$
$613$	− 6.60744i	− 0.266872i	0.991057	−	0.133436i	$-0.0426010\pi$
$614$	23.5413	0.950051
$615$	0	0
$616$	−0.0792486	−0.00319302
$617$	25.1919i	1.01419i	0.861891	+	0.507094i	$0.169280\pi$
$617$	25.1919i	1.01419i	−0.861891	+	0.507094i	$0.830720\pi$
$618$	37.3556i	1.50266i
$619$	−1.45782	−0.0585949	−0.0292975	−	0.999571i	$-0.509327\pi$
$619$	−1.45782	−0.0585949	−0.0292975	+	0.999571i	$0.509327\pi$
$620$	0	0
$621$	−8.36239	−0.335571
$622$	13.4018i	0.537365i
$623$	7.62514i	0.305495i
$624$	21.7710	0.871537
$625$	0	0
$626$	−25.4321	−1.01647
$627$	2.91305i	0.116336i
$628$	9.44950i	0.377076i
$629$	−53.9818	−2.15239
$630$	0	0
$631$	15.0828	0.600435	0.300218	−	0.953871i	$-0.402941\pi$
$631$	15.0828	0.600435	0.300218	+	0.953871i	$0.402941\pi$
$632$	− 0.432859i	− 0.0172182i
$633$	− 5.46907i	− 0.217376i
$634$	−23.7911	−0.944865
$635$	0	0
$636$	−22.8982	−0.907974
$637$	− 39.0247i	− 1.54621i
$638$	− 6.81434i	− 0.269782i
$639$	3.79321	0.150057
$640$	0	0
$641$	−5.23264	−0.206677	−0.103338	−	0.994646i	$-0.532952\pi$
$641$	−5.23264	−0.206677	−0.103338	+	0.994646i	$0.532952\pi$
$642$	− 35.6045i	− 1.40520i
$643$	− 36.4602i	− 1.43785i	−0.695088	−	0.718925i	$-0.744634\pi$
$643$	− 36.4602i	− 1.43785i	0.695088	−	0.718925i	$-0.255366\pi$
$644$	−8.93161	−0.351955
$645$	0	0
$646$	40.7568	1.60355
$647$	5.06588i	0.199160i	0.995030	+	0.0995801i	$0.0317500\pi$
$647$	5.06588i	0.199160i	−0.995030	+	0.0995801i	$0.968250\pi$
$648$	− 0.227977i	− 0.00895579i
$649$	4.79071	0.188052
$650$	0	0
$651$	−1.35936	−0.0532776
$652$	− 30.1862i	− 1.18218i
$653$	− 21.3639i	− 0.836033i	−0.908439	−	0.418017i	$-0.862725\pi$
$653$	− 21.3639i	− 0.836033i	0.908439	−	0.418017i	$-0.137275\pi$
$654$	−23.1380	−0.904767
$655$	0	0
$656$	−0.542731	−0.0211901
$657$	10.9252i	0.426234i
$658$	6.26124i	0.244089i
$659$	47.2176	1.83934	0.919668	−	0.392696i	$-0.128458\pi$
$659$	47.2176	1.83934	0.919668	+	0.392696i	$0.128458\pi$
$660$	0	0
$661$	−23.7835	−0.925072	−0.462536	−	0.886601i	$-0.653060\pi$
$661$	−23.7835	−0.925072	−0.462536	+	0.886601i	$0.653060\pi$
$662$	16.5525i	0.643332i
$663$	− 27.4462i	− 1.06592i
$664$	0.574159	0.0222817
$665$	0	0
$666$	23.0787	0.894283
$667$	− 40.8718i	− 1.58256i
$668$	− 0.999821i	− 0.0386842i
$669$	−22.8887	−0.884928
$670$	0	0
$671$	−2.73659	−0.105645
$672$	4.08840i	0.157714i
$673$	− 26.1124i	− 1.00656i	−0.864124	−	0.503279i	$-0.832127\pi$
$673$	− 26.1124i	− 1.00656i	0.864124	−	0.503279i	$-0.167873\pi$
$674$	−22.6067	−0.870778
$675$	0	0
$676$	43.2644	1.66402
$677$	11.8091i	0.453861i	0.973911	+	0.226931i	$0.0728691\pi$
$677$	11.8091i	0.453861i	−0.973911	+	0.226931i	$0.927131\pi$
$678$	19.5658i	0.751421i
$679$	−0.593560	−0.0227787
$680$	0	0
$681$	−12.9219	−0.495169
$682$	3.74839i	0.143533i
