LMFDB - Embedded newform 4235.2.a.bc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.288385.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 2x^{2} + 10x + 3 $ x^5 - 7x^3 - 2x^2 + 10*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.43438$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43438 q^{2} +2.36534 q^{3} +3.92619 q^{4} +1.00000 q^{5} -5.75812 q^{6} -1.00000 q^{7} -4.68908 q^{8} +2.59481 q^{9} +O(q^{10})$	\(q-2.43438 q^{2} +2.36534 q^{3} +3.92619 q^{4} +1.00000 q^{5} -5.75812 q^{6} -1.00000 q^{7} -4.68908 q^{8} +2.59481 q^{9} -2.43438 q^{10} +9.28676 q^{12} -1.34011 q^{13} +2.43438 q^{14} +2.36534 q^{15} +3.56260 q^{16} -1.53341 q^{17} -6.31675 q^{18} +1.50342 q^{19} +3.92619 q^{20} -2.36534 q^{21} +2.62990 q^{23} -11.0912 q^{24} +1.00000 q^{25} +3.26234 q^{26} -0.958406 q^{27} -3.92619 q^{28} -7.31897 q^{29} -5.75812 q^{30} -7.31675 q^{31} +0.705448 q^{32} +3.73290 q^{34} -1.00000 q^{35} +10.1877 q^{36} -11.6357 q^{37} -3.65989 q^{38} -3.16981 q^{39} -4.68908 q^{40} -4.01758 q^{41} +5.75812 q^{42} +12.8330 q^{43} +2.59481 q^{45} -6.40216 q^{46} -6.51878 q^{47} +8.42674 q^{48} +1.00000 q^{49} -2.43438 q^{50} -3.62703 q^{51} -5.26154 q^{52} -0.974777 q^{53} +2.33312 q^{54} +4.68908 q^{56} +3.55609 q^{57} +17.8171 q^{58} -0.145722 q^{59} +9.28676 q^{60} -4.83193 q^{61} +17.8117 q^{62} -2.59481 q^{63} -8.84252 q^{64} -1.34011 q^{65} -6.74062 q^{67} -6.02046 q^{68} +6.22059 q^{69} +2.43438 q^{70} +4.55387 q^{71} -12.1673 q^{72} +5.13506 q^{73} +28.3257 q^{74} +2.36534 q^{75} +5.90271 q^{76} +7.71652 q^{78} -13.2106 q^{79} +3.56260 q^{80} -10.0514 q^{81} +9.78032 q^{82} +3.80966 q^{83} -9.28676 q^{84} -1.53341 q^{85} -31.2403 q^{86} -17.3118 q^{87} +14.0109 q^{89} -6.31675 q^{90} +1.34011 q^{91} +10.3255 q^{92} -17.3066 q^{93} +15.8692 q^{94} +1.50342 q^{95} +1.66862 q^{96} +11.7534 q^{97} -2.43438 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	−2.43438	−1.72136	−0.860682	−	0.509142i	$-0.829963\pi$
$2$	−2.43438	−1.72136	−0.860682	+	0.509142i	$0.829963\pi$
$3$	2.36534	1.36563	0.682814	−	0.730593i	$-0.260756\pi$
$3$	2.36534	1.36563	0.682814	+	0.730593i	$0.260756\pi$
$4$	3.92619	1.96310
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.75812	−2.35074
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.68908	−1.65784
$9$	2.59481	0.864937
$10$	−2.43438	−0.769818
$11$	0	0
$11$	0	0
$12$	9.28676	2.68086
$13$	−1.34011	−0.371680	−0.185840	−	0.982580i	$-0.559501\pi$
$13$	−1.34011	−0.371680	−0.185840	+	0.982580i	$0.559501\pi$
$14$	2.43438	0.650615
$15$	2.36534	0.610727
$16$	3.56260	0.890649
$17$	−1.53341	−0.371906	−0.185953	−	0.982559i	$-0.559537\pi$
$17$	−1.53341	−0.371906	−0.185953	+	0.982559i	$0.559537\pi$
$18$	−6.31675	−1.48887
$19$	1.50342	0.344908	0.172454	−	0.985018i	$-0.444830\pi$
$19$	1.50342	0.344908	0.172454	+	0.985018i	$0.444830\pi$
$20$	3.92619	0.877923
$21$	−2.36534	−0.516159
$22$	0	0
$23$	2.62990	0.548372	0.274186	−	0.961677i	$-0.411592\pi$
$23$	2.62990	0.548372	0.274186	+	0.961677i	$0.411592\pi$
$24$	−11.0912	−2.26399
$25$	1.00000	0.200000
$26$	3.26234	0.639797
$27$	−0.958406	−0.184445
$28$	−3.92619	−0.741980
$29$	−7.31897	−1.35910	−0.679550	−	0.733629i	$-0.737825\pi$
$29$	−7.31897	−1.35910	−0.679550	+	0.733629i	$0.737825\pi$
$30$	−5.75812	−1.05128
$31$	−7.31675	−1.31413	−0.657064	−	0.753835i	$-0.728202\pi$
$31$	−7.31675	−1.31413	−0.657064	+	0.753835i	$0.728202\pi$
$32$	0.705448	0.124707
$33$	0	0
$34$	3.73290	0.640186
$35$	−1.00000	−0.169031
$36$	10.1877	1.69795
$37$	−11.6357	−1.91290	−0.956451	−	0.291894i	$-0.905715\pi$
$37$	−11.6357	−1.91290	−0.956451	+	0.291894i	$0.905715\pi$
$38$	−3.65989	−0.593712
$39$	−3.16981	−0.507577
$40$	−4.68908	−0.741408
$41$	−4.01758	−0.627441	−0.313721	−	0.949515i	$-0.601576\pi$
$41$	−4.01758	−0.627441	−0.313721	+	0.949515i	$0.601576\pi$
$42$	5.75812	0.888497
$43$	12.8330	1.95701	0.978506	−	0.206218i	$-0.0661156\pi$
$43$	12.8330	1.95701	0.978506	+	0.206218i	$0.0661156\pi$
$44$	0	0
$45$	2.59481	0.386812
$46$	−6.40216	−0.943947
$47$	−6.51878	−0.950862	−0.475431	−	0.879753i	$-0.657708\pi$
$47$	−6.51878	−0.950862	−0.475431	+	0.879753i	$0.657708\pi$
$48$	8.42674	1.21629
$49$	1.00000	0.142857
$50$	−2.43438	−0.344273
$51$	−3.62703	−0.507885
$52$	−5.26154	−0.729644
$53$	−0.974777	−0.133896	−0.0669479	−	0.997756i	$-0.521326\pi$
$53$	−0.974777	−0.133896	−0.0669479	+	0.997756i	$0.521326\pi$
$54$	2.33312	0.317498
$55$	0	0
$56$	4.68908	0.626604
$57$	3.55609	0.471016
$58$	17.8171	2.33951
$59$	−0.145722	−0.0189713	−0.00948567	−	0.999955i	$-0.503019\pi$
$59$	−0.145722	−0.0189713	−0.00948567	+	0.999955i	$0.503019\pi$
$60$	9.28676	1.19892
$61$	−4.83193	−0.618665	−0.309332	−	0.950954i	$-0.600106\pi$
$61$	−4.83193	−0.618665	−0.309332	+	0.950954i	$0.600106\pi$
$62$	17.8117	2.26209
$63$	−2.59481	−0.326916
$64$	−8.84252	−1.10532
$65$	−1.34011	−0.166220
$66$	0	0
$67$	−6.74062	−0.823497	−0.411749	−	0.911297i	$-0.635082\pi$
$67$	−6.74062	−0.823497	−0.411749	+	0.911297i	$0.635082\pi$
$68$	−6.02046	−0.730088
$69$	6.22059	0.748871
$70$	2.43438	0.290964
$71$	4.55387	0.540444	0.270222	−	0.962798i	$-0.412903\pi$
$71$	4.55387	0.540444	0.270222	+	0.962798i	$0.412903\pi$
$72$	−12.1673	−1.43393
$73$	5.13506	0.601013	0.300507	−	0.953780i	$-0.402844\pi$
$73$	5.13506	0.601013	0.300507	+	0.953780i	$0.402844\pi$
$74$	28.3257	3.29280
