LMFDB - Embedded newform 4017.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.950625$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.950625 q^{2} +1.00000 q^{3} -1.09631 q^{4} -0.0164301 q^{5} -0.950625 q^{6} +3.21492 q^{7} +2.94343 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.950625 q^{2} +1.00000 q^{3} -1.09631 q^{4} -0.0164301 q^{5} -0.950625 q^{6} +3.21492 q^{7} +2.94343 q^{8} +1.00000 q^{9} +0.0156189 q^{10} +1.39492 q^{11} -1.09631 q^{12} +1.00000 q^{13} -3.05618 q^{14} -0.0164301 q^{15} -0.605479 q^{16} -0.435090 q^{17} -0.950625 q^{18} -5.48416 q^{19} +0.0180125 q^{20} +3.21492 q^{21} -1.32604 q^{22} -3.31493 q^{23} +2.94343 q^{24} -4.99973 q^{25} -0.950625 q^{26} +1.00000 q^{27} -3.52455 q^{28} -8.82776 q^{29} +0.0156189 q^{30} -2.13167 q^{31} -5.31128 q^{32} +1.39492 q^{33} +0.413608 q^{34} -0.0528215 q^{35} -1.09631 q^{36} -9.14059 q^{37} +5.21338 q^{38} +1.00000 q^{39} -0.0483610 q^{40} -10.3930 q^{41} -3.05618 q^{42} -0.975040 q^{43} -1.52926 q^{44} -0.0164301 q^{45} +3.15126 q^{46} +5.71305 q^{47} -0.605479 q^{48} +3.33568 q^{49} +4.75287 q^{50} -0.435090 q^{51} -1.09631 q^{52} +1.19749 q^{53} -0.950625 q^{54} -0.0229187 q^{55} +9.46289 q^{56} -5.48416 q^{57} +8.39189 q^{58} +4.72448 q^{59} +0.0180125 q^{60} -6.39181 q^{61} +2.02642 q^{62} +3.21492 q^{63} +6.26000 q^{64} -0.0164301 q^{65} -1.32604 q^{66} -2.71316 q^{67} +0.476994 q^{68} -3.31493 q^{69} +0.0502135 q^{70} -8.17697 q^{71} +2.94343 q^{72} -0.674825 q^{73} +8.68928 q^{74} -4.99973 q^{75} +6.01235 q^{76} +4.48454 q^{77} -0.950625 q^{78} -6.74186 q^{79} +0.00994810 q^{80} +1.00000 q^{81} +9.87984 q^{82} +11.7076 q^{83} -3.52455 q^{84} +0.00714859 q^{85} +0.926898 q^{86} -8.82776 q^{87} +4.10584 q^{88} +4.39255 q^{89} +0.0156189 q^{90} +3.21492 q^{91} +3.63420 q^{92} -2.13167 q^{93} -5.43097 q^{94} +0.0901055 q^{95} -5.31128 q^{96} +6.62553 q^{97} -3.17099 q^{98} +1.39492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * 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 $

$2$	−0.950625	−0.672194	−0.336097	−	0.941827i	$-0.609107\pi$
$2$	−0.950625	−0.672194	−0.336097	+	0.941827i	$0.609107\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.09631	−0.548156
$5$	−0.0164301	−0.00734778	−0.00367389	−	0.999993i	$-0.501169\pi$
$5$	−0.0164301	−0.00734778	−0.00367389	+	0.999993i	$0.501169\pi$
$6$	−0.950625	−0.388091
$7$	3.21492	1.21512	0.607562	−	0.794272i	$-0.292148\pi$
$7$	3.21492	1.21512	0.607562	+	0.794272i	$0.292148\pi$
$8$	2.94343	1.04066
$9$	1.00000	0.333333
$10$	0.0156189	0.00493913
$11$	1.39492	0.420583	0.210291	−	0.977639i	$-0.432559\pi$
$11$	1.39492	0.420583	0.210291	+	0.977639i	$0.432559\pi$
$12$	−1.09631	−0.316478
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.05618	−0.816799
$15$	−0.0164301	−0.00424224
$16$	−0.605479	−0.151370
$17$	−0.435090	−0.105525	−0.0527624	−	0.998607i	$-0.516803\pi$
$17$	−0.435090	−0.105525	−0.0527624	+	0.998607i	$0.516803\pi$
$18$	−0.950625	−0.224065
$19$	−5.48416	−1.25815	−0.629076	−	0.777344i	$-0.716567\pi$
$19$	−5.48416	−1.25815	−0.629076	+	0.777344i	$0.716567\pi$
$20$	0.0180125	0.00402773
$21$	3.21492	0.701552
$22$	−1.32604	−0.282713
$23$	−3.31493	−0.691211	−0.345606	−	0.938380i	$-0.612327\pi$
$23$	−3.31493	−0.691211	−0.345606	+	0.938380i	$0.612327\pi$
$24$	2.94343	0.600826
$25$	−4.99973	−0.999946
$26$	−0.950625	−0.186433
$27$	1.00000	0.192450
$28$	−3.52455	−0.666077
$29$	−8.82776	−1.63927	−0.819637	−	0.572884i	$-0.805825\pi$
$29$	−8.82776	−1.63927	−0.819637	+	0.572884i	$0.805825\pi$
$30$	0.0156189	0.00285161
$31$	−2.13167	−0.382859	−0.191429	−	0.981506i	$-0.561312\pi$
$31$	−2.13167	−0.382859	−0.191429	+	0.981506i	$0.561312\pi$
$32$	−5.31128	−0.938911
$33$	1.39492	0.242824
$34$	0.413608	0.0709331
$35$	−0.0528215	−0.00892846
$36$	−1.09631	−0.182719
$37$	−9.14059	−1.50270	−0.751352	−	0.659902i	$-0.770598\pi$
