LMFDB - Embedded newform 4235.2.a.i.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
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			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.618034 q^{3} -1.00000 q^{4} +1.00000 q^{5} +0.618034 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.618034 q^{3} -1.00000 q^{4} +1.00000 q^{5} +0.618034 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} +0.618034 q^{12} -4.61803 q^{13} -1.00000 q^{14} -0.618034 q^{15} -1.00000 q^{16} +2.38197 q^{17} +2.61803 q^{18} -0.763932 q^{19} -1.00000 q^{20} -0.618034 q^{21} +4.47214 q^{23} -1.85410 q^{24} +1.00000 q^{25} +4.61803 q^{26} +3.47214 q^{27} -1.00000 q^{28} -4.09017 q^{29} +0.618034 q^{30} +5.70820 q^{31} -5.00000 q^{32} -2.38197 q^{34} +1.00000 q^{35} +2.61803 q^{36} -3.23607 q^{37} +0.763932 q^{38} +2.85410 q^{39} +3.00000 q^{40} +8.94427 q^{41} +0.618034 q^{42} -1.23607 q^{43} -2.61803 q^{45} -4.47214 q^{46} -6.85410 q^{47} +0.618034 q^{48} +1.00000 q^{49} -1.00000 q^{50} -1.47214 q^{51} +4.61803 q^{52} -5.52786 q^{53} -3.47214 q^{54} +3.00000 q^{56} +0.472136 q^{57} +4.09017 q^{58} -6.76393 q^{59} +0.618034 q^{60} +4.76393 q^{61} -5.70820 q^{62} -2.61803 q^{63} +7.00000 q^{64} -4.61803 q^{65} -9.70820 q^{67} -2.38197 q^{68} -2.76393 q^{69} -1.00000 q^{70} -9.56231 q^{71} -7.85410 q^{72} +14.5623 q^{73} +3.23607 q^{74} -0.618034 q^{75} +0.763932 q^{76} -2.85410 q^{78} +13.8541 q^{79} -1.00000 q^{80} +5.70820 q^{81} -8.94427 q^{82} -4.61803 q^{83} +0.618034 q^{84} +2.38197 q^{85} +1.23607 q^{86} +2.52786 q^{87} -2.29180 q^{89} +2.61803 q^{90} -4.61803 q^{91} -4.47214 q^{92} -3.52786 q^{93} +6.85410 q^{94} -0.763932 q^{95} +3.09017 q^{96} -5.61803 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{12} - 7 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} + 7 q^{17} + 3 q^{18} - 6 q^{19} - 2 q^{20} + q^{21} + 3 q^{24} + 2 q^{25} + 7 q^{26} - 2 q^{27} - 2 q^{28} + 3 q^{29} - q^{30} - 2 q^{31} - 10 q^{32} - 7 q^{34} + 2 q^{35} + 3 q^{36} - 2 q^{37} + 6 q^{38} - q^{39} + 6 q^{40} - q^{42} + 2 q^{43} - 3 q^{45} - 7 q^{47} - q^{48} + 2 q^{49} - 2 q^{50} + 6 q^{51} + 7 q^{52} - 20 q^{53} + 2 q^{54} + 6 q^{56} - 8 q^{57} - 3 q^{58} - 18 q^{59} - q^{60} + 14 q^{61} + 2 q^{62} - 3 q^{63} + 14 q^{64} - 7 q^{65} - 6 q^{67} - 7 q^{68} - 10 q^{69} - 2 q^{70} + q^{71} - 9 q^{72} + 9 q^{73} + 2 q^{74} + q^{75} + 6 q^{76} + q^{78} + 21 q^{79} - 2 q^{80} - 2 q^{81} - 7 q^{83} - q^{84} + 7 q^{85} - 2 q^{86} + 14 q^{87} - 18 q^{89} + 3 q^{90} - 7 q^{91} - 16 q^{93} + 7 q^{94} - 6 q^{95} - 5 q^{96} - 9 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 2 * q^10 - q^12 - 7 * q^13 - 2 * q^14 + q^15 - 2 * q^16 + 7 * q^17 + 3 * q^18 - 6 * q^19 - 2 * q^20 + q^21 + 3 * q^24 + 2 * q^25 + 7 * q^26 - 2 * q^27 - 2 * q^28 + 3 * q^29 - q^30 - 2 * q^31 - 10 * q^32 - 7 * q^34 + 2 * q^35 + 3 * q^36 - 2 * q^37 + 6 * q^38 - q^39 + 6 * q^40 - q^42 + 2 * q^43 - 3 * q^45 - 7 * q^47 - q^48 + 2 * q^49 - 2 * q^50 + 6 * q^51 + 7 * q^52 - 20 * q^53 + 2 * q^54 + 6 * q^56 - 8 * q^57 - 3 * q^58 - 18 * q^59 - q^60 + 14 * q^61 + 2 * q^62 - 3 * q^63 + 14 * q^64 - 7 * q^65 - 6 * q^67 - 7 * q^68 - 10 * q^69 - 2 * q^70 + q^71 - 9 * q^72 + 9 * q^73 + 2 * q^74 + q^75 + 6 * q^76 + q^78 + 21 * q^79 - 2 * q^80 - 2 * q^81 - 7 * q^83 - q^84 + 7 * q^85 - 2 * q^86 + 14 * q^87 - 18 * q^89 + 3 * q^90 - 7 * q^91 - 16 * q^93 + 7 * q^94 - 6 * q^95 - 5 * q^96 - 9 * 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 $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.618034	0.252311
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00000	1.06066
$9$	−2.61803	−0.872678
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	0.618034	0.178411
$13$	−4.61803	−1.28081	−0.640406	−	0.768036i	$-0.721234\pi$
$13$	−4.61803	−1.28081	−0.640406	+	0.768036i	$0.721234\pi$
$14$	−1.00000	−0.267261
$15$	−0.618034	−0.159576
$16$	−1.00000	−0.250000
$17$	2.38197	0.577712	0.288856	−	0.957373i	$-0.406725\pi$
$17$	2.38197	0.577712	0.288856	+	0.957373i	$0.406725\pi$
$18$	2.61803	0.617077
$19$	−0.763932	−0.175258	−0.0876290	−	0.996153i	$-0.527929\pi$
$19$	−0.763932	−0.175258	−0.0876290	+	0.996153i	$0.527929\pi$
$20$	−1.00000	−0.223607
$21$	−0.618034	−0.134866
$22$	0	0
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	−1.85410	−0.378467
$25$	1.00000	0.200000
$26$	4.61803	0.905671
$27$	3.47214	0.668213
$28$	−1.00000	−0.188982
$29$	−4.09017	−0.759525	−0.379763	−	0.925084i	$-0.623994\pi$
$29$	−4.09017	−0.759525	−0.379763	+	0.925084i	$0.623994\pi$
$30$	0.618034	0.112837
$31$	5.70820	1.02522	0.512612	−	0.858620i	$-0.328678\pi$
$31$	5.70820	1.02522	0.512612	+	0.858620i	$0.328678\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	−2.38197	−0.408504
$35$	1.00000	0.169031
$36$	2.61803	0.436339
$37$	−3.23607	−0.532006	−0.266003	−	0.963972i	$-0.585703\pi$
$37$	−3.23607	−0.532006	−0.266003	+	0.963972i	$0.585703\pi$
$38$	0.763932	0.123926
$39$	2.85410	0.457022
$40$	3.00000	0.474342
$41$	8.94427	1.39686	0.698430	−	0.715678i	$-0.253882\pi$
$41$	8.94427	1.39686	0.698430	+	0.715678i	$0.253882\pi$
$42$	0.618034	0.0953647
$43$	−1.23607	−0.188499	−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607	−0.188499	−0.0942493	+	0.995549i	$0.530045\pi$
$44$	0	0
$45$	−2.61803	−0.390273
$46$	−4.47214	−0.659380
$47$	−6.85410	−0.999774	−0.499887	−	0.866091i	$-0.666625\pi$
$47$	−6.85410	−0.999774	−0.499887	+	0.866091i	$0.666625\pi$
$48$	0.618034	0.0892055
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−1.47214	−0.206140
$52$	4.61803	0.640406
$53$	−5.52786	−0.759311	−0.379655	−	0.925128i	$-0.623957\pi$
$53$	−5.52786	−0.759311	−0.379655	+	0.925128i	$0.623957\pi$
