LMFDB - Embedded newform 845.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.a (trivial)

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:	yes
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 $ x^9 - 17x^7 - 9x^6 + 59x^5 + 32x^4 - 44x^3 - 23x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.07331$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.271374 q^{2} -0.319618 q^{3} -1.92636 q^{4} +1.00000 q^{5} +0.0867358 q^{6} -3.38151 q^{7} +1.06551 q^{8} -2.89784 q^{9} -0.271374 q^{10} -1.75204 q^{11} +0.615697 q^{12} +0.917654 q^{14} -0.319618 q^{15} +3.56356 q^{16} +1.95419 q^{17} +0.786399 q^{18} +7.13261 q^{19} -1.92636 q^{20} +1.08079 q^{21} +0.475459 q^{22} +7.61420 q^{23} -0.340556 q^{24} +1.00000 q^{25} +1.88505 q^{27} +6.51400 q^{28} +3.98380 q^{29} +0.0867358 q^{30} -4.86923 q^{31} -3.09808 q^{32} +0.559984 q^{33} -0.530316 q^{34} -3.38151 q^{35} +5.58228 q^{36} -10.5010 q^{37} -1.93560 q^{38} +1.06551 q^{40} -0.911110 q^{41} -0.293298 q^{42} +4.58553 q^{43} +3.37506 q^{44} -2.89784 q^{45} -2.06629 q^{46} +8.58491 q^{47} -1.13898 q^{48} +4.43464 q^{49} -0.271374 q^{50} -0.624593 q^{51} +11.9646 q^{53} -0.511554 q^{54} -1.75204 q^{55} -3.60304 q^{56} -2.27971 q^{57} -1.08110 q^{58} -3.82297 q^{59} +0.615697 q^{60} +7.98476 q^{61} +1.32138 q^{62} +9.79910 q^{63} -6.28638 q^{64} -0.151965 q^{66} -0.472749 q^{67} -3.76446 q^{68} -2.43363 q^{69} +0.917654 q^{70} +5.50312 q^{71} -3.08768 q^{72} -2.93857 q^{73} +2.84969 q^{74} -0.319618 q^{75} -13.7400 q^{76} +5.92456 q^{77} +4.09938 q^{79} +3.56356 q^{80} +8.09104 q^{81} +0.247252 q^{82} +11.7733 q^{83} -2.08199 q^{84} +1.95419 q^{85} -1.24439 q^{86} -1.27329 q^{87} -1.86682 q^{88} +3.85992 q^{89} +0.786399 q^{90} -14.6677 q^{92} +1.55629 q^{93} -2.32972 q^{94} +7.13261 q^{95} +0.990200 q^{96} +6.95775 q^{97} -1.20345 q^{98} +5.07715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9} + 3 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{14} + 7 q^{15} + 37 q^{16} - q^{17} - 10 q^{18} - 4 q^{19} + 17 q^{20} - q^{21}+ \cdots - q^{99}+O(q^{100}) $ 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9 + 3 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^14 + 7 * q^15 + 37 * q^16 - q^17 - 10 * q^18 - 4 * q^19 + 17 * q^20 - q^21 + 12 * q^22 + 14 * q^23 - 35 * q^24 + 9 * q^25 + 22 * q^27 + 18 * q^28 + 12 * q^29 - 2 * q^30 - 7 * q^31 + 22 * q^32 - 8 * q^33 - 30 * q^34 + 7 * q^35 + 3 * q^36 - 5 * q^37 - 47 * q^38 + 12 * q^40 - 10 * q^41 - 11 * q^42 + 39 * q^43 - 25 * q^44 + 16 * q^45 + 6 * q^46 + 36 * q^47 - 3 * q^48 + 16 * q^49 + 3 * q^50 + 43 * q^51 - 8 * q^53 - 2 * q^54 - 9 * q^55 - 29 * q^56 - 32 * q^57 + 21 * q^58 - 21 * q^59 + 12 * q^60 - 3 * q^61 - 10 * q^62 + 35 * q^63 + 34 * q^64 - 49 * q^66 + q^67 - 20 * q^68 - 13 * q^69 - 2 * q^70 - q^71 - 3 * q^72 - 15 * q^74 + 7 * q^75 - 5 * q^76 - 4 * q^77 + 39 * q^79 + 37 * q^80 + 29 * q^81 - 4 * q^82 + 7 * q^83 + 12 * q^84 - q^85 - 24 * q^86 + 16 * q^87 + 42 * q^88 - 19 * q^89 - 10 * q^90 - 27 * q^92 + 31 * q^93 + 16 * q^94 - 4 * q^95 - 7 * q^96 - 34 * q^97 + 48 * q^98 - q^99

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 $

$2$	−0.271374	−0.191890	−0.0959451	−	0.995387i	$-0.530587\pi$
$2$	−0.271374	−0.191890	−0.0959451	+	0.995387i	$0.530587\pi$
$3$	−0.319618	−0.184531	−0.0922656	−	0.995734i	$-0.529411\pi$
$3$	−0.319618	−0.184531	−0.0922656	+	0.995734i	$0.529411\pi$
$4$	−1.92636	−0.963178
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0867358	0.0354098
$7$	−3.38151	−1.27809	−0.639046	−	0.769168i	$-0.720671\pi$
$7$	−3.38151	−1.27809	−0.639046	+	0.769168i	$0.720671\pi$
$8$	1.06551	0.376715
$9$	−2.89784	−0.965948
$10$	−0.271374	−0.0858159
$11$	−1.75204	−0.528261	−0.264131	−	0.964487i	$-0.585085\pi$
$11$	−1.75204	−0.528261	−0.264131	+	0.964487i	$0.585085\pi$
$12$	0.615697	0.177736
$13$	0	0
$13$	0	0
$14$	0.917654	0.245253
$15$	−0.319618	−0.0825249
$16$	3.56356	0.890890
$17$	1.95419	0.473960	0.236980	−	0.971514i	$-0.423842\pi$
$17$	1.95419	0.473960	0.236980	+	0.971514i	$0.423842\pi$
$18$	0.786399	0.185356
$19$	7.13261	1.63633	0.818167	−	0.574981i	$-0.194990\pi$
$19$	7.13261	1.63633	0.818167	+	0.574981i	$0.194990\pi$
$20$	−1.92636	−0.430746
$21$	1.08079	0.235848
$22$	0.475459	0.101368
$23$	7.61420	1.58767	0.793835	−	0.608133i	$-0.208081\pi$
$23$	7.61420	1.58767	0.793835	+	0.608133i	$0.208081\pi$
$24$	−0.340556	−0.0695157
$25$	1.00000	0.200000
$26$	0	0
$27$	1.88505	0.362779
$28$	6.51400	1.23103
$29$	3.98380	0.739773	0.369886	−	0.929077i	$-0.379397\pi$
$29$	3.98380	0.739773	0.369886	+	0.929077i	$0.379397\pi$
$30$	0.0867358	0.0158357
$31$	−4.86923	−0.874540	−0.437270	−	0.899330i	$-0.644055\pi$
$31$	−4.86923	−0.874540	−0.437270	+	0.899330i	$0.644055\pi$
$32$	−3.09808	−0.547668
$33$	0.559984	0.0974807
$34$	−0.530316	−0.0909484
$35$	−3.38151	−0.571580
$36$	5.58228	0.930380
$37$	−10.5010	−1.72635	−0.863176	−	0.504903i	$-0.831528\pi$
$37$	−10.5010	−1.72635	−0.863176	+	0.504903i	$0.831528\pi$
$38$	−1.93560	−0.313997
$39$	0	0
$40$	1.06551	0.168472
$41$	−0.911110	−0.142292	−0.0711458	−	0.997466i	$-0.522666\pi$
$41$	−0.911110	−0.142292	−0.0711458	+	0.997466i	$0.522666\pi$
$42$	−0.293298	−0.0452569
$43$	4.58553	0.699286	0.349643	−	0.936883i	$-0.386303\pi$
$43$	4.58553	0.699286	0.349643	+	0.936883i	$0.386303\pi$
$44$	3.37506	0.508810
$45$	−2.89784	−0.431985
$46$	−2.06629	−0.304658
$47$	8.58491	1.25224	0.626119	−	0.779728i	$-0.284643\pi$
$47$	8.58491	1.25224	0.626119	+	0.779728i	$0.284643\pi$
$48$	−1.13898	−0.164397
$49$	4.43464	0.633520
$50$	−0.271374	−0.0383781
$51$	−0.624593	−0.0874605
$52$	0	0
$53$	11.9646	1.64347	0.821734	−	0.569871i	$-0.193007\pi$
$53$	11.9646	1.64347	0.821734	+	0.569871i	$0.193007\pi$
$54$	−0.511554	−0.0696137
$55$	−1.75204	−0.236246
$56$	−3.60304	−0.481476
$57$	−2.27971	−0.301955
$58$	−1.08110	−0.141955