$75$	2.36534	0.273125
$76$	5.90271	0.677087
$77$	0	0
$78$	7.71652	0.873724
$79$	−13.2106	−1.48631	−0.743155	−	0.669120i	$-0.766671\pi$
$79$	−13.2106	−1.48631	−0.743155	+	0.669120i	$0.766671\pi$
$80$	3.56260	0.398311
$81$	−10.0514	−1.11682
$82$	9.78032	1.08006
$83$	3.80966	0.418164	0.209082	−	0.977898i	$-0.432952\pi$
$83$	3.80966	0.418164	0.209082	+	0.977898i	$0.432952\pi$
$84$	−9.28676	−1.01327
$85$	−1.53341	−0.166322
$86$	−31.2403	−3.36873
$87$	−17.3118	−1.85602
$88$	0	0
$89$	14.0109	1.48515	0.742577	−	0.669760i	$-0.233603\pi$
$89$	14.0109	1.48515	0.742577	+	0.669760i	$0.233603\pi$
$90$	−6.31675	−0.665844
$91$	1.34011	0.140482
$92$	10.3255	1.07651
$93$	−17.3066	−1.79461
$94$	15.8692	1.63678
$95$	1.50342	0.154247
$96$	1.66862	0.170303
$97$	11.7534	1.19337	0.596686	−	0.802475i	$-0.296484\pi$
$97$	11.7534	1.19337	0.596686	+	0.802475i	$0.296484\pi$
$98$	−2.43438	−0.245909
$99$	0	0
$100$	3.92619	0.392619
$101$	−16.1011	−1.60212	−0.801060	−	0.598584i	$-0.795730\pi$
$101$	−16.1011	−1.60212	−0.801060	+	0.598584i	$0.795730\pi$
$102$	8.82955	0.874256
$103$	−17.8420	−1.75803	−0.879015	−	0.476795i	$-0.841798\pi$
$103$	−17.8420	−1.75803	−0.879015	+	0.476795i	$0.841798\pi$
$104$	6.28389	0.616186
$105$	−2.36534	−0.230833
$106$	2.37297	0.230484
$107$	−3.94268	−0.381154	−0.190577	−	0.981672i	$-0.561036\pi$
$107$	−3.94268	−0.381154	−0.190577	+	0.981672i	$0.561036\pi$
$108$	−3.76289	−0.362084
$109$	−1.21104	−0.115996	−0.0579981	−	0.998317i	$-0.518472\pi$
$109$	−1.21104	−0.115996	−0.0579981	+	0.998317i	$0.518472\pi$
$110$	0	0
$111$	−27.5224	−2.61231
$112$	−3.56260	−0.336634
$113$	17.5424	1.65025	0.825125	−	0.564950i	$-0.191105\pi$
$113$	17.5424	1.65025	0.825125	+	0.564950i	$0.191105\pi$
$114$	−8.65686	−0.810789
$115$	2.62990	0.245239
$116$	−28.7357	−2.66804
$117$	−3.47734	−0.321480
$118$	0.354741	0.0326566
$119$	1.53341	0.140567
$120$	−11.0912	−1.01249
$121$	0	0
$122$	11.7627	1.06495
$123$	−9.50294	−0.856851
$124$	−28.7270	−2.57976
$125$	1.00000	0.0894427
$126$	6.31675	0.562741
$127$	−10.8300	−0.961010	−0.480505	−	0.876992i	$-0.659547\pi$
$127$	−10.8300	−0.961010	−0.480505	+	0.876992i	$0.659547\pi$
$128$	20.1151	1.77794
$129$	30.3543	2.67255
$130$	3.26234	0.286126
$131$	−13.8644	−1.21134	−0.605669	−	0.795717i	$-0.707094\pi$
$131$	−13.8644	−1.21134	−0.605669	+	0.795717i	$0.707094\pi$
$132$	0	0
$133$	−1.50342	−0.130363
$134$	16.4092	1.41754
$135$	−0.958406	−0.0824864
$136$	7.19027	0.616561
$137$	14.6642	1.25285	0.626425	−	0.779482i	$-0.284518\pi$
$137$	14.6642	1.25285	0.626425	+	0.779482i	$0.284518\pi$
$138$	−15.1433	−1.28908
$139$	6.14694	0.521376	0.260688	−	0.965423i	$-0.416051\pi$
$139$	6.14694	0.521376	0.260688	+	0.965423i	$0.416051\pi$
$140$	−3.92619	−0.331824
$141$	−15.4191	−1.29852
$142$	−11.0858	−0.930302
$143$	0	0
$144$	9.24427	0.770356
$145$	−7.31897	−0.607808
$146$	−12.5007	−1.03456
$147$	2.36534	0.195090
$148$	−45.6841	−3.75521
$149$	−11.1720	−0.915249	−0.457625	−	0.889146i	$-0.651300\pi$
$149$	−11.1720	−0.915249	−0.457625	+	0.889146i	$0.651300\pi$
$150$	−5.75812	−0.470148
$151$	9.70941	0.790141	0.395070	−	0.918651i	$-0.370720\pi$
$151$	9.70941	0.790141	0.395070	+	0.918651i	$0.370720\pi$
$152$	−7.04965	−0.571802
$153$	−3.97891	−0.321676
$154$	0	0
$155$	−7.31675	−0.587696
$156$	−12.4453	−0.996421
$157$	−23.6446	−1.88704	−0.943521	−	0.331312i	$-0.892509\pi$
$157$	−23.6446	−1.88704	−0.943521	+	0.331312i	$0.892509\pi$
$158$	32.1596	2.55848
$159$	−2.30567	−0.182852
$160$	0.705448	0.0557705
$161$	−2.62990	−0.207265
$162$	24.4689	1.92246
$163$	−1.20062	−0.0940395	−0.0470198	−	0.998894i	$-0.514972\pi$
$163$	−1.20062	−0.0940395	−0.0470198	+	0.998894i	$0.514972\pi$
$164$	−15.7738	−1.23173
$165$	0	0
$166$	−9.27415	−0.719813
$167$	8.52165	0.659425	0.329713	−	0.944081i	$-0.393048\pi$
$167$	8.52165	0.659425	0.329713	+	0.944081i	$0.393048\pi$
$168$	11.0912	0.855708
$169$	−11.2041	−0.861854
$170$	3.73290	0.286300
$171$	3.90109	0.298324
$172$	50.3848	3.84180
$173$	2.71422	0.206358	0.103179	−	0.994663i	$-0.467099\pi$
$173$	2.71422	0.206358	0.103179	+	0.994663i	$0.467099\pi$
$174$	42.1435	3.19489
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−0.344681	−0.0259078
$178$	−34.1079	−2.55649
$179$	−21.9786	−1.64276	−0.821378	−	0.570384i	$-0.806795\pi$
$179$	−21.9786	−1.64276	−0.821378	+	0.570384i	$0.806795\pi$
$180$	10.1877	0.759348
$181$	5.74826	0.427264	0.213632	−	0.976914i	$-0.431471\pi$
$181$	5.74826	0.427264	0.213632	+	0.976914i	$0.431471\pi$
$182$	−3.26234	−0.241821
$183$	−11.4291	−0.844865
$184$	−12.3318	−0.909112
$185$	−11.6357	−0.855476
$186$	42.1307	3.08917
$187$	0	0
$188$	−25.5940	−1.86663
$189$	0.958406	0.0697138
$190$	−3.65989	−0.265516
$191$	−10.3586	−0.749525	−0.374762	−	0.927121i	$-0.622276\pi$
$191$	−10.3586	−0.749525	−0.374762	+	0.927121i	$0.622276\pi$
$192$	−20.9155	−1.50945
$193$	−2.99798	−0.215800	−0.107900	−	0.994162i	$-0.534413\pi$
$193$	−2.99798	−0.215800	−0.107900	+	0.994162i	$0.534413\pi$
$194$	−28.6121	−2.05423
$195$	−3.16981	−0.226995
$196$	3.92619	0.280442
$197$	−5.64425	−0.402136	−0.201068	−	0.979577i	$-0.564441\pi$
$197$	−5.64425	−0.402136	−0.201068	+	0.979577i	$0.564441\pi$
$198$	0	0
$199$	−9.49615	−0.673165	−0.336582	−	0.941654i	$-0.609271\pi$
$199$	−9.49615	−0.673165	−0.336582	+	0.941654i	$0.609271\pi$
$200$	−4.68908	−0.331568
$201$	−15.9438	−1.12459
