LMFDB - Embedded newform 1850.2.b.p.149.4

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			149.4
Root			$-3.13264i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.p.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.13264i q^{3} -1.00000 q^{4} +3.13264 q^{6} +4.13264i q^{7} -1.00000i q^{8} -6.81342 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.13264i q^{3} -1.00000 q^{4} +3.13264 q^{6} +4.13264i q^{7} -1.00000i q^{8} -6.81342 q^{9} -3.68078 q^{11} +3.13264i q^{12} +0.132637i q^{13} -4.13264 q^{14} +1.00000 q^{16} -5.13264i q^{17} -6.81342i q^{18} -0.451857 q^{19} +12.9461 q^{21} -3.68078i q^{22} +4.26527i q^{23} -3.13264 q^{24} -0.132637 q^{26} +11.9461i q^{27} -4.13264i q^{28} +10.2653 q^{29} +5.58449 q^{31} +1.00000i q^{32} +11.5305i q^{33} +5.13264 q^{34} +6.81342 q^{36} +1.00000i q^{37} -0.451857i q^{38} +0.415505 q^{39} +10.3616 q^{41} +12.9461i q^{42} +5.07869i q^{43} +3.68078 q^{44} -4.26527 q^{46} -3.13264i q^{48} -10.0787 q^{49} -16.0787 q^{51} -0.132637i q^{52} +11.6268i q^{53} -11.9461 q^{54} +4.13264 q^{56} +1.41551i q^{57} +10.2653i q^{58} +13.0787 q^{59} -4.39791 q^{61} +5.58449i q^{62} -28.1574i q^{63} -1.00000 q^{64} -11.5305 q^{66} -0.228923i q^{67} +5.13264i q^{68} +13.3616 q^{69} +9.49420 q^{71} +6.81342i q^{72} -3.54814i q^{73} -1.00000 q^{74} +0.451857 q^{76} -15.2113i q^{77} +0.415505i q^{78} +0.903715 q^{79} +16.9824 q^{81} +10.3616i q^{82} +13.9461i q^{83} -12.9461 q^{84} -5.07869 q^{86} -32.1574i q^{87} +3.68078i q^{88} -0.777066 q^{89} -0.548143 q^{91} -4.26527i q^{92} -17.4942i q^{93} +3.13264 q^{96} +0.638440i q^{97} -10.0787i q^{98} +25.0787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	− 3.13264i	− 1.80863i	−0.426867	−	0.904315i	$-0.640383\pi$
$3$	− 3.13264i	− 1.80863i	0.426867	−	0.904315i	$-0.359617\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	3.13264	1.27889
$7$	4.13264i	1.56199i	0.624537	+	0.780995i	$0.285288\pi$
$7$	4.13264i	1.56199i	−0.624537	+	0.780995i	$0.714712\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−6.81342	−2.27114
$10$	0	0
$11$	−3.68078	−1.10980	−0.554898	−	0.831918i	$-0.687243\pi$
$11$	−3.68078	−1.10980	−0.554898	+	0.831918i	$0.687243\pi$
$12$	3.13264i	0.904315i
$13$	0.132637i	0.0367870i	0.999831	+	0.0183935i	$0.00585517\pi$
$13$	0.132637i	0.0367870i	−0.999831	+	0.0183935i	$0.994145\pi$
$14$	−4.13264	−1.10449
$15$	0	0
$16$	1.00000	0.250000
$17$	− 5.13264i	− 1.24485i	−0.782680	−	0.622424i	$-0.786148\pi$
$17$	− 5.13264i	− 1.24485i	0.782680	−	0.622424i	$-0.213852\pi$
$18$	− 6.81342i	− 1.60594i
$19$	−0.451857	−0.103663	−0.0518316	−	0.998656i	$-0.516506\pi$
$19$	−0.451857	−0.103663	−0.0518316	+	0.998656i	$0.516506\pi$
$20$	0	0
$21$	12.9461	2.82506
$22$	− 3.68078i	− 0.784745i
$23$	4.26527i	0.889371i	0.895687	+	0.444686i	$0.146685\pi$
$23$	4.26527i	0.889371i	−0.895687	+	0.444686i	$0.853315\pi$
$24$	−3.13264	−0.639447
$25$	0	0
$26$	−0.132637	−0.0260124
$27$	11.9461i	2.29902i
$28$	− 4.13264i	− 0.780995i
$29$	10.2653	1.90621	0.953107	−	0.302634i	$-0.0978660\pi$
$29$	10.2653	1.90621	0.953107	+	0.302634i	$0.0978660\pi$
$30$	0	0
$31$	5.58449	1.00300	0.501502	−	0.865156i	$-0.332781\pi$
$31$	5.58449	1.00300	0.501502	+	0.865156i	$0.332781\pi$
$32$	1.00000i	0.176777i
$33$	11.5305i	2.00721i
$34$	5.13264	0.880240
$35$	0	0
$36$	6.81342	1.13557
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	− 0.451857i	− 0.0733009i
$39$	0.415505	0.0665341
$40$	0	0
$41$	10.3616	1.61820	0.809102	−	0.587668i	$-0.199954\pi$
$41$	10.3616	1.61820	0.809102	+	0.587668i	$0.199954\pi$
$42$	12.9461i	1.99762i
$43$	5.07869i	0.774493i	0.921976	+	0.387247i	$0.126574\pi$
$43$	5.07869i	0.774493i	−0.921976	+	0.387247i	$0.873426\pi$
$44$	3.68078	0.554898
$45$	0	0
$46$	−4.26527	−0.628880
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	− 3.13264i	− 0.452157i
$49$	−10.0787	−1.43981
$50$	0	0
$51$	−16.0787	−2.25147
$52$	− 0.132637i	− 0.0183935i
$53$	11.6268i	1.59707i	0.601949	+	0.798534i	$0.294391\pi$
$53$	11.6268i	1.59707i	−0.601949	+	0.798534i	$0.705609\pi$
$54$	−11.9461	−1.62565
$55$	0	0
$56$	4.13264	0.552247
$57$	1.41551i	0.187488i
$58$	10.2653i	1.34790i
$59$	13.0787	1.70270	0.851350	−	0.524597i	$-0.175784\pi$
$59$	13.0787	1.70270	0.851350	+	0.524597i	$0.175784\pi$
$60$	0	0
$61$	−4.39791	−0.563095	−0.281547	−	0.959547i	$-0.590848\pi$
$61$	−4.39791	−0.563095	−0.281547	+	0.959547i	$0.590848\pi$
$62$	5.58449i	0.709232i
$63$	− 28.1574i	− 3.54750i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−11.5305	−1.41931
$67$	− 0.228923i	− 0.0279674i	−0.999902	−	0.0139837i	$-0.995549\pi$
$67$	− 0.228923i	− 0.0279674i	0.999902	−	0.0139837i	$-0.00445129\pi$
$68$	5.13264i	0.622424i
$69$	13.3616	1.60854
$70$	0	0
$71$	9.49420	1.12675	0.563377	−	0.826200i	$-0.309502\pi$
$71$	9.49420	1.12675	0.563377	+	0.826200i	$0.309502\pi$
$72$	6.81342i	0.802969i
$73$	− 3.54814i	− 0.415279i	−0.978205	−	0.207639i	$-0.933422\pi$
$73$	− 3.54814i	− 0.415279i	0.978205	−	0.207639i	$-0.0665780\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	0.451857	0.0518316
$77$	− 15.2113i	− 1.73349i
$78$	0.415505i	0.0470467i
$79$	0.903715	0.101676	0.0508379	−	0.998707i	$-0.483811\pi$
$79$	0.903715	0.101676	0.0508379	+	0.998707i	$0.483811\pi$
$80$	0	0
$81$	16.9824	1.88693
$82$	10.3616i	1.14424i
