LMFDB - Embedded newform 4598.2.a.cb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 $ x^8 - 16x^6 - 4x^5 + 75x^4 + 32x^3 - 90x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.93433$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.48823 q^{3} +1.00000 q^{4} +3.25915 q^{5} -2.48823 q^{6} +4.58972 q^{7} +1.00000 q^{8} +3.19127 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.48823 q^{3} +1.00000 q^{4} +3.25915 q^{5} -2.48823 q^{6} +4.58972 q^{7} +1.00000 q^{8} +3.19127 q^{9} +3.25915 q^{10} -2.48823 q^{12} -4.82326 q^{13} +4.58972 q^{14} -8.10950 q^{15} +1.00000 q^{16} +1.77745 q^{17} +3.19127 q^{18} -1.00000 q^{19} +3.25915 q^{20} -11.4203 q^{21} +6.51169 q^{23} -2.48823 q^{24} +5.62205 q^{25} -4.82326 q^{26} -0.475914 q^{27} +4.58972 q^{28} -0.0103559 q^{29} -8.10950 q^{30} -3.91892 q^{31} +1.00000 q^{32} +1.77745 q^{34} +14.9586 q^{35} +3.19127 q^{36} +0.688142 q^{37} -1.00000 q^{38} +12.0014 q^{39} +3.25915 q^{40} +3.27479 q^{41} -11.4203 q^{42} +1.38020 q^{43} +10.4008 q^{45} +6.51169 q^{46} -6.30125 q^{47} -2.48823 q^{48} +14.0655 q^{49} +5.62205 q^{50} -4.42270 q^{51} -4.82326 q^{52} +14.4636 q^{53} -0.475914 q^{54} +4.58972 q^{56} +2.48823 q^{57} -0.0103559 q^{58} -9.20149 q^{59} -8.10950 q^{60} +13.4651 q^{61} -3.91892 q^{62} +14.6470 q^{63} +1.00000 q^{64} -15.7197 q^{65} +5.08657 q^{67} +1.77745 q^{68} -16.2026 q^{69} +14.9586 q^{70} +9.43943 q^{71} +3.19127 q^{72} -15.2769 q^{73} +0.688142 q^{74} -13.9889 q^{75} -1.00000 q^{76} +12.0014 q^{78} +12.9416 q^{79} +3.25915 q^{80} -8.38962 q^{81} +3.27479 q^{82} +2.32216 q^{83} -11.4203 q^{84} +5.79298 q^{85} +1.38020 q^{86} +0.0257678 q^{87} -6.04905 q^{89} +10.4008 q^{90} -22.1374 q^{91} +6.51169 q^{92} +9.75117 q^{93} -6.30125 q^{94} -3.25915 q^{95} -2.48823 q^{96} -19.4094 q^{97} +14.0655 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.48823	−1.43658	−0.718289	−	0.695745i	$-0.755074\pi$
$3$	−2.48823	−1.43658	−0.718289	+	0.695745i	$0.755074\pi$
$4$	1.00000	0.500000
$5$	3.25915	1.45754	0.728768	−	0.684761i	$-0.240093\pi$
$5$	3.25915	1.45754	0.728768	+	0.684761i	$0.240093\pi$
$6$	−2.48823	−1.01581
$7$	4.58972	1.73475	0.867376	−	0.497654i	$-0.165805\pi$
$7$	4.58972	1.73475	0.867376	+	0.497654i	$0.165805\pi$
$8$	1.00000	0.353553
$9$	3.19127	1.06376
$10$	3.25915	1.03063
$11$	0	0
$11$	0	0
$12$	−2.48823	−0.718289
$13$	−4.82326	−1.33773	−0.668865	−	0.743384i	$-0.733220\pi$
$13$	−4.82326	−1.33773	−0.668865	+	0.743384i	$0.733220\pi$
$14$	4.58972	1.22665
$15$	−8.10950	−2.09386
$16$	1.00000	0.250000
$17$	1.77745	0.431095	0.215548	−	0.976493i	$-0.430846\pi$
$17$	1.77745	0.431095	0.215548	+	0.976493i	$0.430846\pi$
$18$	3.19127	0.752189
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.25915	0.728768
$21$	−11.4203	−2.49210
$22$	0	0
$23$	6.51169	1.35778	0.678891	−	0.734239i	$-0.262461\pi$
$23$	6.51169	1.35778	0.678891	+	0.734239i	$0.262461\pi$
$24$	−2.48823	−0.507907
$25$	5.62205	1.12441
$26$	−4.82326	−0.945919
$27$	−0.475914	−0.0915896
$28$	4.58972	0.867376
$29$	−0.0103559	−0.00192304	−0.000961522	−	1.00000i	$-0.500306\pi$
$29$	−0.0103559	−0.00192304	−0.000961522		1.00000i	$0.500306\pi$
$30$	−8.10950	−1.48059
$31$	−3.91892	−0.703860	−0.351930	−	0.936026i	$-0.614474\pi$
$31$	−3.91892	−0.703860	−0.351930	+	0.936026i	$0.614474\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.77745	0.304830
$35$	14.9586	2.52846
$36$	3.19127	0.531878
$37$	0.688142	0.113130	0.0565650	−	0.998399i	$-0.481985\pi$
$37$	0.688142	0.113130	0.0565650	+	0.998399i	$0.481985\pi$
$38$	−1.00000	−0.162221
$39$	12.0014	1.92175
$40$	3.25915	0.515317
$41$	3.27479	0.511436	0.255718	−	0.966751i	$-0.417688\pi$
$41$	3.27479	0.511436	0.255718	+	0.966751i	$0.417688\pi$
$42$	−11.4203	−1.76218
$43$	1.38020	0.210479	0.105240	−	0.994447i	$-0.466439\pi$
$43$	1.38020	0.210479	0.105240	+	0.994447i	$0.466439\pi$
$44$	0	0
$45$	10.4008	1.55046
$46$	6.51169	0.960096
$47$	−6.30125	−0.919132	−0.459566	−	0.888144i	$-0.651995\pi$
$47$	−6.30125	−0.919132	−0.459566	+	0.888144i	$0.651995\pi$
$48$	−2.48823	−0.359144
$49$	14.0655	2.00936
$50$	5.62205	0.795078
$51$	−4.42270	−0.619302
$52$	−4.82326	−0.668865
$53$	14.4636	1.98673	0.993365	−	0.115003i	$-0.0366877\pi$
$53$	14.4636	1.98673	0.993365	+	0.115003i	$0.0366877\pi$
$54$	−0.475914	−0.0647636
$55$	0	0
$56$	4.58972	0.613327
$57$	2.48823	0.329574
$58$	−0.0103559	−0.00135980
$59$	−9.20149	−1.19793	−0.598966	−	0.800775i	$-0.704421\pi$
$59$	−9.20149	−1.19793	−0.598966	+	0.800775i	$0.704421\pi$
$60$	−8.10950	−1.04693
$61$	13.4651	1.72403	0.862017	−	0.506879i	$-0.169201\pi$
$61$	13.4651	1.72403	0.862017	+	0.506879i	$0.169201\pi$
$62$	−3.91892	−0.497704
$63$	14.6470	1.84535
$64$	1.00000	0.125000
$65$	−15.7197	−1.94979
$66$	0	0
$67$	5.08657	0.621424	0.310712	−	0.950504i	$-0.399433\pi$
$67$	5.08657	0.621424	0.310712	+	0.950504i	$0.399433\pi$
$68$	1.77745	0.215548
$69$	−16.2026	−1.95056
$70$	14.9586	1.78789
$71$	9.43943	1.12025	0.560127	−	0.828406i	$-0.310752\pi$
$71$	9.43943	1.12025	0.560127	+	0.828406i	$0.310752\pi$
$72$	3.19127	0.376094
$73$	−15.2769	−1.78803	−0.894014	−	0.448039i	$-0.852123\pi$
$73$	−15.2769	−1.78803	−0.894014	+	0.448039i	$0.852123\pi$
$74$	0.688142	0.0799949
$75$	−13.9889	−1.61530
$76$	−1.00000	−0.114708
$77$	0	0
$78$	12.0014	1.35889
$79$	12.9416	1.45604	0.728019	−	0.685557i	$-0.240441\pi$
