LMFDB - Embedded newform 4598.2.a.cd.1.4

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
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			1.4
Root			$-1.28398$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.28398 q^{3} +1.00000 q^{4} -1.35936 q^{5} -1.28398 q^{6} -3.16828 q^{7} +1.00000 q^{8} -1.35139 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.28398 q^{3} +1.00000 q^{4} -1.35936 q^{5} -1.28398 q^{6} -3.16828 q^{7} +1.00000 q^{8} -1.35139 q^{9} -1.35936 q^{10} -1.28398 q^{12} -0.907331 q^{13} -3.16828 q^{14} +1.74539 q^{15} +1.00000 q^{16} -2.83364 q^{17} -1.35139 q^{18} +1.00000 q^{19} -1.35936 q^{20} +4.06801 q^{21} +2.86075 q^{23} -1.28398 q^{24} -3.15215 q^{25} -0.907331 q^{26} +5.58711 q^{27} -3.16828 q^{28} +4.97073 q^{29} +1.74539 q^{30} -7.84147 q^{31} +1.00000 q^{32} -2.83364 q^{34} +4.30681 q^{35} -1.35139 q^{36} -6.25846 q^{37} +1.00000 q^{38} +1.16500 q^{39} -1.35936 q^{40} -10.7884 q^{41} +4.06801 q^{42} +0.172752 q^{43} +1.83702 q^{45} +2.86075 q^{46} -5.76623 q^{47} -1.28398 q^{48} +3.03797 q^{49} -3.15215 q^{50} +3.63835 q^{51} -0.907331 q^{52} +13.5008 q^{53} +5.58711 q^{54} -3.16828 q^{56} -1.28398 q^{57} +4.97073 q^{58} +0.804852 q^{59} +1.74539 q^{60} +10.0100 q^{61} -7.84147 q^{62} +4.28157 q^{63} +1.00000 q^{64} +1.23339 q^{65} +11.5211 q^{67} -2.83364 q^{68} -3.67315 q^{69} +4.30681 q^{70} -13.1925 q^{71} -1.35139 q^{72} +3.55023 q^{73} -6.25846 q^{74} +4.04731 q^{75} +1.00000 q^{76} +1.16500 q^{78} -5.66991 q^{79} -1.35936 q^{80} -3.11959 q^{81} -10.7884 q^{82} +3.19923 q^{83} +4.06801 q^{84} +3.85193 q^{85} +0.172752 q^{86} -6.38234 q^{87} +18.5862 q^{89} +1.83702 q^{90} +2.87467 q^{91} +2.86075 q^{92} +10.0683 q^{93} -5.76623 q^{94} -1.35936 q^{95} -1.28398 q^{96} +4.04401 q^{97} +3.03797 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * 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
$3$	−1.28398	−0.741308	−0.370654	−	0.928771i	$-0.620866\pi$
$3$	−1.28398	−0.741308	−0.370654	+	0.928771i	$0.620866\pi$
$4$	1.00000	0.500000
$5$	−1.35936	−0.607922	−0.303961	−	0.952684i	$-0.598309\pi$
$5$	−1.35936	−0.607922	−0.303961	+	0.952684i	$0.598309\pi$
$6$	−1.28398	−0.524184
$7$	−3.16828	−1.19750	−0.598748	−	0.800938i	$-0.704335\pi$
$7$	−3.16828	−1.19750	−0.598748	+	0.800938i	$0.704335\pi$
$8$	1.00000	0.353553
$9$	−1.35139	−0.450462
$10$	−1.35936	−0.429866
$11$	0	0
$11$	0	0
$12$	−1.28398	−0.370654
$13$	−0.907331	−0.251648	−0.125824	−	0.992053i	$-0.540158\pi$
$13$	−0.907331	−0.251648	−0.125824	+	0.992053i	$0.540158\pi$
$14$	−3.16828	−0.846757
$15$	1.74539	0.450658
$16$	1.00000	0.250000
$17$	−2.83364	−0.687259	−0.343630	−	0.939105i	$-0.611656\pi$
$17$	−2.83364	−0.687259	−0.343630	+	0.939105i	$0.611656\pi$
$18$	−1.35139	−0.318525
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.35936	−0.303961
$21$	4.06801	0.887713
$22$	0	0
$23$	2.86075	0.596507	0.298254	−	0.954487i	$-0.403596\pi$
$23$	2.86075	0.596507	0.298254	+	0.954487i	$0.403596\pi$
$24$	−1.28398	−0.262092
$25$	−3.15215	−0.630430
$26$	−0.907331	−0.177942
$27$	5.58711	1.07524
$28$	−3.16828	−0.598748
$29$	4.97073	0.923042	0.461521	−	0.887129i	$-0.347304\pi$
$29$	4.97073	0.923042	0.461521	+	0.887129i	$0.347304\pi$
$30$	1.74539	0.318663
$31$	−7.84147	−1.40837	−0.704185	−	0.710017i	$-0.748687\pi$
$31$	−7.84147	−1.40837	−0.704185	+	0.710017i	$0.748687\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.83364	−0.485966
$35$	4.30681	0.727984
$36$	−1.35139	−0.225231
$37$	−6.25846	−1.02888	−0.514442	−	0.857525i	$-0.672001\pi$
$37$	−6.25846	−1.02888	−0.514442	+	0.857525i	$0.672001\pi$
$38$	1.00000	0.162221
$39$	1.16500	0.186549
$40$	−1.35936	−0.214933
$41$	−10.7884	−1.68486	−0.842430	−	0.538807i	$-0.818875\pi$
$41$	−10.7884	−1.68486	−0.842430	+	0.538807i	$0.818875\pi$
$42$	4.06801	0.627708
$43$	0.172752	0.0263445	0.0131722	−	0.999913i	$-0.495807\pi$
$43$	0.172752	0.0263445	0.0131722	+	0.999913i	$0.495807\pi$
$44$	0	0
$45$	1.83702	0.273846
$46$	2.86075	0.421794
$47$	−5.76623	−0.841091	−0.420546	−	0.907271i	$-0.638161\pi$
$47$	−5.76623	−0.841091	−0.420546	+	0.907271i	$0.638161\pi$
$48$	−1.28398	−0.185327
$49$	3.03797	0.433996
$50$	−3.15215	−0.445782
$51$	3.63835	0.509471
$52$	−0.907331	−0.125824
$53$	13.5008	1.85448	0.927238	−	0.374473i	$-0.122176\pi$
$53$	13.5008	1.85448	0.927238	+	0.374473i	$0.122176\pi$
$54$	5.58711	0.760309
$55$	0	0
$56$	−3.16828	−0.423379
$57$	−1.28398	−0.170068
$58$	4.97073	0.652689
$59$	0.804852	0.104783	0.0523914	−	0.998627i	$-0.483316\pi$
$59$	0.804852	0.104783	0.0523914	+	0.998627i	$0.483316\pi$
$60$	1.74539	0.225329
$61$	10.0100	1.28165	0.640826	−	0.767686i	$-0.278592\pi$
$61$	10.0100	1.28165	0.640826	+	0.767686i	$0.278592\pi$
$62$	−7.84147	−0.995868
$63$	4.28157	0.539427
$64$	1.00000	0.125000
$65$	1.23339	0.152983
$66$	0	0
$67$	11.5211	1.40752	0.703760	−	0.710438i	$-0.251503\pi$
$67$	11.5211	1.40752	0.703760	+	0.710438i	$0.251503\pi$
$68$	−2.83364	−0.343630
$69$	−3.67315	−0.442196
$70$	4.30681	0.514763
$71$	−13.1925	−1.56566	−0.782828	−	0.622238i	$-0.786224\pi$
$71$	−13.1925	−1.56566	−0.782828	+	0.622238i	$0.786224\pi$
$72$	−1.35139	−0.159262
$73$	3.55023	0.415523	0.207762	−	0.978179i	$-0.433382\pi$
$73$	3.55023	0.415523	0.207762	+	0.978179i	$0.433382\pi$
$74$	−6.25846	−0.727531
$75$	4.04731	0.467343
$76$	1.00000	0.114708
$77$	0	0
$78$	1.16500	0.131910