$83$	13.9461i	1.53078i	0.643568	+	0.765389i	$0.277454\pi$
$83$	13.9461i	1.53078i	−0.643568	+	0.765389i	$0.722546\pi$
$84$	−12.9461	−1.41253
$85$	0	0
$86$	−5.07869	−0.547650
$87$	− 32.1574i	− 3.44763i
$88$	3.68078i	0.392372i
$89$	−0.777066	−0.0823688	−0.0411844	−	0.999152i	$-0.513113\pi$
$89$	−0.777066	−0.0823688	−0.0411844	+	0.999152i	$0.513113\pi$
$90$	0	0
$91$	−0.548143	−0.0574610
$92$	− 4.26527i	− 0.444686i
$93$	− 17.4942i	− 1.81406i
$94$	0	0
$95$	0	0
$96$	3.13264	0.319723
$97$	0.638440i	0.0648237i	0.999475	+	0.0324119i	$0.0103188\pi$
$97$	0.638440i	0.0648237i	−0.999475	+	0.0324119i	$0.989681\pi$
$98$	− 10.0787i	− 1.01810i
$99$	25.0787	2.52050
$100$	0	0
$101$	−5.62684	−0.559891	−0.279946	−	0.960016i	$-0.590316\pi$
$101$	−5.62684	−0.559891	−0.279946	+	0.960016i	$0.590316\pi$
$102$	− 16.0787i	− 1.59203i
$103$	− 10.0423i	− 0.989501i	−0.869035	−	0.494751i	$-0.835259\pi$
$103$	− 10.0423i	− 0.989501i	0.869035	−	0.494751i	$-0.164741\pi$
$104$	0.132637	0.0130062
$105$	0	0
$106$	−11.6268	−1.12930
$107$	19.6632i	1.90091i	0.310859	+	0.950456i	$0.399383\pi$
$107$	19.6632i	1.90091i	−0.310859	+	0.950456i	$0.600617\pi$
$108$	− 11.9461i	− 1.14951i
$109$	−13.6268	−1.30521	−0.652607	−	0.757697i	$-0.726325\pi$
$109$	−13.6268	−1.30521	−0.652607	+	0.757697i	$0.726325\pi$
$110$	0	0
$111$	3.13264	0.297337
$112$	4.13264i	0.390498i
$113$	− 7.94606i	− 0.747502i	−0.927529	−	0.373751i	$-0.878071\pi$
$113$	− 7.94606i	− 0.747502i	0.927529	−	0.373751i	$-0.121929\pi$
$114$	−1.41551	−0.132574
$115$	0	0
$116$	−10.2653	−0.953107
$117$	− 0.903715i	− 0.0835484i
$118$	13.0787i	1.20399i
$119$	21.2113	1.94444
$120$	0	0
$121$	2.54814	0.231649
$122$	− 4.39791i	− 0.398168i
$123$	− 32.4590i	− 2.92673i
$124$	−5.58449	−0.501502
$125$	0	0
$126$	28.1574	2.50846
$127$	17.4942i	1.55236i	0.630512	+	0.776180i	$0.282845\pi$
$127$	17.4942i	1.55236i	−0.630512	+	0.776180i	$0.717155\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	15.9097	1.40077
$130$	0	0
$131$	8.81342	0.770032	0.385016	−	0.922910i	$-0.374196\pi$
$131$	8.81342	0.770032	0.385016	+	0.922910i	$0.374196\pi$
$132$	− 11.5305i	− 1.00361i
$133$	− 1.86736i	− 0.161921i
$134$	0.228923	0.0197759
$135$	0	0
$136$	−5.13264	−0.440120
$137$	18.8921i	1.61406i	0.590509	+	0.807031i	$0.298927\pi$
$137$	18.8921i	1.61406i	−0.590509	+	0.807031i	$0.701073\pi$
$138$	13.3616i	1.13741i
$139$	14.8498	1.25954	0.629771	−	0.776781i	$-0.283149\pi$
$139$	14.8498	1.25954	0.629771	+	0.776781i	$0.283149\pi$
$140$	0	0
$141$	0	0
$142$	9.49420i	0.796735i
$143$	− 0.488209i	− 0.0408261i
$144$	−6.81342	−0.567785
$145$	0	0
$146$	3.54814	0.293646
$147$	31.5729i	2.60409i
$148$	− 1.00000i	− 0.0821995i
$149$	2.41551	0.197886	0.0989429	−	0.995093i	$-0.468454\pi$
$149$	2.41551	0.197886	0.0989429	+	0.995093i	$0.468454\pi$
$150$	0	0
$151$	10.7231	0.872635	0.436318	−	0.899793i	$-0.356282\pi$
$151$	10.7231	0.872635	0.436318	+	0.899793i	$0.356282\pi$
$152$	0.451857i	0.0366505i
$153$	34.9708i	2.82722i
$154$	15.2113	1.22576
$155$	0	0
$156$	−0.415505	−0.0332670
$157$	− 3.31922i	− 0.264903i	−0.991190	−	0.132451i	$-0.957715\pi$
$157$	− 3.31922i	− 0.264903i	0.991190	−	0.132451i	$-0.0422848\pi$
$158$	0.903715i	0.0718957i
$159$	36.4227	2.88850
$160$	0	0
$161$	−17.6268	−1.38919
$162$	16.9824i	1.33426i
$163$	− 15.5481i	− 1.21782i	−0.793238	−	0.608912i	$-0.791606\pi$
$163$	− 15.5481i	− 1.21782i	0.793238	−	0.608912i	$-0.208394\pi$
$164$	−10.3616	−0.809102
$165$	0	0
$166$	−13.9461	−1.08242
$167$	− 3.77707i	− 0.292278i	−0.989264	−	0.146139i	$-0.953315\pi$
$167$	− 3.77707i	− 0.292278i	0.989264	−	0.146139i	$-0.0466847\pi$
$168$	− 12.9461i	− 0.998810i
$169$	12.9824	0.998647
$170$	0	0
$171$	3.07869	0.235434
$172$	− 5.07869i	− 0.387247i
$173$	− 20.1574i	− 1.53254i	−0.642520	−	0.766269i	$-0.722111\pi$
$173$	− 20.1574i	− 1.53254i	0.642520	−	0.766269i	$-0.277889\pi$
$174$	32.1574	2.43785
$175$	0	0
$176$	−3.68078	−0.277449
$177$	− 40.9708i	− 3.07955i
$178$	− 0.777066i	− 0.0582435i
$179$	−20.2537	−1.51383	−0.756915	−	0.653513i	$-0.773294\pi$
$179$	−20.2537	−1.51383	−0.756915	+	0.653513i	$0.773294\pi$
$180$	0	0
$181$	−17.1690	−1.27616	−0.638080	−	0.769970i	$-0.720271\pi$
$181$	−17.1690	−1.27616	−0.638080	+	0.769970i	$0.720271\pi$
$182$	− 0.548143i	− 0.0406310i
$183$	13.7771i	1.01843i
$184$	4.26527	0.314440
$185$	0	0
$186$	17.4942	1.28274
$187$	18.8921i	1.38153i
$188$	0	0
$189$	−49.3687	−3.59105
$190$	0	0
$191$	−0.192571	−0.0139339	−0.00696696	−	0.999976i	$-0.502218\pi$
$191$	−0.192571	−0.0139339	−0.00696696	+	0.999976i	$0.502218\pi$
$192$	3.13264i	0.226079i
$193$	14.6692i	1.05591i	0.849272	+	0.527955i	$0.177041\pi$
$193$	14.6692i	1.05591i	−0.849272	+	0.527955i	$0.822959\pi$
$194$	−0.638440	−0.0458373
$195$	0	0
$196$	10.0787	0.719907
$197$	− 7.84977i	− 0.559273i	−0.960106	−	0.279636i	$-0.909786\pi$
$197$	− 7.84977i	− 0.559273i	0.960106	−	0.279636i	$-0.0902139\pi$
$198$	25.0787i	1.78227i
$199$	11.3616	0.805400	0.402700	−	0.915332i	$-0.368072\pi$
$199$	11.3616	0.805400	0.402700	+	0.915332i	$0.368072\pi$
$200$	0	0
$201$	−0.717132	−0.0505826
$202$	− 5.62684i	− 0.395903i
$203$	42.4227i	2.97749i
$204$	16.0787	1.12573
$205$	0	0
$206$	10.0423	0.699683
$207$	− 29.0611i	− 2.01989i
$208$	0.132637i	0.00919676i
$209$	1.66319	0.115045
$210$	0	0
