LMFDB - Embedded newform 2850.2.d.x.799.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(799,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2850.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.d (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:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.3
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2850.799
Dual form			2850.2.d.x.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -0.732051i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -0.732051i q^{7} -1.00000i q^{8} -1.00000 q^{9} +3.73205 q^{11} +1.00000i q^{12} -2.73205i q^{13} +0.732051 q^{14} +1.00000 q^{16} +6.19615i q^{17} -1.00000i q^{18} +1.00000 q^{19} -0.732051 q^{21} +3.73205i q^{22} +5.92820i q^{23} -1.00000 q^{24} +2.73205 q^{26} +1.00000i q^{27} +0.732051i q^{28} +1.73205 q^{29} -2.46410 q^{31} +1.00000i q^{32} -3.73205i q^{33} -6.19615 q^{34} +1.00000 q^{36} +2.00000i q^{37} +1.00000i q^{38} -2.73205 q^{39} -2.92820 q^{41} -0.732051i q^{42} -8.19615i q^{43} -3.73205 q^{44} -5.92820 q^{46} -3.46410i q^{47} -1.00000i q^{48} +6.46410 q^{49} +6.19615 q^{51} +2.73205i q^{52} -1.73205i q^{53} -1.00000 q^{54} -0.732051 q^{56} -1.00000i q^{57} +1.73205i q^{58} +8.19615 q^{59} +10.6603 q^{61} -2.46410i q^{62} +0.732051i q^{63} -1.00000 q^{64} +3.73205 q^{66} +0.267949i q^{67} -6.19615i q^{68} +5.92820 q^{69} +12.1962 q^{71} +1.00000i q^{72} -2.46410i q^{73} -2.00000 q^{74} -1.00000 q^{76} -2.73205i q^{77} -2.73205i q^{78} +5.53590 q^{79} +1.00000 q^{81} -2.92820i q^{82} +3.73205i q^{83} +0.732051 q^{84} +8.19615 q^{86} -1.73205i q^{87} -3.73205i q^{88} -10.8564 q^{89} -2.00000 q^{91} -5.92820i q^{92} +2.46410i q^{93} +3.46410 q^{94} +1.00000 q^{96} +15.1244i q^{97} +6.46410i q^{98} -3.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} - 4 q^{24} + 4 q^{26} + 4 q^{31} - 4 q^{34} + 4 q^{36} - 4 q^{39} + 16 q^{41} - 8 q^{44} + 4 q^{46} + 12 q^{49} + 4 q^{51} - 4 q^{54} + 4 q^{56} + 12 q^{59} + 8 q^{61} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 28 q^{71} - 8 q^{74} - 4 q^{76} + 36 q^{79} + 4 q^{81} - 4 q^{84} + 12 q^{86} + 12 q^{89} - 8 q^{91} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 - 4 * q^24 + 4 * q^26 + 4 * q^31 - 4 * q^34 + 4 * q^36 - 4 * q^39 + 16 * q^41 - 8 * q^44 + 4 * q^46 + 12 * q^49 + 4 * q^51 - 4 * q^54 + 4 * q^56 + 12 * q^59 + 8 * q^61 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 28 * q^71 - 8 * q^74 - 4 * q^76 + 36 * q^79 + 4 * q^81 - 4 * q^84 + 12 * q^86 + 12 * q^89 - 8 * q^91 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times$.

$n$	$1027$	$1351$	$1901$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	− 0.732051i	− 0.276689i	−0.990384	−	0.138345i	$-0.955822\pi$
$7$	− 0.732051i	− 0.276689i	0.990384	−	0.138345i	$-0.0441781\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	3.73205	1.12526	0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205	1.12526	0.562628	+	0.826710i	$0.309790\pi$
$12$	1.00000i	0.288675i
$13$	− 2.73205i	− 0.757735i	−0.925451	−	0.378867i	$-0.876314\pi$
$13$	− 2.73205i	− 0.757735i	0.925451	−	0.378867i	$-0.123686\pi$
$14$	0.732051	0.195649
$15$	0	0
$16$	1.00000	0.250000
$17$	6.19615i	1.50279i	0.659854	+	0.751394i	$0.270618\pi$
$17$	6.19615i	1.50279i	−0.659854	+	0.751394i	$0.729382\pi$
$18$	− 1.00000i	− 0.235702i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−0.732051	−0.159747
$22$	3.73205i	0.795676i
$23$	5.92820i	1.23612i	0.786133	+	0.618058i	$0.212080\pi$
$23$	5.92820i	1.23612i	−0.786133	+	0.618058i	$0.787920\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	2.73205	0.535799
$27$	1.00000i	0.192450i
$28$	0.732051i	0.138345i
$29$	1.73205	0.321634	0.160817	−	0.986984i	$-0.448587\pi$
$29$	1.73205	0.321634	0.160817	+	0.986984i	$0.448587\pi$
$30$	0	0
$31$	−2.46410	−0.442566	−0.221283	−	0.975210i	$-0.571024\pi$
$31$	−2.46410	−0.442566	−0.221283	+	0.975210i	$0.571024\pi$
$32$	1.00000i	0.176777i
$33$	− 3.73205i	− 0.649667i
$34$	−6.19615	−1.06263
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000i	0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	2.00000i	0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	1.00000i	0.162221i
$39$	−2.73205	−0.437478
$40$	0	0
$41$	−2.92820	−0.457309	−0.228654	−	0.973508i	$-0.573433\pi$
$41$	−2.92820	−0.457309	−0.228654	+	0.973508i	$0.573433\pi$
$42$	− 0.732051i	− 0.112958i
$43$	− 8.19615i	− 1.24990i	−0.780664	−	0.624951i	$-0.785119\pi$
$43$	− 8.19615i	− 1.24990i	0.780664	−	0.624951i	$-0.214881\pi$
$44$	−3.73205	−0.562628
$45$	0	0
$46$	−5.92820	−0.874066
$47$	− 3.46410i	− 0.505291i	−0.967559	−	0.252646i	$-0.918699\pi$
$47$	− 3.46410i	− 0.505291i	0.967559	−	0.252646i	$-0.0813007\pi$
$48$	− 1.00000i	− 0.144338i
$49$	6.46410	0.923443
$50$	0	0
$51$	6.19615	0.867635
$52$	2.73205i	0.378867i
$53$	− 1.73205i	− 0.237915i	−0.992899	−	0.118958i	$-0.962045\pi$
$53$	− 1.73205i	− 0.237915i	0.992899	−	0.118958i	$-0.0379553\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−0.732051	−0.0978244
$57$	− 1.00000i	− 0.132453i
$58$	1.73205i	0.227429i
$59$	8.19615	1.06705	0.533524	−	0.845785i	$-0.320867\pi$
$59$	8.19615	1.06705	0.533524	+	0.845785i	$0.320867\pi$
$60$	0	0
$61$	10.6603	1.36491	0.682453	−	0.730930i	$-0.260913\pi$
$61$	10.6603	1.36491	0.682453	+	0.730930i	$0.260913\pi$
$62$	− 2.46410i	− 0.312941i
$63$	0.732051i	0.0922297i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.73205	0.459384
$67$	0.267949i	0.0327352i	0.999866	+	0.0163676i	$0.00521020\pi$
$67$	0.267949i	0.0327352i	−0.999866	+	0.0163676i	$0.994790\pi$