$54$	−3.47214	−0.472498
$55$	0	0
$56$	3.00000	0.400892
$57$	0.472136	0.0625359
$58$	4.09017	0.537066
$59$	−6.76393	−0.880589	−0.440294	−	0.897853i	$-0.645126\pi$
$59$	−6.76393	−0.880589	−0.440294	+	0.897853i	$0.645126\pi$
$60$	0.618034	0.0797878
$61$	4.76393	0.609959	0.304979	−	0.952359i	$-0.401350\pi$
$61$	4.76393	0.609959	0.304979	+	0.952359i	$0.401350\pi$
$62$	−5.70820	−0.724943
$63$	−2.61803	−0.329841
$64$	7.00000	0.875000
$65$	−4.61803	−0.572797
$66$	0	0
$67$	−9.70820	−1.18605	−0.593023	−	0.805186i	$-0.702066\pi$
$67$	−9.70820	−1.18605	−0.593023	+	0.805186i	$0.702066\pi$
$68$	−2.38197	−0.288856
$69$	−2.76393	−0.332738
$70$	−1.00000	−0.119523
$71$	−9.56231	−1.13484	−0.567418	−	0.823430i	$-0.692058\pi$
$71$	−9.56231	−1.13484	−0.567418	+	0.823430i	$0.692058\pi$
$72$	−7.85410	−0.925615
$73$	14.5623	1.70439	0.852194	−	0.523225i	$-0.175271\pi$
$73$	14.5623	1.70439	0.852194	+	0.523225i	$0.175271\pi$
$74$	3.23607	0.376185
$75$	−0.618034	−0.0713644
$76$	0.763932	0.0876290
$77$	0	0
$78$	−2.85410	−0.323163
$79$	13.8541	1.55871	0.779354	−	0.626584i	$-0.215547\pi$
$79$	13.8541	1.55871	0.779354	+	0.626584i	$0.215547\pi$
$80$	−1.00000	−0.111803
$81$	5.70820	0.634245
$82$	−8.94427	−0.987730
$83$	−4.61803	−0.506895	−0.253448	−	0.967349i	$-0.581565\pi$
$83$	−4.61803	−0.506895	−0.253448	+	0.967349i	$0.581565\pi$
$84$	0.618034	0.0674330
$85$	2.38197	0.258360
$86$	1.23607	0.133289
$87$	2.52786	0.271015
$88$	0	0
$89$	−2.29180	−0.242930	−0.121465	−	0.992596i	$-0.538759\pi$
$89$	−2.29180	−0.242930	−0.121465	+	0.992596i	$0.538759\pi$
$90$	2.61803	0.275965
$91$	−4.61803	−0.484102
$92$	−4.47214	−0.466252
$93$	−3.52786	−0.365822
$94$	6.85410	0.706947
$95$	−0.763932	−0.0783778
$96$	3.09017	0.315389
$97$	−5.61803	−0.570425	−0.285212	−	0.958464i	$-0.592064\pi$
$97$	−5.61803	−0.570425	−0.285212	+	0.958464i	$0.592064\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	4.18034	0.415959	0.207980	−	0.978133i	$-0.433311\pi$
$101$	4.18034	0.415959	0.207980	+	0.978133i	$0.433311\pi$
$102$	1.47214	0.145763
$103$	−11.6180	−1.14476	−0.572379	−	0.819989i	$-0.693980\pi$
$103$	−11.6180	−1.14476	−0.572379	+	0.819989i	$0.693980\pi$
$104$	−13.8541	−1.35851
$105$	−0.618034	−0.0603139
$106$	5.52786	0.536914
$107$	5.70820	0.551833	0.275916	−	0.961182i	$-0.411019\pi$
$107$	5.70820	0.551833	0.275916	+	0.961182i	$0.411019\pi$
$108$	−3.47214	−0.334106
$109$	−13.4164	−1.28506	−0.642529	−	0.766261i	$-0.722115\pi$
$109$	−13.4164	−1.28506	−0.642529	+	0.766261i	$0.722115\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	18.4721	1.73771	0.868856	−	0.495065i	$-0.164856\pi$
$113$	18.4721	1.73771	0.868856	+	0.495065i	$0.164856\pi$
$114$	−0.472136	−0.0442196
$115$	4.47214	0.417029
$116$	4.09017	0.379763
$117$	12.0902	1.11774
$118$	6.76393	0.622670
$119$	2.38197	0.218354
$120$	−1.85410	−0.169256
$121$	0	0
$122$	−4.76393	−0.431306
$123$	−5.52786	−0.498431
$124$	−5.70820	−0.512612
$125$	1.00000	0.0894427
$126$	2.61803	0.233233
$127$	7.70820	0.683992	0.341996	−	0.939701i	$-0.388897\pi$
$127$	7.70820	0.683992	0.341996	+	0.939701i	$0.388897\pi$
$128$	3.00000	0.265165
$129$	0.763932	0.0672605
$130$	4.61803	0.405028
$131$	−15.4164	−1.34694	−0.673469	−	0.739216i	$-0.735196\pi$
$131$	−15.4164	−1.34694	−0.673469	+	0.739216i	$0.735196\pi$
$132$	0	0
$133$	−0.763932	−0.0662413
$134$	9.70820	0.838661
$135$	3.47214	0.298834
$136$	7.14590	0.612756
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	2.76393	0.235282
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−1.00000	−0.0845154
$141$	4.23607	0.356741
$142$	9.56231	0.802451
$143$	0	0
$144$	2.61803	0.218169
$145$	−4.09017	−0.339670
$146$	−14.5623	−1.20519
$147$	−0.618034	−0.0509746
$148$	3.23607	0.266003
$149$	−9.85410	−0.807279	−0.403640	−	0.914918i	$-0.632255\pi$
$149$	−9.85410	−0.807279	−0.403640	+	0.914918i	$0.632255\pi$
$150$	0.618034	0.0504623
$151$	2.67376	0.217588	0.108794	−	0.994064i	$-0.465301\pi$
$151$	2.67376	0.217588	0.108794	+	0.994064i	$0.465301\pi$
$152$	−2.29180	−0.185889
$153$	−6.23607	−0.504156
$154$	0	0
$155$	5.70820	0.458494
$156$	−2.85410	−0.228511
$157$	5.03444	0.401792	0.200896	−	0.979613i	$-0.435615\pi$
$157$	5.03444	0.401792	0.200896	+	0.979613i	$0.435615\pi$
$158$	−13.8541	−1.10217
$159$	3.41641	0.270939
$160$	−5.00000	−0.395285
$161$	4.47214	0.352454
$162$	−5.70820	−0.448479
$163$	−1.23607	−0.0968163	−0.0484082	−	0.998828i	$-0.515415\pi$
$163$	−1.23607	−0.0968163	−0.0484082	+	0.998828i	$0.515415\pi$
$164$	−8.94427	−0.698430
$165$	0	0
$166$	4.61803	0.358429
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	−1.85410	−0.143047
$169$	8.32624	0.640480
$170$	−2.38197	−0.182688
$171$	2.00000	0.152944
$172$	1.23607	0.0942493
$173$	−11.3820	−0.865355	−0.432677	−	0.901549i	$-0.642431\pi$
$173$	−11.3820	−0.865355	−0.432677	+	0.901549i	$0.642431\pi$
$174$	−2.52786	−0.191637
$175$	1.00000	0.0755929
$176$	0	0
$177$	4.18034	0.314214
$178$	2.29180	0.171777
$179$	−9.32624	−0.697076	−0.348538	−	0.937295i	$-0.613322\pi$
$179$	−9.32624	−0.697076	−0.348538	+	0.937295i	$0.613322\pi$
$180$	2.61803	0.195137
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	4.61803	0.342311
$183$	−2.94427	−0.217647
$184$	13.4164	0.989071
$185$	−3.23607	−0.237920
$186$	3.52786	0.258676
$187$	0	0
$188$	6.85410	0.499887
$189$	3.47214	0.252561
$190$	0.763932	0.0554215
$191$	−23.7426	−1.71796	−0.858979	−	0.512011i	$-0.828901\pi$
$191$	−23.7426	−1.71796	−0.858979	+	0.512011i	$0.828901\pi$
$192$	−4.32624	−0.312219
$193$	17.8885	1.28765	0.643823	−	0.765175i	$-0.277347\pi$
$193$	17.8885	1.28765	0.643823	+	0.765175i	$0.277347\pi$
$194$	5.61803	0.403351
$195$	2.85410	0.204386