$683$	5.41899i	0.207352i	0.994611	+	0.103676i	$0.0330605\pi$
$683$	5.41899i	0.207352i	−0.994611	+	0.103676i	$0.966940\pi$
$684$	−8.95051	−0.342231
$685$	0	0
$686$	14.0926	0.538059
$687$	14.5252i	0.554170i
$688$	− 22.3660i	− 0.852696i
$689$	62.7221	2.38952
$690$	0	0
$691$	48.1513	1.83176	0.915880	−	0.401451i	$-0.131494\pi$
$691$	48.1513	1.83176	0.915880	+	0.401451i	$0.131494\pi$
$692$	− 4.54041i	− 0.172600i
$693$	0.347616i	0.0132049i
$694$	−20.8782	−0.792524
$695$	0	0
$696$	1.11426	0.0422358
$697$	0.684210i	0.0259163i
$698$	− 42.2390i	− 1.59877i
$699$	9.94748	0.376248
$700$	0	0
$701$	46.4747	1.75532	0.877662	−	0.479280i	$-0.159102\pi$
$701$	46.4747	1.75532	0.877662	+	0.479280i	$0.159102\pi$
$702$	11.7340i	0.442873i
$703$	− 48.2204i	− 1.81867i
$704$	6.10007	0.229905
$705$	0	0
$706$	−56.0038	−2.10773
$707$	− 3.65691i	− 0.137532i
$708$	14.7197i	0.553200i
$709$	−2.73598	−0.102752	−0.0513760	−	0.998679i	$-0.516361\pi$
$709$	−2.73598	−0.102752	−0.0513760	+	0.998679i	$0.516361\pi$
$710$	0	0
$711$	−1.89869	−0.0712066
$712$	3.43811i	0.128849i
$713$	22.4826i	0.841979i
$714$	4.86353	0.182013
$715$	0	0
$716$	−2.86931	−0.107231
$717$	1.58509i	0.0591964i
$718$	− 39.0213i	− 1.45626i
$719$	−21.7083	−0.809584	−0.404792	−	0.914409i	$-0.632656\pi$
$719$	−21.7083	−0.809584	−0.404792	+	0.914409i	$0.632656\pi$
$720$	0	0
$721$	9.31378	0.346863
$722$	− 2.12338i	− 0.0790242i
$723$	− 23.7485i	− 0.883217i
$724$	−7.13418	−0.265140
$725$	0	0
$726$	−21.3485	−0.792316
$727$	25.8542i	0.958879i	0.877575	+	0.479439i	$0.159160\pi$
$727$	25.8542i	0.958879i	−0.877575	+	0.479439i	$0.840840\pi$
$728$	0.666975i	0.0247197i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−28.1964	−1.04288
$732$	− 8.40832i	− 0.310781i
$733$	6.28263i	0.232054i	0.993246	+	0.116027i	$0.0370159\pi$
$733$	6.28263i	0.232054i	−0.993246	+	0.116027i	$0.962984\pi$
$734$	16.6917	0.616100
$735$	0	0
$736$	67.6184	2.49245
$737$	0.903054i	0.0332644i
$738$	− 0.292519i	− 0.0107678i
$739$	−23.7681	−0.874325	−0.437162	−	0.899383i	$-0.644017\pi$
$739$	−23.7681	−0.874325	−0.437162	+	0.899383i	$0.644017\pi$
$740$	0	0
$741$	24.5170	0.900653
$742$	11.1145i	0.408026i
$743$	14.8532i	0.544912i	0.962168	+	0.272456i	$0.0878359\pi$
$743$	14.8532i	0.544912i	−0.962168	+	0.272456i	$0.912164\pi$
$744$	−0.612924	−0.0224709
$745$	0	0
$746$	−59.1873	−2.16700
$747$	− 2.51849i	− 0.0921469i
$748$	− 6.88882i	− 0.251880i
$749$	−8.87719	−0.324365
$750$	0	0
$751$	26.1668	0.954841	0.477421	−	0.878675i	$-0.341572\pi$
$751$	26.1668	0.954841	0.477421	+	0.878675i	$0.341572\pi$
$752$	− 22.9758i	− 0.837843i
$753$	− 20.2887i	− 0.739363i
$754$	−57.3511	−2.08860
$755$	0	0
$756$	−1.06807	−0.0388453
$757$	13.1012i	0.476170i	0.971244	+	0.238085i	$0.0765197\pi$
$757$	13.1012i	0.476170i	−0.971244	+	0.238085i	$0.923480\pi$