$202$	39.1962	2.75783
$203$	7.31897	0.513691
$204$	−14.2404	−0.997027
$205$	−4.01758	−0.280600
$206$	43.4343	3.02621
$207$	6.82409	0.474307
$208$	−4.77428	−0.331037
$209$	0	0
$210$	5.75812	0.397348
$211$	−16.3629	−1.12647	−0.563235	−	0.826297i	$-0.690443\pi$
$211$	−16.3629	−1.12647	−0.563235	+	0.826297i	$0.690443\pi$
$212$	−3.82716	−0.262850
$213$	10.7714	0.738045
$214$	9.59798	0.656104
$215$	12.8330	0.875202
$216$	4.49404	0.305781
$217$	7.31675	0.496693
$218$	2.94812	0.199672
$219$	12.1461	0.820760
$220$	0	0
$221$	2.05494	0.138230
$222$	66.9999	4.49674
$223$	−11.2872	−0.755845	−0.377923	−	0.925837i	$-0.623361\pi$
$223$	−11.2872	−0.755845	−0.377923	+	0.925837i	$0.623361\pi$
$224$	−0.705448	−0.0471347
$225$	2.59481	0.172987
$226$	−42.7048	−2.84068
$227$	−1.49294	−0.0990902	−0.0495451	−	0.998772i	$-0.515777\pi$
$227$	−1.49294	−0.0990902	−0.0495451	+	0.998772i	$0.515777\pi$
$228$	13.9619	0.924649
$229$	25.0777	1.65718	0.828592	−	0.559853i	$-0.189142\pi$
$229$	25.0777	1.65718	0.828592	+	0.559853i	$0.189142\pi$
$230$	−6.40216	−0.422146
$231$	0	0
$232$	34.3192	2.25317
$233$	9.28818	0.608489	0.304245	−	0.952594i	$-0.401596\pi$
$233$	9.28818	0.608489	0.304245	+	0.952594i	$0.401596\pi$
$234$	8.46515	0.553384
$235$	−6.51878	−0.425238
$236$	−0.572131	−0.0372426
$237$	−31.2475	−2.02974
$238$	−3.73290	−0.241968
$239$	16.7853	1.08575	0.542874	−	0.839814i	$-0.317336\pi$
$239$	16.7853	1.08575	0.542874	+	0.839814i	$0.317336\pi$
$240$	8.42674	0.543944
$241$	6.92216	0.445895	0.222948	−	0.974830i	$-0.428432\pi$
$241$	6.92216	0.445895	0.222948	+	0.974830i	$0.428432\pi$
$242$	0	0
$243$	−20.8997	−1.34072
$244$	−18.9711	−1.21450
$245$	1.00000	0.0638877
$246$	23.1337	1.47495
$247$	−2.01475	−0.128195
$248$	34.3088	2.17861
$249$	9.01112	0.571057
$250$	−2.43438	−0.153964
$251$	11.6895	0.737837	0.368918	−	0.929462i	$-0.379728\pi$
$251$	11.6895	0.737837	0.368918	+	0.929462i	$0.379728\pi$
$252$	−10.1877	−0.641767
$253$	0	0
$254$	26.3644	1.65425
$255$	−3.62703	−0.227133
$256$	−31.2828	−1.95517
$257$	2.27495	0.141908	0.0709538	−	0.997480i	$-0.477396\pi$
$257$	2.27495	0.141908	0.0709538	+	0.997480i	$0.477396\pi$
$258$	−73.8939	−4.60043
$259$	11.6357	0.723009
$260$	−5.26154	−0.326307
$261$	−18.9914	−1.17554
$262$	33.7512	2.08515
$263$	1.71866	0.105977	0.0529887	−	0.998595i	$-0.483125\pi$
$263$	1.71866	0.105977	0.0529887	+	0.998595i	$0.483125\pi$
$264$	0	0
$265$	−0.974777	−0.0598801
$266$	3.65989	0.224402
$267$	33.1405	2.02817
$268$	−26.4650	−1.61660
$269$	30.1037	1.83545	0.917727	−	0.397211i	$-0.130022\pi$
$269$	30.1037	1.83545	0.917727	+	0.397211i	$0.130022\pi$
$270$	2.33312	0.141989
$271$	11.0588	0.671774	0.335887	−	0.941902i	$-0.390964\pi$
$271$	11.0588	0.671774	0.335887	+	0.941902i	$0.390964\pi$
$272$	−5.46292	−0.331238
$273$	3.16981	0.191846
$274$	−35.6983	−2.15661
$275$	0	0
$276$	24.4232	1.47011
$277$	31.5604	1.89628	0.948139	−	0.317856i	$-0.102963\pi$
$277$	31.5604	1.89628	0.948139	+	0.317856i	$0.102963\pi$
$278$	−14.9640	−0.897479
$279$	−18.9856	−1.13664
$280$	4.68908	0.280226
$281$	17.3779	1.03668	0.518339	−	0.855175i	$-0.326551\pi$
$281$	17.3779	1.03668	0.518339	+	0.855175i	$0.326551\pi$
$282$	37.5359	2.23523
$283$	−13.3616	−0.794266	−0.397133	−	0.917761i	$-0.629995\pi$
$283$	−13.3616	−0.794266	−0.397133	+	0.917761i	$0.629995\pi$
$284$	17.8793	1.06094
$285$	3.55609	0.210645
$286$	0	0
$287$	4.01758	0.237151
$288$	1.83050	0.107863
$289$	−14.6487	−0.861686
$290$	17.8171	1.04626
$291$	27.8006	1.62970
$292$	20.1612	1.17985
$293$	27.1076	1.58364	0.791822	−	0.610752i	$-0.209133\pi$
$293$	27.1076	1.58364	0.791822	+	0.610752i	$0.209133\pi$
$294$	−5.75812	−0.335820
$295$	−0.145722	−0.00848424
$296$	54.5608	3.17128
$297$	0	0
$298$	27.1970	1.57548
$299$	−3.52436	−0.203819
$300$	9.28676	0.536171
$301$	−12.8330	−0.739681
$302$	−23.6364	−1.36012
$303$	−38.0845	−2.18790
$304$	5.35608	0.307192
$305$	−4.83193	−0.276675
$306$	9.68616	0.553721
$307$	−1.06169	−0.0605940	−0.0302970	−	0.999541i	$-0.509645\pi$
$307$	−1.06169	−0.0605940	−0.0302970	+	0.999541i	$0.509645\pi$
$308$	0	0
$309$	−42.2024	−2.40081
$310$	17.8117	1.01164
$311$	8.24957	0.467790	0.233895	−	0.972262i	$-0.424853\pi$
$311$	8.24957	0.467790	0.233895	+	0.972262i	$0.424853\pi$
$312$	14.8635	0.841480
$313$	19.4652	1.10024	0.550120	−	0.835086i	$-0.314582\pi$
$313$	19.4652	1.10024	0.550120	+	0.835086i	$0.314582\pi$
$314$	57.5598	3.24829
$315$	−2.59481	−0.146201
$316$	−51.8674	−2.91777
$317$	−11.2092	−0.629571	−0.314786	−	0.949163i	$-0.601933\pi$
$317$	−11.2092	−0.629571	−0.314786	+	0.949163i	$0.601933\pi$
$318$	5.61288	0.314755
$319$	0	0
$320$	−8.84252	−0.494312
$321$	−9.32577	−0.520514
$322$	6.40216	0.356779
$323$	−2.30536	−0.128273
$324$	−39.4637	−2.19243
$325$	−1.34011	−0.0743360
$326$	2.92275	0.161876
$327$	−2.86450	−0.158407
$328$	18.8388	1.04020
$329$	6.51878	0.359392
$330$	0	0
$331$	−4.42204	−0.243057	−0.121529	−	0.992588i	$-0.538780\pi$
$331$	−4.42204	−0.243057	−0.121529	+	0.992588i	$0.538780\pi$
$332$	14.9575	0.820897
$333$	−30.1925	−1.65454
$334$	−20.7449	−1.13511
$335$	−6.74062	−0.368279
$336$	−8.42674	−0.459716
$337$	−19.5705	−1.06607	−0.533035	−	0.846093i	$-0.678949\pi$
$337$	−19.5705	−1.06607	−0.533035	+	0.846093i	$0.678949\pi$
$338$	27.2750	1.48356
$339$	41.4937	2.25363
$340$	−6.02046	−0.326505
$341$	0	0
$342$	−9.49672	−0.513524
