LMFDB - Embedded newform 4235.2.a.ba.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.580017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 4x^{2} + 6x + 3 $ x^5 - 7x^3 - 4x^2 + 6*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.941569$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.941569 q^{2} +1.53997 q^{3} -1.11345 q^{4} -1.00000 q^{5} +1.44999 q^{6} -1.00000 q^{7} -2.93153 q^{8} -0.628495 q^{9} +O(q^{10})$	\(q+0.941569 q^{2} +1.53997 q^{3} -1.11345 q^{4} -1.00000 q^{5} +1.44999 q^{6} -1.00000 q^{7} -2.93153 q^{8} -0.628495 q^{9} -0.941569 q^{10} -1.71467 q^{12} -1.39156 q^{13} -0.941569 q^{14} -1.53997 q^{15} -0.533340 q^{16} +2.87651 q^{17} -0.591771 q^{18} +1.39301 q^{19} +1.11345 q^{20} -1.53997 q^{21} +6.46428 q^{23} -4.51446 q^{24} +1.00000 q^{25} -1.31025 q^{26} -5.58777 q^{27} +1.11345 q^{28} +2.72955 q^{29} -1.44999 q^{30} -2.10106 q^{31} +5.36088 q^{32} +2.70843 q^{34} +1.00000 q^{35} +0.699796 q^{36} -6.54173 q^{37} +1.31162 q^{38} -2.14296 q^{39} +2.93153 q^{40} +7.54422 q^{41} -1.44999 q^{42} -5.24119 q^{43} +0.628495 q^{45} +6.08657 q^{46} +8.87972 q^{47} -0.821328 q^{48} +1.00000 q^{49} +0.941569 q^{50} +4.42974 q^{51} +1.54943 q^{52} +7.31070 q^{53} -5.26127 q^{54} +2.93153 q^{56} +2.14520 q^{57} +2.57006 q^{58} -8.87651 q^{59} +1.71467 q^{60} +1.70038 q^{61} -1.97829 q^{62} +0.628495 q^{63} +6.11432 q^{64} +1.39156 q^{65} +0.00145621 q^{67} -3.20284 q^{68} +9.95479 q^{69} +0.941569 q^{70} +6.94923 q^{71} +1.84245 q^{72} -0.0957409 q^{73} -6.15949 q^{74} +1.53997 q^{75} -1.55105 q^{76} -2.01774 q^{78} +9.24782 q^{79} +0.533340 q^{80} -6.71951 q^{81} +7.10340 q^{82} +13.2464 q^{83} +1.71467 q^{84} -2.87651 q^{85} -4.93494 q^{86} +4.20343 q^{87} +0.516504 q^{89} +0.591771 q^{90} +1.39156 q^{91} -7.19764 q^{92} -3.23557 q^{93} +8.36088 q^{94} -1.39301 q^{95} +8.25558 q^{96} +0.474323 q^{97} +0.941569 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.941569	0.665790	0.332895	−	0.942964i	$-0.391975\pi$
$2$	0.941569	0.665790	0.332895	+	0.942964i	$0.391975\pi$
$3$	1.53997	0.889102	0.444551	−	0.895754i	$-0.353363\pi$
$3$	1.53997	0.889102	0.444551	+	0.895754i	$0.353363\pi$
$4$	−1.11345	−0.556724
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.44999	0.591955
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.93153	−1.03645
$9$	−0.628495	−0.209498
$10$	−0.941569	−0.297750
$11$	0	0
$11$	0	0
$12$	−1.71467	−0.494984
$13$	−1.39156	−0.385948	−0.192974	−	0.981204i	$-0.561813\pi$
$13$	−1.39156	−0.385948	−0.192974	+	0.981204i	$0.561813\pi$
$14$	−0.941569	−0.251645
$15$	−1.53997	−0.397618
$16$	−0.533340	−0.133335
$17$	2.87651	0.697656	0.348828	−	0.937187i	$-0.386580\pi$
$17$	2.87651	0.697656	0.348828	+	0.937187i	$0.386580\pi$
$18$	−0.591771	−0.139482
$19$	1.39301	0.319579	0.159790	−	0.987151i	$-0.448918\pi$
$19$	1.39301	0.319579	0.159790	+	0.987151i	$0.448918\pi$
$20$	1.11345	0.248974
$21$	−1.53997	−0.336049
$22$	0	0
$23$	6.46428	1.34790	0.673948	−	0.738779i	$-0.264597\pi$
$23$	6.46428	1.34790	0.673948	+	0.738779i	$0.264597\pi$
$24$	−4.51446	−0.921510
$25$	1.00000	0.200000
$26$	−1.31025	−0.256961
$27$	−5.58777	−1.07537
$28$	1.11345	0.210422
$29$	2.72955	0.506865	0.253433	−	0.967353i	$-0.418440\pi$
$29$	2.72955	0.506865	0.253433	+	0.967353i	$0.418440\pi$
$30$	−1.44999	−0.264730
$31$	−2.10106	−0.377361	−0.188681	−	0.982038i	$-0.560421\pi$
$31$	−2.10106	−0.377361	−0.188681	+	0.982038i	$0.560421\pi$
$32$	5.36088	0.947678
$33$	0	0
$34$	2.70843	0.464492
$35$	1.00000	0.169031
$36$	0.699796	0.116633
$37$	−6.54173	−1.07545	−0.537727	−	0.843119i	$-0.680717\pi$
$37$	−6.54173	−1.07545	−0.537727	+	0.843119i	$0.680717\pi$
$38$	1.31162	0.212773
$39$	−2.14296	−0.343147
$40$	2.93153	0.463515
$41$	7.54422	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$41$	7.54422	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$42$	−1.44999	−0.223738
$43$	−5.24119	−0.799273	−0.399637	−	0.916674i	$-0.630864\pi$
$43$	−5.24119	−0.799273	−0.399637	+	0.916674i	$0.630864\pi$
$44$	0	0
$45$	0.628495	0.0936904
$46$	6.08657	0.897415
$47$	8.87972	1.29524	0.647620	−	0.761963i	$-0.275764\pi$
$47$	8.87972	1.29524	0.647620	+	0.761963i	$0.275764\pi$
$48$	−0.821328	−0.118548
$49$	1.00000	0.142857
$50$	0.941569	0.133158
$51$	4.42974	0.620287
$52$	1.54943	0.214867
$53$	7.31070	1.00420	0.502101	−	0.864809i	$-0.332561\pi$
$53$	7.31070	1.00420	0.502101	+	0.864809i	$0.332561\pi$
$54$	−5.26127	−0.715969
$55$	0	0
$56$	2.93153	0.391742
$57$	2.14520	0.284138
$58$	2.57006	0.337466
$59$	−8.87651	−1.15562	−0.577812	−	0.816170i	$-0.696093\pi$
$59$	−8.87651	−1.15562	−0.577812	+	0.816170i	$0.696093\pi$
$60$	1.71467	0.221364
$61$	1.70038	0.217712	0.108856	−	0.994058i	$-0.465281\pi$
$61$	1.70038	0.217712	0.108856	+	0.994058i	$0.465281\pi$
$62$	−1.97829	−0.251243
$63$	0.628495	0.0791829
$64$	6.11432	0.764290
$65$	1.39156	0.172601
$66$	0	0
$67$	0.00145621	0.000177904 0	8.89522e−5	−	1.00000i	$-0.499972\pi$
$67$	0.00145621	0.000177904 0	8.89522e−5		1.00000i	$0.499972\pi$
$68$	−3.20284	−0.388402
$69$	9.95479	1.19842
$70$	0.941569	0.112539
$71$	6.94923	0.824722	0.412361	−	0.911020i	$-0.364704\pi$
$71$	6.94923	0.824722	0.412361	+	0.911020i	$0.364704\pi$
$72$	1.84245	0.217135
$73$	−0.0957409	−0.0112056	−0.00560281	−	0.999984i	$-0.501783\pi$
$73$	−0.0957409	−0.0112056	−0.00560281	+	0.999984i	$0.501783\pi$
$74$	−6.15949	−0.716026
$75$	1.53997	0.177820