$59$	−3.82297	−0.497708	−0.248854	−	0.968541i	$-0.580054\pi$
$59$	−3.82297	−0.497708	−0.248854	+	0.968541i	$0.580054\pi$
$60$	0.615697	0.0794862
$61$	7.98476	1.02234	0.511172	−	0.859479i	$-0.329212\pi$
$61$	7.98476	1.02234	0.511172	+	0.859479i	$0.329212\pi$
$62$	1.32138	0.167816
$63$	9.79910	1.23457
$64$	−6.28638	−0.785798
$65$	0	0
$66$	−0.151965	−0.0187056
$67$	−0.472749	−0.0577554	−0.0288777	−	0.999583i	$-0.509193\pi$
$67$	−0.472749	−0.0577554	−0.0288777	+	0.999583i	$0.509193\pi$
$68$	−3.76446	−0.456508
$69$	−2.43363	−0.292975
$70$	0.917654	0.109681
$71$	5.50312	0.653101	0.326550	−	0.945180i	$-0.394114\pi$
$71$	5.50312	0.653101	0.326550	+	0.945180i	$0.394114\pi$
$72$	−3.08768	−0.363887
$73$	−2.93857	−0.343934	−0.171967	−	0.985103i	$-0.555012\pi$
$73$	−2.93857	−0.343934	−0.171967	+	0.985103i	$0.555012\pi$
$74$	2.84969	0.331270
$75$	−0.319618	−0.0369063
$76$	−13.7400	−1.57608
$77$	5.92456	0.675167
$78$	0	0
$79$	4.09938	0.461216	0.230608	−	0.973047i	$-0.425928\pi$
$79$	4.09938	0.461216	0.230608	+	0.973047i	$0.425928\pi$
$80$	3.56356	0.398418
$81$	8.09104	0.899004
$82$	0.247252	0.0273044
$83$	11.7733	1.29229	0.646144	−	0.763215i	$-0.276381\pi$
$83$	11.7733	1.29229	0.646144	+	0.763215i	$0.276381\pi$
$84$	−2.08199	−0.227164
$85$	1.95419	0.211961
$86$	−1.24439	−0.134186
$87$	−1.27329	−0.136511
$88$	−1.86682	−0.199004
$89$	3.85992	0.409151	0.204576	−	0.978851i	$-0.434419\pi$
$89$	3.85992	0.409151	0.204576	+	0.978851i	$0.434419\pi$
$90$	0.786399	0.0828937
$91$	0	0
$92$	−14.6677	−1.52921
$93$	1.55629	0.161380
$94$	−2.32972	−0.240292
$95$	7.13261	0.731791
$96$	0.990200	0.101062
$97$	6.95775	0.706453	0.353226	−	0.935538i	$-0.385085\pi$
$97$	6.95775	0.706453	0.353226	+	0.935538i	$0.385085\pi$
$98$	−1.20345	−0.121566
$99$	5.07715	0.510273
$100$	−1.92636	−0.192636
$101$	−17.8923	−1.78035	−0.890175	−	0.455619i	$-0.849418\pi$
$101$	−17.8923	−1.78035	−0.890175	+	0.455619i	$0.849418\pi$
$102$	0.169498	0.0167828
$103$	10.2561	1.01056	0.505281	−	0.862955i	$-0.331389\pi$
$103$	10.2561	1.01056	0.505281	+	0.862955i	$0.331389\pi$
$104$	0	0
$105$	1.08079	0.105474
$106$	−3.24689	−0.315366
$107$	12.8986	1.24696	0.623478	−	0.781841i	$-0.285719\pi$
$107$	12.8986	1.24696	0.623478	+	0.781841i	$0.285719\pi$
$108$	−3.63129	−0.349421
$109$	−10.4476	−1.00070	−0.500348	−	0.865825i	$-0.666794\pi$
$109$	−10.4476	−1.00070	−0.500348	+	0.865825i	$0.666794\pi$
$110$	0.475459	0.0453332
$111$	3.35630	0.318566
$112$	−12.0502	−1.13864
$113$	−18.9766	−1.78516	−0.892582	−	0.450884i	$-0.851109\pi$
$113$	−18.9766	−1.78516	−0.892582	+	0.450884i	$0.851109\pi$
$114$	0.618653	0.0579422
$115$	7.61420	0.710028
$116$	−7.67421	−0.712533
$117$	0	0
$118$	1.03745	0.0955054
$119$	−6.60812	−0.605765
$120$	−0.340556	−0.0310883
$121$	−7.93034	−0.720940
$122$	−2.16685	−0.196178
$123$	0.291207	0.0262572
$124$	9.37987	0.842337
$125$	1.00000	0.0894427
$126$	−2.65922	−0.236902
$127$	−9.88489	−0.877142	−0.438571	−	0.898697i	$-0.644515\pi$
$127$	−9.88489	−0.877142	−0.438571	+	0.898697i	$0.644515\pi$
$128$	7.90212	0.698455
$129$	−1.46561	−0.129040
$130$	0	0
$131$	−11.4705	−1.00218	−0.501089	−	0.865396i	$-0.667067\pi$
$131$	−11.4705	−1.00218	−0.501089	+	0.865396i	$0.667067\pi$
$132$	−1.07873	−0.0938913
$133$	−24.1190	−2.09139
$134$	0.128292	0.0110827
$135$	1.88505	0.162240
$136$	2.08221	0.178548
$137$	13.0826	1.11772	0.558861	−	0.829261i	$-0.311239\pi$
$137$	13.0826	1.11772	0.558861	+	0.829261i	$0.311239\pi$
$138$	0.660424	0.0562190
$139$	11.9762	1.01581	0.507904	−	0.861414i	$-0.330421\pi$
$139$	11.9762	1.01581	0.507904	+	0.861414i	$0.330421\pi$
$140$	6.51400	0.550534
$141$	−2.74389	−0.231077
$142$	−1.49340	−0.125324
$143$	0	0
$144$	−10.3266	−0.860554
$145$	3.98380	0.330836
$146$	0.797452	0.0659976
$147$	−1.41739	−0.116904
$148$	20.2287	1.66278
$149$	−16.3052	−1.33577	−0.667887	−	0.744262i	$-0.732801\pi$
$149$	−16.3052	−1.33577	−0.667887	+	0.744262i	$0.732801\pi$
$150$	0.0867358	0.00708195
$151$	−8.75415	−0.712402	−0.356201	−	0.934409i	$-0.615928\pi$
$151$	−8.75415	−0.712402	−0.356201	+	0.934409i	$0.615928\pi$
$152$	7.59987	0.616431
$153$	−5.66293	−0.457821
$154$	−1.60777	−0.129558
$155$	−4.86923	−0.391106
$156$	0	0
$157$	6.48821	0.517816	0.258908	−	0.965902i	$-0.416637\pi$
$157$	6.48821	0.517816	0.258908	+	0.965902i	$0.416637\pi$
$158$	−1.11246	−0.0885029
$159$	−3.82411	−0.303271
$160$	−3.09808	−0.244925
$161$	−25.7475	−2.02919
$162$	−2.19570	−0.172510
$163$	3.84933	0.301503	0.150751	−	0.988572i	$-0.451831\pi$
$163$	3.84933	0.301503	0.150751	+	0.988572i	$0.451831\pi$
$164$	1.75512	0.137052
$165$	0.559984	0.0435947
$166$	−3.19497	−0.247977
$167$	6.85894	0.530760	0.265380	−	0.964144i	$-0.414503\pi$
$167$	6.85894	0.530760	0.265380	+	0.964144i	$0.414503\pi$
$168$	1.15159	0.0888474
$169$	0	0
$170$	−0.530316	−0.0406733
$171$	−20.6692	−1.58061
$172$	−8.83336	−0.673537
$173$	16.0204	1.21801	0.609005	−	0.793166i	$-0.291569\pi$
$173$	16.0204	1.21801	0.609005	+	0.793166i	$0.291569\pi$
$174$	0.345538	0.0261952
$175$	−3.38151	−0.255618
$176$	−6.24352	−0.470623
$177$	1.22189	0.0918428
$178$	−1.04748	−0.0785121
$179$	−8.08309	−0.604158	−0.302079	−	0.953283i	$-0.597681\pi$
$179$	−8.08309	−0.604158	−0.302079	+	0.953283i	$0.597681\pi$
$180$	5.58228	0.416079
$181$	11.0898	0.824298	0.412149	−	0.911117i	$-0.364778\pi$
$181$	11.0898	0.824298	0.412149	+	0.911117i	$0.364778\pi$
$182$	0	0
$183$	−2.55207	−0.188654
$184$	8.11301	0.598099
$185$	−10.5010	−0.772048
$186$	−0.422337	−0.0309672
$187$	−3.42382	−0.250375
$188$	−16.5376	−1.20613
$189$	−6.37434	−0.463665
$190$	−1.93560	−0.140424
$191$	21.7532	1.57401	0.787003	−	0.616949i	$-0.211631\pi$
$191$	21.7532	1.57401	0.787003	+	0.616949i	$0.211631\pi$
$192$	2.00924	0.145004
$193$	22.5285	1.62164	0.810820	−	0.585296i	$-0.199022\pi$
$193$	22.5285	1.62164	0.810820	+	0.585296i	$0.199022\pi$
