LMFDB - Embedded newform 1850.2.b.k.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.k.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +3.44949i q^{3} -1.00000 q^{4} +3.44949 q^{6} +2.44949i q^{7} +1.00000i q^{8} -8.89898 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +3.44949i q^{3} -1.00000 q^{4} +3.44949 q^{6} +2.44949i q^{7} +1.00000i q^{8} -8.89898 q^{9} -1.44949 q^{11} -3.44949i q^{12} +4.44949i q^{13} +2.44949 q^{14} +1.00000 q^{16} +1.44949i q^{17} +8.89898i q^{18} +5.00000 q^{19} -8.44949 q^{21} +1.44949i q^{22} +2.00000i q^{23} -3.44949 q^{24} +4.44949 q^{26} -20.3485i q^{27} -2.44949i q^{28} -8.89898 q^{29} -0.449490 q^{31} -1.00000i q^{32} -5.00000i q^{33} +1.44949 q^{34} +8.89898 q^{36} +1.00000i q^{37} -5.00000i q^{38} -15.3485 q^{39} +1.00000 q^{41} +8.44949i q^{42} -10.8990i q^{43} +1.44949 q^{44} +2.00000 q^{46} +9.79796i q^{47} +3.44949i q^{48} +1.00000 q^{49} -5.00000 q^{51} -4.44949i q^{52} +6.00000i q^{53} -20.3485 q^{54} -2.44949 q^{56} +17.2474i q^{57} +8.89898i q^{58} +2.00000 q^{59} -1.55051 q^{61} +0.449490i q^{62} -21.7980i q^{63} -1.00000 q^{64} -5.00000 q^{66} -9.44949i q^{67} -1.44949i q^{68} -6.89898 q^{69} -12.4495 q^{71} -8.89898i q^{72} -6.79796i q^{73} +1.00000 q^{74} -5.00000 q^{76} -3.55051i q^{77} +15.3485i q^{78} +11.7980 q^{79} +43.4949 q^{81} -1.00000i q^{82} -1.44949i q^{83} +8.44949 q^{84} -10.8990 q^{86} -30.6969i q^{87} -1.44949i q^{88} +0.348469 q^{89} -10.8990 q^{91} -2.00000i q^{92} -1.55051i q^{93} +9.79796 q^{94} +3.44949 q^{96} -14.0000i q^{97} -1.00000i q^{98} +12.8990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9} + 4 q^{11} + 4 q^{16} + 20 q^{19} - 24 q^{21} - 4 q^{24} + 8 q^{26} - 16 q^{29} + 8 q^{31} - 4 q^{34} + 16 q^{36} - 32 q^{39} + 4 q^{41} - 4 q^{44} + 8 q^{46} + 4 q^{49} - 20 q^{51} - 52 q^{54} + 8 q^{59} - 16 q^{61} - 4 q^{64} - 20 q^{66} - 8 q^{69} - 40 q^{71} + 4 q^{74} - 20 q^{76} + 8 q^{79} + 76 q^{81} + 24 q^{84} - 24 q^{86} - 28 q^{89} - 24 q^{91} + 4 q^{96} + 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9 + 4 * q^11 + 4 * q^16 + 20 * q^19 - 24 * q^21 - 4 * q^24 + 8 * q^26 - 16 * q^29 + 8 * q^31 - 4 * q^34 + 16 * q^36 - 32 * q^39 + 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^49 - 20 * q^51 - 52 * q^54 + 8 * q^59 - 16 * q^61 - 4 * q^64 - 20 * q^66 - 8 * q^69 - 40 * q^71 + 4 * q^74 - 20 * q^76 + 8 * q^79 + 76 * q^81 + 24 * q^84 - 24 * q^86 - 28 * q^89 - 24 * q^91 + 4 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	3.44949i	1.99156i	0.0917517	+	0.995782i	$0.470753\pi$
$3$	3.44949i	1.99156i	−0.0917517	+	0.995782i	$0.529247\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	3.44949	1.40825
$7$	2.44949i	0.925820i	0.886405	+	0.462910i	$0.153195\pi$
$7$	2.44949i	0.925820i	−0.886405	+	0.462910i	$0.846805\pi$
$8$	1.00000i	0.353553i
$9$	−8.89898	−2.96633
$10$	0	0
$11$	−1.44949	−0.437038	−0.218519	−	0.975833i	$-0.570122\pi$
$11$	−1.44949	−0.437038	−0.218519	+	0.975833i	$0.570122\pi$
$12$	− 3.44949i	− 0.995782i
$13$	4.44949i	1.23407i	0.786937	+	0.617033i	$0.211666\pi$
$13$	4.44949i	1.23407i	−0.786937	+	0.617033i	$0.788334\pi$
$14$	2.44949	0.654654
$15$	0	0
$16$	1.00000	0.250000
$17$	1.44949i	0.351553i	0.984430	+	0.175776i	$0.0562436\pi$
$17$	1.44949i	0.351553i	−0.984430	+	0.175776i	$0.943756\pi$
$18$	8.89898i	2.09751i
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	−8.44949	−1.84383
$22$	1.44949i	0.309032i
$23$	2.00000i	0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$	2.00000i	0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$	−3.44949	−0.704124
$25$	0	0
$26$	4.44949	0.872617
$27$	− 20.3485i	− 3.91606i
$28$	− 2.44949i	− 0.462910i
$29$	−8.89898	−1.65250	−0.826250	−	0.563304i	$-0.809530\pi$
$29$	−8.89898	−1.65250	−0.826250	+	0.563304i	$0.809530\pi$
$30$	0	0
$31$	−0.449490	−0.0807307	−0.0403654	−	0.999185i	$-0.512852\pi$
$31$	−0.449490	−0.0807307	−0.0403654	+	0.999185i	$0.512852\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.00000i	− 0.870388i
$34$	1.44949	0.248585
$35$	0	0
$36$	8.89898	1.48316
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	− 5.00000i	− 0.811107i
$39$	−15.3485	−2.45772
$40$	0	0
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	8.44949i	1.30378i
$43$	− 10.8990i	− 1.66208i	−0.556214	−	0.831039i	$-0.687746\pi$
$43$	− 10.8990i	− 1.66208i	0.556214	−	0.831039i	$-0.312254\pi$
$44$	1.44949	0.218519
$45$	0	0
$46$	2.00000	0.294884
$47$	9.79796i	1.42918i	0.699544	+	0.714590i	$0.253387\pi$
$47$	9.79796i	1.42918i	−0.699544	+	0.714590i	$0.746613\pi$
$48$	3.44949i	0.497891i
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.00000	−0.700140
$52$	− 4.44949i	− 0.617033i
$53$	6.00000i	0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$	6.00000i	0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−20.3485	−2.76908
$55$	0	0
$56$	−2.44949	−0.327327
$57$	17.2474i	2.28448i
$58$	8.89898i	1.16849i
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−1.55051	−0.198522	−0.0992612	−	0.995061i	$-0.531648\pi$
$61$	−1.55051	−0.198522	−0.0992612	+	0.995061i	$0.531648\pi$
$62$	0.449490i	0.0570853i
$63$	− 21.7980i	− 2.74628i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.00000	−0.615457
$67$	− 9.44949i	− 1.15444i	−0.816589	−	0.577219i	$-0.804138\pi$
$67$	− 9.44949i	− 1.15444i	0.816589	−	0.577219i	$-0.195862\pi$
$68$	− 1.44949i	− 0.175776i
$69$	−6.89898	−0.830540
$70$	0	0
$71$	−12.4495	−1.47748	−0.738741	−	0.673989i	$-0.764579\pi$
