LMFDB - Embedded newform 4235.2.a.bp.1.2

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.64654$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64654 q^{2} +2.16636 q^{3} +5.00419 q^{4} +1.00000 q^{5} -5.73337 q^{6} +1.00000 q^{7} -7.95071 q^{8} +1.69313 q^{9} +O(q^{10})$	\(q-2.64654 q^{2} +2.16636 q^{3} +5.00419 q^{4} +1.00000 q^{5} -5.73337 q^{6} +1.00000 q^{7} -7.95071 q^{8} +1.69313 q^{9} -2.64654 q^{10} +10.8409 q^{12} -3.12586 q^{13} -2.64654 q^{14} +2.16636 q^{15} +11.0335 q^{16} -5.62397 q^{17} -4.48094 q^{18} +6.54172 q^{19} +5.00419 q^{20} +2.16636 q^{21} -5.20325 q^{23} -17.2241 q^{24} +1.00000 q^{25} +8.27272 q^{26} -2.83116 q^{27} +5.00419 q^{28} +8.40125 q^{29} -5.73337 q^{30} -1.15843 q^{31} -13.2993 q^{32} +14.8841 q^{34} +1.00000 q^{35} +8.47274 q^{36} +9.45459 q^{37} -17.3129 q^{38} -6.77174 q^{39} -7.95071 q^{40} -6.53391 q^{41} -5.73337 q^{42} +5.24561 q^{43} +1.69313 q^{45} +13.7706 q^{46} +2.63246 q^{47} +23.9026 q^{48} +1.00000 q^{49} -2.64654 q^{50} -12.1836 q^{51} -15.6424 q^{52} -1.14106 q^{53} +7.49278 q^{54} -7.95071 q^{56} +14.1717 q^{57} -22.2343 q^{58} +2.82897 q^{59} +10.8409 q^{60} +8.70510 q^{61} +3.06585 q^{62} +1.69313 q^{63} +13.1300 q^{64} -3.12586 q^{65} -2.54623 q^{67} -28.1434 q^{68} -11.2721 q^{69} -2.64654 q^{70} +11.3717 q^{71} -13.4616 q^{72} +8.89267 q^{73} -25.0220 q^{74} +2.16636 q^{75} +32.7360 q^{76} +17.9217 q^{78} -3.27231 q^{79} +11.0335 q^{80} -11.2127 q^{81} +17.2923 q^{82} +0.721782 q^{83} +10.8409 q^{84} -5.62397 q^{85} -13.8827 q^{86} +18.2001 q^{87} -0.247052 q^{89} -4.48094 q^{90} -3.12586 q^{91} -26.0381 q^{92} -2.50959 q^{93} -6.96693 q^{94} +6.54172 q^{95} -28.8111 q^{96} +7.36031 q^{97} -2.64654 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.64654	−1.87139	−0.935694	−	0.352812i	$-0.885225\pi$
$2$	−2.64654	−1.87139	−0.935694	+	0.352812i	$0.885225\pi$
$3$	2.16636	1.25075	0.625375	−	0.780324i	$-0.284946\pi$
$3$	2.16636	1.25075	0.625375	+	0.780324i	$0.284946\pi$
$4$	5.00419	2.50209
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.73337	−2.34064
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.95071	−2.81100
$9$	1.69313	0.564376
$10$	−2.64654	−0.836910
$11$	0	0
$11$	0	0
$12$	10.8409	3.12950
$13$	−3.12586	−0.866957	−0.433479	−	0.901164i	$-0.642714\pi$
$13$	−3.12586	−0.866957	−0.433479	+	0.901164i	$0.642714\pi$
$14$	−2.64654	−0.707318
$15$	2.16636	0.559353
$16$	11.0335	2.75838
$17$	−5.62397	−1.36401	−0.682007	−	0.731346i	$-0.738893\pi$
$17$	−5.62397	−1.36401	−0.682007	+	0.731346i	$0.738893\pi$
$18$	−4.48094	−1.05617
$19$	6.54172	1.50077	0.750387	−	0.660999i	$-0.229867\pi$
$19$	6.54172	1.50077	0.750387	+	0.660999i	$0.229867\pi$
$20$	5.00419	1.11897
$21$	2.16636	0.472739
$22$	0	0
$23$	−5.20325	−1.08495	−0.542477	−	0.840071i	$-0.682513\pi$
$23$	−5.20325	−1.08495	−0.542477	+	0.840071i	$0.682513\pi$
$24$	−17.2241	−3.51586
$25$	1.00000	0.200000
$26$	8.27272	1.62241
$27$	−2.83116	−0.544857
$28$	5.00419	0.945703
$29$	8.40125	1.56007	0.780036	−	0.625734i	$-0.215201\pi$
$29$	8.40125	1.56007	0.780036	+	0.625734i	$0.215201\pi$
$30$	−5.73337	−1.04677
$31$	−1.15843	−0.208061	−0.104030	−	0.994574i	$-0.533174\pi$
$31$	−1.15843	−0.208061	−0.104030	+	0.994574i	$0.533174\pi$
$32$	−13.2993	−2.35100
$33$	0	0
$34$	14.8841	2.55260
$35$	1.00000	0.169031
$36$	8.47274	1.41212
$37$	9.45459	1.55433	0.777163	−	0.629300i	$-0.216658\pi$
$37$	9.45459	1.55433	0.777163	+	0.629300i	$0.216658\pi$
$38$	−17.3129	−2.80853
$39$	−6.77174	−1.08435
$40$	−7.95071	−1.25712
$41$	−6.53391	−1.02042	−0.510212	−	0.860048i	$-0.670433\pi$
$41$	−6.53391	−1.02042	−0.510212	+	0.860048i	$0.670433\pi$
$42$	−5.73337	−0.884679
$43$	5.24561	0.799949	0.399974	−	0.916526i	$-0.369019\pi$
$43$	5.24561	0.799949	0.399974	+	0.916526i	$0.369019\pi$
$44$	0	0
$45$	1.69313	0.252397
$46$	13.7706	2.03037
$47$	2.63246	0.383984	0.191992	−	0.981396i	$-0.438505\pi$
$47$	2.63246	0.383984	0.191992	+	0.981396i	$0.438505\pi$
$48$	23.9026	3.45005
$49$	1.00000	0.142857
$50$	−2.64654	−0.374278
$51$	−12.1836	−1.70604
$52$	−15.6424	−2.16921
$53$	−1.14106	−0.156736	−0.0783681	−	0.996924i	$-0.524971\pi$
$53$	−1.14106	−0.156736	−0.0783681	+	0.996924i	$0.524971\pi$
$54$	7.49278	1.01964
$55$	0	0
$56$	−7.95071	−1.06246
$57$	14.1717	1.87709
$58$	−22.2343	−2.91950
$59$	2.82897	0.368300	0.184150	−	0.982898i	$-0.441047\pi$
$59$	2.82897	0.368300	0.184150	+	0.982898i	$0.441047\pi$
$60$	10.8409	1.39955
$61$	8.70510	1.11457	0.557287	−	0.830320i	$-0.311842\pi$
$61$	8.70510	1.11457	0.557287	+	0.830320i	$0.311842\pi$
$62$	3.06585	0.389363
$63$	1.69313	0.213314
$64$	13.1300	1.64126
$65$	−3.12586	−0.387715
$66$	0	0
$67$	−2.54623	−0.311071	−0.155536	−	0.987830i	$-0.549710\pi$
$67$	−2.54623	−0.311071	−0.155536	+	0.987830i	$0.549710\pi$
$68$	−28.1434	−3.41289
$69$	−11.2721	−1.35701
$70$	−2.64654	−0.316322
$71$	11.3717	1.34958	0.674788	−	0.738012i	$-0.264235\pi$
$71$	11.3717	1.34958	0.674788	+	0.738012i	$0.264235\pi$
$72$	−13.4616	−1.58646
$73$	8.89267	1.04081	0.520404	−	0.853920i	$-0.325781\pi$
$73$	8.89267	1.04081	0.520404	+	0.853920i	$0.325781\pi$
$74$	−25.0220	−2.90875
$75$	2.16636	0.250150
$76$	32.7360	3.75508
$77$	0	0
$78$	17.9217	2.02923
$79$	−3.27231	−0.368164	−0.184082	−	0.982911i	$-0.558931\pi$
$79$	−3.27231	−0.368164	−0.184082	+	0.982911i	$0.558931\pi$
