LMFDB - Embedded newform 3850.2.c.z.1849.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3182656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 25x^{2} - 10x + 2 $ x^6 - 2x^3 + 25x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.6
Root			$-1.67298 - 1.67298i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.z.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +3.34596i q^{3} -1.00000 q^{4} -3.34596 q^{6} +1.00000i q^{7} -1.00000i q^{8} -8.19547 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +3.34596i q^{3} -1.00000 q^{4} -3.34596 q^{6} +1.00000i q^{7} -1.00000i q^{8} -8.19547 q^{9} +1.00000 q^{11} -3.34596i q^{12} +6.69193i q^{13} -1.00000 q^{14} +1.00000 q^{16} +7.19547i q^{17} -8.19547i q^{18} +1.84951 q^{19} -3.34596 q^{21} +1.00000i q^{22} +1.84951i q^{23} +3.34596 q^{24} -6.69193 q^{26} -17.3839i q^{27} -1.00000i q^{28} -6.84242 q^{29} +6.00000 q^{31} +1.00000i q^{32} +3.34596i q^{33} -7.19547 q^{34} +8.19547 q^{36} +6.54143i q^{37} +1.84951i q^{38} -22.3909 q^{39} -9.34596 q^{41} -3.34596i q^{42} +0.503544i q^{43} -1.00000 q^{44} -1.84951 q^{46} +1.49646i q^{47} +3.34596i q^{48} -1.00000 q^{49} -24.0758 q^{51} -6.69193i q^{52} +6.84242i q^{53} +17.3839 q^{54} +1.00000 q^{56} +6.18838i q^{57} -6.84242i q^{58} +7.88740 q^{59} +4.50354 q^{61} +6.00000i q^{62} -8.19547i q^{63} -1.00000 q^{64} -3.34596 q^{66} -8.00000i q^{67} -7.19547i q^{68} -6.18838 q^{69} +0.300986 q^{71} +8.19547i q^{72} -10.1884i q^{73} -6.54143 q^{74} -1.84951 q^{76} +1.00000i q^{77} -22.3909i q^{78} +12.2404 q^{79} +33.5793 q^{81} -9.34596i q^{82} -1.30807i q^{83} +3.34596 q^{84} -0.503544 q^{86} -22.8945i q^{87} -1.00000i q^{88} +8.69193 q^{89} -6.69193 q^{91} -1.84951i q^{92} +20.0758i q^{93} -1.49646 q^{94} -3.34596 q^{96} -3.84951i q^{97} -1.00000i q^{98} -8.19547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 22 * q^9	$ 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	3.34596i	1.93179i	0.258929	+	0.965896i	$0.416630\pi$
$3$	3.34596i	1.93179i	−0.258929	+	0.965896i	$0.583370\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−3.34596	−1.36598
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−8.19547	−2.73182
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	− 3.34596i	− 0.965896i
$13$	6.69193i	1.85601i	0.372572	+	0.928003i	$0.378476\pi$
$13$	6.69193i	1.85601i	−0.372572	+	0.928003i	$0.621524\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	7.19547i	1.74516i	0.488473	+	0.872579i	$0.337554\pi$
$17$	7.19547i	1.74516i	−0.488473	+	0.872579i	$0.662446\pi$
$18$	− 8.19547i	− 1.93169i
$19$	1.84951	0.424306	0.212153	−	0.977236i	$-0.431952\pi$
$19$	1.84951	0.424306	0.212153	+	0.977236i	$0.431952\pi$
$20$	0	0
$21$	−3.34596	−0.730149
$22$	1.00000i	0.213201i
$23$	1.84951i	0.385649i	0.981233	+	0.192824i	$0.0617648\pi$
$23$	1.84951i	0.385649i	−0.981233	+	0.192824i	$0.938235\pi$
$24$	3.34596	0.682992
$25$	0	0
$26$	−6.69193	−1.31239
$27$	− 17.3839i	− 3.34552i
$28$	− 1.00000i	− 0.188982i
$29$	−6.84242	−1.27061	−0.635303	−	0.772263i	$-0.719125\pi$
$29$	−6.84242	−1.27061	−0.635303	+	0.772263i	$0.719125\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000i	0.176777i
$33$	3.34596i	0.582457i
$34$	−7.19547	−1.23401
$35$	0	0
$36$	8.19547	1.36591
$37$	6.54143i	1.07541i	0.843135	+	0.537703i	$0.180708\pi$
$37$	6.54143i	1.07541i	−0.843135	+	0.537703i	$0.819292\pi$
$38$	1.84951i	0.300030i
$39$	−22.3909	−3.58542
$40$	0	0
$41$	−9.34596	−1.45959	−0.729797	−	0.683664i	$-0.760385\pi$
$41$	−9.34596	−1.45959	−0.729797	+	0.683664i	$0.760385\pi$
$42$	− 3.34596i	− 0.516293i
$43$	0.503544i	0.0767897i	0.999263	+	0.0383949i	$0.0122245\pi$
$43$	0.503544i	0.0767897i	−0.999263	+	0.0383949i	$0.987776\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.84951	−0.272695
$47$	1.49646i	0.218281i	0.994026	+	0.109140i	$0.0348098\pi$
$47$	1.49646i	0.218281i	−0.994026	+	0.109140i	$0.965190\pi$
$48$	3.34596i	0.482948i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−24.0758	−3.37128
$52$	− 6.69193i	− 0.928003i
$53$	6.84242i	0.939879i	0.882699	+	0.469939i	$0.155724\pi$
$53$	6.84242i	0.939879i	−0.882699	+	0.469939i	$0.844276\pi$
$54$	17.3839	2.36564
$55$	0	0
$56$	1.00000	0.133631
$57$	6.18838i	0.819671i
$58$	− 6.84242i	− 0.898454i
$59$	7.88740	1.02685	0.513426	−	0.858134i	$-0.328376\pi$
$59$	7.88740	1.02685	0.513426	+	0.858134i	$0.328376\pi$
$60$	0	0
$61$	4.50354	0.576620	0.288310	−	0.957537i	$-0.406907\pi$
$61$	4.50354	0.576620	0.288310	+	0.957537i	$0.406907\pi$
$62$	6.00000i	0.762001i
$63$	− 8.19547i	− 1.03253i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−3.34596	−0.411860
$67$	− 8.00000i	− 0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$	− 8.00000i	− 0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$	− 7.19547i	− 0.872579i
$69$	−6.18838	−0.744994
$70$	0	0
$71$	0.300986	0.0357204	0.0178602	−	0.999840i	$-0.494315\pi$
$71$	0.300986	0.0357204	0.0178602	+	0.999840i	$0.494315\pi$
$72$	8.19547i	0.965845i
$73$	− 10.1884i	− 1.19246i	−0.802814	−	0.596230i	$-0.796665\pi$
$73$	− 10.1884i	− 1.19246i	0.802814	−	0.596230i	$-0.203335\pi$
$74$	−6.54143	−0.760426
$75$	0	0
$76$	−1.84951	−0.212153
$77$	1.00000i	0.113961i
$78$	− 22.3909i	− 2.53527i
$79$	12.2404	1.37716	0.688579	−	0.725161i	$-0.258235\pi$
$79$	12.2404	1.37716	0.688579	+	0.725161i	$0.258235\pi$
$80$	0	0
$81$	33.5793	3.73104
$82$	− 9.34596i	− 1.03209i
