LMFDB - Embedded newform 5415.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, 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("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.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:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.8797896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 $ x^5 - x^4 - 8x^3 + 5x^2 + 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.69159$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69159 q^{2} -1.00000 q^{3} +5.24466 q^{4} +1.00000 q^{5} +2.69159 q^{6} -0.797044 q^{7} -8.73329 q^{8} +1.00000 q^{9} -2.69159 q^{10} +2.59225 q^{11} -5.24466 q^{12} -2.79704 q^{13} +2.14532 q^{14} -1.00000 q^{15} +13.0171 q^{16} -5.77247 q^{17} -2.69159 q^{18} +5.24466 q^{20} +0.797044 q^{21} -6.97727 q^{22} -3.10614 q^{23} +8.73329 q^{24} +1.00000 q^{25} +7.52850 q^{26} -1.00000 q^{27} -4.18023 q^{28} -4.79093 q^{29} +2.69159 q^{30} -9.48932 q^{31} -17.5702 q^{32} -2.59225 q^{33} +15.5371 q^{34} -0.797044 q^{35} +5.24466 q^{36} +7.69227 q^{37} +2.79704 q^{39} -8.73329 q^{40} +7.38318 q^{41} -2.14532 q^{42} -2.79704 q^{43} +13.5955 q^{44} +1.00000 q^{45} +8.36045 q^{46} -11.0773 q^{47} -13.0171 q^{48} -6.36472 q^{49} -2.69159 q^{50} +5.77247 q^{51} -14.6695 q^{52} -8.87861 q^{53} +2.69159 q^{54} +2.59225 q^{55} +6.96082 q^{56} +12.8952 q^{58} +1.08020 q^{59} -5.24466 q^{60} +4.07225 q^{61} +25.5414 q^{62} -0.797044 q^{63} +21.2575 q^{64} -2.79704 q^{65} +6.97727 q^{66} +13.7757 q^{67} -30.2747 q^{68} +3.10614 q^{69} +2.14532 q^{70} -11.9754 q^{71} -8.73329 q^{72} +8.50778 q^{73} -20.7045 q^{74} -1.00000 q^{75} -2.06614 q^{77} -7.52850 q^{78} +6.48184 q^{79} +13.0171 q^{80} +1.00000 q^{81} -19.8725 q^{82} -2.79520 q^{83} +4.18023 q^{84} -5.77247 q^{85} +7.52850 q^{86} +4.79093 q^{87} -22.6389 q^{88} -13.3586 q^{89} -2.69159 q^{90} +2.22937 q^{91} -16.2906 q^{92} +9.48932 q^{93} +29.8155 q^{94} +17.5702 q^{96} +2.00000 q^{97} +17.1312 q^{98} +2.59225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} - 7 q^{12} - 8 q^{13} - 4 q^{14} - 5 q^{15} + 7 q^{16} + 10 q^{17} - q^{18} + 7 q^{20} - 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 5 * q - q^2 - 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 5 * q^9 - q^10 + 5 * q^11 - 7 * q^12 - 8 * q^13 - 4 * q^14 - 5 * q^15 + 7 * q^16 + 10 * q^17 - q^18 + 7 * q^20 - 2 * q^21 + 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 - 5 * q^27 + 10 * q^28 - 7 * q^29 + q^30 - 9 * q^31 - 23 * q^32 - 5 * q^33 + 25 * q^34 + 2 * q^35 + 7 * q^36 + 6 * q^37 + 8 * q^39 - 6 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 - 20 * q^46 + 6 * q^47 - 7 * q^48 + 15 * q^49 - q^50 - 10 * q^51 - 4 * q^52 + 8 * q^53 + q^54 + 5 * q^55 + 36 * q^56 + 38 * q^58 - q^59 - 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 - 8 * q^65 - 2 * q^66 - 14 * q^67 - q^68 + 2 * q^69 - 4 * q^70 - 27 * q^71 - 6 * q^72 + 26 * q^73 - 18 * q^74 - 5 * q^75 + 14 * q^77 + 2 * q^78 + 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 - 10 * q^84 + 10 * q^85 - 2 * q^86 + 7 * q^87 - 9 * q^89 - q^90 + 46 * q^91 - 52 * q^92 + 9 * q^93 + 45 * q^94 + 23 * q^96 + 10 * q^97 + 21 * q^98 + 5 * q^99

Coefficient data

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

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

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

$2$	−2.69159	−1.90324	−0.951621	−	0.307274i	$-0.900583\pi$
$2$	−2.69159	−1.90324	−0.951621	+	0.307274i	$0.900583\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.24466	2.62233
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.69159	1.09884
$7$	−0.797044	−0.301254	−0.150627	−	0.988591i	$-0.548129\pi$
$7$	−0.797044	−0.301254	−0.150627	+	0.988591i	$0.548129\pi$
$8$	−8.73329	−3.08769
$9$	1.00000	0.333333
$10$	−2.69159	−0.851156
$11$	2.59225	0.781592	0.390796	−	0.920477i	$-0.372200\pi$
$11$	2.59225	0.781592	0.390796	+	0.920477i	$0.372200\pi$
$12$	−5.24466	−1.51400
$13$	−2.79704	−0.775760	−0.387880	−	0.921710i	$-0.626793\pi$
$13$	−2.79704	−0.775760	−0.387880	+	0.921710i	$0.626793\pi$
$14$	2.14532	0.573360
$15$	−1.00000	−0.258199
$16$	13.0171	3.25428
$17$	−5.77247	−1.40003	−0.700015	−	0.714128i	$-0.746823\pi$
$17$	−5.77247	−1.40003	−0.700015	+	0.714128i	$0.746823\pi$
$18$	−2.69159	−0.634414
$19$	0	0
$19$	0	0
$20$	5.24466	1.17274
$21$	0.797044	0.173929
$22$	−6.97727	−1.48756
$23$	−3.10614	−0.647674	−0.323837	−	0.946113i	$-0.604973\pi$
$23$	−3.10614	−0.647674	−0.323837	+	0.946113i	$0.604973\pi$
$24$	8.73329	1.78268
$25$	1.00000	0.200000
$26$	7.52850	1.47646
$27$	−1.00000	−0.192450
$28$	−4.18023	−0.789988
$29$	−4.79093	−0.889654	−0.444827	−	0.895617i	$-0.646735\pi$
$29$	−4.79093	−0.889654	−0.444827	+	0.895617i	$0.646735\pi$
$30$	2.69159	0.491415
$31$	−9.48932	−1.70433	−0.852166	−	0.523272i	$-0.824711\pi$
$31$	−9.48932	−1.70433	−0.852166	+	0.523272i	$0.824711\pi$
$32$	−17.5702	−3.10600
$33$	−2.59225	−0.451252
$34$	15.5371	2.66460
$35$	−0.797044	−0.134725
$36$	5.24466	0.874110
$37$	7.69227	1.26460	0.632301	−	0.774723i	$-0.282111\pi$
$37$	7.69227	1.26460	0.632301	+	0.774723i	$0.282111\pi$
$38$	0	0
$39$	2.79704	0.447886
$40$	−8.73329	−1.38086
$41$	7.38318	1.15306	0.576530	−	0.817076i	$-0.304407\pi$
$41$	7.38318	1.15306	0.576530	+	0.817076i	$0.304407\pi$
$42$	−2.14532	−0.331030
$43$	−2.79704	−0.426545	−0.213273	−	0.976993i	$-0.568412\pi$
$43$	−2.79704	−0.426545	−0.213273	+	0.976993i	$0.568412\pi$
$44$	13.5955	2.04959
$45$	1.00000	0.149071
$46$	8.36045	1.23268
$47$	−11.0773	−1.61579	−0.807895	−	0.589327i	$-0.799393\pi$
$47$	−11.0773	−1.61579	−0.807895	+	0.589327i	$0.799393\pi$
$48$	−13.0171	−1.87886
$49$	−6.36472	−0.909246
$50$	−2.69159	−0.380648
$51$	5.77247	0.808308