$37$	−9.14059	−1.50270	−0.751352	+	0.659902i	$0.770598\pi$
$38$	5.21338	0.845722
$39$	1.00000	0.160128
$40$	−0.0483610	−0.00764654
$41$	−10.3930	−1.62311	−0.811556	−	0.584274i	$-0.801379\pi$
$41$	−10.3930	−1.62311	−0.811556	+	0.584274i	$0.801379\pi$
$42$	−3.05618	−0.471579
$43$	−0.975040	−0.148692	−0.0743461	−	0.997233i	$-0.523687\pi$
$43$	−0.975040	−0.148692	−0.0743461	+	0.997233i	$0.523687\pi$
$44$	−1.52926	−0.230545
$45$	−0.0164301	−0.00244926
$46$	3.15126	0.464628
$47$	5.71305	0.833335	0.416667	−	0.909059i	$-0.363198\pi$
$47$	5.71305	0.833335	0.416667	+	0.909059i	$0.363198\pi$
$48$	−0.605479	−0.0873933
$49$	3.33568	0.476526
$50$	4.75287	0.672157
$51$	−0.435090	−0.0609248
$52$	−1.09631	−0.152031
$53$	1.19749	0.164488	0.0822441	−	0.996612i	$-0.473791\pi$
$53$	1.19749	0.164488	0.0822441	+	0.996612i	$0.473791\pi$
$54$	−0.950625	−0.129364
$55$	−0.0229187	−0.00309035
$56$	9.46289	1.26453
$57$	−5.48416	−0.726395
$58$	8.39189	1.10191
$59$	4.72448	0.615076	0.307538	−	0.951536i	$-0.400495\pi$
$59$	4.72448	0.615076	0.307538	+	0.951536i	$0.400495\pi$
$60$	0.0180125	0.00232541
$61$	−6.39181	−0.818388	−0.409194	−	0.912447i	$-0.634190\pi$
$61$	−6.39181	−0.818388	−0.409194	+	0.912447i	$0.634190\pi$
$62$	2.02642	0.257355
$63$	3.21492	0.405041
$64$	6.26000	0.782500
$65$	−0.0164301	−0.00203791
$66$	−1.32604	−0.163225
$67$	−2.71316	−0.331465	−0.165732	−	0.986171i	$-0.552999\pi$
$67$	−2.71316	−0.331465	−0.165732	+	0.986171i	$0.552999\pi$
$68$	0.476994	0.0578440
$69$	−3.31493	−0.399071
$70$	0.0502135	0.00600166
$71$	−8.17697	−0.970428	−0.485214	−	0.874395i	$-0.661258\pi$
$71$	−8.17697	−0.970428	−0.485214	+	0.874395i	$0.661258\pi$
$72$	2.94343	0.346887
$73$	−0.674825	−0.0789823	−0.0394911	−	0.999220i	$-0.512574\pi$
$73$	−0.674825	−0.0789823	−0.0394911	+	0.999220i	$0.512574\pi$
$74$	8.68928	1.01011
$75$	−4.99973	−0.577319
$76$	6.01235	0.689663
$77$	4.48454	0.511060
$78$	−0.950625	−0.107637
$79$	−6.74186	−0.758518	−0.379259	−	0.925290i	$-0.623821\pi$
$79$	−6.74186	−0.758518	−0.379259	+	0.925290i	$0.623821\pi$
$80$	0.00994810	0.00111223
$81$	1.00000	0.111111
$82$	9.87984	1.09105
$83$	11.7076	1.28508	0.642538	−	0.766254i	$-0.277882\pi$
$83$	11.7076	1.28508	0.642538	+	0.766254i	$0.277882\pi$
$84$	−3.52455	−0.384560
$85$	0.00714859	0.000775373 0
$86$	0.926898	0.0999499
$87$	−8.82776	−0.946435
$88$	4.10584	0.437684
$89$	4.39255	0.465609	0.232805	−	0.972524i	$-0.425210\pi$
$89$	4.39255	0.465609	0.232805	+	0.972524i	$0.425210\pi$
$90$	0.0156189	0.00164638
$91$	3.21492	0.337015
$92$	3.63420	0.378891
$93$	−2.13167	−0.221044
$94$	−5.43097	−0.560162
$95$	0.0901055	0.00924463
$96$	−5.31128	−0.542080
$97$	6.62553	0.672721	0.336360	−	0.941733i	$-0.390804\pi$
$97$	6.62553	0.672721	0.336360	+	0.941733i	$0.390804\pi$
$98$	−3.17099	−0.320318
$99$	1.39492	0.140194
$100$	5.48126	0.548126
$101$	−1.55974	−0.155200	−0.0776001	−	0.996985i	$-0.524726\pi$
$101$	−1.55974	−0.155200	−0.0776001	+	0.996985i	$0.524726\pi$
$102$	0.413608	0.0409532
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.94343	0.288627
$105$	−0.0528215	−0.00515485
$106$	−1.13837	−0.110568
$107$	−7.84552	−0.758455	−0.379227	−	0.925303i	$-0.623810\pi$
$107$	−7.84552	−0.758455	−0.379227	+	0.925303i	$0.623810\pi$
$108$	−1.09631	−0.105493
$109$	4.45900	0.427094	0.213547	−	0.976933i	$-0.431498\pi$
$109$	4.45900	0.427094	0.213547	+	0.976933i	$0.431498\pi$
$110$	0.0217871	0.00207731
$111$	−9.14059	−0.867587
$112$	−1.94656	−0.183933
$113$	−2.93295	−0.275908	−0.137954	−	0.990439i	$-0.544053\pi$
$113$	−2.93295	−0.275908	−0.137954	+	0.990439i	$0.544053\pi$
$114$	5.21338	0.488278
$115$	0.0544648	0.00507887
$116$	9.67797	0.898577
$117$	1.00000	0.0924500
$118$	−4.49122	−0.413450
$119$	−1.39878	−0.128226
$120$	−0.0483610	−0.00441473
$121$	−9.05421	−0.823110
$122$	6.07622	0.550115
$123$	−10.3930	−0.937105
$124$	2.33697	0.209866
