LMFDB - Embedded newform 1850.2.b.n.149.3

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:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
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			149.3
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.n.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.21432i q^{3} -1.00000 q^{4} +1.21432 q^{6} +3.59210i q^{7} +1.00000i q^{8} +1.52543 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.21432i q^{3} -1.00000 q^{4} +1.21432 q^{6} +3.59210i q^{7} +1.00000i q^{8} +1.52543 q^{9} -4.73975 q^{11} -1.21432i q^{12} -1.78568i q^{13} +3.59210 q^{14} +1.00000 q^{16} +1.83654i q^{17} -1.52543i q^{18} -3.28100 q^{19} -4.36196 q^{21} +4.73975i q^{22} +1.80642i q^{23} -1.21432 q^{24} -1.78568 q^{26} +5.49532i q^{27} -3.59210i q^{28} +0.755569 q^{29} -2.06668 q^{31} -1.00000i q^{32} -5.75557i q^{33} +1.83654 q^{34} -1.52543 q^{36} +1.00000i q^{37} +3.28100i q^{38} +2.16839 q^{39} -2.57136 q^{41} +4.36196i q^{42} -9.19850i q^{43} +4.73975 q^{44} +1.80642 q^{46} +1.24443i q^{47} +1.21432i q^{48} -5.90321 q^{49} -2.23014 q^{51} +1.78568i q^{52} -6.56199i q^{53} +5.49532 q^{54} -3.59210 q^{56} -3.98418i q^{57} -0.755569i q^{58} -9.19850 q^{59} -9.39853 q^{61} +2.06668i q^{62} +5.47949i q^{63} -1.00000 q^{64} -5.75557 q^{66} -2.39853i q^{67} -1.83654i q^{68} -2.19358 q^{69} -9.39853 q^{71} +1.52543i q^{72} -8.09679i q^{73} +1.00000 q^{74} +3.28100 q^{76} -17.0257i q^{77} -2.16839i q^{78} -11.8064 q^{79} -2.09679 q^{81} +2.57136i q^{82} +15.4035i q^{83} +4.36196 q^{84} -9.19850 q^{86} +0.917502i q^{87} -4.73975i q^{88} +0.933323 q^{89} +6.41435 q^{91} -1.80642i q^{92} -2.50961i q^{93} +1.24443 q^{94} +1.21432 q^{96} -2.42864i q^{97} +5.90321i q^{98} -7.23014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{11} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 6 q^{24} - 24 q^{26} + 4 q^{29} - 12 q^{31} - 2 q^{34} + 4 q^{36} - 40 q^{39} - 42 q^{41} + 2 q^{44} - 16 q^{46} - 22 q^{49} - 26 q^{51} + 6 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} - 6 q^{64} - 34 q^{66} - 40 q^{69} - 16 q^{71} + 6 q^{74} + 6 q^{76} - 44 q^{79} - 26 q^{81} - 16 q^{86} + 6 q^{89} + 24 q^{91} + 8 q^{94} - 6 q^{96} - 56 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^11 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 6 * q^24 - 24 * q^26 + 4 * q^29 - 12 * q^31 - 2 * q^34 + 4 * q^36 - 40 * q^39 - 42 * q^41 + 2 * q^44 - 16 * q^46 - 22 * q^49 - 26 * q^51 + 6 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 - 6 * q^64 - 34 * q^66 - 40 * q^69 - 16 * q^71 + 6 * q^74 + 6 * q^76 - 44 * q^79 - 26 * q^81 - 16 * q^86 + 6 * q^89 + 24 * q^91 + 8 * q^94 - 6 * q^96 - 56 * 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
$3$	1.21432i	0.701088i	0.936546	+	0.350544i	$0.114003\pi$
$3$	1.21432i	0.701088i	−0.936546	+	0.350544i	$0.885997\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.21432	0.495744
$7$	3.59210i	1.35769i	0.734283	+	0.678844i	$0.237519\pi$
$7$	3.59210i	1.35769i	−0.734283	+	0.678844i	$0.762481\pi$
$8$	1.00000i	0.353553i
$9$	1.52543	0.508476
$10$	0	0
$11$	−4.73975	−1.42909	−0.714544	−	0.699591i	$-0.753366\pi$
$11$	−4.73975	−1.42909	−0.714544	+	0.699591i	$0.753366\pi$
$12$	− 1.21432i	− 0.350544i
$13$	− 1.78568i	− 0.495259i	−0.968855	−	0.247629i	$-0.920348\pi$
$13$	− 1.78568i	− 0.495259i	0.968855	−	0.247629i	$-0.0796515\pi$
$14$	3.59210	0.960030
$15$	0	0
$16$	1.00000	0.250000
$17$	1.83654i	0.445425i	0.974884	+	0.222713i	$0.0714912\pi$
$17$	1.83654i	0.445425i	−0.974884	+	0.222713i	$0.928509\pi$
$18$	− 1.52543i	− 0.359547i
$19$	−3.28100	−0.752712	−0.376356	−	0.926475i	$-0.622823\pi$
$19$	−3.28100	−0.752712	−0.376356	+	0.926475i	$0.622823\pi$
$20$	0	0
$21$	−4.36196	−0.951858
$22$	4.73975i	1.01052i
$23$	1.80642i	0.376665i	0.982105	+	0.188333i	$0.0603083\pi$
$23$	1.80642i	0.376665i	−0.982105	+	0.188333i	$0.939692\pi$
$24$	−1.21432	−0.247872
$25$	0	0
$26$	−1.78568	−0.350201
$27$	5.49532i	1.05757i
$28$	− 3.59210i	− 0.678844i
$29$	0.755569	0.140306	0.0701528	−	0.997536i	$-0.477651\pi$
$29$	0.755569	0.140306	0.0701528	+	0.997536i	$0.477651\pi$
$30$	0	0
$31$	−2.06668	−0.371186	−0.185593	−	0.982627i	$-0.559421\pi$
$31$	−2.06668	−0.371186	−0.185593	+	0.982627i	$0.559421\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.75557i	− 1.00192i
$34$	1.83654	0.314963
$35$	0	0
$36$	−1.52543	−0.254238
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	3.28100i	0.532248i
$39$	2.16839	0.347220
$40$	0	0
$41$	−2.57136	−0.401579	−0.200790	−	0.979634i	$-0.564351\pi$
$41$	−2.57136	−0.401579	−0.200790	+	0.979634i	$0.564351\pi$
$42$	4.36196i	0.673065i
$43$	− 9.19850i	− 1.40276i	−0.712789	−	0.701379i	$-0.752568\pi$
$43$	− 9.19850i	− 1.40276i	0.712789	−	0.701379i	$-0.247432\pi$
$44$	4.73975	0.714544
$45$	0	0
$46$	1.80642	0.266343
$47$	1.24443i	0.181519i	0.995873	+	0.0907595i	$0.0289294\pi$
$47$	1.24443i	0.181519i	−0.995873	+	0.0907595i	$0.971071\pi$
$48$	1.21432i	0.175272i
$49$	−5.90321	−0.843316
$50$	0	0
$51$	−2.23014	−0.312282
$52$	1.78568i	0.247629i
$53$	− 6.56199i	− 0.901359i	−0.892686	−	0.450680i	$-0.851182\pi$
$53$	− 6.56199i	− 0.901359i	0.892686	−	0.450680i	$-0.148818\pi$
$54$	5.49532	0.747818
$55$	0	0
$56$	−3.59210	−0.480015
$57$	− 3.98418i	− 0.527717i
$58$	− 0.755569i	− 0.0992110i
$59$	−9.19850	−1.19754	−0.598771	−	0.800920i	$-0.704344\pi$
$59$	−9.19850	−1.19754	−0.598771	+	0.800920i	$0.704344\pi$
$60$	0	0
$61$	−9.39853	−1.20336	−0.601679	−	0.798738i	$-0.705501\pi$
$61$	−9.39853	−1.20336	−0.601679	+	0.798738i	$0.705501\pi$
$62$	2.06668i	0.262468i