$52$	−14.6695	−2.03430
$53$	−8.87861	−1.21957	−0.609785	−	0.792567i	$-0.708744\pi$
$53$	−8.87861	−1.21957	−0.609785	+	0.792567i	$0.708744\pi$
$54$	2.69159	0.366279
$55$	2.59225	0.349539
$56$	6.96082	0.930179
$57$	0	0
$58$	12.8952	1.69323
$59$	1.08020	0.140630	0.0703149	−	0.997525i	$-0.477600\pi$
$59$	1.08020	0.140630	0.0703149	+	0.997525i	$0.477600\pi$
$60$	−5.24466	−0.677083
$61$	4.07225	0.521398	0.260699	−	0.965420i	$-0.416047\pi$
$61$	4.07225	0.521398	0.260699	+	0.965420i	$0.416047\pi$
$62$	25.5414	3.24376
$63$	−0.797044	−0.100418
$64$	21.2575	2.65719
$65$	−2.79704	−0.346931
$66$	6.97727	0.858842
$67$	13.7757	1.68297	0.841484	−	0.540283i	$-0.181683\pi$
$67$	13.7757	1.68297	0.841484	+	0.540283i	$0.181683\pi$
$68$	−30.2747	−3.67134
$69$	3.10614	0.373935
$70$	2.14532	0.256414
$71$	−11.9754	−1.42122	−0.710611	−	0.703585i	$-0.751581\pi$
$71$	−11.9754	−1.42122	−0.710611	+	0.703585i	$0.751581\pi$
$72$	−8.73329	−1.02923
$73$	8.50778	0.995760	0.497880	−	0.867246i	$-0.334112\pi$
$73$	8.50778	0.995760	0.497880	+	0.867246i	$0.334112\pi$
$74$	−20.7045	−2.40684
$75$	−1.00000	−0.115470
$76$	0	0
$77$	−2.06614	−0.235458
$78$	−7.52850	−0.852434
$79$	6.48184	0.729264	0.364632	−	0.931152i	$-0.381195\pi$
$79$	6.48184	0.729264	0.364632	+	0.931152i	$0.381195\pi$
$80$	13.0171	1.45536
$81$	1.00000	0.111111
$82$	−19.8725	−2.19455
$83$	−2.79520	−0.306813	−0.153407	−	0.988163i	$-0.549024\pi$
$83$	−2.79520	−0.306813	−0.153407	+	0.988163i	$0.549024\pi$
$84$	4.18023	0.456100
$85$	−5.77247	−0.626113
$86$	7.52850	0.811819
$87$	4.79093	0.513642
$88$	−22.6389	−2.41331
$89$	−13.3586	−1.41601	−0.708005	−	0.706208i	$-0.750405\pi$
$89$	−13.3586	−1.41601	−0.708005	+	0.706208i	$0.750405\pi$
$90$	−2.69159	−0.283719
$91$	2.22937	0.233701
$92$	−16.2906	−1.69842
$93$	9.48932	0.983996
$94$	29.8155	3.07524
$95$	0	0
$96$	17.5702	1.79325
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	17.1312	1.73051
$99$	2.59225	0.260531
$100$	5.24466	0.524466
$101$	13.0816	1.30166	0.650832	−	0.759222i	$-0.274420\pi$
$101$	13.0816	1.30166	0.650832	+	0.759222i	$0.274420\pi$
$102$	−15.5371	−1.53841
$103$	14.4586	1.42465	0.712326	−	0.701849i	$-0.247642\pi$
$103$	14.4586	1.42465	0.712326	+	0.701849i	$0.247642\pi$
$104$	24.4274	2.39530
$105$	0.797044	0.0777835
$106$	23.8976	2.32114
$107$	3.20480	0.309819	0.154910	−	0.987929i	$-0.450491\pi$
$107$	3.20480	0.309819	0.154910	+	0.987929i	$0.450491\pi$
$108$	−5.24466	−0.504668
$109$	7.79841	0.746952	0.373476	−	0.927640i	$-0.378166\pi$
$109$	7.79841	0.746952	0.373476	+	0.927640i	$0.378166\pi$
$110$	−6.97727	−0.665257
$111$	−7.69227	−0.730118
$112$	−10.3752	−0.980367
$113$	8.26042	0.777075	0.388538	−	0.921433i	$-0.372980\pi$
$113$	8.26042	0.777075	0.388538	+	0.921433i	$0.372980\pi$
$114$	0	0
$115$	−3.10614	−0.289649
$116$	−25.1268	−2.33297
$117$	−2.79704	−0.258587
$118$	−2.90745	−0.267653
$119$	4.60092	0.421765
$120$	8.73329	0.797237
$121$	−4.28025	−0.389114
$122$	−10.9608	−0.992346
$123$	−7.38318	−0.665719
$124$	−49.7682	−4.46932
$125$	1.00000	0.0894427
$126$	2.14532	0.191120
$127$	4.48932	0.398363	0.199181	−	0.979963i	$-0.436172\pi$
$127$	4.48932	0.398363	0.199181	+	0.979963i	$0.436172\pi$
$128$	−22.0761	−1.95127
$129$	2.79704	0.246266
$130$	7.52850	0.660293
$131$	19.4788	1.70187	0.850936	−	0.525270i	$-0.176036\pi$
$131$	19.4788	1.70187	0.850936	+	0.525270i	$0.176036\pi$
$132$	−13.5955	−1.18333
$133$	0	0
$134$	−37.0785	−3.20309
$135$	−1.00000	−0.0860663
$136$	50.4127	4.32285
$137$	4.22753	0.361182	0.180591	−	0.983558i	$-0.442199\pi$
$137$	4.22753	0.361182	0.180591	+	0.983558i	$0.442199\pi$
$138$	−8.36045	−0.711689
$139$	7.79093	0.660818	0.330409	−	0.943838i	$-0.392813\pi$
$139$	7.79093	0.660818	0.330409	+	0.943838i	$0.392813\pi$
$140$	−4.18023	−0.353294
$141$	11.0773	0.932877
$142$	32.2329	2.70493
$143$	−7.25063	−0.606328
$144$	13.0171	1.08476
$145$	−4.79093	−0.397865
$146$	−22.8995	−1.89517
$147$	6.36472	0.524953
$148$	40.3434	3.31620
$149$	−0.0907073	−0.00743103	−0.00371552	−	0.999993i	$-0.501183\pi$
$149$	−0.0907073	−0.00743103	−0.00371552	+	0.999993i	$0.501183\pi$
$150$	2.69159	0.219767
$151$	−4.49727	−0.365983	−0.182991	−	0.983115i	$-0.558578\pi$
$151$	−4.49727	−0.365983	−0.182991	+	0.983115i	$0.558578\pi$
$152$	0	0
$153$	−5.77247	−0.466677
$154$	5.56119	0.448134
$155$	−9.48932	−0.762200
$156$	14.6695	1.17450
$157$	17.6468	1.40837	0.704184	−	0.710017i	$-0.251313\pi$
$157$	17.6468	1.40837	0.704184	+	0.710017i	$0.251313\pi$
$158$	−17.4465	−1.38797
$159$	8.87861	0.704120
$160$	−17.5702	−1.38905
$161$	2.47573	0.195115
$162$	−2.69159	−0.211471
$163$	4.25858	0.333558	0.166779	−	0.985994i	$-0.446663\pi$
$163$	4.25858	0.333558	0.166779	+	0.985994i	$0.446663\pi$
$164$	38.7223	3.02370
$165$	−2.59225	−0.201806
$166$	7.52354	0.583940
$167$	3.97970	0.307958	0.153979	−	0.988074i	$-0.450791\pi$
$167$	3.97970	0.307958	0.153979	+	0.988074i	$0.450791\pi$
$168$	−6.96082	−0.537039
$169$	−5.17654	−0.398196
$170$	15.5371	1.19164
$171$	0	0
$172$	−14.6695	−1.11854
$173$	11.1723	0.849412	0.424706	−	0.905331i	$-0.360377\pi$
$173$	11.1723	0.849412	0.424706	+	0.905331i	$0.360377\pi$
$174$	−12.8952	−0.977585
$175$	−0.797044	−0.0602509
$176$	33.7436	2.54352
$177$	−1.08020	−0.0811927
$178$	35.9559	2.69501
$179$	9.63565	0.720203	0.360101	−	0.932913i	$-0.382742\pi$
$179$	9.63565	0.720203	0.360101	+	0.932913i	$0.382742\pi$
$180$	5.24466	0.390914
$181$	4.10003	0.304753	0.152376	−	0.988323i	$-0.451307\pi$
$181$	4.10003	0.304753	0.152376	+	0.988323i	$0.451307\pi$
$182$	−6.00055	−0.444790
$183$	−4.07225	−0.301029
$184$	27.1268	1.99982
$185$	7.69227	0.565547
$186$	−25.5414	−1.87278
$187$	−14.9637	−1.09425
$188$	−58.0966	−4.23713
$189$	0.797044	0.0579764
$190$	0	0
$191$	−22.6143	−1.63631	−0.818156	−	0.574996i	$-0.805004\pi$
