LMFDB - Embedded newform 4730.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.38197 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.38197 q^{7} +1.00000 q^{8} -2.61803 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.618034 q^{12} -1.38197 q^{14} -0.618034 q^{15} +1.00000 q^{16} -1.61803 q^{17} -2.61803 q^{18} -1.14590 q^{19} +1.00000 q^{20} +0.854102 q^{21} -1.00000 q^{22} +4.00000 q^{23} -0.618034 q^{24} +1.00000 q^{25} +3.47214 q^{27} -1.38197 q^{28} +5.70820 q^{29} -0.618034 q^{30} -1.52786 q^{31} +1.00000 q^{32} +0.618034 q^{33} -1.61803 q^{34} -1.38197 q^{35} -2.61803 q^{36} -1.14590 q^{38} +1.00000 q^{40} -7.23607 q^{41} +0.854102 q^{42} -1.00000 q^{43} -1.00000 q^{44} -2.61803 q^{45} +4.00000 q^{46} +2.61803 q^{47} -0.618034 q^{48} -5.09017 q^{49} +1.00000 q^{50} +1.00000 q^{51} -10.8541 q^{53} +3.47214 q^{54} -1.00000 q^{55} -1.38197 q^{56} +0.708204 q^{57} +5.70820 q^{58} -3.38197 q^{59} -0.618034 q^{60} -0.763932 q^{61} -1.52786 q^{62} +3.61803 q^{63} +1.00000 q^{64} +0.618034 q^{66} -11.4164 q^{67} -1.61803 q^{68} -2.47214 q^{69} -1.38197 q^{70} -12.7984 q^{71} -2.61803 q^{72} +4.76393 q^{73} -0.618034 q^{75} -1.14590 q^{76} +1.38197 q^{77} -3.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -7.23607 q^{82} -0.326238 q^{83} +0.854102 q^{84} -1.61803 q^{85} -1.00000 q^{86} -3.52786 q^{87} -1.00000 q^{88} -2.29180 q^{89} -2.61803 q^{90} +4.00000 q^{92} +0.944272 q^{93} +2.61803 q^{94} -1.14590 q^{95} -0.618034 q^{96} -12.4721 q^{97} -5.09017 q^{98} +2.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} - 2 q^{11} + q^{12} - 5 q^{14} + q^{15} + 2 q^{16} - q^{17} - 3 q^{18} - 9 q^{19} + 2 q^{20} - 5 q^{21} - 2 q^{22} + 8 q^{23} + q^{24} + 2 q^{25} - 2 q^{27} - 5 q^{28} - 2 q^{29} + q^{30} - 12 q^{31} + 2 q^{32} - q^{33} - q^{34} - 5 q^{35} - 3 q^{36} - 9 q^{38} + 2 q^{40} - 10 q^{41} - 5 q^{42} - 2 q^{43} - 2 q^{44} - 3 q^{45} + 8 q^{46} + 3 q^{47} + q^{48} + q^{49} + 2 q^{50} + 2 q^{51} - 15 q^{53} - 2 q^{54} - 2 q^{55} - 5 q^{56} - 12 q^{57} - 2 q^{58} - 9 q^{59} + q^{60} - 6 q^{61} - 12 q^{62} + 5 q^{63} + 2 q^{64} - q^{66} + 4 q^{67} - q^{68} + 4 q^{69} - 5 q^{70} - q^{71} - 3 q^{72} + 14 q^{73} + q^{75} - 9 q^{76} + 5 q^{77} - q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} + 15 q^{83} - 5 q^{84} - q^{85} - 2 q^{86} - 16 q^{87} - 2 q^{88} - 18 q^{89} - 3 q^{90} + 8 q^{92} - 16 q^{93} + 3 q^{94} - 9 q^{95} + q^{96} - 16 q^{97} + q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 - 2 * q^11 + q^12 - 5 * q^14 + q^15 + 2 * q^16 - q^17 - 3 * q^18 - 9 * q^19 + 2 * q^20 - 5 * q^21 - 2 * q^22 + 8 * q^23 + q^24 + 2 * q^25 - 2 * q^27 - 5 * q^28 - 2 * q^29 + q^30 - 12 * q^31 + 2 * q^32 - q^33 - q^34 - 5 * q^35 - 3 * q^36 - 9 * q^38 + 2 * q^40 - 10 * q^41 - 5 * q^42 - 2 * q^43 - 2 * q^44 - 3 * q^45 + 8 * q^46 + 3 * q^47 + q^48 + q^49 + 2 * q^50 + 2 * q^51 - 15 * q^53 - 2 * q^54 - 2 * q^55 - 5 * q^56 - 12 * q^57 - 2 * q^58 - 9 * q^59 + q^60 - 6 * q^61 - 12 * q^62 + 5 * q^63 + 2 * q^64 - q^66 + 4 * q^67 - q^68 + 4 * q^69 - 5 * q^70 - q^71 - 3 * q^72 + 14 * q^73 + q^75 - 9 * q^76 + 5 * q^77 - q^79 + 2 * q^80 - 2 * q^81 - 10 * q^82 + 15 * q^83 - 5 * q^84 - q^85 - 2 * q^86 - 16 * q^87 - 2 * q^88 - 18 * q^89 - 3 * q^90 + 8 * q^92 - 16 * q^93 + 3 * q^94 - 9 * q^95 + q^96 - 16 * q^97 + q^98 + 3 * q^99

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
$2$	1.00000	0.707107
$3$	−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
$7$	−1.38197	−0.522334	−0.261167	−	0.965294i	$-0.584107\pi$
$7$	−1.38197	−0.522334	−0.261167	+	0.965294i	$0.584107\pi$
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.618034	−0.178411
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.38197	−0.369346
$15$	−0.618034	−0.159576
$16$	1.00000	0.250000
$17$	−1.61803	−0.392431	−0.196215	−	0.980561i	$-0.562865\pi$
$17$	−1.61803	−0.392431	−0.196215	+	0.980561i	$0.562865\pi$
$18$	−2.61803	−0.617077
$19$	−1.14590	−0.262887	−0.131444	−	0.991324i	$-0.541961\pi$
$19$	−1.14590	−0.262887	−0.131444	+	0.991324i	$0.541961\pi$
$20$	1.00000	0.223607
$21$	0.854102	0.186380
$22$	−1.00000	−0.213201
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−0.618034	−0.126156
$25$	1.00000	0.200000
$26$	0	0
$27$	3.47214	0.668213
$28$	−1.38197	−0.261167
$29$	5.70820	1.05999	0.529993	−	0.848002i	$-0.322194\pi$
$29$	5.70820	1.05999	0.529993	+	0.848002i	$0.322194\pi$
$30$	−0.618034	−0.112837
$31$	−1.52786	−0.274412	−0.137206	−	0.990543i	$-0.543812\pi$
$31$	−1.52786	−0.274412	−0.137206	+	0.990543i	$0.543812\pi$
$32$	1.00000	0.176777
$33$	0.618034	0.107586
$34$	−1.61803	−0.277491
$35$	−1.38197	−0.233595
$36$	−2.61803	−0.436339
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−1.14590	−0.185889
$39$	0	0
$40$	1.00000	0.158114
$41$	−7.23607	−1.13008	−0.565042	−	0.825062i	$-0.691140\pi$
$41$	−7.23607	−1.13008	−0.565042	+	0.825062i	$0.691140\pi$
$42$	0.854102	0.131791
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	−2.61803	−0.390273
$46$	4.00000	0.589768
$47$	2.61803	0.381880	0.190940	−	0.981602i	$-0.438846\pi$
$47$	2.61803	0.381880	0.190940	+	0.981602i	$0.438846\pi$
$48$	−0.618034	−0.0892055
$49$	−5.09017	−0.727167
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	0	0
$53$	−10.8541	−1.49093	−0.745463	−	0.666547i	$-0.767771\pi$
$53$	−10.8541	−1.49093	−0.745463	+	0.666547i	$0.767771\pi$
$54$	3.47214	0.472498
$55$	−1.00000	−0.134840
$56$	−1.38197	−0.184673
$57$	0.708204	0.0938039
$58$	5.70820	0.749524
$59$	−3.38197	−0.440294	−0.220147	−	0.975467i	$-0.570654\pi$
$59$	−3.38197	−0.440294	−0.220147	+	0.975467i	$0.570654\pi$
$60$	−0.618034	−0.0797878
$61$	−0.763932	−0.0978115	−0.0489057	−	0.998803i	$-0.515573\pi$