$83$	− 1.30807i	− 0.143580i	−0.997420	−	0.0717899i	$-0.977129\pi$
$83$	− 1.30807i	− 0.143580i	0.997420	−	0.0717899i	$-0.0228711\pi$
$84$	3.34596	0.365075
$85$	0	0
$86$	−0.503544	−0.0542985
$87$	− 22.8945i	− 2.45455i
$88$	− 1.00000i	− 0.106600i
$89$	8.69193	0.921342	0.460671	−	0.887571i	$-0.347609\pi$
$89$	8.69193	0.921342	0.460671	+	0.887571i	$0.347609\pi$
$90$	0	0
$91$	−6.69193	−0.701505
$92$	− 1.84951i	− 0.192824i
$93$	20.0758i	2.08176i
$94$	−1.49646	−0.154348
$95$	0	0
$96$	−3.34596	−0.341496
$97$	− 3.84951i	− 0.390858i	−0.980718	−	0.195429i	$-0.937390\pi$
$97$	− 3.84951i	− 0.390858i	0.980718	−	0.195429i	$-0.0626100\pi$
$98$	− 1.00000i	− 0.101015i
$99$	−8.19547	−0.823676
$100$	0	0
$101$	6.89448	0.686027	0.343013	−	0.939331i	$-0.388552\pi$
$101$	6.89448	0.686027	0.343013	+	0.939331i	$0.388552\pi$
$102$	− 24.0758i	− 2.38386i
$103$	− 10.5793i	− 1.04241i	−0.853431	−	0.521206i	$-0.825482\pi$
$103$	− 10.5793i	− 1.04241i	0.853431	−	0.521206i	$-0.174518\pi$
$104$	6.69193	0.656197
$105$	0	0
$106$	−6.84242	−0.664595
$107$	7.49646i	0.724710i	0.932040	+	0.362355i	$0.118027\pi$
$107$	7.49646i	0.724710i	−0.932040	+	0.362355i	$0.881973\pi$
$108$	17.3839i	1.67276i
$109$	−1.45857	−0.139705	−0.0698527	−	0.997557i	$-0.522253\pi$
$109$	−1.45857	−0.139705	−0.0698527	+	0.997557i	$0.522253\pi$
$110$	0	0
$111$	−21.8874	−2.07746
$112$	1.00000i	0.0944911i
$113$	− 14.0000i	− 1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	− 14.0000i	− 1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−6.18838	−0.579595
$115$	0	0
$116$	6.84242	0.635303
$117$	− 54.8435i	− 5.07028i
$118$	7.88740i	0.726094i
$119$	−7.19547	−0.659608
$120$	0	0
$121$	1.00000	0.0909091
$122$	4.50354i	0.407732i
$123$	− 31.2713i	− 2.81963i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	8.19547	0.730111
$127$	19.7748i	1.75473i	0.479824	+	0.877365i	$0.340700\pi$
$127$	19.7748i	1.75473i	−0.479824	+	0.877365i	$0.659300\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.68484	−0.148342
$130$	0	0
$131$	2.15049	0.187889	0.0939447	−	0.995577i	$-0.470052\pi$
$131$	2.15049	0.187889	0.0939447	+	0.995577i	$0.470052\pi$
$132$	− 3.34596i	− 0.291229i
$133$	1.84951i	0.160373i
$134$	8.00000	0.691095
$135$	0	0
$136$	7.19547	0.617006
$137$	8.39094i	0.716886i	0.933552	+	0.358443i	$0.116692\pi$
$137$	8.39094i	0.716886i	−0.933552	+	0.358443i	$0.883308\pi$
$138$	− 6.18838i	− 0.526790i
$139$	−17.9253	−1.52040	−0.760201	−	0.649687i	$-0.774900\pi$
$139$	−17.9253	−1.52040	−0.760201	+	0.649687i	$0.774900\pi$
$140$	0	0
$141$	−5.00709	−0.421673
$142$	0.300986i	0.0252582i
$143$	6.69193i	0.559607i
$144$	−8.19547	−0.682956
$145$	0	0
$146$	10.1884	0.843197
$147$	− 3.34596i	− 0.275970i
$148$	− 6.54143i	− 0.537703i
$149$	0.451479	0.0369866	0.0184933	−	0.999829i	$-0.494113\pi$
$149$	0.451479	0.0369866	0.0184933	+	0.999829i	$0.494113\pi$
$150$	0	0
$151$	19.2334	1.56519	0.782594	−	0.622532i	$-0.213896\pi$
$151$	19.2334	1.56519	0.782594	+	0.622532i	$0.213896\pi$
$152$	− 1.84951i	− 0.150015i
$153$	− 58.9703i	− 4.76746i
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	22.3909	1.79271
$157$	9.69901i	0.774066i	0.922066	+	0.387033i	$0.126500\pi$
$157$	9.69901i	0.774066i	−0.922066	+	0.387033i	$0.873500\pi$
$158$	12.2404i	0.973798i
$159$	−22.8945	−1.81565
$160$	0	0
$161$	−1.84951	−0.145762
$162$	33.5793i	2.63824i
$163$	− 8.00000i	− 0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$	− 8.00000i	− 0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$	9.34596	0.729797
$165$	0	0
$166$	1.30807	0.101526
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	3.34596i	0.258147i
$169$	−31.7819	−2.44476
$170$	0	0
$171$	−15.1576	−1.15913
$172$	− 0.503544i	− 0.0383949i
$173$	− 15.4965i	− 1.17817i	−0.808070	−	0.589087i	$-0.799488\pi$
$173$	− 15.4965i	− 1.17817i	0.808070	−	0.589087i	$-0.200512\pi$
$174$	22.8945	1.73563
$175$	0	0
$176$	1.00000	0.0753778
$177$	26.3909i	1.98366i
$178$	8.69193i	0.651487i
$179$	13.8874	1.03799	0.518996	−	0.854776i	$-0.326306\pi$
$179$	13.8874	1.03799	0.518996	+	0.854776i	$0.326306\pi$
$180$	0	0
$181$	18.7819	1.39605	0.698023	−	0.716075i	$-0.254063\pi$
$181$	18.7819	1.39605	0.698023	+	0.716075i	$0.254063\pi$
$182$	− 6.69193i	− 0.496039i
$183$	15.0687i	1.11391i
$184$	1.84951	0.136347
$185$	0	0
$186$	−20.0758	−1.47203
$187$	7.19547i	0.526185i
$188$	− 1.49646i	− 0.109140i
$189$	17.3839	1.26449
$190$	0	0
$191$	−6.39094	−0.462432	−0.231216	−	0.972902i	$-0.574270\pi$
$191$	−6.39094	−0.462432	−0.231216	+	0.972902i	$0.574270\pi$
$192$	− 3.34596i	− 0.241474i
$193$	− 13.1955i	− 0.949831i	−0.880031	−	0.474915i	$-0.842479\pi$
$193$	− 13.1955i	− 0.949831i	0.880031	−	0.474915i	$-0.157521\pi$
$194$	3.84951	0.276379
$195$	0	0
$196$	1.00000	0.0714286
$197$	4.69193i	0.334286i	0.985933	+	0.167143i	$0.0534541\pi$
$197$	4.69193i	0.334286i	−0.985933	+	0.167143i	$0.946546\pi$
$198$	− 8.19547i	− 0.582427i
$199$	9.49646	0.673186	0.336593	−	0.941650i	$-0.390725\pi$
$199$	9.49646	0.673186	0.336593	+	0.941650i	$0.390725\pi$
$200$	0	0
$201$	26.7677	1.88805
$202$	6.89448i	0.485094i
$203$	− 6.84242i	− 0.480244i
$204$	24.0758	1.68564
$205$	0	0
$206$	10.5793	0.737096
$207$	− 15.1576i	− 1.05352i
$208$	6.69193i	0.464002i
$209$	1.84951	0.127933
$210$	0	0
$211$	−2.39094	−0.164599	−0.0822996	−	0.996608i	$-0.526226\pi$
$211$	−2.39094	−0.164599	−0.0822996	+	0.996608i	$0.526226\pi$
