LMFDB - Embedded newform 4334.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} + \cdots - 400 $ x^17 - 7x^16 - 7x^15 + 137x^14 - 98x^13 - 1048x^12 + 1313x^11 + 4085x^10 - 6021x^9 - 8879x^8 + 13530x^7 + 11150x^6 - 15676x^5 - 8037x^4 + 8646x^3 + 3040x^2 - 1640x - 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.87628$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.87628 q^{3} +1.00000 q^{4} -2.40821 q^{5} +1.87628 q^{6} +1.70446 q^{7} +1.00000 q^{8} +0.520431 q^{9} -2.40821 q^{10} -1.00000 q^{11} +1.87628 q^{12} +0.0419654 q^{13} +1.70446 q^{14} -4.51847 q^{15} +1.00000 q^{16} -4.96548 q^{17} +0.520431 q^{18} -8.54692 q^{19} -2.40821 q^{20} +3.19804 q^{21} -1.00000 q^{22} -2.98767 q^{23} +1.87628 q^{24} +0.799457 q^{25} +0.0419654 q^{26} -4.65237 q^{27} +1.70446 q^{28} +1.32735 q^{29} -4.51847 q^{30} -8.45192 q^{31} +1.00000 q^{32} -1.87628 q^{33} -4.96548 q^{34} -4.10468 q^{35} +0.520431 q^{36} +4.04689 q^{37} -8.54692 q^{38} +0.0787390 q^{39} -2.40821 q^{40} +10.0542 q^{41} +3.19804 q^{42} -8.36404 q^{43} -1.00000 q^{44} -1.25330 q^{45} -2.98767 q^{46} +0.374163 q^{47} +1.87628 q^{48} -4.09483 q^{49} +0.799457 q^{50} -9.31664 q^{51} +0.0419654 q^{52} +7.53465 q^{53} -4.65237 q^{54} +2.40821 q^{55} +1.70446 q^{56} -16.0364 q^{57} +1.32735 q^{58} -2.04260 q^{59} -4.51847 q^{60} +2.53017 q^{61} -8.45192 q^{62} +0.887052 q^{63} +1.00000 q^{64} -0.101061 q^{65} -1.87628 q^{66} +2.97228 q^{67} -4.96548 q^{68} -5.60571 q^{69} -4.10468 q^{70} -9.85440 q^{71} +0.520431 q^{72} +5.29069 q^{73} +4.04689 q^{74} +1.50001 q^{75} -8.54692 q^{76} -1.70446 q^{77} +0.0787390 q^{78} +0.855219 q^{79} -2.40821 q^{80} -10.2904 q^{81} +10.0542 q^{82} -2.00289 q^{83} +3.19804 q^{84} +11.9579 q^{85} -8.36404 q^{86} +2.49049 q^{87} -1.00000 q^{88} +3.10139 q^{89} -1.25330 q^{90} +0.0715283 q^{91} -2.98767 q^{92} -15.8582 q^{93} +0.374163 q^{94} +20.5827 q^{95} +1.87628 q^{96} +11.8510 q^{97} -4.09483 q^{98} -0.520431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

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
$3$	1.87628	1.08327	0.541636	−	0.840613i	$-0.317805\pi$
$3$	1.87628	1.08327	0.541636	+	0.840613i	$0.317805\pi$
$4$	1.00000	0.500000
$5$	−2.40821	−1.07698	−0.538491	−	0.842631i	$-0.681006\pi$
$5$	−2.40821	−1.07698	−0.538491	+	0.842631i	$0.681006\pi$
$6$	1.87628	0.765989
$7$	1.70446	0.644224	0.322112	−	0.946702i	$-0.395607\pi$
$7$	1.70446	0.644224	0.322112	+	0.946702i	$0.395607\pi$
$8$	1.00000	0.353553
$9$	0.520431	0.173477
$10$	−2.40821	−0.761542
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.87628	0.541636
$13$	0.0419654	0.0116391	0.00581956	−	0.999983i	$-0.498148\pi$
$13$	0.0419654	0.0116391	0.00581956	+	0.999983i	$0.498148\pi$
$14$	1.70446	0.455535
$15$	−4.51847	−1.16666
$16$	1.00000	0.250000
$17$	−4.96548	−1.20431	−0.602153	−	0.798380i	$-0.705690\pi$
$17$	−4.96548	−1.20431	−0.602153	+	0.798380i	$0.705690\pi$
$18$	0.520431	0.122667
$19$	−8.54692	−1.96080	−0.980399	−	0.197022i	$-0.936873\pi$
$19$	−8.54692	−1.96080	−0.980399	+	0.197022i	$0.936873\pi$
$20$	−2.40821	−0.538491
$21$	3.19804	0.697869
$22$	−1.00000	−0.213201
$23$	−2.98767	−0.622972	−0.311486	−	0.950251i	$-0.600827\pi$
$23$	−2.98767	−0.622972	−0.311486	+	0.950251i	$0.600827\pi$
$24$	1.87628	0.382994
$25$	0.799457	0.159891
$26$	0.0419654	0.00823010
$27$	−4.65237	−0.895349
$28$	1.70446	0.322112
$29$	1.32735	0.246484	0.123242	−	0.992377i	$-0.460671\pi$
$29$	1.32735	0.246484	0.123242	+	0.992377i	$0.460671\pi$
$30$	−4.51847	−0.824956
$31$	−8.45192	−1.51801	−0.759005	−	0.651085i	$-0.774314\pi$
$31$	−8.45192	−1.51801	−0.759005	+	0.651085i	$0.774314\pi$
$32$	1.00000	0.176777
$33$	−1.87628	−0.326619
$34$	−4.96548	−0.851573
$35$	−4.10468	−0.693818
$36$	0.520431	0.0867385
$37$	4.04689	0.665305	0.332652	−	0.943050i	$-0.392056\pi$
$37$	4.04689	0.665305	0.332652	+	0.943050i	$0.392056\pi$
$38$	−8.54692	−1.38649
$39$	0.0787390	0.0126083
$40$	−2.40821	−0.380771
$41$	10.0542	1.57020	0.785098	−	0.619372i	$-0.212613\pi$
$41$	10.0542	1.57020	0.785098	+	0.619372i	$0.212613\pi$
$42$	3.19804	0.493468
$43$	−8.36404	−1.27550	−0.637752	−	0.770242i	$-0.720136\pi$
$43$	−8.36404	−1.27550	−0.637752	+	0.770242i	$0.720136\pi$
$44$	−1.00000	−0.150756
$45$	−1.25330	−0.186832
$46$	−2.98767	−0.440508
$47$	0.374163	0.0545773	0.0272886	−	0.999628i	$-0.491313\pi$
$47$	0.374163	0.0545773	0.0272886	+	0.999628i	$0.491313\pi$
$48$	1.87628	0.270818
$49$	−4.09483	−0.584975
$50$	0.799457	0.113060
$51$	−9.31664	−1.30459
$52$	0.0419654	0.00581956
$53$	7.53465	1.03496	0.517482	−	0.855694i	$-0.326869\pi$
$53$	7.53465	1.03496	0.517482	+	0.855694i	$0.326869\pi$
$54$	−4.65237	−0.633107
$55$	2.40821	0.324722
$56$	1.70446	0.227768
$57$	−16.0364	−2.12408
$58$	1.32735	0.174290
$59$	−2.04260	−0.265924	−0.132962	−	0.991121i	$-0.542449\pi$
$59$	−2.04260	−0.265924	−0.132962	+	0.991121i	$0.542449\pi$
$60$	−4.51847	−0.583332
$61$	2.53017	0.323955	0.161978	−	0.986794i	$-0.448213\pi$
$61$	2.53017	0.323955	0.161978	+	0.986794i	$0.448213\pi$
$62$	−8.45192	−1.07339
$63$	0.887052	0.111758
$64$	1.00000	0.125000
$65$	−0.101061	−0.0125351
$66$	−1.87628	−0.230954
$67$	2.97228	0.363121	0.181561	−	0.983380i	$-0.441885\pi$
$67$	2.97228	0.363121	0.181561	+	0.983380i	$0.441885\pi$
$68$	−4.96548	−0.602153
$69$	−5.60571	−0.674848
$70$	−4.10468	−0.490603
$71$	−9.85440	−1.16950	−0.584751	−	0.811213i	$-0.698808\pi$
$71$	−9.85440	−1.16950	−0.584751	+	0.811213i	$0.698808\pi$
$72$	0.520431	0.0613334
$73$	5.29069	0.619229	0.309614	−	0.950862i	$-0.399800\pi$
$73$	5.29069	0.619229	0.309614	+	0.950862i	$0.399800\pi$