$71$	−12.4495	−1.47748	−0.738741	+	0.673989i	$0.764579\pi$
$72$	− 8.89898i	− 1.04875i
$73$	− 6.79796i	− 0.795641i	−0.917463	−	0.397820i	$-0.869767\pi$
$73$	− 6.79796i	− 0.795641i	0.917463	−	0.397820i	$-0.130233\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−5.00000	−0.573539
$77$	− 3.55051i	− 0.404618i
$78$	15.3485i	1.73787i
$79$	11.7980	1.32737	0.663687	−	0.748010i	$-0.268991\pi$
$79$	11.7980	1.32737	0.663687	+	0.748010i	$0.268991\pi$
$80$	0	0
$81$	43.4949	4.83277
$82$	− 1.00000i	− 0.110432i
$83$	− 1.44949i	− 0.159102i	−0.996831	−	0.0795511i	$-0.974651\pi$
$83$	− 1.44949i	− 0.159102i	0.996831	−	0.0795511i	$-0.0253487\pi$
$84$	8.44949	0.921915
$85$	0	0
$86$	−10.8990	−1.17527
$87$	− 30.6969i	− 3.29106i
$88$	− 1.44949i	− 0.154516i
$89$	0.348469	0.0369377	0.0184688	−	0.999829i	$-0.494121\pi$
$89$	0.348469	0.0369377	0.0184688	+	0.999829i	$0.494121\pi$
$90$	0	0
$91$	−10.8990	−1.14252
$92$	− 2.00000i	− 0.208514i
$93$	− 1.55051i	− 0.160780i
$94$	9.79796	1.01058
$95$	0	0
$96$	3.44949	0.352062
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	− 1.00000i	− 0.101015i
$99$	12.8990	1.29640
$100$	0	0
$101$	10.8990	1.08449	0.542244	−	0.840221i	$-0.317575\pi$
$101$	10.8990	1.08449	0.542244	+	0.840221i	$0.317575\pi$
$102$	5.00000i	0.495074i
$103$	1.55051i	0.152776i	0.997078	+	0.0763882i	$0.0243388\pi$
$103$	1.55051i	0.152776i	−0.997078	+	0.0763882i	$0.975661\pi$
$104$	−4.44949	−0.436308
$105$	0	0
$106$	6.00000	0.582772
$107$	13.4495i	1.30021i	0.759844	+	0.650106i	$0.225275\pi$
$107$	13.4495i	1.30021i	−0.759844	+	0.650106i	$0.774725\pi$
$108$	20.3485i	1.95803i
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	−3.44949	−0.327411
$112$	2.44949i	0.231455i
$113$	− 9.44949i	− 0.888933i	−0.895795	−	0.444467i	$-0.853393\pi$
$113$	− 9.44949i	− 0.888933i	0.895795	−	0.444467i	$-0.146607\pi$
$114$	17.2474	1.61537
$115$	0	0
$116$	8.89898	0.826250
$117$	− 39.5959i	− 3.66064i
$118$	− 2.00000i	− 0.184115i
$119$	−3.55051	−0.325475
$120$	0	0
$121$	−8.89898	−0.808998
$122$	1.55051i	0.140377i
$123$	3.44949i	0.311030i
$124$	0.449490	0.0403654
$125$	0	0
$126$	−21.7980	−1.94192
$127$	− 8.24745i	− 0.731843i	−0.930646	−	0.365921i	$-0.880754\pi$
$127$	− 8.24745i	− 0.731843i	0.930646	−	0.365921i	$-0.119246\pi$
$128$	1.00000i	0.0883883i
$129$	37.5959	3.31014
$130$	0	0
$131$	−20.6969	−1.80830	−0.904150	−	0.427215i	$-0.859495\pi$
$131$	−20.6969	−1.80830	−0.904150	+	0.427215i	$0.859495\pi$
$132$	5.00000i	0.435194i
$133$	12.2474i	1.06199i
$134$	−9.44949	−0.816312
$135$	0	0
$136$	−1.44949	−0.124293
$137$	19.6969i	1.68282i	0.540395	+	0.841412i	$0.318275\pi$
$137$	19.6969i	1.68282i	−0.540395	+	0.841412i	$0.681725\pi$
$138$	6.89898i	0.587280i
$139$	17.4495	1.48005	0.740023	−	0.672581i	$-0.234814\pi$
$139$	17.4495	1.48005	0.740023	+	0.672581i	$0.234814\pi$
$140$	0	0
$141$	−33.7980	−2.84630
$142$	12.4495i	1.04474i
$143$	− 6.44949i	− 0.539333i
$144$	−8.89898	−0.741582
$145$	0	0
$146$	−6.79796	−0.562603
$147$	3.44949i	0.284509i
$148$	− 1.00000i	− 0.0821995i
$149$	19.3485	1.58509	0.792544	−	0.609814i	$-0.208756\pi$
$149$	19.3485	1.58509	0.792544	+	0.609814i	$0.208756\pi$
$150$	0	0
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	5.00000i	0.405554i
$153$	− 12.8990i	− 1.04282i
$154$	−3.55051	−0.286108
$155$	0	0
$156$	15.3485	1.22886
$157$	− 11.5505i	− 0.921831i	−0.887444	−	0.460916i	$-0.847521\pi$
$157$	− 11.5505i	− 0.921831i	0.887444	−	0.460916i	$-0.152479\pi$
$158$	− 11.7980i	− 0.938595i
$159$	−20.6969	−1.64137
$160$	0	0
$161$	−4.89898	−0.386094
$162$	− 43.4949i	− 3.41728i
$163$	19.8990i	1.55861i	0.626646	+	0.779304i	$0.284427\pi$
$163$	19.8990i	1.55861i	−0.626646	+	0.779304i	$0.715573\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	−1.44949	−0.112502
$167$	5.55051i	0.429511i	0.976668	+	0.214756i	$0.0688955\pi$
$167$	5.55051i	0.429511i	−0.976668	+	0.214756i	$0.931104\pi$
$168$	− 8.44949i	− 0.651892i
$169$	−6.79796	−0.522920
$170$	0	0
$171$	−44.4949	−3.40261
$172$	10.8990i	0.831039i
$173$	22.6969i	1.72562i	0.505532	+	0.862808i	$0.331296\pi$
$173$	22.6969i	1.72562i	−0.505532	+	0.862808i	$0.668704\pi$
$174$	−30.6969	−2.32713
$175$	0	0
$176$	−1.44949	−0.109259
$177$	6.89898i	0.518559i
$178$	− 0.348469i	− 0.0261189i
$179$	−18.7980	−1.40503	−0.702513	−	0.711671i	$-0.747939\pi$
$179$	−18.7980	−1.40503	−0.702513	+	0.711671i	$0.747939\pi$
$180$	0	0
$181$	−2.89898	−0.215479	−0.107740	−	0.994179i	$-0.534361\pi$
$181$	−2.89898	−0.215479	−0.107740	+	0.994179i	$0.534361\pi$
$182$	10.8990i	0.807886i
$183$	− 5.34847i	− 0.395370i
$184$	−2.00000	−0.147442
$185$	0	0
$186$	−1.55051	−0.113689
$187$	− 2.10102i	− 0.153642i
$188$	− 9.79796i	− 0.714590i
$189$	49.8434	3.62557
$190$	0	0
$191$	11.7980	0.853670	0.426835	−	0.904329i	$-0.359628\pi$
$191$	11.7980	0.853670	0.426835	+	0.904329i	$0.359628\pi$
$192$	− 3.44949i	− 0.248945i
$193$	− 7.44949i	− 0.536226i	−0.963387	−	0.268113i	$-0.913600\pi$
$193$	− 7.44949i	− 0.536226i	0.963387	−	0.268113i	$-0.0864001\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	2.65153i	0.188914i	0.995529	+	0.0944569i	$0.0301114\pi$
$197$	2.65153i	0.188914i	−0.995529	+	0.0944569i	$0.969889\pi$
$198$	− 12.8990i	− 0.916691i
$199$	−23.5959	−1.67267	−0.836335	−	0.548219i	$-0.815306\pi$
$199$	−23.5959	−1.67267	−0.836335	+	0.548219i	$0.815306\pi$
$200$	0	0
$201$	32.5959	2.29914
$202$	− 10.8990i	− 0.766850i
$203$	− 21.7980i	− 1.52992i
$204$	5.00000	0.350070
$205$	0	0