$63$	5.47949i	0.690351i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.75557	−0.708462
$67$	− 2.39853i	− 0.293027i	−0.989209	−	0.146513i	$-0.953195\pi$
$67$	− 2.39853i	− 0.293027i	0.989209	−	0.146513i	$-0.0468052\pi$
$68$	− 1.83654i	− 0.222713i
$69$	−2.19358	−0.264076
$70$	0	0
$71$	−9.39853	−1.11540	−0.557700	−	0.830043i	$-0.688316\pi$
$71$	−9.39853	−1.11540	−0.557700	+	0.830043i	$0.688316\pi$
$72$	1.52543i	0.179773i
$73$	− 8.09679i	− 0.947657i	−0.880617	−	0.473829i	$-0.842872\pi$
$73$	− 8.09679i	− 0.947657i	0.880617	−	0.473829i	$-0.157128\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	3.28100	0.376356
$77$	− 17.0257i	− 1.94025i
$78$	− 2.16839i	− 0.245521i
$79$	−11.8064	−1.32833	−0.664163	−	0.747588i	$-0.731212\pi$
$79$	−11.8064	−1.32833	−0.664163	+	0.747588i	$0.731212\pi$
$80$	0	0
$81$	−2.09679	−0.232976
$82$	2.57136i	0.283959i
$83$	15.4035i	1.69075i	0.534175	+	0.845374i	$0.320622\pi$
$83$	15.4035i	1.69075i	−0.534175	+	0.845374i	$0.679378\pi$
$84$	4.36196	0.475929
$85$	0	0
$86$	−9.19850	−0.991900
$87$	0.917502i	0.0983665i
$88$	− 4.73975i	− 0.505259i
$89$	0.933323	0.0989321	0.0494660	−	0.998776i	$-0.484248\pi$
$89$	0.933323	0.0989321	0.0494660	+	0.998776i	$0.484248\pi$
$90$	0	0
$91$	6.41435	0.672407
$92$	− 1.80642i	− 0.188333i
$93$	− 2.50961i	− 0.260234i
$94$	1.24443	0.128353
$95$	0	0
$96$	1.21432	0.123936
$97$	− 2.42864i	− 0.246591i	−0.992370	−	0.123295i	$-0.960654\pi$
$97$	− 2.42864i	− 0.246591i	0.992370	−	0.123295i	$-0.0393463\pi$
$98$	5.90321i	0.596314i
$99$	−7.23014	−0.726657
$100$	0	0
$101$	8.04149	0.800158	0.400079	−	0.916481i	$-0.368983\pi$
$101$	8.04149	0.800158	0.400079	+	0.916481i	$0.368983\pi$
$102$	2.23014i	0.220817i
$103$	− 0.495316i	− 0.0488049i	−0.999702	−	0.0244025i	$-0.992232\pi$
$103$	− 0.495316i	− 0.0488049i	0.999702	−	0.0244025i	$-0.00776832\pi$
$104$	1.78568	0.175100
$105$	0	0
$106$	−6.56199	−0.637357
$107$	13.4494i	1.30020i	0.759848	+	0.650100i	$0.225273\pi$
$107$	13.4494i	1.30020i	−0.759848	+	0.650100i	$0.774727\pi$
$108$	− 5.49532i	− 0.528787i
$109$	−10.2351	−0.980341	−0.490171	−	0.871626i	$-0.663066\pi$
$109$	−10.2351	−0.980341	−0.490171	+	0.871626i	$0.663066\pi$
$110$	0	0
$111$	−1.21432	−0.115258
$112$	3.59210i	0.339422i
$113$	7.49532i	0.705100i	0.935793	+	0.352550i	$0.114685\pi$
$113$	7.49532i	0.705100i	−0.935793	+	0.352550i	$0.885315\pi$
$114$	−3.98418	−0.373153
$115$	0	0
$116$	−0.755569	−0.0701528
$117$	− 2.72393i	− 0.251827i
$118$	9.19850i	0.846790i
$119$	−6.59703	−0.604748
$120$	0	0
$121$	11.4652	1.04229
$122$	9.39853i	0.850903i
$123$	− 3.12245i	− 0.281542i
$124$	2.06668	0.185593
$125$	0	0
$126$	5.47949	0.488152
$127$	3.45875i	0.306915i	0.988155	+	0.153457i	$0.0490407\pi$
$127$	3.45875i	0.306915i	−0.988155	+	0.153457i	$0.950959\pi$
$128$	1.00000i	0.0883883i
$129$	11.1699	0.983456
$130$	0	0
$131$	16.0874	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$131$	16.0874	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$132$	5.75557i	0.500958i
$133$	− 11.7857i	− 1.02195i
$134$	−2.39853	−0.207201
$135$	0	0
$136$	−1.83654	−0.157482
$137$	15.9906i	1.36617i	0.730338	+	0.683086i	$0.239363\pi$
$137$	15.9906i	1.36617i	−0.730338	+	0.683086i	$0.760637\pi$
$138$	2.19358i	0.186730i
$139$	−11.0350	−0.935979	−0.467990	−	0.883734i	$-0.655022\pi$
$139$	−11.0350	−0.935979	−0.467990	+	0.883734i	$0.655022\pi$
$140$	0	0
$141$	−1.51114	−0.127261
$142$	9.39853i	0.788707i
$143$	8.46367i	0.707768i
$144$	1.52543	0.127119
$145$	0	0
$146$	−8.09679	−0.670095
$147$	− 7.16839i	− 0.591239i
$148$	− 1.00000i	− 0.0821995i
$149$	−13.9748	−1.14486	−0.572431	−	0.819953i	$-0.693999\pi$
$149$	−13.9748	−1.14486	−0.572431	+	0.819953i	$0.693999\pi$
$150$	0	0
$151$	8.42864	0.685913	0.342956	−	0.939351i	$-0.388572\pi$
$151$	8.42864	0.685913	0.342956	+	0.939351i	$0.388572\pi$
$152$	− 3.28100i	− 0.266124i
$153$	2.80150i	0.226488i
$154$	−17.0257	−1.37197
$155$	0	0
$156$	−2.16839	−0.173610
$157$	9.17775i	0.732465i	0.930523	+	0.366232i	$0.119352\pi$
$157$	9.17775i	0.732465i	−0.930523	+	0.366232i	$0.880648\pi$
$158$	11.8064i	0.939269i
$159$	7.96836	0.631932
$160$	0	0
$161$	−6.48886	−0.511394
$162$	2.09679i	0.164739i
$163$	− 13.9447i	− 1.09223i	−0.837709	−	0.546117i	$-0.816106\pi$
$163$	− 13.9447i	− 1.09223i	0.837709	−	0.546117i	$-0.183894\pi$
$164$	2.57136	0.200790
$165$	0	0
$166$	15.4035	1.19554
$167$	17.6795i	1.36808i	0.729443	+	0.684041i	$0.239779\pi$
$167$	17.6795i	1.36808i	−0.729443	+	0.684041i	$0.760221\pi$
$168$	− 4.36196i	− 0.336533i
$169$	9.81135	0.754719
$170$	0	0
$171$	−5.00492	−0.382736
$172$	9.19850i	0.701379i
$173$	− 15.2859i	− 1.16217i	−0.813844	−	0.581083i	$-0.802629\pi$
$173$	− 15.2859i	− 1.16217i	0.813844	−	0.581083i	$-0.197371\pi$
$174$	0.917502	0.0695556
$175$	0	0
$176$	−4.73975	−0.357272
$177$	− 11.1699i	− 0.839582i
$178$	− 0.933323i	− 0.0699556i
$179$	−18.2859	−1.36675	−0.683377	−	0.730066i	$-0.739489\pi$
$179$	−18.2859	−1.36675	−0.683377	+	0.730066i	$0.739489\pi$
$180$	0	0
$181$	−8.23506	−0.612107	−0.306054	−	0.952014i	$-0.599009\pi$
$181$	−8.23506	−0.612107	−0.306054	+	0.952014i	$0.599009\pi$
$182$	− 6.41435i	− 0.475463i
$183$	− 11.4128i	− 0.843660i
$184$	−1.80642	−0.133171
$185$	0	0
$186$	−2.50961	−0.184013
$187$	− 8.70471i	− 0.636552i
$188$	− 1.24443i	− 0.0907595i
$189$	−19.7397	−1.43586
$190$	0	0
$191$	17.3461	1.25512	0.627561	−	0.778567i	$-0.284053\pi$
$191$	17.3461	1.25512	0.627561	+	0.778567i	$0.284053\pi$
$192$	− 1.21432i	− 0.0876360i
$193$	12.0257i	0.865626i	0.901484	+	0.432813i	$0.142479\pi$
$193$	12.0257i	0.865626i	−0.901484	+	0.432813i	$0.857521\pi$
$194$	−2.42864	−0.174366