$79$	−5.66991	−0.637915	−0.318957	−	0.947769i	$-0.603333\pi$
$79$	−5.66991	−0.637915	−0.318957	+	0.947769i	$0.603333\pi$
$80$	−1.35936	−0.151981
$81$	−3.11959	−0.346621
$82$	−10.7884	−1.19138
$83$	3.19923	0.351161	0.175581	−	0.984465i	$-0.443820\pi$
$83$	3.19923	0.351161	0.175581	+	0.984465i	$0.443820\pi$
$84$	4.06801	0.443857
$85$	3.85193	0.417800
$86$	0.172752	0.0186284
$87$	−6.38234	−0.684258
$88$	0	0
$89$	18.5862	1.97014	0.985068	−	0.172167i	$-0.0550767\pi$
$89$	18.5862	1.97014	0.985068	+	0.172167i	$0.0550767\pi$
$90$	1.83702	0.193638
$91$	2.87467	0.301348
$92$	2.86075	0.298254
$93$	10.0683	1.04404
$94$	−5.76623	−0.594741
$95$	−1.35936	−0.139467
$96$	−1.28398	−0.131046
$97$	4.04401	0.410607	0.205303	−	0.978698i	$-0.434182\pi$
$97$	4.04401	0.410607	0.205303	+	0.978698i	$0.434182\pi$
$98$	3.03797	0.306881
$99$	0	0
$100$	−3.15215	−0.315215
$101$	0.972957	0.0968129	0.0484064	−	0.998828i	$-0.484586\pi$
$101$	0.972957	0.0968129	0.0484064	+	0.998828i	$0.484586\pi$
$102$	3.63835	0.360250
$103$	−3.04190	−0.299727	−0.149864	−	0.988707i	$-0.547883\pi$
$103$	−3.04190	−0.299727	−0.149864	+	0.988707i	$0.547883\pi$
$104$	−0.907331	−0.0889711
$105$	−5.52988	−0.539661
$106$	13.5008	1.31131
$107$	9.11810	0.881480	0.440740	−	0.897635i	$-0.354716\pi$
$107$	9.11810	0.881480	0.440740	+	0.897635i	$0.354716\pi$
$108$	5.58711	0.537620
$109$	18.3209	1.75483	0.877414	−	0.479734i	$-0.159267\pi$
$109$	18.3209	1.75483	0.877414	+	0.479734i	$0.159267\pi$
$110$	0	0
$111$	8.03575	0.762720
$112$	−3.16828	−0.299374
$113$	2.14352	0.201646	0.100823	−	0.994904i	$-0.467852\pi$
$113$	2.14352	0.201646	0.100823	+	0.994904i	$0.467852\pi$
$114$	−1.28398	−0.120256
$115$	−3.88877	−0.362630
$116$	4.97073	0.461521
$117$	1.22616	0.113358
$118$	0.804852	0.0740926
$119$	8.97776	0.822990
$120$	1.74539	0.159332
$121$	0	0
$122$	10.0100	0.906264
$123$	13.8521	1.24900
$124$	−7.84147	−0.704185
$125$	11.0817	0.991175
$126$	4.28157	0.381432
$127$	−0.621182	−0.0551209	−0.0275605	−	0.999620i	$-0.508774\pi$
$127$	−0.621182	−0.0551209	−0.0275605	+	0.999620i	$0.508774\pi$
$128$	1.00000	0.0883883
$129$	−0.221811	−0.0195294
$130$	1.23339	0.108175
$131$	15.3839	1.34409	0.672047	−	0.740508i	$-0.265415\pi$
$131$	15.3839	1.34409	0.672047	+	0.740508i	$0.265415\pi$
$132$	0	0
$133$	−3.16828	−0.274724
$134$	11.5211	0.995267
$135$	−7.59487	−0.653662
$136$	−2.83364	−0.242983
$137$	9.75028	0.833023	0.416512	−	0.909130i	$-0.363253\pi$
$137$	9.75028	0.833023	0.416512	+	0.909130i	$0.363253\pi$
$138$	−3.67315	−0.312680
$139$	−0.217437	−0.0184428	−0.00922138	−	0.999957i	$-0.502935\pi$
$139$	−0.217437	−0.0184428	−0.00922138	+	0.999957i	$0.502935\pi$
$140$	4.30681	0.363992
$141$	7.40374	0.623508
$142$	−13.1925	−1.10709
$143$	0	0
$144$	−1.35139	−0.112616
$145$	−6.75699	−0.561138
$146$	3.55023	0.293819
$147$	−3.90070	−0.321725
$148$	−6.25846	−0.514442
$149$	8.98107	0.735758	0.367879	−	0.929874i	$-0.380084\pi$
$149$	8.98107	0.735758	0.367879	+	0.929874i	$0.380084\pi$
$150$	4.04731	0.330461
$151$	10.9550	0.891506	0.445753	−	0.895156i	$-0.352936\pi$
$151$	10.9550	0.891506	0.445753	+	0.895156i	$0.352936\pi$
$152$	1.00000	0.0811107
$153$	3.82935	0.309584
$154$	0	0
$155$	10.6593	0.856180
$156$	1.16500	0.0932745
$157$	−22.5862	−1.80258	−0.901288	−	0.433219i	$-0.857378\pi$
$157$	−22.5862	−1.80258	−0.901288	+	0.433219i	$0.857378\pi$
$158$	−5.66991	−0.451074
$159$	−17.3348	−1.37474
$160$	−1.35936	−0.107467
$161$	−9.06364	−0.714315
$162$	−3.11959	−0.245098
$163$	12.9872	1.01724	0.508618	−	0.860992i	$-0.330156\pi$
$163$	12.9872	1.01724	0.508618	+	0.860992i	$0.330156\pi$
$164$	−10.7884	−0.842430
$165$	0	0
$166$	3.19923	0.248309
$167$	−2.68269	−0.207592	−0.103796	−	0.994599i	$-0.533099\pi$
$167$	−2.68269	−0.207592	−0.103796	+	0.994599i	$0.533099\pi$
$168$	4.06801	0.313854
$169$	−12.1768	−0.936673
$170$	3.85193	0.295429
$171$	−1.35139	−0.103343
$172$	0.172752	0.0131722
$173$	−2.63532	−0.200360	−0.100180	−	0.994969i	$-0.531942\pi$
$173$	−2.63532	−0.200360	−0.100180	+	0.994969i	$0.531942\pi$
$174$	−6.38234	−0.483844
$175$	9.98689	0.754938
$176$	0	0
$177$	−1.03342	−0.0776763
$178$	18.5862	1.39310
$179$	12.5675	0.939341	0.469671	−	0.882842i	$-0.344373\pi$
$179$	12.5675	0.939341	0.469671	+	0.882842i	$0.344373\pi$
$180$	1.83702	0.136923
$181$	7.32871	0.544739	0.272369	−	0.962193i	$-0.412193\pi$
$181$	7.32871	0.544739	0.272369	+	0.962193i	$0.412193\pi$
$182$	2.87467	0.213085
$183$	−12.8527	−0.950099
$184$	2.86075	0.210897
$185$	8.50747	0.625482
$186$	10.0683	0.738245
$187$	0	0
$188$	−5.76623	−0.420546
$189$	−17.7015	−1.28759
$190$	−1.35936	−0.0986180
$191$	12.1727	0.880783	0.440392	−	0.897806i	$-0.354840\pi$
$191$	12.1727	0.880783	0.440392	+	0.897806i	$0.354840\pi$
$192$	−1.28398	−0.0926635
$193$	−14.3405	−1.03225	−0.516126	−	0.856512i	$-0.672627\pi$
$193$	−14.3405	−1.03225	−0.516126	+	0.856512i	$0.672627\pi$
$194$	4.04401	0.290343
$195$	−1.58365	−0.113407
$196$	3.03797	0.216998
$197$	−15.6720	−1.11659	−0.558293	−	0.829644i	$-0.688543\pi$
$197$	−15.6720	−1.11659	−0.558293	+	0.829644i	$0.688543\pi$
$198$	0	0
$199$	1.37651	0.0975783	0.0487891	−	0.998809i	$-0.484464\pi$
$199$	1.37651	0.0975783	0.0487891	+	0.998809i	$0.484464\pi$
$200$	−3.15215	−0.222891
$201$	−14.7928	−1.04341
$202$	0.972957	0.0684570
$203$	−15.7486	−1.10534
$204$	3.63835	0.254735
$205$	14.6652	1.02426
$206$	−3.04190	−0.211939
$207$	−3.86598	−0.268704
$208$	−0.907331	−0.0629121