$206$	1.55051	0.108029
$207$	− 17.7980i	− 1.23704i
$208$	4.44949i	0.308517i
$209$	−7.24745	−0.501317
$210$	0	0
$211$	−9.44949	−0.650530	−0.325265	−	0.945623i	$-0.605453\pi$
$211$	−9.44949	−0.650530	−0.325265	+	0.945623i	$0.605453\pi$
$212$	− 6.00000i	− 0.412082i
$213$	− 42.9444i	− 2.94250i
$214$	13.4495	0.919388
$215$	0	0
$216$	20.3485	1.38454
$217$	− 1.10102i	− 0.0747421i
$218$	14.0000i	0.948200i
$219$	23.4495	1.58457
$220$	0	0
$221$	−6.44949	−0.433840
$222$	3.44949i	0.231515i
$223$	2.20204i	0.147460i	0.997278	+	0.0737298i	$0.0234902\pi$
$223$	2.20204i	0.147460i	−0.997278	+	0.0737298i	$0.976510\pi$
$224$	2.44949	0.163663
$225$	0	0
$226$	−9.44949	−0.628571
$227$	− 12.6969i	− 0.842725i	−0.906892	−	0.421363i	$-0.861552\pi$
$227$	− 12.6969i	− 0.842725i	0.906892	−	0.421363i	$-0.138448\pi$
$228$	− 17.2474i	− 1.14224i
$229$	13.7980	0.911795	0.455897	−	0.890032i	$-0.349318\pi$
$229$	13.7980	0.911795	0.455897	+	0.890032i	$0.349318\pi$
$230$	0	0
$231$	12.2474	0.805823
$232$	− 8.89898i	− 0.584247i
$233$	20.4949i	1.34267i	0.741156	+	0.671333i	$0.234278\pi$
$233$	20.4949i	1.34267i	−0.741156	+	0.671333i	$0.765722\pi$
$234$	−39.5959	−2.58847
$235$	0	0
$236$	−2.00000	−0.130189
$237$	40.6969i	2.64355i
$238$	3.55051i	0.230145i
$239$	8.89898	0.575627	0.287814	−	0.957686i	$-0.407072\pi$
$239$	8.89898	0.575627	0.287814	+	0.957686i	$0.407072\pi$
$240$	0	0
$241$	−7.44949	−0.479864	−0.239932	−	0.970790i	$-0.577125\pi$
$241$	−7.44949	−0.479864	−0.239932	+	0.970790i	$0.577125\pi$
$242$	8.89898i	0.572048i
$243$	88.9898i	5.70870i
$244$	1.55051	0.0992612
$245$	0	0
$246$	3.44949	0.219931
$247$	22.2474i	1.41557i
$248$	− 0.449490i	− 0.0285426i
$249$	5.00000	0.316862
$250$	0	0
$251$	−11.2020	−0.707067	−0.353533	−	0.935422i	$-0.615020\pi$
$251$	−11.2020	−0.707067	−0.353533	+	0.935422i	$0.615020\pi$
$252$	21.7980i	1.37314i
$253$	− 2.89898i	− 0.182257i
$254$	−8.24745	−0.517491
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 2.89898i	− 0.180833i	−0.995904	−	0.0904167i	$-0.971180\pi$
$257$	− 2.89898i	− 0.180833i	0.995904	−	0.0904167i	$-0.0288199\pi$
$258$	− 37.5959i	− 2.34062i
$259$	−2.44949	−0.152204
$260$	0	0
$261$	79.1918	4.90185
$262$	20.6969i	1.27866i
$263$	19.7980i	1.22079i	0.792095	+	0.610397i	$0.208990\pi$
$263$	19.7980i	1.22079i	−0.792095	+	0.610397i	$0.791010\pi$
$264$	5.00000	0.307729
$265$	0	0
$266$	12.2474	0.750939
$267$	1.20204i	0.0735637i
$268$	9.44949i	0.577219i
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	−14.0454	−0.853198	−0.426599	−	0.904441i	$-0.640288\pi$
$271$	−14.0454	−0.853198	−0.426599	+	0.904441i	$0.640288\pi$
$272$	1.44949i	0.0878882i
$273$	− 37.5959i	− 2.27541i
$274$	19.6969	1.18994
$275$	0	0
$276$	6.89898	0.415270
$277$	13.7980i	0.829039i	0.910040	+	0.414520i	$0.136050\pi$
$277$	13.7980i	0.829039i	−0.910040	+	0.414520i	$0.863950\pi$
$278$	− 17.4495i	− 1.04655i
$279$	4.00000	0.239474
$280$	0	0
$281$	−0.898979	−0.0536286	−0.0268143	−	0.999640i	$-0.508536\pi$
$281$	−0.898979	−0.0536286	−0.0268143	+	0.999640i	$0.508536\pi$
$282$	33.7980i	2.01264i
$283$	17.6969i	1.05197i	0.850493	+	0.525987i	$0.176304\pi$
$283$	17.6969i	1.05197i	−0.850493	+	0.525987i	$0.823696\pi$
$284$	12.4495	0.738741
$285$	0	0
$286$	−6.44949	−0.381366
$287$	2.44949i	0.144589i
$288$	8.89898i	0.524377i
$289$	14.8990	0.876411
$290$	0	0
$291$	48.2929	2.83098
$292$	6.79796i	0.397820i
$293$	16.0454i	0.937383i	0.883362	+	0.468691i	$0.155274\pi$
$293$	16.0454i	0.937383i	−0.883362	+	0.468691i	$0.844726\pi$
$294$	3.44949	0.201178
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	29.4949i	1.71147i
$298$	− 19.3485i	− 1.12083i
$299$	−8.89898	−0.514641
$300$	0	0
$301$	26.6969	1.53879
$302$	14.0000i	0.805609i
$303$	37.5959i	2.15983i
$304$	5.00000	0.286770
$305$	0	0
$306$	−12.8990	−0.737386
$307$	− 22.3485i	− 1.27549i	−0.770246	−	0.637747i	$-0.779866\pi$
$307$	− 22.3485i	− 1.27549i	0.770246	−	0.637747i	$-0.220134\pi$
$308$	3.55051i	0.202309i
$309$	−5.34847	−0.304264
$310$	0	0
$311$	−3.55051	−0.201331	−0.100665	−	0.994920i	$-0.532097\pi$
$311$	−3.55051	−0.201331	−0.100665	+	0.994920i	$0.532097\pi$
$312$	− 15.3485i	− 0.868936i
$313$	− 0.898979i	− 0.0508133i	−0.999677	−	0.0254067i	$-0.991912\pi$
$313$	− 0.898979i	− 0.0508133i	0.999677	−	0.0254067i	$-0.00808806\pi$
$314$	−11.5505	−0.651833
$315$	0	0
$316$	−11.7980	−0.663687
$317$	14.4495i	0.811564i	0.913970	+	0.405782i	$0.133001\pi$
$317$	14.4495i	0.811564i	−0.913970	+	0.405782i	$0.866999\pi$
$318$	20.6969i	1.16063i
$319$	12.8990	0.722204
$320$	0	0
$321$	−46.3939	−2.58945
$322$	4.89898i	0.273009i
$323$	7.24745i	0.403259i
$324$	−43.4949	−2.41638
$325$	0	0
$326$	19.8990	1.10210
$327$	− 48.2929i	− 2.67060i
$328$	1.00000i	0.0552158i
$329$	−24.0000	−1.32316
$330$	0	0
$331$	10.1010	0.555202	0.277601	−	0.960696i	$-0.410461\pi$
$331$	10.1010	0.555202	0.277601	+	0.960696i	$0.410461\pi$
$332$	1.44949i	0.0795511i
$333$	− 8.89898i	− 0.487661i
$334$	5.55051	0.303710
$335$	0	0
$336$	−8.44949	−0.460957
$337$	13.6969i	0.746120i	0.927807	+	0.373060i	$0.121691\pi$
$337$	13.6969i	0.746120i	−0.927807	+	0.373060i	$0.878309\pi$
$338$	6.79796i	0.369760i
$339$	32.5959	1.77037
$340$	0	0
$341$	0.651531	0.0352824
$342$	44.4949i	2.40601i
$343$	19.5959i	1.05808i
$344$	10.8990	0.587634
$345$	0	0
$346$	22.6969	1.22019
$347$	− 0.797959i	− 0.0428367i	−0.999771	−	0.0214183i	$-0.993182\pi$
$347$	− 0.797959i	− 0.0428367i	0.999771	−	0.0214183i	$-0.00681819\pi$
$348$	30.6969i	1.64553i