$79$	12.9416	1.45604	0.728019	+	0.685557i	$0.240441\pi$
$80$	3.25915	0.364384
$81$	−8.38962	−0.932180
$82$	3.27479	0.361640
$83$	2.32216	0.254890	0.127445	−	0.991846i	$-0.459322\pi$
$83$	2.32216	0.254890	0.127445	+	0.991846i	$0.459322\pi$
$84$	−11.4203	−1.24605
$85$	5.79298	0.628337
$86$	1.38020	0.148831
$87$	0.0257678	0.00276260
$88$	0	0
$89$	−6.04905	−0.641198	−0.320599	−	0.947215i	$-0.603884\pi$
$89$	−6.04905	−0.641198	−0.320599	+	0.947215i	$0.603884\pi$
$90$	10.4008	1.09634
$91$	−22.1374	−2.32063
$92$	6.51169	0.678891
$93$	9.75117	1.01115
$94$	−6.30125	−0.649924
$95$	−3.25915	−0.334382
$96$	−2.48823	−0.253953
$97$	−19.4094	−1.97073	−0.985364	−	0.170462i	$-0.945474\pi$
$97$	−19.4094	−1.97073	−0.985364	+	0.170462i	$0.945474\pi$
$98$	14.0655	1.42083
$99$	0	0
$100$	5.62205	0.562205
$101$	−7.13850	−0.710308	−0.355154	−	0.934808i	$-0.615572\pi$
$101$	−7.13850	−0.710308	−0.355154	+	0.934808i	$0.615572\pi$
$102$	−4.42270	−0.437912
$103$	8.65120	0.852428	0.426214	−	0.904622i	$-0.359847\pi$
$103$	8.65120	0.852428	0.426214	+	0.904622i	$0.359847\pi$
$104$	−4.82326	−0.472959
$105$	−37.2203	−3.63233
$106$	14.4636	1.40483
$107$	−13.3149	−1.28720	−0.643599	−	0.765363i	$-0.722560\pi$
$107$	−13.3149	−1.28720	−0.643599	+	0.765363i	$0.722560\pi$
$108$	−0.475914	−0.0457948
$109$	−14.3467	−1.37416	−0.687080	−	0.726581i	$-0.741108\pi$
$109$	−14.3467	−1.37416	−0.687080	+	0.726581i	$0.741108\pi$
$110$	0	0
$111$	−1.71225	−0.162520
$112$	4.58972	0.433688
$113$	17.6690	1.66216	0.831080	−	0.556153i	$-0.187723\pi$
$113$	17.6690	1.66216	0.831080	+	0.556153i	$0.187723\pi$
$114$	2.48823	0.233044
$115$	21.2226	1.97902
$116$	−0.0103559	−0.000961522 0
$117$	−15.3923	−1.42302
$118$	−9.20149	−0.847065
$119$	8.15800	0.747843
$120$	−8.10950	−0.740293
$121$	0	0
$122$	13.4651	1.21908
$123$	−8.14842	−0.734718
$124$	−3.91892	−0.351930
$125$	2.02737	0.181333
$126$	14.6470	1.30486
$127$	−10.6201	−0.942381	−0.471191	−	0.882031i	$-0.656176\pi$
$127$	−10.6201	−0.942381	−0.471191	+	0.882031i	$0.656176\pi$
$128$	1.00000	0.0883883
$129$	−3.43426	−0.302369
$130$	−15.7197	−1.37871
$131$	16.9361	1.47971	0.739856	−	0.672765i	$-0.234894\pi$
$131$	16.9361	1.47971	0.739856	+	0.672765i	$0.234894\pi$
$132$	0	0
$133$	−4.58972	−0.397979
$134$	5.08657	0.439413
$135$	−1.55107	−0.133495
$136$	1.77745	0.152415
$137$	−8.12858	−0.694472	−0.347236	−	0.937778i	$-0.612880\pi$
$137$	−8.12858	−0.694472	−0.347236	+	0.937778i	$0.612880\pi$
$138$	−16.2026	−1.37925
$139$	−0.909211	−0.0771183	−0.0385591	−	0.999256i	$-0.512277\pi$
$139$	−0.909211	−0.0771183	−0.0385591	+	0.999256i	$0.512277\pi$
$140$	14.9586	1.26423
$141$	15.6789	1.32040
$142$	9.43943	0.792140
$143$	0	0
$144$	3.19127	0.265939
$145$	−0.0337514	−0.00280290
$146$	−15.2769	−1.26433
$147$	−34.9982	−2.88660
$148$	0.688142	0.0565650
$149$	13.2547	1.08587	0.542933	−	0.839776i	$-0.317314\pi$
$149$	13.2547	1.08587	0.542933	+	0.839776i	$0.317314\pi$
$150$	−13.9889	−1.14219
$151$	2.29362	0.186652	0.0933261	−	0.995636i	$-0.470250\pi$
$151$	2.29362	0.186652	0.0933261	+	0.995636i	$0.470250\pi$
$152$	−1.00000	−0.0811107
$153$	5.67232	0.458580
$154$	0	0
$155$	−12.7724	−1.02590
$156$	12.0014	0.960877
$157$	−11.2813	−0.900345	−0.450172	−	0.892942i	$-0.648637\pi$
$157$	−11.2813	−0.900345	−0.450172	+	0.892942i	$0.648637\pi$
$158$	12.9416	1.02957
$159$	−35.9887	−2.85409
$160$	3.25915	0.257658
$161$	29.8868	2.35541
$162$	−8.38962	−0.659151
$163$	−6.52158	−0.510810	−0.255405	−	0.966834i	$-0.582209\pi$
$163$	−6.52158	−0.510810	−0.255405	+	0.966834i	$0.582209\pi$
$164$	3.27479	0.255718
$165$	0	0
$166$	2.32216	0.180235
$167$	20.7099	1.60258	0.801289	−	0.598278i	$-0.204148\pi$
$167$	20.7099	1.60258	0.801289	+	0.598278i	$0.204148\pi$
$168$	−11.4203	−0.881092
$169$	10.2638	0.789524
$170$	5.79298	0.444301
$171$	−3.19127	−0.244042
$172$	1.38020	0.105240
$173$	−2.02529	−0.153980	−0.0769899	−	0.997032i	$-0.524531\pi$
$173$	−2.02529	−0.153980	−0.0769899	+	0.997032i	$0.524531\pi$
$174$	0.0257678	0.00195345
$175$	25.8037	1.95057
$176$	0	0
$177$	22.8954	1.72092
$178$	−6.04905	−0.453395
$179$	20.7205	1.54873	0.774363	−	0.632742i	$-0.218071\pi$
$179$	20.7205	1.54873	0.774363	+	0.632742i	$0.218071\pi$
$180$	10.4008	0.775231
$181$	−7.63695	−0.567650	−0.283825	−	0.958876i	$-0.591604\pi$
$181$	−7.63695	−0.567650	−0.283825	+	0.958876i	$0.591604\pi$
$182$	−22.1374	−1.64093
$183$	−33.5043	−2.47671
$184$	6.51169	0.480048
$185$	2.24276	0.164891
$186$	9.75117	0.714990
$187$	0	0
$188$	−6.30125	−0.459566
$189$	−2.18431	−0.158885
$190$	−3.25915	−0.236444
$191$	20.6340	1.49302	0.746512	−	0.665372i	$-0.231727\pi$
$191$	20.6340	1.49302	0.746512	+	0.665372i	$0.231727\pi$
$192$	−2.48823	−0.179572
$193$	8.64747	0.622458	0.311229	−	0.950335i	$-0.399259\pi$
$193$	8.64747	0.622458	0.311229	+	0.950335i	$0.399259\pi$
$194$	−19.4094	−1.39352
$195$	39.1142	2.80103
$196$	14.0655	1.00468
$197$	−10.6030	−0.755430	−0.377715	−	0.925922i	$-0.623290\pi$
$197$	−10.6030	−0.755430	−0.377715	+	0.925922i	$0.623290\pi$
$198$	0	0
$199$	2.19833	0.155836	0.0779179	−	0.996960i	$-0.475173\pi$
$199$	2.19833	0.155836	0.0779179	+	0.996960i	$0.475173\pi$
$200$	5.62205	0.397539
$201$	−12.6565	−0.892724
$202$	−7.13850	−0.502263
$203$	−0.0475307	−0.00333600
$204$	−4.42270	−0.309651
$205$	10.6730	0.745437
$206$	8.65120	0.602758
$207$	20.7805	1.44435
$208$	−4.82326	−0.334433