$76$	−1.55105	−0.177917
$77$	0	0
$78$	−2.01774	−0.228464
$79$	9.24782	1.04046	0.520230	−	0.854026i	$-0.325846\pi$
$79$	9.24782	1.04046	0.520230	+	0.854026i	$0.325846\pi$
$80$	0.533340	0.0596293
$81$	−6.71951	−0.746612
$82$	7.10340	0.784440
$83$	13.2464	1.45398	0.726988	−	0.686650i	$-0.240919\pi$
$83$	13.2464	1.45398	0.726988	+	0.686650i	$0.240919\pi$
$84$	1.71467	0.187086
$85$	−2.87651	−0.312001
$86$	−4.93494	−0.532148
$87$	4.20343	0.450655
$88$	0	0
$89$	0.516504	0.0547493	0.0273746	−	0.999625i	$-0.491285\pi$
$89$	0.516504	0.0547493	0.0273746	+	0.999625i	$0.491285\pi$
$90$	0.591771	0.0623782
$91$	1.39156	0.145875
$92$	−7.19764	−0.750405
$93$	−3.23557	−0.335513
$94$	8.36088	0.862358
$95$	−1.39301	−0.142920
$96$	8.25558	0.842582
$97$	0.474323	0.0481602	0.0240801	−	0.999710i	$-0.492334\pi$
$97$	0.474323	0.0481602	0.0240801	+	0.999710i	$0.492334\pi$
$98$	0.941569	0.0951129
$99$	0	0
$100$	−1.11345	−0.111345
$101$	9.70989	0.966170	0.483085	−	0.875573i	$-0.339516\pi$
$101$	9.70989	0.966170	0.483085	+	0.875573i	$0.339516\pi$
$102$	4.17090	0.412981
$103$	0.722725	0.0712122	0.0356061	−	0.999366i	$-0.488664\pi$
$103$	0.722725	0.0712122	0.0356061	+	0.999366i	$0.488664\pi$
$104$	4.07939	0.400017
$105$	1.53997	0.150286
$106$	6.88353	0.668587
$107$	12.0970	1.16946	0.584732	−	0.811227i	$-0.301200\pi$
$107$	12.0970	1.16946	0.584732	+	0.811227i	$0.301200\pi$
$108$	6.22169	0.598682
$109$	2.06951	0.198223	0.0991115	−	0.995076i	$-0.468400\pi$
$109$	2.06951	0.198223	0.0991115	+	0.995076i	$0.468400\pi$
$110$	0	0
$111$	−10.0741	−0.956187
$112$	0.533340	0.0503959
$113$	18.3350	1.72481	0.862404	−	0.506220i	$-0.168958\pi$
$113$	18.3350	1.72481	0.862404	+	0.506220i	$0.168958\pi$
$114$	2.01985	0.189176
$115$	−6.46428	−0.602797
$116$	−3.03921	−0.282184
$117$	0.874586	0.0808555
$118$	−8.35785	−0.769402
$119$	−2.87651	−0.263689
$120$	4.51446	0.412112
$121$	0	0
$122$	1.60103	0.144950
$123$	11.6179	1.04755
$124$	2.33942	0.210086
$125$	−1.00000	−0.0894427
$126$	0.591771	0.0527192
$127$	−15.6786	−1.39125	−0.695625	−	0.718405i	$-0.744872\pi$
$127$	−15.6786	−1.39125	−0.695625	+	0.718405i	$0.744872\pi$
$128$	−4.96470	−0.438821
$129$	−8.07127	−0.710635
$130$	1.31025	0.114916
$131$	14.8387	1.29646	0.648230	−	0.761445i	$-0.275510\pi$
$131$	14.8387	1.29646	0.648230	+	0.761445i	$0.275510\pi$
$132$	0	0
$133$	−1.39301	−0.120790
$134$	0.00137112	0.000118447 0
$135$	5.58777	0.480919
$136$	−8.43256	−0.723086
$137$	13.0351	1.11366	0.556830	−	0.830626i	$-0.312017\pi$
$137$	13.0351	1.11366	0.556830	+	0.830626i	$0.312017\pi$
$138$	9.37313	0.797894
$139$	18.9218	1.60492	0.802462	−	0.596703i	$-0.203523\pi$
$139$	18.9218	1.60492	0.802462	+	0.596703i	$0.203523\pi$
$140$	−1.11345	−0.0941035
$141$	13.6745	1.15160
$142$	6.54318	0.549092
$143$	0	0
$144$	0.335202	0.0279335
$145$	−2.72955	−0.226677
$146$	−0.0901467	−0.00746060
$147$	1.53997	0.127015
$148$	7.28387	0.598730
$149$	−5.13736	−0.420869	−0.210435	−	0.977608i	$-0.567488\pi$
$149$	−5.13736	−0.420869	−0.210435	+	0.977608i	$0.567488\pi$
$150$	1.44999	0.118391
$151$	9.51339	0.774189	0.387094	−	0.922040i	$-0.373479\pi$
$151$	9.51339	0.774189	0.387094	+	0.922040i	$0.373479\pi$
$152$	−4.08365	−0.331228
$153$	−1.80787	−0.146158
$154$	0	0
$155$	2.10106	0.168761
$156$	2.38607	0.191038
$157$	−4.94602	−0.394735	−0.197368	−	0.980330i	$-0.563239\pi$
$157$	−4.94602	−0.394735	−0.197368	+	0.980330i	$0.563239\pi$
$158$	8.70746	0.692728
$159$	11.2582	0.892837
$160$	−5.36088	−0.423814
$161$	−6.46428	−0.509457
$162$	−6.32688	−0.497087
$163$	−19.1488	−1.49985	−0.749926	−	0.661522i	$-0.769911\pi$
$163$	−19.1488	−1.49985	−0.749926	+	0.661522i	$0.769911\pi$
$164$	−8.40009	−0.655937
$165$	0	0
$166$	12.4724	0.968043
$167$	−11.7906	−0.912382	−0.456191	−	0.889882i	$-0.650787\pi$
$167$	−11.7906	−0.912382	−0.456191	+	0.889882i	$0.650787\pi$
$168$	4.51446	0.348298
$169$	−11.0636	−0.851044
$170$	−2.70843	−0.207727
$171$	−0.875501	−0.0669513
$172$	5.83579	0.444974
$173$	22.0859	1.67916	0.839582	−	0.543233i	$-0.182800\pi$
$173$	22.0859	1.67916	0.839582	+	0.543233i	$0.182800\pi$
$174$	3.95782	0.300042
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−13.6696	−1.02747
$178$	0.486324	0.0364515
$179$	−14.5651	−1.08865	−0.544325	−	0.838875i	$-0.683214\pi$
$179$	−14.5651	−1.08865	−0.544325	+	0.838875i	$0.683214\pi$
$180$	−0.699796	−0.0521597
$181$	4.14710	0.308252	0.154126	−	0.988051i	$-0.450744\pi$
$181$	4.14710	0.308252	0.154126	+	0.988051i	$0.450744\pi$
$182$	1.31025	0.0971220
$183$	2.61854	0.193568
$184$	−18.9502	−1.39703
$185$	6.54173	0.480957
$186$	−3.04651	−0.223381
$187$	0	0
$188$	−9.88711	−0.721091
$189$	5.58777	0.406450
$190$	−1.31162	−0.0951548
$191$	−13.3933	−0.969106	−0.484553	−	0.874762i	$-0.661018\pi$
$191$	−13.3933	−0.969106	−0.484553	+	0.874762i	$0.661018\pi$
$192$	9.41586	0.679531
$193$	14.7344	1.06060	0.530302	−	0.847809i	$-0.322078\pi$
$193$	14.7344	1.06060	0.530302	+	0.847809i	$0.322078\pi$
$194$	0.446608	0.0320646
$195$	2.14296	0.153460
$196$	−1.11345	−0.0795320
$197$	3.94112	0.280793	0.140397	−	0.990095i	$-0.455162\pi$
$197$	3.94112	0.280793	0.140397	+	0.990095i	$0.455162\pi$
$198$	0	0
$199$	−10.2444	−0.726206	−0.363103	−	0.931749i	$-0.618283\pi$
$199$	−10.2444	−0.726206	−0.363103	+	0.931749i	$0.618283\pi$
$200$	−2.93153	−0.207290
$201$	0.00224252	0.000158175 0
$202$	9.14253	0.643266
$203$	−2.72955	−0.191577
$204$	−4.93228	−0.345329
$205$	−7.54422	−0.526911
