LMFDB - Embedded newform 1850.2.b.p.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.37161216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 15x^{4} + 51x^{2} + 1 $ x^6 + 15x^4 + 51x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$-2.27307i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.p.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.27307i q^{3} -1.00000 q^{4} -2.27307 q^{6} +1.27307i q^{7} +1.00000i q^{8} -2.16686 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.27307i q^{3} -1.00000 q^{4} -2.27307 q^{6} +1.27307i q^{7} +1.00000i q^{8} -2.16686 q^{9} -4.43993 q^{11} +2.27307i q^{12} +5.27307i q^{13} +1.27307 q^{14} +1.00000 q^{16} -0.273073i q^{17} +2.16686i q^{18} +5.71301 q^{19} +2.89379 q^{21} +4.43993i q^{22} +6.54615i q^{23} +2.27307 q^{24} +5.27307 q^{26} -1.89379i q^{27} -1.27307i q^{28} -0.546146 q^{29} -5.98608 q^{31} -1.00000i q^{32} +10.0923i q^{33} -0.273073 q^{34} +2.16686 q^{36} -1.00000i q^{37} -5.71301i q^{38} +11.9861 q^{39} +11.8799 q^{41} -2.89379i q^{42} +10.3793i q^{43} +4.43993 q^{44} +6.54615 q^{46} -2.27307i q^{48} +5.37929 q^{49} -0.620715 q^{51} -5.27307i q^{52} -2.33372i q^{53} -1.89379 q^{54} -1.27307 q^{56} -12.9861i q^{57} +0.546146i q^{58} -2.37929 q^{59} +11.8192 q^{61} +5.98608i q^{62} -2.75857i q^{63} -1.00000 q^{64} +10.0923 q^{66} +7.15294i q^{67} +0.273073i q^{68} +14.8799 q^{69} +5.60679 q^{71} -2.16686i q^{72} +9.71301i q^{73} -1.00000 q^{74} -5.71301 q^{76} -5.65236i q^{77} -11.9861i q^{78} -11.4260 q^{79} -10.8053 q^{81} -11.8799i q^{82} -3.89379i q^{83} -2.89379 q^{84} +10.3793 q^{86} +1.24143i q^{87} -4.43993i q^{88} -13.8659 q^{89} -6.71301 q^{91} -6.54615i q^{92} +13.6068i q^{93} -2.27307 q^{96} +0.879866i q^{97} -5.37929i q^{98} +9.62071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{6} - 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^6 - 12 * q^9	$ 6 q - 6 q^{4} + 2 q^{6} - 12 q^{9} - 10 q^{11} - 8 q^{14} + 6 q^{16} + 2 q^{19} + 32 q^{21} - 2 q^{24} + 16 q^{26} + 28 q^{29} + 12 q^{31} + 14 q^{34} + 12 q^{36} + 24 q^{39} + 38 q^{41} + 10 q^{44} + 8 q^{46} + 2 q^{49} - 34 q^{51} - 26 q^{54} + 8 q^{56} + 16 q^{59} + 24 q^{61} - 6 q^{64} - 2 q^{66} + 56 q^{69} + 16 q^{71} - 6 q^{74} - 2 q^{76} - 4 q^{79} + 30 q^{81} - 32 q^{84} + 32 q^{86} - 2 q^{89} - 8 q^{91} + 2 q^{96} + 88 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^6 - 12 * q^9 - 10 * q^11 - 8 * q^14 + 6 * q^16 + 2 * q^19 + 32 * q^21 - 2 * q^24 + 16 * q^26 + 28 * q^29 + 12 * q^31 + 14 * q^34 + 12 * q^36 + 24 * q^39 + 38 * q^41 + 10 * q^44 + 8 * q^46 + 2 * q^49 - 34 * q^51 - 26 * q^54 + 8 * q^56 + 16 * q^59 + 24 * q^61 - 6 * q^64 - 2 * q^66 + 56 * q^69 + 16 * q^71 - 6 * q^74 - 2 * q^76 - 4 * q^79 + 30 * q^81 - 32 * q^84 + 32 * q^86 - 2 * q^89 - 8 * q^91 + 2 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 2.27307i	− 1.31236i	−0.754605	−	0.656180i	$-0.772171\pi$
$3$	− 2.27307i	− 1.31236i	0.754605	−	0.656180i	$-0.227829\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2.27307	−0.927978
$7$	1.27307i	0.481176i	0.970627	+	0.240588i	$0.0773403\pi$
$7$	1.27307i	0.481176i	−0.970627	+	0.240588i	$0.922660\pi$
$8$	1.00000i	0.353553i
$9$	−2.16686	−0.722287
$10$	0	0
$11$	−4.43993	−1.33869	−0.669345	−	0.742952i	$-0.733425\pi$
$11$	−4.43993	−1.33869	−0.669345	+	0.742952i	$0.733425\pi$
$12$	2.27307i	0.656180i
$13$	5.27307i	1.46249i	0.682116	+	0.731244i	$0.261060\pi$
$13$	5.27307i	1.46249i	−0.682116	+	0.731244i	$0.738940\pi$
$14$	1.27307	0.340243
$15$	0	0
$16$	1.00000	0.250000
$17$	− 0.273073i	− 0.0662299i	−0.999452	−	0.0331149i	$-0.989457\pi$
$17$	− 0.273073i	− 0.0662299i	0.999452	−	0.0331149i	$-0.0105427\pi$
$18$	2.16686i	0.510734i
$19$	5.71301	1.31065	0.655327	−	0.755346i	$-0.272531\pi$
$19$	5.71301	1.31065	0.655327	+	0.755346i	$0.272531\pi$
$20$	0	0
$21$	2.89379	0.631476
$22$	4.43993i	0.946597i
$23$	6.54615i	1.36497i	0.730902	+	0.682483i	$0.239100\pi$
$23$	6.54615i	1.36497i	−0.730902	+	0.682483i	$0.760900\pi$
$24$	2.27307	0.463989
$25$	0	0
$26$	5.27307	1.03413
$27$	− 1.89379i	− 0.364460i
$28$	− 1.27307i	− 0.240588i
$29$	−0.546146	−0.101417	−0.0507084	−	0.998714i	$-0.516148\pi$
$29$	−0.546146	−0.101417	−0.0507084	+	0.998714i	$0.516148\pi$
$30$	0	0
$31$	−5.98608	−1.07513	−0.537566	−	0.843222i	$-0.680656\pi$
$31$	−5.98608	−1.07513	−0.537566	+	0.843222i	$0.680656\pi$
$32$	− 1.00000i	− 0.176777i
$33$	10.0923i	1.75684i
$34$	−0.273073	−0.0468316
$35$	0	0
$36$	2.16686	0.361143
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	− 5.71301i	− 0.926772i
$39$	11.9861	1.91931
$40$	0	0
$41$	11.8799	1.85532	0.927662	−	0.373422i	$-0.121816\pi$
$41$	11.8799	1.85532	0.927662	+	0.373422i	$0.121816\pi$
$42$	− 2.89379i	− 0.446521i
$43$	10.3793i	1.58283i	0.611282	+	0.791413i	$0.290654\pi$
$43$	10.3793i	1.58283i	−0.611282	+	0.791413i	$0.709346\pi$
$44$	4.43993	0.669345
$45$	0	0
$46$	6.54615	0.965177
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	− 2.27307i	− 0.328090i
$49$	5.37929	0.768469
$50$	0	0
$51$	−0.620715	−0.0869174
$52$	− 5.27307i	− 0.731244i
$53$	− 2.33372i	− 0.320561i	−0.987071	−	0.160281i	$-0.948760\pi$
$53$	− 2.33372i	− 0.320561i	0.987071	−	0.160281i	$-0.0512399\pi$
$54$	−1.89379	−0.257712
$55$	0	0
$56$	−1.27307	−0.170122
$57$	− 12.9861i	− 1.72005i
$58$	0.546146i	0.0717124i
$59$	−2.37929	−0.309757	−0.154878	−	0.987934i	$-0.549499\pi$
$59$	−2.37929	−0.309757	−0.154878	+	0.987934i	$0.549499\pi$
$60$	0	0
$61$	11.8192	1.51330	0.756648	−	0.653823i	$-0.226836\pi$
$61$	11.8192	1.51330	0.756648	+	0.653823i	$0.226836\pi$