$209$	0	0
$210$	−37.2203	−2.56845
$211$	−13.9756	−0.962118	−0.481059	−	0.876688i	$-0.659748\pi$
$211$	−13.9756	−0.962118	−0.481059	+	0.876688i	$0.659748\pi$
$212$	14.4636	0.993365
$213$	−23.4874	−1.60933
$214$	−13.3149	−0.910187
$215$	4.49829	0.306781
$216$	−0.475914	−0.0323818
$217$	−17.9868	−1.22102
$218$	−14.3467	−0.971678
$219$	38.0124	2.56864
$220$	0	0
$221$	−8.57310	−0.576689
$222$	−1.71225	−0.114919
$223$	8.82515	0.590976	0.295488	−	0.955346i	$-0.404518\pi$
$223$	8.82515	0.590976	0.295488	+	0.955346i	$0.404518\pi$
$224$	4.58972	0.306664
$225$	17.9415	1.19610
$226$	17.6690	1.17532
$227$	−4.53586	−0.301055	−0.150528	−	0.988606i	$-0.548097\pi$
$227$	−4.53586	−0.301055	−0.150528	+	0.988606i	$0.548097\pi$
$228$	2.48823	0.164787
$229$	−6.29059	−0.415694	−0.207847	−	0.978161i	$-0.566646\pi$
$229$	−6.29059	−0.415694	−0.207847	+	0.978161i	$0.566646\pi$
$230$	21.2226	1.39938
$231$	0	0
$232$	−0.0103559	−0.000679898 0
$233$	−16.6897	−1.09338	−0.546689	−	0.837336i	$-0.684112\pi$
$233$	−16.6897	−1.09338	−0.546689	+	0.837336i	$0.684112\pi$
$234$	−15.3923	−1.00623
$235$	−20.5367	−1.33967
$236$	−9.20149	−0.598966
$237$	−32.2015	−2.09171
$238$	8.15800	0.528805
$239$	−7.23299	−0.467863	−0.233932	−	0.972253i	$-0.575159\pi$
$239$	−7.23299	−0.467863	−0.233932	+	0.972253i	$0.575159\pi$
$240$	−8.10950	−0.523466
$241$	13.5156	0.870618	0.435309	−	0.900281i	$-0.356639\pi$
$241$	13.5156	0.870618	0.435309	+	0.900281i	$0.356639\pi$
$242$	0	0
$243$	22.3030	1.43074
$244$	13.4651	0.862017
$245$	45.8417	2.92872
$246$	−8.14842	−0.519524
$247$	4.82326	0.306897
$248$	−3.91892	−0.248852
$249$	−5.77806	−0.366170
$250$	2.02737	0.128222
$251$	3.08810	0.194919	0.0974595	−	0.995239i	$-0.468928\pi$
$251$	3.08810	0.194919	0.0974595	+	0.995239i	$0.468928\pi$
$252$	14.6470	0.922676
$253$	0	0
$254$	−10.6201	−0.666364
$255$	−14.4142	−0.902654
$256$	1.00000	0.0625000
$257$	17.3396	1.08161	0.540806	−	0.841147i	$-0.318119\pi$
$257$	17.3396	1.08161	0.540806	+	0.841147i	$0.318119\pi$
$258$	−3.43426	−0.213808
$259$	3.15838	0.196252
$260$	−15.7197	−0.974895
$261$	−0.0330484	−0.00204565
$262$	16.9361	1.04631
$263$	−16.8383	−1.03830	−0.519148	−	0.854684i	$-0.673751\pi$
$263$	−16.8383	−1.03830	−0.519148	+	0.854684i	$0.673751\pi$
$264$	0	0
$265$	47.1391	2.89573
$266$	−4.58972	−0.281414
$267$	15.0514	0.921130
$268$	5.08657	0.310712
$269$	−4.84616	−0.295475	−0.147738	−	0.989027i	$-0.547199\pi$
$269$	−4.84616	−0.295475	−0.147738	+	0.989027i	$0.547199\pi$
$270$	−1.55107	−0.0943953
$271$	5.89504	0.358098	0.179049	−	0.983840i	$-0.442698\pi$
$271$	5.89504	0.358098	0.179049	+	0.983840i	$0.442698\pi$
$272$	1.77745	0.107774
$273$	55.0828	3.33377
$274$	−8.12858	−0.491066
$275$	0	0
$276$	−16.2026	−0.975279
$277$	30.7017	1.84468	0.922342	−	0.386375i	$-0.126273\pi$
$277$	30.7017	1.84468	0.922342	+	0.386375i	$0.126273\pi$
$278$	−0.909211	−0.0545309
$279$	−12.5063	−0.748734
$280$	14.9586	0.893946
$281$	−14.4108	−0.859678	−0.429839	−	0.902905i	$-0.641430\pi$
$281$	−14.4108	−0.859678	−0.429839	+	0.902905i	$0.641430\pi$
$282$	15.6789	0.933667
$283$	15.1624	0.901313	0.450657	−	0.892697i	$-0.351190\pi$
$283$	15.1624	0.901313	0.450657	+	0.892697i	$0.351190\pi$
$284$	9.43943	0.560127
$285$	8.10950	0.480365
$286$	0	0
$287$	15.0304	0.887215
$288$	3.19127	0.188047
$289$	−13.8407	−0.814157
$290$	−0.0337514	−0.00198195
$291$	48.2950	2.83110
$292$	−15.2769	−0.894014
$293$	−30.5088	−1.78234	−0.891172	−	0.453665i	$-0.850116\pi$
$293$	−30.5088	−1.78234	−0.891172	+	0.453665i	$0.850116\pi$
$294$	−34.9982	−2.04114
$295$	−29.9890	−1.74603
$296$	0.688142	0.0399975
$297$	0	0
$298$	13.2547	0.767823
$299$	−31.4076	−1.81635
$300$	−13.9889	−0.807652
$301$	6.33475	0.365129
$302$	2.29362	0.131983
$303$	17.7622	1.02041
$304$	−1.00000	−0.0573539
$305$	43.8849	2.51284
$306$	5.67232	0.324265
$307$	−10.4099	−0.594123	−0.297062	−	0.954858i	$-0.596007\pi$
$307$	−10.4099	−0.594123	−0.297062	+	0.954858i	$0.596007\pi$
$308$	0	0
$309$	−21.5261	−1.22458
$310$	−12.7724	−0.725421
$311$	28.6601	1.62516	0.812582	−	0.582847i	$-0.198061\pi$
$311$	28.6601	1.62516	0.812582	+	0.582847i	$0.198061\pi$
$312$	12.0014	0.679443
$313$	32.8105	1.85456	0.927279	−	0.374370i	$-0.122141\pi$
$313$	32.8105	1.85456	0.927279	+	0.374370i	$0.122141\pi$
$314$	−11.2813	−0.636640
$315$	47.7368	2.68967
$316$	12.9416	0.728019
$317$	−11.3871	−0.639564	−0.319782	−	0.947491i	$-0.603610\pi$
$317$	−11.3871	−0.639564	−0.319782	+	0.947491i	$0.603610\pi$
$318$	−35.9887	−2.01815
$319$	0	0
$320$	3.25915	0.182192
$321$	33.1304	1.84916
$322$	29.8868	1.66553
$323$	−1.77745	−0.0989000
$324$	−8.38962	−0.466090
$325$	−27.1166	−1.50416
$326$	−6.52158	−0.361197
$327$	35.6977	1.97409
$328$	3.27479	0.180820
$329$	−28.9210	−1.59446
$330$	0	0
$331$	13.1649	0.723609	0.361805	−	0.932254i	$-0.382161\pi$
$331$	13.1649	0.723609	0.361805	+	0.932254i	$0.382161\pi$
$332$	2.32216	0.127445
$333$	2.19605	0.120343
$334$	20.7099	1.13319
$335$	16.5779	0.905747
$336$	−11.4203	−0.623026
$337$	−17.3554	−0.945407	−0.472704	−	0.881221i	$-0.656722\pi$
$337$	−17.3554	−0.945407	−0.472704	+	0.881221i	$0.656722\pi$
$338$	10.2638	0.558278
$339$	−43.9644	−2.38782
$340$	5.79298	0.314168
$341$	0	0
$342$	−3.19127	−0.172564
$343$	32.4288	1.75099
$344$	1.38020	0.0744156
$345$	−52.8065	−2.84301
$346$	−2.02529	−0.108880
