LMFDB - Embedded newform 4235.2.a.bo.1.17

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			1.17
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	$-0.114775\pi$
$2$	2.64654	1.87139	0.935694	+	0.352812i	$0.114775\pi$
$3$	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	$-0.357286\pi$
$13$	3.12586	0.866957	0.433479	+	0.901164i	$0.357286\pi$
$14$	−2.64654	−0.707318
$15$	2.16636	0.559353
$16$	11.0335	2.75838
$17$	5.62397	1.36401	0.682007	−	0.731346i	$-0.261107\pi$
$17$	5.62397	1.36401	0.682007	+	0.731346i	$0.261107\pi$
$18$	4.48094	1.05617
$19$	−6.54172	−1.50077	−0.750387	−	0.660999i	$-0.770133\pi$
$19$	−6.54172	−1.50077	−0.750387	+	0.660999i	$0.770133\pi$
$20$	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	$-0.784799\pi$
$29$	−8.40125	−1.56007	−0.780036	+	0.625734i	$0.784799\pi$
$30$	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	$-0.329567\pi$
$41$	6.53391	1.02042	0.510212	+	0.860048i	$0.329567\pi$
$42$	−5.73337	−0.884679
$43$	−5.24561	−0.799949	−0.399974	−	0.916526i	$-0.630981\pi$
$43$	−5.24561	−0.799949	−0.399974	+	0.916526i	$0.630981\pi$
$44$	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	$-0.688158\pi$
$61$	−8.70510	−1.11457	−0.557287	+	0.830320i	$0.688158\pi$
$62$	−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	$-0.674219\pi$
$73$	−8.89267	−1.04081	−0.520404	+	0.853920i	$0.674219\pi$
$74$	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	$-0.441069\pi$
$79$	3.27231	0.368164	0.184082	+	0.982911i	$0.441069\pi$
$80$	11.0335	1.23359
$81$	−11.2127	−1.24586
$82$	17.2923	1.90961
$83$	−0.721782	−0.0792259	−0.0396129	−	0.999215i	$-0.512612\pi$
$83$	−0.721782	−0.0792259	−0.0396129	+	0.999215i	$0.512612\pi$
$84$	−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	$-0.755803\pi$
$101$	−14.4694	−1.43976	−0.719879	+	0.694100i	$0.755803\pi$
$102$	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	$-0.693177\pi$
$107$	−11.7986	−1.14062	−0.570309	+	0.821430i	$0.693177\pi$
$108$	−14.1676	−1.36328
$109$	−5.74042	−0.549832	−0.274916	−	0.961468i	$-0.588650\pi$
$109$	−5.74042	−0.549832	−0.274916	+	0.961468i	$0.588650\pi$
$110$	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	$-0.422921\pi$
$127$	5.40464	0.479584	0.239792	+	0.970824i	$0.422921\pi$
$128$	8.15068	0.720425
$129$	−11.3639	−1.00054
$130$	8.27272	0.725565
$131$	−20.2994	−1.77357	−0.886784	−	0.462184i	$-0.847066\pi$
$131$	−20.2994	−1.77357	−0.886784	+	0.462184i	$0.847066\pi$
$132$	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	$-0.579406\pi$
$139$	−5.82139	−0.493764	−0.246882	+	0.969046i	$0.579406\pi$
$140$	−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	$-0.338869\pi$
$149$	11.8371	0.969729	0.484865	+	0.874589i	$0.338869\pi$
$150$	5.73337	0.468128
$151$	−6.06549	−0.493602	−0.246801	−	0.969066i	$-0.579379\pi$
$151$	−6.06549	−0.493602	−0.246801	+	0.969066i	$0.579379\pi$
$152$	−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	$-0.662409\pi$
$167$	−12.6223	−0.976744	−0.488372	+	0.872635i	$0.662409\pi$
$168$	−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	$-0.310300\pi$
$173$	14.7656	1.12261	0.561305	+	0.827609i	$0.310300\pi$
$174$	−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	$-0.400673\pi$
$193$	8.53014	0.614013	0.307007	+	0.951707i	$0.400673\pi$
$194$	19.4794	1.39854
$195$	6.77174	0.484935
$196$	5.00419	0.357442
$197$	23.5163	1.67547	0.837733	−	0.546080i	$-0.183880\pi$
$197$	23.5163	1.67547	0.837733	+	0.546080i	$0.183880\pi$
$198$	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	$-0.563101\pi$
$211$	−5.72148	−0.393883	−0.196941	+	0.980415i	$0.563101\pi$
$212$	−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	$-0.350973\pi$
$227$	13.5980	0.902530	0.451265	+	0.892390i	$0.350973\pi$
$228$	−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	$-0.565429\pi$
$233$	−6.23109	−0.408212	−0.204106	+	0.978949i	$0.565429\pi$
$234$	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	$-0.365899\pi$
$239$	12.6440	0.817875	0.408938	+	0.912562i	$0.365899\pi$
$240$	23.9026	1.54291
$241$	−8.45907	−0.544897	−0.272448	−	0.962170i	$-0.587833\pi$
$241$	−8.45907	−0.544897	−0.272448	+	0.962170i	$0.587833\pi$