$343$	−1.00000	−0.0539949
$344$	−60.1749	−3.24441
$345$	6.22059	0.334905
$346$	−6.60743	−0.355217
$347$	28.3803	1.52354	0.761768	−	0.647849i	$-0.224331\pi$
$347$	28.3803	1.52354	0.761768	+	0.647849i	$0.224331\pi$
$348$	−67.9696	−3.64355
$349$	−33.6629	−1.80194	−0.900968	−	0.433886i	$-0.857142\pi$
$349$	−33.6629	−1.80194	−0.900968	+	0.433886i	$0.857142\pi$
$350$	2.43438	0.130123
$351$	1.28437	0.0685547
$352$	0	0
$353$	−14.1144	−0.751236	−0.375618	−	0.926775i	$-0.622570\pi$
$353$	−14.1144	−0.751236	−0.375618	+	0.926775i	$0.622570\pi$
$354$	0.839083	0.0445967
$355$	4.55387	0.241694
$356$	55.0096	2.91550
$357$	3.62703	0.191963
$358$	53.5042	2.82778
$359$	−1.60776	−0.0848541	−0.0424270	−	0.999100i	$-0.513509\pi$
$359$	−1.60776	−0.0848541	−0.0424270	+	0.999100i	$0.513509\pi$
$360$	−12.1673	−0.641272
$361$	−16.7397	−0.881039
$362$	−13.9934	−0.735478
$363$	0	0
$364$	5.26154	0.275779
$365$	5.13506	0.268781
$366$	27.8228	1.45432
$367$	27.8927	1.45599	0.727994	−	0.685584i	$-0.240453\pi$
$367$	27.8927	1.45599	0.727994	+	0.685584i	$0.240453\pi$
$368$	9.36927	0.488407
$369$	−10.4249	−0.542697
$370$	28.3257	1.47259
$371$	0.974777	0.0506079
$372$	−67.9489	−3.52299
$373$	−4.95974	−0.256806	−0.128403	−	0.991722i	$-0.540985\pi$
$373$	−4.95974	−0.256806	−0.128403	+	0.991722i	$0.540985\pi$
$374$	0	0
$375$	2.36534	0.122145
$376$	30.5671	1.57638
$377$	9.80825	0.505150
$378$	−2.33312	−0.120003
$379$	−22.7034	−1.16619	−0.583097	−	0.812403i	$-0.698159\pi$
$379$	−22.7034	−1.16619	−0.583097	+	0.812403i	$0.698159\pi$
$380$	5.90271	0.302803
$381$	−25.6167	−1.31238
$382$	25.2168	1.29021
$383$	−8.25745	−0.421936	−0.210968	−	0.977493i	$-0.567662\pi$
$383$	−8.25745	−0.421936	−0.210968	+	0.977493i	$0.567662\pi$
$384$	47.5790	2.42801
$385$	0	0
$386$	7.29823	0.371470
$387$	33.2992	1.69269
$388$	46.1459	2.34270
$389$	5.49137	0.278424	0.139212	−	0.990263i	$-0.455543\pi$
$389$	5.49137	0.278424	0.139212	+	0.990263i	$0.455543\pi$
$390$	7.71652	0.390741
$391$	−4.03271	−0.203943
$392$	−4.68908	−0.236834
$393$	−32.7940	−1.65424
$394$	13.7402	0.692223
$395$	−13.2106	−0.664698
$396$	0	0
$397$	26.4027	1.32511	0.662556	−	0.749013i	$-0.269472\pi$
$397$	26.4027	1.32511	0.662556	+	0.749013i	$0.269472\pi$
$398$	23.1172	1.15876
$399$	−3.55609	−0.178027
$400$	3.56260	0.178130
$401$	9.39065	0.468947	0.234473	−	0.972123i	$-0.424663\pi$
$401$	9.39065	0.468947	0.234473	+	0.972123i	$0.424663\pi$
$402$	38.8133	1.93583
$403$	9.80527	0.488435
$404$	−63.2160	−3.14511
$405$	−10.0514	−0.499457
$406$	−17.8171	−0.884250
$407$	0	0
$408$	17.0074	0.841992
$409$	−16.6149	−0.821552	−0.410776	−	0.911736i	$-0.634742\pi$
$409$	−16.6149	−0.821552	−0.410776	+	0.911736i	$0.634742\pi$
$410$	9.78032	0.483015
$411$	34.6858	1.71093
$412$	−70.0513	−3.45118
$413$	0.145722	0.00717049
$414$	−16.6124	−0.816455
$415$	3.80966	0.187009
$416$	−0.945379	−0.0463510
$417$	14.5396	0.712006
$418$	0	0
$419$	−15.7433	−0.769112	−0.384556	−	0.923102i	$-0.625645\pi$
$419$	−15.7433	−0.769112	−0.384556	+	0.923102i	$0.625645\pi$
$420$	−9.28676	−0.453148
$421$	−32.8440	−1.60072	−0.800360	−	0.599519i	$-0.795358\pi$
$421$	−32.8440	−1.60072	−0.800360	+	0.599519i	$0.795358\pi$
$422$	39.8335	1.93906
$423$	−16.9150	−0.822436
$424$	4.57080	0.221978
$425$	−1.53341	−0.0743812
$426$	−26.2217	−1.27045
$427$	4.83193	0.233833
$428$	−15.4797	−0.748241
$429$	0	0
$430$	−31.2403	−1.50654
$431$	5.37185	0.258753	0.129377	−	0.991596i	$-0.458702\pi$
$431$	5.37185	0.258753	0.129377	+	0.991596i	$0.458702\pi$
$432$	−3.41441	−0.164276
$433$	−38.7699	−1.86316	−0.931582	−	0.363532i	$-0.881571\pi$
$433$	−38.7699	−1.86316	−0.931582	+	0.363532i	$0.881571\pi$
$434$	−17.8117	−0.854990
$435$	−17.3118	−0.830039
$436$	−4.75476	−0.227711
$437$	3.95384	0.189138
$438$	−29.5683	−1.41283
$439$	−0.00322934	−0.000154128 0	−7.70639e−5	−	1.00000i	$-0.500025\pi$
$439$	−0.00322934	−0.000154128 0	−7.70639e−5		1.00000i	$0.500025\pi$
$440$	0	0
$441$	2.59481	0.123562
$442$	−5.00250	−0.237945
$443$	13.0852	0.621697	0.310848	−	0.950460i	$-0.399387\pi$
$443$	13.0852	0.621697	0.310848	+	0.950460i	$0.399387\pi$
$444$	−108.058	−5.12821
$445$	14.0109	0.664181
$446$	27.4772	1.30108
$447$	−26.4256	−1.24989
$448$	8.84252	0.417770
$449$	−23.5135	−1.10967	−0.554835	−	0.831960i	$-0.687219\pi$
$449$	−23.5135	−1.10967	−0.554835	+	0.831960i	$0.687219\pi$
$450$	−6.31675	−0.297774
$451$	0	0
$452$	68.8748	3.23960
$453$	22.9660	1.07904
$454$	3.63439	0.170570
$455$	1.34011	0.0628254
$456$	−16.6748	−0.780868
$457$	−19.5267	−0.913423	−0.456711	−	0.889615i	$-0.650973\pi$
$457$	−19.5267	−0.913423	−0.456711	+	0.889615i	$0.650973\pi$
$458$	−61.0487	−2.85262
$459$	1.46963	0.0685964
$460$	10.3255	0.481428
$461$	−35.0700	−1.63337	−0.816686	−	0.577082i	$-0.804191\pi$
$461$	−35.0700	−1.63337	−0.816686	+	0.577082i	$0.804191\pi$
$462$	0	0
$463$	0.275759	0.0128156	0.00640781	−	0.999979i	$-0.497960\pi$
$463$	0.275759	0.0128156	0.00640781	+	0.999979i	$0.497960\pi$
$464$	−26.0746	−1.21048
$465$	−17.3066	−0.802573
$466$	−22.6109	−1.04743
$467$	10.9082	0.504772	0.252386	−	0.967627i	$-0.418785\pi$
$467$	10.9082	0.504772	0.252386	+	0.967627i	$0.418785\pi$
$468$	−13.6527	−0.631096
$469$	6.74062	0.311253
$470$	15.8692	0.731990
$471$	−55.9274	−2.57700
$472$	0.683300	0.0314514
$473$	0	0
$474$	76.0682	3.49393
$475$	1.50342	0.0689816
$476$	6.02046	0.275947