$347$	5.01412	0.269172	0.134586	−	0.990902i	$-0.457030\pi$
$347$	5.01412	0.269172	0.134586	+	0.990902i	$0.457030\pi$
$348$	0.0257678	0.00138130
$349$	−36.1563	−1.93540	−0.967701	−	0.252100i	$-0.918879\pi$
$349$	−36.1563	−1.93540	−0.967701	+	0.252100i	$0.918879\pi$
$350$	25.8037	1.37926
$351$	2.29545	0.122522
$352$	0	0
$353$	16.1472	0.859429	0.429714	−	0.902965i	$-0.358614\pi$
$353$	16.1472	0.859429	0.429714	+	0.902965i	$0.358614\pi$
$354$	22.8954	1.21688
$355$	30.7645	1.63281
$356$	−6.04905	−0.320599
$357$	−20.2990	−1.07433
$358$	20.7205	1.09511
$359$	8.01403	0.422964	0.211482	−	0.977382i	$-0.432171\pi$
$359$	8.01403	0.422964	0.211482	+	0.977382i	$0.432171\pi$
$360$	10.4008	0.548171
$361$	1.00000	0.0526316
$362$	−7.63695	−0.401389
$363$	0	0
$364$	−22.1374	−1.16032
$365$	−49.7898	−2.60612
$366$	−33.5043	−1.75130
$367$	22.3199	1.16509	0.582544	−	0.812799i	$-0.302058\pi$
$367$	22.3199	1.16509	0.582544	+	0.812799i	$0.302058\pi$
$368$	6.51169	0.339445
$369$	10.4507	0.544043
$370$	2.24276	0.116595
$371$	66.3839	3.44648
$372$	9.75117	0.505574
$373$	−11.0167	−0.570423	−0.285211	−	0.958465i	$-0.592064\pi$
$373$	−11.0167	−0.570423	−0.285211	+	0.958465i	$0.592064\pi$
$374$	0	0
$375$	−5.04454	−0.260499
$376$	−6.30125	−0.324962
$377$	0.0499492	0.00257251
$378$	−2.18431	−0.112349
$379$	19.2812	0.990410	0.495205	−	0.868776i	$-0.335093\pi$
$379$	19.2812	0.990410	0.495205	+	0.868776i	$0.335093\pi$
$380$	−3.25915	−0.167191
$381$	26.4252	1.35380
$382$	20.6340	1.05573
$383$	15.5005	0.792039	0.396019	−	0.918242i	$-0.370391\pi$
$383$	15.5005	0.792039	0.396019	+	0.918242i	$0.370391\pi$
$384$	−2.48823	−0.126977
$385$	0	0
$386$	8.64747	0.440145
$387$	4.40460	0.223898
$388$	−19.4094	−0.985364
$389$	2.57878	0.130749	0.0653746	−	0.997861i	$-0.479176\pi$
$389$	2.57878	0.130749	0.0653746	+	0.997861i	$0.479176\pi$
$390$	39.1142	1.98062
$391$	11.5742	0.585333
$392$	14.0655	0.710417
$393$	−42.1408	−2.12572
$394$	−10.6030	−0.534170
$395$	42.1784	2.12223
$396$	0	0
$397$	4.30951	0.216288	0.108144	−	0.994135i	$-0.465509\pi$
$397$	4.30951	0.216288	0.108144	+	0.994135i	$0.465509\pi$
$398$	2.19833	0.110193
$399$	11.4203	0.571728
$400$	5.62205	0.281103
$401$	−12.0460	−0.601551	−0.300775	−	0.953695i	$-0.597245\pi$
$401$	−12.0460	−0.601551	−0.300775	+	0.953695i	$0.597245\pi$
$402$	−12.6565	−0.631251
$403$	18.9020	0.941575
$404$	−7.13850	−0.355154
$405$	−27.3430	−1.35869
$406$	−0.0475307	−0.00235891
$407$	0	0
$408$	−4.42270	−0.218956
$409$	−35.2394	−1.74248	−0.871239	−	0.490859i	$-0.836683\pi$
$409$	−35.2394	−1.74248	−0.871239	+	0.490859i	$0.836683\pi$
$410$	10.6730	0.527104
$411$	20.2257	0.997663
$412$	8.65120	0.426214
$413$	−42.2322	−2.07811
$414$	20.7805	1.02131
$415$	7.56827	0.371512
$416$	−4.82326	−0.236480
$417$	2.26232	0.110786
$418$	0	0
$419$	−8.29185	−0.405083	−0.202542	−	0.979274i	$-0.564920\pi$
$419$	−8.29185	−0.405083	−0.202542	+	0.979274i	$0.564920\pi$
$420$	−37.2203	−1.81617
$421$	−25.2575	−1.23098	−0.615488	−	0.788146i	$-0.711041\pi$
$421$	−25.2575	−1.23098	−0.615488	+	0.788146i	$0.711041\pi$
$422$	−13.9756	−0.680320
$423$	−20.1090	−0.977731
$424$	14.4636	0.702415
$425$	9.99292	0.484728
$426$	−23.4874	−1.13797
$427$	61.8012	2.99077
$428$	−13.3149	−0.643599
$429$	0	0
$430$	4.49829	0.216927
$431$	−5.62638	−0.271013	−0.135507	−	0.990776i	$-0.543266\pi$
$431$	−5.62638	−0.271013	−0.135507	+	0.990776i	$0.543266\pi$
$432$	−0.475914	−0.0228974
$433$	24.2774	1.16670	0.583349	−	0.812222i	$-0.301742\pi$
$433$	24.2774	1.16670	0.583349	+	0.812222i	$0.301742\pi$
$434$	−17.9868	−0.863392
$435$	0.0839812	0.00402659
$436$	−14.3467	−0.687080
$437$	−6.51169	−0.311496
$438$	38.0124	1.81630
$439$	−23.6907	−1.13070	−0.565348	−	0.824853i	$-0.691258\pi$
$439$	−23.6907	−1.13070	−0.565348	+	0.824853i	$0.691258\pi$
$440$	0	0
$441$	44.8869	2.13747
$442$	−8.57310	−0.407781
$443$	−26.9144	−1.27874	−0.639371	−	0.768899i	$-0.720805\pi$
$443$	−26.9144	−1.27874	−0.639371	+	0.768899i	$0.720805\pi$
$444$	−1.71225	−0.0812600
$445$	−19.7147	−0.934569
$446$	8.82515	0.417883
$447$	−32.9806	−1.55993
$448$	4.58972	0.216844
$449$	15.5953	0.735987	0.367993	−	0.929828i	$-0.380045\pi$
$449$	15.5953	0.735987	0.367993	+	0.929828i	$0.380045\pi$
$450$	17.9415	0.845769
$451$	0	0
$452$	17.6690	0.831080
$453$	−5.70705	−0.268140
$454$	−4.53586	−0.212878
$455$	−72.1491	−3.38240
$456$	2.48823	0.116522
$457$	−24.0214	−1.12367	−0.561837	−	0.827248i	$-0.689905\pi$
$457$	−24.0214	−1.12367	−0.561837	+	0.827248i	$0.689905\pi$
$458$	−6.29059	−0.293940
$459$	−0.845913	−0.0394838
$460$	21.2226	0.989508
$461$	−19.8822	−0.926005	−0.463003	−	0.886357i	$-0.653228\pi$
$461$	−19.8822	−0.926005	−0.463003	+	0.886357i	$0.653228\pi$
$462$	0	0
$463$	37.7710	1.75537	0.877684	−	0.479240i	$-0.159087\pi$
$463$	37.7710	1.75537	0.877684	+	0.479240i	$0.159087\pi$
$464$	−0.0103559	−0.000480761 0
$465$	31.7805	1.47379
$466$	−16.6897	−0.773135
$467$	−42.9098	−1.98563	−0.992815	−	0.119656i	$-0.961821\pi$
$467$	−42.9098	−1.98563	−0.992815	+	0.119656i	$0.961821\pi$
$468$	−15.3923	−0.711509
$469$	23.3459	1.07802
$470$	−20.5367	−0.947288
$471$	28.0704	1.29342
$472$	−9.20149	−0.423533
$473$	0	0
$474$	−32.2015	−1.47906
$475$	−5.62205	−0.257958
$476$	8.15800	0.373921
$477$	46.1572	2.11340
$478$	−7.23299	−0.330829
$479$	26.1271	1.19378	0.596888	−	0.802324i	$-0.296404\pi$
$479$	26.1271	1.19378	0.596888	+	0.802324i	$0.296404\pi$