$194$	−1.88815	−0.135561
$195$	0	0
$196$	−8.54270	−0.610193
$197$	−17.2749	−1.23078	−0.615392	−	0.788221i	$-0.711002\pi$
$197$	−17.2749	−1.23078	−0.615392	+	0.788221i	$0.711002\pi$
$198$	−1.37781	−0.0979164
$199$	17.4901	1.23984	0.619919	−	0.784666i	$-0.287166\pi$
$199$	17.4901	1.23984	0.619919	+	0.784666i	$0.287166\pi$
$200$	1.06551	0.0753430
$201$	0.151099	0.0106577
$202$	4.85550	0.341632
$203$	−13.4713	−0.945498
$204$	1.20319	0.0842400
$205$	−0.911110	−0.0636347
$206$	−2.78323	−0.193917
$207$	−22.0648	−1.53361
$208$	0	0
$209$	−12.4967	−0.864412
$210$	−0.293298	−0.0202395
$211$	6.33563	0.436163	0.218081	−	0.975931i	$-0.430020\pi$
$211$	6.33563	0.436163	0.218081	+	0.975931i	$0.430020\pi$
$212$	−23.0481	−1.58295
$213$	−1.75889	−0.120517
$214$	−3.50034	−0.239279
$215$	4.58553	0.312730
$216$	2.00855	0.136664
$217$	16.4654	1.11774
$218$	2.83520	0.192024
$219$	0.939220	0.0634666
$220$	3.37506	0.227547
$221$	0	0
$222$	−0.910812	−0.0611297
$223$	23.4948	1.57333	0.786664	−	0.617381i	$-0.211806\pi$
$223$	23.4948	1.57333	0.786664	+	0.617381i	$0.211806\pi$
$224$	10.4762	0.699970
$225$	−2.89784	−0.193190
$226$	5.14974	0.342556
$227$	9.59397	0.636774	0.318387	−	0.947961i	$-0.396859\pi$
$227$	9.59397	0.636774	0.318387	+	0.947961i	$0.396859\pi$
$228$	4.39153	0.290836
$229$	−7.23000	−0.477772	−0.238886	−	0.971048i	$-0.576782\pi$
$229$	−7.23000	−0.477772	−0.238886	+	0.971048i	$0.576782\pi$
$230$	−2.06629	−0.136247
$231$	−1.89359	−0.124589
$232$	4.24478	0.278683
$233$	−0.429924	−0.0281652	−0.0140826	−	0.999901i	$-0.504483\pi$
$233$	−0.429924	−0.0281652	−0.0140826	+	0.999901i	$0.504483\pi$
$234$	0	0
$235$	8.58491	0.560017
$236$	7.36440	0.479382
$237$	−1.31023	−0.0851088
$238$	1.79327	0.116240
$239$	−12.7450	−0.824405	−0.412203	−	0.911092i	$-0.635240\pi$
$239$	−12.7450	−0.824405	−0.412203	+	0.911092i	$0.635240\pi$
$240$	−1.13898	−0.0735206
$241$	19.1338	1.23252	0.616258	−	0.787545i	$-0.288648\pi$
$241$	19.1338	1.23252	0.616258	+	0.787545i	$0.288648\pi$
$242$	2.15209	0.138341
$243$	−8.24120	−0.528673
$244$	−15.3815	−0.984699
$245$	4.43464	0.283319
$246$	−0.0790259	−0.00503851
$247$	0	0
$248$	−5.18821	−0.329452
$249$	−3.76295	−0.238468
$250$	−0.271374	−0.0171632
$251$	0.411815	0.0259935	0.0129968	−	0.999916i	$-0.495863\pi$
$251$	0.411815	0.0259935	0.0129968	+	0.999916i	$0.495863\pi$
$252$	−18.8766	−1.18911
$253$	−13.3404	−0.838705
$254$	2.68250	0.168315
$255$	−0.624593	−0.0391135
$256$	10.4283	0.651771
$257$	−2.47556	−0.154421	−0.0772105	−	0.997015i	$-0.524601\pi$
$257$	−2.47556	−0.154421	−0.0772105	+	0.997015i	$0.524601\pi$
$258$	0.397729	0.0247616
$259$	35.5093	2.20644
$260$	0	0
$261$	−11.5444	−0.714582
$262$	3.11278	0.192308
$263$	−11.3591	−0.700430	−0.350215	−	0.936669i	$-0.613892\pi$
$263$	−11.3591	−0.700430	−0.350215	+	0.936669i	$0.613892\pi$
$264$	0.596669	0.0367224
$265$	11.9646	0.734981
$266$	6.54527	0.401317
$267$	−1.23370	−0.0755012
$268$	0.910682	0.0556288
$269$	−29.6888	−1.81016	−0.905078	−	0.425245i	$-0.860188\pi$
$269$	−29.6888	−1.81016	−0.905078	+	0.425245i	$0.860188\pi$
$270$	−0.511554	−0.0311322
$271$	−14.7761	−0.897583	−0.448792	−	0.893636i	$-0.648145\pi$
$271$	−14.7761	−0.897583	−0.448792	+	0.893636i	$0.648145\pi$
$272$	6.96387	0.422247
$273$	0	0
$274$	−3.55028	−0.214480
$275$	−1.75204	−0.105652
$276$	4.68804	0.282187
$277$	−1.94652	−0.116955	−0.0584774	−	0.998289i	$-0.518625\pi$
$277$	−1.94652	−0.116955	−0.0584774	+	0.998289i	$0.518625\pi$
$278$	−3.25002	−0.194924
$279$	14.1103	0.844760
$280$	−3.60304	−0.215323
$281$	18.5256	1.10515	0.552573	−	0.833464i	$-0.313646\pi$
$281$	18.5256	1.10515	0.552573	+	0.833464i	$0.313646\pi$
$282$	0.744619	0.0443414
$283$	13.0952	0.778427	0.389214	−	0.921148i	$-0.372747\pi$
$283$	13.0952	0.778427	0.389214	+	0.921148i	$0.372747\pi$
$284$	−10.6010	−0.629052
$285$	−2.27971	−0.135038
$286$	0	0
$287$	3.08093	0.181862
$288$	8.97775	0.529019
$289$	−13.1811	−0.775362
$290$	−1.08110	−0.0634843
$291$	−2.22382	−0.130363
$292$	5.66074	0.331270
$293$	−1.20753	−0.0705445	−0.0352722	−	0.999378i	$-0.511230\pi$
$293$	−1.20753	−0.0705445	−0.0352722	+	0.999378i	$0.511230\pi$
$294$	0.384642	0.0224328
$295$	−3.82297	−0.222582
$296$	−11.1889	−0.650342
$297$	−3.30270	−0.191642
$298$	4.42481	0.256322
$299$	0	0
$300$	0.615697	0.0355473
$301$	−15.5060	−0.893752
$302$	2.37565	0.136703
$303$	5.71869	0.328530
$304$	25.4175	1.45779
$305$	7.98476	0.457206
$306$	1.53677	0.0878514
$307$	−21.9275	−1.25147	−0.625733	−	0.780037i	$-0.715200\pi$
$307$	−21.9275	−1.25147	−0.625733	+	0.780037i	$0.715200\pi$
$308$	−11.4128	−0.650306
$309$	−3.27802	−0.186480
$310$	1.32138	0.0750494
$311$	−12.5966	−0.714288	−0.357144	−	0.934049i	$-0.616249\pi$
$311$	−12.5966	−0.714288	−0.357144	+	0.934049i	$0.616249\pi$
$312$	0	0
$313$	26.8268	1.51634	0.758169	−	0.652058i	$-0.226094\pi$
$313$	26.8268	1.51634	0.758169	+	0.652058i	$0.226094\pi$
$314$	−1.76073	−0.0993638
$315$	9.79910	0.552117
$316$	−7.89687	−0.444234
$317$	17.1279	0.961999	0.481000	−	0.876721i	$-0.340274\pi$
$317$	17.1279	0.961999	0.481000	+	0.876721i	$0.340274\pi$
$318$	1.03776	0.0581948
$319$	−6.97979	−0.390793
$320$	−6.28638	−0.351420
$321$	−4.12262	−0.230102
$322$	6.98720	0.389382
$323$	13.9385	0.775557
$324$	−15.5862	−0.865901
$325$	0	0
$326$	−1.04461	−0.0578555
$327$	3.33923	0.184660
$328$	−0.970798	−0.0536033
$329$	−29.0300	−1.60047
$330$	−0.151965	−0.00836540
$331$	−1.43062	−0.0786338	−0.0393169	−	0.999227i	$-0.512518\pi$
$331$	−1.43062	−0.0786338	−0.0393169	+	0.999227i	$0.512518\pi$
$332$	−22.6796	−1.24470
$333$	30.4302	1.66757
$334$	−1.86134	−0.101848
$335$	−0.472749	−0.0258290
$336$	3.85147	0.210115
$337$	−7.48872	−0.407937	−0.203968	−	0.978977i	$-0.565384\pi$
$337$	−7.48872	−0.407937	−0.203968	+	0.978977i	$0.565384\pi$
$338$	0	0
$339$	6.06524	0.329419
$340$	−3.76446	−0.204157