$196$	−1.00000	−0.0714286
$197$	17.5279	1.24881	0.624404	−	0.781101i	$-0.285342\pi$
$197$	17.5279	1.24881	0.624404	+	0.781101i	$0.285342\pi$
$198$	0	0
$199$	−6.00000	−0.425329	−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000	−0.425329	−0.212664	+	0.977125i	$0.568214\pi$
$200$	3.00000	0.212132
$201$	6.00000	0.423207
$202$	−4.18034	−0.294128
$203$	−4.09017	−0.287074
$204$	1.47214	0.103070
$205$	8.94427	0.624695
$206$	11.6180	0.809467
$207$	−11.7082	−0.813776
$208$	4.61803	0.320203
$209$	0	0
$210$	0.618034	0.0426484
$211$	−16.3262	−1.12394	−0.561972	−	0.827156i	$-0.689957\pi$
$211$	−16.3262	−1.12394	−0.561972	+	0.827156i	$0.689957\pi$
$212$	5.52786	0.379655
$213$	5.90983	0.404935
$214$	−5.70820	−0.390205
$215$	−1.23607	−0.0842991
$216$	10.4164	0.708747
$217$	5.70820	0.387498
$218$	13.4164	0.908674
$219$	−9.00000	−0.608164
$220$	0	0
$221$	−11.0000	−0.739940
$222$	−2.00000	−0.134231
$223$	6.47214	0.433406	0.216703	−	0.976238i	$-0.430470\pi$
$223$	6.47214	0.433406	0.216703	+	0.976238i	$0.430470\pi$
$224$	−5.00000	−0.334077
$225$	−2.61803	−0.174536
$226$	−18.4721	−1.22875
$227$	13.8541	0.919529	0.459765	−	0.888041i	$-0.347934\pi$
$227$	13.8541	0.919529	0.459765	+	0.888041i	$0.347934\pi$
$228$	−0.472136	−0.0312680
$229$	−16.7639	−1.10779	−0.553896	−	0.832586i	$-0.686859\pi$
$229$	−16.7639	−1.10779	−0.553896	+	0.832586i	$0.686859\pi$
$230$	−4.47214	−0.294884
$231$	0	0
$232$	−12.2705	−0.805598
$233$	−19.2361	−1.26020	−0.630098	−	0.776515i	$-0.716985\pi$
$233$	−19.2361	−1.26020	−0.630098	+	0.776515i	$0.716985\pi$
$234$	−12.0902	−0.790359
$235$	−6.85410	−0.447112
$236$	6.76393	0.440294
$237$	−8.56231	−0.556182
$238$	−2.38197	−0.154400
$239$	−21.8541	−1.41362	−0.706812	−	0.707401i	$-0.749867\pi$
$239$	−21.8541	−1.41362	−0.706812	+	0.707401i	$0.749867\pi$
$240$	0.618034	0.0398939
$241$	22.6525	1.45917	0.729587	−	0.683888i	$-0.239712\pi$
$241$	22.6525	1.45917	0.729587	+	0.683888i	$0.239712\pi$
$242$	0	0
$243$	−13.9443	−0.894525
$244$	−4.76393	−0.304979
$245$	1.00000	0.0638877
$246$	5.52786	0.352444
$247$	3.52786	0.224473
$248$	17.1246	1.08741
$249$	2.85410	0.180871
$250$	−1.00000	−0.0632456
$251$	13.2361	0.835453	0.417727	−	0.908573i	$-0.362827\pi$
$251$	13.2361	0.835453	0.417727	+	0.908573i	$0.362827\pi$
$252$	2.61803	0.164921
$253$	0	0
$254$	−7.70820	−0.483656
$255$	−1.47214	−0.0921887
$256$	−17.0000	−1.06250
$257$	−31.5066	−1.96533	−0.982663	−	0.185400i	$-0.940642\pi$
$257$	−31.5066	−1.96533	−0.982663	+	0.185400i	$0.940642\pi$
$258$	−0.763932	−0.0475603
$259$	−3.23607	−0.201079
$260$	4.61803	0.286398
$261$	10.7082	0.662821
$262$	15.4164	0.952429
$263$	0.652476	0.0402334	0.0201167	−	0.999798i	$-0.493596\pi$
$263$	0.652476	0.0402334	0.0201167	+	0.999798i	$0.493596\pi$
$264$	0	0
$265$	−5.52786	−0.339574
$266$	0.763932	0.0468397
$267$	1.41641	0.0866828
$268$	9.70820	0.593023
$269$	−22.6525	−1.38115	−0.690573	−	0.723263i	$-0.742642\pi$
$269$	−22.6525	−1.38115	−0.690573	+	0.723263i	$0.742642\pi$
$270$	−3.47214	−0.211307
$271$	−20.1803	−1.22587	−0.612934	−	0.790134i	$-0.710011\pi$
$271$	−20.1803	−1.22587	−0.612934	+	0.790134i	$0.710011\pi$
$272$	−2.38197	−0.144428
$273$	2.85410	0.172738
$274$	0	0
$275$	0	0
$276$	2.76393	0.166369
$277$	−26.3607	−1.58386	−0.791930	−	0.610612i	$-0.790923\pi$
$277$	−26.3607	−1.58386	−0.791930	+	0.610612i	$0.790923\pi$
$278$	−4.00000	−0.239904
$279$	−14.9443	−0.894690
$280$	3.00000	0.179284
$281$	9.41641	0.561736	0.280868	−	0.959746i	$-0.409378\pi$
$281$	9.41641	0.561736	0.280868	+	0.959746i	$0.409378\pi$
$282$	−4.23607	−0.252254
$283$	−24.5623	−1.46008	−0.730039	−	0.683406i	$-0.760498\pi$
$283$	−24.5623	−1.46008	−0.730039	+	0.683406i	$0.760498\pi$
$284$	9.56231	0.567418
$285$	0.472136	0.0279669
$286$	0	0
$287$	8.94427	0.527964
$288$	13.0902	0.771346
$289$	−11.3262	−0.666249
$290$	4.09017	0.240183
$291$	3.47214	0.203540
$292$	−14.5623	−0.852194
$293$	−24.4721	−1.42968	−0.714839	−	0.699289i	$-0.753500\pi$
$293$	−24.4721	−1.42968	−0.714839	+	0.699289i	$0.753500\pi$
$294$	0.618034	0.0360445
$295$	−6.76393	−0.393811
$296$	−9.70820	−0.564278
$297$	0	0
$298$	9.85410	0.570833
$299$	−20.6525	−1.19436
$300$	0.618034	0.0356822
$301$	−1.23607	−0.0712458
$302$	−2.67376	−0.153858
$303$	−2.58359	−0.148423
$304$	0.763932	0.0438145
$305$	4.76393	0.272782
$306$	6.23607	0.356492
$307$	−13.3262	−0.760569	−0.380284	−	0.924870i	$-0.624174\pi$
$307$	−13.3262	−0.760569	−0.380284	+	0.924870i	$0.624174\pi$
$308$	0	0
$309$	7.18034	0.408475
$310$	−5.70820	−0.324204
$311$	34.6525	1.96496	0.982481	−	0.186364i	$-0.0596703\pi$
$311$	34.6525	1.96496	0.982481	+	0.186364i	$0.0596703\pi$
$312$	8.56231	0.484745
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−5.03444	−0.284110
$315$	−2.61803	−0.147510
$316$	−13.8541	−0.779354
$317$	−9.88854	−0.555396	−0.277698	−	0.960668i	$-0.589571\pi$
$317$	−9.88854	−0.555396	−0.277698	+	0.960668i	$0.589571\pi$
$318$	−3.41641	−0.191583
$319$	0	0
$320$	7.00000	0.391312
$321$	−3.52786	−0.196906
$322$	−4.47214	−0.249222
$323$	−1.81966	−0.101249
$324$	−5.70820	−0.317122
$325$	−4.61803	−0.256162
$326$	1.23607	0.0684595
$327$	8.29180	0.458537
$328$	26.8328	1.48159
$329$	−6.85410	−0.377879
$330$	0	0
$331$	−34.5066	−1.89665	−0.948327	−	0.317296i	$-0.897225\pi$
$331$	−34.5066	−1.89665	−0.948327	+	0.317296i	$0.897225\pi$
$332$	4.61803	0.253448
$333$	8.47214	0.464270
$334$	−4.00000	−0.218870
$335$	−9.70820	−0.530416
$336$	0.618034	0.0337165
$337$	12.9443	0.705119	0.352560	−	0.935789i	$-0.385311\pi$
$337$	12.9443	0.705119	0.352560	+	0.935789i	$0.385311\pi$
$338$	−8.32624	−0.452888
$339$	−11.4164	−0.620054
$340$	−2.38197	−0.129180
$341$	0	0
$342$	−2.00000	−0.108148