$212$	− 6.84242i	− 0.469939i
$213$	1.00709i	0.0690045i
$214$	−7.49646	−0.512447
$215$	0	0
$216$	−17.3839	−1.18282
$217$	6.00000i	0.407307i
$218$	− 1.45857i	− 0.0987866i
$219$	34.0900	2.30359
$220$	0	0
$221$	−48.1516	−3.23902
$222$	− 21.8874i	− 1.46899i
$223$	0.188383i	0.0126150i	0.999980	+	0.00630752i	$0.00200776\pi$
$223$	0.188383i	0.0126150i	−0.999980	+	0.00630752i	$0.997992\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	14.0000	0.931266
$227$	6.99291i	0.464136i	0.972700	+	0.232068i	$0.0745492\pi$
$227$	6.99291i	0.464136i	−0.972700	+	0.232068i	$0.925451\pi$
$228$	− 6.18838i	− 0.409836i
$229$	9.19547	0.607654	0.303827	−	0.952727i	$-0.401736\pi$
$229$	9.19547	0.607654	0.303827	+	0.952727i	$0.401736\pi$
$230$	0	0
$231$	−3.34596	−0.220148
$232$	6.84242i	0.449227i
$233$	− 0.992912i	− 0.0650479i	−0.999471	−	0.0325239i	$-0.989645\pi$
$233$	− 0.992912i	− 0.0650479i	0.999471	−	0.0325239i	$-0.0103545\pi$
$234$	54.8435	3.58523
$235$	0	0
$236$	−7.88740	−0.513426
$237$	40.9561i	2.66038i
$238$	− 7.19547i	− 0.466413i
$239$	1.14341	0.0739607	0.0369804	−	0.999316i	$-0.488226\pi$
$239$	1.14341	0.0739607	0.0369804	+	0.999316i	$0.488226\pi$
$240$	0	0
$241$	8.33888	0.537154	0.268577	−	0.963258i	$-0.413447\pi$
$241$	8.33888	0.537154	0.268577	+	0.963258i	$0.413447\pi$
$242$	1.00000i	0.0642824i
$243$	60.2036i	3.86206i
$244$	−4.50354	−0.288310
$245$	0	0
$246$	31.2713	1.99378
$247$	12.3768i	0.787515i
$248$	− 6.00000i	− 0.381000i
$249$	4.37677	0.277366
$250$	0	0
$251$	23.8874	1.50776	0.753880	−	0.657013i	$-0.228180\pi$
$251$	23.8874	1.50776	0.753880	+	0.657013i	$0.228180\pi$
$252$	8.19547i	0.516266i
$253$	1.84951i	0.116278i
$254$	−19.7748	−1.24078
$255$	0	0
$256$	1.00000	0.0625000
$257$	31.6243i	1.97267i	0.164753	+	0.986335i	$0.447317\pi$
$257$	31.6243i	1.97267i	−0.164753	+	0.986335i	$0.552683\pi$
$258$	− 1.68484i	− 0.104893i
$259$	−6.54143	−0.406465
$260$	0	0
$261$	56.0768	3.47107
$262$	2.15049i	0.132858i
$263$	13.3839i	0.825284i	0.910893	+	0.412642i	$0.135394\pi$
$263$	13.3839i	0.825284i	−0.910893	+	0.412642i	$0.864606\pi$
$264$	3.34596	0.205930
$265$	0	0
$266$	−1.84951	−0.113401
$267$	29.0829i	1.77984i
$268$	8.00000i	0.488678i
$269$	−5.79744	−0.353476	−0.176738	−	0.984258i	$-0.556555\pi$
$269$	−5.79744	−0.353476	−0.176738	+	0.984258i	$0.556555\pi$
$270$	0	0
$271$	−20.0758	−1.21952	−0.609758	−	0.792587i	$-0.708734\pi$
$271$	−20.0758	−1.21952	−0.609758	+	0.792587i	$0.708734\pi$
$272$	7.19547i	0.436289i
$273$	− 22.3909i	− 1.35516i
$274$	−8.39094	−0.506915
$275$	0	0
$276$	6.18838	0.372497
$277$	− 22.0000i	− 1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$	− 22.0000i	− 1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$	− 17.9253i	− 1.07509i
$279$	−49.1728	−2.94390
$280$	0	0
$281$	−6.30099	−0.375885	−0.187943	−	0.982180i	$-0.560182\pi$
$281$	−6.30099	−0.375885	−0.187943	+	0.982180i	$0.560182\pi$
$282$	− 5.00709i	− 0.298168i
$283$	22.3909i	1.33100i	0.746396	+	0.665502i	$0.231782\pi$
$283$	22.3909i	1.33100i	−0.746396	+	0.665502i	$0.768218\pi$
$284$	−0.300986	−0.0178602
$285$	0	0
$286$	−6.69193	−0.395702
$287$	− 9.34596i	− 0.551675i
$288$	− 8.19547i	− 0.482923i
$289$	−34.7748	−2.04558
$290$	0	0
$291$	12.8803	0.755057
$292$	10.1884i	0.596230i
$293$	− 10.6919i	− 0.624629i	−0.949979	−	0.312315i	$-0.898896\pi$
$293$	− 10.6919i	− 0.624629i	0.949979	−	0.312315i	$-0.101104\pi$
$294$	3.34596	0.195141
$295$	0	0
$296$	6.54143	0.380213
$297$	− 17.3839i	− 1.00871i
$298$	0.451479i	0.0261535i
$299$	−12.3768	−0.715767
$300$	0	0
$301$	−0.503544	−0.0290238
$302$	19.2334i	1.10676i
$303$	23.0687i	1.32526i
$304$	1.84951	0.106077
$305$	0	0
$306$	58.9703	3.37111
$307$	9.08287i	0.518387i	0.965825	+	0.259193i	$0.0834567\pi$
$307$	9.08287i	0.518387i	−0.965825	+	0.259193i	$0.916543\pi$
$308$	− 1.00000i	− 0.0569803i
$309$	35.3980	2.01372
$310$	0	0
$311$	−11.3839	−0.645519	−0.322760	−	0.946481i	$-0.604611\pi$
$311$	−11.3839	−0.645519	−0.322760	+	0.946481i	$0.604611\pi$
$312$	22.3909i	1.26764i
$313$	− 23.6243i	− 1.33532i	−0.744464	−	0.667662i	$-0.767295\pi$
$313$	− 23.6243i	− 1.33532i	0.744464	−	0.667662i	$-0.232705\pi$
$314$	−9.69901	−0.547347
$315$	0	0
$316$	−12.2404	−0.688579
$317$	9.53435i	0.535502i	0.963488	+	0.267751i	$0.0862805\pi$
$317$	9.53435i	0.535502i	−0.963488	+	0.267751i	$0.913720\pi$
$318$	− 22.8945i	− 1.28386i
$319$	−6.84242	−0.383102
$320$	0	0
$321$	−25.0829	−1.39999
$322$	− 1.84951i	− 0.103069i
$323$	13.3081i	0.740481i
$324$	−33.5793	−1.86552
$325$	0	0
$326$	8.00000	0.443079
$327$	− 4.88031i	− 0.269882i
$328$	9.34596i	0.516044i
$329$	−1.49646	−0.0825023
$330$	0	0
$331$	0.503544	0.0276773	0.0138386	−	0.999904i	$-0.495595\pi$
$331$	0.503544	0.0276773	0.0138386	+	0.999904i	$0.495595\pi$
$332$	1.30807i	0.0717899i
$333$	− 53.6101i	− 2.93782i
$334$	8.00000	0.437741
$335$	0	0
$336$	−3.34596	−0.182537
$337$	− 12.3909i	− 0.674978i	−0.941330	−	0.337489i	$-0.890422\pi$
$337$	− 12.3909i	− 0.674978i	0.941330	−	0.337489i	$-0.109578\pi$
$338$	− 31.7819i	− 1.72871i
$339$	46.8435	2.54419
$340$	0	0
$341$	6.00000	0.324918
$342$	− 15.1576i	− 0.819628i
$343$	− 1.00000i	− 0.0539949i
$344$	0.503544	0.0271493
$345$	0	0
$346$	15.4965	0.833095
$347$	− 20.8803i	− 1.12091i	−0.828184	−	0.560457i	$-0.810626\pi$
$347$	− 20.8803i	− 1.12091i	0.828184	−	0.560457i	$-0.189374\pi$
$348$	22.8945i	1.22727i
$349$	22.1884	1.18772	0.593858	−	0.804570i	$-0.297604\pi$