$195$	0	0
$196$	5.90321	0.421658
$197$	13.9146i	0.991373i	0.868501	+	0.495687i	$0.165084\pi$
$197$	13.9146i	0.991373i	−0.868501	+	0.495687i	$0.834916\pi$
$198$	7.23014i	0.513824i
$199$	−24.5718	−1.74185	−0.870926	−	0.491415i	$-0.836480\pi$
$199$	−24.5718	−1.74185	−0.870926	+	0.491415i	$0.836480\pi$
$200$	0	0
$201$	2.91258	0.205438
$202$	− 8.04149i	− 0.565797i
$203$	2.71408i	0.190491i
$204$	2.23014	0.156141
$205$	0	0
$206$	−0.495316	−0.0345103
$207$	2.75557i	0.191525i
$208$	− 1.78568i	− 0.123815i
$209$	15.5511	1.07569
$210$	0	0
$211$	−14.3383	−0.987090	−0.493545	−	0.869720i	$-0.664299\pi$
$211$	−14.3383	−0.987090	−0.493545	+	0.869720i	$0.664299\pi$
$212$	6.56199i	0.450680i
$213$	− 11.4128i	− 0.781993i
$214$	13.4494	0.919381
$215$	0	0
$216$	−5.49532	−0.373909
$217$	− 7.42372i	− 0.503955i
$218$	10.2351i	0.693206i
$219$	9.83209	0.664391
$220$	0	0
$221$	3.27946	0.220601
$222$	1.21432i	0.0814998i
$223$	9.09234i	0.608868i	0.952533	+	0.304434i	$0.0984674\pi$
$223$	9.09234i	0.608868i	−0.952533	+	0.304434i	$0.901533\pi$
$224$	3.59210	0.240008
$225$	0	0
$226$	7.49532	0.498581
$227$	− 21.3319i	− 1.41584i	−0.706290	−	0.707922i	$-0.749633\pi$
$227$	− 21.3319i	− 1.41584i	0.706290	−	0.707922i	$-0.250367\pi$
$228$	3.98418i	0.263859i
$229$	24.0098	1.58662	0.793308	−	0.608821i	$-0.208357\pi$
$229$	24.0098	1.58662	0.793308	+	0.608821i	$0.208357\pi$
$230$	0	0
$231$	20.6746	1.36029
$232$	0.755569i	0.0496055i
$233$	− 8.28100i	− 0.542506i	−0.962508	−	0.271253i	$-0.912562\pi$
$233$	− 8.28100i	− 0.542506i	0.962508	−	0.271253i	$-0.0874380\pi$
$234$	−2.72393	−0.178069
$235$	0	0
$236$	9.19850	0.598771
$237$	− 14.3368i	− 0.931274i
$238$	6.59703i	0.427622i
$239$	25.5812	1.65471	0.827355	−	0.561679i	$-0.189844\pi$
$239$	25.5812	1.65471	0.827355	+	0.561679i	$0.189844\pi$
$240$	0	0
$241$	2.72546	0.175562	0.0877811	−	0.996140i	$-0.472022\pi$
$241$	2.72546	0.175562	0.0877811	+	0.996140i	$0.472022\pi$
$242$	− 11.4652i	− 0.737011i
$243$	13.9398i	0.894237i
$244$	9.39853	0.601679
$245$	0	0
$246$	−3.12245	−0.199080
$247$	5.85881i	0.372787i
$248$	− 2.06668i	− 0.131234i
$249$	−18.7047	−1.18536
$250$	0	0
$251$	−10.2859	−0.649241	−0.324621	−	0.945844i	$-0.605237\pi$
$251$	−10.2859	−0.649241	−0.324621	+	0.945844i	$0.605237\pi$
$252$	− 5.47949i	− 0.345176i
$253$	− 8.56199i	− 0.538288i
$254$	3.45875	0.217021
$255$	0	0
$256$	1.00000	0.0625000
$257$	5.14272i	0.320794i	0.987053	+	0.160397i	$0.0512775\pi$
$257$	5.14272i	0.320794i	−0.987053	+	0.160397i	$0.948723\pi$
$258$	− 11.1699i	− 0.695409i
$259$	−3.59210	−0.223202
$260$	0	0
$261$	1.15257	0.0713420
$262$	− 16.0874i	− 0.993884i
$263$	− 7.09234i	− 0.437333i	−0.975800	−	0.218666i	$-0.929829\pi$
$263$	− 7.09234i	− 0.437333i	0.975800	−	0.218666i	$-0.0701706\pi$
$264$	5.75557	0.354231
$265$	0	0
$266$	−11.7857	−0.722626
$267$	1.13335i	0.0693601i
$268$	2.39853i	0.146513i
$269$	26.0830	1.59031	0.795154	−	0.606408i	$-0.207390\pi$
$269$	26.0830	1.59031	0.795154	+	0.606408i	$0.207390\pi$
$270$	0	0
$271$	1.84590	0.112131	0.0560653	−	0.998427i	$-0.482144\pi$
$271$	1.84590	0.112131	0.0560653	+	0.998427i	$0.482144\pi$
$272$	1.83654i	0.111356i
$273$	7.78907i	0.471416i
$274$	15.9906	0.966029
$275$	0	0
$276$	2.19358	0.132038
$277$	− 22.9906i	− 1.38137i	−0.723154	−	0.690687i	$-0.757308\pi$
$277$	− 22.9906i	− 1.38137i	0.723154	−	0.690687i	$-0.242692\pi$
$278$	11.0350i	0.661837i
$279$	−3.15257	−0.188739
$280$	0	0
$281$	8.60793	0.513506	0.256753	−	0.966477i	$-0.417347\pi$
$281$	8.60793	0.513506	0.256753	+	0.966477i	$0.417347\pi$
$282$	1.51114i	0.0899869i
$283$	− 30.7605i	− 1.82852i	−0.405126	−	0.914261i	$-0.632772\pi$
$283$	− 30.7605i	− 1.82852i	0.405126	−	0.914261i	$-0.367228\pi$
$284$	9.39853	0.557700
$285$	0	0
$286$	8.46367	0.500467
$287$	− 9.23659i	− 0.545219i
$288$	− 1.52543i	− 0.0898867i
$289$	13.6271	0.801596
$290$	0	0
$291$	2.94914	0.172882
$292$	8.09679i	0.473829i
$293$	14.2286i	0.831244i	0.909537	+	0.415622i	$0.136436\pi$
$293$	14.2286i	0.831244i	−0.909537	+	0.415622i	$0.863564\pi$
$294$	−7.16839	−0.418069
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 26.0464i	− 1.51137i
$298$	13.9748i	0.809539i
$299$	3.22570	0.186547
$300$	0	0
$301$	33.0420	1.90451
$302$	− 8.42864i	− 0.485014i
$303$	9.76494i	0.560981i
$304$	−3.28100	−0.188178
$305$	0	0
$306$	2.80150	0.160151
$307$	29.2514i	1.66946i	0.550657	+	0.834732i	$0.314377\pi$
$307$	29.2514i	1.66946i	−0.550657	+	0.834732i	$0.685623\pi$
$308$	17.0257i	0.970127i
$309$	0.601472	0.0342165
$310$	0	0
$311$	−14.5970	−0.827721	−0.413861	−	0.910340i	$-0.635820\pi$
$311$	−14.5970	−0.827721	−0.413861	+	0.910340i	$0.635820\pi$
$312$	2.16839i	0.122761i
$313$	0.516060i	0.0291694i	0.999894	+	0.0145847i	$0.00464262\pi$
$313$	0.516060i	0.0291694i	−0.999894	+	0.0145847i	$0.995357\pi$
$314$	9.17775	0.517931
$315$	0	0
$316$	11.8064	0.664163
$317$	28.8736i	1.62170i	0.585253	+	0.810851i	$0.300995\pi$
$317$	28.8736i	1.62170i	−0.585253	+	0.810851i	$0.699005\pi$
$318$	− 7.96836i	− 0.446843i
$319$	−3.58120	−0.200509
$320$	0	0
$321$	−16.3319	−0.911555
$322$	6.48886i	0.361610i
$323$	− 6.02567i	− 0.335277i
$324$	2.09679	0.116488
$325$	0	0
$326$	−13.9447	−0.772325
$327$	− 12.4286i	− 0.687305i
$328$	− 2.57136i	− 0.141980i
$329$	−4.47013	−0.246446
$330$	0	0
$331$	6.55707	0.360409	0.180205	−	0.983629i	$-0.442324\pi$
$331$	6.55707	0.360409	0.180205	+	0.983629i	$0.442324\pi$
$332$	− 15.4035i	− 0.845374i
$333$	1.52543i	0.0835929i
$334$	17.6795	0.967381
$335$	0	0
$336$	−4.36196	−0.237965
$337$	− 29.0098i	− 1.58027i	−0.612935	−	0.790133i	$-0.710011\pi$