$191$	−22.6143	−1.63631	−0.818156	+	0.574996i	$0.805004\pi$
$192$	−21.2575	−1.53413
$193$	16.6034	1.19514	0.597570	−	0.801817i	$-0.296133\pi$
$193$	16.6034	1.19514	0.597570	+	0.801817i	$0.296133\pi$
$194$	−5.38318	−0.386490
$195$	2.79704	0.200300
$196$	−33.3808	−2.38434
$197$	−17.6450	−1.25715	−0.628576	−	0.777748i	$-0.716362\pi$
$197$	−17.6450	−1.25715	−0.628576	+	0.777748i	$0.716362\pi$
$198$	−6.97727	−0.495853
$199$	19.0631	1.35135	0.675674	−	0.737201i	$-0.263853\pi$
$199$	19.0631	1.35135	0.675674	+	0.737201i	$0.263853\pi$
$200$	−8.73329	−0.617537
$201$	−13.7757	−0.971662
$202$	−35.2102	−2.47738
$203$	3.81859	0.268012
$204$	30.2747	2.11965
$205$	7.38318	0.515664
$206$	−38.9167	−2.71146
$207$	−3.10614	−0.215891
$208$	−36.4095	−2.52454
$209$	0	0
$210$	−2.14532	−0.148041
$211$	−14.0434	−0.966788	−0.483394	−	0.875403i	$-0.660596\pi$
$211$	−14.0434	−0.966788	−0.483394	+	0.875403i	$0.660596\pi$
$212$	−46.5653	−3.19812
$213$	11.9754	0.820543
$214$	−8.62600	−0.589661
$215$	−2.79704	−0.190757
$216$	8.73329	0.594225
$217$	7.56341	0.513437
$218$	−20.9901	−1.42163
$219$	−8.50778	−0.574902
$220$	13.5955	0.916605
$221$	16.1459	1.08609
$222$	20.7045	1.38959
$223$	−24.1853	−1.61957	−0.809783	−	0.586730i	$-0.800415\pi$
$223$	−24.1853	−1.61957	−0.809783	+	0.586730i	$0.800415\pi$
$224$	14.0042	0.935697
$225$	1.00000	0.0666667
$226$	−22.2337	−1.47896
$227$	3.38455	0.224640	0.112320	−	0.993672i	$-0.464172\pi$
$227$	3.38455	0.224640	0.112320	+	0.993672i	$0.464172\pi$
$228$	0	0
$229$	−25.9664	−1.71591	−0.857955	−	0.513726i	$-0.828265\pi$
$229$	−25.9664	−1.71591	−0.857955	+	0.513726i	$0.828265\pi$
$230$	8.36045	0.551272
$231$	2.06614	0.135942
$232$	41.8406	2.74697
$233$	−6.71821	−0.440125	−0.220062	−	0.975486i	$-0.570626\pi$
$233$	−6.71821	−0.440125	−0.220062	+	0.975486i	$0.570626\pi$
$234$	7.52850	0.492153
$235$	−11.0773	−0.722603
$236$	5.66527	0.368778
$237$	−6.48184	−0.421041
$238$	−12.3838	−0.802721
$239$	25.7818	1.66769	0.833843	−	0.552002i	$-0.186136\pi$
$239$	25.7818	1.66769	0.833843	+	0.552002i	$0.186136\pi$
$240$	−13.0171	−0.840252
$241$	−7.77858	−0.501063	−0.250531	−	0.968108i	$-0.580605\pi$
$241$	−7.77858	−0.501063	−0.250531	+	0.968108i	$0.580605\pi$
$242$	11.5207	0.740578
$243$	−1.00000	−0.0641500
$244$	21.3575	1.36728
$245$	−6.36472	−0.406627
$246$	19.8725	1.26702
$247$	0	0
$248$	82.8730	5.26244
$249$	2.79520	0.177139
$250$	−2.69159	−0.170231
$251$	10.8743	0.686382	0.343191	−	0.939266i	$-0.388492\pi$
$251$	10.8743	0.686382	0.343191	+	0.939266i	$0.388492\pi$
$252$	−4.18023	−0.263329
$253$	−8.05188	−0.506217
$254$	−12.0834	−0.758180
$255$	5.77247	0.361486
$256$	16.9049	1.05656
$257$	11.2543	0.702025	0.351012	−	0.936371i	$-0.385838\pi$
$257$	11.2543	0.702025	0.351012	+	0.936371i	$0.385838\pi$
$258$	−7.52850	−0.468704
$259$	−6.13108	−0.380967
$260$	−14.6695	−0.909766
$261$	−4.79093	−0.296551
$262$	−52.4290	−3.23907
$263$	−13.3387	−0.822500	−0.411250	−	0.911523i	$-0.634908\pi$
$263$	−13.3387	−0.822500	−0.411250	+	0.911523i	$0.634908\pi$
$264$	22.6389	1.39333
$265$	−8.87861	−0.545409
$266$	0	0
$267$	13.3586	0.817534
$268$	72.2488	4.41330
$269$	−7.06798	−0.430942	−0.215471	−	0.976510i	$-0.569129\pi$
$269$	−7.06798	−0.430942	−0.215471	+	0.976510i	$0.569129\pi$
$270$	2.69159	0.163805
$271$	−23.0578	−1.40066	−0.700330	−	0.713819i	$-0.746964\pi$
$271$	−23.0578	−1.40066	−0.700330	+	0.713819i	$0.746964\pi$
$272$	−75.1410	−4.55609
$273$	−2.22937	−0.134927
$274$	−11.3788	−0.687417
$275$	2.59225	0.156318
$276$	16.2906	0.980581
$277$	18.8461	1.13235	0.566176	−	0.824284i	$-0.308422\pi$
$277$	18.8461	1.13235	0.566176	+	0.824284i	$0.308422\pi$
$278$	−20.9700	−1.25770
$279$	−9.48932	−0.568111
$280$	6.96082	0.415989
$281$	16.6497	0.993239	0.496619	−	0.867968i	$-0.334574\pi$
$281$	16.6497	0.993239	0.496619	+	0.867968i	$0.334574\pi$
$282$	−29.8155	−1.77549
$283$	13.0519	0.775858	0.387929	−	0.921689i	$-0.373191\pi$
$283$	13.0519	0.775858	0.387929	+	0.921689i	$0.373191\pi$
$284$	−62.8070	−3.72691
$285$	0	0
$286$	19.5157	1.15399
$287$	−5.88472	−0.347364
$288$	−17.5702	−1.03533
$289$	16.3214	0.960085
$290$	12.8952	0.757234
$291$	−2.00000	−0.117242
$292$	44.6204	2.61121
$293$	−3.07225	−0.179483	−0.0897413	−	0.995965i	$-0.528604\pi$
$293$	−3.07225	−0.179483	−0.0897413	+	0.995965i	$0.528604\pi$
$294$	−17.1312	−0.999113
$295$	1.08020	0.0628916
$296$	−67.1789	−3.90469
$297$	−2.59225	−0.150417
$298$	0.244147	0.0141430
$299$	8.68800	0.502440
$300$	−5.24466	−0.302801
$301$	2.22937	0.128499
$302$	12.1048	0.696554
$303$	−13.0816	−0.751516
$304$	0	0
$305$	4.07225	0.233176
$306$	15.5371	0.888199
$307$	23.4615	1.33902	0.669510	−	0.742803i	$-0.266504\pi$
$307$	23.4615	1.33902	0.669510	+	0.742803i	$0.266504\pi$
$308$	−10.8362	−0.617449
$309$	−14.4586	−0.822523
$310$	25.5414	1.45065
$311$	−5.59041	−0.317003	−0.158501	−	0.987359i	$-0.550666\pi$
$311$	−5.59041	−0.317003	−0.158501	+	0.987359i	$0.550666\pi$
$312$	−24.4274	−1.38293
$313$	−28.4280	−1.60684	−0.803421	−	0.595411i	$-0.796989\pi$
$313$	−28.4280	−1.60684	−0.803421	+	0.595411i	$0.796989\pi$
$314$	−47.4980	−2.68047
$315$	−0.797044	−0.0449084
$316$	33.9950	1.91237
$317$	−10.5096	−0.590279	−0.295140	−	0.955454i	$-0.595366\pi$
$317$	−10.5096	−0.590279	−0.295140	+	0.955454i	$0.595366\pi$
$318$	−23.8976	−1.34011
$319$	−12.4193	−0.695347
$320$	21.2575	1.18833
$321$	−3.20480	−0.178874
$322$	−6.66365	−0.371351
$323$	0	0
$324$	5.24466	0.291370
$325$	−2.79704	−0.155152
$326$	−11.4624	−0.634841
$327$	−7.79841	−0.431253
$328$	−64.4795	−3.56028
$329$	8.82909	0.486764
$330$	6.97727	0.384086
$331$	−6.39618	−0.351566	−0.175783	−	0.984429i	$-0.556246\pi$
$331$	−6.39618	−0.351566	−0.175783	+	0.984429i	$0.556246\pi$
$332$	−14.6599	−0.804566
$333$	7.69227	0.421534