$480$	−8.10950	−0.370146
$481$	−3.31909	−0.151337
$482$	13.5156	0.615620
$483$	−74.3652	−3.38373
$484$	0	0
$485$	−63.2582	−2.87241
$486$	22.3030	1.01168
$487$	13.0467	0.591204	0.295602	−	0.955311i	$-0.404480\pi$
$487$	13.0467	0.591204	0.295602	+	0.955311i	$0.404480\pi$
$488$	13.4651	0.609538
$489$	16.2272	0.733818
$490$	45.8417	2.07092
$491$	−16.0017	−0.722145	−0.361072	−	0.932538i	$-0.617589\pi$
$491$	−16.0017	−0.722145	−0.361072	+	0.932538i	$0.617589\pi$
$492$	−8.14842	−0.367359
$493$	−0.0184071	−0.000829015 0
$494$	4.82326	0.217009
$495$	0	0
$496$	−3.91892	−0.175965
$497$	43.3244	1.94336
$498$	−5.77806	−0.258921
$499$	−29.3850	−1.31545	−0.657727	−	0.753256i	$-0.728482\pi$
$499$	−29.3850	−1.31545	−0.657727	+	0.753256i	$0.728482\pi$
$500$	2.02737	0.0906665
$501$	−51.5308	−2.30223
$502$	3.08810	0.137829
$503$	−8.80839	−0.392747	−0.196373	−	0.980529i	$-0.562916\pi$
$503$	−8.80839	−0.392747	−0.196373	+	0.980529i	$0.562916\pi$
$504$	14.6470	0.652430
$505$	−23.2655	−1.03530
$506$	0	0
$507$	−25.5387	−1.13421
$508$	−10.6201	−0.471191
$509$	−15.7974	−0.700209	−0.350104	−	0.936711i	$-0.613854\pi$
$509$	−15.7974	−0.700209	−0.350104	+	0.936711i	$0.613854\pi$
$510$	−14.4142	−0.638273
$511$	−70.1168	−3.10178
$512$	1.00000	0.0441942
$513$	0.475914	0.0210121
$514$	17.3396	0.764815
$515$	28.1955	1.24244
$516$	−3.43426	−0.151185
$517$	0	0
$518$	3.15838	0.138771
$519$	5.03938	0.221204
$520$	−15.7197	−0.689355
$521$	27.2791	1.19512	0.597560	−	0.801824i	$-0.296137\pi$
$521$	27.2791	1.19512	0.597560	+	0.801824i	$0.296137\pi$
$522$	−0.0330484	−0.00144649
$523$	−24.3662	−1.06546	−0.532730	−	0.846285i	$-0.678834\pi$
$523$	−24.3662	−1.06546	−0.532730	+	0.846285i	$0.678834\pi$
$524$	16.9361	0.739856
$525$	−64.2053	−2.80215
$526$	−16.8383	−0.734186
$527$	−6.96570	−0.303430
$528$	0	0
$529$	19.4021	0.843571
$530$	47.1391	2.04759
$531$	−29.3644	−1.27431
$532$	−4.58972	−0.198990
$533$	−15.7952	−0.684164
$534$	15.0514	0.651337
$535$	−43.3952	−1.87614
$536$	5.08657	0.219706
$537$	−51.5574	−2.22486
$538$	−4.84616	−0.208933
$539$	0	0
$540$	−1.55107	−0.0667476
$541$	15.4651	0.664897	0.332449	−	0.943121i	$-0.392125\pi$
$541$	15.4651	0.664897	0.332449	+	0.943121i	$0.392125\pi$
$542$	5.89504	0.253214
$543$	19.0025	0.815474
$544$	1.77745	0.0762076
$545$	−46.7579	−2.00289
$546$	55.0828	2.35733
$547$	−1.33234	−0.0569667	−0.0284834	−	0.999594i	$-0.509068\pi$
$547$	−1.33234	−0.0569667	−0.0284834	+	0.999594i	$0.509068\pi$
$548$	−8.12858	−0.347236
$549$	42.9708	1.83395
$550$	0	0
$551$	0.0103559	0.000441176 0
$552$	−16.2026	−0.689627
$553$	59.3981	2.52586
$554$	30.7017	1.30439
$555$	−5.58049	−0.236879
$556$	−0.909211	−0.0385591
$557$	26.6638	1.12978	0.564892	−	0.825165i	$-0.308918\pi$
$557$	26.6638	1.12978	0.564892	+	0.825165i	$0.308918\pi$
$558$	−12.5063	−0.529435
$559$	−6.65708	−0.281564
$560$	14.9586	0.632116
$561$	0	0
$562$	−14.4108	−0.607884
$563$	−25.1226	−1.05879	−0.529396	−	0.848375i	$-0.677582\pi$
$563$	−25.1226	−1.05879	−0.529396	+	0.848375i	$0.677582\pi$
$564$	15.6789	0.660202
$565$	57.5859	2.42266
$566$	15.1624	0.637325
$567$	−38.5060	−1.61710
$568$	9.43943	0.396070
$569$	−16.6061	−0.696162	−0.348081	−	0.937464i	$-0.613167\pi$
$569$	−16.6061	−0.696162	−0.348081	+	0.937464i	$0.613167\pi$
$570$	8.10950	0.339670
$571$	−27.1795	−1.13743	−0.568713	−	0.822536i	$-0.692558\pi$
$571$	−27.1795	−1.13743	−0.568713	+	0.822536i	$0.692558\pi$
$572$	0	0
$573$	−51.3421	−2.14485
$574$	15.0304	0.627356
$575$	36.6091	1.52670
$576$	3.19127	0.132969
$577$	−20.5578	−0.855831	−0.427915	−	0.903819i	$-0.640752\pi$
$577$	−20.5578	−0.855831	−0.427915	+	0.903819i	$0.640752\pi$
$578$	−13.8407	−0.575696
$579$	−21.5168	−0.894210
$580$	−0.0337514	−0.00140145
$581$	10.6581	0.442171
$582$	48.2950	2.00189
$583$	0	0
$584$	−15.2769	−0.632163
$585$	−50.1658	−2.07410
$586$	−30.5088	−1.26031
$587$	−13.6615	−0.563872	−0.281936	−	0.959433i	$-0.590977\pi$
$587$	−13.6615	−0.563872	−0.281936	+	0.959433i	$0.590977\pi$
$588$	−34.9982	−1.44330
$589$	3.91892	0.161476
$590$	−29.9890	−1.23463
$591$	26.3826	1.08523
$592$	0.688142	0.0282825
$593$	8.26443	0.339380	0.169690	−	0.985498i	$-0.445723\pi$
$593$	8.26443	0.339380	0.169690	+	0.985498i	$0.445723\pi$
$594$	0	0
$595$	26.5881	1.09001
$596$	13.2547	0.542933
$597$	−5.46995	−0.223870
$598$	−31.4076	−1.28435
$599$	−11.3663	−0.464413	−0.232207	−	0.972666i	$-0.574595\pi$
$599$	−11.3663	−0.464413	−0.232207	+	0.972666i	$0.574595\pi$
$600$	−13.9889	−0.571096
$601$	−17.2129	−0.702130	−0.351065	−	0.936351i	$-0.614180\pi$
$601$	−17.2129	−0.702130	−0.351065	+	0.936351i	$0.614180\pi$
$602$	6.33475	0.258185
$603$	16.2326	0.661043
$604$	2.29362	0.0933261
$605$	0	0
$606$	17.7622	0.721540
$607$	−2.71425	−0.110168	−0.0550841	−	0.998482i	$-0.517543\pi$
$607$	−2.71425	−0.110168	−0.0550841	+	0.998482i	$0.517543\pi$
$608$	−1.00000	−0.0405554
$609$	0.118267	0.00479242
$610$	43.8849	1.77685
$611$	30.3925	1.22955
$612$	5.67232	0.229290
$613$	−0.970155	−0.0391842	−0.0195921	−	0.999808i	$-0.506237\pi$
$613$	−0.970155	−0.0391842	−0.0195921	+	0.999808i	$0.506237\pi$
$614$	−10.4099	−0.420109
$615$	−26.5569	−1.07088
$616$	0	0
$617$	0.377035	0.0151789	0.00758944	−	0.999971i	$-0.497584\pi$
$617$	0.377035	0.0151789	0.00758944	+	0.999971i	$0.497584\pi$
$618$	−21.5261	−0.865908
$619$	−11.6033	−0.466377	−0.233188	−	0.972432i	$-0.574916\pi$