$477$	−2.52936	−0.115812
$478$	−40.8616	−1.86897
$479$	−40.5238	−1.85158	−0.925790	−	0.378038i	$-0.876599\pi$
$479$	−40.5238	−1.85158	−0.925790	+	0.378038i	$0.876599\pi$
$480$	1.66862	0.0761617
$481$	15.5932	0.710988
$482$	−16.8511	−0.767548
$483$	−6.22059	−0.283047
$484$	0	0
$485$	11.7534	0.533692
$486$	50.8777	2.30786
$487$	24.0857	1.09143	0.545714	−	0.837972i	$-0.316259\pi$
$487$	24.0857	1.09143	0.545714	+	0.837972i	$0.316259\pi$
$488$	22.6573	1.02565
$489$	−2.83986	−0.128423
$490$	−2.43438	−0.109974
$491$	18.6951	0.843700	0.421850	−	0.906666i	$-0.361381\pi$
$491$	18.6951	0.843700	0.421850	+	0.906666i	$0.361381\pi$
$492$	−37.3103	−1.68208
$493$	11.2230	0.505458
$494$	4.90466	0.220671
$495$	0	0
$496$	−26.0666	−1.17043
$497$	−4.55387	−0.204269
$498$	−21.9365	−0.982997
$499$	7.18660	0.321716	0.160858	−	0.986978i	$-0.448574\pi$
$499$	7.18660	0.321716	0.160858	+	0.986978i	$0.448574\pi$
$500$	3.92619	0.175585
$501$	20.1566	0.900529
$502$	−28.4567	−1.27009
$503$	31.1808	1.39028	0.695142	−	0.718872i	$-0.255341\pi$
$503$	31.1808	1.39028	0.695142	+	0.718872i	$0.255341\pi$
$504$	12.1673	0.541973
$505$	−16.1011	−0.716490
$506$	0	0
$507$	−26.5015	−1.17697
$508$	−42.5208	−1.88655
$509$	−16.1794	−0.717141	−0.358571	−	0.933503i	$-0.616736\pi$
$509$	−16.1794	−0.717141	−0.358571	+	0.933503i	$0.616736\pi$
$510$	8.82955	0.390979
$511$	−5.13506	−0.227162
$512$	35.9238	1.58762
$513$	−1.44089	−0.0636166
$514$	−5.53809	−0.244275
$515$	−17.8420	−0.786215
$516$	119.177	5.24647
$517$	0	0
$518$	−28.3257	−1.24456
$519$	6.42003	0.281808
$520$	6.28389	0.275567
$521$	33.2339	1.45600	0.728001	−	0.685576i	$-0.240450\pi$
$521$	33.2339	1.45600	0.728001	+	0.685576i	$0.240450\pi$
$522$	46.2321	2.02353
$523$	−26.8322	−1.17329	−0.586646	−	0.809844i	$-0.699552\pi$
$523$	−26.8322	−1.17329	−0.586646	+	0.809844i	$0.699552\pi$
$524$	−54.4343	−2.37797
$525$	−2.36534	−0.103232
$526$	−4.18388	−0.182426
$527$	11.2196	0.488732
$528$	0	0
$529$	−16.0836	−0.699289
$530$	2.37297	0.103075
$531$	−0.378120	−0.0164090
$532$	−5.90271	−0.255915
$533$	5.38401	0.233208
$534$	−80.6766	−3.49122
$535$	−3.94268	−0.170457
$536$	31.6073	1.36523
$537$	−51.9867	−2.24339
$538$	−73.2837	−3.15949
$539$	0	0
$540$	−3.76289	−0.161929
$541$	−43.2563	−1.85973	−0.929866	−	0.367899i	$-0.880077\pi$
$541$	−43.2563	−1.85973	−0.929866	+	0.367899i	$0.880077\pi$
$542$	−26.9213	−1.15637
$543$	13.5966	0.583484
$544$	−1.08174	−0.0463792
$545$	−1.21104	−0.0518750
$546$	−7.71652	−0.330237
$547$	−44.8652	−1.91830	−0.959148	−	0.282903i	$-0.908702\pi$
$547$	−44.8652	−1.91830	−0.959148	+	0.282903i	$0.908702\pi$
$548$	57.5746	2.45946
$549$	−12.5379	−0.535106
$550$	0	0
$551$	−11.0035	−0.468764
$552$	−29.1688	−1.24151
$553$	13.2106	0.561772
$554$	−76.8298	−3.26419
$555$	−27.5224	−1.16826
$556$	24.1340	1.02351
$557$	36.5892	1.55033	0.775167	−	0.631756i	$-0.217665\pi$
$557$	36.5892	1.55033	0.775167	+	0.631756i	$0.217665\pi$
$558$	46.2181	1.95657
$559$	−17.1976	−0.727383
$560$	−3.56260	−0.150547
$561$	0	0
$562$	−42.3043	−1.78450
$563$	−33.8293	−1.42574	−0.712868	−	0.701298i	$-0.752604\pi$
$563$	−33.8293	−1.42574	−0.712868	+	0.701298i	$0.752604\pi$
$564$	−60.5383	−2.54912
$565$	17.5424	0.738014
$566$	32.5272	1.36722
$567$	10.0514	0.422119
$568$	−21.3534	−0.895970
$569$	−8.04376	−0.337212	−0.168606	−	0.985684i	$-0.553927\pi$
$569$	−8.04376	−0.337212	−0.168606	+	0.985684i	$0.553927\pi$
$570$	−8.65686	−0.362596
$571$	−32.0830	−1.34263	−0.671316	−	0.741171i	$-0.734271\pi$
$571$	−32.0830	−1.34263	−0.671316	+	0.741171i	$0.734271\pi$
$572$	0	0
$573$	−24.5017	−1.02357
$574$	−9.78032	−0.408223
$575$	2.62990	0.109674
$576$	−22.9447	−0.956028
$577$	6.33279	0.263638	0.131819	−	0.991274i	$-0.457918\pi$
$577$	6.33279	0.263638	0.131819	+	0.991274i	$0.457918\pi$
$578$	35.6604	1.48328
$579$	−7.09124	−0.294702
$580$	−28.7357	−1.19318
$581$	−3.80966	−0.158051
$582$	−67.6772	−2.80531
$583$	0	0
$584$	−24.0787	−0.996383
$585$	−3.47734	−0.143770
$586$	−65.9902	−2.72603
$587$	−13.1445	−0.542530	−0.271265	−	0.962505i	$-0.587442\pi$
$587$	−13.1445	−0.542530	−0.271265	+	0.962505i	$0.587442\pi$
$588$	9.28676	0.382980
$589$	−11.0001	−0.453253
$590$	0.354741	0.0146045
$591$	−13.3506	−0.549168
$592$	−41.4534	−1.70372
$593$	22.6909	0.931802	0.465901	−	0.884837i	$-0.345730\pi$
$593$	22.6909	0.931802	0.465901	+	0.884837i	$0.345730\pi$
$594$	0	0
$595$	1.53341	0.0628636
$596$	−43.8636	−1.79672
$597$	−22.4616	−0.919292
$598$	8.57962	0.350847
$599$	16.1228	0.658758	0.329379	−	0.944198i	$-0.393161\pi$
$599$	16.1228	0.658758	0.329379	+	0.944198i	$0.393161\pi$
$600$	−11.0912	−0.452798
$601$	0.160957	0.00656559	0.00328279	−	0.999995i	$-0.498955\pi$
$601$	0.160957	0.00656559	0.00328279	+	0.999995i	$0.498955\pi$
$602$	31.2403	1.27326
$603$	−17.4906	−0.712274
$604$	38.1210	1.55112
$605$	0	0
$606$	92.7121	3.76617
$607$	32.1249	1.30391	0.651955	−	0.758258i	$-0.273949\pi$
$607$	32.1249	1.30391	0.651955	+	0.758258i	$0.273949\pi$
$608$	1.06058	0.0430123
$609$	17.3118	0.701511
$610$	11.7627	0.476259
$611$	8.73590	0.353416
$612$	−15.6220	−0.631480
$613$	7.43932	0.300471	0.150236	−	0.988650i	$-0.451997\pi$
$613$	7.43932	0.300471	0.150236	+	0.988650i	$0.451997\pi$
$614$	2.58456	0.104304
$615$	−9.50294	−0.383195
$616$	0	0
$617$	32.0092	1.28864	0.644320	−	0.764756i	$-0.277140\pi$
$617$	32.0092	1.28864	0.644320	+	0.764756i	$0.277140\pi$