$206$	0.680496	0.0474124
$207$	−4.06277	−0.282382
$208$	0.742174	0.0514605
$209$	0	0
$210$	1.44999	0.100059
$211$	8.32284	0.572968	0.286484	−	0.958085i	$-0.407514\pi$
$211$	8.32284	0.572968	0.286484	+	0.958085i	$0.407514\pi$
$212$	−8.14007	−0.559063
$213$	10.7016	0.733262
$214$	11.3902	0.778617
$215$	5.24119	0.357446
$216$	16.3807	1.11457
$217$	2.10106	0.142629
$218$	1.94859	0.131975
$219$	−0.147438	−0.00996294
$220$	0	0
$221$	−4.00283	−0.269259
$222$	−9.48543	−0.636620
$223$	20.0014	1.33939	0.669695	−	0.742636i	$-0.266425\pi$
$223$	20.0014	1.33939	0.669695	+	0.742636i	$0.266425\pi$
$224$	−5.36088	−0.358189
$225$	−0.628495	−0.0418996
$226$	17.2636	1.14836
$227$	−13.2057	−0.876494	−0.438247	−	0.898854i	$-0.644401\pi$
$227$	−13.2057	−0.876494	−0.438247	+	0.898854i	$0.644401\pi$
$228$	−2.38856	−0.158187
$229$	−25.7475	−1.70144	−0.850720	−	0.525618i	$-0.823834\pi$
$229$	−25.7475	−1.70144	−0.850720	+	0.525618i	$0.823834\pi$
$230$	−6.08657	−0.401336
$231$	0	0
$232$	−8.00176	−0.525341
$233$	−11.9028	−0.779776	−0.389888	−	0.920862i	$-0.627486\pi$
$233$	−11.9028	−0.779776	−0.389888	+	0.920862i	$0.627486\pi$
$234$	0.823483	0.0538328
$235$	−8.87972	−0.579249
$236$	9.88353	0.643363
$237$	14.2414	0.925075
$238$	−2.70843	−0.175562
$239$	−17.4196	−1.12678	−0.563390	−	0.826191i	$-0.690503\pi$
$239$	−17.4196	−1.12678	−0.563390	+	0.826191i	$0.690503\pi$
$240$	0.821328	0.0530165
$241$	2.30561	0.148517	0.0742587	−	0.997239i	$-0.476341\pi$
$241$	2.30561	0.148517	0.0742587	+	0.997239i	$0.476341\pi$
$242$	0	0
$243$	6.41547	0.411553
$244$	−1.89329	−0.121205
$245$	−1.00000	−0.0638877
$246$	10.9390	0.697447
$247$	−1.93846	−0.123341
$248$	6.15931	0.391117
$249$	20.3990	1.29273
$250$	−0.941569	−0.0595501
$251$	−9.53947	−0.602126	−0.301063	−	0.953604i	$-0.597341\pi$
$251$	−9.53947	−0.602126	−0.301063	+	0.953604i	$0.597341\pi$
$252$	−0.699796	−0.0440830
$253$	0	0
$254$	−14.7625	−0.926280
$255$	−4.42974	−0.277401
$256$	−16.9032	−1.05645
$257$	−29.4161	−1.83493	−0.917463	−	0.397821i	$-0.869767\pi$
$257$	−29.4161	−1.83493	−0.917463	+	0.397821i	$0.869767\pi$
$258$	−7.59966	−0.473134
$259$	6.54173	0.406483
$260$	−1.54943	−0.0960913
$261$	−1.71551	−0.106187
$262$	13.9716	0.863170
$263$	−3.05267	−0.188236	−0.0941179	−	0.995561i	$-0.530003\pi$
$263$	−3.05267	−0.188236	−0.0941179	+	0.995561i	$0.530003\pi$
$264$	0	0
$265$	−7.31070	−0.449092
$266$	−1.31162	−0.0804205
$267$	0.795400	0.0486777
$268$	−0.00162141	−9.90436e−5 0
$269$	−2.00386	−0.122178	−0.0610888	−	0.998132i	$-0.519457\pi$
$269$	−2.00386	−0.122178	−0.0610888	+	0.998132i	$0.519457\pi$
$270$	5.26127	0.320191
$271$	23.7039	1.43991	0.719955	−	0.694021i	$-0.244163\pi$
$271$	23.7039	1.43991	0.719955	+	0.694021i	$0.244163\pi$
$272$	−1.53416	−0.0930221
$273$	2.14296	0.129698
$274$	12.2734	0.741464
$275$	0	0
$276$	−11.0841	−0.667187
$277$	18.9545	1.13886	0.569432	−	0.822038i	$-0.307163\pi$
$277$	18.9545	1.13886	0.569432	+	0.822038i	$0.307163\pi$
$278$	17.8162	1.06854
$279$	1.32050	0.0790565
$280$	−2.93153	−0.175192
$281$	−1.50221	−0.0896144	−0.0448072	−	0.998996i	$-0.514267\pi$
$281$	−1.50221	−0.0896144	−0.0448072	+	0.998996i	$0.514267\pi$
$282$	12.8755	0.766724
$283$	−1.69585	−0.100808	−0.0504038	−	0.998729i	$-0.516051\pi$
$283$	−1.69585	−0.100808	−0.0504038	+	0.998729i	$0.516051\pi$
$284$	−7.73760	−0.459142
$285$	−2.14520	−0.127071
$286$	0	0
$287$	−7.54422	−0.445321
$288$	−3.36928	−0.198537
$289$	−8.72569	−0.513276
$290$	−2.57006	−0.150919
$291$	0.730443	0.0428193
$292$	0.106602	0.00623844
$293$	−8.76253	−0.511912	−0.255956	−	0.966688i	$-0.582390\pi$
$293$	−8.76253	−0.511912	−0.255956	+	0.966688i	$0.582390\pi$
$294$	1.44999	0.0845650
$295$	8.87651	0.516810
$296$	19.1772	1.11465
$297$	0	0
$298$	−4.83718	−0.280210
$299$	−8.99541	−0.520218
$300$	−1.71467	−0.0989968
$301$	5.24119	0.302097
$302$	8.95752	0.515447
$303$	14.9529	0.859023
$304$	−0.742950	−0.0426111
$305$	−1.70038	−0.0973636
$306$	−1.70224	−0.0973103
$307$	15.6989	0.895985	0.447992	−	0.894037i	$-0.352139\pi$
$307$	15.6989	0.895985	0.447992	+	0.894037i	$0.352139\pi$
$308$	0	0
$309$	1.11297	0.0633149
$310$	1.97829	0.112359
$311$	4.53471	0.257140	0.128570	−	0.991700i	$-0.458961\pi$
$311$	4.53471	0.257140	0.128570	+	0.991700i	$0.458961\pi$
$312$	6.28213	0.355656
$313$	−2.68654	−0.151852	−0.0759261	−	0.997113i	$-0.524191\pi$
$313$	−2.68654	−0.151852	−0.0759261	+	0.997113i	$0.524191\pi$
$314$	−4.65702	−0.262811
$315$	−0.628495	−0.0354117
$316$	−10.2970	−0.579249
$317$	−14.0343	−0.788244	−0.394122	−	0.919058i	$-0.628951\pi$
$317$	−14.0343	−0.788244	−0.394122	+	0.919058i	$0.628951\pi$
$318$	10.6004	0.594442
$319$	0	0
$320$	−6.11432	−0.341801
$321$	18.6290	1.03977
$322$	−6.08657	−0.339191
$323$	4.00702	0.222956
$324$	7.48182	0.415657
$325$	−1.39156	−0.0771897
$326$	−18.0299	−0.998586
$327$	3.18698	0.176240
$328$	−22.1161	−1.22116
$329$	−8.87972	−0.489555
$330$	0	0
$331$	21.5349	1.18367	0.591833	−	0.806060i	$-0.298404\pi$
$331$	21.5349	1.18367	0.591833	+	0.806060i	$0.298404\pi$
$332$	−14.7491	−0.809463
$333$	4.11144	0.225306
$334$	−11.1016	−0.607455
$335$	−0.00145621	−7.95613e−5 0
$336$	0.821328	0.0448071
$337$	−26.0578	−1.41946	−0.709730	−	0.704474i	$-0.751183\pi$
$337$	−26.0578	−1.41946	−0.709730	+	0.704474i	$0.751183\pi$
$338$	−10.4171	−0.566616
$339$	28.2353	1.53353
$340$	3.20284	0.173698
$341$	0	0
$342$	−0.824345	−0.0445755
$343$	−1.00000	−0.0539949