$211$	−12.2289	−0.841874	−0.420937	−	0.907090i	$-0.638299\pi$
$211$	−12.2289	−0.841874	−0.420937	+	0.907090i	$0.638299\pi$
$212$	− 11.6268i	− 0.798534i
$213$	− 29.7419i	− 2.03788i
$214$	−19.6632	−1.34415
$215$	0	0
$216$	11.9461	0.812826
$217$	23.0787i	1.56668i
$218$	− 13.6268i	− 0.922926i
$219$	−11.1150	−0.751085
$220$	0	0
$221$	0.680780	0.0457942
$222$	3.13264i	0.210249i
$223$	− 28.1574i	− 1.88556i	−0.333418	−	0.942779i	$-0.608202\pi$
$223$	− 28.1574i	− 1.88556i	0.333418	−	0.942779i	$-0.391798\pi$
$224$	−4.13264	−0.276123
$225$	0	0
$226$	7.94606	0.528564
$227$	0.282868i	0.0187746i	0.999956	+	0.00938729i	$0.00298811\pi$
$227$	0.282868i	0.0187746i	−0.999956	+	0.00938729i	$0.997012\pi$
$228$	− 1.41551i	− 0.0937441i
$229$	8.45785	0.558910	0.279455	−	0.960159i	$-0.409846\pi$
$229$	8.45785	0.558910	0.279455	+	0.960159i	$0.409846\pi$
$230$	0	0
$231$	−47.6516	−3.13524
$232$	− 10.2653i	− 0.673948i
$233$	14.2477i	0.933397i	0.884417	+	0.466698i	$0.154557\pi$
$233$	14.2477i	0.933397i	−0.884417	+	0.466698i	$0.845443\pi$
$234$	0.903715	0.0590777
$235$	0	0
$236$	−13.0787	−0.851350
$237$	− 2.83101i	− 0.183894i
$238$	21.2113i	1.37493i
$239$	−21.8921	−1.41608	−0.708041	−	0.706171i	$-0.750421\pi$
$239$	−21.8921	−1.41608	−0.708041	+	0.706171i	$0.750421\pi$
$240$	0	0
$241$	−9.13264	−0.588285	−0.294142	−	0.955762i	$-0.595034\pi$
$241$	−9.13264	−0.588285	−0.294142	+	0.955762i	$0.595034\pi$
$242$	2.54814i	0.163801i
$243$	− 17.3616i	− 1.11374i
$244$	4.39791	0.281547
$245$	0	0
$246$	32.4590	2.06951
$247$	− 0.0599332i	− 0.00381346i
$248$	− 5.58449i	− 0.354616i
$249$	43.6879	2.76861
$250$	0	0
$251$	−9.00000	−0.568075	−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000	−0.568075	−0.284037	+	0.958813i	$0.591674\pi$
$252$	28.1574i	1.77375i
$253$	− 15.6995i	− 0.987022i
$254$	−17.4942	−1.09768
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 8.90371i	− 0.555398i	−0.960668	−	0.277699i	$-0.910428\pi$
$257$	− 8.90371i	− 0.555398i	0.960668	−	0.277699i	$-0.0895719\pi$
$258$	15.9097i	0.990495i
$259$	−4.13264	−0.256790
$260$	0	0
$261$	−69.9416	−4.32928
$262$	8.81342i	0.544495i
$263$	14.9037i	0.919002i	0.888177	+	0.459501i	$0.151972\pi$
$263$	14.9037i	0.919002i	−0.888177	+	0.459501i	$0.848028\pi$
$264$	11.5305	0.709656
$265$	0	0
$266$	1.86736	0.114495
$267$	2.43426i	0.148975i
$268$	0.228923i	0.0139837i
$269$	1.55413	0.0947570	0.0473785	−	0.998877i	$-0.484913\pi$
$269$	1.55413	0.0947570	0.0473785	+	0.998877i	$0.484913\pi$
$270$	0	0
$271$	5.68677	0.345447	0.172723	−	0.984970i	$-0.444743\pi$
$271$	5.68677	0.345447	0.172723	+	0.984970i	$0.444743\pi$
$272$	− 5.13264i	− 0.311212i
$273$	1.71713i	0.103926i
$274$	−18.8921	−1.14131
$275$	0	0
$276$	−13.3616	−0.804271
$277$	− 12.9037i	− 0.775309i	−0.921805	−	0.387655i	$-0.873285\pi$
$277$	− 12.9037i	− 0.775309i	0.921805	−	0.387655i	$-0.126715\pi$
$278$	14.8498i	0.890630i
$279$	−38.0495	−2.27796
$280$	0	0
$281$	−12.2829	−0.732734	−0.366367	−	0.930470i	$-0.619399\pi$
$281$	−12.2829	−0.732734	−0.366367	+	0.930470i	$0.619399\pi$
$282$	0	0
$283$	26.8745i	1.59752i	0.601647	+	0.798762i	$0.294511\pi$
$283$	26.8745i	1.59752i	−0.601647	+	0.798762i	$0.705489\pi$
$284$	−9.49420	−0.563377
$285$	0	0
$286$	0.488209	0.0288684
$287$	42.8206i	2.52762i
$288$	− 6.81342i	− 0.401484i
$289$	−9.34397	−0.549645
$290$	0	0
$291$	2.00000	0.117242
$292$	3.54814i	0.207639i
$293$	16.7535i	0.978749i	0.872074	+	0.489375i	$0.162775\pi$
$293$	16.7535i	0.978749i	−0.872074	+	0.489375i	$0.837225\pi$
$294$	−31.5729	−1.84137
$295$	0	0
$296$	1.00000	0.0581238
$297$	− 43.9708i	− 2.55144i
$298$	2.41551i	0.139926i
$299$	−0.565735	−0.0327173
$300$	0	0
$301$	−20.9884	−1.20975
$302$	10.7231i	0.617046i
$303$	17.6268i	1.01264i
$304$	−0.451857	−0.0259158
$305$	0	0
$306$	−34.9708	−1.99915
$307$	− 8.47661i	− 0.483785i	−0.970303	−	0.241893i	$-0.922232\pi$
$307$	− 8.47661i	− 0.483785i	0.970303	−	0.241893i	$-0.0777682\pi$
$308$	15.2113i	0.866746i
$309$	−31.4590	−1.78964
$310$	0	0
$311$	32.4650	1.84092	0.920461	−	0.390835i	$-0.127814\pi$
$311$	32.4650	1.84092	0.920461	+	0.390835i	$0.127814\pi$
$312$	− 0.415505i	− 0.0235233i
$313$	− 28.8134i	− 1.62863i	−0.580423	−	0.814315i	$-0.697113\pi$
$313$	− 28.8134i	− 1.62863i	0.580423	−	0.814315i	$-0.302887\pi$
$314$	3.31922	0.187314
$315$	0	0
$316$	−0.903715	−0.0508379
$317$	− 6.87335i	− 0.386046i	−0.981194	−	0.193023i	$-0.938171\pi$
$317$	− 6.87335i	− 0.386046i	0.981194	−	0.193023i	$-0.0618292\pi$
$318$	36.4227i	2.04248i
$319$	−37.7842	−2.11551
$320$	0	0
$321$	61.5976	3.43804
$322$	− 17.6268i	− 0.982305i
$323$	2.31922i	0.129045i
$324$	−16.9824	−0.943467
$325$	0	0
$326$	15.5481	0.861132
$327$	42.6879i	2.36065i
$328$	− 10.3616i	− 0.572121i
$329$	0	0
$330$	0	0
$331$	−1.65603	−0.0910238	−0.0455119	−	0.998964i	$-0.514492\pi$
$331$	−1.65603	−0.0910238	−0.0455119	+	0.998964i	$0.514492\pi$
$332$	− 13.9461i	− 0.765389i
$333$	− 6.81342i	− 0.373373i
$334$	3.77707	0.206672
$335$	0	0
$336$	12.9461	0.706265
$337$	10.2537i	0.558553i	0.960211	+	0.279277i	$0.0900946\pi$
$337$	10.2537i	0.558553i	−0.960211	+	0.279277i	$0.909905\pi$
$338$	12.9824i	0.706150i
$339$	−24.8921	−1.35195
$340$	0	0
$341$	−20.5553	−1.11313
$342$	3.07869i	0.166477i
$343$	− 12.7231i	− 0.686984i
$344$	5.07869	0.273825
$345$	0	0
$346$	20.1574	1.08367