$618$	102.737	4.13267
$619$	16.8003	0.675262	0.337631	−	0.941279i	$-0.390374\pi$
$619$	16.8003	0.675262	0.337631	+	0.941279i	$0.390374\pi$
$620$	−28.7270	−1.15370
$621$	−2.52051	−0.101145
$622$	−20.0826	−0.805238
$623$	−14.0109	−0.561336
$624$	−11.2928	−0.452073
$625$	1.00000	0.0400000
$626$	−47.3857	−1.89391
$627$	0	0
$628$	−92.8331	−3.70445
$629$	17.8423	0.711420
$630$	6.31675	0.251665
$631$	−20.2166	−0.804810	−0.402405	−	0.915462i	$-0.631826\pi$
$631$	−20.2166	−0.804810	−0.402405	+	0.915462i	$0.631826\pi$
$632$	61.9456	2.46406
$633$	−38.7038	−1.53834
$634$	27.2874	1.08372
$635$	−10.8300	−0.429777
$636$	−9.05252	−0.358956
$637$	−1.34011	−0.0530972
$638$	0	0
$639$	11.8164	0.467451
$640$	20.1151	0.795121
$641$	−14.6462	−0.578491	−0.289246	−	0.957255i	$-0.593404\pi$
$641$	−14.6462	−0.578491	−0.289246	+	0.957255i	$0.593404\pi$
$642$	22.7024	0.895994
$643$	14.4119	0.568351	0.284176	−	0.958772i	$-0.408280\pi$
$643$	14.4119	0.568351	0.284176	+	0.958772i	$0.408280\pi$
$644$	−10.3255	−0.406881
$645$	30.3543	1.19520
$646$	5.61210	0.220805
$647$	23.4980	0.923800	0.461900	−	0.886932i	$-0.347168\pi$
$647$	23.4980	0.923800	0.461900	+	0.886932i	$0.347168\pi$
$648$	47.1317	1.85151
$649$	0	0
$650$	3.26234	0.127959
$651$	17.3066	0.678298
$652$	−4.71385	−0.184609
$653$	−43.3028	−1.69457	−0.847286	−	0.531137i	$-0.821765\pi$
$653$	−43.3028	−1.69457	−0.847286	+	0.531137i	$0.821765\pi$
$654$	6.97328	0.272677
$655$	−13.8644	−0.541727
$656$	−14.3130	−0.558830
$657$	13.3245	0.519839
$658$	−15.8692	−0.618645
$659$	−9.68581	−0.377306	−0.188653	−	0.982044i	$-0.560412\pi$
$659$	−9.68581	−0.377306	−0.188653	+	0.982044i	$0.560412\pi$
$660$	0	0
$661$	18.1345	0.705352	0.352676	−	0.935746i	$-0.385272\pi$
$661$	18.1345	0.705352	0.352676	+	0.935746i	$0.385272\pi$
$662$	10.7649	0.418390
$663$	4.86062	0.188771
$664$	−17.8638	−0.693249
$665$	−1.50342	−0.0583001
$666$	73.5000	2.84807
$667$	−19.2482	−0.745292
$668$	33.4576	1.29451
$669$	−26.6980	−1.03220
$670$	16.4092	0.633943
$671$	0	0
$672$	−1.66862	−0.0643684
$673$	4.10637	0.158289	0.0791444	−	0.996863i	$-0.474781\pi$
$673$	4.10637	0.158289	0.0791444	+	0.996863i	$0.474781\pi$
$674$	47.6419	1.83510
$675$	−0.958406	−0.0368891
$676$	−43.9894	−1.69190
$677$	−24.1327	−0.927496	−0.463748	−	0.885967i	$-0.653496\pi$
$677$	−24.1327	−0.927496	−0.463748	+	0.885967i	$0.653496\pi$
$678$	−101.011	−3.87931
$679$	−11.7534	−0.451052
$680$	7.19027	0.275734
$681$	−3.53132	−0.135320
$682$	0	0
$683$	−34.0135	−1.30149	−0.650746	−	0.759296i	$-0.725544\pi$
$683$	−34.0135	−1.30149	−0.650746	+	0.759296i	$0.725544\pi$
$684$	15.3164	0.585638
$685$	14.6642	0.560291
$686$	2.43438	0.0929449
$687$	59.3173	2.26309
$688$	45.7188	1.74301
$689$	1.30631	0.0497664
$690$	−15.1433	−0.576494
$691$	16.7932	0.638842	0.319421	−	0.947613i	$-0.396512\pi$
$691$	16.7932	0.638842	0.319421	+	0.947613i	$0.396512\pi$
$692$	10.6565	0.405101
$693$	0	0
$694$	−69.0885	−2.62256
$695$	6.14694	0.233167
$696$	81.1765	3.07699
$697$	6.16060	0.233349
$698$	81.9483	3.10179
$699$	21.9697	0.830969
$700$	−3.92619	−0.148396
$701$	13.3071	0.502603	0.251301	−	0.967909i	$-0.419142\pi$
$701$	13.3071	0.502603	0.251301	+	0.967909i	$0.419142\pi$
$702$	−3.12664	−0.118008
$703$	−17.4934	−0.659775
$704$	0	0
$705$	−15.4191	−0.580717
$706$	34.3599	1.29315
$707$	16.1011	0.605544
$708$	−1.35328	−0.0508595
$709$	−21.5427	−0.809053	−0.404526	−	0.914526i	$-0.632564\pi$
$709$	−21.5427	−0.809053	−0.404526	+	0.914526i	$0.632564\pi$
$710$	−11.0858	−0.416044
$711$	−34.2790	−1.28556
$712$	−65.6983	−2.46215
$713$	−19.2423	−0.720630
$714$	−8.82955	−0.330438
$715$	0	0
$716$	−86.2922	−3.22489
$717$	39.7028	1.48273
$718$	3.91388	0.146065
$719$	31.1227	1.16068	0.580341	−	0.814373i	$-0.302919\pi$
$719$	31.1227	1.16068	0.580341	+	0.814373i	$0.302919\pi$
$720$	9.24427	0.344514
$721$	17.8420	0.664473
$722$	40.7508	1.51659
$723$	16.3732	0.608927
$724$	22.5688	0.838761
$725$	−7.31897	−0.271820
$726$	0	0
$727$	−6.28012	−0.232917	−0.116458	−	0.993196i	$-0.537154\pi$
$727$	−6.28012	−0.232917	−0.116458	+	0.993196i	$0.537154\pi$
$728$	−6.28389	−0.232896
$729$	−19.2806	−0.714096
$730$	−12.5007	−0.462670
$731$	−19.6782	−0.727825
$732$	−44.8729	−1.65855
$733$	30.1727	1.11445	0.557227	−	0.830361i	$-0.311865\pi$
$733$	30.1727	1.11445	0.557227	+	0.830361i	$0.311865\pi$
$734$	−67.9014	−2.50628
$735$	2.36534	0.0872467
$736$	1.85526	0.0683856
$737$	0	0
$738$	25.3781	0.934180
$739$	38.6060	1.42015	0.710073	−	0.704128i	$-0.248662\pi$
$739$	38.6060	1.42015	0.710073	+	0.704128i	$0.248662\pi$
$740$	−45.6841	−1.67938
$741$	−4.76556	−0.175067
$742$	−2.37297	−0.0871146
$743$	53.2030	1.95183	0.975915	−	0.218152i	$-0.0700027\pi$
$743$	53.2030	1.95183	0.975915	+	0.218152i	$0.0700027\pi$
$744$	81.1518	2.97517
$745$	−11.1720	−0.409312
$746$	12.0739	0.442056
$747$	9.88535	0.361686
$748$	0	0
$749$	3.94268	0.144062
$750$	−5.75812	−0.210257
$751$	30.7735	1.12294	0.561471	−	0.827496i	$-0.310236\pi$
$751$	30.7735	1.12294	0.561471	+	0.827496i	$0.310236\pi$
$752$	−23.2238	−0.846884
$753$	27.6497	1.00761
$754$	−23.8770	−0.869548
$755$	9.70941	0.353362
$756$	3.76289	0.136855
$757$	29.8373	1.08445	0.542227	−	0.840232i	$-0.317581\pi$
$757$	29.8373	1.08445	0.542227	+	0.840232i	$0.317581\pi$
$758$	55.2685	2.00744
$759$	0	0
$760$	−7.04965	−0.255718
