LMFDB - Embedded newform 3179.2.a.bd.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, 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("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.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:	$25.3844428026$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 40 x^{11} + 126 x^{10} - 284 x^{9} - 338 x^{8} + 860 x^{7} + 312 x^{6} + \cdots + 2 $ x^14 - 2x^13 - 19x^12 + 40x^11 + 126x^10 - 284x^9 - 338x^8 + 860x^7 + 312x^6 - 1076x^5 - 38x^4 + 480x^3 - 8x^2 - 48*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.0421125$ of defining polynomial
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0421125 q^{2} -0.623078 q^{3} -1.99823 q^{4} -3.21410 q^{5} -0.0262394 q^{6} +4.28743 q^{7} -0.168375 q^{8} -2.61177 q^{9} +O(q^{10})$	\(q+0.0421125 q^{2} -0.623078 q^{3} -1.99823 q^{4} -3.21410 q^{5} -0.0262394 q^{6} +4.28743 q^{7} -0.168375 q^{8} -2.61177 q^{9} -0.135354 q^{10} -1.00000 q^{11} +1.24505 q^{12} -3.32292 q^{13} +0.180554 q^{14} +2.00264 q^{15} +3.98936 q^{16} -0.109988 q^{18} +5.85419 q^{19} +6.42250 q^{20} -2.67140 q^{21} -0.0421125 q^{22} +5.39146 q^{23} +0.104911 q^{24} +5.33044 q^{25} -0.139937 q^{26} +3.49657 q^{27} -8.56725 q^{28} -0.872197 q^{29} +0.0843361 q^{30} -8.88302 q^{31} +0.504753 q^{32} +0.623078 q^{33} -13.7802 q^{35} +5.21891 q^{36} -0.753308 q^{37} +0.246535 q^{38} +2.07044 q^{39} +0.541175 q^{40} +5.94085 q^{41} -0.112499 q^{42} -0.849123 q^{43} +1.99823 q^{44} +8.39450 q^{45} +0.227048 q^{46} +8.83981 q^{47} -2.48569 q^{48} +11.3820 q^{49} +0.224478 q^{50} +6.63995 q^{52} -3.41117 q^{53} +0.147250 q^{54} +3.21410 q^{55} -0.721897 q^{56} -3.64762 q^{57} -0.0367304 q^{58} +12.4757 q^{59} -4.00172 q^{60} -11.8966 q^{61} -0.374086 q^{62} -11.1978 q^{63} -7.95747 q^{64} +10.6802 q^{65} +0.0262394 q^{66} +4.87083 q^{67} -3.35930 q^{69} -0.580320 q^{70} -3.50485 q^{71} +0.439758 q^{72} +4.39102 q^{73} -0.0317237 q^{74} -3.32128 q^{75} -11.6980 q^{76} -4.28743 q^{77} +0.0871915 q^{78} -6.22872 q^{79} -12.8222 q^{80} +5.65668 q^{81} +0.250184 q^{82} -6.33683 q^{83} +5.33807 q^{84} -0.0357587 q^{86} +0.543447 q^{87} +0.168375 q^{88} -0.373263 q^{89} +0.353514 q^{90} -14.2468 q^{91} -10.7734 q^{92} +5.53482 q^{93} +0.372267 q^{94} -18.8159 q^{95} -0.314501 q^{96} -11.9714 q^{97} +0.479326 q^{98} +2.61177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 14 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 + 14 * q^4 - 8 * q^5 - 16 * q^6 - 12 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q + 2 q^{2} + 14 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} - 6 q^{8} + 14 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} + 36 q^{14} + 22 q^{16} + 2 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{21} - 2 q^{22} - 4 q^{23} - 52 q^{24} + 14 q^{25} - 36 q^{28} - 24 q^{29} + 4 q^{30} - 28 q^{31} - 30 q^{32} - 16 q^{35} + 38 q^{36} - 16 q^{37} + 4 q^{38} + 36 q^{39} - 36 q^{40} - 16 q^{41} - 4 q^{42} + 16 q^{43} - 14 q^{44} - 36 q^{45} - 56 q^{46} + 8 q^{47} + 68 q^{48} + 22 q^{49} + 30 q^{50} - 8 q^{52} + 4 q^{53} - 40 q^{54} + 8 q^{55} + 56 q^{56} - 36 q^{57} + 20 q^{58} + 12 q^{59} + 20 q^{60} - 60 q^{61} - 12 q^{62} - 40 q^{63} + 6 q^{64} + 8 q^{65} + 16 q^{66} - 8 q^{67} - 20 q^{69} - 24 q^{70} - 8 q^{71} - 10 q^{72} + 4 q^{73} - 44 q^{74} - 20 q^{75} - 8 q^{76} + 12 q^{77} - 20 q^{78} - 64 q^{79} - 60 q^{80} - 6 q^{81} + 8 q^{82} - 24 q^{83} - 76 q^{84} - 12 q^{86} - 24 q^{87} + 6 q^{88} - 4 q^{89} - 64 q^{90} - 44 q^{91} + 28 q^{92} - 40 q^{93} - 60 q^{94} - 24 q^{95} - 80 q^{96} - 80 q^{97} - 82 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 + 14 * q^4 - 8 * q^5 - 16 * q^6 - 12 * q^7 - 6 * q^8 + 14 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 + 36 * q^14 + 22 * q^16 + 2 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^21 - 2 * q^22 - 4 * q^23 - 52 * q^24 + 14 * q^25 - 36 * q^28 - 24 * q^29 + 4 * q^30 - 28 * q^31 - 30 * q^32 - 16 * q^35 + 38 * q^36 - 16 * q^37 + 4 * q^38 + 36 * q^39 - 36 * q^40 - 16 * q^41 - 4 * q^42 + 16 * q^43 - 14 * q^44 - 36 * q^45 - 56 * q^46 + 8 * q^47 + 68 * q^48 + 22 * q^49 + 30 * q^50 - 8 * q^52 + 4 * q^53 - 40 * q^54 + 8 * q^55 + 56 * q^56 - 36 * q^57 + 20 * q^58 + 12 * q^59 + 20 * q^60 - 60 * q^61 - 12 * q^62 - 40 * q^63 + 6 * q^64 + 8 * q^65 + 16 * q^66 - 8 * q^67 - 20 * q^69 - 24 * q^70 - 8 * q^71 - 10 * q^72 + 4 * q^73 - 44 * q^74 - 20 * q^75 - 8 * q^76 + 12 * q^77 - 20 * q^78 - 64 * q^79 - 60 * q^80 - 6 * q^81 + 8 * q^82 - 24 * q^83 - 76 * q^84 - 12 * q^86 - 24 * q^87 + 6 * q^88 - 4 * q^89 - 64 * q^90 - 44 * q^91 + 28 * q^92 - 40 * q^93 - 60 * q^94 - 24 * q^95 - 80 * q^96 - 80 * q^97 - 82 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.0421125	0.0297780	0.0148890	−	0.999889i	$-0.495261\pi$
$2$	0.0421125	0.0297780	0.0148890	+	0.999889i	$0.495261\pi$
$3$	−0.623078	−0.359734	−0.179867	−	0.983691i	$-0.557567\pi$
$3$	−0.623078	−0.359734	−0.179867	+	0.983691i	$0.557567\pi$
$4$	−1.99823	−0.999113
$5$	−3.21410	−1.43739	−0.718695	−	0.695326i	$-0.755260\pi$
$5$	−3.21410	−1.43739	−0.718695	+	0.695326i	$0.755260\pi$
$6$	−0.0262394	−0.0107122
$7$	4.28743	1.62049	0.810247	−	0.586088i	$-0.199333\pi$
$7$	4.28743	1.62049	0.810247	+	0.586088i	$0.199333\pi$
$8$	−0.168375	−0.0595297
$9$	−2.61177	−0.870591
$10$	−0.135354	−0.0428027
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.24505	0.359415
$13$	−3.32292	−0.921613	−0.460806	−	0.887501i	$-0.652440\pi$
$13$	−3.32292	−0.921613	−0.460806	+	0.887501i	$0.652440\pi$
$14$	0.180554	0.0482552
$15$	2.00264	0.517078
$16$	3.98936	0.997341
$17$	0	0
$17$	0	0
$18$	−0.109988	−0.0259245
$19$	5.85419	1.34304	0.671521	−	0.740985i	$-0.265641\pi$
$19$	5.85419	1.34304	0.671521	+	0.740985i	$0.265641\pi$
$20$	6.42250	1.43611
$21$	−2.67140	−0.582948
$22$	−0.0421125	−0.00897842
$23$	5.39146	1.12420	0.562098	−	0.827070i	$-0.309994\pi$
$23$	5.39146	1.12420	0.562098	+	0.827070i	$0.309994\pi$
$24$	0.104911	0.0214149
$25$	5.33044	1.06609
$26$	−0.139937	−0.0274438
$27$	3.49657	0.672916
$28$	−8.56725	−1.61906
$29$	−0.872197	−0.161963	−0.0809815	−	0.996716i	$-0.525805\pi$