$74$	4.04689	0.470441
$75$	1.50001	0.173206
$76$	−8.54692	−0.980399
$77$	−1.70446	−0.194241
$78$	0.0787390	0.00891543
$79$	0.855219	0.0962196	0.0481098	−	0.998842i	$-0.484680\pi$
$79$	0.855219	0.0962196	0.0481098	+	0.998842i	$0.484680\pi$
$80$	−2.40821	−0.269246
$81$	−10.2904	−1.14338
$82$	10.0542	1.11030
$83$	−2.00289	−0.219846	−0.109923	−	0.993940i	$-0.535060\pi$
$83$	−2.00289	−0.219846	−0.109923	+	0.993940i	$0.535060\pi$
$84$	3.19804	0.348935
$85$	11.9579	1.29702
$86$	−8.36404	−0.901918
$87$	2.49049	0.267009
$88$	−1.00000	−0.106600
$89$	3.10139	0.328747	0.164373	−	0.986398i	$-0.447440\pi$
$89$	3.10139	0.328747	0.164373	+	0.986398i	$0.447440\pi$
$90$	−1.25330	−0.132110
$91$	0.0715283	0.00749820
$92$	−2.98767	−0.311486
$93$	−15.8582	−1.64442
$94$	0.374163	0.0385920
$95$	20.5827	2.11175
$96$	1.87628	0.191497
$97$	11.8510	1.20329	0.601643	−	0.798765i	$-0.294513\pi$
$97$	11.8510	1.20329	0.601643	+	0.798765i	$0.294513\pi$
$98$	−4.09483	−0.413640
$99$	−0.520431	−0.0523053
$100$	0.799457	0.0799457
$101$	1.68016	0.167182	0.0835910	−	0.996500i	$-0.473361\pi$
$101$	1.68016	0.167182	0.0835910	+	0.996500i	$0.473361\pi$
$102$	−9.31664	−0.922485
$103$	−2.42599	−0.239039	−0.119520	−	0.992832i	$-0.538135\pi$
$103$	−2.42599	−0.239039	−0.119520	+	0.992832i	$0.538135\pi$
$104$	0.0419654	0.00411505
$105$	−7.70154	−0.751593
$106$	7.53465	0.731830
$107$	−19.9178	−1.92552	−0.962762	−	0.270350i	$-0.912861\pi$
$107$	−19.9178	−1.92552	−0.962762	+	0.270350i	$0.912861\pi$
$108$	−4.65237	−0.447674
$109$	12.6390	1.21060	0.605299	−	0.795998i	$-0.293053\pi$
$109$	12.6390	1.21060	0.605299	+	0.795998i	$0.293053\pi$
$110$	2.40821	0.229613
$111$	7.59310	0.720705
$112$	1.70446	0.161056
$113$	14.0958	1.32602	0.663011	−	0.748610i	$-0.269278\pi$
$113$	14.0958	1.32602	0.663011	+	0.748610i	$0.269278\pi$
$114$	−16.0364	−1.50195
$115$	7.19493	0.670930
$116$	1.32735	0.123242
$117$	0.0218401	0.00201912
$118$	−2.04260	−0.188037
$119$	−8.46345	−0.775843
$120$	−4.51847	−0.412478
$121$	1.00000	0.0909091
$122$	2.53017	0.229071
$123$	18.8644	1.70095
$124$	−8.45192	−0.759005
$125$	10.1158	0.904782
$126$	0.887052	0.0790248
$127$	−11.0676	−0.982093	−0.491047	−	0.871133i	$-0.663386\pi$
$127$	−11.0676	−0.982093	−0.491047	+	0.871133i	$0.663386\pi$
$128$	1.00000	0.0883883
$129$	−15.6933	−1.38172
$130$	−0.101061	−0.00886367
$131$	−15.6723	−1.36930	−0.684648	−	0.728874i	$-0.740044\pi$
$131$	−15.6723	−1.36930	−0.684648	+	0.728874i	$0.740044\pi$
$132$	−1.87628	−0.163309
$133$	−14.5679	−1.26319
$134$	2.97228	0.256765
$135$	11.2039	0.964275
$136$	−4.96548	−0.425787
$137$	3.35052	0.286254	0.143127	−	0.989704i	$-0.454284\pi$
$137$	3.35052	0.286254	0.143127	+	0.989704i	$0.454284\pi$
$138$	−5.60571	−0.477190
$139$	11.4461	0.970847	0.485424	−	0.874279i	$-0.338665\pi$
$139$	11.4461	0.970847	0.485424	+	0.874279i	$0.338665\pi$
$140$	−4.10468	−0.346909
$141$	0.702035	0.0591220
$142$	−9.85440	−0.826963
$143$	−0.0419654	−0.00350933
$144$	0.520431	0.0433692
$145$	−3.19654	−0.265459
$146$	5.29069	0.437861
$147$	−7.68305	−0.633687
$148$	4.04689	0.332652
$149$	−2.80403	−0.229715	−0.114858	−	0.993382i	$-0.536641\pi$
$149$	−2.80403	−0.229715	−0.114858	+	0.993382i	$0.536641\pi$
$150$	1.50001	0.122475
$151$	5.19141	0.422471	0.211235	−	0.977435i	$-0.432251\pi$
$151$	5.19141	0.422471	0.211235	+	0.977435i	$0.432251\pi$
$152$	−8.54692	−0.693247
$153$	−2.58419	−0.208919
$154$	−1.70446	−0.137349
$155$	20.3540	1.63487
$156$	0.0787390	0.00630416
$157$	1.64185	0.131034	0.0655170	−	0.997851i	$-0.479130\pi$
$157$	1.64185	0.131034	0.0655170	+	0.997851i	$0.479130\pi$
$158$	0.855219	0.0680376
$159$	14.1371	1.12115
$160$	−2.40821	−0.190385
$161$	−5.09235	−0.401334
$162$	−10.2904	−0.808494
$163$	−16.1985	−1.26876	−0.634382	−	0.773019i	$-0.718746\pi$
$163$	−16.1985	−1.26876	−0.634382	+	0.773019i	$0.718746\pi$
$164$	10.0542	0.785098
$165$	4.51847	0.351763
$166$	−2.00289	−0.155455
$167$	−6.30982	−0.488268	−0.244134	−	0.969741i	$-0.578504\pi$
$167$	−6.30982	−0.488268	−0.244134	+	0.969741i	$0.578504\pi$
$168$	3.19804	0.246734
$169$	−12.9982	−0.999865
$170$	11.9579	0.917130
$171$	−4.44808	−0.340153
$172$	−8.36404	−0.637752
$173$	−4.95476	−0.376704	−0.188352	−	0.982102i	$-0.560315\pi$
$173$	−4.95476	−0.376704	−0.188352	+	0.982102i	$0.560315\pi$
$174$	2.49049	0.188804
$175$	1.36264	0.103006
$176$	−1.00000	−0.0753778
$177$	−3.83249	−0.288068
$178$	3.10139	0.232459
$179$	18.5569	1.38701	0.693505	−	0.720452i	$-0.256065\pi$
$179$	18.5569	1.38701	0.693505	+	0.720452i	$0.256065\pi$
$180$	−1.25330	−0.0934158
$181$	8.53533	0.634426	0.317213	−	0.948354i	$-0.397253\pi$
$181$	8.53533	0.634426	0.317213	+	0.948354i	$0.397253\pi$
$182$	0.0715283	0.00530203
$183$	4.74731	0.350931
$184$	−2.98767	−0.220254
$185$	−9.74574	−0.716521
$186$	−15.8582	−1.16278
$187$	4.96548	0.363112
$188$	0.374163	0.0272886
$189$	−7.92976	−0.576805
$190$	20.5827	1.49323
$191$	−5.88789	−0.426033	−0.213016	−	0.977049i	$-0.568329\pi$
$191$	−5.88789	−0.426033	−0.213016	+	0.977049i	$0.568329\pi$
$192$	1.87628	0.135409
$193$	7.07445	0.509230	0.254615	−	0.967043i	$-0.418051\pi$
$193$	7.07445	0.509230	0.254615	+	0.967043i	$0.418051\pi$
$194$	11.8510	0.850851
$195$	−0.189620	−0.0135789
$196$	−4.09483	−0.292488
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−0.520431	−0.0369854
$199$	−6.66336	−0.472353	−0.236177	−	0.971710i	$-0.575894\pi$
$199$	−6.66336	−0.472353	−0.236177	+	0.971710i	$0.575894\pi$
$200$	0.799457	0.0565302
$201$	5.57682	0.393359
$202$	1.68016	0.118215
$203$	2.26242	0.158791
$204$	−9.31664	−0.652296