$68$	− 6.19615i	− 0.751394i
$69$	5.92820	0.713672
$70$	0	0
$71$	12.1962	1.44742	0.723708	−	0.690106i	$-0.242436\pi$
$71$	12.1962	1.44742	0.723708	+	0.690106i	$0.242436\pi$
$72$	1.00000i	0.117851i
$73$	− 2.46410i	− 0.288401i	−0.989548	−	0.144201i	$-0.953939\pi$
$73$	− 2.46410i	− 0.288401i	0.989548	−	0.144201i	$-0.0460611\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 2.73205i	− 0.311346i
$78$	− 2.73205i	− 0.309344i
$79$	5.53590	0.622837	0.311419	−	0.950273i	$-0.399196\pi$
$79$	5.53590	0.622837	0.311419	+	0.950273i	$0.399196\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 2.92820i	− 0.323366i
$83$	3.73205i	0.409646i	0.978799	+	0.204823i	$0.0656618\pi$
$83$	3.73205i	0.409646i	−0.978799	+	0.204823i	$0.934338\pi$
$84$	0.732051	0.0798733
$85$	0	0
$86$	8.19615	0.883814
$87$	− 1.73205i	− 0.185695i
$88$	− 3.73205i	− 0.397838i
$89$	−10.8564	−1.15078	−0.575388	−	0.817880i	$-0.695149\pi$
$89$	−10.8564	−1.15078	−0.575388	+	0.817880i	$0.695149\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	− 5.92820i	− 0.618058i
$93$	2.46410i	0.255515i
$94$	3.46410	0.357295
$95$	0	0
$96$	1.00000	0.102062
$97$	15.1244i	1.53565i	0.640662	+	0.767823i	$0.278660\pi$
$97$	15.1244i	1.53565i	−0.640662	+	0.767823i	$0.721340\pi$
$98$	6.46410i	0.652973i
$99$	−3.73205	−0.375085
$100$	0	0
$101$	9.26795	0.922195	0.461098	−	0.887349i	$-0.347456\pi$
$101$	9.26795	0.922195	0.461098	+	0.887349i	$0.347456\pi$
$102$	6.19615i	0.613511i
$103$	− 3.53590i	− 0.348402i	−0.984710	−	0.174201i	$-0.944266\pi$
$103$	− 3.53590i	− 0.348402i	0.984710	−	0.174201i	$-0.0557343\pi$
$104$	−2.73205	−0.267900
$105$	0	0
$106$	1.73205	0.168232
$107$	− 2.19615i	− 0.212310i	−0.994350	−	0.106155i	$-0.966146\pi$
$107$	− 2.19615i	− 0.212310i	0.994350	−	0.106155i	$-0.0338540\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−2.39230	−0.229141	−0.114571	−	0.993415i	$-0.536549\pi$
$109$	−2.39230	−0.229141	−0.114571	+	0.993415i	$0.536549\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	− 0.732051i	− 0.0691723i
$113$	− 13.3923i	− 1.25984i	−0.776659	−	0.629921i	$-0.783087\pi$
$113$	− 13.3923i	− 1.25984i	0.776659	−	0.629921i	$-0.216913\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−1.73205	−0.160817
$117$	2.73205i	0.252578i
$118$	8.19615i	0.754517i
$119$	4.53590	0.415805
$120$	0	0
$121$	2.92820	0.266200
$122$	10.6603i	0.965134i
$123$	2.92820i	0.264027i
$124$	2.46410	0.221283
$125$	0	0
$126$	−0.732051	−0.0652163
$127$	5.00000i	0.443678i	0.975083	+	0.221839i	$0.0712060\pi$
$127$	5.00000i	0.443678i	−0.975083	+	0.221839i	$0.928794\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−8.19615	−0.721631
$130$	0	0
$131$	10.2679	0.897115	0.448557	−	0.893754i	$-0.351938\pi$
$131$	10.2679	0.897115	0.448557	+	0.893754i	$0.351938\pi$
$132$	3.73205i	0.324833i
$133$	− 0.732051i	− 0.0634769i
$134$	−0.267949	−0.0231473
$135$	0	0
$136$	6.19615	0.531316
$137$	12.3923i	1.05875i	0.848389	+	0.529373i	$0.177573\pi$
$137$	12.3923i	1.05875i	−0.848389	+	0.529373i	$0.822427\pi$
$138$	5.92820i	0.504642i
$139$	21.1244	1.79174	0.895872	−	0.444312i	$-0.146552\pi$
$139$	21.1244	1.79174	0.895872	+	0.444312i	$0.146552\pi$
$140$	0	0
$141$	−3.46410	−0.291730
$142$	12.1962i	1.02348i
$143$	− 10.1962i	− 0.852645i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	2.46410	0.203931
$147$	− 6.46410i	− 0.533150i
$148$	− 2.00000i	− 0.164399i
$149$	21.8564	1.79055	0.895273	−	0.445517i	$-0.146980\pi$
$149$	21.8564	1.79055	0.895273	+	0.445517i	$0.146980\pi$
$150$	0	0
$151$	−11.4641	−0.932935	−0.466468	−	0.884538i	$-0.654474\pi$
$151$	−11.4641	−0.932935	−0.466468	+	0.884538i	$0.654474\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	− 6.19615i	− 0.500929i
$154$	2.73205	0.220155
$155$	0	0
$156$	2.73205	0.218739
$157$	− 13.8564i	− 1.10586i	−0.833227	−	0.552931i	$-0.813509\pi$
$157$	− 13.8564i	− 1.10586i	0.833227	−	0.552931i	$-0.186491\pi$
$158$	5.53590i	0.440412i
$159$	−1.73205	−0.137361
$160$	0	0
$161$	4.33975	0.342020
$162$	1.00000i	0.0785674i
$163$	− 2.00000i	− 0.156652i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	− 2.00000i	− 0.156652i	0.996928	−	0.0783260i	$-0.0249575\pi$
$164$	2.92820	0.228654
$165$	0	0
$166$	−3.73205	−0.289663
$167$	8.92820i	0.690885i	0.938440	+	0.345443i	$0.112271\pi$
$167$	8.92820i	0.690885i	−0.938440	+	0.345443i	$0.887729\pi$
$168$	0.732051i	0.0564789i
$169$	5.53590	0.425838
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	8.19615i	0.624951i
$173$	13.5885i	1.03311i	0.856254	+	0.516556i	$0.172786\pi$
$173$	13.5885i	1.03311i	−0.856254	+	0.516556i	$0.827214\pi$
$174$	1.73205	0.131306
$175$	0	0
$176$	3.73205	0.281314
$177$	− 8.19615i	− 0.616061i
$178$	− 10.8564i	− 0.813722i
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−16.5885	−1.23301	−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885	−1.23301	−0.616505	+	0.787351i	$0.711452\pi$
$182$	− 2.00000i	− 0.148250i
$183$	− 10.6603i	− 0.788029i
$184$	5.92820	0.437033
$185$	0	0
$186$	−2.46410	−0.180677
$187$	23.1244i	1.69102i
$188$	3.46410i	0.252646i
$189$	0.732051	0.0532489
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	1.00000i	0.0721688i
$193$	22.0526i	1.58738i	0.608324	+	0.793689i	$0.291842\pi$
$193$	22.0526i	1.58738i	−0.608324	+	0.793689i	$0.708158\pi$
$194$	−15.1244	−1.08587
$195$	0	0
$196$	−6.46410	−0.461722
$197$	− 24.5885i	− 1.75186i	−0.482443	−	0.875928i	$-0.660250\pi$
$197$	− 24.5885i	− 1.75186i	0.482443	−	0.875928i	$-0.339750\pi$
$198$	− 3.73205i	− 0.265225i
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	0	0