$334$	−10.7117	−0.586119
$335$	13.7757	0.752646
$336$	10.3752	0.566015
$337$	−18.2772	−0.995624	−0.497812	−	0.867285i	$-0.665863\pi$
$337$	−18.2772	−0.995624	−0.497812	+	0.867285i	$0.665863\pi$
$338$	13.9331	0.757863
$339$	−8.26042	−0.448645
$340$	−30.2747	−1.64187
$341$	−24.5987	−1.33209
$342$	0	0
$343$	10.6523	0.575169
$344$	24.4274	1.31704
$345$	3.10614	0.167229
$346$	−30.0712	−1.61664
$347$	−31.6586	−1.69952	−0.849760	−	0.527169i	$-0.823253\pi$
$347$	−31.6586	−1.69952	−0.849760	+	0.527169i	$0.823253\pi$
$348$	25.1268	1.34694
$349$	12.0802	0.646638	0.323319	−	0.946290i	$-0.395201\pi$
$349$	12.0802	0.646638	0.323319	+	0.946290i	$0.395201\pi$
$350$	2.14532	0.114672
$351$	2.79704	0.149295
$352$	−45.5463	−2.42763
$353$	3.63101	0.193259	0.0966296	−	0.995320i	$-0.469194\pi$
$353$	3.63101	0.193259	0.0966296	+	0.995320i	$0.469194\pi$
$354$	2.90745	0.154529
$355$	−11.9754	−0.635590
$356$	−70.0614	−3.71324
$357$	−4.60092	−0.243506
$358$	−25.9352	−1.37072
$359$	−5.91796	−0.312338	−0.156169	−	0.987730i	$-0.549914\pi$
$359$	−5.91796	−0.312338	−0.156169	+	0.987730i	$0.549914\pi$
$360$	−8.73329	−0.460285
$361$	0	0
$362$	−11.0356	−0.580018
$363$	4.28025	0.224655
$364$	11.6923	0.612842
$365$	8.50778	0.445317
$366$	10.9608	0.572931
$367$	6.18159	0.322677	0.161338	−	0.986899i	$-0.448419\pi$
$367$	6.18159	0.322677	0.161338	+	0.986899i	$0.448419\pi$
$368$	−40.4330	−2.10772
$369$	7.38318	0.384353
$370$	−20.7045	−1.07637
$371$	7.07664	0.367401
$372$	49.7682	2.58036
$373$	−7.24346	−0.375052	−0.187526	−	0.982260i	$-0.560047\pi$
$373$	−7.24346	−0.375052	−0.187526	+	0.982260i	$0.560047\pi$
$374$	40.2761	2.08263
$375$	−1.00000	−0.0516398
$376$	96.7413	4.98905
$377$	13.4005	0.690158
$378$	−2.14532	−0.110343
$379$	15.4483	0.793524	0.396762	−	0.917922i	$-0.370134\pi$
$379$	15.4483	0.793524	0.396762	+	0.917922i	$0.370134\pi$
$380$	0	0
$381$	−4.48932	−0.229995
$382$	60.8684	3.11430
$383$	−19.5161	−0.997226	−0.498613	−	0.866825i	$-0.666157\pi$
$383$	−19.5161	−0.997226	−0.498613	+	0.866825i	$0.666157\pi$
$384$	22.0761	1.12657
$385$	−2.06614	−0.105300
$386$	−44.6896	−2.27464
$387$	−2.79704	−0.142182
$388$	10.4893	0.532514
$389$	14.2575	0.722885	0.361443	−	0.932394i	$-0.382284\pi$
$389$	14.2575	0.722885	0.361443	+	0.932394i	$0.382284\pi$
$390$	−7.52850	−0.381220
$391$	17.9301	0.906764
$392$	55.5850	2.80747
$393$	−19.4788	−0.982576
$394$	47.4930	2.39266
$395$	6.48184	0.326137
$396$	13.5955	0.683197
$397$	27.9080	1.40066	0.700330	−	0.713819i	$-0.253036\pi$
$397$	27.9080	1.40066	0.700330	+	0.713819i	$0.253036\pi$
$398$	−51.3101	−2.57194
$399$	0	0
$400$	13.0171	0.650857
$401$	19.7241	0.984975	0.492487	−	0.870320i	$-0.336088\pi$
$401$	19.7241	0.984975	0.492487	+	0.870320i	$0.336088\pi$
$402$	37.0785	1.84931
$403$	26.5420	1.32215
$404$	68.6084	3.41339
$405$	1.00000	0.0496904
$406$	−10.2781	−0.510092
$407$	19.9403	0.988403
$408$	−50.4127	−2.49580
$409$	19.2311	0.950917	0.475459	−	0.879738i	$-0.342282\pi$
$409$	19.2311	0.950917	0.475459	+	0.879738i	$0.342282\pi$
$410$	−19.8725	−0.981433
$411$	−4.22753	−0.208529
$412$	75.8306	3.73591
$413$	−0.860966	−0.0423654
$414$	8.36045	0.410894
$415$	−2.79520	−0.137211
$416$	49.1446	2.40951
$417$	−7.79093	−0.381524
$418$	0	0
$419$	−4.45253	−0.217520	−0.108760	−	0.994068i	$-0.534688\pi$
$419$	−4.45253	−0.217520	−0.108760	+	0.994068i	$0.534688\pi$
$420$	4.18023	0.203974
$421$	12.0893	0.589198	0.294599	−	0.955621i	$-0.404814\pi$
$421$	12.0893	0.589198	0.294599	+	0.955621i	$0.404814\pi$
$422$	37.7991	1.84003
$423$	−11.0773	−0.538597
$424$	77.5395	3.76565
$425$	−5.77247	−0.280006
$426$	−32.2329	−1.56169
$427$	−3.24576	−0.157073
$428$	16.8081	0.812449
$429$	7.25063	0.350064
$430$	7.52850	0.363056
$431$	−20.5431	−0.989527	−0.494763	−	0.869028i	$-0.664745\pi$
$431$	−20.5431	−0.989527	−0.494763	+	0.869028i	$0.664745\pi$
$432$	−13.0171	−0.626287
$433$	−19.3735	−0.931029	−0.465514	−	0.885040i	$-0.654131\pi$
$433$	−19.3735	−0.931029	−0.465514	+	0.885040i	$0.654131\pi$
$434$	−20.3576	−0.977196
$435$	4.79093	0.229708
$436$	40.9000	1.95876
$437$	0	0
$438$	22.8995	1.09418
$439$	17.2316	0.822419	0.411209	−	0.911541i	$-0.365107\pi$
$439$	17.2316	0.822419	0.411209	+	0.911541i	$0.365107\pi$
$440$	−22.6389	−1.07927
$441$	−6.36472	−0.303082
$442$	−43.4580	−2.06709
$443$	16.6555	0.791326	0.395663	−	0.918396i	$-0.370515\pi$
$443$	16.6555	0.791326	0.395663	+	0.918396i	$0.370515\pi$
$444$	−40.3434	−1.91461
$445$	−13.3586	−0.633259
$446$	65.0969	3.08243
$447$	0.0907073	0.00429031
$448$	−16.9432	−0.800490
$449$	−18.4698	−0.871644	−0.435822	−	0.900033i	$-0.643542\pi$
$449$	−18.4698	−0.871644	−0.435822	+	0.900033i	$0.643542\pi$
$450$	−2.69159	−0.126883
$451$	19.1390	0.901222
$452$	43.3231	2.03775
$453$	4.49727	0.211300
$454$	−9.10982	−0.427545
$455$	2.22937	0.104514
$456$	0	0
$457$	3.40669	0.159358	0.0796791	−	0.996821i	$-0.474610\pi$
$457$	3.40669	0.159358	0.0796791	+	0.996821i	$0.474610\pi$
$458$	69.8910	3.26579
$459$	5.77247	0.269436
$460$	−16.2906	−0.759555
$461$	40.4057	1.88188	0.940940	−	0.338572i	$-0.109944\pi$
$461$	40.4057	1.88188	0.940940	+	0.338572i	$0.109944\pi$
$462$	−5.56119	−0.258730
$463$	−22.9724	−1.06762	−0.533809	−	0.845605i	$-0.679240\pi$
$463$	−22.9724	−1.06762	−0.533809	+	0.845605i	$0.679240\pi$
$464$	−62.3642	−2.89519
$465$	9.48932	0.440057
$466$	18.0827	0.837664
$467$	7.02174	0.324927	0.162464	−	0.986715i	$-0.448056\pi$
$467$	7.02174	0.324927	0.162464	+	0.986715i	$0.448056\pi$
$468$	−14.6695	−0.678100
$469$	−10.9798	−0.507001
$470$	29.8155	1.37529
$471$	−17.6468	−0.813122
$472$	−9.43369	−0.434221
$473$	−7.25063	−0.333384
$474$	17.4465	0.801342
$475$	0	0
$476$	24.1302	1.10601
$477$	−8.87861	−0.406524
$478$	−69.3940	−3.17401