$341$	8.53111	0.461985
$342$	5.60908	0.303304
$343$	8.67480	0.468395
$344$	4.88593	0.263431
$345$	−2.43363	−0.131022
$346$	−4.34752	−0.233724
$347$	6.96813	0.374069	0.187034	−	0.982353i	$-0.440112\pi$
$347$	6.96813	0.374069	0.187034	+	0.982353i	$0.440112\pi$
$348$	2.45281	0.131485
$349$	−21.9738	−1.17623	−0.588116	−	0.808777i	$-0.700130\pi$
$349$	−21.9738	−1.17623	−0.588116	+	0.808777i	$0.700130\pi$
$350$	0.917654	0.0490507
$351$	0	0
$352$	5.42797	0.289312
$353$	−13.0184	−0.692899	−0.346450	−	0.938069i	$-0.612613\pi$
$353$	−13.0184	−0.692899	−0.346450	+	0.938069i	$0.612613\pi$
$354$	−0.331589	−0.0176237
$355$	5.50312	0.292075
$356$	−7.43559	−0.394085
$357$	2.11207	0.111783
$358$	2.19354	0.115932
$359$	−9.99211	−0.527363	−0.263682	−	0.964610i	$-0.584937\pi$
$359$	−9.99211	−0.527363	−0.263682	+	0.964610i	$0.584937\pi$
$360$	−3.08768	−0.162735
$361$	31.8742	1.67759
$362$	−3.00948	−0.158175
$363$	2.53468	0.133036
$364$	0	0
$365$	−2.93857	−0.153812
$366$	0.692564	0.0362009
$367$	25.2882	1.32004	0.660018	−	0.751250i	$-0.270549\pi$
$367$	25.2882	1.32004	0.660018	+	0.751250i	$0.270549\pi$
$368$	27.1337	1.41444
$369$	2.64026	0.137446
$370$	2.84969	0.148149
$371$	−40.4586	−2.10050
$372$	−2.99797	−0.155438
$373$	14.2703	0.738887	0.369444	−	0.929253i	$-0.379548\pi$
$373$	14.2703	0.738887	0.369444	+	0.929253i	$0.379548\pi$
$374$	0.929136	0.0480445
$375$	−0.319618	−0.0165050
$376$	9.14730	0.471736
$377$	0	0
$378$	1.72983	0.0889728
$379$	−7.01341	−0.360255	−0.180127	−	0.983643i	$-0.557651\pi$
$379$	−7.01341	−0.360255	−0.180127	+	0.983643i	$0.557651\pi$
$380$	−13.7400	−0.704845
$381$	3.15938	0.161860
$382$	−5.90325	−0.302036
$383$	−4.69336	−0.239820	−0.119910	−	0.992785i	$-0.538261\pi$
$383$	−4.69336	−0.239820	−0.119910	+	0.992785i	$0.538261\pi$
$384$	−2.52565	−0.128887
$385$	5.92456	0.301944
$386$	−6.11365	−0.311177
$387$	−13.2881	−0.675474
$388$	−13.4031	−0.680440
$389$	−9.34682	−0.473902	−0.236951	−	0.971522i	$-0.576148\pi$
$389$	−9.34682	−0.473902	−0.236951	+	0.971522i	$0.576148\pi$
$390$	0	0
$391$	14.8796	0.752493
$392$	4.72515	0.238656
$393$	3.66616	0.184933
$394$	4.68795	0.236176
$395$	4.09938	0.206262
$396$	−9.78041	−0.491484
$397$	21.2133	1.06467	0.532334	−	0.846535i	$-0.321315\pi$
$397$	21.2133	1.06467	0.532334	+	0.846535i	$0.321315\pi$
$398$	−4.74634	−0.237913
$399$	7.70887	0.385926
$400$	3.56356	0.178178
$401$	−18.2172	−0.909725	−0.454863	−	0.890562i	$-0.650312\pi$
$401$	−18.2172	−0.909725	−0.454863	+	0.890562i	$0.650312\pi$
$402$	−0.0410042	−0.00204511
$403$	0	0
$404$	34.4669	1.71479
$405$	8.09104	0.402047
$406$	3.65575	0.181432
$407$	18.3982	0.911965
$408$	−0.665510	−0.0329477
$409$	4.36136	0.215655	0.107828	−	0.994170i	$-0.465611\pi$
$409$	4.36136	0.215655	0.107828	+	0.994170i	$0.465611\pi$
$410$	0.247252	0.0122109
$411$	−4.18143	−0.206255
$412$	−19.7569	−0.973351
$413$	12.9274	0.636117
$414$	5.98780	0.294284
$415$	11.7733	0.577929
$416$	0	0
$417$	−3.82780	−0.187448
$418$	3.39127	0.165872
$419$	17.0555	0.833214	0.416607	−	0.909087i	$-0.363219\pi$
$419$	17.0555	0.833214	0.416607	+	0.909087i	$0.363219\pi$
$420$	−2.08199	−0.101591
$421$	−1.27996	−0.0623816	−0.0311908	−	0.999513i	$-0.509930\pi$
$421$	−1.27996	−0.0623816	−0.0311908	+	0.999513i	$0.509930\pi$
$422$	−1.71932	−0.0836954
$423$	−24.8777	−1.20960
$424$	12.7484	0.619119
$425$	1.95419	0.0947921
$426$	0.477318	0.0231261
$427$	−27.0006	−1.30665
$428$	−24.8473	−1.20104
$429$	0	0
$430$	−1.24439	−0.0600099
$431$	32.8733	1.58345	0.791725	−	0.610878i	$-0.209183\pi$
$431$	32.8733	1.58345	0.791725	+	0.610878i	$0.209183\pi$
$432$	6.71751	0.323196
$433$	−28.2622	−1.35819	−0.679097	−	0.734048i	$-0.737628\pi$
$433$	−28.2622	−1.35819	−0.679097	+	0.734048i	$0.737628\pi$
$434$	−4.46827	−0.214484
$435$	−1.27329	−0.0610497
$436$	20.1257	0.963848
$437$	54.3091	2.59796
$438$	−0.254880	−0.0121786
$439$	26.2621	1.25342	0.626711	−	0.779252i	$-0.284401\pi$
$439$	26.2621	1.25342	0.626711	+	0.779252i	$0.284401\pi$
$440$	−1.86682	−0.0889972
$441$	−12.8509	−0.611948
$442$	0	0
$443$	−14.0477	−0.667427	−0.333714	−	0.942674i	$-0.608302\pi$
$443$	−14.0477	−0.667427	−0.333714	+	0.942674i	$0.608302\pi$
$444$	−6.46543	−0.306836
$445$	3.85992	0.182978
$446$	−6.37588	−0.301906
$447$	5.21143	0.246492
$448$	21.2575	1.00432
$449$	−4.45904	−0.210435	−0.105218	−	0.994449i	$-0.533554\pi$
$449$	−4.45904	−0.210435	−0.105218	+	0.994449i	$0.533554\pi$
$450$	0.786399	0.0370712
$451$	1.59631	0.0751671
$452$	36.5556	1.71943
$453$	2.79798	0.131461
$454$	−2.60355	−0.122191
$455$	0	0
$456$	−2.42905	−0.113751
$457$	16.4149	0.767855	0.383927	−	0.923363i	$-0.374571\pi$
$457$	16.4149	0.767855	0.383927	+	0.923363i	$0.374571\pi$
$458$	1.96203	0.0916798
$459$	3.68375	0.171943
$460$	−14.6677	−0.683883
$461$	20.5455	0.956899	0.478449	−	0.878115i	$-0.341199\pi$
$461$	20.5455	0.956899	0.478449	+	0.878115i	$0.341199\pi$
$462$	0.513872	0.0239075
$463$	1.58359	0.0735958	0.0367979	−	0.999323i	$-0.488284\pi$
$463$	1.58359	0.0735958	0.0367979	+	0.999323i	$0.488284\pi$
$464$	14.1965	0.659056
$465$	1.55629	0.0721713
$466$	0.116670	0.00540463
$467$	5.14277	0.237979	0.118990	−	0.992896i	$-0.462034\pi$
$467$	5.14277	0.237979	0.118990	+	0.992896i	$0.462034\pi$
$468$	0	0
$469$	1.59861	0.0738168
$470$	−2.32972	−0.107462
$471$	−2.07375	−0.0955532
$472$	−4.07341	−0.187494
$473$	−8.03405	−0.369406
$474$	0.355563	0.0163316
$475$	7.13261	0.327267
$476$	12.7296	0.583460
$477$	−34.6716	−1.58751
$478$	3.45866	0.158195
$479$	22.2914	1.01852	0.509260	−	0.860613i	$-0.329919\pi$
$479$	22.2914	1.01852	0.509260	+	0.860613i	$0.329919\pi$
$480$	0.990200	0.0451962
$481$	0	0
$482$	−5.19241	−0.236508
$483$	8.22936	0.374449
$484$	15.2767	0.694394
$485$	6.95775	0.315935
$486$	2.23645	0.101447
$487$	−23.4185	−1.06119	−0.530597	−	0.847624i	$-0.678032\pi$
$487$	−23.4185	−1.06119	−0.530597	+	0.847624i	$0.678032\pi$
