LMFDB - Embedded newform 4598.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -2.85410 q^{5} -1.23607 q^{6} -2.85410 q^{7} -1.00000 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -2.85410 q^{5} -1.23607 q^{6} -2.85410 q^{7} -1.00000 q^{8} -1.47214 q^{9} +2.85410 q^{10} +1.23607 q^{12} +4.00000 q^{13} +2.85410 q^{14} -3.52786 q^{15} +1.00000 q^{16} +0.618034 q^{17} +1.47214 q^{18} -1.00000 q^{19} -2.85410 q^{20} -3.52786 q^{21} -5.85410 q^{23} -1.23607 q^{24} +3.14590 q^{25} -4.00000 q^{26} -5.52786 q^{27} -2.85410 q^{28} -7.70820 q^{29} +3.52786 q^{30} -7.23607 q^{31} -1.00000 q^{32} -0.618034 q^{34} +8.14590 q^{35} -1.47214 q^{36} +1.23607 q^{37} +1.00000 q^{38} +4.94427 q^{39} +2.85410 q^{40} +8.47214 q^{41} +3.52786 q^{42} +5.38197 q^{43} +4.20163 q^{45} +5.85410 q^{46} +5.85410 q^{47} +1.23607 q^{48} +1.14590 q^{49} -3.14590 q^{50} +0.763932 q^{51} +4.00000 q^{52} +6.76393 q^{53} +5.52786 q^{54} +2.85410 q^{56} -1.23607 q^{57} +7.70820 q^{58} -10.9443 q^{59} -3.52786 q^{60} +7.85410 q^{61} +7.23607 q^{62} +4.20163 q^{63} +1.00000 q^{64} -11.4164 q^{65} -4.76393 q^{67} +0.618034 q^{68} -7.23607 q^{69} -8.14590 q^{70} -7.23607 q^{71} +1.47214 q^{72} -6.94427 q^{73} -1.23607 q^{74} +3.88854 q^{75} -1.00000 q^{76} -4.94427 q^{78} +4.76393 q^{79} -2.85410 q^{80} -2.41641 q^{81} -8.47214 q^{82} -8.85410 q^{83} -3.52786 q^{84} -1.76393 q^{85} -5.38197 q^{86} -9.52786 q^{87} +8.18034 q^{89} -4.20163 q^{90} -11.4164 q^{91} -5.85410 q^{92} -8.94427 q^{93} -5.85410 q^{94} +2.85410 q^{95} -1.23607 q^{96} -0.944272 q^{97} -1.14590 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9} - q^{10} - 2 q^{12} + 8 q^{13} - q^{14} - 16 q^{15} + 2 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + q^{20} - 16 q^{21} - 5 q^{23} + 2 q^{24} + 13 q^{25} - 8 q^{26} - 20 q^{27} + q^{28} - 2 q^{29} + 16 q^{30} - 10 q^{31} - 2 q^{32} + q^{34} + 23 q^{35} + 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{39} - q^{40} + 8 q^{41} + 16 q^{42} + 13 q^{43} + 33 q^{45} + 5 q^{46} + 5 q^{47} - 2 q^{48} + 9 q^{49} - 13 q^{50} + 6 q^{51} + 8 q^{52} + 18 q^{53} + 20 q^{54} - q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} - 16 q^{60} + 9 q^{61} + 10 q^{62} + 33 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{67} - q^{68} - 10 q^{69} - 23 q^{70} - 10 q^{71} - 6 q^{72} + 4 q^{73} + 2 q^{74} - 28 q^{75} - 2 q^{76} + 8 q^{78} + 14 q^{79} + q^{80} + 22 q^{81} - 8 q^{82} - 11 q^{83} - 16 q^{84} - 8 q^{85} - 13 q^{86} - 28 q^{87} - 6 q^{89} - 33 q^{90} + 4 q^{91} - 5 q^{92} - 5 q^{94} - q^{95} + 2 q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9 - q^10 - 2 * q^12 + 8 * q^13 - q^14 - 16 * q^15 + 2 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + q^20 - 16 * q^21 - 5 * q^23 + 2 * q^24 + 13 * q^25 - 8 * q^26 - 20 * q^27 + q^28 - 2 * q^29 + 16 * q^30 - 10 * q^31 - 2 * q^32 + q^34 + 23 * q^35 + 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^39 - q^40 + 8 * q^41 + 16 * q^42 + 13 * q^43 + 33 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 + 9 * q^49 - 13 * q^50 + 6 * q^51 + 8 * q^52 + 18 * q^53 + 20 * q^54 - q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 - 16 * q^60 + 9 * q^61 + 10 * q^62 + 33 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^67 - q^68 - 10 * q^69 - 23 * q^70 - 10 * q^71 - 6 * q^72 + 4 * q^73 + 2 * q^74 - 28 * q^75 - 2 * q^76 + 8 * q^78 + 14 * q^79 + q^80 + 22 * q^81 - 8 * q^82 - 11 * q^83 - 16 * q^84 - 8 * q^85 - 13 * q^86 - 28 * q^87 - 6 * q^89 - 33 * q^90 + 4 * q^91 - 5 * q^92 - 5 * q^94 - q^95 + 2 * q^96 + 16 * q^97 - 9 * 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
$2$	−1.00000	−0.707107
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	1.00000	0.500000
$5$	−2.85410	−1.27639	−0.638197	−	0.769873i	$-0.720319\pi$
$5$	−2.85410	−1.27639	−0.638197	+	0.769873i	$0.720319\pi$
$6$	−1.23607	−0.504623
$7$	−2.85410	−1.07875	−0.539375	−	0.842066i	$-0.681339\pi$
$7$	−2.85410	−1.07875	−0.539375	+	0.842066i	$0.681339\pi$
$8$	−1.00000	−0.353553
$9$	−1.47214	−0.490712
$10$	2.85410	0.902546
$11$	0	0
$11$	0	0
$12$	1.23607	0.356822
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	2.85410	0.762791
$15$	−3.52786	−0.910891
$16$	1.00000	0.250000
$17$	0.618034	0.149895	0.0749476	−	0.997187i	$-0.476121\pi$
$17$	0.618034	0.149895	0.0749476	+	0.997187i	$0.476121\pi$
$18$	1.47214	0.346986
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.85410	−0.638197
$21$	−3.52786	−0.769843
$22$	0	0
$23$	−5.85410	−1.22066	−0.610332	−	0.792145i	$-0.708964\pi$
$23$	−5.85410	−1.22066	−0.610332	+	0.792145i	$0.708964\pi$
$24$	−1.23607	−0.252311
$25$	3.14590	0.629180
$26$	−4.00000	−0.784465
$27$	−5.52786	−1.06384
$28$	−2.85410	−0.539375
$29$	−7.70820	−1.43138	−0.715689	−	0.698419i	$-0.753887\pi$
$29$	−7.70820	−1.43138	−0.715689	+	0.698419i	$0.753887\pi$
$30$	3.52786	0.644097
$31$	−7.23607	−1.29964	−0.649818	−	0.760090i	$-0.725155\pi$
$31$	−7.23607	−1.29964	−0.649818	+	0.760090i	$0.725155\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.618034	−0.105992
$35$	8.14590	1.37691
$36$	−1.47214	−0.245356
$37$	1.23607	0.203208	0.101604	−	0.994825i	$-0.467602\pi$
$37$	1.23607	0.203208	0.101604	+	0.994825i	$0.467602\pi$
$38$	1.00000	0.162221
$39$	4.94427	0.791717
$40$	2.85410	0.451273
$41$	8.47214	1.32313	0.661563	−	0.749890i	$-0.269894\pi$
$41$	8.47214	1.32313	0.661563	+	0.749890i	$0.269894\pi$
$42$	3.52786	0.544361
$43$	5.38197	0.820742	0.410371	−	0.911919i	$-0.365399\pi$
$43$	5.38197	0.820742	0.410371	+	0.911919i	$0.365399\pi$
$44$	0	0
$45$	4.20163	0.626341
$46$	5.85410	0.863140
$47$	5.85410	0.853909	0.426954	−	0.904273i	$-0.359587\pi$
$47$	5.85410	0.853909	0.426954	+	0.904273i	$0.359587\pi$
$48$	1.23607	0.178411
$49$	1.14590	0.163700
$50$	−3.14590	−0.444897
$51$	0.763932	0.106972