$343$	1.00000	0.0539949
$344$	−3.70820	−0.199933
$345$	−2.76393	−0.148805
$346$	11.3820	0.611898
$347$	20.9443	1.12435	0.562174	−	0.827019i	$-0.309965\pi$
$347$	20.9443	1.12435	0.562174	+	0.827019i	$0.309965\pi$
$348$	−2.52786	−0.135508
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	−1.00000	−0.0534522
$351$	−16.0344	−0.855855
$352$	0	0
$353$	11.6738	0.621332	0.310666	−	0.950519i	$-0.399448\pi$
$353$	11.6738	0.621332	0.310666	+	0.950519i	$0.399448\pi$
$354$	−4.18034	−0.222183
$355$	−9.56231	−0.507515
$356$	2.29180	0.121465
$357$	−1.47214	−0.0779137
$358$	9.32624	0.492907
$359$	−27.0902	−1.42976	−0.714882	−	0.699245i	$-0.753520\pi$
$359$	−27.0902	−1.42976	−0.714882	+	0.699245i	$0.753520\pi$
$360$	−7.85410	−0.413948
$361$	−18.4164	−0.969285
$362$	8.00000	0.420471
$363$	0	0
$364$	4.61803	0.242051
$365$	14.5623	0.762226
$366$	2.94427	0.153900
$367$	−4.32624	−0.225828	−0.112914	−	0.993605i	$-0.536018\pi$
$367$	−4.32624	−0.225828	−0.112914	+	0.993605i	$0.536018\pi$
$368$	−4.47214	−0.233126
$369$	−23.4164	−1.21901
$370$	3.23607	0.168235
$371$	−5.52786	−0.286992
$372$	3.52786	0.182911
$373$	−21.2361	−1.09956	−0.549781	−	0.835309i	$-0.685289\pi$
$373$	−21.2361	−1.09956	−0.549781	+	0.835309i	$0.685289\pi$
$374$	0	0
$375$	−0.618034	−0.0319151
$376$	−20.5623	−1.06042
$377$	18.8885	0.972809
$378$	−3.47214	−0.178587
$379$	−35.0344	−1.79960	−0.899799	−	0.436304i	$-0.856287\pi$
$379$	−35.0344	−1.79960	−0.899799	+	0.436304i	$0.856287\pi$
$380$	0.763932	0.0391889
$381$	−4.76393	−0.244064
$382$	23.7426	1.21478
$383$	29.9230	1.52899	0.764497	−	0.644628i	$-0.222988\pi$
$383$	29.9230	1.52899	0.764497	+	0.644628i	$0.222988\pi$
$384$	−1.85410	−0.0946167
$385$	0	0
$386$	−17.8885	−0.910503
$387$	3.23607	0.164499
$388$	5.61803	0.285212
$389$	5.27051	0.267225	0.133613	−	0.991034i	$-0.457342\pi$
$389$	5.27051	0.267225	0.133613	+	0.991034i	$0.457342\pi$
$390$	−2.85410	−0.144523
$391$	10.6525	0.538719
$392$	3.00000	0.151523
$393$	9.52786	0.480617
$394$	−17.5279	−0.883041
$395$	13.8541	0.697076
$396$	0	0
$397$	−28.3262	−1.42165	−0.710827	−	0.703367i	$-0.751679\pi$
$397$	−28.3262	−1.42165	−0.710827	+	0.703367i	$0.751679\pi$
$398$	6.00000	0.300753
$399$	0.472136	0.0236364
$400$	−1.00000	−0.0500000
$401$	−12.2705	−0.612760	−0.306380	−	0.951909i	$-0.599118\pi$
$401$	−12.2705	−0.612760	−0.306380	+	0.951909i	$0.599118\pi$
$402$	−6.00000	−0.299253
$403$	−26.3607	−1.31312
$404$	−4.18034	−0.207980
$405$	5.70820	0.283643
$406$	4.09017	0.202992
$407$	0	0
$408$	−4.41641	−0.218645
$409$	23.5967	1.16678	0.583392	−	0.812191i	$-0.301725\pi$
$409$	23.5967	1.16678	0.583392	+	0.812191i	$0.301725\pi$
$410$	−8.94427	−0.441726
$411$	0	0
$412$	11.6180	0.572379
$413$	−6.76393	−0.332831
$414$	11.7082	0.575427
$415$	−4.61803	−0.226690
$416$	23.0902	1.13209
$417$	−2.47214	−0.121061
$418$	0	0
$419$	40.8328	1.99481	0.997407	−	0.0719701i	$-0.0229286\pi$
$419$	40.8328	1.99481	0.997407	+	0.0719701i	$0.0229286\pi$
$420$	0.618034	0.0301570
$421$	2.43769	0.118806	0.0594030	−	0.998234i	$-0.481080\pi$
$421$	2.43769	0.118806	0.0594030	+	0.998234i	$0.481080\pi$
$422$	16.3262	0.794749
$423$	17.9443	0.872480
$424$	−16.5836	−0.805370
$425$	2.38197	0.115542
$426$	−5.90983	−0.286332
$427$	4.76393	0.230543
$428$	−5.70820	−0.275916
$429$	0	0
$430$	1.23607	0.0596085
$431$	15.6180	0.752294	0.376147	−	0.926560i	$-0.377249\pi$
$431$	15.6180	0.752294	0.376147	+	0.926560i	$0.377249\pi$
$432$	−3.47214	−0.167053
$433$	−7.09017	−0.340732	−0.170366	−	0.985381i	$-0.554495\pi$
$433$	−7.09017	−0.340732	−0.170366	+	0.985381i	$0.554495\pi$
$434$	−5.70820	−0.274003
$435$	2.52786	0.121202
$436$	13.4164	0.642529
$437$	−3.41641	−0.163429
$438$	9.00000	0.430037
$439$	15.7082	0.749712	0.374856	−	0.927083i	$-0.377692\pi$
$439$	15.7082	0.749712	0.374856	+	0.927083i	$0.377692\pi$
$440$	0	0
$441$	−2.61803	−0.124668
$442$	11.0000	0.523217
$443$	−18.7639	−0.891501	−0.445751	−	0.895157i	$-0.647063\pi$
$443$	−18.7639	−0.891501	−0.445751	+	0.895157i	$0.647063\pi$
$444$	−2.00000	−0.0949158
$445$	−2.29180	−0.108642
$446$	−6.47214	−0.306465
$447$	6.09017	0.288055
$448$	7.00000	0.330719
$449$	−27.1591	−1.28171	−0.640857	−	0.767660i	$-0.721421\pi$
$449$	−27.1591	−1.28171	−0.640857	+	0.767660i	$0.721421\pi$
$450$	2.61803	0.123415
$451$	0	0
$452$	−18.4721	−0.868856
$453$	−1.65248	−0.0776401
$454$	−13.8541	−0.650205
$455$	−4.61803	−0.216497
$456$	1.41641	0.0663294
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	16.7639	0.783327
$459$	8.27051	0.386034
$460$	−4.47214	−0.208514
$461$	−2.18034	−0.101549	−0.0507743	−	0.998710i	$-0.516169\pi$
$461$	−2.18034	−0.101549	−0.0507743	+	0.998710i	$0.516169\pi$
$462$	0	0
$463$	−14.6525	−0.680958	−0.340479	−	0.940252i	$-0.610589\pi$
$463$	−14.6525	−0.680958	−0.340479	+	0.940252i	$0.610589\pi$
$464$	4.09017	0.189881
$465$	−3.52786	−0.163601
$466$	19.2361	0.891094
$467$	13.2705	0.614086	0.307043	−	0.951696i	$-0.400660\pi$
$467$	13.2705	0.614086	0.307043	+	0.951696i	$0.400660\pi$
$468$	−12.0902	−0.558868
$469$	−9.70820	−0.448283
$470$	6.85410	0.316156
$471$	−3.11146	−0.143368
$472$	−20.2918	−0.934006
$473$	0	0
$474$	8.56231	0.393280
$475$	−0.763932	−0.0350516
$476$	−2.38197	−0.109177
$477$	14.4721	0.662634
$478$	21.8541	0.999583
$479$	−1.70820	−0.0780498	−0.0390249	−	0.999238i	$-0.512425\pi$
$479$	−1.70820	−0.0780498	−0.0390249	+	0.999238i	$0.512425\pi$
$480$	3.09017	0.141046
$481$	14.9443	0.681400
$482$	−22.6525	−1.03179
$483$	−2.76393	−0.125763
$484$	0	0
$485$	−5.61803	−0.255102
$486$	13.9443	0.632525
$487$	34.1803	1.54886	0.774430	−	0.632660i	$-0.218037\pi$
$487$	34.1803	1.54886	0.774430	+	0.632660i	$0.218037\pi$
$488$	14.2918	0.646959