$62$	5.98608i	0.760233i
$63$	− 2.75857i	− 0.347547i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	10.0923	1.24228
$67$	7.15294i	0.873871i	0.899493	+	0.436935i	$0.143936\pi$
$67$	7.15294i	0.873871i	−0.899493	+	0.436935i	$0.856064\pi$
$68$	0.273073i	0.0331149i
$69$	14.8799	1.79133
$70$	0	0
$71$	5.60679	0.665404	0.332702	−	0.943032i	$-0.392040\pi$
$71$	5.60679	0.665404	0.332702	+	0.943032i	$0.392040\pi$
$72$	− 2.16686i	− 0.255367i
$73$	9.71301i	1.13682i	0.822745	+	0.568411i	$0.192442\pi$
$73$	9.71301i	1.13682i	−0.822745	+	0.568411i	$0.807558\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	−5.71301	−0.655327
$77$	− 5.65236i	− 0.644146i
$78$	− 11.9861i	− 1.35716i
$79$	−11.4260	−1.28553	−0.642763	−	0.766065i	$-0.722212\pi$
$79$	−11.4260	−1.28553	−0.642763	+	0.766065i	$0.722212\pi$
$80$	0	0
$81$	−10.8053	−1.20059
$82$	− 11.8799i	− 1.31191i
$83$	− 3.89379i	− 0.427399i	−0.976899	−	0.213699i	$-0.931449\pi$
$83$	− 3.89379i	− 0.427399i	0.976899	−	0.213699i	$-0.0685513\pi$
$84$	−2.89379	−0.315738
$85$	0	0
$86$	10.3793	1.11923
$87$	1.24143i	0.133095i
$88$	− 4.43993i	− 0.473298i
$89$	−13.8659	−1.46979	−0.734894	−	0.678182i	$-0.762768\pi$
$89$	−13.8659	−1.46979	−0.734894	+	0.678182i	$0.762768\pi$
$90$	0	0
$91$	−6.71301	−0.703714
$92$	− 6.54615i	− 0.682483i
$93$	13.6068i	1.41096i
$94$	0	0
$95$	0	0
$96$	−2.27307	−0.231995
$97$	0.879866i	0.0893369i	0.999002	+	0.0446684i	$0.0142231\pi$
$97$	0.879866i	0.0893369i	−0.999002	+	0.0446684i	$0.985777\pi$
$98$	− 5.37929i	− 0.543390i
$99$	9.62071	0.966918
$100$	0	0
$101$	3.66628	0.364808	0.182404	−	0.983224i	$-0.441612\pi$
$101$	3.66628	0.364808	0.182404	+	0.983224i	$0.441612\pi$
$102$	0.620715i	0.0614599i
$103$	12.3198i	1.21391i	0.794738	+	0.606953i	$0.207608\pi$
$103$	12.3198i	1.21391i	−0.794738	+	0.606953i	$0.792392\pi$
$104$	−5.27307	−0.517067
$105$	0	0
$106$	−2.33372	−0.226671
$107$	7.36536i	0.712037i	0.934479	+	0.356018i	$0.115866\pi$
$107$	7.36536i	0.712037i	−0.934479	+	0.356018i	$0.884134\pi$
$108$	1.89379i	0.182230i
$109$	−4.33372	−0.415095	−0.207548	−	0.978225i	$-0.566548\pi$
$109$	−4.33372	−0.415095	−0.207548	+	0.978225i	$0.566548\pi$
$110$	0	0
$111$	−2.27307	−0.215751
$112$	1.27307i	0.120294i
$113$	− 2.10621i	− 0.198136i	−0.995081	−	0.0990679i	$-0.968414\pi$
$113$	− 2.10621i	− 0.198136i	0.995081	−	0.0990679i	$-0.0315861\pi$
$114$	−12.9861	−1.21626
$115$	0	0
$116$	0.546146	0.0507084
$117$	− 11.4260i	− 1.05634i
$118$	2.37929i	0.219031i
$119$	0.347642	0.0318683
$120$	0	0
$121$	8.71301	0.792091
$122$	− 11.8192i	− 1.07006i
$123$	− 27.0038i	− 2.43485i
$124$	5.98608	0.537566
$125$	0	0
$126$	−2.75857	−0.245753
$127$	− 13.6068i	− 1.20741i	−0.797209	−	0.603704i	$-0.793691\pi$
$127$	− 13.6068i	− 1.20741i	0.797209	−	0.603704i	$-0.206309\pi$
$128$	1.00000i	0.0883883i
$129$	23.5929	2.07724
$130$	0	0
$131$	4.16686	0.364060	0.182030	−	0.983293i	$-0.441733\pi$
$131$	4.16686	0.364060	0.182030	+	0.983293i	$0.441733\pi$
$132$	− 10.0923i	− 0.878421i
$133$	7.27307i	0.630655i
$134$	7.15294	0.617920
$135$	0	0
$136$	0.273073	0.0234158
$137$	1.21243i	0.103584i	0.998658	+	0.0517922i	$0.0164934\pi$
$137$	1.21243i	0.103584i	−0.998658	+	0.0517922i	$0.983507\pi$
$138$	− 14.8799i	− 1.26666i
$139$	−7.53222	−0.638875	−0.319437	−	0.947607i	$-0.603494\pi$
$139$	−7.53222	−0.638875	−0.319437	+	0.947607i	$0.603494\pi$
$140$	0	0
$141$	0	0
$142$	− 5.60679i	− 0.470512i
$143$	− 23.4121i	− 1.95782i
$144$	−2.16686	−0.180572
$145$	0	0
$146$	9.71301	0.803854
$147$	− 12.2275i	− 1.00851i
$148$	1.00000i	0.0821995i
$149$	13.9861	1.14578	0.572892	−	0.819631i	$-0.305821\pi$
$149$	13.9861	1.14578	0.572892	+	0.819631i	$0.305821\pi$
$150$	0	0
$151$	13.7597	1.11975	0.559876	−	0.828577i	$-0.310849\pi$
$151$	13.7597	1.11975	0.559876	+	0.828577i	$0.310849\pi$
$152$	5.71301i	0.463386i
$153$	0.591711i	0.0478370i
$154$	−5.65236	−0.455480
$155$	0	0
$156$	−11.9861	−0.959654
$157$	2.56007i	0.204316i	0.994768	+	0.102158i	$0.0325747\pi$
$157$	2.56007i	0.204316i	−0.994768	+	0.102158i	$0.967425\pi$
$158$	11.4260i	0.909005i
$159$	−5.30472	−0.420691
$160$	0	0
$161$	−8.33372	−0.656789
$162$	10.8053i	0.848944i
$163$	21.7130i	1.70069i	0.526222	+	0.850347i	$0.323608\pi$
$163$	21.7130i	1.70069i	−0.526222	+	0.850347i	$0.676392\pi$
$164$	−11.8799	−0.927662
$165$	0	0
$166$	−3.89379	−0.302217
$167$	16.8659i	1.30513i	0.757734	+	0.652563i	$0.226306\pi$
$167$	16.8659i	1.30513i	−0.757734	+	0.652563i	$0.773694\pi$
$168$	2.89379i	0.223261i
$169$	−14.8053	−1.13887
$170$	0	0
$171$	−12.3793	−0.946668
$172$	− 10.3793i	− 0.791413i
$173$	− 10.7586i	− 0.817959i	−0.912544	−	0.408980i	$-0.865885\pi$
$173$	− 10.7586i	− 0.817959i	0.912544	−	0.408980i	$-0.134115\pi$
$174$	1.24143	0.0941125
$175$	0	0
$176$	−4.43993	−0.334673
$177$	5.40829i	0.406512i
$178$	13.8659i	1.03930i
$179$	−1.66744	−0.124630	−0.0623152	−	0.998057i	$-0.519848\pi$
$179$	−1.66744	−0.124630	−0.0623152	+	0.998057i	$0.519848\pi$
$180$	0	0
$181$	5.97216	0.443907	0.221953	−	0.975057i	$-0.428757\pi$
$181$	5.97216	0.443907	0.221953	+	0.975057i	$0.428757\pi$
$182$	6.71301i	0.497601i
$183$	− 26.8659i	− 1.98599i
$184$	−6.54615	−0.482588
$185$	0	0
$186$	13.6068	0.997698
$187$	1.21243i	0.0886613i
$188$	0	0
$189$	2.41093	0.175369
$190$	0	0
$191$	−24.8520	−1.79823	−0.899115	−	0.437713i	$-0.855789\pi$
$191$	−24.8520	−1.79823	−0.899115	+	0.437713i	$0.855789\pi$
$192$	2.27307i	0.164045i
$193$	− 7.65352i	− 0.550912i	−0.961314	−	0.275456i	$-0.911171\pi$
$193$	− 7.65352i	− 0.550912i	0.961314	−	0.275456i	$-0.0888289\pi$
$194$	0.879866	0.0631707
$195$	0	0