$201$	0.267949	0.0188997
$202$	9.26795i	0.652091i
$203$	− 1.26795i	− 0.0889926i
$204$	−6.19615	−0.433817
$205$	0	0
$206$	3.53590	0.246358
$207$	− 5.92820i	− 0.412039i
$208$	− 2.73205i	− 0.189434i
$209$	3.73205	0.258151
$210$	0	0
$211$	−10.2679	−0.706875	−0.353437	−	0.935458i	$-0.614987\pi$
$211$	−10.2679	−0.706875	−0.353437	+	0.935458i	$0.614987\pi$
$212$	1.73205i	0.118958i
$213$	− 12.1962i	− 0.835667i
$214$	2.19615	0.150126
$215$	0	0
$216$	1.00000	0.0680414
$217$	1.80385i	0.122453i
$218$	− 2.39230i	− 0.162027i
$219$	−2.46410	−0.166509
$220$	0	0
$221$	16.9282	1.13871
$222$	2.00000i	0.134231i
$223$	− 3.53590i	− 0.236781i	−0.992967	−	0.118391i	$-0.962226\pi$
$223$	− 3.53590i	− 0.236781i	0.992967	−	0.118391i	$-0.0377735\pi$
$224$	0.732051	0.0489122
$225$	0	0
$226$	13.3923	0.890843
$227$	6.00000i	0.398234i	0.979976	+	0.199117i	$0.0638074\pi$
$227$	6.00000i	0.398234i	−0.979976	+	0.199117i	$0.936193\pi$
$228$	1.00000i	0.0662266i
$229$	6.26795	0.414198	0.207099	−	0.978320i	$-0.433598\pi$
$229$	6.26795	0.414198	0.207099	+	0.978320i	$0.433598\pi$
$230$	0	0
$231$	−2.73205	−0.179756
$232$	− 1.73205i	− 0.113715i
$233$	− 21.1244i	− 1.38390i	−0.721944	−	0.691951i	$-0.756751\pi$
$233$	− 21.1244i	− 1.38390i	0.721944	−	0.691951i	$-0.243249\pi$
$234$	−2.73205	−0.178600
$235$	0	0
$236$	−8.19615	−0.533524
$237$	− 5.53590i	− 0.359595i
$238$	4.53590i	0.294019i
$239$	14.0000	0.905585	0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000	0.905585	0.452792	+	0.891616i	$0.350428\pi$
$240$	0	0
$241$	−30.1962	−1.94511	−0.972553	−	0.232683i	$-0.925249\pi$
$241$	−30.1962	−1.94511	−0.972553	+	0.232683i	$0.925249\pi$
$242$	2.92820i	0.188232i
$243$	− 1.00000i	− 0.0641500i
$244$	−10.6603	−0.682453
$245$	0	0
$246$	−2.92820	−0.186695
$247$	− 2.73205i	− 0.173836i
$248$	2.46410i	0.156471i
$249$	3.73205	0.236509
$250$	0	0
$251$	11.4641	0.723608	0.361804	−	0.932254i	$-0.382161\pi$
$251$	11.4641	0.723608	0.361804	+	0.932254i	$0.382161\pi$
$252$	− 0.732051i	− 0.0461149i
$253$	22.1244i	1.39095i
$254$	−5.00000	−0.313728
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 9.00000i	− 0.561405i	−0.959795	−	0.280702i	$-0.909433\pi$
$257$	− 9.00000i	− 0.561405i	0.959795	−	0.280702i	$-0.0905674\pi$
$258$	− 8.19615i	− 0.510270i
$259$	1.46410	0.0909748
$260$	0	0
$261$	−1.73205	−0.107211
$262$	10.2679i	0.634356i
$263$	15.0000i	0.924940i	0.886635	+	0.462470i	$0.153037\pi$
$263$	15.0000i	0.924940i	−0.886635	+	0.462470i	$0.846963\pi$
$264$	−3.73205	−0.229692
$265$	0	0
$266$	0.732051	0.0448849
$267$	10.8564i	0.664401i
$268$	− 0.267949i	− 0.0163676i
$269$	20.5359	1.25210	0.626048	−	0.779785i	$-0.284671\pi$
$269$	20.5359	1.25210	0.626048	+	0.779785i	$0.284671\pi$
$270$	0	0
$271$	−15.8038	−0.960015	−0.480008	−	0.877264i	$-0.659366\pi$
$271$	−15.8038	−0.960015	−0.480008	+	0.877264i	$0.659366\pi$
$272$	6.19615i	0.375697i
$273$	2.00000i	0.121046i
$274$	−12.3923	−0.748647
$275$	0	0
$276$	−5.92820	−0.356836
$277$	− 11.1962i	− 0.672712i	−0.941735	−	0.336356i	$-0.890806\pi$
$277$	− 11.1962i	− 0.672712i	0.941735	−	0.336356i	$-0.109194\pi$
$278$	21.1244i	1.26695i
$279$	2.46410	0.147522
$280$	0	0
$281$	17.7846	1.06094	0.530470	−	0.847703i	$-0.322015\pi$
$281$	17.7846	1.06094	0.530470	+	0.847703i	$0.322015\pi$
$282$	− 3.46410i	− 0.206284i
$283$	4.00000i	0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$	4.00000i	0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	−12.1962	−0.723708
$285$	0	0
$286$	10.1962	0.602911
$287$	2.14359i	0.126532i
$288$	− 1.00000i	− 0.0589256i
$289$	−21.3923	−1.25837
$290$	0	0
$291$	15.1244	0.886605
$292$	2.46410i	0.144201i
$293$	− 27.7321i	− 1.62012i	−0.586344	−	0.810062i	$-0.699433\pi$
$293$	− 27.7321i	− 1.62012i	0.586344	−	0.810062i	$-0.300567\pi$
$294$	6.46410	0.376994
$295$	0	0
$296$	2.00000	0.116248
$297$	3.73205i	0.216556i
$298$	21.8564i	1.26611i
$299$	16.1962	0.936648
$300$	0	0
$301$	−6.00000	−0.345834
$302$	− 11.4641i	− 0.659685i
$303$	− 9.26795i	− 0.532430i
$304$	1.00000	0.0573539
$305$	0	0
$306$	6.19615	0.354210
$307$	20.2679i	1.15675i	0.815770	+	0.578376i	$0.196314\pi$
$307$	20.2679i	1.15675i	−0.815770	+	0.578376i	$0.803686\pi$
$308$	2.73205i	0.155673i
$309$	−3.53590	−0.201150
$310$	0	0
$311$	−29.3205	−1.66261	−0.831307	−	0.555814i	$-0.812407\pi$
$311$	−29.3205	−1.66261	−0.831307	+	0.555814i	$0.812407\pi$
$312$	2.73205i	0.154672i
$313$	− 3.92820i	− 0.222035i	−0.993818	−	0.111018i	$-0.964589\pi$
$313$	− 3.92820i	− 0.222035i	0.993818	−	0.111018i	$-0.0354110\pi$
$314$	13.8564	0.781962
$315$	0	0
$316$	−5.53590	−0.311419
$317$	1.73205i	0.0972817i	0.998816	+	0.0486408i	$0.0154890\pi$
$317$	1.73205i	0.0972817i	−0.998816	+	0.0486408i	$0.984511\pi$
$318$	− 1.73205i	− 0.0971286i
$319$	6.46410	0.361920
$320$	0	0
$321$	−2.19615	−0.122577
$322$	4.33975i	0.241845i
$323$	6.19615i	0.344763i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	2.00000	0.110770
$327$	2.39230i	0.132295i
$328$	2.92820i	0.161683i
$329$	−2.53590	−0.139809
$330$	0	0
$331$	−22.2679	−1.22396	−0.611979	−	0.790874i	$-0.709626\pi$
$331$	−22.2679	−1.22396	−0.611979	+	0.790874i	$0.709626\pi$
$332$	− 3.73205i	− 0.204823i
$333$	− 2.00000i	− 0.109599i
$334$	−8.92820	−0.488530
$335$	0	0
$336$	−0.732051	−0.0399366
$337$	− 10.5359i	− 0.573927i	−0.957942	−	0.286963i	$-0.907354\pi$
$337$	− 10.5359i	− 0.573927i	0.957942	−	0.286963i	$-0.0926458\pi$
$338$	5.53590i	0.301113i
$339$	−13.3923	−0.727370
$340$	0	0
$341$	−9.19615	−0.498000
$342$	− 1.00000i	− 0.0540738i
$343$	− 9.85641i	− 0.532196i
$344$	−8.19615	−0.441907