$479$	−2.92117	−0.133472	−0.0667358	−	0.997771i	$-0.521258\pi$
$479$	−2.92117	−0.133472	−0.0667358	+	0.997771i	$0.521258\pi$
$480$	17.5702	0.801966
$481$	−21.5156	−0.981028
$482$	20.9368	0.953643
$483$	−2.47573	−0.112650
$484$	−22.4485	−1.02038
$485$	2.00000	0.0908153
$486$	2.69159	0.122093
$487$	19.2038	0.870207	0.435104	−	0.900380i	$-0.356712\pi$
$487$	19.2038	0.870207	0.435104	+	0.900380i	$0.356712\pi$
$488$	−35.5641	−1.60991
$489$	−4.25858	−0.192580
$490$	17.1312	0.773910
$491$	10.4369	0.471011	0.235505	−	0.971873i	$-0.424325\pi$
$491$	10.4369	0.471011	0.235505	+	0.971873i	$0.424325\pi$
$492$	−38.7223	−1.74573
$493$	27.6555	1.24554
$494$	0	0
$495$	2.59225	0.116513
$496$	−123.524	−5.54638
$497$	9.54495	0.428149
$498$	−7.52354	−0.337138
$499$	26.1700	1.17153	0.585766	−	0.810481i	$-0.300794\pi$
$499$	26.1700	1.17153	0.585766	+	0.810481i	$0.300794\pi$
$500$	5.24466	0.234548
$501$	−3.97970	−0.177800
$502$	−29.2693	−1.30635
$503$	5.35094	0.238586	0.119293	−	0.992859i	$-0.461937\pi$
$503$	5.35094	0.238586	0.119293	+	0.992859i	$0.461937\pi$
$504$	6.96082	0.310060
$505$	13.0816	0.582122
$506$	21.6724	0.963454
$507$	5.17654	0.229898
$508$	23.5449	1.04464
$509$	9.78909	0.433894	0.216947	−	0.976183i	$-0.430390\pi$
$509$	9.78909	0.433894	0.216947	+	0.976183i	$0.430390\pi$
$510$	−15.5371	−0.687996
$511$	−6.78108	−0.299977
$512$	−1.34875	−0.0596067
$513$	0	0
$514$	−30.2920	−1.33612
$515$	14.4586	0.637124
$516$	14.6695	0.645791
$517$	−28.7151	−1.26289
$518$	16.5024	0.725072
$519$	−11.1723	−0.490408
$520$	24.4274	1.07121
$521$	26.4315	1.15799	0.578993	−	0.815333i	$-0.303446\pi$
$521$	26.4315	1.15799	0.578993	+	0.815333i	$0.303446\pi$
$522$	12.8952	0.564409
$523$	28.6624	1.25332	0.626659	−	0.779294i	$-0.284422\pi$
$523$	28.6624	1.25332	0.626659	+	0.779294i	$0.284422\pi$
$524$	102.160	4.46287
$525$	0.797044	0.0347859
$526$	35.9024	1.56542
$527$	54.7768	2.38612
$528$	−33.7436	−1.46850
$529$	−13.3519	−0.580518
$530$	23.8976	1.03804
$531$	1.08020	0.0468766
$532$	0	0
$533$	−20.6511	−0.894498
$534$	−35.9559	−1.55596
$535$	3.20480	0.138555
$536$	−120.307	−5.19647
$537$	−9.63565	−0.415809
$538$	19.0241	0.820187
$539$	−16.4989	−0.710659
$540$	−5.24466	−0.225694
$541$	−24.1946	−1.04021	−0.520103	−	0.854103i	$-0.674107\pi$
$541$	−24.1946	−1.04021	−0.520103	+	0.854103i	$0.674107\pi$
$542$	62.0621	2.66579
$543$	−4.10003	−0.175949
$544$	101.424	4.34850
$545$	7.79841	0.334047
$546$	6.00055	0.256800
$547$	30.9917	1.32511	0.662555	−	0.749013i	$-0.269472\pi$
$547$	30.9917	1.32511	0.662555	+	0.749013i	$0.269472\pi$
$548$	22.1719	0.947138
$549$	4.07225	0.173799
$550$	−6.97727	−0.297512
$551$	0	0
$552$	−27.1268	−1.15459
$553$	−5.16631	−0.219694
$554$	−50.7259	−2.15514
$555$	−7.69227	−0.326519
$556$	40.8608	1.73288
$557$	12.7664	0.540928	0.270464	−	0.962730i	$-0.412823\pi$
$557$	12.7664	0.540928	0.270464	+	0.962730i	$0.412823\pi$
$558$	25.5414	1.08125
$559$	7.82346	0.330897
$560$	−10.3752	−0.438433
$561$	14.9637	0.631767
$562$	−44.8142	−1.89037
$563$	−8.11088	−0.341833	−0.170916	−	0.985286i	$-0.554673\pi$
$563$	−8.11088	−0.341833	−0.170916	+	0.985286i	$0.554673\pi$
$564$	58.0966	2.44631
$565$	8.26042	0.347519
$566$	−35.1305	−1.47664
$567$	−0.797044	−0.0334727
$568$	104.585	4.38829
$569$	21.0412	0.882091	0.441046	−	0.897485i	$-0.354608\pi$
$569$	21.0412	0.882091	0.441046	+	0.897485i	$0.354608\pi$
$570$	0	0
$571$	−8.45300	−0.353747	−0.176873	−	0.984234i	$-0.556598\pi$
$571$	−8.45300	−0.353747	−0.176873	+	0.984234i	$0.556598\pi$
$572$	−38.0271	−1.58999
$573$	22.6143	0.944726
$574$	15.8393	0.661118
$575$	−3.10614	−0.129535
$576$	21.2575	0.885730
$577$	23.4005	0.974174	0.487087	−	0.873354i	$-0.338060\pi$
$577$	23.4005	0.974174	0.487087	+	0.873354i	$0.338060\pi$
$578$	−43.9306	−1.82727
$579$	−16.6034	−0.690014
$580$	−25.1268	−1.04333
$581$	2.22790	0.0924289
$582$	5.38318	0.223140
$583$	−23.0156	−0.953207
$584$	−74.3009	−3.07459
$585$	−2.79704	−0.115644
$586$	8.26923	0.341599
$587$	30.1675	1.24515	0.622574	−	0.782561i	$-0.286087\pi$
$587$	30.1675	1.24515	0.622574	+	0.782561i	$0.286087\pi$
$588$	33.3808	1.37660
$589$	0	0
$590$	−2.90745	−0.119698
$591$	17.6450	0.725817
$592$	100.131	4.11537
$593$	22.6992	0.932146	0.466073	−	0.884746i	$-0.345668\pi$
$593$	22.6992	0.932146	0.466073	+	0.884746i	$0.345668\pi$
$594$	6.97727	0.286281
$595$	4.60092	0.188619
$596$	−0.475729	−0.0194866
$597$	−19.0631	−0.780201
$598$	−23.3845	−0.956265
$599$	−19.9267	−0.814183	−0.407091	−	0.913387i	$-0.633457\pi$
$599$	−19.9267	−0.814183	−0.407091	+	0.913387i	$0.633457\pi$
$600$	8.73329	0.356535
$601$	24.8942	1.01545	0.507727	−	0.861518i	$-0.330486\pi$
$601$	24.8942	1.01545	0.507727	+	0.861518i	$0.330486\pi$
$602$	−6.00055	−0.244564
$603$	13.7757	0.560989
$604$	−23.5866	−0.959727
$605$	−4.28025	−0.174017
$606$	35.2102	1.43032
$607$	−11.3318	−0.459945	−0.229972	−	0.973197i	$-0.573864\pi$
$607$	−11.3318	−0.459945	−0.229972	+	0.973197i	$0.573864\pi$
$608$	0	0
$609$	−3.81859	−0.154737
$610$	−10.9608	−0.443791
$611$	30.9837	1.25347
$612$	−30.2747	−1.22378
$613$	−6.96854	−0.281457	−0.140728	−	0.990048i	$-0.544944\pi$
$613$	−6.96854	−0.281457	−0.140728	+	0.990048i	$0.544944\pi$
$614$	−63.1489	−2.54848
$615$	−7.38318	−0.297719
$616$	18.0442	0.727020
$617$	−4.93998	−0.198876	−0.0994380	−	0.995044i	$-0.531704\pi$
$617$	−4.93998	−0.198876	−0.0994380	+	0.995044i	$0.531704\pi$
$618$	38.9167	1.56546
$619$	−17.7750	−0.714439	−0.357219	−	0.934021i	$-0.616275\pi$
$619$	−17.7750	−0.714439	−0.357219	+	0.934021i	$0.616275\pi$
$620$	−49.7682	−1.99874
$621$	3.10614	0.124645
$622$	15.0471	0.603333
$623$	10.6474	0.426579
$624$	36.4095	1.45755
$625$	1.00000	0.0400000
$626$	76.5164	3.05821
$627$	0	0
$628$	92.5515	3.69321
$629$	−44.4034	−1.77048
$630$	2.14532	0.0854715
