LMFDB - Embedded newform 230.2.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +3.30278 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.30278 q^{6} -0.302776 q^{7} -1.00000 q^{8} +7.90833 q^{9} -1.00000 q^{10} -5.30278 q^{11} +3.30278 q^{12} -0.302776 q^{13} +0.302776 q^{14} +3.30278 q^{15} +1.00000 q^{16} -3.90833 q^{17} -7.90833 q^{18} -4.90833 q^{19} +1.00000 q^{20} -1.00000 q^{21} +5.30278 q^{22} -1.00000 q^{23} -3.30278 q^{24} +1.00000 q^{25} +0.302776 q^{26} +16.2111 q^{27} -0.302776 q^{28} +4.60555 q^{29} -3.30278 q^{30} +2.90833 q^{31} -1.00000 q^{32} -17.5139 q^{33} +3.90833 q^{34} -0.302776 q^{35} +7.90833 q^{36} +8.00000 q^{37} +4.90833 q^{38} -1.00000 q^{39} -1.00000 q^{40} -9.90833 q^{41} +1.00000 q^{42} +5.21110 q^{43} -5.30278 q^{44} +7.90833 q^{45} +1.00000 q^{46} +4.60555 q^{47} +3.30278 q^{48} -6.90833 q^{49} -1.00000 q^{50} -12.9083 q^{51} -0.302776 q^{52} +3.21110 q^{53} -16.2111 q^{54} -5.30278 q^{55} +0.302776 q^{56} -16.2111 q^{57} -4.60555 q^{58} -10.6056 q^{59} +3.30278 q^{60} -6.51388 q^{61} -2.90833 q^{62} -2.39445 q^{63} +1.00000 q^{64} -0.302776 q^{65} +17.5139 q^{66} -4.00000 q^{67} -3.90833 q^{68} -3.30278 q^{69} +0.302776 q^{70} -12.6972 q^{71} -7.90833 q^{72} +15.8167 q^{73} -8.00000 q^{74} +3.30278 q^{75} -4.90833 q^{76} +1.60555 q^{77} +1.00000 q^{78} +14.4222 q^{79} +1.00000 q^{80} +29.8167 q^{81} +9.90833 q^{82} -3.21110 q^{83} -1.00000 q^{84} -3.90833 q^{85} -5.21110 q^{86} +15.2111 q^{87} +5.30278 q^{88} -7.90833 q^{90} +0.0916731 q^{91} -1.00000 q^{92} +9.60555 q^{93} -4.60555 q^{94} -4.90833 q^{95} -3.30278 q^{96} +2.69722 q^{97} +6.90833 q^{98} -41.9361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 2 q^{8} + 5 q^{9} - 2 q^{10} - 7 q^{11} + 3 q^{12} + 3 q^{13} - 3 q^{14} + 3 q^{15} + 2 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} + 2 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 2 * q^8 + 5 * q^9 - 2 * q^10 - 7 * q^11 + 3 * q^12 + 3 * q^13 - 3 * q^14 + 3 * q^15 + 2 * q^16 + 3 * q^17 - 5 * q^18 + q^19 + 2 * q^20 - 2 * q^21 + 7 * q^22 - 2 * q^23 - 3 * q^24 + 2 * q^25 - 3 * q^26 + 18 * q^27 + 3 * q^28 + 2 * q^29 - 3 * q^30 - 5 * q^31 - 2 * q^32 - 17 * q^33 - 3 * q^34 + 3 * q^35 + 5 * q^36 + 16 * q^37 - q^38 - 2 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - 4 * q^43 - 7 * q^44 + 5 * q^45 + 2 * q^46 + 2 * q^47 + 3 * q^48 - 3 * q^49 - 2 * q^50 - 15 * q^51 + 3 * q^52 - 8 * q^53 - 18 * q^54 - 7 * q^55 - 3 * q^56 - 18 * q^57 - 2 * q^58 - 14 * q^59 + 3 * q^60 + 5 * q^61 + 5 * q^62 - 12 * q^63 + 2 * q^64 + 3 * q^65 + 17 * q^66 - 8 * q^67 + 3 * q^68 - 3 * q^69 - 3 * q^70 - 29 * q^71 - 5 * q^72 + 10 * q^73 - 16 * q^74 + 3 * q^75 + q^76 - 4 * q^77 + 2 * q^78 + 2 * q^80 + 38 * q^81 + 9 * q^82 + 8 * q^83 - 2 * q^84 + 3 * q^85 + 4 * q^86 + 16 * q^87 + 7 * q^88 - 5 * q^90 + 11 * q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 + q^95 - 3 * q^96 + 9 * q^97 + 3 * q^98 - 37 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.30278	1.90686	0.953429	−	0.301617i	$-0.0975264\pi$
$3$	3.30278	1.90686	0.953429	+	0.301617i	$0.0975264\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.30278	−1.34835
$7$	−0.302776	−0.114438	−0.0572192	−	0.998362i	$-0.518223\pi$
$7$	−0.302776	−0.114438	−0.0572192	+	0.998362i	$0.518223\pi$
$8$	−1.00000	−0.353553
$9$	7.90833	2.63611
$10$	−1.00000	−0.316228
$11$	−5.30278	−1.59885	−0.799424	−	0.600768i	$-0.794862\pi$
$11$	−5.30278	−1.59885	−0.799424	+	0.600768i	$0.794862\pi$
$12$	3.30278	0.953429
$13$	−0.302776	−0.0839749	−0.0419874	−	0.999118i	$-0.513369\pi$
$13$	−0.302776	−0.0839749	−0.0419874	+	0.999118i	$0.513369\pi$
$14$	0.302776	0.0809202
$15$	3.30278	0.852773
$16$	1.00000	0.250000
$17$	−3.90833	−0.947909	−0.473954	−	0.880549i	$-0.657174\pi$
$17$	−3.90833	−0.947909	−0.473954	+	0.880549i	$0.657174\pi$
$18$	−7.90833	−1.86401
$19$	−4.90833	−1.12605	−0.563024	−	0.826441i	$-0.690362\pi$
$19$	−4.90833	−1.12605	−0.563024	+	0.826441i	$0.690362\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	5.30278	1.13056
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.30278	−0.674176
$25$	1.00000	0.200000
$26$	0.302776	0.0593792
$27$	16.2111	3.11983
$28$	−0.302776	−0.0572192
$29$	4.60555	0.855229	0.427615	−	0.903961i	$-0.359354\pi$
$29$	4.60555	0.855229	0.427615	+	0.903961i	$0.359354\pi$
$30$	−3.30278	−0.603002
$31$	2.90833	0.522351	0.261175	−	0.965291i	$-0.415890\pi$
$31$	2.90833	0.522351	0.261175	+	0.965291i	$0.415890\pi$
$32$	−1.00000	−0.176777
$33$	−17.5139	−3.04877
$34$	3.90833	0.670273
$35$	−0.302776	−0.0511784
$36$	7.90833	1.31805
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	4.90833	0.796236
$39$	−1.00000	−0.160128
$40$	−1.00000	−0.158114
$41$	−9.90833	−1.54742	−0.773710	−	0.633540i	$-0.781601\pi$
$41$	−9.90833	−1.54742	−0.773710	+	0.633540i	$0.781601\pi$
$42$	1.00000	0.154303
$43$	5.21110	0.794686	0.397343	−	0.917670i	$-0.369932\pi$
$43$	5.21110	0.794686	0.397343	+	0.917670i	$0.369932\pi$
$44$	−5.30278	−0.799424
$45$	7.90833	1.17890
$46$	1.00000	0.147442
$47$	4.60555	0.671789	0.335894	−	0.941900i	$-0.390961\pi$
$47$	4.60555	0.671789	0.335894	+	0.941900i	$0.390961\pi$
$48$	3.30278	0.476715
$49$	−6.90833	−0.986904
$50$	−1.00000	−0.141421
$51$	−12.9083	−1.80753
$52$	−0.302776	−0.0419874
$53$	3.21110	0.441079	0.220539	−	0.975378i	$-0.429218\pi$
$53$	3.21110	0.441079	0.220539	+	0.975378i	$0.429218\pi$
$54$	−16.2111	−2.20605
$55$	−5.30278	−0.715026
$56$	0.302776	0.0404601
$57$	−16.2111	−2.14721
$58$	−4.60555	−0.604739
$59$	−10.6056	−1.38073	−0.690363	−	0.723464i	$-0.742549\pi$
$59$	−10.6056	−1.38073	−0.690363	+	0.723464i	$0.742549\pi$
$60$	3.30278	0.426387
$61$	−6.51388	−0.834017	−0.417008	−	0.908903i	$-0.636921\pi$
$61$	−6.51388	−0.834017	−0.417008	+	0.908903i	$0.636921\pi$
