LMFDB - Embedded newform 4235.2.a.bo.1.12

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			1.12
Root			$-0.740902$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.740902 q^{2} +3.32552 q^{3} -1.45106 q^{4} +1.00000 q^{5} +2.46389 q^{6} -1.00000 q^{7} -2.55690 q^{8} +8.05911 q^{9} +O(q^{10})$	\(q+0.740902 q^{2} +3.32552 q^{3} -1.45106 q^{4} +1.00000 q^{5} +2.46389 q^{6} -1.00000 q^{7} -2.55690 q^{8} +8.05911 q^{9} +0.740902 q^{10} -4.82555 q^{12} +0.588588 q^{13} -0.740902 q^{14} +3.32552 q^{15} +1.00771 q^{16} -4.88277 q^{17} +5.97101 q^{18} +4.21562 q^{19} -1.45106 q^{20} -3.32552 q^{21} +4.20377 q^{23} -8.50304 q^{24} +1.00000 q^{25} +0.436086 q^{26} +16.8242 q^{27} +1.45106 q^{28} -0.124718 q^{29} +2.46389 q^{30} +6.32361 q^{31} +5.86042 q^{32} -3.61765 q^{34} -1.00000 q^{35} -11.6943 q^{36} +0.686995 q^{37} +3.12336 q^{38} +1.95736 q^{39} -2.55690 q^{40} +7.78513 q^{41} -2.46389 q^{42} -0.533845 q^{43} +8.05911 q^{45} +3.11458 q^{46} -11.2602 q^{47} +3.35118 q^{48} +1.00000 q^{49} +0.740902 q^{50} -16.2378 q^{51} -0.854079 q^{52} +11.6652 q^{53} +12.4651 q^{54} +2.55690 q^{56} +14.0191 q^{57} -0.0924040 q^{58} -10.6492 q^{59} -4.82555 q^{60} -0.361742 q^{61} +4.68518 q^{62} -8.05911 q^{63} +2.32657 q^{64} +0.588588 q^{65} +4.73740 q^{67} +7.08521 q^{68} +13.9797 q^{69} -0.740902 q^{70} +3.22187 q^{71} -20.6063 q^{72} +9.81141 q^{73} +0.508996 q^{74} +3.32552 q^{75} -6.11713 q^{76} +1.45021 q^{78} +13.6286 q^{79} +1.00771 q^{80} +31.7719 q^{81} +5.76802 q^{82} -16.2270 q^{83} +4.82555 q^{84} -4.88277 q^{85} -0.395527 q^{86} -0.414754 q^{87} +13.3986 q^{89} +5.97101 q^{90} -0.588588 q^{91} -6.09993 q^{92} +21.0293 q^{93} -8.34273 q^{94} +4.21562 q^{95} +19.4890 q^{96} -7.19044 q^{97} +0.740902 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.740902	0.523897	0.261948	−	0.965082i	$-0.415635\pi$
$2$	0.740902	0.523897	0.261948	+	0.965082i	$0.415635\pi$
$3$	3.32552	1.91999	0.959996	−	0.280013i	$-0.0903389\pi$
$3$	3.32552	1.91999	0.959996	+	0.280013i	$0.0903389\pi$
$4$	−1.45106	−0.725532
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.46389	1.00588
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.55690	−0.904001
$9$	8.05911	2.68637
$10$	0.740902	0.234294
$11$	0	0
$11$	0	0
$12$	−4.82555	−1.39302
$13$	0.588588	0.163245	0.0816225	−	0.996663i	$-0.473990\pi$
$13$	0.588588	0.163245	0.0816225	+	0.996663i	$0.473990\pi$
$14$	−0.740902	−0.198014
$15$	3.32552	0.858647
$16$	1.00771	0.251929
$17$	−4.88277	−1.18425	−0.592123	−	0.805848i	$-0.701710\pi$
$17$	−4.88277	−1.18425	−0.592123	+	0.805848i	$0.701710\pi$
$18$	5.97101	1.40738
$19$	4.21562	0.967130	0.483565	−	0.875309i	$-0.339342\pi$
$19$	4.21562	0.967130	0.483565	+	0.875309i	$0.339342\pi$
$20$	−1.45106	−0.324468
$21$	−3.32552	−0.725689
$22$	0	0
$23$	4.20377	0.876546	0.438273	−	0.898842i	$-0.355590\pi$
$23$	4.20377	0.876546	0.438273	+	0.898842i	$0.355590\pi$
$24$	−8.50304	−1.73567
$25$	1.00000	0.200000
$26$	0.436086	0.0855235
$27$	16.8242	3.23782
$28$	1.45106	0.274225
$29$	−0.124718	−0.0231596	−0.0115798	−	0.999933i	$-0.503686\pi$
$29$	−0.124718	−0.0231596	−0.0115798	+	0.999933i	$0.503686\pi$
$30$	2.46389	0.449842
$31$	6.32361	1.13575	0.567877	−	0.823114i	$-0.307765\pi$
$31$	6.32361	1.13575	0.567877	+	0.823114i	$0.307765\pi$
$32$	5.86042	1.03599
$33$	0	0
$34$	−3.61765	−0.620423
$35$	−1.00000	−0.169031
$36$	−11.6943	−1.94905
$37$	0.686995	0.112941	0.0564706	−	0.998404i	$-0.482015\pi$
$37$	0.686995	0.112941	0.0564706	+	0.998404i	$0.482015\pi$
$38$	3.12336	0.506676
$39$	1.95736	0.313429
$40$	−2.55690	−0.404282
$41$	7.78513	1.21583	0.607917	−	0.794001i	$-0.292005\pi$
$41$	7.78513	1.21583	0.607917	+	0.794001i	$0.292005\pi$
$42$	−2.46389	−0.380186
$43$	−0.533845	−0.0814106	−0.0407053	−	0.999171i	$-0.512960\pi$
$43$	−0.533845	−0.0814106	−0.0407053	+	0.999171i	$0.512960\pi$
$44$	0	0
$45$	8.05911	1.20138
$46$	3.11458	0.459220
$47$	−11.2602	−1.64247	−0.821237	−	0.570588i	$-0.806715\pi$
$47$	−11.2602	−1.64247	−0.821237	+	0.570588i	$0.806715\pi$
$48$	3.35118	0.483701
$49$	1.00000	0.142857
$50$	0.740902	0.104779
$51$	−16.2378	−2.27374
$52$	−0.854079	−0.118439
$53$	11.6652	1.60234	0.801168	−	0.598439i	$-0.204212\pi$
$53$	11.6652	1.60234	0.801168	+	0.598439i	$0.204212\pi$
$54$	12.4651	1.69628
$55$	0	0
$56$	2.55690	0.341680
$57$	14.0191	1.85688
$58$	−0.0924040	−0.0121332
$59$	−10.6492	−1.38641	−0.693205	−	0.720741i	$-0.743802\pi$
$59$	−10.6492	−1.38641	−0.693205	+	0.720741i	$0.743802\pi$
$60$	−4.82555	−0.622976
$61$	−0.361742	−0.0463164	−0.0231582	−	0.999732i	$-0.507372\pi$
$61$	−0.361742	−0.0463164	−0.0231582	+	0.999732i	$0.507372\pi$
$62$	4.68518	0.595018
$63$	−8.05911	−1.01535
$64$	2.32657	0.290821
$65$	0.588588	0.0730053
$66$	0	0
$67$	4.73740	0.578765	0.289383	−	0.957213i	$-0.406550\pi$
$67$	4.73740	0.578765	0.289383	+	0.957213i	$0.406550\pi$
$68$	7.08521	0.859208
$69$	13.9797	1.68296
$70$	−0.740902	−0.0885548
$71$	3.22187	0.382366	0.191183	−	0.981554i	$-0.438768\pi$
$71$	3.22187	0.382366	0.191183	+	0.981554i	$0.438768\pi$
$72$	−20.6063	−2.42848
$73$	9.81141	1.14834	0.574169	−	0.818737i	$-0.305325\pi$
$73$	9.81141	1.14834	0.574169	+	0.818737i	$0.305325\pi$
$74$	0.508996	0.0591696
$75$	3.32552	0.383998
$76$	−6.11713	−0.701683
$77$	0	0
$78$	1.45021	0.164204
$79$	13.6286	1.53334	0.766668	−	0.642044i	$-0.221913\pi$
$79$	13.6286	1.53334	0.766668	+	0.642044i	$0.221913\pi$