$631$	−10.2984	−0.409973	−0.204987	−	0.978765i	$-0.565715\pi$
$631$	−10.2984	−0.409973	−0.204987	+	0.978765i	$0.565715\pi$
$632$	−56.6078	−2.25174
$633$	14.0434	0.558175
$634$	28.2876	1.12344
$635$	4.48932	0.178153
$636$	46.5653	1.84643
$637$	17.8024	0.705357
$638$	33.4276	1.32341
$639$	−11.9754	−0.473741
$640$	−22.0761	−0.872636
$641$	24.9490	0.985427	0.492713	−	0.870192i	$-0.336005\pi$
$641$	24.9490	0.985427	0.492713	+	0.870192i	$0.336005\pi$
$642$	8.62600	0.340441
$643$	−5.69227	−0.224481	−0.112241	−	0.993681i	$-0.535803\pi$
$643$	−5.69227	−0.224481	−0.112241	+	0.993681i	$0.535803\pi$
$644$	12.9844	0.511655
$645$	2.79704	0.110134
$646$	0	0
$647$	−19.9379	−0.783840	−0.391920	−	0.919999i	$-0.628189\pi$
$647$	−19.9379	−0.783840	−0.391920	+	0.919999i	$0.628189\pi$
$648$	−8.73329	−0.343076
$649$	2.80014	0.109915
$650$	7.52850	0.295292
$651$	−7.56341	−0.296433
$652$	22.3348	0.874699
$653$	21.5636	0.843848	0.421924	−	0.906631i	$-0.361355\pi$
$653$	21.5636	0.843848	0.421924	+	0.906631i	$0.361355\pi$
$654$	20.9901	0.820779
$655$	19.4788	0.761100
$656$	96.1078	3.75238
$657$	8.50778	0.331920
$658$	−23.7643	−0.926429
$659$	−40.6511	−1.58354	−0.791771	−	0.610818i	$-0.790841\pi$
$659$	−40.6511	−1.58354	−0.791771	+	0.610818i	$0.790841\pi$
$660$	−13.5955	−0.529202
$661$	−39.5102	−1.53677	−0.768384	−	0.639989i	$-0.778939\pi$
$661$	−39.5102	−1.53677	−0.768384	+	0.639989i	$0.778939\pi$
$662$	17.2159	0.669115
$663$	−16.1459	−0.627053
$664$	24.4113	0.947343
$665$	0	0
$666$	−20.7045	−0.802281
$667$	14.8813	0.576206
$668$	20.8722	0.807568
$669$	24.1853	0.935057
$670$	−37.0785	−1.43247
$671$	10.5563	0.407520
$672$	−14.0042	−0.540225
$673$	6.47351	0.249536	0.124768	−	0.992186i	$-0.460181\pi$
$673$	6.47351	0.249536	0.124768	+	0.992186i	$0.460181\pi$
$674$	49.1948	1.89491
$675$	−1.00000	−0.0384900
$676$	−27.1492	−1.04420
$677$	45.8593	1.76252	0.881258	−	0.472636i	$-0.156697\pi$
$677$	45.8593	1.76252	0.881258	+	0.472636i	$0.156697\pi$
$678$	22.2337	0.853879
$679$	−1.59409	−0.0611755
$680$	50.4127	1.93324
$681$	−3.38455	−0.129696
$682$	66.2095	2.53529
$683$	−7.04406	−0.269533	−0.134767	−	0.990877i	$-0.543028\pi$
$683$	−7.04406	−0.269533	−0.134767	+	0.990877i	$0.543028\pi$
$684$	0	0
$685$	4.22753	0.161526
$686$	−28.6716	−1.09469
$687$	25.9664	0.990681
$688$	−36.4095	−1.38810
$689$	24.8339	0.946095
$690$	−8.36045	−0.318277
$691$	6.01990	0.229008	0.114504	−	0.993423i	$-0.463472\pi$
$691$	6.01990	0.229008	0.114504	+	0.993423i	$0.463472\pi$
$692$	58.5948	2.22744
$693$	−2.06614	−0.0784860
$694$	85.2119	3.23460
$695$	7.79093	0.295527
$696$	−41.8406	−1.58596
$697$	−42.6192	−1.61432
$698$	−32.5149	−1.23071
$699$	6.71821	0.254106
$700$	−4.18023	−0.157998
$701$	0.537093	0.0202857	0.0101429	−	0.999949i	$-0.496771\pi$
$701$	0.537093	0.0202857	0.0101429	+	0.999949i	$0.496771\pi$
$702$	−7.52850	−0.284145
$703$	0	0
$704$	55.1048	2.07684
$705$	11.0773	0.417195
$706$	−9.77319	−0.367819
$707$	−10.4266	−0.392132
$708$	−5.66527	−0.212914
$709$	22.7572	0.854665	0.427333	−	0.904094i	$-0.359453\pi$
$709$	22.7572	0.854665	0.427333	+	0.904094i	$0.359453\pi$
$710$	32.2329	1.20968
$711$	6.48184	0.243088
$712$	116.665	4.37219
$713$	29.4751	1.10385
$714$	12.3838	0.463451
$715$	−7.25063	−0.271158
$716$	50.5357	1.88861
$717$	−25.7818	−0.962839
$718$	15.9287	0.594455
$719$	2.59593	0.0968118	0.0484059	−	0.998828i	$-0.484586\pi$
$719$	2.59593	0.0968118	0.0484059	+	0.998828i	$0.484586\pi$
$720$	13.0171	0.485120
$721$	−11.5242	−0.429183
$722$	0	0
$723$	7.77858	0.289289
$724$	21.5032	0.799162
$725$	−4.79093	−0.177931
$726$	−11.5207	−0.427573
$727$	24.1511	0.895714	0.447857	−	0.894105i	$-0.352187\pi$
$727$	24.1511	0.895714	0.447857	+	0.894105i	$0.352187\pi$
$728$	−19.4697	−0.721596
$729$	1.00000	0.0370370
$730$	−22.8995	−0.847547
$731$	16.1459	0.597176
$732$	−21.3575	−0.789398
$733$	0.0870881	0.00321667	0.00160834	−	0.999999i	$-0.499488\pi$
$733$	0.0870881	0.00321667	0.00160834	+	0.999999i	$0.499488\pi$
$734$	−16.6383	−0.614131
$735$	6.36472	0.234766
$736$	54.5755	2.01168
$737$	35.7100	1.31539
$738$	−19.8725	−0.731517
$739$	−21.3761	−0.786332	−0.393166	−	0.919468i	$-0.628620\pi$
$739$	−21.3761	−0.786332	−0.393166	+	0.919468i	$0.628620\pi$
$740$	40.3434	1.48305
$741$	0	0
$742$	−19.0474	−0.699253
$743$	−20.7233	−0.760263	−0.380131	−	0.924933i	$-0.624121\pi$
$743$	−20.7233	−0.760263	−0.380131	+	0.924933i	$0.624121\pi$
$744$	−82.8730	−3.03827
$745$	−0.0907073	−0.00332326
$746$	19.4964	0.713815
$747$	−2.79520	−0.102271
$748$	−78.4794	−2.86949
$749$	−2.55436	−0.0933344
$750$	2.69159	0.0982830
$751$	13.6338	0.497505	0.248752	−	0.968567i	$-0.419979\pi$
$751$	13.6338	0.497505	0.248752	+	0.968567i	$0.419979\pi$
$752$	−144.195	−5.25824
$753$	−10.8743	−0.396283
$754$	−36.0685	−1.31354
$755$	−4.49727	−0.163672
$756$	4.18023	0.152033
$757$	−8.81200	−0.320278	−0.160139	−	0.987095i	$-0.551194\pi$
$757$	−8.81200	−0.320278	−0.160139	+	0.987095i	$0.551194\pi$
$758$	−41.5804	−1.51027
$759$	8.05188	0.292265
$760$	0	0
$761$	36.5972	1.32665	0.663323	−	0.748333i	$-0.269145\pi$
$761$	36.5972	1.32665	0.663323	+	0.748333i	$0.269145\pi$
$762$	12.0834	0.437736
$763$	−6.21568	−0.225023
$764$	−118.604	−4.29095
$765$	−5.77247	−0.208704
$766$	52.5294	1.89796
$767$	−3.02136	−0.109095
$768$	−16.9049	−0.610002
$769$	11.8277	0.426519	0.213259	−	0.976996i	$-0.431592\pi$
$769$	11.8277	0.426519	0.213259	+	0.976996i	$0.431592\pi$
$770$	5.56119	0.200411
$771$	−11.2543	−0.405314
$772$	87.0792	3.13405
$773$	−13.1564	−0.473202	−0.236601	−	0.971607i	$-0.576033\pi$
$773$	−13.1564	−0.473202	−0.236601	+	0.971607i	$0.576033\pi$
$774$	7.52850	0.270606
$775$	−9.48932	−0.340866
$776$	−17.4666	−0.627014
$777$	6.13108	0.219951
$778$	−38.3754	−1.37583
$779$	0	0
$780$	14.6695	0.525254