$62$	−2.90833	−0.369358
$63$	−2.39445	−0.301672
$64$	1.00000	0.125000
$65$	−0.302776	−0.0375547
$66$	17.5139	2.15581
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−3.90833	−0.473954
$69$	−3.30278	−0.397607
$70$	0.302776	0.0361886
$71$	−12.6972	−1.50688	−0.753442	−	0.657515i	$-0.771608\pi$
$71$	−12.6972	−1.50688	−0.753442	+	0.657515i	$0.771608\pi$
$72$	−7.90833	−0.932005
$73$	15.8167	1.85120	0.925600	−	0.378504i	$-0.123561\pi$
$73$	15.8167	1.85120	0.925600	+	0.378504i	$0.123561\pi$
$74$	−8.00000	−0.929981
$75$	3.30278	0.381372
$76$	−4.90833	−0.563024
$77$	1.60555	0.182970
$78$	1.00000	0.113228
$79$	14.4222	1.62262	0.811312	−	0.584613i	$-0.198754\pi$
$79$	14.4222	1.62262	0.811312	+	0.584613i	$0.198754\pi$
$80$	1.00000	0.111803
$81$	29.8167	3.31296
$82$	9.90833	1.09419
$83$	−3.21110	−0.352464	−0.176232	−	0.984349i	$-0.556391\pi$
$83$	−3.21110	−0.352464	−0.176232	+	0.984349i	$0.556391\pi$
$84$	−1.00000	−0.109109
$85$	−3.90833	−0.423918
$86$	−5.21110	−0.561928
$87$	15.2111	1.63080
$88$	5.30278	0.565278
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−7.90833	−0.833611
$91$	0.0916731	0.00960995
$92$	−1.00000	−0.104257
$93$	9.60555	0.996049
$94$	−4.60555	−0.475026
$95$	−4.90833	−0.503584
$96$	−3.30278	−0.337088
$97$	2.69722	0.273862	0.136931	−	0.990581i	$-0.456276\pi$
$97$	2.69722	0.273862	0.136931	+	0.990581i	$0.456276\pi$
$98$	6.90833	0.697846
$99$	−41.9361	−4.21473
$100$	1.00000	0.100000
$101$	−4.60555	−0.458269	−0.229135	−	0.973395i	$-0.573590\pi$
$101$	−4.60555	−0.458269	−0.229135	+	0.973395i	$0.573590\pi$
$102$	12.9083	1.27811
$103$	−17.1194	−1.68683	−0.843414	−	0.537265i	$-0.819458\pi$
$103$	−17.1194	−1.68683	−0.843414	+	0.537265i	$0.819458\pi$
$104$	0.302776	0.0296896
$105$	−1.00000	−0.0975900
$106$	−3.21110	−0.311890
$107$	4.60555	0.445235	0.222618	−	0.974906i	$-0.428540\pi$
$107$	4.60555	0.445235	0.222618	+	0.974906i	$0.428540\pi$
$108$	16.2111	1.55991
$109$	19.5139	1.86909	0.934545	−	0.355844i	$-0.115807\pi$
$109$	19.5139	1.86909	0.934545	+	0.355844i	$0.115807\pi$
$110$	5.30278	0.505600
$111$	26.4222	2.50788
$112$	−0.302776	−0.0286096
$113$	12.4222	1.16858	0.584291	−	0.811544i	$-0.301373\pi$
$113$	12.4222	1.16858	0.584291	+	0.811544i	$0.301373\pi$
$114$	16.2111	1.51831
$115$	−1.00000	−0.0932505
$116$	4.60555	0.427615
$117$	−2.39445	−0.221367
$118$	10.6056	0.976320
$119$	1.18335	0.108477
$120$	−3.30278	−0.301501
$121$	17.1194	1.55631
$122$	6.51388	0.589739
$123$	−32.7250	−2.95071
$124$	2.90833	0.261175
$125$	1.00000	0.0894427
$126$	2.39445	0.213314
$127$	−11.8167	−1.04856	−0.524279	−	0.851546i	$-0.675665\pi$
$127$	−11.8167	−1.04856	−0.524279	+	0.851546i	$0.675665\pi$
$128$	−1.00000	−0.0883883
$129$	17.2111	1.51535
$130$	0.302776	0.0265552
$131$	3.21110	0.280555	0.140278	−	0.990112i	$-0.455200\pi$
$131$	3.21110	0.280555	0.140278	+	0.990112i	$0.455200\pi$
$132$	−17.5139	−1.52439
$133$	1.48612	0.128863
$134$	4.00000	0.345547
$135$	16.2111	1.39523
$136$	3.90833	0.335136
$137$	−6.90833	−0.590218	−0.295109	−	0.955464i	$-0.595356\pi$
$137$	−6.90833	−0.590218	−0.295109	+	0.955464i	$0.595356\pi$
$138$	3.30278	0.281151
$139$	−5.39445	−0.457551	−0.228776	−	0.973479i	$-0.573472\pi$
$139$	−5.39445	−0.457551	−0.228776	+	0.973479i	$0.573472\pi$
$140$	−0.302776	−0.0255892
$141$	15.2111	1.28101
$142$	12.6972	1.06553
$143$	1.60555	0.134263
$144$	7.90833	0.659027
$145$	4.60555	0.382470
$146$	−15.8167	−1.30900
$147$	−22.8167	−1.88189
$148$	8.00000	0.657596
$149$	9.69722	0.794428	0.397214	−	0.917726i	$-0.369977\pi$
$149$	9.69722	0.794428	0.397214	+	0.917726i	$0.369977\pi$
$150$	−3.30278	−0.269671
$151$	−1.90833	−0.155297	−0.0776487	−	0.996981i	$-0.524741\pi$
$151$	−1.90833	−0.155297	−0.0776487	+	0.996981i	$0.524741\pi$
$152$	4.90833	0.398118
$153$	−30.9083	−2.49879
$154$	−1.60555	−0.129379
$155$	2.90833	0.233602
$156$	−1.00000	−0.0800641
$157$	−11.3944	−0.909376	−0.454688	−	0.890651i	$-0.650249\pi$
$157$	−11.3944	−0.909376	−0.454688	+	0.890651i	$0.650249\pi$
$158$	−14.4222	−1.14737
$159$	10.6056	0.841075
$160$	−1.00000	−0.0790569
$161$	0.302776	0.0238621
$162$	−29.8167	−2.34262
$163$	5.69722	0.446241	0.223121	−	0.974791i	$-0.428376\pi$
$163$	5.69722	0.446241	0.223121	+	0.974791i	$0.428376\pi$
$164$	−9.90833	−0.773710
$165$	−17.5139	−1.36345
$166$	3.21110	0.249230
$167$	21.2111	1.64136	0.820682	−	0.571385i	$-0.193594\pi$
$167$	21.2111	1.64136	0.820682	+	0.571385i	$0.193594\pi$
$168$	1.00000	0.0771517
$169$	−12.9083	−0.992948
$170$	3.90833	0.299755
$171$	−38.8167	−2.96838
$172$	5.21110	0.397343
$173$	23.3028	1.77168	0.885839	−	0.463993i	$-0.153584\pi$
$173$	23.3028	1.77168	0.885839	+	0.463993i	$0.153584\pi$
$174$	−15.2111	−1.15315
$175$	−0.302776	−0.0228877
$176$	−5.30278	−0.399712
$177$	−35.0278	−2.63285
$178$	0	0
$179$	16.6056	1.24116	0.620579	−	0.784144i	$-0.286898\pi$
$179$	16.6056	1.24116	0.620579	+	0.784144i	$0.286898\pi$
$180$	7.90833	0.589452
$181$	−8.11943	−0.603512	−0.301756	−	0.953385i	$-0.597573\pi$
$181$	−8.11943	−0.603512	−0.301756	+	0.953385i	$0.597573\pi$
$182$	−0.0916731	−0.00679526
$183$	−21.5139	−1.59035
$184$	1.00000	0.0737210
$185$	8.00000	0.588172
$186$	−9.60555	−0.704313
$187$	20.7250	1.51556
$188$	4.60555	0.335894
$189$	−4.90833	−0.357028
$190$	4.90833	0.356087
$191$	−1.39445	−0.100899	−0.0504494	−	0.998727i	$-0.516065\pi$
$191$	−1.39445	−0.100899	−0.0504494	+	0.998727i	$0.516065\pi$
$192$	3.30278	0.238357
$193$	3.81665	0.274729	0.137364	−	0.990521i	$-0.456137\pi$
$193$	3.81665	0.274729	0.137364	+	0.990521i	$0.456137\pi$
$194$	−2.69722	−0.193649
$195$	−1.00000	−0.0716115
$196$	−6.90833	−0.493452
$197$	0.697224	0.0496752	0.0248376	−	0.999691i	$-0.492093\pi$
$197$	0.697224	0.0496752	0.0248376	+	0.999691i	$0.492093\pi$