$80$	1.00771	0.112666
$81$	31.7719	3.53021
$82$	5.76802	0.636971
$83$	−16.2270	−1.78114	−0.890571	−	0.454844i	$-0.849695\pi$
$83$	−16.2270	−1.78114	−0.890571	+	0.454844i	$0.849695\pi$
$84$	4.82555	0.526510
$85$	−4.88277	−0.529611
$86$	−0.395527	−0.0426508
$87$	−0.414754	−0.0444663
$88$	0	0
$89$	13.3986	1.42025	0.710126	−	0.704075i	$-0.248638\pi$
$89$	13.3986	1.42025	0.710126	+	0.704075i	$0.248638\pi$
$90$	5.97101	0.629400
$91$	−0.588588	−0.0617008
$92$	−6.09993	−0.635962
$93$	21.0293	2.18064
$94$	−8.34273	−0.860487
$95$	4.21562	0.432514
$96$	19.4890	1.98908
$97$	−7.19044	−0.730079	−0.365039	−	0.930992i	$-0.618944\pi$
$97$	−7.19044	−0.730079	−0.365039	+	0.930992i	$0.618944\pi$
$98$	0.740902	0.0748424
$99$	0	0
$100$	−1.45106	−0.145106
$101$	−16.6830	−1.66002	−0.830012	−	0.557746i	$-0.811666\pi$
$101$	−16.6830	−1.66002	−0.830012	+	0.557746i	$0.811666\pi$
$102$	−12.0306	−1.19121
$103$	−4.62225	−0.455444	−0.227722	−	0.973726i	$-0.573128\pi$
$103$	−4.62225	−0.455444	−0.227722	+	0.973726i	$0.573128\pi$
$104$	−1.50496	−0.147574
$105$	−3.32552	−0.324538
$106$	8.64276	0.839459
$107$	−6.26645	−0.605801	−0.302900	−	0.953022i	$-0.597955\pi$
$107$	−6.26645	−0.605801	−0.302900	+	0.953022i	$0.597955\pi$
$108$	−24.4130	−2.34914
$109$	12.8690	1.23262	0.616312	−	0.787502i	$-0.288626\pi$
$109$	12.8690	1.23262	0.616312	+	0.787502i	$0.288626\pi$
$110$	0	0
$111$	2.28462	0.216846
$112$	−1.00771	−0.0952200
$113$	0.516482	0.0485866	0.0242933	−	0.999705i	$-0.492266\pi$
$113$	0.516482	0.0485866	0.0242933	+	0.999705i	$0.492266\pi$
$114$	10.3868	0.972815
$115$	4.20377	0.392003
$116$	0.180974	0.0168030
$117$	4.74349	0.438536
$118$	−7.89002	−0.726336
$119$	4.88277	0.447603
$120$	−8.50304	−0.776217
$121$	0	0
$122$	−0.268016	−0.0242650
$123$	25.8896	2.33439
$124$	−9.17596	−0.824026
$125$	1.00000	0.0894427
$126$	−5.97101	−0.531940
$127$	−8.74072	−0.775614	−0.387807	−	0.921741i	$-0.626767\pi$
$127$	−8.74072	−0.775614	−0.387807	+	0.921741i	$0.626767\pi$
$128$	−9.99708	−0.883625
$129$	−1.77531	−0.156308
$130$	0.436086	0.0382473
$131$	4.10058	0.358269	0.179135	−	0.983825i	$-0.442670\pi$
$131$	4.10058	0.358269	0.179135	+	0.983825i	$0.442670\pi$
$132$	0	0
$133$	−4.21562	−0.365541
$134$	3.50995	0.303213
$135$	16.8242	1.44800
$136$	12.4848	1.07056
$137$	−17.3543	−1.48268	−0.741341	−	0.671128i	$-0.765810\pi$
$137$	−17.3543	−1.48268	−0.741341	+	0.671128i	$0.765810\pi$
$138$	10.3576	0.881698
$139$	−6.02294	−0.510859	−0.255430	−	0.966828i	$-0.582217\pi$
$139$	−6.02294	−0.510859	−0.255430	+	0.966828i	$0.582217\pi$
$140$	1.45106	0.122637
$141$	−37.4462	−3.15354
$142$	2.38709	0.200320
$143$	0	0
$144$	8.12128	0.676773
$145$	−0.124718	−0.0103573
$146$	7.26930	0.601611
$147$	3.32552	0.274285
$148$	−0.996873	−0.0819425
$149$	15.0872	1.23599	0.617995	−	0.786182i	$-0.287945\pi$
$149$	15.0872	1.23599	0.617995	+	0.786182i	$0.287945\pi$
$150$	2.46389	0.201176
$151$	8.22954	0.669711	0.334855	−	0.942270i	$-0.391313\pi$
$151$	8.22954	0.669711	0.334855	+	0.942270i	$0.391313\pi$
$152$	−10.7789	−0.874286
$153$	−39.3508	−3.18132
$154$	0	0
$155$	6.32361	0.507924
$156$	−2.84026	−0.227403
$157$	−4.76691	−0.380441	−0.190221	−	0.981741i	$-0.560920\pi$
$157$	−4.76691	−0.380441	−0.190221	+	0.981741i	$0.560920\pi$
$158$	10.0975	0.803310
$159$	38.7929	3.07647
$160$	5.86042	0.463307
$161$	−4.20377	−0.331303
$162$	23.5399	1.84947
$163$	9.15700	0.717231	0.358616	−	0.933485i	$-0.383249\pi$
$163$	9.15700	0.717231	0.358616	+	0.933485i	$0.383249\pi$
$164$	−11.2967	−0.882126
$165$	0	0
$166$	−12.0226	−0.933135
$167$	−16.7861	−1.29895	−0.649475	−	0.760383i	$-0.725011\pi$
$167$	−16.7861	−1.29895	−0.649475	+	0.760383i	$0.725011\pi$
$168$	8.50304	0.656023
$169$	−12.6536	−0.973351
$170$	−3.61765	−0.277461
$171$	33.9741	2.59807
$172$	0.774643	0.0590660
$173$	−7.42591	−0.564582	−0.282291	−	0.959329i	$-0.591094\pi$
$173$	−7.42591	−0.564582	−0.282291	+	0.959329i	$0.591094\pi$
$174$	−0.307292	−0.0232957
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−35.4142	−2.66189
$178$	9.92707	0.744065
$179$	−2.45750	−0.183682	−0.0918410	−	0.995774i	$-0.529275\pi$
$179$	−2.45750	−0.183682	−0.0918410	+	0.995774i	$0.529275\pi$
$180$	−11.6943	−0.871640
$181$	−3.91995	−0.291367	−0.145684	−	0.989331i	$-0.546538\pi$
$181$	−3.91995	−0.291367	−0.145684	+	0.989331i	$0.546538\pi$
$182$	−0.436086	−0.0323249
$183$	−1.20298	−0.0889271
$184$	−10.7486	−0.792398
$185$	0.686995	0.0505089
$186$	15.5807	1.14243
$187$	0	0
$188$	16.3393	1.19167
$189$	−16.8242	−1.22378
$190$	3.12336	0.226593
$191$	−12.8515	−0.929899	−0.464950	−	0.885337i	$-0.653928\pi$
$191$	−12.8515	−0.929899	−0.464950	+	0.885337i	$0.653928\pi$
$192$	7.73706	0.558374
$193$	−8.90911	−0.641292	−0.320646	−	0.947199i	$-0.603900\pi$
$193$	−8.90911	−0.641292	−0.320646	+	0.947199i	$0.603900\pi$
$194$	−5.32741	−0.382486
$195$	1.95736	0.140170
$196$	−1.45106	−0.103647
$197$	2.60486	0.185588	0.0927942	−	0.995685i	$-0.470420\pi$
$197$	2.60486	0.185588	0.0927942	+	0.995685i	$0.470420\pi$
$198$	0	0
$199$	6.85953	0.486259	0.243130	−	0.969994i	$-0.421826\pi$
$199$	6.85953	0.486259	0.243130	+	0.969994i	$0.421826\pi$
$200$	−2.55690	−0.180800
$201$	15.7543	1.11122
$202$	−12.3605	−0.869681
$203$	0.124718	0.00875351
$204$	23.5620	1.64967
$205$	7.78513	0.543737
$206$	−3.42464	−0.238606
$207$	33.8786	2.35473
$208$	0.593128	0.0411261
$209$	0	0
$210$	−2.46389	−0.170024