$61$	−0.763932	−0.0978115	−0.0489057	+	0.998803i	$0.515573\pi$
$62$	−1.52786	−0.194039
$63$	3.61803	0.455829
$64$	1.00000	0.125000
$65$	0	0
$66$	0.618034	0.0760747
$67$	−11.4164	−1.39474	−0.697368	−	0.716713i	$-0.745646\pi$
$67$	−11.4164	−1.39474	−0.697368	+	0.716713i	$0.745646\pi$
$68$	−1.61803	−0.196215
$69$	−2.47214	−0.297610
$70$	−1.38197	−0.165177
$71$	−12.7984	−1.51889	−0.759444	−	0.650573i	$-0.774529\pi$
$71$	−12.7984	−1.51889	−0.759444	+	0.650573i	$0.774529\pi$
$72$	−2.61803	−0.308538
$73$	4.76393	0.557576	0.278788	−	0.960353i	$-0.410067\pi$
$73$	4.76393	0.557576	0.278788	+	0.960353i	$0.410067\pi$
$74$	0	0
$75$	−0.618034	−0.0713644
$76$	−1.14590	−0.131444
$77$	1.38197	0.157490
$78$	0	0
$79$	−3.85410	−0.433620	−0.216810	−	0.976214i	$-0.569565\pi$
$79$	−3.85410	−0.433620	−0.216810	+	0.976214i	$0.569565\pi$
$80$	1.00000	0.111803
$81$	5.70820	0.634245
$82$	−7.23607	−0.799090
$83$	−0.326238	−0.0358093	−0.0179046	−	0.999840i	$-0.505700\pi$
$83$	−0.326238	−0.0358093	−0.0179046	+	0.999840i	$0.505700\pi$
$84$	0.854102	0.0931902
$85$	−1.61803	−0.175500
$86$	−1.00000	−0.107833
$87$	−3.52786	−0.378227
$88$	−1.00000	−0.106600
$89$	−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
$91$	0	0
$92$	4.00000	0.417029
$93$	0.944272	0.0979164
$94$	2.61803	0.270030
$95$	−1.14590	−0.117567
$96$	−0.618034	−0.0630778
$97$	−12.4721	−1.26635	−0.633177	−	0.774007i	$-0.718249\pi$
$97$	−12.4721	−1.26635	−0.633177	+	0.774007i	$0.718249\pi$
$98$	−5.09017	−0.514185
$99$	2.61803	0.263122
$100$	1.00000	0.100000
$101$	−14.3262	−1.42551	−0.712757	−	0.701411i	$-0.752554\pi$
$101$	−14.3262	−1.42551	−0.712757	+	0.701411i	$0.752554\pi$
$102$	1.00000	0.0990148
$103$	−6.56231	−0.646603	−0.323302	−	0.946296i	$-0.604793\pi$
$103$	−6.56231	−0.646603	−0.323302	+	0.946296i	$0.604793\pi$
$104$	0	0
$105$	0.854102	0.0833518
$106$	−10.8541	−1.05424
$107$	−15.6180	−1.50985	−0.754926	−	0.655810i	$-0.772327\pi$
$107$	−15.6180	−1.50985	−0.754926	+	0.655810i	$0.772327\pi$
$108$	3.47214	0.334106
$109$	−2.67376	−0.256100	−0.128050	−	0.991768i	$-0.540872\pi$
$109$	−2.67376	−0.256100	−0.128050	+	0.991768i	$0.540872\pi$
$110$	−1.00000	−0.0953463
$111$	0	0
$112$	−1.38197	−0.130584
$113$	−9.79837	−0.921753	−0.460877	−	0.887464i	$-0.652465\pi$
$113$	−9.79837	−0.921753	−0.460877	+	0.887464i	$0.652465\pi$
$114$	0.708204	0.0663294
$115$	4.00000	0.373002
$116$	5.70820	0.529993
$117$	0	0
$118$	−3.38197	−0.311335
$119$	2.23607	0.204980
$120$	−0.618034	−0.0564185
$121$	1.00000	0.0909091
$122$	−0.763932	−0.0691632
$123$	4.47214	0.403239
$124$	−1.52786	−0.137206
$125$	1.00000	0.0894427
$126$	3.61803	0.322320
$127$	1.52786	0.135576	0.0677880	−	0.997700i	$-0.478406\pi$
$127$	1.52786	0.135576	0.0677880	+	0.997700i	$0.478406\pi$
$128$	1.00000	0.0883883
$129$	0.618034	0.0544149
$130$	0	0
$131$	16.9443	1.48043	0.740214	−	0.672371i	$-0.234724\pi$
$131$	16.9443	1.48043	0.740214	+	0.672371i	$0.234724\pi$
$132$	0.618034	0.0537930
$133$	1.58359	0.137315
$134$	−11.4164	−0.986227
$135$	3.47214	0.298834
$136$	−1.61803	−0.138745
$137$	0.472136	0.0403373	0.0201686	−	0.999797i	$-0.493580\pi$
$137$	0.472136	0.0403373	0.0201686	+	0.999797i	$0.493580\pi$
$138$	−2.47214	−0.210442
$139$	−13.8885	−1.17801	−0.589005	−	0.808129i	$-0.700480\pi$
$139$	−13.8885	−1.17801	−0.589005	+	0.808129i	$0.700480\pi$
$140$	−1.38197	−0.116797
$141$	−1.61803	−0.136263
$142$	−12.7984	−1.07402
$143$	0	0
$144$	−2.61803	−0.218169
$145$	5.70820	0.474041
$146$	4.76393	0.394266
$147$	3.14590	0.259469
$148$	0	0
$149$	3.70820	0.303788	0.151894	−	0.988397i	$-0.451463\pi$
$149$	3.70820	0.303788	0.151894	+	0.988397i	$0.451463\pi$
$150$	−0.618034	−0.0504623
$151$	−2.76393	−0.224926	−0.112463	−	0.993656i	$-0.535874\pi$
$151$	−2.76393	−0.224926	−0.112463	+	0.993656i	$0.535874\pi$
$152$	−1.14590	−0.0929446
$153$	4.23607	0.342466
$154$	1.38197	0.111362
$155$	−1.52786	−0.122721
$156$	0	0
$157$	13.4164	1.07075	0.535373	−	0.844616i	$-0.320171\pi$
$157$	13.4164	1.07075	0.535373	+	0.844616i	$0.320171\pi$
$158$	−3.85410	−0.306616
$159$	6.70820	0.531995
$160$	1.00000	0.0790569
$161$	−5.52786	−0.435657
$162$	5.70820	0.448479
$163$	3.79837	0.297512	0.148756	−	0.988874i	$-0.452473\pi$
$163$	3.79837	0.297512	0.148756	+	0.988874i	$0.452473\pi$
$164$	−7.23607	−0.565042
$165$	0.618034	0.0481139
$166$	−0.326238	−0.0253210
$167$	−2.29180	−0.177345	−0.0886723	−	0.996061i	$-0.528262\pi$
$167$	−2.29180	−0.177345	−0.0886723	+	0.996061i	$0.528262\pi$
$168$	0.854102	0.0658954
$169$	−13.0000	−1.00000
$170$	−1.61803	−0.124098
$171$	3.00000	0.229416
$172$	−1.00000	−0.0762493
$173$	−22.9443	−1.74442	−0.872210	−	0.489131i	$-0.837314\pi$
$173$	−22.9443	−1.74442	−0.872210	+	0.489131i	$0.837314\pi$
$174$	−3.52786	−0.267447
$175$	−1.38197	−0.104467
$176$	−1.00000	−0.0753778
$177$	2.09017	0.157107
$178$	−2.29180	−0.171777
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−2.61803	−0.195137
$181$	8.29180	0.616324	0.308162	−	0.951334i	$-0.400286\pi$
$181$	8.29180	0.616324	0.308162	+	0.951334i	$0.400286\pi$
$182$	0	0
$183$	0.472136	0.0349013
$184$	4.00000	0.294884
$185$	0	0
$186$	0.944272	0.0692374
$187$	1.61803	0.118322
$188$	2.61803	0.190940
$189$	−4.79837	−0.349030
$190$	−1.14590	−0.0831322
$191$	6.56231	0.474832	0.237416	−	0.971408i	$-0.423700\pi$
$191$	6.56231	0.474832	0.237416	+	0.971408i	$0.423700\pi$
$192$	−0.618034	−0.0446028
$193$	26.2148	1.88698	0.943491	−	0.331399i	$-0.107521\pi$
$193$	26.2148	1.88698	0.943491	+	0.331399i	$0.107521\pi$
$194$	−12.4721	−0.895447
$195$	0	0
$196$	−5.09017	−0.363584
$197$	−10.7639	−0.766898	−0.383449	−	0.923562i	$-0.625264\pi$
$197$	−10.7639	−0.766898	−0.383449	+	0.923562i	$0.625264\pi$
$198$	2.61803	0.186056