$52$	4.00000	0.554700
$53$	6.76393	0.929098	0.464549	−	0.885548i	$-0.346217\pi$
$53$	6.76393	0.929098	0.464549	+	0.885548i	$0.346217\pi$
$54$	5.52786	0.752247
$55$	0	0
$56$	2.85410	0.381395
$57$	−1.23607	−0.163721
$58$	7.70820	1.01214
$59$	−10.9443	−1.42482	−0.712411	−	0.701762i	$-0.752397\pi$
$59$	−10.9443	−1.42482	−0.712411	+	0.701762i	$0.752397\pi$
$60$	−3.52786	−0.455445
$61$	7.85410	1.00561	0.502807	−	0.864398i	$-0.332301\pi$
$61$	7.85410	1.00561	0.502807	+	0.864398i	$0.332301\pi$
$62$	7.23607	0.918982
$63$	4.20163	0.529355
$64$	1.00000	0.125000
$65$	−11.4164	−1.41603
$66$	0	0
$67$	−4.76393	−0.582007	−0.291003	−	0.956722i	$-0.593989\pi$
$67$	−4.76393	−0.582007	−0.291003	+	0.956722i	$0.593989\pi$
$68$	0.618034	0.0749476
$69$	−7.23607	−0.871120
$70$	−8.14590	−0.973621
$71$	−7.23607	−0.858763	−0.429382	−	0.903123i	$-0.641268\pi$
$71$	−7.23607	−0.858763	−0.429382	+	0.903123i	$0.641268\pi$
$72$	1.47214	0.173493
$73$	−6.94427	−0.812766	−0.406383	−	0.913703i	$-0.633210\pi$
$73$	−6.94427	−0.812766	−0.406383	+	0.913703i	$0.633210\pi$
$74$	−1.23607	−0.143690
$75$	3.88854	0.449010
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−4.94427	−0.559829
$79$	4.76393	0.535984	0.267992	−	0.963421i	$-0.413640\pi$
$79$	4.76393	0.535984	0.267992	+	0.963421i	$0.413640\pi$
$80$	−2.85410	−0.319098
$81$	−2.41641	−0.268490
$82$	−8.47214	−0.935591
$83$	−8.85410	−0.971864	−0.485932	−	0.873997i	$-0.661520\pi$
$83$	−8.85410	−0.971864	−0.485932	+	0.873997i	$0.661520\pi$
$84$	−3.52786	−0.384922
$85$	−1.76393	−0.191325
$86$	−5.38197	−0.580352
$87$	−9.52786	−1.02149
$88$	0	0
$89$	8.18034	0.867114	0.433557	−	0.901126i	$-0.357258\pi$
$89$	8.18034	0.867114	0.433557	+	0.901126i	$0.357258\pi$
$90$	−4.20163	−0.442890
$91$	−11.4164	−1.19676
$92$	−5.85410	−0.610332
$93$	−8.94427	−0.927478
$94$	−5.85410	−0.603805
$95$	2.85410	0.292825
$96$	−1.23607	−0.126156
$97$	−0.944272	−0.0958763	−0.0479381	−	0.998850i	$-0.515265\pi$
$97$	−0.944272	−0.0958763	−0.0479381	+	0.998850i	$0.515265\pi$
$98$	−1.14590	−0.115753
$99$	0	0
$100$	3.14590	0.314590
$101$	16.5623	1.64801	0.824006	−	0.566582i	$-0.191734\pi$
$101$	16.5623	1.64801	0.824006	+	0.566582i	$0.191734\pi$
$102$	−0.763932	−0.0756405
$103$	10.9443	1.07837	0.539186	−	0.842187i	$-0.318732\pi$
$103$	10.9443	1.07837	0.539186	+	0.842187i	$0.318732\pi$
$104$	−4.00000	−0.392232
$105$	10.0689	0.982622
$106$	−6.76393	−0.656971
$107$	−6.47214	−0.625685	−0.312842	−	0.949805i	$-0.601281\pi$
$107$	−6.47214	−0.625685	−0.312842	+	0.949805i	$0.601281\pi$
$108$	−5.52786	−0.531919
$109$	16.9443	1.62297	0.811483	−	0.584375i	$-0.198660\pi$
$109$	16.9443	1.62297	0.811483	+	0.584375i	$0.198660\pi$
$110$	0	0
$111$	1.52786	0.145018
$112$	−2.85410	−0.269687
$113$	−16.4721	−1.54957	−0.774784	−	0.632226i	$-0.782141\pi$
$113$	−16.4721	−1.54957	−0.774784	+	0.632226i	$0.782141\pi$
$114$	1.23607	0.115768
$115$	16.7082	1.55805
$116$	−7.70820	−0.715689
$117$	−5.88854	−0.544396
$118$	10.9443	1.00750
$119$	−1.76393	−0.161699
$120$	3.52786	0.322048
$121$	0	0
$122$	−7.85410	−0.711077
$123$	10.4721	0.944241
$124$	−7.23607	−0.649818
$125$	5.29180	0.473313
$126$	−4.20163	−0.374311
$127$	15.7082	1.39388	0.696939	−	0.717131i	$-0.254545\pi$
$127$	15.7082	1.39388	0.696939	+	0.717131i	$0.254545\pi$
$128$	−1.00000	−0.0883883
$129$	6.65248	0.585718
$130$	11.4164	1.00129
$131$	−7.14590	−0.624340	−0.312170	−	0.950026i	$-0.601056\pi$
$131$	−7.14590	−0.624340	−0.312170	+	0.950026i	$0.601056\pi$
$132$	0	0
$133$	2.85410	0.247482
$134$	4.76393	0.411541
$135$	15.7771	1.35788
$136$	−0.618034	−0.0529960
$137$	10.5623	0.902399	0.451199	−	0.892423i	$-0.350996\pi$
$137$	10.5623	0.902399	0.451199	+	0.892423i	$0.350996\pi$
$138$	7.23607	0.615975
$139$	−2.90983	−0.246809	−0.123404	−	0.992356i	$-0.539381\pi$
$139$	−2.90983	−0.246809	−0.123404	+	0.992356i	$0.539381\pi$
$140$	8.14590	0.688454
$141$	7.23607	0.609387
$142$	7.23607	0.607237
$143$	0	0
$144$	−1.47214	−0.122678
$145$	22.0000	1.82700
$146$	6.94427	0.574712
$147$	1.41641	0.116823
$148$	1.23607	0.101604
$149$	12.4721	1.02176	0.510879	−	0.859653i	$-0.329320\pi$
$149$	12.4721	1.02176	0.510879	+	0.859653i	$0.329320\pi$
$150$	−3.88854	−0.317498
$151$	15.2361	1.23989	0.619947	−	0.784644i	$-0.287154\pi$
$151$	15.2361	1.23989	0.619947	+	0.784644i	$0.287154\pi$
$152$	1.00000	0.0811107
$153$	−0.909830	−0.0735554
$154$	0	0
$155$	20.6525	1.65885
$156$	4.94427	0.395859
$157$	−6.67376	−0.532624	−0.266312	−	0.963887i	$-0.585805\pi$
$157$	−6.67376	−0.532624	−0.266312	+	0.963887i	$0.585805\pi$
$158$	−4.76393	−0.378998
$159$	8.36068	0.663045
$160$	2.85410	0.225637
$161$	16.7082	1.31679
$162$	2.41641	0.189851
$163$	−16.2705	−1.27440	−0.637202	−	0.770697i	$-0.719908\pi$
$163$	−16.2705	−1.27440	−0.637202	+	0.770697i	$0.719908\pi$
$164$	8.47214	0.661563
$165$	0	0
$166$	8.85410	0.687212
$167$	−19.7082	−1.52507	−0.762533	−	0.646949i	$-0.776045\pi$
$167$	−19.7082	−1.52507	−0.762533	+	0.646949i	$0.776045\pi$
$168$	3.52786	0.272181
$169$	3.00000	0.230769
$170$	1.76393	0.135287
$171$	1.47214	0.112577
$172$	5.38197	0.410371
$173$	−4.00000	−0.304114	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−4.00000	−0.304114	−0.152057	+	0.988372i	$0.548590\pi$
$174$	9.52786	0.722306
$175$	−8.97871	−0.678727
$176$	0	0
$177$	−13.5279	−1.01682
$178$	−8.18034	−0.613142
$179$	19.1246	1.42944	0.714720	−	0.699410i	$-0.246554\pi$
$179$	19.1246	1.42944	0.714720	+	0.699410i	$0.246554\pi$
$180$	4.20163	0.313171
$181$	21.4164	1.59187	0.795935	−	0.605383i	$-0.206980\pi$
$181$	21.4164	1.59187	0.795935	+	0.605383i	$0.206980\pi$
$182$	11.4164	0.846240
$183$	9.70820	0.717651
$184$	5.85410	0.431570
$185$	−3.52786	−0.259374
$186$	8.94427	0.655826
$187$	0	0
$188$	5.85410	0.426954
$189$	15.7771	1.14761
$190$	−2.85410	−0.207058