$337$	− 29.0098i	− 1.58027i	0.612935	−	0.790133i	$-0.289989\pi$
$338$	− 9.81135i	− 0.533667i
$339$	−9.10171	−0.494337
$340$	0	0
$341$	9.79552	0.530457
$342$	5.00492i	0.270635i
$343$	3.93978i	0.212728i
$344$	9.19850	0.495950
$345$	0	0
$346$	−15.2859	−0.821776
$347$	24.8479i	1.33391i	0.745100	+	0.666953i	$0.232402\pi$
$347$	24.8479i	1.33391i	−0.745100	+	0.666953i	$0.767598\pi$
$348$	− 0.917502i	− 0.0491833i
$349$	−24.0765	−1.28879	−0.644393	−	0.764694i	$-0.722890\pi$
$349$	−24.0765	−1.28879	−0.644393	+	0.764694i	$0.722890\pi$
$350$	0	0
$351$	9.81288	0.523773
$352$	4.73975i	0.252629i
$353$	32.5433i	1.73210i	0.499955	+	0.866051i	$0.333350\pi$
$353$	32.5433i	1.73210i	−0.499955	+	0.866051i	$0.666650\pi$
$354$	−11.1699	−0.593674
$355$	0	0
$356$	−0.933323	−0.0494660
$357$	− 8.01090i	− 0.423982i
$358$	18.2859i	0.966441i
$359$	23.0923	1.21877	0.609384	−	0.792876i	$-0.291417\pi$
$359$	23.0923	1.21877	0.609384	+	0.792876i	$0.291417\pi$
$360$	0	0
$361$	−8.23506	−0.433424
$362$	8.23506i	0.432825i
$363$	13.9224i	0.730738i
$364$	−6.41435	−0.336203
$365$	0	0
$366$	−11.4128	−0.596558
$367$	15.4717i	0.807614i	0.914844	+	0.403807i	$0.132313\pi$
$367$	15.4717i	0.807614i	−0.914844	+	0.403807i	$0.867687\pi$
$368$	1.80642i	0.0941664i
$369$	−3.92242	−0.204193
$370$	0	0
$371$	23.5714	1.22376
$372$	2.50961i	0.130117i
$373$	− 17.6064i	− 0.911625i	−0.890076	−	0.455812i	$-0.849349\pi$
$373$	− 17.6064i	− 0.911625i	0.890076	−	0.455812i	$-0.150651\pi$
$374$	−8.70471	−0.450110
$375$	0	0
$376$	−1.24443	−0.0641766
$377$	− 1.34920i	− 0.0694875i
$378$	19.7397i	1.01530i
$379$	9.68445	0.497457	0.248728	−	0.968573i	$-0.419987\pi$
$379$	9.68445	0.497457	0.248728	+	0.968573i	$0.419987\pi$
$380$	0	0
$381$	−4.20003	−0.215174
$382$	− 17.3461i	− 0.887506i
$383$	1.50468i	0.0768858i	0.999261	+	0.0384429i	$0.0122398\pi$
$383$	1.50468i	0.0768858i	−0.999261	+	0.0384429i	$0.987760\pi$
$384$	−1.21432	−0.0619680
$385$	0	0
$386$	12.0257	0.612090
$387$	− 14.0316i	− 0.713268i
$388$	2.42864i	0.123295i
$389$	−5.59210	−0.283531	−0.141765	−	0.989900i	$-0.545278\pi$
$389$	−5.59210	−0.283531	−0.141765	+	0.989900i	$0.545278\pi$
$390$	0	0
$391$	−3.31756	−0.167776
$392$	− 5.90321i	− 0.298157i
$393$	19.5353i	0.985424i
$394$	13.9146	0.701007
$395$	0	0
$396$	7.23014	0.363328
$397$	27.5274i	1.38156i	0.723064	+	0.690781i	$0.242733\pi$
$397$	27.5274i	1.38156i	−0.723064	+	0.690781i	$0.757267\pi$
$398$	24.5718i	1.23167i
$399$	14.3116	0.716475
$400$	0	0
$401$	−4.83161	−0.241279	−0.120640	−	0.992696i	$-0.538495\pi$
$401$	−4.83161	−0.241279	−0.120640	+	0.992696i	$0.538495\pi$
$402$	− 2.91258i	− 0.145266i
$403$	3.69042i	0.183833i
$404$	−8.04149	−0.400079
$405$	0	0
$406$	2.71408	0.134698
$407$	− 4.73975i	− 0.234941i
$408$	− 2.23014i	− 0.110408i
$409$	33.7447	1.66857	0.834283	−	0.551336i	$-0.185882\pi$
$409$	33.7447	1.66857	0.834283	+	0.551336i	$0.185882\pi$
$410$	0	0
$411$	−19.4177	−0.957806
$412$	0.495316i	0.0244025i
$413$	− 33.0420i	− 1.62589i
$414$	2.75557	0.135429
$415$	0	0
$416$	−1.78568	−0.0875502
$417$	− 13.4001i	− 0.656204i
$418$	− 15.5511i	− 0.760629i
$419$	−15.0479	−0.735140	−0.367570	−	0.929996i	$-0.619810\pi$
$419$	−15.0479	−0.735140	−0.367570	+	0.929996i	$0.619810\pi$
$420$	0	0
$421$	−21.2859	−1.03741	−0.518706	−	0.854953i	$-0.673586\pi$
$421$	−21.2859	−1.03741	−0.518706	+	0.854953i	$0.673586\pi$
$422$	14.3383i	0.697978i
$423$	1.89829i	0.0922980i
$424$	6.56199	0.318679
$425$	0	0
$426$	−11.4128	−0.552953
$427$	− 33.7605i	− 1.63378i
$428$	− 13.4494i	− 0.650100i
$429$	−10.2776	−0.496207
$430$	0	0
$431$	35.8479	1.72673	0.863367	−	0.504577i	$-0.168352\pi$
$431$	35.8479	1.72673	0.863367	+	0.504577i	$0.168352\pi$
$432$	5.49532i	0.264394i
$433$	19.1847i	0.921957i	0.887411	+	0.460979i	$0.152501\pi$
$433$	19.1847i	0.921957i	−0.887411	+	0.460979i	$0.847499\pi$
$434$	−7.42372	−0.356350
$435$	0	0
$436$	10.2351	0.490171
$437$	− 5.92687i	− 0.283521i
$438$	− 9.83209i	− 0.469795i
$439$	11.1427	0.531813	0.265907	−	0.963999i	$-0.414329\pi$
$439$	11.1427	0.531813	0.265907	+	0.963999i	$0.414329\pi$
$440$	0	0
$441$	−9.00492	−0.428806
$442$	− 3.27946i	− 0.155988i
$443$	− 2.13627i	− 0.101497i	−0.998711	−	0.0507486i	$-0.983839\pi$
$443$	− 2.13627i	− 0.101497i	0.998711	−	0.0507486i	$-0.0161607\pi$
$444$	1.21432	0.0576291
$445$	0	0
$446$	9.09234	0.430535
$447$	− 16.9699i	− 0.802648i
$448$	− 3.59210i	− 0.169711i
$449$	0.711167	0.0335621	0.0167810	−	0.999859i	$-0.494658\pi$
$449$	0.711167	0.0335621	0.0167810	+	0.999859i	$0.494658\pi$
$450$	0	0
$451$	12.1876	0.573892
$452$	− 7.49532i	− 0.352550i
$453$	10.2351i	0.480885i
$454$	−21.3319	−1.00115
$455$	0	0
$456$	3.98418	0.186576
$457$	− 29.8321i	− 1.39549i	−0.716348	−	0.697743i	$-0.754188\pi$
$457$	− 29.8321i	− 1.39549i	0.716348	−	0.697743i	$-0.245812\pi$
$458$	− 24.0098i	− 1.12191i
$459$	−10.0923	−0.471070
$460$	0	0
$461$	4.10171	0.191036	0.0955178	−	0.995428i	$-0.469549\pi$
$461$	4.10171	0.191036	0.0955178	+	0.995428i	$0.469549\pi$
$462$	− 20.6746i	− 0.961870i
$463$	− 13.2924i	− 0.617749i	−0.951103	−	0.308874i	$-0.900048\pi$
$463$	− 13.2924i	− 0.617749i	0.951103	−	0.308874i	$-0.0999523\pi$
$464$	0.755569	0.0350764
$465$	0	0
$466$	−8.28100	−0.383610
$467$	− 34.7052i	− 1.60596i	−0.596003	−	0.802982i	$-0.703245\pi$
$467$	− 34.7052i	− 1.60596i	0.596003	−	0.802982i	$-0.296755\pi$
$468$	2.72393i	0.125914i
$469$	8.61576	0.397839
$470$	0	0
$471$	−11.1447	−0.513522
$472$	− 9.19850i	− 0.423395i
$473$	43.5986i	2.00466i
$474$	−14.3368	−0.658510
$475$	0	0
$476$	6.59703	0.302374
$477$	− 10.0098i	− 0.458319i
$478$	− 25.5812i	− 1.17006i
$479$	−2.89231	−0.132153	−0.0660766	−	0.997815i	$-0.521048\pi$