$347$	25.8805i	1.38934i	0.719329	+	0.694669i	$0.244449\pi$
$347$	25.8805i	1.38934i	−0.719329	+	0.694669i	$0.755551\pi$
$348$	32.1574i	1.72382i
$349$	−12.7535	−0.682678	−0.341339	−	0.939940i	$-0.610880\pi$
$349$	−12.7535	−0.682678	−0.341339	+	0.939940i	$0.610880\pi$
$350$	0	0
$351$	−1.58449	−0.0845741
$352$	− 3.68078i	− 0.196186i
$353$	− 8.72312i	− 0.464285i	−0.972682	−	0.232142i	$-0.925426\pi$
$353$	− 8.72312i	− 0.464285i	0.972682	−	0.232142i	$-0.0745735\pi$
$354$	40.9708	2.17757
$355$	0	0
$356$	0.777066	0.0411844
$357$	− 66.4474i	− 3.51677i
$358$	− 20.2537i	− 1.07044i
$359$	−14.9037	−0.786588	−0.393294	−	0.919413i	$-0.628665\pi$
$359$	−14.9037	−0.786588	−0.393294	+	0.919413i	$0.628665\pi$
$360$	0	0
$361$	−18.7958	−0.989254
$362$	− 17.1690i	− 0.902382i
$363$	− 7.98241i	− 0.418968i
$364$	0.548143	0.0287305
$365$	0	0
$366$	−13.7771	−0.720139
$367$	− 14.8558i	− 0.775464i	−0.921772	−	0.387732i	$-0.873259\pi$
$367$	− 14.8558i	− 0.775464i	0.921772	−	0.387732i	$-0.126741\pi$
$368$	4.26527i	0.222343i
$369$	−70.5976	−3.67517
$370$	0	0
$371$	−48.0495	−2.49461
$372$	17.4942i	0.907032i
$373$	1.77707i	0.0920130i	0.998941	+	0.0460065i	$0.0146495\pi$
$373$	1.77707i	0.0920130i	−0.998941	+	0.0460065i	$0.985351\pi$
$374$	−18.8921	−0.976888
$375$	0	0
$376$	0	0
$377$	1.36156i	0.0701239i
$378$	− 49.3687i	− 2.53925i
$379$	26.3863	1.35537	0.677687	−	0.735351i	$-0.262983\pi$
$379$	26.3863	1.35537	0.677687	+	0.735351i	$0.262983\pi$
$380$	0	0
$381$	54.8030	2.80764
$382$	− 0.192571i	− 0.00985277i
$383$	− 4.57289i	− 0.233664i	−0.993152	−	0.116832i	$-0.962726\pi$
$383$	− 4.57289i	− 0.233664i	0.993152	−	0.116832i	$-0.0372739\pi$
$384$	−3.13264	−0.159862
$385$	0	0
$386$	−14.6692	−0.746641
$387$	− 34.6033i	− 1.75898i
$388$	− 0.638440i	− 0.0324119i
$389$	−5.03635	−0.255353	−0.127677	−	0.991816i	$-0.540752\pi$
$389$	−5.03635	−0.255353	−0.127677	+	0.991816i	$0.540752\pi$
$390$	0	0
$391$	21.8921	1.10713
$392$	10.0787i	0.509051i
$393$	− 27.6092i	− 1.39270i
$394$	7.84977	0.395466
$395$	0	0
$396$	−25.0787	−1.26025
$397$	34.4650i	1.72975i	0.501988	+	0.864874i	$0.332602\pi$
$397$	34.4650i	1.72975i	−0.501988	+	0.864874i	$0.667398\pi$
$398$	11.3616i	0.569504i
$399$	−5.84977	−0.292855
$400$	0	0
$401$	−4.47661	−0.223551	−0.111775	−	0.993733i	$-0.535654\pi$
$401$	−4.47661	−0.223551	−0.111775	+	0.993733i	$0.535654\pi$
$402$	− 0.717132i	− 0.0357673i
$403$	0.740713i	0.0368976i
$404$	5.62684	0.279946
$405$	0	0
$406$	−42.4227	−2.10540
$407$	− 3.68078i	− 0.182449i
$408$	16.0787i	0.796014i
$409$	34.7243	1.71701	0.858503	−	0.512809i	$-0.171395\pi$
$409$	34.7243	1.71701	0.858503	+	0.512809i	$0.171395\pi$
$410$	0	0
$411$	59.1821	2.91924
$412$	10.0423i	0.494751i
$413$	54.0495i	2.65960i
$414$	29.0611	1.42828
$415$	0	0
$416$	−0.132637	−0.00650309
$417$	− 46.5189i	− 2.27804i
$418$	1.66319i	0.0813492i
$419$	7.15023	0.349312	0.174656	−	0.984630i	$-0.444119\pi$
$419$	7.15023	0.349312	0.174656	+	0.984630i	$0.444119\pi$
$420$	0	0
$421$	26.6033	1.29656	0.648282	−	0.761401i	$-0.275488\pi$
$421$	26.6033	1.29656	0.648282	+	0.761401i	$0.275488\pi$
$422$	− 12.2289i	− 0.595295i
$423$	0	0
$424$	11.6268	0.564649
$425$	0	0
$426$	29.7419	1.44100
$427$	− 18.1750i	− 0.879549i
$428$	− 19.6632i	− 0.950456i
$429$	−1.52938	−0.0738393
$430$	0	0
$431$	−1.16899	−0.0563082	−0.0281541	−	0.999604i	$-0.508963\pi$
$431$	−1.16899	−0.0563082	−0.0281541	+	0.999604i	$0.508963\pi$
$432$	11.9461i	0.574755i
$433$	− 5.00000i	− 0.240285i	−0.992757	−	0.120142i	$-0.961665\pi$
$433$	− 5.00000i	− 0.240285i	0.992757	−	0.120142i	$-0.0383351\pi$
$434$	−23.0787	−1.10781
$435$	0	0
$436$	13.6268	0.652607
$437$	− 1.92730i	− 0.0921951i
$438$	− 11.1150i	− 0.531097i
$439$	32.3148	1.54230	0.771150	−	0.636654i	$-0.219682\pi$
$439$	32.3148	1.54230	0.771150	+	0.636654i	$0.219682\pi$
$440$	0	0
$441$	68.6703	3.27002
$442$	0.680780i	0.0323814i
$443$	17.4155i	0.827436i	0.910405	+	0.413718i	$0.135770\pi$
$443$	17.4155i	0.827436i	−0.910405	+	0.413718i	$0.864230\pi$
$444$	−3.13264	−0.148668
$445$	0	0
$446$	28.1574	1.33329
$447$	− 7.56690i	− 0.357902i
$448$	− 4.13264i	− 0.195249i
$449$	7.38032	0.348299	0.174149	−	0.984719i	$-0.444282\pi$
$449$	7.38032	0.348299	0.174149	+	0.984719i	$0.444282\pi$
$450$	0	0
$451$	−38.1386	−1.79588
$452$	7.94606i	0.373751i
$453$	− 33.5916i	− 1.57827i
$454$	−0.282868	−0.0132756
$455$	0	0
$456$	1.41551	0.0662871
$457$	22.7419i	1.06382i	0.846801	+	0.531910i	$0.178526\pi$
$457$	22.7419i	1.06382i	−0.846801	+	0.531910i	$0.821474\pi$
$458$	8.45785i	0.395209i
$459$	61.3148	2.86193
$460$	0	0
$461$	39.7115	1.84955	0.924775	−	0.380515i	$-0.124253\pi$
$461$	39.7115	1.84955	0.924775	+	0.380515i	$0.124253\pi$
$462$	− 47.6516i	− 2.21695i
$463$	30.6456i	1.42422i	0.702067	+	0.712111i	$0.252261\pi$
$463$	30.6456i	1.42422i	−0.702067	+	0.712111i	$0.747739\pi$
$464$	10.2653	0.476553
$465$	0	0
$466$	−14.2477	−0.660011
$467$	24.7958i	1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$467$	24.7958i	1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$468$	0.903715i	0.0417742i
$469$	0.946055	0.0436848
$470$	0	0
$471$	−10.3979	−0.479111
$472$	− 13.0787i	− 0.601996i
$473$	− 18.6936i	− 0.859530i
$474$	2.83101	0.130033
$475$	0	0
$476$	−21.2113	−0.972220
$477$	− 79.2185i	− 3.62717i
$478$	− 21.8921i	− 1.00132i