$489$	0.763932	0.0345462
$490$	−1.00000	−0.0451754
$491$	24.9443	1.12572	0.562860	−	0.826553i	$-0.309701\pi$
$491$	24.9443	1.12572	0.562860	+	0.826553i	$0.309701\pi$
$492$	5.52786	0.249215
$493$	−9.74265	−0.438787
$494$	−3.52786	−0.158726
$495$	0	0
$496$	−5.70820	−0.256306
$497$	−9.56231	−0.428928
$498$	−2.85410	−0.127895
$499$	25.6869	1.14990	0.574952	−	0.818187i	$-0.305021\pi$
$499$	25.6869	1.14990	0.574952	+	0.818187i	$0.305021\pi$
$500$	−1.00000	−0.0447214
$501$	−2.47214	−0.110447
$502$	−13.2361	−0.590755
$503$	−19.0902	−0.851189	−0.425594	−	0.904914i	$-0.639935\pi$
$503$	−19.0902	−0.851189	−0.425594	+	0.904914i	$0.639935\pi$
$504$	−7.85410	−0.349850
$505$	4.18034	0.186023
$506$	0	0
$507$	−5.14590	−0.228537
$508$	−7.70820	−0.341996
$509$	−40.8328	−1.80988	−0.904941	−	0.425536i	$-0.860085\pi$
$509$	−40.8328	−1.80988	−0.904941	+	0.425536i	$0.860085\pi$
$510$	1.47214	0.0651873
$511$	14.5623	0.644198
$512$	11.0000	0.486136
$513$	−2.65248	−0.117110
$514$	31.5066	1.38970
$515$	−11.6180	−0.511952
$516$	−0.763932	−0.0336302
$517$	0	0
$518$	3.23607	0.142185
$519$	7.03444	0.308778
$520$	−13.8541	−0.607543
$521$	−38.1803	−1.67271	−0.836356	−	0.548187i	$-0.815318\pi$
$521$	−38.1803	−1.67271	−0.836356	+	0.548187i	$0.815318\pi$
$522$	−10.7082	−0.468685
$523$	16.7426	0.732105	0.366052	−	0.930594i	$-0.380709\pi$
$523$	16.7426	0.732105	0.366052	+	0.930594i	$0.380709\pi$
$524$	15.4164	0.673469
$525$	−0.618034	−0.0269732
$526$	−0.652476	−0.0284493
$527$	13.5967	0.592284
$528$	0	0
$529$	−3.00000	−0.130435
$530$	5.52786	0.240115
$531$	17.7082	0.768471
$532$	0.763932	0.0331207
$533$	−41.3050	−1.78912
$534$	−1.41641	−0.0612940
$535$	5.70820	0.246787
$536$	−29.1246	−1.25799
$537$	5.76393	0.248732
$538$	22.6525	0.976618
$539$	0	0
$540$	−3.47214	−0.149417
$541$	−30.7984	−1.32413	−0.662063	−	0.749448i	$-0.730319\pi$
$541$	−30.7984	−1.32413	−0.662063	+	0.749448i	$0.730319\pi$
$542$	20.1803	0.866820
$543$	4.94427	0.212179
$544$	−11.9098	−0.510630
$545$	−13.4164	−0.574696
$546$	−2.85410	−0.122144
$547$	−24.5410	−1.04930	−0.524649	−	0.851319i	$-0.675803\pi$
$547$	−24.5410	−1.04930	−0.524649	+	0.851319i	$0.675803\pi$
$548$	0	0
$549$	−12.4721	−0.532298
$550$	0	0
$551$	3.12461	0.133113
$552$	−8.29180	−0.352922
$553$	13.8541	0.589136
$554$	26.3607	1.11996
$555$	2.00000	0.0848953
$556$	−4.00000	−0.169638
$557$	20.7639	0.879796	0.439898	−	0.898048i	$-0.355015\pi$
$557$	20.7639	0.879796	0.439898	+	0.898048i	$0.355015\pi$
$558$	14.9443	0.632641
$559$	5.70820	0.241431
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−9.41641	−0.397207
$563$	−23.2148	−0.978386	−0.489193	−	0.872175i	$-0.662709\pi$
$563$	−23.2148	−0.978386	−0.489193	+	0.872175i	$0.662709\pi$
$564$	−4.23607	−0.178371
$565$	18.4721	0.777129
$566$	24.5623	1.03243
$567$	5.70820	0.239722
$568$	−28.6869	−1.20368
$569$	−11.9098	−0.499286	−0.249643	−	0.968338i	$-0.580313\pi$
$569$	−11.9098	−0.499286	−0.249643	+	0.968338i	$0.580313\pi$
$570$	−0.472136	−0.0197756
$571$	30.6312	1.28188	0.640938	−	0.767593i	$-0.278546\pi$
$571$	30.6312	1.28188	0.640938	+	0.767593i	$0.278546\pi$
$572$	0	0
$573$	14.6738	0.613005
$574$	−8.94427	−0.373327
$575$	4.47214	0.186501
$576$	−18.3262	−0.763593
$577$	−41.2148	−1.71579	−0.857897	−	0.513822i	$-0.828229\pi$
$577$	−41.2148	−1.71579	−0.857897	+	0.513822i	$0.828229\pi$
$578$	11.3262	0.471109
$579$	−11.0557	−0.459460
$580$	4.09017	0.169835
$581$	−4.61803	−0.191588
$582$	−3.47214	−0.143925
$583$	0	0
$584$	43.6869	1.80778
$585$	12.0902	0.499867
$586$	24.4721	1.01093
$587$	23.3820	0.965077	0.482539	−	0.875875i	$-0.339715\pi$
$587$	23.3820	0.965077	0.482539	+	0.875875i	$0.339715\pi$
$588$	0.618034	0.0254873
$589$	−4.36068	−0.179679
$590$	6.76393	0.278467
$591$	−10.8328	−0.445602
$592$	3.23607	0.133002
$593$	32.0902	1.31779	0.658893	−	0.752237i	$-0.271025\pi$
$593$	32.0902	1.31779	0.658893	+	0.752237i	$0.271025\pi$
$594$	0	0
$595$	2.38197	0.0976511
$596$	9.85410	0.403640
$597$	3.70820	0.151767
$598$	20.6525	0.844543
$599$	−20.5623	−0.840153	−0.420077	−	0.907489i	$-0.637997\pi$
$599$	−20.5623	−0.840153	−0.420077	+	0.907489i	$0.637997\pi$
$600$	−1.85410	−0.0756934
$601$	−4.94427	−0.201681	−0.100841	−	0.994903i	$-0.532153\pi$
$601$	−4.94427	−0.201681	−0.100841	+	0.994903i	$0.532153\pi$
$602$	1.23607	0.0503784
$603$	25.4164	1.03504
$604$	−2.67376	−0.108794
$605$	0	0
$606$	2.58359	0.104951
$607$	−25.1459	−1.02064	−0.510320	−	0.859984i	$-0.670473\pi$
$607$	−25.1459	−1.02064	−0.510320	+	0.859984i	$0.670473\pi$
$608$	3.81966	0.154908
$609$	2.52786	0.102434
$610$	−4.76393	−0.192886
$611$	31.6525	1.28052
$612$	6.23607	0.252078
$613$	22.0000	0.888572	0.444286	−	0.895885i	$-0.353457\pi$
$613$	22.0000	0.888572	0.444286	+	0.895885i	$0.353457\pi$
$614$	13.3262	0.537803
$615$	−5.52786	−0.222905
$616$	0	0
$617$	17.5967	0.708418	0.354209	−	0.935166i	$-0.384750\pi$
$617$	17.5967	0.708418	0.354209	+	0.935166i	$0.384750\pi$
$618$	−7.18034	−0.288836
$619$	1.52786	0.0614100	0.0307050	−	0.999528i	$-0.490225\pi$
$619$	1.52786	0.0614100	0.0307050	+	0.999528i	$0.490225\pi$
$620$	−5.70820	−0.229247
$621$	15.5279	0.623112
$622$	−34.6525	−1.38944
$623$	−2.29180	−0.0918189
$624$	−2.85410	−0.114256
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	−5.03444	−0.200896
$629$	−7.70820	−0.307346
$630$	2.61803	0.104305
$631$	36.1591	1.43947	0.719735	−	0.694249i	$-0.244263\pi$
$631$	36.1591	1.43947	0.719735	+	0.694249i	$0.244263\pi$
$632$	41.5623	1.65326
$633$	10.0902	0.401048
$634$	9.88854	0.392724
$635$	7.70820	0.305891
$636$	−3.41641	−0.135469
$637$	−4.61803	−0.182973
$638$	0	0
$639$	25.0344	0.990347
$640$	3.00000	0.118585