$488$	8.50784	0.385132
$489$	−1.23031	−0.0556367
$490$	−1.20345	−0.0543661
$491$	3.39791	0.153345	0.0766727	−	0.997056i	$-0.475570\pi$
$491$	3.39791	0.153345	0.0766727	+	0.997056i	$0.475570\pi$
$492$	−0.560968	−0.0252904
$493$	7.78509	0.350623
$494$	0	0
$495$	5.07715	0.228201
$496$	−17.3518	−0.779119
$497$	−18.6089	−0.834723
$498$	1.02117	0.0457596
$499$	−4.87712	−0.218330	−0.109165	−	0.994024i	$-0.534818\pi$
$499$	−4.87712	−0.218330	−0.109165	+	0.994024i	$0.534818\pi$
$500$	−1.92636	−0.0861493
$501$	−2.19224	−0.0979419
$502$	−0.111756	−0.00498791
$503$	−13.9853	−0.623572	−0.311786	−	0.950152i	$-0.600927\pi$
$503$	−13.9853	−0.623572	−0.311786	+	0.950152i	$0.600927\pi$
$504$	10.4410	0.465081
$505$	−17.8923	−0.796196
$506$	3.62024	0.160939
$507$	0	0
$508$	19.0418	0.844844
$509$	37.0157	1.64069	0.820347	−	0.571866i	$-0.193780\pi$
$509$	37.0157	1.64069	0.820347	+	0.571866i	$0.193780\pi$
$510$	0.169498	0.00750550
$511$	9.93683	0.439579
$512$	−18.6342	−0.823524
$513$	13.4454	0.593627
$514$	0.671801	0.0296319
$515$	10.2561	0.451937
$516$	2.82330	0.124289
$517$	−15.0411	−0.661508
$518$	−9.63628	−0.423394
$519$	−5.12041	−0.224761
$520$	0	0
$521$	21.5328	0.943370	0.471685	−	0.881767i	$-0.343646\pi$
$521$	21.5328	0.943370	0.471685	+	0.881767i	$0.343646\pi$
$522$	3.13286	0.137121
$523$	36.0055	1.57441	0.787204	−	0.616692i	$-0.211528\pi$
$523$	36.0055	1.57441	0.787204	+	0.616692i	$0.211528\pi$
$524$	22.0962	0.965277
$525$	1.08079	0.0471696
$526$	3.08255	0.134406
$527$	−9.51539	−0.414497
$528$	1.99554	0.0868446
$529$	34.9760	1.52070
$530$	−3.24689	−0.141036
$531$	11.0784	0.480761
$532$	46.4619	2.01438
$533$	0	0
$534$	0.334794	0.0144879
$535$	12.8986	0.557656
$536$	−0.503718	−0.0217573
$537$	2.58350	0.111486
$538$	8.05676	0.347351
$539$	−7.76969	−0.334664
$540$	−3.63129	−0.156266
$541$	0.123280	0.00530020	0.00265010	−	0.999996i	$-0.499156\pi$
$541$	0.123280	0.00530020	0.00265010	+	0.999996i	$0.499156\pi$
$542$	4.00984	0.172238
$543$	−3.54449	−0.152109
$544$	−6.05423	−0.259573
$545$	−10.4476	−0.447525
$546$	0	0
$547$	2.52166	0.107818	0.0539092	−	0.998546i	$-0.482832\pi$
$547$	2.52166	0.107818	0.0539092	+	0.998546i	$0.482832\pi$
$548$	−25.2018	−1.07657
$549$	−23.1386	−0.987531
$550$	0.475459	0.0202736
$551$	28.4149	1.21052
$552$	−2.59306	−0.110368
$553$	−13.8621	−0.589477
$554$	0.528233	0.0224425
$555$	3.35630	0.142467
$556$	−23.0704	−0.978403
$557$	−0.974960	−0.0413104	−0.0206552	−	0.999787i	$-0.506575\pi$
$557$	−0.974960	−0.0413104	−0.0206552	+	0.999787i	$0.506575\pi$
$558$	−3.82916	−0.162101
$559$	0	0
$560$	−12.0502	−0.509215
$561$	1.09431	0.0462020
$562$	−5.02737	−0.212067
$563$	−31.5376	−1.32915	−0.664576	−	0.747220i	$-0.731388\pi$
$563$	−31.5376	−1.32915	−0.664576	+	0.747220i	$0.731388\pi$
$564$	5.28570	0.222568
$565$	−18.9766	−0.798350
$566$	−3.55369	−0.149373
$567$	−27.3600	−1.14901
$568$	5.86363	0.246033
$569$	24.8762	1.04287	0.521433	−	0.853292i	$-0.325398\pi$
$569$	24.8762	1.04287	0.521433	+	0.853292i	$0.325398\pi$
$570$	0.618653	0.0259125
$571$	−7.92958	−0.331843	−0.165921	−	0.986139i	$-0.553060\pi$
$571$	−7.92958	−0.331843	−0.165921	+	0.986139i	$0.553060\pi$
$572$	0	0
$573$	−6.95271	−0.290453
$574$	−0.836085	−0.0348975
$575$	7.61420	0.317534
$576$	18.2170	0.759040
$577$	19.0769	0.794180	0.397090	−	0.917780i	$-0.370020\pi$
$577$	19.0769	0.794180	0.397090	+	0.917780i	$0.370020\pi$
$578$	3.57702	0.148784
$579$	−7.20051	−0.299243
$580$	−7.67421	−0.318654
$581$	−39.8116	−1.65166
$582$	0.603487	0.0250153
$583$	−20.9626	−0.868181
$584$	−3.13108	−0.129565
$585$	0	0
$586$	0.327691	0.0135368
$587$	−19.1196	−0.789149	−0.394574	−	0.918864i	$-0.629108\pi$
$587$	−19.1196	−0.789149	−0.394574	+	0.918864i	$0.629108\pi$
$588$	2.73040	0.112600
$589$	−34.7303	−1.43104
$590$	1.03745	0.0427113
$591$	5.52136	0.227118
$592$	−37.4209	−1.53799
$593$	−36.9354	−1.51676	−0.758379	−	0.651814i	$-0.774008\pi$
$593$	−36.9354	−1.51676	−0.758379	+	0.651814i	$0.774008\pi$
$594$	0.896266	0.0367742
$595$	−6.60812	−0.270906
$596$	31.4096	1.28659
$597$	−5.59013	−0.228789
$598$	0	0
$599$	−5.19953	−0.212447	−0.106224	−	0.994342i	$-0.533876\pi$
$599$	−5.19953	−0.212447	−0.106224	+	0.994342i	$0.533876\pi$
$600$	−0.340556	−0.0139031
$601$	−28.3207	−1.15523	−0.577613	−	0.816311i	$-0.696016\pi$
$601$	−28.3207	−1.15523	−0.577613	+	0.816311i	$0.696016\pi$
$602$	4.20793	0.171502
$603$	1.36995	0.0557887
$604$	16.8636	0.686170
$605$	−7.93034	−0.322414
$606$	−1.55190	−0.0630417
$607$	20.1615	0.818332	0.409166	−	0.912460i	$-0.365820\pi$
$607$	20.1615	0.818332	0.409166	+	0.912460i	$0.365820\pi$
$608$	−22.0974	−0.896168
$609$	4.30565	0.174474
$610$	−2.16685	−0.0877333
$611$	0	0
$612$	10.9088	0.440963
$613$	−18.8190	−0.760094	−0.380047	−	0.924967i	$-0.624092\pi$
$613$	−18.8190	−0.760094	−0.380047	+	0.924967i	$0.624092\pi$
$614$	5.95054	0.240144
$615$	0.291207	0.0117426
$616$	6.31268	0.254345
$617$	2.82492	0.113727	0.0568634	−	0.998382i	$-0.481890\pi$
$617$	2.82492	0.113727	0.0568634	+	0.998382i	$0.481890\pi$
$618$	0.889570	0.0357837
$619$	−15.6686	−0.629773	−0.314886	−	0.949129i	$-0.601966\pi$
$619$	−15.6686	−0.629773	−0.314886	+	0.949129i	$0.601966\pi$
$620$	9.37987	0.376705
$621$	14.3532	0.575973
$622$	3.41839	0.137065
$623$	−13.0524	−0.522933
$624$	0	0
$625$	1.00000	0.0400000
$626$	−7.28008	−0.290971
$627$	3.99415	0.159511
$628$	−12.4986	−0.498749
$629$	−20.5209	−0.818223
$630$	−2.65922	−0.105946
$631$	−10.1149	−0.402667	−0.201333	−	0.979523i	$-0.564527\pi$
$631$	−10.1149	−0.402667	−0.201333	+	0.979523i	$0.564527\pi$
$632$	4.36793	0.173747
$633$	−2.02498	−0.0804857
$634$	−4.64807	−0.184598
$635$	−9.88489	−0.392270
$636$	7.36659	0.292104
$637$	0	0
$638$	1.89413	0.0749894
$639$	−15.9472	−0.630861
$640$	7.90212	0.312359
$641$	−17.6173	−0.695843	−0.347922	−	0.937524i	$-0.613112\pi$