$125$	0.164297	0.0146952
$126$	−3.05618	−0.272266
$127$	2.66115	0.236139	0.118069	−	0.993005i	$-0.462329\pi$
$127$	2.66115	0.236139	0.118069	+	0.993005i	$0.462329\pi$
$128$	4.67165	0.412919
$129$	−0.975040	−0.0858475
$130$	0.0156189	0.00136987
$131$	−5.82525	−0.508954	−0.254477	−	0.967079i	$-0.581903\pi$
$131$	−5.82525	−0.508954	−0.254477	+	0.967079i	$0.581903\pi$
$132$	−1.52926	−0.133105
$133$	−17.6311	−1.52881
$134$	2.57919	0.222808
$135$	−0.0164301	−0.00141408
$136$	−1.28066	−0.109815
$137$	−4.46201	−0.381215	−0.190608	−	0.981666i	$-0.561046\pi$
$137$	−4.46201	−0.381215	−0.190608	+	0.981666i	$0.561046\pi$
$138$	3.15126	0.268253
$139$	7.85685	0.666409	0.333205	−	0.942855i	$-0.391870\pi$
$139$	7.85685	0.666409	0.333205	+	0.942855i	$0.391870\pi$
$140$	0.0579088	0.00489419
$141$	5.71305	0.481126
$142$	7.77324	0.652316
$143$	1.39492	0.116649
$144$	−0.605479	−0.0504566
$145$	0.145041	0.0120450
$146$	0.641505	0.0530914
$147$	3.33568	0.275123
$148$	10.0209	0.823716
$149$	2.52642	0.206972	0.103486	−	0.994631i	$-0.467000\pi$
$149$	2.52642	0.206972	0.103486	+	0.994631i	$0.467000\pi$
$150$	4.75287	0.388070
$151$	−6.68554	−0.544061	−0.272031	−	0.962289i	$-0.587695\pi$
$151$	−6.68554	−0.544061	−0.272031	+	0.962289i	$0.587695\pi$
$152$	−16.1423	−1.30931
$153$	−0.435090	−0.0351749
$154$	−4.26311	−0.343532
$155$	0.0350236	0.00281316
$156$	−1.09631	−0.0877752
$157$	−24.3825	−1.94594	−0.972968	−	0.230940i	$-0.925820\pi$
$157$	−24.3825	−1.94594	−0.972968	+	0.230940i	$0.925820\pi$
$158$	6.40898	0.509871
$159$	1.19749	0.0949673
$160$	0.0872651	0.00689891
$161$	−10.6572	−0.839907
$162$	−0.950625	−0.0746882
$163$	21.8985	1.71523	0.857613	−	0.514296i	$-0.171947\pi$
$163$	21.8985	1.71523	0.857613	+	0.514296i	$0.171947\pi$
$164$	11.3940	0.889718
$165$	−0.0229187	−0.00178422
$166$	−11.1295	−0.863820
$167$	20.6879	1.60088	0.800439	−	0.599414i	$-0.204600\pi$
$167$	20.6879	1.60088	0.800439	+	0.599414i	$0.204600\pi$
$168$	9.46289	0.730078
$169$	1.00000	0.0769231
$170$	−0.00679563	−0.000521201 0
$171$	−5.48416	−0.419384
$172$	1.06895	0.0815065
$173$	15.2656	1.16062	0.580310	−	0.814396i	$-0.302931\pi$
$173$	15.2656	1.16062	0.580310	+	0.814396i	$0.302931\pi$
$174$	8.39189	0.636187
$175$	−16.0737	−1.21506
$176$	−0.844592	−0.0636635
$177$	4.72448	0.355114
$178$	−4.17567	−0.312979
$179$	4.26012	0.318416	0.159208	−	0.987245i	$-0.449106\pi$
$179$	4.26012	0.318416	0.159208	+	0.987245i	$0.449106\pi$
$180$	0.0180125	0.00134258
$181$	−23.7399	−1.76457	−0.882286	−	0.470714i	$-0.843996\pi$
$181$	−23.7399	−1.76457	−0.882286	+	0.470714i	$0.843996\pi$
$182$	−3.05618	−0.226539
$183$	−6.39181	−0.472496
$184$	−9.75728	−0.719316
$185$	0.150181	0.0110415
$186$	2.02642	0.148584
$187$	−0.606914	−0.0443819
$188$	−6.26329	−0.456797
$189$	3.21492	0.233851
$190$	−0.0856566	−0.00621418
$191$	6.43848	0.465872	0.232936	−	0.972492i	$-0.425167\pi$
$191$	6.43848	0.465872	0.232936	+	0.972492i	$0.425167\pi$
$192$	6.26000	0.451776
$193$	−5.47374	−0.394009	−0.197004	−	0.980403i	$-0.563121\pi$
$193$	−5.47374	−0.394009	−0.197004	+	0.980403i	$0.563121\pi$
$194$	−6.29840	−0.452199
$195$	−0.0164301	−0.00117659
$196$	−3.65695	−0.261211
$197$	12.0329	0.857310	0.428655	−	0.903468i	$-0.358988\pi$
$197$	12.0329	0.857310	0.428655	+	0.903468i	$0.358988\pi$
$198$	−1.32604	−0.0942377
$199$	9.16912	0.649982	0.324991	−	0.945717i	$-0.394639\pi$
$199$	9.16912	0.649982	0.324991	+	0.945717i	$0.394639\pi$
$200$	−14.7164	−1.04060
$201$	−2.71316	−0.191371
$202$	1.48273	0.104325
$203$	−28.3805	−1.99192
$204$	0.476994	0.0333963
$205$	0.170758	0.0119263
$206$	0.950625	0.0662332
$207$	−3.31493	−0.230404
$208$	−0.605479	−0.0419824
$209$	−7.64994	−0.529157
$210$	0.0502135	0.00346506
$211$	4.15253	0.285872	0.142936	−	0.989732i	$-0.454346\pi$
$211$	4.15253	0.285872	0.142936	+	0.989732i	$0.454346\pi$
$212$	−1.31282	−0.0901652