$242$	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	$-0.739394\pi$
$263$	−22.1579	−1.36632	−0.683158	+	0.730270i	$0.739394\pi$
$264$	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	$-0.682593\pi$
$271$	−17.8675	−1.08538	−0.542688	+	0.839935i	$0.682593\pi$
$272$	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	$-0.186988\pi$
$277$	27.7065	1.66472	0.832362	+	0.554232i	$0.186988\pi$
$278$	−15.4065	−0.924023
$279$	−1.96138	−0.117425
$280$	−7.95071	−0.475146
$281$	6.28484	0.374922	0.187461	−	0.982272i	$-0.439974\pi$
$281$	6.28484	0.374922	0.187461	+	0.982272i	$0.439974\pi$
$282$	15.0929	0.898768
$283$	2.33268	0.138663	0.0693317	−	0.997594i	$-0.477913\pi$
$283$	2.33268	0.138663	0.0693317	+	0.997594i	$0.477913\pi$
$284$	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	$-0.247048\pi$
$293$	24.4309	1.42727	0.713633	+	0.700520i	$0.247048\pi$
$294$	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	$-0.451830\pi$
$307$	5.28285	0.301508	0.150754	+	0.988571i	$0.451830\pi$
$308$	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	$-0.406916\pi$
$337$	10.5843	0.576564	0.288282	+	0.957546i	$0.406916\pi$
$338$	−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	$-0.343166\pi$
$347$	17.6225	0.946026	0.473013	+	0.881055i	$0.343166\pi$
$348$	−91.0770	−4.88224
$349$	−15.5902	−0.834527	−0.417263	−	0.908786i	$-0.637011\pi$
$349$	−15.5902	−0.834527	−0.417263	+	0.908786i	$0.637011\pi$
$350$	−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	$-0.330346\pi$
$359$	19.2545	1.01621	0.508106	+	0.861294i	$0.330346\pi$
$360$	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	$-0.510675\pi$
$373$	−1.29514	−0.0670600	−0.0335300	+	0.999438i	$0.510675\pi$
$374$	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	$-0.863641\pi$
$409$	−36.7926	−1.81928	−0.909638	+	0.415401i	$0.863641\pi$
$410$	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	$-0.485166\pi$
$431$	1.93426	0.0931702	0.0465851	+	0.998914i	$0.485166\pi$
$432$	−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	$-0.509225\pi$
$439$	−1.21426	−0.0579534	−0.0289767	+	0.999580i	$0.509225\pi$
$440$	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	$-0.172573\pi$
$457$	36.6240	1.71320	0.856599	+	0.515983i	$0.172573\pi$
$458$	−33.5774	−1.56897
$459$	−15.9224	−0.743192
$460$	−26.0381	−1.21403
$461$	33.1867	1.54566	0.772828	−	0.634615i	$-0.218841\pi$
$461$	33.1867	1.54566	0.772828	+	0.634615i	$0.218841\pi$
$462$	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	$-0.659248\pi$
$479$	−20.9967	−0.959364	−0.479682	+	0.877442i	$0.659248\pi$
$480$	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	$-0.328004\pi$
$491$	22.7980	1.02886	0.514429	+	0.857533i	$0.328004\pi$
$492$	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	$-0.586031\pi$
$503$	−11.9762	−0.533994	−0.266997	+	0.963697i	$0.586031\pi$
$504$	−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	$-0.501072\pi$
$523$	−0.154037	−0.00673555	−0.00336777	+	0.999994i	$0.501072\pi$
$524$	−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	$-0.742856\pi$
$541$	−32.1473	−1.38212	−0.691060	+	0.722797i	$0.742856\pi$
$542$	−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	$-0.524764\pi$
$547$	−3.63549	−0.155442	−0.0777212	+	0.996975i	$0.524764\pi$
$548$	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	$-0.610195\pi$
$557$	−16.0162	−0.678629	−0.339314	+	0.940673i	$0.610195\pi$
$558$	−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	$-0.673861\pi$
$563$	−24.6504	−1.03889	−0.519444	+	0.854504i	$0.673861\pi$
$564$	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	$-0.312709\pi$
$569$	26.4787	1.11005	0.555023	+	0.831835i	$0.312709\pi$
$570$	−37.5061	−1.57096
$571$	24.5231	1.02626	0.513129	−	0.858311i	$-0.328486\pi$
$571$	24.5231	1.02626	0.513129	+	0.858311i	$0.328486\pi$
$572$	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	$-0.545920\pi$
$593$	−7.00160	−0.287521	−0.143761	+	0.989612i	$0.545920\pi$
$594$	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	$-0.656244\pi$
$601$	−23.1120	−0.942760	−0.471380	+	0.881930i	$0.656244\pi$
$602$	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	$-0.504371\pi$