$80$	11.0335	1.23359
$81$	−11.2127	−1.24586
$82$	17.2923	1.90961
$83$	0.721782	0.0792259	0.0396129	−	0.999215i	$-0.487388\pi$
$83$	0.721782	0.0792259	0.0396129	+	0.999215i	$0.487388\pi$
$84$	10.8409	1.18284
$85$	−5.62397	−0.610006
$86$	−13.8827	−1.49701
$87$	18.2001	1.95126
$88$	0	0
$89$	−0.247052	−0.0261874	−0.0130937	−	0.999914i	$-0.504168\pi$
$89$	−0.247052	−0.0261874	−0.0130937	+	0.999914i	$0.504168\pi$
$90$	−4.48094	−0.472332
$91$	−3.12586	−0.327679
$92$	−26.0381	−2.71466
$93$	−2.50959	−0.260232
$94$	−6.96693	−0.718583
$95$	6.54172	0.671166
$96$	−28.8111	−2.94052
$97$	7.36031	0.747326	0.373663	−	0.927564i	$-0.378102\pi$
$97$	7.36031	0.747326	0.373663	+	0.927564i	$0.378102\pi$
$98$	−2.64654	−0.267341
$99$	0	0
$100$	5.00419	0.500419
$101$	14.4694	1.43976	0.719879	−	0.694100i	$-0.244197\pi$
$101$	14.4694	1.43976	0.719879	+	0.694100i	$0.244197\pi$
$102$	32.2443	3.19266
$103$	−9.53701	−0.939710	−0.469855	−	0.882744i	$-0.655694\pi$
$103$	−9.53701	−0.939710	−0.469855	+	0.882744i	$0.655694\pi$
$104$	24.8528	2.43702
$105$	2.16636	0.211415
$106$	3.01986	0.293314
$107$	11.7986	1.14062	0.570309	−	0.821430i	$-0.306823\pi$
$107$	11.7986	1.14062	0.570309	+	0.821430i	$0.306823\pi$
$108$	−14.1676	−1.36328
$109$	5.74042	0.549832	0.274916	−	0.961468i	$-0.411350\pi$
$109$	5.74042	0.549832	0.274916	+	0.961468i	$0.411350\pi$
$110$	0	0
$111$	20.4821	1.94407
$112$	11.0335	1.04257
$113$	12.6578	1.19075	0.595375	−	0.803448i	$-0.297004\pi$
$113$	12.6578	1.19075	0.595375	+	0.803448i	$0.297004\pi$
$114$	−37.5061	−3.51277
$115$	−5.20325	−0.485206
$116$	42.0414	3.90345
$117$	−5.29248	−0.489290
$118$	−7.48698	−0.689233
$119$	−5.62397	−0.515549
$120$	−17.2241	−1.57234
$121$	0	0
$122$	−23.0384	−2.08580
$123$	−14.1548	−1.27630
$124$	−5.79703	−0.520588
$125$	1.00000	0.0894427
$126$	−4.48094	−0.399194
$127$	−5.40464	−0.479584	−0.239792	−	0.970824i	$-0.577079\pi$
$127$	−5.40464	−0.479584	−0.239792	+	0.970824i	$0.577079\pi$
$128$	−8.15068	−0.720425
$129$	11.3639	1.00054
$130$	8.27272	0.725565
$131$	20.2994	1.77357	0.886784	−	0.462184i	$-0.152934\pi$
$131$	20.2994	1.77357	0.886784	+	0.462184i	$0.152934\pi$
$132$	0	0
$133$	6.54172	0.567239
$134$	6.73870	0.582135
$135$	−2.83116	−0.243667
$136$	44.7146	3.83425
$137$	18.3214	1.56530	0.782652	−	0.622459i	$-0.213866\pi$
$137$	18.3214	1.56530	0.782652	+	0.622459i	$0.213866\pi$
$138$	29.8322	2.53949
$139$	5.82139	0.493764	0.246882	−	0.969046i	$-0.420594\pi$
$139$	5.82139	0.493764	0.246882	+	0.969046i	$0.420594\pi$
$140$	5.00419	0.422931
$141$	5.70287	0.480268
$142$	−30.0958	−2.52558
$143$	0	0
$144$	18.6812	1.55677
$145$	8.40125	0.697686
$146$	−23.5348	−1.94776
$147$	2.16636	0.178679
$148$	47.3126	3.88907
$149$	−11.8371	−0.969729	−0.484865	−	0.874589i	$-0.661131\pi$
$149$	−11.8371	−0.969729	−0.484865	+	0.874589i	$0.661131\pi$
$150$	−5.73337	−0.468128
$151$	6.06549	0.493602	0.246801	−	0.969066i	$-0.420621\pi$
$151$	6.06549	0.493602	0.246801	+	0.969066i	$0.420621\pi$
$152$	−52.0113	−4.21868
$153$	−9.52211	−0.769817
$154$	0	0
$155$	−1.15843	−0.0930477
$156$	−33.8871	−2.71314
$157$	17.6595	1.40938	0.704690	−	0.709515i	$-0.251086\pi$
$157$	17.6595	1.40938	0.704690	+	0.709515i	$0.251086\pi$
$158$	8.66031	0.688977
$159$	−2.47194	−0.196038
$160$	−13.2993	−1.05140
$161$	−5.20325	−0.410074
$162$	29.6749	2.33148
$163$	14.5382	1.13872	0.569358	−	0.822089i	$-0.307192\pi$
$163$	14.5382	1.13872	0.569358	+	0.822089i	$0.307192\pi$
$164$	−32.6969	−2.55320
$165$	0	0
$166$	−1.91023	−0.148262
$167$	12.6223	0.976744	0.488372	−	0.872635i	$-0.337591\pi$
$167$	12.6223	0.976744	0.488372	+	0.872635i	$0.337591\pi$
$168$	−17.2241	−1.32887
$169$	−3.22901	−0.248385
$170$	14.8841	1.14156
$171$	11.0760	0.847001
$172$	26.2500	2.00155
$173$	−14.7656	−1.12261	−0.561305	−	0.827609i	$-0.689700\pi$
$173$	−14.7656	−1.12261	−0.561305	+	0.827609i	$0.689700\pi$
$174$	−48.1675	−3.65157
$175$	1.00000	0.0755929
$176$	0	0
$177$	6.12857	0.460652
$178$	0.653833	0.0490068
$179$	5.25923	0.393093	0.196547	−	0.980494i	$-0.437027\pi$
$179$	5.25923	0.393093	0.196547	+	0.980494i	$0.437027\pi$
$180$	8.47274	0.631520
$181$	8.10300	0.602291	0.301145	−	0.953578i	$-0.402631\pi$
$181$	8.10300	0.602291	0.301145	+	0.953578i	$0.402631\pi$
$182$	8.27272	0.613215
$183$	18.8584	1.39405
$184$	41.3696	3.04981
$185$	9.45459	0.695116
$186$	6.64174	0.486996
$187$	0	0
$188$	13.1733	0.960765
$189$	−2.83116	−0.205936
$190$	−17.3129	−1.25601
$191$	−25.3264	−1.83256	−0.916279	−	0.400541i	$-0.868822\pi$
$191$	−25.3264	−1.83256	−0.916279	+	0.400541i	$0.868822\pi$
$192$	28.4444	2.05280
$193$	−8.53014	−0.614013	−0.307007	−	0.951707i	$-0.599327\pi$
$193$	−8.53014	−0.614013	−0.307007	+	0.951707i	$0.599327\pi$
$194$	−19.4794	−1.39854
$195$	−6.77174	−0.484935
$196$	5.00419	0.357442
$197$	−23.5163	−1.67547	−0.837733	−	0.546080i	$-0.816120\pi$
$197$	−23.5163	−1.67547	−0.837733	+	0.546080i	$0.816120\pi$
$198$	0	0
$199$	16.0115	1.13502	0.567511	−	0.823366i	$-0.307906\pi$
$199$	16.0115	1.13502	0.567511	+	0.823366i	$0.307906\pi$
$200$	−7.95071	−0.562200
$201$	−5.51605	−0.389072
$202$	−38.2938	−2.69435
$203$	8.40125	0.589652
$204$	−60.9689	−4.26867
$205$	−6.53391	−0.456348
$206$	25.2401	1.75856
$207$	−8.80978	−0.612322
$208$	−34.4893	−2.39140
$209$	0	0
$210$	−5.73337	−0.395640
$211$	5.72148	0.393883	0.196941	−	0.980415i	$-0.436899\pi$