$345$	0	0
$346$	−13.5885	−0.730520
$347$	20.7846i	1.11578i	0.829916	+	0.557888i	$0.188388\pi$
$347$	20.7846i	1.11578i	−0.829916	+	0.557888i	$0.811612\pi$
$348$	1.73205i	0.0928477i
$349$	17.0526	0.912803	0.456401	−	0.889774i	$-0.349138\pi$
$349$	17.0526	0.912803	0.456401	+	0.889774i	$0.349138\pi$
$350$	0	0
$351$	2.73205	0.145826
$352$	3.73205i	0.198919i
$353$	16.0526i	0.854391i	0.904159	+	0.427196i	$0.140498\pi$
$353$	16.0526i	0.854391i	−0.904159	+	0.427196i	$0.859502\pi$
$354$	8.19615	0.435621
$355$	0	0
$356$	10.8564	0.575388
$357$	− 4.53590i	− 0.240065i
$358$	12.0000i	0.634220i
$359$	16.9282	0.893436	0.446718	−	0.894675i	$-0.352593\pi$
$359$	16.9282	0.893436	0.446718	+	0.894675i	$0.352593\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 16.5885i	− 0.871870i
$363$	− 2.92820i	− 0.153691i
$364$	2.00000	0.104828
$365$	0	0
$366$	10.6603	0.557220
$367$	13.2679i	0.692581i	0.938127	+	0.346291i	$0.112559\pi$
$367$	13.2679i	0.692581i	−0.938127	+	0.346291i	$0.887441\pi$
$368$	5.92820i	0.309029i
$369$	2.92820	0.152436
$370$	0	0
$371$	−1.26795	−0.0658286
$372$	− 2.46410i	− 0.127758i
$373$	− 31.5167i	− 1.63187i	−0.578143	−	0.815935i	$-0.696222\pi$
$373$	− 31.5167i	− 1.63187i	0.578143	−	0.815935i	$-0.303778\pi$
$374$	−23.1244	−1.19573
$375$	0	0
$376$	−3.46410	−0.178647
$377$	− 4.73205i	− 0.243713i
$378$	0.732051i	0.0376526i
$379$	0.392305	0.0201513	0.0100757	−	0.999949i	$-0.496793\pi$
$379$	0.392305	0.0201513	0.0100757	+	0.999949i	$0.496793\pi$
$380$	0	0
$381$	5.00000	0.256158
$382$	3.00000i	0.153493i
$383$	− 19.5167i	− 0.997255i	−0.866816	−	0.498627i	$-0.833838\pi$
$383$	− 19.5167i	− 0.997255i	0.866816	−	0.498627i	$-0.166162\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−22.0526	−1.12245
$387$	8.19615i	0.416634i
$388$	− 15.1244i	− 0.767823i
$389$	−21.7128	−1.10088	−0.550442	−	0.834874i	$-0.685541\pi$
$389$	−21.7128	−1.10088	−0.550442	+	0.834874i	$0.685541\pi$
$390$	0	0
$391$	−36.7321	−1.85762
$392$	− 6.46410i	− 0.326486i
$393$	− 10.2679i	− 0.517950i
$394$	24.5885	1.23875
$395$	0	0
$396$	3.73205	0.187543
$397$	− 11.7321i	− 0.588815i	−0.955680	−	0.294407i	$-0.904878\pi$
$397$	− 11.7321i	− 0.588815i	0.955680	−	0.294407i	$-0.0951222\pi$
$398$	14.0000i	0.701757i
$399$	−0.732051	−0.0366484
$400$	0	0
$401$	16.8564	0.841769	0.420884	−	0.907114i	$-0.361720\pi$
$401$	16.8564	0.841769	0.420884	+	0.907114i	$0.361720\pi$
$402$	0.267949i	0.0133641i
$403$	6.73205i	0.335347i
$404$	−9.26795	−0.461098
$405$	0	0
$406$	1.26795	0.0629273
$407$	7.46410i	0.369982i
$408$	− 6.19615i	− 0.306755i
$409$	−1.60770	−0.0794954	−0.0397477	−	0.999210i	$-0.512655\pi$
$409$	−1.60770	−0.0794954	−0.0397477	+	0.999210i	$0.512655\pi$
$410$	0	0
$411$	12.3923	0.611267
$412$	3.53590i	0.174201i
$413$	− 6.00000i	− 0.295241i
$414$	5.92820	0.291355
$415$	0	0
$416$	2.73205	0.133950
$417$	− 21.1244i	− 1.03446i
$418$	3.73205i	0.182541i
$419$	−13.8564	−0.676930	−0.338465	−	0.940979i	$-0.609908\pi$
$419$	−13.8564	−0.676930	−0.338465	+	0.940979i	$0.609908\pi$
$420$	0	0
$421$	6.78461	0.330662	0.165331	−	0.986238i	$-0.447131\pi$
$421$	6.78461	0.330662	0.165331	+	0.986238i	$0.447131\pi$
$422$	− 10.2679i	− 0.499836i
$423$	3.46410i	0.168430i
$424$	−1.73205	−0.0841158
$425$	0	0
$426$	12.1962	0.590906
$427$	− 7.80385i	− 0.377655i
$428$	2.19615i	0.106155i
$429$	−10.1962	−0.492275
$430$	0	0
$431$	−29.3205	−1.41232	−0.706160	−	0.708053i	$-0.749574\pi$
$431$	−29.3205	−1.41232	−0.706160	+	0.708053i	$0.749574\pi$
$432$	1.00000i	0.0481125i
$433$	24.1962i	1.16279i	0.813620	+	0.581396i	$0.197493\pi$
$433$	24.1962i	1.16279i	−0.813620	+	0.581396i	$0.802507\pi$
$434$	−1.80385	−0.0865875
$435$	0	0
$436$	2.39230	0.114571
$437$	5.92820i	0.283584i
$438$	− 2.46410i	− 0.117739i
$439$	−25.7846	−1.23063	−0.615316	−	0.788280i	$-0.710972\pi$
$439$	−25.7846	−1.23063	−0.615316	+	0.788280i	$0.710972\pi$
$440$	0	0
$441$	−6.46410	−0.307814
$442$	16.9282i	0.805193i
$443$	3.33975i	0.158676i	0.996848	+	0.0793381i	$0.0252807\pi$
$443$	3.33975i	0.158676i	−0.996848	+	0.0793381i	$0.974719\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	3.53590	0.167430
$447$	− 21.8564i	− 1.03377i
$448$	0.732051i	0.0345861i
$449$	−24.4641	−1.15453	−0.577266	−	0.816556i	$-0.695880\pi$
$449$	−24.4641	−1.15453	−0.577266	+	0.816556i	$0.695880\pi$
$450$	0	0
$451$	−10.9282	−0.514589
$452$	13.3923i	0.629921i
$453$	11.4641i	0.538630i
$454$	−6.00000	−0.281594
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	− 5.07180i	− 0.237249i	−0.992939	−	0.118624i	$-0.962152\pi$
$457$	− 5.07180i	− 0.237249i	0.992939	−	0.118624i	$-0.0378484\pi$
$458$	6.26795i	0.292882i
$459$	−6.19615	−0.289212
$460$	0	0
$461$	−17.8564	−0.831656	−0.415828	−	0.909443i	$-0.636508\pi$
$461$	−17.8564	−0.831656	−0.415828	+	0.909443i	$0.636508\pi$
$462$	− 2.73205i	− 0.127107i
$463$	35.3205i	1.64148i	0.571300	+	0.820742i	$0.306439\pi$
$463$	35.3205i	1.64148i	−0.571300	+	0.820742i	$0.693561\pi$
$464$	1.73205	0.0804084
$465$	0	0
$466$	21.1244	0.978567
$467$	7.19615i	0.332998i	0.986042	+	0.166499i	$0.0532463\pi$
$467$	7.19615i	0.332998i	−0.986042	+	0.166499i	$0.946754\pi$
$468$	− 2.73205i	− 0.126289i
$469$	0.196152	0.00905748
$470$	0	0
$471$	−13.8564	−0.638470
$472$	− 8.19615i	− 0.377258i
$473$	− 30.5885i	− 1.40646i
$474$	5.53590	0.254272
$475$	0	0
$476$	−4.53590	−0.207903
$477$	1.73205i	0.0793052i
$478$	14.0000i	0.640345i
$479$	−3.14359	−0.143634	−0.0718172	−	0.997418i	$-0.522880\pi$
$479$	−3.14359	−0.143634	−0.0718172	+	0.997418i	$0.522880\pi$
$480$	0	0
$481$	5.46410	0.249142
$482$	− 30.1962i	− 1.37540i