$479$	15.5845	0.712074	0.356037	−	0.934472i	$-0.384128\pi$
$479$	15.5845	0.712074	0.356037	+	0.934472i	$0.384128\pi$
$480$	0	0
$481$	−0.132637	−0.00604775
$482$	− 9.13264i	− 0.415980i
$483$	55.2185i	2.51253i
$484$	−2.54814	−0.115825
$485$	0	0
$486$	17.3616	0.787536
$487$	3.65720i	0.165724i	0.996561	+	0.0828618i	$0.0264060\pi$
$487$	3.65720i	0.165724i	−0.996561	+	0.0828618i	$0.973594\pi$
$488$	4.39791i	0.199084i
$489$	−48.7067	−2.20259
$490$	0	0
$491$	33.3264	1.50400	0.751999	−	0.659164i	$-0.229090\pi$
$491$	33.3264	1.50400	0.751999	+	0.659164i	$0.229090\pi$
$492$	32.4590i	1.46337i
$493$	− 52.6879i	− 2.37295i
$494$	0.0599332	0.00269652
$495$	0	0
$496$	5.58449	0.250751
$497$	39.2361i	1.75998i
$498$	43.6879i	1.95770i
$499$	−7.53654	−0.337382	−0.168691	−	0.985669i	$-0.553954\pi$
$499$	−7.53654	−0.337382	−0.168691	+	0.985669i	$0.553954\pi$
$500$	0	0
$501$	−11.8322	−0.528623
$502$	− 9.00000i	− 0.401690i
$503$	24.0000i	1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$	24.0000i	1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	−28.1574	−1.25423
$505$	0	0
$506$	15.6995	0.697930
$507$	− 40.6692i	− 1.80618i
$508$	− 17.4942i	− 0.776180i
$509$	−24.1150	−1.06888	−0.534440	−	0.845206i	$-0.679478\pi$
$509$	−24.1150	−1.06888	−0.534440	+	0.845206i	$0.679478\pi$
$510$	0	0
$511$	14.6632	0.648661
$512$	1.00000i	0.0441942i
$513$	− 5.39791i	− 0.238324i
$514$	8.90371	0.392726
$515$	0	0
$516$	−15.9097	−0.700386
$517$	0	0
$518$	− 4.13264i	− 0.181578i
$519$	−63.1458	−2.77179
$520$	0	0
$521$	−11.8134	−0.517555	−0.258778	−	0.965937i	$-0.583320\pi$
$521$	−11.8134	−0.517555	−0.258778	+	0.965937i	$0.583320\pi$
$522$	− 69.9416i	− 3.06126i
$523$	33.9532i	1.48467i	0.670029	+	0.742335i	$0.266282\pi$
$523$	33.9532i	1.48467i	−0.670029	+	0.742335i	$0.733718\pi$
$524$	−8.81342	−0.385016
$525$	0	0
$526$	−14.9037	−0.649833
$527$	− 28.6632i	− 1.24859i
$528$	11.5305i	0.501803i
$529$	4.80743	0.209019
$530$	0	0
$531$	−89.1106	−3.86707
$532$	1.86736i	0.0809604i
$533$	1.37433i	0.0595289i
$534$	−2.43426	−0.105341
$535$	0	0
$536$	−0.228923	−0.00988796
$537$	63.4474i	2.73796i
$538$	1.55413i	0.0670033i
$539$	37.0975	1.59790
$540$	0	0
$541$	−33.4590	−1.43852	−0.719258	−	0.694743i	$-0.755518\pi$
$541$	−33.4590	−1.43852	−0.719258	+	0.694743i	$0.755518\pi$
$542$	5.68677i	0.244268i
$543$	53.7842i	2.30810i
$544$	5.13264	0.220060
$545$	0	0
$546$	−1.71713	−0.0734865
$547$	− 42.1514i	− 1.80226i	−0.433545	−	0.901132i	$-0.642738\pi$
$547$	− 42.1514i	− 1.80226i	0.433545	−	0.901132i	$-0.357262\pi$
$548$	− 18.8921i	− 0.807031i
$549$	29.9648	1.27887
$550$	0	0
$551$	−4.63844	−0.197604
$552$	− 13.3616i	− 0.568706i
$553$	3.73473i	0.158817i
$554$	12.9037	0.548226
$555$	0	0
$556$	−14.8498	−0.629771
$557$	12.3732i	0.524268i	0.965032	+	0.262134i	$0.0844262\pi$
$557$	12.3732i	0.524268i	−0.965032	+	0.262134i	$0.915574\pi$
$558$	− 38.0495i	− 1.61076i
$559$	−0.673625	−0.0284913
$560$	0	0
$561$	59.1821	2.49867
$562$	− 12.2829i	− 0.518122i
$563$	− 40.7782i	− 1.71860i	−0.511474	−	0.859299i	$-0.670900\pi$
$563$	− 40.7782i	− 1.71860i	0.511474	−	0.859299i	$-0.329100\pi$
$564$	0	0
$565$	0	0
$566$	−26.8745	−1.12962
$567$	70.1821i	2.94737i
$568$	− 9.49420i	− 0.398368i
$569$	20.7419	0.869545	0.434772	−	0.900540i	$-0.356829\pi$
$569$	20.7419	0.869545	0.434772	+	0.900540i	$0.356829\pi$
$570$	0	0
$571$	−37.1458	−1.55450	−0.777251	−	0.629190i	$-0.783387\pi$
$571$	−37.1458	−1.55450	−0.777251	+	0.629190i	$0.783387\pi$
$572$	0.488209i	0.0204131i
$573$	0.603254i	0.0252013i
$574$	−42.8206	−1.78730
$575$	0	0
$576$	6.81342	0.283892
$577$	− 23.0975i	− 0.961560i	−0.876841	−	0.480780i	$-0.840354\pi$
$577$	− 23.0975i	− 0.961560i	0.876841	−	0.480780i	$-0.159646\pi$
$578$	− 9.34397i	− 0.388658i
$579$	45.9532	1.90975
$580$	0	0
$581$	−57.6340	−2.39106
$582$	2.00000i	0.0829027i
$583$	− 42.7958i	− 1.77242i
$584$	−3.54814	−0.146823
$585$	0	0
$586$	−16.7535	−0.692080
$587$	11.0176i	0.454745i	0.973808	+	0.227372i	$0.0730134\pi$
$587$	11.0176i	0.454745i	−0.973808	+	0.227372i	$0.926987\pi$
$588$	− 31.5729i	− 1.30204i
$589$	−2.52339	−0.103975
$590$	0	0
$591$	−24.5905	−1.01152
$592$	1.00000i	0.0410997i
$593$	0.469450i	0.0192780i	0.999954	+	0.00963900i	$0.00306824\pi$
$593$	0.469450i	0.0192780i	−0.999954	+	0.00963900i	$0.996932\pi$
$594$	43.9708	1.80414
$595$	0	0
$596$	−2.41551	−0.0989429
$597$	− 35.5916i	− 1.45667i
$598$	− 0.565735i	− 0.0231346i
$599$	24.7711	1.01212	0.506059	−	0.862499i	$-0.331102\pi$
$599$	24.7711	1.01212	0.506059	+	0.862499i	$0.331102\pi$
$600$	0	0
$601$	−23.4051	−0.954713	−0.477356	−	0.878710i	$-0.658405\pi$
$601$	−23.4051	−0.954713	−0.477356	+	0.878710i	$0.658405\pi$
$602$	− 20.9884i	− 0.855423i
$603$	1.55975i	0.0635178i
$604$	−10.7231	−0.436318
$605$	0	0
$606$	−17.6268	−0.716041
$607$	0.342801i	0.0139139i	0.999976	+	0.00695693i	$0.00221448\pi$
$607$	0.342801i	0.0139139i	−0.999976	+	0.00695693i	$0.997786\pi$
$608$	− 0.451857i	− 0.0183252i
$609$	132.895	5.38517
$610$	0	0
$611$	0	0
$612$	− 34.9708i	− 1.41361i
$613$	− 35.8921i	− 1.44967i	−0.688923	−	0.724834i	$-0.741916\pi$
$613$	− 35.8921i	− 1.44967i	0.688923	−	0.724834i	$-0.258084\pi$
$614$	8.47661	0.342088
$615$	0	0
$616$	−15.2113	−0.612882
$617$	7.64443i	0.307753i	0.988090	+	0.153877i	$0.0491758\pi$
$617$	7.64443i	0.307753i	−0.988090	+	0.153877i	$0.950824\pi$