$191$	−15.6180	−1.13008	−0.565041	−	0.825063i	$-0.691140\pi$
$191$	−15.6180	−1.13008	−0.565041	+	0.825063i	$0.691140\pi$
$192$	1.23607	0.0892055
$193$	9.52786	0.685831	0.342915	−	0.939366i	$-0.388586\pi$
$193$	9.52786	0.685831	0.342915	+	0.939366i	$0.388586\pi$
$194$	0.944272	0.0677948
$195$	−14.1115	−1.01054
$196$	1.14590	0.0818499
$197$	−6.94427	−0.494759	−0.247379	−	0.968919i	$-0.579569\pi$
$197$	−6.94427	−0.494759	−0.247379	+	0.968919i	$0.579569\pi$
$198$	0	0
$199$	24.3820	1.72839	0.864196	−	0.503156i	$-0.167828\pi$
$199$	24.3820	1.72839	0.864196	+	0.503156i	$0.167828\pi$
$200$	−3.14590	−0.222449
$201$	−5.88854	−0.415346
$202$	−16.5623	−1.16532
$203$	22.0000	1.54410
$204$	0.763932	0.0534859
$205$	−24.1803	−1.68883
$206$	−10.9443	−0.762524
$207$	8.61803	0.598995
$208$	4.00000	0.277350
$209$	0	0
$210$	−10.0689	−0.694819
$211$	2.94427	0.202692	0.101346	−	0.994851i	$-0.467685\pi$
$211$	2.94427	0.202692	0.101346	+	0.994851i	$0.467685\pi$
$212$	6.76393	0.464549
$213$	−8.94427	−0.612851
$214$	6.47214	0.442426
$215$	−15.3607	−1.04759
$216$	5.52786	0.376124
$217$	20.6525	1.40198
$218$	−16.9443	−1.14761
$219$	−8.58359	−0.580025
$220$	0	0
$221$	2.47214	0.166294
$222$	−1.52786	−0.102544
$223$	20.6525	1.38299	0.691496	−	0.722380i	$-0.256952\pi$
$223$	20.6525	1.38299	0.691496	+	0.722380i	$0.256952\pi$
$224$	2.85410	0.190698
$225$	−4.63119	−0.308746
$226$	16.4721	1.09571
$227$	3.81966	0.253520	0.126760	−	0.991933i	$-0.459542\pi$
$227$	3.81966	0.253520	0.126760	+	0.991933i	$0.459542\pi$
$228$	−1.23607	−0.0818606
$229$	−4.14590	−0.273969	−0.136984	−	0.990573i	$-0.543741\pi$
$229$	−4.14590	−0.273969	−0.136984	+	0.990573i	$0.543741\pi$
$230$	−16.7082	−1.10171
$231$	0	0
$232$	7.70820	0.506068
$233$	−15.3262	−1.00406	−0.502028	−	0.864852i	$-0.667412\pi$
$233$	−15.3262	−1.00406	−0.502028	+	0.864852i	$0.667412\pi$
$234$	5.88854	0.384946
$235$	−16.7082	−1.08992
$236$	−10.9443	−0.712411
$237$	5.88854	0.382502
$238$	1.76393	0.114339
$239$	−0.326238	−0.0211026	−0.0105513	−	0.999944i	$-0.503359\pi$
$239$	−0.326238	−0.0211026	−0.0105513	+	0.999944i	$0.503359\pi$
$240$	−3.52786	−0.227723
$241$	28.4721	1.83405	0.917026	−	0.398828i	$-0.130583\pi$
$241$	28.4721	1.83405	0.917026	+	0.398828i	$0.130583\pi$
$242$	0	0
$243$	13.5967	0.872232
$244$	7.85410	0.502807
$245$	−3.27051	−0.208945
$246$	−10.4721	−0.667679
$247$	−4.00000	−0.254514
$248$	7.23607	0.459491
$249$	−10.9443	−0.693565
$250$	−5.29180	−0.334683
$251$	−14.6180	−0.922682	−0.461341	−	0.887223i	$-0.652632\pi$
$251$	−14.6180	−0.922682	−0.461341	+	0.887223i	$0.652632\pi$
$252$	4.20163	0.264678
$253$	0	0
$254$	−15.7082	−0.985620
$255$	−2.18034	−0.136538
$256$	1.00000	0.0625000
$257$	4.18034	0.260762	0.130381	−	0.991464i	$-0.458380\pi$
$257$	4.18034	0.260762	0.130381	+	0.991464i	$0.458380\pi$
$258$	−6.65248	−0.414165
$259$	−3.52786	−0.219211
$260$	−11.4164	−0.708016
$261$	11.3475	0.702394
$262$	7.14590	0.441475
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	−19.3050	−1.18589
$266$	−2.85410	−0.174996
$267$	10.1115	0.618811
$268$	−4.76393	−0.291003
$269$	6.29180	0.383618	0.191809	−	0.981432i	$-0.438565\pi$
$269$	6.29180	0.383618	0.191809	+	0.981432i	$0.438565\pi$
$270$	−15.7771	−0.960163
$271$	−16.9098	−1.02720	−0.513600	−	0.858030i	$-0.671688\pi$
$271$	−16.9098	−1.02720	−0.513600	+	0.858030i	$0.671688\pi$
$272$	0.618034	0.0374738
$273$	−14.1115	−0.854064
$274$	−10.5623	−0.638092
$275$	0	0
$276$	−7.23607	−0.435560
$277$	11.5279	0.692642	0.346321	−	0.938116i	$-0.387431\pi$
$277$	11.5279	0.692642	0.346321	+	0.938116i	$0.387431\pi$
$278$	2.90983	0.174520
$279$	10.6525	0.637747
$280$	−8.14590	−0.486811
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	−7.23607	−0.430902
$283$	3.14590	0.187004	0.0935021	−	0.995619i	$-0.470194\pi$
$283$	3.14590	0.187004	0.0935021	+	0.995619i	$0.470194\pi$
$284$	−7.23607	−0.429382
$285$	3.52786	0.208973
$286$	0	0
$287$	−24.1803	−1.42732
$288$	1.47214	0.0867464
$289$	−16.6180	−0.977531
$290$	−22.0000	−1.29188
$291$	−1.16718	−0.0684216
$292$	−6.94427	−0.406383
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	−1.41641	−0.0826066
$295$	31.2361	1.81863
$296$	−1.23607	−0.0718450
$297$	0	0
$298$	−12.4721	−0.722491
$299$	−23.4164	−1.35421
$300$	3.88854	0.224505
$301$	−15.3607	−0.885375
$302$	−15.2361	−0.876737
$303$	20.4721	1.17609
$304$	−1.00000	−0.0573539
$305$	−22.4164	−1.28356
$306$	0.909830	0.0520115
$307$	10.4721	0.597676	0.298838	−	0.954304i	$-0.403401\pi$
$307$	10.4721	0.597676	0.298838	+	0.954304i	$0.403401\pi$
$308$	0	0
$309$	13.5279	0.769573
$310$	−20.6525	−1.17298
$311$	25.5623	1.44951	0.724753	−	0.689009i	$-0.241954\pi$
$311$	25.5623	1.44951	0.724753	+	0.689009i	$0.241954\pi$
$312$	−4.94427	−0.279914
$313$	22.5066	1.27215	0.636073	−	0.771628i	$-0.280558\pi$
$313$	22.5066	1.27215	0.636073	+	0.771628i	$0.280558\pi$
$314$	6.67376	0.376622
$315$	−11.9919	−0.675665
$316$	4.76393	0.267992
$317$	0.472136	0.0265178	0.0132589	−	0.999912i	$-0.495779\pi$
$317$	0.472136	0.0265178	0.0132589	+	0.999912i	$0.495779\pi$
$318$	−8.36068	−0.468844
$319$	0	0
$320$	−2.85410	−0.159549
$321$	−8.00000	−0.446516
$322$	−16.7082	−0.931112
$323$	−0.618034	−0.0343883
$324$	−2.41641	−0.134245
$325$	12.5836	0.698012
$326$	16.2705	0.901140
$327$	20.9443	1.15822
$328$	−8.47214	−0.467795
$329$	−16.7082	−0.921153
$330$	0	0
$331$	−1.52786	−0.0839790	−0.0419895	−	0.999118i	$-0.513370\pi$
$331$	−1.52786	−0.0839790	−0.0419895	+	0.999118i	$0.513370\pi$
$332$	−8.85410	−0.485932
$333$	−1.81966	−0.0997168
$334$	19.7082	1.07838
$335$	13.5967	0.742870
$336$	−3.52786	−0.192461
$337$	−3.81966	−0.208070	−0.104035	−	0.994574i	$-0.533175\pi$
$337$	−3.81966	−0.208070	−0.104035	+	0.994574i	$0.533175\pi$
$338$	−3.00000	−0.163178
$339$	−20.3607	−1.10584
$340$	−1.76393	−0.0956626