$761$	−21.1281	−0.765893	−0.382947	−	0.923770i	$-0.625091\pi$
$761$	−21.1281	−0.765893	−0.382947	+	0.923770i	$0.625091\pi$
$762$	62.3606	2.25909
$763$	1.21104	0.0438424
$764$	−40.6700	−1.47139
$765$	−3.97891	−0.143858
$766$	20.1017	0.726306
$767$	0.195283	0.00705127
$768$	−73.9943	−2.67004
$769$	2.88706	0.104110	0.0520550	−	0.998644i	$-0.483423\pi$
$769$	2.88706	0.104110	0.0520550	+	0.998644i	$0.483423\pi$
$770$	0	0
$771$	5.38103	0.193793
$772$	−11.7707	−0.423635
$773$	−0.535717	−0.0192684	−0.00963419	−	0.999954i	$-0.503067\pi$
$773$	−0.535717	−0.0192684	−0.00963419	+	0.999954i	$0.503067\pi$
$774$	−81.0628	−2.91374
$775$	−7.31675	−0.262825
$776$	−55.1124	−1.97842
$777$	27.5224	0.987360
$778$	−13.3681	−0.479268
$779$	−6.04011	−0.216409
$780$	−12.4453	−0.445613
$781$	0	0
$782$	9.81713	0.351060
$783$	7.01455	0.250680
$784$	3.56260	0.127236
$785$	−23.6446	−0.843911
$786$	79.8329	2.84754
$787$	−13.4545	−0.479602	−0.239801	−	0.970822i	$-0.577082\pi$
$787$	−13.4545	−0.479602	−0.239801	+	0.970822i	$0.577082\pi$
$788$	−22.1604	−0.789432
$789$	4.06522	0.144726
$790$	32.1596	1.14419
$791$	−17.5424	−0.623736
$792$	0	0
$793$	6.47532	0.229945
$794$	−64.2740	−2.28100
$795$	−2.30567	−0.0817738
$796$	−37.2837	−1.32149
$797$	43.3906	1.53697	0.768487	−	0.639865i	$-0.221010\pi$
$797$	43.3906	1.53697	0.768487	+	0.639865i	$0.221010\pi$
$798$	8.65686	0.306450
$799$	9.99595	0.353631
$800$	0.705448	0.0249413
$801$	36.3557	1.28457
$802$	−22.8604	−0.807228
$803$	0	0
$804$	−62.5985	−2.20768
$805$	−2.62990	−0.0926917
$806$	−23.8697	−0.840775
$807$	71.2053	2.50655
$808$	75.4993	2.65606
$809$	8.36441	0.294077	0.147039	−	0.989131i	$-0.453026\pi$
$809$	8.36441	0.294077	0.147039	+	0.989131i	$0.453026\pi$
$810$	24.4689	0.859748
$811$	28.2293	0.991263	0.495632	−	0.868533i	$-0.334937\pi$
$811$	28.2293	0.991263	0.495632	+	0.868533i	$0.334937\pi$
$812$	28.7357	1.00843
$813$	26.1578	0.917392
$814$	0	0
$815$	−1.20062	−0.0420558
$816$	−12.9216	−0.452348
$817$	19.2934	0.674989
$818$	40.4468	1.41419
$819$	3.47734	0.121508
$820$	−15.7738	−0.550845
$821$	−46.8204	−1.63404	−0.817022	−	0.576607i	$-0.804376\pi$
$821$	−46.8204	−1.63404	−0.817022	+	0.576607i	$0.804376\pi$
$822$	−84.4384	−2.94513
$823$	−14.2851	−0.497948	−0.248974	−	0.968510i	$-0.580093\pi$
$823$	−14.2851	−0.497948	−0.248974	+	0.968510i	$0.580093\pi$
$824$	83.6627	2.91453
$825$	0	0
$826$	−0.354741	−0.0123430
$827$	−49.5751	−1.72389	−0.861947	−	0.506998i	$-0.830755\pi$
$827$	−49.5751	−1.72389	−0.861947	+	0.506998i	$0.830755\pi$
$828$	26.7927	0.931110
$829$	28.0658	0.974767	0.487383	−	0.873188i	$-0.337951\pi$
$829$	28.0658	0.974767	0.487383	+	0.873188i	$0.337951\pi$
$830$	−9.27415	−0.321910
$831$	74.6508	2.58961
$832$	11.8500	0.410824
$833$	−1.53341	−0.0531295
$834$	−35.3948	−1.22562
$835$	8.52165	0.294904
$836$	0	0
$837$	7.01242	0.242385
$838$	38.3252	1.32392
$839$	29.9123	1.03269	0.516344	−	0.856381i	$-0.327293\pi$
$839$	29.9123	1.03269	0.516344	+	0.856381i	$0.327293\pi$
$840$	11.0912	0.382684
$841$	24.5674	0.847151
$842$	79.9548	2.75542
$843$	41.1045	1.41571
$844$	−64.2439	−2.21137
$845$	−11.2041	−0.385433
$846$	41.1775	1.41571
$847$	0	0
$848$	−3.47274	−0.119254
$849$	−31.6047	−1.08467
$850$	3.73290	0.128037
$851$	−30.6008	−1.04898
$852$	42.2907	1.44885
$853$	−22.9248	−0.784929	−0.392464	−	0.919767i	$-0.628377\pi$
$853$	−22.9248	−0.784929	−0.392464	+	0.919767i	$0.628377\pi$
$854$	−11.7627	−0.402512
$855$	3.90109	0.133414
$856$	18.4875	0.631891
$857$	−32.2930	−1.10311	−0.551553	−	0.834140i	$-0.685965\pi$
$857$	−32.2930	−1.10311	−0.551553	+	0.834140i	$0.685965\pi$
$858$	0	0
$859$	−34.5206	−1.17783	−0.588915	−	0.808195i	$-0.700445\pi$
$859$	−34.5206	−1.17783	−0.588915	+	0.808195i	$0.700445\pi$
$860$	50.3848	1.71811
$861$	9.50294	0.323859
$862$	−13.0771	−0.445408
$863$	−15.7056	−0.534626	−0.267313	−	0.963610i	$-0.586136\pi$
$863$	−15.7056	−0.534626	−0.267313	+	0.963610i	$0.586136\pi$
$864$	−0.676105	−0.0230016
$865$	2.71422	0.0922861
$866$	94.3806	3.20718
$867$	−34.6490	−1.17674
$868$	28.7270	0.975057
$869$	0	0
$870$	42.1435	1.42880
$871$	9.03318	0.306078
$872$	5.67864	0.192303
$873$	30.4977	1.03219
$874$	−9.62513	−0.325575
$875$	−1.00000	−0.0338062
$876$	47.6881	1.61123
$877$	−6.93152	−0.234061	−0.117030	−	0.993128i	$-0.537338\pi$
$877$	−6.93152	−0.234061	−0.117030	+	0.993128i	$0.537338\pi$
$878$	0.00786143	0.000265310 0
$879$	64.1186	2.16267
$880$	0	0
$881$	−21.1349	−0.712054	−0.356027	−	0.934476i	$-0.615869\pi$
$881$	−21.1349	−0.712054	−0.356027	+	0.934476i	$0.615869\pi$
$882$	−6.31675	−0.212696
$883$	47.2496	1.59007	0.795037	−	0.606561i	$-0.207451\pi$
$883$	47.2496	1.59007	0.795037	+	0.606561i	$0.207451\pi$
$884$	8.06809	0.271359
$885$	−0.344681	−0.0115863
$886$	−31.8543	−1.07017
$887$	−46.5946	−1.56449	−0.782247	−	0.622969i	$-0.785926\pi$
$887$	−46.5946	−1.56449	−0.782247	+	0.622969i	$0.785926\pi$
$888$	129.055	4.33079
$889$	10.8300	0.363228
$890$	−34.1079	−1.14330
$891$	0	0
$892$	−44.3156	−1.48380
$893$	−9.80045	−0.327960
$894$	64.3299	2.15151
$895$	−21.9786	−0.734663
$896$	−20.1151	−0.671999
$897$	−8.33629	−0.278341
$898$	57.2407	1.91015
$899$	53.5511	1.78603
$900$	10.1877	0.339591
$901$	1.49473	0.0497967
$902$	0	0
$903$	−30.3543	−1.01013
$904$	−82.2577	−2.73585
$905$	5.74826	0.191078
$906$	−55.9080	−1.85742
$907$	27.4396	0.911119	0.455559	−	0.890205i	$-0.349439\pi$