$205$	−24.2125	−1.69107
$206$	−2.42599	−0.169026
$207$	−1.55488	−0.108071
$208$	0.0419654	0.00290978
$209$	8.54692	0.591203
$210$	−7.70154	−0.531457
$211$	−1.97095	−0.135686	−0.0678430	−	0.997696i	$-0.521612\pi$
$211$	−1.97095	−0.135686	−0.0678430	+	0.997696i	$0.521612\pi$
$212$	7.53465	0.517482
$213$	−18.4896	−1.26689
$214$	−19.9178	−1.36155
$215$	20.1423	1.37370
$216$	−4.65237	−0.316554
$217$	−14.4059	−0.977938
$218$	12.6390	0.856023
$219$	9.92682	0.670793
$220$	2.40821	0.162361
$221$	−0.208379	−0.0140171
$222$	7.59310	0.509616
$223$	−11.0359	−0.739015	−0.369508	−	0.929228i	$-0.620474\pi$
$223$	−11.0359	−0.739015	−0.369508	+	0.929228i	$0.620474\pi$
$224$	1.70446	0.113884
$225$	0.416062	0.0277375
$226$	14.0958	0.937639
$227$	9.96423	0.661349	0.330675	−	0.943745i	$-0.392724\pi$
$227$	9.96423	0.661349	0.330675	+	0.943745i	$0.392724\pi$
$228$	−16.0364	−1.06204
$229$	−14.4346	−0.953866	−0.476933	−	0.878940i	$-0.658252\pi$
$229$	−14.4346	−0.953866	−0.476933	+	0.878940i	$0.658252\pi$
$230$	7.19493	0.474419
$231$	−3.19804	−0.210416
$232$	1.32735	0.0871451
$233$	16.7948	1.10027	0.550133	−	0.835077i	$-0.314577\pi$
$233$	16.7948	1.10027	0.550133	+	0.835077i	$0.314577\pi$
$234$	0.0218401	0.00142773
$235$	−0.901062	−0.0587788
$236$	−2.04260	−0.132962
$237$	1.60463	0.104232
$238$	−8.46345	−0.548604
$239$	24.8879	1.60987	0.804934	−	0.593365i	$-0.202201\pi$
$239$	24.8879	1.60987	0.804934	+	0.593365i	$0.202201\pi$
$240$	−4.51847	−0.291666
$241$	−17.5898	−1.13306	−0.566528	−	0.824043i	$-0.691714\pi$
$241$	−17.5898	−1.13306	−0.566528	+	0.824043i	$0.691714\pi$
$242$	1.00000	0.0642824
$243$	−5.35066	−0.343245
$244$	2.53017	0.161978
$245$	9.86119	0.630008
$246$	18.8644	1.20275
$247$	−0.358675	−0.0228220
$248$	−8.45192	−0.536697
$249$	−3.75799	−0.238153
$250$	10.1158	0.639778
$251$	−27.1453	−1.71340	−0.856698	−	0.515818i	$-0.827488\pi$
$251$	−27.1453	−1.71340	−0.856698	+	0.515818i	$0.827488\pi$
$252$	0.887052	0.0558790
$253$	2.98767	0.187833
$254$	−11.0676	−0.694445
$255$	22.4364	1.40502
$256$	1.00000	0.0625000
$257$	−24.2591	−1.51324	−0.756620	−	0.653855i	$-0.773150\pi$
$257$	−24.2591	−1.51324	−0.756620	+	0.653855i	$0.773150\pi$
$258$	−15.6933	−0.977021
$259$	6.89775	0.428605
$260$	−0.101061	−0.00626756
$261$	0.690796	0.0427592
$262$	−15.6723	−0.968238
$263$	−8.84355	−0.545316	−0.272658	−	0.962111i	$-0.587903\pi$
$263$	−8.84355	−0.545316	−0.272658	+	0.962111i	$0.587903\pi$
$264$	−1.87628	−0.115477
$265$	−18.1450	−1.11464
$266$	−14.5679	−0.893212
$267$	5.81908	0.356122
$268$	2.97228	0.181561
$269$	−21.9464	−1.33810	−0.669048	−	0.743219i	$-0.733298\pi$
$269$	−21.9464	−1.33810	−0.669048	+	0.743219i	$0.733298\pi$
$270$	11.2039	0.681845
$271$	9.20821	0.559359	0.279680	−	0.960093i	$-0.409772\pi$
$271$	9.20821	0.559359	0.279680	+	0.960093i	$0.409772\pi$
$272$	−4.96548	−0.301077
$273$	0.134207	0.00812259
$274$	3.35052	0.202412
$275$	−0.799457	−0.0482091
$276$	−5.60571	−0.337424
$277$	−25.4499	−1.52914	−0.764568	−	0.644543i	$-0.777048\pi$
$277$	−25.4499	−1.52914	−0.764568	+	0.644543i	$0.777048\pi$
$278$	11.4461	0.686493
$279$	−4.39864	−0.263340
$280$	−4.10468	−0.245302
$281$	−12.9781	−0.774211	−0.387106	−	0.922035i	$-0.626525\pi$
$281$	−12.9781	−0.774211	−0.387106	+	0.922035i	$0.626525\pi$
$282$	0.702035	0.0418056
$283$	−4.06933	−0.241896	−0.120948	−	0.992659i	$-0.538593\pi$
$283$	−4.06933	−0.241896	−0.120948	+	0.992659i	$0.538593\pi$
$284$	−9.85440	−0.584751
$285$	38.6190	2.28759
$286$	−0.0419654	−0.00248147
$287$	17.1369	1.01156
$288$	0.520431	0.0306667
$289$	7.65603	0.450355
$290$	−3.19654	−0.187708
$291$	22.2358	1.30348
$292$	5.29069	0.309614
$293$	34.2111	1.99863	0.999316	−	0.0369875i	$-0.0117762\pi$
$293$	34.2111	1.99863	0.999316	+	0.0369875i	$0.0117762\pi$
$294$	−7.68305	−0.448084
$295$	4.91900	0.286395
$296$	4.04689	0.235221
$297$	4.65237	0.269958
$298$	−2.80403	−0.162433
$299$	−0.125379	−0.00725085
$300$	1.50001	0.0866029
$301$	−14.2561	−0.821710
$302$	5.19141	0.298732
$303$	3.15245	0.181103
$304$	−8.54692	−0.490199
$305$	−6.09317	−0.348894
$306$	−2.58419	−0.147728
$307$	−9.55211	−0.545168	−0.272584	−	0.962132i	$-0.587878\pi$
$307$	−9.55211	−0.545168	−0.272584	+	0.962132i	$0.587878\pi$
$308$	−1.70446	−0.0971204
$309$	−4.55183	−0.258945
$310$	20.3540	1.15603
$311$	−20.5365	−1.16452	−0.582259	−	0.813003i	$-0.697831\pi$
$311$	−20.5365	−1.16452	−0.582259	+	0.813003i	$0.697831\pi$
$312$	0.0787390	0.00445772
$313$	−23.2423	−1.31373	−0.656866	−	0.754007i	$-0.728118\pi$
$313$	−23.2423	−1.31373	−0.656866	+	0.754007i	$0.728118\pi$
$314$	1.64185	0.0926550
$315$	−2.13620	−0.120361
$316$	0.855219	0.0481098
$317$	3.45907	0.194281	0.0971405	−	0.995271i	$-0.469030\pi$
$317$	3.45907	0.194281	0.0971405	+	0.995271i	$0.469030\pi$
$318$	14.1371	0.792771
$319$	−1.32735	−0.0743176
$320$	−2.40821	−0.134623
$321$	−37.3713	−2.08587
$322$	−5.09235	−0.283786
$323$	42.4396	2.36140
$324$	−10.2904	−0.571691
$325$	0.0335496	0.00186100
$326$	−16.1985	−0.897152
$327$	23.7144	1.31141
$328$	10.0542	0.555148
$329$	0.637745	0.0351600
$330$	4.51847	0.248734
$331$	5.11299	0.281035	0.140518	−	0.990078i	$-0.455123\pi$
$331$	5.11299	0.281035	0.140518	+	0.990078i	$0.455123\pi$
$332$	−2.00289	−0.109923
$333$	2.10613	0.115415
$334$	−6.30982	−0.345258
$335$	−7.15785	−0.391075
$336$	3.19804	0.174467
$337$	5.31525	0.289540	0.144770	−	0.989465i	$-0.453756\pi$
$337$	5.31525	0.289540	0.144770	+	0.989465i	$0.453756\pi$
$338$	−12.9982	−0.707011
$339$	26.4477	1.43644
$340$	11.9579	0.648509
$341$	8.45192	0.457697
$342$	−4.44808	−0.240525