$213$	−8.17697	−0.560277
$214$	7.45815	0.509829
$215$	0.0160200	0.00109256
$216$	2.94343	0.200275
$217$	−6.85314	−0.465221
$218$	−4.23883	−0.287090
$219$	−0.674825	−0.0456004
$220$	0.0251260	0.00169399
$221$	−0.435090	−0.0292673
$222$	8.68928	0.583186
$223$	−4.20727	−0.281740	−0.140870	−	0.990028i	$-0.544990\pi$
$223$	−4.20727	−0.281740	−0.140870	+	0.990028i	$0.544990\pi$
$224$	−17.0753	−1.14089
$225$	−4.99973	−0.333315
$226$	2.78813	0.185464
$227$	−1.75542	−0.116511	−0.0582555	−	0.998302i	$-0.518554\pi$
$227$	−1.75542	−0.116511	−0.0582555	+	0.998302i	$0.518554\pi$
$228$	6.01235	0.398177
$229$	−20.6717	−1.36603	−0.683013	−	0.730406i	$-0.739331\pi$
$229$	−20.6717	−1.36603	−0.683013	+	0.730406i	$0.739331\pi$
$230$	−0.0517756	−0.00341398
$231$	4.48454	0.295061
$232$	−25.9839	−1.70593
$233$	−4.34930	−0.284932	−0.142466	−	0.989800i	$-0.545503\pi$
$233$	−4.34930	−0.284932	−0.142466	+	0.989800i	$0.545503\pi$
$234$	−0.950625	−0.0621443
$235$	−0.0938663	−0.00612316
$236$	−5.17951	−0.337157
$237$	−6.74186	−0.437931
$238$	1.32971	0.0861925
$239$	11.0044	0.711813	0.355907	−	0.934522i	$-0.384172\pi$
$239$	11.0044	0.711813	0.355907	+	0.934522i	$0.384172\pi$
$240$	0.00994810	0.000642147 0
$241$	−17.4809	−1.12605	−0.563023	−	0.826442i	$-0.690362\pi$
$241$	−17.4809	−1.12605	−0.563023	+	0.826442i	$0.690362\pi$
$242$	8.60716	0.553289
$243$	1.00000	0.0641500
$244$	7.00742	0.448604
$245$	−0.0548057	−0.00350141
$246$	9.87984	0.629916
$247$	−5.48416	−0.348949
$248$	−6.27442	−0.398426
$249$	11.7076	0.741939
$250$	−0.156185	−0.00987800
$251$	−29.2508	−1.84629	−0.923146	−	0.384450i	$-0.874391\pi$
$251$	−29.2508	−1.84629	−0.923146	+	0.384450i	$0.874391\pi$
$252$	−3.52455	−0.222026
$253$	−4.62405	−0.290712
$254$	−2.52976	−0.158731
$255$	0.00714859	0.000447662 0
$256$	−16.9610	−1.06006
$257$	−9.57585	−0.597325	−0.298663	−	0.954359i	$-0.596541\pi$
$257$	−9.57585	−0.597325	−0.298663	+	0.954359i	$0.596541\pi$
$258$	0.926898	0.0577061
$259$	−29.3862	−1.82597
$260$	0.0180125	0.00111709
$261$	−8.82776	−0.546424
$262$	5.53763	0.342116
$263$	6.91080	0.426138	0.213069	−	0.977037i	$-0.431654\pi$
$263$	6.91080	0.426138	0.213069	+	0.977037i	$0.431654\pi$
$264$	4.10584	0.252697
$265$	−0.0196750	−0.00120862
$266$	16.7606	1.02766
$267$	4.39255	0.268820
$268$	2.97446	0.181694
$269$	12.5944	0.767892	0.383946	−	0.923355i	$-0.374565\pi$
$269$	12.5944	0.767892	0.383946	+	0.923355i	$0.374565\pi$
$270$	0.0156189	0.000950536 0
$271$	−17.5377	−1.06534	−0.532670	−	0.846323i	$-0.678811\pi$
$271$	−17.5377	−1.06534	−0.532670	+	0.846323i	$0.678811\pi$
$272$	0.263438	0.0159733
$273$	3.21492	0.194576
$274$	4.24170	0.256250
$275$	−6.97420	−0.420560
$276$	3.63420	0.218753
$277$	19.6368	1.17986	0.589930	−	0.807454i	$-0.299155\pi$
$277$	19.6368	1.17986	0.589930	+	0.807454i	$0.299155\pi$
$278$	−7.46892	−0.447956
$279$	−2.13167	−0.127620
$280$	−0.155477	−0.00929150
$281$	25.0995	1.49731	0.748654	−	0.662961i	$-0.230700\pi$
$281$	25.0995	1.49731	0.748654	+	0.662961i	$0.230700\pi$
$282$	−5.43097	−0.323410
$283$	−2.15995	−0.128396	−0.0641980	−	0.997937i	$-0.520449\pi$
$283$	−2.15995	−0.128396	−0.0641980	+	0.997937i	$0.520449\pi$
$284$	8.96451	0.531946
$285$	0.0901055	0.00533739
$286$	−1.32604	−0.0784105
$287$	−33.4126	−1.97228
$288$	−5.31128	−0.312970
$289$	−16.8107	−0.988865
$290$	−0.137880	−0.00809659
$291$	6.62553	0.388396
$292$	0.739818	0.0432946
$293$	13.1915	0.770658	0.385329	−	0.922779i	$-0.374088\pi$
$293$	13.1915	0.770658	0.385329	+	0.922779i	$0.374088\pi$
$294$	−3.17099	−0.184936
$295$	−0.0776239	−0.00451944
$296$	−26.9047	−1.56380
$297$	1.39492	0.0809412
$298$	−2.40168	−0.139125
$299$	−3.31493	−0.191708
$300$	5.48126	0.316461
$301$	−3.13467	−0.180679
$302$	6.35544	0.365715
$303$	−1.55974	−0.0896049
$304$	3.32054	0.190446
$305$	0.105018	0.00601333
$306$	0.413608	0.0236444