$349$	7.55051	0.404170	0.202085	−	0.979368i	$-0.435228\pi$
$349$	7.55051	0.404170	0.202085	+	0.979368i	$0.435228\pi$
$350$	0	0
$351$	90.5403	4.83268
$352$	1.44949i	0.0772581i
$353$	5.10102i	0.271500i	0.990743	+	0.135750i	$0.0433444\pi$
$353$	5.10102i	0.271500i	−0.990743	+	0.135750i	$0.956656\pi$
$354$	6.89898	0.366677
$355$	0	0
$356$	−0.348469	−0.0184688
$357$	− 12.2474i	− 0.648204i
$358$	18.7980i	0.993503i
$359$	−27.3939	−1.44579	−0.722897	−	0.690956i	$-0.757190\pi$
$359$	−27.3939	−1.44579	−0.722897	+	0.690956i	$0.757190\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	2.89898i	0.152367i
$363$	− 30.6969i	− 1.61117i
$364$	10.8990	0.571262
$365$	0	0
$366$	−5.34847	−0.279569
$367$	− 10.2474i	− 0.534912i	−0.963570	−	0.267456i	$-0.913817\pi$
$367$	− 10.2474i	− 0.534912i	0.963570	−	0.267456i	$-0.0861831\pi$
$368$	2.00000i	0.104257i
$369$	−8.89898	−0.463262
$370$	0	0
$371$	−14.6969	−0.763027
$372$	1.55051i	0.0803902i
$373$	24.0454i	1.24502i	0.782610	+	0.622512i	$0.213888\pi$
$373$	24.0454i	1.24502i	−0.782610	+	0.622512i	$0.786112\pi$
$374$	−2.10102	−0.108641
$375$	0	0
$376$	−9.79796	−0.505291
$377$	− 39.5959i	− 2.03929i
$378$	− 49.8434i	− 2.56367i
$379$	−23.0454	−1.18376	−0.591882	−	0.806025i	$-0.701615\pi$
$379$	−23.0454	−1.18376	−0.591882	+	0.806025i	$0.701615\pi$
$380$	0	0
$381$	28.4495	1.45751
$382$	− 11.7980i	− 0.603636i
$383$	9.34847i	0.477684i	0.971058	+	0.238842i	$0.0767679\pi$
$383$	9.34847i	0.477684i	−0.971058	+	0.238842i	$0.923232\pi$
$384$	−3.44949	−0.176031
$385$	0	0
$386$	−7.44949	−0.379169
$387$	96.9898i	4.93027i
$388$	14.0000i	0.710742i
$389$	21.1464	1.07217	0.536083	−	0.844165i	$-0.319903\pi$
$389$	21.1464	1.07217	0.536083	+	0.844165i	$0.319903\pi$
$390$	0	0
$391$	−2.89898	−0.146608
$392$	1.00000i	0.0505076i
$393$	− 71.3939i	− 3.60134i
$394$	2.65153	0.133582
$395$	0	0
$396$	−12.8990	−0.648198
$397$	0.651531i	0.0326994i	0.999866	+	0.0163497i	$0.00520450\pi$
$397$	0.651531i	0.0326994i	−0.999866	+	0.0163497i	$0.994795\pi$
$398$	23.5959i	1.18276i
$399$	−42.2474	−2.11502
$400$	0	0
$401$	−37.9444	−1.89485	−0.947426	−	0.319975i	$-0.896326\pi$
$401$	−37.9444	−1.89485	−0.947426	+	0.319975i	$0.896326\pi$
$402$	− 32.5959i	− 1.62574i
$403$	− 2.00000i	− 0.0996271i
$404$	−10.8990	−0.542244
$405$	0	0
$406$	−21.7980	−1.08181
$407$	− 1.44949i	− 0.0718485i
$408$	− 5.00000i	− 0.247537i
$409$	−0.146428	−0.00724041	−0.00362020	−	0.999993i	$-0.501152\pi$
$409$	−0.146428	−0.00724041	−0.00362020	+	0.999993i	$0.501152\pi$
$410$	0	0
$411$	−67.9444	−3.35145
$412$	− 1.55051i	− 0.0763882i
$413$	4.89898i	0.241063i
$414$	−17.7980	−0.874722
$415$	0	0
$416$	4.44949	0.218154
$417$	60.1918i	2.94761i
$418$	7.24745i	0.354484i
$419$	16.5505	0.808545	0.404273	−	0.914639i	$-0.367525\pi$
$419$	16.5505	0.808545	0.404273	+	0.914639i	$0.367525\pi$
$420$	0	0
$421$	23.1010	1.12587	0.562937	−	0.826500i	$-0.309671\pi$
$421$	23.1010	1.12587	0.562937	+	0.826500i	$0.309671\pi$
$422$	9.44949i	0.459994i
$423$	− 87.1918i	− 4.23941i
$424$	−6.00000	−0.291386
$425$	0	0
$426$	−42.9444	−2.08066
$427$	− 3.79796i	− 0.183796i
$428$	− 13.4495i	− 0.650106i
$429$	22.2474	1.07412
$430$	0	0
$431$	8.69694	0.418917	0.209458	−	0.977818i	$-0.432830\pi$
$431$	8.69694	0.418917	0.209458	+	0.977818i	$0.432830\pi$
$432$	− 20.3485i	− 0.979016i
$433$	19.0000i	0.913082i	0.889702	+	0.456541i	$0.150912\pi$
$433$	19.0000i	0.913082i	−0.889702	+	0.456541i	$0.849088\pi$
$434$	−1.10102	−0.0528507
$435$	0	0
$436$	14.0000	0.670478
$437$	10.0000i	0.478365i
$438$	− 23.4495i	− 1.12046i
$439$	−19.5959	−0.935262	−0.467631	−	0.883924i	$-0.654892\pi$
$439$	−19.5959	−0.935262	−0.467631	+	0.883924i	$0.654892\pi$
$440$	0	0
$441$	−8.89898	−0.423761
$442$	6.44949i	0.306771i
$443$	− 12.5505i	− 0.596293i	−0.954520	−	0.298146i	$-0.903632\pi$
$443$	− 12.5505i	− 0.596293i	0.954520	−	0.298146i	$-0.0963684\pi$
$444$	3.44949	0.163706
$445$	0	0
$446$	2.20204	0.104270
$447$	66.7423i	3.15680i
$448$	− 2.44949i	− 0.115728i
$449$	−8.75255	−0.413058	−0.206529	−	0.978440i	$-0.566217\pi$
$449$	−8.75255	−0.413058	−0.206529	+	0.978440i	$0.566217\pi$
$450$	0	0
$451$	−1.44949	−0.0682538
$452$	9.44949i	0.444467i
$453$	− 48.2929i	− 2.26900i
$454$	−12.6969	−0.595897
$455$	0	0
$456$	−17.2474	−0.807686
$457$	9.24745i	0.432577i	0.976329	+	0.216289i	$0.0693952\pi$
$457$	9.24745i	0.432577i	−0.976329	+	0.216289i	$0.930605\pi$
$458$	− 13.7980i	− 0.644736i
$459$	29.4949	1.37670
$460$	0	0
$461$	38.6969	1.80230	0.901148	−	0.433511i	$-0.142726\pi$
$461$	38.6969	1.80230	0.901148	+	0.433511i	$0.142726\pi$
$462$	− 12.2474i	− 0.569803i
$463$	14.4495i	0.671525i	0.941947	+	0.335762i	$0.108994\pi$
$463$	14.4495i	0.671525i	−0.941947	+	0.335762i	$0.891006\pi$
$464$	−8.89898	−0.413125
$465$	0	0
$466$	20.4949	0.949408
$467$	12.0000i	0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$	12.0000i	0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$	39.5959i	1.83032i
$469$	23.1464	1.06880
$470$	0	0
$471$	39.8434	1.83589
$472$	2.00000i	0.0920575i
$473$	15.7980i	0.726391i
$474$	40.6969	1.86927
$475$	0	0
$476$	3.55051	0.162737
$477$	− 53.3939i	− 2.44474i
$478$	− 8.89898i	− 0.407030i
$479$	18.2474	0.833747	0.416874	−	0.908964i	$-0.363126\pi$
$479$	18.2474	0.833747	0.416874	+	0.908964i	$0.363126\pi$
$480$	0	0
$481$	−4.44949	−0.202879
$482$	7.44949i	0.339315i
$483$	− 16.8990i	− 0.768930i
$484$	8.89898	0.404499
$485$	0	0
$486$	88.9898	4.03666
$487$	− 42.7423i	− 1.93684i	−0.249323	−	0.968420i	$-0.580208\pi$