$479$	−2.89231	−0.132153	−0.0660766	+	0.997815i	$0.521048\pi$
$480$	0	0
$481$	1.78568	0.0814200
$482$	− 2.72546i	− 0.124141i
$483$	− 7.87955i	− 0.358532i
$484$	−11.4652	−0.521146
$485$	0	0
$486$	13.9398	0.632321
$487$	39.5560i	1.79245i	0.443596	+	0.896227i	$0.353703\pi$
$487$	39.5560i	1.79245i	−0.443596	+	0.896227i	$0.646297\pi$
$488$	− 9.39853i	− 0.425451i
$489$	16.9333	0.765751
$490$	0	0
$491$	26.5018	1.19601	0.598004	−	0.801493i	$-0.295961\pi$
$491$	26.5018	1.19601	0.598004	+	0.801493i	$0.295961\pi$
$492$	3.12245i	0.140771i
$493$	1.38763i	0.0624957i
$494$	5.85881	0.263600
$495$	0	0
$496$	−2.06668	−0.0927965
$497$	− 33.7605i	− 1.51436i
$498$	18.7047i	0.838178i
$499$	41.3319	1.85027	0.925134	−	0.379641i	$-0.123952\pi$
$499$	41.3319	1.85027	0.925134	+	0.379641i	$0.123952\pi$
$500$	0	0
$501$	−21.4686	−0.959146
$502$	10.2859i	0.459083i
$503$	2.87601i	0.128235i	0.997942	+	0.0641176i	$0.0204233\pi$
$503$	2.87601i	0.128235i	−0.997942	+	0.0641176i	$0.979577\pi$
$504$	−5.47949	−0.244076
$505$	0	0
$506$	−8.56199	−0.380627
$507$	11.9141i	0.529124i
$508$	− 3.45875i	− 0.153457i
$509$	11.3713	0.504025	0.252013	−	0.967724i	$-0.418908\pi$
$509$	11.3713	0.504025	0.252013	+	0.967724i	$0.418908\pi$
$510$	0	0
$511$	29.0845	1.28662
$512$	− 1.00000i	− 0.0441942i
$513$	− 18.0301i	− 0.796049i
$514$	5.14272	0.226836
$515$	0	0
$516$	−11.1699	−0.491728
$517$	− 5.89829i	− 0.259406i
$518$	3.59210i	0.157828i
$519$	18.5620	0.814781
$520$	0	0
$521$	−19.2908	−0.845147	−0.422574	−	0.906329i	$-0.638873\pi$
$521$	−19.2908	−0.845147	−0.422574	+	0.906329i	$0.638873\pi$
$522$	− 1.15257i	− 0.0504464i
$523$	− 12.9813i	− 0.567631i	−0.958879	−	0.283816i	$-0.908400\pi$
$523$	− 12.9813i	− 0.567631i	0.958879	−	0.283816i	$-0.0916003\pi$
$524$	−16.0874	−0.702782
$525$	0	0
$526$	−7.09234	−0.309241
$527$	− 3.79552i	− 0.165336i
$528$	− 5.75557i	− 0.250479i
$529$	19.7368	0.858123
$530$	0	0
$531$	−14.0316	−0.608921
$532$	11.7857i	0.510974i
$533$	4.59163i	0.198885i
$534$	1.13335	0.0490450
$535$	0	0
$536$	2.39853	0.103601
$537$	− 22.2050i	− 0.958214i
$538$	− 26.0830i	− 1.12452i
$539$	27.9797	1.20517
$540$	0	0
$541$	−16.3160	−0.701481	−0.350740	−	0.936473i	$-0.614070\pi$
$541$	−16.3160	−0.701481	−0.350740	+	0.936473i	$0.614070\pi$
$542$	− 1.84590i	− 0.0792883i
$543$	− 10.0000i	− 0.429141i
$544$	1.83654	0.0787408
$545$	0	0
$546$	7.78907	0.333341
$547$	0.677517i	0.0289685i	0.999895	+	0.0144843i	$0.00461064\pi$
$547$	0.677517i	0.0289685i	−0.999895	+	0.0144843i	$0.995389\pi$
$548$	− 15.9906i	− 0.683086i
$549$	−14.3368	−0.611879
$550$	0	0
$551$	−2.47902	−0.105610
$552$	− 2.19358i	− 0.0933648i
$553$	− 42.4099i	− 1.80345i
$554$	−22.9906	−0.976778
$555$	0	0
$556$	11.0350	0.467990
$557$	− 3.11108i	− 0.131821i	−0.997826	−	0.0659103i	$-0.979005\pi$
$557$	− 3.11108i	− 0.131821i	0.997826	−	0.0659103i	$-0.0209951\pi$
$558$	3.15257i	0.133459i
$559$	−16.4256	−0.694728
$560$	0	0
$561$	10.5703	0.446279
$562$	− 8.60793i	− 0.363103i
$563$	22.1891i	0.935160i	0.883951	+	0.467580i	$0.154874\pi$
$563$	22.1891i	0.935160i	−0.883951	+	0.467580i	$0.845126\pi$
$564$	1.51114	0.0636304
$565$	0	0
$566$	−30.7605	−1.29296
$567$	− 7.53188i	− 0.316309i
$568$	− 9.39853i	− 0.394353i
$569$	−17.5783	−0.736920	−0.368460	−	0.929644i	$-0.620115\pi$
$569$	−17.5783	−0.736920	−0.368460	+	0.929644i	$0.620115\pi$
$570$	0	0
$571$	30.5303	1.27766	0.638828	−	0.769350i	$-0.279420\pi$
$571$	30.5303	1.27766	0.638828	+	0.769350i	$0.279420\pi$
$572$	− 8.46367i	− 0.353884i
$573$	21.0638i	0.879951i
$574$	−9.23659	−0.385528
$575$	0	0
$576$	−1.52543	−0.0635595
$577$	14.2335i	0.592550i	0.955103	+	0.296275i	$0.0957444\pi$
$577$	14.2335i	0.592550i	−0.955103	+	0.296275i	$0.904256\pi$
$578$	− 13.6271i	− 0.566814i
$579$	−14.6030	−0.606880
$580$	0	0
$581$	−55.3308	−2.29551
$582$	− 2.94914i	− 0.122246i
$583$	31.1022i	1.28812i
$584$	8.09679	0.335047
$585$	0	0
$586$	14.2286	0.587778
$587$	− 10.5254i	− 0.434431i	−0.976124	−	0.217215i	$-0.930303\pi$
$587$	− 10.5254i	− 0.434431i	0.976124	−	0.217215i	$-0.0696974\pi$
$588$	7.16839i	0.295619i
$589$	6.78076	0.279396
$590$	0	0
$591$	−16.8968	−0.695040
$592$	1.00000i	0.0410997i
$593$	22.8163i	0.936952i	0.883476	+	0.468476i	$0.155197\pi$
$593$	22.8163i	0.936952i	−0.883476	+	0.468476i	$0.844803\pi$
$594$	−26.0464	−1.06870
$595$	0	0
$596$	13.9748	0.572431
$597$	− 29.8381i	− 1.22119i
$598$	− 3.22570i	− 0.131908i
$599$	7.23659	0.295679	0.147840	−	0.989011i	$-0.452768\pi$
$599$	7.23659	0.295679	0.147840	+	0.989011i	$0.452768\pi$
$600$	0	0
$601$	−17.2623	−0.704142	−0.352071	−	0.935973i	$-0.614522\pi$
$601$	−17.2623	−0.704142	−0.352071	+	0.935973i	$0.614522\pi$
$602$	− 33.0420i	− 1.34669i
$603$	− 3.65878i	− 0.148997i
$604$	−8.42864	−0.342956
$605$	0	0
$606$	9.76494	0.396673
$607$	30.8825i	1.25348i	0.779228	+	0.626740i	$0.215611\pi$
$607$	30.8825i	1.25348i	−0.779228	+	0.626740i	$0.784389\pi$
$608$	3.28100i	0.133062i
$609$	−3.29576	−0.133551
$610$	0	0
$611$	2.22216	0.0898988
$612$	− 2.80150i	− 0.113244i
$613$	− 16.3180i	− 0.659079i	−0.944142	−	0.329540i	$-0.893106\pi$
$613$	− 16.3180i	− 0.659079i	0.944142	−	0.329540i	$-0.106894\pi$
$614$	29.2514	1.18049
$615$	0	0
$616$	17.0257	0.685984
$617$	− 3.16992i	− 0.127616i	−0.997962	−	0.0638080i	$-0.979675\pi$
$617$	− 3.16992i	− 0.127616i	0.997962	−	0.0638080i	$-0.0203245\pi$
$618$	− 0.601472i	− 0.0241948i
$619$	−30.5018	−1.22597	−0.612985	−	0.790095i	$-0.710031\pi$
$619$	−30.5018	−1.22597	−0.612985	+	0.790095i	$0.710031\pi$
$620$	0	0
$621$	−9.92687	−0.398352
$622$	14.5970i	0.585287i
$623$	3.35260i	0.134319i
$624$	2.16839	0.0868049