$196$	−5.37929	−0.384235
$197$	− 14.5322i	− 1.03538i	−0.855569	−	0.517689i	$-0.826792\pi$
$197$	− 14.5322i	− 1.03538i	0.855569	−	0.517689i	$-0.173208\pi$
$198$	− 9.62071i	− 0.683714i
$199$	12.8799	0.913030	0.456515	−	0.889716i	$-0.349098\pi$
$199$	12.8799	0.913030	0.456515	+	0.889716i	$0.349098\pi$
$200$	0	0
$201$	16.2592	1.14683
$202$	− 3.66628i	− 0.257959i
$203$	− 0.695283i	− 0.0487993i
$204$	0.620715	0.0434587
$205$	0	0
$206$	12.3198	0.858361
$207$	− 14.1846i	− 0.985897i
$208$	5.27307i	0.365622i
$209$	−25.3654	−1.75456
$210$	0	0
$211$	−19.1529	−1.31854	−0.659271	−	0.751905i	$-0.729135\pi$
$211$	−19.1529	−1.31854	−0.659271	+	0.751905i	$0.729135\pi$
$212$	2.33372i	0.160281i
$213$	− 12.7446i	− 0.873249i
$214$	7.36536	0.503486
$215$	0	0
$216$	1.89379	0.128856
$217$	− 7.62071i	− 0.517328i
$218$	4.33372i	0.293517i
$219$	22.0784	1.49192
$220$	0	0
$221$	1.43993	0.0968604
$222$	2.27307i	0.152559i
$223$	− 2.75857i	− 0.184728i	−0.995725	−	0.0923638i	$-0.970558\pi$
$223$	− 2.75857i	− 0.184728i	0.995725	−	0.0923638i	$-0.0294423\pi$
$224$	1.27307	0.0850608
$225$	0	0
$226$	−2.10621	−0.140103
$227$	− 17.2592i	− 1.14553i	−0.819720	−	0.572765i	$-0.805871\pi$
$227$	− 17.2592i	− 1.14553i	0.819720	−	0.572765i	$-0.194129\pi$
$228$	12.9861i	0.860024i
$229$	22.3059	1.47401	0.737007	−	0.675885i	$-0.236238\pi$
$229$	22.3059	1.47401	0.737007	+	0.675885i	$0.236238\pi$
$230$	0	0
$231$	−12.8482	−0.845351
$232$	− 0.546146i	− 0.0358562i
$233$	24.3514i	1.59532i	0.603110	+	0.797658i	$0.293928\pi$
$233$	24.3514i	1.59532i	−0.603110	+	0.797658i	$0.706072\pi$
$234$	−11.4260	−0.746942
$235$	0	0
$236$	2.37929	0.154878
$237$	25.9722i	1.68707i
$238$	− 0.347642i	− 0.0225343i
$239$	−1.78757	−0.115629	−0.0578143	−	0.998327i	$-0.518413\pi$
$239$	−1.78757	−0.115629	−0.0578143	+	0.998327i	$0.518413\pi$
$240$	0	0
$241$	−3.72693	−0.240072	−0.120036	−	0.992770i	$-0.538301\pi$
$241$	−3.72693	−0.240072	−0.120036	+	0.992770i	$0.538301\pi$
$242$	− 8.71301i	− 0.560093i
$243$	18.8799i	1.21114i
$244$	−11.8192	−0.756648
$245$	0	0
$246$	−27.0038	−1.72170
$247$	30.1251i	1.91681i
$248$	− 5.98608i	− 0.380116i
$249$	−8.85086	−0.560901
$250$	0	0
$251$	−9.00000	−0.568075	−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000	−0.568075	−0.284037	+	0.958813i	$0.591674\pi$
$252$	2.75857i	0.173774i
$253$	− 29.0644i	− 1.82727i
$254$	−13.6068	−0.853766
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 3.42601i	− 0.213709i	−0.994275	−	0.106854i	$-0.965922\pi$
$257$	− 3.42601i	− 0.213709i	0.994275	−	0.106854i	$-0.0340779\pi$
$258$	− 23.5929i	− 1.46883i
$259$	1.27307	0.0791049
$260$	0	0
$261$	1.18342	0.0732519
$262$	− 4.16686i	− 0.257429i
$263$	− 2.57399i	− 0.158719i	−0.996846	−	0.0793595i	$-0.974713\pi$
$263$	− 2.57399i	− 0.158719i	0.996846	−	0.0793595i	$-0.0252875\pi$
$264$	−10.0923	−0.621138
$265$	0	0
$266$	7.27307	0.445941
$267$	31.5183i	1.92889i
$268$	− 7.15294i	− 0.436935i
$269$	27.7319	1.69084	0.845422	−	0.534100i	$-0.179349\pi$
$269$	27.7319	1.69084	0.845422	+	0.534100i	$0.179349\pi$
$270$	0	0
$271$	26.4588	1.60726	0.803629	−	0.595130i	$-0.202899\pi$
$271$	26.4588	1.60726	0.803629	+	0.595130i	$0.202899\pi$
$272$	− 0.273073i	− 0.0165575i
$273$	15.2592i	0.923526i
$274$	1.21243	0.0732453
$275$	0	0
$276$	−14.8799	−0.895663
$277$	0.573988i	0.0344876i	0.999851	+	0.0172438i	$0.00548914\pi$
$277$	0.573988i	0.0344876i	−0.999851	+	0.0172438i	$0.994511\pi$
$278$	7.53222i	0.451753i
$279$	12.9710	0.776553
$280$	0	0
$281$	−29.2592	−1.74545	−0.872727	−	0.488208i	$-0.837651\pi$
$281$	−29.2592	−1.74545	−0.872727	+	0.488208i	$0.837651\pi$
$282$	0	0
$283$	21.0177i	1.24937i	0.780875	+	0.624687i	$0.214773\pi$
$283$	21.0177i	1.24937i	−0.780875	+	0.624687i	$0.785227\pi$
$284$	−5.60679	−0.332702
$285$	0	0
$286$	−23.4121	−1.38439
$287$	15.1239i	0.892738i
$288$	2.16686i	0.127683i
$289$	16.9254	0.995614
$290$	0	0
$291$	2.00000	0.117242
$292$	− 9.71301i	− 0.568411i
$293$	17.9582i	1.04913i	0.851370	+	0.524566i	$0.175772\pi$
$293$	17.9582i	1.04913i	−0.851370	+	0.524566i	$0.824228\pi$
$294$	−12.2275	−0.713123
$295$	0	0
$296$	1.00000	0.0581238
$297$	8.40829i	0.487898i
$298$	− 13.9861i	− 0.810192i
$299$	−34.5183	−1.99625
$300$	0	0
$301$	−13.2136	−0.761618
$302$	− 13.7597i	− 0.791784i
$303$	− 8.33372i	− 0.478760i
$304$	5.71301	0.327663
$305$	0	0
$306$	0.591711	0.0338259
$307$	− 23.1985i	− 1.32401i	−0.749500	−	0.662004i	$-0.769706\pi$
$307$	− 23.1985i	− 1.32401i	0.749500	−	0.662004i	$-0.230294\pi$
$308$	5.65236i	0.322073i
$309$	28.0038	1.59308
$310$	0	0
$311$	−6.98492	−0.396078	−0.198039	−	0.980194i	$-0.563457\pi$
$311$	−6.98492	−0.396078	−0.198039	+	0.980194i	$0.563457\pi$
$312$	11.9861i	0.678578i
$313$	24.1669i	1.36599i	0.730422	+	0.682996i	$0.239323\pi$
$313$	24.1669i	1.36599i	−0.730422	+	0.682996i	$0.760677\pi$
$314$	2.56007	0.144473
$315$	0	0
$316$	11.4260	0.642763
$317$	32.2920i	1.81370i	0.421457	+	0.906848i	$0.361519\pi$
$317$	32.2920i	1.81370i	−0.421457	+	0.906848i	$0.638481\pi$
$318$	5.30472i	0.297474i
$319$	2.42485	0.135766
$320$	0	0
$321$	16.7420	0.934448
$322$	8.33372i	0.464420i
$323$	− 1.56007i	− 0.0868044i
$324$	10.8053	0.600294
$325$	0	0
$326$	21.7130	1.20257
$327$	9.85086i	0.544754i
$328$	11.8799i	0.655956i
$329$	0	0
$330$	0	0
$331$	−27.9254	−1.53492	−0.767460	−	0.641097i	$-0.778480\pi$
$331$	−27.9254	−1.53492	−0.767460	+	0.641097i	$0.778480\pi$
$332$	3.89379i	0.213699i
$333$	2.16686i	0.118743i
$334$	16.8659	0.922863
$335$	0	0
$336$	2.89379	0.157869
$337$	8.33256i	0.453903i	0.973906	+	0.226952i	$0.0728760\pi$
$337$	8.33256i	0.453903i	−0.973906	+	0.226952i	$0.927124\pi$