$307$	−7.50778	−0.428492	−0.214246	−	0.976780i	$-0.568729\pi$
$307$	−7.50778	−0.428492	−0.214246	+	0.976780i	$0.568729\pi$
$308$	−4.91645	−0.280141
$309$	−1.00000	−0.0568880
$310$	−0.0332943	−0.00189099
$311$	2.58125	0.146369	0.0731846	−	0.997318i	$-0.476684\pi$
$311$	2.58125	0.146369	0.0731846	+	0.997318i	$0.476684\pi$
$312$	2.94343	0.166639
$313$	35.0024	1.97846	0.989228	−	0.146386i	$-0.0467641\pi$
$313$	35.0024	1.97846	0.989228	+	0.146386i	$0.0467641\pi$
$314$	23.1786	1.30805
$315$	−0.0528215	−0.00297615
$316$	7.39118	0.415786
$317$	1.24437	0.0698907	0.0349453	−	0.999389i	$-0.488874\pi$
$317$	1.24437	0.0698907	0.0349453	+	0.999389i	$0.488874\pi$
$318$	−1.13837	−0.0638364
$319$	−12.3140	−0.689450
$320$	−0.102853	−0.00574963
$321$	−7.84552	−0.437894
$322$	10.1310	0.564580
$323$	2.38610	0.132766
$324$	−1.09631	−0.0609062
$325$	−4.99973	−0.277335
$326$	−20.8173	−1.15296
$327$	4.45900	0.246583
$328$	−30.5911	−1.68911
$329$	18.3670	1.01260
$330$	0.0217871	0.00119934
$331$	2.55054	0.140190	0.0700952	−	0.997540i	$-0.477670\pi$
$331$	2.55054	0.140190	0.0700952	+	0.997540i	$0.477670\pi$
$332$	−12.8352	−0.704422
$333$	−9.14059	−0.500901
$334$	−19.6664	−1.07610
$335$	0.0445775	0.00243553
$336$	−1.94656	−0.106194
$337$	25.9589	1.41407	0.707035	−	0.707178i	$-0.250032\pi$
$337$	25.9589	1.41407	0.707035	+	0.707178i	$0.250032\pi$
$338$	−0.950625	−0.0517072
$339$	−2.93295	−0.159296
$340$	−0.00783708	−0.000425025 0
$341$	−2.97350	−0.161024
$342$	5.21338	0.281907
$343$	−11.7805	−0.636085
$344$	−2.86996	−0.154738
$345$	0.0544648	0.00293229
$346$	−14.5118	−0.780161
$347$	11.6601	0.625948	0.312974	−	0.949762i	$-0.398675\pi$
$347$	11.6601	0.625948	0.312974	+	0.949762i	$0.398675\pi$
$348$	9.67797	0.518794
$349$	10.8337	0.579914	0.289957	−	0.957040i	$-0.406359\pi$
$349$	10.8337	0.579914	0.289957	+	0.957040i	$0.406359\pi$
$350$	15.2801	0.816755
$351$	1.00000	0.0533761
$352$	−7.40879	−0.394890
$353$	−10.3011	−0.548272	−0.274136	−	0.961691i	$-0.588392\pi$
$353$	−10.3011	−0.548272	−0.274136	+	0.961691i	$0.588392\pi$
$354$	−4.49122	−0.238705
$355$	0.134349	0.00713049
$356$	−4.81560	−0.255226
$357$	−1.39878	−0.0740312
$358$	−4.04978	−0.214037
$359$	−32.5678	−1.71886	−0.859432	−	0.511250i	$-0.829183\pi$
$359$	−32.5678	−1.71886	−0.859432	+	0.511250i	$0.829183\pi$
$360$	−0.0483610	−0.00254885
$361$	11.0760	0.582948
$362$	22.5677	1.18613
$363$	−9.05421	−0.475223
$364$	−3.52455	−0.184737
$365$	0.0110875	0.000580344 0
$366$	6.07622	0.317609
$367$	−1.41233	−0.0737230	−0.0368615	−	0.999320i	$-0.511736\pi$
$367$	−1.41233	−0.0737230	−0.0368615	+	0.999320i	$0.511736\pi$
$368$	2.00712	0.104628
$369$	−10.3930	−0.541038
$370$	−0.142766	−0.00742205
$371$	3.84984	0.199874
$372$	2.33697	0.121166
$373$	20.8514	1.07964	0.539822	−	0.841779i	$-0.318491\pi$
$373$	20.8514	1.07964	0.539822	+	0.841779i	$0.318491\pi$
$374$	0.576948	0.0298333
$375$	0.164297	0.00848426
$376$	16.8160	0.867218
$377$	−8.82776	−0.454653
$378$	−3.05618	−0.157193
$379$	17.8996	0.919440	0.459720	−	0.888064i	$-0.347950\pi$
$379$	17.8996	0.919440	0.459720	+	0.888064i	$0.347950\pi$
$380$	−0.0987837	−0.00506750
$381$	2.66115	0.136335
$382$	−6.12058	−0.313156
$383$	9.38207	0.479402	0.239701	−	0.970847i	$-0.422951\pi$
$383$	9.38207	0.479402	0.239701	+	0.970847i	$0.422951\pi$
$384$	4.67165	0.238399
$385$	−0.0736816	−0.00375516
$386$	5.20348	0.264850
$387$	−0.975040	−0.0495641
$388$	−7.26364	−0.368756
$389$	27.1914	1.37866	0.689329	−	0.724448i	$-0.257905\pi$
$389$	27.1914	1.37866	0.689329	+	0.724448i	$0.257905\pi$
$390$	0.0156189	0.000790894 0
$391$	1.44229	0.0729399
$392$	9.81836	0.495902
$393$	−5.82525	−0.293845
$394$	−11.4388	−0.576279
$395$	0.110770	0.00557343
$396$	−1.52926	−0.0768483
$397$	−9.02232	−0.452817	−0.226409	−	0.974032i	$-0.572698\pi$
$397$	−9.02232	−0.452817	−0.226409	+	0.974032i	$0.572698\pi$
$398$	−8.71640	−0.436914
$399$	−17.6311	−0.882660