$211$	5.72148	0.393883	0.196941	+	0.980415i	$0.436899\pi$
$212$	−5.71007	−0.392169
$213$	24.6353	1.68798
$214$	−31.2256	−2.13454
$215$	5.24561	0.357748
$216$	22.5097	1.53159
$217$	−1.15843	−0.0786397
$218$	−15.1923	−1.02895
$219$	19.2647	1.30179
$220$	0	0
$221$	17.5797	1.18254
$222$	−54.2067	−3.63812
$223$	4.57966	0.306677	0.153338	−	0.988174i	$-0.450998\pi$
$223$	4.57966	0.306677	0.153338	+	0.988174i	$0.450998\pi$
$224$	−13.2993	−0.888595
$225$	1.69313	0.112875
$226$	−33.4995	−2.22836
$227$	−13.5980	−0.902530	−0.451265	−	0.892390i	$-0.649027\pi$
$227$	−13.5980	−0.902530	−0.451265	+	0.892390i	$0.649027\pi$
$228$	70.9181	4.69666
$229$	−12.6873	−0.838398	−0.419199	−	0.907894i	$-0.637689\pi$
$229$	−12.6873	−0.838398	−0.419199	+	0.907894i	$0.637689\pi$
$230$	13.7706	0.908009
$231$	0	0
$232$	−66.7959	−4.38537
$233$	6.23109	0.408212	0.204106	−	0.978949i	$-0.434571\pi$
$233$	6.23109	0.408212	0.204106	+	0.978949i	$0.434571\pi$
$234$	14.0068	0.915652
$235$	2.63246	0.171723
$236$	14.1567	0.921522
$237$	−7.08901	−0.460481
$238$	14.8841	0.964792
$239$	−12.6440	−0.817875	−0.408938	−	0.912562i	$-0.634101\pi$
$239$	−12.6440	−0.817875	−0.408938	+	0.912562i	$0.634101\pi$
$240$	23.9026	1.54291
$241$	8.45907	0.544897	0.272448	−	0.962170i	$-0.412167\pi$
$241$	8.45907	0.544897	0.272448	+	0.962170i	$0.412167\pi$
$242$	0	0
$243$	−15.7973	−1.01340
$244$	43.5620	2.78877
$245$	1.00000	0.0638877
$246$	37.4613	2.38845
$247$	−20.4485	−1.30111
$248$	9.21038	0.584860
$249$	1.56364	0.0990918
$250$	−2.64654	−0.167382
$251$	−7.83979	−0.494843	−0.247422	−	0.968908i	$-0.579583\pi$
$251$	−7.83979	−0.494843	−0.247422	+	0.968908i	$0.579583\pi$
$252$	8.47274	0.533732
$253$	0	0
$254$	14.3036	0.897488
$255$	−12.1836	−0.762965
$256$	−4.68897	−0.293061
$257$	−6.35452	−0.396384	−0.198192	−	0.980163i	$-0.563507\pi$
$257$	−6.35452	−0.396384	−0.198192	+	0.980163i	$0.563507\pi$
$258$	−30.0751	−1.87239
$259$	9.45459	0.587480
$260$	−15.6424	−0.970100
$261$	14.2244	0.880468
$262$	−53.7233	−3.31904
$263$	22.1579	1.36632	0.683158	−	0.730270i	$-0.260606\pi$
$263$	22.1579	1.36632	0.683158	+	0.730270i	$0.260606\pi$
$264$	0	0
$265$	−1.14106	−0.0700946
$266$	−17.3129	−1.06152
$267$	−0.535203	−0.0327539
$268$	−12.7418	−0.778329
$269$	−18.1912	−1.10914	−0.554568	−	0.832139i	$-0.687116\pi$
$269$	−18.1912	−1.10914	−0.554568	+	0.832139i	$0.687116\pi$
$270$	7.49278	0.455996
$271$	17.8675	1.08538	0.542688	−	0.839935i	$-0.317407\pi$
$271$	17.8675	1.08538	0.542688	+	0.839935i	$0.317407\pi$
$272$	−62.0523	−3.76247
$273$	−6.77174	−0.409845
$274$	−48.4884	−2.92929
$275$	0	0
$276$	−56.4079	−3.39536
$277$	−27.7065	−1.66472	−0.832362	−	0.554232i	$-0.813012\pi$
$277$	−27.7065	−1.66472	−0.832362	+	0.554232i	$0.813012\pi$
$278$	−15.4065	−0.924023
$279$	−1.96138	−0.117425
$280$	−7.95071	−0.475146
$281$	−6.28484	−0.374922	−0.187461	−	0.982272i	$-0.560026\pi$
$281$	−6.28484	−0.374922	−0.187461	+	0.982272i	$0.560026\pi$
$282$	−15.0929	−0.898768
$283$	−2.33268	−0.138663	−0.0693317	−	0.997594i	$-0.522087\pi$
$283$	−2.33268	−0.138663	−0.0693317	+	0.997594i	$0.522087\pi$
$284$	56.9063	3.37677
$285$	14.1717	0.839461
$286$	0	0
$287$	−6.53391	−0.385684
$288$	−22.5174	−1.32685
$289$	14.6291	0.860534
$290$	−22.2343	−1.30564
$291$	15.9451	0.934719
$292$	44.5006	2.60420
$293$	−24.4309	−1.42727	−0.713633	−	0.700520i	$-0.752952\pi$
$293$	−24.4309	−1.42727	−0.713633	+	0.700520i	$0.752952\pi$
$294$	−5.73337	−0.334377
$295$	2.82897	0.164709
$296$	−75.1708	−4.36921
$297$	0	0
$298$	31.3273	1.81474
$299$	16.2646	0.940608
$300$	10.8409	0.625899
$301$	5.24561	0.302352
$302$	−16.0526	−0.923722
$303$	31.3459	1.80078
$304$	72.1783	4.13971
$305$	8.70510	0.498453
$306$	25.2007	1.44063
$307$	−5.28285	−0.301508	−0.150754	−	0.988571i	$-0.548170\pi$
$307$	−5.28285	−0.301508	−0.150754	+	0.988571i	$0.548170\pi$
$308$	0	0
$309$	−20.6606	−1.17534
$310$	3.06585	0.174128
$311$	5.56805	0.315735	0.157867	−	0.987460i	$-0.449538\pi$
$311$	5.56805	0.315735	0.157867	+	0.987460i	$0.449538\pi$
$312$	53.8402	3.04810
$313$	−13.7796	−0.778871	−0.389435	−	0.921054i	$-0.627330\pi$
$313$	−13.7796	−0.778871	−0.389435	+	0.921054i	$0.627330\pi$
$314$	−46.7366	−2.63750
$315$	1.69313	0.0953970
$316$	−16.3753	−0.921181
$317$	−28.4970	−1.60055	−0.800276	−	0.599632i	$-0.795314\pi$
$317$	−28.4970	−1.60055	−0.800276	+	0.599632i	$0.795314\pi$
$318$	6.54211	0.366863
$319$	0	0
$320$	13.1300	0.733992
$321$	25.5602	1.42663
$322$	13.7706	0.767408
$323$	−36.7905	−2.04708
$324$	−56.1105	−3.11725
$325$	−3.12586	−0.173391
$326$	−38.4759	−2.13098
$327$	12.4358	0.687703
$328$	51.9492	2.86842
$329$	2.63246	0.145132
$330$	0	0
$331$	−27.4360	−1.50802	−0.754011	−	0.656862i	$-0.771883\pi$
$331$	−27.4360	−1.50802	−0.754011	+	0.656862i	$0.771883\pi$
$332$	3.61193	0.198231
$333$	16.0078	0.877224
$334$	−33.4055	−1.82787
$335$	−2.54623	−0.139115
$336$	23.9026	1.30400
$337$	−10.5843	−0.576564	−0.288282	−	0.957546i	$-0.593084\pi$
$337$	−10.5843	−0.576564	−0.288282	+	0.957546i	$0.593084\pi$
$338$	8.54571	0.464825
$339$	27.4215	1.48933
$340$	−28.1434	−1.52629
$341$	0	0
$342$	−29.3130	−1.58507
$343$	1.00000	0.0539949
$344$	−41.7064	−2.24866
$345$	−11.2721	−0.606871
$346$	39.0779	2.10084
$347$	−17.6225	−0.946026	−0.473013	−	0.881055i	$-0.656834\pi$