$209$	0	0
$210$	−5.52988	−0.381598
$211$	−9.04401	−0.622615	−0.311308	−	0.950309i	$-0.600767\pi$
$211$	−9.04401	−0.622615	−0.311308	+	0.950309i	$0.600767\pi$
$212$	13.5008	0.927238
$213$	16.9389	1.16063
$214$	9.11810	0.623300
$215$	−0.234832	−0.0160154
$216$	5.58711	0.380155
$217$	24.8439	1.68652
$218$	18.3209	1.24085
$219$	−4.55844	−0.308031
$220$	0	0
$221$	2.57105	0.172948
$222$	8.03575	0.539325
$223$	−2.78430	−0.186451	−0.0932253	−	0.995645i	$-0.529718\pi$
$223$	−2.78430	−0.186451	−0.0932253	+	0.995645i	$0.529718\pi$
$224$	−3.16828	−0.211689
$225$	4.25978	0.283985
$226$	2.14352	0.142585
$227$	3.01179	0.199900	0.0999498	−	0.994992i	$-0.468132\pi$
$227$	3.01179	0.199900	0.0999498	+	0.994992i	$0.468132\pi$
$228$	−1.28398	−0.0850339
$229$	−20.8123	−1.37532	−0.687659	−	0.726034i	$-0.741362\pi$
$229$	−20.8123	−1.37532	−0.687659	+	0.726034i	$0.741362\pi$
$230$	−3.88877	−0.256418
$231$	0	0
$232$	4.97073	0.326345
$233$	−15.7607	−1.03252	−0.516258	−	0.856433i	$-0.672675\pi$
$233$	−15.7607	−1.03252	−0.516258	+	0.856433i	$0.672675\pi$
$234$	1.22616	0.0801563
$235$	7.83836	0.511318
$236$	0.804852	0.0523914
$237$	7.28007	0.472891
$238$	8.97776	0.581942
$239$	25.3585	1.64031	0.820153	−	0.572144i	$-0.193888\pi$
$239$	25.3585	1.64031	0.820153	+	0.572144i	$0.193888\pi$
$240$	1.74539	0.112664
$241$	−7.85507	−0.505989	−0.252995	−	0.967468i	$-0.581415\pi$
$241$	−7.85507	−0.505989	−0.252995	+	0.967468i	$0.581415\pi$
$242$	0	0
$243$	−12.7558	−0.818286
$244$	10.0100	0.640826
$245$	−4.12968	−0.263836
$246$	13.8521	0.883176
$247$	−0.907331	−0.0577321
$248$	−7.84147	−0.497934
$249$	−4.10776	−0.260319
$250$	11.0817	0.700867
$251$	6.91129	0.436237	0.218118	−	0.975922i	$-0.430008\pi$
$251$	6.91129	0.436237	0.218118	+	0.975922i	$0.430008\pi$
$252$	4.28157	0.269713
$253$	0	0
$254$	−0.621182	−0.0389764
$255$	−4.94581	−0.309719
$256$	1.00000	0.0625000
$257$	−7.45372	−0.464950	−0.232475	−	0.972602i	$-0.574682\pi$
$257$	−7.45372	−0.464950	−0.232475	+	0.972602i	$0.574682\pi$
$258$	−0.221811	−0.0138093
$259$	19.8285	1.23208
$260$	1.23339	0.0764913
$261$	−6.71738	−0.415796
$262$	15.3839	0.950418
$263$	9.10723	0.561576	0.280788	−	0.959770i	$-0.409404\pi$
$263$	9.10723	0.561576	0.280788	+	0.959770i	$0.409404\pi$
$264$	0	0
$265$	−18.3524	−1.12738
$266$	−3.16828	−0.194259
$267$	−23.8644	−1.46048
$268$	11.5211	0.703760
$269$	−15.7555	−0.960631	−0.480315	−	0.877096i	$-0.659478\pi$
$269$	−15.7555	−0.960631	−0.480315	+	0.877096i	$0.659478\pi$
$270$	−7.59487	−0.462209
$271$	21.0008	1.27571	0.637853	−	0.770158i	$-0.279823\pi$
$271$	21.0008	1.27571	0.637853	+	0.770158i	$0.279823\pi$
$272$	−2.83364	−0.171815
$273$	−3.69103	−0.223392
$274$	9.75028	0.589036
$275$	0	0
$276$	−3.67315	−0.221098
$277$	13.8546	0.832442	0.416221	−	0.909264i	$-0.363354\pi$
$277$	13.8546	0.832442	0.416221	+	0.909264i	$0.363354\pi$
$278$	−0.217437	−0.0130410
$279$	10.5969	0.634418
$280$	4.30681	0.257381
$281$	−9.64862	−0.575589	−0.287794	−	0.957692i	$-0.592922\pi$
$281$	−9.64862	−0.575589	−0.287794	+	0.957692i	$0.592922\pi$
$282$	7.40374	0.440886
$283$	18.4701	1.09794	0.548968	−	0.835844i	$-0.315021\pi$
$283$	18.4701	1.09794	0.548968	+	0.835844i	$0.315021\pi$
$284$	−13.1925	−0.782828
$285$	1.74539	0.103388
$286$	0	0
$287$	34.1805	2.01761
$288$	−1.35139	−0.0796312
$289$	−8.97047	−0.527675
$290$	−6.75699	−0.396784
$291$	−5.19244	−0.304386
$292$	3.55023	0.207762
$293$	6.73690	0.393574	0.196787	−	0.980446i	$-0.436949\pi$
$293$	6.73690	0.393574	0.196787	+	0.980446i	$0.436949\pi$
$294$	−3.90070	−0.227494
$295$	−1.09408	−0.0636998
$296$	−6.25846	−0.363765
$297$	0	0
$298$	8.98107	0.520259
$299$	−2.59565	−0.150110
$300$	4.04731	0.233672
$301$	−0.547327	−0.0315474
$302$	10.9550	0.630390
$303$	−1.24926	−0.0717682
$304$	1.00000	0.0573539
$305$	−13.6072	−0.779145
$306$	3.82935	0.218909
$307$	13.8179	0.788632	0.394316	−	0.918975i	$-0.370982\pi$
$307$	13.8179	0.788632	0.394316	+	0.918975i	$0.370982\pi$
$308$	0	0
$309$	3.90575	0.222190
$310$	10.6593	0.605410
$311$	−23.1524	−1.31285	−0.656427	−	0.754389i	$-0.727933\pi$
$311$	−23.1524	−1.31285	−0.656427	+	0.754389i	$0.727933\pi$
$312$	1.16500	0.0659550
$313$	−17.0322	−0.962719	−0.481359	−	0.876523i	$-0.659857\pi$
$313$	−17.0322	−0.962719	−0.481359	+	0.876523i	$0.659857\pi$
$314$	−22.5862	−1.27461
$315$	−5.82017	−0.327930
$316$	−5.66991	−0.318957
$317$	−32.0159	−1.79819	−0.899096	−	0.437752i	$-0.855775\pi$
$317$	−32.0159	−1.79819	−0.899096	+	0.437752i	$0.855775\pi$
$318$	−17.3348	−0.972086
$319$	0	0
$320$	−1.35936	−0.0759903
$321$	−11.7075	−0.653448
$322$	−9.06364	−0.505097
$323$	−2.83364	−0.157668
$324$	−3.11959	−0.173311
$325$	2.86005	0.158647
$326$	12.9872	0.719295
$327$	−23.5238	−1.30087
$328$	−10.7884	−0.595688
$329$	18.2690	1.00720
$330$	0	0
$331$	−19.8146	−1.08911	−0.544554	−	0.838726i	$-0.683301\pi$
$331$	−19.8146	−1.08911	−0.544554	+	0.838726i	$0.683301\pi$
$332$	3.19923	0.175581
$333$	8.45760	0.463474
$334$	−2.68269	−0.146790
$335$	−15.6612	−0.855663
$336$	4.06801	0.221928
$337$	32.5368	1.77239	0.886195	−	0.463312i	$-0.153339\pi$
$337$	32.5368	1.77239	0.886195	+	0.463312i	$0.153339\pi$
$338$	−12.1768	−0.662328
$339$	−2.75225	−0.149482
$340$	3.85193	0.208900
$341$	0	0
$342$	−1.35139	−0.0730746
$343$	12.5528	0.677787
$344$	0.172752	0.00931418
$345$	4.99312	0.268821
$346$	−2.63532	−0.141676
$347$	7.35177	0.394664	0.197332	−	0.980337i	$-0.436772\pi$