$487$	− 42.7423i	− 1.93684i	0.249323	−	0.968420i	$-0.419792\pi$
$488$	− 1.55051i	− 0.0701883i
$489$	−68.6413	−3.10407
$490$	0	0
$491$	−22.2020	−1.00196	−0.500982	−	0.865458i	$-0.667028\pi$
$491$	−22.2020	−1.00196	−0.500982	+	0.865458i	$0.667028\pi$
$492$	− 3.44949i	− 0.155515i
$493$	− 12.8990i	− 0.580941i
$494$	22.2474	1.00096
$495$	0	0
$496$	−0.449490	−0.0201827
$497$	− 30.4949i	− 1.36788i
$498$	− 5.00000i	− 0.224055i
$499$	−22.0000	−0.984855	−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000	−0.984855	−0.492428	+	0.870353i	$0.663890\pi$
$500$	0	0
$501$	−19.1464	−0.855399
$502$	11.2020i	0.499972i
$503$	− 9.79796i	− 0.436869i	−0.975852	−	0.218435i	$-0.929905\pi$
$503$	− 9.79796i	− 0.436869i	0.975852	−	0.218435i	$-0.0700951\pi$
$504$	21.7980	0.970958
$505$	0	0
$506$	−2.89898	−0.128875
$507$	− 23.4495i	− 1.04143i
$508$	8.24745i	0.365921i
$509$	−14.6515	−0.649418	−0.324709	−	0.945814i	$-0.605266\pi$
$509$	−14.6515	−0.649418	−0.324709	+	0.945814i	$0.605266\pi$
$510$	0	0
$511$	16.6515	0.736620
$512$	− 1.00000i	− 0.0441942i
$513$	− 101.742i	− 4.49203i
$514$	−2.89898	−0.127869
$515$	0	0
$516$	−37.5959	−1.65507
$517$	− 14.2020i	− 0.624605i
$518$	2.44949i	0.107624i
$519$	−78.2929	−3.43667
$520$	0	0
$521$	19.8990	0.871790	0.435895	−	0.899997i	$-0.356432\pi$
$521$	19.8990	0.871790	0.435895	+	0.899997i	$0.356432\pi$
$522$	− 79.1918i	− 3.46613i
$523$	40.3939i	1.76630i	0.469090	+	0.883150i	$0.344582\pi$
$523$	40.3939i	1.76630i	−0.469090	+	0.883150i	$0.655418\pi$
$524$	20.6969	0.904150
$525$	0	0
$526$	19.7980	0.863232
$527$	− 0.651531i	− 0.0283811i
$528$	− 5.00000i	− 0.217597i
$529$	19.0000	0.826087
$530$	0	0
$531$	−17.7980	−0.772366
$532$	− 12.2474i	− 0.530994i
$533$	4.44949i	0.192729i
$534$	1.20204	0.0520174
$535$	0	0
$536$	9.44949	0.408156
$537$	− 64.8434i	− 2.79820i
$538$	4.00000i	0.172452i
$539$	−1.44949	−0.0624339
$540$	0	0
$541$	10.6515	0.457945	0.228973	−	0.973433i	$-0.426463\pi$
$541$	10.6515	0.457945	0.228973	+	0.973433i	$0.426463\pi$
$542$	14.0454i	0.603302i
$543$	− 10.0000i	− 0.429141i
$544$	1.44949	0.0621464
$545$	0	0
$546$	−37.5959	−1.60896
$547$	25.6969i	1.09872i	0.835585	+	0.549361i	$0.185129\pi$
$547$	25.6969i	1.09872i	−0.835585	+	0.549361i	$0.814871\pi$
$548$	− 19.6969i	− 0.841412i
$549$	13.7980	0.588883
$550$	0	0
$551$	−44.4949	−1.89555
$552$	− 6.89898i	− 0.293640i
$553$	28.8990i	1.22891i
$554$	13.7980	0.586219
$555$	0	0
$556$	−17.4495	−0.740023
$557$	2.20204i	0.0933035i	0.998911	+	0.0466517i	$0.0148551\pi$
$557$	2.20204i	0.0933035i	−0.998911	+	0.0466517i	$0.985145\pi$
$558$	− 4.00000i	− 0.169334i
$559$	48.4949	2.05112
$560$	0	0
$561$	7.24745	0.305988
$562$	0.898979i	0.0379212i
$563$	− 1.59592i	− 0.0672599i	−0.999434	−	0.0336300i	$-0.989293\pi$
$563$	− 1.59592i	− 0.0672599i	0.999434	−	0.0336300i	$-0.0107068\pi$
$564$	33.7980	1.42315
$565$	0	0
$566$	17.6969	0.743858
$567$	106.540i	4.47427i
$568$	− 12.4495i	− 0.522369i
$569$	17.0454	0.714581	0.357290	−	0.933993i	$-0.383701\pi$
$569$	17.0454	0.714581	0.357290	+	0.933993i	$0.383701\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	6.44949i	0.269667i
$573$	40.6969i	1.70014i
$574$	2.44949	0.102240
$575$	0	0
$576$	8.89898	0.370791
$577$	23.0454i	0.959393i	0.877435	+	0.479696i	$0.159253\pi$
$577$	23.0454i	0.959393i	−0.877435	+	0.479696i	$0.840747\pi$
$578$	− 14.8990i	− 0.619716i
$579$	25.6969	1.06793
$580$	0	0
$581$	3.55051	0.147300
$582$	− 48.2929i	− 2.00180i
$583$	− 8.69694i	− 0.360190i
$584$	6.79796	0.281302
$585$	0	0
$586$	16.0454	0.662830
$587$	35.6969i	1.47337i	0.676236	+	0.736685i	$0.263610\pi$
$587$	35.6969i	1.47337i	−0.676236	+	0.736685i	$0.736390\pi$
$588$	− 3.44949i	− 0.142255i
$589$	−2.24745	−0.0926045
$590$	0	0
$591$	−9.14643	−0.376234
$592$	1.00000i	0.0410997i
$593$	− 12.3939i	− 0.508956i	−0.967079	−	0.254478i	$-0.918096\pi$
$593$	− 12.3939i	− 0.508956i	0.967079	−	0.254478i	$-0.0819036\pi$
$594$	29.4949	1.21019
$595$	0	0
$596$	−19.3485	−0.792544
$597$	− 81.3939i	− 3.33123i
$598$	8.89898i	0.363906i
$599$	14.9444	0.610611	0.305306	−	0.952254i	$-0.401241\pi$
$599$	14.9444	0.610611	0.305306	+	0.952254i	$0.401241\pi$
$600$	0	0
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	− 26.6969i	− 1.08809i
$603$	84.0908i	3.42444i
$604$	14.0000	0.569652
$605$	0	0
$606$	37.5959	1.52723
$607$	− 44.7423i	− 1.81604i	−0.418931	−	0.908018i	$-0.637595\pi$
$607$	− 44.7423i	− 1.81604i	0.418931	−	0.908018i	$-0.362405\pi$
$608$	− 5.00000i	− 0.202777i
$609$	75.1918	3.04693
$610$	0	0
$611$	−43.5959	−1.76370
$612$	12.8990i	0.521410i
$613$	14.4949i	0.585443i	0.956198	+	0.292722i	$0.0945609\pi$
$613$	14.4949i	0.585443i	−0.956198	+	0.292722i	$0.905439\pi$
$614$	−22.3485	−0.901911
$615$	0	0
$616$	3.55051	0.143054
$617$	− 4.89898i	− 0.197225i	−0.995126	−	0.0986127i	$-0.968559\pi$
$617$	− 4.89898i	− 0.197225i	0.995126	−	0.0986127i	$-0.0314405\pi$
$618$	5.34847i	0.215147i
$619$	23.1010	0.928508	0.464254	−	0.885702i	$-0.346322\pi$
$619$	23.1010	0.928508	0.464254	+	0.885702i	$0.346322\pi$
$620$	0	0
$621$	40.6969	1.63311
$622$	3.55051i	0.142362i
$623$	0.853572i	0.0341976i
$624$	−15.3485	−0.614431
$625$	0	0
$626$	−0.898979	−0.0359304
$627$	− 25.0000i	− 0.998404i
$628$	11.5505i	0.460916i
$629$	−1.44949	−0.0577949
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	11.7980i	0.469298i
$633$	− 32.5959i	− 1.29557i
$634$	14.4495	0.573863
$635$	0	0
$636$	20.6969	0.820687
$637$	4.44949i	0.176295i