$641$	−36.9098	−1.45785	−0.728925	−	0.684593i	$-0.759980\pi$
$641$	−36.9098	−1.45785	−0.728925	+	0.684593i	$0.759980\pi$
$642$	3.52786	0.139234
$643$	42.1459	1.66207	0.831036	−	0.556219i	$-0.187748\pi$
$643$	42.1459	1.66207	0.831036	+	0.556219i	$0.187748\pi$
$644$	−4.47214	−0.176227
$645$	0.763932	0.0300798
$646$	1.81966	0.0715936
$647$	−7.97871	−0.313676	−0.156838	−	0.987624i	$-0.550130\pi$
$647$	−7.97871	−0.313676	−0.156838	+	0.987624i	$0.550130\pi$
$648$	17.1246	0.672718
$649$	0	0
$650$	4.61803	0.181134
$651$	−3.52786	−0.138268
$652$	1.23607	0.0484082
$653$	11.1246	0.435340	0.217670	−	0.976022i	$-0.430154\pi$
$653$	11.1246	0.435340	0.217670	+	0.976022i	$0.430154\pi$
$654$	−8.29180	−0.324235
$655$	−15.4164	−0.602369
$656$	−8.94427	−0.349215
$657$	−38.1246	−1.48738
$658$	6.85410	0.267201
$659$	5.85410	0.228043	0.114022	−	0.993478i	$-0.463627\pi$
$659$	5.85410	0.228043	0.114022	+	0.993478i	$0.463627\pi$
$660$	0	0
$661$	−1.05573	−0.0410631	−0.0205315	−	0.999789i	$-0.506536\pi$
$661$	−1.05573	−0.0410631	−0.0205315	+	0.999789i	$0.506536\pi$
$662$	34.5066	1.34114
$663$	6.79837	0.264027
$664$	−13.8541	−0.537643
$665$	−0.763932	−0.0296240
$666$	−8.47214	−0.328289
$667$	−18.2918	−0.708261
$668$	−4.00000	−0.154765
$669$	−4.00000	−0.154649
$670$	9.70820	0.375061
$671$	0	0
$672$	3.09017	0.119206
$673$	33.3050	1.28381	0.641906	−	0.766784i	$-0.278144\pi$
$673$	33.3050	1.28381	0.641906	+	0.766784i	$0.278144\pi$
$674$	−12.9443	−0.498595
$675$	3.47214	0.133643
$676$	−8.32624	−0.320240
$677$	4.09017	0.157198	0.0785990	−	0.996906i	$-0.474955\pi$
$677$	4.09017	0.157198	0.0785990	+	0.996906i	$0.474955\pi$
$678$	11.4164	0.438445
$679$	−5.61803	−0.215600
$680$	7.14590	0.274033
$681$	−8.56231	−0.328108
$682$	0	0
$683$	−25.2361	−0.965631	−0.482816	−	0.875722i	$-0.660386\pi$
$683$	−25.2361	−0.965631	−0.482816	+	0.875722i	$0.660386\pi$
$684$	−2.00000	−0.0764719
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	10.3607	0.395285
$688$	1.23607	0.0471246
$689$	25.5279	0.972534
$690$	2.76393	0.105221
$691$	−11.4164	−0.434301	−0.217150	−	0.976138i	$-0.569676\pi$
$691$	−11.4164	−0.434301	−0.217150	+	0.976138i	$0.569676\pi$
$692$	11.3820	0.432677
$693$	0	0
$694$	−20.9443	−0.795034
$695$	4.00000	0.151729
$696$	7.58359	0.287455
$697$	21.3050	0.806983
$698$	22.0000	0.832712
$699$	11.8885	0.449666
$700$	−1.00000	−0.0377964
$701$	−15.5279	−0.586479	−0.293240	−	0.956039i	$-0.594733\pi$
$701$	−15.5279	−0.586479	−0.293240	+	0.956039i	$0.594733\pi$
$702$	16.0344	0.605181
$703$	2.47214	0.0932384
$704$	0	0
$705$	4.23607	0.159540
$706$	−11.6738	−0.439348
$707$	4.18034	0.157218
$708$	−4.18034	−0.157107
$709$	37.9230	1.42423	0.712114	−	0.702064i	$-0.247738\pi$
$709$	37.9230	1.42423	0.712114	+	0.702064i	$0.247738\pi$
$710$	9.56231	0.358867
$711$	−36.2705	−1.36025
$712$	−6.87539	−0.257666
$713$	25.5279	0.956026
$714$	1.47214	0.0550933
$715$	0	0
$716$	9.32624	0.348538
$717$	13.5066	0.504412
$718$	27.0902	1.01100
$719$	−15.4164	−0.574935	−0.287467	−	0.957790i	$-0.592813\pi$
$719$	−15.4164	−0.574935	−0.287467	+	0.957790i	$0.592813\pi$
$720$	2.61803	0.0975684
$721$	−11.6180	−0.432678
$722$	18.4164	0.685388
$723$	−14.0000	−0.520666
$724$	8.00000	0.297318
$725$	−4.09017	−0.151905
$726$	0	0
$727$	−0.326238	−0.0120995	−0.00604975	−	0.999982i	$-0.501926\pi$
$727$	−0.326238	−0.0120995	−0.00604975	+	0.999982i	$0.501926\pi$
$728$	−13.8541	−0.513467
$729$	−8.50658	−0.315058
$730$	−14.5623	−0.538975
$731$	−2.94427	−0.108898
$732$	2.94427	0.108823
$733$	−37.9230	−1.40072	−0.700359	−	0.713791i	$-0.746977\pi$
$733$	−37.9230	−1.40072	−0.700359	+	0.713791i	$0.746977\pi$
$734$	4.32624	0.159684
$735$	−0.618034	−0.0227965
$736$	−22.3607	−0.824226
$737$	0	0
$738$	23.4164	0.861970
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	3.23607	0.118960
$741$	−2.18034	−0.0800968
$742$	5.52786	0.202934
$743$	−6.65248	−0.244056	−0.122028	−	0.992527i	$-0.538940\pi$
$743$	−6.65248	−0.244056	−0.122028	+	0.992527i	$0.538940\pi$
$744$	−10.5836	−0.388013
$745$	−9.85410	−0.361026
$746$	21.2361	0.777508
$747$	12.0902	0.442356
$748$	0	0
$749$	5.70820	0.208573
$750$	0.618034	0.0225674
$751$	−12.5623	−0.458405	−0.229203	−	0.973379i	$-0.573612\pi$
$751$	−12.5623	−0.458405	−0.229203	+	0.973379i	$0.573612\pi$
$752$	6.85410	0.249943
$753$	−8.18034	−0.298108
$754$	−18.8885	−0.687880
$755$	2.67376	0.0973082
$756$	−3.47214	−0.126280
$757$	−7.23607	−0.262999	−0.131500	−	0.991316i	$-0.541979\pi$
$757$	−7.23607	−0.262999	−0.131500	+	0.991316i	$0.541979\pi$
$758$	35.0344	1.27251
$759$	0	0
$760$	−2.29180	−0.0831322
$761$	−33.4164	−1.21134	−0.605672	−	0.795714i	$-0.707096\pi$
$761$	−33.4164	−1.21134	−0.605672	+	0.795714i	$0.707096\pi$
$762$	4.76393	0.172579
$763$	−13.4164	−0.485707
$764$	23.7426	0.858979
$765$	−6.23607	−0.225466
$766$	−29.9230	−1.08116
$767$	31.2361	1.12787
$768$	10.5066	0.379123
$769$	−52.0689	−1.87765	−0.938826	−	0.344392i	$-0.888085\pi$
$769$	−52.0689	−1.87765	−0.938826	+	0.344392i	$0.888085\pi$
$770$	0	0
$771$	19.4721	0.701272
$772$	−17.8885	−0.643823
$773$	−2.72949	−0.0981729	−0.0490865	−	0.998795i	$-0.515631\pi$
$773$	−2.72949	−0.0981729	−0.0490865	+	0.998795i	$0.515631\pi$
$774$	−3.23607	−0.116318
$775$	5.70820	0.205045
$776$	−16.8541	−0.605027
$777$	2.00000	0.0717496
$778$	−5.27051	−0.188957
$779$	−6.83282	−0.244811
$780$	−2.85410	−0.102193
$781$	0	0
$782$	−10.6525	−0.380932
$783$	−14.2016	−0.507525
$784$	−1.00000	−0.0357143
$785$	5.03444	0.179687
$786$	−9.52786	−0.339848
$787$	−36.9787	−1.31815	−0.659074	−	0.752078i	$-0.729052\pi$
$787$	−36.9787	−1.31815	−0.659074	+	0.752078i	$0.729052\pi$
$788$	−17.5279	−0.624404
$789$	−0.403252	−0.0143562
$790$	−13.8541	−0.492907