$344$	15.3647	0.828408
$345$	−9.95479	−0.535948
$346$	20.7954	1.11797
$347$	29.2251	1.56888	0.784442	−	0.620202i	$-0.212950\pi$
$347$	29.2251	1.56888	0.784442	+	0.620202i	$0.212950\pi$
$348$	−4.68030	−0.250890
$349$	−7.70633	−0.412510	−0.206255	−	0.978498i	$-0.566128\pi$
$349$	−7.70633	−0.412510	−0.206255	+	0.978498i	$0.566128\pi$
$350$	−0.941569	−0.0503290
$351$	7.77570	0.415036
$352$	0	0
$353$	−22.2765	−1.18566	−0.592829	−	0.805328i	$-0.701989\pi$
$353$	−22.2765	−1.18566	−0.592829	+	0.805328i	$0.701989\pi$
$354$	−12.8708	−0.684077
$355$	−6.94923	−0.368827
$356$	−0.575099	−0.0304802
$357$	−4.42974	−0.234447
$358$	−13.7141	−0.724812
$359$	1.69238	0.0893205	0.0446603	−	0.999002i	$-0.485779\pi$
$359$	1.69238	0.0893205	0.0446603	+	0.999002i	$0.485779\pi$
$360$	−1.84245	−0.0971056
$361$	−17.0595	−0.897869
$362$	3.90478	0.205231
$363$	0	0
$364$	−1.54943	−0.0812120
$365$	0.0957409	0.00501131
$366$	2.46553	0.128876
$367$	−13.2925	−0.693862	−0.346931	−	0.937891i	$-0.612776\pi$
$367$	−13.2925	−0.693862	−0.346931	+	0.937891i	$0.612776\pi$
$368$	−3.44766	−0.179722
$369$	−4.74150	−0.246833
$370$	6.15949	0.320217
$371$	−7.31070	−0.379552
$372$	3.60263	0.186788
$373$	−5.17666	−0.268037	−0.134019	−	0.990979i	$-0.542788\pi$
$373$	−5.17666	−0.268037	−0.134019	+	0.990979i	$0.542788\pi$
$374$	0	0
$375$	−1.53997	−0.0795237
$376$	−26.0311	−1.34245
$377$	−3.79833	−0.195624
$378$	5.26127	0.270611
$379$	20.8034	1.06860	0.534299	−	0.845295i	$-0.320576\pi$
$379$	20.8034	1.06860	0.534299	+	0.845295i	$0.320576\pi$
$380$	1.55105	0.0795670
$381$	−24.1445	−1.23696
$382$	−12.6107	−0.645221
$383$	−5.55781	−0.283991	−0.141996	−	0.989867i	$-0.545352\pi$
$383$	−5.55781	−0.283991	−0.141996	+	0.989867i	$0.545352\pi$
$384$	−7.64548	−0.390157
$385$	0	0
$386$	13.8734	0.706140
$387$	3.29406	0.167446
$388$	−0.528134	−0.0268119
$389$	30.9206	1.56774	0.783869	−	0.620927i	$-0.213244\pi$
$389$	30.9206	1.56774	0.783869	+	0.620927i	$0.213244\pi$
$390$	2.01774	0.102172
$391$	18.5946	0.940368
$392$	−2.93153	−0.148064
$393$	22.8511	1.15268
$394$	3.71084	0.186949
$395$	−9.24782	−0.465308
$396$	0	0
$397$	30.4744	1.52946	0.764732	−	0.644348i	$-0.222871\pi$
$397$	30.4744	1.52946	0.764732	+	0.644348i	$0.222871\pi$
$398$	−9.64581	−0.483501
$399$	−2.14520	−0.107394
$400$	−0.533340	−0.0266670
$401$	−27.1836	−1.35749	−0.678743	−	0.734376i	$-0.737475\pi$
$401$	−27.1836	−1.35749	−0.678743	+	0.734376i	$0.737475\pi$
$402$	0.00211149	0.000105311 0
$403$	2.92374	0.145642
$404$	−10.8115	−0.537890
$405$	6.71951	0.333895
$406$	−2.57006	−0.127550
$407$	0	0
$408$	−12.9859	−0.642897
$409$	12.4138	0.613822	0.306911	−	0.951738i	$-0.400705\pi$
$409$	12.4138	0.613822	0.306911	+	0.951738i	$0.400705\pi$
$410$	−7.10340	−0.350812
$411$	20.0736	0.990158
$412$	−0.804717	−0.0396455
$413$	8.87651	0.436784
$414$	−3.82537	−0.188007
$415$	−13.2464	−0.650238
$416$	−7.45996	−0.365755
$417$	29.1390	1.42694
$418$	0	0
$419$	10.5333	0.514585	0.257292	−	0.966334i	$-0.417170\pi$
$419$	10.5333	0.514585	0.257292	+	0.966334i	$0.417170\pi$
$420$	−1.71467	−0.0836676
$421$	19.6680	0.958560	0.479280	−	0.877662i	$-0.340898\pi$
$421$	19.6680	0.958560	0.479280	+	0.877662i	$0.340898\pi$
$422$	7.83653	0.381476
$423$	−5.58086	−0.271351
$424$	−21.4315	−1.04081
$425$	2.87651	0.139531
$426$	10.0763	0.488198
$427$	−1.70038	−0.0822873
$428$	−13.4694	−0.651068
$429$	0	0
$430$	4.93494	0.237984
$431$	15.7944	0.760788	0.380394	−	0.924824i	$-0.375788\pi$
$431$	15.7944	0.760788	0.380394	+	0.924824i	$0.375788\pi$
$432$	2.98018	0.143384
$433$	7.09301	0.340868	0.170434	−	0.985369i	$-0.445483\pi$
$433$	7.09301	0.340868	0.170434	+	0.985369i	$0.445483\pi$
$434$	1.97829	0.0949611
$435$	−4.20343	−0.201539
$436$	−2.30429	−0.110355
$437$	9.00483	0.430759
$438$	−0.138823	−0.00663323
$439$	−24.5227	−1.17040	−0.585202	−	0.810888i	$-0.698985\pi$
$439$	−24.5227	−1.17040	−0.585202	+	0.810888i	$0.698985\pi$
$440$	0	0
$441$	−0.628495	−0.0299283
$442$	−3.76894	−0.179270
$443$	−10.0332	−0.476693	−0.238346	−	0.971180i	$-0.576605\pi$
$443$	−10.0332	−0.476693	−0.238346	+	0.971180i	$0.576605\pi$
$444$	11.2169	0.532332
$445$	−0.516504	−0.0244846
$446$	18.8327	0.891753
$447$	−7.91138	−0.374195
$448$	−6.11432	−0.288874
$449$	28.3911	1.33986	0.669929	−	0.742425i	$-0.266325\pi$
$449$	28.3911	1.33986	0.669929	+	0.742425i	$0.266325\pi$
$450$	−0.591771	−0.0278964
$451$	0	0
$452$	−20.4150	−0.960242
$453$	14.6503	0.688333
$454$	−12.4341	−0.583561
$455$	−1.39156	−0.0652372
$456$	−6.28870	−0.294496
$457$	−17.9107	−0.837825	−0.418913	−	0.908027i	$-0.637589\pi$
$457$	−17.9107	−0.837825	−0.418913	+	0.908027i	$0.637589\pi$
$458$	−24.2430	−1.13280
$459$	−16.0733	−0.750236
$460$	7.19764	0.335591
$461$	−22.3455	−1.04073	−0.520366	−	0.853943i	$-0.674204\pi$
$461$	−22.3455	−1.04073	−0.520366	+	0.853943i	$0.674204\pi$
$462$	0	0
$463$	−31.7804	−1.47696	−0.738480	−	0.674275i	$-0.764456\pi$
$463$	−31.7804	−1.47696	−0.738480	+	0.674275i	$0.764456\pi$
$464$	−1.45578	−0.0675830
$465$	3.23557	0.150046
$466$	−11.2073	−0.519167
$467$	13.4270	0.621328	0.310664	−	0.950520i	$-0.399449\pi$
$467$	13.4270	0.621328	0.310664	+	0.950520i	$0.399449\pi$
$468$	−0.973806	−0.0450142
$469$	−0.00145621	−6.72415e−5 0
$470$	−8.36088	−0.385658
$471$	−7.61672	−0.350960
$472$	26.0217	1.19775
$473$	0	0
$474$	13.4092	0.615906
$475$	1.39301	0.0639158
$476$	3.20284	0.146802
$477$	−4.59473	−0.210378
$478$	−16.4018	−0.750199