$347$	−17.6225	−0.946026	−0.473013	+	0.881055i	$0.656834\pi$
$348$	91.0770	4.88224
$349$	15.5902	0.834527	0.417263	−	0.908786i	$-0.362989\pi$
$349$	15.5902	0.834527	0.417263	+	0.908786i	$0.362989\pi$
$350$	−2.64654	−0.141464
$351$	8.84980	0.472367
$352$	0	0
$353$	−32.3843	−1.72364	−0.861822	−	0.507211i	$-0.830677\pi$
$353$	−32.3843	−1.72364	−0.861822	+	0.507211i	$0.830677\pi$
$354$	−16.2195	−0.862058
$355$	11.3717	0.603549
$356$	−1.23629	−0.0655234
$357$	−12.1836	−0.644823
$358$	−13.9188	−0.735630
$359$	−19.2545	−1.01621	−0.508106	−	0.861294i	$-0.669654\pi$
$359$	−19.2545	−1.01621	−0.508106	+	0.861294i	$0.669654\pi$
$360$	−13.4616	−0.709488
$361$	23.7941	1.25232
$362$	−21.4449	−1.12712
$363$	0	0
$364$	−15.6424	−0.819884
$365$	8.89267	0.465464
$366$	−49.9096	−2.60882
$367$	−1.69271	−0.0883586	−0.0441793	−	0.999024i	$-0.514067\pi$
$367$	−1.69271	−0.0883586	−0.0441793	+	0.999024i	$0.514067\pi$
$368$	−57.4103	−2.99272
$369$	−11.0627	−0.575903
$370$	−25.0220	−1.30083
$371$	−1.14106	−0.0592407
$372$	−12.5585	−0.651126
$373$	1.29514	0.0670600	0.0335300	−	0.999438i	$-0.489325\pi$
$373$	1.29514	0.0670600	0.0335300	+	0.999438i	$0.489325\pi$
$374$	0	0
$375$	2.16636	0.111871
$376$	−20.9300	−1.07938
$377$	−26.2611	−1.35252
$378$	7.49278	0.385387
$379$	14.4379	0.741624	0.370812	−	0.928708i	$-0.379079\pi$
$379$	14.4379	0.741624	0.370812	+	0.928708i	$0.379079\pi$
$380$	32.7360	1.67932
$381$	−11.7084	−0.599840
$382$	67.0275	3.42943
$383$	7.14078	0.364877	0.182439	−	0.983217i	$-0.441601\pi$
$383$	7.14078	0.364877	0.182439	+	0.983217i	$0.441601\pi$
$384$	−17.6573	−0.901072
$385$	0	0
$386$	22.5754	1.14906
$387$	8.88150	0.451472
$388$	36.8324	1.86988
$389$	25.1690	1.27612	0.638060	−	0.769987i	$-0.279737\pi$
$389$	25.1690	1.27612	0.638060	+	0.769987i	$0.279737\pi$
$390$	17.9217	0.907501
$391$	29.2630	1.47989
$392$	−7.95071	−0.401572
$393$	43.9759	2.21829
$394$	62.2369	3.13545
$395$	−3.27231	−0.164648
$396$	0	0
$397$	−5.80386	−0.291288	−0.145644	−	0.989337i	$-0.546525\pi$
$397$	−5.80386	−0.291288	−0.145644	+	0.989337i	$0.546525\pi$
$398$	−42.3750	−2.12407
$399$	14.1717	0.709474
$400$	11.0335	0.551676
$401$	12.4874	0.623593	0.311796	−	0.950149i	$-0.399069\pi$
$401$	12.4874	0.623593	0.311796	+	0.950149i	$0.399069\pi$
$402$	14.5985	0.728105
$403$	3.62110	0.180380
$404$	72.4075	3.60241
$405$	−11.2127	−0.557164
$406$	−22.2343	−1.10347
$407$	0	0
$408$	96.8681	4.79568
$409$	36.7926	1.81928	0.909638	−	0.415401i	$-0.136359\pi$
$409$	36.7926	1.81928	0.909638	+	0.415401i	$0.136359\pi$
$410$	17.2923	0.854004
$411$	39.6909	1.95781
$412$	−47.7250	−2.35124
$413$	2.82897	0.139204
$414$	23.3155	1.14589
$415$	0.721782	0.0354309
$416$	41.5717	2.03822
$417$	12.6112	0.617575
$418$	0	0
$419$	11.9413	0.583370	0.291685	−	0.956514i	$-0.405784\pi$
$419$	11.9413	0.583370	0.291685	+	0.956514i	$0.405784\pi$
$420$	10.8409	0.528981
$421$	22.8265	1.11250	0.556248	−	0.831017i	$-0.312241\pi$
$421$	22.8265	1.11250	0.556248	+	0.831017i	$0.312241\pi$
$422$	−15.1421	−0.737107
$423$	4.45710	0.216712
$424$	9.07222	0.440586
$425$	−5.62397	−0.272803
$426$	−65.1983	−3.15887
$427$	8.70510	0.421269
$428$	59.0427	2.85393
$429$	0	0
$430$	−13.8827	−0.669485
$431$	−1.93426	−0.0931702	−0.0465851	−	0.998914i	$-0.514834\pi$
$431$	−1.93426	−0.0931702	−0.0465851	+	0.998914i	$0.514834\pi$
$432$	−31.2377	−1.50292
$433$	31.4068	1.50932	0.754658	−	0.656119i	$-0.227803\pi$
$433$	31.4068	1.50932	0.754658	+	0.656119i	$0.227803\pi$
$434$	3.06585	0.147165
$435$	18.2001	0.872630
$436$	28.7261	1.37573
$437$	−34.0382	−1.62827
$438$	−50.9850	−2.43616
$439$	1.21426	0.0579534	0.0289767	−	0.999580i	$-0.490775\pi$
$439$	1.21426	0.0579534	0.0289767	+	0.999580i	$0.490775\pi$
$440$	0	0
$441$	1.69313	0.0806252
$442$	−46.5255	−2.21299
$443$	−2.94837	−0.140081	−0.0700407	−	0.997544i	$-0.522313\pi$
$443$	−2.94837	−0.140081	−0.0700407	+	0.997544i	$0.522313\pi$
$444$	102.496	4.86425
$445$	−0.247052	−0.0117114
$446$	−12.1203	−0.573912
$447$	−25.6434	−1.21289
$448$	13.1300	0.620336
$449$	2.77180	0.130809	0.0654047	−	0.997859i	$-0.479166\pi$
$449$	2.77180	0.130809	0.0654047	+	0.997859i	$0.479166\pi$
$450$	−4.48094	−0.211233
$451$	0	0
$452$	63.3422	2.97937
$453$	13.1400	0.617373
$454$	35.9876	1.68898
$455$	−3.12586	−0.146543
$456$	−112.675	−5.27651
$457$	−36.6240	−1.71320	−0.856599	−	0.515983i	$-0.827427\pi$
$457$	−36.6240	−1.71320	−0.856599	+	0.515983i	$0.827427\pi$
$458$	33.5774	1.56897
$459$	15.9224	0.743192
$460$	−26.0381	−1.21403
$461$	−33.1867	−1.54566	−0.772828	−	0.634615i	$-0.781159\pi$
$461$	−33.1867	−1.54566	−0.772828	+	0.634615i	$0.781159\pi$
$462$	0	0
$463$	14.0968	0.655135	0.327568	−	0.944828i	$-0.393771\pi$
$463$	14.0968	0.655135	0.327568	+	0.944828i	$0.393771\pi$
$464$	92.6954	4.30328
$465$	−2.50959	−0.116379
$466$	−16.4908	−0.763924
$467$	16.1107	0.745516	0.372758	−	0.927929i	$-0.378412\pi$
$467$	16.1107	0.745516	0.372758	+	0.927929i	$0.378412\pi$
$468$	−26.4846	−1.22425
$469$	−2.54623	−0.117574
$470$	−6.96693	−0.321360
$471$	38.2568	1.76278
$472$	−22.4923	−1.03529
$473$	0	0
$474$	18.7614	0.861739
$475$	6.54172	0.300155
$476$	−28.1434	−1.28995
$477$	−1.93196	−0.0884582
$478$	33.4630	1.53056
$479$	20.9967	0.959364	0.479682	−	0.877442i	$-0.340752\pi$
$479$	20.9967	0.959364	0.479682	+	0.877442i	$0.340752\pi$
$480$	−28.8111	−1.31504