$198$	41.9361	2.98027
$199$	8.42221	0.597034	0.298517	−	0.954404i	$-0.403508\pi$
$199$	8.42221	0.597034	0.298517	+	0.954404i	$0.403508\pi$
$200$	−1.00000	−0.0707107
$201$	−13.2111	−0.931839
$202$	4.60555	0.324045
$203$	−1.39445	−0.0978711
$204$	−12.9083	−0.903764
$205$	−9.90833	−0.692028
$206$	17.1194	1.19277
$207$	−7.90833	−0.549667
$208$	−0.302776	−0.0209937
$209$	26.0278	1.80038
$210$	1.00000	0.0690066
$211$	−7.21110	−0.496433	−0.248216	−	0.968705i	$-0.579844\pi$
$211$	−7.21110	−0.496433	−0.248216	+	0.968705i	$0.579844\pi$
$212$	3.21110	0.220539
$213$	−41.9361	−2.87341
$214$	−4.60555	−0.314829
$215$	5.21110	0.355394
$216$	−16.2111	−1.10303
$217$	−0.880571	−0.0597770
$218$	−19.5139	−1.32165
$219$	52.2389	3.52997
$220$	−5.30278	−0.357513
$221$	1.18335	0.0796005
$222$	−26.4222	−1.77334
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	0.302776	0.0202300
$225$	7.90833	0.527222
$226$	−12.4222	−0.826313
$227$	−7.39445	−0.490787	−0.245393	−	0.969424i	$-0.578917\pi$
$227$	−7.39445	−0.490787	−0.245393	+	0.969424i	$0.578917\pi$
$228$	−16.2111	−1.07361
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	1.00000	0.0659380
$231$	5.30278	0.348897
$232$	−4.60555	−0.302369
$233$	4.18335	0.274060	0.137030	−	0.990567i	$-0.456244\pi$
$233$	4.18335	0.274060	0.137030	+	0.990567i	$0.456244\pi$
$234$	2.39445	0.156530
$235$	4.60555	0.300433
$236$	−10.6056	−0.690363
$237$	47.6333	3.09412
$238$	−1.18335	−0.0767049
$239$	−9.21110	−0.595817	−0.297908	−	0.954594i	$-0.596289\pi$
$239$	−9.21110	−0.595817	−0.297908	+	0.954594i	$0.596289\pi$
$240$	3.30278	0.213193
$241$	14.4222	0.929016	0.464508	−	0.885569i	$-0.346231\pi$
$241$	14.4222	0.929016	0.464508	+	0.885569i	$0.346231\pi$
$242$	−17.1194	−1.10048
$243$	49.8444	3.19752
$244$	−6.51388	−0.417008
$245$	−6.90833	−0.441357
$246$	32.7250	2.08647
$247$	1.48612	0.0945597
$248$	−2.90833	−0.184679
$249$	−10.6056	−0.672100
$250$	−1.00000	−0.0632456
$251$	−5.51388	−0.348033	−0.174016	−	0.984743i	$-0.555675\pi$
$251$	−5.51388	−0.348033	−0.174016	+	0.984743i	$0.555675\pi$
$252$	−2.39445	−0.150836
$253$	5.30278	0.333383
$254$	11.8167	0.741443
$255$	−12.9083	−0.808351
$256$	1.00000	0.0625000
$257$	19.8167	1.23613	0.618064	−	0.786127i	$-0.287917\pi$
$257$	19.8167	1.23613	0.618064	+	0.786127i	$0.287917\pi$
$258$	−17.2111	−1.07152
$259$	−2.42221	−0.150509
$260$	−0.302776	−0.0187773
$261$	36.4222	2.25448
$262$	−3.21110	−0.198383
$263$	−14.5139	−0.894964	−0.447482	−	0.894293i	$-0.647679\pi$
$263$	−14.5139	−0.894964	−0.447482	+	0.894293i	$0.647679\pi$
$264$	17.5139	1.07790
$265$	3.21110	0.197256
$266$	−1.48612	−0.0911200
$267$	0	0
$268$	−4.00000	−0.244339
$269$	25.8167	1.57407	0.787035	−	0.616909i	$-0.211615\pi$
$269$	25.8167	1.57407	0.787035	+	0.616909i	$0.211615\pi$
$270$	−16.2111	−0.986576
$271$	−6.30278	−0.382866	−0.191433	−	0.981506i	$-0.561314\pi$
$271$	−6.30278	−0.382866	−0.191433	+	0.981506i	$0.561314\pi$
$272$	−3.90833	−0.236977
$273$	0.302776	0.0183248
$274$	6.90833	0.417347
$275$	−5.30278	−0.319769
$276$	−3.30278	−0.198804
$277$	−12.7889	−0.768410	−0.384205	−	0.923248i	$-0.625524\pi$
$277$	−12.7889	−0.768410	−0.384205	+	0.923248i	$0.625524\pi$
$278$	5.39445	0.323538
$279$	23.0000	1.37697
$280$	0.302776	0.0180943
$281$	−19.3944	−1.15698	−0.578488	−	0.815691i	$-0.696357\pi$
$281$	−19.3944	−1.15698	−0.578488	+	0.815691i	$0.696357\pi$
$282$	−15.2111	−0.905808
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	−12.6972	−0.753442
$285$	−16.2111	−0.960263
$286$	−1.60555	−0.0949382
$287$	3.00000	0.177084
$288$	−7.90833	−0.466003
$289$	−1.72498	−0.101469
$290$	−4.60555	−0.270447
$291$	8.90833	0.522215
$292$	15.8167	0.925600
$293$	8.78890	0.513453	0.256726	−	0.966484i	$-0.417356\pi$
$293$	8.78890	0.513453	0.256726	+	0.966484i	$0.417356\pi$
$294$	22.8167	1.33069
$295$	−10.6056	−0.617479
$296$	−8.00000	−0.464991
$297$	−85.9638	−4.98813
$298$	−9.69722	−0.561745
$299$	0.302776	0.0175100
$300$	3.30278	0.190686
$301$	−1.57779	−0.0909426
$302$	1.90833	0.109812
$303$	−15.2111	−0.873855
$304$	−4.90833	−0.281512
$305$	−6.51388	−0.372984
$306$	30.9083	1.76691
$307$	−15.3028	−0.873376	−0.436688	−	0.899613i	$-0.643849\pi$
$307$	−15.3028	−0.873376	−0.436688	+	0.899613i	$0.643849\pi$
$308$	1.60555	0.0914848
$309$	−56.5416	−3.21654
$310$	−2.90833	−0.165182
$311$	−6.42221	−0.364170	−0.182085	−	0.983283i	$-0.558285\pi$
$311$	−6.42221	−0.364170	−0.182085	+	0.983283i	$0.558285\pi$
$312$	1.00000	0.0566139
$313$	−12.7250	−0.719258	−0.359629	−	0.933095i	$-0.617097\pi$
$313$	−12.7250	−0.719258	−0.359629	+	0.933095i	$0.617097\pi$
$314$	11.3944	0.643026
$315$	−2.39445	−0.134912
$316$	14.4222	0.811312
$317$	−14.7250	−0.827037	−0.413519	−	0.910496i	$-0.635700\pi$
$317$	−14.7250	−0.827037	−0.413519	+	0.910496i	$0.635700\pi$
$318$	−10.6056	−0.594730
$319$	−24.4222	−1.36738
$320$	1.00000	0.0559017
$321$	15.2111	0.849001
$322$	−0.302776	−0.0168730
$323$	19.1833	1.06739
$324$	29.8167	1.65648
$325$	−0.302776	−0.0167950
$326$	−5.69722	−0.315540
$327$	64.4500	3.56409
$328$	9.90833	0.547096
$329$	−1.39445	−0.0768784
$330$	17.5139	0.964107
$331$	9.39445	0.516366	0.258183	−	0.966096i	$-0.416876\pi$
$331$	9.39445	0.516366	0.258183	+	0.966096i	$0.416876\pi$
$332$	−3.21110	−0.176232
$333$	63.2666	3.46699
$334$	−21.2111	−1.16062
$335$	−4.00000	−0.218543
$336$	−1.00000	−0.0545545
$337$	−4.48612	−0.244375	−0.122187	−	0.992507i	$-0.538991\pi$
$337$	−4.48612	−0.244375	−0.122187	+	0.992507i	$0.538991\pi$
$338$	12.9083	0.702120
$339$	41.0278	2.22832
$340$	−3.90833	−0.211959
$341$	−15.4222	−0.835159
$342$	38.8167	2.09896
$343$	4.21110	0.227378
$344$	−5.21110	−0.280964
$345$	−3.30278	−0.177815
$346$	−23.3028	−1.25276
$347$	−25.5416	−1.37115	−0.685573	−	0.728004i	$-0.740448\pi$