$483$	− 4.33975i	− 0.197465i
$484$	−2.92820	−0.133100
$485$	0	0
$486$	1.00000	0.0453609
$487$	2.14359i	0.0971355i	0.998820	+	0.0485677i	$0.0154657\pi$
$487$	2.14359i	0.0971355i	−0.998820	+	0.0485677i	$0.984534\pi$
$488$	− 10.6603i	− 0.482567i
$489$	−2.00000	−0.0904431
$490$	0	0
$491$	−2.92820	−0.132148	−0.0660740	−	0.997815i	$-0.521047\pi$
$491$	−2.92820	−0.132148	−0.0660740	+	0.997815i	$0.521047\pi$
$492$	− 2.92820i	− 0.132014i
$493$	10.7321i	0.483347i
$494$	2.73205	0.122921
$495$	0	0
$496$	−2.46410	−0.110641
$497$	− 8.92820i	− 0.400485i
$498$	3.73205i	0.167237i
$499$	−41.3731	−1.85211	−0.926056	−	0.377385i	$-0.876823\pi$
$499$	−41.3731	−1.85211	−0.926056	+	0.377385i	$0.876823\pi$
$500$	0	0
$501$	8.92820	0.398883
$502$	11.4641i	0.511668i
$503$	17.8564i	0.796178i	0.917347	+	0.398089i	$0.130326\pi$
$503$	17.8564i	0.796178i	−0.917347	+	0.398089i	$0.869674\pi$
$504$	0.732051	0.0326081
$505$	0	0
$506$	−22.1244	−0.983548
$507$	− 5.53590i	− 0.245858i
$508$	− 5.00000i	− 0.221839i
$509$	−13.8756	−0.615027	−0.307514	−	0.951544i	$-0.599497\pi$
$509$	−13.8756	−0.615027	−0.307514	+	0.951544i	$0.599497\pi$
$510$	0	0
$511$	−1.80385	−0.0797975
$512$	1.00000i	0.0441942i
$513$	1.00000i	0.0441511i
$514$	9.00000	0.396973
$515$	0	0
$516$	8.19615	0.360815
$517$	− 12.9282i	− 0.568582i
$518$	1.46410i	0.0643289i
$519$	13.5885	0.596467
$520$	0	0
$521$	24.1769	1.05921	0.529605	−	0.848244i	$-0.322340\pi$
$521$	24.1769	1.05921	0.529605	+	0.848244i	$0.322340\pi$
$522$	− 1.73205i	− 0.0758098i
$523$	− 4.00000i	− 0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$	− 4.00000i	− 0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	−10.2679	−0.448557
$525$	0	0
$526$	−15.0000	−0.654031
$527$	− 15.2679i	− 0.665082i
$528$	− 3.73205i	− 0.162417i
$529$	−12.1436	−0.527982
$530$	0	0
$531$	−8.19615	−0.355683
$532$	0.732051i	0.0317384i
$533$	8.00000i	0.346518i
$534$	−10.8564	−0.469803
$535$	0	0
$536$	0.267949	0.0115736
$537$	− 12.0000i	− 0.517838i
$538$	20.5359i	0.885365i
$539$	24.1244	1.03911
$540$	0	0
$541$	17.1962	0.739320	0.369660	−	0.929167i	$-0.379474\pi$
$541$	17.1962	0.739320	0.369660	+	0.929167i	$0.379474\pi$
$542$	− 15.8038i	− 0.678833i
$543$	16.5885i	0.711879i
$544$	−6.19615	−0.265658
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	− 43.4449i	− 1.85757i	−0.370621	−	0.928784i	$-0.620855\pi$
$547$	− 43.4449i	− 1.85757i	0.370621	−	0.928784i	$-0.379145\pi$
$548$	− 12.3923i	− 0.529373i
$549$	−10.6603	−0.454969
$550$	0	0
$551$	1.73205	0.0737878
$552$	− 5.92820i	− 0.252321i
$553$	− 4.05256i	− 0.172332i
$554$	11.1962	0.475679
$555$	0	0
$556$	−21.1244	−0.895872
$557$	− 3.80385i	− 0.161174i	−0.996748	−	0.0805871i	$-0.974320\pi$
$557$	− 3.80385i	− 0.161174i	0.996748	−	0.0805871i	$-0.0256795\pi$
$558$	2.46410i	0.104314i
$559$	−22.3923	−0.947094
$560$	0	0
$561$	23.1244	0.976311
$562$	17.7846i	0.750198i
$563$	7.66025i	0.322841i	0.986886	+	0.161421i	$0.0516076\pi$
$563$	7.66025i	0.322841i	−0.986886	+	0.161421i	$0.948392\pi$
$564$	3.46410	0.145865
$565$	0	0
$566$	−4.00000	−0.168133
$567$	− 0.732051i	− 0.0307432i
$568$	− 12.1962i	− 0.511739i
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	−6.19615	−0.259301	−0.129650	−	0.991560i	$-0.541386\pi$
$571$	−6.19615	−0.259301	−0.129650	+	0.991560i	$0.541386\pi$
$572$	10.1962i	0.426323i
$573$	− 3.00000i	− 0.125327i
$574$	−2.14359	−0.0894719
$575$	0	0
$576$	1.00000	0.0416667
$577$	17.2487i	0.718073i	0.933323	+	0.359037i	$0.116895\pi$
$577$	17.2487i	0.718073i	−0.933323	+	0.359037i	$0.883105\pi$
$578$	− 21.3923i	− 0.889803i
$579$	22.0526	0.916473
$580$	0	0
$581$	2.73205	0.113345
$582$	15.1244i	0.626925i
$583$	− 6.46410i	− 0.267716i
$584$	−2.46410	−0.101965
$585$	0	0
$586$	27.7321	1.14560
$587$	12.2679i	0.506352i	0.967420	+	0.253176i	$0.0814752\pi$
$587$	12.2679i	0.506352i	−0.967420	+	0.253176i	$0.918525\pi$
$588$	6.46410i	0.266575i
$589$	−2.46410	−0.101532
$590$	0	0
$591$	−24.5885	−1.01143
$592$	2.00000i	0.0821995i
$593$	− 27.6077i	− 1.13371i	−0.823817	−	0.566856i	$-0.808160\pi$
$593$	− 27.6077i	− 1.13371i	0.823817	−	0.566856i	$-0.191840\pi$
$594$	−3.73205	−0.153128
$595$	0	0
$596$	−21.8564	−0.895273
$597$	− 14.0000i	− 0.572982i
$598$	16.1962i	0.662310i
$599$	3.66025	0.149554	0.0747770	−	0.997200i	$-0.476176\pi$
$599$	3.66025	0.149554	0.0747770	+	0.997200i	$0.476176\pi$
$600$	0	0
$601$	−10.0526	−0.410052	−0.205026	−	0.978756i	$-0.565728\pi$
$601$	−10.0526	−0.410052	−0.205026	+	0.978756i	$0.565728\pi$
$602$	− 6.00000i	− 0.244542i
$603$	− 0.267949i	− 0.0109117i
$604$	11.4641	0.466468
$605$	0	0
$606$	9.26795	0.376485
$607$	11.7846i	0.478323i	0.970980	+	0.239161i	$0.0768725\pi$
$607$	11.7846i	0.478323i	−0.970980	+	0.239161i	$0.923128\pi$
$608$	1.00000i	0.0405554i
$609$	−1.26795	−0.0513799
$610$	0	0
$611$	−9.46410	−0.382877
$612$	6.19615i	0.250465i
$613$	38.7846i	1.56650i	0.621710	+	0.783248i	$0.286438\pi$
$613$	38.7846i	1.56650i	−0.621710	+	0.783248i	$0.713562\pi$
$614$	−20.2679	−0.817948
$615$	0	0
$616$	−2.73205	−0.110077
$617$	− 46.3923i	− 1.86768i	−0.357686	−	0.933842i	$-0.616434\pi$
$617$	− 46.3923i	− 1.86768i	0.357686	−	0.933842i	$-0.383566\pi$
$618$	− 3.53590i	− 0.142235i
$619$	0.196152	0.00788403	0.00394202	−	0.999992i	$-0.498745\pi$
$619$	0.196152	0.00788403	0.00394202	+	0.999992i	$0.498745\pi$
$620$	0	0
$621$	−5.92820	−0.237891
$622$	− 29.3205i	− 1.17565i
$623$	7.94744i	0.318408i
$624$	−2.73205	−0.109370
$625$	0	0
$626$	3.92820	0.157003
$627$	− 3.73205i	− 0.149044i
$628$	13.8564i	0.552931i
$629$	−12.3923	−0.494114
$630$	0	0