$349$	22.1884	1.18772	0.593858	+	0.804570i	$0.297604\pi$
$350$	0	0
$351$	116.331	6.20931
$352$	1.00000i	0.0533002i
$353$	− 31.6243i	− 1.68319i	−0.540108	−	0.841596i	$-0.681617\pi$
$353$	− 31.6243i	− 1.68319i	0.540108	−	0.841596i	$-0.318383\pi$
$354$	−26.3909	−1.40266
$355$	0	0
$356$	−8.69193	−0.460671
$357$	− 24.0758i	− 1.27423i
$358$	13.8874i	0.733972i
$359$	−30.5273	−1.61117	−0.805584	−	0.592482i	$-0.798148\pi$
$359$	−30.5273	−1.61117	−0.805584	+	0.592482i	$0.798148\pi$
$360$	0	0
$361$	−15.5793	−0.819964
$362$	18.7819i	0.987154i
$363$	3.34596i	0.175618i
$364$	6.69193	0.350752
$365$	0	0
$366$	−15.0687	−0.787653
$367$	10.5793i	0.552236i	0.961124	+	0.276118i	$0.0890481\pi$
$367$	10.5793i	0.552236i	−0.961124	+	0.276118i	$0.910952\pi$
$368$	1.84951i	0.0964122i
$369$	76.5946	3.98735
$370$	0	0
$371$	−6.84242	−0.355241
$372$	− 20.0758i	− 1.04088i
$373$	36.4667i	1.88818i	0.329695	+	0.944088i	$0.393054\pi$
$373$	36.4667i	1.88818i	−0.329695	+	0.944088i	$0.606946\pi$
$374$	−7.19547	−0.372069
$375$	0	0
$376$	1.49646	0.0771738
$377$	− 45.7890i	− 2.35825i
$378$	17.3839i	0.894129i
$379$	−14.9929	−0.770134	−0.385067	−	0.922889i	$-0.625822\pi$
$379$	−14.9929	−0.770134	−0.385067	+	0.922889i	$0.625822\pi$
$380$	0	0
$381$	−66.1657	−3.38977
$382$	− 6.39094i	− 0.326989i
$383$	35.1813i	1.79768i	0.438277	+	0.898840i	$0.355589\pi$
$383$	35.1813i	1.79768i	−0.438277	+	0.898840i	$0.644411\pi$
$384$	3.34596	0.170748
$385$	0	0
$386$	13.1955	0.671632
$387$	− 4.12678i	− 0.209776i
$388$	3.84951i	0.195429i
$389$	−2.30099	−0.116665	−0.0583323	−	0.998297i	$-0.518578\pi$
$389$	−2.30099	−0.116665	−0.0583323	+	0.998297i	$0.518578\pi$
$390$	0	0
$391$	−13.3081	−0.673018
$392$	1.00000i	0.0505076i
$393$	7.19547i	0.362963i
$394$	−4.69193	−0.236376
$395$	0	0
$396$	8.19547	0.411838
$397$	− 18.0758i	− 0.907197i	−0.891206	−	0.453599i	$-0.850140\pi$
$397$	− 18.0758i	− 0.907197i	0.891206	−	0.453599i	$-0.149860\pi$
$398$	9.49646i	0.476014i
$399$	−6.18838	−0.309807
$400$	0	0
$401$	22.5793	1.12756	0.563779	−	0.825926i	$-0.309347\pi$
$401$	22.5793	1.12756	0.563779	+	0.825926i	$0.309347\pi$
$402$	26.7677i	1.33505i
$403$	40.1516i	2.00009i
$404$	−6.89448	−0.343013
$405$	0	0
$406$	6.84242	0.339584
$407$	6.54143i	0.324247i
$408$	24.0758i	1.19193i
$409$	−1.04498	−0.0516708	−0.0258354	−	0.999666i	$-0.508225\pi$
$409$	−1.04498	−0.0516708	−0.0258354	+	0.999666i	$0.508225\pi$
$410$	0	0
$411$	−28.0758	−1.38488
$412$	10.5793i	0.521206i
$413$	7.88740i	0.388113i
$414$	15.1576	0.744954
$415$	0	0
$416$	−6.69193	−0.328099
$417$	− 59.9774i	− 2.93710i
$418$	1.84951i	0.0904623i
$419$	−5.49646	−0.268519	−0.134260	−	0.990946i	$-0.542866\pi$
$419$	−5.49646	−0.268519	−0.134260	+	0.990946i	$0.542866\pi$
$420$	0	0
$421$	2.60197	0.126812	0.0634062	−	0.997988i	$-0.479804\pi$
$421$	2.60197	0.126812	0.0634062	+	0.997988i	$0.479804\pi$
$422$	− 2.39094i	− 0.116389i
$423$	− 12.2642i	− 0.596304i
$424$	6.84242	0.332297
$425$	0	0
$426$	−1.00709	−0.0487936
$427$	4.50354i	0.217942i
$428$	− 7.49646i	− 0.362355i
$429$	−22.3909	−1.08104
$430$	0	0
$431$	19.2334	0.926438	0.463219	−	0.886244i	$-0.346694\pi$
$431$	19.2334	0.926438	0.463219	+	0.886244i	$0.346694\pi$
$432$	− 17.3839i	− 0.836381i
$433$	− 8.93237i	− 0.429263i	−0.976695	−	0.214631i	$-0.931145\pi$
$433$	− 8.93237i	− 0.429263i	0.976695	−	0.214631i	$-0.0688550\pi$
$434$	−6.00000	−0.288009
$435$	0	0
$436$	1.45857	0.0698527
$437$	3.42068i	0.163633i
$438$	34.0900i	1.62888i
$439$	0.300986	0.0143653	0.00718264	−	0.999974i	$-0.497714\pi$
$439$	0.300986	0.0143653	0.00718264	+	0.999974i	$0.497714\pi$
$440$	0	0
$441$	8.19547	0.390260
$442$	− 48.1516i	− 2.29034i
$443$	30.7677i	1.46182i	0.682475	+	0.730909i	$0.260904\pi$
$443$	30.7677i	1.46182i	−0.682475	+	0.730909i	$0.739096\pi$
$444$	21.8874	1.03873
$445$	0	0
$446$	−0.188383	−0.00892018
$447$	1.51063i	0.0714504i
$448$	− 1.00000i	− 0.0472456i
$449$	1.19547	0.0564177	0.0282089	−	0.999602i	$-0.491020\pi$
$449$	1.19547	0.0564177	0.0282089	+	0.999602i	$0.491020\pi$
$450$	0	0
$451$	−9.34596	−0.440084
$452$	14.0000i	0.658505i
$453$	64.3541i	3.02362i
$454$	−6.99291	−0.328194
$455$	0	0
$456$	6.18838	0.289798
$457$	25.7748i	1.20569i	0.797857	+	0.602847i	$0.205967\pi$
$457$	25.7748i	1.20569i	−0.797857	+	0.602847i	$0.794033\pi$
$458$	9.19547i	0.429676i
$459$	125.085	5.83847
$460$	0	0
$461$	11.5722	0.538973	0.269486	−	0.963004i	$-0.413146\pi$
$461$	11.5722	0.538973	0.269486	+	0.963004i	$0.413146\pi$
$462$	− 3.34596i	− 0.155668i
$463$	− 32.9182i	− 1.52984i	−0.644126	−	0.764919i	$-0.722779\pi$
$463$	− 32.9182i	− 1.52984i	0.644126	−	0.764919i	$-0.277221\pi$
$464$	−6.84242	−0.317651
$465$	0	0
$466$	0.992912	0.0459958
$467$	14.6399i	0.677452i	0.940885	+	0.338726i	$0.109996\pi$
$467$	14.6399i	0.677452i	−0.940885	+	0.338726i	$0.890004\pi$
$468$	54.8435i	2.53514i
$469$	8.00000	0.369406
$470$	0	0
$471$	−32.4525	−1.49533
$472$	− 7.88740i	− 0.363047i
$473$	0.503544i	0.0231530i
$474$	−40.9561	−1.88118
$475$	0	0
$476$	7.19547	0.329804
$477$	− 56.0768i	− 2.56758i
$478$	1.14341i	0.0522981i
$479$	−10.3909	−0.474774	−0.237387	−	0.971415i	$-0.576291\pi$
$479$	−10.3909	−0.474774	−0.237387	+	0.971415i	$0.576291\pi$
$480$	0	0
$481$	−43.7748	−1.99596
$482$	8.33888i	0.379825i
$483$	− 6.18838i	− 0.281581i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	−60.2036	−2.73089
$487$	− 39.3091i	− 1.78127i	−0.454722	−	0.890634i	$-0.650261\pi$