$638$	− 12.8990i	− 0.510675i
$639$	110.788	4.38270
$640$	0	0
$641$	−17.5959	−0.694997	−0.347498	−	0.937681i	$-0.612969\pi$
$641$	−17.5959	−0.694997	−0.347498	+	0.937681i	$0.612969\pi$
$642$	46.3939i	1.83102i
$643$	− 36.2929i	− 1.43125i	−0.698484	−	0.715625i	$-0.746142\pi$
$643$	− 36.2929i	− 1.43125i	0.698484	−	0.715625i	$-0.253858\pi$
$644$	4.89898	0.193047
$645$	0	0
$646$	7.24745	0.285147
$647$	15.7526i	0.619297i	0.950851	+	0.309648i	$0.100211\pi$
$647$	15.7526i	0.619297i	−0.950851	+	0.309648i	$0.899789\pi$
$648$	43.4949i	1.70864i
$649$	−2.89898	−0.113795
$650$	0	0
$651$	3.79796	0.148854
$652$	− 19.8990i	− 0.779304i
$653$	34.0454i	1.33230i	0.745818	+	0.666150i	$0.232059\pi$
$653$	34.0454i	1.33230i	−0.745818	+	0.666150i	$0.767941\pi$
$654$	−48.2929	−1.88840
$655$	0	0
$656$	1.00000	0.0390434
$657$	60.4949i	2.36013i
$658$	24.0000i	0.935617i
$659$	−11.4495	−0.446009	−0.223004	−	0.974817i	$-0.571586\pi$
$659$	−11.4495	−0.446009	−0.223004	+	0.974817i	$0.571586\pi$
$660$	0	0
$661$	6.20204	0.241231	0.120616	−	0.992699i	$-0.461513\pi$
$661$	6.20204	0.241231	0.120616	+	0.992699i	$0.461513\pi$
$662$	− 10.1010i	− 0.392587i
$663$	− 22.2474i	− 0.864019i
$664$	1.44949	0.0562511
$665$	0	0
$666$	−8.89898	−0.344828
$667$	− 17.7980i	− 0.689140i
$668$	− 5.55051i	− 0.214756i
$669$	−7.59592	−0.293675
$670$	0	0
$671$	2.24745	0.0867618
$672$	8.44949i	0.325946i
$673$	− 13.7980i	− 0.531872i	−0.963991	−	0.265936i	$-0.914319\pi$
$673$	− 13.7980i	− 0.531872i	0.963991	−	0.265936i	$-0.0856810\pi$
$674$	13.6969	0.527586
$675$	0	0
$676$	6.79796	0.261460
$677$	4.40408i	0.169263i	0.996412	+	0.0846313i	$0.0269712\pi$
$677$	4.40408i	0.169263i	−0.996412	+	0.0846313i	$0.973029\pi$
$678$	− 32.5959i	− 1.25184i
$679$	34.2929	1.31604
$680$	0	0
$681$	43.7980	1.67834
$682$	− 0.651531i	− 0.0249484i
$683$	− 7.00000i	− 0.267848i	−0.990992	−	0.133924i	$-0.957242\pi$
$683$	− 7.00000i	− 0.267848i	0.990992	−	0.133924i	$-0.0427577\pi$
$684$	44.4949	1.70130
$685$	0	0
$686$	19.5959	0.748176
$687$	47.5959i	1.81590i
$688$	− 10.8990i	− 0.415520i
$689$	−26.6969	−1.01707
$690$	0	0
$691$	44.3485	1.68710	0.843548	−	0.537054i	$-0.180463\pi$
$691$	44.3485	1.68710	0.843548	+	0.537054i	$0.180463\pi$
$692$	− 22.6969i	− 0.862808i
$693$	31.5959i	1.20023i
$694$	−0.797959	−0.0302901
$695$	0	0
$696$	30.6969	1.16356
$697$	1.44949i	0.0549033i
$698$	− 7.55051i	− 0.285791i
$699$	−70.6969	−2.67400
$700$	0	0
$701$	−9.75255	−0.368349	−0.184174	−	0.982894i	$-0.558961\pi$
$701$	−9.75255	−0.368349	−0.184174	+	0.982894i	$0.558961\pi$
$702$	− 90.5403i	− 3.41722i
$703$	5.00000i	0.188579i
$704$	1.44949	0.0546297
$705$	0	0
$706$	5.10102	0.191979
$707$	26.6969i	1.00404i
$708$	− 6.89898i	− 0.259280i
$709$	−7.10102	−0.266684	−0.133342	−	0.991070i	$-0.542571\pi$
$709$	−7.10102	−0.266684	−0.133342	+	0.991070i	$0.542571\pi$
$710$	0	0
$711$	−104.990	−3.93742
$712$	0.348469i	0.0130594i
$713$	− 0.898979i	− 0.0336670i
$714$	−12.2474	−0.458349
$715$	0	0
$716$	18.7980	0.702513
$717$	30.6969i	1.14640i
$718$	27.3939i	1.02233i
$719$	15.3485	0.572401	0.286201	−	0.958170i	$-0.407608\pi$
$719$	15.3485	0.572401	0.286201	+	0.958170i	$0.407608\pi$
$720$	0	0
$721$	−3.79796	−0.141443
$722$	− 6.00000i	− 0.223297i
$723$	− 25.6969i	− 0.955679i
$724$	2.89898	0.107740
$725$	0	0
$726$	−30.6969	−1.13927
$727$	− 36.0000i	− 1.33517i	−0.744535	−	0.667583i	$-0.767329\pi$
$727$	− 36.0000i	− 1.33517i	0.744535	−	0.667583i	$-0.232671\pi$
$728$	− 10.8990i	− 0.403943i
$729$	−176.485	−6.53647
$730$	0	0
$731$	15.7980	0.584309
$732$	5.34847i	0.197685i
$733$	23.5959i	0.871535i	0.900059	+	0.435768i	$0.143523\pi$
$733$	23.5959i	0.871535i	−0.900059	+	0.435768i	$0.856477\pi$
$734$	−10.2474	−0.378240
$735$	0	0
$736$	2.00000	0.0737210
$737$	13.6969i	0.504533i
$738$	8.89898i	0.327576i
$739$	−7.59592	−0.279420	−0.139710	−	0.990192i	$-0.544617\pi$
$739$	−7.59592	−0.279420	−0.139710	+	0.990192i	$0.544617\pi$
$740$	0	0
$741$	−76.7423	−2.81920
$742$	14.6969i	0.539542i
$743$	− 45.5959i	− 1.67275i	−0.548156	−	0.836376i	$-0.684670\pi$
$743$	− 45.5959i	− 1.67275i	0.548156	−	0.836376i	$-0.315330\pi$
$744$	1.55051	0.0568445
$745$	0	0
$746$	24.0454	0.880365
$747$	12.8990i	0.471949i
$748$	2.10102i	0.0768209i
$749$	−32.9444	−1.20376
$750$	0	0
$751$	−1.30306	−0.0475494	−0.0237747	−	0.999717i	$-0.507568\pi$
$751$	−1.30306	−0.0475494	−0.0237747	+	0.999717i	$0.507568\pi$
$752$	9.79796i	0.357295i
$753$	− 38.6413i	− 1.40817i
$754$	−39.5959	−1.44200
$755$	0	0
$756$	−49.8434	−1.81279
$757$	− 5.79796i	− 0.210730i	−0.994434	−	0.105365i	$-0.966399\pi$
$757$	− 5.79796i	− 0.210730i	0.994434	−	0.105365i	$-0.0336012\pi$
$758$	23.0454i	0.837047i
$759$	10.0000	0.362977
$760$	0	0
$761$	−43.6969	−1.58401	−0.792006	−	0.610513i	$-0.790963\pi$
$761$	−43.6969	−1.58401	−0.792006	+	0.610513i	$0.790963\pi$
$762$	− 28.4495i	− 1.03062i
$763$	− 34.2929i	− 1.24148i
$764$	−11.7980	−0.426835
$765$	0	0
$766$	9.34847	0.337774
$767$	8.89898i	0.321324i
$768$	3.44949i	0.124473i
$769$	−28.7526	−1.03684	−0.518422	−	0.855125i	$-0.673480\pi$
$769$	−28.7526	−1.03684	−0.518422	+	0.855125i	$0.673480\pi$
$770$	0	0
$771$	10.0000	0.360141
$772$	7.44949i	0.268113i
$773$	− 22.0454i	− 0.792918i	−0.918052	−	0.396459i	$-0.870239\pi$
$773$	− 22.0454i	− 0.792918i	0.918052	−	0.396459i	$-0.129761\pi$
$774$	96.9898	3.48623
$775$	0	0
$776$	14.0000	0.502571
$777$	− 8.44949i	− 0.303124i
$778$	− 21.1464i	− 0.758136i
$779$	5.00000	0.179144
$780$	0	0