$631$	2.92820	0.116570	0.0582850	−	0.998300i	$-0.481437\pi$
$631$	2.92820	0.116570	0.0582850	+	0.998300i	$0.481437\pi$
$632$	− 5.53590i	− 0.220206i
$633$	10.2679i	0.408114i
$634$	−1.73205	−0.0687885
$635$	0	0
$636$	1.73205	0.0686803
$637$	− 17.6603i	− 0.699725i
$638$	6.46410i	0.255916i
$639$	−12.1962	−0.482472
$640$	0	0
$641$	10.5359	0.416143	0.208071	−	0.978114i	$-0.433281\pi$
$641$	10.5359	0.416143	0.208071	+	0.978114i	$0.433281\pi$
$642$	− 2.19615i	− 0.0866752i
$643$	27.0718i	1.06761i	0.845608	+	0.533804i	$0.179238\pi$
$643$	27.0718i	1.06761i	−0.845608	+	0.533804i	$0.820762\pi$
$644$	−4.33975	−0.171010
$645$	0	0
$646$	−6.19615	−0.243784
$647$	− 9.39230i	− 0.369250i	−0.982809	−	0.184625i	$-0.940893\pi$
$647$	− 9.39230i	− 0.369250i	0.982809	−	0.184625i	$-0.0591070\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	30.5885	1.20070
$650$	0	0
$651$	1.80385	0.0706984
$652$	2.00000i	0.0783260i
$653$	− 17.4641i	− 0.683423i	−0.939805	−	0.341712i	$-0.888993\pi$
$653$	− 17.4641i	− 0.683423i	0.939805	−	0.341712i	$-0.111007\pi$
$654$	−2.39230	−0.0935465
$655$	0	0
$656$	−2.92820	−0.114327
$657$	2.46410i	0.0961338i
$658$	− 2.53590i	− 0.0988596i
$659$	−7.41154	−0.288713	−0.144356	−	0.989526i	$-0.546111\pi$
$659$	−7.41154	−0.288713	−0.144356	+	0.989526i	$0.546111\pi$
$660$	0	0
$661$	−22.6410	−0.880633	−0.440317	−	0.897843i	$-0.645134\pi$
$661$	−22.6410	−0.880633	−0.440317	+	0.897843i	$0.645134\pi$
$662$	− 22.2679i	− 0.865468i
$663$	− 16.9282i	− 0.657437i
$664$	3.73205	0.144832
$665$	0	0
$666$	2.00000	0.0774984
$667$	10.2679i	0.397577i
$668$	− 8.92820i	− 0.345443i
$669$	−3.53590	−0.136706
$670$	0	0
$671$	39.7846	1.53587
$672$	− 0.732051i	− 0.0282395i
$673$	6.98076i	0.269089i	0.990908	+	0.134544i	$0.0429571\pi$
$673$	6.98076i	0.269089i	−0.990908	+	0.134544i	$0.957043\pi$
$674$	10.5359	0.405828
$675$	0	0
$676$	−5.53590	−0.212919
$677$	8.66025i	0.332841i	0.986055	+	0.166420i	$0.0532208\pi$
$677$	8.66025i	0.332841i	−0.986055	+	0.166420i	$0.946779\pi$
$678$	− 13.3923i	− 0.514328i
$679$	11.0718	0.424897
$680$	0	0
$681$	6.00000	0.229920
$682$	− 9.19615i	− 0.352139i
$683$	46.9808i	1.79767i	0.438288	+	0.898834i	$0.355585\pi$
$683$	46.9808i	1.79767i	−0.438288	+	0.898834i	$0.644415\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	9.85641	0.376319
$687$	− 6.26795i	− 0.239137i
$688$	− 8.19615i	− 0.312475i
$689$	−4.73205	−0.180277
$690$	0	0
$691$	−22.1962	−0.844381	−0.422191	−	0.906507i	$-0.638739\pi$
$691$	−22.1962	−0.844381	−0.422191	+	0.906507i	$0.638739\pi$
$692$	− 13.5885i	− 0.516556i
$693$	2.73205i	0.103782i
$694$	−20.7846	−0.788973
$695$	0	0
$696$	−1.73205	−0.0656532
$697$	− 18.1436i	− 0.687238i
$698$	17.0526i	0.645449i
$699$	−21.1244	−0.798997
$700$	0	0
$701$	3.60770	0.136261	0.0681304	−	0.997676i	$-0.478297\pi$
$701$	3.60770	0.136261	0.0681304	+	0.997676i	$0.478297\pi$
$702$	2.73205i	0.103115i
$703$	2.00000i	0.0754314i
$704$	−3.73205	−0.140657
$705$	0	0
$706$	−16.0526	−0.604146
$707$	− 6.78461i	− 0.255162i
$708$	8.19615i	0.308030i
$709$	−47.3013	−1.77644	−0.888218	−	0.459422i	$-0.848057\pi$
$709$	−47.3013	−1.77644	−0.888218	+	0.459422i	$0.848057\pi$
$710$	0	0
$711$	−5.53590	−0.207612
$712$	10.8564i	0.406861i
$713$	− 14.6077i	− 0.547062i
$714$	4.53590	0.169752
$715$	0	0
$716$	−12.0000	−0.448461
$717$	− 14.0000i	− 0.522840i
$718$	16.9282i	0.631755i
$719$	−12.1769	−0.454122	−0.227061	−	0.973881i	$-0.572912\pi$
$719$	−12.1769	−0.454122	−0.227061	+	0.973881i	$0.572912\pi$
$720$	0	0
$721$	−2.58846	−0.0963992
$722$	1.00000i	0.0372161i
$723$	30.1962i	1.12301i
$724$	16.5885	0.616505
$725$	0	0
$726$	2.92820	0.108676
$727$	38.1051i	1.41324i	0.707593	+	0.706620i	$0.249781\pi$
$727$	38.1051i	1.41324i	−0.707593	+	0.706620i	$0.750219\pi$
$728$	2.00000i	0.0741249i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	50.7846	1.87834
$732$	10.6603i	0.394014i
$733$	− 20.5167i	− 0.757800i	−0.925438	−	0.378900i	$-0.876302\pi$
$733$	− 20.5167i	− 0.757800i	0.925438	−	0.378900i	$-0.123698\pi$
$734$	−13.2679	−0.489729
$735$	0	0
$736$	−5.92820	−0.218516
$737$	1.00000i	0.0368355i
$738$	2.92820i	0.107789i
$739$	53.1769	1.95614	0.978072	−	0.208266i	$-0.0667820\pi$
$739$	53.1769	1.95614	0.978072	+	0.208266i	$0.0667820\pi$
$740$	0	0
$741$	−2.73205	−0.100364
$742$	− 1.26795i	− 0.0465479i
$743$	− 5.07180i	− 0.186066i	−0.995663	−	0.0930331i	$-0.970344\pi$
$743$	− 5.07180i	− 0.186066i	0.995663	−	0.0930331i	$-0.0296562\pi$
$744$	2.46410	0.0903383
$745$	0	0
$746$	31.5167	1.15391
$747$	− 3.73205i	− 0.136549i
$748$	− 23.1244i	− 0.845510i
$749$	−1.60770	−0.0587439
$750$	0	0
$751$	7.46410	0.272369	0.136184	−	0.990683i	$-0.456516\pi$
$751$	7.46410	0.272369	0.136184	+	0.990683i	$0.456516\pi$
$752$	− 3.46410i	− 0.126323i
$753$	− 11.4641i	− 0.417775i
$754$	4.73205	0.172331
$755$	0	0
$756$	−0.732051	−0.0266244
$757$	13.5885i	0.493881i	0.969031	+	0.246940i	$0.0794252\pi$
$757$	13.5885i	0.493881i	−0.969031	+	0.246940i	$0.920575\pi$
$758$	0.392305i	0.0142492i
$759$	22.1244	0.803063
$760$	0	0
$761$	1.26795	0.0459631	0.0229816	−	0.999736i	$-0.492684\pi$
$761$	1.26795	0.0459631	0.0229816	+	0.999736i	$0.492684\pi$
$762$	5.00000i	0.181131i
$763$	1.75129i	0.0634009i
$764$	−3.00000	−0.108536
$765$	0	0
$766$	19.5167	0.705166
$767$	− 22.3923i	− 0.808539i
$768$	− 1.00000i	− 0.0360844i
$769$	34.7128	1.25178	0.625888	−	0.779913i	$-0.284737\pi$
$769$	34.7128	1.25178	0.625888	+	0.779913i	$0.284737\pi$
$770$	0	0
$771$	−9.00000	−0.324127
$772$	− 22.0526i	− 0.793689i
$773$	− 45.3205i	− 1.63007i	−0.579415	−	0.815033i	$-0.696719\pi$