$758$	8.81602i	0.320212i
$759$	5.74925	0.208685
$760$	0	0
$761$	−36.3328	−1.31706	−0.658531	−	0.752554i	$-0.728822\pi$
$761$	−36.3328	−1.31706	−0.658531	+	0.752554i	$0.728822\pi$
$762$	− 8.77687i	− 0.317953i
$763$	5.76894i	0.208850i
$764$	−46.2496	−1.67325
$765$	0	0
$766$	45.8762	1.65758
$767$	− 40.3198i	− 1.45586i
$768$	− 14.0526i	− 0.507080i
$769$	18.6504	0.672550	0.336275	−	0.941764i	$-0.390833\pi$
$769$	18.6504	0.672550	0.336275	+	0.941764i	$0.390833\pi$
$770$	0	0
$771$	21.8997	0.788699
$772$	− 43.0702i	− 1.55013i
$773$	− 9.15449i	− 0.329264i	−0.986355	−	0.164632i	$-0.947356\pi$
$773$	− 9.15449i	− 0.329264i	0.986355	−	0.164632i	$-0.0526437\pi$
$774$	12.0548	0.433299
$775$	0	0
$776$	−0.267631	−0.00960740
$777$	− 5.75417i	− 0.206430i
$778$	− 22.8869i	− 0.820536i
$779$	−0.611186	−0.0218980
$780$	0	0
$781$	−2.60788	−0.0933174
$782$	− 80.4383i	− 2.87647i
$783$	− 4.88758i	− 0.174668i
$784$	−25.3758	−0.906278
$785$	0	0
$786$	−20.6120	−0.735206
$787$	36.1383i	1.28819i	0.764945	+	0.644095i	$0.222766\pi$
$787$	36.1383i	1.28819i	−0.764945	+	0.644095i	$0.777234\pi$
$788$	52.7446i	1.87895i
$789$	−4.76922	−0.169789
$790$	0	0
$791$	4.87830	0.173452
$792$	0.156737i	0.00556942i
$793$	23.0318i	0.817884i
$794$	−18.3852	−0.652465
$795$	0	0
$796$	−21.5759	−0.764736
$797$	15.1491i	0.536608i	0.963334	+	0.268304i	$0.0864631\pi$
$797$	15.1491i	0.536608i	−0.963334	+	0.268304i	$0.913537\pi$
$798$	4.34446i	0.153792i
$799$	−28.9652	−1.02471
$800$	0	0
$801$	15.0809	0.532859
$802$	− 24.2740i	− 0.857146i
$803$	− 7.51124i	− 0.265066i
$804$	−2.77468	−0.0978554
$805$	0	0
$806$	31.5474	1.11121
$807$	− 12.0532i	− 0.424294i
$808$	− 1.64887i	− 0.0580071i
$809$	−33.2017	−1.16731	−0.583654	−	0.812002i	$-0.698378\pi$
$809$	−33.2017	−1.16731	−0.583654	+	0.812002i	$0.698378\pi$
$810$	0	0
$811$	26.6013	0.934098	0.467049	−	0.884231i	$-0.345317\pi$
$811$	26.6013	0.934098	0.467049	+	0.884231i	$0.345317\pi$
$812$	− 5.22028i	− 0.183196i
$813$	− 27.5843i	− 0.967422i
$814$	−15.8669	−0.556136
$815$	0	0
$816$	−17.8469	−0.624766
$817$	− 25.1870i	− 0.881183i
$818$	46.8909i	1.63950i
$819$	2.92562	0.102230
$820$	0	0
$821$	2.75480	0.0961432	0.0480716	−	0.998844i	$-0.484692\pi$
$821$	2.75480	0.0961432	0.0480716	+	0.998844i	$0.484692\pi$
$822$	− 11.3058i	− 0.394335i
$823$	− 4.73309i	− 0.164985i	−0.996592	−	0.0824926i	$-0.973712\pi$
$823$	− 4.73309i	− 0.164985i	0.996592	−	0.0824926i	$-0.0262881\pi$
$824$	4.19951	0.146297
$825$	0	0
$826$	7.14475	0.248598
$827$	39.6187i	1.37768i	0.724916	+	0.688838i	$0.241879\pi$
$827$	39.6187i	1.37768i	−0.724916	+	0.688838i	$0.758121\pi$
$828$	17.6649i	0.613897i
$829$	16.0834	0.558600	0.279300	−	0.960204i	$-0.409898\pi$
$829$	16.0834	0.558600	0.279300	+	0.960204i	$0.409898\pi$