$347$	7.35177	0.394664	0.197332	+	0.980337i	$0.436772\pi$
$348$	−6.38234	−0.342129
$349$	20.4037	1.09219	0.546093	−	0.837725i	$-0.316115\pi$
$349$	20.4037	1.09219	0.546093	+	0.837725i	$0.316115\pi$
$350$	9.98689	0.533822
$351$	−5.06936	−0.270582
$352$	0	0
$353$	−20.7451	−1.10415	−0.552076	−	0.833794i	$-0.686164\pi$
$353$	−20.7451	−1.10415	−0.552076	+	0.833794i	$0.686164\pi$
$354$	−1.03342	−0.0549254
$355$	17.9332	0.951798
$356$	18.5862	0.985068
$357$	−11.5273	−0.610089
$358$	12.5675	0.664214
$359$	29.4812	1.55596	0.777979	−	0.628290i	$-0.216245\pi$
$359$	29.4812	1.55596	0.777979	+	0.628290i	$0.216245\pi$
$360$	1.83702	0.0968192
$361$	1.00000	0.0526316
$362$	7.32871	0.385188
$363$	0	0
$364$	2.87467	0.150674
$365$	−4.82603	−0.252606
$366$	−12.8527	−0.671821
$367$	29.5576	1.54289	0.771447	−	0.636293i	$-0.219533\pi$
$367$	29.5576	1.54289	0.771447	+	0.636293i	$0.219533\pi$
$368$	2.86075	0.149127
$369$	14.5793	0.758966
$370$	8.50747	0.442282
$371$	−42.7742	−2.22073
$372$	10.0683	0.522018
$373$	14.7023	0.761256	0.380628	−	0.924728i	$-0.375708\pi$
$373$	14.7023	0.761256	0.380628	+	0.924728i	$0.375708\pi$
$374$	0	0
$375$	−14.2287	−0.734766
$376$	−5.76623	−0.297371
$377$	−4.51010	−0.232282
$378$	−17.7015	−0.910467
$379$	3.03085	0.155684	0.0778422	−	0.996966i	$-0.475197\pi$
$379$	3.03085	0.155684	0.0778422	+	0.996966i	$0.475197\pi$
$380$	−1.35936	−0.0697335
$381$	0.797587	0.0408616
$382$	12.1727	0.622808
$383$	−12.5120	−0.639332	−0.319666	−	0.947530i	$-0.603571\pi$
$383$	−12.5120	−0.639332	−0.319666	+	0.947530i	$0.603571\pi$
$384$	−1.28398	−0.0655230
$385$	0	0
$386$	−14.3405	−0.729913
$387$	−0.233455	−0.0118672
$388$	4.04401	0.205303
$389$	−10.2328	−0.518822	−0.259411	−	0.965767i	$-0.583528\pi$
$389$	−10.2328	−0.518822	−0.259411	+	0.965767i	$0.583528\pi$
$390$	−1.58365	−0.0801911
$391$	−8.10634	−0.409955
$392$	3.03797	0.153441
$393$	−19.7526	−0.996388
$394$	−15.6720	−0.789545
$395$	7.70743	0.387803
$396$	0	0
$397$	0.277416	0.0139231	0.00696156	−	0.999976i	$-0.497784\pi$
$397$	0.277416	0.0139231	0.00696156	+	0.999976i	$0.497784\pi$
$398$	1.37651	0.0689983
$399$	4.06801	0.203655
$400$	−3.15215	−0.157608
$401$	7.27854	0.363473	0.181737	−	0.983347i	$-0.441828\pi$
$401$	7.27854	0.363473	0.181737	+	0.983347i	$0.441828\pi$
$402$	−14.7928	−0.737800
$403$	7.11481	0.354414
$404$	0.972957	0.0484064
$405$	4.24063	0.210719
$406$	−15.7486	−0.781592
$407$	0	0
$408$	3.63835	0.180125
$409$	−7.55844	−0.373741	−0.186870	−	0.982385i	$-0.559834\pi$
$409$	−7.55844	−0.373741	−0.186870	+	0.982385i	$0.559834\pi$
$410$	14.6652	0.724264
$411$	−12.5192	−0.617527
$412$	−3.04190	−0.149864
$413$	−2.54999	−0.125477
$414$	−3.86598	−0.190002
$415$	−4.34890	−0.213479
$416$	−0.907331	−0.0444856
$417$	0.279185	0.0136718
$418$	0	0
$419$	34.8385	1.70197	0.850986	−	0.525189i	$-0.176005\pi$
$419$	34.8385	1.70197	0.850986	+	0.525189i	$0.176005\pi$
$420$	−5.52988	−0.269830
$421$	−12.1865	−0.593934	−0.296967	−	0.954888i	$-0.595975\pi$
$421$	−12.1865	−0.593934	−0.296967	+	0.954888i	$0.595975\pi$
$422$	−9.04401	−0.440255
$423$	7.79241	0.378880
$424$	13.5008	0.655656
$425$	8.93207	0.433269
$426$	16.9389	0.820692
$427$	−31.7145	−1.53477
$428$	9.11810	0.440740
$429$	0	0
$430$	−0.234832	−0.0113246
$431$	−29.8641	−1.43850	−0.719251	−	0.694750i	$-0.755515\pi$
$431$	−29.8641	−1.43850	−0.719251	+	0.694750i	$0.755515\pi$
$432$	5.58711	0.268810
$433$	0.226900	0.0109041	0.00545206	−	0.999985i	$-0.498265\pi$
$433$	0.226900	0.0109041	0.00545206	+	0.999985i	$0.498265\pi$
$434$	24.8439	1.19255
$435$	8.67587	0.415976
$436$	18.3209	0.877414
$437$	2.86075	0.136848
$438$	−4.55844	−0.217811
$439$	−15.7258	−0.750552	−0.375276	−	0.926913i	$-0.622452\pi$
$439$	−15.7258	−0.750552	−0.375276	+	0.926913i	$0.622452\pi$
$440$	0	0
$441$	−4.10548	−0.195499
$442$	2.57105	0.122292
$443$	28.4832	1.35328	0.676638	−	0.736316i	$-0.263436\pi$
$443$	28.4832	1.35328	0.676638	+	0.736316i	$0.263436\pi$
$444$	8.03575	0.381360
$445$	−25.2653	−1.19769
$446$	−2.78430	−0.131840
$447$	−11.5315	−0.545423
$448$	−3.16828	−0.149687
$449$	−16.3373	−0.771003	−0.385501	−	0.922707i	$-0.625972\pi$
$449$	−16.3373	−0.771003	−0.385501	+	0.922707i	$0.625972\pi$
$450$	4.25978	0.200808
$451$	0	0
$452$	2.14352	0.100823
$453$	−14.0661	−0.660881
$454$	3.01179	0.141350
$455$	−3.90771	−0.183196
$456$	−1.28398	−0.0601280
$457$	21.6394	1.01225	0.506125	−	0.862460i	$-0.331077\pi$
$457$	21.6394	1.01225	0.506125	+	0.862460i	$0.331077\pi$
$458$	−20.8123	−0.972497
$459$	−15.8319	−0.738968
$460$	−3.88877	−0.181315
$461$	9.99146	0.465349	0.232674	−	0.972555i	$-0.425252\pi$
$461$	9.99146	0.465349	0.232674	+	0.972555i	$0.425252\pi$
$462$	0	0
$463$	18.7196	0.869972	0.434986	−	0.900437i	$-0.356753\pi$
$463$	18.7196	0.869972	0.434986	+	0.900437i	$0.356753\pi$
$464$	4.97073	0.230760
$465$	−13.6864	−0.634693
$466$	−15.7607	−0.730099
$467$	−35.7800	−1.65570	−0.827851	−	0.560949i	$-0.810436\pi$
$467$	−35.7800	−1.65570	−0.827851	+	0.560949i	$0.810436\pi$
$468$	1.22616	0.0566791
$469$	−36.5019	−1.68550
$470$	7.83836	0.361557
$471$	29.0003	1.33626
$472$	0.804852	0.0370463
$473$	0	0
$474$	7.28007	0.334385
$475$	−3.15215	−0.144631
$476$	8.97776	0.411495
$477$	−18.2448	−0.835372
$478$	25.3585	1.15987
$479$	−12.3527	−0.564409	−0.282205	−	0.959354i	$-0.591066\pi$
$479$	−12.3527	−0.564409	−0.282205	+	0.959354i	$0.591066\pi$