$338$	14.8053i	0.805302i
$339$	−4.78757	−0.260025
$340$	0	0
$341$	26.5778	1.43927
$342$	12.3793i	0.669395i
$343$	15.7597i	0.850946i
$344$	−10.3793	−0.559614
$345$	0	0
$346$	−10.7586	−0.578384
$347$	1.99884i	0.107303i	0.998560	+	0.0536516i	$0.0170861\pi$
$347$	1.99884i	0.107303i	−0.998560	+	0.0536516i	$0.982914\pi$
$348$	− 1.24143i	− 0.0665476i
$349$	21.9582	1.17540	0.587699	−	0.809080i	$-0.300034\pi$
$349$	21.9582	1.17540	0.587699	+	0.809080i	$0.300034\pi$
$350$	0	0
$351$	9.98608	0.533017
$352$	4.43993i	0.236649i
$353$	11.7597i	0.625907i	0.949768	+	0.312954i	$0.101318\pi$
$353$	11.7597i	0.625907i	−0.949768	+	0.312954i	$0.898682\pi$
$354$	5.40829	0.287447
$355$	0	0
$356$	13.8659	0.734894
$357$	− 0.790215i	− 0.0418226i
$358$	1.66744i	0.0881270i
$359$	−2.57399	−0.135850	−0.0679249	−	0.997690i	$-0.521638\pi$
$359$	−2.57399	−0.135850	−0.0679249	+	0.997690i	$0.521638\pi$
$360$	0	0
$361$	13.6384	0.717812
$362$	− 5.97216i	− 0.313890i
$363$	− 19.8053i	− 1.03951i
$364$	6.71301	0.351857
$365$	0	0
$366$	−26.8659	−1.40431
$367$	12.4867i	0.651798i	0.945405	+	0.325899i	$0.105667\pi$
$367$	12.4867i	0.651798i	−0.945405	+	0.325899i	$0.894333\pi$
$368$	6.54615i	0.341241i
$369$	−25.7420	−1.34008
$370$	0	0
$371$	2.97100	0.154246
$372$	− 13.6068i	− 0.705479i
$373$	− 14.8659i	− 0.769729i	−0.922973	−	0.384865i	$-0.874248\pi$
$373$	− 14.8659i	− 0.769729i	0.922973	−	0.384865i	$-0.125752\pi$
$374$	1.21243	0.0626930
$375$	0	0
$376$	0	0
$377$	− 2.87987i	− 0.148321i
$378$	− 2.41093i	− 0.124005i
$379$	2.39437	0.122990	0.0614952	−	0.998107i	$-0.480413\pi$
$379$	2.39437	0.122990	0.0614952	+	0.998107i	$0.480413\pi$
$380$	0	0
$381$	−30.9292	−1.58455
$382$	24.8520i	1.27154i
$383$	− 14.7725i	− 0.754839i	−0.926042	−	0.377420i	$-0.876811\pi$
$383$	− 14.7725i	− 0.754839i	0.926042	−	0.377420i	$-0.123189\pi$
$384$	2.27307	0.115997
$385$	0	0
$386$	−7.65352	−0.389554
$387$	− 22.4905i	− 1.14325i
$388$	− 0.879866i	− 0.0446684i
$389$	12.6991	0.643869	0.321935	−	0.946762i	$-0.395667\pi$
$389$	12.6991	0.643869	0.321935	+	0.946762i	$0.395667\pi$
$390$	0	0
$391$	1.78757	0.0904015
$392$	5.37929i	0.271695i
$393$	− 9.47158i	− 0.477778i
$394$	−14.5322	−0.732123
$395$	0	0
$396$	−9.62071	−0.483459
$397$	4.98492i	0.250186i	0.992145	+	0.125093i	$0.0399229\pi$
$397$	4.98492i	0.250186i	−0.992145	+	0.125093i	$0.960077\pi$
$398$	− 12.8799i	− 0.645609i
$399$	16.5322	0.827646
$400$	0	0
$401$	27.1985	1.35823	0.679114	−	0.734033i	$-0.262364\pi$
$401$	27.1985	1.35823	0.679114	+	0.734033i	$0.262364\pi$
$402$	− 16.2592i	− 0.810933i
$403$	− 31.5650i	− 1.57237i
$404$	−3.66628	−0.182404
$405$	0	0
$406$	−0.695283	−0.0345063
$407$	4.43993i	0.220079i
$408$	− 0.620715i	− 0.0307299i
$409$	−35.5499	−1.75783	−0.878916	−	0.476977i	$-0.841733\pi$
$409$	−35.5499	−1.75783	−0.878916	+	0.476977i	$0.841733\pi$
$410$	0	0
$411$	2.75593	0.135940
$412$	− 12.3198i	− 0.606953i
$413$	− 3.02900i	− 0.149048i
$414$	−14.1846	−0.697134
$415$	0	0
$416$	5.27307	0.258534
$417$	17.1213i	0.838433i
$418$	25.3654i	1.24066i
$419$	29.5322	1.44274	0.721372	−	0.692548i	$-0.243512\pi$
$419$	29.5322	1.44274	0.721372	+	0.692548i	$0.243512\pi$
$420$	0	0
$421$	−30.4905	−1.48601	−0.743007	−	0.669284i	$-0.766601\pi$
$421$	−30.4905	−1.48601	−0.743007	+	0.669284i	$0.766601\pi$
$422$	19.1529i	0.932350i
$423$	0	0
$424$	2.33372	0.113335
$425$	0	0
$426$	−12.7446	−0.617480
$427$	15.0467i	0.728162i
$428$	− 7.36536i	− 0.356018i
$429$	−53.2174	−2.56936
$430$	0	0
$431$	21.9722	1.05836	0.529181	−	0.848509i	$-0.322499\pi$
$431$	21.9722	1.05836	0.529181	+	0.848509i	$0.322499\pi$
$432$	− 1.89379i	− 0.0911149i
$433$	5.00000i	0.240285i	0.992757	+	0.120142i	$0.0383351\pi$
$433$	5.00000i	0.240285i	−0.992757	+	0.120142i	$0.961665\pi$
$434$	−7.62071	−0.365806
$435$	0	0
$436$	4.33372	0.207548
$437$	37.3982i	1.78900i
$438$	− 22.0784i	− 1.05495i
$439$	−29.5171	−1.40878	−0.704388	−	0.709815i	$-0.748779\pi$
$439$	−29.5171	−1.40878	−0.704388	+	0.709815i	$0.748779\pi$
$440$	0	0
$441$	−11.6562	−0.555055
$442$	− 1.43993i	− 0.0684906i
$443$	− 28.9861i	− 1.37717i	−0.725156	−	0.688585i	$-0.758232\pi$
$443$	− 28.9861i	− 1.37717i	0.725156	−	0.688585i	$-0.241768\pi$
$444$	2.27307	0.107875
$445$	0	0
$446$	−2.75857	−0.130622
$447$	− 31.7914i	− 1.50368i
$448$	− 1.27307i	− 0.0601470i
$449$	−36.6245	−1.72842	−0.864209	−	0.503133i	$-0.832181\pi$
$449$	−36.6245	−1.72842	−0.864209	+	0.503133i	$0.832181\pi$
$450$	0	0
$451$	−52.7458	−2.48370
$452$	2.10621i	0.0990679i
$453$	− 31.2769i	− 1.46952i
$454$	−17.2592	−0.810012
$455$	0	0
$456$	12.9861	0.608129
$457$	19.7446i	0.923616i	0.886980	+	0.461808i	$0.152799\pi$
$457$	19.7446i	0.923616i	−0.886980	+	0.461808i	$0.847201\pi$
$458$	− 22.3059i	− 1.04229i
$459$	−0.517142	−0.0241381
$460$	0	0
$461$	34.9733	1.62887	0.814435	−	0.580255i	$-0.197047\pi$
$461$	34.9733	1.62887	0.814435	+	0.580255i	$0.197047\pi$
$462$	12.8482i	0.597753i
$463$	24.1707i	1.12331i	0.827373	+	0.561653i	$0.189834\pi$
$463$	24.1707i	1.12331i	−0.827373	+	0.561653i	$0.810166\pi$
$464$	−0.546146	−0.0253542
$465$	0	0
$466$	24.3514	1.12806
$467$	7.63844i	0.353465i	0.984259	+	0.176732i	$0.0565527\pi$
$467$	7.63844i	0.353465i	−0.984259	+	0.176732i	$0.943447\pi$
$468$	11.4260i	0.528168i
$469$	−9.10621	−0.420486
$470$	0	0
$471$	5.81922	0.268135
$472$	− 2.37929i	− 0.109515i
$473$	− 46.0833i	− 2.11891i
$474$	25.9722	1.19294
$475$	0	0
$476$	−0.347642	−0.0159341
$477$	5.05685i	0.231537i
$478$	1.78757i	0.0817618i
$479$	4.01392	0.183401	0.0917004	−	0.995787i	$-0.470770\pi$