$625$	0	0
$626$	0.516060	0.0206259
$627$	18.8840i	0.754154i
$628$	− 9.17775i	− 0.366232i
$629$	−1.83654	−0.0732275
$630$	0	0
$631$	−13.3274	−0.530556	−0.265278	−	0.964172i	$-0.585464\pi$
$631$	−13.3274	−0.530556	−0.265278	+	0.964172i	$0.585464\pi$
$632$	− 11.8064i	− 0.469634i
$633$	− 17.4113i	− 0.692037i
$634$	28.8736	1.14672
$635$	0	0
$636$	−7.96836	−0.315966
$637$	10.5412i	0.417659i
$638$	3.58120i	0.141781i
$639$	−14.3368	−0.567154
$640$	0	0
$641$	−26.9403	−1.06408	−0.532038	−	0.846720i	$-0.678574\pi$
$641$	−26.9403	−1.06408	−0.532038	+	0.846720i	$0.678574\pi$
$642$	16.3319i	0.644567i
$643$	28.0370i	1.10567i	0.833290	+	0.552836i	$0.186455\pi$
$643$	28.0370i	1.10567i	−0.833290	+	0.552836i	$0.813545\pi$
$644$	6.48886	0.255697
$645$	0	0
$646$	−6.02567	−0.237077
$647$	− 3.81288i	− 0.149900i	−0.997187	−	0.0749498i	$-0.976120\pi$
$647$	− 3.81288i	− 0.149900i	0.997187	−	0.0749498i	$-0.0238797\pi$
$648$	− 2.09679i	− 0.0823696i
$649$	43.5986	1.71139
$650$	0	0
$651$	9.01477	0.353317
$652$	13.9447i	0.546117i
$653$	− 1.53188i	− 0.0599471i	−0.999551	−	0.0299736i	$-0.990458\pi$
$653$	− 1.53188i	− 0.0599471i	0.999551	−	0.0299736i	$-0.00954231\pi$
$654$	−12.4286	−0.485998
$655$	0	0
$656$	−2.57136	−0.100395
$657$	− 12.3511i	− 0.481861i
$658$	4.47013i	0.174264i
$659$	−30.9101	−1.20409	−0.602044	−	0.798463i	$-0.705647\pi$
$659$	−30.9101	−1.20409	−0.602044	+	0.798463i	$0.705647\pi$
$660$	0	0
$661$	−11.8163	−0.459600	−0.229800	−	0.973238i	$-0.573807\pi$
$661$	−11.8163	−0.459600	−0.229800	+	0.973238i	$0.573807\pi$
$662$	− 6.55707i	− 0.254848i
$663$	3.98232i	0.154660i
$664$	−15.4035	−0.597770
$665$	0	0
$666$	1.52543	0.0591091
$667$	1.36488i	0.0528483i
$668$	− 17.6795i	− 0.684041i
$669$	−11.0410	−0.426870
$670$	0	0
$671$	44.5466	1.71970
$672$	4.36196i	0.168266i
$673$	− 10.6780i	− 0.411606i	−0.978593	−	0.205803i	$-0.934019\pi$
$673$	− 10.6780i	− 0.411606i	0.978593	−	0.205803i	$-0.0659807\pi$
$674$	−29.0098	−1.11742
$675$	0	0
$676$	−9.81135	−0.377359
$677$	0.828699i	0.0318495i	0.999873	+	0.0159247i	$0.00506922\pi$
$677$	0.828699i	0.0318495i	−0.999873	+	0.0159247i	$0.994931\pi$
$678$	9.10171i	0.349549i
$679$	8.72393	0.334794
$680$	0	0
$681$	25.9037	0.992631
$682$	− 9.79552i	− 0.375090i
$683$	12.3921i	0.474170i	0.971489	+	0.237085i	$0.0761919\pi$
$683$	12.3921i	0.474170i	−0.971489	+	0.237085i	$0.923808\pi$
$684$	5.00492	0.191368
$685$	0	0
$686$	3.93978	0.150421
$687$	29.1556i	1.11236i
$688$	− 9.19850i	− 0.350689i
$689$	−11.7176	−0.446406
$690$	0	0
$691$	22.9146	0.871712	0.435856	−	0.900016i	$-0.356446\pi$
$691$	22.9146	0.871712	0.435856	+	0.900016i	$0.356446\pi$
$692$	15.2859i	0.581083i
$693$	− 25.9714i	− 0.986573i
$694$	24.8479	0.943214
$695$	0	0
$696$	−0.917502	−0.0347778
$697$	− 4.72239i	− 0.178873i
$698$	24.0765i	0.911310i
$699$	10.0558	0.380344
$700$	0	0
$701$	−42.7161	−1.61336	−0.806682	−	0.590985i	$-0.798739\pi$
$701$	−42.7161	−1.61336	−0.806682	+	0.590985i	$0.798739\pi$
$702$	− 9.81288i	− 0.370363i
$703$	− 3.28100i	− 0.123745i
$704$	4.73975	0.178636
$705$	0	0
$706$	32.5433	1.22478
$707$	28.8859i	1.08636i
$708$	11.1699i	0.419791i
$709$	47.0005	1.76514	0.882570	−	0.470181i	$-0.155811\pi$
$709$	47.0005	1.76514	0.882570	+	0.470181i	$0.155811\pi$
$710$	0	0
$711$	−18.0098	−0.675422
$712$	0.933323i	0.0349778i
$713$	− 3.73329i	− 0.139813i
$714$	−8.01090	−0.299800
$715$	0	0
$716$	18.2859	0.683377
$717$	31.0638i	1.16010i
$718$	− 23.0923i	− 0.861799i
$719$	−5.82717	−0.217317	−0.108658	−	0.994079i	$-0.534655\pi$
$719$	−5.82717	−0.217317	−0.108658	+	0.994079i	$0.534655\pi$
$720$	0	0
$721$	1.77923	0.0662619
$722$	8.23506i	0.306477i
$723$	3.30958i	0.123084i
$724$	8.23506	0.306054
$725$	0	0
$726$	13.9224	0.516710
$727$	− 15.4479i	− 0.572929i	−0.958091	−	0.286465i	$-0.907520\pi$
$727$	− 15.4479i	− 0.572929i	0.958091	−	0.286465i	$-0.0924801\pi$
$728$	6.41435i	0.237732i
$729$	−23.2177	−0.859915
$730$	0	0
$731$	16.8934	0.624824
$732$	11.4128i	0.421830i
$733$	− 15.4479i	− 0.570579i	−0.958441	−	0.285290i	$-0.907910\pi$
$733$	− 15.4479i	− 0.570579i	0.958441	−	0.285290i	$-0.0920898\pi$
$734$	15.4717	0.571069
$735$	0	0
$736$	1.80642	0.0665857
$737$	11.3684i	0.418761i
$738$	3.92242i	0.144386i
$739$	−52.2034	−1.92033	−0.960167	−	0.279427i	$-0.909855\pi$
$739$	−52.2034	−1.92033	−0.960167	+	0.279427i	$0.909855\pi$
$740$	0	0
$741$	−7.11447	−0.261357
$742$	− 23.5714i	− 0.865332i
$743$	16.7556i	0.614702i	0.951596	+	0.307351i	$0.0994426\pi$
$743$	16.7556i	0.614702i	−0.951596	+	0.307351i	$0.900557\pi$
$744$	2.50961	0.0920066
$745$	0	0
$746$	−17.6064	−0.644616
$747$	23.4968i	0.859705i
$748$	8.70471i	0.318276i
$749$	−48.3116	−1.76527
$750$	0	0
$751$	9.67307	0.352975	0.176488	−	0.984303i	$-0.443526\pi$
$751$	9.67307	0.352975	0.176488	+	0.984303i	$0.443526\pi$
$752$	1.24443i	0.0453797i
$753$	− 12.4904i	− 0.455175i
$754$	−1.34920	−0.0491351
$755$	0	0
$756$	19.7397	0.717928
$757$	− 5.98126i	− 0.217393i	−0.994075	−	0.108696i	$-0.965332\pi$
$757$	− 5.98126i	− 0.217393i	0.994075	−	0.108696i	$-0.0346676\pi$
$758$	− 9.68445i	− 0.351755i
$759$	10.3970	0.377387
$760$	0	0
$761$	−27.6365	−1.00182	−0.500911	−	0.865499i	$-0.667002\pi$
$761$	−27.6365	−1.00182	−0.500911	+	0.865499i	$0.667002\pi$
$762$	4.20003i	0.152151i
$763$	− 36.7654i	− 1.33100i
$764$	−17.3461	−0.627561
$765$	0	0
$766$	1.50468	0.0543664
$767$	16.4256i	0.593093i
$768$	1.21432i	0.0438180i
$769$	9.64740	0.347894	0.173947	−	0.984755i	$-0.444348\pi$
$769$	9.64740	0.347894	0.173947	+	0.984755i	$0.444348\pi$
$770$	0	0
$771$	−6.24491	−0.224905
$772$	− 12.0257i	− 0.432813i