$199$	26.5623	1.88295	0.941476	−	0.337080i	$-0.109439\pi$
$199$	26.5623	1.88295	0.941476	+	0.337080i	$0.109439\pi$
$200$	1.00000	0.0707107
$201$	7.05573	0.497673
$202$	−14.3262	−1.00799
$203$	−7.88854	−0.553667
$204$	1.00000	0.0700140
$205$	−7.23607	−0.505389
$206$	−6.56231	−0.457218
$207$	−10.4721	−0.727864
$208$	0	0
$209$	1.14590	0.0792634
$210$	0.854102	0.0589386
$211$	−11.0902	−0.763479	−0.381739	−	0.924270i	$-0.624675\pi$
$211$	−11.0902	−0.763479	−0.381739	+	0.924270i	$0.624675\pi$
$212$	−10.8541	−0.745463
$213$	7.90983	0.541973
$214$	−15.6180	−1.06763
$215$	−1.00000	−0.0681994
$216$	3.47214	0.236249
$217$	2.11146	0.143335
$218$	−2.67376	−0.181090
$219$	−2.94427	−0.198955
$220$	−1.00000	−0.0674200
$221$	0	0
$222$	0	0
$223$	26.4721	1.77271	0.886353	−	0.463011i	$-0.153231\pi$
$223$	26.4721	1.77271	0.886353	+	0.463011i	$0.153231\pi$
$224$	−1.38197	−0.0923365
$225$	−2.61803	−0.174536
$226$	−9.79837	−0.651778
$227$	19.4164	1.28871	0.644356	−	0.764726i	$-0.277125\pi$
$227$	19.4164	1.28871	0.644356	+	0.764726i	$0.277125\pi$
$228$	0.708204	0.0469020
$229$	14.4721	0.956346	0.478173	−	0.878266i	$-0.341299\pi$
$229$	14.4721	0.956346	0.478173	+	0.878266i	$0.341299\pi$
$230$	4.00000	0.263752
$231$	−0.854102	−0.0561958
$232$	5.70820	0.374762
$233$	−11.2361	−0.736099	−0.368050	−	0.929806i	$-0.619974\pi$
$233$	−11.2361	−0.736099	−0.368050	+	0.929806i	$0.619974\pi$
$234$	0	0
$235$	2.61803	0.170782
$236$	−3.38197	−0.220147
$237$	2.38197	0.154725
$238$	2.23607	0.144943
$239$	25.7984	1.66876	0.834379	−	0.551191i	$-0.185826\pi$
$239$	25.7984	1.66876	0.834379	+	0.551191i	$0.185826\pi$
$240$	−0.618034	−0.0398939
$241$	−15.0902	−0.972043	−0.486022	−	0.873947i	$-0.661552\pi$
$241$	−15.0902	−0.972043	−0.486022	+	0.873947i	$0.661552\pi$
$242$	1.00000	0.0642824
$243$	−13.9443	−0.894525
$244$	−0.763932	−0.0489057
$245$	−5.09017	−0.325199
$246$	4.47214	0.285133
$247$	0	0
$248$	−1.52786	−0.0970195
$249$	0.201626	0.0127775
$250$	1.00000	0.0632456
$251$	−22.2705	−1.40570	−0.702851	−	0.711337i	$-0.748090\pi$
$251$	−22.2705	−1.40570	−0.702851	+	0.711337i	$0.748090\pi$
$252$	3.61803	0.227915
$253$	−4.00000	−0.251478
$254$	1.52786	0.0958667
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−17.6180	−1.09898	−0.549491	−	0.835499i	$-0.685178\pi$
$257$	−17.6180	−1.09898	−0.549491	+	0.835499i	$0.685178\pi$
$258$	0.618034	0.0384771
$259$	0	0
$260$	0	0
$261$	−14.9443	−0.925027
$262$	16.9443	1.04682
$263$	−5.43769	−0.335303	−0.167651	−	0.985846i	$-0.553618\pi$
$263$	−5.43769	−0.335303	−0.167651	+	0.985846i	$0.553618\pi$
$264$	0.618034	0.0380374
$265$	−10.8541	−0.666762
$266$	1.58359	0.0970963
$267$	1.41641	0.0866828
$268$	−11.4164	−0.697368
$269$	11.7082	0.713862	0.356931	−	0.934131i	$-0.383823\pi$
$269$	11.7082	0.713862	0.356931	+	0.934131i	$0.383823\pi$
$270$	3.47214	0.211307
$271$	−15.4164	−0.936480	−0.468240	−	0.883601i	$-0.655112\pi$
$271$	−15.4164	−0.936480	−0.468240	+	0.883601i	$0.655112\pi$
$272$	−1.61803	−0.0981077
$273$	0	0
$274$	0.472136	0.0285228
$275$	−1.00000	−0.0603023
$276$	−2.47214	−0.148805
$277$	−20.7426	−1.24630	−0.623152	−	0.782100i	$-0.714148\pi$
$277$	−20.7426	−1.24630	−0.623152	+	0.782100i	$0.714148\pi$
$278$	−13.8885	−0.832980
$279$	4.00000	0.239474
$280$	−1.38197	−0.0825883
$281$	−13.2361	−0.789598	−0.394799	−	0.918768i	$-0.629186\pi$
$281$	−13.2361	−0.789598	−0.394799	+	0.918768i	$0.629186\pi$
$282$	−1.61803	−0.0963525
$283$	−25.5066	−1.51621	−0.758104	−	0.652133i	$-0.773874\pi$
$283$	−25.5066	−1.51621	−0.758104	+	0.652133i	$0.773874\pi$
$284$	−12.7984	−0.759444
$285$	0.708204	0.0419504
$286$	0	0
$287$	10.0000	0.590281
$288$	−2.61803	−0.154269
$289$	−14.3820	−0.845998
$290$	5.70820	0.335197
$291$	7.70820	0.451863
$292$	4.76393	0.278788
$293$	19.1246	1.11727	0.558636	−	0.829413i	$-0.311325\pi$
$293$	19.1246	1.11727	0.558636	+	0.829413i	$0.311325\pi$
$294$	3.14590	0.183472
$295$	−3.38197	−0.196906
$296$	0	0
$297$	−3.47214	−0.201474
$298$	3.70820	0.214810
$299$	0	0
$300$	−0.618034	−0.0356822
$301$	1.38197	0.0796552
$302$	−2.76393	−0.159046
$303$	8.85410	0.508655
$304$	−1.14590	−0.0657218
$305$	−0.763932	−0.0437426
$306$	4.23607	0.242160
$307$	−6.14590	−0.350765	−0.175382	−	0.984500i	$-0.556116\pi$
$307$	−6.14590	−0.350765	−0.175382	+	0.984500i	$0.556116\pi$
$308$	1.38197	0.0787448
$309$	4.05573	0.230722
$310$	−1.52786	−0.0867768
$311$	28.9443	1.64128	0.820640	−	0.571446i	$-0.193617\pi$
$311$	28.9443	1.64128	0.820640	+	0.571446i	$0.193617\pi$
$312$	0	0
$313$	−28.4508	−1.60814	−0.804069	−	0.594537i	$-0.797336\pi$
$313$	−28.4508	−1.60814	−0.804069	+	0.594537i	$0.797336\pi$
$314$	13.4164	0.757132
$315$	3.61803	0.203853
$316$	−3.85410	−0.216810
$317$	31.5623	1.77272	0.886358	−	0.463001i	$-0.153227\pi$
$317$	31.5623	1.77272	0.886358	+	0.463001i	$0.153227\pi$
$318$	6.70820	0.376177
$319$	−5.70820	−0.319598
$320$	1.00000	0.0559017
$321$	9.65248	0.538749
$322$	−5.52786	−0.308056
$323$	1.85410	0.103165
$324$	5.70820	0.317122
$325$	0	0
$326$	3.79837	0.210372
$327$	1.65248	0.0913821
$328$	−7.23607	−0.399545
$329$	−3.61803	−0.199469
$330$	0.618034	0.0340217
$331$	17.4164	0.957292	0.478646	−	0.878008i	$-0.341128\pi$
$331$	17.4164	0.957292	0.478646	+	0.878008i	$0.341128\pi$
$332$	−0.326238	−0.0179046
$333$	0	0
$334$	−2.29180	−0.125402
$335$	−11.4164	−0.623745
$336$	0.854102	0.0465951
$337$	23.5066	1.28048	0.640242	−	0.768173i	$-0.278834\pi$
$337$	23.5066	1.28048	0.640242	+	0.768173i	$0.278834\pi$
$338$	−13.0000	−0.707107
$339$	6.05573	0.328902
$340$	−1.61803	−0.0877502
$341$	1.52786	0.0827385
$342$	3.00000	0.162221
$343$	16.7082	0.902158
$344$	−1.00000	−0.0539164
$345$	−2.47214	−0.133095
$346$	−22.9443	−1.23349