$347$	−25.5416	−1.37115	−0.685573	+	0.728004i	$0.740448\pi$
$348$	15.2111	0.815401
$349$	−12.7889	−0.684574	−0.342287	−	0.939595i	$-0.611202\pi$
$349$	−12.7889	−0.684574	−0.342287	+	0.939595i	$0.611202\pi$
$350$	0.302776	0.0161840
$351$	−4.90833	−0.261987
$352$	5.30278	0.282639
$353$	18.4222	0.980515	0.490258	−	0.871578i	$-0.336903\pi$
$353$	18.4222	0.980515	0.490258	+	0.871578i	$0.336903\pi$
$354$	35.0278	1.86170
$355$	−12.6972	−0.673899
$356$	0	0
$357$	3.90833	0.206851
$358$	−16.6056	−0.877631
$359$	−3.21110	−0.169476	−0.0847378	−	0.996403i	$-0.527005\pi$
$359$	−3.21110	−0.169476	−0.0847378	+	0.996403i	$0.527005\pi$
$360$	−7.90833	−0.416805
$361$	5.09167	0.267983
$362$	8.11943	0.426748
$363$	56.5416	2.96767
$364$	0.0916731	0.00480498
$365$	15.8167	0.827881
$366$	21.5139	1.12455
$367$	29.2111	1.52481	0.762404	−	0.647102i	$-0.224019\pi$
$367$	29.2111	1.52481	0.762404	+	0.647102i	$0.224019\pi$
$368$	−1.00000	−0.0521286
$369$	−78.3583	−4.07917
$370$	−8.00000	−0.415900
$371$	−0.972244	−0.0504764
$372$	9.60555	0.498025
$373$	−2.60555	−0.134910	−0.0674552	−	0.997722i	$-0.521488\pi$
$373$	−2.60555	−0.134910	−0.0674552	+	0.997722i	$0.521488\pi$
$374$	−20.7250	−1.07166
$375$	3.30278	0.170555
$376$	−4.60555	−0.237513
$377$	−1.39445	−0.0718178
$378$	4.90833	0.252457
$379$	4.09167	0.210175	0.105088	−	0.994463i	$-0.466488\pi$
$379$	4.09167	0.210175	0.105088	+	0.994463i	$0.466488\pi$
$380$	−4.90833	−0.251792
$381$	−39.0278	−1.99945
$382$	1.39445	0.0713462
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−3.30278	−0.168544
$385$	1.60555	0.0818265
$386$	−3.81665	−0.194263
$387$	41.2111	2.09488
$388$	2.69722	0.136931
$389$	20.9361	1.06150	0.530751	−	0.847528i	$-0.321910\pi$
$389$	20.9361	1.06150	0.530751	+	0.847528i	$0.321910\pi$
$390$	1.00000	0.0506370
$391$	3.90833	0.197653
$392$	6.90833	0.348923
$393$	10.6056	0.534979
$394$	−0.697224	−0.0351257
$395$	14.4222	0.725660
$396$	−41.9361	−2.10737
$397$	−21.7250	−1.09035	−0.545173	−	0.838324i	$-0.683536\pi$
$397$	−21.7250	−1.09035	−0.545173	+	0.838324i	$0.683536\pi$
$398$	−8.42221	−0.422167
$399$	4.90833	0.245724
$400$	1.00000	0.0500000
$401$	−1.39445	−0.0696354	−0.0348177	−	0.999394i	$-0.511085\pi$
$401$	−1.39445	−0.0696354	−0.0348177	+	0.999394i	$0.511085\pi$
$402$	13.2111	0.658910
$403$	−0.880571	−0.0438643
$404$	−4.60555	−0.229135
$405$	29.8167	1.48160
$406$	1.39445	0.0692053
$407$	−42.4222	−2.10279
$408$	12.9083	0.639057
$409$	−15.0917	−0.746235	−0.373118	−	0.927784i	$-0.621711\pi$
$409$	−15.0917	−0.746235	−0.373118	+	0.927784i	$0.621711\pi$
$410$	9.90833	0.489337
$411$	−22.8167	−1.12546
$412$	−17.1194	−0.843414
$413$	3.21110	0.158008
$414$	7.90833	0.388673
$415$	−3.21110	−0.157627
$416$	0.302776	0.0148448
$417$	−17.8167	−0.872485
$418$	−26.0278	−1.27306
$419$	−39.6333	−1.93621	−0.968107	−	0.250538i	$-0.919393\pi$
$419$	−39.6333	−1.93621	−0.968107	+	0.250538i	$0.919393\pi$
$420$	−1.00000	−0.0487950
$421$	34.3028	1.67181	0.835907	−	0.548870i	$-0.184942\pi$
$421$	34.3028	1.67181	0.835907	+	0.548870i	$0.184942\pi$
$422$	7.21110	0.351031
$423$	36.4222	1.77091
$424$	−3.21110	−0.155945
$425$	−3.90833	−0.189582
$426$	41.9361	2.03181
$427$	1.97224	0.0954436
$428$	4.60555	0.222618
$429$	5.30278	0.256020
$430$	−5.21110	−0.251302
$431$	20.2389	0.974872	0.487436	−	0.873159i	$-0.337932\pi$
$431$	20.2389	0.974872	0.487436	+	0.873159i	$0.337932\pi$
$432$	16.2111	0.779957
$433$	−34.9083	−1.67759	−0.838794	−	0.544450i	$-0.816739\pi$
$433$	−34.9083	−1.67759	−0.838794	+	0.544450i	$0.816739\pi$
$434$	0.880571	0.0422687
$435$	15.2111	0.729317
$436$	19.5139	0.934545
$437$	4.90833	0.234797
$438$	−52.2389	−2.49607
$439$	−18.3028	−0.873544	−0.436772	−	0.899572i	$-0.643878\pi$
$439$	−18.3028	−0.873544	−0.436772	+	0.899572i	$0.643878\pi$
$440$	5.30278	0.252800
$441$	−54.6333	−2.60159
$442$	−1.18335	−0.0562860
$443$	35.5139	1.68732	0.843658	−	0.536882i	$-0.180398\pi$
$443$	35.5139	1.68732	0.843658	+	0.536882i	$0.180398\pi$
$444$	26.4222	1.25394
$445$	0	0
$446$	4.00000	0.189405
$447$	32.0278	1.51486
$448$	−0.302776	−0.0143048
$449$	−12.9083	−0.609182	−0.304591	−	0.952483i	$-0.598520\pi$
$449$	−12.9083	−0.609182	−0.304591	+	0.952483i	$0.598520\pi$
$450$	−7.90833	−0.372802
$451$	52.5416	2.47409
$452$	12.4222	0.584291
$453$	−6.30278	−0.296130
$454$	7.39445	0.347039
$455$	0.0916731	0.00429770
$456$	16.2111	0.759154
$457$	−3.57779	−0.167362	−0.0836811	−	0.996493i	$-0.526668\pi$
$457$	−3.57779	−0.167362	−0.0836811	+	0.996493i	$0.526668\pi$
$458$	−2.00000	−0.0934539
$459$	−63.3583	−2.95731
$460$	−1.00000	−0.0466252
$461$	31.8167	1.48185	0.740925	−	0.671588i	$-0.234388\pi$
$461$	31.8167	1.48185	0.740925	+	0.671588i	$0.234388\pi$
$462$	−5.30278	−0.246707
$463$	−25.6333	−1.19128	−0.595640	−	0.803251i	$-0.703102\pi$
$463$	−25.6333	−1.19128	−0.595640	+	0.803251i	$0.703102\pi$
$464$	4.60555	0.213807
$465$	9.60555	0.445447
$466$	−4.18335	−0.193790
$467$	19.8167	0.917005	0.458503	−	0.888693i	$-0.348386\pi$
$467$	19.8167	0.917005	0.458503	+	0.888693i	$0.348386\pi$
$468$	−2.39445	−0.110683
$469$	1.21110	0.0559235
$470$	−4.60555	−0.212438
$471$	−37.6333	−1.73405
$472$	10.6056	0.488160
$473$	−27.6333	−1.27058
$474$	−47.6333	−2.18787
$475$	−4.90833	−0.225209
$476$	1.18335	0.0542386
$477$	25.3944	1.16273
$478$	9.21110	0.421306
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	−3.30278	−0.150750
$481$	−2.42221	−0.110443
$482$	−14.4222	−0.656913
$483$	1.00000	0.0455016
$484$	17.1194	0.778156
$485$	2.69722	0.122475
$486$	−49.8444	−2.26099
$487$	−11.8167	−0.535464	−0.267732	−	0.963493i	$-0.586274\pi$
$487$	−11.8167	−0.535464	−0.267732	+	0.963493i	$0.586274\pi$
$488$	6.51388	0.294869
$489$	18.8167	0.850918
$490$	6.90833	0.312086
$491$	−25.8167	−1.16509	−0.582545	−	0.812799i	$-0.697943\pi$