$211$	10.3377	0.711679	0.355839	−	0.934547i	$-0.384195\pi$
$211$	10.3377	0.711679	0.355839	+	0.934547i	$0.384195\pi$
$212$	−16.9269	−1.16255
$213$	10.7144	0.734140
$214$	−4.64283	−0.317377
$215$	−0.533845	−0.0364079
$216$	−43.0178	−2.92699
$217$	−6.32361	−0.429275
$218$	9.53465	0.645768
$219$	32.6281	2.20480
$220$	0	0
$221$	−2.87394	−0.193322
$222$	1.69268	0.113605
$223$	7.56625	0.506673	0.253337	−	0.967378i	$-0.418472\pi$
$223$	7.56625	0.506673	0.253337	+	0.967378i	$0.418472\pi$
$224$	−5.86042	−0.391566
$225$	8.05911	0.537274
$226$	0.382663	0.0254544
$227$	3.63619	0.241343	0.120671	−	0.992693i	$-0.461495\pi$
$227$	3.63619	0.241343	0.120671	+	0.992693i	$0.461495\pi$
$228$	−20.3427	−1.34723
$229$	1.33243	0.0880497	0.0440249	−	0.999030i	$-0.485982\pi$
$229$	1.33243	0.0880497	0.0440249	+	0.999030i	$0.485982\pi$
$230$	3.11458	0.205369
$231$	0	0
$232$	0.318892	0.0209363
$233$	−25.3530	−1.66093	−0.830465	−	0.557071i	$-0.811925\pi$
$233$	−25.3530	−1.66093	−0.830465	+	0.557071i	$0.811925\pi$
$234$	3.51447	0.229748
$235$	−11.2602	−0.734536
$236$	15.4527	1.00588
$237$	45.3222	2.94399
$238$	3.61765	0.234498
$239$	−8.76596	−0.567023	−0.283511	−	0.958969i	$-0.591499\pi$
$239$	−8.76596	−0.567023	−0.283511	+	0.958969i	$0.591499\pi$
$240$	3.35118	0.216318
$241$	−6.18506	−0.398415	−0.199207	−	0.979957i	$-0.563837\pi$
$241$	−6.18506	−0.398415	−0.199207	+	0.979957i	$0.563837\pi$
$242$	0	0
$243$	55.1857	3.54017
$244$	0.524911	0.0336040
$245$	1.00000	0.0638877
$246$	19.1817	1.22298
$247$	2.48126	0.157879
$248$	−16.1688	−1.02672
$249$	−53.9632	−3.41978
$250$	0.740902	0.0468588
$251$	−12.9305	−0.816163	−0.408082	−	0.912945i	$-0.633802\pi$
$251$	−12.9305	−0.816163	−0.408082	+	0.912945i	$0.633802\pi$
$252$	11.6943	0.736671
$253$	0	0
$254$	−6.47602	−0.406342
$255$	−16.2378	−1.01685
$256$	−12.0600	−0.753750
$257$	12.9055	0.805022	0.402511	−	0.915415i	$-0.368138\pi$
$257$	12.9055	0.805022	0.402511	+	0.915415i	$0.368138\pi$
$258$	−1.31533	−0.0818891
$259$	−0.686995	−0.0426878
$260$	−0.854079	−0.0529677
$261$	−1.00512	−0.0622153
$262$	3.03813	0.187696
$263$	12.0469	0.742844	0.371422	−	0.928464i	$-0.378870\pi$
$263$	12.0469	0.742844	0.371422	+	0.928464i	$0.378870\pi$
$264$	0	0
$265$	11.6652	0.716587
$266$	−3.12336	−0.191506
$267$	44.5574	2.72687
$268$	−6.87427	−0.419913
$269$	12.4887	0.761447	0.380723	−	0.924689i	$-0.375675\pi$
$269$	12.4887	0.761447	0.380723	+	0.924689i	$0.375675\pi$
$270$	12.4651	0.758601
$271$	10.9493	0.665121	0.332560	−	0.943082i	$-0.392087\pi$
$271$	10.9493	0.665121	0.332560	+	0.943082i	$0.392087\pi$
$272$	−4.92044	−0.298345
$273$	−1.95736	−0.118465
$274$	−12.8579	−0.776773
$275$	0	0
$276$	−20.2855	−1.22104
$277$	−17.6527	−1.06065	−0.530324	−	0.847795i	$-0.677930\pi$
$277$	−17.6527	−1.06065	−0.530324	+	0.847795i	$0.677930\pi$
$278$	−4.46241	−0.267638
$279$	50.9627	3.05105
$280$	2.55690	0.152804
$281$	5.99127	0.357409	0.178705	−	0.983903i	$-0.442809\pi$
$281$	5.99127	0.357409	0.178705	+	0.983903i	$0.442809\pi$
$282$	−27.7439	−1.65213
$283$	−26.3958	−1.56907	−0.784535	−	0.620085i	$-0.787098\pi$
$283$	−26.3958	−1.56907	−0.784535	+	0.620085i	$0.787098\pi$
$284$	−4.67514	−0.277419
$285$	14.0191	0.830423
$286$	0	0
$287$	−7.78513	−0.459542
$288$	47.2298	2.78304
$289$	6.84143	0.402437
$290$	−0.0924040	−0.00542615
$291$	−23.9120	−1.40175
$292$	−14.2370	−0.833156
$293$	−17.6166	−1.02917	−0.514587	−	0.857438i	$-0.672055\pi$
$293$	−17.6166	−1.02917	−0.514587	+	0.857438i	$0.672055\pi$
$294$	2.46389	0.143697
$295$	−10.6492	−0.620021
$296$	−1.75658	−0.102099
$297$	0	0
$298$	11.1781	0.647532
$299$	2.47429	0.143092
$300$	−4.82555	−0.278603
$301$	0.533845	0.0307703
$302$	6.09729	0.350859
$303$	−55.4798	−3.18723
$304$	4.24814	0.243648
$305$	−0.361742	−0.0207133
$306$	−29.1551	−1.66668
$307$	29.3775	1.67667	0.838333	−	0.545159i	$-0.183531\pi$
$307$	29.3775	1.67667	0.838333	+	0.545159i	$0.183531\pi$
$308$	0	0
$309$	−15.3714	−0.874449
$310$	4.68518	0.266100
$311$	−12.5665	−0.712580	−0.356290	−	0.934375i	$-0.615958\pi$
$311$	−12.5665	−0.712580	−0.356290	+	0.934375i	$0.615958\pi$
$312$	−5.00478	−0.283340
$313$	−0.0329153	−0.00186048	−0.000930240	−	1.00000i	$-0.500296\pi$
$313$	−0.0329153	−0.00186048	−0.000930240		1.00000i	$0.500296\pi$
$314$	−3.53182	−0.199312
$315$	−8.05911	−0.454079
$316$	−19.7760	−1.11248
$317$	−12.6357	−0.709690	−0.354845	−	0.934925i	$-0.615466\pi$
$317$	−12.6357	−0.709690	−0.354845	+	0.934925i	$0.615466\pi$
$318$	28.7417	1.61176
$319$	0	0
$320$	2.32657	0.130059
$321$	−20.8392	−1.16313
$322$	−3.11458	−0.173569
$323$	−20.5839	−1.14532
$324$	−46.1031	−2.56128
$325$	0.588588	0.0326490
$326$	6.78444	0.375755
$327$	42.7961	2.36663
$328$	−19.9058	−1.09911
$329$	11.2602	0.620797
$330$	0	0
$331$	−31.5396	−1.73358	−0.866788	−	0.498677i	$-0.833819\pi$
$331$	−31.5396	−1.73358	−0.866788	+	0.498677i	$0.833819\pi$
$332$	23.5464	1.29228
$333$	5.53657	0.303402
$334$	−12.4369	−0.680516
$335$	4.73740	0.258832
$336$	−3.35118	−0.182822
$337$	−22.5080	−1.22609	−0.613044	−	0.790049i	$-0.710055\pi$
$337$	−22.5080	−1.22609	−0.613044	+	0.790049i	$0.710055\pi$
$338$	−9.37505	−0.509936
$339$	1.71757	0.0932859
$340$	7.08521	0.384249
$341$	0	0
$342$	25.1715	1.36112
$343$	−1.00000	−0.0539949
$344$	1.36499	0.0735952
$345$	13.9797	0.752643
$346$	−5.50187	−0.295783
$347$	25.5314	1.37060	0.685299	−	0.728262i	$-0.259672\pi$