$400$	3.02723	0.151362
$401$	8.06447	0.402721	0.201360	−	0.979517i	$-0.435464\pi$
$401$	8.06447	0.402721	0.201360	+	0.979517i	$0.435464\pi$
$402$	2.57919	0.128639
$403$	−2.13167	−0.106186
$404$	1.70996	0.0850739
$405$	−0.0164301	−0.000816420 0
$406$	26.9792	1.33896
$407$	−12.7504	−0.632012
$408$	−1.28066	−0.0634020
$409$	−30.9453	−1.53015	−0.765073	−	0.643944i	$-0.777297\pi$
$409$	−30.9453	−1.53015	−0.765073	+	0.643944i	$0.777297\pi$
$410$	−0.162327	−0.00801677
$411$	−4.46201	−0.220095
$412$	1.09631	0.0540114
$413$	15.1888	0.747393
$414$	3.15126	0.154876
$415$	−0.192357	−0.00944245
$416$	−5.31128	−0.260407
$417$	7.85685	0.384752
$418$	7.27223	0.355696
$419$	34.8422	1.70215	0.851077	−	0.525040i	$-0.175950\pi$
$419$	34.8422	1.70215	0.851077	+	0.525040i	$0.175950\pi$
$420$	0.0579088	0.00282566
$421$	−23.8064	−1.16025	−0.580126	−	0.814527i	$-0.696997\pi$
$421$	−23.8064	−1.16025	−0.580126	+	0.814527i	$0.696997\pi$
$422$	−3.94750	−0.192161
$423$	5.71305	0.277778
$424$	3.52474	0.171176
$425$	2.17533	0.105519
$426$	7.77324	0.376615
$427$	−20.5491	−0.994443
$428$	8.60113	0.415751
$429$	1.39492	0.0673472
$430$	−0.0152291	−0.000734410 0
$431$	7.11742	0.342834	0.171417	−	0.985199i	$-0.445165\pi$
$431$	7.11742	0.342834	0.171417	+	0.985199i	$0.445165\pi$
$432$	−0.605479	−0.0291311
$433$	−11.1433	−0.535512	−0.267756	−	0.963487i	$-0.586282\pi$
$433$	−11.1433	−0.535512	−0.267756	+	0.963487i	$0.586282\pi$
$434$	6.51476	0.312719
$435$	0.145041	0.00695420
$436$	−4.88845	−0.234114
$437$	18.1796	0.869649
$438$	0.641505	0.0306523
$439$	14.5227	0.693132	0.346566	−	0.938026i	$-0.387348\pi$
$439$	14.5227	0.693132	0.346566	+	0.938026i	$0.387348\pi$
$440$	−0.0674595	−0.00321601
$441$	3.33568	0.158842
$442$	0.413608	0.0196733
$443$	35.5144	1.68734	0.843670	−	0.536863i	$-0.180391\pi$
$443$	35.5144	1.68734	0.843670	+	0.536863i	$0.180391\pi$
$444$	10.0209	0.475572
$445$	−0.0721702	−0.00342119
$446$	3.99954	0.189384
$447$	2.52642	0.119496
$448$	20.1254	0.950834
$449$	24.1094	1.13779	0.568896	−	0.822409i	$-0.307371\pi$
$449$	24.1094	1.13779	0.568896	+	0.822409i	$0.307371\pi$
$450$	4.75287	0.224052
$451$	−14.4973	−0.682653
$452$	3.21542	0.151241
$453$	−6.68554	−0.314114
$454$	1.66874	0.0783180
$455$	−0.0528215	−0.00247631
$456$	−16.1423	−0.755930
$457$	−0.926627	−0.0433458	−0.0216729	−	0.999765i	$-0.506899\pi$
$457$	−0.926627	−0.0433458	−0.0216729	+	0.999765i	$0.506899\pi$
$458$	19.6511	0.918234
$459$	−0.435090	−0.0203083
$460$	−0.0597104	−0.00278401
$461$	−21.7398	−1.01252	−0.506261	−	0.862380i	$-0.668973\pi$
$461$	−21.7398	−1.01252	−0.506261	+	0.862380i	$0.668973\pi$
$462$	−4.26311	−0.198338
$463$	15.4446	0.717771	0.358885	−	0.933382i	$-0.383157\pi$
$463$	15.4446	0.717771	0.358885	+	0.933382i	$0.383157\pi$
$464$	5.34502	0.248136
$465$	0.0350236	0.00162418
$466$	4.13455	0.191529
$467$	12.0135	0.555919	0.277960	−	0.960593i	$-0.410342\pi$
$467$	12.0135	0.555919	0.277960	+	0.960593i	$0.410342\pi$
$468$	−1.09631	−0.0506770
$469$	−8.72257	−0.402771
$470$	0.0892317	0.00411595
$471$	−24.3825	−1.12349
$472$	13.9062	0.640085
$473$	−1.36010	−0.0625374
$474$	6.40898	0.294374
$475$	27.4193	1.25808
$476$	1.53350	0.0702877
$477$	1.19749	0.0548294
$478$	−10.4610	−0.478476
$479$	−6.93105	−0.316688	−0.158344	−	0.987384i	$-0.550615\pi$
$479$	−6.93105	−0.316688	−0.158344	+	0.987384i	$0.550615\pi$
$480$	0.0872651	0.00398309
$481$	−9.14059	−0.416775
$482$	16.6178	0.756920
$483$	−10.6572	−0.484921
$484$	9.92623	0.451192
$485$	−0.108858	−0.00494300
$486$	−0.950625	−0.0431212
$487$	10.2062	0.462489	0.231244	−	0.972896i	$-0.425720\pi$
$487$	10.2062	0.462489	0.231244	+	0.972896i	$0.425720\pi$
$488$	−18.8139	−0.851664
$489$	21.8985	0.990286
$490$	0.0520997	0.00235363
$491$	−33.1158	−1.49450	−0.747248	−	0.664546i	$-0.768625\pi$
$491$	−33.1158	−1.49450	−0.747248	+	0.664546i	$0.768625\pi$