$907$	27.4396	0.911119	0.455559	+	0.890205i	$0.349439\pi$
$908$	−5.86159	−0.194524
$909$	−41.7793	−1.38573
$910$	−3.26234	−0.108145
$911$	27.1675	0.900099	0.450050	−	0.893004i	$-0.351406\pi$
$911$	27.1675	0.900099	0.450050	+	0.893004i	$0.351406\pi$
$912$	12.6689	0.419510
$913$	0	0
$914$	47.5355	1.57233
$915$	−11.4291	−0.377835
$916$	98.4600	3.25321
$917$	13.8644	0.457843
$918$	−3.57763	−0.118079
$919$	8.17692	0.269732	0.134866	−	0.990864i	$-0.456940\pi$
$919$	8.17692	0.269732	0.134866	+	0.990864i	$0.456940\pi$
$920$	−12.3318	−0.406567
$921$	−2.51126	−0.0827488
$922$	85.3736	2.81163
$923$	−6.10269	−0.200872
$924$	0	0
$925$	−11.6357	−0.382580
$926$	−0.671302	−0.0220604
$927$	−46.2968	−1.52059
$928$	−5.16315	−0.169489
$929$	−10.8786	−0.356914	−0.178457	−	0.983948i	$-0.557110\pi$
$929$	−10.8786	−0.356914	−0.178457	+	0.983948i	$0.557110\pi$
$930$	42.1307	1.38152
$931$	1.50342	0.0492726
$932$	36.4672	1.19452
$933$	19.5130	0.638827
$934$	−26.5547	−0.868896
$935$	0	0
$936$	16.3055	0.532962
$937$	−17.2856	−0.564697	−0.282348	−	0.959312i	$-0.591113\pi$
$937$	−17.2856	−0.564697	−0.282348	+	0.959312i	$0.591113\pi$
$938$	−16.4092	−0.535780
$939$	46.0418	1.50252
$940$	−25.5940	−0.834783
$941$	−15.0622	−0.491014	−0.245507	−	0.969395i	$-0.578954\pi$
$941$	−15.0622	−0.491014	−0.245507	+	0.969395i	$0.578954\pi$
$942$	136.148	4.43595
$943$	−10.5658	−0.344071
$944$	−0.519148	−0.0168968
$945$	0.958406	0.0311769
$946$	0	0
$947$	9.48480	0.308215	0.154107	−	0.988054i	$-0.450750\pi$
$947$	9.48480	0.308215	0.154107	+	0.988054i	$0.450750\pi$
$948$	−122.684	−3.98458
$949$	−6.88155	−0.223385
$950$	−3.65989	−0.118742
$951$	−26.5135	−0.859759
$952$	−7.19027	−0.233038
$953$	23.9737	0.776585	0.388293	−	0.921536i	$-0.373065\pi$
$953$	23.9737	0.776585	0.388293	+	0.921536i	$0.373065\pi$
$954$	6.15742	0.199354
$955$	−10.3586	−0.335198
$956$	65.9021	2.13143
$957$	0	0
$958$	98.6502	3.18724
$959$	−14.6642	−0.473533
$960$	−20.9155	−0.675046
$961$	22.5348	0.726930
$962$	−37.9597	−1.22387
$963$	−10.2305	−0.329674
$964$	27.1777	0.875335
$965$	−2.99798	−0.0965085
$966$	15.1433	0.487226
$967$	12.7099	0.408722	0.204361	−	0.978896i	$-0.434488\pi$
$967$	12.7099	0.408722	0.204361	+	0.978896i	$0.434488\pi$
$968$	0	0
$969$	−5.45294	−0.175174
$970$	−28.6121	−0.918679
$971$	−39.2102	−1.25831	−0.629157	−	0.777278i	$-0.716600\pi$
$971$	−39.2102	−1.25831	−0.629157	+	0.777278i	$0.716600\pi$
$972$	−82.0562	−2.63195
$973$	−6.14694	−0.197062
$974$	−58.6337	−1.87874
$975$	−3.16981	−0.101515
$976$	−17.2142	−0.551013
$977$	15.3991	0.492660	0.246330	−	0.969186i	$-0.420775\pi$
$977$	15.3991	0.492660	0.246330	+	0.969186i	$0.420775\pi$
$978$	6.91329	0.221063
$979$	0	0
$980$	3.92619	0.125418
$981$	−3.14241	−0.100329
$982$	−45.5110	−1.45232
$983$	60.1481	1.91843	0.959214	−	0.282682i	$-0.0912240\pi$
$983$	60.1481	1.91843	0.959214	+	0.282682i	$0.0912240\pi$
$984$	44.5600	1.42052
$985$	−5.64425	−0.179841
$986$	−27.3210	−0.870077
$987$	15.4191	0.490795
$988$	−7.91029	−0.251660
$989$	33.7494	1.07317
$990$	0	0
$991$	−3.21037	−0.101981	−0.0509904	−	0.998699i	$-0.516238\pi$
$991$	−3.21037	−0.101981	−0.0509904	+	0.998699i	$0.516238\pi$
$992$	−5.16158	−0.163880
$993$	−10.4596	−0.331926
$994$	11.0858	0.351621
$995$	−9.49615	−0.301048
$996$	35.3794	1.12104
$997$	−20.4013	−0.646115	−0.323057	−	0.946379i	$-0.604711\pi$
$997$	−20.4013	−0.646115	−0.323057	+	0.946379i	$0.604711\pi$
$998$	−17.4949	−0.553791
$999$	11.1517	0.352826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bc.1.1	✓	5
11.10	odd	2		4235.2.a.bd.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bc.1.1	✓	5	1.1	even	1	trivial
4235.2.a.bd.1.5	yes	5	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43438 q^{2} +2.36534 q^{3} +3.92619 q^{4} +1.00000 q^{5} -5.75812 q^{6} -1.00000 q^{7} -4.68908 q^{8} +2.59481 q^{9} +O(q^{10})\)	\(q-2.43438 q^{2} +2.36534 q^{3} +3.92619 q^{4} +1.00000 q^{5} -5.75812 q^{6} -1.00000 q^{7} -4.68908 q^{8} +2.59481 q^{9} -2.43438 q^{10} +9.28676 q^{12} -1.34011 q^{13} +2.43438 q^{14} +2.36534 q^{15} +3.56260 q^{16} -1.53341 q^{17} -6.31675 q^{18} +1.50342 q^{19} +3.92619 q^{20} -2.36534 q^{21} +2.62990 q^{23} -11.0912 q^{24} +1.00000 q^{25} +3.26234 q^{26} -0.958406 q^{27} -3.92619 q^{28} -7.31897 q^{29} -5.75812 q^{30} -7.31675 q^{31} +0.705448 q^{32} +3.73290 q^{34} -1.00000 q^{35} +10.1877 q^{36} -11.6357 q^{37} -3.65989 q^{38} -3.16981 q^{39} -4.68908 q^{40} -4.01758 q^{41} +5.75812 q^{42} +12.8330 q^{43} +2.59481 q^{45} -6.40216 q^{46} -6.51878 q^{47} +8.42674 q^{48} +1.00000 q^{49} -2.43438 q^{50} -3.62703 q^{51} -5.26154 q^{52} -0.974777 q^{53} +2.33312 q^{54} +4.68908 q^{56} +3.55609 q^{57} +17.8171 q^{58} -0.145722 q^{59} +9.28676 q^{60} -4.83193 q^{61} +17.8117 q^{62} -2.59481 q^{63} -8.84252 q^{64} -1.34011 q^{65} -6.74062 q^{67} -6.02046 q^{68} +6.22059 q^{69} +2.43438 q^{70} +4.55387 q^{71} -12.1673 q^{72} +5.13506 q^{73} +28.3257 q^{74} +2.36534 q^{75} +5.90271 q^{76} +7.71652 q^{78} -13.2106 q^{79} +3.56260 q^{80} -10.0514 q^{81} +9.78032 q^{82} +3.80966 q^{83} -9.28676 q^{84} -1.53341 q^{85} -31.2403 q^{86} -17.3118 q^{87} +14.0109 q^{89} -6.31675 q^{90} +1.34011 q^{91} +10.3255 q^{92} -17.3066 q^{93} +15.8692 q^{94} +1.50342 q^{95} +1.66862 q^{96} +11.7534 q^{97} -2.43438 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more