$479$	4.01392	0.183401	0.0917004	+	0.995787i	$0.470770\pi$
$480$	0	0
$481$	5.27307	0.240431
$482$	3.72693i	0.169757i
$483$	18.9432i	0.861943i
$484$	−8.71301	−0.396046
$485$	0	0
$486$	18.8799	0.856408
$487$	43.3842i	1.96593i	0.183798	+	0.982964i	$0.441161\pi$
$487$	43.3842i	1.96593i	−0.183798	+	0.982964i	$0.558839\pi$
$488$	11.8192i	0.535031i
$489$	49.3552	2.23192
$490$	0	0
$491$	−20.7307	−0.935565	−0.467782	−	0.883844i	$-0.654947\pi$
$491$	−20.7307	−0.935565	−0.467782	+	0.883844i	$0.654947\pi$
$492$	27.0038i	1.21743i
$493$	0.149138i	0.00671682i
$494$	30.1251	1.35539
$495$	0	0
$496$	−5.98608	−0.268783
$497$	7.13786i	0.320177i
$498$	8.85086i	0.396617i
$499$	−5.92659	−0.265311	−0.132655	−	0.991162i	$-0.542350\pi$
$499$	−5.92659	−0.265311	−0.132655	+	0.991162i	$0.542350\pi$
$500$	0	0
$501$	38.3375	1.71279
$502$	9.00000i	0.401690i
$503$	− 24.0000i	− 1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$	− 24.0000i	− 1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$	2.75857	0.122877
$505$	0	0
$506$	−29.0644	−1.29207
$507$	33.6535i	1.49461i
$508$	13.6068i	0.603704i
$509$	9.07837	0.402392	0.201196	−	0.979551i	$-0.435517\pi$
$509$	9.07837	0.402392	0.201196	+	0.979551i	$0.435517\pi$
$510$	0	0
$511$	−12.3654	−0.547012
$512$	− 1.00000i	− 0.0441942i
$513$	− 10.8192i	− 0.477680i
$514$	−3.42601	−0.151115
$515$	0	0
$516$	−23.5929	−1.03862
$517$	0	0
$518$	− 1.27307i	− 0.0559356i
$519$	−24.4550	−1.07346
$520$	0	0
$521$	−7.16686	−0.313986	−0.156993	−	0.987600i	$-0.550180\pi$
$521$	−7.16686	−0.313986	−0.156993	+	0.987600i	$0.550180\pi$
$522$	− 1.18342i	− 0.0517970i
$523$	29.3970i	1.28544i	0.766101	+	0.642721i	$0.222194\pi$
$523$	29.3970i	1.28544i	−0.766101	+	0.642721i	$0.777806\pi$
$524$	−4.16686	−0.182030
$525$	0	0
$526$	−2.57399	−0.112231
$527$	1.63464i	0.0712058i
$528$	10.0923i	0.439211i
$529$	−19.8520	−0.863131
$530$	0	0
$531$	5.15558	0.223733
$532$	− 7.27307i	− 0.315328i
$533$	62.6434i	2.71339i
$534$	31.5183	1.36393
$535$	0	0
$536$	−7.15294	−0.308960
$537$	3.79021i	0.163560i
$538$	− 27.7319i	− 1.19561i
$539$	−23.8837	−1.02874
$540$	0	0
$541$	26.0038	1.11799	0.558995	−	0.829171i	$-0.311187\pi$
$541$	26.0038	1.11799	0.558995	+	0.829171i	$0.311187\pi$
$542$	− 26.4588i	− 1.13650i
$543$	− 13.5751i	− 0.582565i
$544$	−0.273073	−0.0117079
$545$	0	0
$546$	15.2592	0.653031
$547$	− 8.77746i	− 0.375297i	−0.982236	−	0.187648i	$-0.939913\pi$
$547$	− 8.77746i	− 0.375297i	0.982236	−	0.187648i	$-0.0600866\pi$
$548$	− 1.21243i	− 0.0517922i
$549$	−25.6106	−1.09303
$550$	0	0
$551$	−3.12013	−0.132922
$552$	14.8799i	0.633329i
$553$	− 14.5461i	− 0.618565i
$554$	0.573988	0.0243864
$555$	0	0
$556$	7.53222	0.319437
$557$	− 21.6663i	− 0.918030i	−0.888429	−	0.459015i	$-0.848202\pi$
$557$	− 21.6663i	− 0.918030i	0.888429	−	0.459015i	$-0.151798\pi$
$558$	− 12.9710i	− 0.549106i
$559$	−54.7307	−2.31486
$560$	0	0
$561$	2.75593	0.116355
$562$	29.2592i	1.23422i
$563$	− 19.4437i	− 0.819456i	−0.912208	−	0.409728i	$-0.865624\pi$
$563$	− 19.4437i	− 0.819456i	0.912208	−	0.409728i	$-0.134376\pi$
$564$	0	0
$565$	0	0
$566$	21.0177	0.883441
$567$	− 13.7559i	− 0.577695i
$568$	5.60679i	0.235256i
$569$	−21.7446	−0.911583	−0.455792	−	0.890087i	$-0.650644\pi$
$569$	−21.7446	−0.911583	−0.455792	+	0.890087i	$0.650644\pi$
$570$	0	0
$571$	1.54498	0.0646556	0.0323278	−	0.999477i	$-0.489708\pi$
$571$	1.54498	0.0646556	0.0323278	+	0.999477i	$0.489708\pi$
$572$	23.4121i	0.978909i
$573$	56.4905i	2.35992i
$574$	15.1239	0.631261
$575$	0	0
$576$	2.16686	0.0902858
$577$	− 37.8837i	− 1.57712i	−0.614959	−	0.788559i	$-0.710828\pi$
$577$	− 37.8837i	− 1.57712i	0.614959	−	0.788559i	$-0.289172\pi$
$578$	− 16.9254i	− 0.704005i
$579$	−17.3970	−0.722995
$580$	0	0
$581$	4.95708	0.205654
$582$	− 2.00000i	− 0.0829027i
$583$	10.3616i	0.429132i
$584$	−9.71301	−0.401927
$585$	0	0
$586$	17.9582	0.741848
$587$	− 38.8053i	− 1.60167i	−0.598888	−	0.800833i	$-0.704390\pi$
$587$	− 38.8053i	− 1.60167i	0.598888	−	0.800833i	$-0.295610\pi$
$588$	12.2275i	0.504254i
$589$	−34.1985	−1.40912
$590$	0	0
$591$	−33.0328	−1.35879
$592$	− 1.00000i	− 0.0410997i
$593$	− 22.0923i	− 0.907222i	−0.891200	−	0.453611i	$-0.850136\pi$
$593$	− 22.0923i	− 0.907222i	0.891200	−	0.453611i	$-0.149864\pi$
$594$	8.40829	0.344996
$595$	0	0
$596$	−13.9861	−0.572892
$597$	− 29.2769i	− 1.19822i
$598$	34.5183i	1.41156i
$599$	17.8471	0.729211	0.364606	−	0.931162i	$-0.381204\pi$
$599$	17.8471	0.729211	0.364606	+	0.931162i	$0.381204\pi$
$600$	0	0
$601$	46.1100	1.88087	0.940433	−	0.339978i	$-0.110420\pi$
$601$	46.1100	1.88087	0.940433	+	0.339978i	$0.110420\pi$
$602$	13.2136i	0.538546i
$603$	− 15.4994i	− 0.631185i
$604$	−13.7597	−0.559876
$605$	0	0
$606$	−8.33372	−0.338534
$607$	− 47.3842i	− 1.92327i	−0.274337	−	0.961634i	$-0.588458\pi$
$607$	− 47.3842i	− 1.92327i	0.274337	−	0.961634i	$-0.411542\pi$
$608$	− 5.71301i	− 0.231693i
$609$	−1.58043	−0.0640422
$610$	0	0
$611$	0	0
$612$	− 0.591711i	− 0.0239185i
$613$	15.7876i	0.637654i	0.947813	+	0.318827i	$0.103289\pi$
$613$	15.7876i	0.637654i	−0.947813	+	0.318827i	$0.896711\pi$
$614$	−23.1985	−0.936215
$615$	0	0
$616$	5.65236	0.227740
$617$	− 26.1390i	− 1.05232i	−0.850386	−	0.526159i	$-0.823632\pi$
$617$	− 26.1390i	− 1.05232i	0.850386	−	0.526159i	$-0.176368\pi$
$618$	− 28.0038i	− 1.12648i
$619$	−31.3047	−1.25824	−0.629121	−	0.777307i	$-0.716585\pi$
$619$	−31.3047	−1.25824	−0.629121	+	0.777307i	$0.716585\pi$
$620$	0	0
$621$	12.3970	0.497475
$622$	6.98492i	0.280070i
$623$	− 17.6524i	− 0.707227i
$624$	11.9861	0.479827
$625$	0	0
$626$	24.1669	0.965902
$627$	57.6573i	2.30261i