$343$	−18.9107	−1.02108
$344$	−8.36404	−0.450959
$345$	13.4997	0.726800
$346$	−4.95476	−0.266370
$347$	−16.9611	−0.910522	−0.455261	−	0.890358i	$-0.650454\pi$
$347$	−16.9611	−0.910522	−0.455261	+	0.890358i	$0.650454\pi$
$348$	2.49049	0.133504
$349$	−16.7962	−0.899079	−0.449540	−	0.893260i	$-0.648412\pi$
$349$	−16.7962	−0.899079	−0.449540	+	0.893260i	$0.648412\pi$
$350$	1.36264	0.0728362
$351$	−0.195239	−0.0104211
$352$	−1.00000	−0.0533002
$353$	25.6462	1.36501	0.682505	−	0.730881i	$-0.260891\pi$
$353$	25.6462	1.36501	0.682505	+	0.730881i	$0.260891\pi$
$354$	−3.83249	−0.203695
$355$	23.7314	1.25953
$356$	3.10139	0.164373
$357$	−15.8798	−0.840449
$358$	18.5569	0.980764
$359$	22.7650	1.20149	0.600746	−	0.799440i	$-0.294870\pi$
$359$	22.7650	1.20149	0.600746	+	0.799440i	$0.294870\pi$
$360$	−1.25330	−0.0660550
$361$	54.0498	2.84473
$362$	8.53533	0.448607
$363$	1.87628	0.0984792
$364$	0.0715283	0.00374910
$365$	−12.7411	−0.666898
$366$	4.74731	0.248146
$367$	19.5005	1.01792	0.508959	−	0.860791i	$-0.330030\pi$
$367$	19.5005	1.01792	0.508959	+	0.860791i	$0.330030\pi$
$368$	−2.98767	−0.155743
$369$	5.23249	0.272393
$370$	−9.74574	−0.506657
$371$	12.8425	0.666749
$372$	−15.8582	−0.822208
$373$	−0.368520	−0.0190813	−0.00954063	−	0.999954i	$-0.503037\pi$
$373$	−0.368520	−0.0190813	−0.00954063	+	0.999954i	$0.503037\pi$
$374$	4.96548	0.256759
$375$	18.9800	0.980125
$376$	0.374163	0.0192960
$377$	0.0557030	0.00286885
$378$	−7.92976	−0.407863
$379$	−27.6329	−1.41940	−0.709702	−	0.704502i	$-0.751171\pi$
$379$	−27.6329	−1.41940	−0.709702	+	0.704502i	$0.751171\pi$
$380$	20.5827	1.05587
$381$	−20.7660	−1.06387
$382$	−5.88789	−0.301251
$383$	5.88684	0.300803	0.150402	−	0.988625i	$-0.451943\pi$
$383$	5.88684	0.300803	0.150402	+	0.988625i	$0.451943\pi$
$384$	1.87628	0.0957486
$385$	4.10468	0.209194
$386$	7.07445	0.360080
$387$	−4.35290	−0.221271
$388$	11.8510	0.601643
$389$	21.5887	1.09459	0.547295	−	0.836940i	$-0.315658\pi$
$389$	21.5887	1.09459	0.547295	+	0.836940i	$0.315658\pi$
$390$	−0.189620	−0.00960177
$391$	14.8352	0.750250
$392$	−4.09483	−0.206820
$393$	−29.4056	−1.48332
$394$	1.00000	0.0503793
$395$	−2.05954	−0.103627
$396$	−0.520431	−0.0261526
$397$	−8.60327	−0.431786	−0.215893	−	0.976417i	$-0.569266\pi$
$397$	−8.60327	−0.431786	−0.215893	+	0.976417i	$0.569266\pi$
$398$	−6.66336	−0.334004
$399$	−27.3334	−1.36838
$400$	0.799457	0.0399729
$401$	20.9056	1.04398	0.521988	−	0.852953i	$-0.325191\pi$
$401$	20.9056	1.04398	0.521988	+	0.852953i	$0.325191\pi$
$402$	5.57682	0.278147
$403$	−0.354689	−0.0176683
$404$	1.68016	0.0835910
$405$	24.7815	1.23140
$406$	2.26242	0.112282
$407$	−4.04689	−0.200597
$408$	−9.31664	−0.461243
$409$	−4.59003	−0.226962	−0.113481	−	0.993540i	$-0.536200\pi$
$409$	−4.59003	−0.226962	−0.113481	+	0.993540i	$0.536200\pi$
$410$	−24.2125	−1.19577
$411$	6.28651	0.310091
$412$	−2.42599	−0.119520
$413$	−3.48152	−0.171315
$414$	−1.55488	−0.0764180
$415$	4.82338	0.236770
$416$	0.0419654	0.00205753
$417$	21.4761	1.05169
$418$	8.54692	0.418044
$419$	20.5895	1.00586	0.502931	−	0.864327i	$-0.332255\pi$
$419$	20.5895	1.00586	0.502931	+	0.864327i	$0.332255\pi$
$420$	−7.70154	−0.375797
$421$	−0.545293	−0.0265759	−0.0132880	−	0.999912i	$-0.504230\pi$
$421$	−0.545293	−0.0265759	−0.0132880	+	0.999912i	$0.504230\pi$
$422$	−1.97095	−0.0959444
$423$	0.194726	0.00946790
$424$	7.53465	0.365915
$425$	−3.96969	−0.192558
$426$	−18.4896	−0.895825
$427$	4.31257	0.208700
$428$	−19.9178	−0.962762
$429$	−0.0787390	−0.00380155
$430$	20.1423	0.971349
$431$	−22.0236	−1.06084	−0.530419	−	0.847735i	$-0.677966\pi$
$431$	−22.0236	−1.06084	−0.530419	+	0.847735i	$0.677966\pi$
$432$	−4.65237	−0.223837
$433$	24.7037	1.18719	0.593593	−	0.804766i	$-0.297709\pi$
$433$	24.7037	1.18719	0.593593	+	0.804766i	$0.297709\pi$
$434$	−14.4059	−0.691507
$435$	−5.99761	−0.287564
$436$	12.6390	0.605299
$437$	25.5354	1.22152
$438$	9.92682	0.474322
$439$	6.60749	0.315358	0.157679	−	0.987490i	$-0.449599\pi$
$439$	6.60749	0.315358	0.157679	+	0.987490i	$0.449599\pi$
$440$	2.40821	0.114807
$441$	−2.13107	−0.101480
$442$	−0.208379	−0.00991157
$443$	37.8275	1.79724	0.898620	−	0.438729i	$-0.144571\pi$
$443$	37.8275	1.79724	0.898620	+	0.438729i	$0.144571\pi$
$444$	7.59310	0.360353
$445$	−7.46879	−0.354054
$446$	−11.0359	−0.522563
$447$	−5.26116	−0.248844
$448$	1.70446	0.0805280
$449$	34.2765	1.61761	0.808805	−	0.588078i	$-0.200115\pi$
$449$	34.2765	1.61761	0.808805	+	0.588078i	$0.200115\pi$
$450$	0.416062	0.0196134
$451$	−10.0542	−0.473432
$452$	14.0958	0.663011
$453$	9.74054	0.457650
$454$	9.96423	0.467645
$455$	−0.172255	−0.00807543
$456$	−16.0364	−0.750974
$457$	−34.3365	−1.60619	−0.803096	−	0.595850i	$-0.796815\pi$
$457$	−34.3365	−1.60619	−0.803096	+	0.595850i	$0.796815\pi$
$458$	−14.4346	−0.674485
$459$	23.1013	1.07827
$460$	7.19493	0.335465
$461$	−0.343935	−0.0160186	−0.00800932	−	0.999968i	$-0.502549\pi$
$461$	−0.343935	−0.0160186	−0.00800932	+	0.999968i	$0.502549\pi$
$462$	−3.19804	−0.148786
$463$	6.86964	0.319259	0.159630	−	0.987177i	$-0.448970\pi$
$463$	6.86964	0.319259	0.159630	+	0.987177i	$0.448970\pi$
$464$	1.32735	0.0616209
$465$	38.1898	1.77101
$466$	16.7948	0.778006
$467$	−6.00587	−0.277919	−0.138959	−	0.990298i	$-0.544376\pi$
$467$	−6.00587	−0.277919	−0.138959	+	0.990298i	$0.544376\pi$
$468$	0.0218401	0.00100956
$469$	5.06611	0.233931
$470$	−0.901062	−0.0415629
$471$	3.08057	0.141945
$472$	−2.04260	−0.0940183
$473$	8.36404	0.384579
$474$	1.60463	0.0737031
$475$	−6.83290	−0.313515
$476$	−8.46345	−0.387922
$477$	3.92127	0.179542