$479$	9.65688	0.441234	0.220617	−	0.975361i	$-0.429193\pi$
$479$	9.65688	0.441234	0.220617	+	0.975361i	$0.429193\pi$
$480$	−8.25558	−0.376814
$481$	9.10319	0.415070
$482$	2.17089	0.0988814
$483$	−9.95479	−0.452959
$484$	0	0
$485$	−0.474323	−0.0215379
$486$	6.04061	0.274008
$487$	−34.1522	−1.54759	−0.773793	−	0.633439i	$-0.781643\pi$
$487$	−34.1522	−1.54759	−0.773793	+	0.633439i	$0.781643\pi$
$488$	−4.98472	−0.225647
$489$	−29.4886	−1.33352
$490$	−0.941569	−0.0425358
$491$	1.54632	0.0697845	0.0348923	−	0.999391i	$-0.488891\pi$
$491$	1.54632	0.0697845	0.0348923	+	0.999391i	$0.488891\pi$
$492$	−12.9359	−0.583195
$493$	7.85159	0.353618
$494$	−1.82519	−0.0821193
$495$	0	0
$496$	1.12058	0.0503155
$497$	−6.94923	−0.311716
$498$	19.2071	0.860689
$499$	−14.9721	−0.670241	−0.335121	−	0.942175i	$-0.608777\pi$
$499$	−14.9721	−0.670241	−0.335121	+	0.942175i	$0.608777\pi$
$500$	1.11345	0.0497949
$501$	−18.1571	−0.811201
$502$	−8.98207	−0.400889
$503$	3.62122	0.161462	0.0807311	−	0.996736i	$-0.474275\pi$
$503$	3.62122	0.161462	0.0807311	+	0.996736i	$0.474275\pi$
$504$	−1.84245	−0.0820692
$505$	−9.70989	−0.432084
$506$	0	0
$507$	−17.0376	−0.756664
$508$	17.4573	0.774542
$509$	−2.39707	−0.106248	−0.0531240	−	0.998588i	$-0.516918\pi$
$509$	−2.39707	−0.106248	−0.0531240	+	0.998588i	$0.516918\pi$
$510$	−4.17090	−0.184691
$511$	0.0957409	0.00423533
$512$	−5.98618	−0.264554
$513$	−7.78384	−0.343665
$514$	−27.6973	−1.22168
$515$	−0.722725	−0.0318471
$516$	8.98693	0.395628
$517$	0	0
$518$	6.15949	0.270632
$519$	34.0117	1.49295
$520$	−4.07939	−0.178893
$521$	41.8248	1.83238	0.916189	−	0.400747i	$-0.131250\pi$
$521$	41.8248	1.83238	0.916189	+	0.400747i	$0.131250\pi$
$522$	−1.61527	−0.0706985
$523$	−28.7142	−1.25559	−0.627793	−	0.778380i	$-0.716042\pi$
$523$	−28.7142	−1.25559	−0.627793	+	0.778380i	$0.716042\pi$
$524$	−16.5221	−0.721770
$525$	−1.53997	−0.0672098
$526$	−2.87430	−0.125326
$527$	−6.04372	−0.263268
$528$	0	0
$529$	18.7869	0.816822
$530$	−6.88353	−0.299001
$531$	5.57884	0.242101
$532$	1.55105	0.0672464
$533$	−10.4982	−0.454728
$534$	0.748924	0.0324091
$535$	−12.0970	−0.523000
$536$	−0.00426892	−0.000184389 0
$537$	−22.4299	−0.967920
$538$	−1.88677	−0.0813446
$539$	0	0
$540$	−6.22169	−0.267739
$541$	41.4908	1.78383	0.891914	−	0.452205i	$-0.149362\pi$
$541$	41.4908	1.78383	0.891914	+	0.452205i	$0.149362\pi$
$542$	22.3189	0.958677
$543$	6.38641	0.274067
$544$	15.4206	0.661153
$545$	−2.06951	−0.0886480
$546$	2.01774	0.0863513
$547$	12.1246	0.518412	0.259206	−	0.965822i	$-0.416539\pi$
$547$	12.1246	0.518412	0.259206	+	0.965822i	$0.416539\pi$
$548$	−14.5139	−0.620001
$549$	−1.06868	−0.0456102
$550$	0	0
$551$	3.80230	0.161984
$552$	−29.1827	−1.24210
$553$	−9.24782	−0.393257
$554$	17.8470	0.758245
$555$	10.0741	0.427620
$556$	−21.0684	−0.893500
$557$	2.35811	0.0999163	0.0499581	−	0.998751i	$-0.484091\pi$
$557$	2.35811	0.0999163	0.0499581	+	0.998751i	$0.484091\pi$
$558$	1.24335	0.0526350
$559$	7.29341	0.308478
$560$	−0.533340	−0.0225377
$561$	0	0
$562$	−1.41444	−0.0596644
$563$	42.3956	1.78676	0.893380	−	0.449302i	$-0.148327\pi$
$563$	42.3956	1.78676	0.893380	+	0.449302i	$0.148327\pi$
$564$	−15.2258	−0.641123
$565$	−18.3350	−0.771358
$566$	−1.59676	−0.0671167
$567$	6.71951	0.282193
$568$	−20.3719	−0.854784
$569$	−2.97701	−0.124803	−0.0624013	−	0.998051i	$-0.519876\pi$
$569$	−2.97701	−0.124803	−0.0624013	+	0.998051i	$0.519876\pi$
$570$	−2.01985	−0.0846023
$571$	46.8050	1.95873	0.979364	−	0.202107i	$-0.0647788\pi$
$571$	46.8050	1.95873	0.979364	+	0.202107i	$0.0647788\pi$
$572$	0	0
$573$	−20.6253	−0.861634
$574$	−7.10340	−0.296490
$575$	6.46428	0.269579
$576$	−3.84282	−0.160117
$577$	−26.4035	−1.09919	−0.549596	−	0.835431i	$-0.685218\pi$
$577$	−26.4035	−1.09919	−0.549596	+	0.835431i	$0.685218\pi$
$578$	−8.21584	−0.341734
$579$	22.6905	0.942985
$580$	3.03921	0.126197
$581$	−13.2464	−0.549552
$582$	0.687762	0.0285087
$583$	0	0
$584$	0.280667	0.0116141
$585$	−0.874586	−0.0361597
$586$	−8.25053	−0.340826
$587$	−33.7101	−1.39136	−0.695682	−	0.718349i	$-0.744898\pi$
$587$	−33.7101	−1.39136	−0.695682	+	0.718349i	$0.744898\pi$
$588$	−1.71467	−0.0707120
$589$	−2.92680	−0.120597
$590$	8.35785	0.344087
$591$	6.06921	0.249654
$592$	3.48897	0.143396
$593$	−34.4146	−1.41324	−0.706620	−	0.707594i	$-0.749781\pi$
$593$	−34.4146	−1.41324	−0.706620	+	0.707594i	$0.749781\pi$
$594$	0	0
$595$	2.87651	0.117925
$596$	5.72018	0.234308
$597$	−15.7761	−0.645671
$598$	−8.46981	−0.346356
$599$	40.4876	1.65428	0.827140	−	0.561996i	$-0.189967\pi$
$599$	40.4876	1.65428	0.827140	+	0.561996i	$0.189967\pi$
$600$	−4.51446	−0.184302
$601$	22.7587	0.928346	0.464173	−	0.885744i	$-0.346352\pi$
$601$	22.7587	0.928346	0.464173	+	0.885744i	$0.346352\pi$
$602$	4.93494	0.201133
$603$	−0.000915220 0	−3.72706e−5 0
$604$	−10.5927	−0.431009
$605$	0	0
$606$	14.0792	0.571929
$607$	−3.61857	−0.146873	−0.0734365	−	0.997300i	$-0.523397\pi$
$607$	−3.61857	−0.146873	−0.0734365	+	0.997300i	$0.523397\pi$
$608$	7.46777	0.302858
$609$	−4.20343	−0.170332
$610$	−1.60103	−0.0648237
$611$	−12.3566	−0.499896
$612$	2.01297	0.0813694
$613$	33.2875	1.34447	0.672235	−	0.740337i	$-0.265334\pi$
$613$	33.2875	1.34447	0.672235	+	0.740337i	$0.265334\pi$
$614$	14.7816	0.596538
$615$	−11.6179	−0.468478
$616$	0	0
$617$	14.2743	0.574662	0.287331	−	0.957831i	$-0.407232\pi$
$617$	14.2743	0.574662	0.287331	+	0.957831i	$0.407232\pi$