$628$	− 2.56007i	− 0.102158i
$629$	−0.273073	−0.0108881
$630$	0	0
$631$	−15.3047	−0.609271	−0.304636	−	0.952469i	$-0.598535\pi$
$631$	−15.3047	−0.609271	−0.304636	+	0.952469i	$0.598535\pi$
$632$	− 11.4260i	− 0.454502i
$633$	43.5360i	1.73040i
$634$	32.2920	1.28248
$635$	0	0
$636$	5.30472	0.210346
$637$	28.3654i	1.12388i
$638$	− 2.42485i	− 0.0960008i
$639$	−12.1491	−0.480612
$640$	0	0
$641$	−12.8520	−0.507624	−0.253812	−	0.967254i	$-0.581685\pi$
$641$	−12.8520	−0.507624	−0.253812	+	0.967254i	$0.581685\pi$
$642$	− 16.7420i	− 0.660754i
$643$	− 0.139018i	− 0.00548233i	−0.999996	−	0.00274117i	$-0.999127\pi$
$643$	− 0.139018i	− 0.00548233i	0.999996	−	0.00274117i	$-0.000872541\pi$
$644$	8.33372	0.328395
$645$	0	0
$646$	−1.56007	−0.0613800
$647$	− 46.8659i	− 1.84249i	−0.388982	−	0.921245i	$-0.627173\pi$
$647$	− 46.8659i	− 1.84249i	0.388982	−	0.921245i	$-0.372827\pi$
$648$	− 10.8053i	− 0.424472i
$649$	10.5639	0.414668
$650$	0	0
$651$	−17.3224	−0.678920
$652$	− 21.7130i	− 0.850347i
$653$	− 7.48550i	− 0.292930i	−0.989216	−	0.146465i	$-0.953210\pi$
$653$	− 7.48550i	− 0.292930i	0.989216	−	0.146465i	$-0.0467896\pi$
$654$	9.85086	0.385199
$655$	0	0
$656$	11.8799	0.463831
$657$	− 21.0467i	− 0.821111i
$658$	0	0
$659$	22.7914	0.887826	0.443913	−	0.896070i	$-0.353590\pi$
$659$	22.7914	0.887826	0.443913	+	0.896070i	$0.353590\pi$
$660$	0	0
$661$	16.4249	0.638853	0.319426	−	0.947611i	$-0.396510\pi$
$661$	16.4249	0.638853	0.319426	+	0.947611i	$0.396510\pi$
$662$	27.9254i	1.08535i
$663$	− 3.27307i	− 0.127116i
$664$	3.89379	0.151108
$665$	0	0
$666$	2.16686	0.0839641
$667$	− 3.57515i	− 0.138430i
$668$	− 16.8659i	− 0.652563i
$669$	−6.27043	−0.242429
$670$	0	0
$671$	−52.4765	−2.02583
$672$	− 2.89379i	− 0.111630i
$673$	51.2035i	1.97375i	0.161490	+	0.986874i	$0.448370\pi$
$673$	51.2035i	1.97375i	−0.161490	+	0.986874i	$0.551630\pi$
$674$	8.33256	0.320958
$675$	0	0
$676$	14.8053	0.569435
$677$	1.00116i	0.0384778i	0.999815	+	0.0192389i	$0.00612430\pi$
$677$	1.00116i	0.0384778i	−0.999815	+	0.0192389i	$0.993876\pi$
$678$	4.78757i	0.183866i
$679$	−1.12013	−0.0429868
$680$	0	0
$681$	−39.2313	−1.50335
$682$	− 26.5778i	− 1.01772i
$683$	28.3526i	1.08488i	0.840094	+	0.542441i	$0.182500\pi$
$683$	28.3526i	1.08488i	−0.840094	+	0.542441i	$0.817500\pi$
$684$	12.3793	0.473334
$685$	0	0
$686$	15.7597	0.601709
$687$	− 50.7029i	− 1.93444i
$688$	10.3793i	0.395707i
$689$	12.3059	0.468817
$690$	0	0
$691$	26.3842	1.00370	0.501852	−	0.864953i	$-0.332652\pi$
$691$	26.3842	1.00370	0.501852	+	0.864953i	$0.332652\pi$
$692$	10.7586i	0.408980i
$693$	12.2479i	0.465258i
$694$	1.99884	0.0758749
$695$	0	0
$696$	−1.24143	−0.0470562
$697$	− 3.24407i	− 0.122878i
$698$	− 21.9582i	− 0.831132i
$699$	55.3526	2.09363
$700$	0	0
$701$	40.5801	1.53269	0.766345	−	0.642429i	$-0.222073\pi$
$701$	40.5801	1.53269	0.766345	+	0.642429i	$0.222073\pi$
$702$	− 9.98608i	− 0.376900i
$703$	− 5.71301i	− 0.215470i
$704$	4.43993	0.167336
$705$	0	0
$706$	11.7597	0.442583
$707$	4.66744i	0.175537i
$708$	− 5.40829i	− 0.203256i
$709$	−14.5461	−0.546292	−0.273146	−	0.961973i	$-0.588064\pi$
$709$	−14.5461	−0.546292	−0.273146	+	0.961973i	$0.588064\pi$
$710$	0	0
$711$	24.7586	0.928519
$712$	− 13.8659i	− 0.519648i
$713$	− 39.1857i	− 1.46752i
$714$	−0.790215	−0.0295730
$715$	0	0
$716$	1.66744	0.0623152
$717$	4.06329i	0.151746i
$718$	2.57399i	0.0960604i
$719$	−21.6701	−0.808158	−0.404079	−	0.914724i	$-0.632408\pi$
$719$	−21.6701	−0.808158	−0.404079	+	0.914724i	$0.632408\pi$
$720$	0	0
$721$	−15.6840	−0.584103
$722$	− 13.6384i	− 0.507570i
$723$	8.47158i	0.315061i
$724$	−5.97216	−0.221953
$725$	0	0
$726$	−19.8053	−0.735044
$727$	− 28.8799i	− 1.07109i	−0.844505	−	0.535547i	$-0.820105\pi$
$727$	− 28.8799i	− 1.07109i	0.844505	−	0.535547i	$-0.179895\pi$
$728$	− 6.71301i	− 0.248801i
$729$	10.4994	0.388867
$730$	0	0
$731$	2.83430	0.104830
$732$	26.8659i	0.992994i
$733$	− 21.9165i	− 0.809503i	−0.914427	−	0.404752i	$-0.867358\pi$
$733$	− 21.9165i	− 0.809503i	0.914427	−	0.404752i	$-0.132642\pi$
$734$	12.4867	0.460891
$735$	0	0
$736$	6.54615	0.241294
$737$	− 31.7586i	− 1.16984i
$738$	25.7420i	0.947576i
$739$	29.7040	1.09268	0.546341	−	0.837563i	$-0.316020\pi$
$739$	29.7040	1.09268	0.546341	+	0.837563i	$0.316020\pi$
$740$	0	0
$741$	68.4765	2.51555
$742$	− 2.97100i	− 0.109069i
$743$	− 39.5171i	− 1.44974i	−0.688884	−	0.724872i	$-0.741899\pi$
$743$	− 39.5171i	− 1.44974i	0.688884	−	0.724872i	$-0.258101\pi$
$744$	−13.6068	−0.498849
$745$	0	0
$746$	−14.8659	−0.544281
$747$	8.43729i	0.308704i
$748$	− 1.21243i	− 0.0443307i
$749$	−9.37665	−0.342615
$750$	0	0
$751$	−11.6384	−0.424693	−0.212346	−	0.977194i	$-0.568110\pi$
$751$	−11.6384	−0.424693	−0.212346	+	0.977194i	$0.568110\pi$
$752$	0	0
$753$	20.4577i	0.745518i
$754$	−2.87987	−0.104879
$755$	0	0
$756$	−2.41093	−0.0876847
$757$	− 21.0923i	− 0.766612i	−0.923621	−	0.383306i	$-0.874785\pi$
$757$	− 21.0923i	− 0.766612i	0.923621	−	0.383306i	$-0.125215\pi$
$758$	− 2.39437i	− 0.0869674i
$759$	−66.0656	−2.39803
$760$	0	0
$761$	−16.8988	−0.612579	−0.306290	−	0.951938i	$-0.599088\pi$
$761$	−16.8988	−0.612579	−0.306290	+	0.951938i	$0.599088\pi$
$762$	30.9292i	1.12045i
$763$	− 5.51714i	− 0.199734i
$764$	24.8520	0.899115
$765$	0	0
$766$	−14.7725	−0.533752
$767$	− 12.5461i	− 0.453015i
$768$	− 2.27307i	− 0.0820225i
$769$	−28.6524	−1.03323	−0.516615	−	0.856218i	$-0.672808\pi$
$769$	−28.6524	−1.03323	−0.516615	+	0.856218i	$0.672808\pi$
$770$	0	0
$771$	−7.78757	−0.280463
$772$	7.65352i	0.275456i
$773$	− 10.3198i	− 0.371177i	−0.982628	−	0.185589i	$-0.940581\pi$