$480$	1.74539	0.0796658
$481$	5.67849	0.258917
$482$	−7.85507	−0.357788
$483$	11.6376	0.529527
$484$	0	0
$485$	−5.49725	−0.249617
$486$	−12.7558	−0.578616
$487$	13.9682	0.632959	0.316479	−	0.948599i	$-0.397499\pi$
$487$	13.9682	0.632959	0.316479	+	0.948599i	$0.397499\pi$
$488$	10.0100	0.453132
$489$	−16.6754	−0.754086
$490$	−4.12968	−0.186560
$491$	−3.44846	−0.155627	−0.0778134	−	0.996968i	$-0.524794\pi$
$491$	−3.44846	−0.155627	−0.0778134	+	0.996968i	$0.524794\pi$
$492$	13.8521	0.624500
$493$	−14.0853	−0.634369
$494$	−0.907331	−0.0408228
$495$	0	0
$496$	−7.84147	−0.352092
$497$	41.7974	1.87487
$498$	−4.10776	−0.184073
$499$	−43.4252	−1.94398	−0.971989	−	0.235028i	$-0.924482\pi$
$499$	−43.4252	−1.94398	−0.971989	+	0.235028i	$0.924482\pi$
$500$	11.0817	0.495588
$501$	3.44452	0.153890
$502$	6.91129	0.308466
$503$	29.2138	1.30258	0.651289	−	0.758830i	$-0.274229\pi$
$503$	29.2138	1.30258	0.651289	+	0.758830i	$0.274229\pi$
$504$	4.28157	0.190716
$505$	−1.32260	−0.0588547
$506$	0	0
$507$	15.6347	0.694363
$508$	−0.621182	−0.0275605
$509$	−37.8491	−1.67763	−0.838816	−	0.544414i	$-0.816752\pi$
$509$	−37.8491	−1.67763	−0.838816	+	0.544414i	$0.816752\pi$
$510$	−4.94581	−0.219004
$511$	−11.2481	−0.497587
$512$	1.00000	0.0441942
$513$	5.58711	0.246677
$514$	−7.45372	−0.328770
$515$	4.13503	0.182211
$516$	−0.221811	−0.00976468
$517$	0	0
$518$	19.8285	0.871215
$519$	3.38371	0.148528
$520$	1.23339	0.0540875
$521$	−26.8499	−1.17632	−0.588158	−	0.808746i	$-0.700147\pi$
$521$	−26.8499	−1.17632	−0.588158	+	0.808746i	$0.700147\pi$
$522$	−6.71738	−0.294012
$523$	−19.9251	−0.871264	−0.435632	−	0.900125i	$-0.643475\pi$
$523$	−19.9251	−0.871264	−0.435632	+	0.900125i	$0.643475\pi$
$524$	15.3839	0.672047
$525$	−12.8230	−0.559641
$526$	9.10723	0.397094
$527$	22.2199	0.967915
$528$	0	0
$529$	−14.8161	−0.644179
$530$	−18.3524	−0.797176
$531$	−1.08767	−0.0472007
$532$	−3.16828	−0.137362
$533$	9.78862	0.423992
$534$	−23.8644	−1.03271
$535$	−12.3947	−0.535871
$536$	11.5211	0.497634
$537$	−16.1365	−0.696341
$538$	−15.7555	−0.679269
$539$	0	0
$540$	−7.59487	−0.326831
$541$	11.8381	0.508961	0.254480	−	0.967078i	$-0.418096\pi$
$541$	11.8381	0.508961	0.254480	+	0.967078i	$0.418096\pi$
$542$	21.0008	0.902060
$543$	−9.40994	−0.403819
$544$	−2.83364	−0.121491
$545$	−24.9047	−1.06680
$546$	−3.69103	−0.157962
$547$	41.1291	1.75855	0.879277	−	0.476310i	$-0.158026\pi$
$547$	41.1291	1.75855	0.879277	+	0.476310i	$0.158026\pi$
$548$	9.75028	0.416512
$549$	−13.5274	−0.577336
$550$	0	0
$551$	4.97073	0.211760
$552$	−3.67315	−0.156340
$553$	17.9638	0.763900
$554$	13.8546	0.588625
$555$	−10.9234	−0.463675
$556$	−0.217437	−0.00922138
$557$	15.3705	0.651269	0.325635	−	0.945496i	$-0.394422\pi$
$557$	15.3705	0.651269	0.325635	+	0.945496i	$0.394422\pi$
$558$	10.5969	0.448601
$559$	−0.156743	−0.00662954
$560$	4.30681	0.181996
$561$	0	0
$562$	−9.64862	−0.407003
$563$	15.6035	0.657611	0.328805	−	0.944398i	$-0.393354\pi$
$563$	15.6035	0.657611	0.328805	+	0.944398i	$0.393354\pi$
$564$	7.40374	0.311754
$565$	−2.91381	−0.122585
$566$	18.4701	0.776358
$567$	9.88373	0.415077
$568$	−13.1925	−0.553543
$569$	−36.2078	−1.51791	−0.758955	−	0.651143i	$-0.774290\pi$
$569$	−36.2078	−1.51791	−0.758955	+	0.651143i	$0.774290\pi$
$570$	1.74539	0.0731063
$571$	−10.4696	−0.438138	−0.219069	−	0.975709i	$-0.570302\pi$
$571$	−10.4696	−0.438138	−0.219069	+	0.975709i	$0.570302\pi$
$572$	0	0
$573$	−15.6295	−0.652932
$574$	34.1805	1.42667
$575$	−9.01751	−0.376056
$576$	−1.35139	−0.0563078
$577$	19.5184	0.812564	0.406282	−	0.913748i	$-0.366825\pi$
$577$	19.5184	0.812564	0.406282	+	0.913748i	$0.366825\pi$
$578$	−8.97047	−0.373123
$579$	18.4130	0.765217
$580$	−6.75699	−0.280569
$581$	−10.1361	−0.420514
$582$	−5.19244	−0.215234
$583$	0	0
$584$	3.55023	0.146910
$585$	−1.66678	−0.0689129
$586$	6.73690	0.278299
$587$	19.2505	0.794555	0.397277	−	0.917699i	$-0.369955\pi$
$587$	19.2505	0.794555	0.397277	+	0.917699i	$0.369955\pi$
$588$	−3.90070	−0.160862
$589$	−7.84147	−0.323102
$590$	−1.09408	−0.0450426
$591$	20.1226	0.827734
$592$	−6.25846	−0.257221
$593$	−8.08792	−0.332131	−0.166066	−	0.986115i	$-0.553106\pi$
$593$	−8.08792	−0.332131	−0.166066	+	0.986115i	$0.553106\pi$
$594$	0	0
$595$	−12.2040	−0.500314
$596$	8.98107	0.367879
$597$	−1.76742	−0.0723356
$598$	−2.59565	−0.106144
$599$	42.2590	1.72665	0.863327	−	0.504644i	$-0.168376\pi$
$599$	42.2590	1.72665	0.863327	+	0.504644i	$0.168376\pi$
$600$	4.04731	0.165231
$601$	−38.8149	−1.58329	−0.791646	−	0.610980i	$-0.790775\pi$
$601$	−38.8149	−1.58329	−0.791646	+	0.610980i	$0.790775\pi$
$602$	−0.547327	−0.0223074
$603$	−15.5694	−0.634035
$604$	10.9550	0.445753
$605$	0	0
$606$	−1.24926	−0.0507478
$607$	−17.0246	−0.691008	−0.345504	−	0.938417i	$-0.612292\pi$
$607$	−17.0246	−0.691008	−0.345504	+	0.938417i	$0.612292\pi$
$608$	1.00000	0.0405554
$609$	20.2210	0.819396
$610$	−13.6072	−0.550938
$611$	5.23188	0.211659
$612$	3.82935	0.154792
$613$	−8.62704	−0.348443	−0.174221	−	0.984706i	$-0.555741\pi$
$613$	−8.62704	−0.348443	−0.174221	+	0.984706i	$0.555741\pi$
$614$	13.8179	0.557647
$615$	−18.8299	−0.759295
$616$	0	0
$617$	27.1013	1.09106	0.545528	−	0.838092i	$-0.316329\pi$
$617$	27.1013	1.09106	0.545528	+	0.838092i	$0.316329\pi$
$618$	3.90575	0.157112
$619$	11.5655	0.464857	0.232429	−	0.972613i	$-0.425333\pi$
$619$	11.5655	0.464857	0.232429	+	0.972613i	$0.425333\pi$