$478$	24.8879	1.13835
$479$	−32.0469	−1.46426	−0.732130	−	0.681165i	$-0.761473\pi$
$479$	−32.0469	−1.46426	−0.732130	+	0.681165i	$0.761473\pi$
$480$	−4.51847	−0.206239
$481$	0.169830	0.00774356
$482$	−17.5898	−0.801191
$483$	−9.55469	−0.434753
$484$	1.00000	0.0454545
$485$	−28.5396	−1.29592
$486$	−5.35066	−0.242711
$487$	−16.8881	−0.765273	−0.382637	−	0.923899i	$-0.624984\pi$
$487$	−16.8881	−0.765273	−0.382637	+	0.923899i	$0.624984\pi$
$488$	2.53017	0.114535
$489$	−30.3929	−1.37442
$490$	9.86119	0.445483
$491$	31.7080	1.43096	0.715481	−	0.698632i	$-0.246208\pi$
$491$	31.7080	1.43096	0.715481	+	0.698632i	$0.246208\pi$
$492$	18.8644	0.850474
$493$	−6.59096	−0.296842
$494$	−0.358675	−0.0161376
$495$	1.25330	0.0563319
$496$	−8.45192	−0.379502
$497$	−16.7964	−0.753421
$498$	−3.75799	−0.168400
$499$	−28.1109	−1.25842	−0.629208	−	0.777237i	$-0.716621\pi$
$499$	−28.1109	−1.25842	−0.629208	+	0.777237i	$0.716621\pi$
$500$	10.1158	0.452391
$501$	−11.8390	−0.528927
$502$	−27.1453	−1.21155
$503$	−34.6747	−1.54607	−0.773034	−	0.634365i	$-0.781262\pi$
$503$	−34.6747	−1.54607	−0.773034	+	0.634365i	$0.781262\pi$
$504$	0.887052	0.0395124
$505$	−4.04617	−0.180052
$506$	2.98767	0.132818
$507$	−24.3883	−1.08312
$508$	−11.0676	−0.491047
$509$	−20.0200	−0.887371	−0.443686	−	0.896182i	$-0.646329\pi$
$509$	−20.0200	−0.887371	−0.443686	+	0.896182i	$0.646329\pi$
$510$	22.4364	0.993500
$511$	9.01775	0.398922
$512$	1.00000	0.0441942
$513$	39.7634	1.75560
$514$	−24.2591	−1.07002
$515$	5.84227	0.257441
$516$	−15.6933	−0.690859
$517$	−0.374163	−0.0164557
$518$	6.89775	0.303070
$519$	−9.29653	−0.408072
$520$	−0.101061	−0.00443184
$521$	13.6175	0.596592	0.298296	−	0.954473i	$-0.403582\pi$
$521$	13.6175	0.596592	0.298296	+	0.954473i	$0.403582\pi$
$522$	0.690796	0.0302353
$523$	5.47057	0.239211	0.119606	−	0.992821i	$-0.461837\pi$
$523$	5.47057	0.239211	0.119606	+	0.992821i	$0.461837\pi$
$524$	−15.6723	−0.684648
$525$	2.55670	0.111583
$526$	−8.84355	−0.385597
$527$	41.9679	1.82815
$528$	−1.87628	−0.0816547
$529$	−14.0738	−0.611906
$530$	−18.1450	−0.788168
$531$	−1.06303	−0.0461317
$532$	−14.5679	−0.631597
$533$	0.421927	0.0182757
$534$	5.81908	0.251816
$535$	47.9661	2.07376
$536$	2.97228	0.128383
$537$	34.8180	1.50251
$538$	−21.9464	−0.946177
$539$	4.09483	0.176377
$540$	11.2039	0.482138
$541$	11.6009	0.498764	0.249382	−	0.968405i	$-0.419773\pi$
$541$	11.6009	0.498764	0.249382	+	0.968405i	$0.419773\pi$
$542$	9.20821	0.395527
$543$	16.0147	0.687256
$544$	−4.96548	−0.212893
$545$	−30.4374	−1.30379
$546$	0.134207	0.00574354
$547$	17.0241	0.727896	0.363948	−	0.931419i	$-0.381429\pi$
$547$	17.0241	0.727896	0.363948	+	0.931419i	$0.381429\pi$
$548$	3.35052	0.143127
$549$	1.31678	0.0561987
$550$	−0.799457	−0.0340890
$551$	−11.3448	−0.483304
$552$	−5.60571	−0.238595
$553$	1.45768	0.0619870
$554$	−25.4499	−1.08126
$555$	−18.2858	−0.776187
$556$	11.4461	0.485424
$557$	27.7694	1.17663	0.588314	−	0.808633i	$-0.299792\pi$
$557$	27.7694	1.17663	0.588314	+	0.808633i	$0.299792\pi$
$558$	−4.39864	−0.186209
$559$	−0.351001	−0.0148457
$560$	−4.10468	−0.173455
$561$	9.31664	0.393349
$562$	−12.9781	−0.547450
$563$	−43.5022	−1.83340	−0.916700	−	0.399575i	$-0.869158\pi$
$563$	−43.5022	−1.83340	−0.916700	+	0.399575i	$0.869158\pi$
$564$	0.702035	0.0295610
$565$	−33.9456	−1.42810
$566$	−4.06933	−0.171047
$567$	−17.5396	−0.736595
$568$	−9.85440	−0.413481
$569$	24.9377	1.04544	0.522722	−	0.852503i	$-0.324917\pi$
$569$	24.9377	1.04544	0.522722	+	0.852503i	$0.324917\pi$
$570$	38.6190	1.61757
$571$	−0.515714	−0.0215820	−0.0107910	−	0.999942i	$-0.503435\pi$
$571$	−0.515714	−0.0215820	−0.0107910	+	0.999942i	$0.503435\pi$
$572$	−0.0419654	−0.00175466
$573$	−11.0473	−0.461509
$574$	17.1369	0.715279
$575$	−2.38851	−0.0996079
$576$	0.520431	0.0216846
$577$	−15.1581	−0.631039	−0.315520	−	0.948919i	$-0.602179\pi$
$577$	−15.1581	−0.631039	−0.315520	+	0.948919i	$0.602179\pi$
$578$	7.65603	0.318449
$579$	13.2736	0.551634
$580$	−3.19654	−0.132729
$581$	−3.41384	−0.141630
$582$	22.2358	0.921703
$583$	−7.53465	−0.312053
$584$	5.29069	0.218930
$585$	−0.0525955	−0.00217456
$586$	34.2111	1.41325
$587$	2.41795	0.0997997	0.0498998	−	0.998754i	$-0.484110\pi$
$587$	2.41795	0.0997997	0.0498998	+	0.998754i	$0.484110\pi$
$588$	−7.68305	−0.316844
$589$	72.2379	2.97651
$590$	4.91900	0.202512
$591$	1.87628	0.0771799
$592$	4.04689	0.166326
$593$	16.6269	0.682787	0.341393	−	0.939921i	$-0.389101\pi$
$593$	16.6269	0.682787	0.341393	+	0.939921i	$0.389101\pi$
$594$	4.65237	0.190889
$595$	20.3817	0.835570
$596$	−2.80403	−0.114858
$597$	−12.5023	−0.511687
$598$	−0.125379	−0.00512712
$599$	7.77552	0.317699	0.158850	−	0.987303i	$-0.449221\pi$
$599$	7.77552	0.317699	0.158850	+	0.987303i	$0.449221\pi$
$600$	1.50001	0.0612375
$601$	5.84421	0.238390	0.119195	−	0.992871i	$-0.461969\pi$
$601$	5.84421	0.238390	0.119195	+	0.992871i	$0.461969\pi$
$602$	−14.2561	−0.581037
$603$	1.54686	0.0629932
$604$	5.19141	0.211235
$605$	−2.40821	−0.0979075
$606$	3.15245	0.128059
$607$	−12.4887	−0.506902	−0.253451	−	0.967348i	$-0.581566\pi$
$607$	−12.4887	−0.506902	−0.253451	+	0.967348i	$0.581566\pi$
$608$	−8.54692	−0.346623
$609$	4.24493	0.172013
$610$	−6.09317	−0.246705
$611$	0.0157019	0.000635232 0
$612$	−2.58419	−0.104460
$613$	−0.763653	−0.0308437	−0.0154218	−	0.999881i	$-0.504909\pi$
$613$	−0.763653	−0.0308437	−0.0154218	+	0.999881i	$0.504909\pi$
$614$	−9.55211	−0.385492
$615$	−45.4294	−1.83189
$616$	−1.70446	−0.0686745
$617$	22.4130	0.902315	0.451157	−	0.892444i	$-0.351011\pi$
$617$	22.4130	0.902315	0.451157	+	0.892444i	$0.351011\pi$