$29$	−0.872197	−0.161963	−0.0809815	+	0.996716i	$0.525805\pi$
$30$	0.0843361	0.0153976
$31$	−8.88302	−1.59544	−0.797719	−	0.603029i	$-0.793960\pi$
$31$	−8.88302	−1.59544	−0.797719	+	0.603029i	$0.793960\pi$
$32$	0.504753	0.0892286
$33$	0.623078	0.108464
$34$	0	0
$35$	−13.7802	−2.32928
$36$	5.21891	0.869819
$37$	−0.753308	−0.123843	−0.0619215	−	0.998081i	$-0.519723\pi$
$37$	−0.753308	−0.123843	−0.0619215	+	0.998081i	$0.519723\pi$
$38$	0.246535	0.0399932
$39$	2.07044	0.331536
$40$	0.541175	0.0855673
$41$	5.94085	0.927805	0.463902	−	0.885886i	$-0.346449\pi$
$41$	5.94085	0.927805	0.463902	+	0.885886i	$0.346449\pi$
$42$	−0.112499	−0.0173590
$43$	−0.849123	−0.129490	−0.0647450	−	0.997902i	$-0.520623\pi$
$43$	−0.849123	−0.129490	−0.0647450	+	0.997902i	$0.520623\pi$
$44$	1.99823	0.301244
$45$	8.39450	1.25138
$46$	0.227048	0.0334764
$47$	8.83981	1.28942	0.644709	−	0.764428i	$-0.276978\pi$
$47$	8.83981	1.28942	0.644709	+	0.764428i	$0.276978\pi$
$48$	−2.48569	−0.358778
$49$	11.3820	1.62600
$50$	0.224478	0.0317460
$51$	0	0
$52$	6.63995	0.920796
$53$	−3.41117	−0.468560	−0.234280	−	0.972169i	$-0.575273\pi$
$53$	−3.41117	−0.468560	−0.234280	+	0.972169i	$0.575273\pi$
$54$	0.147250	0.0200381
$55$	3.21410	0.433389
$56$	−0.721897	−0.0964676
$57$	−3.64762	−0.483139
$58$	−0.0367304	−0.00482294
$59$	12.4757	1.62419	0.812096	−	0.583524i	$-0.198326\pi$
$59$	12.4757	1.62419	0.812096	+	0.583524i	$0.198326\pi$
$60$	−4.00172	−0.516620
$61$	−11.8966	−1.52320	−0.761600	−	0.648047i	$-0.775586\pi$
$61$	−11.8966	−1.52320	−0.761600	+	0.648047i	$0.775586\pi$
$62$	−0.374086	−0.0475090
$63$	−11.1978	−1.41079
$64$	−7.95747	−0.994684
$65$	10.6802	1.32472
$66$	0.0262394	0.00322985
$67$	4.87083	0.595066	0.297533	−	0.954711i	$-0.403836\pi$
$67$	4.87083	0.595066	0.297533	+	0.954711i	$0.403836\pi$
$68$	0	0
$69$	−3.35930	−0.404412
$70$	−0.580320	−0.0693615
$71$	−3.50485	−0.415949	−0.207974	−	0.978134i	$-0.566687\pi$
$71$	−3.50485	−0.415949	−0.207974	+	0.978134i	$0.566687\pi$
$72$	0.439758	0.0518260
$73$	4.39102	0.513930	0.256965	−	0.966421i	$-0.417277\pi$
$73$	4.39102	0.513930	0.256965	+	0.966421i	$0.417277\pi$
$74$	−0.0317237	−0.00368780
$75$	−3.32128	−0.383509
$76$	−11.6980	−1.34185
$77$	−4.28743	−0.488598
$78$	0.0871915	0.00987249
$79$	−6.22872	−0.700785	−0.350393	−	0.936603i	$-0.613952\pi$
$79$	−6.22872	−0.700785	−0.350393	+	0.936603i	$0.613952\pi$
$80$	−12.8222	−1.43357
$81$	5.65668	0.628520
$82$	0.250184	0.0276282
$83$	−6.33683	−0.695557	−0.347779	−	0.937577i	$-0.613064\pi$
$83$	−6.33683	−0.695557	−0.347779	+	0.937577i	$0.613064\pi$
$84$	5.33807	0.582431
$85$	0	0
$86$	−0.0357587	−0.00385596
$87$	0.543447	0.0582637
$88$	0.168375	0.0179489
$89$	−0.373263	−0.0395658	−0.0197829	−	0.999804i	$-0.506298\pi$
$89$	−0.373263	−0.0395658	−0.0197829	+	0.999804i	$0.506298\pi$
$90$	0.353514	0.0372636
$91$	−14.2468	−1.49347
$92$	−10.7734	−1.12320
$93$	5.53482	0.573934
$94$	0.372267	0.0383964
$95$	−18.8159	−1.93048
$96$	−0.314501	−0.0320986
$97$	−11.9714	−1.21551	−0.607756	−	0.794124i	$-0.707930\pi$
$97$	−11.9714	−1.21551	−0.607756	+	0.794124i	$0.707930\pi$
$98$	0.479326	0.0484192
$99$	2.61177	0.262493
$100$	−10.6514	−1.06514
$101$	3.81697	0.379803	0.189902	−	0.981803i	$-0.439183\pi$
$101$	3.81697	0.379803	0.189902	+	0.981803i	$0.439183\pi$
$102$	0	0
$103$	−9.47135	−0.933240	−0.466620	−	0.884458i	$-0.654528\pi$
$103$	−9.47135	−0.933240	−0.466620	+	0.884458i	$0.654528\pi$
$104$	0.559498	0.0548633
$105$	8.58616	0.837923
$106$	−0.143653	−0.0139528
$107$	−5.42549	−0.524502	−0.262251	−	0.965000i	$-0.584465\pi$
$107$	−5.42549	−0.524502	−0.262251	+	0.965000i	$0.584465\pi$
$108$	−6.98695	−0.672319
$109$	−17.4392	−1.67037	−0.835187	−	0.549966i	$-0.814641\pi$
$109$	−17.4392	−1.67037	−0.835187	+	0.549966i	$0.814641\pi$
$110$	0.135354	0.0129055
$111$	0.469370	0.0445506
$112$	17.1041	1.61619
$113$	−5.66399	−0.532824	−0.266412	−	0.963859i	$-0.585838\pi$
$113$	−5.66399	−0.532824	−0.266412	+	0.963859i	$0.585838\pi$
$114$	−0.153610	−0.0143869
$115$	−17.3287	−1.61591
$116$	1.74285	0.161819
$117$	8.67872	0.802348
$118$	0.525381	0.0483653
$119$	0	0
$120$	−0.337195	−0.0307815
$121$	1.00000	0.0909091
$122$	−0.500995	−0.0453579
$123$	−3.70161	−0.333763
$124$	17.7503	1.59402
$125$	−1.06207	−0.0949943
$126$	−0.471567	−0.0420105
$127$	−11.5162	−1.02190	−0.510950	−	0.859610i	$-0.670706\pi$
$127$	−11.5162	−1.02190	−0.510950	+	0.859610i	$0.670706\pi$
$128$	−1.34461	−0.118848
$129$	0.529070	0.0465820
$130$	0.449770	0.0394475
$131$	−2.43224	−0.212506	−0.106253	−	0.994339i	$-0.533885\pi$
$131$	−2.43224	−0.212506	−0.106253	+	0.994339i	$0.533885\pi$
$132$	−1.24505	−0.108368
$133$	25.0994	2.17639
$134$	0.205123	0.0177199
$135$	−11.2383	−0.967242
$136$	0	0
$137$	9.77215	0.834891	0.417445	−	0.908702i	$-0.362925\pi$
$137$	9.77215	0.834891	0.417445	+	0.908702i	$0.362925\pi$
$138$	−0.141469	−0.0120426
$139$	−3.23738	−0.274591	−0.137296	−	0.990530i	$-0.543841\pi$
$139$	−3.23738	−0.274591	−0.137296	+	0.990530i	$0.543841\pi$
$140$	27.5360	2.32722
$141$	−5.50789	−0.463848
$142$	−0.147598	−0.0123861
$143$	3.32292	0.277877
$144$	−10.4193	−0.868276
$145$	2.80333	0.232804
$146$	0.184917	0.0153038
$147$	−7.09189	−0.584929
$148$	1.50528	0.123733
$149$	12.9589	1.06164	0.530818	−	0.847486i	$-0.321885\pi$
$149$	12.9589	1.06164	0.530818	+	0.847486i	$0.321885\pi$
$150$	−0.139868	−0.0114201
$151$	−12.3703	−1.00668	−0.503342	−	0.864087i	$-0.667897\pi$
$151$	−12.3703	−1.00668	−0.503342	+	0.864087i	$0.667897\pi$
$152$	−0.985701	−0.0799509
$153$	0	0
$154$	−0.180554	−0.0145495
$155$	28.5509	2.29327
$156$	−4.13721	−0.331242
$157$	−1.85459	−0.148012	−0.0740062	−	0.997258i	$-0.523578\pi$
$157$	−1.85459	−0.148012	−0.0740062	+	0.997258i	$0.523578\pi$
$158$	−0.262307	−0.0208680
$159$	2.12543	0.168557
$160$	−1.62233	−0.128256
$161$	23.1155	1.82176
$162$	0.238217	0.0187161
$163$	−6.69097	−0.524077	−0.262039	−	0.965057i	$-0.584395\pi$
$163$	−6.69097	−0.524077	−0.262039	+	0.965057i	$0.584395\pi$
$164$	−11.8712	−0.926982
$165$	−2.00264	−0.155905
$166$	−0.266860	−0.0207123
$167$	14.6693	1.13514	0.567572	−	0.823324i	$-0.307883\pi$
$167$	14.6693	1.13514	0.567572	+	0.823324i	$0.307883\pi$
$168$	0.449798	0.0347027