$491$	−25.8167	−1.16509	−0.582545	+	0.812799i	$0.697943\pi$
$492$	−32.7250	−1.47536
$493$	−18.0000	−0.810679
$494$	−1.48612	−0.0668638
$495$	−41.9361	−1.88489
$496$	2.90833	0.130588
$497$	3.84441	0.172445
$498$	10.6056	0.475246
$499$	11.6333	0.520778	0.260389	−	0.965504i	$-0.416149\pi$
$499$	11.6333	0.520778	0.260389	+	0.965504i	$0.416149\pi$
$500$	1.00000	0.0447214
$501$	70.0555	3.12985
$502$	5.51388	0.246096
$503$	−2.72498	−0.121501	−0.0607504	−	0.998153i	$-0.519349\pi$
$503$	−2.72498	−0.121501	−0.0607504	+	0.998153i	$0.519349\pi$
$504$	2.39445	0.106657
$505$	−4.60555	−0.204944
$506$	−5.30278	−0.235737
$507$	−42.6333	−1.89341
$508$	−11.8167	−0.524279
$509$	29.4500	1.30535	0.652673	−	0.757639i	$-0.273647\pi$
$509$	29.4500	1.30535	0.652673	+	0.757639i	$0.273647\pi$
$510$	12.9083	0.571590
$511$	−4.78890	−0.211848
$512$	−1.00000	−0.0441942
$513$	−79.5694	−3.51307
$514$	−19.8167	−0.874075
$515$	−17.1194	−0.754372
$516$	17.2111	0.757677
$517$	−24.4222	−1.07409
$518$	2.42221	0.106426
$519$	76.9638	3.37834
$520$	0.302776	0.0132776
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	−36.4222	−1.59416
$523$	8.42221	0.368277	0.184139	−	0.982900i	$-0.441050\pi$
$523$	8.42221	0.368277	0.184139	+	0.982900i	$0.441050\pi$
$524$	3.21110	0.140278
$525$	−1.00000	−0.0436436
$526$	14.5139	0.632835
$527$	−11.3667	−0.495141
$528$	−17.5139	−0.762194
$529$	1.00000	0.0434783
$530$	−3.21110	−0.139481
$531$	−83.8722	−3.63974
$532$	1.48612	0.0644316
$533$	3.00000	0.129944
$534$	0	0
$535$	4.60555	0.199115
$536$	4.00000	0.172774
$537$	54.8444	2.36671
$538$	−25.8167	−1.11303
$539$	36.6333	1.57791
$540$	16.2111	0.697615
$541$	−28.8444	−1.24012	−0.620059	−	0.784555i	$-0.712891\pi$
$541$	−28.8444	−1.24012	−0.620059	+	0.784555i	$0.712891\pi$
$542$	6.30278	0.270727
$543$	−26.8167	−1.15081
$544$	3.90833	0.167568
$545$	19.5139	0.835883
$546$	−0.302776	−0.0129576
$547$	7.51388	0.321270	0.160635	−	0.987014i	$-0.448646\pi$
$547$	7.51388	0.321270	0.160635	+	0.987014i	$0.448646\pi$
$548$	−6.90833	−0.295109
$549$	−51.5139	−2.19856
$550$	5.30278	0.226111
$551$	−22.6056	−0.963029
$552$	3.30278	0.140575
$553$	−4.36669	−0.185691
$554$	12.7889	0.543348
$555$	26.4222	1.12156
$556$	−5.39445	−0.228776
$557$	−6.42221	−0.272118	−0.136059	−	0.990701i	$-0.543444\pi$
$557$	−6.42221	−0.272118	−0.136059	+	0.990701i	$0.543444\pi$
$558$	−23.0000	−0.973668
$559$	−1.57779	−0.0667336
$560$	−0.302776	−0.0127946
$561$	68.4500	2.88996
$562$	19.3944	0.818105
$563$	39.6333	1.67034	0.835172	−	0.549988i	$-0.185368\pi$
$563$	39.6333	1.67034	0.835172	+	0.549988i	$0.185368\pi$
$564$	15.2111	0.640503
$565$	12.4222	0.522606
$566$	−2.00000	−0.0840663
$567$	−9.02776	−0.379130
$568$	12.6972	0.532764
$569$	−0.422205	−0.0176998	−0.00884988	−	0.999961i	$-0.502817\pi$
$569$	−0.422205	−0.0176998	−0.00884988	+	0.999961i	$0.502817\pi$
$570$	16.2111	0.679008
$571$	9.11943	0.381636	0.190818	−	0.981625i	$-0.438886\pi$
$571$	9.11943	0.381636	0.190818	+	0.981625i	$0.438886\pi$
$572$	1.60555	0.0671315
$573$	−4.60555	−0.192400
$574$	−3.00000	−0.125218
$575$	−1.00000	−0.0417029
$576$	7.90833	0.329514
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	1.72498	0.0717497
$579$	12.6056	0.523869
$580$	4.60555	0.191235
$581$	0.972244	0.0403355
$582$	−8.90833	−0.369262
$583$	−17.0278	−0.705218
$584$	−15.8167	−0.654498
$585$	−2.39445	−0.0989983
$586$	−8.78890	−0.363066
$587$	−37.5416	−1.54951	−0.774755	−	0.632262i	$-0.782127\pi$
$587$	−37.5416	−1.54951	−0.774755	+	0.632262i	$0.782127\pi$
$588$	−22.8167	−0.940943
$589$	−14.2750	−0.588192
$590$	10.6056	0.436624
$591$	2.30278	0.0947235
$592$	8.00000	0.328798
$593$	19.8167	0.813772	0.406886	−	0.913479i	$-0.366615\pi$
$593$	19.8167	0.813772	0.406886	+	0.913479i	$0.366615\pi$
$594$	85.9638	3.52714
$595$	1.18335	0.0485125
$596$	9.69722	0.397214
$597$	27.8167	1.13846
$598$	−0.302776	−0.0123814
$599$	4.33053	0.176941	0.0884704	−	0.996079i	$-0.471802\pi$
$599$	4.33053	0.176941	0.0884704	+	0.996079i	$0.471802\pi$
$600$	−3.30278	−0.134835
$601$	−3.93608	−0.160556	−0.0802781	−	0.996773i	$-0.525581\pi$
$601$	−3.93608	−0.160556	−0.0802781	+	0.996773i	$0.525581\pi$
$602$	1.57779	0.0643061
$603$	−31.6333	−1.28821
$604$	−1.90833	−0.0776487
$605$	17.1194	0.696004
$606$	15.2111	0.617909
$607$	−26.0555	−1.05756	−0.528780	−	0.848759i	$-0.677350\pi$
$607$	−26.0555	−1.05756	−0.528780	+	0.848759i	$0.677350\pi$
$608$	4.90833	0.199059
$609$	−4.60555	−0.186626
$610$	6.51388	0.263739
$611$	−1.39445	−0.0564134
$612$	−30.9083	−1.24940
$613$	32.4222	1.30952	0.654760	−	0.755837i	$-0.272770\pi$
$613$	32.4222	1.30952	0.654760	+	0.755837i	$0.272770\pi$
$614$	15.3028	0.617570
$615$	−32.7250	−1.31960
$616$	−1.60555	−0.0646895
$617$	8.09167	0.325758	0.162879	−	0.986646i	$-0.447922\pi$
$617$	8.09167	0.325758	0.162879	+	0.986646i	$0.447922\pi$
$618$	56.5416	2.27444
$619$	27.3305	1.09851	0.549253	−	0.835656i	$-0.314912\pi$
$619$	27.3305	1.09851	0.549253	+	0.835656i	$0.314912\pi$
$620$	2.90833	0.116801
$621$	−16.2111	−0.650529
$622$	6.42221	0.257507
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	1.00000	0.0400000
$626$	12.7250	0.508593
$627$	85.9638	3.43307
$628$	−11.3944	−0.454688
$629$	−31.2666	−1.24668
$630$	2.39445	0.0953971
$631$	30.6056	1.21839	0.609194	−	0.793021i	$-0.291493\pi$
$631$	30.6056	1.21839	0.609194	+	0.793021i	$0.291493\pi$
$632$	−14.4222	−0.573685
$633$	−23.8167	−0.946627
$634$	14.7250	0.584804
$635$	−11.8167	−0.468930
$636$	10.6056	0.420537
$637$	2.09167	0.0828751
$638$	24.4222	0.966884
$639$	−100.414	−3.97231
$640$	−1.00000	−0.0395285
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	−15.2111	−0.600334
$643$	16.2389	0.640398	0.320199	−	0.947350i	$-0.396250\pi$
$643$	16.2389	0.640398	0.320199	+	0.947350i	$0.396250\pi$