$773$	− 10.3198i	− 0.371177i	0.982628	−	0.185589i	$-0.0594192\pi$
$774$	−22.4905	−0.808403
$775$	0	0
$776$	−0.879866	−0.0315854
$777$	− 2.89379i	− 0.103814i
$778$	− 12.6991i	− 0.455284i
$779$	67.8697	2.43169
$780$	0	0
$781$	−24.8938	−0.890770
$782$	− 1.78757i	− 0.0639235i
$783$	1.03428i	0.0369623i
$784$	5.37929	0.192117
$785$	0	0
$786$	−9.47158	−0.337840
$787$	− 16.3337i	− 0.582234i	−0.956687	−	0.291117i	$-0.905973\pi$
$787$	− 16.3337i	− 0.582234i	0.956687	−	0.291117i	$-0.0940269\pi$
$788$	14.5322i	0.517689i
$789$	−5.85086	−0.208296
$790$	0	0
$791$	2.68136	0.0953383
$792$	9.62071i	0.341857i
$793$	62.3236i	2.21318i
$794$	4.98492	0.176908
$795$	0	0
$796$	−12.8799	−0.456515
$797$	− 2.96719i	− 0.105103i	−0.998618	−	0.0525517i	$-0.983265\pi$
$797$	− 2.96719i	− 0.105103i	0.998618	−	0.0525517i	$-0.0167354\pi$
$798$	− 16.5322i	− 0.585234i
$799$	0	0
$800$	0	0
$801$	30.0456	1.06161
$802$	− 27.1985i	− 0.960413i
$803$	− 43.1251i	− 1.52185i
$804$	−16.2592	−0.573416
$805$	0	0
$806$	−31.5650	−1.11183
$807$	− 63.0366i	− 2.21899i
$808$	3.66628i	0.128979i
$809$	7.87870	0.277001	0.138500	−	0.990362i	$-0.455772\pi$
$809$	7.87870	0.277001	0.138500	+	0.990362i	$0.455772\pi$
$810$	0	0
$811$	−48.6396	−1.70797	−0.853984	−	0.520300i	$-0.825820\pi$
$811$	−48.6396	−1.70797	−0.853984	+	0.520300i	$0.825820\pi$
$812$	0.695283i	0.0243997i
$813$	− 60.1428i	− 2.10930i
$814$	4.43993	0.155620
$815$	0	0
$816$	−0.620715	−0.0217294
$817$	59.2969i	2.07454i
$818$	35.5499i	1.24297i
$819$	14.5461	0.508283
$820$	0	0
$821$	−7.68020	−0.268041	−0.134020	−	0.990979i	$-0.542789\pi$
$821$	−7.68020	−0.268041	−0.134020	+	0.990979i	$0.542789\pi$
$822$	− 2.75593i	− 0.0961241i
$823$	− 26.3654i	− 0.919039i	−0.888168	−	0.459519i	$-0.848022\pi$
$823$	− 26.3654i	− 0.919039i	0.888168	−	0.459519i	$-0.151978\pi$
$824$	−12.3198	−0.429181
$825$	0	0
$826$	−3.02900	−0.105393
$827$	17.8343i	0.620159i	0.950711	+	0.310080i	$0.100356\pi$
$827$	17.8343i	0.620159i	−0.950711	+	0.310080i	$0.899644\pi$
$828$	14.1846i	0.492948i
$829$	5.17962	0.179896	0.0899478	−	0.995946i	$-0.471330\pi$
$829$	5.17962	0.179896	0.0899478	+	0.995946i	$0.471330\pi$
$830$	0	0
$831$	1.30472	0.0452601
$832$	− 5.27307i	− 0.182811i
$833$	− 1.46894i	− 0.0508956i
$834$	17.1213	0.592862
$835$	0	0
$836$	25.3654	0.877279
$837$	11.3364i	0.391842i
$838$	− 29.5322i	− 1.02017i
$839$	6.15294	0.212423	0.106212	−	0.994344i	$-0.466128\pi$
$839$	6.15294	0.212423	0.106212	+	0.994344i	$0.466128\pi$
$840$	0	0
$841$	−28.7017	−0.989715
$842$	30.4905i	1.05077i
$843$	66.5082i	2.29066i
$844$	19.1529	0.659271
$845$	0	0
$846$	0	0
$847$	11.0923i	0.381136i
$848$	− 2.33372i	− 0.0801403i
$849$	47.7748	1.63963
$850$	0	0
$851$	6.54615	0.224399
$852$	12.7446i	0.436625i
$853$	− 30.8837i	− 1.05744i	−0.848797	−	0.528718i	$-0.822673\pi$
$853$	− 30.8837i	− 1.05744i	0.848797	−	0.528718i	$-0.177327\pi$
$854$	15.0467	0.514888
$855$	0	0
$856$	−7.36536	−0.251743
$857$	− 15.1529i	− 0.517615i	−0.965929	−	0.258807i	$-0.916671\pi$
$857$	− 15.1529i	− 0.517615i	0.965929	−	0.258807i	$-0.0833295\pi$
$858$	53.2174i	1.81681i
$859$	7.28583	0.248589	0.124295	−	0.992245i	$-0.460333\pi$
$859$	7.28583	0.248589	0.124295	+	0.992245i	$0.460333\pi$
$860$	0	0
$861$	34.3778	1.17159
$862$	− 21.9722i	− 0.748375i
$863$	− 51.7357i	− 1.76110i	−0.473950	−	0.880552i	$-0.657172\pi$
$863$	− 51.7357i	− 1.76110i	0.473950	−	0.880552i	$-0.342828\pi$
$864$	−1.89379	−0.0644280
$865$	0	0
$866$	5.00000	0.169907
$867$	− 38.4727i	− 1.30660i
$868$	7.62071i	0.258664i
$869$	50.7307	1.72092
$870$	0	0
$871$	−37.7180	−1.27802
$872$	− 4.33372i	− 0.146758i
$873$	− 1.90655i	− 0.0645268i
$874$	37.3982	1.26501
$875$	0	0
$876$	−22.0784	−0.745959
$877$	50.4109i	1.70226i	0.524958	+	0.851128i	$0.324081\pi$
$877$	50.4109i	1.70226i	−0.524958	+	0.851128i	$0.675919\pi$
$878$	29.5171i	0.996155i
$879$	40.8204	1.37684
$880$	0	0
$881$	−45.0822	−1.51886	−0.759428	−	0.650591i	$-0.774521\pi$
$881$	−45.0822	−1.51886	−0.759428	+	0.650591i	$0.774521\pi$
$882$	11.6562i	0.392483i
$883$	− 17.9988i	− 0.605709i	−0.953037	−	0.302855i	$-0.902060\pi$
$883$	− 17.9988i	− 0.605709i	0.953037	−	0.302855i	$-0.0979396\pi$
$884$	−1.43993	−0.0484302
$885$	0	0
$886$	−28.9861	−0.973806
$887$	38.2502i	1.28432i	0.766572	+	0.642158i	$0.221961\pi$
$887$	38.2502i	1.28432i	−0.766572	+	0.642158i	$0.778039\pi$
$888$	− 2.27307i	− 0.0762793i
$889$	17.3224	0.580976
$890$	0	0
$891$	47.9748	1.60722
$892$	2.75857i	0.0923638i
$893$	0	0
$894$	−31.7914	−1.06326
$895$	0	0
$896$	−1.27307	−0.0425304
$897$	78.4626i	2.61979i
$898$	36.6245i	1.22218i
$899$	3.26927	0.109036
$900$	0	0
$901$	−0.637276	−0.0212307
$902$	52.7458i	1.75624i
$903$	30.0354i	0.999517i
$904$	2.10621	0.0700516
$905$	0	0
$906$	−31.2769	−1.03910
$907$	− 10.0734i	− 0.334482i	−0.985916	−	0.167241i	$-0.946514\pi$
$907$	− 10.0734i	− 0.334482i	0.985916	−	0.167241i	$-0.0534858\pi$
$908$	17.2592i	0.572765i
$909$	−7.94432	−0.263496
$910$	0	0
$911$	−5.56123	−0.184252	−0.0921259	−	0.995747i	$-0.529366\pi$
$911$	−5.56123	−0.184252	−0.0921259	+	0.995747i	$0.529366\pi$
$912$	− 12.9861i	− 0.430012i
$913$	17.2882i	0.572154i
$914$	19.7446	0.653095
$915$	0	0
$916$	−22.3059	−0.737007
$917$	5.30472i	0.175177i
$918$	0.517142i	0.0170682i
$919$	3.75973	0.124022	0.0620111	−	0.998075i	$-0.480249\pi$
$919$	3.75973	0.124022	0.0620111	+	0.998075i	$0.480249\pi$
$920$	0	0
$921$	−52.7319	−1.73757
$922$	− 34.9733i	− 1.15178i
$923$	29.5650i	0.973145i
$924$	12.8482	0.422675
$925$	0	0
$926$	24.1707	0.794297
$927$	− 26.6953i	− 0.876788i
$928$	0.546146i	0.0179281i