$618$	− 31.4590i	− 1.26547i
$619$	10.4227	0.418922	0.209461	−	0.977817i	$-0.432829\pi$
$619$	10.4227	0.418922	0.209461	+	0.977817i	$0.432829\pi$
$620$	0	0
$621$	−50.9532	−2.04468
$622$	32.4650i	1.30173i
$623$	− 3.21133i	− 0.128659i
$624$	0.415505	0.0166335
$625$	0	0
$626$	28.8134	1.15162
$627$	− 5.21016i	− 0.208074i
$628$	3.31922i	0.132451i
$629$	5.13264	0.204652
$630$	0	0
$631$	26.4227	1.05187	0.525935	−	0.850525i	$-0.323716\pi$
$631$	26.4227	1.05187	0.525935	+	0.850525i	$0.323716\pi$
$632$	− 0.903715i	− 0.0359478i
$633$	38.3088i	1.52264i
$634$	6.87335	0.272976
$635$	0	0
$636$	−36.4227	−1.44425
$637$	− 1.33681i	− 0.0529664i
$638$	− 37.7842i	− 1.49589i
$639$	−64.6879	−2.55902
$640$	0	0
$641$	11.8074	0.466365	0.233183	−	0.972433i	$-0.425086\pi$
$641$	11.8074	0.466365	0.233183	+	0.972433i	$0.425086\pi$
$642$	61.5976i	2.43106i
$643$	− 18.3556i	− 0.723873i	−0.932203	−	0.361937i	$-0.882116\pi$
$643$	− 18.3556i	− 0.723873i	0.932203	−	0.361937i	$-0.117884\pi$
$644$	17.6268	0.694595
$645$	0	0
$646$	−2.31922	−0.0912485
$647$	33.7771i	1.32791i	0.747771	+	0.663957i	$0.231124\pi$
$647$	33.7771i	1.32791i	−0.747771	+	0.663957i	$0.768876\pi$
$648$	− 16.9824i	− 0.667132i
$649$	−48.1398	−1.88965
$650$	0	0
$651$	72.2972	2.83355
$652$	15.5481i	0.608912i
$653$	− 18.0247i	− 0.705363i	−0.935743	−	0.352681i	$-0.885270\pi$
$653$	− 18.0247i	− 0.705363i	0.935743	−	0.352681i	$-0.114730\pi$
$654$	−42.6879	−1.66923
$655$	0	0
$656$	10.3616	0.404551
$657$	24.1750i	0.943156i
$658$	0	0
$659$	−16.5669	−0.645355	−0.322677	−	0.946509i	$-0.604583\pi$
$659$	−16.5669	−0.645355	−0.322677	+	0.946509i	$0.604583\pi$
$660$	0	0
$661$	−23.7842	−0.925099	−0.462549	−	0.886593i	$-0.653065\pi$
$661$	−23.7842	−0.925099	−0.462549	+	0.886593i	$0.653065\pi$
$662$	− 1.65603i	− 0.0643635i
$663$	− 2.13264i	− 0.0828248i
$664$	13.9461	0.541212
$665$	0	0
$666$	6.81342	0.264015
$667$	43.7842i	1.69533i
$668$	3.77707i	0.146139i
$669$	−88.2069	−3.41028
$670$	0	0
$671$	16.1877	0.624921
$672$	12.9461i	0.499405i
$673$	12.0551i	0.464690i	0.972633	+	0.232345i	$0.0746399\pi$
$673$	12.0551i	0.464690i	−0.972633	+	0.232345i	$0.925360\pi$
$674$	−10.2537	−0.394957
$675$	0	0
$676$	−12.9824	−0.499323
$677$	− 28.8805i	− 1.10997i	−0.831861	−	0.554984i	$-0.812724\pi$
$677$	− 28.8805i	− 1.10997i	0.831861	−	0.554984i	$-0.187276\pi$
$678$	− 24.8921i	− 0.955976i
$679$	−2.63844	−0.101254
$680$	0	0
$681$	0.886122	0.0339563
$682$	− 20.5553i	− 0.787103i
$683$	− 17.6328i	− 0.674701i	−0.941379	−	0.337351i	$-0.890469\pi$
$683$	− 17.6328i	− 0.674701i	0.941379	−	0.337351i	$-0.109531\pi$
$684$	−3.07869	−0.117717
$685$	0	0
$686$	12.7231	0.485771
$687$	− 26.4954i	− 1.01086i
$688$	5.07869i	0.193623i
$689$	−1.54215	−0.0587514
$690$	0	0
$691$	−20.6572	−0.785837	−0.392918	−	0.919573i	$-0.628535\pi$
$691$	−20.6572	−0.785837	−0.392918	+	0.919573i	$0.628535\pi$
$692$	20.1574i	0.766269i
$693$	103.641i	3.93700i
$694$	−25.8805	−0.982411
$695$	0	0
$696$	−32.1574	−1.21892
$697$	− 53.1821i	− 2.01442i
$698$	− 12.7535i	− 0.482727i
$699$	44.6328	1.68817
$700$	0	0
$701$	49.2057	1.85847	0.929237	−	0.369484i	$-0.120466\pi$
$701$	49.2057	1.85847	0.929237	+	0.369484i	$0.120466\pi$
$702$	− 1.58449i	− 0.0598029i
$703$	− 0.451857i	− 0.0170421i
$704$	3.68078	0.138725
$705$	0	0
$706$	8.72312	0.328299
$707$	− 23.2537i	− 0.874544i
$708$	40.9708i	1.53978i
$709$	−3.73473	−0.140261	−0.0701303	−	0.997538i	$-0.522341\pi$
$709$	−3.73473	−0.140261	−0.0701303	+	0.997538i	$0.522341\pi$
$710$	0	0
$711$	−6.15739	−0.230920
$712$	0.777066i	0.0291218i
$713$	23.8194i	0.892044i
$714$	66.4474	2.48673
$715$	0	0
$716$	20.2537	0.756915
$717$	68.5800i	2.56117i
$718$	− 14.9037i	− 0.556202i
$719$	47.0858	1.75601	0.878003	−	0.478655i	$-0.158876\pi$
$719$	47.0858	1.75601	0.878003	+	0.478655i	$0.158876\pi$
$720$	0	0
$721$	41.5014	1.54559
$722$	− 18.7958i	− 0.699508i
$723$	28.6092i	1.06399i
$724$	17.1690	0.638080
$725$	0	0
$726$	7.98241	0.296255
$727$	27.3616i	1.01478i	0.861715	+	0.507392i	$0.169390\pi$
$727$	27.3616i	1.01478i	−0.861715	+	0.507392i	$0.830610\pi$
$728$	0.548143i	0.0203155i
$729$	−3.44025	−0.127417
$730$	0	0
$731$	26.0671	0.964126
$732$	− 13.7771i	− 0.509215i
$733$	− 47.5070i	− 1.75471i	−0.479842	−	0.877355i	$-0.659306\pi$
$733$	− 47.5070i	− 1.75471i	0.479842	−	0.877355i	$-0.340694\pi$
$734$	14.8558	0.548336
$735$	0	0
$736$	−4.26527	−0.157220
$737$	0.842615i	0.0310381i
$738$	− 70.5976i	− 2.59873i
$739$	−19.6149	−0.721544	−0.360772	−	0.932654i	$-0.617487\pi$
$739$	−19.6149	−0.721544	−0.360772	+	0.932654i	$0.617487\pi$
$740$	0	0
$741$	−0.187749	−0.00689713
$742$	− 48.0495i	− 1.76395i
$743$	− 22.3148i	− 0.818650i	−0.912389	−	0.409325i	$-0.865764\pi$
$743$	− 22.3148i	− 0.818650i	0.912389	−	0.409325i	$-0.134236\pi$
$744$	−17.4942	−0.641368
$745$	0	0
$746$	−1.77707	−0.0650630
$747$	− 95.0203i	− 3.47661i
$748$	− 18.8921i	− 0.690764i
$749$	−81.2608	−2.96921
$750$	0	0
$751$	20.7958	0.758850	0.379425	−	0.925222i	$-0.376122\pi$
$751$	20.7958	0.758850	0.379425	+	0.925222i	$0.376122\pi$
$752$	0	0
$753$	28.1937i	1.02744i
$754$	−1.36156	−0.0495851
$755$	0	0
$756$	49.3687	1.79552
$757$	− 0.530550i	− 0.0192832i	−0.999954	−	0.00964158i	$-0.996931\pi$
$757$	− 0.530550i	− 0.0192832i	0.999954	−	0.00964158i	$-0.00306906\pi$
$758$	26.3863i	0.958394i