$618$	−4.55183	−0.183102
$619$	18.2027	0.731626	0.365813	−	0.930688i	$-0.380791\pi$
$619$	18.2027	0.731626	0.365813	+	0.930688i	$0.380791\pi$
$620$	20.3540	0.817435
$621$	13.8997	0.557777
$622$	−20.5365	−0.823439
$623$	5.28619	0.211787
$624$	0.0787390	0.00315208
$625$	−28.3582	−1.13433
$626$	−23.2423	−0.928949
$627$	16.0364	0.640433
$628$	1.64185	0.0655170
$629$	−20.0948	−0.801231
$630$	−2.13620	−0.0851084
$631$	−15.3306	−0.610302	−0.305151	−	0.952304i	$-0.598707\pi$
$631$	−15.3306	−0.610302	−0.305151	+	0.952304i	$0.598707\pi$
$632$	0.855219	0.0340188
$633$	−3.69806	−0.146985
$634$	3.45907	0.137377
$635$	26.6531	1.05770
$636$	14.1371	0.560574
$637$	−0.171841	−0.00680860
$638$	−1.32735	−0.0525505
$639$	−5.12853	−0.202882
$640$	−2.40821	−0.0951927
$641$	20.6817	0.816879	0.408439	−	0.912785i	$-0.366073\pi$
$641$	20.6817	0.816879	0.408439	+	0.912785i	$0.366073\pi$
$642$	−37.3713	−1.47493
$643$	−4.09439	−0.161467	−0.0807335	−	0.996736i	$-0.525726\pi$
$643$	−4.09439	−0.161467	−0.0807335	+	0.996736i	$0.525726\pi$
$644$	−5.09235	−0.200667
$645$	37.7927	1.48809
$646$	42.4396	1.66976
$647$	21.3797	0.840523	0.420262	−	0.907403i	$-0.361938\pi$
$647$	21.3797	0.840523	0.420262	+	0.907403i	$0.361938\pi$
$648$	−10.2904	−0.404247
$649$	2.04260	0.0801791
$650$	0.0335496	0.00131592
$651$	−27.0296	−1.05937
$652$	−16.1985	−0.634382
$653$	15.4836	0.605919	0.302959	−	0.953003i	$-0.402025\pi$
$653$	15.4836	0.605919	0.302959	+	0.953003i	$0.402025\pi$
$654$	23.7144	0.927305
$655$	37.7421	1.47471
$656$	10.0542	0.392549
$657$	2.75344	0.107422
$658$	0.637745	0.0248619
$659$	36.7103	1.43003	0.715015	−	0.699109i	$-0.246420\pi$
$659$	36.7103	1.43003	0.715015	+	0.699109i	$0.246420\pi$
$660$	4.51847	0.175881
$661$	−35.6168	−1.38533	−0.692666	−	0.721258i	$-0.743564\pi$
$661$	−35.6168	−1.38533	−0.692666	+	0.721258i	$0.743564\pi$
$662$	5.11299	0.198722
$663$	−0.390977	−0.0151843
$664$	−2.00289	−0.0777273
$665$	35.0824	1.36044
$666$	2.10613	0.0816107
$667$	−3.96570	−0.153552
$668$	−6.30982	−0.244134
$669$	−20.7064	−0.800554
$670$	−7.15785	−0.276532
$671$	−2.53017	−0.0976762
$672$	3.19804	0.123367
$673$	−5.23076	−0.201631	−0.100816	−	0.994905i	$-0.532145\pi$
$673$	−5.23076	−0.201631	−0.100816	+	0.994905i	$0.532145\pi$
$674$	5.31525	0.204736
$675$	−3.71937	−0.143159
$676$	−12.9982	−0.499932
$677$	−11.7675	−0.452263	−0.226131	−	0.974097i	$-0.572608\pi$
$677$	−11.7675	−0.452263	−0.226131	+	0.974097i	$0.572608\pi$
$678$	26.4477	1.01572
$679$	20.1995	0.775186
$680$	11.9579	0.458565
$681$	18.6957	0.716421
$682$	8.45192	0.323641
$683$	28.7929	1.10173	0.550865	−	0.834594i	$-0.314298\pi$
$683$	28.7929	1.10173	0.550865	+	0.834594i	$0.314298\pi$
$684$	−4.44808	−0.170077
$685$	−8.06874	−0.308291
$686$	−18.9107	−0.722012
$687$	−27.0834	−1.03330
$688$	−8.36404	−0.318876
$689$	0.316195	0.0120461
$690$	13.4997	0.513925
$691$	−12.2366	−0.465501	−0.232751	−	0.972536i	$-0.574773\pi$
$691$	−12.2366	−0.465501	−0.232751	+	0.972536i	$0.574773\pi$
$692$	−4.95476	−0.188352
$693$	−0.887052	−0.0336963
$694$	−16.9611	−0.643836
$695$	−27.5646	−1.04559
$696$	2.49049	0.0944018
$697$	−49.9237	−1.89100
$698$	−16.7962	−0.635745
$699$	31.5119	1.19189
$700$	1.36264	0.0515030
$701$	19.6685	0.742871	0.371435	−	0.928459i	$-0.378866\pi$
$701$	19.6685	0.742871	0.371435	+	0.928459i	$0.378866\pi$
$702$	−0.195239	−0.00736881
$703$	−34.5884	−1.30453
$704$	−1.00000	−0.0376889
$705$	−1.69065	−0.0636734
$706$	25.6462	0.965207
$707$	2.86376	0.107703
$708$	−3.83249	−0.144034
$709$	−26.7301	−1.00387	−0.501936	−	0.864905i	$-0.667379\pi$
$709$	−26.7301	−1.00387	−0.501936	+	0.864905i	$0.667379\pi$
$710$	23.7314	0.890625
$711$	0.445082	0.0166919
$712$	3.10139	0.116230
$713$	25.2515	0.945678
$714$	−15.8798	−0.594287
$715$	0.101061	0.00377948
$716$	18.5569	0.693505
$717$	46.6968	1.74392
$718$	22.7650	0.849583
$719$	48.6144	1.81301	0.906505	−	0.422194i	$-0.138740\pi$
$719$	48.6144	1.81301	0.906505	+	0.422194i	$0.138740\pi$
$720$	−1.25330	−0.0467079
$721$	−4.13499	−0.153995
$722$	54.0498	2.01153
$723$	−33.0033	−1.22741
$724$	8.53533	0.317213
$725$	1.06116	0.0394106
$726$	1.87628	0.0696353
$727$	−5.62286	−0.208540	−0.104270	−	0.994549i	$-0.533251\pi$
$727$	−5.62286	−0.208540	−0.104270	+	0.994549i	$0.533251\pi$
$728$	0.0715283	0.00265101
$729$	20.8320	0.771555
$730$	−12.7411	−0.471568
$731$	41.5315	1.53610
$732$	4.74731	0.175466
$733$	−38.1632	−1.40959	−0.704795	−	0.709411i	$-0.748961\pi$
$733$	−38.1632	−1.40959	−0.704795	+	0.709411i	$0.748961\pi$
$734$	19.5005	0.719777
$735$	18.5024	0.682470
$736$	−2.98767	−0.110127
$737$	−2.97228	−0.109485
$738$	5.23249	0.192611
$739$	13.6636	0.502623	0.251311	−	0.967906i	$-0.419138\pi$
$739$	13.6636	0.502623	0.251311	+	0.967906i	$0.419138\pi$
$740$	−9.74574	−0.358261
$741$	−0.672976	−0.0247224
$742$	12.8425	0.471463
$743$	−13.3942	−0.491384	−0.245692	−	0.969348i	$-0.579015\pi$
$743$	−13.3942	−0.491384	−0.245692	+	0.969348i	$0.579015\pi$
$744$	−15.8582	−0.581389
$745$	6.75269	0.247400
$746$	−0.368520	−0.0134925
$747$	−1.04237	−0.0381382
$748$	4.96548	0.181556
$749$	−33.9490	−1.24047
$750$	18.9800	0.693053
$751$	26.2938	0.959475	0.479737	−	0.877412i	$-0.340732\pi$
$751$	26.2938	0.959475	0.479737	+	0.877412i	$0.340732\pi$
$752$	0.374163	0.0136443
$753$	−50.9322	−1.85607
$754$	0.0557030	0.00202858
$755$	−12.5020	−0.454994
$756$	−7.92976	−0.288403
$757$	−19.8549	−0.721639	−0.360819	−	0.932636i	$-0.617503\pi$
$757$	−19.8549	−0.721639	−0.360819	+	0.932636i	$0.617503\pi$
$758$	−27.6329	−1.00367
$759$	5.60571	0.203474