$169$	−1.95819	−0.150630
$170$	0	0
$171$	−15.2898	−1.16924
$172$	1.69674	0.129375
$173$	−13.7751	−1.04730	−0.523650	−	0.851933i	$-0.675430\pi$
$173$	−13.7751	−1.04730	−0.523650	+	0.851933i	$0.675430\pi$
$174$	0.0228859	0.00173498
$175$	22.8539	1.72759
$176$	−3.98936	−0.300710
$177$	−7.77331	−0.584278
$178$	−0.0157191	−0.00117819
$179$	−8.44838	−0.631462	−0.315731	−	0.948849i	$-0.602250\pi$
$179$	−8.44838	−0.631462	−0.315731	+	0.948849i	$0.602250\pi$
$180$	−16.7741	−1.25027
$181$	−23.0799	−1.71552	−0.857758	−	0.514054i	$-0.828143\pi$
$181$	−23.0799	−1.71552	−0.857758	+	0.514054i	$0.828143\pi$
$182$	−0.599968	−0.0444726
$183$	7.41250	0.547948
$184$	−0.907789	−0.0669231
$185$	2.42121	0.178011
$186$	0.233085	0.0170906
$187$	0	0
$188$	−17.6639	−1.28828
$189$	14.9913	1.09046
$190$	−0.792387	−0.0574858
$191$	−23.4963	−1.70013	−0.850067	−	0.526675i	$-0.823439\pi$
$191$	−23.4963	−1.70013	−0.850067	+	0.526675i	$0.823439\pi$
$192$	4.95813	0.357822
$193$	−2.72933	−0.196461	−0.0982306	−	0.995164i	$-0.531318\pi$
$193$	−2.72933	−0.196461	−0.0982306	+	0.995164i	$0.531318\pi$
$194$	−0.504146	−0.0361956
$195$	−6.65461	−0.476546
$196$	−22.7439	−1.62456
$197$	7.69328	0.548124	0.274062	−	0.961712i	$-0.411633\pi$
$197$	7.69328	0.548124	0.274062	+	0.961712i	$0.411633\pi$
$198$	0.109988	0.00781653
$199$	−10.4388	−0.739990	−0.369995	−	0.929034i	$-0.620641\pi$
$199$	−10.4388	−0.739990	−0.369995	+	0.929034i	$0.620641\pi$
$200$	−0.897515	−0.0634639
$201$	−3.03491	−0.214066
$202$	0.160742	0.0113098
$203$	−3.73948	−0.262460
$204$	0	0
$205$	−19.0945	−1.33362
$206$	−0.398862	−0.0277901
$207$	−14.0813	−0.978716
$208$	−13.2563	−0.919162
$209$	−5.85419	−0.404943
$210$	0.361585	0.0249517
$211$	10.4219	0.717472	0.358736	−	0.933439i	$-0.383208\pi$
$211$	10.4219	0.717472	0.358736	+	0.933439i	$0.383208\pi$
$212$	6.81629	0.468145
$213$	2.18379	0.149631
$214$	−0.228481	−0.0156186
$215$	2.72917	0.186128
$216$	−0.588737	−0.0400585
$217$	−38.0853	−2.58540
$218$	−0.734409	−0.0497405
$219$	−2.73595	−0.184878
$220$	−6.42250	−0.433005
$221$	0	0
$222$	0.0197663	0.00132663
$223$	−23.8482	−1.59699	−0.798496	−	0.602000i	$-0.794371\pi$
$223$	−23.8482	−1.59699	−0.798496	+	0.602000i	$0.794371\pi$
$224$	2.16409	0.144594
$225$	−13.9219	−0.928127
$226$	−0.238525	−0.0158665
$227$	−20.2337	−1.34296	−0.671479	−	0.741024i	$-0.734341\pi$
$227$	−20.2337	−1.34296	−0.671479	+	0.741024i	$0.734341\pi$
$228$	7.28877	0.482710
$229$	27.5015	1.81735	0.908676	−	0.417501i	$-0.137094\pi$
$229$	27.5015	1.81735	0.908676	+	0.417501i	$0.137094\pi$
$230$	−0.729755	−0.0481186
$231$	2.67140	0.175765
$232$	0.146857	0.00964161
$233$	28.8378	1.88923	0.944614	−	0.328184i	$-0.106437\pi$
$233$	28.8378	1.88923	0.944614	+	0.328184i	$0.106437\pi$
$234$	0.365483	0.0238924
$235$	−28.4120	−1.85340
$236$	−24.9292	−1.62275
$237$	3.88098	0.252097
$238$	0	0
$239$	15.8428	1.02479	0.512394	−	0.858751i	$-0.328759\pi$
$239$	15.8428	1.02479	0.512394	+	0.858751i	$0.328759\pi$
$240$	7.98924	0.515703
$241$	14.2136	0.915580	0.457790	−	0.889060i	$-0.348641\pi$
$241$	14.2136	0.915580	0.457790	+	0.889060i	$0.348641\pi$
$242$	0.0421125	0.00270710
$243$	−14.0143	−0.899016
$244$	23.7721	1.52185
$245$	−36.5830	−2.33720
$246$	−0.155884	−0.00993882
$247$	−19.4530	−1.23777
$248$	1.49568	0.0949759
$249$	3.94834	0.250216
$250$	−0.0447264	−0.00282874
$251$	−0.885722	−0.0559063	−0.0279532	−	0.999609i	$-0.508899\pi$
$251$	−0.885722	−0.0559063	−0.0279532	+	0.999609i	$0.508899\pi$
$252$	22.3757	1.40954
$253$	−5.39146	−0.338958
$254$	−0.484978	−0.0304302
$255$	0	0
$256$	15.8583	0.991144
$257$	6.69991	0.417929	0.208964	−	0.977923i	$-0.432991\pi$
$257$	6.69991	0.417929	0.208964	+	0.977923i	$0.432991\pi$
$258$	0.0222805	0.00138712
$259$	−3.22975	−0.200687
$260$	−21.3415	−1.32354
$261$	2.27798	0.141004
$262$	−0.102428	−0.00632802
$263$	−4.25215	−0.262199	−0.131099	−	0.991369i	$-0.541851\pi$
$263$	−4.25215	−0.262199	−0.131099	+	0.991369i	$0.541851\pi$
$264$	−0.104911	−0.00645683
$265$	10.9638	0.673504
$266$	1.05700	0.0648088
$267$	0.232572	0.0142332
$268$	−9.73302	−0.594539
$269$	−25.9407	−1.58163	−0.790816	−	0.612053i	$-0.790344\pi$
$269$	−25.9407	−1.58163	−0.790816	+	0.612053i	$0.790344\pi$
$270$	−0.473275	−0.0288026
$271$	14.9592	0.908704	0.454352	−	0.890822i	$-0.349871\pi$
$271$	14.9592	0.908704	0.454352	+	0.890822i	$0.349871\pi$
$272$	0	0
$273$	8.87686	0.537252
$274$	0.411530	0.0248614
$275$	−5.33044	−0.321438
$276$	6.71264	0.404054
$277$	−9.81435	−0.589687	−0.294844	−	0.955546i	$-0.595268\pi$
$277$	−9.81435	−0.589687	−0.294844	+	0.955546i	$0.595268\pi$
$278$	−0.136334	−0.00817679
$279$	23.2004	1.38897
$280$	2.32025	0.138661
$281$	12.7856	0.762726	0.381363	−	0.924425i	$-0.375455\pi$
$281$	12.7856	0.762726	0.381363	+	0.924425i	$0.375455\pi$
$282$	−0.231951	−0.0138125
$283$	12.3625	0.734873	0.367436	−	0.930049i	$-0.380236\pi$
$283$	12.3625	0.734873	0.367436	+	0.930049i	$0.380236\pi$
$284$	7.00348	0.415580
$285$	11.7238	0.694458
$286$	0.139937	0.00827463
$287$	25.4710	1.50350
$288$	−1.31830	−0.0776816
$289$	0	0
$290$	0.118055	0.00693244
$291$	7.45912	0.437261
$292$	−8.77426	−0.513475
$293$	−15.5310	−0.907333	−0.453667	−	0.891171i	$-0.649884\pi$
$293$	−15.5310	−0.907333	−0.453667	+	0.891171i	$0.649884\pi$
$294$	−0.298658	−0.0174181
$295$	−40.0980	−2.33460
$296$	0.126838	0.00737234
$297$	−3.49657	−0.202892
$298$	0.545733	0.0316134
$299$	−17.9154	−1.03607
$300$	6.63667	0.383169
$301$	−3.64055	−0.209838
$302$	−0.520947	−0.0299771
$303$	−2.37827	−0.136628
$304$	23.3545	1.33947
$305$	38.2368	2.18943
$306$	0	0
$307$	−29.4466	−1.68060	−0.840302	−	0.542119i	$-0.817622\pi$
$307$	−29.4466	−1.68060	−0.840302	+	0.542119i	$0.817622\pi$
$308$	8.56725	0.488164
$309$	5.90139	0.335718
$310$	1.20235	0.0682890
$311$	−12.0658	−0.684189	−0.342095	−	0.939665i	$-0.611136\pi$
$311$	−12.0658	−0.684189	−0.342095	+	0.939665i	$0.611136\pi$
$312$	−0.348611	−0.0197362
$313$	8.44197	0.477168	0.238584	−	0.971122i	$-0.423317\pi$
$313$	8.44197	0.477168	0.238584	+	0.971122i	$0.423317\pi$
$314$	−0.0781014	−0.00440752
$315$	35.9908	2.02785
$316$	12.4464	0.700164
$317$	−20.0872	−1.12821	−0.564105	−	0.825703i	$-0.690779\pi$