$487$	− 39.3091i	− 1.78127i	0.454722	−	0.890634i	$-0.349739\pi$
$488$	− 4.50354i	− 0.203866i
$489$	26.7677	1.21048
$490$	0	0
$491$	23.7748	1.07294	0.536471	−	0.843919i	$-0.319757\pi$
$491$	23.7748	1.07294	0.536471	+	0.843919i	$0.319757\pi$
$492$	31.2713i	1.40982i
$493$	− 49.2344i	− 2.21741i
$494$	−12.3768	−0.556857
$495$	0	0
$496$	6.00000	0.269408
$497$	0.300986i	0.0135011i
$498$	4.37677i	0.196128i
$499$	6.11260	0.273638	0.136819	−	0.990596i	$-0.456312\pi$
$499$	6.11260	0.273638	0.136819	+	0.990596i	$0.456312\pi$
$500$	0	0
$501$	26.7677	1.19589
$502$	23.8874i	1.06615i
$503$	− 13.1586i	− 0.586715i	−0.956003	−	0.293358i	$-0.905227\pi$
$503$	− 13.1586i	− 0.586715i	0.956003	−	0.293358i	$-0.0947726\pi$
$504$	−8.19547	−0.365055
$505$	0	0
$506$	−1.84951	−0.0822206
$507$	− 106.341i	− 4.72277i
$508$	− 19.7748i	− 0.877365i
$509$	−34.1799	−1.51500	−0.757499	−	0.652836i	$-0.773579\pi$
$509$	−34.1799	−1.51500	−0.757499	+	0.652836i	$0.773579\pi$
$510$	0	0
$511$	10.1884	0.450708
$512$	1.00000i	0.0441942i
$513$	− 32.1516i	− 1.41953i
$514$	−31.6243	−1.39489
$515$	0	0
$516$	1.68484	0.0741709
$517$	1.49646i	0.0658141i
$518$	− 6.54143i	− 0.287414i
$519$	51.8506	2.27599
$520$	0	0
$521$	−26.6778	−1.16877	−0.584387	−	0.811475i	$-0.698665\pi$
$521$	−26.6778	−1.16877	−0.584387	+	0.811475i	$0.698665\pi$
$522$	56.0768i	2.45442i
$523$	25.4880i	1.11451i	0.830341	+	0.557256i	$0.188146\pi$
$523$	25.4880i	1.11451i	−0.830341	+	0.557256i	$0.811854\pi$
$524$	−2.15049	−0.0939447
$525$	0	0
$526$	−13.3839	−0.583564
$527$	43.1728i	1.88064i
$528$	3.34596i	0.145614i
$529$	19.5793	0.851275
$530$	0	0
$531$	−64.6409	−2.80518
$532$	− 1.84951i	− 0.0801863i
$533$	− 62.5425i	− 2.70902i
$534$	−29.0829	−1.25854
$535$	0	0
$536$	−8.00000	−0.345547
$537$	46.4667i	2.00519i
$538$	− 5.79744i	− 0.249945i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	4.45148	0.191384	0.0956920	−	0.995411i	$-0.469494\pi$
$541$	4.45148	0.191384	0.0956920	+	0.995411i	$0.469494\pi$
$542$	− 20.0758i	− 0.862329i
$543$	62.8435i	2.69687i
$544$	−7.19547	−0.308503
$545$	0	0
$546$	22.3909	0.958244
$547$	1.38385i	0.0591693i	0.999562	+	0.0295846i	$0.00941846\pi$
$547$	1.38385i	0.0591693i	−0.999562	+	0.0295846i	$0.990582\pi$
$548$	− 8.39094i	− 0.358443i
$549$	−36.9087	−1.57522
$550$	0	0
$551$	−12.6551	−0.539126
$552$	6.18838i	0.263395i
$553$	12.2404i	0.520517i
$554$	22.0000	0.934690
$555$	0	0
$556$	17.9253	0.760201
$557$	6.70610i	0.284147i	0.989856	+	0.142073i	$0.0453769\pi$
$557$	6.70610i	0.284147i	−0.989856	+	0.142073i	$0.954623\pi$
$558$	− 49.1728i	− 2.08165i
$559$	−3.36968	−0.142522
$560$	0	0
$561$	−24.0758	−1.01648
$562$	− 6.30099i	− 0.265791i
$563$	3.59488i	0.151506i	0.997127	+	0.0757532i	$0.0241361\pi$
$563$	3.59488i	0.151506i	−0.997127	+	0.0757532i	$0.975864\pi$
$564$	5.00709	0.210836
$565$	0	0
$566$	−22.3909	−0.941161
$567$	33.5793i	1.41020i
$568$	− 0.300986i	− 0.0126291i
$569$	−31.7606	−1.33147	−0.665737	−	0.746186i	$-0.731883\pi$
$569$	−31.7606	−1.33147	−0.665737	+	0.746186i	$0.731883\pi$
$570$	0	0
$571$	−5.68484	−0.237903	−0.118952	−	0.992900i	$-0.537953\pi$
$571$	−5.68484	−0.237903	−0.118952	+	0.992900i	$0.537953\pi$
$572$	− 6.69193i	− 0.279804i
$573$	− 21.3839i	− 0.893323i
$574$	9.34596	0.390093
$575$	0	0
$576$	8.19547	0.341478
$577$	− 13.5343i	− 0.563442i	−0.959496	−	0.281721i	$-0.909095\pi$
$577$	− 13.5343i	− 0.563442i	0.959496	−	0.281721i	$-0.0909053\pi$
$578$	− 34.7748i	− 1.44644i
$579$	44.1516	1.83488
$580$	0	0
$581$	1.30807	0.0542680
$582$	12.8803i	0.533906i
$583$	6.84242i	0.283384i
$584$	−10.1884	−0.421598
$585$	0	0
$586$	10.6919	0.441679
$587$	0.0520650i	0.00214895i	0.999999	+	0.00107448i	$0.000342017\pi$
$587$	0.0520650i	0.00214895i	−0.999999	+	0.00107448i	$0.999658\pi$
$588$	3.34596i	0.137985i
$589$	11.0970	0.457246
$590$	0	0
$591$	−15.6990	−0.645771
$592$	6.54143i	0.268851i
$593$	31.9774i	1.31315i	0.754260	+	0.656576i	$0.227996\pi$
$593$	31.9774i	1.31315i	−0.754260	+	0.656576i	$0.772004\pi$
$594$	17.3839	0.713268
$595$	0	0
$596$	−0.451479	−0.0184933
$597$	31.7748i	1.30046i
$598$	− 12.3768i	− 0.506124i
$599$	−21.0829	−0.861423	−0.430711	−	0.902490i	$-0.641737\pi$
$599$	−21.0829	−0.861423	−0.430711	+	0.902490i	$0.641737\pi$
$600$	0	0
$601$	−21.6469	−0.882997	−0.441499	−	0.897262i	$-0.645553\pi$
$601$	−21.6469	−0.882997	−0.441499	+	0.897262i	$0.645553\pi$
$602$	− 0.503544i	− 0.0205229i
$603$	65.5638i	2.66996i
$604$	−19.2334	−0.782594
$605$	0	0
$606$	−23.0687	−0.937102
$607$	− 21.6622i	− 0.879241i	−0.898184	−	0.439621i	$-0.855113\pi$
$607$	− 21.6622i	− 0.879241i	0.898184	−	0.439621i	$-0.144887\pi$
$608$	1.84951i	0.0750074i
$609$	22.8945	0.927731
$610$	0	0
$611$	−10.0142	−0.405130
$612$	58.9703i	2.38373i
$613$	8.31516i	0.335846i	0.985800	+	0.167923i	$0.0537060\pi$
$613$	8.31516i	0.335846i	−0.985800	+	0.167923i	$0.946294\pi$
$614$	−9.08287	−0.366555
$615$	0	0
$616$	1.00000	0.0402911
$617$	− 12.4667i	− 0.501891i	−0.968001	−	0.250946i	$-0.919258\pi$
$617$	− 12.4667i	− 0.501891i	0.968001	−	0.250946i	$-0.0807415\pi$
$618$	35.3980i	1.42392i
$619$	−5.27125	−0.211869	−0.105935	−	0.994373i	$-0.533783\pi$
$619$	−5.27125	−0.211869	−0.105935	+	0.994373i	$0.533783\pi$
$620$	0	0
$621$	32.1516	1.29020
$622$	− 11.3839i	− 0.456451i
$623$	8.69193i	0.348235i
$624$	−22.3909	−0.896355
$625$	0	0
$626$	23.6243	0.944217
$627$	6.18838i	0.247140i