$781$	18.0454	0.645715
$782$	2.89898i	0.103667i
$783$	181.081i	6.47129i
$784$	1.00000	0.0357143
$785$	0	0
$786$	−71.3939	−2.54654
$787$	− 1.30306i	− 0.0464491i	−0.999730	−	0.0232246i	$-0.992607\pi$
$787$	− 1.30306i	− 0.0464491i	0.999730	−	0.0232246i	$-0.00739327\pi$
$788$	− 2.65153i	− 0.0944569i
$789$	−68.2929	−2.43129
$790$	0	0
$791$	23.1464	0.822992
$792$	12.8990i	0.458345i
$793$	− 6.89898i	− 0.244990i
$794$	0.651531	0.0231220
$795$	0	0
$796$	23.5959	0.836335
$797$	20.2474i	0.717201i	0.933491	+	0.358601i	$0.116746\pi$
$797$	20.2474i	0.717201i	−0.933491	+	0.358601i	$0.883254\pi$
$798$	42.2474i	1.49554i
$799$	−14.2020	−0.502432
$800$	0	0
$801$	−3.10102	−0.109569
$802$	37.9444i	1.33986i
$803$	9.85357i	0.347725i
$804$	−32.5959	−1.14957
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	− 13.7980i	− 0.485711i
$808$	10.8990i	0.383425i
$809$	−19.3939	−0.681852	−0.340926	−	0.940090i	$-0.610741\pi$
$809$	−19.3939	−0.681852	−0.340926	+	0.940090i	$0.610741\pi$
$810$	0	0
$811$	−13.7980	−0.484512	−0.242256	−	0.970212i	$-0.577887\pi$
$811$	−13.7980	−0.484512	−0.242256	+	0.970212i	$0.577887\pi$
$812$	21.7980i	0.764958i
$813$	− 48.4495i	− 1.69920i
$814$	−1.44949	−0.0508046
$815$	0	0
$816$	−5.00000	−0.175035
$817$	− 54.4949i	− 1.90654i
$818$	0.146428i	0.00511974i
$819$	96.9898	3.38910
$820$	0	0
$821$	−40.0454	−1.39759	−0.698797	−	0.715320i	$-0.746281\pi$
$821$	−40.0454	−1.39759	−0.698797	+	0.715320i	$0.746281\pi$
$822$	67.9444i	2.36983i
$823$	− 29.8434i	− 1.04027i	−0.854083	−	0.520137i	$-0.825881\pi$
$823$	− 29.8434i	− 1.04027i	0.854083	−	0.520137i	$-0.174119\pi$
$824$	−1.55051	−0.0540146
$825$	0	0
$826$	4.89898	0.170457
$827$	− 27.0000i	− 0.938882i	−0.882964	−	0.469441i	$-0.844455\pi$
$827$	− 27.0000i	− 0.938882i	0.882964	−	0.469441i	$-0.155545\pi$
$828$	17.7980i	0.618522i
$829$	−6.65153	−0.231017	−0.115509	−	0.993306i	$-0.536850\pi$
$829$	−6.65153	−0.231017	−0.115509	+	0.993306i	$0.536850\pi$
$830$	0	0
$831$	−47.5959	−1.65108
$832$	− 4.44949i	− 0.154258i
$833$	1.44949i	0.0502218i
$834$	60.1918	2.08427
$835$	0	0
$836$	7.24745	0.250658
$837$	9.14643i	0.316147i
$838$	− 16.5505i	− 0.571728i
$839$	−13.3485	−0.460840	−0.230420	−	0.973091i	$-0.574010\pi$
$839$	−13.3485	−0.460840	−0.230420	+	0.973091i	$0.574010\pi$
$840$	0	0
$841$	50.1918	1.73075
$842$	− 23.1010i	− 0.796114i
$843$	− 3.10102i	− 0.106805i
$844$	9.44949	0.325265
$845$	0	0
$846$	−87.1918	−2.99772
$847$	− 21.7980i	− 0.748987i
$848$	6.00000i	0.206041i
$849$	−61.0454	−2.09507
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	42.9444i	1.47125i
$853$	− 4.65153i	− 0.159265i	−0.996824	−	0.0796327i	$-0.974625\pi$
$853$	− 4.65153i	− 0.159265i	0.996824	−	0.0796327i	$-0.0253747\pi$
$854$	−3.79796	−0.129963
$855$	0	0
$856$	−13.4495	−0.459694
$857$	− 2.14643i	− 0.0733206i	−0.999328	−	0.0366603i	$-0.988328\pi$
$857$	− 2.14643i	− 0.0733206i	0.999328	−	0.0366603i	$-0.0116719\pi$
$858$	− 22.2474i	− 0.759515i
$859$	−39.4949	−1.34755	−0.673774	−	0.738937i	$-0.735328\pi$
$859$	−39.4949	−1.34755	−0.673774	+	0.738937i	$0.735328\pi$
$860$	0	0
$861$	−8.44949	−0.287958
$862$	− 8.69694i	− 0.296219i
$863$	− 6.24745i	− 0.212666i	−0.994331	−	0.106333i	$-0.966089\pi$
$863$	− 6.24745i	− 0.212666i	0.994331	−	0.106333i	$-0.0339109\pi$
$864$	−20.3485	−0.692269
$865$	0	0
$866$	19.0000	0.645646
$867$	51.3939i	1.74543i
$868$	1.10102i	0.0373711i
$869$	−17.1010	−0.580112
$870$	0	0
$871$	42.0454	1.42465
$872$	− 14.0000i	− 0.474100i
$873$	124.586i	4.21659i
$874$	10.0000	0.338255
$875$	0	0
$876$	−23.4495	−0.792285
$877$	− 19.3485i	− 0.653351i	−0.945136	−	0.326676i	$-0.894072\pi$
$877$	− 19.3485i	− 0.653351i	0.945136	−	0.326676i	$-0.105928\pi$
$878$	19.5959i	0.661330i
$879$	−55.3485	−1.86686
$880$	0	0
$881$	−34.2929	−1.15536	−0.577678	−	0.816265i	$-0.696041\pi$
$881$	−34.2929	−1.15536	−0.577678	+	0.816265i	$0.696041\pi$
$882$	8.89898i	0.299644i
$883$	35.8990i	1.20810i	0.796948	+	0.604048i	$0.206447\pi$
$883$	35.8990i	1.20810i	−0.796948	+	0.604048i	$0.793553\pi$
$884$	6.44949	0.216920
$885$	0	0
$886$	−12.5505	−0.421643
$887$	− 21.3031i	− 0.715287i	−0.933858	−	0.357643i	$-0.883580\pi$
$887$	− 21.3031i	− 0.715287i	0.933858	−	0.357643i	$-0.116420\pi$
$888$	− 3.44949i	− 0.115757i
$889$	20.2020	0.677555
$890$	0	0
$891$	−63.0454	−2.11210
$892$	− 2.20204i	− 0.0737298i
$893$	48.9898i	1.63938i
$894$	66.7423	2.23220
$895$	0	0
$896$	−2.44949	−0.0818317
$897$	− 30.6969i	− 1.02494i
$898$	8.75255i	0.292076i
$899$	4.00000	0.133407
$900$	0	0
$901$	−8.69694	−0.289737
$902$	1.44949i	0.0482627i
$903$	92.0908i	3.06459i
$904$	9.44949	0.314285
$905$	0	0
$906$	−48.2929	−1.60442
$907$	25.1010i	0.833466i	0.909029	+	0.416733i	$0.136825\pi$
$907$	25.1010i	0.833466i	−0.909029	+	0.416733i	$0.863175\pi$
$908$	12.6969i	0.421363i
$909$	−96.9898	−3.21695
$910$	0	0
$911$	8.24745	0.273250	0.136625	−	0.990623i	$-0.456374\pi$
$911$	8.24745	0.273250	0.136625	+	0.990623i	$0.456374\pi$
$912$	17.2474i	0.571120i
$913$	2.10102i	0.0695336i
$914$	9.24745	0.305878
$915$	0	0
$916$	−13.7980	−0.455897
$917$	− 50.6969i	− 1.67416i
$918$	− 29.4949i	− 0.973477i
$919$	32.2020	1.06225	0.531124	−	0.847294i	$-0.321770\pi$
$919$	32.2020	1.06225	0.531124	+	0.847294i	$0.321770\pi$
$920$	0	0
$921$	77.0908	2.54023
$922$	− 38.6969i	− 1.27442i
$923$	− 55.3939i	− 1.82331i
$924$	−12.2474	−0.402911
$925$	0	0
$926$	14.4495	0.474840
$927$	− 13.7980i	− 0.453184i
$928$	8.89898i	0.292123i
$929$	−13.7980	−0.452696	−0.226348	−	0.974046i	$-0.572679\pi$