$791$	18.4721	0.656794
$792$	0	0
$793$	−22.0000	−0.781243
$794$	28.3262	1.00526
$795$	3.41641	0.121168
$796$	6.00000	0.212664
$797$	49.5623	1.75559	0.877793	−	0.479039i	$-0.159015\pi$
$797$	49.5623	1.75559	0.877793	+	0.479039i	$0.159015\pi$
$798$	−0.472136	−0.0167134
$799$	−16.3262	−0.577581
$800$	−5.00000	−0.176777
$801$	6.00000	0.212000
$802$	12.2705	0.433287
$803$	0	0
$804$	−6.00000	−0.211604
$805$	4.47214	0.157622
$806$	26.3607	0.928515
$807$	14.0000	0.492823
$808$	12.5410	0.441192
$809$	38.7984	1.36408	0.682039	−	0.731316i	$-0.261093\pi$
$809$	38.7984	1.36408	0.682039	+	0.731316i	$0.261093\pi$
$810$	−5.70820	−0.200566
$811$	−29.8885	−1.04953	−0.524764	−	0.851248i	$-0.675847\pi$
$811$	−29.8885	−1.04953	−0.524764	+	0.851248i	$0.675847\pi$
$812$	4.09017	0.143537
$813$	12.4721	0.437417
$814$	0	0
$815$	−1.23607	−0.0432976
$816$	1.47214	0.0515351
$817$	0.944272	0.0330359
$818$	−23.5967	−0.825041
$819$	12.0902	0.422465
$820$	−8.94427	−0.312348
$821$	−38.3820	−1.33954	−0.669770	−	0.742569i	$-0.733607\pi$
$821$	−38.3820	−1.33954	−0.669770	+	0.742569i	$0.733607\pi$
$822$	0	0
$823$	−13.5279	−0.471552	−0.235776	−	0.971807i	$-0.575763\pi$
$823$	−13.5279	−0.471552	−0.235776	+	0.971807i	$0.575763\pi$
$824$	−34.8541	−1.21420
$825$	0	0
$826$	6.76393	0.235347
$827$	42.8328	1.48944	0.744721	−	0.667375i	$-0.232582\pi$
$827$	42.8328	1.48944	0.744721	+	0.667375i	$0.232582\pi$
$828$	11.7082	0.406888
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	4.61803	0.160294
$831$	16.2918	0.565156
$832$	−32.3262	−1.12071
$833$	2.38197	0.0825302
$834$	2.47214	0.0856031
$835$	4.00000	0.138426
$836$	0	0
$837$	19.8197	0.685068
$838$	−40.8328	−1.41055
$839$	−26.4721	−0.913920	−0.456960	−	0.889487i	$-0.651062\pi$
$839$	−26.4721	−0.913920	−0.456960	+	0.889487i	$0.651062\pi$
$840$	−1.85410	−0.0639726
$841$	−12.2705	−0.423121
$842$	−2.43769	−0.0840085
$843$	−5.81966	−0.200440
$844$	16.3262	0.561972
$845$	8.32624	0.286431
$846$	−17.9443	−0.616937
$847$	0	0
$848$	5.52786	0.189828
$849$	15.1803	0.520988
$850$	−2.38197	−0.0817008
$851$	−14.4721	−0.496098
$852$	−5.90983	−0.202467
$853$	14.7295	0.504328	0.252164	−	0.967684i	$-0.418858\pi$
$853$	14.7295	0.504328	0.252164	+	0.967684i	$0.418858\pi$
$854$	−4.76393	−0.163018
$855$	2.00000	0.0683986
$856$	17.1246	0.585307
$857$	16.4721	0.562677	0.281339	−	0.959609i	$-0.409222\pi$
$857$	16.4721	0.562677	0.281339	+	0.959609i	$0.409222\pi$
$858$	0	0
$859$	7.63932	0.260650	0.130325	−	0.991471i	$-0.458398\pi$
$859$	7.63932	0.260650	0.130325	+	0.991471i	$0.458398\pi$
$860$	1.23607	0.0421496
$861$	−5.52786	−0.188389
$862$	−15.6180	−0.531952
$863$	44.9443	1.52992	0.764960	−	0.644077i	$-0.222759\pi$
$863$	44.9443	1.52992	0.764960	+	0.644077i	$0.222759\pi$
$864$	−17.3607	−0.590622
$865$	−11.3820	−0.386998
$866$	7.09017	0.240934
$867$	7.00000	0.237732
$868$	−5.70820	−0.193749
$869$	0	0
$870$	−2.52786	−0.0857026
$871$	44.8328	1.51910
$872$	−40.2492	−1.36301
$873$	14.7082	0.497797
$874$	3.41641	0.115562
$875$	1.00000	0.0338062
$876$	9.00000	0.304082
$877$	26.0689	0.880284	0.440142	−	0.897928i	$-0.354928\pi$
$877$	26.0689	0.880284	0.440142	+	0.897928i	$0.354928\pi$
$878$	−15.7082	−0.530126
$879$	15.1246	0.510140
$880$	0	0
$881$	38.1803	1.28633	0.643164	−	0.765728i	$-0.277621\pi$
$881$	38.1803	1.28633	0.643164	+	0.765728i	$0.277621\pi$
$882$	2.61803	0.0881538
$883$	43.1246	1.45126	0.725629	−	0.688086i	$-0.241549\pi$
$883$	43.1246	1.45126	0.725629	+	0.688086i	$0.241549\pi$
$884$	11.0000	0.369970
$885$	4.18034	0.140521
$886$	18.7639	0.630387
$887$	27.9787	0.939433	0.469717	−	0.882817i	$-0.344356\pi$
$887$	27.9787	0.939433	0.469717	+	0.882817i	$0.344356\pi$
$888$	6.00000	0.201347
$889$	7.70820	0.258525
$890$	2.29180	0.0768212
$891$	0	0
$892$	−6.47214	−0.216703
$893$	5.23607	0.175218
$894$	−6.09017	−0.203686
$895$	−9.32624	−0.311742
$896$	3.00000	0.100223
$897$	12.7639	0.426175
$898$	27.1591	0.906309
$899$	−23.3475	−0.778684
$900$	2.61803	0.0872678
$901$	−13.1672	−0.438663
$902$	0	0
$903$	0.763932	0.0254221
$904$	55.4164	1.84312
$905$	−8.00000	−0.265929
$906$	1.65248	0.0548998
$907$	30.3607	1.00811	0.504055	−	0.863672i	$-0.331841\pi$
$907$	30.3607	1.00811	0.504055	+	0.863672i	$0.331841\pi$
$908$	−13.8541	−0.459765
$909$	−10.9443	−0.362999
$910$	4.61803	0.153086
$911$	−43.3951	−1.43774	−0.718872	−	0.695142i	$-0.755341\pi$
$911$	−43.3951	−1.43774	−0.718872	+	0.695142i	$0.755341\pi$
$912$	−0.472136	−0.0156340
$913$	0	0
$914$	−26.0000	−0.860004
$915$	−2.94427	−0.0973346
$916$	16.7639	0.553896
$917$	−15.4164	−0.509095
$918$	−8.27051	−0.272967
$919$	−38.4508	−1.26838	−0.634188	−	0.773179i	$-0.718666\pi$
$919$	−38.4508	−1.26838	−0.634188	+	0.773179i	$0.718666\pi$
$920$	13.4164	0.442326
$921$	8.23607	0.271388
$922$	2.18034	0.0718057
$923$	44.1591	1.45351
$924$	0	0
$925$	−3.23607	−0.106401
$926$	14.6525	0.481510
$927$	30.4164	0.999006
$928$	20.4508	0.671332
$929$	20.9443	0.687159	0.343580	−	0.939124i	$-0.388360\pi$
$929$	20.9443	0.687159	0.343580	+	0.939124i	$0.388360\pi$
$930$	3.52786	0.115683
$931$	−0.763932	−0.0250369
$932$	19.2361	0.630098
$933$	−21.4164	−0.701142
$934$	−13.2705	−0.434224
$935$	0	0
$936$	36.2705	1.18554
$937$	6.72949	0.219843	0.109921	−	0.993940i	$-0.464940\pi$
$937$	6.72949	0.219843	0.109921	+	0.993940i	$0.464940\pi$
$938$	9.70820	0.316984
$939$	8.65248	0.282363
$940$	6.85410	0.223556
$941$	−12.6525	−0.412459	−0.206229	−	0.978504i	$-0.566119\pi$
$941$	−12.6525	−0.412459	−0.206229	+	0.978504i	$0.566119\pi$
$942$	3.11146	0.101377
$943$	40.0000	1.30258
$944$	6.76393	0.220147
$945$	3.47214	0.112949
$946$	0	0
$947$	46.2918	1.50428	0.752141	−	0.659003i	$-0.229021\pi$