$644$	0.302776	0.0119310
$645$	17.2111	0.677687
$646$	−19.1833	−0.754759
$647$	−30.8444	−1.21262	−0.606309	−	0.795229i	$-0.707351\pi$
$647$	−30.8444	−1.21262	−0.606309	+	0.795229i	$0.707351\pi$
$648$	−29.8167	−1.17131
$649$	56.2389	2.20757
$650$	0.302776	0.0118758
$651$	−2.90833	−0.113986
$652$	5.69722	0.223121
$653$	9.27502	0.362960	0.181480	−	0.983395i	$-0.441911\pi$
$653$	9.27502	0.362960	0.181480	+	0.983395i	$0.441911\pi$
$654$	−64.4500	−2.52019
$655$	3.21110	0.125468
$656$	−9.90833	−0.386855
$657$	125.083	4.87996
$658$	1.39445	0.0543613
$659$	−27.6333	−1.07644	−0.538220	−	0.842804i	$-0.680903\pi$
$659$	−27.6333	−1.07644	−0.538220	+	0.842804i	$0.680903\pi$
$660$	−17.5139	−0.681727
$661$	−24.0917	−0.937057	−0.468529	−	0.883448i	$-0.655216\pi$
$661$	−24.0917	−0.937057	−0.468529	+	0.883448i	$0.655216\pi$
$662$	−9.39445	−0.365126
$663$	3.90833	0.151787
$664$	3.21110	0.124615
$665$	1.48612	0.0576293
$666$	−63.2666	−2.45153
$667$	−4.60555	−0.178328
$668$	21.2111	0.820682
$669$	−13.2111	−0.510771
$670$	4.00000	0.154533
$671$	34.5416	1.33347
$672$	1.00000	0.0385758
$673$	5.63331	0.217148	0.108574	−	0.994088i	$-0.465372\pi$
$673$	5.63331	0.217148	0.108574	+	0.994088i	$0.465372\pi$
$674$	4.48612	0.172799
$675$	16.2111	0.623966
$676$	−12.9083	−0.496474
$677$	−12.4222	−0.477424	−0.238712	−	0.971090i	$-0.576725\pi$
$677$	−12.4222	−0.477424	−0.238712	+	0.971090i	$0.576725\pi$
$678$	−41.0278	−1.57566
$679$	−0.816654	−0.0313403
$680$	3.90833	0.149877
$681$	−24.4222	−0.935861
$682$	15.4222	0.590547
$683$	−32.7250	−1.25219	−0.626093	−	0.779748i	$-0.715347\pi$
$683$	−32.7250	−1.25219	−0.626093	+	0.779748i	$0.715347\pi$
$684$	−38.8167	−1.48419
$685$	−6.90833	−0.263954
$686$	−4.21110	−0.160781
$687$	6.60555	0.252018
$688$	5.21110	0.198671
$689$	−0.972244	−0.0370395
$690$	3.30278	0.125735
$691$	30.1833	1.14823	0.574114	−	0.818775i	$-0.305347\pi$
$691$	30.1833	1.14823	0.574114	+	0.818775i	$0.305347\pi$
$692$	23.3028	0.885839
$693$	12.6972	0.482328
$694$	25.5416	0.969547
$695$	−5.39445	−0.204623
$696$	−15.2111	−0.576575
$697$	38.7250	1.46681
$698$	12.7889	0.484067
$699$	13.8167	0.522594
$700$	−0.302776	−0.0114438
$701$	42.9083	1.62063	0.810313	−	0.585998i	$-0.199297\pi$
$701$	42.9083	1.62063	0.810313	+	0.585998i	$0.199297\pi$
$702$	4.90833	0.185253
$703$	−39.2666	−1.48097
$704$	−5.30278	−0.199856
$705$	15.2111	0.572883
$706$	−18.4222	−0.693329
$707$	1.39445	0.0524436
$708$	−35.0278	−1.31642
$709$	−41.1194	−1.54427	−0.772136	−	0.635457i	$-0.780812\pi$
$709$	−41.1194	−1.54427	−0.772136	+	0.635457i	$0.780812\pi$
$710$	12.6972	0.476518
$711$	114.056	4.27742
$712$	0	0
$713$	−2.90833	−0.108918
$714$	−3.90833	−0.146265
$715$	1.60555	0.0600442
$716$	16.6056	0.620579
$717$	−30.4222	−1.13614
$718$	3.21110	0.119837
$719$	14.3028	0.533404	0.266702	−	0.963779i	$-0.414066\pi$
$719$	14.3028	0.533404	0.266702	+	0.963779i	$0.414066\pi$
$720$	7.90833	0.294726
$721$	5.18335	0.193038
$722$	−5.09167	−0.189492
$723$	47.6333	1.77150
$724$	−8.11943	−0.301756
$725$	4.60555	0.171046
$726$	−56.5416	−2.09846
$727$	−7.90833	−0.293304	−0.146652	−	0.989188i	$-0.546850\pi$
$727$	−7.90833	−0.293304	−0.146652	+	0.989188i	$0.546850\pi$
$728$	−0.0916731	−0.00339763
$729$	75.1749	2.78426
$730$	−15.8167	−0.585401
$731$	−20.3667	−0.753289
$732$	−21.5139	−0.795176
$733$	−13.6333	−0.503558	−0.251779	−	0.967785i	$-0.581016\pi$
$733$	−13.6333	−0.503558	−0.251779	+	0.967785i	$0.581016\pi$
$734$	−29.2111	−1.07820
$735$	−22.8167	−0.841605
$736$	1.00000	0.0368605
$737$	21.2111	0.781321
$738$	78.3583	2.88441
$739$	−7.63331	−0.280796	−0.140398	−	0.990095i	$-0.544838\pi$
$739$	−7.63331	−0.280796	−0.140398	+	0.990095i	$0.544838\pi$
$740$	8.00000	0.294086
$741$	4.90833	0.180312
$742$	0.972244	0.0356922
$743$	7.33053	0.268931	0.134466	−	0.990918i	$-0.457068\pi$
$743$	7.33053	0.268931	0.134466	+	0.990918i	$0.457068\pi$
$744$	−9.60555	−0.352157
$745$	9.69722	0.355279
$746$	2.60555	0.0953960
$747$	−25.3944	−0.929134
$748$	20.7250	0.757780
$749$	−1.39445	−0.0509520
$750$	−3.30278	−0.120600
$751$	0.183346	0.00669040	0.00334520	−	0.999994i	$-0.498935\pi$
$751$	0.183346	0.00669040	0.00334520	+	0.999994i	$0.498935\pi$
$752$	4.60555	0.167947
$753$	−18.2111	−0.663649
$754$	1.39445	0.0507828
$755$	−1.90833	−0.0694511
$756$	−4.90833	−0.178514
$757$	−1.21110	−0.0440183	−0.0220091	−	0.999758i	$-0.507006\pi$
$757$	−1.21110	−0.0440183	−0.0220091	+	0.999758i	$0.507006\pi$
$758$	−4.09167	−0.148616
$759$	17.5139	0.635714
$760$	4.90833	0.178044
$761$	4.54163	0.164634	0.0823171	−	0.996606i	$-0.473768\pi$
$761$	4.54163	0.164634	0.0823171	+	0.996606i	$0.473768\pi$
$762$	39.0278	1.41383
$763$	−5.90833	−0.213896
$764$	−1.39445	−0.0504494
$765$	−30.9083	−1.11749
$766$	0	0
$767$	3.21110	0.115946
$768$	3.30278	0.119179
$769$	−41.2666	−1.48811	−0.744056	−	0.668117i	$-0.767100\pi$
$769$	−41.2666	−1.48811	−0.744056	+	0.668117i	$0.767100\pi$
$770$	−1.60555	−0.0578601
$771$	65.4500	2.35712
$772$	3.81665	0.137364
$773$	12.0000	0.431610	0.215805	−	0.976436i	$-0.430762\pi$
$773$	12.0000	0.431610	0.215805	+	0.976436i	$0.430762\pi$
$774$	−41.2111	−1.48130
$775$	2.90833	0.104470
$776$	−2.69722	−0.0968247
$777$	−8.00000	−0.286998
$778$	−20.9361	−0.750595
$779$	48.6333	1.74247
$780$	−1.00000	−0.0358057
$781$	67.3305	2.40928
$782$	−3.90833	−0.139761
$783$	74.6611	2.66817
$784$	−6.90833	−0.246726
$785$	−11.3944	−0.406685
$786$	−10.6056	−0.378287
$787$	−27.4500	−0.978485	−0.489243	−	0.872148i	$-0.662727\pi$
$787$	−27.4500	−0.978485	−0.489243	+	0.872148i	$0.662727\pi$
$788$	0.697224	0.0248376
$789$	−47.9361	−1.70657
$790$	−14.4222	−0.513119
$791$	−3.76114	−0.133731
$792$	41.9361	1.49013
$793$	1.97224	0.0700364
$794$	21.7250	0.770991
$795$	10.6056	0.376140