$641$	−17.6173	−0.695843	−0.347922	+	0.937524i	$0.613112\pi$
$642$	1.11877	0.0441544
$643$	19.0312	0.750519	0.375260	−	0.926920i	$-0.377554\pi$
$643$	19.0312	0.750519	0.375260	+	0.926920i	$0.377554\pi$
$644$	49.5989	1.95447
$645$	−1.46561	−0.0577085
$646$	−3.78254	−0.148822
$647$	−26.6972	−1.04957	−0.524787	−	0.851233i	$-0.675855\pi$
$647$	−26.6972	−1.04957	−0.524787	+	0.851233i	$0.675855\pi$
$648$	8.62108	0.338668
$649$	6.69802	0.262920
$650$	0	0
$651$	−5.26262	−0.206258
$652$	−7.41518	−0.290401
$653$	−3.16076	−0.123690	−0.0618451	−	0.998086i	$-0.519698\pi$
$653$	−3.16076	−0.123690	−0.0618451	+	0.998086i	$0.519698\pi$
$654$	−0.906178	−0.0354344
$655$	−11.4705	−0.448188
$656$	−3.24680	−0.126766
$657$	8.51553	0.332222
$658$	7.87798	0.307116
$659$	−18.0060	−0.701413	−0.350706	−	0.936486i	$-0.614058\pi$
$659$	−18.0060	−0.701413	−0.350706	+	0.936486i	$0.614058\pi$
$660$	−1.07873	−0.0419895
$661$	3.51786	0.136829	0.0684145	−	0.997657i	$-0.478206\pi$
$661$	3.51786	0.136829	0.0684145	+	0.997657i	$0.478206\pi$
$662$	0.388232	0.0150891
$663$	0	0
$664$	12.5446	0.486824
$665$	−24.1190	−0.935296
$666$	−8.25797	−0.319990
$667$	30.3334	1.17452
$668$	−13.2128	−0.511217
$669$	−7.50935	−0.290328
$670$	0.128292	0.00495634
$671$	−13.9896	−0.540064
$672$	−3.34838	−0.129166
$673$	−26.0032	−1.00235	−0.501175	−	0.865346i	$-0.667099\pi$
$673$	−26.0032	−1.00235	−0.501175	+	0.865346i	$0.667099\pi$
$674$	2.03224	0.0782791
$675$	1.88505	0.0725558
$676$	0	0
$677$	−28.5157	−1.09595	−0.547975	−	0.836495i	$-0.684601\pi$
$677$	−28.5157	−1.09595	−0.547975	+	0.836495i	$0.684601\pi$
$678$	−1.64595	−0.0632122
$679$	−23.5277	−0.902912
$680$	2.08221	0.0798490
$681$	−3.06640	−0.117505
$682$	−2.31512	−0.0886505
$683$	28.9493	1.10771	0.553857	−	0.832612i	$-0.313155\pi$
$683$	28.9493	1.10771	0.553857	+	0.832612i	$0.313155\pi$
$684$	39.8163	1.52241
$685$	13.0826	0.499861
$686$	−2.35411	−0.0898805
$687$	2.31084	0.0881639
$688$	16.3408	0.622987
$689$	0	0
$690$	0.660424	0.0251419
$691$	21.6566	0.823854	0.411927	−	0.911217i	$-0.364856\pi$
$691$	21.6566	0.823854	0.411927	+	0.911217i	$0.364856\pi$
$692$	−30.8611	−1.17316
$693$	−17.1685	−0.652176
$694$	−1.89097	−0.0717801
$695$	11.9762	0.454283
$696$	−1.35671	−0.0514258
$697$	−1.78048	−0.0674405
$698$	5.96312	0.225707
$699$	0.137411	0.00519737
$700$	6.51400	0.246206
$701$	25.0376	0.945656	0.472828	−	0.881155i	$-0.343233\pi$
$701$	25.0376	0.945656	0.472828	+	0.881155i	$0.343233\pi$
$702$	0	0
$703$	−74.8995	−2.82489
$704$	11.0140	0.415107
$705$	−2.74389	−0.103341
$706$	3.53285	0.132961
$707$	60.5030	2.27545
$708$	−2.35379	−0.0884610
$709$	25.6247	0.962355	0.481178	−	0.876623i	$-0.340209\pi$
$709$	25.6247	0.962355	0.481178	+	0.876623i	$0.340209\pi$
$710$	−1.49340	−0.0560464
$711$	−11.8794	−0.445511
$712$	4.11279	0.154133
$713$	−37.0753	−1.38848
$714$	−0.573160	−0.0214500
$715$	0	0
$716$	15.5709	0.581912
$717$	4.07352	0.152129
$718$	2.71160	0.101196
$719$	14.8064	0.552186	0.276093	−	0.961131i	$-0.410960\pi$
$719$	14.8064	0.552186	0.276093	+	0.961131i	$0.410960\pi$
$720$	−10.3266	−0.384851
$721$	−34.6811	−1.29159
$722$	−8.64982	−0.321913
$723$	−6.11549	−0.227438
$724$	−21.3629	−0.793945
$725$	3.98380	0.147955
$726$	−0.687845	−0.0255283
$727$	−30.1688	−1.11890	−0.559449	−	0.828865i	$-0.688987\pi$
$727$	−30.1688	−1.11890	−0.559449	+	0.828865i	$0.688987\pi$
$728$	0	0
$729$	−21.6391	−0.801447
$730$	0.797452	0.0295150
$731$	8.96098	0.331434
$732$	4.91619	0.181708
$733$	−49.8997	−1.84309	−0.921544	−	0.388275i	$-0.873071\pi$
$733$	−49.8997	−1.84309	−0.921544	+	0.388275i	$0.873071\pi$
$734$	−6.86257	−0.253302
$735$	−1.41739	−0.0522812
$736$	−23.5894	−0.869516
$737$	0.828276	0.0305100
$738$	−0.716496	−0.0263746
$739$	31.5796	1.16167	0.580836	−	0.814020i	$-0.302726\pi$
$739$	31.5796	1.16167	0.580836	+	0.814020i	$0.302726\pi$
$740$	20.2287	0.743620
$741$	0	0
$742$	10.9794	0.403066
$743$	−1.60448	−0.0588625	−0.0294312	−	0.999567i	$-0.509370\pi$
$743$	−1.60448	−0.0588625	−0.0294312	+	0.999567i	$0.509370\pi$
$744$	1.65824	0.0607942
$745$	−16.3052	−0.597377
$746$	−3.87258	−0.141785
$747$	−34.1172	−1.24828
$748$	6.59551	0.241156
$749$	−43.6168	−1.59372
$750$	0.0867358	0.00316714
$751$	10.7873	0.393634	0.196817	−	0.980440i	$-0.436940\pi$
$751$	10.7873	0.393634	0.196817	+	0.980440i	$0.436940\pi$
$752$	30.5928	1.11561
$753$	−0.131623	−0.00479662
$754$	0	0
$755$	−8.75415	−0.318596
$756$	12.2792	0.446592
$757$	−6.40389	−0.232753	−0.116377	−	0.993205i	$-0.537128\pi$
$757$	−6.40389	−0.232753	−0.116377	+	0.993205i	$0.537128\pi$
$758$	1.90326	0.0691294
$759$	4.26383	0.154767
$760$	7.59987	0.275676
$761$	50.2655	1.82212	0.911062	−	0.412269i	$-0.135264\pi$
$761$	50.2655	1.82212	0.911062	+	0.412269i	$0.135264\pi$
$762$	−0.857374	−0.0310594
$763$	35.3286	1.27898
$764$	−41.9044	−1.51605
$765$	−5.66293	−0.204744
$766$	1.27366	0.0460191
$767$	0	0
$768$	−3.33308	−0.120272
$769$	4.10457	0.148015	0.0740074	−	0.997258i	$-0.476421\pi$
$769$	4.10457	0.148015	0.0740074	+	0.997258i	$0.476421\pi$
$770$	−1.60777	−0.0579401
$771$	0.791232	0.0284955
$772$	−43.3980	−1.56193
$773$	−1.17851	−0.0423882	−0.0211941	−	0.999775i	$-0.506747\pi$
$773$	−1.17851	−0.0423882	−0.0211941	+	0.999775i	$0.506747\pi$
$774$	3.60605	0.129617
$775$	−4.86923	−0.174908
$776$	7.41356	0.266131
$777$	−11.3494	−0.407157
$778$	2.53648	0.0909373
$779$	−6.49860	−0.232836
$780$	0	0
$781$	−9.64172	−0.345008
$782$	−4.03793	−0.144396
$783$	7.50968	0.268374
$784$	15.8031	0.564397
$785$	6.48821	0.231574
$786$	−0.994900	−0.0354869
$787$	33.4916	1.19385	0.596923	−	0.802298i	$-0.296390\pi$
$787$	33.4916	1.19385	0.596923	+	0.802298i	$0.296390\pi$
$788$	33.2776	1.18546
$789$	3.63056	0.129251
$790$	−1.11246	−0.0395797
$791$	64.1695	2.28161
$792$	5.40976	0.192227
$793$	0	0
$794$	−5.75675	−0.204299
$795$	−3.82411	−0.135627