$341$	0	0
$342$	−1.47214	−0.0796040
$343$	16.7082	0.902158
$344$	−5.38197	−0.290176
$345$	20.6525	1.11189
$346$	4.00000	0.215041
$347$	20.7984	1.11652	0.558258	−	0.829668i	$-0.311470\pi$
$347$	20.7984	1.11652	0.558258	+	0.829668i	$0.311470\pi$
$348$	−9.52786	−0.510747
$349$	−25.3262	−1.35568	−0.677841	−	0.735208i	$-0.737084\pi$
$349$	−25.3262	−1.35568	−0.677841	+	0.735208i	$0.737084\pi$
$350$	8.97871	0.479932
$351$	−22.1115	−1.18022
$352$	0	0
$353$	30.9230	1.64586	0.822932	−	0.568140i	$-0.192337\pi$
$353$	30.9230	1.64586	0.822932	+	0.568140i	$0.192337\pi$
$354$	13.5279	0.718998
$355$	20.6525	1.09612
$356$	8.18034	0.433557
$357$	−2.18034	−0.115396
$358$	−19.1246	−1.01077
$359$	26.7984	1.41436	0.707182	−	0.707032i	$-0.249966\pi$
$359$	26.7984	1.41436	0.707182	+	0.707032i	$0.249966\pi$
$360$	−4.20163	−0.221445
$361$	1.00000	0.0526316
$362$	−21.4164	−1.12562
$363$	0	0
$364$	−11.4164	−0.598382
$365$	19.8197	1.03741
$366$	−9.70820	−0.507456
$367$	−2.09017	−0.109106	−0.0545530	−	0.998511i	$-0.517373\pi$
$367$	−2.09017	−0.109106	−0.0545530	+	0.998511i	$0.517373\pi$
$368$	−5.85410	−0.305166
$369$	−12.4721	−0.649273
$370$	3.52786	0.183405
$371$	−19.3050	−1.00226
$372$	−8.94427	−0.463739
$373$	9.52786	0.493334	0.246667	−	0.969100i	$-0.420665\pi$
$373$	9.52786	0.493334	0.246667	+	0.969100i	$0.420665\pi$
$374$	0	0
$375$	6.54102	0.337777
$376$	−5.85410	−0.301902
$377$	−30.8328	−1.58797
$378$	−15.7771	−0.811486
$379$	−27.8885	−1.43254	−0.716269	−	0.697824i	$-0.754152\pi$
$379$	−27.8885	−1.43254	−0.716269	+	0.697824i	$0.754152\pi$
$380$	2.85410	0.146412
$381$	19.4164	0.994733
$382$	15.6180	0.799088
$383$	12.6525	0.646511	0.323256	−	0.946312i	$-0.395223\pi$
$383$	12.6525	0.646511	0.323256	+	0.946312i	$0.395223\pi$
$384$	−1.23607	−0.0630778
$385$	0	0
$386$	−9.52786	−0.484956
$387$	−7.92299	−0.402748
$388$	−0.944272	−0.0479381
$389$	−31.2705	−1.58548	−0.792739	−	0.609561i	$-0.791346\pi$
$389$	−31.2705	−1.58548	−0.792739	+	0.609561i	$0.791346\pi$
$390$	14.1115	0.714561
$391$	−3.61803	−0.182972
$392$	−1.14590	−0.0578766
$393$	−8.83282	−0.445557
$394$	6.94427	0.349847
$395$	−13.5967	−0.684127
$396$	0	0
$397$	−3.56231	−0.178787	−0.0893935	−	0.995996i	$-0.528493\pi$
$397$	−3.56231	−0.178787	−0.0893935	+	0.995996i	$0.528493\pi$
$398$	−24.3820	−1.22216
$399$	3.52786	0.176614
$400$	3.14590	0.157295
$401$	−14.7639	−0.737276	−0.368638	−	0.929573i	$-0.620176\pi$
$401$	−14.7639	−0.737276	−0.368638	+	0.929573i	$0.620176\pi$
$402$	5.88854	0.293694
$403$	−28.9443	−1.44182
$404$	16.5623	0.824006
$405$	6.89667	0.342699
$406$	−22.0000	−1.09184
$407$	0	0
$408$	−0.763932	−0.0378203
$409$	−38.4721	−1.90232	−0.951162	−	0.308691i	$-0.900109\pi$
$409$	−38.4721	−1.90232	−0.951162	+	0.308691i	$0.900109\pi$
$410$	24.1803	1.19418
$411$	13.0557	0.643992
$412$	10.9443	0.539186
$413$	31.2361	1.53703
$414$	−8.61803	−0.423553
$415$	25.2705	1.24048
$416$	−4.00000	−0.196116
$417$	−3.59675	−0.176133
$418$	0	0
$419$	13.7426	0.671372	0.335686	−	0.941974i	$-0.391032\pi$
$419$	13.7426	0.671372	0.335686	+	0.941974i	$0.391032\pi$
$420$	10.0689	0.491311
$421$	15.5279	0.756782	0.378391	−	0.925646i	$-0.376478\pi$
$421$	15.5279	0.756782	0.378391	+	0.925646i	$0.376478\pi$
$422$	−2.94427	−0.143325
$423$	−8.61803	−0.419023
$424$	−6.76393	−0.328486
$425$	1.94427	0.0943110
$426$	8.94427	0.433351
$427$	−22.4164	−1.08481
$428$	−6.47214	−0.312842
$429$	0	0
$430$	15.3607	0.740758
$431$	−37.4164	−1.80228	−0.901142	−	0.433523i	$-0.857270\pi$
$431$	−37.4164	−1.80228	−0.901142	+	0.433523i	$0.857270\pi$
$432$	−5.52786	−0.265959
$433$	−23.8885	−1.14801	−0.574005	−	0.818852i	$-0.694611\pi$
$433$	−23.8885	−1.14801	−0.574005	+	0.818852i	$0.694611\pi$
$434$	−20.6525	−0.991351
$435$	27.1935	1.30383
$436$	16.9443	0.811483
$437$	5.85410	0.280040
$438$	8.58359	0.410140
$439$	26.3607	1.25813	0.629063	−	0.777354i	$-0.283439\pi$
$439$	26.3607	1.25813	0.629063	+	0.777354i	$0.283439\pi$
$440$	0	0
$441$	−1.68692	−0.0803294
$442$	−2.47214	−0.117588
$443$	12.2705	0.582990	0.291495	−	0.956572i	$-0.405847\pi$
$443$	12.2705	0.582990	0.291495	+	0.956572i	$0.405847\pi$
$444$	1.52786	0.0725092
$445$	−23.3475	−1.10678
$446$	−20.6525	−0.977923
$447$	15.4164	0.729171
$448$	−2.85410	−0.134844
$449$	2.29180	0.108157	0.0540783	−	0.998537i	$-0.482778\pi$
$449$	2.29180	0.108157	0.0540783	+	0.998537i	$0.482778\pi$
$450$	4.63119	0.218316
$451$	0	0
$452$	−16.4721	−0.774784
$453$	18.8328	0.884843
$454$	−3.81966	−0.179266
$455$	32.5836	1.52754
$456$	1.23607	0.0578842
$457$	0.0901699	0.00421797	0.00210899	−	0.999998i	$-0.499329\pi$
$457$	0.0901699	0.00421797	0.00210899	+	0.999998i	$0.499329\pi$
$458$	4.14590	0.193725
$459$	−3.41641	−0.159464
$460$	16.7082	0.779024
$461$	−29.6869	−1.38266	−0.691329	−	0.722540i	$-0.742974\pi$
$461$	−29.6869	−1.38266	−0.691329	+	0.722540i	$0.742974\pi$
$462$	0	0
$463$	39.2148	1.82247	0.911233	−	0.411892i	$-0.135132\pi$
$463$	39.2148	1.82247	0.911233	+	0.411892i	$0.135132\pi$
$464$	−7.70820	−0.357844
$465$	25.5279	1.18383
$466$	15.3262	0.709974
$467$	−24.2705	−1.12311	−0.561553	−	0.827441i	$-0.689796\pi$
$467$	−24.2705	−1.12311	−0.561553	+	0.827441i	$0.689796\pi$
$468$	−5.88854	−0.272198
$469$	13.5967	0.627839
$470$	16.7082	0.770692
$471$	−8.24922	−0.380104
$472$	10.9443	0.503751
$473$	0	0
$474$	−5.88854	−0.270470
$475$	−3.14590	−0.144344
$476$	−1.76393	−0.0808497
$477$	−9.95743	−0.455919
$478$	0.326238	0.0149218
$479$	−31.0902	−1.42055	−0.710273	−	0.703926i	$-0.751429\pi$
$479$	−31.0902	−1.42055	−0.710273	+	0.703926i	$0.751429\pi$
$480$	3.52786	0.161024
$481$	4.94427	0.225439
$482$	−28.4721	−1.29687
$483$	20.6525	0.939720
$484$	0	0
$485$	2.69505	0.122376
$486$	−13.5967	−0.616761
$487$	−5.41641	−0.245441	−0.122720	−	0.992441i	$-0.539162\pi$
$487$	−5.41641	−0.245441	−0.122720	+	0.992441i	$0.539162\pi$