$347$	−14.3607	−0.770922	−0.385461	−	0.922724i	$-0.625958\pi$
$347$	−14.3607	−0.770922	−0.385461	+	0.922724i	$0.625958\pi$
$348$	−3.52786	−0.189113
$349$	2.94427	0.157603	0.0788016	−	0.996890i	$-0.474891\pi$
$349$	2.94427	0.157603	0.0788016	+	0.996890i	$0.474891\pi$
$350$	−1.38197	−0.0738692
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	0.180340	0.00959852	0.00479926	−	0.999988i	$-0.498472\pi$
$353$	0.180340	0.00959852	0.00479926	+	0.999988i	$0.498472\pi$
$354$	2.09017	0.111091
$355$	−12.7984	−0.679267
$356$	−2.29180	−0.121465
$357$	−1.38197	−0.0731414
$358$	20.0000	1.05703
$359$	4.00000	0.211112	0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000	0.211112	0.105556	+	0.994413i	$0.466338\pi$
$360$	−2.61803	−0.137983
$361$	−17.6869	−0.930890
$362$	8.29180	0.435807
$363$	−0.618034	−0.0324384
$364$	0	0
$365$	4.76393	0.249356
$366$	0.472136	0.0246789
$367$	13.9787	0.729683	0.364841	−	0.931070i	$-0.381123\pi$
$367$	13.9787	0.729683	0.364841	+	0.931070i	$0.381123\pi$
$368$	4.00000	0.208514
$369$	18.9443	0.986199
$370$	0	0
$371$	15.0000	0.778761
$372$	0.944272	0.0489582
$373$	−18.3262	−0.948897	−0.474448	−	0.880283i	$-0.657352\pi$
$373$	−18.3262	−0.948897	−0.474448	+	0.880283i	$0.657352\pi$
$374$	1.61803	0.0836665
$375$	−0.618034	−0.0319151
$376$	2.61803	0.135015
$377$	0	0
$378$	−4.79837	−0.246802
$379$	28.0344	1.44003	0.720016	−	0.693957i	$-0.244134\pi$
$379$	28.0344	1.44003	0.720016	+	0.693957i	$0.244134\pi$
$380$	−1.14590	−0.0587833
$381$	−0.944272	−0.0483765
$382$	6.56231	0.335757
$383$	−13.1246	−0.670636	−0.335318	−	0.942105i	$-0.608844\pi$
$383$	−13.1246	−0.670636	−0.335318	+	0.942105i	$0.608844\pi$
$384$	−0.618034	−0.0315389
$385$	1.38197	0.0704315
$386$	26.2148	1.33430
$387$	2.61803	0.133082
$388$	−12.4721	−0.633177
$389$	9.09017	0.460890	0.230445	−	0.973085i	$-0.425982\pi$
$389$	9.09017	0.460890	0.230445	+	0.973085i	$0.425982\pi$
$390$	0	0
$391$	−6.47214	−0.327310
$392$	−5.09017	−0.257092
$393$	−10.4721	−0.528249
$394$	−10.7639	−0.542279
$395$	−3.85410	−0.193921
$396$	2.61803	0.131561
$397$	−21.4508	−1.07659	−0.538294	−	0.842757i	$-0.680931\pi$
$397$	−21.4508	−1.07659	−0.538294	+	0.842757i	$0.680931\pi$
$398$	26.5623	1.33145
$399$	−0.978714	−0.0489970
$400$	1.00000	0.0500000
$401$	−18.7426	−0.935963	−0.467982	−	0.883738i	$-0.655019\pi$
$401$	−18.7426	−0.935963	−0.467982	+	0.883738i	$0.655019\pi$
$402$	7.05573	0.351908
$403$	0	0
$404$	−14.3262	−0.712757
$405$	5.70820	0.283643
$406$	−7.88854	−0.391502
$407$	0	0
$408$	1.00000	0.0495074
$409$	22.3820	1.10672	0.553358	−	0.832943i	$-0.313346\pi$
$409$	22.3820	1.10672	0.553358	+	0.832943i	$0.313346\pi$
$410$	−7.23607	−0.357364
$411$	−0.291796	−0.0143932
$412$	−6.56231	−0.323302
$413$	4.67376	0.229981
$414$	−10.4721	−0.514677
$415$	−0.326238	−0.0160144
$416$	0	0
$417$	8.58359	0.420340
$418$	1.14590	0.0560477
$419$	−13.1246	−0.641179	−0.320590	−	0.947218i	$-0.603881\pi$
$419$	−13.1246	−0.641179	−0.320590	+	0.947218i	$0.603881\pi$
$420$	0.854102	0.0416759
$421$	−3.61803	−0.176332	−0.0881661	−	0.996106i	$-0.528101\pi$
$421$	−3.61803	−0.176332	−0.0881661	+	0.996106i	$0.528101\pi$
$422$	−11.0902	−0.539861
$423$	−6.85410	−0.333258
$424$	−10.8541	−0.527122
$425$	−1.61803	−0.0784862
$426$	7.90983	0.383233
$427$	1.05573	0.0510903
$428$	−15.6180	−0.754926
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	−0.145898	−0.00702766	−0.00351383	−	0.999994i	$-0.501118\pi$
$431$	−0.145898	−0.00702766	−0.00351383	+	0.999994i	$0.501118\pi$
$432$	3.47214	0.167053
$433$	15.8885	0.763555	0.381777	−	0.924254i	$-0.375312\pi$
$433$	15.8885	0.763555	0.381777	+	0.924254i	$0.375312\pi$
$434$	2.11146	0.101353
$435$	−3.52786	−0.169148
$436$	−2.67376	−0.128050
$437$	−4.58359	−0.219263
$438$	−2.94427	−0.140683
$439$	21.7984	1.04038	0.520190	−	0.854051i	$-0.325861\pi$
$439$	21.7984	1.04038	0.520190	+	0.854051i	$0.325861\pi$
$440$	−1.00000	−0.0476731
$441$	13.3262	0.634583
$442$	0	0
$443$	−31.8885	−1.51507	−0.757535	−	0.652794i	$-0.773597\pi$
$443$	−31.8885	−1.51507	−0.757535	+	0.652794i	$0.773597\pi$
$444$	0	0
$445$	−2.29180	−0.108642
$446$	26.4721	1.25349
$447$	−2.29180	−0.108398
$448$	−1.38197	−0.0652918
$449$	−1.05573	−0.0498229	−0.0249114	−	0.999690i	$-0.507930\pi$
$449$	−1.05573	−0.0498229	−0.0249114	+	0.999690i	$0.507930\pi$
$450$	−2.61803	−0.123415
$451$	7.23607	0.340733
$452$	−9.79837	−0.460877
$453$	1.70820	0.0802584
$454$	19.4164	0.911257
$455$	0	0
$456$	0.708204	0.0331647
$457$	8.18034	0.382660	0.191330	−	0.981526i	$-0.438720\pi$
$457$	8.18034	0.382660	0.191330	+	0.981526i	$0.438720\pi$
$458$	14.4721	0.676239
$459$	−5.61803	−0.262227
$460$	4.00000	0.186501
$461$	−35.9787	−1.67570	−0.837848	−	0.545904i	$-0.816186\pi$
$461$	−35.9787	−1.67570	−0.837848	+	0.545904i	$0.816186\pi$
$462$	−0.854102	−0.0397364
$463$	−14.9443	−0.694519	−0.347260	−	0.937769i	$-0.612888\pi$
$463$	−14.9443	−0.694519	−0.347260	+	0.937769i	$0.612888\pi$
$464$	5.70820	0.264997
$465$	0.944272	0.0437896
$466$	−11.2361	−0.520501
$467$	25.1459	1.16361	0.581807	−	0.813327i	$-0.302346\pi$
$467$	25.1459	1.16361	0.581807	+	0.813327i	$0.302346\pi$
$468$	0	0
$469$	15.7771	0.728518
$470$	2.61803	0.120761
$471$	−8.29180	−0.382066
$472$	−3.38197	−0.155668
$473$	1.00000	0.0459800
$474$	2.38197	0.109407
$475$	−1.14590	−0.0525774
$476$	2.23607	0.102490
$477$	28.4164	1.30110
$478$	25.7984	1.17999
$479$	−7.41641	−0.338864	−0.169432	−	0.985542i	$-0.554193\pi$
$479$	−7.41641	−0.338864	−0.169432	+	0.985542i	$0.554193\pi$
$480$	−0.618034	−0.0282093
$481$	0	0
$482$	−15.0902	−0.687338
$483$	3.41641	0.155452
$484$	1.00000	0.0454545
$485$	−12.4721	−0.566331
$486$	−13.9443	−0.632525
$487$	18.0344	0.817219	0.408609	−	0.912709i	$-0.366014\pi$