$317$	−20.0872	−1.12821	−0.564105	+	0.825703i	$0.690779\pi$
$318$	0.0895071	0.00501931
$319$	0.872197	0.0488337
$320$	25.5761	1.42975
$321$	3.38050	0.188681
$322$	0.973451	0.0542483
$323$	0	0
$324$	−11.3033	−0.627963
$325$	−17.7126	−0.982521
$326$	−0.281774	−0.0156060
$327$	10.8660	0.600891
$328$	−1.00029	−0.0552319
$329$	37.9000	2.08950
$330$	−0.0843361	−0.00464255
$331$	−6.00340	−0.329976	−0.164988	−	0.986296i	$-0.552759\pi$
$331$	−6.00340	−0.329976	−0.164988	+	0.986296i	$0.552759\pi$
$332$	12.6624	0.694941
$333$	1.96747	0.107817
$334$	0.617761	0.0338024
$335$	−15.6553	−0.855342
$336$	−10.6572	−0.581398
$337$	−25.8240	−1.40672	−0.703361	−	0.710833i	$-0.748318\pi$
$337$	−25.8240	−1.40672	−0.703361	+	0.710833i	$0.748318\pi$
$338$	−0.0824641	−0.00448546
$339$	3.52911	0.191675
$340$	0	0
$341$	8.88302	0.481043
$342$	−0.643893	−0.0348177
$343$	18.7876	1.01444
$344$	0.142971	0.00770850
$345$	10.7971	0.581298
$346$	−0.580104	−0.0311866
$347$	−10.5922	−0.568617	−0.284308	−	0.958733i	$-0.591764\pi$
$347$	−10.5922	−0.568617	−0.284308	+	0.958733i	$0.591764\pi$
$348$	−1.08593	−0.0582120
$349$	−14.7061	−0.787198	−0.393599	−	0.919282i	$-0.628770\pi$
$349$	−14.7061	−0.787198	−0.393599	+	0.919282i	$0.628770\pi$
$350$	0.962434	0.0514443
$351$	−11.6188	−0.620168
$352$	−0.504753	−0.0269034
$353$	31.0800	1.65422	0.827110	−	0.562040i	$-0.189983\pi$
$353$	31.0800	1.65422	0.827110	+	0.562040i	$0.189983\pi$
$354$	−0.327354	−0.0173987
$355$	11.2649	0.597880
$356$	0.745865	0.0395308
$357$	0	0
$358$	−0.355783	−0.0188037
$359$	14.3294	0.756276	0.378138	−	0.925749i	$-0.376565\pi$
$359$	14.3294	0.756276	0.378138	+	0.925749i	$0.376565\pi$
$360$	−1.41343	−0.0744942
$361$	15.2715	0.803764
$362$	−0.971953	−0.0510847
$363$	−0.623078	−0.0327031
$364$	28.4683	1.49214
$365$	−14.1132	−0.738718
$366$	0.312159	0.0163168
$367$	−21.3733	−1.11568	−0.557838	−	0.829950i	$-0.688369\pi$
$367$	−21.3733	−1.11568	−0.557838	+	0.829950i	$0.688369\pi$
$368$	21.5085	1.12121
$369$	−15.5162	−0.807739
$370$	0.101963	0.00530081
$371$	−14.6251	−0.759300
$372$	−11.0598	−0.573425
$373$	−4.14225	−0.214477	−0.107239	−	0.994233i	$-0.534201\pi$
$373$	−4.14225	−0.214477	−0.107239	+	0.994233i	$0.534201\pi$
$374$	0	0
$375$	0.661752	0.0341727
$376$	−1.48841	−0.0767587
$377$	2.89824	0.149267
$378$	0.631322	0.0324717
$379$	−3.87716	−0.199156	−0.0995781	−	0.995030i	$-0.531749\pi$
$379$	−3.87716	−0.199156	−0.0995781	+	0.995030i	$0.531749\pi$
$380$	37.5985	1.92876
$381$	7.17552	0.367613
$382$	−0.989489	−0.0506267
$383$	−17.8600	−0.912604	−0.456302	−	0.889825i	$-0.650826\pi$
$383$	−17.8600	−0.912604	−0.456302	+	0.889825i	$0.650826\pi$
$384$	0.837800	0.0427538
$385$	13.7802	0.702305
$386$	−0.114939	−0.00585023
$387$	2.21772	0.112733
$388$	23.9216	1.21443
$389$	10.6554	0.540249	0.270124	−	0.962825i	$-0.412935\pi$
$389$	10.6554	0.540249	0.270124	+	0.962825i	$0.412935\pi$
$390$	−0.280242	−0.0141906
$391$	0	0
$392$	−1.91645	−0.0967955
$393$	1.51548	0.0764457
$394$	0.323984	0.0163221
$395$	20.0197	1.00730
$396$	−5.21891	−0.262260
$397$	−3.13989	−0.157587	−0.0787933	−	0.996891i	$-0.525107\pi$
$397$	−3.13989	−0.157587	−0.0787933	+	0.996891i	$0.525107\pi$
$398$	−0.439606	−0.0220355
$399$	−15.6389	−0.782924
$400$	21.2651	1.06325
$401$	−7.68154	−0.383598	−0.191799	−	0.981434i	$-0.561432\pi$
$401$	−7.68154	−0.383598	−0.191799	+	0.981434i	$0.561432\pi$
$402$	−0.127808	−0.00637446
$403$	29.5176	1.47038
$404$	−7.62718	−0.379466
$405$	−18.1811	−0.903428
$406$	−0.157479	−0.00781555
$407$	0.753308	0.0373401
$408$	0	0
$409$	18.2193	0.900889	0.450444	−	0.892805i	$-0.351266\pi$
$409$	18.2193	0.900889	0.450444	+	0.892805i	$0.351266\pi$
$410$	−0.804117	−0.0397125
$411$	−6.08881	−0.300339
$412$	18.9259	0.932412
$413$	53.4885	2.63200
$414$	−0.592998	−0.0291442
$415$	20.3672	0.999787
$416$	−1.67725	−0.0822342
$417$	2.01714	0.0987799
$418$	−0.246535	−0.0120584
$419$	5.51417	0.269385	0.134692	−	0.990887i	$-0.456995\pi$
$419$	5.51417	0.269385	0.134692	+	0.990887i	$0.456995\pi$
$420$	−17.1571	−0.837180
$421$	15.5720	0.758933	0.379467	−	0.925205i	$-0.376107\pi$
$421$	15.5720	0.758933	0.379467	+	0.925205i	$0.376107\pi$
$422$	0.438892	0.0213649
$423$	−23.0876	−1.12256
$424$	0.574357	0.0278933
$425$	0	0
$426$	0.0919651	0.00445572
$427$	−51.0057	−2.46834
$428$	10.8414	0.524037
$429$	−2.07044	−0.0999618
$430$	0.114932	0.00554252
$431$	24.6870	1.18913	0.594566	−	0.804047i	$-0.297324\pi$
$431$	24.6870	1.18913	0.594566	+	0.804047i	$0.297324\pi$
$432$	13.9491	0.671126
$433$	27.4120	1.31734	0.658669	−	0.752433i	$-0.271120\pi$
$433$	27.4120	1.31734	0.658669	+	0.752433i	$0.271120\pi$
$434$	−1.60387	−0.0769881
$435$	−1.74669	−0.0837476
$436$	34.8475	1.66889
$437$	31.5626	1.50984
$438$	−0.115218	−0.00550532
$439$	−7.97677	−0.380711	−0.190355	−	0.981715i	$-0.560964\pi$
$439$	−7.97677	−0.380711	−0.190355	+	0.981715i	$0.560964\pi$
$440$	−0.541175	−0.0257995
$441$	−29.7273	−1.41558
$442$	0	0
$443$	−19.4155	−0.922458	−0.461229	−	0.887281i	$-0.652591\pi$
$443$	−19.4155	−0.922458	−0.461229	+	0.887281i	$0.652591\pi$
$444$	−0.937907	−0.0445111
$445$	1.19971	0.0568715
$446$	−1.00431	−0.0475553
$447$	−8.07442	−0.381907
$448$	−34.1171	−1.61188
$449$	4.59585	0.216892	0.108446	−	0.994102i	$-0.465413\pi$
$449$	4.59585	0.216892	0.108446	+	0.994102i	$0.465413\pi$
$450$	−0.586286	−0.0276378
$451$	−5.94085	−0.279744
$452$	11.3179	0.532351
$453$	7.70770	0.362139
$454$	−0.852092	−0.0399907
$455$	45.7906	2.14670
$456$	0.614169	0.0287611
$457$	15.5847	0.729023	0.364511	−	0.931199i	$-0.381236\pi$
$457$	15.5847	0.729023	0.364511	+	0.931199i	$0.381236\pi$
$458$	1.15816	0.0541172
$459$	0	0
$460$	34.6266	1.61448
$461$	−27.3289	−1.27284	−0.636418	−	0.771344i	$-0.719585\pi$
$461$	−27.3289	−1.27284	−0.636418	+	0.771344i	$0.719585\pi$
$462$	0.112499	0.00523395
$463$	2.64550	0.122947	0.0614734	−	0.998109i	$-0.480420\pi$
$463$	2.64550	0.122947	0.0614734	+	0.998109i	$0.480420\pi$
$464$	−3.47951	−0.161532
$465$	−17.7895	−0.824966
$466$	1.21443	0.0562575
$467$	−13.4709	−0.623358	−0.311679	−	0.950187i	$-0.600891\pi$
$467$	−13.4709	−0.623358	−0.311679	+	0.950187i	$0.600891\pi$
$468$	−17.3421	−0.801637
$469$	20.8833	0.964302