$607$	−0.676620	−0.0274632	−0.0137316	+	0.999906i	$0.504371\pi$
$608$	−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	$-0.268523\pi$
$613$	32.9186	1.32957	0.664786	+	0.747034i	$0.268523\pi$
$614$	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	$-0.243882\pi$
$659$	36.9953	1.44113	0.720566	+	0.693386i	$0.243882\pi$
$660$	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	$-0.764227\pi$
$673$	−38.2905	−1.47599	−0.737994	+	0.674807i	$0.764227\pi$
$674$	28.0118	1.07898
$675$	−2.83116	−0.108971
$676$	−16.1586	−0.621483
$677$	−1.96344	−0.0754611	−0.0377305	−	0.999288i	$-0.512013\pi$
$677$	−1.96344	−0.0754611	−0.0377305	+	0.999288i	$0.512013\pi$
$678$	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	$-0.617904\pi$
$701$	−19.1685	−0.723986	−0.361993	+	0.932181i	$0.617904\pi$
$702$	−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	$-0.272360\pi$
$733$	35.5065	1.31146	0.655731	+	0.754994i	$0.272360\pi$
$734$	−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	$-0.187619\pi$
$739$	45.1950	1.66252	0.831262	+	0.555881i	$0.187619\pi$
$740$	47.3126	1.73924
$741$	−44.2989	−1.62736
$742$	3.01986	0.110862
$743$	−19.5096	−0.715738	−0.357869	−	0.933772i	$-0.616496\pi$
$743$	−19.5096	−0.715738	−0.357869	+	0.933772i	$0.616496\pi$
$744$	−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	$-0.479126\pi$
$761$	3.61552	0.131063	0.0655313	+	0.997851i	$0.479126\pi$
$762$	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	$-0.591144\pi$
$769$	−15.6646	−0.564879	−0.282439	+	0.959285i	$0.591144\pi$
$770$	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	$-0.317708\pi$
$787$	30.4041	1.08379	0.541894	+	0.840447i	$0.317708\pi$
$788$	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	$-0.819579\pi$
$809$	−47.9900	−1.68724	−0.843619	+	0.536942i	$0.819579\pi$
$810$	−29.6749	−1.04267
$811$	−4.28841	−0.150587	−0.0752933	−	0.997161i	$-0.523989\pi$
$811$	−4.28841	−0.150587	−0.0752933	+	0.997161i	$0.523989\pi$
$812$	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	$-0.686504\pi$
$821$	−31.6883	−1.10593	−0.552965	+	0.833204i	$0.686504\pi$
$822$	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	$-0.206316\pi$
$827$	45.8509	1.59439	0.797195	+	0.603721i	$0.206316\pi$
$828$	−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	$-0.553059\pi$
$853$	−9.69177	−0.331840	−0.165920	+	0.986139i	$0.553059\pi$
$854$	23.0384	0.788358
$855$	−11.0760	−0.378790
$856$	−93.8077	−3.20628
$857$	−53.2018	−1.81734	−0.908670	−	0.417515i	$-0.862901\pi$
$857$	−53.2018	−1.81734	−0.908670	+	0.417515i	$0.862901\pi$
$858$	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	$-0.258499\pi$
$877$	40.7478	1.37595	0.687977	+	0.725732i	$0.258499\pi$
$878$	−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	$-0.206370\pi$
$887$	47.4789	1.59419	0.797093	+	0.603856i	$0.206370\pi$
$888$	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	$-0.588178\pi$
$919$	−16.5817	−0.546981	−0.273490	+	0.961875i	$0.588178\pi$
$920$	−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	$-0.385120\pi$
$937$	21.6184	0.706242	0.353121	+	0.935578i	$0.385120\pi$
$938$	6.73870	0.220026
$939$	−29.8517	−0.974173
$940$	13.1733	0.429667
$941$	5.68138	0.185208	0.0926039	−	0.995703i	$-0.470481\pi$
$941$	5.68138	0.185208	0.0926039	+	0.995703i	$0.470481\pi$
$942$	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	$-0.789089\pi$
$953$	−48.6768	−1.57680	−0.788398	+	0.615166i	$0.789089\pi$
$954$	−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	$-0.513119\pi$
$967$	−2.56263	−0.0824086	−0.0412043	+	0.999151i	$0.513119\pi$
$968$	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	$-0.412089\pi$
$997$	17.2201	0.545365	0.272683	+	0.962104i	$0.412089\pi$
$998$	−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.bo.1.17		18
11.5	even	5		385.2.n.f.36.1	✓	36
11.9	even	5		385.2.n.f.246.1	yes	36
11.10	odd	2		4235.2.a.bp.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.1	✓	36	11.5	even	5
385.2.n.f.246.1	yes	36	11.9	even	5
4235.2.a.bo.1.17		18	1.1	even	1	trivial
4235.2.a.bp.1.2		18	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)

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