$347$	25.5314	1.37060	0.685299	+	0.728262i	$0.259672\pi$
$348$	0.601834	0.0322617
$349$	23.7564	1.27165	0.635825	−	0.771834i	$-0.280660\pi$
$349$	23.7564	1.27165	0.635825	+	0.771834i	$0.280660\pi$
$350$	−0.740902	−0.0396029
$351$	9.90252	0.528557
$352$	0	0
$353$	−5.70882	−0.303850	−0.151925	−	0.988392i	$-0.548547\pi$
$353$	−5.70882	−0.303850	−0.151925	+	0.988392i	$0.548547\pi$
$354$	−26.2385	−1.39456
$355$	3.22187	0.170999
$356$	−19.4423	−1.03044
$357$	16.2378	0.859394
$358$	−1.82077	−0.0962305
$359$	22.1184	1.16737	0.583683	−	0.811981i	$-0.301611\pi$
$359$	22.1184	1.16737	0.583683	+	0.811981i	$0.301611\pi$
$360$	−20.6063	−1.08605
$361$	−1.22854	−0.0646602
$362$	−2.90430	−0.152646
$363$	0	0
$364$	0.854079	0.0447659
$365$	9.81141	0.513553
$366$	−0.891293	−0.0465886
$367$	12.4927	0.652112	0.326056	−	0.945351i	$-0.394280\pi$
$367$	12.4927	0.652112	0.326056	+	0.945351i	$0.394280\pi$
$368$	4.23619	0.220827
$369$	62.7412	3.26618
$370$	0.508996	0.0264614
$371$	−11.6652	−0.605626
$372$	−30.5149	−1.58212
$373$	−8.13646	−0.421290	−0.210645	−	0.977563i	$-0.567556\pi$
$373$	−8.13646	−0.421290	−0.210645	+	0.977563i	$0.567556\pi$
$374$	0	0
$375$	3.32552	0.171729
$376$	28.7913	1.48480
$377$	−0.0734077	−0.00378069
$378$	−12.4651	−0.641135
$379$	−3.13927	−0.161253	−0.0806266	−	0.996744i	$-0.525692\pi$
$379$	−3.13927	−0.161253	−0.0806266	+	0.996744i	$0.525692\pi$
$380$	−6.11713	−0.313802
$381$	−29.0675	−1.48917
$382$	−9.52168	−0.487171
$383$	−13.7587	−0.703038	−0.351519	−	0.936181i	$-0.614335\pi$
$383$	−13.7587	−0.703038	−0.351519	+	0.936181i	$0.614335\pi$
$384$	−33.2455	−1.69655
$385$	0	0
$386$	−6.60078	−0.335971
$387$	−4.30231	−0.218699
$388$	10.4338	0.529695
$389$	25.5233	1.29408	0.647040	−	0.762456i	$-0.276007\pi$
$389$	25.5233	1.29408	0.647040	+	0.762456i	$0.276007\pi$
$390$	1.45021	0.0734345
$391$	−20.5260	−1.03805
$392$	−2.55690	−0.129143
$393$	13.6366	0.687874
$394$	1.92994	0.0972292
$395$	13.6286	0.685729
$396$	0	0
$397$	22.0365	1.10598	0.552991	−	0.833187i	$-0.313486\pi$
$397$	22.0365	1.10598	0.552991	+	0.833187i	$0.313486\pi$
$398$	5.08224	0.254750
$399$	−14.0191	−0.701835
$400$	1.00771	0.0503857
$401$	5.89093	0.294179	0.147090	−	0.989123i	$-0.453009\pi$
$401$	5.89093	0.294179	0.147090	+	0.989123i	$0.453009\pi$
$402$	11.6724	0.582167
$403$	3.72200	0.185406
$404$	24.2081	1.20440
$405$	31.7719	1.57876
$406$	0.0924040	0.00458594
$407$	0	0
$408$	41.5184	2.05547
$409$	−1.22680	−0.0606614	−0.0303307	−	0.999540i	$-0.509656\pi$
$409$	−1.22680	−0.0606614	−0.0303307	+	0.999540i	$0.509656\pi$
$410$	5.76802	0.284862
$411$	−57.7123	−2.84674
$412$	6.70718	0.330439
$413$	10.6492	0.524013
$414$	25.1007	1.23363
$415$	−16.2270	−0.796551
$416$	3.44937	0.169119
$417$	−20.0294	−0.980846
$418$	0	0
$419$	−36.3705	−1.77681	−0.888407	−	0.459056i	$-0.848188\pi$
$419$	−36.3705	−1.77681	−0.888407	+	0.459056i	$0.848188\pi$
$420$	4.82555	0.235463
$421$	−31.1666	−1.51897	−0.759485	−	0.650525i	$-0.774549\pi$
$421$	−31.1666	−1.51897	−0.759485	+	0.650525i	$0.774549\pi$
$422$	7.65925	0.372846
$423$	−90.7474	−4.41229
$424$	−29.8267	−1.44851
$425$	−4.88277	−0.236849
$426$	7.93834	0.384614
$427$	0.361742	0.0175059
$428$	9.09302	0.439528
$429$	0	0
$430$	−0.395527	−0.0190740
$431$	1.70892	0.0823160	0.0411580	−	0.999153i	$-0.486895\pi$
$431$	1.70892	0.0823160	0.0411580	+	0.999153i	$0.486895\pi$
$432$	16.9540	0.815699
$433$	−8.09654	−0.389095	−0.194547	−	0.980893i	$-0.562324\pi$
$433$	−8.09654	−0.389095	−0.194547	+	0.980893i	$0.562324\pi$
$434$	−4.68518	−0.224896
$435$	−0.414754	−0.0198859
$436$	−18.6737	−0.894308
$437$	17.7215	0.847733
$438$	24.1742	1.15509
$439$	−28.7595	−1.37262	−0.686308	−	0.727311i	$-0.740770\pi$
$439$	−28.7595	−1.37262	−0.686308	+	0.727311i	$0.740770\pi$
$440$	0	0
$441$	8.05911	0.383767
$442$	−2.12931	−0.101281
$443$	−11.4903	−0.545922	−0.272961	−	0.962025i	$-0.588003\pi$
$443$	−11.4903	−0.545922	−0.272961	+	0.962025i	$0.588003\pi$
$444$	−3.31513	−0.157329
$445$	13.3986	0.635156
$446$	5.60585	0.265445
$447$	50.1728	2.37309
$448$	−2.32657	−0.109920
$449$	5.41676	0.255633	0.127816	−	0.991798i	$-0.459203\pi$
$449$	5.41676	0.255633	0.127816	+	0.991798i	$0.459203\pi$
$450$	5.97101	0.281476
$451$	0	0
$452$	−0.749449	−0.0352511
$453$	27.3675	1.28584
$454$	2.69406	0.126439
$455$	−0.588588	−0.0275934
$456$	−35.8456	−1.67862
$457$	−29.3300	−1.37200	−0.686000	−	0.727601i	$-0.740635\pi$
$457$	−29.3300	−1.37200	−0.686000	+	0.727601i	$0.740635\pi$
$458$	0.987204	0.0461290
$459$	−82.1486	−3.83437
$460$	−6.09993	−0.284411
$461$	17.5986	0.819648	0.409824	−	0.912165i	$-0.365590\pi$
$461$	17.5986	0.819648	0.409824	+	0.912165i	$0.365590\pi$
$462$	0	0
$463$	16.7601	0.778908	0.389454	−	0.921046i	$-0.372664\pi$
$463$	16.7601	0.778908	0.389454	+	0.921046i	$0.372664\pi$
$464$	−0.125680	−0.00583456
$465$	21.0293	0.975211
$466$	−18.7841	−0.870156
$467$	23.7167	1.09748	0.548739	−	0.835993i	$-0.315108\pi$
$467$	23.7167	1.09748	0.548739	+	0.835993i	$0.315108\pi$
$468$	−6.88311	−0.318172
$469$	−4.73740	−0.218753
$470$	−8.34273	−0.384821
$471$	−15.8525	−0.730444
$472$	27.2290	1.25332
$473$	0	0
$474$	33.5793	1.54235
$475$	4.21562	0.193426
$476$	−7.08521	−0.324750
$477$	94.0110	4.30447
$478$	−6.49472	−0.297062
$479$	−31.9677	−1.46064	−0.730320	−	0.683105i	$-0.760629\pi$
$479$	−31.9677	−1.46064	−0.730320	+	0.683105i	$0.760629\pi$
$480$	19.4890	0.889546
$481$	0.404357	0.0184371