$470$	−1.19650	−0.0551905
$471$	1.15555	0.0532451
$472$	−2.10059	−0.0966877
$473$	0.849123	0.0390427
$474$	0.163438	0.00750694
$475$	31.2054	1.43180
$476$	0	0
$477$	8.90921	0.407925
$478$	0.667182	0.0305162
$479$	36.8230	1.68249	0.841244	−	0.540656i	$-0.181824\pi$
$479$	36.8230	1.68249	0.841244	+	0.540656i	$0.181824\pi$
$480$	1.01084	0.0461382
$481$	2.50318	0.114135
$482$	0.598572	0.0272642
$483$	−14.4028	−0.655348
$484$	−1.99823	−0.0908285
$485$	38.4773	1.74716
$486$	−0.590177	−0.0267710
$487$	21.6191	0.979656	0.489828	−	0.871819i	$-0.337060\pi$
$487$	21.6191	0.979656	0.489828	+	0.871819i	$0.337060\pi$
$488$	2.00309	0.0906757
$489$	4.16900	0.188529
$490$	−1.54060	−0.0695973
$491$	−14.5982	−0.658806	−0.329403	−	0.944189i	$-0.606847\pi$
$491$	−14.5982	−0.658806	−0.329403	+	0.944189i	$0.606847\pi$
$492$	7.39666	0.333467
$493$	0	0
$494$	−0.819215	−0.0368582
$495$	−8.39450	−0.377305
$496$	−35.4376	−1.59119
$497$	−15.0268	−0.674043
$498$	0.166275	0.00745094
$499$	5.08257	0.227527	0.113763	−	0.993508i	$-0.463709\pi$
$499$	5.08257	0.227527	0.113763	+	0.993508i	$0.463709\pi$
$500$	2.12225	0.0949101
$501$	−9.14012	−0.408351
$502$	−0.0373000	−0.00166478
$503$	−10.9987	−0.490406	−0.245203	−	0.969472i	$-0.578855\pi$
$503$	−10.9987	−0.490406	−0.245203	+	0.969472i	$0.578855\pi$
$504$	1.88543	0.0839838
$505$	−12.2681	−0.545925
$506$	−0.227048	−0.0100935
$507$	1.22010	0.0541867
$508$	23.0120	1.02099
$509$	−25.8733	−1.14681	−0.573406	−	0.819271i	$-0.694378\pi$
$509$	−25.8733	−1.14681	−0.573406	+	0.819271i	$0.694378\pi$
$510$	0	0
$511$	18.8262	0.832822
$512$	3.35706	0.148363
$513$	20.4696	0.903755
$514$	0.282150	0.0124451
$515$	30.4419	1.34143
$516$	−1.05720	−0.0465407
$517$	−8.83981	−0.388774
$518$	−0.136013	−0.00597607
$519$	8.58296	0.376750
$520$	−1.79828	−0.0788600
$521$	3.16515	0.138668	0.0693338	−	0.997594i	$-0.477913\pi$
$521$	3.16515	0.138668	0.0693338	+	0.997594i	$0.477913\pi$
$522$	0.0959315	0.00419881
$523$	−35.3598	−1.54618	−0.773088	−	0.634299i	$-0.781289\pi$
$523$	−35.3598	−1.54618	−0.773088	+	0.634299i	$0.781289\pi$
$524$	4.86017	0.212318
$525$	−14.2398	−0.621474
$526$	−0.179069	−0.00780776
$527$	0	0
$528$	2.48569	0.108176
$529$	6.06782	0.263818
$530$	0.461715	0.0200556
$531$	−32.5836	−1.41401
$532$	−50.1543	−2.17446
$533$	−19.7410	−0.855077
$534$	0.00979421	0.000423837 0
$535$	17.4381	0.753913
$536$	−0.820128	−0.0354241
$537$	5.26400	0.227158
$538$	−1.09243	−0.0470979
$539$	−11.3820	−0.490259
$540$	22.4568	0.966385
$541$	−2.39033	−0.102768	−0.0513842	−	0.998679i	$-0.516363\pi$
$541$	−2.39033	−0.102768	−0.0513842	+	0.998679i	$0.516363\pi$
$542$	0.629968	0.0270594
$543$	14.3806	0.617130
$544$	0	0
$545$	56.0514	2.40098
$546$	0.373827	0.0159983
$547$	19.1928	0.820623	0.410312	−	0.911945i	$-0.365420\pi$
$547$	19.1928	0.820623	0.410312	+	0.911945i	$0.365420\pi$
$548$	−19.5270	−0.834150
$549$	31.0712	1.32608
$550$	−0.224478	−0.00957179
$551$	−5.10601	−0.217523
$552$	0.565624	0.0240745
$553$	−26.7052	−1.13562
$554$	−0.413307	−0.0175597
$555$	−1.50860	−0.0640366
$556$	6.46902	0.274348
$557$	3.48978	0.147867	0.0739334	−	0.997263i	$-0.476445\pi$
$557$	3.48978	0.147867	0.0739334	+	0.997263i	$0.476445\pi$
$558$	0.977029	0.0413609
$559$	2.82157	0.119340
$560$	−54.9743	−2.32309
$561$	0	0
$562$	0.538434	0.0227125
$563$	5.42665	0.228706	0.114353	−	0.993440i	$-0.463520\pi$
$563$	5.42665	0.228706	0.114353	+	0.993440i	$0.463520\pi$
$564$	11.0060	0.463437
$565$	18.2046	0.765875
$566$	0.520615	0.0218831
$567$	24.2526	1.01851
$568$	0.590130	0.0247613
$569$	16.3440	0.685175	0.342588	−	0.939486i	$-0.388697\pi$
$569$	16.3440	0.685175	0.342588	+	0.939486i	$0.388697\pi$
$570$	0.493719	0.0206796
$571$	27.8433	1.16520	0.582602	−	0.812757i	$-0.302035\pi$
$571$	27.8433	1.16520	0.582602	+	0.812757i	$0.302035\pi$
$572$	−6.63995	−0.277630
$573$	14.6400	0.611597
$574$	1.07265	0.0447714
$575$	28.7388	1.19849
$576$	20.7831	0.865963
$577$	−30.8328	−1.28359	−0.641794	−	0.766877i	$-0.721810\pi$
$577$	−30.8328	−1.28359	−0.641794	+	0.766877i	$0.721810\pi$
$578$	0	0
$579$	1.70058	0.0706739
$580$	−5.60169	−0.232597
$581$	−27.1687	−1.12715
$582$	0.314122	0.0130208
$583$	3.41117	0.141276
$584$	−0.739340	−0.0305941
$585$	−27.8943	−1.15329
$586$	−0.654052	−0.0270186
$587$	−13.1242	−0.541695	−0.270848	−	0.962622i	$-0.587304\pi$
$587$	−13.1242	−0.541695	−0.270848	+	0.962622i	$0.587304\pi$
$588$	14.1712	0.584411
$589$	−52.0029	−2.14274
$590$	−1.68863	−0.0695197
$591$	−4.79352	−0.197179
$592$	−3.00522	−0.123514
$593$	−9.08497	−0.373075	−0.186538	−	0.982448i	$-0.559727\pi$
$593$	−9.08497	−0.373075	−0.186538	+	0.982448i	$0.559727\pi$
$594$	−0.147250	−0.00604172
$595$	0	0
$596$	−25.8948	−1.06069
$597$	6.50422	0.266200
$598$	−0.754463	−0.0308523
$599$	29.2400	1.19471	0.597357	−	0.801975i	$-0.296217\pi$
$599$	29.2400	1.19471	0.597357	+	0.801975i	$0.296217\pi$
$600$	0.559222	0.0228301
$601$	11.0737	0.451704	0.225852	−	0.974162i	$-0.427483\pi$
$601$	11.0737	0.451704	0.225852	+	0.974162i	$0.427483\pi$
$602$	−0.153313	−0.00624856
$603$	−12.7215	−0.518060
$604$	24.7188	1.00579
$605$	−3.21410	−0.130672
$606$	−0.100155	−0.00406852
$607$	−5.63482	−0.228710	−0.114355	−	0.993440i	$-0.536480\pi$
$607$	−5.63482	−0.228710	−0.114355	+	0.993440i	$0.536480\pi$
$608$	2.95492	0.119838
$609$	2.32999	0.0944160
$610$	1.61025	0.0651970
$611$	−29.3740	−1.18835
$612$	0	0
$613$	15.3457	0.619806	0.309903	−	0.950768i	$-0.399703\pi$
$613$	15.3457	0.619806	0.309903	+	0.950768i	$0.399703\pi$
$614$	−1.24007	−0.0500451
$615$	11.8974	0.479748
$616$	0.721897	0.0290861
$617$	−34.4778	−1.38803	−0.694013	−	0.719963i	$-0.744159\pi$
$617$	−34.4778	−1.38803	−0.694013	+	0.719963i	$0.744159\pi$
$618$	0.248522	0.00999704
$619$	5.39548	0.216863	0.108431	−	0.994104i	$-0.465417\pi$
$619$	5.39548	0.216863	0.108431	+	0.994104i	$0.465417\pi$
$620$	−57.0512	−2.29123
$621$	18.8516	0.756490
$622$	−0.508122	−0.0203738
$623$	−1.60034	−0.0641162
$624$	8.25974	0.330654
$625$	−23.2386	−0.929544
$626$	0.355513	0.0142091
$627$	3.64762	0.145672
$628$	3.70589	0.147881
$629$	0	0
$630$	1.51566	0.0603855
$631$	10.7782	0.429071	0.214536	−	0.976716i	$-0.431176\pi$