$488$	−7.85410	−0.355538
$489$	−20.1115	−0.909471
$490$	3.27051	0.147747
$491$	−18.7426	−0.845844	−0.422922	−	0.906166i	$-0.638996\pi$
$491$	−18.7426	−0.845844	−0.422922	+	0.906166i	$0.638996\pi$
$492$	10.4721	0.472120
$493$	−4.76393	−0.214557
$494$	4.00000	0.179969
$495$	0	0
$496$	−7.23607	−0.324909
$497$	20.6525	0.926390
$498$	10.9443	0.490425
$499$	9.03444	0.404437	0.202219	−	0.979340i	$-0.435185\pi$
$499$	9.03444	0.404437	0.202219	+	0.979340i	$0.435185\pi$
$500$	5.29180	0.236656
$501$	−24.3607	−1.08835
$502$	14.6180	0.652435
$503$	−7.05573	−0.314599	−0.157300	−	0.987551i	$-0.550279\pi$
$503$	−7.05573	−0.314599	−0.157300	+	0.987551i	$0.550279\pi$
$504$	−4.20163	−0.187155
$505$	−47.2705	−2.10351
$506$	0	0
$507$	3.70820	0.164687
$508$	15.7082	0.696939
$509$	18.7639	0.831697	0.415848	−	0.909434i	$-0.363485\pi$
$509$	18.7639	0.831697	0.415848	+	0.909434i	$0.363485\pi$
$510$	2.18034	0.0965471
$511$	19.8197	0.876770
$512$	−1.00000	−0.0441942
$513$	5.52786	0.244061
$514$	−4.18034	−0.184387
$515$	−31.2361	−1.37643
$516$	6.65248	0.292859
$517$	0	0
$518$	3.52786	0.155005
$519$	−4.94427	−0.217029
$520$	11.4164	0.500643
$521$	3.41641	0.149676	0.0748378	−	0.997196i	$-0.476156\pi$
$521$	3.41641	0.149676	0.0748378	+	0.997196i	$0.476156\pi$
$522$	−11.3475	−0.496668
$523$	2.58359	0.112973	0.0564863	−	0.998403i	$-0.482010\pi$
$523$	2.58359	0.112973	0.0564863	+	0.998403i	$0.482010\pi$
$524$	−7.14590	−0.312170
$525$	−11.0983	−0.484370
$526$	−16.0000	−0.697633
$527$	−4.47214	−0.194809
$528$	0	0
$529$	11.2705	0.490022
$530$	19.3050	0.838554
$531$	16.1115	0.699178
$532$	2.85410	0.123741
$533$	33.8885	1.46788
$534$	−10.1115	−0.437566
$535$	18.4721	0.798620
$536$	4.76393	0.205771
$537$	23.6393	1.02011
$538$	−6.29180	−0.271259
$539$	0	0
$540$	15.7771	0.678938
$541$	−8.14590	−0.350220	−0.175110	−	0.984549i	$-0.556028\pi$
$541$	−8.14590	−0.350220	−0.175110	+	0.984549i	$0.556028\pi$
$542$	16.9098	0.726339
$543$	26.4721	1.13603
$544$	−0.618034	−0.0264980
$545$	−48.3607	−2.07154
$546$	14.1115	0.603915
$547$	−19.3050	−0.825420	−0.412710	−	0.910862i	$-0.635418\pi$
$547$	−19.3050	−0.825420	−0.412710	+	0.910862i	$0.635418\pi$
$548$	10.5623	0.451199
$549$	−11.5623	−0.493467
$550$	0	0
$551$	7.70820	0.328381
$552$	7.23607	0.307988
$553$	−13.5967	−0.578193
$554$	−11.5279	−0.489772
$555$	−4.36068	−0.185101
$556$	−2.90983	−0.123404
$557$	−34.8541	−1.47682	−0.738408	−	0.674354i	$-0.764422\pi$
$557$	−34.8541	−1.47682	−0.738408	+	0.674354i	$0.764422\pi$
$558$	−10.6525	−0.450955
$559$	21.5279	0.910532
$560$	8.14590	0.344227
$561$	0	0
$562$	−4.00000	−0.168730
$563$	−15.0557	−0.634523	−0.317262	−	0.948338i	$-0.602763\pi$
$563$	−15.0557	−0.634523	−0.317262	+	0.948338i	$0.602763\pi$
$564$	7.23607	0.304693
$565$	47.0132	1.97786
$566$	−3.14590	−0.132232
$567$	6.89667	0.289633
$568$	7.23607	0.303619
$569$	8.18034	0.342938	0.171469	−	0.985190i	$-0.445149\pi$
$569$	8.18034	0.342938	0.171469	+	0.985190i	$0.445149\pi$
$570$	−3.52786	−0.147766
$571$	37.2148	1.55739	0.778695	−	0.627403i	$-0.215882\pi$
$571$	37.2148	1.55739	0.778695	+	0.627403i	$0.215882\pi$
$572$	0	0
$573$	−19.3050	−0.806476
$574$	24.1803	1.00927
$575$	−18.4164	−0.768017
$576$	−1.47214	−0.0613390
$577$	−23.3050	−0.970198	−0.485099	−	0.874459i	$-0.661216\pi$
$577$	−23.3050	−0.970198	−0.485099	+	0.874459i	$0.661216\pi$
$578$	16.6180	0.691219
$579$	11.7771	0.489439
$580$	22.0000	0.913500
$581$	25.2705	1.04840
$582$	1.16718	0.0483813
$583$	0	0
$584$	6.94427	0.287356
$585$	16.8065	0.694863
$586$	−24.0000	−0.991431
$587$	42.4721	1.75301	0.876506	−	0.481390i	$-0.159868\pi$
$587$	42.4721	1.75301	0.876506	+	0.481390i	$0.159868\pi$
$588$	1.41641	0.0584117
$589$	7.23607	0.298157
$590$	−31.2361	−1.28597
$591$	−8.58359	−0.353082
$592$	1.23607	0.0508021
$593$	31.7426	1.30351	0.651757	−	0.758428i	$-0.274032\pi$
$593$	31.7426	1.30351	0.651757	+	0.758428i	$0.274032\pi$
$594$	0	0
$595$	5.03444	0.206392
$596$	12.4721	0.510879
$597$	30.1378	1.23346
$598$	23.4164	0.957568
$599$	2.58359	0.105563	0.0527814	−	0.998606i	$-0.483191\pi$
$599$	2.58359	0.105563	0.0527814	+	0.998606i	$0.483191\pi$
$600$	−3.88854	−0.158749
$601$	33.3050	1.35854	0.679269	−	0.733890i	$-0.262297\pi$
$601$	33.3050	1.35854	0.679269	+	0.733890i	$0.262297\pi$
$602$	15.3607	0.626055
$603$	7.01316	0.285598
$604$	15.2361	0.619947
$605$	0	0
$606$	−20.4721	−0.831624
$607$	4.76393	0.193362	0.0966810	−	0.995315i	$-0.469177\pi$
$607$	4.76393	0.193362	0.0966810	+	0.995315i	$0.469177\pi$
$608$	1.00000	0.0405554
$609$	27.1935	1.10194
$610$	22.4164	0.907614
$611$	23.4164	0.947326
$612$	−0.909830	−0.0367777
$613$	−31.2705	−1.26300	−0.631502	−	0.775374i	$-0.717561\pi$
$613$	−31.2705	−1.26300	−0.631502	+	0.775374i	$0.717561\pi$
$614$	−10.4721	−0.422621
$615$	−29.8885	−1.20522
$616$	0	0
$617$	−42.3607	−1.70538	−0.852688	−	0.522420i	$-0.825029\pi$
$617$	−42.3607	−1.70538	−0.852688	+	0.522420i	$0.825029\pi$
$618$	−13.5279	−0.544170
$619$	0.729490	0.0293207	0.0146603	−	0.999893i	$-0.495333\pi$
$619$	0.729490	0.0293207	0.0146603	+	0.999893i	$0.495333\pi$
$620$	20.6525	0.829423
$621$	32.3607	1.29859
$622$	−25.5623	−1.02496
$623$	−23.3475	−0.935399
$624$	4.94427	0.197929
$625$	−30.8328	−1.23331
$626$	−22.5066	−0.899544
$627$	0	0
$628$	−6.67376	−0.266312
$629$	0.763932	0.0304600
$630$	11.9919	0.477768
$631$	−22.4721	−0.894602	−0.447301	−	0.894384i	$-0.647615\pi$
$631$	−22.4721	−0.894602	−0.447301	+	0.894384i	$0.647615\pi$
$632$	−4.76393	−0.189499
$633$	3.63932	0.144650
$634$	−0.472136	−0.0187509
$635$	−44.8328	−1.77914
$636$	8.36068	0.331523
$637$	4.58359	0.181609
$638$	0	0
$639$	10.6525	0.421405
$640$	2.85410	0.112818
$641$	37.8885	1.49651	0.748254	−	0.663413i	$-0.230893\pi$
$641$	37.8885	1.49651	0.748254	+	0.663413i	$0.230893\pi$