$773$	− 4.56845i	− 0.164316i	−0.996619	−	0.0821578i	$-0.973819\pi$
$773$	− 4.56845i	− 0.164316i	0.996619	−	0.0821578i	$-0.0261811\pi$
$774$	−14.0316	−0.504357
$775$	0	0
$776$	2.42864	0.0871831
$777$	− 4.36196i	− 0.156485i
$778$	5.59210i	0.200487i
$779$	8.43662	0.302273
$780$	0	0
$781$	44.5466	1.59400
$782$	3.31756i	0.118636i
$783$	4.15209i	0.148384i
$784$	−5.90321	−0.210829
$785$	0	0
$786$	19.5353	0.696800
$787$	25.3274i	0.902825i	0.892316	+	0.451412i	$0.149080\pi$
$787$	25.3274i	0.902825i	−0.892316	+	0.451412i	$0.850920\pi$
$788$	− 13.9146i	− 0.495687i
$789$	8.61237	0.306609
$790$	0	0
$791$	−26.9240	−0.957306
$792$	− 7.23014i	− 0.256912i
$793$	16.7828i	0.595973i
$794$	27.5274	0.976912
$795$	0	0
$796$	24.5718	0.870926
$797$	8.98862i	0.318393i	0.987247	+	0.159197i	$0.0508904\pi$
$797$	8.98862i	0.318393i	−0.987247	+	0.159197i	$0.949110\pi$
$798$	− 14.3116i	− 0.506625i
$799$	−2.28544	−0.0808531
$800$	0	0
$801$	1.42372	0.0503046
$802$	4.83161i	0.170610i
$803$	38.3767i	1.35429i
$804$	−2.91258	−0.102719
$805$	0	0
$806$	3.69042	0.129990
$807$	31.6731i	1.11494i
$808$	8.04149i	0.282899i
$809$	−36.8256	−1.29472	−0.647360	−	0.762184i	$-0.724127\pi$
$809$	−36.8256	−1.29472	−0.647360	+	0.762184i	$0.724127\pi$
$810$	0	0
$811$	16.4286	0.576888	0.288444	−	0.957497i	$-0.406862\pi$
$811$	16.4286	0.576888	0.288444	+	0.957497i	$0.406862\pi$
$812$	− 2.71408i	− 0.0952456i
$813$	2.24152i	0.0786134i
$814$	−4.73975	−0.166128
$815$	0	0
$816$	−2.23014	−0.0780706
$817$	30.1802i	1.05587i
$818$	− 33.7447i	− 1.17985i
$819$	9.78463	0.341902
$820$	0	0
$821$	42.5881	1.48634	0.743168	−	0.669105i	$-0.233322\pi$
$821$	42.5881	1.48634	0.743168	+	0.669105i	$0.233322\pi$
$822$	19.4177i	0.677271i
$823$	3.79552i	0.132304i	0.997810	+	0.0661518i	$0.0210722\pi$
$823$	3.79552i	0.132304i	−0.997810	+	0.0661518i	$0.978928\pi$
$824$	0.495316	0.0172552
$825$	0	0
$826$	−33.0420	−1.14968
$827$	− 9.61777i	− 0.334443i	−0.985919	−	0.167221i	$-0.946521\pi$
$827$	− 9.61777i	− 0.334443i	0.985919	−	0.167221i	$-0.0534794\pi$
$828$	− 2.75557i	− 0.0957626i
$829$	30.2657	1.05117	0.525585	−	0.850741i	$-0.323847\pi$
$829$	30.2657	1.05117	0.525585	+	0.850741i	$0.323847\pi$
$830$	0	0
$831$	27.9180	0.968464
$832$	1.78568i	0.0619073i
$833$	− 10.8415i	− 0.375634i
$834$	−13.4001	−0.464006
$835$	0	0
$836$	−15.5511	−0.537846
$837$	− 11.3570i	− 0.392557i
$838$	15.0479i	0.519822i
$839$	−8.05239	−0.277999	−0.139000	−	0.990292i	$-0.544389\pi$
$839$	−8.05239	−0.277999	−0.139000	+	0.990292i	$0.544389\pi$
$840$	0	0
$841$	−28.4291	−0.980314
$842$	21.2859i	0.733561i
$843$	10.4528i	0.360013i
$844$	14.3383	0.493545
$845$	0	0
$846$	1.89829	0.0652645
$847$	41.1842i	1.41511i
$848$	− 6.56199i	− 0.225340i
$849$	37.3531	1.28195
$850$	0	0
$851$	−1.80642	−0.0619234
$852$	11.4128i	0.390997i
$853$	25.0845i	0.858877i	0.903096	+	0.429439i	$0.141289\pi$
$853$	25.0845i	0.858877i	−0.903096	+	0.429439i	$0.858711\pi$
$854$	−33.7605	−1.15526
$855$	0	0
$856$	−13.4494	−0.459690
$857$	20.5506i	0.701996i	0.936376	+	0.350998i	$0.114158\pi$
$857$	20.5506i	0.701996i	−0.936376	+	0.350998i	$0.885842\pi$
$858$	10.2776i	0.350872i
$859$	49.2810	1.68145	0.840723	−	0.541466i	$-0.182130\pi$
$859$	49.2810	1.68145	0.840723	+	0.541466i	$0.182130\pi$
$860$	0	0
$861$	11.2162	0.382246
$862$	− 35.8479i	− 1.22098i
$863$	37.6849i	1.28281i	0.767203	+	0.641405i	$0.221648\pi$
$863$	37.6849i	1.28281i	−0.767203	+	0.641405i	$0.778352\pi$
$864$	5.49532	0.186954
$865$	0	0
$866$	19.1847	0.651922
$867$	16.5477i	0.561989i
$868$	7.42372i	0.251977i
$869$	55.9595	1.89829
$870$	0	0
$871$	−4.28300	−0.145124
$872$	− 10.2351i	− 0.346603i
$873$	− 3.70471i	− 0.125386i
$874$	−5.92687	−0.200479
$875$	0	0
$876$	−9.83209	−0.332196
$877$	50.9022i	1.71884i	0.511267	+	0.859422i	$0.329176\pi$
$877$	50.9022i	1.71884i	−0.511267	+	0.859422i	$0.670824\pi$
$878$	− 11.1427i	− 0.376049i
$879$	−17.2781	−0.582775
$880$	0	0
$881$	5.39207	0.181664	0.0908318	−	0.995866i	$-0.471047\pi$
$881$	5.39207	0.181664	0.0908318	+	0.995866i	$0.471047\pi$
$882$	9.00492i	0.303212i
$883$	30.6356i	1.03097i	0.856899	+	0.515485i	$0.172388\pi$
$883$	30.6356i	1.03097i	−0.856899	+	0.515485i	$0.827612\pi$
$884$	−3.27946	−0.110300
$885$	0	0
$886$	−2.13627	−0.0717693
$887$	37.3087i	1.25270i	0.779541	+	0.626351i	$0.215452\pi$
$887$	37.3087i	1.25270i	−0.779541	+	0.626351i	$0.784548\pi$
$888$	− 1.21432i	− 0.0407499i
$889$	−12.4242	−0.416694
$890$	0	0
$891$	9.93825	0.332944
$892$	− 9.09234i	− 0.304434i
$893$	− 4.08297i	− 0.136632i
$894$	−16.9699	−0.567558
$895$	0	0
$896$	−3.59210	−0.120004
$897$	3.91703i	0.130786i
$898$	− 0.711167i	− 0.0237320i
$899$	−1.56152	−0.0520795
$900$	0	0
$901$	12.0513	0.401488
$902$	− 12.1876i	− 0.405803i
$903$	40.1235i	1.33523i
$904$	−7.49532	−0.249291
$905$	0	0
$906$	10.2351	0.340037
$907$	− 18.0973i	− 0.600910i	−0.953796	−	0.300455i	$-0.902862\pi$
$907$	− 18.0973i	− 0.600910i	0.953796	−	0.300455i	$-0.0971385\pi$
$908$	21.3319i	0.707922i
$909$	12.2667	0.406861
$910$	0	0
$911$	−44.9753	−1.49010	−0.745049	−	0.667010i	$-0.767574\pi$
$911$	−44.9753	−1.49010	−0.745049	+	0.667010i	$0.767574\pi$
$912$	− 3.98418i	− 0.131929i
$913$	− 73.0085i	− 2.41623i
$914$	−29.8321	−0.986758
$915$	0	0
$916$	−24.0098	−0.793308
$917$	57.7877i	1.90832i
$918$	10.0923i	0.333097i
$919$	−5.87955	−0.193949	−0.0969743	−	0.995287i	$-0.530916\pi$
$919$	−5.87955	−0.193949	−0.0969743	+	0.995287i	$0.530916\pi$
$920$	0	0
$921$	−35.5205	−1.17044
$922$	− 4.10171i	− 0.135083i
$923$	16.7828i	0.552411i
$924$	−20.6746	−0.680144
$925$	0	0
$926$	−13.2924	−0.436814
$927$	− 0.755569i	− 0.0248161i
$928$	− 0.755569i	− 0.0248028i