$796$	8.42221	0.298517
$797$	−19.8167	−0.701942	−0.350971	−	0.936386i	$-0.614148\pi$
$797$	−19.8167	−0.701942	−0.350971	+	0.936386i	$0.614148\pi$
$798$	−4.90833	−0.173753
$799$	−18.0000	−0.636794
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	1.39445	0.0492397
$803$	−83.8722	−2.95978
$804$	−13.2111	−0.465920
$805$	0.302776	0.0106714
$806$	0.880571	0.0310168
$807$	85.2666	3.00153
$808$	4.60555	0.162023
$809$	18.2750	0.642515	0.321258	−	0.946992i	$-0.395894\pi$
$809$	18.2750	0.642515	0.321258	+	0.946992i	$0.395894\pi$
$810$	−29.8167	−1.04765
$811$	−4.97224	−0.174599	−0.0872995	−	0.996182i	$-0.527824\pi$
$811$	−4.97224	−0.174599	−0.0872995	+	0.996182i	$0.527824\pi$
$812$	−1.39445	−0.0489356
$813$	−20.8167	−0.730072
$814$	42.4222	1.48690
$815$	5.69722	0.199565
$816$	−12.9083	−0.451882
$817$	−25.5778	−0.894854
$818$	15.0917	0.527668
$819$	0.724981	0.0253329
$820$	−9.90833	−0.346014
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	22.8167	0.795822
$823$	−0.788897	−0.0274992	−0.0137496	−	0.999905i	$-0.504377\pi$
$823$	−0.788897	−0.0274992	−0.0137496	+	0.999905i	$0.504377\pi$
$824$	17.1194	0.596384
$825$	−17.5139	−0.609755
$826$	−3.21110	−0.111729
$827$	35.4500	1.23272	0.616358	−	0.787466i	$-0.288607\pi$
$827$	35.4500	1.23272	0.616358	+	0.787466i	$0.288607\pi$
$828$	−7.90833	−0.274833
$829$	16.7889	0.583103	0.291551	−	0.956555i	$-0.405829\pi$
$829$	16.7889	0.583103	0.291551	+	0.956555i	$0.405829\pi$
$830$	3.21110	0.111459
$831$	−42.2389	−1.46525
$832$	−0.302776	−0.0104969
$833$	27.0000	0.935495
$834$	17.8167	0.616940
$835$	21.2111	0.734040
$836$	26.0278	0.900189
$837$	47.1472	1.62965
$838$	39.6333	1.36911
$839$	−22.1833	−0.765854	−0.382927	−	0.923779i	$-0.625084\pi$
$839$	−22.1833	−0.765854	−0.382927	+	0.923779i	$0.625084\pi$
$840$	1.00000	0.0345033
$841$	−7.78890	−0.268583
$842$	−34.3028	−1.18215
$843$	−64.0555	−2.20619
$844$	−7.21110	−0.248216
$845$	−12.9083	−0.444060
$846$	−36.4222	−1.25222
$847$	−5.18335	−0.178102
$848$	3.21110	0.110270
$849$	6.60555	0.226702
$850$	3.90833	0.134055
$851$	−8.00000	−0.274236
$852$	−41.9361	−1.43671
$853$	10.7250	0.367216	0.183608	−	0.983000i	$-0.441222\pi$
$853$	10.7250	0.367216	0.183608	+	0.983000i	$0.441222\pi$
$854$	−1.97224	−0.0674888
$855$	−38.8167	−1.32750
$856$	−4.60555	−0.157415
$857$	−33.6333	−1.14889	−0.574446	−	0.818543i	$-0.694782\pi$
$857$	−33.6333	−1.14889	−0.574446	+	0.818543i	$0.694782\pi$
$858$	−5.30278	−0.181034
$859$	−14.1833	−0.483930	−0.241965	−	0.970285i	$-0.577792\pi$
$859$	−14.1833	−0.483930	−0.241965	+	0.970285i	$0.577792\pi$
$860$	5.21110	0.177697
$861$	9.90833	0.337675
$862$	−20.2389	−0.689338
$863$	23.4500	0.798246	0.399123	−	0.916897i	$-0.369315\pi$
$863$	23.4500	0.798246	0.399123	+	0.916897i	$0.369315\pi$
$864$	−16.2111	−0.551513
$865$	23.3028	0.792318
$866$	34.9083	1.18623
$867$	−5.69722	−0.193488
$868$	−0.880571	−0.0298885
$869$	−76.4777	−2.59433
$870$	−15.2111	−0.515705
$871$	1.21110	0.0410366
$872$	−19.5139	−0.660823
$873$	21.3305	0.721929
$874$	−4.90833	−0.166027
$875$	−0.302776	−0.0102357
$876$	52.2389	1.76499
$877$	49.1749	1.66052	0.830260	−	0.557376i	$-0.188192\pi$
$877$	49.1749	1.66052	0.830260	+	0.557376i	$0.188192\pi$
$878$	18.3028	0.617689
$879$	29.0278	0.979082
$880$	−5.30278	−0.178757
$881$	−31.2666	−1.05340	−0.526700	−	0.850052i	$-0.676571\pi$
$881$	−31.2666	−1.05340	−0.526700	+	0.850052i	$0.676571\pi$
$882$	54.6333	1.83960
$883$	40.7250	1.37050	0.685252	−	0.728306i	$-0.259692\pi$
$883$	40.7250	1.37050	0.685252	+	0.728306i	$0.259692\pi$
$884$	1.18335	0.0398002
$885$	−35.0278	−1.17745
$886$	−35.5139	−1.19311
$887$	−15.6333	−0.524915	−0.262458	−	0.964944i	$-0.584533\pi$
$887$	−15.6333	−0.524915	−0.262458	+	0.964944i	$0.584533\pi$
$888$	−26.4222	−0.886671
$889$	3.57779	0.119995
$890$	0	0
$891$	−158.111	−5.29692
$892$	−4.00000	−0.133930
$893$	−22.6056	−0.756466
$894$	−32.0278	−1.07117
$895$	16.6056	0.555062
$896$	0.302776	0.0101150
$897$	1.00000	0.0333890
$898$	12.9083	0.430756
$899$	13.3944	0.446730
$900$	7.90833	0.263611
$901$	−12.5500	−0.418102
$902$	−52.5416	−1.74945
$903$	−5.21110	−0.173415
$904$	−12.4222	−0.413156
$905$	−8.11943	−0.269899
$906$	6.30278	0.209396
$907$	−30.6611	−1.01808	−0.509042	−	0.860742i	$-0.670000\pi$
$907$	−30.6611	−1.01808	−0.509042	+	0.860742i	$0.670000\pi$
$908$	−7.39445	−0.245393
$909$	−36.4222	−1.20805
$910$	−0.0916731	−0.00303893
$911$	−25.8167	−0.855344	−0.427672	−	0.903934i	$-0.640666\pi$
$911$	−25.8167	−0.855344	−0.427672	+	0.903934i	$0.640666\pi$
$912$	−16.2111	−0.536803
$913$	17.0278	0.563536
$914$	3.57779	0.118343
$915$	−21.5139	−0.711227
$916$	2.00000	0.0660819
$917$	−0.972244	−0.0321063
$918$	63.3583	2.09114
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	1.00000	0.0329690
$921$	−50.5416	−1.66540
$922$	−31.8167	−1.04783
$923$	3.84441	0.126540
$924$	5.30278	0.174449
$925$	8.00000	0.263038
$926$	25.6333	0.842363
$927$	−135.386	−4.44666
$928$	−4.60555	−0.151185
$929$	−57.6333	−1.89089	−0.945444	−	0.325785i	$-0.894371\pi$
$929$	−57.6333	−1.89089	−0.945444	+	0.325785i	$0.894371\pi$
$930$	−9.60555	−0.314978
$931$	33.9083	1.11130
$932$	4.18335	0.137030
$933$	−21.2111	−0.694420
$934$	−19.8167	−0.648421
$935$	20.7250	0.677779
$936$	2.39445	0.0782650
$937$	−44.9638	−1.46890	−0.734452	−	0.678660i	$-0.762561\pi$
$937$	−44.9638	−1.46890	−0.734452	+	0.678660i	$0.762561\pi$
$938$	−1.21110	−0.0395439
$939$	−42.0278	−1.37152
$940$	4.60555	0.150217
$941$	−20.9361	−0.682497	−0.341248	−	0.939973i	$-0.610850\pi$
$941$	−20.9361	−0.682497	−0.341248	+	0.939973i	$0.610850\pi$
$942$	37.6333	1.22616
$943$	9.90833	0.322660
$944$	−10.6056	−0.345181
$945$	−4.90833	−0.159668
$946$	27.6333	0.898436
$947$	41.9361	1.36274	0.681370	−	0.731939i	$-0.261385\pi$