$481$	−29.5537	−1.34753
$482$	−22.3873	−1.01971
$483$	−11.2721	−0.512900
$484$	0	0
$485$	7.36031	0.334215
$486$	41.8083	1.89646
$487$	16.1833	0.733338	0.366669	−	0.930352i	$-0.380498\pi$
$487$	16.1833	0.733338	0.366669	+	0.930352i	$0.380498\pi$
$488$	−69.2118	−3.13307
$489$	31.4949	1.42425
$490$	−2.64654	−0.119559
$491$	−22.7980	−1.02886	−0.514429	−	0.857533i	$-0.671996\pi$
$491$	−22.7980	−1.02886	−0.514429	+	0.857533i	$0.671996\pi$
$492$	−70.8334	−3.19341
$493$	−47.2484	−2.12796
$494$	54.1178	2.43488
$495$	0	0
$496$	−12.7816	−0.573912
$497$	11.3717	0.510092
$498$	−4.13825	−0.185439
$499$	−36.0556	−1.61407	−0.807034	−	0.590505i	$-0.798929\pi$
$499$	−36.0556	−1.61407	−0.807034	+	0.590505i	$0.798929\pi$
$500$	5.00419	0.223794
$501$	27.3445	1.22166
$502$	20.7483	0.926044
$503$	11.9762	0.533994	0.266997	−	0.963697i	$-0.413969\pi$
$503$	11.9762	0.533994	0.266997	+	0.963697i	$0.413969\pi$
$504$	−13.4616	−0.599627
$505$	14.4694	0.643879
$506$	0	0
$507$	−6.99520	−0.310668
$508$	−27.0458	−1.19997
$509$	−10.5351	−0.466962	−0.233481	−	0.972361i	$-0.575012\pi$
$509$	−10.5351	−0.466962	−0.233481	+	0.972361i	$0.575012\pi$
$510$	32.2443	1.42780
$511$	8.89267	0.393389
$512$	28.7109	1.26886
$513$	−18.5206	−0.817706
$514$	16.8175	0.741788
$515$	−9.53701	−0.420251
$516$	56.8671	2.50344
$517$	0	0
$518$	−25.0220	−1.09940
$519$	−31.9877	−1.40410
$520$	24.8528	1.08987
$521$	−40.6225	−1.77970	−0.889852	−	0.456248i	$-0.849193\pi$
$521$	−40.6225	−1.77970	−0.889852	+	0.456248i	$0.849193\pi$
$522$	−37.6455	−1.64770
$523$	0.154037	0.00673555	0.00336777	−	0.999994i	$-0.498928\pi$
$523$	0.154037	0.00673555	0.00336777	+	0.999994i	$0.498928\pi$
$524$	101.582	4.43764
$525$	2.16636	0.0945478
$526$	−58.6419	−2.55691
$527$	6.51500	0.283798
$528$	0	0
$529$	4.07386	0.177124
$530$	3.01986	0.131174
$531$	4.78981	0.207860
$532$	32.7360	1.41929
$533$	20.4241	0.884665
$534$	1.41644	0.0612953
$535$	11.7986	0.510100
$536$	20.2443	0.874421
$537$	11.3934	0.491661
$538$	48.1437	2.07562
$539$	0	0
$540$	−14.1676	−0.609679
$541$	32.1473	1.38212	0.691060	−	0.722797i	$-0.257144\pi$
$541$	32.1473	1.38212	0.691060	+	0.722797i	$0.257144\pi$
$542$	−47.2872	−2.03116
$543$	17.5540	0.753316
$544$	74.7948	3.20680
$545$	5.74042	0.245893
$546$	17.9217	0.766978
$547$	3.63549	0.155442	0.0777212	−	0.996975i	$-0.475236\pi$
$547$	3.63549	0.155442	0.0777212	+	0.996975i	$0.475236\pi$
$548$	91.6839	3.91654
$549$	14.7389	0.629039
$550$	0	0
$551$	54.9586	2.34132
$552$	89.6215	3.81455
$553$	−3.27231	−0.139153
$554$	73.3265	3.11534
$555$	20.4821	0.869416
$556$	29.1313	1.23544
$557$	16.0162	0.678629	0.339314	−	0.940673i	$-0.389805\pi$
$557$	16.0162	0.678629	0.339314	+	0.940673i	$0.389805\pi$
$558$	5.19087	0.219747
$559$	−16.3970	−0.693521
$560$	11.0335	0.466252
$561$	0	0
$562$	16.6331	0.701625
$563$	24.6504	1.03889	0.519444	−	0.854504i	$-0.326139\pi$
$563$	24.6504	1.03889	0.519444	+	0.854504i	$0.326139\pi$
$564$	28.5382	1.20168
$565$	12.6578	0.532520
$566$	6.17353	0.259493
$567$	−11.2127	−0.470889
$568$	−90.4134	−3.79366
$569$	−26.4787	−1.11005	−0.555023	−	0.831835i	$-0.687291\pi$
$569$	−26.4787	−1.11005	−0.555023	+	0.831835i	$0.687291\pi$
$570$	−37.5061	−1.57096
$571$	−24.5231	−1.02626	−0.513129	−	0.858311i	$-0.671514\pi$
$571$	−24.5231	−1.02626	−0.513129	+	0.858311i	$0.671514\pi$
$572$	0	0
$573$	−54.8663	−2.29207
$574$	17.2923	0.721765
$575$	−5.20325	−0.216991
$576$	22.2309	0.926286
$577$	−1.34244	−0.0558867	−0.0279433	−	0.999610i	$-0.508896\pi$
$577$	−1.34244	−0.0558867	−0.0279433	+	0.999610i	$0.508896\pi$
$578$	−38.7165	−1.61039
$579$	−18.4794	−0.767977
$580$	42.0414	1.74568
$581$	0.721782	0.0299446
$582$	−42.1994	−1.74922
$583$	0	0
$584$	−70.7031	−2.92571
$585$	−5.29248	−0.218817
$586$	64.6573	2.67097
$587$	38.7935	1.60118	0.800590	−	0.599212i	$-0.204520\pi$
$587$	38.7935	1.60118	0.800590	+	0.599212i	$0.204520\pi$
$588$	10.8409	0.447071
$589$	−7.57815	−0.312252
$590$	−7.48698	−0.308234
$591$	−50.9448	−2.09559
$592$	104.318	4.28742
$593$	7.00160	0.287521	0.143761	−	0.989612i	$-0.454080\pi$
$593$	7.00160	0.287521	0.143761	+	0.989612i	$0.454080\pi$
$594$	0	0
$595$	−5.62397	−0.230560
$596$	−59.2349	−2.42635
$597$	34.6866	1.41963
$598$	−43.0451	−1.76024
$599$	22.4428	0.916988	0.458494	−	0.888698i	$-0.348389\pi$
$599$	22.4428	0.916988	0.458494	+	0.888698i	$0.348389\pi$
$600$	−17.2241	−0.703172
$601$	23.1120	0.942760	0.471380	−	0.881930i	$-0.343756\pi$
$601$	23.1120	0.942760	0.471380	+	0.881930i	$0.343756\pi$
$602$	−13.8827	−0.565818
$603$	−4.31109	−0.175561
$604$	30.3528	1.23504
$605$	0	0
$606$	−82.9584	−3.36995
$607$	0.676620	0.0274632	0.0137316	−	0.999906i	$-0.495629\pi$
$607$	0.676620	0.0274632	0.0137316	+	0.999906i	$0.495629\pi$
$608$	−87.0001	−3.52832
$609$	18.2001	0.737507
$610$	−23.0384	−0.932798
$611$	−8.22871	−0.332898
$612$	−47.6504	−1.92615
$613$	−32.9186	−1.32957	−0.664786	−	0.747034i	$-0.731477\pi$
$613$	−32.9186	−1.32957	−0.664786	+	0.747034i	$0.731477\pi$
$614$	13.9813	0.564239
$615$	−14.1548	−0.570777
$616$	0	0
$617$	−16.6795	−0.671490	−0.335745	−	0.941953i	$-0.608988\pi$
$617$	−16.6795	−0.671490	−0.335745	+	0.941953i	$0.608988\pi$
$618$	54.6792	2.19952
$619$	−16.7611	−0.673687	−0.336843	−	0.941561i	$-0.609359\pi$
$619$	−16.7611	−0.673687	−0.336843	+	0.941561i	$0.609359\pi$
$620$	−5.79703	−0.232814