$482$	−4.58253	−0.208728
$483$	−13.9797	−0.636100
$484$	0	0
$485$	−7.19044	−0.326501
$486$	40.8872	1.85468
$487$	12.0804	0.547414	0.273707	−	0.961813i	$-0.411750\pi$
$487$	12.0804	0.547414	0.273707	+	0.961813i	$0.411750\pi$
$488$	0.924939	0.0418700
$489$	30.4518	1.37708
$490$	0.740902	0.0334706
$491$	−2.06484	−0.0931850	−0.0465925	−	0.998914i	$-0.514836\pi$
$491$	−2.06484	−0.0931850	−0.0465925	+	0.998914i	$0.514836\pi$
$492$	−37.5675	−1.69367
$493$	0.608971	0.0274267
$494$	1.83837	0.0827123
$495$	0	0
$496$	6.37239	0.286129
$497$	−3.22187	−0.144521
$498$	−39.9815	−1.79161
$499$	−17.4767	−0.782362	−0.391181	−	0.920314i	$-0.627933\pi$
$499$	−17.4767	−0.782362	−0.391181	+	0.920314i	$0.627933\pi$
$500$	−1.45106	−0.0648935
$501$	−55.8227	−2.49397
$502$	−9.58020	−0.427585
$503$	24.4505	1.09019	0.545097	−	0.838373i	$-0.316493\pi$
$503$	24.4505	1.09019	0.545097	+	0.838373i	$0.316493\pi$
$504$	20.6063	0.917880
$505$	−16.6830	−0.742385
$506$	0	0
$507$	−42.0797	−1.86883
$508$	12.6833	0.562733
$509$	−23.2420	−1.03019	−0.515093	−	0.857135i	$-0.672242\pi$
$509$	−23.2420	−1.03019	−0.515093	+	0.857135i	$0.672242\pi$
$510$	−12.0306	−0.532724
$511$	−9.81141	−0.434031
$512$	11.0589	0.488738
$513$	70.9244	3.13139
$514$	9.56170	0.421749
$515$	−4.62225	−0.203681
$516$	2.57609	0.113406
$517$	0	0
$518$	−0.508996	−0.0223640
$519$	−24.6950	−1.08399
$520$	−1.50496	−0.0659969
$521$	1.45214	0.0636193	0.0318097	−	0.999494i	$-0.489873\pi$
$521$	1.45214	0.0636193	0.0318097	+	0.999494i	$0.489873\pi$
$522$	−0.744694	−0.0325944
$523$	−9.04231	−0.395393	−0.197696	−	0.980263i	$-0.563346\pi$
$523$	−9.04231	−0.395393	−0.197696	+	0.980263i	$0.563346\pi$
$524$	−5.95020	−0.259936
$525$	−3.32552	−0.145138
$526$	8.92558	0.389174
$527$	−30.8767	−1.34501
$528$	0	0
$529$	−5.32835	−0.231667
$530$	8.64276	0.375418
$531$	−85.8232	−3.72441
$532$	6.11713	0.265211
$533$	4.58223	0.198479
$534$	33.0127	1.42860
$535$	−6.26645	−0.270922
$536$	−12.1131	−0.523204
$537$	−8.17247	−0.352668
$538$	9.25287	0.398920
$539$	0	0
$540$	−24.4130	−1.05057
$541$	−29.6058	−1.27285	−0.636426	−	0.771338i	$-0.719588\pi$
$541$	−29.6058	−1.27285	−0.636426	+	0.771338i	$0.719588\pi$
$542$	8.11234	0.348455
$543$	−13.0359	−0.559423
$544$	−28.6151	−1.22686
$545$	12.8690	0.551246
$546$	−1.45021	−0.0620635
$547$	17.8524	0.763314	0.381657	−	0.924304i	$-0.375354\pi$
$547$	17.8524	0.763314	0.381657	+	0.924304i	$0.375354\pi$
$548$	25.1823	1.07573
$549$	−2.91532	−0.124423
$550$	0	0
$551$	−0.525765	−0.0223983
$552$	−35.7448	−1.52140
$553$	−13.6286	−0.579547
$554$	−13.0789	−0.555670
$555$	2.28462	0.0969766
$556$	8.73968	0.370645
$557$	14.5225	0.615338	0.307669	−	0.951493i	$-0.400451\pi$
$557$	14.5225	0.615338	0.307669	+	0.951493i	$0.400451\pi$
$558$	37.7583	1.59844
$559$	−0.314215	−0.0132899
$560$	−1.00771	−0.0425837
$561$	0	0
$562$	4.43895	0.187246
$563$	28.2880	1.19220	0.596098	−	0.802912i	$-0.296717\pi$
$563$	28.2880	1.19220	0.596098	+	0.802912i	$0.296717\pi$
$564$	54.3368	2.28799
$565$	0.516482	0.0217286
$566$	−19.5567	−0.822031
$567$	−31.7719	−1.33430
$568$	−8.23801	−0.345659
$569$	−15.3419	−0.643165	−0.321582	−	0.946882i	$-0.604215\pi$
$569$	−15.3419	−0.643165	−0.321582	+	0.946882i	$0.604215\pi$
$570$	10.3868	0.435056
$571$	−2.01209	−0.0842034	−0.0421017	−	0.999113i	$-0.513405\pi$
$571$	−2.01209	−0.0842034	−0.0421017	+	0.999113i	$0.513405\pi$
$572$	0	0
$573$	−42.7379	−1.78540
$574$	−5.76802	−0.240753
$575$	4.20377	0.175309
$576$	18.7501	0.781253
$577$	−34.5987	−1.44036	−0.720182	−	0.693785i	$-0.755942\pi$
$577$	−34.5987	−1.44036	−0.720182	+	0.693785i	$0.755942\pi$
$578$	5.06883	0.210836
$579$	−29.6274	−1.23127
$580$	0.180974	0.00751454
$581$	16.2270	0.673208
$582$	−17.7164	−0.734370
$583$	0	0
$584$	−25.0868	−1.03810
$585$	4.74349	0.196119
$586$	−13.0522	−0.539181
$587$	−38.9041	−1.60574	−0.802871	−	0.596153i	$-0.796695\pi$
$587$	−38.9041	−1.60574	−0.802871	+	0.596153i	$0.796695\pi$
$588$	−4.82555	−0.199002
$589$	26.6579	1.09842
$590$	−7.89002	−0.324827
$591$	8.66251	0.356328
$592$	0.692294	0.0284531
$593$	−1.23232	−0.0506053	−0.0253027	−	0.999680i	$-0.508055\pi$
$593$	−1.23232	−0.0506053	−0.0253027	+	0.999680i	$0.508055\pi$
$594$	0	0
$595$	4.88277	0.200174
$596$	−21.8925	−0.896750
$597$	22.8115	0.933614
$598$	1.83320	0.0749653
$599$	26.4285	1.07984	0.539920	−	0.841716i	$-0.318454\pi$
$599$	26.4285	1.07984	0.539920	+	0.841716i	$0.318454\pi$
$600$	−8.50304	−0.347135
$601$	11.6244	0.474169	0.237084	−	0.971489i	$-0.423808\pi$
$601$	11.6244	0.474169	0.237084	+	0.971489i	$0.423808\pi$
$602$	0.395527	0.0161205
$603$	38.1792	1.55478
$604$	−11.9416	−0.485896
$605$	0	0
$606$	−41.1051	−1.66978
$607$	2.59642	0.105385	0.0526927	−	0.998611i	$-0.483220\pi$
$607$	2.59642	0.105385	0.0526927	+	0.998611i	$0.483220\pi$
$608$	24.7053	1.00193
$609$	0.414754	0.0168067
$610$	−0.268016	−0.0108516
$611$	−6.62764	−0.268125
$612$	57.1005	2.30815
$613$	−47.3500	−1.91245	−0.956224	−	0.292635i	$-0.905468\pi$
$613$	−47.3500	−1.91245	−0.956224	+	0.292635i	$0.905468\pi$
$614$	21.7659	0.878400
$615$	25.8896	1.04397
$616$	0	0
$617$	−39.7038	−1.59841	−0.799206	−	0.601057i	$-0.794747\pi$
$617$	−39.7038	−1.59841	−0.799206	+	0.601057i	$0.794747\pi$
$618$	−11.3887	−0.458121
$619$	19.3632	0.778273	0.389137	−	0.921180i	$-0.372773\pi$
$619$	19.3632	0.778273	0.389137	+	0.921180i	$0.372773\pi$
$620$	−9.17596	−0.368515
$621$	70.7250	2.83810