$492$	11.3940	0.513679
$493$	3.84087	0.172984
$494$	5.21338	0.234561
$495$	−0.0229187	−0.00103012
$496$	1.29068	0.0579532
$497$	−26.2883	−1.17919
$498$	−11.1295	−0.498727
$499$	−28.6992	−1.28475	−0.642377	−	0.766389i	$-0.722051\pi$
$499$	−28.6992	−1.28475	−0.642377	+	0.766389i	$0.722051\pi$
$500$	−0.180121	−0.00805524
$501$	20.6879	0.924267
$502$	27.8065	1.24107
$503$	−12.8013	−0.570783	−0.285392	−	0.958411i	$-0.592124\pi$
$503$	−12.8013	−0.570783	−0.285392	+	0.958411i	$0.592124\pi$
$504$	9.46289	0.421510
$505$	0.0256268	0.00114038
$506$	4.39574	0.195415
$507$	1.00000	0.0444116
$508$	−2.91745	−0.129441
$509$	−39.6562	−1.75773	−0.878864	−	0.477072i	$-0.841698\pi$
$509$	−39.6562	−1.75773	−0.878864	+	0.477072i	$0.841698\pi$
$510$	−0.00679563	−0.000300915 0
$511$	−2.16950	−0.0959732
$512$	6.78024	0.299647
$513$	−5.48416	−0.242132
$514$	9.10305	0.401518
$515$	0.0164301	0.000723998 0
$516$	1.06895	0.0470578
$517$	7.96923	0.350486
$518$	27.9353	1.22741
$519$	15.2656	0.670084
$520$	−0.0483610	−0.00212077
$521$	5.13169	0.224823	0.112412	−	0.993662i	$-0.464142\pi$
$521$	5.13169	0.224823	0.112412	+	0.993662i	$0.464142\pi$
$522$	8.39189	0.367303
$523$	−29.5915	−1.29395	−0.646973	−	0.762513i	$-0.723965\pi$
$523$	−29.5915	−1.29395	−0.646973	+	0.762513i	$0.723965\pi$
$524$	6.38629	0.278986
$525$	−16.0737	−0.701514
$526$	−6.56958	−0.286447
$527$	0.927468	0.0404011
$528$	−0.844592	−0.0367561
$529$	−12.0112	−0.522227
$530$	0.0187035	0.000812429 0
$531$	4.72448	0.205025
$532$	19.3292	0.838027
$533$	−10.3930	−0.450170
$534$	−4.17567	−0.180699
$535$	0.128903	0.00557296
$536$	−7.98599	−0.344942
$537$	4.26012	0.183838
$538$	−11.9725	−0.516172
$539$	4.65300	0.200419
$540$	0.0180125	0.000775137 0
$541$	−5.47847	−0.235538	−0.117769	−	0.993041i	$-0.537574\pi$
$541$	−5.47847	−0.235538	−0.117769	+	0.993041i	$0.537574\pi$
$542$	16.6718	0.716115
$543$	−23.7399	−1.01878
$544$	2.31088	0.0990784
$545$	−0.0732619	−0.00313820
$546$	−3.05618	−0.130792
$547$	−4.71551	−0.201621	−0.100810	−	0.994906i	$-0.532144\pi$
$547$	−4.71551	−0.201621	−0.100810	+	0.994906i	$0.532144\pi$
$548$	4.89175	0.208965
$549$	−6.39181	−0.272796
$550$	6.62985	0.282698
$551$	48.4128	2.06246
$552$	−9.75728	−0.415297
$553$	−21.6745	−0.921694
$554$	−18.6672	−0.793094
$555$	0.150181	0.00637484
$556$	−8.61355	−0.365296
$557$	14.9111	0.631804	0.315902	−	0.948792i	$-0.397693\pi$
$557$	14.9111	0.631804	0.315902	+	0.948792i	$0.397693\pi$
$558$	2.02642	0.0857851
$559$	−0.975040	−0.0412398
$560$	0.0319823	0.00135150
$561$	−0.606914	−0.0256239
$562$	−23.8602	−1.00648
$563$	22.5691	0.951172	0.475586	−	0.879669i	$-0.342236\pi$
$563$	22.5691	0.951172	0.475586	+	0.879669i	$0.342236\pi$
$564$	−6.26329	−0.263732
$565$	0.0481887	0.00202731
$566$	2.05331	0.0863069
$567$	3.21492	0.135014
$568$	−24.0684	−1.00989
$569$	−32.2449	−1.35178	−0.675888	−	0.737004i	$-0.736240\pi$
$569$	−32.2449	−1.35178	−0.675888	+	0.737004i	$0.736240\pi$
$570$	−0.0856566	−0.00358776
$571$	23.1180	0.967460	0.483730	−	0.875217i	$-0.339282\pi$
$571$	23.1180	0.967460	0.483730	+	0.875217i	$0.339282\pi$
$572$	−1.52926	−0.0639417
$573$	6.43848	0.268971
$574$	31.7629	1.32576
$575$	16.5738	0.691174
$576$	6.26000	0.260833
$577$	−38.4911	−1.60241	−0.801203	−	0.598392i	$-0.795806\pi$
$577$	−38.4911	−1.60241	−0.801203	+	0.598392i	$0.795806\pi$
$578$	15.9807	0.664708
$579$	−5.47374	−0.227481
$580$	−0.159010	−0.00660255
$581$	37.6389	1.56153
$582$	−6.29840	−0.261077
$583$	1.67040	0.0691810
$584$	−1.98630	−0.0821937
$585$	−0.0164301	−0.000679303 0
$586$	−12.5402	−0.518031
$587$	8.64673	0.356889	0.178444	−	0.983950i	$-0.442894\pi$
$587$	8.64673	0.356889	0.178444	+	0.983950i	$0.442894\pi$
$588$	−3.65695	−0.150810
$589$	11.6904	0.481695
$590$	0.0737913	0.00303794
$591$	12.0329	0.494968
$592$	5.53443	0.227464
$593$	−41.0949	−1.68756	−0.843782	−	0.536685i	$-0.819676\pi$