$759$	−49.1810	−1.78516
$760$	0	0
$761$	4.63245	0.167926	0.0839631	−	0.996469i	$-0.473242\pi$
$761$	4.63245	0.167926	0.0839631	+	0.996469i	$0.473242\pi$
$762$	54.8030i	1.98530i
$763$	− 56.3148i	− 2.03873i
$764$	0.192571	0.00696696
$765$	0	0
$766$	4.57289	0.165225
$767$	1.73473i	0.0626373i
$768$	− 3.13264i	− 0.113039i
$769$	−7.78867	−0.280867	−0.140433	−	0.990090i	$-0.544850\pi$
$769$	−7.78867	−0.280867	−0.140433	+	0.990090i	$0.544850\pi$
$770$	0	0
$771$	−27.8921	−1.00451
$772$	− 14.6692i	− 0.527955i
$773$	8.04234i	0.289263i	0.989486	+	0.144631i	$0.0461997\pi$
$773$	8.04234i	0.289263i	−0.989486	+	0.144631i	$0.953800\pi$
$774$	34.6033	1.24379
$775$	0	0
$776$	0.638440	0.0229186
$777$	12.9461i	0.464437i
$778$	− 5.03635i	− 0.180562i
$779$	−4.68195	−0.167748
$780$	0	0
$781$	−34.9461	−1.25047
$782$	21.8921i	0.782860i
$783$	122.630i	4.38242i
$784$	−10.0787	−0.359953
$785$	0	0
$786$	27.6092	0.984789
$787$	25.6268i	0.913498i	0.889596	+	0.456749i	$0.150986\pi$
$787$	25.6268i	0.913498i	−0.889596	+	0.456749i	$0.849014\pi$
$788$	7.84977i	0.279636i
$789$	46.6879	1.66213
$790$	0	0
$791$	32.8382	1.16759
$792$	− 25.0787i	− 0.891133i
$793$	− 0.583328i	− 0.0207146i
$794$	−34.4650	−1.22312
$795$	0	0
$796$	−11.3616	−0.402700
$797$	11.4095i	0.404146i	0.979370	+	0.202073i	$0.0647678\pi$
$797$	11.4095i	0.404146i	−0.979370	+	0.202073i	$0.935232\pi$
$798$	− 5.84977i	− 0.207080i
$799$	0	0
$800$	0	0
$801$	5.29447	0.187071
$802$	− 4.47661i	− 0.158074i
$803$	13.0599i	0.460875i
$804$	0.717132	0.0252913
$805$	0	0
$806$	−0.740713	−0.0260905
$807$	− 4.86853i	− 0.171380i
$808$	5.62684i	0.197951i
$809$	−21.5189	−0.756566	−0.378283	−	0.925690i	$-0.623485\pi$
$809$	−21.5189	−0.756566	−0.378283	+	0.925690i	$0.623485\pi$
$810$	0	0
$811$	−44.0847	−1.54802	−0.774011	−	0.633172i	$-0.781753\pi$
$811$	−44.0847	−1.54802	−0.774011	+	0.633172i	$0.781753\pi$
$812$	− 42.4227i	− 1.48874i
$813$	− 17.8146i	− 0.624785i
$814$	3.68078	0.129011
$815$	0	0
$816$	−16.0787	−0.562867
$817$	− 2.29484i	− 0.0802864i
$818$	34.7243i	1.21411i
$819$	3.73473	0.130502
$820$	0	0
$821$	−9.95766	−0.347525	−0.173762	−	0.984788i	$-0.555592\pi$
$821$	−9.95766	−0.347525	−0.173762	+	0.984788i	$0.555592\pi$
$822$	59.1821i	2.06421i
$823$	− 0.663187i	− 0.0231173i	−0.999933	−	0.0115586i	$-0.996321\pi$
$823$	− 0.663187i	− 0.0231173i	0.999933	−	0.0115586i	$-0.00367931\pi$
$824$	−10.0423	−0.349842
$825$	0	0
$826$	−54.0495	−1.88062
$827$	− 41.0671i	− 1.42804i	−0.700124	−	0.714021i	$-0.746872\pi$
$827$	− 41.0671i	− 1.42804i	0.700124	−	0.714021i	$-0.253128\pi$
$828$	29.0611i	1.00994i
$829$	−6.48259	−0.225150	−0.112575	−	0.993643i	$-0.535910\pi$
$829$	−6.48259	−0.225150	−0.112575	+	0.993643i	$0.535910\pi$
$830$	0	0
$831$	−40.4227	−1.40225
$832$	− 0.132637i	− 0.00459838i
$833$	51.7303i	1.79235i
$834$	46.5189	1.61082
$835$	0	0
$836$	−1.66319	−0.0575225
$837$	66.7127i	2.30593i
$838$	7.15023i	0.247001i
$839$	−0.771077	−0.0266205	−0.0133103	−	0.999911i	$-0.504237\pi$
$839$	−0.771077	−0.0266205	−0.0133103	+	0.999911i	$0.504237\pi$
$840$	0	0
$841$	76.3759	2.63365
$842$	26.6033i	0.916809i
$843$	38.4778i	1.32524i
$844$	12.2289	0.420937
$845$	0	0
$846$	0	0
$847$	10.5305i	0.361834i
$848$	11.6268i	0.399267i
$849$	84.1881	2.88933
$850$	0	0
$851$	−4.26527	−0.146212
$852$	29.7419i	1.01894i
$853$	− 30.0975i	− 1.03052i	−0.857035	−	0.515259i	$-0.827696\pi$
$853$	− 30.0975i	− 1.03052i	0.857035	−	0.515259i	$-0.172304\pi$
$854$	18.1750	0.621935
$855$	0	0
$856$	19.6632	0.672074
$857$	8.22892i	0.281095i	0.990074	+	0.140547i	$0.0448862\pi$
$857$	8.22892i	0.281095i	−0.990074	+	0.140547i	$0.955114\pi$
$858$	− 1.52938i	− 0.0522123i
$859$	−14.4286	−0.492299	−0.246150	−	0.969232i	$-0.579165\pi$
$859$	−14.4286	−0.492299	−0.246150	+	0.969232i	$0.579165\pi$
$860$	0	0
$861$	134.141	4.57152
$862$	− 1.16899i	− 0.0398159i
$863$	− 33.9049i	− 1.15414i	−0.816696	−	0.577068i	$-0.804197\pi$
$863$	− 33.9049i	− 1.15414i	0.816696	−	0.577068i	$-0.195803\pi$
$864$	−11.9461	−0.406413
$865$	0	0
$866$	5.00000	0.169907
$867$	29.2713i	0.994104i
$868$	− 23.0787i	− 0.783342i
$869$	−3.32637	−0.112840
$870$	0	0
$871$	0.0303638	0.00102884
$872$	13.6268i	0.461463i
$873$	− 4.34996i	− 0.147224i
$874$	1.92730	0.0651918
$875$	0	0
$876$	11.1150	0.375543
$877$	1.36872i	0.0462182i	0.999733	+	0.0231091i	$0.00735652\pi$
$877$	1.36872i	0.0462182i	−0.999733	+	0.0231091i	$0.992643\pi$
$878$	32.3148i	1.09057i
$879$	52.4826	1.77019
$880$	0	0
$881$	47.5741	1.60281	0.801405	−	0.598122i	$-0.204086\pi$
$881$	47.5741	1.60281	0.801405	+	0.598122i	$0.204086\pi$
$882$	68.6703i	2.31225i
$883$	− 9.88051i	− 0.332506i	−0.986083	−	0.166253i	$-0.946833\pi$
$883$	− 9.88051i	− 0.332506i	0.986083	−	0.166253i	$-0.0531668\pi$
$884$	−0.680780	−0.0228971
$885$	0	0
$886$	−17.4155	−0.585085
$887$	21.8801i	0.734663i	0.930090	+	0.367331i	$0.119729\pi$
$887$	21.8801i	0.734663i	−0.930090	+	0.367331i	$0.880271\pi$
$888$	− 3.13264i	− 0.105124i
$889$	−72.2972	−2.42477
$890$	0	0
$891$	−62.5085	−2.09411
$892$	28.1574i	0.942779i
$893$	0	0
$894$	7.56690	0.253075
$895$	0	0
$896$	4.13264	0.138062
$897$	1.77224i	0.0591735i
$898$	7.38032i	0.246284i
$899$	57.3264	1.91194
$900$	0	0
$901$	59.6763	1.98811
$902$	− 38.1386i	− 1.26988i
$903$	65.7490i	2.18799i
$904$	−7.94606	−0.264282
$905$	0	0