$929$	−13.7980	−0.452696	−0.226348	+	0.974046i	$0.572679\pi$
$930$	0	0
$931$	5.00000	0.163868
$932$	− 20.4949i	− 0.671333i
$933$	− 12.2474i	− 0.400963i
$934$	12.0000	0.392652
$935$	0	0
$936$	39.5959	1.29423
$937$	24.5959i	0.803514i	0.915746	+	0.401757i	$0.131600\pi$
$937$	24.5959i	0.803514i	−0.915746	+	0.401757i	$0.868400\pi$
$938$	− 23.1464i	− 0.755758i
$939$	3.10102	0.101198
$940$	0	0
$941$	17.3939	0.567024	0.283512	−	0.958969i	$-0.408500\pi$
$941$	17.3939	0.567024	0.283512	+	0.958969i	$0.408500\pi$
$942$	− 39.8434i	− 1.29817i
$943$	2.00000i	0.0651290i
$944$	2.00000	0.0650945
$945$	0	0
$946$	15.7980	0.513636
$947$	− 32.0000i	− 1.03986i	−0.854209	−	0.519930i	$-0.825958\pi$
$947$	− 32.0000i	− 1.03986i	0.854209	−	0.519930i	$-0.174042\pi$
$948$	− 40.6969i	− 1.32178i
$949$	30.2474	0.981874
$950$	0	0
$951$	−49.8434	−1.61628
$952$	− 3.55051i	− 0.115073i
$953$	− 23.4949i	− 0.761074i	−0.924766	−	0.380537i	$-0.875739\pi$
$953$	− 23.4949i	− 0.761074i	0.924766	−	0.380537i	$-0.124261\pi$
$954$	−53.3939	−1.72869
$955$	0	0
$956$	−8.89898	−0.287814
$957$	44.4949i	1.43832i
$958$	− 18.2474i	− 0.589548i
$959$	−48.2474	−1.55799
$960$	0	0
$961$	−30.7980	−0.993483
$962$	4.44949i	0.143457i
$963$	− 119.687i	− 3.85685i
$964$	7.44949	0.239932
$965$	0	0
$966$	−16.8990	−0.543716
$967$	44.0000i	1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$	44.0000i	1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$	− 8.89898i	− 0.286024i
$969$	−25.0000	−0.803116
$970$	0	0
$971$	39.5403	1.26891	0.634454	−	0.772960i	$-0.281225\pi$
$971$	39.5403	1.26891	0.634454	+	0.772960i	$0.281225\pi$
$972$	− 88.9898i	− 2.85435i
$973$	42.7423i	1.37026i
$974$	−42.7423	−1.36955
$975$	0	0
$976$	−1.55051	−0.0496306
$977$	− 49.7423i	− 1.59140i	−0.605692	−	0.795699i	$-0.707104\pi$
$977$	− 49.7423i	− 1.59140i	0.605692	−	0.795699i	$-0.292896\pi$
$978$	68.6413i	2.19491i
$979$	−0.505103	−0.0161431
$980$	0	0
$981$	124.586	3.97772
$982$	22.2020i	0.708496i
$983$	− 30.4949i	− 0.972636i	−0.873782	−	0.486318i	$-0.838340\pi$
$983$	− 30.4949i	− 0.972636i	0.873782	−	0.486318i	$-0.161660\pi$
$984$	−3.44949	−0.109966
$985$	0	0
$986$	−12.8990	−0.410787
$987$	− 82.7878i	− 2.63516i
$988$	− 22.2474i	− 0.707786i
$989$	21.7980	0.693135
$990$	0	0
$991$	−11.5505	−0.366914	−0.183457	−	0.983028i	$-0.558729\pi$
$991$	−11.5505	−0.366914	−0.183457	+	0.983028i	$0.558729\pi$
$992$	0.449490i	0.0142713i
$993$	34.8434i	1.10572i
$994$	−30.4949	−0.967239
$995$	0	0
$996$	−5.00000	−0.158431
$997$	− 44.4495i	− 1.40773i	−0.710334	−	0.703865i	$-0.751456\pi$
$997$	− 44.4495i	− 1.40773i	0.710334	−	0.703865i	$-0.248544\pi$
$998$	22.0000i	0.696398i
$999$	20.3485	0.643797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.k.149.2		4
5.2	odd	4		1850.2.a.w.1.2	yes	2
5.3	odd	4		1850.2.a.r.1.1	✓	2
5.4	even	2	inner	1850.2.b.k.149.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.r.1.1	✓	2	5.3	odd	4
1850.2.a.w.1.2	yes	2	5.2	odd	4
1850.2.b.k.149.2		4	1.1	even	1	trivial
1850.2.b.k.149.3		4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.44949i q^{3} -1.00000 q^{4} +3.44949 q^{6} +2.44949i q^{7} +1.00000i q^{8} -8.89898 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +3.44949i q^{3} -1.00000 q^{4} +3.44949 q^{6} +2.44949i q^{7} +1.00000i q^{8} -8.89898 q^{9} -1.44949 q^{11} -3.44949i q^{12} +4.44949i q^{13} +2.44949 q^{14} +1.00000 q^{16} +1.44949i q^{17} +8.89898i q^{18} +5.00000 q^{19} -8.44949 q^{21} +1.44949i q^{22} +2.00000i q^{23} -3.44949 q^{24} +4.44949 q^{26} -20.3485i q^{27} -2.44949i q^{28} -8.89898 q^{29} -0.449490 q^{31} -1.00000i q^{32} -5.00000i q^{33} +1.44949 q^{34} +8.89898 q^{36} +1.00000i q^{37} -5.00000i q^{38} -15.3485 q^{39} +1.00000 q^{41} +8.44949i q^{42} -10.8990i q^{43} +1.44949 q^{44} +2.00000 q^{46} +9.79796i q^{47} +3.44949i q^{48} +1.00000 q^{49} -5.00000 q^{51} -4.44949i q^{52} +6.00000i q^{53} -20.3485 q^{54} -2.44949 q^{56} +17.2474i q^{57} +8.89898i q^{58} +2.00000 q^{59} -1.55051 q^{61} +0.449490i q^{62} -21.7980i q^{63} -1.00000 q^{64} -5.00000 q^{66} -9.44949i q^{67} -1.44949i q^{68} -6.89898 q^{69} -12.4495 q^{71} -8.89898i q^{72} -6.79796i q^{73} +1.00000 q^{74} -5.00000 q^{76} -3.55051i q^{77} +15.3485i q^{78} +11.7980 q^{79} +43.4949 q^{81} -1.00000i q^{82} -1.44949i q^{83} +8.44949 q^{84} -10.8990 q^{86} -30.6969i q^{87} -1.44949i q^{88} +0.348469 q^{89} -10.8990 q^{91} -2.00000i q^{92} -1.55051i q^{93} +9.79796 q^{94} +3.44949 q^{96} -14.0000i q^{97} -1.00000i q^{98} +12.8990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9} + 4 q^{11} + 4 q^{16} + 20 q^{19} - 24 q^{21} - 4 q^{24} + 8 q^{26} - 16 q^{29} + 8 q^{31} - 4 q^{34} + 16 q^{36} - 32 q^{39} + 4 q^{41} - 4 q^{44} + 8 q^{46} + 4 q^{49} - 20 q^{51} - 52 q^{54} + 8 q^{59} - 16 q^{61} - 4 q^{64} - 20 q^{66} - 8 q^{69} - 40 q^{71} + 4 q^{74} - 20 q^{76} + 8 q^{79} + 76 q^{81} + 24 q^{84} - 24 q^{86} - 28 q^{89} - 24 q^{91} + 4 q^{96} + 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9 + 4 * q^11 + 4 * q^16 + 20 * q^19 - 24 * q^21 - 4 * q^24 + 8 * q^26 - 16 * q^29 + 8 * q^31 - 4 * q^34 + 16 * q^36 - 32 * q^39 + 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^49 - 20 * q^51 - 52 * q^54 + 8 * q^59 - 16 * q^61 - 4 * q^64 - 20 * q^66 - 8 * q^69 - 40 * q^71 + 4 * q^74 - 20 * q^76 + 8 * q^79 + 76 * q^81 + 24 * q^84 - 24 * q^86 - 28 * q^89 - 24 * q^91 + 4 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more