$796$	−33.6921	−1.19418
$797$	−24.9394	−0.883400	−0.441700	−	0.897163i	$-0.645624\pi$
$797$	−24.9394	−0.883400	−0.441700	+	0.897163i	$0.645624\pi$
$798$	−2.09198	−0.0740555
$799$	16.7765	0.593511
$800$	−3.09808	−0.109534
$801$	−11.1855	−0.395219
$802$	4.94368	0.174567
$803$	5.14851	0.181687
$804$	−0.291070	−0.0102652
$805$	−25.7475	−0.907481
$806$	0	0
$807$	9.48906	0.334031
$808$	−19.0644	−0.670684
$809$	12.8221	0.450802	0.225401	−	0.974266i	$-0.427631\pi$
$809$	12.8221	0.450802	0.225401	+	0.974266i	$0.427631\pi$
$810$	−2.19570	−0.0771489
$811$	29.8424	1.04791	0.523954	−	0.851746i	$-0.324456\pi$
$811$	29.8424	1.04791	0.523954	+	0.851746i	$0.324456\pi$
$812$	25.9505	0.910683
$813$	4.72270	0.165632
$814$	−4.99279	−0.174997
$815$	3.84933	0.134836
$816$	−2.22577	−0.0779177
$817$	32.7068	1.14427
$818$	−1.18356	−0.0413822
$819$	0	0
$820$	1.75512	0.0612916
$821$	19.6918	0.687249	0.343624	−	0.939107i	$-0.388345\pi$
$821$	19.6918	0.687249	0.343624	+	0.939107i	$0.388345\pi$
$822$	1.13473	0.0395783
$823$	41.9069	1.46078	0.730390	−	0.683030i	$-0.239338\pi$
$823$	41.9069	1.46078	0.730390	+	0.683030i	$0.239338\pi$
$824$	10.9280	0.380693
$825$	0.559984	0.0194961
$826$	−3.50817	−0.122065
$827$	21.7734	0.757134	0.378567	−	0.925574i	$-0.376417\pi$
$827$	21.7734	0.757134	0.378567	+	0.925574i	$0.376417\pi$
$828$	42.5046	1.47714
$829$	−5.87683	−0.204111	−0.102055	−	0.994779i	$-0.532542\pi$
$829$	−5.87683	−0.204111	−0.102055	+	0.994779i	$0.532542\pi$
$830$	−3.19497	−0.110899
$831$	0.622141	0.0215818
$832$	0	0
$833$	8.66612	0.300263
$834$	1.03876	0.0359695
$835$	6.85894	0.237363
$836$	24.0730	0.832583
$837$	−9.17876	−0.317265
$838$	−4.62841	−0.159886
$839$	−54.1116	−1.86814	−0.934069	−	0.357092i	$-0.883768\pi$
$839$	−54.1116	−1.86814	−0.934069	+	0.357092i	$0.883768\pi$
$840$	1.15159	0.0397338
$841$	−13.1294	−0.452736
$842$	0.347348	0.0119704
$843$	−5.92112	−0.203934
$844$	−12.2047	−0.420103
$845$	0	0
$846$	6.75116	0.232110
$847$	26.8166	0.921428
$848$	42.6367	1.46415
$849$	−4.18545	−0.143644
$850$	−0.530316	−0.0181897
$851$	−79.9567	−2.74088
$852$	3.38826	0.116080
$853$	10.8001	0.369787	0.184893	−	0.982759i	$-0.440806\pi$
$853$	10.8001	0.369787	0.184893	+	0.982759i	$0.440806\pi$
$854$	7.32725	0.250733
$855$	−20.6692	−0.706872
$856$	13.7436	0.469747
$857$	−12.0558	−0.411817	−0.205908	−	0.978571i	$-0.566015\pi$
$857$	−12.0558	−0.411817	−0.205908	+	0.978571i	$0.566015\pi$
$858$	0	0
$859$	−47.6819	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$859$	−47.6819	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$860$	−8.83336	−0.301215
$861$	−0.984720	−0.0335592
$862$	−8.92095	−0.303849
$863$	−46.2292	−1.57366	−0.786831	−	0.617169i	$-0.788279\pi$
$863$	−46.2292	−1.57366	−0.786831	+	0.617169i	$0.788279\pi$
$864$	−5.84005	−0.198682
$865$	16.0204	0.544711
$866$	7.66962	0.260624
$867$	4.21293	0.143078
$868$	−31.7182	−1.07658
$869$	−7.18230	−0.243643
$870$	0.345538	0.0117148
$871$	0	0
$872$	−11.1320	−0.376977
$873$	−20.1625	−0.682397
$874$	−14.7381	−0.498523
$875$	−3.38151	−0.114316
$876$	−1.80927	−0.0611296
$877$	−25.2281	−0.851893	−0.425947	−	0.904748i	$-0.640059\pi$
$877$	−25.2281	−0.851893	−0.425947	+	0.904748i	$0.640059\pi$
$878$	−7.12684	−0.240519
$879$	0.385947	0.0130177
$880$	−6.24352	−0.210469
$881$	−12.5086	−0.421425	−0.210712	−	0.977548i	$-0.567578\pi$
$881$	−12.5086	−0.421425	−0.210712	+	0.977548i	$0.567578\pi$
$882$	3.48740	0.117427
$883$	−11.2289	−0.377881	−0.188941	−	0.981989i	$-0.560505\pi$
$883$	−11.2289	−0.377881	−0.188941	+	0.981989i	$0.560505\pi$
$884$	0	0
$885$	1.22189	0.0410733
$886$	3.81218	0.128073
$887$	−54.5383	−1.83122	−0.915609	−	0.402069i	$-0.868291\pi$
$887$	−54.5383	−1.83122	−0.915609	+	0.402069i	$0.868291\pi$
$888$	3.57617	0.120009
$889$	33.4259	1.12107
$890$	−1.04748	−0.0351117
$891$	−14.1759	−0.474909
$892$	−45.2594	−1.51540
$893$	61.2328	2.04908
$894$	−1.41425	−0.0472995
$895$	−8.08309	−0.270188
$896$	−26.7211	−0.892690
$897$	0	0
$898$	1.21007	0.0403805
$899$	−19.3980	−0.646960
$900$	5.58228	0.186076
$901$	23.3811	0.778939
$902$	−0.433196	−0.0144238
$903$	4.95600	0.164925
$904$	−20.2197	−0.672498
$905$	11.0898	0.368637
$906$	−0.759298	−0.0252260
$907$	28.9083	0.959883	0.479942	−	0.877300i	$-0.340658\pi$
$907$	28.9083	0.959883	0.479942	+	0.877300i	$0.340658\pi$
$908$	−18.4814	−0.613327
$909$	51.8491	1.71973
$910$	0	0
$911$	−7.04371	−0.233369	−0.116684	−	0.993169i	$-0.537227\pi$
$911$	−7.04371	−0.233369	−0.116684	+	0.993169i	$0.537227\pi$
$912$	−8.12388	−0.269009
$913$	−20.6274	−0.682666
$914$	−4.45456	−0.147344
$915$	−2.55207	−0.0843688
$916$	13.9276	0.460180
$917$	38.7875	1.28088
$918$	−0.999674	−0.0329942
$919$	−17.3638	−0.572780	−0.286390	−	0.958113i	$-0.592455\pi$
$919$	−17.3638	−0.572780	−0.286390	+	0.958113i	$0.592455\pi$
$920$	8.11301	0.267478
$921$	7.00840	0.230935
$922$	−5.57551	−0.183620
$923$	0	0
$924$	3.64774	0.120002
$925$	−10.5010	−0.345271
$926$	−0.429745	−0.0141223
$927$	−29.7205	−0.976150
$928$	−12.3421	−0.405150
$929$	−30.9381	−1.01504	−0.507522	−	0.861639i	$-0.669439\pi$
$929$	−30.9381	−1.01504	−0.507522	+	0.861639i	$0.669439\pi$
$930$	−0.422337	−0.0138490
$931$	31.6306	1.03665
$932$	0.828186	0.0271281
$933$	4.02610	0.131808
$934$	−1.39561	−0.0456659
$935$	−3.42382	−0.111971
$936$	0	0
$937$	30.5009	0.996422	0.498211	−	0.867056i	$-0.333990\pi$
$937$	30.5009	0.996422	0.498211	+	0.867056i	$0.333990\pi$
$938$	−0.433820	−0.0141647
$939$	−8.57431	−0.279812
$940$	−16.5376	−0.539397
$941$	32.0423	1.04455	0.522275	−	0.852777i	$-0.325083\pi$
$941$	32.0423	1.04455	0.522275	+	0.852777i	$0.325083\pi$
$942$	0.562761	0.0183357
$943$	−6.93738	−0.225912
$944$	−13.6234	−0.443404
$945$	−6.37434	−0.207357
$946$	2.18023	0.0708854
$947$	8.63395	0.280566	0.140283	−	0.990111i	$-0.455199\pi$
$947$	8.63395	0.280566	0.140283	+	0.990111i	$0.455199\pi$