$830$	0	0
$831$	−28.9858	−1.00551
$832$	− 51.3396i	− 1.77988i
$833$	31.9907i	1.10841i
$834$	−18.7399	−0.648908
$835$	0	0
$836$	6.15359	0.212826
$837$	2.68853i	0.0929293i
$838$	66.6328i	2.30179i
$839$	36.4617	1.25880	0.629400	−	0.777082i	$-0.283301\pi$
$839$	36.4617	1.25880	0.629400	+	0.777082i	$0.283301\pi$
$840$	0	0
$841$	−5.11156	−0.176261
$842$	17.6436i	0.608039i
$843$	− 5.93418i	− 0.204384i
$844$	−11.5530	−0.397670
$845$	0	0
$846$	12.3834	0.425751
$847$	5.32277i	0.182892i
$848$	− 40.7850i	− 1.40056i
$849$	−15.2381	−0.522971
$850$	0	0
$851$	−95.1686	−3.26234
$852$	− 8.01286i	− 0.274516i
$853$	− 25.0460i	− 0.857560i	−0.903409	−	0.428780i	$-0.858944\pi$
$853$	− 25.0460i	− 0.857560i	0.903409	−	0.428780i	$-0.141056\pi$
$854$	−4.08129	−0.139659
$855$	0	0
$856$	−4.00265	−0.136808
$857$	15.1391i	0.517140i	0.965993	+	0.258570i	$0.0832513\pi$
$857$	15.1391i	0.517140i	−0.965993	+	0.258570i	$0.916749\pi$
$858$	− 8.06731i	− 0.275413i
$859$	−24.3545	−0.830966	−0.415483	−	0.909601i	$-0.636387\pi$
$859$	−24.3545	−0.830966	−0.415483	+	0.909601i	$0.636387\pi$
$860$	0	0
$861$	−0.0729331	−0.00248555
$862$	11.5720i	0.394142i
$863$	29.0380i	0.988466i	0.869329	+	0.494233i	$0.164551\pi$
$863$	29.0380i	0.988466i	−0.869329	+	0.494233i	$0.835449\pi$
$864$	8.08601	0.275092
$865$	0	0
$866$	36.9529	1.25571
$867$	5.49921i	0.186763i
$868$	2.87154i	0.0974665i
$869$	1.30538	0.0442819
$870$	0	0
$871$	7.60031	0.257527
$872$	2.60117i	0.0880866i
$873$	1.17394i	0.0397318i
$874$	71.8533	2.43047
$875$	0	0
$876$	23.0787	0.779756
$877$	16.8629i	0.569420i	0.958614	+	0.284710i	$0.0918973\pi$
$877$	16.8629i	0.569420i	−0.958614	+	0.284710i	$0.908103\pi$
$878$	− 26.8534i	− 0.906259i
$879$	1.73298	0.0584518
$880$	0	0
$881$	−50.2279	−1.69222	−0.846110	−	0.533008i	$-0.821062\pi$
$881$	−50.2279	−1.69222	−0.846110	+	0.533008i	$0.821062\pi$
$882$	− 13.6769i	− 0.460527i
$883$	− 7.42047i	− 0.249719i	−0.992174	−	0.124859i	$-0.960152\pi$
$883$	− 7.42047i	− 0.249719i	0.992174	−	0.124859i	$-0.0398480\pi$
$884$	−57.9780	−1.95001
$885$	0	0
$886$	−53.3900	−1.79367
$887$	− 39.7855i	− 1.33587i	−0.744221	−	0.667933i	$-0.767179\pi$
$887$	− 39.7855i	− 1.33587i	0.744221	−	0.667933i	$-0.232821\pi$
$888$	− 2.59451i	− 0.0870660i
$889$	−2.18832	−0.0733938
$890$	0	0
$891$	0.687513	0.0230326
$892$	48.3505i	1.61890i
$893$	− 25.8738i	− 0.865833i
$894$	20.0998	0.672237
$895$	0	0
$896$	0.920691	0.0307581
$897$	− 48.3871i	− 1.61560i
$898$	− 45.2086i	− 1.50863i
$899$	−13.1404	−0.438258
$900$	0	0
$901$	−51.4168	−1.71294
$902$	0.201111i	0.00669626i
$903$	− 3.00558i	− 0.100020i
$904$	2.19958	0.0731571
$905$	0	0
$906$	−44.3800	−1.47443
$907$	− 46.5970i	− 1.54723i	−0.633657	−	0.773614i	$-0.718447\pi$
$907$	− 46.5970i	− 1.54723i	0.633657	−	0.773614i	$-0.281553\pi$