$642$	8.00000	0.315735
$643$	13.6738	0.539241	0.269620	−	0.962967i	$-0.413102\pi$
$643$	13.6738	0.539241	0.269620	+	0.962967i	$0.413102\pi$
$644$	16.7082	0.658395
$645$	−18.9868	−0.747606
$646$	0.618034	0.0243162
$647$	29.3050	1.15210	0.576048	−	0.817416i	$-0.304594\pi$
$647$	29.3050	1.15210	0.576048	+	0.817416i	$0.304594\pi$
$648$	2.41641	0.0949255
$649$	0	0
$650$	−12.5836	−0.493569
$651$	25.5279	1.00052
$652$	−16.2705	−0.637202
$653$	25.3820	0.993273	0.496637	−	0.867959i	$-0.334568\pi$
$653$	25.3820	0.993273	0.496637	+	0.867959i	$0.334568\pi$
$654$	−20.9443	−0.818986
$655$	20.3951	0.796903
$656$	8.47214	0.330781
$657$	10.2229	0.398834
$658$	16.7082	0.651354
$659$	−2.58359	−0.100642	−0.0503212	−	0.998733i	$-0.516025\pi$
$659$	−2.58359	−0.100642	−0.0503212	+	0.998733i	$0.516025\pi$
$660$	0	0
$661$	7.41641	0.288465	0.144232	−	0.989544i	$-0.453929\pi$
$661$	7.41641	0.288465	0.144232	+	0.989544i	$0.453929\pi$
$662$	1.52786	0.0593821
$663$	3.05573	0.118675
$664$	8.85410	0.343606
$665$	−8.14590	−0.315884
$666$	1.81966	0.0705104
$667$	45.1246	1.74723
$668$	−19.7082	−0.762533
$669$	25.5279	0.986964
$670$	−13.5967	−0.525288
$671$	0	0
$672$	3.52786	0.136090
$673$	−6.65248	−0.256434	−0.128217	−	0.991746i	$-0.540925\pi$
$673$	−6.65248	−0.256434	−0.128217	+	0.991746i	$0.540925\pi$
$674$	3.81966	0.147128
$675$	−17.3901	−0.669345
$676$	3.00000	0.115385
$677$	−9.41641	−0.361902	−0.180951	−	0.983492i	$-0.557918\pi$
$677$	−9.41641	−0.361902	−0.180951	+	0.983492i	$0.557918\pi$
$678$	20.3607	0.781947
$679$	2.69505	0.103426
$680$	1.76393	0.0676437
$681$	4.72136	0.180923
$682$	0	0
$683$	3.70820	0.141890	0.0709452	−	0.997480i	$-0.477398\pi$
$683$	3.70820	0.141890	0.0709452	+	0.997480i	$0.477398\pi$
$684$	1.47214	0.0562885
$685$	−30.1459	−1.15182
$686$	−16.7082	−0.637922
$687$	−5.12461	−0.195516
$688$	5.38197	0.205186
$689$	27.0557	1.03074
$690$	−20.6525	−0.786226
$691$	−37.2148	−1.41572	−0.707859	−	0.706354i	$-0.750339\pi$
$691$	−37.2148	−1.41572	−0.707859	+	0.706354i	$0.750339\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	−20.7984	−0.789495
$695$	8.30495	0.315025
$696$	9.52786	0.361153
$697$	5.23607	0.198330
$698$	25.3262	0.958612
$699$	−18.9443	−0.716538
$700$	−8.97871	−0.339363
$701$	−30.9098	−1.16745	−0.583724	−	0.811952i	$-0.698405\pi$
$701$	−30.9098	−1.16745	−0.583724	+	0.811952i	$0.698405\pi$
$702$	22.1115	0.834543
$703$	−1.23607	−0.0466192
$704$	0	0
$705$	−20.6525	−0.777817
$706$	−30.9230	−1.16380
$707$	−47.2705	−1.77779
$708$	−13.5279	−0.508408
$709$	16.9656	0.637155	0.318577	−	0.947897i	$-0.396795\pi$
$709$	16.9656	0.637155	0.318577	+	0.947897i	$0.396795\pi$
$710$	−20.6525	−0.775074
$711$	−7.01316	−0.263014
$712$	−8.18034	−0.306571
$713$	42.3607	1.58642
$714$	2.18034	0.0815972
$715$	0	0
$716$	19.1246	0.714720
$717$	−0.403252	−0.0150597
$718$	−26.7984	−1.00011
$719$	−42.2705	−1.57642	−0.788212	−	0.615404i	$-0.788993\pi$
$719$	−42.2705	−1.57642	−0.788212	+	0.615404i	$0.788993\pi$
$720$	4.20163	0.156585
$721$	−31.2361	−1.16329
$722$	−1.00000	−0.0372161
$723$	35.1935	1.30886
$724$	21.4164	0.795935
$725$	−24.2492	−0.900594
$726$	0	0
$727$	−35.1591	−1.30398	−0.651989	−	0.758229i	$-0.726065\pi$
$727$	−35.1591	−1.30398	−0.651989	+	0.758229i	$0.726065\pi$
$728$	11.4164	0.423120
$729$	24.0557	0.890953
$730$	−19.8197	−0.733559
$731$	3.32624	0.123025
$732$	9.70820	0.358826
$733$	3.79837	0.140296	0.0701481	−	0.997537i	$-0.477653\pi$
$733$	3.79837	0.140296	0.0701481	+	0.997537i	$0.477653\pi$
$734$	2.09017	0.0771496
$735$	−4.04257	−0.149113
$736$	5.85410	0.215785
$737$	0	0
$738$	12.4721	0.459106
$739$	−5.21478	−0.191829	−0.0959144	−	0.995390i	$-0.530578\pi$
$739$	−5.21478	−0.191829	−0.0959144	+	0.995390i	$0.530578\pi$
$740$	−3.52786	−0.129687
$741$	−4.94427	−0.181632
$742$	19.3050	0.708707
$743$	23.4164	0.859065	0.429532	−	0.903051i	$-0.358678\pi$
$743$	23.4164	0.859065	0.429532	+	0.903051i	$0.358678\pi$
$744$	8.94427	0.327913
$745$	−35.5967	−1.30416
$746$	−9.52786	−0.348840
$747$	13.0344	0.476905
$748$	0	0
$749$	18.4721	0.674957
$750$	−6.54102	−0.238844
$751$	−2.11146	−0.0770481	−0.0385241	−	0.999258i	$-0.512266\pi$
$751$	−2.11146	−0.0770481	−0.0385241	+	0.999258i	$0.512266\pi$
$752$	5.85410	0.213477
$753$	−18.0689	−0.658467
$754$	30.8328	1.12286
$755$	−43.4853	−1.58259
$756$	15.7771	0.573807
$757$	−14.3607	−0.521948	−0.260974	−	0.965346i	$-0.584044\pi$
$757$	−14.3607	−0.521948	−0.260974	+	0.965346i	$0.584044\pi$
$758$	27.8885	1.01296
$759$	0	0
$760$	−2.85410	−0.103529
$761$	40.4721	1.46711	0.733557	−	0.679628i	$-0.237859\pi$
$761$	40.4721	1.46711	0.733557	+	0.679628i	$0.237859\pi$
$762$	−19.4164	−0.703382
$763$	−48.3607	−1.75077
$764$	−15.6180	−0.565041
$765$	2.59675	0.0938856
$766$	−12.6525	−0.457153
$767$	−43.7771	−1.58070
$768$	1.23607	0.0446028
$769$	−20.2705	−0.730973	−0.365487	−	0.930817i	$-0.619097\pi$
$769$	−20.2705	−0.730973	−0.365487	+	0.930817i	$0.619097\pi$
$770$	0	0
$771$	5.16718	0.186092
$772$	9.52786	0.342915
$773$	−30.3607	−1.09200	−0.545999	−	0.837786i	$-0.683850\pi$
$773$	−30.3607	−1.09200	−0.545999	+	0.837786i	$0.683850\pi$
$774$	7.92299	0.284786
$775$	−22.7639	−0.817705
$776$	0.944272	0.0338974
$777$	−4.36068	−0.156439
$778$	31.2705	1.12110
$779$	−8.47214	−0.303546
$780$	−14.1115	−0.505271
$781$	0	0
$782$	3.61803	0.129381
$783$	42.6099	1.52275
$784$	1.14590	0.0409249
$785$	19.0476	0.679838
$786$	8.83282	0.315056
$787$	9.41641	0.335659	0.167829	−	0.985816i	$-0.446324\pi$
$787$	9.41641	0.335659	0.167829	+	0.985816i	$0.446324\pi$
$788$	−6.94427	−0.247379
$789$	19.7771	0.704083
$790$	13.5967	0.483751
$791$	47.0132	1.67160
$792$	0	0
$793$	31.4164	1.11563
$794$	3.56231	0.126422
$795$	−23.8622	−0.846306
$796$	24.3820	0.864196
$797$	34.0000	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$798$	−3.52786	−0.124885