$929$	−3.40597	−0.111746	−0.0558731	−	0.998438i	$-0.517794\pi$
$929$	−3.40597	−0.111746	−0.0558731	+	0.998438i	$0.517794\pi$
$930$	0	0
$931$	30.7319	1.00720
$932$	− 24.3514i	− 0.797658i
$933$	15.8772i	0.519797i
$934$	7.63844	0.249937
$935$	0	0
$936$	11.4260	0.373471
$937$	− 34.8053i	− 1.13704i	−0.822670	−	0.568520i	$-0.807516\pi$
$937$	− 34.8053i	− 1.13704i	0.822670	−	0.568520i	$-0.192484\pi$
$938$	9.10621i	0.297328i
$939$	54.9330	1.79267
$940$	0	0
$941$	−1.63844	−0.0534115	−0.0267058	−	0.999643i	$-0.508502\pi$
$941$	−1.63844	−0.0534115	−0.0267058	+	0.999643i	$0.508502\pi$
$942$	− 5.81922i	− 0.189600i
$943$	77.7673i	2.53245i
$944$	−2.37929	−0.0774391
$945$	0	0
$946$	−46.0833	−1.49830
$947$	− 30.8520i	− 1.00256i	−0.865286	−	0.501278i	$-0.832863\pi$
$947$	− 30.8520i	− 1.00256i	0.865286	−	0.501278i	$-0.167137\pi$
$948$	− 25.9722i	− 0.843536i
$949$	−51.2174	−1.66259
$950$	0	0
$951$	73.4020	2.38022
$952$	0.347642i	0.0112671i
$953$	− 34.0467i	− 1.10288i	−0.834214	−	0.551441i	$-0.814078\pi$
$953$	− 34.0467i	− 1.10288i	0.834214	−	0.551441i	$-0.185922\pi$
$954$	5.05685	0.163721
$955$	0	0
$956$	1.78757	0.0578143
$957$	− 5.51186i	− 0.178173i
$958$	− 4.01392i	− 0.129684i
$959$	−1.54351	−0.0498424
$960$	0	0
$961$	4.83314	0.155908
$962$	− 5.27307i	− 0.170011i
$963$	− 15.9597i	− 0.514295i
$964$	3.72693	0.120036
$965$	0	0
$966$	18.9432	0.609486
$967$	− 58.2757i	− 1.87402i	−0.349302	−	0.937010i	$-0.613581\pi$
$967$	− 58.2757i	− 1.87402i	0.349302	−	0.937010i	$-0.386419\pi$
$968$	8.71301i	0.280047i
$969$	−3.54615	−0.113919
$970$	0	0
$971$	57.6611	1.85043	0.925217	−	0.379439i	$-0.123883\pi$
$971$	57.6611	1.85043	0.925217	+	0.379439i	$0.123883\pi$
$972$	− 18.8799i	− 0.605572i
$973$	− 9.58907i	− 0.307411i
$974$	43.3842	1.39012
$975$	0	0
$976$	11.8192	0.378324
$977$	3.78261i	0.121016i	0.998168	+	0.0605082i	$0.0192721\pi$
$977$	3.78261i	0.121016i	−0.998168	+	0.0605082i	$0.980728\pi$
$978$	− 49.3552i	− 1.57821i
$979$	61.5639	1.96759
$980$	0	0
$981$	9.39057	0.299818
$982$	20.7307i	0.661544i
$983$	41.3047i	1.31742i	0.752399	+	0.658708i	$0.228897\pi$
$983$	41.3047i	1.31742i	−0.752399	+	0.658708i	$0.771103\pi$
$984$	27.0038	0.860850
$985$	0	0
$986$	0.149138	0.00474951
$987$	0	0
$988$	− 30.1251i	− 0.958407i
$989$	−67.9443	−2.16050
$990$	0	0
$991$	−9.89263	−0.314250	−0.157125	−	0.987579i	$-0.550222\pi$
$991$	−9.89263	−0.314250	−0.157125	+	0.987579i	$0.550222\pi$
$992$	5.98608i	0.190058i
$993$	63.4765i	2.01437i
$994$	7.13786	0.226399
$995$	0	0
$996$	8.85086	0.280450
$997$	44.5221i	1.41003i	0.709193	+	0.705015i	$0.249060\pi$
$997$	44.5221i	1.41003i	−0.709193	+	0.705015i	$0.750940\pi$
$998$	5.92659i	0.187603i
$999$	−1.89379	−0.0599168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.p.149.1		6
5.2	odd	4		1850.2.a.bc.1.1	yes	3
5.3	odd	4		1850.2.a.y.1.3	✓	3
5.4	even	2	inner	1850.2.b.p.149.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.y.1.3	✓	3	5.3	odd	4
1850.2.a.bc.1.1	yes	3	5.2	odd	4
1850.2.b.p.149.1		6	1.1	even	1	trivial
1850.2.b.p.149.6		6	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.27307i q^{3} -1.00000 q^{4} -2.27307 q^{6} +1.27307i q^{7} +1.00000i q^{8} -2.16686 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.27307i q^{3} -1.00000 q^{4} -2.27307 q^{6} +1.27307i q^{7} +1.00000i q^{8} -2.16686 q^{9} -4.43993 q^{11} +2.27307i q^{12} +5.27307i q^{13} +1.27307 q^{14} +1.00000 q^{16} -0.273073i q^{17} +2.16686i q^{18} +5.71301 q^{19} +2.89379 q^{21} +4.43993i q^{22} +6.54615i q^{23} +2.27307 q^{24} +5.27307 q^{26} -1.89379i q^{27} -1.27307i q^{28} -0.546146 q^{29} -5.98608 q^{31} -1.00000i q^{32} +10.0923i q^{33} -0.273073 q^{34} +2.16686 q^{36} -1.00000i q^{37} -5.71301i q^{38} +11.9861 q^{39} +11.8799 q^{41} -2.89379i q^{42} +10.3793i q^{43} +4.43993 q^{44} +6.54615 q^{46} -2.27307i q^{48} +5.37929 q^{49} -0.620715 q^{51} -5.27307i q^{52} -2.33372i q^{53} -1.89379 q^{54} -1.27307 q^{56} -12.9861i q^{57} +0.546146i q^{58} -2.37929 q^{59} +11.8192 q^{61} +5.98608i q^{62} -2.75857i q^{63} -1.00000 q^{64} +10.0923 q^{66} +7.15294i q^{67} +0.273073i q^{68} +14.8799 q^{69} +5.60679 q^{71} -2.16686i q^{72} +9.71301i q^{73} -1.00000 q^{74} -5.71301 q^{76} -5.65236i q^{77} -11.9861i q^{78} -11.4260 q^{79} -10.8053 q^{81} -11.8799i q^{82} -3.89379i q^{83} -2.89379 q^{84} +10.3793 q^{86} +1.24143i q^{87} -4.43993i q^{88} -13.8659 q^{89} -6.71301 q^{91} -6.54615i q^{92} +13.6068i q^{93} -2.27307 q^{96} +0.879866i q^{97} -5.37929i q^{98} +9.62071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^6 - 12 * q^9	\( 6 q - 6 q^{4} + 2 q^{6} - 12 q^{9} - 10 q^{11} - 8 q^{14} + 6 q^{16} + 2 q^{19} + 32 q^{21} - 2 q^{24} + 16 q^{26} + 28 q^{29} + 12 q^{31} + 14 q^{34} + 12 q^{36} + 24 q^{39} + 38 q^{41} + 10 q^{44} + 8 q^{46} + 2 q^{49} - 34 q^{51} - 26 q^{54} + 8 q^{56} + 16 q^{59} + 24 q^{61} - 6 q^{64} - 2 q^{66} + 56 q^{69} + 16 q^{71} - 6 q^{74} - 2 q^{76} - 4 q^{79} + 30 q^{81} - 32 q^{84} + 32 q^{86} - 2 q^{89} - 8 q^{91} + 2 q^{96} + 88 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^6 - 12 * q^9 - 10 * q^11 - 8 * q^14 + 6 * q^16 + 2 * q^19 + 32 * q^21 - 2 * q^24 + 16 * q^26 + 28 * q^29 + 12 * q^31 + 14 * q^34 + 12 * q^36 + 24 * q^39 + 38 * q^41 + 10 * q^44 + 8 * q^46 + 2 * q^49 - 34 * q^51 - 26 * q^54 + 8 * q^56 + 16 * q^59 + 24 * q^61 - 6 * q^64 - 2 * q^66 + 56 * q^69 + 16 * q^71 - 6 * q^74 - 2 * q^76 - 4 * q^79 + 30 * q^81 - 32 * q^84 + 32 * q^86 - 2 * q^89 - 8 * q^91 + 2 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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