$620$	10.6593	0.428090
$621$	15.9833	0.641388
$622$	−23.1524	−0.928328
$623$	−58.8863	−2.35923
$624$	1.16500	0.0466372
$625$	0.696820	0.0278728
$626$	−17.0322	−0.680745
$627$	0	0
$628$	−22.5862	−0.901288
$629$	17.7342	0.707110
$630$	−5.82017	−0.231881
$631$	0.180197	0.00717353	0.00358676	−	0.999994i	$-0.498858\pi$
$631$	0.180197	0.00717353	0.00358676	+	0.999994i	$0.498858\pi$
$632$	−5.66991	−0.225537
$633$	11.6124	0.461550
$634$	−32.0159	−1.27151
$635$	0.844407	0.0335093
$636$	−17.3348	−0.687369
$637$	−2.75645	−0.109214
$638$	0	0
$639$	17.8281	0.705270
$640$	−1.35936	−0.0537333
$641$	−3.56024	−0.140621	−0.0703105	−	0.997525i	$-0.522399\pi$
$641$	−3.56024	−0.140621	−0.0703105	+	0.997525i	$0.522399\pi$
$642$	−11.7075	−0.462058
$643$	23.3365	0.920302	0.460151	−	0.887841i	$-0.347795\pi$
$643$	23.3365	0.920302	0.460151	+	0.887841i	$0.347795\pi$
$644$	−9.06364	−0.357157
$645$	0.301520	0.0118723
$646$	−2.83364	−0.111488
$647$	−35.4209	−1.39254	−0.696270	−	0.717780i	$-0.745158\pi$
$647$	−35.4209	−1.39254	−0.696270	+	0.717780i	$0.745158\pi$
$648$	−3.11959	−0.122549
$649$	0	0
$650$	2.86005	0.112180
$651$	−31.8992	−1.25023
$652$	12.9872	0.508618
$653$	−19.4650	−0.761724	−0.380862	−	0.924632i	$-0.624373\pi$
$653$	−19.4650	−0.761724	−0.380862	+	0.924632i	$0.624373\pi$
$654$	−23.5238	−0.919853
$655$	−20.9121	−0.817105
$656$	−10.7884	−0.421215
$657$	−4.79774	−0.187178
$658$	18.2690	0.712200
$659$	40.4633	1.57622	0.788112	−	0.615531i	$-0.211059\pi$
$659$	40.4633	1.57622	0.788112	+	0.615531i	$0.211059\pi$
$660$	0	0
$661$	30.5618	1.18872	0.594358	−	0.804201i	$-0.297406\pi$
$661$	30.5618	1.18872	0.594358	+	0.804201i	$0.297406\pi$
$662$	−19.8146	−0.770115
$663$	−3.30119	−0.128207
$664$	3.19923	0.124154
$665$	4.30681	0.167011
$666$	8.45760	0.327725
$667$	14.2200	0.550601
$668$	−2.68269	−0.103796
$669$	3.57499	0.138217
$670$	−15.6612	−0.605045
$671$	0	0
$672$	4.06801	0.156927
$673$	49.1890	1.89610	0.948048	−	0.318127i	$-0.103054\pi$
$673$	49.1890	1.89610	0.948048	+	0.318127i	$0.103054\pi$
$674$	32.5368	1.25327
$675$	−17.6114	−0.677864
$676$	−12.1768	−0.468337
$677$	−3.15874	−0.121400	−0.0607002	−	0.998156i	$-0.519333\pi$
$677$	−3.15874	−0.121400	−0.0607002	+	0.998156i	$0.519333\pi$
$678$	−2.75225	−0.105699
$679$	−12.8125	−0.491700
$680$	3.85193	0.147715
$681$	−3.86709	−0.148187
$682$	0	0
$683$	−32.2822	−1.23524	−0.617621	−	0.786476i	$-0.711904\pi$
$683$	−32.2822	−1.23524	−0.617621	+	0.786476i	$0.711904\pi$
$684$	−1.35139	−0.0516716
$685$	−13.2541	−0.506413
$686$	12.5528	0.479268
$687$	26.7227	1.01953
$688$	0.172752	0.00658612
$689$	−12.2497	−0.466676
$690$	4.99312	0.190085
$691$	19.5991	0.745585	0.372792	−	0.927915i	$-0.378400\pi$
$691$	19.5991	0.745585	0.372792	+	0.927915i	$0.378400\pi$
$692$	−2.63532	−0.100180
$693$	0	0
$694$	7.35177	0.279069
$695$	0.295574	0.0112118
$696$	−6.38234	−0.241922
$697$	30.5704	1.15793
$698$	20.4037	0.772292
$699$	20.2364	0.765412
$700$	9.98689	0.377469
$701$	19.1206	0.722176	0.361088	−	0.932532i	$-0.382405\pi$
$701$	19.1206	0.722176	0.361088	+	0.932532i	$0.382405\pi$
$702$	−5.06936	−0.191331
$703$	−6.25846	−0.236042
$704$	0	0
$705$	−10.0643	−0.379044
$706$	−20.7451	−0.780753
$707$	−3.08260	−0.115933
$708$	−1.03342	−0.0388382
$709$	−2.97244	−0.111632	−0.0558161	−	0.998441i	$-0.517776\pi$
$709$	−2.97244	−0.111632	−0.0558161	+	0.998441i	$0.517776\pi$
$710$	17.9332	0.673023
$711$	7.66225	0.287357
$712$	18.5862	0.696548
$713$	−22.4325	−0.840103
$714$	−11.5273	−0.431398
$715$	0	0
$716$	12.5675	0.469671
$717$	−32.5599	−1.21597
$718$	29.4812	1.10023
$719$	39.2747	1.46470	0.732349	−	0.680929i	$-0.238424\pi$
$719$	39.2747	1.46470	0.732349	+	0.680929i	$0.238424\pi$
$720$	1.83702	0.0684615
$721$	9.63758	0.358922
$722$	1.00000	0.0372161
$723$	10.0858	0.375094
$724$	7.32871	0.272369
$725$	−15.6685	−0.581913
$726$	0	0
$727$	−5.38463	−0.199705	−0.0998525	−	0.995002i	$-0.531837\pi$
$727$	−5.38463	−0.199705	−0.0998525	+	0.995002i	$0.531837\pi$
$728$	2.87467	0.106543
$729$	25.7370	0.953223
$730$	−4.82603	−0.178619
$731$	−0.489518	−0.0181055
$732$	−12.8527	−0.475049
$733$	−2.28940	−0.0845610	−0.0422805	−	0.999106i	$-0.513462\pi$
$733$	−2.28940	−0.0845610	−0.0422805	+	0.999106i	$0.513462\pi$
$734$	29.5576	1.09099
$735$	5.30244	0.195584
$736$	2.86075	0.105449
$737$	0	0
$738$	14.5793	0.536670
$739$	−29.5536	−1.08715	−0.543573	−	0.839362i	$-0.682929\pi$
$739$	−29.5536	−1.08715	−0.543573	+	0.839362i	$0.682929\pi$
$740$	8.50747	0.312741
$741$	1.16500	0.0427973
$742$	−42.7742	−1.57029
$743$	−21.8256	−0.800704	−0.400352	−	0.916361i	$-0.631112\pi$
$743$	−21.8256	−0.800704	−0.400352	+	0.916361i	$0.631112\pi$
$744$	10.0683	0.369122
$745$	−12.2085	−0.447283
$746$	14.7023	0.538289
$747$	−4.32340	−0.158185
$748$	0	0
$749$	−28.8886	−1.05557
$750$	−14.2287	−0.519558
$751$	−18.2267	−0.665100	−0.332550	−	0.943086i	$-0.607909\pi$
$751$	−18.2267	−0.665100	−0.332550	+	0.943086i	$0.607909\pi$
$752$	−5.76623	−0.210273
$753$	−8.87398	−0.323386
$754$	−4.51010	−0.164248
$755$	−14.8918	−0.541967
$756$	−17.7015	−0.643797
$757$	4.09038	0.148667	0.0743336	−	0.997233i	$-0.476317\pi$
$757$	4.09038	0.148667	0.0743336	+	0.997233i	$0.476317\pi$
$758$	3.03085	0.110085
$759$	0	0
$760$	−1.35936	−0.0493090
$761$	−1.41069	−0.0511374	−0.0255687	−	0.999673i	$-0.508140\pi$
$761$	−1.41069	−0.0511374	−0.0255687	+	0.999673i	$0.508140\pi$
$762$	0.797587	0.0288935