$487$	18.0344	0.817219	0.408609	+	0.912709i	$0.366014\pi$
$488$	−0.763932	−0.0345816
$489$	−2.34752	−0.106159
$490$	−5.09017	−0.229950
$491$	21.5623	0.973093	0.486547	−	0.873655i	$-0.338256\pi$
$491$	21.5623	0.973093	0.486547	+	0.873655i	$0.338256\pi$
$492$	4.47214	0.201619
$493$	−9.23607	−0.415972
$494$	0	0
$495$	2.61803	0.117672
$496$	−1.52786	−0.0686031
$497$	17.6869	0.793367
$498$	0.201626	0.00903508
$499$	−26.9443	−1.20619	−0.603096	−	0.797669i	$-0.706066\pi$
$499$	−26.9443	−1.20619	−0.603096	+	0.797669i	$0.706066\pi$
$500$	1.00000	0.0447214
$501$	1.41641	0.0632804
$502$	−22.2705	−0.993981
$503$	21.9787	0.979982	0.489991	−	0.871727i	$-0.337000\pi$
$503$	21.9787	0.979982	0.489991	+	0.871727i	$0.337000\pi$
$504$	3.61803	0.161160
$505$	−14.3262	−0.637509
$506$	−4.00000	−0.177822
$507$	8.03444	0.356822
$508$	1.52786	0.0677880
$509$	26.1803	1.16042	0.580212	−	0.814466i	$-0.302970\pi$
$509$	26.1803	1.16042	0.580212	+	0.814466i	$0.302970\pi$
$510$	1.00000	0.0442807
$511$	−6.58359	−0.291241
$512$	1.00000	0.0441942
$513$	−3.97871	−0.175665
$514$	−17.6180	−0.777098
$515$	−6.56231	−0.289170
$516$	0.618034	0.0272074
$517$	−2.61803	−0.115141
$518$	0	0
$519$	14.1803	0.622448
$520$	0	0
$521$	12.9443	0.567099	0.283549	−	0.958958i	$-0.408488\pi$
$521$	12.9443	0.567099	0.283549	+	0.958958i	$0.408488\pi$
$522$	−14.9443	−0.654093
$523$	10.9443	0.478560	0.239280	−	0.970951i	$-0.423089\pi$
$523$	10.9443	0.478560	0.239280	+	0.970951i	$0.423089\pi$
$524$	16.9443	0.740214
$525$	0.854102	0.0372761
$526$	−5.43769	−0.237095
$527$	2.47214	0.107688
$528$	0.618034	0.0268965
$529$	−7.00000	−0.304348
$530$	−10.8541	−0.471472
$531$	8.85410	0.384235
$532$	1.58359	0.0686574
$533$	0	0
$534$	1.41641	0.0612940
$535$	−15.6180	−0.675226
$536$	−11.4164	−0.493114
$537$	−12.3607	−0.533403
$538$	11.7082	0.504777
$539$	5.09017	0.219249
$540$	3.47214	0.149417
$541$	3.56231	0.153155	0.0765777	−	0.997064i	$-0.475601\pi$
$541$	3.56231	0.153155	0.0765777	+	0.997064i	$0.475601\pi$
$542$	−15.4164	−0.662191
$543$	−5.12461	−0.219918
$544$	−1.61803	−0.0693726
$545$	−2.67376	−0.114531
$546$	0	0
$547$	−42.2148	−1.80497	−0.902487	−	0.430717i	$-0.858261\pi$
$547$	−42.2148	−1.80497	−0.902487	+	0.430717i	$0.858261\pi$
$548$	0.472136	0.0201686
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	−6.54102	−0.278657
$552$	−2.47214	−0.105221
$553$	5.32624	0.226495
$554$	−20.7426	−0.881271
$555$	0	0
$556$	−13.8885	−0.589005
$557$	−24.8328	−1.05220	−0.526100	−	0.850423i	$-0.676346\pi$
$557$	−24.8328	−1.05220	−0.526100	+	0.850423i	$0.676346\pi$
$558$	4.00000	0.169334
$559$	0	0
$560$	−1.38197	−0.0583987
$561$	−1.00000	−0.0422200
$562$	−13.2361	−0.558330
$563$	3.05573	0.128784	0.0643918	−	0.997925i	$-0.479489\pi$
$563$	3.05573	0.128784	0.0643918	+	0.997925i	$0.479489\pi$
$564$	−1.61803	−0.0681315
$565$	−9.79837	−0.412221
$566$	−25.5066	−1.07212
$567$	−7.88854	−0.331288
$568$	−12.7984	−0.537008
$569$	28.1803	1.18138	0.590691	−	0.806898i	$-0.298855\pi$
$569$	28.1803	1.18138	0.590691	+	0.806898i	$0.298855\pi$
$570$	0.708204	0.0296634
$571$	34.0902	1.42663	0.713315	−	0.700844i	$-0.247193\pi$
$571$	34.0902	1.42663	0.713315	+	0.700844i	$0.247193\pi$
$572$	0	0
$573$	−4.05573	−0.169430
$574$	10.0000	0.417392
$575$	4.00000	0.166812
$576$	−2.61803	−0.109085
$577$	−17.5623	−0.731128	−0.365564	−	0.930786i	$-0.619124\pi$
$577$	−17.5623	−0.731128	−0.365564	+	0.930786i	$0.619124\pi$
$578$	−14.3820	−0.598211
$579$	−16.2016	−0.673317
$580$	5.70820	0.237020
$581$	0.450850	0.0187044
$582$	7.70820	0.319515
$583$	10.8541	0.449531
$584$	4.76393	0.197133
$585$	0	0
$586$	19.1246	0.790030
$587$	4.03444	0.166519	0.0832596	−	0.996528i	$-0.473467\pi$
$587$	4.03444	0.166519	0.0832596	+	0.996528i	$0.473467\pi$
$588$	3.14590	0.129735
$589$	1.75078	0.0721395
$590$	−3.38197	−0.139233
$591$	6.65248	0.273646
$592$	0	0
$593$	6.76393	0.277761	0.138881	−	0.990309i	$-0.455650\pi$
$593$	6.76393	0.277761	0.138881	+	0.990309i	$0.455650\pi$
$594$	−3.47214	−0.142463
$595$	2.23607	0.0916698
$596$	3.70820	0.151894
$597$	−16.4164	−0.671879
$598$	0	0
$599$	14.6525	0.598684	0.299342	−	0.954146i	$-0.403233\pi$
$599$	14.6525	0.598684	0.299342	+	0.954146i	$0.403233\pi$
$600$	−0.618034	−0.0252311
$601$	13.5623	0.553218	0.276609	−	0.960983i	$-0.410789\pi$
$601$	13.5623	0.553218	0.276609	+	0.960983i	$0.410789\pi$
$602$	1.38197	0.0563247
$603$	29.8885	1.21716
$604$	−2.76393	−0.112463
$605$	1.00000	0.0406558
$606$	8.85410	0.359673
$607$	−30.3820	−1.23317	−0.616583	−	0.787290i	$-0.711484\pi$
$607$	−30.3820	−1.23317	−0.616583	+	0.787290i	$0.711484\pi$
$608$	−1.14590	−0.0464723
$609$	4.87539	0.197561
$610$	−0.763932	−0.0309307
$611$	0	0
$612$	4.23607	0.171233
$613$	3.70820	0.149773	0.0748865	−	0.997192i	$-0.476141\pi$
$613$	3.70820	0.149773	0.0748865	+	0.997192i	$0.476141\pi$
$614$	−6.14590	−0.248028
$615$	4.47214	0.180334
$616$	1.38197	0.0556810
$617$	−14.2918	−0.575366	−0.287683	−	0.957726i	$-0.592885\pi$
$617$	−14.2918	−0.575366	−0.287683	+	0.957726i	$0.592885\pi$
$618$	4.05573	0.163145
$619$	46.4508	1.86702	0.933509	−	0.358555i	$-0.116730\pi$
$619$	46.4508	1.86702	0.933509	+	0.358555i	$0.116730\pi$
$620$	−1.52786	−0.0613605
$621$	13.8885	0.557328
$622$	28.9443	1.16056
$623$	3.16718	0.126891
$624$	0	0
$625$	1.00000	0.0400000
$626$	−28.4508	−1.13712
$627$	−0.708204	−0.0282829
$628$	13.4164	0.535373
$629$	0	0
$630$	3.61803	0.144146
$631$	14.9787	0.596293	0.298147	−	0.954520i	$-0.403632\pi$
$631$	14.9787	0.596293	0.298147	+	0.954520i	$0.403632\pi$
$632$	−3.85410	−0.153308
$633$	6.85410	0.272426
$634$	31.5623	1.25350
$635$	1.52786	0.0606314
$636$	6.70820	0.265998
$637$	0	0
$638$	−5.70820	−0.225990