$619$	−11.6033	−0.466377	−0.233188	+	0.972432i	$0.574916\pi$
$620$	−12.7724	−0.512950
$621$	−3.09900	−0.124359
$622$	28.6601	1.14916
$623$	−27.7634	−1.11232
$624$	12.0014	0.480439
$625$	−21.5028	−0.860111
$626$	32.8105	1.31137
$627$	0	0
$628$	−11.2813	−0.450172
$629$	1.22314	0.0487698
$630$	47.7368	1.90188
$631$	13.9531	0.555464	0.277732	−	0.960659i	$-0.410417\pi$
$631$	13.9531	0.555464	0.277732	+	0.960659i	$0.410417\pi$
$632$	12.9416	0.514787
$633$	34.7744	1.38216
$634$	−11.3871	−0.452240
$635$	−34.6125	−1.37355
$636$	−35.9887	−1.42705
$637$	−67.8417	−2.68799
$638$	0	0
$639$	30.1238	1.19168
$640$	3.25915	0.128829
$641$	3.80584	0.150322	0.0751608	−	0.997171i	$-0.476053\pi$
$641$	3.80584	0.150322	0.0751608	+	0.997171i	$0.476053\pi$
$642$	33.1304	1.30755
$643$	8.46396	0.333786	0.166893	−	0.985975i	$-0.446627\pi$
$643$	8.46396	0.333786	0.166893	+	0.985975i	$0.446627\pi$
$644$	29.8868	1.17771
$645$	−11.1928	−0.440714
$646$	−1.77745	−0.0699329
$647$	−10.1179	−0.397775	−0.198888	−	0.980022i	$-0.563733\pi$
$647$	−10.1179	−0.397775	−0.198888	+	0.980022i	$0.563733\pi$
$648$	−8.38962	−0.329575
$649$	0	0
$650$	−27.1166	−1.06360
$651$	44.7551	1.75409
$652$	−6.52158	−0.255405
$653$	7.24197	0.283400	0.141700	−	0.989910i	$-0.454743\pi$
$653$	7.24197	0.283400	0.141700	+	0.989910i	$0.454743\pi$
$654$	35.6977	1.39589
$655$	55.1972	2.15673
$656$	3.27479	0.127859
$657$	−48.7527	−1.90202
$658$	−28.9210	−1.12746
$659$	−11.1870	−0.435783	−0.217891	−	0.975973i	$-0.569918\pi$
$659$	−11.1870	−0.435783	−0.217891	+	0.975973i	$0.569918\pi$
$660$	0	0
$661$	6.73868	0.262104	0.131052	−	0.991375i	$-0.458164\pi$
$661$	6.73868	0.262104	0.131052	+	0.991375i	$0.458164\pi$
$662$	13.1649	0.511669
$663$	21.3318	0.828459
$664$	2.32216	0.0901173
$665$	−14.9586	−0.580069
$666$	2.19605	0.0850950
$667$	−0.0674344	−0.00261107
$668$	20.7099	0.801289
$669$	−21.9590	−0.848983
$670$	16.5779	0.640460
$671$	0	0
$672$	−11.4203	−0.440546
$673$	3.80683	0.146743	0.0733713	−	0.997305i	$-0.476624\pi$
$673$	3.80683	0.146743	0.0733713	+	0.997305i	$0.476624\pi$
$674$	−17.3554	−0.668504
$675$	−2.67561	−0.102984
$676$	10.2638	0.394762
$677$	14.9987	0.576446	0.288223	−	0.957563i	$-0.406936\pi$
$677$	14.9987	0.576446	0.288223	+	0.957563i	$0.406936\pi$
$678$	−43.9644	−1.68844
$679$	−89.0838	−3.41872
$680$	5.79298	0.222151
$681$	11.2862	0.432489
$682$	0	0
$683$	−12.7603	−0.488260	−0.244130	−	0.969742i	$-0.578502\pi$
$683$	−12.7603	−0.488260	−0.244130	+	0.969742i	$0.578502\pi$
$684$	−3.19127	−0.122021
$685$	−26.4923	−1.01222
$686$	32.4288	1.23814
$687$	15.6524	0.597177
$688$	1.38020	0.0526198
$689$	−69.7617	−2.65771
$690$	−52.8065	−2.01031
$691$	29.5740	1.12505	0.562525	−	0.826780i	$-0.309830\pi$
$691$	29.5740	1.12505	0.562525	+	0.826780i	$0.309830\pi$
$692$	−2.02529	−0.0769899
$693$	0	0
$694$	5.01412	0.190333
$695$	−2.96326	−0.112403
$696$	0.0257678	0.000976727 0
$697$	5.82078	0.220478
$698$	−36.1563	−1.36854
$699$	41.5277	1.57072
$700$	25.8037	0.975286
$701$	−35.4860	−1.34029	−0.670143	−	0.742232i	$-0.733767\pi$
$701$	−35.4860	−1.34029	−0.670143	+	0.742232i	$0.733767\pi$
$702$	2.29545	0.0866363
$703$	−0.688142	−0.0259538
$704$	0	0
$705$	51.1000	1.92454
$706$	16.1472	0.607708
$707$	−32.7637	−1.23221
$708$	22.8954	0.860461
$709$	7.58291	0.284782	0.142391	−	0.989810i	$-0.454521\pi$
$709$	7.58291	0.284782	0.142391	+	0.989810i	$0.454521\pi$
$710$	30.7645	1.15457
$711$	41.2999	1.54887
$712$	−6.04905	−0.226698
$713$	−25.5188	−0.955687
$714$	−20.2990	−0.759669
$715$	0	0
$716$	20.7205	0.774363
$717$	17.9973	0.672122
$718$	8.01403	0.299081
$719$	10.5644	0.393985	0.196993	−	0.980405i	$-0.436883\pi$
$719$	10.5644	0.393985	0.196993	+	0.980405i	$0.436883\pi$
$720$	10.4008	0.387615
$721$	39.7066	1.47875
$722$	1.00000	0.0372161
$723$	−33.6299	−1.25071
$724$	−7.63695	−0.283825
$725$	−0.0582214	−0.00216229
$726$	0	0
$727$	−13.9031	−0.515638	−0.257819	−	0.966193i	$-0.583004\pi$
$727$	−13.9031	−0.515638	−0.257819	+	0.966193i	$0.583004\pi$
$728$	−22.1374	−0.820467
$729$	−30.3260	−1.12319
$730$	−49.7898	−1.84280
$731$	2.45324	0.0907365
$732$	−33.5043	−1.23835
$733$	24.9256	0.920649	0.460325	−	0.887751i	$-0.347733\pi$
$733$	24.9256	0.920649	0.460325	+	0.887751i	$0.347733\pi$
$734$	22.3199	0.823841
$735$	−114.064	−4.20733
$736$	6.51169	0.240024
$737$	0	0
$738$	10.4507	0.384697
$739$	−9.43289	−0.346995	−0.173497	−	0.984834i	$-0.555507\pi$
$739$	−9.43289	−0.346995	−0.173497	+	0.984834i	$0.555507\pi$
$740$	2.24276	0.0824455
$741$	−12.0014	−0.440881
$742$	66.3839	2.43703
$743$	50.6746	1.85907	0.929535	−	0.368735i	$-0.120209\pi$
$743$	50.6746	1.85907	0.929535	+	0.368735i	$0.120209\pi$
$744$	9.75117	0.357495
$745$	43.1990	1.58269
$746$	−11.0167	−0.403350
$747$	7.41063	0.271141
$748$	0	0
$749$	−61.1116	−2.23297
$750$	−5.04454	−0.184201
$751$	53.0962	1.93751	0.968754	−	0.248025i	$-0.0797815\pi$
$751$	53.0962	1.93751	0.968754	+	0.248025i	$0.0797815\pi$
$752$	−6.30125	−0.229783
$753$	−7.68388	−0.280016
$754$	0.0499492	0.00181904
$755$	7.47525	0.272052
$756$	−2.18431	−0.0794426
$757$	−30.2934	−1.10103	−0.550517	−	0.834824i	$-0.685569\pi$
$757$	−30.2934	−1.10103	−0.550517	+	0.834824i	$0.685569\pi$
$758$	19.2812	0.700326
$759$	0	0
$760$	−3.25915	−0.118222
$761$	−4.83983	−0.175444	−0.0877219	−	0.996145i	$-0.527959\pi$