$947$	41.9361	1.36274	0.681370	+	0.731939i	$0.261385\pi$
$948$	47.6333	1.54706
$949$	−4.78890	−0.155454
$950$	4.90833	0.159247
$951$	−48.6333	−1.57704
$952$	−1.18335	−0.0383525
$953$	−1.66947	−0.0540794	−0.0270397	−	0.999634i	$-0.508608\pi$
$953$	−1.66947	−0.0540794	−0.0270397	+	0.999634i	$0.508608\pi$
$954$	−25.3944	−0.822176
$955$	−1.39445	−0.0451233
$956$	−9.21110	−0.297908
$957$	−80.6611	−2.60740
$958$	30.0000	0.969256
$959$	2.09167	0.0675436
$960$	3.30278	0.106597
$961$	−22.5416	−0.727150
$962$	2.42221	0.0780950
$963$	36.4222	1.17369
$964$	14.4222	0.464508
$965$	3.81665	0.122862
$966$	−1.00000	−0.0321745
$967$	−5.39445	−0.173474	−0.0867369	−	0.996231i	$-0.527644\pi$
$967$	−5.39445	−0.173474	−0.0867369	+	0.996231i	$0.527644\pi$
$968$	−17.1194	−0.550239
$969$	63.3583	2.03536
$970$	−2.69722	−0.0866027
$971$	−27.9083	−0.895621	−0.447810	−	0.894129i	$-0.647796\pi$
$971$	−27.9083	−0.895621	−0.447810	+	0.894129i	$0.647796\pi$
$972$	49.8444	1.59876
$973$	1.63331	0.0523614
$974$	11.8167	0.378630
$975$	−1.00000	−0.0320256
$976$	−6.51388	−0.208504
$977$	−11.5139	−0.368362	−0.184181	−	0.982892i	$-0.558963\pi$
$977$	−11.5139	−0.368362	−0.184181	+	0.982892i	$0.558963\pi$
$978$	−18.8167	−0.601690
$979$	0	0
$980$	−6.90833	−0.220678
$981$	154.322	4.92713
$982$	25.8167	0.823843
$983$	−19.5416	−0.623281	−0.311641	−	0.950200i	$-0.600879\pi$
$983$	−19.5416	−0.623281	−0.311641	+	0.950200i	$0.600879\pi$
$984$	32.7250	1.04323
$985$	0.697224	0.0222154
$986$	18.0000	0.573237
$987$	−4.60555	−0.146596
$988$	1.48612	0.0472798
$989$	−5.21110	−0.165703
$990$	41.9361	1.33282
$991$	24.3305	0.772885	0.386442	−	0.922314i	$-0.373704\pi$
$991$	24.3305	0.772885	0.386442	+	0.922314i	$0.373704\pi$
$992$	−2.90833	−0.0923395
$993$	31.0278	0.984636
$994$	−3.84441	−0.121937
$995$	8.42221	0.267002
$996$	−10.6056	−0.336050
$997$	−31.2111	−0.988466	−0.494233	−	0.869330i	$-0.664551\pi$
$997$	−31.2111	−0.988466	−0.494233	+	0.869330i	$0.664551\pi$
$998$	−11.6333	−0.368246
$999$	129.689	4.10317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.a.b.1.2	✓	2
3.2	odd	2		2070.2.a.w.1.1		2
4.3	odd	2		1840.2.a.j.1.1		2
5.2	odd	4		1150.2.b.f.599.1		4
5.3	odd	4		1150.2.b.f.599.4		4
5.4	even	2		1150.2.a.m.1.1		2
8.3	odd	2		7360.2.a.bu.1.2		2
8.5	even	2		7360.2.a.bc.1.1		2
20.19	odd	2		9200.2.a.ca.1.2		2
23.22	odd	2		5290.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.b.1.2	✓	2	1.1	even	1	trivial
1150.2.a.m.1.1		2	5.4	even	2
1150.2.b.f.599.1		4	5.2	odd	4
1150.2.b.f.599.4		4	5.3	odd	4
1840.2.a.j.1.1		2	4.3	odd	2
2070.2.a.w.1.1		2	3.2	odd	2
5290.2.a.j.1.2		2	23.22	odd	2
7360.2.a.bc.1.1		2	8.5	even	2
7360.2.a.bu.1.2		2	8.3	odd	2
9200.2.a.ca.1.2		2	20.19	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.30278 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.30278 q^{6} -0.302776 q^{7} -1.00000 q^{8} +7.90833 q^{9} -1.00000 q^{10} -5.30278 q^{11} +3.30278 q^{12} -0.302776 q^{13} +0.302776 q^{14} +3.30278 q^{15} +1.00000 q^{16} -3.90833 q^{17} -7.90833 q^{18} -4.90833 q^{19} +1.00000 q^{20} -1.00000 q^{21} +5.30278 q^{22} -1.00000 q^{23} -3.30278 q^{24} +1.00000 q^{25} +0.302776 q^{26} +16.2111 q^{27} -0.302776 q^{28} +4.60555 q^{29} -3.30278 q^{30} +2.90833 q^{31} -1.00000 q^{32} -17.5139 q^{33} +3.90833 q^{34} -0.302776 q^{35} +7.90833 q^{36} +8.00000 q^{37} +4.90833 q^{38} -1.00000 q^{39} -1.00000 q^{40} -9.90833 q^{41} +1.00000 q^{42} +5.21110 q^{43} -5.30278 q^{44} +7.90833 q^{45} +1.00000 q^{46} +4.60555 q^{47} +3.30278 q^{48} -6.90833 q^{49} -1.00000 q^{50} -12.9083 q^{51} -0.302776 q^{52} +3.21110 q^{53} -16.2111 q^{54} -5.30278 q^{55} +0.302776 q^{56} -16.2111 q^{57} -4.60555 q^{58} -10.6056 q^{59} +3.30278 q^{60} -6.51388 q^{61} -2.90833 q^{62} -2.39445 q^{63} +1.00000 q^{64} -0.302776 q^{65} +17.5139 q^{66} -4.00000 q^{67} -3.90833 q^{68} -3.30278 q^{69} +0.302776 q^{70} -12.6972 q^{71} -7.90833 q^{72} +15.8167 q^{73} -8.00000 q^{74} +3.30278 q^{75} -4.90833 q^{76} +1.60555 q^{77} +1.00000 q^{78} +14.4222 q^{79} +1.00000 q^{80} +29.8167 q^{81} +9.90833 q^{82} -3.21110 q^{83} -1.00000 q^{84} -3.90833 q^{85} -5.21110 q^{86} +15.2111 q^{87} +5.30278 q^{88} -7.90833 q^{90} +0.0916731 q^{91} -1.00000 q^{92} +9.60555 q^{93} -4.60555 q^{94} -4.90833 q^{95} -3.30278 q^{96} +2.69722 q^{97} +6.90833 q^{98} -41.9361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 2 q^{8} + 5 q^{9} - 2 q^{10} - 7 q^{11} + 3 q^{12} + 3 q^{13} - 3 q^{14} + 3 q^{15} + 2 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} + 2 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 2 * q^8 + 5 * q^9 - 2 * q^10 - 7 * q^11 + 3 * q^12 + 3 * q^13 - 3 * q^14 + 3 * q^15 + 2 * q^16 + 3 * q^17 - 5 * q^18 + q^19 + 2 * q^20 - 2 * q^21 + 7 * q^22 - 2 * q^23 - 3 * q^24 + 2 * q^25 - 3 * q^26 + 18 * q^27 + 3 * q^28 + 2 * q^29 - 3 * q^30 - 5 * q^31 - 2 * q^32 - 17 * q^33 - 3 * q^34 + 3 * q^35 + 5 * q^36 + 16 * q^37 - q^38 - 2 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - 4 * q^43 - 7 * q^44 + 5 * q^45 + 2 * q^46 + 2 * q^47 + 3 * q^48 - 3 * q^49 - 2 * q^50 - 15 * q^51 + 3 * q^52 - 8 * q^53 - 18 * q^54 - 7 * q^55 - 3 * q^56 - 18 * q^57 - 2 * q^58 - 14 * q^59 + 3 * q^60 + 5 * q^61 + 5 * q^62 - 12 * q^63 + 2 * q^64 + 3 * q^65 + 17 * q^66 - 8 * q^67 + 3 * q^68 - 3 * q^69 - 3 * q^70 - 29 * q^71 - 5 * q^72 + 10 * q^73 - 16 * q^74 + 3 * q^75 + q^76 - 4 * q^77 + 2 * q^78 + 2 * q^80 + 38 * q^81 + 9 * q^82 + 8 * q^83 - 2 * q^84 + 3 * q^85 + 4 * q^86 + 16 * q^87 + 7 * q^88 - 5 * q^90 + 11 * q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 + q^95 - 3 * q^96 + 9 * q^97 + 3 * q^98 - 37 * q^99

Introduction

L-functions

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Database

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