$639$	33.5066	1.32550
$640$	1.00000	0.0395285
$641$	0.944272	0.0372965	0.0186482	−	0.999826i	$-0.494064\pi$
$641$	0.944272	0.0372965	0.0186482	+	0.999826i	$0.494064\pi$
$642$	9.65248	0.380953
$643$	−31.7771	−1.25317	−0.626583	−	0.779355i	$-0.715547\pi$
$643$	−31.7771	−1.25317	−0.626583	+	0.779355i	$0.715547\pi$
$644$	−5.52786	−0.217828
$645$	0.618034	0.0243351
$646$	1.85410	0.0729487
$647$	4.18034	0.164346	0.0821731	−	0.996618i	$-0.473814\pi$
$647$	4.18034	0.164346	0.0821731	+	0.996618i	$0.473814\pi$
$648$	5.70820	0.224239
$649$	3.38197	0.132754
$650$	0	0
$651$	−1.30495	−0.0511451
$652$	3.79837	0.148756
$653$	−28.4721	−1.11420	−0.557100	−	0.830445i	$-0.688086\pi$
$653$	−28.4721	−1.11420	−0.557100	+	0.830445i	$0.688086\pi$
$654$	1.65248	0.0646169
$655$	16.9443	0.662067
$656$	−7.23607	−0.282521
$657$	−12.4721	−0.486584
$658$	−3.61803	−0.141046
$659$	−7.81966	−0.304611	−0.152305	−	0.988333i	$-0.548670\pi$
$659$	−7.81966	−0.304611	−0.152305	+	0.988333i	$0.548670\pi$
$660$	0.618034	0.0240569
$661$	−33.5967	−1.30676	−0.653381	−	0.757029i	$-0.726650\pi$
$661$	−33.5967	−1.30676	−0.653381	+	0.757029i	$0.726650\pi$
$662$	17.4164	0.676908
$663$	0	0
$664$	−0.326238	−0.0126605
$665$	1.58359	0.0614091
$666$	0	0
$667$	22.8328	0.884090
$668$	−2.29180	−0.0886723
$669$	−16.3607	−0.632540
$670$	−11.4164	−0.441054
$671$	0.763932	0.0294913
$672$	0.854102	0.0329477
$673$	−29.0132	−1.11837	−0.559187	−	0.829041i	$-0.688887\pi$
$673$	−29.0132	−1.11837	−0.559187	+	0.829041i	$0.688887\pi$
$674$	23.5066	0.905440
$675$	3.47214	0.133643
$676$	−13.0000	−0.500000
$677$	12.2148	0.469452	0.234726	−	0.972062i	$-0.424581\pi$
$677$	12.2148	0.469452	0.234726	+	0.972062i	$0.424581\pi$
$678$	6.05573	0.232569
$679$	17.2361	0.661460
$680$	−1.61803	−0.0620488
$681$	−12.0000	−0.459841
$682$	1.52786	0.0585049
$683$	−12.2918	−0.470333	−0.235166	−	0.971955i	$-0.575563\pi$
$683$	−12.2918	−0.470333	−0.235166	+	0.971955i	$0.575563\pi$
$684$	3.00000	0.114708
$685$	0.472136	0.0180394
$686$	16.7082	0.637922
$687$	−8.94427	−0.341245
$688$	−1.00000	−0.0381246
$689$	0	0
$690$	−2.47214	−0.0941126
$691$	−41.7082	−1.58665	−0.793327	−	0.608795i	$-0.791653\pi$
$691$	−41.7082	−1.58665	−0.793327	+	0.608795i	$0.791653\pi$
$692$	−22.9443	−0.872210
$693$	−3.61803	−0.137438
$694$	−14.3607	−0.545124
$695$	−13.8885	−0.526822
$696$	−3.52786	−0.133723
$697$	11.7082	0.443480
$698$	2.94427	0.111442
$699$	6.94427	0.262656
$700$	−1.38197	−0.0522334
$701$	23.9787	0.905664	0.452832	−	0.891596i	$-0.350414\pi$
$701$	23.9787	0.905664	0.452832	+	0.891596i	$0.350414\pi$
$702$	0	0
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	−1.61803	−0.0609387
$706$	0.180340	0.00678718
$707$	19.7984	0.744594
$708$	2.09017	0.0785534
$709$	13.3475	0.501277	0.250638	−	0.968081i	$-0.419359\pi$
$709$	13.3475	0.501277	0.250638	+	0.968081i	$0.419359\pi$
$710$	−12.7984	−0.480314
$711$	10.0902	0.378411
$712$	−2.29180	−0.0858887
$713$	−6.11146	−0.228876
$714$	−1.38197	−0.0517188
$715$	0	0
$716$	20.0000	0.747435
$717$	−15.9443	−0.595450
$718$	4.00000	0.149279
$719$	41.4164	1.54457	0.772286	−	0.635275i	$-0.219113\pi$
$719$	41.4164	1.54457	0.772286	+	0.635275i	$0.219113\pi$
$720$	−2.61803	−0.0975684
$721$	9.06888	0.337743
$722$	−17.6869	−0.658239
$723$	9.32624	0.346847
$724$	8.29180	0.308162
$725$	5.70820	0.211997
$726$	−0.618034	−0.0229374
$727$	46.2492	1.71529	0.857644	−	0.514243i	$-0.171927\pi$
$727$	46.2492	1.71529	0.857644	+	0.514243i	$0.171927\pi$
$728$	0	0
$729$	−8.50658	−0.315058
$730$	4.76393	0.176321
$731$	1.61803	0.0598451
$732$	0.472136	0.0174506
$733$	−29.5066	−1.08985	−0.544925	−	0.838485i	$-0.683442\pi$
$733$	−29.5066	−1.08985	−0.544925	+	0.838485i	$0.683442\pi$
$734$	13.9787	0.515964
$735$	3.14590	0.116038
$736$	4.00000	0.147442
$737$	11.4164	0.420529
$738$	18.9443	0.697348
$739$	34.7984	1.28008	0.640039	−	0.768342i	$-0.278918\pi$
$739$	34.7984	1.28008	0.640039	+	0.768342i	$0.278918\pi$
$740$	0	0
$741$	0	0
$742$	15.0000	0.550667
$743$	26.9787	0.989753	0.494877	−	0.868963i	$-0.335213\pi$
$743$	26.9787	0.989753	0.494877	+	0.868963i	$0.335213\pi$
$744$	0.944272	0.0346187
$745$	3.70820	0.135858
$746$	−18.3262	−0.670971
$747$	0.854102	0.0312500
$748$	1.61803	0.0591612
$749$	21.5836	0.788647
$750$	−0.618034	−0.0225674
$751$	−23.5623	−0.859801	−0.429900	−	0.902876i	$-0.641451\pi$
$751$	−23.5623	−0.859801	−0.429900	+	0.902876i	$0.641451\pi$
$752$	2.61803	0.0954699
$753$	13.7639	0.501586
$754$	0	0
$755$	−2.76393	−0.100590
$756$	−4.79837	−0.174515
$757$	−22.6525	−0.823318	−0.411659	−	0.911338i	$-0.635051\pi$
$757$	−22.6525	−0.823318	−0.411659	+	0.911338i	$0.635051\pi$
$758$	28.0344	1.01826
$759$	2.47214	0.0897329
$760$	−1.14590	−0.0415661
$761$	−40.2492	−1.45903	−0.729517	−	0.683963i	$-0.760255\pi$
$761$	−40.2492	−1.45903	−0.729517	+	0.683963i	$0.760255\pi$
$762$	−0.944272	−0.0342074
$763$	3.69505	0.133770
$764$	6.56231	0.237416
$765$	4.23607	0.153155
$766$	−13.1246	−0.474212
$767$	0	0
$768$	−0.618034	−0.0223014
$769$	23.1246	0.833895	0.416947	−	0.908931i	$-0.363100\pi$
$769$	23.1246	0.833895	0.416947	+	0.908931i	$0.363100\pi$
$770$	1.38197	0.0498026
$771$	10.8885	0.392141
$772$	26.2148	0.943491
$773$	12.8328	0.461564	0.230782	−	0.973005i	$-0.425872\pi$
$773$	12.8328	0.461564	0.230782	+	0.973005i	$0.425872\pi$
$774$	2.61803	0.0941033
$775$	−1.52786	−0.0548825
$776$	−12.4721	−0.447724
$777$	0	0
$778$	9.09017	0.325898
$779$	8.29180	0.297084
$780$	0	0
$781$	12.7984	0.457962
$782$	−6.47214	−0.231443
$783$	19.8197	0.708297
$784$	−5.09017	−0.181792
$785$	13.4164	0.478852
$786$	−10.4721	−0.373529
$787$	−3.03444	−0.108166	−0.0540831	−	0.998536i	$-0.517224\pi$
$787$	−3.03444	−0.108166	−0.0540831	+	0.998536i	$0.517224\pi$