$761$	−4.83983	−0.175444	−0.0877219	+	0.996145i	$0.527959\pi$
$762$	26.4252	0.957284
$763$	−65.8471	−2.38383
$764$	20.6340	0.746512
$765$	18.4869	0.668397
$766$	15.5005	0.560056
$767$	44.3811	1.60251
$768$	−2.48823	−0.0897861
$769$	−30.9675	−1.11672	−0.558358	−	0.829600i	$-0.688568\pi$
$769$	−30.9675	−1.11672	−0.558358	+	0.829600i	$0.688568\pi$
$770$	0	0
$771$	−43.1447	−1.55382
$772$	8.64747	0.311229
$773$	−30.9296	−1.11246	−0.556229	−	0.831029i	$-0.687752\pi$
$773$	−30.9296	−1.11246	−0.556229	+	0.831029i	$0.687752\pi$
$774$	4.40460	0.158320
$775$	−22.0324	−0.791427
$776$	−19.4094	−0.696758
$777$	−7.85877	−0.281932
$778$	2.57878	0.0924536
$779$	−3.27479	−0.117332
$780$	39.1142	1.40051
$781$	0	0
$782$	11.5742	0.413893
$783$	0.00492852	0.000176131 0
$784$	14.0655	0.502340
$785$	−36.7674	−1.31228
$786$	−42.1408	−1.50311
$787$	−7.58212	−0.270274	−0.135137	−	0.990827i	$-0.543147\pi$
$787$	−7.58212	−0.270274	−0.135137	+	0.990827i	$0.543147\pi$
$788$	−10.6030	−0.377715
$789$	41.8975	1.49159
$790$	42.1784	1.50064
$791$	81.0957	2.88343
$792$	0	0
$793$	−64.9458	−2.30629
$794$	4.30951	0.152939
$795$	−117.293	−4.15994
$796$	2.19833	0.0779179
$797$	−1.66912	−0.0591232	−0.0295616	−	0.999563i	$-0.509411\pi$
$797$	−1.66912	−0.0591232	−0.0295616	+	0.999563i	$0.509411\pi$
$798$	11.4203	0.404273
$799$	−11.2002	−0.396233
$800$	5.62205	0.198770
$801$	−19.3041	−0.682078
$802$	−12.0460	−0.425361
$803$	0	0
$804$	−12.6565	−0.446362
$805$	97.4057	3.43310
$806$	18.9020	0.665794
$807$	12.0583	0.424473
$808$	−7.13850	−0.251132
$809$	27.4251	0.964215	0.482107	−	0.876112i	$-0.339871\pi$
$809$	27.4251	0.964215	0.482107	+	0.876112i	$0.339871\pi$
$810$	−27.3430	−0.960736
$811$	−52.1412	−1.83093	−0.915463	−	0.402401i	$-0.868176\pi$
$811$	−52.1412	−1.83093	−0.915463	+	0.402401i	$0.868176\pi$
$812$	−0.0475307	−0.00166800
$813$	−14.6682	−0.514436
$814$	0	0
$815$	−21.2548	−0.744523
$816$	−4.42270	−0.154825
$817$	−1.38020	−0.0482872
$818$	−35.2394	−1.23212
$819$	−70.6463	−2.46858
$820$	10.6730	0.372718
$821$	−19.2406	−0.671502	−0.335751	−	0.941951i	$-0.608990\pi$
$821$	−19.2406	−0.671502	−0.335751	+	0.941951i	$0.608990\pi$
$822$	20.2257	0.705454
$823$	23.7426	0.827614	0.413807	−	0.910365i	$-0.364199\pi$
$823$	23.7426	0.827614	0.413807	+	0.910365i	$0.364199\pi$
$824$	8.65120	0.301379
$825$	0	0
$826$	−42.2322	−1.46945
$827$	−19.7786	−0.687769	−0.343885	−	0.939012i	$-0.611743\pi$
$827$	−19.7786	−0.687769	−0.343885	+	0.939012i	$0.611743\pi$
$828$	20.7805	0.722174
$829$	9.35784	0.325011	0.162506	−	0.986708i	$-0.448042\pi$
$829$	9.35784	0.325011	0.162506	+	0.986708i	$0.448042\pi$
$830$	7.56827	0.262698
$831$	−76.3926	−2.65003
$832$	−4.82326	−0.167216
$833$	25.0008	0.866226
$834$	2.26232	0.0783378
$835$	67.4965	2.33581
$836$	0	0
$837$	1.86507	0.0644662
$838$	−8.29185	−0.286437
$839$	−7.65538	−0.264293	−0.132147	−	0.991230i	$-0.542187\pi$
$839$	−7.65538	−0.264293	−0.132147	+	0.991230i	$0.542187\pi$
$840$	−37.2203	−1.28422
$841$	−28.9999	−0.999996
$842$	−25.2575	−0.870431
$843$	35.8574	1.23499
$844$	−13.9756	−0.481059
$845$	33.4513	1.15076
$846$	−20.1090	−0.691360
$847$	0	0
$848$	14.4636	0.496683
$849$	−37.7276	−1.29481
$850$	9.99292	0.342754
$851$	4.48097	0.153606
$852$	−23.4874	−0.804667
$853$	27.9084	0.955565	0.477783	−	0.878478i	$-0.341441\pi$
$853$	27.9084	0.955565	0.477783	+	0.878478i	$0.341441\pi$
$854$	61.8012	2.11479
$855$	−10.4008	−0.355700
$856$	−13.3149	−0.455093
$857$	38.8157	1.32592	0.662960	−	0.748655i	$-0.269300\pi$
$857$	38.8157	1.32592	0.662960	+	0.748655i	$0.269300\pi$
$858$	0	0
$859$	−12.5352	−0.427697	−0.213848	−	0.976867i	$-0.568600\pi$
$859$	−12.5352	−0.427697	−0.213848	+	0.976867i	$0.568600\pi$
$860$	4.49829	0.153390
$861$	−37.3990	−1.27455
$862$	−5.62638	−0.191635
$863$	−12.4527	−0.423896	−0.211948	−	0.977281i	$-0.567981\pi$
$863$	−12.4527	−0.423896	−0.211948	+	0.977281i	$0.567981\pi$
$864$	−0.475914	−0.0161909
$865$	−6.60072	−0.224431
$866$	24.2774	0.824980
$867$	34.4387	1.16960
$868$	−17.9868	−0.610511
$869$	0	0
$870$	0.0839812	0.00284723
$871$	−24.5338	−0.831298
$872$	−14.3467	−0.485839
$873$	−61.9406	−2.09637
$874$	−6.51169	−0.220261
$875$	9.30504	0.314568
$876$	38.0124	1.28432
$877$	−11.4582	−0.386917	−0.193458	−	0.981108i	$-0.561970\pi$
$877$	−11.4582	−0.386917	−0.193458	+	0.981108i	$0.561970\pi$
$878$	−23.6907	−0.799523
$879$	75.9128	2.56048
$880$	0	0
$881$	26.3649	0.888257	0.444129	−	0.895963i	$-0.353513\pi$
$881$	26.3649	0.888257	0.444129	+	0.895963i	$0.353513\pi$
$882$	44.8869	1.51142
$883$	52.5648	1.76895	0.884474	−	0.466590i	$-0.154517\pi$
$883$	52.5648	1.76895	0.884474	+	0.466590i	$0.154517\pi$
$884$	−8.57310	−0.288345
$885$	74.6194	2.50830
$886$	−26.9144	−0.904207
$887$	29.5635	0.992644	0.496322	−	0.868138i	$-0.334683\pi$
$887$	29.5635	0.992644	0.496322	+	0.868138i	$0.334683\pi$
$888$	−1.71225	−0.0574595
$889$	−48.7433	−1.63480
$890$	−19.7147	−0.660840
$891$	0	0
$892$	8.82515	0.295488
$893$	6.30125	0.210863
$894$	−32.9806	−1.10304
$895$	67.5313	2.25732
$896$	4.58972	0.153332
$897$	78.1491	2.60932
$898$	15.5953	0.520421
$899$	0.0405840	0.00135355
$900$	17.9415	0.598049
$901$	25.7084	0.856470
$902$	0	0
$903$	−15.7623	−0.524536
$904$	17.6690	0.587662
$905$	−24.8900	−0.827371
$906$	−5.70705	−0.189604
$907$	49.2004	1.63367	0.816836	−	0.576870i	$-0.195726\pi$
$907$	49.2004	1.63367	0.816836	+	0.576870i	$0.195726\pi$