$618$	1.04794	0.0421544
$619$	−40.8425	−1.64160	−0.820800	−	0.571216i	$-0.806472\pi$
$619$	−40.8425	−1.64160	−0.820800	+	0.571216i	$0.806472\pi$
$620$	−2.33942	−0.0939533
$621$	−36.1209	−1.44948
$622$	4.26975	0.171201
$623$	−0.516504	−0.0206933
$624$	1.14292	0.0457536
$625$	1.00000	0.0400000
$626$	−2.52956	−0.101102
$627$	0	0
$628$	5.50713	0.219758
$629$	−18.8173	−0.750297
$630$	−0.591771	−0.0235767
$631$	19.6251	0.781264	0.390632	−	0.920547i	$-0.372256\pi$
$631$	19.6251	0.781264	0.390632	+	0.920547i	$0.372256\pi$
$632$	−27.1102	−1.07839
$633$	12.8169	0.509426
$634$	−13.2142	−0.524805
$635$	15.6786	0.622186
$636$	−12.5355	−0.497063
$637$	−1.39156	−0.0551355
$638$	0	0
$639$	−4.36756	−0.172778
$640$	4.96470	0.196247
$641$	−1.26648	−0.0500228	−0.0250114	−	0.999687i	$-0.507962\pi$
$641$	−1.26648	−0.0500228	−0.0250114	+	0.999687i	$0.507962\pi$
$642$	17.5405	0.692270
$643$	−1.93346	−0.0762481	−0.0381241	−	0.999273i	$-0.512138\pi$
$643$	−1.93346	−0.0762481	−0.0381241	+	0.999273i	$0.512138\pi$
$644$	7.19764	0.283627
$645$	8.07127	0.317806
$646$	3.77288	0.148442
$647$	7.99759	0.314418	0.157209	−	0.987565i	$-0.449750\pi$
$647$	7.99759	0.314418	0.157209	+	0.987565i	$0.449750\pi$
$648$	19.6984	0.773827
$649$	0	0
$650$	−1.31025	−0.0513921
$651$	3.23557	0.126812
$652$	21.3212	0.835003
$653$	46.2529	1.81002	0.905009	−	0.425393i	$-0.139864\pi$
$653$	46.2529	1.81002	0.905009	+	0.425393i	$0.139864\pi$
$654$	3.00076	0.117339
$655$	−14.8387	−0.579795
$656$	−4.02364	−0.157097
$657$	0.0601727	0.00234756
$658$	−8.36088	−0.325941
$659$	−15.8183	−0.616193	−0.308097	−	0.951355i	$-0.599692\pi$
$659$	−15.8183	−0.616193	−0.308097	+	0.951355i	$0.599692\pi$
$660$	0	0
$661$	15.2510	0.593195	0.296597	−	0.955003i	$-0.404148\pi$
$661$	15.2510	0.593195	0.296597	+	0.955003i	$0.404148\pi$
$662$	20.2766	0.788073
$663$	−6.16423	−0.239399
$664$	−38.8321	−1.50698
$665$	1.39301	0.0540187
$666$	3.87121	0.150006
$667$	17.6446	0.683202
$668$	13.1282	0.507945
$669$	30.8015	1.19085
$670$	−0.00137112	−5.29711e−5 0
$671$	0	0
$672$	−8.25558	−0.318466
$673$	13.4813	0.519666	0.259833	−	0.965654i	$-0.416333\pi$
$673$	13.4813	0.519666	0.259833	+	0.965654i	$0.416333\pi$
$674$	−24.5352	−0.945062
$675$	−5.58777	−0.215073
$676$	12.3187	0.473796
$677$	−2.21002	−0.0849381	−0.0424690	−	0.999098i	$-0.513522\pi$
$677$	−2.21002	−0.0849381	−0.0424690	+	0.999098i	$0.513522\pi$
$678$	26.5855	1.02101
$679$	−0.474323	−0.0182028
$680$	8.43256	0.323374
$681$	−20.3364	−0.779293
$682$	0	0
$683$	44.4249	1.69987	0.849935	−	0.526888i	$-0.176641\pi$
$683$	44.4249	1.69987	0.849935	+	0.526888i	$0.176641\pi$
$684$	0.974825	0.0372733
$685$	−13.0351	−0.498044
$686$	−0.941569	−0.0359493
$687$	−39.6503	−1.51275
$688$	2.79534	0.106571
$689$	−10.1732	−0.387570
$690$	−9.37313	−0.356829
$691$	29.0538	1.10526	0.552629	−	0.833427i	$-0.313625\pi$
$691$	29.0538	1.10526	0.552629	+	0.833427i	$0.313625\pi$
$692$	−24.5915	−0.934830
$693$	0	0
$694$	27.5174	1.04455
$695$	−18.9218	−0.717744
$696$	−12.3225	−0.467082
$697$	21.7010	0.821985
$698$	−7.25604	−0.274645
$699$	−18.3299	−0.693300
$700$	1.11345	0.0420844
$701$	26.7632	1.01083	0.505416	−	0.862876i	$-0.331339\pi$
$701$	26.7632	1.01083	0.505416	+	0.862876i	$0.331339\pi$
$702$	7.32136	0.276327
$703$	−9.11271	−0.343692
$704$	0	0
$705$	−13.6745	−0.515012
$706$	−20.9749	−0.789399
$707$	−9.70989	−0.365178
$708$	15.2203	0.572015
$709$	9.52139	0.357583	0.178792	−	0.983887i	$-0.442781\pi$
$709$	9.52139	0.357583	0.178792	+	0.983887i	$0.442781\pi$
$710$	−6.54318	−0.245561
$711$	−5.81220	−0.217975
$712$	−1.51414	−0.0567449
$713$	−13.5818	−0.508644
$714$	−4.17090	−0.156092
$715$	0	0
$716$	16.2175	0.606077
$717$	−26.8257	−1.00182
$718$	1.59350	0.0594687
$719$	−28.4864	−1.06236	−0.531182	−	0.847258i	$-0.678252\pi$
$719$	−28.4864	−1.06236	−0.531182	+	0.847258i	$0.678252\pi$
$720$	−0.335202	−0.0124922
$721$	−0.722725	−0.0269157
$722$	−16.0627	−0.597792
$723$	3.55057	0.132047
$724$	−4.61758	−0.171611
$725$	2.72955	0.101373
$726$	0	0
$727$	48.7611	1.80845	0.904225	−	0.427057i	$-0.140449\pi$
$727$	48.7611	1.80845	0.904225	+	0.427057i	$0.140449\pi$
$728$	−4.07939	−0.151192
$729$	30.0382	1.11252
$730$	0.0901467	0.00333648
$731$	−15.0763	−0.557618
$732$	−2.91560	−0.107764
$733$	29.8881	1.10394	0.551972	−	0.833863i	$-0.313876\pi$
$733$	29.8881	1.10394	0.551972	+	0.833863i	$0.313876\pi$
$734$	−12.5158	−0.461967
$735$	−1.53997	−0.0568026
$736$	34.6542	1.27737
$737$	0	0
$738$	−4.46445	−0.164339
$739$	15.1162	0.556058	0.278029	−	0.960573i	$-0.410319\pi$
$739$	15.1162	0.556058	0.278029	+	0.960573i	$0.410319\pi$
$740$	−7.28387	−0.267760
$741$	−2.98516	−0.109663
$742$	−6.88353	−0.252702
$743$	−42.9453	−1.57551	−0.787756	−	0.615988i	$-0.788757\pi$
$743$	−42.9453	−1.57551	−0.787756	+	0.615988i	$0.788757\pi$
$744$	9.48515	0.347742
$745$	5.13736	0.188218
$746$	−4.87418	−0.178457
$747$	−8.32527	−0.304606
$748$	0	0
$749$	−12.0970	−0.442016
$750$	−1.44999	−0.0529461
$751$	−17.3139	−0.631793	−0.315896	−	0.948794i	$-0.602305\pi$
$751$	−17.3139	−0.631793	−0.315896	+	0.948794i	$0.602305\pi$
$752$	−4.73592	−0.172701
$753$	−14.6905	−0.535351
$754$	−3.57639	−0.130244
$755$	−9.51339	−0.346228
$756$	−6.22169	−0.226281
$757$	10.0094	0.363798	0.181899	−	0.983317i	$-0.441776\pi$
$757$	10.0094	0.363798	0.181899	+	0.983317i	$0.441776\pi$
$758$	19.5878	0.711462
$759$	0	0
$760$	4.08365	0.148130
$761$	−47.8699	−1.73528	−0.867642	−	0.497190i	$-0.834365\pi$