$760$	20.5827	0.746615
$761$	−7.52743	−0.272869	−0.136435	−	0.990649i	$-0.543564\pi$
$761$	−7.52743	−0.272869	−0.136435	+	0.990649i	$0.543564\pi$
$762$	−20.7660	−0.752272
$763$	21.5427	0.779897
$764$	−5.88789	−0.213016
$765$	6.22326	0.225003
$766$	5.88684	0.212700
$767$	−0.0857186	−0.00309512
$768$	1.87628	0.0677045
$769$	25.1185	0.905798	0.452899	−	0.891562i	$-0.350390\pi$
$769$	25.1185	0.905798	0.452899	+	0.891562i	$0.350390\pi$
$770$	4.10468	0.147923
$771$	−45.5168	−1.63925
$772$	7.07445	0.254615
$773$	0.424823	0.0152798	0.00763991	−	0.999971i	$-0.497568\pi$
$773$	0.424823	0.0152798	0.00763991	+	0.999971i	$0.497568\pi$
$774$	−4.35290	−0.156462
$775$	−6.75695	−0.242717
$776$	11.8510	0.425426
$777$	12.9421	0.464296
$778$	21.5887	0.773992
$779$	−85.9321	−3.07884
$780$	−0.189620	−0.00678947
$781$	9.85440	0.352618
$782$	14.8352	0.530507
$783$	−6.17534	−0.220689
$784$	−4.09483	−0.146244
$785$	−3.95392	−0.141121
$786$	−29.4056	−1.04886
$787$	−22.7385	−0.810541	−0.405271	−	0.914197i	$-0.632823\pi$
$787$	−22.7385	−0.810541	−0.405271	+	0.914197i	$0.632823\pi$
$788$	1.00000	0.0356235
$789$	−16.5930	−0.590726
$790$	−2.05954	−0.0732753
$791$	24.0257	0.854255
$792$	−0.520431	−0.0184927
$793$	0.106180	0.00377055
$794$	−8.60327	−0.305319
$795$	−34.0451	−1.20746
$796$	−6.66336	−0.236177
$797$	46.9378	1.66262	0.831310	−	0.555809i	$-0.187591\pi$
$797$	46.9378	1.66262	0.831310	+	0.555809i	$0.187591\pi$
$798$	−27.3334	−0.967592
$799$	−1.85790	−0.0657278
$800$	0.799457	0.0282651
$801$	1.61406	0.0570300
$802$	20.9056	0.738202
$803$	−5.29069	−0.186704
$804$	5.57682	0.196679
$805$	12.2634	0.432229
$806$	−0.354689	−0.0124934
$807$	−41.1776	−1.44952
$808$	1.68016	0.0591077
$809$	−55.3470	−1.94590	−0.972949	−	0.231019i	$-0.925794\pi$
$809$	−55.3470	−1.94590	−0.972949	+	0.231019i	$0.925794\pi$
$810$	24.7815	0.870734
$811$	−17.3938	−0.610778	−0.305389	−	0.952228i	$-0.598786\pi$
$811$	−17.3938	−0.610778	−0.305389	+	0.952228i	$0.598786\pi$
$812$	2.26242	0.0793953
$813$	17.2772	0.605938
$814$	−4.04689	−0.141843
$815$	39.0093	1.36644
$816$	−9.31664	−0.326148
$817$	71.4868	2.50101
$818$	−4.59003	−0.160487
$819$	0.0372255	0.00130076
$820$	−24.2125	−0.845536
$821$	−47.9222	−1.67250	−0.836248	−	0.548352i	$-0.815255\pi$
$821$	−47.9222	−1.67250	−0.836248	+	0.548352i	$0.815255\pi$
$822$	6.28651	0.219267
$823$	−9.34377	−0.325703	−0.162852	−	0.986651i	$-0.552069\pi$
$823$	−9.34377	−0.325703	−0.162852	+	0.986651i	$0.552069\pi$
$824$	−2.42599	−0.0845132
$825$	−1.50001	−0.0522235
$826$	−3.48152	−0.121138
$827$	14.1179	0.490929	0.245464	−	0.969406i	$-0.421060\pi$
$827$	14.1179	0.490929	0.245464	+	0.969406i	$0.421060\pi$
$828$	−1.55488	−0.0540357
$829$	−50.7623	−1.76305	−0.881525	−	0.472138i	$-0.843482\pi$
$829$	−50.7623	−1.76305	−0.881525	+	0.472138i	$0.843482\pi$
$830$	4.82338	0.167422
$831$	−47.7512	−1.65647
$832$	0.0419654	0.00145489
$833$	20.3328	0.704490
$834$	21.4761	0.743658
$835$	15.1953	0.525856
$836$	8.54692	0.295601
$837$	39.3214	1.35915
$838$	20.5895	0.711252
$839$	−26.7496	−0.923499	−0.461750	−	0.887010i	$-0.652778\pi$
$839$	−26.7496	−0.923499	−0.461750	+	0.887010i	$0.652778\pi$
$840$	−7.70154	−0.265728
$841$	−27.2381	−0.939246
$842$	−0.545293	−0.0187920
$843$	−24.3507	−0.838681
$844$	−1.97095	−0.0678430
$845$	31.3024	1.07684
$846$	0.194726	0.00669482
$847$	1.70446	0.0585658
$848$	7.53465	0.258741
$849$	−7.63520	−0.262039
$850$	−3.96969	−0.136159
$851$	−12.0908	−0.414466
$852$	−18.4896	−0.633444
$853$	−24.1631	−0.827329	−0.413664	−	0.910429i	$-0.635751\pi$
$853$	−24.1631	−0.827329	−0.413664	+	0.910429i	$0.635751\pi$
$854$	4.31257	0.147573
$855$	10.7119	0.366339
$856$	−19.9178	−0.680776
$857$	−34.1833	−1.16768	−0.583839	−	0.811869i	$-0.698450\pi$
$857$	−34.1833	−1.16768	−0.583839	+	0.811869i	$0.698450\pi$
$858$	−0.0787390	−0.00268810
$859$	−26.3380	−0.898639	−0.449320	−	0.893371i	$-0.648334\pi$
$859$	−26.3380	−0.898639	−0.449320	+	0.893371i	$0.648334\pi$
$860$	20.1423	0.686848
$861$	32.1536	1.09579
$862$	−22.0236	−0.750126
$863$	−40.9829	−1.39507	−0.697537	−	0.716549i	$-0.745721\pi$
$863$	−40.9829	−1.39507	−0.697537	+	0.716549i	$0.745721\pi$
$864$	−4.65237	−0.158277
$865$	11.9321	0.405703
$866$	24.7037	0.839467
$867$	14.3649	0.487856
$868$	−14.4059	−0.488969
$869$	−0.855219	−0.0290113
$870$	−5.99761	−0.203338
$871$	0.124733	0.00422641
$872$	12.6390	0.428011
$873$	6.16762	0.208742
$874$	25.5354	0.863747
$875$	17.2419	0.582882
$876$	9.92682	0.335396
$877$	−51.5191	−1.73968	−0.869839	−	0.493336i	$-0.835777\pi$
$877$	−51.5191	−1.73968	−0.869839	+	0.493336i	$0.835777\pi$
$878$	6.60749	0.222992
$879$	64.1896	2.16506
$880$	2.40821	0.0811806
$881$	−45.3704	−1.52857	−0.764283	−	0.644881i	$-0.776907\pi$
$881$	−45.3704	−1.52857	−0.764283	+	0.644881i	$0.776907\pi$
$882$	−2.13107	−0.0717570
$883$	−15.0235	−0.505580	−0.252790	−	0.967521i	$-0.581348\pi$
$883$	−15.0235	−0.505580	−0.252790	+	0.967521i	$0.581348\pi$
$884$	−0.208379	−0.00700854
$885$	9.22943	0.310244
$886$	37.8275	1.27084
$887$	−37.4267	−1.25666	−0.628332	−	0.777945i	$-0.716262\pi$
$887$	−37.4267	−1.25666	−0.628332	+	0.777945i	$0.716262\pi$
$888$	7.59310	0.254808
$889$	−18.8643	−0.632688
$890$	−7.46879	−0.250354
$891$	10.2904	0.344743
$892$	−11.0359	−0.369508
$893$	−3.19794	−0.107015
$894$	−5.26116	−0.175959
$895$	−44.6889	−1.49379
$896$	1.70446	0.0569419
$897$	−0.235246	−0.00785464
$898$	34.2765	1.14382
$899$	−11.2187	−0.374164
$900$	0.416062	0.0138687
$901$	−37.4132	−1.24641
$902$	−10.0542	−0.334767
$903$	−26.7485	−0.890135
$904$	14.0958	0.468820
$905$	−20.5548	−0.683266