$621$	14.7312	0.591144
$622$	−14.7361	−0.590863
$623$	−0.247052	−0.00989791
$624$	−74.7162	−2.99104
$625$	1.00000	0.0400000
$626$	36.4684	1.45757
$627$	0	0
$628$	88.3714	3.52640
$629$	−53.1724	−2.12012
$630$	−4.48094	−0.178525
$631$	−23.6295	−0.940676	−0.470338	−	0.882486i	$-0.655868\pi$
$631$	−23.6295	−0.940676	−0.470338	+	0.882486i	$0.655868\pi$
$632$	26.0172	1.03491
$633$	12.3948	0.492649
$634$	75.4186	2.99525
$635$	−5.40464	−0.214477
$636$	−12.3701	−0.490505
$637$	−3.12586	−0.123851
$638$	0	0
$639$	19.2538	0.761668
$640$	−8.15068	−0.322184
$641$	−0.129991	−0.00513434	−0.00256717	−	0.999997i	$-0.500817\pi$
$641$	−0.129991	−0.00513434	−0.00256717	+	0.999997i	$0.500817\pi$
$642$	−67.6460	−2.66978
$643$	−5.41167	−0.213415	−0.106708	−	0.994290i	$-0.534031\pi$
$643$	−5.41167	−0.213415	−0.106708	+	0.994290i	$0.534031\pi$
$644$	−26.0381	−1.02604
$645$	11.3639	0.447453
$646$	97.3675	3.83087
$647$	19.7906	0.778049	0.389025	−	0.921227i	$-0.372812\pi$
$647$	19.7906	0.778049	0.389025	+	0.921227i	$0.372812\pi$
$648$	89.1490	3.50210
$649$	0	0
$650$	8.27272	0.324483
$651$	−2.50959	−0.0983586
$652$	72.7517	2.84918
$653$	4.53855	0.177607	0.0888035	−	0.996049i	$-0.471696\pi$
$653$	4.53855	0.177607	0.0888035	+	0.996049i	$0.471696\pi$
$654$	−32.9120	−1.28696
$655$	20.2994	0.793164
$656$	−72.0920	−2.81472
$657$	15.0564	0.587407
$658$	−6.96693	−0.271599
$659$	−36.9953	−1.44113	−0.720566	−	0.693386i	$-0.756118\pi$
$659$	−36.9953	−1.44113	−0.720566	+	0.693386i	$0.756118\pi$
$660$	0	0
$661$	3.49539	0.135955	0.0679775	−	0.997687i	$-0.478345\pi$
$661$	3.49539	0.135955	0.0679775	+	0.997687i	$0.478345\pi$
$662$	72.6107	2.82209
$663$	38.0841	1.47906
$664$	−5.73868	−0.222704
$665$	6.54172	0.253677
$666$	−42.3654	−1.64163
$667$	−43.7138	−1.69261
$668$	63.1645	2.44391
$669$	9.92121	0.383576
$670$	6.73870	0.260339
$671$	0	0
$672$	−28.8111	−1.11141
$673$	38.2905	1.47599	0.737994	−	0.674807i	$-0.235773\pi$
$673$	38.2905	1.47599	0.737994	+	0.674807i	$0.235773\pi$
$674$	28.0118	1.07898
$675$	−2.83116	−0.108971
$676$	−16.1586	−0.621483
$677$	1.96344	0.0754611	0.0377305	−	0.999288i	$-0.487987\pi$
$677$	1.96344	0.0754611	0.0377305	+	0.999288i	$0.487987\pi$
$678$	−72.5721	−2.78712
$679$	7.36031	0.282463
$680$	44.7146	1.71473
$681$	−29.4582	−1.12884
$682$	0	0
$683$	4.22053	0.161494	0.0807470	−	0.996735i	$-0.474269\pi$
$683$	4.22053	0.161494	0.0807470	+	0.996735i	$0.474269\pi$
$684$	55.4263	2.11928
$685$	18.3214	0.700026
$686$	−2.64654	−0.101045
$687$	−27.4852	−1.04863
$688$	57.8776	2.20656
$689$	3.56678	0.135884
$690$	29.8322	1.13569
$691$	23.9254	0.910167	0.455083	−	0.890449i	$-0.349609\pi$
$691$	23.9254	0.910167	0.455083	+	0.890449i	$0.349609\pi$
$692$	−73.8900	−2.80888
$693$	0	0
$694$	46.6387	1.77038
$695$	5.82139	0.220818
$696$	−144.704	−5.48500
$697$	36.7465	1.39187
$698$	−41.2603	−1.56172
$699$	13.4988	0.510572
$700$	5.00419	0.189141
$701$	19.1685	0.723986	0.361993	−	0.932181i	$-0.382096\pi$
$701$	19.1685	0.723986	0.361993	+	0.932181i	$0.382096\pi$
$702$	−23.4214	−0.883983
$703$	61.8493	2.33269
$704$	0	0
$705$	5.70287	0.214783
$706$	85.7065	3.22561
$707$	14.4694	0.544177
$708$	30.6685	1.15259
$709$	13.2804	0.498757	0.249378	−	0.968406i	$-0.419774\pi$
$709$	13.2804	0.498757	0.249378	+	0.968406i	$0.419774\pi$
$710$	−30.0958	−1.12947
$711$	−5.54044	−0.207783
$712$	1.96424	0.0736129
$713$	6.02763	0.225736
$714$	32.2443	1.20671
$715$	0	0
$716$	26.3182	0.983556
$717$	−27.3916	−1.02296
$718$	50.9578	1.90173
$719$	5.99419	0.223546	0.111773	−	0.993734i	$-0.464347\pi$
$719$	5.99419	0.223546	0.111773	+	0.993734i	$0.464347\pi$
$720$	18.6812	0.696207
$721$	−9.53701	−0.355177
$722$	−62.9721	−2.34358
$723$	18.3254	0.681530
$724$	40.5489	1.50699
$725$	8.40125	0.312014
$726$	0	0
$727$	−16.6536	−0.617649	−0.308824	−	0.951119i	$-0.599936\pi$
$727$	−16.6536	−0.617649	−0.308824	+	0.951119i	$0.599936\pi$
$728$	24.8528	0.921106
$729$	−0.584598	−0.0216518
$730$	−23.5348	−0.871063
$731$	−29.5012	−1.09114
$732$	94.3710	3.48805
$733$	−35.5065	−1.31146	−0.655731	−	0.754994i	$-0.727640\pi$
$733$	−35.5065	−1.31146	−0.655731	+	0.754994i	$0.727640\pi$
$734$	4.47982	0.165353
$735$	2.16636	0.0799075
$736$	69.1995	2.55073
$737$	0	0
$738$	29.2780	1.07774
$739$	−45.1950	−1.66252	−0.831262	−	0.555881i	$-0.812381\pi$
$739$	−45.1950	−1.66252	−0.831262	+	0.555881i	$0.812381\pi$
$740$	47.3126	1.73924
$741$	−44.2989	−1.62736
$742$	3.01986	0.110862
$743$	19.5096	0.715738	0.357869	−	0.933772i	$-0.383504\pi$
$743$	19.5096	0.715738	0.357869	+	0.933772i	$0.383504\pi$
$744$	19.9530	0.731514
$745$	−11.8371	−0.433676
$746$	−3.42765	−0.125495
$747$	1.22207	0.0447132
$748$	0	0
$749$	11.7986	0.431113
$750$	−5.73337	−0.209353
$751$	−7.39109	−0.269705	−0.134852	−	0.990866i	$-0.543056\pi$
$751$	−7.39109	−0.269705	−0.134852	+	0.990866i	$0.543056\pi$
$752$	29.0454	1.05917
$753$	−16.9838	−0.618925
$754$	69.5011	2.53108
$755$	6.06549	0.220746
$756$	−14.1676	−0.515272
$757$	−26.7323	−0.971602	−0.485801	−	0.874069i	$-0.661472\pi$
$757$	−26.7323	−0.971602	−0.485801	+	0.874069i	$0.661472\pi$
$758$	−38.2105	−1.38787
$759$	0	0
$760$	−52.0113	−1.88665
$761$	−3.61552	−0.131063	−0.0655313	−	0.997851i	$-0.520874\pi$
$761$	−3.61552	−0.131063	−0.0655313	+	0.997851i	$0.520874\pi$
$762$	30.9868	1.12253
$763$	5.74042	0.207817
$764$	−126.738	−4.58523