$781$	−31.0433	−1.11082
$782$	−48.2605	−1.72579
$783$	4.79093	0.171214
$784$	−82.8504	−2.95894
$785$	17.6468	0.629842
$786$	52.4290	1.87008
$787$	4.59331	0.163734	0.0818669	−	0.996643i	$-0.473912\pi$
$787$	4.59331	0.163734	0.0818669	+	0.996643i	$0.473912\pi$
$788$	−92.5419	−3.29667
$789$	13.3387	0.474871
$790$	−17.4465	−0.620717
$791$	−6.58392	−0.234097
$792$	−22.6389	−0.804437
$793$	−11.3903	−0.404480
$794$	−75.1168	−2.66579
$795$	8.87861	0.314892
$796$	99.9795	3.54368
$797$	10.1848	0.360764	0.180382	−	0.983597i	$-0.442267\pi$
$797$	10.1848	0.360764	0.180382	+	0.983597i	$0.442267\pi$
$798$	0	0
$799$	63.9434	2.26215
$800$	−17.5702	−0.621200
$801$	−13.3586	−0.472003
$802$	−53.0892	−1.87465
$803$	22.0543	0.778278
$804$	−72.2488	−2.54802
$805$	2.47573	0.0872580
$806$	−71.4403	−2.51638
$807$	7.06798	0.248805
$808$	−114.245	−4.01913
$809$	31.9669	1.12390	0.561948	−	0.827173i	$-0.310052\pi$
$809$	31.9669	1.12390	0.561948	+	0.827173i	$0.310052\pi$
$810$	−2.69159	−0.0945728
$811$	22.2359	0.780806	0.390403	−	0.920644i	$-0.372336\pi$
$811$	22.2359	0.780806	0.390403	+	0.920644i	$0.372336\pi$
$812$	20.0272	0.702816
$813$	23.0578	0.808671
$814$	−53.6711	−1.88117
$815$	4.25858	0.149172
$816$	75.1410	2.63046
$817$	0	0
$818$	−51.7623	−1.80983
$819$	2.22937	0.0779004
$820$	38.7223	1.35224
$821$	51.1209	1.78413	0.892065	−	0.451906i	$-0.149256\pi$
$821$	51.1209	1.78413	0.892065	+	0.451906i	$0.149256\pi$
$822$	11.3788	0.396880
$823$	−34.2289	−1.19315	−0.596573	−	0.802559i	$-0.703471\pi$
$823$	−34.2289	−1.19315	−0.596573	+	0.802559i	$0.703471\pi$
$824$	−126.272	−4.39888
$825$	−2.59225	−0.0902505
$826$	2.31737	0.0806315
$827$	8.57712	0.298256	0.149128	−	0.988818i	$-0.452353\pi$
$827$	8.57712	0.298256	0.149128	+	0.988818i	$0.452353\pi$
$828$	−16.2906	−0.566139
$829$	−13.4230	−0.466199	−0.233099	−	0.972453i	$-0.574887\pi$
$829$	−13.4230	−0.466199	−0.233099	+	0.972453i	$0.574887\pi$
$830$	7.52354	0.261146
$831$	−18.8461	−0.653764
$832$	−59.4582	−2.06134
$833$	36.7402	1.27297
$834$	20.9700	0.726132
$835$	3.97970	0.137723
$836$	0	0
$837$	9.48932	0.327999
$838$	11.9844	0.413993
$839$	39.6388	1.36848	0.684242	−	0.729255i	$-0.260133\pi$
$839$	39.6388	1.36848	0.684242	+	0.729255i	$0.260133\pi$
$840$	−6.96082	−0.240171
$841$	−6.04696	−0.208516
$842$	−32.5396	−1.12139
$843$	−16.6497	−0.573447
$844$	−73.6529	−2.53524
$845$	−5.17654	−0.178079
$846$	29.8155	1.02508
$847$	3.41155	0.117222
$848$	−115.574	−3.96883
$849$	−13.0519	−0.447942
$850$	15.5371	0.532919
$851$	−23.8933	−0.819050
$852$	62.8070	2.15173
$853$	−6.04904	−0.207115	−0.103558	−	0.994623i	$-0.533023\pi$
$853$	−6.04904	−0.207115	−0.103558	+	0.994623i	$0.533023\pi$
$854$	8.73626	0.298949
$855$	0	0
$856$	−27.9884	−0.956625
$857$	51.3361	1.75361	0.876803	−	0.480849i	$-0.159672\pi$
$857$	51.3361	1.75361	0.876803	+	0.480849i	$0.159672\pi$
$858$	−19.5157	−0.666256
$859$	12.0743	0.411969	0.205984	−	0.978555i	$-0.433960\pi$
$859$	12.0743	0.411969	0.205984	+	0.978555i	$0.433960\pi$
$860$	−14.6695	−0.500227
$861$	5.88472	0.200551
$862$	55.2936	1.88331
$863$	−12.8023	−0.435797	−0.217898	−	0.975971i	$-0.569920\pi$
$863$	−12.8023	−0.435797	−0.217898	+	0.975971i	$0.569920\pi$
$864$	17.5702	0.597750
$865$	11.1723	0.379869
$866$	52.1454	1.77197
$867$	−16.3214	−0.554305
$868$	39.6675	1.34640
$869$	16.8025	0.569987
$870$	−12.8952	−0.437189
$871$	−38.5312	−1.30558
$872$	−68.1058	−2.30635
$873$	2.00000	0.0676897
$874$	0	0
$875$	−0.797044	−0.0269450
$876$	−44.6204	−1.50758
$877$	−30.5367	−1.03115	−0.515575	−	0.856845i	$-0.672422\pi$
$877$	−30.5367	−1.03115	−0.515575	+	0.856845i	$0.672422\pi$
$878$	−46.3804	−1.56526
$879$	3.07225	0.103624
$880$	33.7436	1.13750
$881$	−6.79947	−0.229080	−0.114540	−	0.993419i	$-0.536539\pi$
$881$	−6.79947	−0.229080	−0.114540	+	0.993419i	$0.536539\pi$
$882$	17.1312	0.576838
$883$	27.0741	0.911116	0.455558	−	0.890206i	$-0.349440\pi$
$883$	27.0741	0.911116	0.455558	+	0.890206i	$0.349440\pi$
$884$	84.6795	2.84808
$885$	−1.08020	−0.0363105
$886$	−44.8297	−1.50608
$887$	−11.2462	−0.377612	−0.188806	−	0.982014i	$-0.560462\pi$
$887$	−11.2462	−0.377612	−0.188806	+	0.982014i	$0.560462\pi$
$888$	67.1789	2.25438
$889$	−3.57819	−0.120008
$890$	35.9559	1.20524
$891$	2.59225	0.0868436
$892$	−126.844	−4.24704
$893$	0	0
$894$	−0.244147	−0.00816549
$895$	9.63565	0.322084
$896$	17.5957	0.587830
$897$	−8.68800	−0.290084
$898$	49.7131	1.65895
$899$	45.4627	1.51627
$900$	5.24466	0.174822
$901$	51.2515	1.70744
$902$	−51.5144	−1.71524
$903$	−2.22937	−0.0741887
$904$	−72.1407	−2.39936
$905$	4.10003	0.136289
$906$	−12.1048	−0.402155
$907$	−42.8755	−1.42366	−0.711829	−	0.702353i	$-0.752133\pi$
$907$	−42.8755	−1.42366	−0.711829	+	0.702353i	$0.752133\pi$
$908$	17.7508	0.589081
$909$	13.0816	0.433888
$910$	−6.00055	−0.198916
$911$	39.7951	1.31847	0.659235	−	0.751937i	$-0.270880\pi$
$911$	39.7951	1.31847	0.659235	+	0.751937i	$0.270880\pi$
$912$	0	0
$913$	−7.24586	−0.239803
$914$	−9.16941	−0.303297
$915$	−4.07225	−0.134624
$916$	−136.185	−4.49968
$917$	−15.5255	−0.512696
$918$	−15.5371	−0.512802
$919$	−51.8927	−1.71178	−0.855891	−	0.517156i	$-0.826991\pi$
$919$	−51.8927	−1.71178	−0.855891	+	0.517156i	$0.826991\pi$
$920$	27.1268	0.894345
$921$	−23.4615	−0.773084
$922$	−108.756	−3.58167
$923$	33.4958	1.10253
$924$	10.8362	0.356484
$925$	7.69227	0.252920
$926$	61.8323	2.03194
$927$	14.4586	0.474884
$928$	84.1777	2.76327
$929$	−26.1323	−0.857374	−0.428687	−	0.903453i	$-0.641024\pi$
$929$	−26.1323	−0.857374	−0.428687	+	0.903453i	$0.641024\pi$
$930$	−25.5414	−0.837534
$931$	0	0
$932$	−35.2347	−1.15415
$933$	5.59041	0.183022
$934$	−18.8996	−0.618415
$935$	−14.9637	−0.489365
$936$	24.4274	0.798435
$937$	32.2318	1.05297	0.526483	−	0.850186i	$-0.323510\pi$