$906$	9.74054	0.323608
$907$	−22.8577	−0.758977	−0.379489	−	0.925196i	$-0.623900\pi$
$907$	−22.8577	−0.758977	−0.379489	+	0.925196i	$0.623900\pi$
$908$	9.96423	0.330675
$909$	0.874406	0.0290022
$910$	−0.172255	−0.00571019
$911$	−0.0167353	−0.000554466 0	−0.000277233	−	1.00000i	$-0.500088\pi$
$911$	−0.0167353	−0.000554466 0	−0.000277233		1.00000i	$0.500088\pi$
$912$	−16.0364	−0.531019
$913$	2.00289	0.0662861
$914$	−34.3365	−1.13575
$915$	−11.4325	−0.377947
$916$	−14.4346	−0.476933
$917$	−26.7128	−0.882133
$918$	23.1013	0.762455
$919$	29.1329	0.961006	0.480503	−	0.876993i	$-0.340454\pi$
$919$	29.1329	0.961006	0.480503	+	0.876993i	$0.340454\pi$
$920$	7.19493	0.237210
$921$	−17.9224	−0.590565
$922$	−0.343935	−0.0113269
$923$	−0.413544	−0.0136120
$924$	−3.19804	−0.105208
$925$	3.23531	0.106376
$926$	6.86964	0.225750
$927$	−1.26256	−0.0414678
$928$	1.32735	0.0435726
$929$	9.31463	0.305603	0.152802	−	0.988257i	$-0.451170\pi$
$929$	9.31463	0.305603	0.152802	+	0.988257i	$0.451170\pi$
$930$	38.1898	1.25229
$931$	34.9982	1.14702
$932$	16.7948	0.550133
$933$	−38.5322	−1.26149
$934$	−6.00587	−0.196518
$935$	−11.9579	−0.391065
$936$	0.0218401	0.000713866 0
$937$	27.0791	0.884637	0.442318	−	0.896858i	$-0.354156\pi$
$937$	27.0791	0.884637	0.442318	+	0.896858i	$0.354156\pi$
$938$	5.06611	0.165415
$939$	−43.6091	−1.42313
$940$	−0.901062	−0.0293894
$941$	16.5510	0.539547	0.269774	−	0.962924i	$-0.413051\pi$
$941$	16.5510	0.539547	0.269774	+	0.962924i	$0.413051\pi$
$942$	3.08057	0.100371
$943$	−30.0385	−0.978188
$944$	−2.04260	−0.0664810
$945$	19.0965	0.621209
$946$	8.36404	0.271938
$947$	−1.62188	−0.0527041	−0.0263520	−	0.999653i	$-0.508389\pi$
$947$	−1.62188	−0.0527041	−0.0263520	+	0.999653i	$0.508389\pi$
$948$	1.60463	0.0521160
$949$	0.222026	0.00720728
$950$	−6.83290	−0.221688
$951$	6.49020	0.210459
$952$	−8.46345	−0.274302
$953$	58.7320	1.90251	0.951257	−	0.308398i	$-0.0997930\pi$
$953$	58.7320	1.90251	0.951257	+	0.308398i	$0.0997930\pi$
$954$	3.92127	0.126956
$955$	14.1793	0.458830
$956$	24.8879	0.804934
$957$	−2.49049	−0.0805061
$958$	−32.0469	−1.03539
$959$	5.71081	0.184412
$960$	−4.51847	−0.145833
$961$	40.4349	1.30435
$962$	0.169830	0.00547552
$963$	−10.3658	−0.334034
$964$	−17.5898	−0.566528
$965$	−17.0367	−0.548432
$966$	−9.55469	−0.307417
$967$	−27.3851	−0.880647	−0.440323	−	0.897839i	$-0.645136\pi$
$967$	−27.3851	−0.880647	−0.440323	+	0.897839i	$0.645136\pi$
$968$	1.00000	0.0321412
$969$	79.6286	2.55804
$970$	−28.5396	−0.916352
$971$	−15.4104	−0.494542	−0.247271	−	0.968946i	$-0.579534\pi$
$971$	−15.4104	−0.494542	−0.247271	+	0.968946i	$0.579534\pi$
$972$	−5.35066	−0.171622
$973$	19.5094	0.625443
$974$	−16.8881	−0.541130
$975$	0.0629484	0.00201596
$976$	2.53017	0.0809888
$977$	20.7467	0.663747	0.331873	−	0.943324i	$-0.392319\pi$
$977$	20.7467	0.663747	0.331873	+	0.943324i	$0.392319\pi$
$978$	−30.3929	−0.971859
$979$	−3.10139	−0.0991209
$980$	9.86119	0.315004
$981$	6.57774	0.210011
$982$	31.7080	1.01184
$983$	−10.7658	−0.343377	−0.171688	−	0.985151i	$-0.554922\pi$
$983$	−10.7658	−0.343377	−0.171688	+	0.985151i	$0.554922\pi$
$984$	18.8644	0.601376
$985$	−2.40821	−0.0767318
$986$	−6.59096	−0.209899
$987$	1.19659	0.0380878
$988$	−0.358675	−0.0114110
$989$	24.9890	0.794604
$990$	1.25330	0.0398326
$991$	14.5127	0.461013	0.230506	−	0.973071i	$-0.425962\pi$
$991$	14.5127	0.461013	0.230506	+	0.973071i	$0.425962\pi$
$992$	−8.45192	−0.268349
$993$	9.59340	0.304437
$994$	−16.7964	−0.532749
$995$	16.0467	0.508716
$996$	−3.75799	−0.119076
$997$	−14.9530	−0.473566	−0.236783	−	0.971563i	$-0.576093\pi$
$997$	−14.9530	−0.473566	−0.236783	+	0.971563i	$0.576093\pi$
$998$	−28.1109	−0.889834
$999$	−18.8276	−0.595680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.15	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.15	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.87628 q^{3} +1.00000 q^{4} -2.40821 q^{5} +1.87628 q^{6} +1.70446 q^{7} +1.00000 q^{8} +0.520431 q^{9} -2.40821 q^{10} -1.00000 q^{11} +1.87628 q^{12} +0.0419654 q^{13} +1.70446 q^{14} -4.51847 q^{15} +1.00000 q^{16} -4.96548 q^{17} +0.520431 q^{18} -8.54692 q^{19} -2.40821 q^{20} +3.19804 q^{21} -1.00000 q^{22} -2.98767 q^{23} +1.87628 q^{24} +0.799457 q^{25} +0.0419654 q^{26} -4.65237 q^{27} +1.70446 q^{28} +1.32735 q^{29} -4.51847 q^{30} -8.45192 q^{31} +1.00000 q^{32} -1.87628 q^{33} -4.96548 q^{34} -4.10468 q^{35} +0.520431 q^{36} +4.04689 q^{37} -8.54692 q^{38} +0.0787390 q^{39} -2.40821 q^{40} +10.0542 q^{41} +3.19804 q^{42} -8.36404 q^{43} -1.00000 q^{44} -1.25330 q^{45} -2.98767 q^{46} +0.374163 q^{47} +1.87628 q^{48} -4.09483 q^{49} +0.799457 q^{50} -9.31664 q^{51} +0.0419654 q^{52} +7.53465 q^{53} -4.65237 q^{54} +2.40821 q^{55} +1.70446 q^{56} -16.0364 q^{57} +1.32735 q^{58} -2.04260 q^{59} -4.51847 q^{60} +2.53017 q^{61} -8.45192 q^{62} +0.887052 q^{63} +1.00000 q^{64} -0.101061 q^{65} -1.87628 q^{66} +2.97228 q^{67} -4.96548 q^{68} -5.60571 q^{69} -4.10468 q^{70} -9.85440 q^{71} +0.520431 q^{72} +5.29069 q^{73} +4.04689 q^{74} +1.50001 q^{75} -8.54692 q^{76} -1.70446 q^{77} +0.0787390 q^{78} +0.855219 q^{79} -2.40821 q^{80} -10.2904 q^{81} +10.0542 q^{82} -2.00289 q^{83} +3.19804 q^{84} +11.9579 q^{85} -8.36404 q^{86} +2.49049 q^{87} -1.00000 q^{88} +3.10139 q^{89} -1.25330 q^{90} +0.0715283 q^{91} -2.98767 q^{92} -15.8582 q^{93} +0.374163 q^{94} +20.5827 q^{95} +1.87628 q^{96} +11.8510 q^{97} -4.09483 q^{98} -0.520431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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