$761$	−47.8699	−1.73528	−0.867642	+	0.497190i	$0.834365\pi$
$762$	−22.7338	−0.823557
$763$	−2.06951	−0.0749212
$764$	14.9128	0.539524
$765$	1.80787	0.0653637
$766$	−5.23307	−0.189078
$767$	12.3522	0.446011
$768$	−26.0305	−0.939294
$769$	−54.1437	−1.95247	−0.976236	−	0.216708i	$-0.930468\pi$
$769$	−54.1437	−1.95247	−0.976236	+	0.216708i	$0.930468\pi$
$770$	0	0
$771$	−45.2999	−1.63144
$772$	−16.4060	−0.590464
$773$	44.3052	1.59355	0.796774	−	0.604278i	$-0.206538\pi$
$773$	44.3052	1.59355	0.796774	+	0.604278i	$0.206538\pi$
$774$	3.10158	0.111484
$775$	−2.10106	−0.0754723
$776$	−1.39049	−0.0499157
$777$	10.0741	0.361405
$778$	29.1139	1.04378
$779$	10.5092	0.376531
$780$	−2.38607	−0.0854349
$781$	0	0
$782$	17.5081	0.626087
$783$	−15.2521	−0.545066
$784$	−0.533340	−0.0190479
$785$	4.94602	0.176531
$786$	21.5159	0.767446
$787$	−30.0712	−1.07192	−0.535961	−	0.844243i	$-0.680051\pi$
$787$	−30.0712	−1.07192	−0.535961	+	0.844243i	$0.680051\pi$
$788$	−4.38823	−0.156324
$789$	−4.70102	−0.167361
$790$	−8.70746	−0.309797
$791$	−18.3350	−0.651916
$792$	0	0
$793$	−2.36618	−0.0840255
$794$	28.6937	1.01830
$795$	−11.2582	−0.399289
$796$	11.4066	0.404296
$797$	−38.1915	−1.35281	−0.676406	−	0.736529i	$-0.736463\pi$
$797$	−38.1915	−1.35281	−0.676406	+	0.736529i	$0.736463\pi$
$798$	−2.01985	−0.0715020
$799$	25.5426	0.903633
$800$	5.36088	0.189536
$801$	−0.324620	−0.0114699
$802$	−25.5953	−0.903801
$803$	0	0
$804$	−0.00249693	−8.80598e−5 0
$805$	6.46428	0.227836
$806$	2.75291	0.0969670
$807$	−3.08589	−0.108628
$808$	−28.4648	−1.00139
$809$	1.13775	0.0400011	0.0200005	−	0.999800i	$-0.493633\pi$
$809$	1.13775	0.0400011	0.0200005	+	0.999800i	$0.493633\pi$
$810$	6.32688	0.222304
$811$	−48.3009	−1.69607	−0.848037	−	0.529937i	$-0.822216\pi$
$811$	−48.3009	−1.69607	−0.848037	+	0.529937i	$0.822216\pi$
$812$	3.03921	0.106656
$813$	36.5033	1.28023
$814$	0	0
$815$	19.1488	0.670754
$816$	−2.36256	−0.0827061
$817$	−7.30104	−0.255431
$818$	11.6884	0.408677
$819$	−0.874586	−0.0305605
$820$	8.40009	0.293344
$821$	−42.5334	−1.48443	−0.742213	−	0.670164i	$-0.766224\pi$
$821$	−42.5334	−1.48443	−0.742213	+	0.670164i	$0.766224\pi$
$822$	18.9007	0.659237
$823$	−16.3459	−0.569781	−0.284891	−	0.958560i	$-0.591957\pi$
$823$	−16.3459	−0.569781	−0.284891	+	0.958560i	$0.591957\pi$
$824$	−2.11869	−0.0738080
$825$	0	0
$826$	8.35785	0.290807
$827$	39.8338	1.38516	0.692578	−	0.721343i	$-0.256475\pi$
$827$	39.8338	1.38516	0.692578	+	0.721343i	$0.256475\pi$
$828$	4.52367	0.157209
$829$	17.9400	0.623081	0.311540	−	0.950233i	$-0.399155\pi$
$829$	17.9400	0.623081	0.311540	+	0.950233i	$0.399155\pi$
$830$	−12.4724	−0.432922
$831$	29.1893	1.01257
$832$	−8.50842	−0.294976
$833$	2.87651	0.0996652
$834$	27.4364	0.950043
$835$	11.7906	0.408030
$836$	0	0
$837$	11.7402	0.405802
$838$	9.91782	0.342605
$839$	−51.5966	−1.78131	−0.890656	−	0.454677i	$-0.849755\pi$
$839$	−51.5966	−1.78131	−0.890656	+	0.454677i	$0.849755\pi$
$840$	−4.51446	−0.155764
$841$	−21.5495	−0.743087
$842$	18.5188	0.638200
$843$	−2.31336	−0.0796763
$844$	−9.26704	−0.318985
$845$	11.0636	0.380598
$846$	−5.25477	−0.180663
$847$	0	0
$848$	−3.89909	−0.133895
$849$	−2.61155	−0.0896282
$850$	2.70843	0.0928985
$851$	−42.2876	−1.44960
$852$	−11.9157	−0.408224
$853$	28.2200	0.966235	0.483117	−	0.875556i	$-0.339504\pi$
$853$	28.2200	0.966235	0.483117	+	0.875556i	$0.339504\pi$
$854$	−1.60103	−0.0547860
$855$	0.875501	0.0299415
$856$	−35.4627	−1.21209
$857$	−6.27743	−0.214433	−0.107216	−	0.994236i	$-0.534194\pi$
$857$	−6.27743	−0.214433	−0.107216	+	0.994236i	$0.534194\pi$
$858$	0	0
$859$	25.9580	0.885675	0.442837	−	0.896602i	$-0.353972\pi$
$859$	25.9580	0.885675	0.442837	+	0.896602i	$0.353972\pi$
$860$	−5.83579	−0.198999
$861$	−11.6179	−0.395936
$862$	14.8715	0.506525
$863$	7.62600	0.259592	0.129796	−	0.991541i	$-0.458568\pi$
$863$	7.62600	0.259592	0.129796	+	0.991541i	$0.458568\pi$
$864$	−29.9553	−1.01910
$865$	−22.0859	−0.750945
$866$	6.67856	0.226947
$867$	−13.4373	−0.456355
$868$	−2.33942	−0.0794050
$869$	0	0
$870$	−3.95782	−0.134183
$871$	−0.00202640	−6.86619e−5 0
$872$	−6.06682	−0.205448
$873$	−0.298109	−0.0100895
$874$	8.47867	0.286795
$875$	1.00000	0.0338062
$876$	0.164165	0.00554661
$877$	25.0934	0.847344	0.423672	−	0.905816i	$-0.360741\pi$
$877$	25.0934	0.847344	0.423672	+	0.905816i	$0.360741\pi$
$878$	−23.0898	−0.779243
$879$	−13.4940	−0.455142
$880$	0	0
$881$	27.4989	0.926463	0.463231	−	0.886237i	$-0.346690\pi$
$881$	27.4989	0.926463	0.463231	+	0.886237i	$0.346690\pi$
$882$	−0.591771	−0.0199260
$883$	−26.9277	−0.906190	−0.453095	−	0.891462i	$-0.649680\pi$
$883$	−26.9277	−0.906190	−0.453095	+	0.891462i	$0.649680\pi$
$884$	4.45694	0.149903
$885$	13.6696	0.459497
$886$	−9.44697	−0.317377
$887$	34.6125	1.16217	0.581087	−	0.813841i	$-0.302628\pi$
$887$	34.6125	1.16217	0.581087	+	0.813841i	$0.302628\pi$
$888$	29.5324	0.991041
$889$	15.6786	0.525843
$890$	−0.486324	−0.0163016
$891$	0	0
$892$	−22.2705	−0.745670
$893$	12.3696	0.413932
$894$	−7.44911	−0.249136
$895$	14.5651	0.486859
$896$	4.96470	0.165859
$897$	−13.8527	−0.462527
$898$	26.7322	0.892064
$899$	−5.73495	−0.191271
$900$	0.699796	0.0233265
$901$	21.0293	0.700587
$902$	0	0
$903$	8.07127	0.268595
$904$	−53.7494	−1.78768
$905$	−4.14710	−0.137854
$906$	13.7943	0.458285
$907$	19.9016	0.660823	0.330411	−	0.943837i	$-0.392813\pi$