$788$	−10.7639	−0.383449
$789$	3.36068	0.119643
$790$	−3.85410	−0.137123
$791$	13.5410	0.481463
$792$	2.61803	0.0930278
$793$	0	0
$794$	−21.4508	−0.761262
$795$	6.70820	0.237915
$796$	26.5623	0.941476
$797$	−52.5755	−1.86232	−0.931159	−	0.364613i	$-0.881201\pi$
$797$	−52.5755	−1.86232	−0.931159	+	0.364613i	$0.881201\pi$
$798$	−0.978714	−0.0346461
$799$	−4.23607	−0.149861
$800$	1.00000	0.0353553
$801$	6.00000	0.212000
$802$	−18.7426	−0.661826
$803$	−4.76393	−0.168116
$804$	7.05573	0.248836
$805$	−5.52786	−0.194832
$806$	0	0
$807$	−7.23607	−0.254722
$808$	−14.3262	−0.503995
$809$	−30.8328	−1.08402	−0.542012	−	0.840371i	$-0.682337\pi$
$809$	−30.8328	−1.08402	−0.542012	+	0.840371i	$0.682337\pi$
$810$	5.70820	0.200566
$811$	14.2148	0.499148	0.249574	−	0.968356i	$-0.419709\pi$
$811$	14.2148	0.499148	0.249574	+	0.968356i	$0.419709\pi$
$812$	−7.88854	−0.276834
$813$	9.52786	0.334157
$814$	0	0
$815$	3.79837	0.133051
$816$	1.00000	0.0350070
$817$	1.14590	0.0400899
$818$	22.3820	0.782567
$819$	0	0
$820$	−7.23607	−0.252694
$821$	−46.3262	−1.61680	−0.808398	−	0.588636i	$-0.799665\pi$
$821$	−46.3262	−1.61680	−0.808398	+	0.588636i	$0.799665\pi$
$822$	−0.291796	−0.0101776
$823$	41.8885	1.46014	0.730071	−	0.683371i	$-0.239487\pi$
$823$	41.8885	1.46014	0.730071	+	0.683371i	$0.239487\pi$
$824$	−6.56231	−0.228609
$825$	0.618034	0.0215172
$826$	4.67376	0.162621
$827$	−40.7214	−1.41602	−0.708010	−	0.706202i	$-0.750407\pi$
$827$	−40.7214	−1.41602	−0.708010	+	0.706202i	$0.750407\pi$
$828$	−10.4721	−0.363932
$829$	35.3050	1.22619	0.613096	−	0.790009i	$-0.289924\pi$
$829$	35.3050	1.22619	0.613096	+	0.790009i	$0.289924\pi$
$830$	−0.326238	−0.0113239
$831$	12.8197	0.444709
$832$	0	0
$833$	8.23607	0.285363
$834$	8.58359	0.297225
$835$	−2.29180	−0.0793109
$836$	1.14590	0.0396317
$837$	−5.30495	−0.183366
$838$	−13.1246	−0.453382
$839$	2.11146	0.0728956	0.0364478	−	0.999336i	$-0.488396\pi$
$839$	2.11146	0.0728956	0.0364478	+	0.999336i	$0.488396\pi$
$840$	0.854102	0.0294693
$841$	3.58359	0.123572
$842$	−3.61803	−0.124686
$843$	8.18034	0.281746
$844$	−11.0902	−0.381739
$845$	−13.0000	−0.447214
$846$	−6.85410	−0.235649
$847$	−1.38197	−0.0474849
$848$	−10.8541	−0.372731
$849$	15.7639	0.541017
$850$	−1.61803	−0.0554981
$851$	0	0
$852$	7.90983	0.270986
$853$	−13.5967	−0.465544	−0.232772	−	0.972531i	$-0.574780\pi$
$853$	−13.5967	−0.465544	−0.232772	+	0.972531i	$0.574780\pi$
$854$	1.05573	0.0361263
$855$	3.00000	0.102598
$856$	−15.6180	−0.533813
$857$	−48.6180	−1.66076	−0.830380	−	0.557197i	$-0.811877\pi$
$857$	−48.6180	−1.66076	−0.830380	+	0.557197i	$0.811877\pi$
$858$	0	0
$859$	7.59675	0.259198	0.129599	−	0.991567i	$-0.458631\pi$
$859$	7.59675	0.259198	0.129599	+	0.991567i	$0.458631\pi$
$860$	−1.00000	−0.0340997
$861$	−6.18034	−0.210625
$862$	−0.145898	−0.00496931
$863$	33.5967	1.14365	0.571823	−	0.820377i	$-0.306236\pi$
$863$	33.5967	1.14365	0.571823	+	0.820377i	$0.306236\pi$
$864$	3.47214	0.118124
$865$	−22.9443	−0.780129
$866$	15.8885	0.539915
$867$	8.88854	0.301871
$868$	2.11146	0.0716675
$869$	3.85410	0.130741
$870$	−3.52786	−0.119606
$871$	0	0
$872$	−2.67376	−0.0905450
$873$	32.6525	1.10512
$874$	−4.58359	−0.155042
$875$	−1.38197	−0.0467190
$876$	−2.94427	−0.0994777
$877$	56.6525	1.91302	0.956509	−	0.291703i	$-0.0942217\pi$
$877$	56.6525	1.91302	0.956509	+	0.291703i	$0.0942217\pi$
$878$	21.7984	0.735659
$879$	−11.8197	−0.398667
$880$	−1.00000	−0.0337100
$881$	17.8541	0.601520	0.300760	−	0.953700i	$-0.402760\pi$
$881$	17.8541	0.601520	0.300760	+	0.953700i	$0.402760\pi$
$882$	13.3262	0.448718
$883$	43.8885	1.47697	0.738484	−	0.674271i	$-0.235542\pi$
$883$	43.8885	1.47697	0.738484	+	0.674271i	$0.235542\pi$
$884$	0	0
$885$	2.09017	0.0702603
$886$	−31.8885	−1.07132
$887$	10.5623	0.354648	0.177324	−	0.984153i	$-0.443256\pi$
$887$	10.5623	0.354648	0.177324	+	0.984153i	$0.443256\pi$
$888$	0	0
$889$	−2.11146	−0.0708160
$890$	−2.29180	−0.0768212
$891$	−5.70820	−0.191232
$892$	26.4721	0.886353
$893$	−3.00000	−0.100391
$894$	−2.29180	−0.0766491
$895$	20.0000	0.668526
$896$	−1.38197	−0.0461682
$897$	0	0
$898$	−1.05573	−0.0352301
$899$	−8.72136	−0.290874
$900$	−2.61803	−0.0872678
$901$	17.5623	0.585085
$902$	7.23607	0.240935
$903$	−0.854102	−0.0284227
$904$	−9.79837	−0.325889
$905$	8.29180	0.275629
$906$	1.70820	0.0567513
$907$	6.47214	0.214904	0.107452	−	0.994210i	$-0.465731\pi$
$907$	6.47214	0.214904	0.107452	+	0.994210i	$0.465731\pi$
$908$	19.4164	0.644356
$909$	37.5066	1.24401
$910$	0	0
$911$	42.9230	1.42210	0.711051	−	0.703140i	$-0.248219\pi$
$911$	42.9230	1.42210	0.711051	+	0.703140i	$0.248219\pi$
$912$	0.708204	0.0234510
$913$	0.326238	0.0107969
$914$	8.18034	0.270582
$915$	0.472136	0.0156083
$916$	14.4721	0.478173
$917$	−23.4164	−0.773278
$918$	−5.61803	−0.185423
$919$	−6.03444	−0.199058	−0.0995289	−	0.995035i	$-0.531734\pi$
$919$	−6.03444	−0.199058	−0.0995289	+	0.995035i	$0.531734\pi$
$920$	4.00000	0.131876
$921$	3.79837	0.125161
$922$	−35.9787	−1.18490
$923$	0	0
$924$	−0.854102	−0.0280979
$925$	0	0
$926$	−14.9443	−0.491099
$927$	17.1803	0.564276
$928$	5.70820	0.187381
$929$	−5.59675	−0.183623	−0.0918117	−	0.995776i	$-0.529266\pi$
$929$	−5.59675	−0.183623	−0.0918117	+	0.995776i	$0.529266\pi$
$930$	0.944272	0.0309639
$931$	5.83282	0.191163
$932$	−11.2361	−0.368050
$933$	−17.8885	−0.585645
$934$	25.1459	0.822799
$935$	1.61803	0.0529154
$936$	0	0
$937$	−9.70820	−0.317153	−0.158577	−	0.987347i	$-0.550690\pi$
$937$	−9.70820	−0.317153	−0.158577	+	0.987347i	$0.550690\pi$
$938$	15.7771	0.515140
$939$	17.5836	0.573819
$940$	2.61803	0.0853909
$941$	27.3951	0.893055	0.446528	−	0.894770i	$-0.352660\pi$