$628$	− 9.69901i	− 0.387033i
$629$	−47.0687	−1.87675
$630$	0	0
$631$	−17.1586	−0.683075	−0.341537	−	0.939868i	$-0.610948\pi$
$631$	−17.1586	−0.683075	−0.341537	+	0.939868i	$0.610948\pi$
$632$	− 12.2404i	− 0.486899i
$633$	− 8.00000i	− 0.317971i
$634$	−9.53435	−0.378657
$635$	0	0
$636$	22.8945	0.907825
$637$	− 6.69193i	− 0.265144i
$638$	− 6.84242i	− 0.270894i
$639$	−2.46672	−0.0975820
$640$	0	0
$641$	24.7677	0.978266	0.489133	−	0.872209i	$-0.337313\pi$
$641$	24.7677	0.978266	0.489133	+	0.872209i	$0.337313\pi$
$642$	− 25.0829i	− 0.989942i
$643$	1.03080i	0.0406509i	0.999793	+	0.0203254i	$0.00647023\pi$
$643$	1.03080i	0.0406509i	−0.999793	+	0.0203254i	$0.993530\pi$
$644$	1.84951	0.0728808
$645$	0	0
$646$	−13.3081	−0.523599
$647$	− 12.7904i	− 0.502841i	−0.967878	−	0.251420i	$-0.919102\pi$
$647$	− 12.7904i	− 0.502841i	0.967878	−	0.251420i	$-0.0808977\pi$
$648$	− 33.5793i	− 1.31912i
$649$	7.88740	0.309607
$650$	0	0
$651$	−20.0758	−0.786832
$652$	8.00000i	0.313304i
$653$	− 22.3162i	− 0.873301i	−0.899631	−	0.436651i	$-0.856165\pi$
$653$	− 22.3162i	− 0.873301i	0.899631	−	0.436651i	$-0.143835\pi$
$654$	4.88031	0.190835
$655$	0	0
$656$	−9.34596	−0.364899
$657$	83.4986i	3.25759i
$658$	− 1.49646i	− 0.0583379i
$659$	−22.6919	−0.883952	−0.441976	−	0.897027i	$-0.645722\pi$
$659$	−22.6919	−0.883952	−0.441976	+	0.897027i	$0.645722\pi$
$660$	0	0
$661$	43.5638	1.69443	0.847217	−	0.531247i	$-0.178276\pi$
$661$	43.5638	1.69443	0.847217	+	0.531247i	$0.178276\pi$
$662$	0.503544i	0.0195708i
$663$	− 161.113i	− 6.25712i
$664$	−1.30807	−0.0507631
$665$	0	0
$666$	53.6101	2.07735
$667$	− 12.6551i	− 0.490008i
$668$	8.00000i	0.309529i
$669$	−0.630322	−0.0243697
$670$	0	0
$671$	4.50354	0.173857
$672$	− 3.34596i	− 0.129073i
$673$	38.0000i	1.46479i	0.680879	+	0.732396i	$0.261598\pi$
$673$	38.0000i	1.46479i	−0.680879	+	0.732396i	$0.738402\pi$
$674$	12.3909	0.477281
$675$	0	0
$676$	31.7819	1.22238
$677$	16.0984i	0.618713i	0.950946	+	0.309356i	$0.100114\pi$
$677$	16.0984i	0.618713i	−0.950946	+	0.309356i	$0.899886\pi$
$678$	46.8435i	1.79901i
$679$	3.84951	0.147731
$680$	0	0
$681$	−23.3980	−0.896614
$682$	6.00000i	0.229752i
$683$	29.0829i	1.11282i	0.830906	+	0.556412i	$0.187823\pi$
$683$	29.0829i	1.11282i	−0.830906	+	0.556412i	$0.812177\pi$
$684$	15.1576	0.579565
$685$	0	0
$686$	1.00000	0.0381802
$687$	30.7677i	1.17386i
$688$	0.503544i	0.0191974i
$689$	−45.7890	−1.74442
$690$	0	0
$691$	7.58641	0.288601	0.144300	−	0.989534i	$-0.453907\pi$
$691$	7.58641	0.288601	0.144300	+	0.989534i	$0.453907\pi$
$692$	15.4965i	0.589087i
$693$	− 8.19547i	− 0.311320i
$694$	20.8803	0.792606
$695$	0	0
$696$	−22.8945	−0.867813
$697$	− 67.2486i	− 2.54722i
$698$	22.1884i	0.839843i
$699$	3.32225	0.125659
$700$	0	0
$701$	4.07471	0.153900	0.0769499	−	0.997035i	$-0.475482\pi$
$701$	4.07471	0.153900	0.0769499	+	0.997035i	$0.475482\pi$
$702$	116.331i	4.39065i
$703$	12.0984i	0.456301i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	31.6243	1.19020
$707$	6.89448i	0.259294i
$708$	− 26.3909i	− 0.991832i
$709$	46.4525	1.74456	0.872281	−	0.489005i	$-0.162640\pi$
$709$	46.4525	1.74456	0.872281	+	0.489005i	$0.162640\pi$
$710$	0	0
$711$	−100.316	−3.76215
$712$	− 8.69193i	− 0.325744i
$713$	11.0970i	0.415588i
$714$	24.0758	0.901013
$715$	0	0
$716$	−13.8874	−0.518996
$717$	3.82579i	0.142877i
$718$	− 30.5273i	− 1.13927i
$719$	17.8732	0.666559	0.333279	−	0.942828i	$-0.391845\pi$
$719$	17.8732	0.666559	0.333279	+	0.942828i	$0.391845\pi$
$720$	0	0
$721$	10.5793	0.393995
$722$	− 15.5793i	− 0.579802i
$723$	27.9016i	1.03767i
$724$	−18.7819	−0.698023
$725$	0	0
$726$	−3.34596	−0.124180
$727$	11.8874i	0.440879i	0.975401	+	0.220440i	$0.0707492\pi$
$727$	11.8874i	0.440879i	−0.975401	+	0.220440i	$0.929251\pi$
$728$	6.69193i	0.248019i
$729$	−100.701	−3.72967
$730$	0	0
$731$	−3.62323	−0.134010
$732$	− 15.0687i	− 0.556955i
$733$	− 31.6764i	− 1.16999i	−0.811036	−	0.584997i	$-0.801096\pi$
$733$	− 31.6764i	− 1.16999i	0.811036	−	0.584997i	$-0.198904\pi$
$734$	−10.5793	−0.390490
$735$	0	0
$736$	−1.84951	−0.0681737
$737$	− 8.00000i	− 0.294684i
$738$	76.5946i	2.81948i
$739$	−28.5567	−1.05047	−0.525237	−	0.850956i	$-0.676023\pi$
$739$	−28.5567	−1.05047	−0.525237	+	0.850956i	$0.676023\pi$
$740$	0	0
$741$	−41.4122	−1.52132
$742$	− 6.84242i	− 0.251193i
$743$	13.9858i	0.513090i	0.966532	+	0.256545i	$0.0825842\pi$
$743$	13.9858i	0.513090i	−0.966532	+	0.256545i	$0.917416\pi$
$744$	20.0758	0.736014
$745$	0	0
$746$	−36.4667	−1.33514
$747$	10.7203i	0.392234i
$748$	− 7.19547i	− 0.263092i
$749$	−7.49646	−0.273915
$750$	0	0
$751$	18.9171	0.690296	0.345148	−	0.938548i	$-0.387829\pi$
$751$	18.9171	0.690296	0.345148	+	0.938548i	$0.387829\pi$
$752$	1.49646i	0.0545701i
$753$	79.9264i	2.91268i
$754$	45.7890	1.66754
$755$	0	0
$756$	−17.3839	−0.632245
$757$	− 10.9182i	− 0.396829i	−0.980118	−	0.198414i	$-0.936421\pi$
$757$	− 10.9182i	− 0.396829i	0.980118	−	0.198414i	$-0.0635792\pi$
$758$	− 14.9929i	− 0.544567i
$759$	−6.18838	−0.224624
$760$	0	0
$761$	−30.3531	−1.10030	−0.550149	−	0.835067i	$-0.685429\pi$
$761$	−30.3531	−1.10030	−0.550149	+	0.835067i	$0.685429\pi$
$762$	− 66.1657i	− 2.39693i
$763$	− 1.45857i	− 0.0528036i
$764$	6.39094	0.231216
$765$	0	0
$766$	−35.1813	−1.27115
$767$	52.7819i	1.90584i
$768$	3.34596i	0.120737i
$769$	19.7369	0.711731	0.355865	−	0.934537i	$-0.384186\pi$
$769$	19.7369	0.711731	0.355865	+	0.934537i	$0.384186\pi$