$799$	3.61803	0.127997
$800$	−3.14590	−0.111224
$801$	−12.0426	−0.425503
$802$	14.7639	0.521333
$803$	0	0
$804$	−5.88854	−0.207673
$805$	−47.6869	−1.68074
$806$	28.9443	1.01952
$807$	7.77709	0.273766
$808$	−16.5623	−0.582660
$809$	−23.9098	−0.840625	−0.420312	−	0.907379i	$-0.638080\pi$
$809$	−23.9098	−0.840625	−0.420312	+	0.907379i	$0.638080\pi$
$810$	−6.89667	−0.242324
$811$	17.2361	0.605240	0.302620	−	0.953111i	$-0.402139\pi$
$811$	17.2361	0.605240	0.302620	+	0.953111i	$0.402139\pi$
$812$	22.0000	0.772049
$813$	−20.9017	−0.733055
$814$	0	0
$815$	46.4377	1.62664
$816$	0.763932	0.0267430
$817$	−5.38197	−0.188291
$818$	38.4721	1.34515
$819$	16.8065	0.587267
$820$	−24.1803	−0.844414
$821$	−45.3820	−1.58384	−0.791921	−	0.610624i	$-0.790919\pi$
$821$	−45.3820	−1.58384	−0.791921	+	0.610624i	$0.790919\pi$
$822$	−13.0557	−0.455371
$823$	40.7426	1.42020	0.710100	−	0.704101i	$-0.248650\pi$
$823$	40.7426	1.42020	0.710100	+	0.704101i	$0.248650\pi$
$824$	−10.9443	−0.381262
$825$	0	0
$826$	−31.2361	−1.08684
$827$	−46.0689	−1.60197	−0.800986	−	0.598683i	$-0.795691\pi$
$827$	−46.0689	−1.60197	−0.800986	+	0.598683i	$0.795691\pi$
$828$	8.61803	0.299497
$829$	−2.36068	−0.0819898	−0.0409949	−	0.999159i	$-0.513053\pi$
$829$	−2.36068	−0.0819898	−0.0409949	+	0.999159i	$0.513053\pi$
$830$	−25.2705	−0.877152
$831$	14.2492	0.494300
$832$	4.00000	0.138675
$833$	0.708204	0.0245378
$834$	3.59675	0.124545
$835$	56.2492	1.94658
$836$	0	0
$837$	40.0000	1.38260
$838$	−13.7426	−0.474732
$839$	−53.0132	−1.83022	−0.915109	−	0.403207i	$-0.867895\pi$
$839$	−53.0132	−1.83022	−0.915109	+	0.403207i	$0.867895\pi$
$840$	−10.0689	−0.347409
$841$	30.4164	1.04884
$842$	−15.5279	−0.535126
$843$	4.94427	0.170290
$844$	2.94427	0.101346
$845$	−8.56231	−0.294552
$846$	8.61803	0.296294
$847$	0	0
$848$	6.76393	0.232274
$849$	3.88854	0.133454
$850$	−1.94427	−0.0666880
$851$	−7.23607	−0.248049
$852$	−8.94427	−0.306426
$853$	−0.145898	−0.00499545	−0.00249773	−	0.999997i	$-0.500795\pi$
$853$	−0.145898	−0.00499545	−0.00249773	+	0.999997i	$0.500795\pi$
$854$	22.4164	0.767074
$855$	−4.20163	−0.143693
$856$	6.47214	0.221213
$857$	26.8328	0.916592	0.458296	−	0.888800i	$-0.348460\pi$
$857$	26.8328	0.916592	0.458296	+	0.888800i	$0.348460\pi$
$858$	0	0
$859$	−22.0344	−0.751805	−0.375903	−	0.926659i	$-0.622667\pi$
$859$	−22.0344	−0.751805	−0.375903	+	0.926659i	$0.622667\pi$
$860$	−15.3607	−0.523795
$861$	−29.8885	−1.01860
$862$	37.4164	1.27441
$863$	−23.2361	−0.790965	−0.395482	−	0.918474i	$-0.629423\pi$
$863$	−23.2361	−0.790965	−0.395482	+	0.918474i	$0.629423\pi$
$864$	5.52786	0.188062
$865$	11.4164	0.388170
$866$	23.8885	0.811766
$867$	−20.5410	−0.697610
$868$	20.6525	0.700991
$869$	0	0
$870$	−27.1935	−0.921946
$871$	−19.0557	−0.645679
$872$	−16.9443	−0.573805
$873$	1.39010	0.0470476
$874$	−5.85410	−0.198018
$875$	−15.1033	−0.510586
$876$	−8.58359	−0.290013
$877$	−1.34752	−0.0455027	−0.0227513	−	0.999741i	$-0.507243\pi$
$877$	−1.34752	−0.0455027	−0.0227513	+	0.999741i	$0.507243\pi$
$878$	−26.3607	−0.889630
$879$	29.6656	1.00060
$880$	0	0
$881$	−21.4164	−0.721537	−0.360769	−	0.932655i	$-0.617486\pi$
$881$	−21.4164	−0.721537	−0.360769	+	0.932655i	$0.617486\pi$
$882$	1.68692	0.0568015
$883$	−1.03444	−0.0348117	−0.0174059	−	0.999849i	$-0.505541\pi$
$883$	−1.03444	−0.0348117	−0.0174059	+	0.999849i	$0.505541\pi$
$884$	2.47214	0.0831469
$885$	38.6099	1.29786
$886$	−12.2705	−0.412236
$887$	−27.3050	−0.916811	−0.458405	−	0.888743i	$-0.651579\pi$
$887$	−27.3050	−0.916811	−0.458405	+	0.888743i	$0.651579\pi$
$888$	−1.52786	−0.0512718
$889$	−44.8328	−1.50364
$890$	23.3475	0.782611
$891$	0	0
$892$	20.6525	0.691496
$893$	−5.85410	−0.195900
$894$	−15.4164	−0.515602
$895$	−54.5836	−1.82453
$896$	2.85410	0.0953489
$897$	−28.9443	−0.966421
$898$	−2.29180	−0.0764782
$899$	55.7771	1.86027
$900$	−4.63119	−0.154373
$901$	4.18034	0.139267
$902$	0	0
$903$	−18.9868	−0.631843
$904$	16.4721	0.547855
$905$	−61.1246	−2.03185
$906$	−18.8328	−0.625678
$907$	48.6525	1.61548	0.807739	−	0.589540i	$-0.200691\pi$
$907$	48.6525	1.61548	0.807739	+	0.589540i	$0.200691\pi$
$908$	3.81966	0.126760
$909$	−24.3820	−0.808699
$910$	−32.5836	−1.08014
$911$	−25.5967	−0.848058	−0.424029	−	0.905649i	$-0.639385\pi$
$911$	−25.5967	−0.848058	−0.424029	+	0.905649i	$0.639385\pi$
$912$	−1.23607	−0.0409303
$913$	0	0
$914$	−0.0901699	−0.00298256
$915$	−27.7082	−0.916005
$916$	−4.14590	−0.136984
$917$	20.3951	0.673506
$918$	3.41641	0.112758
$919$	38.6312	1.27433	0.637163	−	0.770729i	$-0.280108\pi$
$919$	38.6312	1.27433	0.637163	+	0.770729i	$0.280108\pi$
$920$	−16.7082	−0.550853
$921$	12.9443	0.426528
$922$	29.6869	0.977687
$923$	−28.9443	−0.952712
$924$	0	0
$925$	3.88854	0.127855
$926$	−39.2148	−1.28868
$927$	−16.1115	−0.529170
$928$	7.70820	0.253034
$929$	−47.3820	−1.55455	−0.777276	−	0.629160i	$-0.783399\pi$
$929$	−47.3820	−1.55455	−0.777276	+	0.629160i	$0.783399\pi$
$930$	−25.5279	−0.837092
$931$	−1.14590	−0.0375553
$932$	−15.3262	−0.502028
$933$	31.5967	1.03443
$934$	24.2705	0.794155
$935$	0	0
$936$	5.88854	0.192473
$937$	46.5066	1.51930	0.759652	−	0.650330i	$-0.225369\pi$
$937$	46.5066	1.51930	0.759652	+	0.650330i	$0.225369\pi$
$938$	−13.5967	−0.443950
$939$	27.8197	0.907860
$940$	−16.7082	−0.544962
$941$	−25.2361	−0.822672	−0.411336	−	0.911484i	$-0.634938\pi$
$941$	−25.2361	−0.822672	−0.411336	+	0.911484i	$0.634938\pi$
$942$	8.24922	0.268774
$943$	−49.5967	−1.61509
$944$	−10.9443	−0.356206
$945$	−45.0294	−1.46481
$946$	0	0
$947$	−39.5066	−1.28379	−0.641896	−	0.766792i	$-0.721852\pi$
$947$	−39.5066	−1.28379	−0.641896	+	0.766792i	$0.721852\pi$
$948$	5.88854	0.191251
$949$	−27.7771	−0.901682
$950$	3.14590	0.102066
$951$	0.583592	0.0189243
$952$	1.76393	0.0571694