$907$	19.9016	0.660823	0.330411	+	0.943837i	$0.392813\pi$
$908$	14.7039	0.487965
$909$	−6.10261	−0.202411
$910$	−1.31025	−0.0434343
$911$	50.4666	1.67203	0.836016	−	0.548704i	$-0.184879\pi$
$911$	50.4666	1.67203	0.836016	+	0.548704i	$0.184879\pi$
$912$	−1.14412	−0.0378856
$913$	0	0
$914$	−16.8641	−0.557816
$915$	−2.61854	−0.0865662
$916$	28.6685	0.947232
$917$	−14.8387	−0.490016
$918$	−15.1341	−0.499500
$919$	6.02847	0.198861	0.0994304	−	0.995045i	$-0.468298\pi$
$919$	6.02847	0.198861	0.0994304	+	0.995045i	$0.468298\pi$
$920$	18.9502	0.624770
$921$	24.1759	0.796622
$922$	−21.0398	−0.692909
$923$	−9.67025	−0.318300
$924$	0	0
$925$	−6.54173	−0.215091
$926$	−29.9234	−0.983345
$927$	−0.454229	−0.0149188
$928$	14.6328	0.480345
$929$	30.9289	1.01474	0.507371	−	0.861727i	$-0.330617\pi$
$929$	30.9289	1.01474	0.507371	+	0.861727i	$0.330617\pi$
$930$	3.04651	0.0998990
$931$	1.39301	0.0456542
$932$	13.2531	0.434120
$933$	6.98332	0.228624
$934$	12.6425	0.413674
$935$	0	0
$936$	−2.56387	−0.0838028
$937$	17.9725	0.587135	0.293568	−	0.955938i	$-0.405157\pi$
$937$	17.9725	0.587135	0.293568	+	0.955938i	$0.405157\pi$
$938$	−0.00137112	−4.47687e−5 0
$939$	−4.13719	−0.135012
$940$	9.88711	0.322482
$941$	−11.1858	−0.364646	−0.182323	−	0.983239i	$-0.558362\pi$
$941$	−11.1858	−0.364646	−0.182323	+	0.983239i	$0.558362\pi$
$942$	−7.17167	−0.233665
$943$	48.7679	1.58810
$944$	4.73420	0.154085
$945$	−5.58777	−0.181770
$946$	0	0
$947$	36.2130	1.17677	0.588383	−	0.808583i	$-0.299765\pi$
$947$	36.2130	1.17677	0.588383	+	0.808583i	$0.299765\pi$
$948$	−15.8570	−0.515011
$949$	0.133229	0.00432480
$950$	1.31162	0.0425545
$951$	−21.6124	−0.700829
$952$	8.43256	0.273301
$953$	−28.0283	−0.907926	−0.453963	−	0.891020i	$-0.649990\pi$
$953$	−28.0283	−0.907926	−0.453963	+	0.891020i	$0.649990\pi$
$954$	−4.32626	−0.140068
$955$	13.3933	0.433398
$956$	19.3958	0.627306
$957$	0	0
$958$	9.09262	0.293769
$959$	−13.0351	−0.420924
$960$	−9.41586	−0.303896
$961$	−26.5856	−0.857598
$962$	8.57128	0.276349
$963$	−7.60291	−0.245000
$964$	−2.56718	−0.0826832
$965$	−14.7344	−0.474317
$966$	−9.37313	−0.301575
$967$	60.9621	1.96041	0.980205	−	0.197985i	$-0.0634397\pi$
$967$	60.9621	1.96041	0.980205	+	0.197985i	$0.0634397\pi$
$968$	0	0
$969$	6.17068	0.198231
$970$	−0.446608	−0.0143397
$971$	−26.9575	−0.865107	−0.432554	−	0.901608i	$-0.642387\pi$
$971$	−26.9575	−0.865107	−0.432554	+	0.901608i	$0.642387\pi$
$972$	−7.14329	−0.229121
$973$	−18.9218	−0.606605
$974$	−32.1567	−1.03037
$975$	−2.14296	−0.0686295
$976$	−0.906883	−0.0290286
$977$	−3.67207	−0.117480	−0.0587400	−	0.998273i	$-0.518708\pi$
$977$	−3.67207	−0.117480	−0.0587400	+	0.998273i	$0.518708\pi$
$978$	−27.7656	−0.887845
$979$	0	0
$980$	1.11345	0.0355678
$981$	−1.30067	−0.0415273
$982$	1.45597	0.0464618
$983$	25.0044	0.797515	0.398758	−	0.917056i	$-0.369442\pi$
$983$	25.0044	0.797515	0.398758	+	0.917056i	$0.369442\pi$
$984$	−34.0581	−1.08573
$985$	−3.94112	−0.125575
$986$	7.39281	0.235435
$987$	−13.6745	−0.435264
$988$	2.15837	0.0686669
$989$	−33.8805	−1.07734
$990$	0	0
$991$	−5.78499	−0.183766	−0.0918831	−	0.995770i	$-0.529289\pi$
$991$	−5.78499	−0.183766	−0.0918831	+	0.995770i	$0.529289\pi$
$992$	−11.2635	−0.357617
$993$	33.1631	1.05240
$994$	−6.54318	−0.207537
$995$	10.2444	0.324769
$996$	−22.7132	−0.719695
$997$	2.01189	0.0637171	0.0318585	−	0.999492i	$-0.489857\pi$
$997$	2.01189	0.0637171	0.0318585	+	0.999492i	$0.489857\pi$
$998$	−14.0972	−0.446240
$999$	36.5537	1.15651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.ba.1.4	✓	5
11.10	odd	2		4235.2.a.bb.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.ba.1.4	✓	5	1.1	even	1	trivial
4235.2.a.bb.1.2	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+0.941569 q^{2} +1.53997 q^{3} -1.11345 q^{4} -1.00000 q^{5} +1.44999 q^{6} -1.00000 q^{7} -2.93153 q^{8} -0.628495 q^{9} +O(q^{10})\)	\(q+0.941569 q^{2} +1.53997 q^{3} -1.11345 q^{4} -1.00000 q^{5} +1.44999 q^{6} -1.00000 q^{7} -2.93153 q^{8} -0.628495 q^{9} -0.941569 q^{10} -1.71467 q^{12} -1.39156 q^{13} -0.941569 q^{14} -1.53997 q^{15} -0.533340 q^{16} +2.87651 q^{17} -0.591771 q^{18} +1.39301 q^{19} +1.11345 q^{20} -1.53997 q^{21} +6.46428 q^{23} -4.51446 q^{24} +1.00000 q^{25} -1.31025 q^{26} -5.58777 q^{27} +1.11345 q^{28} +2.72955 q^{29} -1.44999 q^{30} -2.10106 q^{31} +5.36088 q^{32} +2.70843 q^{34} +1.00000 q^{35} +0.699796 q^{36} -6.54173 q^{37} +1.31162 q^{38} -2.14296 q^{39} +2.93153 q^{40} +7.54422 q^{41} -1.44999 q^{42} -5.24119 q^{43} +0.628495 q^{45} +6.08657 q^{46} +8.87972 q^{47} -0.821328 q^{48} +1.00000 q^{49} +0.941569 q^{50} +4.42974 q^{51} +1.54943 q^{52} +7.31070 q^{53} -5.26127 q^{54} +2.93153 q^{56} +2.14520 q^{57} +2.57006 q^{58} -8.87651 q^{59} +1.71467 q^{60} +1.70038 q^{61} -1.97829 q^{62} +0.628495 q^{63} +6.11432 q^{64} +1.39156 q^{65} +0.00145621 q^{67} -3.20284 q^{68} +9.95479 q^{69} +0.941569 q^{70} +6.94923 q^{71} +1.84245 q^{72} -0.0957409 q^{73} -6.15949 q^{74} +1.53997 q^{75} -1.55105 q^{76} -2.01774 q^{78} +9.24782 q^{79} +0.533340 q^{80} -6.71951 q^{81} +7.10340 q^{82} +13.2464 q^{83} +1.71467 q^{84} -2.87651 q^{85} -4.93494 q^{86} +4.20343 q^{87} +0.516504 q^{89} +0.591771 q^{90} +1.39156 q^{91} -7.19764 q^{92} -3.23557 q^{93} +8.36088 q^{94} -1.39301 q^{95} +8.25558 q^{96} +0.474323 q^{97} +0.941569 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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