$770$	0	0
$771$	−105.814	−3.81079
$772$	13.1955i	0.474915i
$773$	− 24.3909i	− 0.877281i	−0.898663	−	0.438641i	$-0.855460\pi$
$773$	− 24.3909i	− 0.877281i	0.898663	−	0.438641i	$-0.144540\pi$
$774$	4.12678	0.148334
$775$	0	0
$776$	−3.84951	−0.138189
$777$	− 21.8874i	− 0.785206i
$778$	− 2.30099i	− 0.0824943i
$779$	−17.2854	−0.619315
$780$	0	0
$781$	0.300986	0.0107701
$782$	− 13.3081i	− 0.475896i
$783$	118.948i	4.25084i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−7.19547	−0.256654
$787$	− 33.7890i	− 1.20445i	−0.798328	−	0.602223i	$-0.794282\pi$
$787$	− 33.7890i	− 1.20445i	0.798328	−	0.602223i	$-0.205718\pi$
$788$	− 4.69193i	− 0.167143i
$789$	−44.7819	−1.59428
$790$	0	0
$791$	14.0000	0.497783
$792$	8.19547i	0.291213i
$793$	30.1374i	1.07021i
$794$	18.0758	0.641485
$795$	0	0
$796$	−9.49646	−0.336593
$797$	− 36.8435i	− 1.30506i	−0.757761	−	0.652532i	$-0.773707\pi$
$797$	− 36.8435i	− 1.30506i	0.757761	−	0.652532i	$-0.226293\pi$
$798$	− 6.18838i	− 0.219066i
$799$	−10.7677	−0.380934
$800$	0	0
$801$	−71.2344	−2.51694
$802$	22.5793i	0.797304i
$803$	− 10.1884i	− 0.359540i
$804$	−26.7677	−0.944024
$805$	0	0
$806$	−40.1516	−1.41428
$807$	− 19.3980i	− 0.682843i
$808$	− 6.89448i	− 0.242547i
$809$	−37.6990	−1.32543	−0.662713	−	0.748873i	$-0.730595\pi$
$809$	−37.6990	−1.32543	−0.662713	+	0.748873i	$0.730595\pi$
$810$	0	0
$811$	38.3304	1.34596	0.672981	−	0.739660i	$-0.265013\pi$
$811$	38.3304	1.34596	0.672981	+	0.739660i	$0.265013\pi$
$812$	6.84242i	0.240122i
$813$	− 67.1728i	− 2.35585i
$814$	−6.54143	−0.229277
$815$	0	0
$816$	−24.0758	−0.842821
$817$	0.931308i	0.0325823i
$818$	− 1.04498i	− 0.0365368i
$819$	54.8435	1.91639
$820$	0	0
$821$	−18.1363	−0.632962	−0.316481	−	0.948599i	$-0.602501\pi$
$821$	−18.1363	−0.632962	−0.316481	+	0.948599i	$0.602501\pi$
$822$	− 28.0758i	− 0.979255i
$823$	− 7.86368i	− 0.274111i	−0.990563	−	0.137055i	$-0.956236\pi$
$823$	− 7.86368i	− 0.274111i	0.990563	−	0.137055i	$-0.0437638\pi$
$824$	−10.5793	−0.368548
$825$	0	0
$826$	−7.88740	−0.274438
$827$	− 12.0000i	− 0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$	− 12.0000i	− 0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	15.1576i	0.526762i
$829$	−2.80453	−0.0974053	−0.0487027	−	0.998813i	$-0.515509\pi$
$829$	−2.80453	−0.0974053	−0.0487027	+	0.998813i	$0.515509\pi$
$830$	0	0
$831$	73.6112	2.55354
$832$	− 6.69193i	− 0.232001i
$833$	− 7.19547i	− 0.249308i
$834$	59.9774	2.07685
$835$	0	0
$836$	−1.84951	−0.0639665
$837$	− 104.303i	− 3.60524i
$838$	− 5.49646i	− 0.189872i
$839$	−36.9929	−1.27714	−0.638569	−	0.769565i	$-0.720473\pi$
$839$	−36.9929	−1.27714	−0.638569	+	0.769565i	$0.720473\pi$
$840$	0	0
$841$	17.8187	0.614438
$842$	2.60197i	0.0896699i
$843$	− 21.0829i	− 0.726133i
$844$	2.39094	0.0822996
$845$	0	0
$846$	12.2642	0.421651
$847$	1.00000i	0.0343604i
$848$	6.84242i	0.234970i
$849$	−74.9193	−2.57122
$850$	0	0
$851$	−12.0984	−0.414729
$852$	− 1.00709i	− 0.0345023i
$853$	− 49.2571i	− 1.68653i	−0.537498	−	0.843265i	$-0.680630\pi$
$853$	− 49.2571i	− 1.68653i	0.537498	−	0.843265i	$-0.319370\pi$
$854$	−4.50354	−0.154108
$855$	0	0
$856$	7.49646	0.256224
$857$	20.3541i	0.695283i	0.937627	+	0.347642i	$0.113017\pi$
$857$	20.3541i	0.695283i	−0.937627	+	0.347642i	$0.886983\pi$
$858$	− 22.3909i	− 0.764414i
$859$	34.2783	1.16956	0.584781	−	0.811191i	$-0.301180\pi$
$859$	34.2783	1.16956	0.584781	+	0.811191i	$0.301180\pi$
$860$	0	0
$861$	31.2713	1.06572
$862$	19.2334i	0.655091i
$863$	− 12.4373i	− 0.423371i	−0.977338	−	0.211685i	$-0.932105\pi$
$863$	− 12.4373i	− 0.423371i	0.977338	−	0.211685i	$-0.0678952\pi$
$864$	17.3839	0.591411
$865$	0	0
$866$	8.93237	0.303534
$867$	− 116.355i	− 3.95163i
$868$	− 6.00000i	− 0.203653i
$869$	12.2404	0.415229
$870$	0	0
$871$	53.5354	1.81398
$872$	1.45857i	0.0493933i
$873$	31.5485i	1.06776i
$874$	−3.42068	−0.115706
$875$	0	0
$876$	−34.0900	−1.15179
$877$	− 34.4809i	− 1.16434i	−0.813068	−	0.582169i	$-0.802204\pi$
$877$	− 34.4809i	− 1.16434i	0.813068	−	0.582169i	$-0.197796\pi$
$878$	0.300986i	0.0101578i
$879$	35.7748	1.20665
$880$	0	0
$881$	27.3839	0.922585	0.461293	−	0.887248i	$-0.347386\pi$
$881$	27.3839	0.922585	0.461293	+	0.887248i	$0.347386\pi$
$882$	8.19547i	0.275956i
$883$	22.0900i	0.743386i	0.928356	+	0.371693i	$0.121223\pi$
$883$	22.0900i	0.743386i	−0.928356	+	0.371693i	$0.878777\pi$
$884$	48.1516	1.61951
$885$	0	0
$886$	−30.7677	−1.03366
$887$	− 25.7890i	− 0.865909i	−0.901416	−	0.432954i	$-0.857471\pi$
$887$	− 25.7890i	− 0.865909i	0.901416	−	0.432954i	$-0.142529\pi$
$888$	21.8874i	0.734493i
$889$	−19.7748	−0.663225
$890$	0	0
$891$	33.5793	1.12495
$892$	− 0.188383i	− 0.00630752i
$893$	2.76771i	0.0926178i
$894$	−1.51063	−0.0505231
$895$	0	0
$896$	1.00000	0.0334077
$897$	− 41.4122i	− 1.38271i
$898$	1.19547i	0.0398934i
$899$	−41.0545	−1.36924
$900$	0	0
$901$	−49.2344	−1.64024
$902$	− 9.34596i	− 0.311187i
$903$	− 1.68484i	− 0.0560679i
$904$	−14.0000	−0.465633
$905$	0	0
$906$	−64.3541	−2.13802
$907$	45.4596i	1.50946i	0.656034	+	0.754731i	$0.272233\pi$
$907$	45.4596i	1.50946i	−0.656034	+	0.754731i	$0.727767\pi$
$908$	− 6.99291i	− 0.232068i
$909$	−56.5035	−1.87410
$910$	0	0
$911$	−15.8506	−0.525153	−0.262576	−	0.964911i	$-0.584572\pi$
$911$	−15.8506	−0.525153	−0.262576	+	0.964911i	$0.584572\pi$
$912$	6.18838i	0.204918i
$913$	− 1.30807i	− 0.0432909i
$914$	−25.7748	−0.852554