$908$	−4.53586	−0.150528
$909$	−22.7809	−0.755594
$910$	−72.1491	−2.39172
$911$	−11.8309	−0.391976	−0.195988	−	0.980606i	$-0.562791\pi$
$911$	−11.8309	−0.391976	−0.195988	+	0.980606i	$0.562791\pi$
$912$	2.48823	0.0823934
$913$	0	0
$914$	−24.0214	−0.794557
$915$	−109.196	−3.60989
$916$	−6.29059	−0.207847
$917$	77.7319	2.56693
$918$	−0.845913	−0.0279193
$919$	8.32413	0.274588	0.137294	−	0.990530i	$-0.456160\pi$
$919$	8.32413	0.274588	0.137294	+	0.990530i	$0.456160\pi$
$920$	21.2226	0.699688
$921$	25.9021	0.853504
$922$	−19.8822	−0.654784
$923$	−45.5288	−1.49860
$924$	0	0
$925$	3.86877	0.127204
$926$	37.7710	1.24123
$927$	27.6083	0.906775
$928$	−0.0103559	−0.000339949 0
$929$	−56.0858	−1.84011	−0.920057	−	0.391784i	$-0.871858\pi$
$929$	−56.0858	−1.84011	−0.920057	+	0.391784i	$0.871858\pi$
$930$	31.7805	1.04212
$931$	−14.0655	−0.460979
$932$	−16.6897	−0.546689
$933$	−71.3127	−2.33467
$934$	−42.9098	−1.40405
$935$	0	0
$936$	−15.3923	−0.503113
$937$	25.2464	0.824764	0.412382	−	0.911011i	$-0.364697\pi$
$937$	25.2464	0.824764	0.412382	+	0.911011i	$0.364697\pi$
$938$	23.3459	0.762272
$939$	−81.6399	−2.66422
$940$	−20.5367	−0.669834
$941$	−2.72172	−0.0887257	−0.0443628	−	0.999015i	$-0.514126\pi$
$941$	−2.72172	−0.0887257	−0.0443628	+	0.999015i	$0.514126\pi$
$942$	28.0704	0.914583
$943$	21.3244	0.694419
$944$	−9.20149	−0.299483
$945$	−7.11899	−0.231581
$946$	0	0
$947$	−28.7838	−0.935347	−0.467674	−	0.883901i	$-0.654908\pi$
$947$	−28.7838	−0.935347	−0.467674	+	0.883901i	$0.654908\pi$
$948$	−32.2015	−1.04586
$949$	73.6845	2.39190
$950$	−5.62205	−0.182404
$951$	28.3337	0.918784
$952$	8.15800	0.264402
$953$	−19.3594	−0.627113	−0.313556	−	0.949570i	$-0.601520\pi$
$953$	−19.3594	−0.627113	−0.313556	+	0.949570i	$0.601520\pi$
$954$	46.1572	1.49440
$955$	67.2493	2.17614
$956$	−7.23299	−0.233932
$957$	0	0
$958$	26.1271	0.844127
$959$	−37.3079	−1.20474
$960$	−8.10950	−0.261733
$961$	−15.6420	−0.504582
$962$	−3.31909	−0.107012
$963$	−42.4913	−1.36926
$964$	13.5156	0.435309
$965$	28.1834	0.907255
$966$	−74.3652	−2.39266
$967$	−16.2018	−0.521016	−0.260508	−	0.965472i	$-0.583890\pi$
$967$	−16.2018	−0.521016	−0.260508	+	0.965472i	$0.583890\pi$
$968$	0	0
$969$	4.42270	0.142078
$970$	−63.2582	−2.03110
$971$	−38.0152	−1.21996	−0.609982	−	0.792415i	$-0.708824\pi$
$971$	−38.0152	−1.21996	−0.609982	+	0.792415i	$0.708824\pi$
$972$	22.3030	0.715369
$973$	−4.17303	−0.133781
$974$	13.0467	0.418044
$975$	67.4722	2.16084
$976$	13.4651	0.431009
$977$	11.0980	0.355055	0.177528	−	0.984116i	$-0.443190\pi$
$977$	11.0980	0.355055	0.177528	+	0.984116i	$0.443190\pi$
$978$	16.2272	0.518888
$979$	0	0
$980$	45.8417	1.46436
$981$	−45.7840	−1.46177
$982$	−16.0017	−0.510633
$983$	−29.1596	−0.930045	−0.465023	−	0.885299i	$-0.653954\pi$
$983$	−29.1596	−0.930045	−0.465023	+	0.885299i	$0.653954\pi$
$984$	−8.14842	−0.259762
$985$	−34.5566	−1.10107
$986$	−0.0184071	−0.000586202 0
$987$	71.9619	2.29057
$988$	4.82326	0.153448
$989$	8.98746	0.285785
$990$	0	0
$991$	7.72841	0.245501	0.122751	−	0.992438i	$-0.460828\pi$
$991$	7.72841	0.245501	0.122751	+	0.992438i	$0.460828\pi$
$992$	−3.91892	−0.124426
$993$	−32.7573	−1.03952
$994$	43.3244	1.37417
$995$	7.16470	0.227136
$996$	−5.77806	−0.183085
$997$	−43.8825	−1.38977	−0.694886	−	0.719120i	$-0.744545\pi$
$997$	−43.8825	−1.38977	−0.694886	+	0.719120i	$0.744545\pi$
$998$	−29.3850	−0.930166
$999$	−0.327496	−0.0103615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cb.1.1	yes	8
11.10	odd	2		4598.2.a.by.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.by.1.1	✓	8	11.10	odd	2
4598.2.a.cb.1.1	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.48823 q^{3} +1.00000 q^{4} +3.25915 q^{5} -2.48823 q^{6} +4.58972 q^{7} +1.00000 q^{8} +3.19127 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.48823 q^{3} +1.00000 q^{4} +3.25915 q^{5} -2.48823 q^{6} +4.58972 q^{7} +1.00000 q^{8} +3.19127 q^{9} +3.25915 q^{10} -2.48823 q^{12} -4.82326 q^{13} +4.58972 q^{14} -8.10950 q^{15} +1.00000 q^{16} +1.77745 q^{17} +3.19127 q^{18} -1.00000 q^{19} +3.25915 q^{20} -11.4203 q^{21} +6.51169 q^{23} -2.48823 q^{24} +5.62205 q^{25} -4.82326 q^{26} -0.475914 q^{27} +4.58972 q^{28} -0.0103559 q^{29} -8.10950 q^{30} -3.91892 q^{31} +1.00000 q^{32} +1.77745 q^{34} +14.9586 q^{35} +3.19127 q^{36} +0.688142 q^{37} -1.00000 q^{38} +12.0014 q^{39} +3.25915 q^{40} +3.27479 q^{41} -11.4203 q^{42} +1.38020 q^{43} +10.4008 q^{45} +6.51169 q^{46} -6.30125 q^{47} -2.48823 q^{48} +14.0655 q^{49} +5.62205 q^{50} -4.42270 q^{51} -4.82326 q^{52} +14.4636 q^{53} -0.475914 q^{54} +4.58972 q^{56} +2.48823 q^{57} -0.0103559 q^{58} -9.20149 q^{59} -8.10950 q^{60} +13.4651 q^{61} -3.91892 q^{62} +14.6470 q^{63} +1.00000 q^{64} -15.7197 q^{65} +5.08657 q^{67} +1.77745 q^{68} -16.2026 q^{69} +14.9586 q^{70} +9.43943 q^{71} +3.19127 q^{72} -15.2769 q^{73} +0.688142 q^{74} -13.9889 q^{75} -1.00000 q^{76} +12.0014 q^{78} +12.9416 q^{79} +3.25915 q^{80} -8.38962 q^{81} +3.27479 q^{82} +2.32216 q^{83} -11.4203 q^{84} +5.79298 q^{85} +1.38020 q^{86} +0.0257678 q^{87} -6.04905 q^{89} +10.4008 q^{90} -22.1374 q^{91} +6.51169 q^{92} +9.75117 q^{93} -6.30125 q^{94} -3.25915 q^{95} -2.48823 q^{96} -19.4094 q^{97} +14.0655 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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