$908$	27.2965i	0.905868i
$909$	−7.23262	−0.239891
$910$	0	0
$911$	47.5250	1.57457	0.787287	−	0.616586i	$-0.211485\pi$
$911$	47.5250	1.57457	0.787287	+	0.616586i	$0.211485\pi$
$912$	− 15.9421i	− 0.527897i
$913$	1.73150i	0.0573042i
$914$	−35.1150	−1.16150
$915$	0	0
$916$	30.6833	1.01380
$917$	5.13914i	0.169709i
$918$	− 9.61905i	− 0.317476i
$919$	29.4578	0.971723	0.485862	−	0.874036i	$-0.338506\pi$
$919$	29.4578	0.971723	0.485862	+	0.874036i	$0.338506\pi$
$920$	0	0
$921$	−11.6087	−0.382518
$922$	− 32.8936i	− 1.08329i
$923$	21.9486i	0.722446i
$924$	0.734312	0.0241571
$925$	0	0
$926$	40.7735	1.33990
$927$	− 18.4207i	− 0.605016i
$928$	39.5210i	1.29734i
$929$	−33.9108	−1.11258	−0.556288	−	0.830989i	$-0.687775\pi$
$929$	−33.9108	−1.11258	−0.556288	+	0.830989i	$0.687775\pi$
$930$	0	0
$931$	−28.5764	−0.936555
$932$	− 21.0133i	− 0.688312i
$933$	− 6.60870i	− 0.216359i
$934$	65.8913	2.15603
$935$	0	0
$936$	1.31914	0.0431174
$937$	− 16.1534i	− 0.527708i	−0.964563	−	0.263854i	$-0.915006\pi$
$937$	− 16.1534i	− 0.527708i	0.964563	−	0.263854i	$-0.0849937\pi$
$938$	1.34679i	0.0439743i
$939$	12.5410	0.409261
$940$	0	0
$941$	32.2573	1.05156	0.525778	−	0.850622i	$-0.323774\pi$
$941$	32.2573	1.05156	0.525778	+	0.850622i	$0.323774\pi$
$942$	− 9.07146i	− 0.295564i
$943$	1.20625i	0.0392808i
$944$	−26.2179	−0.853320
$945$	0	0
$946$	−8.28780	−0.269460
$947$	20.9811i	0.681796i	0.940100	+	0.340898i	$0.110731\pi$
$947$	20.9811i	0.681796i	−0.940100	+	0.340898i	$0.889269\pi$
$948$	4.01084i	0.130266i
$949$	−63.2164	−2.05209
$950$	0	0
$951$	11.7318	0.380431
$952$	− 0.546757i	− 0.0177205i
$953$	− 19.0273i	− 0.616354i	−0.951329	−	0.308177i	$-0.900281\pi$
$953$	− 19.0273i	− 0.616354i	0.951329	−	0.308177i	$-0.0997188\pi$
$954$	21.9822	0.711699
$955$	0	0
$956$	3.34838	0.108294
$957$	3.36028i	0.108622i
$958$	18.2505i	0.589647i
$959$	−2.81885	−0.0910253
$960$	0	0
$961$	−23.7718	−0.766832
$962$	133.540i	4.30550i
$963$	17.5572i	0.565774i
$964$	−50.1669	−1.61577
$965$	0	0
$966$	8.57429	0.275873
$967$	− 17.7570i	− 0.571027i	−0.958375	−	0.285513i	$-0.907836\pi$
$967$	− 17.7570i	− 0.571027i	0.958375	−	0.285513i	$-0.0921641\pi$
$968$	2.39999i	0.0771386i
$969$	−20.0979	−0.645638
$970$	0	0
$971$	−19.0906	−0.612648	−0.306324	−	0.951927i	$-0.599099\pi$
$971$	−19.0906	−0.612648	−0.306324	+	0.951927i	$0.599099\pi$
$972$	2.11242i	0.0677559i
$973$	4.67236i	0.149789i
$974$	−81.3502	−2.60663
$975$	0	0
$976$	14.9764	0.479384
$977$	− 3.22285i	− 0.103108i	−0.998670	−	0.0515541i	$-0.983583\pi$
$977$	− 3.22285i	− 0.103108i	0.998670	−	0.0515541i	$-0.0164175\pi$
$978$	28.9785i	0.926631i
$979$	−10.3684	−0.331374
$980$	0	0
$981$	11.4098	0.364286
$982$	− 72.5530i	− 2.31526i
$983$	− 35.6008i	− 1.13549i	−0.823205	−	0.567744i	$-0.807816\pi$