$947$	46.2918	1.50428	0.752141	+	0.659003i	$0.229021\pi$
$948$	8.56231	0.278091
$949$	−67.2492	−2.18300
$950$	0.763932	0.0247852
$951$	6.11146	0.198178
$952$	7.14590	0.231600
$953$	45.4164	1.47118	0.735591	−	0.677426i	$-0.236905\pi$
$953$	45.4164	1.47118	0.735591	+	0.677426i	$0.236905\pi$
$954$	−14.4721	−0.468553
$955$	−23.7426	−0.768294
$956$	21.8541	0.706812
$957$	0	0
$958$	1.70820	0.0551896
$959$	0	0
$960$	−4.32624	−0.139629
$961$	1.58359	0.0510836
$962$	−14.9443	−0.481823
$963$	−14.9443	−0.481572
$964$	−22.6525	−0.729587
$965$	17.8885	0.575853
$966$	2.76393	0.0889281
$967$	1.34752	0.0433335	0.0216667	−	0.999765i	$-0.493103\pi$
$967$	1.34752	0.0433335	0.0216667	+	0.999765i	$0.493103\pi$
$968$	0	0
$969$	1.12461	0.0361277
$970$	5.61803	0.180384
$971$	18.5836	0.596376	0.298188	−	0.954507i	$-0.403618\pi$
$971$	18.5836	0.596376	0.298188	+	0.954507i	$0.403618\pi$
$972$	13.9443	0.447263
$973$	4.00000	0.128234
$974$	−34.1803	−1.09521
$975$	2.85410	0.0914044
$976$	−4.76393	−0.152490
$977$	−39.1246	−1.25171	−0.625854	−	0.779941i	$-0.715249\pi$
$977$	−39.1246	−1.25171	−0.625854	+	0.779941i	$0.715249\pi$
$978$	−0.763932	−0.0244279
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	35.1246	1.12144
$982$	−24.9443	−0.796004
$983$	26.0902	0.832147	0.416074	−	0.909331i	$-0.363406\pi$
$983$	26.0902	0.832147	0.416074	+	0.909331i	$0.363406\pi$
$984$	−16.5836	−0.528666
$985$	17.5279	0.558484
$986$	9.74265	0.310269
$987$	4.23607	0.134836
$988$	−3.52786	−0.112236
$989$	−5.52786	−0.175776
$990$	0	0
$991$	−4.03444	−0.128158	−0.0640791	−	0.997945i	$-0.520411\pi$
$991$	−4.03444	−0.128158	−0.0640791	+	0.997945i	$0.520411\pi$
$992$	−28.5410	−0.906178
$993$	21.3262	0.676768
$994$	9.56231	0.303298
$995$	−6.00000	−0.190213
$996$	−2.85410	−0.0904357
$997$	−39.5066	−1.25119	−0.625593	−	0.780150i	$-0.715143\pi$
$997$	−39.5066	−1.25119	−0.625593	+	0.780150i	$0.715143\pi$
$998$	−25.6869	−0.813105
$999$	−11.2361	−0.355493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.i.1.1		2
11.5	even	5		385.2.n.a.36.1	✓	4
11.9	even	5		385.2.n.a.246.1	yes	4
11.10	odd	2		4235.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.a.36.1	✓	4	11.5	even	5
385.2.n.a.246.1	yes	4	11.9	even	5
4235.2.a.i.1.1		2	1.1	even	1	trivial
4235.2.a.n.1.1		2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.618034 q^{3} -1.00000 q^{4} +1.00000 q^{5} +0.618034 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.618034 q^{3} -1.00000 q^{4} +1.00000 q^{5} +0.618034 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} +0.618034 q^{12} -4.61803 q^{13} -1.00000 q^{14} -0.618034 q^{15} -1.00000 q^{16} +2.38197 q^{17} +2.61803 q^{18} -0.763932 q^{19} -1.00000 q^{20} -0.618034 q^{21} +4.47214 q^{23} -1.85410 q^{24} +1.00000 q^{25} +4.61803 q^{26} +3.47214 q^{27} -1.00000 q^{28} -4.09017 q^{29} +0.618034 q^{30} +5.70820 q^{31} -5.00000 q^{32} -2.38197 q^{34} +1.00000 q^{35} +2.61803 q^{36} -3.23607 q^{37} +0.763932 q^{38} +2.85410 q^{39} +3.00000 q^{40} +8.94427 q^{41} +0.618034 q^{42} -1.23607 q^{43} -2.61803 q^{45} -4.47214 q^{46} -6.85410 q^{47} +0.618034 q^{48} +1.00000 q^{49} -1.00000 q^{50} -1.47214 q^{51} +4.61803 q^{52} -5.52786 q^{53} -3.47214 q^{54} +3.00000 q^{56} +0.472136 q^{57} +4.09017 q^{58} -6.76393 q^{59} +0.618034 q^{60} +4.76393 q^{61} -5.70820 q^{62} -2.61803 q^{63} +7.00000 q^{64} -4.61803 q^{65} -9.70820 q^{67} -2.38197 q^{68} -2.76393 q^{69} -1.00000 q^{70} -9.56231 q^{71} -7.85410 q^{72} +14.5623 q^{73} +3.23607 q^{74} -0.618034 q^{75} +0.763932 q^{76} -2.85410 q^{78} +13.8541 q^{79} -1.00000 q^{80} +5.70820 q^{81} -8.94427 q^{82} -4.61803 q^{83} +0.618034 q^{84} +2.38197 q^{85} +1.23607 q^{86} +2.52786 q^{87} -2.29180 q^{89} +2.61803 q^{90} -4.61803 q^{91} -4.47214 q^{92} -3.52786 q^{93} +6.85410 q^{94} -0.763932 q^{95} +3.09017 q^{96} -5.61803 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{12} - 7 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} + 7 q^{17} + 3 q^{18} - 6 q^{19} - 2 q^{20} + q^{21} + 3 q^{24} + 2 q^{25} + 7 q^{26} - 2 q^{27} - 2 q^{28} + 3 q^{29} - q^{30} - 2 q^{31} - 10 q^{32} - 7 q^{34} + 2 q^{35} + 3 q^{36} - 2 q^{37} + 6 q^{38} - q^{39} + 6 q^{40} - q^{42} + 2 q^{43} - 3 q^{45} - 7 q^{47} - q^{48} + 2 q^{49} - 2 q^{50} + 6 q^{51} + 7 q^{52} - 20 q^{53} + 2 q^{54} + 6 q^{56} - 8 q^{57} - 3 q^{58} - 18 q^{59} - q^{60} + 14 q^{61} + 2 q^{62} - 3 q^{63} + 14 q^{64} - 7 q^{65} - 6 q^{67} - 7 q^{68} - 10 q^{69} - 2 q^{70} + q^{71} - 9 q^{72} + 9 q^{73} + 2 q^{74} + q^{75} + 6 q^{76} + q^{78} + 21 q^{79} - 2 q^{80} - 2 q^{81} - 7 q^{83} - q^{84} + 7 q^{85} - 2 q^{86} + 14 q^{87} - 18 q^{89} + 3 q^{90} - 7 q^{91} - 16 q^{93} + 7 q^{94} - 6 q^{95} - 5 q^{96} - 9 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 2 * q^10 - q^12 - 7 * q^13 - 2 * q^14 + q^15 - 2 * q^16 + 7 * q^17 + 3 * q^18 - 6 * q^19 - 2 * q^20 + q^21 + 3 * q^24 + 2 * q^25 + 7 * q^26 - 2 * q^27 - 2 * q^28 + 3 * q^29 - q^30 - 2 * q^31 - 10 * q^32 - 7 * q^34 + 2 * q^35 + 3 * q^36 - 2 * q^37 + 6 * q^38 - q^39 + 6 * q^40 - q^42 + 2 * q^43 - 3 * q^45 - 7 * q^47 - q^48 + 2 * q^49 - 2 * q^50 + 6 * q^51 + 7 * q^52 - 20 * q^53 + 2 * q^54 + 6 * q^56 - 8 * q^57 - 3 * q^58 - 18 * q^59 - q^60 + 14 * q^61 + 2 * q^62 - 3 * q^63 + 14 * q^64 - 7 * q^65 - 6 * q^67 - 7 * q^68 - 10 * q^69 - 2 * q^70 + q^71 - 9 * q^72 + 9 * q^73 + 2 * q^74 + q^75 + 6 * q^76 + q^78 + 21 * q^79 - 2 * q^80 - 2 * q^81 - 7 * q^83 - q^84 + 7 * q^85 - 2 * q^86 + 14 * q^87 - 18 * q^89 + 3 * q^90 - 7 * q^91 - 16 * q^93 + 7 * q^94 - 6 * q^95 - 5 * q^96 - 9 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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