$765$	−9.52211	−0.344273
$766$	−18.8984	−0.682827
$767$	−8.84295	−0.319301
$768$	−10.1580	−0.366546
$769$	15.6646	0.564879	0.282439	−	0.959285i	$-0.408856\pi$
$769$	15.6646	0.564879	0.282439	+	0.959285i	$0.408856\pi$
$770$	0	0
$771$	−13.7662	−0.495777
$772$	−42.6864	−1.53632
$773$	−7.60801	−0.273641	−0.136820	−	0.990596i	$-0.543688\pi$
$773$	−7.60801	−0.273641	−0.136820	+	0.990596i	$0.543688\pi$
$774$	−23.5053	−0.844879
$775$	−1.15843	−0.0416122
$776$	−58.5197	−2.10074
$777$	20.4821	0.734791
$778$	−66.6109	−2.38812
$779$	−42.7430	−1.53143
$780$	−33.8871	−1.21335
$781$	0	0
$782$	−77.4457	−2.76945
$783$	−23.7853	−0.850016
$784$	11.0335	0.394055
$785$	17.6595	0.630294
$786$	−116.384	−4.15128
$787$	−30.4041	−1.08379	−0.541894	−	0.840447i	$-0.682292\pi$
$787$	−30.4041	−1.08379	−0.541894	+	0.840447i	$0.682292\pi$
$788$	−117.680	−4.19217
$789$	48.0021	1.70892
$790$	8.66031	0.308120
$791$	12.6578	0.450061
$792$	0	0
$793$	−27.2109	−0.966288
$794$	15.3602	0.545112
$795$	−2.47194	−0.0876708
$796$	80.1243	2.83993
$797$	30.2413	1.07120	0.535601	−	0.844471i	$-0.320085\pi$
$797$	30.2413	1.07120	0.535601	+	0.844471i	$0.320085\pi$
$798$	−37.5061	−1.32770
$799$	−14.8049	−0.523760
$800$	−13.2993	−0.470200
$801$	−0.418290	−0.0147796
$802$	−33.0485	−1.16698
$803$	0	0
$804$	−27.6034	−0.973495
$805$	−5.20325	−0.183391
$806$	−9.58340	−0.337561
$807$	−39.4087	−1.38725
$808$	−115.042	−4.04716
$809$	47.9900	1.68724	0.843619	−	0.536942i	$-0.180421\pi$
$809$	47.9900	1.68724	0.843619	+	0.536942i	$0.180421\pi$
$810$	29.6749	1.04267
$811$	4.28841	0.150587	0.0752933	−	0.997161i	$-0.476011\pi$
$811$	4.28841	0.150587	0.0752933	+	0.997161i	$0.476011\pi$
$812$	42.0414	1.47536
$813$	38.7076	1.35753
$814$	0	0
$815$	14.5382	0.509250
$816$	−134.428	−4.70591
$817$	34.3153	1.20054
$818$	−97.3732	−3.40457
$819$	−5.29248	−0.184934
$820$	−32.6969	−1.14183
$821$	31.6883	1.10593	0.552965	−	0.833204i	$-0.313496\pi$
$821$	31.6883	1.10593	0.552965	+	0.833204i	$0.313496\pi$
$822$	−105.044	−3.66381
$823$	3.54472	0.123561	0.0617805	−	0.998090i	$-0.480322\pi$
$823$	3.54472	0.123561	0.0617805	+	0.998090i	$0.480322\pi$
$824$	75.8261	2.64153
$825$	0	0
$826$	−7.48698	−0.260505
$827$	−45.8509	−1.59439	−0.797195	−	0.603721i	$-0.793684\pi$
$827$	−45.8509	−1.59439	−0.797195	+	0.603721i	$0.793684\pi$
$828$	−44.0858	−1.53209
$829$	1.76505	0.0613026	0.0306513	−	0.999530i	$-0.490242\pi$
$829$	1.76505	0.0613026	0.0306513	+	0.999530i	$0.490242\pi$
$830$	−1.91023	−0.0663050
$831$	−60.0224	−2.08215
$832$	−41.0427	−1.42290
$833$	−5.62397	−0.194859
$834$	−33.3762	−1.15572
$835$	12.6223	0.436813
$836$	0	0
$837$	3.27971	0.113363
$838$	−31.6031	−1.09171
$839$	−7.70939	−0.266158	−0.133079	−	0.991105i	$-0.542486\pi$
$839$	−7.70939	−0.266158	−0.133079	+	0.991105i	$0.542486\pi$
$840$	−17.2241	−0.594289
$841$	41.5809	1.43383
$842$	−60.4113	−2.08191
$843$	−13.6153	−0.468934
$844$	28.6313	0.985531
$845$	−3.22901	−0.111081
$846$	−11.7959	−0.405551
$847$	0	0
$848$	−12.5899	−0.432339
$849$	−5.05343	−0.173433
$850$	14.8841	0.510520
$851$	−49.1947	−1.68637
$852$	123.280	4.22349
$853$	9.69177	0.331840	0.165920	−	0.986139i	$-0.446941\pi$
$853$	9.69177	0.331840	0.165920	+	0.986139i	$0.446941\pi$
$854$	−23.0384	−0.788358
$855$	11.0760	0.378790
$856$	−93.8077	−3.20628
$857$	53.2018	1.81734	0.908670	−	0.417515i	$-0.137099\pi$
$857$	53.2018	1.81734	0.908670	+	0.417515i	$0.137099\pi$
$858$	0	0
$859$	−49.7581	−1.69772	−0.848862	−	0.528615i	$-0.822711\pi$
$859$	−49.7581	−1.69772	−0.848862	+	0.528615i	$0.822711\pi$
$860$	26.2500	0.895119
$861$	−14.1548	−0.482395
$862$	5.11911	0.174358
$863$	34.9784	1.19068	0.595339	−	0.803475i	$-0.297018\pi$
$863$	34.9784	1.19068	0.595339	+	0.803475i	$0.297018\pi$
$864$	37.6524	1.28096
$865$	−14.7656	−0.502046
$866$	−83.1195	−2.82452
$867$	31.6919	1.07631
$868$	−5.79703	−0.196764
$869$	0	0
$870$	−48.1675	−1.63303
$871$	7.95914	0.269685
$872$	−45.6404	−1.54558
$873$	12.4620	0.421773
$874$	90.0836	3.04712
$875$	1.00000	0.0338062
$876$	96.4044	3.25720
$877$	−40.7478	−1.37595	−0.687977	−	0.725732i	$-0.741501\pi$
$877$	−40.7478	−1.37595	−0.687977	+	0.725732i	$0.741501\pi$
$878$	−3.21359	−0.108453
$879$	−52.9261	−1.78515
$880$	0	0
$881$	35.7741	1.20526	0.602630	−	0.798021i	$-0.294120\pi$
$881$	35.7741	1.20526	0.602630	+	0.798021i	$0.294120\pi$
$882$	−4.48094	−0.150881
$883$	−35.6583	−1.20000	−0.599999	−	0.800001i	$-0.704832\pi$
$883$	−35.6583	−1.20000	−0.599999	+	0.800001i	$0.704832\pi$
$884$	87.9724	2.95883
$885$	6.12857	0.206010
$886$	7.80300	0.262147
$887$	−47.4789	−1.59419	−0.797093	−	0.603856i	$-0.793630\pi$
$887$	−47.4789	−1.59419	−0.797093	+	0.603856i	$0.793630\pi$
$888$	−162.847	−5.46479
$889$	−5.40464	−0.181266
$890$	0.653833	0.0219165
$891$	0	0
$892$	22.9175	0.767335
$893$	17.2208	0.576273
$894$	67.8662	2.26979
$895$	5.25923	0.175797
$896$	−8.15068	−0.272295
$897$	35.2351	1.17647
$898$	−7.33569	−0.244795
$899$	−9.73229	−0.324590
$900$	8.47274	0.282425
$901$	6.41728	0.213790
$902$	0	0
$903$	11.3639	0.378167
$904$	−100.639	−3.34720
$905$	8.10300	0.269353
$906$	−34.7757	−1.15535
$907$	3.64231	0.120941	0.0604705	−	0.998170i	$-0.480740\pi$
$907$	3.64231	0.120941	0.0604705	+	0.998170i	$0.480740\pi$
$908$	−68.0469	−2.25821
$909$	24.4985	0.812565
$910$	8.27272	0.274238