$983$	− 35.6008i	− 1.13549i	0.823205	−	0.567744i	$-0.192184\pi$
$984$	−0.0328849	−0.00104833
$985$	0	0
$986$	47.0139	1.49723
$987$	− 3.08753i	− 0.0982773i
$988$	− 51.7901i	− 1.64766i
$989$	−49.7096	−1.58067
$990$	0	0
$991$	−17.0654	−0.542100	−0.271050	−	0.962565i	$-0.587371\pi$
$991$	−17.0654	−0.542100	−0.271050	+	0.962565i	$0.587371\pi$
$992$	− 21.7395i	− 0.690230i
$993$	− 8.16236i	− 0.259025i
$994$	−3.88933	−0.123362
$995$	0	0
$996$	−5.32012	−0.168574
$997$	− 36.5010i	− 1.15600i	−0.816038	−	0.577998i	$-0.803834\pi$
$997$	− 36.5010i	− 1.15600i	0.816038	−	0.577998i	$-0.196166\pi$
$998$	− 30.3359i	− 0.960265i
$999$	−11.3806	−0.360065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.e.1249.9		12
5.2	odd	4		1875.2.a.l.1.2	yes	6
5.3	odd	4		1875.2.a.i.1.5	✓	6
5.4	even	2	inner	1875.2.b.e.1249.4		12
15.2	even	4		5625.2.a.o.1.5		6
15.8	even	4		5625.2.a.r.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.5	✓	6	5.3	odd	4
1875.2.a.l.1.2	yes	6	5.2	odd	4
1875.2.b.e.1249.4		12	5.4	even	2	inner
1875.2.b.e.1249.9		12	1.1	even	1	trivial
5625.2.a.o.1.5		6	15.2	even	4
5625.2.a.r.1.2		6	15.8	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.02791i q^{2} -1.00000i q^{3} -2.11242 q^{4} +2.02791 q^{6} -0.505614i q^{7} -0.227977i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.02791i q^{2} -1.00000i q^{3} -2.11242 q^{4} +2.02791 q^{6} -0.505614i q^{7} -0.227977i q^{8} -1.00000 q^{9} +0.687513 q^{11} +2.11242i q^{12} -5.78627i q^{13} +1.02534 q^{14} -3.76252 q^{16} +4.74333i q^{17} -2.02791i q^{18} -4.23709 q^{19} -0.505614 q^{21} +1.39422i q^{22} +8.36239i q^{23} -0.227977 q^{24} +11.7340 q^{26} +1.00000i q^{27} +1.06807i q^{28} -4.88758 q^{29} +2.68853 q^{31} -8.08601i q^{32} -0.687513i q^{33} -9.61905 q^{34} +2.11242 q^{36} +11.3806i q^{37} -8.59244i q^{38} -5.78627 q^{39} +0.144247 q^{41} -1.02534i q^{42} +5.94442i q^{43} -1.45232 q^{44} -16.9582 q^{46} +6.10650i q^{47} +3.76252i q^{48} +6.74435 q^{49} +4.74333 q^{51} +12.2230i q^{52} +10.8398i q^{53} -2.02791 q^{54} -0.115269 q^{56} +4.23709i q^{57} -9.91157i q^{58} +6.96817 q^{59} -3.98042 q^{61} +5.45211i q^{62} +0.505614i q^{63} +8.87266 q^{64} +1.39422 q^{66} +1.31351i q^{67} -10.0199i q^{68} +8.36239 q^{69} -3.79321 q^{71} +0.227977i q^{72} -10.9252i q^{73} -23.0787 q^{74} +8.95051 q^{76} -0.347616i q^{77} -11.7340i q^{78} +1.89869 q^{79} +1.00000 q^{81} +0.292519i q^{82} +2.51849i q^{83} +1.06807 q^{84} -12.0548 q^{86} +4.88758i q^{87} -0.156737i q^{88} -15.0809 q^{89} -2.92562 q^{91} -17.6649i q^{92} -2.68853i q^{93} -12.3834 q^{94} -8.08601 q^{96} -1.17394i q^{97} +13.6769i q^{98} -0.687513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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