$631$	10.7782	0.429071	0.214536	+	0.976716i	$0.431176\pi$
$632$	1.04876	0.0417175
$633$	−6.49365	−0.258100
$634$	−0.845922	−0.0335959
$635$	37.0143	1.46887
$636$	−4.24708	−0.168408
$637$	−37.8216	−1.49855
$638$	0.0367304	0.00145417
$639$	9.15387	0.362121
$640$	4.32173	0.170831
$641$	−22.2713	−0.879662	−0.439831	−	0.898080i	$-0.644962\pi$
$641$	−22.2713	−0.879662	−0.439831	+	0.898080i	$0.644962\pi$
$642$	0.142362	0.00561856
$643$	−20.7636	−0.818835	−0.409418	−	0.912347i	$-0.634268\pi$
$643$	−20.7636	−0.818835	−0.409418	+	0.912347i	$0.634268\pi$
$644$	−46.1900	−1.82014
$645$	−1.70048	−0.0669565
$646$	0	0
$647$	5.79889	0.227978	0.113989	−	0.993482i	$-0.463637\pi$
$647$	5.79889	0.227978	0.113989	+	0.993482i	$0.463637\pi$
$648$	−0.952446	−0.0374156
$649$	−12.4757	−0.489712
$650$	−0.745924	−0.0292575
$651$	23.7301	0.930057
$652$	13.3701	0.523612
$653$	−0.509407	−0.0199346	−0.00996732	−	0.999950i	$-0.503173\pi$
$653$	−0.509407	−0.0199346	−0.00996732	+	0.999950i	$0.503173\pi$
$654$	0.457594	0.0178934
$655$	7.81747	0.305454
$656$	23.7002	0.925337
$657$	−11.4684	−0.447423
$658$	1.59607	0.0622211
$659$	−27.7963	−1.08279	−0.541395	−	0.840768i	$-0.682104\pi$
$659$	−27.7963	−1.08279	−0.541395	+	0.840768i	$0.682104\pi$
$660$	4.00172	0.155767
$661$	3.34455	0.130088	0.0650439	−	0.997882i	$-0.479281\pi$
$661$	3.34455	0.130088	0.0650439	+	0.997882i	$0.479281\pi$
$662$	−0.252818	−0.00982606
$663$	0	0
$664$	1.06697	0.0414063
$665$	−80.6720	−3.12833
$666$	0.0828551	0.00321057
$667$	−4.70242	−0.182078
$668$	−29.3126	−1.13414
$669$	14.8593	0.574493
$670$	−0.659285	−0.0254704
$671$	11.8966	0.459262
$672$	−1.34840	−0.0520156
$673$	8.09204	0.311925	0.155963	−	0.987763i	$-0.450152\pi$
$673$	8.09204	0.311925	0.155963	+	0.987763i	$0.450152\pi$
$674$	−1.08751	−0.0418894
$675$	18.6383	0.717388
$676$	3.91290	0.150496
$677$	−34.3293	−1.31938	−0.659691	−	0.751537i	$-0.729313\pi$
$677$	−34.3293	−1.31938	−0.659691	+	0.751537i	$0.729313\pi$
$678$	0.148620	0.00570771
$679$	−51.3265	−1.96973
$680$	0	0
$681$	12.6072	0.483108
$682$	0.374086	0.0143245
$683$	6.25725	0.239427	0.119714	−	0.992808i	$-0.461802\pi$
$683$	6.25725	0.239427	0.119714	+	0.992808i	$0.461802\pi$
$684$	30.5525	1.16820
$685$	−31.4087	−1.20006
$686$	0.791194	0.0302079
$687$	−17.1356	−0.653764
$688$	−3.38746	−0.129146
$689$	11.3351	0.431831
$690$	0.454694	0.0173099
$691$	44.6726	1.69942	0.849712	−	0.527247i	$-0.176776\pi$
$691$	44.6726	1.69942	0.849712	+	0.527247i	$0.176776\pi$
$692$	27.5258	1.04637
$693$	11.1978	0.425369
$694$	−0.446062	−0.0169323
$695$	10.4053	0.394695
$696$	−0.0915031	−0.00346842
$697$	0	0
$698$	−0.619309	−0.0234412
$699$	−17.9682	−0.679620
$700$	−45.6672	−1.72606
$701$	−46.1860	−1.74442	−0.872210	−	0.489132i	$-0.837314\pi$
$701$	−46.1860	−1.74442	−0.872210	+	0.489132i	$0.837314\pi$
$702$	−0.489299	−0.0184674
$703$	−4.41000	−0.166326
$704$	7.95747	0.299908
$705$	17.7029	0.666731
$706$	1.30886	0.0492594
$707$	16.3650	0.615469
$708$	15.5328	0.583760
$709$	48.3425	1.81554	0.907770	−	0.419468i	$-0.137784\pi$
$709$	48.3425	1.81554	0.907770	+	0.419468i	$0.137784\pi$
$710$	0.474395	0.0178037
$711$	16.2680	0.610097
$712$	0.0628484	0.00235534
$713$	−47.8924	−1.79359
$714$	0	0
$715$	−10.6802	−0.399417
$716$	16.8818	0.630902
$717$	−9.87133	−0.368651
$718$	0.603446	0.0225204
$719$	10.5335	0.392833	0.196416	−	0.980521i	$-0.437070\pi$
$719$	10.5335	0.392833	0.196416	+	0.980521i	$0.437070\pi$
$720$	33.4887	1.24805
$721$	−40.6077	−1.51231
$722$	0.643122	0.0239345
$723$	−8.85620	−0.329366
$724$	46.1189	1.71399
$725$	−4.64920	−0.172667
$726$	−0.0262394	−0.000973835 0
$727$	47.6233	1.76625	0.883125	−	0.469137i	$-0.155435\pi$
$727$	47.6233	1.76625	0.883125	+	0.469137i	$0.155435\pi$
$728$	2.39881	0.0889058
$729$	−8.23805	−0.305113
$730$	−0.594342	−0.0219976
$731$	0	0
$732$	−14.8119	−0.547462
$733$	42.3340	1.56364	0.781821	−	0.623503i	$-0.214291\pi$
$733$	42.3340	1.56364	0.781821	+	0.623503i	$0.214291\pi$
$734$	−0.900083	−0.0332227
$735$	22.7941	0.840771
$736$	2.72135	0.100310
$737$	−4.87083	−0.179419
$738$	−0.653424	−0.0240529
$739$	18.3674	0.675657	0.337828	−	0.941208i	$-0.390308\pi$
$739$	18.3674	0.675657	0.337828	+	0.941208i	$0.390308\pi$
$740$	−4.83812	−0.177853
$741$	12.1208	0.445267
$742$	−0.615902	−0.0226105
$743$	31.7761	1.16575	0.582875	−	0.812562i	$-0.301928\pi$
$743$	31.7761	1.16575	0.582875	+	0.812562i	$0.301928\pi$
$744$	−0.931927	−0.0341661
$745$	−41.6513	−1.52598
$746$	−0.174441	−0.00638672
$747$	16.5504	0.605546
$748$	0	0
$749$	−23.2614	−0.849953
$750$	0.0278680	0.00101760
$751$	−36.7758	−1.34197	−0.670984	−	0.741472i	$-0.734128\pi$
$751$	−36.7758	−1.34197	−0.670984	+	0.741472i	$0.734128\pi$
$752$	35.2652	1.28599
$753$	0.551874	0.0201114
$754$	0.122052	0.00444488
$755$	39.7595	1.44700
$756$	−29.9560	−1.08949
$757$	6.40521	0.232801	0.116401	−	0.993202i	$-0.462864\pi$
$757$	6.40521	0.232801	0.116401	+	0.993202i	$0.462864\pi$
$758$	−0.163277	−0.00593048
$759$	3.35930	0.121935
$760$	3.16814	0.114921
$761$	−25.8600	−0.937424	−0.468712	−	0.883351i	$-0.655282\pi$
$761$	−25.8600	−0.937424	−0.468712	+	0.883351i	$0.655282\pi$
$762$	0.302179	0.0109468
$763$	−74.7693	−2.70683
$764$	46.9510	1.69863
$765$	0	0
$766$	−0.752130	−0.0271756
$767$	−41.4556	−1.49688
$768$	−9.88097	−0.356549
$769$	7.38242	0.266217	0.133108	−	0.991101i	$-0.457504\pi$
$769$	7.38242	0.266217	0.133108	+	0.991101i	$0.457504\pi$
$770$	0.580320	0.0209133
$771$	−4.17457	−0.150343
$772$	5.45381	0.196287
$773$	−0.0674286	−0.00242524	−0.00121262	−	0.999999i	$-0.500386\pi$
$773$	−0.0674286	−0.00242524	−0.00121262	+	0.999999i	$0.500386\pi$
$774$	0.0933936	0.00335696
$775$	−47.3504	−1.70088
$776$	2.01569	0.0723590
$777$	2.01239	0.0721940
$778$	0.448724	0.0160875
$779$	34.7788	1.24608
$780$	13.2974	0.476124
$781$	3.50485	0.125413
$782$	0	0
$783$	−3.04970	−0.108987
$784$	45.4070	1.62168
$785$	5.96084	0.212751
$786$	0.0638206	0.00227641
$787$	−27.0059	−0.962657	−0.481328	−	0.876540i	$-0.659846\pi$
$787$	−27.0059	−0.962657	−0.481328	+	0.876540i	$0.659846\pi$
$788$	−15.3729	−0.547638
$789$	2.64942	0.0943219
$790$	0.843081	0.0299955
$791$	−24.2840	−0.863438
$792$	−0.439758	−0.0156261
$793$	39.5314	1.40380