$622$	−9.31054	−0.373318
$623$	−13.3986	−0.536805
$624$	1.97246	0.0789617
$625$	1.00000	0.0400000
$626$	−0.0243870	−0.000974700 0
$627$	0	0
$628$	6.91710	0.276022
$629$	−3.35444	−0.133750
$630$	−5.97101	−0.237891
$631$	−46.2315	−1.84045	−0.920224	−	0.391392i	$-0.871994\pi$
$631$	−46.2315	−1.84045	−0.920224	+	0.391392i	$0.871994\pi$
$632$	−34.8470	−1.38614
$633$	34.3784	1.36642
$634$	−9.36180	−0.371804
$635$	−8.74072	−0.346865
$636$	−56.2909	−2.23208
$637$	0.588588	0.0233207
$638$	0	0
$639$	25.9654	1.02718
$640$	−9.99708	−0.395169
$641$	27.7825	1.09734	0.548672	−	0.836038i	$-0.315134\pi$
$641$	27.7825	1.09734	0.548672	+	0.836038i	$0.315134\pi$
$642$	−15.4398	−0.609362
$643$	27.3219	1.07747	0.538735	−	0.842475i	$-0.318902\pi$
$643$	27.3219	1.07747	0.538735	+	0.842475i	$0.318902\pi$
$644$	6.09993	0.240371
$645$	−1.77531	−0.0699029
$646$	−15.2507	−0.600029
$647$	35.1807	1.38310	0.691548	−	0.722330i	$-0.256929\pi$
$647$	35.1807	1.38310	0.691548	+	0.722330i	$0.256929\pi$
$648$	−81.2377	−3.19132
$649$	0	0
$650$	0.436086	0.0171047
$651$	−21.0293	−0.824204
$652$	−13.2874	−0.520374
$653$	6.16841	0.241389	0.120694	−	0.992690i	$-0.461488\pi$
$653$	6.16841	0.241389	0.120694	+	0.992690i	$0.461488\pi$
$654$	31.7077	1.23987
$655$	4.10058	0.160223
$656$	7.84519	0.306303
$657$	79.0712	3.08486
$658$	8.34273	0.325233
$659$	17.6870	0.688989	0.344494	−	0.938788i	$-0.388050\pi$
$659$	17.6870	0.688989	0.344494	+	0.938788i	$0.388050\pi$
$660$	0	0
$661$	−24.0951	−0.937191	−0.468596	−	0.883413i	$-0.655240\pi$
$661$	−24.0951	−0.937191	−0.468596	+	0.883413i	$0.655240\pi$
$662$	−23.3678	−0.908215
$663$	−9.55735	−0.371177
$664$	41.4908	1.61015
$665$	−4.21562	−0.163475
$666$	4.10205	0.158951
$667$	−0.524286	−0.0203005
$668$	24.3578	0.942430
$669$	25.1617	0.972809
$670$	3.50995	0.135601
$671$	0	0
$672$	−19.4890	−0.751803
$673$	40.2274	1.55065	0.775326	−	0.631562i	$-0.217586\pi$
$673$	40.2274	1.55065	0.775326	+	0.631562i	$0.217586\pi$
$674$	−16.6762	−0.642344
$675$	16.8242	0.647563
$676$	18.3611	0.706197
$677$	24.2527	0.932106	0.466053	−	0.884757i	$-0.345676\pi$
$677$	24.2527	0.932106	0.466053	+	0.884757i	$0.345676\pi$
$678$	1.27256	0.0488722
$679$	7.19044	0.275944
$680$	12.4848	0.478769
$681$	12.0923	0.463376
$682$	0	0
$683$	−5.54703	−0.212251	−0.106126	−	0.994353i	$-0.533845\pi$
$683$	−5.54703	−0.212251	−0.106126	+	0.994353i	$0.533845\pi$
$684$	−49.2987	−1.88498
$685$	−17.3543	−0.663076
$686$	−0.740902	−0.0282878
$687$	4.43104	0.169055
$688$	−0.537963	−0.0205096
$689$	6.86599	0.261573
$690$	10.3576	0.394307
$691$	2.56865	0.0977162	0.0488581	−	0.998806i	$-0.484442\pi$
$691$	2.56865	0.0977162	0.0488581	+	0.998806i	$0.484442\pi$
$692$	10.7755	0.409622
$693$	0	0
$694$	18.9163	0.718052
$695$	−6.02294	−0.228463
$696$	1.06048	0.0401975
$697$	−38.0130	−1.43985
$698$	17.6011	0.666213
$699$	−84.3120	−3.18897
$700$	1.45106	0.0548451
$701$	27.0302	1.02092	0.510458	−	0.859903i	$-0.329476\pi$
$701$	27.0302	1.02092	0.510458	+	0.859903i	$0.329476\pi$
$702$	7.33680	0.276910
$703$	2.89611	0.109229
$704$	0	0
$705$	−37.4462	−1.41030
$706$	−4.22968	−0.159186
$707$	16.6830	0.627430
$708$	51.3883	1.93129
$709$	47.4716	1.78283	0.891417	−	0.453185i	$-0.149712\pi$
$709$	47.4716	1.78283	0.891417	+	0.453185i	$0.149712\pi$
$710$	2.38709	0.0895860
$711$	109.834	4.11911
$712$	−34.2590	−1.28391
$713$	26.5830	0.995540
$714$	12.0306	0.450234
$715$	0	0
$716$	3.56599	0.133267
$717$	−29.1514	−1.08868
$718$	16.3876	0.611580
$719$	−26.4519	−0.986491	−0.493245	−	0.869890i	$-0.664190\pi$
$719$	−26.4519	−0.986491	−0.493245	+	0.869890i	$0.664190\pi$
$720$	8.12128	0.302662
$721$	4.62225	0.172142
$722$	−0.910231	−0.0338753
$723$	−20.5686	−0.764953
$724$	5.68809	0.211396
$725$	−0.124718	−0.00463192
$726$	0	0
$727$	15.0260	0.557282	0.278641	−	0.960395i	$-0.410116\pi$
$727$	15.0260	0.557282	0.278641	+	0.960395i	$0.410116\pi$
$728$	1.50496	0.0557776
$729$	88.2057	3.26688
$730$	7.26930	0.269049
$731$	2.60664	0.0964101
$732$	1.74560	0.0645194
$733$	25.8873	0.956168	0.478084	−	0.878314i	$-0.341331\pi$
$733$	25.8873	0.956168	0.478084	+	0.878314i	$0.341331\pi$
$734$	9.25584	0.341639
$735$	3.32552	0.122664
$736$	24.6358	0.908089
$737$	0	0
$738$	46.4851	1.71114
$739$	14.7159	0.541334	0.270667	−	0.962673i	$-0.412756\pi$
$739$	14.7159	0.541334	0.270667	+	0.962673i	$0.412756\pi$
$740$	−0.996873	−0.0366458
$741$	8.25150	0.303126
$742$	−8.64276	−0.317286
$743$	25.9049	0.950359	0.475180	−	0.879889i	$-0.342383\pi$
$743$	25.9049	0.950359	0.475180	+	0.879889i	$0.342383\pi$
$744$	−53.7699	−1.97130
$745$	15.0872	0.552752
$746$	−6.02832	−0.220712
$747$	−130.775	−4.78481
$748$	0	0
$749$	6.26645	0.228971
$750$	2.46389	0.0899685
$751$	45.8236	1.67213	0.836063	−	0.548633i	$-0.184851\pi$
$751$	45.8236	1.67213	0.836063	+	0.548633i	$0.184851\pi$
$752$	−11.3471	−0.413786
$753$	−43.0005	−1.56703
$754$	−0.0543879	−0.00198069
$755$	8.22954	0.299504
$756$	24.4130	0.887891
$757$	−42.8514	−1.55746	−0.778730	−	0.627360i	$-0.784136\pi$
$757$	−42.8514	−1.55746	−0.778730	+	0.627360i	$0.784136\pi$
$758$	−2.32589	−0.0844801
$759$	0	0
$760$	−10.7789	−0.390993
$761$	−37.9050	−1.37406	−0.687028	−	0.726631i	$-0.741085\pi$
$761$	−37.9050	−1.37406	−0.687028	+	0.726631i	$0.741085\pi$
$762$	−21.5362	−0.780173
$763$	−12.8690	−0.465888
$764$	18.6483	0.674672
$765$	−39.3508	−1.42273
$766$	−10.1939	−0.368319
$767$	−6.26800	−0.226324