$937$	32.2318	1.05297	0.526483	+	0.850186i	$0.323510\pi$
$938$	29.5532	0.964946
$939$	28.4280	0.927711
$940$	−58.0966	−1.89490
$941$	−33.9341	−1.10622	−0.553110	−	0.833109i	$-0.686559\pi$
$941$	−33.9341	−1.10622	−0.553110	+	0.833109i	$0.686559\pi$
$942$	47.4980	1.54757
$943$	−22.9332	−0.746807
$944$	14.0611	0.457649
$945$	0.797044	0.0259278
$946$	19.5157	0.634511
$947$	0.896598	0.0291355	0.0145678	−	0.999894i	$-0.495363\pi$
$947$	0.896598	0.0291355	0.0145678	+	0.999894i	$0.495363\pi$
$948$	−33.9950	−1.10411
$949$	−23.7966	−0.772471
$950$	0	0
$951$	10.5096	0.340798
$952$	−40.1812	−1.30228
$953$	−30.7219	−0.995180	−0.497590	−	0.867412i	$-0.665782\pi$
$953$	−30.7219	−0.995180	−0.497590	+	0.867412i	$0.665782\pi$
$954$	23.8976	0.773713
$955$	−22.6143	−0.731781
$956$	135.217	4.37322
$957$	12.4193	0.401458
$958$	7.86259	0.254029
$959$	−3.36953	−0.108808
$960$	−21.2575	−0.686084
$961$	59.0472	1.90475
$962$	57.9113	1.86713
$963$	3.20480	0.103273
$964$	−40.7960	−1.31395
$965$	16.6034	0.534483
$966$	6.66365	0.214399
$967$	−13.6554	−0.439127	−0.219563	−	0.975598i	$-0.570463\pi$
$967$	−13.6554	−0.439127	−0.219563	+	0.975598i	$0.570463\pi$
$968$	37.3807	1.20146
$969$	0	0
$970$	−5.38318	−0.172844
$971$	38.3313	1.23011	0.615055	−	0.788484i	$-0.289134\pi$
$971$	38.3313	1.23011	0.615055	+	0.788484i	$0.289134\pi$
$972$	−5.24466	−0.168223
$973$	−6.20972	−0.199074
$974$	−51.6888	−1.65622
$975$	2.79704	0.0895771
$976$	53.0090	1.69678
$977$	−57.0555	−1.82537	−0.912684	−	0.408666i	$-0.865994\pi$
$977$	−57.0555	−1.82537	−0.912684	+	0.408666i	$0.865994\pi$
$978$	11.4624	0.366526
$979$	−34.6288	−1.10674
$980$	−33.3808	−1.06631
$981$	7.79841	0.248984
$982$	−28.0919	−0.896447
$983$	−28.9251	−0.922567	−0.461284	−	0.887253i	$-0.652611\pi$
$983$	−28.9251	−0.922567	−0.461284	+	0.887253i	$0.652611\pi$
$984$	64.4795	2.05553
$985$	−17.6450	−0.562216
$986$	−74.4374	−2.37057
$987$	−8.82909	−0.281033
$988$	0	0
$989$	8.68800	0.276262
$990$	−6.97727	−0.221752
$991$	8.14129	0.258616	0.129308	−	0.991604i	$-0.458724\pi$
$991$	8.14129	0.258616	0.129308	+	0.991604i	$0.458724\pi$
$992$	166.729	5.29366
$993$	6.39618	0.202977
$994$	−25.6911	−0.814872
$995$	19.0631	0.604341
$996$	14.6599	0.464516
$997$	43.7693	1.38619	0.693095	−	0.720847i	$-0.256247\pi$
$997$	43.7693	1.38619	0.693095	+	0.720847i	$0.256247\pi$
$998$	−70.4390	−2.22971
$999$	−7.69227	−0.243373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.y.1.1		5
19.7	even	3		285.2.i.f.106.5	✓	10
19.11	even	3		285.2.i.f.121.5	yes	10
19.18	odd	2		5415.2.a.z.1.5		5
57.11	odd	6		855.2.k.i.406.1		10
57.26	odd	6		855.2.k.i.676.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.5	✓	10	19.7	even	3
285.2.i.f.121.5	yes	10	19.11	even	3
855.2.k.i.406.1		10	57.11	odd	6
855.2.k.i.676.1		10	57.26	odd	6
5415.2.a.y.1.1		5	1.1	even	1	trivial
5415.2.a.z.1.5		5	19.18	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:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69159 q^{2} -1.00000 q^{3} +5.24466 q^{4} +1.00000 q^{5} +2.69159 q^{6} -0.797044 q^{7} -8.73329 q^{8} +1.00000 q^{9} -2.69159 q^{10} +2.59225 q^{11} -5.24466 q^{12} -2.79704 q^{13} +2.14532 q^{14} -1.00000 q^{15} +13.0171 q^{16} -5.77247 q^{17} -2.69159 q^{18} +5.24466 q^{20} +0.797044 q^{21} -6.97727 q^{22} -3.10614 q^{23} +8.73329 q^{24} +1.00000 q^{25} +7.52850 q^{26} -1.00000 q^{27} -4.18023 q^{28} -4.79093 q^{29} +2.69159 q^{30} -9.48932 q^{31} -17.5702 q^{32} -2.59225 q^{33} +15.5371 q^{34} -0.797044 q^{35} +5.24466 q^{36} +7.69227 q^{37} +2.79704 q^{39} -8.73329 q^{40} +7.38318 q^{41} -2.14532 q^{42} -2.79704 q^{43} +13.5955 q^{44} +1.00000 q^{45} +8.36045 q^{46} -11.0773 q^{47} -13.0171 q^{48} -6.36472 q^{49} -2.69159 q^{50} +5.77247 q^{51} -14.6695 q^{52} -8.87861 q^{53} +2.69159 q^{54} +2.59225 q^{55} +6.96082 q^{56} +12.8952 q^{58} +1.08020 q^{59} -5.24466 q^{60} +4.07225 q^{61} +25.5414 q^{62} -0.797044 q^{63} +21.2575 q^{64} -2.79704 q^{65} +6.97727 q^{66} +13.7757 q^{67} -30.2747 q^{68} +3.10614 q^{69} +2.14532 q^{70} -11.9754 q^{71} -8.73329 q^{72} +8.50778 q^{73} -20.7045 q^{74} -1.00000 q^{75} -2.06614 q^{77} -7.52850 q^{78} +6.48184 q^{79} +13.0171 q^{80} +1.00000 q^{81} -19.8725 q^{82} -2.79520 q^{83} +4.18023 q^{84} -5.77247 q^{85} +7.52850 q^{86} +4.79093 q^{87} -22.6389 q^{88} -13.3586 q^{89} -2.69159 q^{90} +2.22937 q^{91} -16.2906 q^{92} +9.48932 q^{93} +29.8155 q^{94} +17.5702 q^{96} +2.00000 q^{97} +17.1312 q^{98} +2.59225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} - 7 q^{12} - 8 q^{13} - 4 q^{14} - 5 q^{15} + 7 q^{16} + 10 q^{17} - q^{18} + 7 q^{20} - 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 5 * q^9 - q^10 + 5 * q^11 - 7 * q^12 - 8 * q^13 - 4 * q^14 - 5 * q^15 + 7 * q^16 + 10 * q^17 - q^18 + 7 * q^20 - 2 * q^21 + 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 - 5 * q^27 + 10 * q^28 - 7 * q^29 + q^30 - 9 * q^31 - 23 * q^32 - 5 * q^33 + 25 * q^34 + 2 * q^35 + 7 * q^36 + 6 * q^37 + 8 * q^39 - 6 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 - 20 * q^46 + 6 * q^47 - 7 * q^48 + 15 * q^49 - q^50 - 10 * q^51 - 4 * q^52 + 8 * q^53 + q^54 + 5 * q^55 + 36 * q^56 + 38 * q^58 - q^59 - 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 - 8 * q^65 - 2 * q^66 - 14 * q^67 - q^68 + 2 * q^69 - 4 * q^70 - 27 * q^71 - 6 * q^72 + 26 * q^73 - 18 * q^74 - 5 * q^75 + 14 * q^77 + 2 * q^78 + 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 - 10 * q^84 + 10 * q^85 - 2 * q^86 + 7 * q^87 - 9 * q^89 - q^90 + 46 * q^91 - 52 * q^92 + 9 * q^93 + 45 * q^94 + 23 * q^96 + 10 * q^97 + 21 * q^98 + 5 * q^99

Introduction

L-functions

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Database

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