$794$	−0.132229	−0.00469262
$795$	−6.83134	−0.242282
$796$	20.8592	0.739334
$797$	34.1361	1.20916	0.604581	−	0.796543i	$-0.293340\pi$
$797$	34.1361	1.20916	0.604581	+	0.796543i	$0.293340\pi$
$798$	−0.658593	−0.0233139
$799$	0	0
$800$	2.69056	0.0951255
$801$	0.974879	0.0344457
$802$	−0.323489	−0.0114228
$803$	−4.39102	−0.154956
$804$	6.06443	0.213876
$805$	−74.2955	−2.61857
$806$	1.24306	0.0437849
$807$	16.1631	0.568968
$808$	−0.642685	−0.0226096
$809$	1.66404	0.0585044	0.0292522	−	0.999572i	$-0.490687\pi$
$809$	1.66404	0.0585044	0.0292522	+	0.999572i	$0.490687\pi$
$810$	−0.765654	−0.0269023
$811$	−5.62692	−0.197588	−0.0987939	−	0.995108i	$-0.531498\pi$
$811$	−5.62692	−0.197588	−0.0987939	+	0.995108i	$0.531498\pi$
$812$	7.47233	0.262227
$813$	−9.32073	−0.326892
$814$	0.0317237	0.00111191
$815$	21.5054	0.753303
$816$	0	0
$817$	−4.97092	−0.173911
$818$	0.767262	0.0268267
$819$	37.2094	1.30020
$820$	38.1551	1.33243
$821$	−23.5211	−0.820893	−0.410447	−	0.911885i	$-0.634627\pi$
$821$	−23.5211	−0.820893	−0.410447	+	0.911885i	$0.634627\pi$
$822$	−0.256415	−0.00894351
$823$	14.4531	0.503802	0.251901	−	0.967753i	$-0.418944\pi$
$823$	14.4531	0.503802	0.251901	+	0.967753i	$0.418944\pi$
$824$	1.59474	0.0555555
$825$	3.32128	0.115632
$826$	2.25253	0.0783757
$827$	12.8313	0.446187	0.223094	−	0.974797i	$-0.428384\pi$
$827$	12.8313	0.446187	0.223094	+	0.974797i	$0.428384\pi$
$828$	28.1376	0.977848
$829$	−39.8821	−1.38516	−0.692580	−	0.721341i	$-0.743526\pi$
$829$	−39.8821	−1.38516	−0.692580	+	0.721341i	$0.743526\pi$
$830$	0.857714	0.0297717
$831$	6.11511	0.212131
$832$	26.4421	0.916713
$833$	0	0
$834$	0.0849470	0.00294147
$835$	−47.1486	−1.63164
$836$	11.6980	0.404584
$837$	−31.0601	−1.07360
$838$	0.232216	0.00802176
$839$	12.1834	0.420616	0.210308	−	0.977635i	$-0.432553\pi$
$839$	12.1834	0.420616	0.210308	+	0.977635i	$0.432553\pi$
$840$	−1.44570	−0.0498813
$841$	−28.2393	−0.973768
$842$	0.655777	0.0225996
$843$	−7.96644	−0.274379
$844$	−20.8253	−0.716836
$845$	6.29380	0.216513
$846$	−0.972276	−0.0334275
$847$	4.28743	0.147318
$848$	−13.6084	−0.467314
$849$	−7.70279	−0.264359
$850$	0	0
$851$	−4.06143	−0.139224
$852$	−4.36372	−0.149498
$853$	−43.0363	−1.47353	−0.736767	−	0.676147i	$-0.763649\pi$
$853$	−43.0363	−1.47353	−0.736767	+	0.676147i	$0.763649\pi$
$854$	−2.14798	−0.0735023
$855$	49.1430	1.68065
$856$	0.913519	0.0312234
$857$	−15.0866	−0.515348	−0.257674	−	0.966232i	$-0.582956\pi$
$857$	−15.0866	−0.515348	−0.257674	+	0.966232i	$0.582956\pi$
$858$	−0.0871915	−0.00297667
$859$	1.91593	0.0653706	0.0326853	−	0.999466i	$-0.489594\pi$
$859$	1.91593	0.0653706	0.0326853	+	0.999466i	$0.489594\pi$
$860$	−5.45349	−0.185963
$861$	−15.8704	−0.540862
$862$	1.03963	0.0354100
$863$	−55.0897	−1.87527	−0.937637	−	0.347616i	$-0.886991\pi$
$863$	−55.0897	−1.87527	−0.937637	+	0.347616i	$0.886991\pi$
$864$	1.76491	0.0600433
$865$	44.2745	1.50538
$866$	1.15439	0.0392278
$867$	0	0
$868$	76.1031	2.58311
$869$	6.22872	0.211295
$870$	−0.0735577	−0.00249384
$871$	−16.1854	−0.548421
$872$	2.93633	0.0994368
$873$	31.2666	1.05821
$874$	1.32918	0.0449602
$875$	−4.55354	−0.153938
$876$	5.46705	0.184715
$877$	−42.6222	−1.43925	−0.719625	−	0.694363i	$-0.755686\pi$
$877$	−42.6222	−1.43925	−0.719625	+	0.694363i	$0.755686\pi$
$878$	−0.335922	−0.0113368
$879$	9.67706	0.326399
$880$	12.8222	0.432237
$881$	−21.4272	−0.721901	−0.360950	−	0.932585i	$-0.617548\pi$
$881$	−21.4272	−0.721901	−0.360950	+	0.932585i	$0.617548\pi$
$882$	−1.25189	−0.0421533
$883$	11.2898	0.379931	0.189965	−	0.981791i	$-0.439162\pi$
$883$	11.2898	0.379931	0.189965	+	0.981791i	$0.439162\pi$
$884$	0	0
$885$	24.9842	0.839835
$886$	−0.817636	−0.0274690
$887$	−51.1225	−1.71653	−0.858263	−	0.513211i	$-0.828456\pi$
$887$	−51.1225	−1.71653	−0.858263	+	0.513211i	$0.828456\pi$
$888$	−0.0790303	−0.00265208
$889$	−49.3750	−1.65598
$890$	0.0505226	0.00169352
$891$	−5.65668	−0.189506
$892$	47.6541	1.59558
$893$	51.7499	1.73174
$894$	−0.340034	−0.0113724
$895$	27.1539	0.907656
$896$	−5.76494	−0.192593
$897$	11.1627	0.372712
$898$	0.193543	0.00645861
$899$	7.74775	0.258402
$900$	27.8191	0.927304
$901$	0	0
$902$	−0.250184	−0.00833022
$903$	2.26835	0.0754859
$904$	0.953677	0.0317188
$905$	74.1811	2.46586
$906$	0.324590	0.0107838
$907$	−3.87594	−0.128699	−0.0643493	−	0.997927i	$-0.520497\pi$
$907$	−3.87594	−0.128699	−0.0643493	+	0.997927i	$0.520497\pi$
$908$	40.4315	1.34177
$909$	−9.96907	−0.330653
$910$	1.92836	0.0639244
$911$	−7.56194	−0.250538	−0.125269	−	0.992123i	$-0.539979\pi$
$911$	−7.56194	−0.250538	−0.125269	+	0.992123i	$0.539979\pi$
$912$	−14.5517	−0.481854
$913$	6.33683	0.209718
$914$	0.656312	0.0217089
$915$	−23.8245	−0.787614
$916$	−54.9543	−1.81574
$917$	−10.4281	−0.344365
$918$	0	0
$919$	33.0326	1.08965	0.544823	−	0.838551i	$-0.316597\pi$
$919$	33.0326	1.08965	0.544823	+	0.838551i	$0.316597\pi$
$920$	2.91772	0.0961945
$921$	18.3475	0.604571
$922$	−1.15089	−0.0379026
$923$	11.6463	0.383344
$924$	−5.33807	−0.175610
$925$	−4.01546	−0.132028
$926$	0.111409	0.00366112
$927$	24.7370	0.812470
$928$	−0.440244	−0.0144517
$929$	−12.9608	−0.425230	−0.212615	−	0.977136i	$-0.568198\pi$
$929$	−12.9608	−0.425230	−0.212615	+	0.977136i	$0.568198\pi$
$930$	−0.749159	−0.0245659
$931$	66.6325	2.18379
$932$	−57.6245	−1.88755
$933$	7.51795	0.246126
$934$	−0.567293	−0.0185624
$935$	0	0
$936$	−1.46128	−0.0477635
$937$	−45.8455	−1.49771	−0.748854	−	0.662735i	$-0.769396\pi$
$937$	−45.8455	−1.49771	−0.748854	+	0.662735i	$0.769396\pi$
$938$	0.879449	0.0287150
$939$	−5.26001	−0.171654
$940$	56.7737	1.85175
$941$	−13.0066	−0.424003	−0.212002	−	0.977269i	$-0.567998\pi$
$941$	−13.0066	−0.424003	−0.212002	+	0.977269i	$0.567998\pi$
$942$	0.0486633	0.00158554
$943$	32.0298	1.04304
$944$	49.7699	1.61987
$945$	−48.1836	−1.56741
$946$	0.0357587	0.00116262
$947$	−21.7184	−0.705752	−0.352876	−	0.935670i	$-0.614796\pi$
$947$	−21.7184	−0.705752	−0.352876	+	0.935670i	$0.614796\pi$
$948$	−7.75507	−0.251873
$949$	−14.5910	−0.473645
$950$	1.31414	0.0426363
$951$	12.5159	0.405856
$952$	0	0
$953$	15.5511	0.503748	0.251874	−	0.967760i	$-0.418953\pi$
$953$	15.5511	0.503748	0.251874	+	0.967760i	$0.418953\pi$