$941$	27.3951	0.893055	0.446528	+	0.894770i	$0.352660\pi$
$942$	−8.29180	−0.270161
$943$	−28.9443	−0.942555
$944$	−3.38197	−0.110074
$945$	−4.79837	−0.156091
$946$	1.00000	0.0325128
$947$	−16.5410	−0.537511	−0.268755	−	0.963208i	$-0.586612\pi$
$947$	−16.5410	−0.537511	−0.268755	+	0.963208i	$0.586612\pi$
$948$	2.38197	0.0773627
$949$	0	0
$950$	−1.14590	−0.0371778
$951$	−19.5066	−0.632544
$952$	2.23607	0.0724714
$953$	−24.8328	−0.804414	−0.402207	−	0.915549i	$-0.631757\pi$
$953$	−24.8328	−0.804414	−0.402207	+	0.915549i	$0.631757\pi$
$954$	28.4164	0.920015
$955$	6.56231	0.212351
$956$	25.7984	0.834379
$957$	3.52786	0.114040
$958$	−7.41641	−0.239613
$959$	−0.652476	−0.0210695
$960$	−0.618034	−0.0199470
$961$	−28.6656	−0.924698
$962$	0	0
$963$	40.8885	1.31761
$964$	−15.0902	−0.486022
$965$	26.2148	0.843884
$966$	3.41641	0.109921
$967$	−26.9443	−0.866469	−0.433235	−	0.901281i	$-0.642628\pi$
$967$	−26.9443	−0.866469	−0.433235	+	0.901281i	$0.642628\pi$
$968$	1.00000	0.0321412
$969$	−1.14590	−0.0368115
$970$	−12.4721	−0.400456
$971$	25.8673	0.830120	0.415060	−	0.909794i	$-0.363761\pi$
$971$	25.8673	0.830120	0.415060	+	0.909794i	$0.363761\pi$
$972$	−13.9443	−0.447263
$973$	19.1935	0.615315
$974$	18.0344	0.577861
$975$	0	0
$976$	−0.763932	−0.0244529
$977$	20.8328	0.666501	0.333250	−	0.942838i	$-0.391855\pi$
$977$	20.8328	0.666501	0.333250	+	0.942838i	$0.391855\pi$
$978$	−2.34752	−0.0750655
$979$	2.29180	0.0732461
$980$	−5.09017	−0.162600
$981$	7.00000	0.223493
$982$	21.5623	0.688081
$983$	−12.5410	−0.399996	−0.199998	−	0.979796i	$-0.564094\pi$
$983$	−12.5410	−0.399996	−0.199998	+	0.979796i	$0.564094\pi$
$984$	4.47214	0.142566
$985$	−10.7639	−0.342967
$986$	−9.23607	−0.294136
$987$	2.23607	0.0711748
$988$	0	0
$989$	−4.00000	−0.127193
$990$	2.61803	0.0832066
$991$	−39.0557	−1.24065	−0.620323	−	0.784346i	$-0.712998\pi$
$991$	−39.0557	−1.24065	−0.620323	+	0.784346i	$0.712998\pi$
$992$	−1.52786	−0.0485097
$993$	−10.7639	−0.341583
$994$	17.6869	0.560995
$995$	26.5623	0.842082
$996$	0.201626	0.00638877
$997$	34.3262	1.08712	0.543561	−	0.839369i	$-0.317075\pi$
$997$	34.3262	1.08712	0.543561	+	0.839369i	$0.317075\pi$
$998$	−26.9443	−0.852906
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.s.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.s.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.38197 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.38197 q^{7} +1.00000 q^{8} -2.61803 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.618034 q^{12} -1.38197 q^{14} -0.618034 q^{15} +1.00000 q^{16} -1.61803 q^{17} -2.61803 q^{18} -1.14590 q^{19} +1.00000 q^{20} +0.854102 q^{21} -1.00000 q^{22} +4.00000 q^{23} -0.618034 q^{24} +1.00000 q^{25} +3.47214 q^{27} -1.38197 q^{28} +5.70820 q^{29} -0.618034 q^{30} -1.52786 q^{31} +1.00000 q^{32} +0.618034 q^{33} -1.61803 q^{34} -1.38197 q^{35} -2.61803 q^{36} -1.14590 q^{38} +1.00000 q^{40} -7.23607 q^{41} +0.854102 q^{42} -1.00000 q^{43} -1.00000 q^{44} -2.61803 q^{45} +4.00000 q^{46} +2.61803 q^{47} -0.618034 q^{48} -5.09017 q^{49} +1.00000 q^{50} +1.00000 q^{51} -10.8541 q^{53} +3.47214 q^{54} -1.00000 q^{55} -1.38197 q^{56} +0.708204 q^{57} +5.70820 q^{58} -3.38197 q^{59} -0.618034 q^{60} -0.763932 q^{61} -1.52786 q^{62} +3.61803 q^{63} +1.00000 q^{64} +0.618034 q^{66} -11.4164 q^{67} -1.61803 q^{68} -2.47214 q^{69} -1.38197 q^{70} -12.7984 q^{71} -2.61803 q^{72} +4.76393 q^{73} -0.618034 q^{75} -1.14590 q^{76} +1.38197 q^{77} -3.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -7.23607 q^{82} -0.326238 q^{83} +0.854102 q^{84} -1.61803 q^{85} -1.00000 q^{86} -3.52786 q^{87} -1.00000 q^{88} -2.29180 q^{89} -2.61803 q^{90} +4.00000 q^{92} +0.944272 q^{93} +2.61803 q^{94} -1.14590 q^{95} -0.618034 q^{96} -12.4721 q^{97} -5.09017 q^{98} +2.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} - 2 q^{11} + q^{12} - 5 q^{14} + q^{15} + 2 q^{16} - q^{17} - 3 q^{18} - 9 q^{19} + 2 q^{20} - 5 q^{21} - 2 q^{22} + 8 q^{23} + q^{24} + 2 q^{25} - 2 q^{27} - 5 q^{28} - 2 q^{29} + q^{30} - 12 q^{31} + 2 q^{32} - q^{33} - q^{34} - 5 q^{35} - 3 q^{36} - 9 q^{38} + 2 q^{40} - 10 q^{41} - 5 q^{42} - 2 q^{43} - 2 q^{44} - 3 q^{45} + 8 q^{46} + 3 q^{47} + q^{48} + q^{49} + 2 q^{50} + 2 q^{51} - 15 q^{53} - 2 q^{54} - 2 q^{55} - 5 q^{56} - 12 q^{57} - 2 q^{58} - 9 q^{59} + q^{60} - 6 q^{61} - 12 q^{62} + 5 q^{63} + 2 q^{64} - q^{66} + 4 q^{67} - q^{68} + 4 q^{69} - 5 q^{70} - q^{71} - 3 q^{72} + 14 q^{73} + q^{75} - 9 q^{76} + 5 q^{77} - q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} + 15 q^{83} - 5 q^{84} - q^{85} - 2 q^{86} - 16 q^{87} - 2 q^{88} - 18 q^{89} - 3 q^{90} + 8 q^{92} - 16 q^{93} + 3 q^{94} - 9 q^{95} + q^{96} - 16 q^{97} + q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 - 2 * q^11 + q^12 - 5 * q^14 + q^15 + 2 * q^16 - q^17 - 3 * q^18 - 9 * q^19 + 2 * q^20 - 5 * q^21 - 2 * q^22 + 8 * q^23 + q^24 + 2 * q^25 - 2 * q^27 - 5 * q^28 - 2 * q^29 + q^30 - 12 * q^31 + 2 * q^32 - q^33 - q^34 - 5 * q^35 - 3 * q^36 - 9 * q^38 + 2 * q^40 - 10 * q^41 - 5 * q^42 - 2 * q^43 - 2 * q^44 - 3 * q^45 + 8 * q^46 + 3 * q^47 + q^48 + q^49 + 2 * q^50 + 2 * q^51 - 15 * q^53 - 2 * q^54 - 2 * q^55 - 5 * q^56 - 12 * q^57 - 2 * q^58 - 9 * q^59 + q^60 - 6 * q^61 - 12 * q^62 + 5 * q^63 + 2 * q^64 - q^66 + 4 * q^67 - q^68 + 4 * q^69 - 5 * q^70 - q^71 - 3 * q^72 + 14 * q^73 + q^75 - 9 * q^76 + 5 * q^77 - q^79 + 2 * q^80 - 2 * q^81 - 10 * q^82 + 15 * q^83 - 5 * q^84 - q^85 - 2 * q^86 - 16 * q^87 - 2 * q^88 - 18 * q^89 - 3 * q^90 + 8 * q^92 - 16 * q^93 + 3 * q^94 - 9 * q^95 + q^96 - 16 * q^97 + q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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