$911$	10.1450	0.336118	0.168059	−	0.985777i	$-0.446250\pi$
$911$	10.1450	0.336118	0.168059	+	0.985777i	$0.446250\pi$
$912$	156.364	5.17774
$913$	0	0
$914$	96.9269	3.20606
$915$	18.8584	0.623440
$916$	−63.4895	−2.09775
$917$	20.2994	0.670346
$918$	−42.1392	−1.39080
$919$	16.5817	0.546981	0.273490	−	0.961875i	$-0.411822\pi$
$919$	16.5817	0.546981	0.273490	+	0.961875i	$0.411822\pi$
$920$	41.3696	1.36391
$921$	−11.4446	−0.377111
$922$	87.8299	2.89252
$923$	−35.5464	−1.17002
$924$	0	0
$925$	9.45459	0.310865
$926$	−37.3079	−1.22601
$927$	−16.1474	−0.530350
$928$	−111.730	−3.66773
$929$	−35.3734	−1.16056	−0.580281	−	0.814416i	$-0.697057\pi$
$929$	−35.3734	−1.16056	−0.580281	+	0.814416i	$0.697057\pi$
$930$	6.64174	0.217791
$931$	6.54172	0.214396
$932$	31.1815	1.02139
$933$	12.0624	0.394906
$934$	−42.6377	−1.39515
$935$	0	0
$936$	42.0790	1.37540
$937$	−21.6184	−0.706242	−0.353121	−	0.935578i	$-0.614880\pi$
$937$	−21.6184	−0.706242	−0.353121	+	0.935578i	$0.614880\pi$
$938$	6.73870	0.220026
$939$	−29.8517	−0.974173
$940$	13.1733	0.429667
$941$	−5.68138	−0.185208	−0.0926039	−	0.995703i	$-0.529519\pi$
$941$	−5.68138	−0.185208	−0.0926039	+	0.995703i	$0.529519\pi$
$942$	−101.248	−3.29885
$943$	33.9976	1.10711
$944$	31.2135	1.01591
$945$	−2.83116	−0.0920976
$946$	0	0
$947$	23.3154	0.757650	0.378825	−	0.925468i	$-0.376328\pi$
$947$	23.3154	0.757650	0.378825	+	0.925468i	$0.376328\pi$
$948$	−35.4748	−1.15217
$949$	−27.7972	−0.902336
$950$	−17.3129	−0.561706
$951$	−61.7349	−2.00189
$952$	44.7146	1.44921
$953$	48.6768	1.57680	0.788398	−	0.615166i	$-0.210911\pi$
$953$	48.6768	1.57680	0.788398	+	0.615166i	$0.210911\pi$
$954$	5.11301	0.165540
$955$	−25.3264	−0.819545
$956$	−63.2732	−2.04640
$957$	0	0
$958$	−55.5687	−1.79534
$959$	18.3214	0.591630
$960$	28.4444	0.918041
$961$	−29.6580	−0.956711
$962$	78.2152	2.52176
$963$	19.9766	0.643738
$964$	42.3308	1.36338
$965$	−8.53014	−0.274595
$966$	29.8322	0.959835
$967$	2.56263	0.0824086	0.0412043	−	0.999151i	$-0.486881\pi$
$967$	2.56263	0.0824086	0.0412043	+	0.999151i	$0.486881\pi$
$968$	0	0
$969$	−79.7015	−2.56038
$970$	−19.4794	−0.625445
$971$	−10.5871	−0.339757	−0.169878	−	0.985465i	$-0.554337\pi$
$971$	−10.5871	−0.339757	−0.169878	+	0.985465i	$0.554337\pi$
$972$	−79.0527	−2.53562
$973$	5.82139	0.186625
$974$	−42.8299	−1.37236
$975$	−6.77174	−0.216869
$976$	96.0480	3.07442
$977$	15.6783	0.501594	0.250797	−	0.968040i	$-0.419307\pi$
$977$	15.6783	0.501594	0.250797	+	0.968040i	$0.419307\pi$
$978$	−83.3527	−2.66533
$979$	0	0
$980$	5.00419	0.159853
$981$	9.71927	0.310312
$982$	60.3358	1.92539
$983$	−8.50300	−0.271204	−0.135602	−	0.990763i	$-0.543297\pi$
$983$	−8.50300	−0.271204	−0.135602	+	0.990763i	$0.543297\pi$
$984$	112.541	3.58767
$985$	−23.5163	−0.749291
$986$	125.045	3.98224
$987$	5.70287	0.181524
$988$	−102.328	−3.25549
$989$	−27.2943	−0.867907
$990$	0	0
$991$	45.5424	1.44670	0.723351	−	0.690480i	$-0.242601\pi$
$991$	45.5424	1.44670	0.723351	+	0.690480i	$0.242601\pi$
$992$	15.4063	0.489152
$993$	−59.4364	−1.88616
$994$	−30.0958	−0.954580
$995$	16.0115	0.507597
$996$	7.82476	0.247937
$997$	−17.2201	−0.545365	−0.272683	−	0.962104i	$-0.587911\pi$
$997$	−17.2201	−0.545365	−0.272683	+	0.962104i	$0.587911\pi$
$998$	95.4226	3.02055
$999$	−26.7674	−0.846885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.2		18
11.2	odd	10		385.2.n.f.246.1	yes	36
11.6	odd	10		385.2.n.f.36.1	✓	36
11.10	odd	2		4235.2.a.bo.1.17		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.1	✓	36	11.6	odd	10
385.2.n.f.246.1	yes	36	11.2	odd	10
4235.2.a.bo.1.17		18	11.10	odd	2
4235.2.a.bp.1.2		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.64654 q^{2} +2.16636 q^{3} +5.00419 q^{4} +1.00000 q^{5} -5.73337 q^{6} +1.00000 q^{7} -7.95071 q^{8} +1.69313 q^{9} +O(q^{10})\)	\(q-2.64654 q^{2} +2.16636 q^{3} +5.00419 q^{4} +1.00000 q^{5} -5.73337 q^{6} +1.00000 q^{7} -7.95071 q^{8} +1.69313 q^{9} -2.64654 q^{10} +10.8409 q^{12} -3.12586 q^{13} -2.64654 q^{14} +2.16636 q^{15} +11.0335 q^{16} -5.62397 q^{17} -4.48094 q^{18} +6.54172 q^{19} +5.00419 q^{20} +2.16636 q^{21} -5.20325 q^{23} -17.2241 q^{24} +1.00000 q^{25} +8.27272 q^{26} -2.83116 q^{27} +5.00419 q^{28} +8.40125 q^{29} -5.73337 q^{30} -1.15843 q^{31} -13.2993 q^{32} +14.8841 q^{34} +1.00000 q^{35} +8.47274 q^{36} +9.45459 q^{37} -17.3129 q^{38} -6.77174 q^{39} -7.95071 q^{40} -6.53391 q^{41} -5.73337 q^{42} +5.24561 q^{43} +1.69313 q^{45} +13.7706 q^{46} +2.63246 q^{47} +23.9026 q^{48} +1.00000 q^{49} -2.64654 q^{50} -12.1836 q^{51} -15.6424 q^{52} -1.14106 q^{53} +7.49278 q^{54} -7.95071 q^{56} +14.1717 q^{57} -22.2343 q^{58} +2.82897 q^{59} +10.8409 q^{60} +8.70510 q^{61} +3.06585 q^{62} +1.69313 q^{63} +13.1300 q^{64} -3.12586 q^{65} -2.54623 q^{67} -28.1434 q^{68} -11.2721 q^{69} -2.64654 q^{70} +11.3717 q^{71} -13.4616 q^{72} +8.89267 q^{73} -25.0220 q^{74} +2.16636 q^{75} +32.7360 q^{76} +17.9217 q^{78} -3.27231 q^{79} +11.0335 q^{80} -11.2127 q^{81} +17.2923 q^{82} +0.721782 q^{83} +10.8409 q^{84} -5.62397 q^{85} -13.8827 q^{86} +18.2001 q^{87} -0.247052 q^{89} -4.48094 q^{90} -3.12586 q^{91} -26.0381 q^{92} -2.50959 q^{93} -6.96693 q^{94} +6.54172 q^{95} -28.8111 q^{96} +7.36031 q^{97} -2.64654 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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