$768$	−40.1058	−1.44719
$769$	50.4597	1.81962	0.909812	−	0.415020i	$-0.136225\pi$
$769$	50.4597	1.81962	0.909812	+	0.415020i	$0.136225\pi$
$770$	0	0
$771$	42.9175	1.54564
$772$	12.9277	0.465277
$773$	−28.7958	−1.03571	−0.517856	−	0.855468i	$-0.673270\pi$
$773$	−28.7958	−1.03571	−0.517856	+	0.855468i	$0.673270\pi$
$774$	−3.18759	−0.114576
$775$	6.32361	0.227151
$776$	18.3852	0.659992
$777$	−2.28462	−0.0819602
$778$	18.9102	0.677965
$779$	32.8192	1.17587
$780$	−2.84026	−0.101698
$781$	0	0
$782$	−15.2078	−0.543829
$783$	−2.09828	−0.0749866
$784$	1.00771	0.0359898
$785$	−4.76691	−0.170138
$786$	10.1034	0.360375
$787$	−14.2233	−0.507006	−0.253503	−	0.967335i	$-0.581583\pi$
$787$	−14.2233	−0.507006	−0.253503	+	0.967335i	$0.581583\pi$
$788$	−3.77981	−0.134650
$789$	40.0623	1.42626
$790$	10.0975	0.359251
$791$	−0.516482	−0.0183640
$792$	0	0
$793$	−0.212917	−0.00756091
$794$	16.3269	0.579421
$795$	38.7929	1.37584
$796$	−9.95362	−0.352797
$797$	−9.21655	−0.326467	−0.163233	−	0.986587i	$-0.552192\pi$
$797$	−9.21655	−0.326467	−0.163233	+	0.986587i	$0.552192\pi$
$798$	−10.3868	−0.367689
$799$	54.9811	1.94509
$800$	5.86042	0.207197
$801$	107.981	3.81532
$802$	4.36461	0.154120
$803$	0	0
$804$	−22.8605	−0.806229
$805$	−4.20377	−0.148163
$806$	2.75764	0.0971337
$807$	41.5313	1.46197
$808$	42.6569	1.50066
$809$	10.6708	0.375165	0.187583	−	0.982249i	$-0.439935\pi$
$809$	10.6708	0.375165	0.187583	+	0.982249i	$0.439935\pi$
$810$	23.5399	0.827107
$811$	−52.1357	−1.83073	−0.915366	−	0.402623i	$-0.868099\pi$
$811$	−52.1357	−1.83073	−0.915366	+	0.402623i	$0.868099\pi$
$812$	−0.180974	−0.00635095
$813$	36.4121	1.27703
$814$	0	0
$815$	9.15700	0.320756
$816$	−16.3630	−0.572820
$817$	−2.25049	−0.0787346
$818$	−0.908939	−0.0317803
$819$	−4.74349	−0.165751
$820$	−11.2967	−0.394499
$821$	32.0144	1.11731	0.558655	−	0.829400i	$-0.311317\pi$
$821$	32.0144	1.11731	0.558655	+	0.829400i	$0.311317\pi$
$822$	−42.7592	−1.49140
$823$	−1.44778	−0.0504666	−0.0252333	−	0.999682i	$-0.508033\pi$
$823$	−1.44778	−0.0504666	−0.0252333	+	0.999682i	$0.508033\pi$
$824$	11.8186	0.411722
$825$	0	0
$826$	7.89002	0.274529
$827$	4.25875	0.148091	0.0740457	−	0.997255i	$-0.476409\pi$
$827$	4.25875	0.148091	0.0740457	+	0.997255i	$0.476409\pi$
$828$	−49.1600	−1.70843
$829$	51.4817	1.78803	0.894017	−	0.448034i	$-0.147875\pi$
$829$	51.4817	1.78803	0.894017	+	0.448034i	$0.147875\pi$
$830$	−12.0226	−0.417311
$831$	−58.7045	−2.03644
$832$	1.36939	0.0474751
$833$	−4.88277	−0.169178
$834$	−14.8399	−0.513862
$835$	−16.7861	−0.580908
$836$	0	0
$837$	106.390	3.67736
$838$	−26.9470	−0.930868
$839$	−26.2598	−0.906588	−0.453294	−	0.891361i	$-0.649751\pi$
$839$	−26.2598	−0.906588	−0.453294	+	0.891361i	$0.649751\pi$
$840$	8.50304	0.293383
$841$	−28.9844	−0.999464
$842$	−23.0914	−0.795783
$843$	19.9241	0.686223
$844$	−15.0007	−0.516346
$845$	−12.6536	−0.435296
$846$	−67.2350	−2.31159
$847$	0	0
$848$	11.7552	0.403674
$849$	−87.7800	−3.01260
$850$	−3.61765	−0.124085
$851$	2.88797	0.0989982
$852$	−15.5473	−0.532642
$853$	−34.8421	−1.19297	−0.596485	−	0.802624i	$-0.703436\pi$
$853$	−34.8421	−1.19297	−0.596485	+	0.802624i	$0.703436\pi$
$854$	0.268016	0.00917131
$855$	33.9741	1.16189
$856$	16.0227	0.547645
$857$	14.5853	0.498223	0.249112	−	0.968475i	$-0.419861\pi$
$857$	14.5853	0.498223	0.249112	+	0.968475i	$0.419861\pi$
$858$	0	0
$859$	1.82183	0.0621599	0.0310799	−	0.999517i	$-0.490105\pi$
$859$	1.82183	0.0621599	0.0310799	+	0.999517i	$0.490105\pi$
$860$	0.774643	0.0264151
$861$	−25.8896	−0.882317
$862$	1.26615	0.0431251
$863$	−6.18666	−0.210596	−0.105298	−	0.994441i	$-0.533580\pi$
$863$	−6.18666	−0.210596	−0.105298	+	0.994441i	$0.533580\pi$
$864$	98.5968	3.35433
$865$	−7.42591	−0.252489
$866$	−5.99875	−0.203846
$867$	22.7514	0.772676
$868$	9.17596	0.311452
$869$	0	0
$870$	−0.307292	−0.0104182
$871$	2.78838	0.0944805
$872$	−32.9047	−1.11429
$873$	−57.9486	−1.96126
$874$	13.1299	0.444125
$875$	−1.00000	−0.0338062
$876$	−47.3454	−1.59965
$877$	15.6413	0.528170	0.264085	−	0.964499i	$-0.414930\pi$
$877$	15.6413	0.528170	0.264085	+	0.964499i	$0.414930\pi$
$878$	−21.3080	−0.719110
$879$	−58.5845	−1.97601
$880$	0	0
$881$	23.0981	0.778196	0.389098	−	0.921196i	$-0.372787\pi$
$881$	23.0981	0.778196	0.389098	+	0.921196i	$0.372787\pi$
$882$	5.97101	0.201054
$883$	−18.7230	−0.630078	−0.315039	−	0.949079i	$-0.602018\pi$
$883$	−18.7230	−0.630078	−0.315039	+	0.949079i	$0.602018\pi$
$884$	4.17027	0.140261
$885$	−35.4142	−1.19044
$886$	−8.51321	−0.286007
$887$	−28.1850	−0.946361	−0.473181	−	0.880965i	$-0.656894\pi$
$887$	−28.1850	−0.946361	−0.473181	+	0.880965i	$0.656894\pi$
$888$	−5.84154	−0.196029
$889$	8.74072	0.293154
$890$	9.92707	0.332756
$891$	0	0
$892$	−10.9791	−0.367608
$893$	−47.4689	−1.58848
$894$	37.1731	1.24326
$895$	−2.45750	−0.0821451
$896$	9.99708	0.333979
$897$	8.22830	0.274735
$898$	4.01329	0.133925
$899$	−0.788670	−0.0263036
$900$	−11.6943	−0.389809
$901$	−56.9584	−1.89756
$902$	0	0
$903$	1.77531	0.0590787
$904$	−1.32059	−0.0439223
$905$	−3.91995	−0.130303
$906$	20.2767	0.673647
$907$	−36.9047	−1.22540	−0.612701	−	0.790315i	$-0.709917\pi$
$907$	−36.9047	−1.22540	−0.612701	+	0.790315i	$0.709917\pi$
$908$	−5.27635	−0.175102
$909$	−134.450	−4.45944
$910$	−0.436086	−0.0144561
$911$	4.19369	0.138943	0.0694716	−	0.997584i	$-0.477869\pi$
$911$	4.19369	0.138943	0.0694716	+	0.997584i	$0.477869\pi$