$929$	−39.0910	−1.28253	−0.641266	−	0.767318i	$-0.721591\pi$
$929$	−39.0910	−1.28253	−0.641266	+	0.767318i	$0.721591\pi$
$930$	0	0
$931$	19.3684	0.634774
$932$	8.28100i	0.271253i
$933$	− 17.7255i	− 0.580305i
$934$	−34.7052	−1.13559
$935$	0	0
$936$	2.72393	0.0890343
$937$	4.36349i	0.142549i	0.997457	+	0.0712746i	$0.0227067\pi$
$937$	4.36349i	0.142549i	−0.997457	+	0.0712746i	$0.977293\pi$
$938$	− 8.61576i	− 0.281315i
$939$	−0.626661	−0.0204503
$940$	0	0
$941$	−12.8671	−0.419456	−0.209728	−	0.977760i	$-0.567258\pi$
$941$	−12.8671	−0.419456	−0.209728	+	0.977760i	$0.567258\pi$
$942$	11.1447i	0.363115i
$943$	− 4.64497i	− 0.151261i
$944$	−9.19850	−0.299386
$945$	0	0
$946$	43.5986	1.41751
$947$	− 17.2444i	− 0.560369i	−0.959946	−	0.280184i	$-0.909604\pi$
$947$	− 17.2444i	− 0.560369i	0.959946	−	0.280184i	$-0.0903956\pi$
$948$	14.3368i	0.465637i
$949$	−14.4583	−0.469335
$950$	0	0
$951$	−35.0618	−1.13696
$952$	− 6.59703i	− 0.213811i
$953$	24.6874i	0.799702i	0.916580	+	0.399851i	$0.130938\pi$
$953$	24.6874i	0.799702i	−0.916580	+	0.399851i	$0.869062\pi$
$954$	−10.0098	−0.324081
$955$	0	0
$956$	−25.5812	−0.827355
$957$	− 4.34873i	− 0.140574i
$958$	2.89231i	0.0934464i
$959$	−57.4400	−1.85483
$960$	0	0
$961$	−26.7288	−0.862221
$962$	− 1.78568i	− 0.0575726i
$963$	20.5161i	0.661121i
$964$	−2.72546	−0.0877811
$965$	0	0
$966$	−7.87955	−0.253520
$967$	− 36.1748i	− 1.16330i	−0.813438	−	0.581652i	$-0.802406\pi$
$967$	− 36.1748i	− 1.16330i	0.813438	−	0.581652i	$-0.197594\pi$
$968$	11.4652i	0.368506i
$969$	7.31708	0.235059
$970$	0	0
$971$	−33.8419	−1.08604	−0.543020	−	0.839720i	$-0.682719\pi$
$971$	−33.8419	−1.08604	−0.543020	+	0.839720i	$0.682719\pi$
$972$	− 13.9398i	− 0.447119i
$973$	− 39.6390i	− 1.27077i
$974$	39.5560	1.26746
$975$	0	0
$976$	−9.39853	−0.300840
$977$	38.7768i	1.24058i	0.784373	+	0.620290i	$0.212985\pi$
$977$	38.7768i	1.24058i	−0.784373	+	0.620290i	$0.787015\pi$
$978$	− 16.9333i	− 0.541468i
$979$	−4.42372	−0.141383
$980$	0	0
$981$	−15.6128	−0.498480
$982$	− 26.5018i	− 0.845705i
$983$	59.3975i	1.89449i	0.320518	+	0.947243i	$0.396143\pi$
$983$	59.3975i	1.89449i	−0.320518	+	0.947243i	$0.603857\pi$
$984$	3.12245	0.0995402
$985$	0	0
$986$	1.38763	0.0441911
$987$	− 5.42816i	− 0.172780i
$988$	− 5.85881i	− 0.186394i
$989$	16.6164	0.528370
$990$	0	0
$991$	36.3245	1.15389	0.576943	−	0.816785i	$-0.304246\pi$
$991$	36.3245	1.15389	0.576943	+	0.816785i	$0.304246\pi$
$992$	2.06668i	0.0656170i
$993$	7.96238i	0.252678i
$994$	−33.7605	−1.07082
$995$	0	0
$996$	18.7047	0.592682
$997$	32.7732i	1.03794i	0.854793	+	0.518970i	$0.173684\pi$
$997$	32.7732i	1.03794i	−0.854793	+	0.518970i	$0.826316\pi$
$998$	− 41.3319i	− 1.30834i
$999$	−5.49532	−0.173864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.n.149.3		6
5.2	odd	4		1850.2.a.bb.1.3	yes	3
5.3	odd	4		1850.2.a.ba.1.1	✓	3
5.4	even	2	inner	1850.2.b.n.149.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.ba.1.1	✓	3	5.3	odd	4
1850.2.a.bb.1.3	yes	3	5.2	odd	4
1850.2.b.n.149.3		6	1.1	even	1	trivial
1850.2.b.n.149.4		6	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.21432i q^{3} -1.00000 q^{4} +1.21432 q^{6} +3.59210i q^{7} +1.00000i q^{8} +1.52543 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.21432i q^{3} -1.00000 q^{4} +1.21432 q^{6} +3.59210i q^{7} +1.00000i q^{8} +1.52543 q^{9} -4.73975 q^{11} -1.21432i q^{12} -1.78568i q^{13} +3.59210 q^{14} +1.00000 q^{16} +1.83654i q^{17} -1.52543i q^{18} -3.28100 q^{19} -4.36196 q^{21} +4.73975i q^{22} +1.80642i q^{23} -1.21432 q^{24} -1.78568 q^{26} +5.49532i q^{27} -3.59210i q^{28} +0.755569 q^{29} -2.06668 q^{31} -1.00000i q^{32} -5.75557i q^{33} +1.83654 q^{34} -1.52543 q^{36} +1.00000i q^{37} +3.28100i q^{38} +2.16839 q^{39} -2.57136 q^{41} +4.36196i q^{42} -9.19850i q^{43} +4.73975 q^{44} +1.80642 q^{46} +1.24443i q^{47} +1.21432i q^{48} -5.90321 q^{49} -2.23014 q^{51} +1.78568i q^{52} -6.56199i q^{53} +5.49532 q^{54} -3.59210 q^{56} -3.98418i q^{57} -0.755569i q^{58} -9.19850 q^{59} -9.39853 q^{61} +2.06668i q^{62} +5.47949i q^{63} -1.00000 q^{64} -5.75557 q^{66} -2.39853i q^{67} -1.83654i q^{68} -2.19358 q^{69} -9.39853 q^{71} +1.52543i q^{72} -8.09679i q^{73} +1.00000 q^{74} +3.28100 q^{76} -17.0257i q^{77} -2.16839i q^{78} -11.8064 q^{79} -2.09679 q^{81} +2.57136i q^{82} +15.4035i q^{83} +4.36196 q^{84} -9.19850 q^{86} +0.917502i q^{87} -4.73975i q^{88} +0.933323 q^{89} +6.41435 q^{91} -1.80642i q^{92} -2.50961i q^{93} +1.24443 q^{94} +1.21432 q^{96} -2.42864i q^{97} +5.90321i q^{98} -7.23014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{11} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 6 q^{24} - 24 q^{26} + 4 q^{29} - 12 q^{31} - 2 q^{34} + 4 q^{36} - 40 q^{39} - 42 q^{41} + 2 q^{44} - 16 q^{46} - 22 q^{49} - 26 q^{51} + 6 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} - 6 q^{64} - 34 q^{66} - 40 q^{69} - 16 q^{71} + 6 q^{74} + 6 q^{76} - 44 q^{79} - 26 q^{81} - 16 q^{86} + 6 q^{89} + 24 q^{91} + 8 q^{94} - 6 q^{96} - 56 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^11 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 6 * q^24 - 24 * q^26 + 4 * q^29 - 12 * q^31 - 2 * q^34 + 4 * q^36 - 40 * q^39 - 42 * q^41 + 2 * q^44 - 16 * q^46 - 22 * q^49 - 26 * q^51 + 6 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 - 6 * q^64 - 34 * q^66 - 40 * q^69 - 16 * q^71 + 6 * q^74 + 6 * q^76 - 44 * q^79 - 26 * q^81 - 16 * q^86 + 6 * q^89 + 24 * q^91 + 8 * q^94 - 6 * q^96 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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