$763$	−58.0458	−2.10140
$764$	12.1727	0.440392
$765$	−5.20545	−0.188203
$766$	−12.5120	−0.452076
$767$	−0.730267	−0.0263684
$768$	−1.28398	−0.0463318
$769$	−43.5034	−1.56877	−0.784387	−	0.620272i	$-0.787022\pi$
$769$	−43.5034	−1.56877	−0.784387	+	0.620272i	$0.787022\pi$
$770$	0	0
$771$	9.57045	0.344671
$772$	−14.3405	−0.516126
$773$	18.5978	0.668917	0.334459	−	0.942410i	$-0.391447\pi$
$773$	18.5978	0.668917	0.334459	+	0.942410i	$0.391447\pi$
$774$	−0.233455	−0.00839137
$775$	24.7175	0.887879
$776$	4.04401	0.145171
$777$	−25.4595	−0.913354
$778$	−10.2328	−0.366863
$779$	−10.7884	−0.386533
$780$	−1.58365	−0.0567036
$781$	0	0
$782$	−8.10634	−0.289882
$783$	27.7720	0.992491
$784$	3.03797	0.108499
$785$	30.7027	1.09583
$786$	−19.7526	−0.704553
$787$	24.5979	0.876819	0.438409	−	0.898775i	$-0.355542\pi$
$787$	24.5979	0.876819	0.438409	+	0.898775i	$0.355542\pi$
$788$	−15.6720	−0.558293
$789$	−11.6935	−0.416301
$790$	7.70743	0.274218
$791$	−6.79127	−0.241470
$792$	0	0
$793$	−9.08240	−0.322525
$794$	0.277416	0.00984513
$795$	23.5641	0.835734
$796$	1.37651	0.0487891
$797$	−2.05011	−0.0726185	−0.0363092	−	0.999341i	$-0.511560\pi$
$797$	−2.05011	−0.0726185	−0.0363092	+	0.999341i	$0.511560\pi$
$798$	4.06801	0.144006
$799$	16.3394	0.578048
$800$	−3.15215	−0.111445
$801$	−25.1172	−0.887472
$802$	7.27854	0.257014
$803$	0	0
$804$	−14.7928	−0.521703
$805$	12.3207	0.434248
$806$	7.11481	0.250608
$807$	20.2298	0.712123
$808$	0.972957	0.0342285
$809$	3.46113	0.121687	0.0608434	−	0.998147i	$-0.480621\pi$
$809$	3.46113	0.121687	0.0608434	+	0.998147i	$0.480621\pi$
$810$	4.24063	0.149001
$811$	12.8868	0.452517	0.226258	−	0.974067i	$-0.427351\pi$
$811$	12.8868	0.452517	0.226258	+	0.974067i	$0.427351\pi$
$812$	−15.7486	−0.552669
$813$	−26.9646	−0.945691
$814$	0	0
$815$	−17.6542	−0.618401
$816$	3.63835	0.127368
$817$	0.172752	0.00604384
$818$	−7.55844	−0.264275
$819$	−3.88480	−0.135746
$820$	14.6652	0.512132
$821$	−18.4965	−0.645531	−0.322766	−	0.946479i	$-0.604613\pi$
$821$	−18.4965	−0.645531	−0.322766	+	0.946479i	$0.604613\pi$
$822$	−12.5192	−0.436657
$823$	50.1844	1.74932	0.874659	−	0.484740i	$-0.161086\pi$
$823$	50.1844	1.74932	0.874659	+	0.484740i	$0.161086\pi$
$824$	−3.04190	−0.105970
$825$	0	0
$826$	−2.54999	−0.0887256
$827$	26.2799	0.913842	0.456921	−	0.889507i	$-0.348952\pi$
$827$	26.2799	0.913842	0.456921	+	0.889507i	$0.348952\pi$
$828$	−3.86598	−0.134352
$829$	−15.8906	−0.551903	−0.275951	−	0.961172i	$-0.588993\pi$
$829$	−15.8906	−0.551903	−0.275951	+	0.961172i	$0.588993\pi$
$830$	−4.34890	−0.150952
$831$	−17.7891	−0.617096
$832$	−0.907331	−0.0314560
$833$	−8.60852	−0.298268
$834$	0.279185	0.00966740
$835$	3.64672	0.126200
$836$	0	0
$837$	−43.8111	−1.51433
$838$	34.8385	1.20348
$839$	4.81166	0.166117	0.0830585	−	0.996545i	$-0.473531\pi$
$839$	4.81166	0.166117	0.0830585	+	0.996545i	$0.473531\pi$
$840$	−5.52988	−0.190799
$841$	−4.29183	−0.147994
$842$	−12.1865	−0.419975
$843$	12.3887	0.426688
$844$	−9.04401	−0.311308
$845$	16.5525	0.569425
$846$	7.79241	0.267909
$847$	0	0
$848$	13.5008	0.463619
$849$	−23.7153	−0.813908
$850$	8.93207	0.306367
$851$	−17.9039	−0.613737
$852$	16.9389	0.580317
$853$	51.1727	1.75212	0.876059	−	0.482203i	$-0.160163\pi$
$853$	51.1727	1.75212	0.876059	+	0.482203i	$0.160163\pi$
$854$	−31.7145	−1.08525
$855$	1.83702	0.0628246
$856$	9.11810	0.311650
$857$	33.0439	1.12876	0.564379	−	0.825516i	$-0.309116\pi$
$857$	33.0439	1.12876	0.564379	+	0.825516i	$0.309116\pi$
$858$	0	0
$859$	−50.3474	−1.71783	−0.858915	−	0.512117i	$-0.828861\pi$
$859$	−50.3474	−1.71783	−0.858915	+	0.512117i	$0.828861\pi$
$860$	−0.234832	−0.00800770
$861$	−43.8872	−1.49567
$862$	−29.8641	−1.01717
$863$	24.3654	0.829408	0.414704	−	0.909956i	$-0.363885\pi$
$863$	24.3654	0.829408	0.414704	+	0.909956i	$0.363885\pi$
$864$	5.58711	0.190077
$865$	3.58234	0.121803
$866$	0.226900	0.00771037
$867$	11.5179	0.391170
$868$	24.8439	0.843258
$869$	0	0
$870$	8.67587	0.294139
$871$	−10.4534	−0.354200
$872$	18.3209	0.620425
$873$	−5.46502	−0.184963
$874$	2.86075	0.0967663
$875$	−35.1098	−1.18693
$876$	−4.55844	−0.154015
$877$	15.0793	0.509190	0.254595	−	0.967048i	$-0.418058\pi$
$877$	15.0793	0.509190	0.254595	+	0.967048i	$0.418058\pi$
$878$	−15.7258	−0.530720
$879$	−8.65007	−0.291760
$880$	0	0
$881$	−28.2858	−0.952973	−0.476487	−	0.879182i	$-0.658090\pi$
$881$	−28.2858	−0.952973	−0.476487	+	0.879182i	$0.658090\pi$
$882$	−4.10548	−0.138239
$883$	−2.02415	−0.0681182	−0.0340591	−	0.999420i	$-0.510843\pi$
$883$	−2.02415	−0.0681182	−0.0340591	+	0.999420i	$0.510843\pi$
$884$	2.57105	0.0864738
$885$	1.40478	0.0472212
$886$	28.4832	0.956910
$887$	21.4355	0.719734	0.359867	−	0.933004i	$-0.382822\pi$
$887$	21.4355	0.719734	0.359867	+	0.933004i	$0.382822\pi$
$888$	8.03575	0.269662
$889$	1.96807	0.0660071
$890$	−25.2653	−0.846894
$891$	0	0
$892$	−2.78430	−0.0932253
$893$	−5.76623	−0.192960
$894$	−11.5315	−0.385672
$895$	−17.0837	−0.571046
$896$	−3.16828	−0.105845
$897$	3.33277	0.111278
$898$	−16.3373	−0.545181
$899$	−38.9778	−1.29998
$900$	4.25978	0.141993
$901$	−38.2564	−1.27451
$902$	0	0
$903$	0.702758	0.0233863
$904$	2.14352	0.0712925
$905$	−9.96233	−0.331159
$906$	−14.0661	−0.467313
$907$	−46.5179	−1.54460	−0.772300	−	0.635257i	$-0.780894\pi$
$907$	−46.5179	−1.54460	−0.772300	+	0.635257i	$0.780894\pi$
$908$	3.01179	0.0999498
$909$	−1.31484	−0.0436106