$915$	0	0
$916$	−9.19547	−0.303827
$917$	2.15049i	0.0710155i
$918$	125.085i	4.12842i
$919$	−18.6314	−0.614593	−0.307296	−	0.951614i	$-0.599424\pi$
$919$	−18.6314	−0.614593	−0.307296	+	0.951614i	$0.599424\pi$
$920$	0	0
$921$	−30.3909	−1.00142
$922$	11.5722i	0.381111i
$923$	2.01418i	0.0662974i
$924$	3.34596	0.110074
$925$	0	0
$926$	32.9182	1.08176
$927$	86.7025i	2.84768i
$928$	− 6.84242i	− 0.224613i
$929$	29.2486	0.959616	0.479808	−	0.877374i	$-0.340706\pi$
$929$	29.2486	0.959616	0.479808	+	0.877374i	$0.340706\pi$
$930$	0	0
$931$	−1.84951	−0.0606151
$932$	0.992912i	0.0325239i
$933$	− 38.0900i	− 1.24701i
$934$	−14.6399	−0.479031
$935$	0	0
$936$	−54.8435	−1.79262
$937$	46.4441i	1.51726i	0.651521	+	0.758631i	$0.274131\pi$
$937$	46.4441i	1.51726i	−0.651521	+	0.758631i	$0.725869\pi$
$938$	8.00000i	0.261209i
$939$	79.0460	2.57957
$940$	0	0
$941$	−39.2713	−1.28021	−0.640103	−	0.768289i	$-0.721108\pi$
$941$	−39.2713	−1.28021	−0.640103	+	0.768289i	$0.721108\pi$
$942$	− 32.4525i	− 1.05736i
$943$	− 17.2854i	− 0.562891i
$944$	7.88740	0.256713
$945$	0	0
$946$	−0.503544	−0.0163716
$947$	− 54.2415i	− 1.76261i	−0.472546	−	0.881306i	$-0.656665\pi$
$947$	− 54.2415i	− 1.76261i	0.472546	−	0.881306i	$-0.343335\pi$
$948$	− 40.9561i	− 1.33019i
$949$	68.1799	2.21321
$950$	0	0
$951$	−31.9016	−1.03448
$952$	7.19547i	0.233207i
$953$	59.3612i	1.92290i	0.274983	+	0.961449i	$0.411328\pi$
$953$	59.3612i	1.92290i	−0.274983	+	0.961449i	$0.588672\pi$
$954$	56.0768	1.81555
$955$	0	0
$956$	−1.14341	−0.0369804
$957$	− 22.8945i	− 0.740074i
$958$	− 10.3909i	− 0.335716i
$959$	−8.39094	−0.270958
$960$	0	0
$961$	5.00000	0.161290
$962$	− 43.7748i	− 1.41136i
$963$	− 61.4370i	− 1.97978i
$964$	−8.33888	−0.268577
$965$	0	0
$966$	6.18838	0.199108
$967$	18.7677i	0.603529i	0.953383	+	0.301764i	$0.0975756\pi$
$967$	18.7677i	0.603529i	−0.953383	+	0.301764i	$0.902424\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	−44.5283	−1.43046
$970$	0	0
$971$	−59.4370	−1.90742	−0.953712	−	0.300722i	$-0.902772\pi$
$971$	−59.4370	−1.90742	−0.953712	+	0.300722i	$0.902772\pi$
$972$	− 60.2036i	− 1.93103i
$973$	− 17.9253i	− 0.574658i
$974$	39.3091	1.25955
$975$	0	0
$976$	4.50354	0.144155
$977$	32.7677i	1.04833i	0.851616	+	0.524166i	$0.175623\pi$
$977$	32.7677i	1.04833i	−0.851616	+	0.524166i	$0.824377\pi$
$978$	26.7677i	0.855937i
$979$	8.69193	0.277795
$980$	0	0
$981$	11.9536	0.381650
$982$	23.7748i	0.758684i
$983$	13.4207i	0.428053i	0.976828	+	0.214027i	$0.0686579\pi$
$983$	13.4207i	0.428053i	−0.976828	+	0.214027i	$0.931342\pi$
$984$	−31.2713	−0.996891
$985$	0	0
$986$	49.2344	1.56794
$987$	− 5.00709i	− 0.159377i
$988$	− 12.3768i	− 0.393757i
$989$	−0.931308	−0.0296139
$990$	0	0
$991$	−38.1657	−1.21237	−0.606187	−	0.795322i	$-0.707302\pi$
$991$	−38.1657	−1.21237	−0.606187	+	0.795322i	$0.707302\pi$
$992$	6.00000i	0.190500i
$993$	1.68484i	0.0534668i
$994$	−0.300986	−0.00954669
$995$	0	0
$996$	−4.37677	−0.138683
$997$	33.6622i	1.06609i	0.846086	+	0.533046i	$0.178953\pi$
$997$	33.6622i	1.06609i	−0.846086	+	0.533046i	$0.821047\pi$
$998$	6.11260i	0.193491i
$999$	113.715	3.59779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.z.1849.6		6
5.2	odd	4		770.2.a.l.1.3	✓	3
5.3	odd	4		3850.2.a.bu.1.1		3
5.4	even	2	inner	3850.2.c.z.1849.1		6
15.2	even	4		6930.2.a.cl.1.3		3
20.7	even	4		6160.2.a.bi.1.1		3
35.27	even	4		5390.2.a.bz.1.1		3
55.32	even	4		8470.2.a.cl.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.l.1.3	✓	3	5.2	odd	4
3850.2.a.bu.1.1		3	5.3	odd	4
3850.2.c.z.1849.1		6	5.4	even	2	inner
3850.2.c.z.1849.6		6	1.1	even	1	trivial
5390.2.a.bz.1.1		3	35.27	even	4
6160.2.a.bi.1.1		3	20.7	even	4
6930.2.a.cl.1.3		3	15.2	even	4
8470.2.a.cl.1.3		3	55.32	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +3.34596i q^{3} -1.00000 q^{4} -3.34596 q^{6} +1.00000i q^{7} -1.00000i q^{8} -8.19547 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +3.34596i q^{3} -1.00000 q^{4} -3.34596 q^{6} +1.00000i q^{7} -1.00000i q^{8} -8.19547 q^{9} +1.00000 q^{11} -3.34596i q^{12} +6.69193i q^{13} -1.00000 q^{14} +1.00000 q^{16} +7.19547i q^{17} -8.19547i q^{18} +1.84951 q^{19} -3.34596 q^{21} +1.00000i q^{22} +1.84951i q^{23} +3.34596 q^{24} -6.69193 q^{26} -17.3839i q^{27} -1.00000i q^{28} -6.84242 q^{29} +6.00000 q^{31} +1.00000i q^{32} +3.34596i q^{33} -7.19547 q^{34} +8.19547 q^{36} +6.54143i q^{37} +1.84951i q^{38} -22.3909 q^{39} -9.34596 q^{41} -3.34596i q^{42} +0.503544i q^{43} -1.00000 q^{44} -1.84951 q^{46} +1.49646i q^{47} +3.34596i q^{48} -1.00000 q^{49} -24.0758 q^{51} -6.69193i q^{52} +6.84242i q^{53} +17.3839 q^{54} +1.00000 q^{56} +6.18838i q^{57} -6.84242i q^{58} +7.88740 q^{59} +4.50354 q^{61} +6.00000i q^{62} -8.19547i q^{63} -1.00000 q^{64} -3.34596 q^{66} -8.00000i q^{67} -7.19547i q^{68} -6.18838 q^{69} +0.300986 q^{71} +8.19547i q^{72} -10.1884i q^{73} -6.54143 q^{74} -1.84951 q^{76} +1.00000i q^{77} -22.3909i q^{78} +12.2404 q^{79} +33.5793 q^{81} -9.34596i q^{82} -1.30807i q^{83} +3.34596 q^{84} -0.503544 q^{86} -22.8945i q^{87} -1.00000i q^{88} +8.69193 q^{89} -6.69193 q^{91} -1.84951i q^{92} +20.0758i q^{93} -1.49646 q^{94} -3.34596 q^{96} -3.84951i q^{97} -1.00000i q^{98} -8.19547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 22 * q^9	\( 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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