$773$	− 45.3205i	− 1.63007i	0.579415	−	0.815033i	$-0.303281\pi$
$774$	−8.19615	−0.294605
$775$	0	0
$776$	15.1244	0.542933
$777$	− 1.46410i	− 0.0525244i
$778$	− 21.7128i	− 0.778442i
$779$	−2.92820	−0.104914
$780$	0	0
$781$	45.5167	1.62871
$782$	− 36.7321i	− 1.31354i
$783$	1.73205i	0.0618984i
$784$	6.46410	0.230861
$785$	0	0
$786$	10.2679	0.366246
$787$	− 2.12436i	− 0.0757251i	−0.999283	−	0.0378626i	$-0.987945\pi$
$787$	− 2.12436i	− 0.0757251i	0.999283	−	0.0378626i	$-0.0120549\pi$
$788$	24.5885i	0.875928i
$789$	15.0000	0.534014
$790$	0	0
$791$	−9.80385	−0.348585
$792$	3.73205i	0.132613i
$793$	− 29.1244i	− 1.03424i
$794$	11.7321	0.416355
$795$	0	0
$796$	−14.0000	−0.496217
$797$	− 20.0000i	− 0.708436i	−0.935163	−	0.354218i	$-0.884747\pi$
$797$	− 20.0000i	− 0.708436i	0.935163	−	0.354218i	$-0.115253\pi$
$798$	− 0.732051i	− 0.0259143i
$799$	21.4641	0.759345
$800$	0	0
$801$	10.8564	0.383592
$802$	16.8564i	0.595220i
$803$	− 9.19615i	− 0.324525i
$804$	−0.267949	−0.00944984
$805$	0	0
$806$	−6.73205	−0.237126
$807$	− 20.5359i	− 0.722898i
$808$	− 9.26795i	− 0.326045i
$809$	−37.5167	−1.31902	−0.659508	−	0.751698i	$-0.729235\pi$
$809$	−37.5167	−1.31902	−0.659508	+	0.751698i	$0.729235\pi$
$810$	0	0
$811$	18.3731	0.645166	0.322583	−	0.946541i	$-0.395449\pi$
$811$	18.3731	0.645166	0.322583	+	0.946541i	$0.395449\pi$
$812$	1.26795i	0.0444963i
$813$	15.8038i	0.554265i
$814$	−7.46410	−0.261617
$815$	0	0
$816$	6.19615	0.216909
$817$	− 8.19615i	− 0.286747i
$818$	− 1.60770i	− 0.0562117i
$819$	2.00000	0.0698857
$820$	0	0
$821$	2.48334	0.0866691	0.0433346	−	0.999061i	$-0.486202\pi$
$821$	2.48334	0.0866691	0.0433346	+	0.999061i	$0.486202\pi$
$822$	12.3923i	0.432231i
$823$	− 6.78461i	− 0.236497i	−0.992984	−	0.118248i	$-0.962272\pi$
$823$	− 6.78461i	− 0.236497i	0.992984	−	0.118248i	$-0.0377279\pi$
$824$	−3.53590	−0.123179
$825$	0	0
$826$	6.00000	0.208767
$827$	− 6.73205i	− 0.234096i	−0.993126	−	0.117048i	$-0.962657\pi$
$827$	− 6.73205i	− 0.234096i	0.993126	−	0.117048i	$-0.0373432\pi$
$828$	5.92820i	0.206019i
$829$	−6.19615	−0.215201	−0.107601	−	0.994194i	$-0.534317\pi$
$829$	−6.19615	−0.215201	−0.107601	+	0.994194i	$0.534317\pi$
$830$	0	0
$831$	−11.1962	−0.388390
$832$	2.73205i	0.0947168i
$833$	40.0526i	1.38774i
$834$	21.1244	0.731477
$835$	0	0
$836$	−3.73205	−0.129076
$837$	− 2.46410i	− 0.0851718i
$838$	− 13.8564i	− 0.478662i
$839$	46.5885	1.60841	0.804206	−	0.594351i	$-0.202591\pi$
$839$	46.5885	1.60841	0.804206	+	0.594351i	$0.202591\pi$
$840$	0	0
$841$	−26.0000	−0.896552
$842$	6.78461i	0.233813i
$843$	− 17.7846i	− 0.612534i
$844$	10.2679	0.353437
$845$	0	0
$846$	−3.46410	−0.119098
$847$	− 2.14359i	− 0.0736547i
$848$	− 1.73205i	− 0.0594789i
$849$	4.00000	0.137280
$850$	0	0
$851$	−11.8564	−0.406432
$852$	12.1962i	0.417833i
$853$	− 4.53590i	− 0.155306i	−0.996980	−	0.0776531i	$-0.975257\pi$
$853$	− 4.53590i	− 0.155306i	0.996980	−	0.0776531i	$-0.0247427\pi$
$854$	7.80385	0.267042
$855$	0	0
$856$	−2.19615	−0.0750629
$857$	42.9282i	1.46640i	0.680013	+	0.733200i	$0.261974\pi$
$857$	42.9282i	1.46640i	−0.680013	+	0.733200i	$0.738026\pi$
$858$	− 10.1962i	− 0.348091i
$859$	−56.9282	−1.94237	−0.971183	−	0.238337i	$-0.923398\pi$
$859$	−56.9282	−1.94237	−0.971183	+	0.238337i	$0.923398\pi$
$860$	0	0
$861$	2.14359	0.0730535
$862$	− 29.3205i	− 0.998660i
$863$	− 55.3205i	− 1.88313i	−0.336829	−	0.941566i	$-0.609354\pi$
$863$	− 55.3205i	− 1.88313i	0.336829	−	0.941566i	$-0.390646\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−24.1962	−0.822219
$867$	21.3923i	0.726521i
$868$	− 1.80385i	− 0.0612266i
$869$	20.6603	0.700851
$870$	0	0
$871$	0.732051	0.0248046
$872$	2.39230i	0.0810137i
$873$	− 15.1244i	− 0.511882i
$874$	−5.92820	−0.200524
$875$	0	0
$876$	2.46410	0.0832543
$877$	− 31.1769i	− 1.05277i	−0.850246	−	0.526385i	$-0.823547\pi$
$877$	− 31.1769i	− 1.05277i	0.850246	−	0.526385i	$-0.176453\pi$
$878$	− 25.7846i	− 0.870188i
$879$	−27.7321	−0.935379
$880$	0	0
$881$	−26.5359	−0.894017	−0.447009	−	0.894530i	$-0.647511\pi$
$881$	−26.5359	−0.894017	−0.447009	+	0.894530i	$0.647511\pi$
$882$	− 6.46410i	− 0.217658i
$883$	27.2679i	0.917640i	0.888529	+	0.458820i	$0.151728\pi$
$883$	27.2679i	0.917640i	−0.888529	+	0.458820i	$0.848272\pi$
$884$	−16.9282	−0.569357
$885$	0	0
$886$	−3.33975	−0.112201
$887$	7.60770i	0.255441i	0.991810	+	0.127721i	$0.0407661\pi$
$887$	7.60770i	0.255441i	−0.991810	+	0.127721i	$0.959234\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	3.66025	0.122761
$890$	0	0
$891$	3.73205	0.125028
$892$	3.53590i	0.118391i
$893$	− 3.46410i	− 0.115922i
$894$	21.8564	0.730988
$895$	0	0
$896$	−0.732051	−0.0244561
$897$	− 16.1962i	− 0.540774i
$898$	− 24.4641i	− 0.816378i
$899$	−4.26795	−0.142344
$900$	0	0
$901$	10.7321	0.357536
$902$	− 10.9282i	− 0.363869i
$903$	6.00000i	0.199667i
$904$	−13.3923	−0.445421
$905$	0	0
$906$	−11.4641	−0.380869
$907$	− 49.3205i	− 1.63766i	−0.574036	−	0.818830i	$-0.694623\pi$
$907$	− 49.3205i	− 1.63766i	0.574036	−	0.818830i	$-0.305377\pi$
$908$	− 6.00000i	− 0.199117i
$909$	−9.26795	−0.307398
$910$	0	0
$911$	34.1051	1.12995	0.564976	−	0.825107i	$-0.308885\pi$
$911$	34.1051	1.12995	0.564976	+	0.825107i	$0.308885\pi$
$912$	− 1.00000i	− 0.0331133i
$913$	13.9282i	0.460956i
$914$	5.07180	0.167760
$915$	0	0
$916$	−6.26795	−0.207099
$917$	− 7.51666i	− 0.248222i
$918$	− 6.19615i	− 0.204504i
$919$	4.48334	0.147892	0.0739459	−	0.997262i	$-0.476441\pi$
$919$	4.48334	0.147892	0.0739459	+	0.997262i	$0.476441\pi$
$920$	0	0
$921$	20.2679	0.667852
$922$	− 17.8564i	− 0.588069i
$923$	− 33.3205i	− 1.09676i