$953$	53.0132	1.71726	0.858632	−	0.512592i	$-0.171315\pi$
$953$	53.0132	1.71726	0.858632	+	0.512592i	$0.171315\pi$
$954$	9.95743	0.322384
$955$	44.5755	1.44243
$956$	−0.326238	−0.0105513
$957$	0	0
$958$	31.0902	1.00448
$959$	−30.1459	−0.973462
$960$	−3.52786	−0.113861
$961$	21.3607	0.689054
$962$	−4.94427	−0.159410
$963$	9.52786	0.307031
$964$	28.4721	0.917026
$965$	−27.1935	−0.875390
$966$	−20.6525	−0.664483
$967$	42.1459	1.35532	0.677660	−	0.735375i	$-0.262994\pi$
$967$	42.1459	1.35532	0.677660	+	0.735375i	$0.262994\pi$
$968$	0	0
$969$	−0.763932	−0.0245410
$970$	−2.69505	−0.0865328
$971$	−15.0557	−0.483161	−0.241581	−	0.970381i	$-0.577666\pi$
$971$	−15.0557	−0.483161	−0.241581	+	0.970381i	$0.577666\pi$
$972$	13.5967	0.436116
$973$	8.30495	0.266245
$974$	5.41641	0.173553
$975$	15.5542	0.498132
$976$	7.85410	0.251404
$977$	−46.8328	−1.49831	−0.749157	−	0.662392i	$-0.769541\pi$
$977$	−46.8328	−1.49831	−0.749157	+	0.662392i	$0.769541\pi$
$978$	20.1115	0.643093
$979$	0	0
$980$	−3.27051	−0.104473
$981$	−24.9443	−0.796409
$982$	18.7426	0.598102
$983$	27.4164	0.874448	0.437224	−	0.899353i	$-0.355962\pi$
$983$	27.4164	0.874448	0.437224	+	0.899353i	$0.355962\pi$
$984$	−10.4721	−0.333840
$985$	19.8197	0.631507
$986$	4.76393	0.151715
$987$	−20.6525	−0.657376
$988$	−4.00000	−0.127257
$989$	−31.5066	−1.00185
$990$	0	0
$991$	−4.94427	−0.157060	−0.0785300	−	0.996912i	$-0.525023\pi$
$991$	−4.94427	−0.157060	−0.0785300	+	0.996912i	$0.525023\pi$
$992$	7.23607	0.229745
$993$	−1.88854	−0.0599311
$994$	−20.6525	−0.655057
$995$	−69.5886	−2.20611
$996$	−10.9443	−0.346783
$997$	24.9230	0.789319	0.394659	−	0.918827i	$-0.370863\pi$
$997$	24.9230	0.789319	0.394659	+	0.918827i	$0.370863\pi$
$998$	−9.03444	−0.285980
$999$	−6.83282	−0.216181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.v.1.2		2
11.7	odd	10		418.2.f.a.115.1	✓	4
11.8	odd	10		418.2.f.a.229.1	yes	4
11.10	odd	2		4598.2.a.be.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.a.115.1	✓	4	11.7	odd	10
418.2.f.a.229.1	yes	4	11.8	odd	10
4598.2.a.v.1.2		2	1.1	even	1	trivial
4598.2.a.be.1.2		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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -2.85410 q^{5} -1.23607 q^{6} -2.85410 q^{7} -1.00000 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -2.85410 q^{5} -1.23607 q^{6} -2.85410 q^{7} -1.00000 q^{8} -1.47214 q^{9} +2.85410 q^{10} +1.23607 q^{12} +4.00000 q^{13} +2.85410 q^{14} -3.52786 q^{15} +1.00000 q^{16} +0.618034 q^{17} +1.47214 q^{18} -1.00000 q^{19} -2.85410 q^{20} -3.52786 q^{21} -5.85410 q^{23} -1.23607 q^{24} +3.14590 q^{25} -4.00000 q^{26} -5.52786 q^{27} -2.85410 q^{28} -7.70820 q^{29} +3.52786 q^{30} -7.23607 q^{31} -1.00000 q^{32} -0.618034 q^{34} +8.14590 q^{35} -1.47214 q^{36} +1.23607 q^{37} +1.00000 q^{38} +4.94427 q^{39} +2.85410 q^{40} +8.47214 q^{41} +3.52786 q^{42} +5.38197 q^{43} +4.20163 q^{45} +5.85410 q^{46} +5.85410 q^{47} +1.23607 q^{48} +1.14590 q^{49} -3.14590 q^{50} +0.763932 q^{51} +4.00000 q^{52} +6.76393 q^{53} +5.52786 q^{54} +2.85410 q^{56} -1.23607 q^{57} +7.70820 q^{58} -10.9443 q^{59} -3.52786 q^{60} +7.85410 q^{61} +7.23607 q^{62} +4.20163 q^{63} +1.00000 q^{64} -11.4164 q^{65} -4.76393 q^{67} +0.618034 q^{68} -7.23607 q^{69} -8.14590 q^{70} -7.23607 q^{71} +1.47214 q^{72} -6.94427 q^{73} -1.23607 q^{74} +3.88854 q^{75} -1.00000 q^{76} -4.94427 q^{78} +4.76393 q^{79} -2.85410 q^{80} -2.41641 q^{81} -8.47214 q^{82} -8.85410 q^{83} -3.52786 q^{84} -1.76393 q^{85} -5.38197 q^{86} -9.52786 q^{87} +8.18034 q^{89} -4.20163 q^{90} -11.4164 q^{91} -5.85410 q^{92} -8.94427 q^{93} -5.85410 q^{94} +2.85410 q^{95} -1.23607 q^{96} -0.944272 q^{97} -1.14590 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9} - q^{10} - 2 q^{12} + 8 q^{13} - q^{14} - 16 q^{15} + 2 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + q^{20} - 16 q^{21} - 5 q^{23} + 2 q^{24} + 13 q^{25} - 8 q^{26} - 20 q^{27} + q^{28} - 2 q^{29} + 16 q^{30} - 10 q^{31} - 2 q^{32} + q^{34} + 23 q^{35} + 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{39} - q^{40} + 8 q^{41} + 16 q^{42} + 13 q^{43} + 33 q^{45} + 5 q^{46} + 5 q^{47} - 2 q^{48} + 9 q^{49} - 13 q^{50} + 6 q^{51} + 8 q^{52} + 18 q^{53} + 20 q^{54} - q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} - 16 q^{60} + 9 q^{61} + 10 q^{62} + 33 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{67} - q^{68} - 10 q^{69} - 23 q^{70} - 10 q^{71} - 6 q^{72} + 4 q^{73} + 2 q^{74} - 28 q^{75} - 2 q^{76} + 8 q^{78} + 14 q^{79} + q^{80} + 22 q^{81} - 8 q^{82} - 11 q^{83} - 16 q^{84} - 8 q^{85} - 13 q^{86} - 28 q^{87} - 6 q^{89} - 33 q^{90} + 4 q^{91} - 5 q^{92} - 5 q^{94} - q^{95} + 2 q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9 - q^10 - 2 * q^12 + 8 * q^13 - q^14 - 16 * q^15 + 2 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + q^20 - 16 * q^21 - 5 * q^23 + 2 * q^24 + 13 * q^25 - 8 * q^26 - 20 * q^27 + q^28 - 2 * q^29 + 16 * q^30 - 10 * q^31 - 2 * q^32 + q^34 + 23 * q^35 + 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^39 - q^40 + 8 * q^41 + 16 * q^42 + 13 * q^43 + 33 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 + 9 * q^49 - 13 * q^50 + 6 * q^51 + 8 * q^52 + 18 * q^53 + 20 * q^54 - q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 - 16 * q^60 + 9 * q^61 + 10 * q^62 + 33 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^67 - q^68 - 10 * q^69 - 23 * q^70 - 10 * q^71 - 6 * q^72 + 4 * q^73 + 2 * q^74 - 28 * q^75 - 2 * q^76 + 8 * q^78 + 14 * q^79 + q^80 + 22 * q^81 - 8 * q^82 - 11 * q^83 - 16 * q^84 - 8 * q^85 - 13 * q^86 - 28 * q^87 - 6 * q^89 - 33 * q^90 + 4 * q^91 - 5 * q^92 - 5 * q^94 - q^95 + 2 * q^96 + 16 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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