$948$	2.52398	0.0819750
$949$	0	0
$950$	−1.93560	−0.0627993
$951$	−5.47438	−0.177519
$952$	−7.04102	−0.228201
$953$	−32.4260	−1.05038	−0.525191	−	0.850984i	$-0.676006\pi$
$953$	−32.4260	−1.05038	−0.525191	+	0.850984i	$0.676006\pi$
$954$	9.40897	0.304627
$955$	21.7532	0.703917
$956$	24.5514	0.794049
$957$	2.23086	0.0721136
$958$	−6.04930	−0.195444
$959$	−44.2390	−1.42855
$960$	2.00924	0.0648479
$961$	−7.29060	−0.235181
$962$	0	0
$963$	−37.3782	−1.20449
$964$	−36.8585	−1.18713
$965$	22.5285	0.725219
$966$	−2.23323	−0.0718531
$967$	27.0744	0.870656	0.435328	−	0.900272i	$-0.356632\pi$
$967$	27.0744	0.870656	0.435328	+	0.900272i	$0.356632\pi$
$968$	−8.44986	−0.271589
$969$	−4.45498	−0.143115
$970$	−1.88815	−0.0606249
$971$	31.8039	1.02063	0.510317	−	0.859986i	$-0.329528\pi$
$971$	31.8039	1.02063	0.510317	+	0.859986i	$0.329528\pi$
$972$	15.8755	0.509207
$973$	−40.4977	−1.29830
$974$	6.35517	0.203633
$975$	0	0
$976$	28.4542	0.910796
$977$	31.3672	1.00353	0.501763	−	0.865005i	$-0.332685\pi$
$977$	31.3672	1.00353	0.501763	+	0.865005i	$0.332685\pi$
$978$	0.333875	0.0106761
$979$	−6.76276	−0.216139
$980$	−8.54270	−0.272886
$981$	30.2754	0.966620
$982$	−0.922103	−0.0294255
$983$	−35.5044	−1.13241	−0.566207	−	0.824263i	$-0.691590\pi$
$983$	−35.5044	−1.13241	−0.566207	+	0.824263i	$0.691590\pi$
$984$	0.310284	0.00989149
$985$	−17.2749	−0.550424
$986$	−2.11267	−0.0672811
$987$	9.27849	0.295338
$988$	0	0
$989$	34.9151	1.11024
$990$	−1.37781	−0.0437896
$991$	−41.0638	−1.30443	−0.652217	−	0.758032i	$-0.726161\pi$
$991$	−41.0638	−1.30443	−0.652217	+	0.758032i	$0.726161\pi$
$992$	15.0853	0.478957
$993$	0.457250	0.0145104
$994$	5.04997	0.160175
$995$	17.4901	0.554472
$996$	7.24879	0.229687
$997$	−44.7904	−1.41853	−0.709264	−	0.704943i	$-0.750972\pi$
$997$	−44.7904	−1.41853	−0.709264	+	0.704943i	$0.750972\pi$
$998$	1.32352	0.0418954
$999$	−19.7949	−0.626284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.o.1.4	yes	9
3.2	odd	2		7605.2.a.cp.1.6		9
5.4	even	2		4225.2.a.bs.1.6		9
13.2	odd	12		845.2.m.j.316.8		36
13.3	even	3		845.2.e.o.191.6		18
13.4	even	6		845.2.e.p.146.4		18
13.5	odd	4		845.2.c.h.506.11		18
13.6	odd	12		845.2.m.j.361.11		36
13.7	odd	12		845.2.m.j.361.8		36
13.8	odd	4		845.2.c.h.506.8		18
13.9	even	3		845.2.e.o.146.6		18
13.10	even	6		845.2.e.p.191.4		18
13.11	odd	12		845.2.m.j.316.11		36
13.12	even	2		845.2.a.n.1.6	✓	9
39.38	odd	2		7605.2.a.cs.1.4		9
65.64	even	2		4225.2.a.bt.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.6	✓	9	13.12	even	2
845.2.a.o.1.4	yes	9	1.1	even	1	trivial
845.2.c.h.506.8		18	13.8	odd	4
845.2.c.h.506.11		18	13.5	odd	4
845.2.e.o.146.6		18	13.9	even	3
845.2.e.o.191.6		18	13.3	even	3
845.2.e.p.146.4		18	13.4	even	6
845.2.e.p.191.4		18	13.10	even	6
845.2.m.j.316.8		36	13.2	odd	12
845.2.m.j.316.11		36	13.11	odd	12
845.2.m.j.361.8		36	13.7	odd	12
845.2.m.j.361.11		36	13.6	odd	12
4225.2.a.bs.1.6		9	5.4	even	2
4225.2.a.bt.1.4		9	65.64	even	2
7605.2.a.cp.1.6		9	3.2	odd	2
7605.2.a.cs.1.4		9	39.38	odd	2

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q-0.271374 q^{2} -0.319618 q^{3} -1.92636 q^{4} +1.00000 q^{5} +0.0867358 q^{6} -3.38151 q^{7} +1.06551 q^{8} -2.89784 q^{9} -0.271374 q^{10} -1.75204 q^{11} +0.615697 q^{12} +0.917654 q^{14} -0.319618 q^{15} +3.56356 q^{16} +1.95419 q^{17} +0.786399 q^{18} +7.13261 q^{19} -1.92636 q^{20} +1.08079 q^{21} +0.475459 q^{22} +7.61420 q^{23} -0.340556 q^{24} +1.00000 q^{25} +1.88505 q^{27} +6.51400 q^{28} +3.98380 q^{29} +0.0867358 q^{30} -4.86923 q^{31} -3.09808 q^{32} +0.559984 q^{33} -0.530316 q^{34} -3.38151 q^{35} +5.58228 q^{36} -10.5010 q^{37} -1.93560 q^{38} +1.06551 q^{40} -0.911110 q^{41} -0.293298 q^{42} +4.58553 q^{43} +3.37506 q^{44} -2.89784 q^{45} -2.06629 q^{46} +8.58491 q^{47} -1.13898 q^{48} +4.43464 q^{49} -0.271374 q^{50} -0.624593 q^{51} +11.9646 q^{53} -0.511554 q^{54} -1.75204 q^{55} -3.60304 q^{56} -2.27971 q^{57} -1.08110 q^{58} -3.82297 q^{59} +0.615697 q^{60} +7.98476 q^{61} +1.32138 q^{62} +9.79910 q^{63} -6.28638 q^{64} -0.151965 q^{66} -0.472749 q^{67} -3.76446 q^{68} -2.43363 q^{69} +0.917654 q^{70} +5.50312 q^{71} -3.08768 q^{72} -2.93857 q^{73} +2.84969 q^{74} -0.319618 q^{75} -13.7400 q^{76} +5.92456 q^{77} +4.09938 q^{79} +3.56356 q^{80} +8.09104 q^{81} +0.247252 q^{82} +11.7733 q^{83} -2.08199 q^{84} +1.95419 q^{85} -1.24439 q^{86} -1.27329 q^{87} -1.86682 q^{88} +3.85992 q^{89} +0.786399 q^{90} -14.6677 q^{92} +1.55629 q^{93} -2.32972 q^{94} +7.13261 q^{95} +0.990200 q^{96} +6.95775 q^{97} -1.20345 q^{98} +5.07715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9} + 3 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{14} + 7 q^{15} + 37 q^{16} - q^{17} - 10 q^{18} - 4 q^{19} + 17 q^{20} - q^{21}+ \cdots - q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9 + 3 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^14 + 7 * q^15 + 37 * q^16 - q^17 - 10 * q^18 - 4 * q^19 + 17 * q^20 - q^21 + 12 * q^22 + 14 * q^23 - 35 * q^24 + 9 * q^25 + 22 * q^27 + 18 * q^28 + 12 * q^29 - 2 * q^30 - 7 * q^31 + 22 * q^32 - 8 * q^33 - 30 * q^34 + 7 * q^35 + 3 * q^36 - 5 * q^37 - 47 * q^38 + 12 * q^40 - 10 * q^41 - 11 * q^42 + 39 * q^43 - 25 * q^44 + 16 * q^45 + 6 * q^46 + 36 * q^47 - 3 * q^48 + 16 * q^49 + 3 * q^50 + 43 * q^51 - 8 * q^53 - 2 * q^54 - 9 * q^55 - 29 * q^56 - 32 * q^57 + 21 * q^58 - 21 * q^59 + 12 * q^60 - 3 * q^61 - 10 * q^62 + 35 * q^63 + 34 * q^64 - 49 * q^66 + q^67 - 20 * q^68 - 13 * q^69 - 2 * q^70 - q^71 - 3 * q^72 - 15 * q^74 + 7 * q^75 - 5 * q^76 - 4 * q^77 + 39 * q^79 + 37 * q^80 + 29 * q^81 - 4 * q^82 + 7 * q^83 + 12 * q^84 - q^85 - 24 * q^86 + 16 * q^87 + 42 * q^88 - 19 * q^89 - 10 * q^90 - 27 * q^92 + 31 * q^93 + 16 * q^94 - 4 * q^95 - 7 * q^96 - 34 * q^97 + 48 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more