$912$	14.1273	0.467801
$913$	0	0
$914$	−21.7307	−0.718787
$915$	−1.20298	−0.0397694
$916$	−1.93345	−0.0638829
$917$	−4.10058	−0.135413
$918$	−60.8641	−2.00882
$919$	−3.41445	−0.112632	−0.0563161	−	0.998413i	$-0.517935\pi$
$919$	−3.41445	−0.112632	−0.0563161	+	0.998413i	$0.517935\pi$
$920$	−10.7486	−0.354371
$921$	97.6957	3.21918
$922$	13.0388	0.429411
$923$	1.89636	0.0624193
$924$	0	0
$925$	0.686995	0.0225882
$926$	12.4176	0.408068
$927$	−37.2512	−1.22349
$928$	−0.730901	−0.0239930
$929$	−35.9599	−1.17981	−0.589904	−	0.807474i	$-0.700834\pi$
$929$	−35.9599	−1.17981	−0.589904	+	0.807474i	$0.700834\pi$
$930$	15.5807	0.510910
$931$	4.21562	0.138161
$932$	36.7888	1.20506
$933$	−41.7901	−1.36815
$934$	17.5718	0.574966
$935$	0	0
$936$	−12.1286	−0.396437
$937$	45.3406	1.48121	0.740606	−	0.671940i	$-0.234539\pi$
$937$	45.3406	1.48121	0.740606	+	0.671940i	$0.234539\pi$
$938$	−3.50995	−0.114604
$939$	−0.109460	−0.00357211
$940$	16.3393	0.532930
$941$	−41.4410	−1.35094	−0.675469	−	0.737388i	$-0.736059\pi$
$941$	−41.4410	−1.35094	−0.675469	+	0.737388i	$0.736059\pi$
$942$	−11.7451	−0.382677
$943$	32.7269	1.06573
$944$	−10.7314	−0.349276
$945$	−16.8242	−0.547291
$946$	0	0
$947$	−39.0899	−1.27025	−0.635126	−	0.772409i	$-0.719052\pi$
$947$	−39.0899	−1.27025	−0.635126	+	0.772409i	$0.719052\pi$
$948$	−65.7654	−2.13596
$949$	5.77488	0.187460
$950$	3.12336	0.101335
$951$	−42.0202	−1.36260
$952$	−12.4848	−0.404633
$953$	39.2439	1.27123	0.635617	−	0.772005i	$-0.280746\pi$
$953$	39.2439	1.27123	0.635617	+	0.772005i	$0.280746\pi$
$954$	69.6530	2.25510
$955$	−12.8515	−0.415864
$956$	12.7200	0.411393
$957$	0	0
$958$	−23.6849	−0.765225
$959$	17.3543	0.560401
$960$	7.73706	0.249713
$961$	8.98803	0.289936
$962$	0.299589	0.00965913
$963$	−50.5020	−1.62741
$964$	8.97492	0.289063
$965$	−8.90911	−0.286794
$966$	−10.3576	−0.333251
$967$	−9.73746	−0.313136	−0.156568	−	0.987667i	$-0.550043\pi$
$967$	−9.73746	−0.313136	−0.156568	+	0.987667i	$0.550043\pi$
$968$	0	0
$969$	−68.4523	−2.19900
$970$	−5.32741	−0.171053
$971$	−25.6845	−0.824256	−0.412128	−	0.911126i	$-0.635214\pi$
$971$	−25.6845	−0.824256	−0.412128	+	0.911126i	$0.635214\pi$
$972$	−80.0780	−2.56850
$973$	6.02294	0.193087
$974$	8.95037	0.286788
$975$	1.95736	0.0626858
$976$	−0.364533	−0.0116684
$977$	−2.89790	−0.0927121	−0.0463561	−	0.998925i	$-0.514761\pi$
$977$	−2.89790	−0.0927121	−0.0463561	+	0.998925i	$0.514761\pi$
$978$	22.5618	0.721447
$979$	0	0
$980$	−1.45106	−0.0463525
$981$	103.712	3.31128
$982$	−1.52985	−0.0488194
$983$	10.2510	0.326955	0.163478	−	0.986547i	$-0.447729\pi$
$983$	10.2510	0.326955	0.163478	+	0.986547i	$0.447729\pi$
$984$	−66.1973	−2.11029
$985$	2.60486	0.0829976
$986$	0.451188	0.0143687
$987$	37.4462	1.19192
$988$	−3.60047	−0.114546
$989$	−2.24416	−0.0713601
$990$	0	0
$991$	17.8568	0.567239	0.283620	−	0.958937i	$-0.408465\pi$
$991$	17.8568	0.567239	0.283620	+	0.958937i	$0.408465\pi$
$992$	37.0590	1.17662
$993$	−104.886	−3.32845
$994$	−2.38709	−0.0757140
$995$	6.85953	0.217462
$996$	78.3040	2.48116
$997$	5.40921	0.171312	0.0856558	−	0.996325i	$-0.472701\pi$
$997$	5.40921	0.171312	0.0856558	+	0.996325i	$0.472701\pi$
$998$	−12.9485	−0.409877
$999$	11.5581	0.365683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bo.1.12		18
11.5	even	5		385.2.n.f.36.4	✓	36
11.9	even	5		385.2.n.f.246.4	yes	36
11.10	odd	2		4235.2.a.bp.1.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.4	✓	36	11.5	even	5
385.2.n.f.246.4	yes	36	11.9	even	5
4235.2.a.bo.1.12		18	1.1	even	1	trivial
4235.2.a.bp.1.7		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)

\(f(q)\)	\(=\)	\(q+0.740902 q^{2} +3.32552 q^{3} -1.45106 q^{4} +1.00000 q^{5} +2.46389 q^{6} -1.00000 q^{7} -2.55690 q^{8} +8.05911 q^{9} +O(q^{10})\)	\(q+0.740902 q^{2} +3.32552 q^{3} -1.45106 q^{4} +1.00000 q^{5} +2.46389 q^{6} -1.00000 q^{7} -2.55690 q^{8} +8.05911 q^{9} +0.740902 q^{10} -4.82555 q^{12} +0.588588 q^{13} -0.740902 q^{14} +3.32552 q^{15} +1.00771 q^{16} -4.88277 q^{17} +5.97101 q^{18} +4.21562 q^{19} -1.45106 q^{20} -3.32552 q^{21} +4.20377 q^{23} -8.50304 q^{24} +1.00000 q^{25} +0.436086 q^{26} +16.8242 q^{27} +1.45106 q^{28} -0.124718 q^{29} +2.46389 q^{30} +6.32361 q^{31} +5.86042 q^{32} -3.61765 q^{34} -1.00000 q^{35} -11.6943 q^{36} +0.686995 q^{37} +3.12336 q^{38} +1.95736 q^{39} -2.55690 q^{40} +7.78513 q^{41} -2.46389 q^{42} -0.533845 q^{43} +8.05911 q^{45} +3.11458 q^{46} -11.2602 q^{47} +3.35118 q^{48} +1.00000 q^{49} +0.740902 q^{50} -16.2378 q^{51} -0.854079 q^{52} +11.6652 q^{53} +12.4651 q^{54} +2.55690 q^{56} +14.0191 q^{57} -0.0924040 q^{58} -10.6492 q^{59} -4.82555 q^{60} -0.361742 q^{61} +4.68518 q^{62} -8.05911 q^{63} +2.32657 q^{64} +0.588588 q^{65} +4.73740 q^{67} +7.08521 q^{68} +13.9797 q^{69} -0.740902 q^{70} +3.22187 q^{71} -20.6063 q^{72} +9.81141 q^{73} +0.508996 q^{74} +3.32552 q^{75} -6.11713 q^{76} +1.45021 q^{78} +13.6286 q^{79} +1.00771 q^{80} +31.7719 q^{81} +5.76802 q^{82} -16.2270 q^{83} +4.82555 q^{84} -4.88277 q^{85} -0.395527 q^{86} -0.414754 q^{87} +13.3986 q^{89} +5.97101 q^{90} -0.588588 q^{91} -6.09993 q^{92} +21.0293 q^{93} -8.34273 q^{94} +4.21562 q^{95} +19.4890 q^{96} -7.19044 q^{97} +0.740902 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) \) 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

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