$954$	0.375189	0.0121472
$955$	75.5195	2.44375
$956$	−31.6576	−1.02388
$957$	−0.543447	−0.0175672
$958$	1.55071	0.0501012
$959$	41.8974	1.35294
$960$	−15.9359	−0.514329
$961$	47.9081	1.54542
$962$	0.105415	0.00339873
$963$	14.1701	0.456627
$964$	−28.4021	−0.914768
$965$	8.77233	0.282391
$966$	−0.606536	−0.0195150
$967$	−14.2821	−0.459282	−0.229641	−	0.973275i	$-0.573755\pi$
$967$	−14.2821	−0.459282	−0.229641	+	0.973275i	$0.573755\pi$
$968$	−0.168375	−0.00541179
$969$	0	0
$970$	1.62037	0.0520271
$971$	−34.3172	−1.10129	−0.550646	−	0.834739i	$-0.685619\pi$
$971$	−34.3172	−1.10129	−0.550646	+	0.834739i	$0.685619\pi$
$972$	28.0037	0.898219
$973$	−13.8800	−0.444974
$974$	0.910436	0.0291722
$975$	11.0364	0.353446
$976$	−47.4598	−1.51915
$977$	−40.5801	−1.29827	−0.649136	−	0.760673i	$-0.724869\pi$
$977$	−40.5801	−1.29827	−0.649136	+	0.760673i	$0.724869\pi$
$978$	0.175567	0.00561401
$979$	0.373263	0.0119296
$980$	73.1011	2.33513
$981$	45.5473	1.45421
$982$	−0.614765	−0.0196180
$983$	9.55314	0.304698	0.152349	−	0.988327i	$-0.451316\pi$
$983$	9.55314	0.304698	0.152349	+	0.988327i	$0.451316\pi$
$984$	0.623261	0.0198688
$985$	−24.7270	−0.787867
$986$	0	0
$987$	−23.6147	−0.751664
$988$	38.8715	1.23667
$989$	−4.57801	−0.145572
$990$	−0.353514	−0.0112354
$991$	−50.1123	−1.59187	−0.795934	−	0.605383i	$-0.793020\pi$
$991$	−50.1123	−1.59187	−0.795934	+	0.605383i	$0.793020\pi$
$992$	−4.48373	−0.142359
$993$	3.74059	0.118704
$994$	−0.632815	−0.0200717
$995$	33.5515	1.06365
$996$	−7.88968	−0.249994
$997$	54.7568	1.73417	0.867083	−	0.498164i	$-0.165992\pi$
$997$	54.7568	1.73417	0.867083	+	0.498164i	$0.165992\pi$
$998$	0.214040	0.00677531
$999$	−2.63400	−0.0833359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bd.1.7		14
17.2	even	8		187.2.e.b.89.7	✓	28
17.9	even	8		187.2.e.b.166.8	yes	28
17.16	even	2		3179.2.a.be.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.7	✓	28	17.2	even	8
187.2.e.b.166.8	yes	28	17.9	even	8
3179.2.a.bd.1.7		14	1.1	even	1	trivial
3179.2.a.be.1.7		14	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0421125 q^{2} -0.623078 q^{3} -1.99823 q^{4} -3.21410 q^{5} -0.0262394 q^{6} +4.28743 q^{7} -0.168375 q^{8} -2.61177 q^{9} +O(q^{10})\)	\(q+0.0421125 q^{2} -0.623078 q^{3} -1.99823 q^{4} -3.21410 q^{5} -0.0262394 q^{6} +4.28743 q^{7} -0.168375 q^{8} -2.61177 q^{9} -0.135354 q^{10} -1.00000 q^{11} +1.24505 q^{12} -3.32292 q^{13} +0.180554 q^{14} +2.00264 q^{15} +3.98936 q^{16} -0.109988 q^{18} +5.85419 q^{19} +6.42250 q^{20} -2.67140 q^{21} -0.0421125 q^{22} +5.39146 q^{23} +0.104911 q^{24} +5.33044 q^{25} -0.139937 q^{26} +3.49657 q^{27} -8.56725 q^{28} -0.872197 q^{29} +0.0843361 q^{30} -8.88302 q^{31} +0.504753 q^{32} +0.623078 q^{33} -13.7802 q^{35} +5.21891 q^{36} -0.753308 q^{37} +0.246535 q^{38} +2.07044 q^{39} +0.541175 q^{40} +5.94085 q^{41} -0.112499 q^{42} -0.849123 q^{43} +1.99823 q^{44} +8.39450 q^{45} +0.227048 q^{46} +8.83981 q^{47} -2.48569 q^{48} +11.3820 q^{49} +0.224478 q^{50} +6.63995 q^{52} -3.41117 q^{53} +0.147250 q^{54} +3.21410 q^{55} -0.721897 q^{56} -3.64762 q^{57} -0.0367304 q^{58} +12.4757 q^{59} -4.00172 q^{60} -11.8966 q^{61} -0.374086 q^{62} -11.1978 q^{63} -7.95747 q^{64} +10.6802 q^{65} +0.0262394 q^{66} +4.87083 q^{67} -3.35930 q^{69} -0.580320 q^{70} -3.50485 q^{71} +0.439758 q^{72} +4.39102 q^{73} -0.0317237 q^{74} -3.32128 q^{75} -11.6980 q^{76} -4.28743 q^{77} +0.0871915 q^{78} -6.22872 q^{79} -12.8222 q^{80} +5.65668 q^{81} +0.250184 q^{82} -6.33683 q^{83} +5.33807 q^{84} -0.0357587 q^{86} +0.543447 q^{87} +0.168375 q^{88} -0.373263 q^{89} +0.353514 q^{90} -14.2468 q^{91} -10.7734 q^{92} +5.53482 q^{93} +0.372267 q^{94} -18.8159 q^{95} -0.314501 q^{96} -11.9714 q^{97} +0.479326 q^{98} +2.61177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 14 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 + 14 * q^4 - 8 * q^5 - 16 * q^6 - 12 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q + 2 q^{2} + 14 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} - 6 q^{8} + 14 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} + 36 q^{14} + 22 q^{16} + 2 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{21} - 2 q^{22} - 4 q^{23} - 52 q^{24} + 14 q^{25} - 36 q^{28} - 24 q^{29} + 4 q^{30} - 28 q^{31} - 30 q^{32} - 16 q^{35} + 38 q^{36} - 16 q^{37} + 4 q^{38} + 36 q^{39} - 36 q^{40} - 16 q^{41} - 4 q^{42} + 16 q^{43} - 14 q^{44} - 36 q^{45} - 56 q^{46} + 8 q^{47} + 68 q^{48} + 22 q^{49} + 30 q^{50} - 8 q^{52} + 4 q^{53} - 40 q^{54} + 8 q^{55} + 56 q^{56} - 36 q^{57} + 20 q^{58} + 12 q^{59} + 20 q^{60} - 60 q^{61} - 12 q^{62} - 40 q^{63} + 6 q^{64} + 8 q^{65} + 16 q^{66} - 8 q^{67} - 20 q^{69} - 24 q^{70} - 8 q^{71} - 10 q^{72} + 4 q^{73} - 44 q^{74} - 20 q^{75} - 8 q^{76} + 12 q^{77} - 20 q^{78} - 64 q^{79} - 60 q^{80} - 6 q^{81} + 8 q^{82} - 24 q^{83} - 76 q^{84} - 12 q^{86} - 24 q^{87} + 6 q^{88} - 4 q^{89} - 64 q^{90} - 44 q^{91} + 28 q^{92} - 40 q^{93} - 60 q^{94} - 24 q^{95} - 80 q^{96} - 80 q^{97} - 82 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 + 14 * q^4 - 8 * q^5 - 16 * q^6 - 12 * q^7 - 6 * q^8 + 14 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 + 36 * q^14 + 22 * q^16 + 2 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^21 - 2 * q^22 - 4 * q^23 - 52 * q^24 + 14 * q^25 - 36 * q^28 - 24 * q^29 + 4 * q^30 - 28 * q^31 - 30 * q^32 - 16 * q^35 + 38 * q^36 - 16 * q^37 + 4 * q^38 + 36 * q^39 - 36 * q^40 - 16 * q^41 - 4 * q^42 + 16 * q^43 - 14 * q^44 - 36 * q^45 - 56 * q^46 + 8 * q^47 + 68 * q^48 + 22 * q^49 + 30 * q^50 - 8 * q^52 + 4 * q^53 - 40 * q^54 + 8 * q^55 + 56 * q^56 - 36 * q^57 + 20 * q^58 + 12 * q^59 + 20 * q^60 - 60 * q^61 - 12 * q^62 - 40 * q^63 + 6 * q^64 + 8 * q^65 + 16 * q^66 - 8 * q^67 - 20 * q^69 - 24 * q^70 - 8 * q^71 - 10 * q^72 + 4 * q^73 - 44 * q^74 - 20 * q^75 - 8 * q^76 + 12 * q^77 - 20 * q^78 - 64 * q^79 - 60 * q^80 - 6 * q^81 + 8 * q^82 - 24 * q^83 - 76 * q^84 - 12 * q^86 - 24 * q^87 + 6 * q^88 - 4 * q^89 - 64 * q^90 - 44 * q^91 + 28 * q^92 - 40 * q^93 - 60 * q^94 - 24 * q^95 - 80 * q^96 - 80 * q^97 - 82 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more