$910$	−3.90771	−0.129539
$911$	21.9576	0.727488	0.363744	−	0.931499i	$-0.381498\pi$
$911$	21.9576	0.727488	0.363744	+	0.931499i	$0.381498\pi$
$912$	−1.28398	−0.0425169
$913$	0	0
$914$	21.6394	0.715769
$915$	17.4714	0.577586
$916$	−20.8123	−0.687659
$917$	−48.7403	−1.60955
$918$	−15.8319	−0.522529
$919$	26.0498	0.859303	0.429651	−	0.902995i	$-0.358636\pi$
$919$	26.0498	0.859303	0.429651	+	0.902995i	$0.358636\pi$
$920$	−3.88877	−0.128209
$921$	−17.7420	−0.584619
$922$	9.99146	0.329051
$923$	11.9699	0.393995
$924$	0	0
$925$	19.7276	0.648640
$926$	18.7196	0.615163
$927$	4.11079	0.135016
$928$	4.97073	0.163172
$929$	−1.51172	−0.0495978	−0.0247989	−	0.999692i	$-0.507895\pi$
$929$	−1.51172	−0.0495978	−0.0247989	+	0.999692i	$0.507895\pi$
$930$	−13.6864	−0.448796
$931$	3.03797	0.0995655
$932$	−15.7607	−0.516258
$933$	29.7273	0.973230
$934$	−35.7800	−1.17076
$935$	0	0
$936$	1.22616	0.0400781
$937$	46.2992	1.51253	0.756265	−	0.654265i	$-0.227022\pi$
$937$	46.2992	1.51253	0.756265	+	0.654265i	$0.227022\pi$
$938$	−36.5019	−1.19183
$939$	21.8691	0.713671
$940$	7.83836	0.255659
$941$	−55.9080	−1.82255	−0.911274	−	0.411801i	$-0.864900\pi$
$941$	−55.9080	−1.82255	−0.911274	+	0.411801i	$0.864900\pi$
$942$	29.0003	0.944882
$943$	−30.8628	−1.00503
$944$	0.804852	0.0261957
$945$	24.0626	0.782758
$946$	0	0
$947$	42.9748	1.39649	0.698247	−	0.715857i	$-0.253964\pi$
$947$	42.9748	1.39649	0.698247	+	0.715857i	$0.253964\pi$
$948$	7.28007	0.236446
$949$	−3.22124	−0.104566
$950$	−3.15215	−0.102269
$951$	41.1079	1.33301
$952$	8.97776	0.290971
$953$	24.2414	0.785257	0.392629	−	0.919697i	$-0.371566\pi$
$953$	24.2414	0.785257	0.392629	+	0.919697i	$0.371566\pi$
$954$	−18.2448	−0.590697
$955$	−16.5470	−0.535448
$956$	25.3585	0.820153
$957$	0	0
$958$	−12.3527	−0.399098
$959$	−30.8916	−0.997541
$960$	1.74539	0.0563322
$961$	30.4887	0.983505
$962$	5.67849	0.183082
$963$	−12.3221	−0.397073
$964$	−7.85507	−0.252995
$965$	19.4939	0.627530
$966$	11.6376	0.374432
$967$	−49.2508	−1.58380	−0.791899	−	0.610653i	$-0.790907\pi$
$967$	−49.2508	−1.58380	−0.791899	+	0.610653i	$0.790907\pi$
$968$	0	0
$969$	3.63835	0.116881
$970$	−5.49725	−0.176506
$971$	40.2607	1.29203	0.646014	−	0.763326i	$-0.276435\pi$
$971$	40.2607	1.29203	0.646014	+	0.763326i	$0.276435\pi$
$972$	−12.7558	−0.409143
$973$	0.688900	0.0220851
$974$	13.9682	0.447570
$975$	−3.67225	−0.117606
$976$	10.0100	0.320413
$977$	4.31832	0.138155	0.0690777	−	0.997611i	$-0.477994\pi$
$977$	4.31832	0.138155	0.0690777	+	0.997611i	$0.477994\pi$
$978$	−16.6754	−0.533219
$979$	0	0
$980$	−4.12968	−0.131918
$981$	−24.7587	−0.790484
$982$	−3.44846	−0.110045
$983$	11.7864	0.375927	0.187963	−	0.982176i	$-0.439811\pi$
$983$	11.7864	0.375927	0.187963	+	0.982176i	$0.439811\pi$
$984$	13.8521	0.441588
$985$	21.3039	0.678797
$986$	−14.0853	−0.448566
$987$	−23.4571	−0.746648
$988$	−0.907331	−0.0288660
$989$	0.494201	0.0157147
$990$	0	0
$991$	15.8154	0.502393	0.251197	−	0.967936i	$-0.419176\pi$
$991$	15.8154	0.502393	0.251197	+	0.967936i	$0.419176\pi$
$992$	−7.84147	−0.248967
$993$	25.4416	0.807364
$994$	41.7974	1.32573
$995$	−1.87117	−0.0593200
$996$	−4.10776	−0.130159
$997$	−37.0811	−1.17437	−0.587185	−	0.809453i	$-0.699764\pi$
$997$	−37.0811	−1.17437	−0.587185	+	0.809453i	$0.699764\pi$
$998$	−43.4252	−1.37460
$999$	−34.9667	−1.10630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.4		10
11.2	odd	10		418.2.f.h.191.2	✓	20
11.6	odd	10		418.2.f.h.267.2	yes	20
11.10	odd	2		4598.2.a.cc.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.2	✓	20	11.2	odd	10
418.2.f.h.267.2	yes	20	11.6	odd	10
4598.2.a.cc.1.4		10	11.10	odd	2
4598.2.a.cd.1.4		10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.28398 q^{3} +1.00000 q^{4} -1.35936 q^{5} -1.28398 q^{6} -3.16828 q^{7} +1.00000 q^{8} -1.35139 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.28398 q^{3} +1.00000 q^{4} -1.35936 q^{5} -1.28398 q^{6} -3.16828 q^{7} +1.00000 q^{8} -1.35139 q^{9} -1.35936 q^{10} -1.28398 q^{12} -0.907331 q^{13} -3.16828 q^{14} +1.74539 q^{15} +1.00000 q^{16} -2.83364 q^{17} -1.35139 q^{18} +1.00000 q^{19} -1.35936 q^{20} +4.06801 q^{21} +2.86075 q^{23} -1.28398 q^{24} -3.15215 q^{25} -0.907331 q^{26} +5.58711 q^{27} -3.16828 q^{28} +4.97073 q^{29} +1.74539 q^{30} -7.84147 q^{31} +1.00000 q^{32} -2.83364 q^{34} +4.30681 q^{35} -1.35139 q^{36} -6.25846 q^{37} +1.00000 q^{38} +1.16500 q^{39} -1.35936 q^{40} -10.7884 q^{41} +4.06801 q^{42} +0.172752 q^{43} +1.83702 q^{45} +2.86075 q^{46} -5.76623 q^{47} -1.28398 q^{48} +3.03797 q^{49} -3.15215 q^{50} +3.63835 q^{51} -0.907331 q^{52} +13.5008 q^{53} +5.58711 q^{54} -3.16828 q^{56} -1.28398 q^{57} +4.97073 q^{58} +0.804852 q^{59} +1.74539 q^{60} +10.0100 q^{61} -7.84147 q^{62} +4.28157 q^{63} +1.00000 q^{64} +1.23339 q^{65} +11.5211 q^{67} -2.83364 q^{68} -3.67315 q^{69} +4.30681 q^{70} -13.1925 q^{71} -1.35139 q^{72} +3.55023 q^{73} -6.25846 q^{74} +4.04731 q^{75} +1.00000 q^{76} +1.16500 q^{78} -5.66991 q^{79} -1.35936 q^{80} -3.11959 q^{81} -10.7884 q^{82} +3.19923 q^{83} +4.06801 q^{84} +3.85193 q^{85} +0.172752 q^{86} -6.38234 q^{87} +18.5862 q^{89} +1.83702 q^{90} +2.87467 q^{91} +2.86075 q^{92} +10.0683 q^{93} -5.76623 q^{94} -1.35936 q^{95} -1.28398 q^{96} +4.04401 q^{97} +3.03797 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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