$924$	2.73205	0.0898779
$925$	0	0
$926$	−35.3205	−1.16070
$927$	3.53590i	0.116134i
$928$	1.73205i	0.0568574i
$929$	−42.9282	−1.40843	−0.704214	−	0.709987i	$-0.748701\pi$
$929$	−42.9282	−1.40843	−0.704214	+	0.709987i	$0.748701\pi$
$930$	0	0
$931$	6.46410	0.211852
$932$	21.1244i	0.691951i
$933$	29.3205i	0.959910i
$934$	−7.19615	−0.235465
$935$	0	0
$936$	2.73205	0.0892999
$937$	13.2154i	0.431728i	0.976423	+	0.215864i	$0.0692568\pi$
$937$	13.2154i	0.431728i	−0.976423	+	0.215864i	$0.930743\pi$
$938$	0.196152i	0.00640460i
$939$	−3.92820	−0.128192
$940$	0	0
$941$	−12.2679	−0.399924	−0.199962	−	0.979804i	$-0.564082\pi$
$941$	−12.2679	−0.399924	−0.199962	+	0.979804i	$0.564082\pi$
$942$	− 13.8564i	− 0.451466i
$943$	− 17.3590i	− 0.565286i
$944$	8.19615	0.266762
$945$	0	0
$946$	30.5885	0.994517
$947$	− 5.85641i	− 0.190308i	−0.995463	−	0.0951538i	$-0.969666\pi$
$947$	− 5.85641i	− 0.190308i	0.995463	−	0.0951538i	$-0.0303343\pi$
$948$	5.53590i	0.179798i
$949$	−6.73205	−0.218532
$950$	0	0
$951$	1.73205	0.0561656
$952$	− 4.53590i	− 0.147009i
$953$	5.24871i	0.170022i	0.996380	+	0.0850112i	$0.0270926\pi$
$953$	5.24871i	0.170022i	−0.996380	+	0.0850112i	$0.972907\pi$
$954$	−1.73205	−0.0560772
$955$	0	0
$956$	−14.0000	−0.452792
$957$	− 6.46410i	− 0.208955i
$958$	− 3.14359i	− 0.101565i
$959$	9.07180	0.292944
$960$	0	0
$961$	−24.9282	−0.804136
$962$	5.46410i	0.176170i
$963$	2.19615i	0.0707700i
$964$	30.1962	0.972553
$965$	0	0
$966$	4.33975	0.139629
$967$	18.1051i	0.582221i	0.956689	+	0.291111i	$0.0940248\pi$
$967$	18.1051i	0.582221i	−0.956689	+	0.291111i	$0.905975\pi$
$968$	− 2.92820i	− 0.0941160i
$969$	6.19615	0.199049
$970$	0	0
$971$	−37.7654	−1.21195	−0.605974	−	0.795484i	$-0.707217\pi$
$971$	−37.7654	−1.21195	−0.605974	+	0.795484i	$0.707217\pi$
$972$	1.00000i	0.0320750i
$973$	− 15.4641i	− 0.495756i
$974$	−2.14359	−0.0686852
$975$	0	0
$976$	10.6603	0.341226
$977$	− 1.46410i	− 0.0468408i	−0.999726	−	0.0234204i	$-0.992544\pi$
$977$	− 1.46410i	− 0.0468408i	0.999726	−	0.0234204i	$-0.00745562\pi$
$978$	− 2.00000i	− 0.0639529i
$979$	−40.5167	−1.29492
$980$	0	0
$981$	2.39230	0.0763804
$982$	− 2.92820i	− 0.0934427i
$983$	30.3397i	0.967688i	0.875154	+	0.483844i	$0.160760\pi$
$983$	30.3397i	0.967688i	−0.875154	+	0.483844i	$0.839240\pi$
$984$	2.92820	0.0933477
$985$	0	0
$986$	−10.7321	−0.341778
$987$	2.53590i	0.0807185i
$988$	2.73205i	0.0869181i
$989$	48.5885	1.54502
$990$	0	0
$991$	−40.3205	−1.28082	−0.640412	−	0.768032i	$-0.721236\pi$
$991$	−40.3205	−1.28082	−0.640412	+	0.768032i	$0.721236\pi$
$992$	− 2.46410i	− 0.0782353i
$993$	22.2679i	0.706652i
$994$	8.92820	0.283185
$995$	0	0
$996$	−3.73205	−0.118255
$997$	− 63.0526i	− 1.99689i	−0.0557047	−	0.998447i	$-0.517741\pi$
$997$	− 63.0526i	− 1.99689i	0.0557047	−	0.998447i	$-0.482259\pi$
$998$	− 41.3731i	− 1.30964i
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.d.x.799.3		4
5.2	odd	4		2850.2.a.bd.1.2	✓	2
5.3	odd	4		2850.2.a.bi.1.1	yes	2
5.4	even	2	inner	2850.2.d.x.799.2		4
15.2	even	4		8550.2.a.by.1.2		2
15.8	even	4		8550.2.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bd.1.2	✓	2	5.2	odd	4
2850.2.a.bi.1.1	yes	2	5.3	odd	4
2850.2.d.x.799.2		4	5.4	even	2	inner
2850.2.d.x.799.3		4	1.1	even	1	trivial
8550.2.a.bs.1.1		2	15.8	even	4
8550.2.a.by.1.2		2	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -0.732051i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -0.732051i q^{7} -1.00000i q^{8} -1.00000 q^{9} +3.73205 q^{11} +1.00000i q^{12} -2.73205i q^{13} +0.732051 q^{14} +1.00000 q^{16} +6.19615i q^{17} -1.00000i q^{18} +1.00000 q^{19} -0.732051 q^{21} +3.73205i q^{22} +5.92820i q^{23} -1.00000 q^{24} +2.73205 q^{26} +1.00000i q^{27} +0.732051i q^{28} +1.73205 q^{29} -2.46410 q^{31} +1.00000i q^{32} -3.73205i q^{33} -6.19615 q^{34} +1.00000 q^{36} +2.00000i q^{37} +1.00000i q^{38} -2.73205 q^{39} -2.92820 q^{41} -0.732051i q^{42} -8.19615i q^{43} -3.73205 q^{44} -5.92820 q^{46} -3.46410i q^{47} -1.00000i q^{48} +6.46410 q^{49} +6.19615 q^{51} +2.73205i q^{52} -1.73205i q^{53} -1.00000 q^{54} -0.732051 q^{56} -1.00000i q^{57} +1.73205i q^{58} +8.19615 q^{59} +10.6603 q^{61} -2.46410i q^{62} +0.732051i q^{63} -1.00000 q^{64} +3.73205 q^{66} +0.267949i q^{67} -6.19615i q^{68} +5.92820 q^{69} +12.1962 q^{71} +1.00000i q^{72} -2.46410i q^{73} -2.00000 q^{74} -1.00000 q^{76} -2.73205i q^{77} -2.73205i q^{78} +5.53590 q^{79} +1.00000 q^{81} -2.92820i q^{82} +3.73205i q^{83} +0.732051 q^{84} +8.19615 q^{86} -1.73205i q^{87} -3.73205i q^{88} -10.8564 q^{89} -2.00000 q^{91} -5.92820i q^{92} +2.46410i q^{93} +3.46410 q^{94} +1.00000 q^{96} +15.1244i q^{97} +6.46410i q^{98} -3.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} - 4 q^{24} + 4 q^{26} + 4 q^{31} - 4 q^{34} + 4 q^{36} - 4 q^{39} + 16 q^{41} - 8 q^{44} + 4 q^{46} + 12 q^{49} + 4 q^{51} - 4 q^{54} + 4 q^{56} + 12 q^{59} + 8 q^{61} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 28 q^{71} - 8 q^{74} - 4 q^{76} + 36 q^{79} + 4 q^{81} - 4 q^{84} + 12 q^{86} + 12 q^{89} - 8 q^{91} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 - 4 * q^24 + 4 * q^26 + 4 * q^31 - 4 * q^34 + 4 * q^36 - 4 * q^39 + 16 * q^41 - 8 * q^44 + 4 * q^46 + 12 * q^49 + 4 * q^51 - 4 * q^54 + 4 * q^56 + 12 * q^59 + 8 * q^61 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 28 * q^71 - 8 * q^74 - 4 * q^76 + 36 * q^79 + 4 * q^81 - 4 * q^84 + 12 * q^86 + 12 * q^89 - 8 * q^91 + 4 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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