$906$	33.5916	1.11601
$907$	8.46346i	0.281025i	0.990079	+	0.140512i	$0.0448750\pi$
$907$	8.46346i	0.281025i	−0.990079	+	0.140512i	$0.955125\pi$
$908$	− 0.282868i	− 0.00938729i
$909$	38.3380	1.27159
$910$	0	0
$911$	−34.1997	−1.13309	−0.566544	−	0.824032i	$-0.691720\pi$
$911$	−34.1997	−1.13309	−0.566544	+	0.824032i	$0.691720\pi$
$912$	1.41551i	0.0468721i
$913$	− 51.3324i	− 1.69885i
$914$	−22.7419	−0.752235
$915$	0	0
$916$	−8.45785	−0.279455
$917$	36.4227i	1.20278i
$918$	61.3148i	2.02369i
$919$	0.723121	0.0238536	0.0119268	−	0.999929i	$-0.496203\pi$
$919$	0.723121	0.0238536	0.0119268	+	0.999929i	$0.496203\pi$
$920$	0	0
$921$	−26.5541	−0.874988
$922$	39.7115i	1.30783i
$923$	1.25929i	0.0414499i
$924$	47.6516	1.56762
$925$	0	0
$926$	−30.6456	−1.00708
$927$	68.4227i	2.24730i
$928$	10.2653i	0.336974i
$929$	16.7902	0.550869	0.275434	−	0.961320i	$-0.411178\pi$
$929$	16.7902	0.550869	0.275434	+	0.961320i	$0.411178\pi$
$930$	0	0
$931$	4.55413	0.149256
$932$	− 14.2477i	− 0.466698i
$933$	− 101.701i	− 3.32954i
$934$	−24.7958	−0.811344
$935$	0	0
$936$	−0.903715	−0.0295388
$937$	7.01759i	0.229255i	0.993409	+	0.114627i	$0.0365674\pi$
$937$	7.01759i	0.229255i	−0.993409	+	0.114627i	$0.963433\pi$
$938$	0.946055i	0.0308898i
$939$	−90.2620	−2.94559
$940$	0	0
$941$	30.7958	1.00392	0.501958	−	0.864892i	$-0.332613\pi$
$941$	30.7958	1.00392	0.501958	+	0.864892i	$0.332613\pi$
$942$	− 10.3979i	− 0.338782i
$943$	44.1949i	1.43918i
$944$	13.0787	0.425675
$945$	0	0
$946$	18.6936	0.607780
$947$	6.19257i	0.201232i	0.994925	+	0.100616i	$0.0320813\pi$
$947$	6.19257i	0.201232i	−0.994925	+	0.100616i	$0.967919\pi$
$948$	2.83101i	0.0919469i
$949$	0.470617	0.0152769
$950$	0	0
$951$	−21.5317	−0.698214
$952$	− 21.2113i	− 0.687463i
$953$	37.1750i	1.20422i	0.798415	+	0.602108i	$0.205672\pi$
$953$	37.1750i	1.20422i	−0.798415	+	0.602108i	$0.794328\pi$
$954$	79.2185	2.56479
$955$	0	0
$956$	21.8921	0.708041
$957$	118.364i	3.82617i
$958$	15.5845i	0.503512i
$959$	−78.0742	−2.52115
$960$	0	0
$961$	0.186582	0.00601878
$962$	− 0.132637i	− 0.00427640i
$963$	− 133.974i	− 4.31724i
$964$	9.13264	0.294142
$965$	0	0
$966$	−55.2185	−1.77663
$967$	− 34.4722i	− 1.10855i	−0.832334	−	0.554275i	$-0.812996\pi$
$967$	− 34.4722i	− 1.10855i	0.832334	−	0.554275i	$-0.187004\pi$
$968$	− 2.54814i	− 0.0819004i
$969$	7.26527	0.233394
$970$	0	0
$971$	−54.2488	−1.74093	−0.870464	−	0.492232i	$-0.836181\pi$
$971$	−54.2488	−1.74093	−0.870464	+	0.492232i	$0.836181\pi$
$972$	17.3616i	0.556872i
$973$	61.3687i	1.96739i
$974$	−3.65720	−0.117184
$975$	0	0
$976$	−4.39791	−0.140774
$977$	− 55.4706i	− 1.77466i	−0.461133	−	0.887331i	$-0.652557\pi$
$977$	− 55.4706i	− 1.77466i	0.461133	−	0.887331i	$-0.347443\pi$
$978$	− 48.7067i	− 1.55747i
$979$	2.86021	0.0914126
$980$	0	0
$981$	92.8453	2.96432
$982$	33.3264i	1.06349i
$983$	0.422660i	0.0134808i	0.999977	+	0.00674038i	$0.00214555\pi$
$983$	0.422660i	0.0134808i	−0.999977	+	0.00674038i	$0.997854\pi$
$984$	−32.4590	−1.03476
$985$	0	0
$986$	52.6879	1.67793
$987$	0	0
$988$	0.0599332i	0.00190673i
$989$	−21.6620	−0.688812
$990$	0	0
$991$	7.93445	0.252046	0.126023	−	0.992027i	$-0.459779\pi$
$991$	7.93445	0.252046	0.126023	+	0.992027i	$0.459779\pi$
$992$	5.58449i	0.177308i
$993$	5.18775i	0.164628i
$994$	−39.2361	−1.24449
$995$	0	0
$996$	−43.6879	−1.38431
$997$	48.8933i	1.54847i	0.632901	+	0.774233i	$0.281864\pi$
$997$	48.8933i	1.54847i	−0.632901	+	0.774233i	$0.718136\pi$
$998$	− 7.53654i	− 0.238565i
$999$	−11.9461	−0.377956

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.y.1.1	✓	3	5.2	odd	4
1850.2.a.bc.1.3	yes	3	5.3	odd	4
1850.2.b.p.149.3		6	5.4	even	2	inner
1850.2.b.p.149.4		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.13264i q^{3} -1.00000 q^{4} +3.13264 q^{6} +4.13264i q^{7} -1.00000i q^{8} -6.81342 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.13264i q^{3} -1.00000 q^{4} +3.13264 q^{6} +4.13264i q^{7} -1.00000i q^{8} -6.81342 q^{9} -3.68078 q^{11} +3.13264i q^{12} +0.132637i q^{13} -4.13264 q^{14} +1.00000 q^{16} -5.13264i q^{17} -6.81342i q^{18} -0.451857 q^{19} +12.9461 q^{21} -3.68078i q^{22} +4.26527i q^{23} -3.13264 q^{24} -0.132637 q^{26} +11.9461i q^{27} -4.13264i q^{28} +10.2653 q^{29} +5.58449 q^{31} +1.00000i q^{32} +11.5305i q^{33} +5.13264 q^{34} +6.81342 q^{36} +1.00000i q^{37} -0.451857i q^{38} +0.415505 q^{39} +10.3616 q^{41} +12.9461i q^{42} +5.07869i q^{43} +3.68078 q^{44} -4.26527 q^{46} -3.13264i q^{48} -10.0787 q^{49} -16.0787 q^{51} -0.132637i q^{52} +11.6268i q^{53} -11.9461 q^{54} +4.13264 q^{56} +1.41551i q^{57} +10.2653i q^{58} +13.0787 q^{59} -4.39791 q^{61} +5.58449i q^{62} -28.1574i q^{63} -1.00000 q^{64} -11.5305 q^{66} -0.228923i q^{67} +5.13264i q^{68} +13.3616 q^{69} +9.49420 q^{71} +6.81342i q^{72} -3.54814i q^{73} -1.00000 q^{74} +0.451857 q^{76} -15.2113i q^{77} +0.415505i q^{78} +0.903715 q^{79} +16.9824 q^{81} +10.3616i q^{82} +13.9461i q^{83} -12.9461 q^{84} -5.07869 q^{86} -32.1574i q^{87} +3.68078i q^{88} -0.777066 q^{89} -0.548143 q^{91} -4.26527i q^{92} -17.4942i q^{93} +3.13264 q^{96} +0.638440i q^{97} -10.0787i q^{98} +25.0787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 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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