$593$	−41.0949	−1.68756	−0.843782	+	0.536685i	$0.819676\pi$
$594$	−1.32604	−0.0544082
$595$	0.0229821	0.000942175 0
$596$	−2.76974	−0.113453
$597$	9.16912	0.375267
$598$	3.15126	0.128865
$599$	35.7184	1.45941	0.729707	−	0.683760i	$-0.239656\pi$
$599$	35.7184	1.45941	0.729707	+	0.683760i	$0.239656\pi$
$600$	−14.7164	−0.600793
$601$	−32.6439	−1.33157	−0.665786	−	0.746142i	$-0.731904\pi$
$601$	−32.6439	−1.33157	−0.665786	+	0.746142i	$0.731904\pi$
$602$	2.97990	0.121452
$603$	−2.71316	−0.110488
$604$	7.32943	0.298230
$605$	0.148762	0.00604803
$606$	1.48273	0.0602318
$607$	−4.57079	−0.185523	−0.0927614	−	0.995688i	$-0.529569\pi$
$607$	−4.57079	−0.185523	−0.0927614	+	0.995688i	$0.529569\pi$
$608$	29.1279	1.18129
$609$	−28.3805	−1.15004
$610$	−0.0998331	−0.00404212
$611$	5.71305	0.231125
$612$	0.476994	0.0192813
$613$	15.6177	0.630793	0.315397	−	0.948960i	$-0.397862\pi$
$613$	15.6177	0.630793	0.315397	+	0.948960i	$0.397862\pi$
$614$	7.13709	0.288029
$615$	0.170758	0.00688564
$616$	13.1999	0.531840
$617$	40.1521	1.61646	0.808231	−	0.588866i	$-0.200425\pi$
$617$	40.1521	1.61646	0.808231	+	0.588866i	$0.200425\pi$
$618$	0.950625	0.0382398
$619$	−41.1949	−1.65576	−0.827882	−	0.560902i	$-0.810454\pi$
$619$	−41.1949	−1.65576	−0.827882	+	0.560902i	$0.810454\pi$
$620$	−0.0383968	−0.00154205
$621$	−3.31493	−0.133024
$622$	−2.45380	−0.0983885
$623$	14.1217	0.565773
$624$	−0.605479	−0.0242385
$625$	24.9960	0.999838
$626$	−33.2742	−1.32991
$627$	−7.64994	−0.305509
$628$	26.7308	1.06668
$629$	3.97698	0.158573
$630$	0.0502135	0.00200055
$631$	−32.8846	−1.30911	−0.654557	−	0.756013i	$-0.727145\pi$
$631$	−32.8846	−1.30911	−0.654557	+	0.756013i	$0.727145\pi$
$632$	−19.8442	−0.789360
$633$	4.15253	0.165048
$634$	−1.18293	−0.0469801
$635$	−0.0437231	−0.00173510
$636$	−1.31282	−0.0520569
$637$	3.33568	0.132165
$638$	11.7060	0.463444
$639$	−8.17697	−0.323476
$640$	−0.0767559	−0.00303404
$641$	−25.3125	−0.999783	−0.499892	−	0.866088i	$-0.666627\pi$
$641$	−25.3125	−0.999783	−0.499892	+	0.866088i	$0.666627\pi$
$642$	7.45815	0.294350
$643$	−5.00044	−0.197198	−0.0985990	−	0.995127i	$-0.531436\pi$
$643$	−5.00044	−0.197198	−0.0985990	+	0.995127i	$0.531436\pi$
$644$	11.6836	0.460400
$645$	0.0160200	0.000630788 0
$646$	−2.26829	−0.0892447
$647$	0.241813	0.00950666	0.00475333	−	0.999989i	$-0.498487\pi$
$647$	0.241813	0.00950666	0.00475333	+	0.999989i	$0.498487\pi$
$648$	2.94343	0.115629
$649$	6.59026	0.258690
$650$	4.75287	0.186423
$651$	−6.85314	−0.268596
$652$	−24.0076	−0.940211
$653$	−38.5805	−1.50977	−0.754885	−	0.655857i	$-0.772307\pi$
$653$	−38.5805	−1.50977	−0.754885	+	0.655857i	$0.772307\pi$
$654$	−4.23883	−0.165752
$655$	0.0957096	0.00373969
$656$	6.29274	0.245690
$657$	−0.674825	−0.0263274
$658$	−17.4601	−0.680667
$659$	16.7615	0.652936	0.326468	−	0.945208i	$-0.394141\pi$
$659$	16.7615	0.652936	0.326468	+	0.945208i	$0.394141\pi$
$660$	0.0251260	0.000978028 0
$661$	−19.1976	−0.746700	−0.373350	−	0.927691i	$-0.621791\pi$
$661$	−19.1976	−0.746700	−0.373350	+	0.927691i	$0.621791\pi$
$662$	−2.42461	−0.0942351
$663$	−0.435090	−0.0168975
$664$	34.4605	1.33733
$665$	0.289682	0.0112334
$666$	8.68928	0.336703
$667$	29.2634	1.13308
$668$	−22.6804	−0.877530
$669$	−4.20727	−0.162662
$670$	−0.0423765	−0.00163715
$671$	−8.91604	−0.344200
$672$	−17.0753	−0.658695
$673$	−12.1221	−0.467272	−0.233636	−	0.972324i	$-0.575062\pi$
$673$	−12.1221	−0.467272	−0.233636	+	0.972324i	$0.575062\pi$
$674$	−24.6772	−0.950529
$675$	−4.99973	−0.192440
$676$	−1.09631	−0.0421658
$677$	43.5940	1.67545	0.837727	−	0.546089i	$-0.183884\pi$
$677$	43.5940	1.67545	0.837727	+	0.546089i	$0.183884\pi$
$678$	2.78813	0.107078
$679$	21.3005	0.817439
$680$	0.0210414	0.000806900 0
$681$	−1.75542	−0.0672677
$682$	2.82668	0.108239
$683$	50.4492	1.93038	0.965192	−	0.261543i	$-0.0842314\pi$
$683$	50.4492	1.93038	0.965192	+	0.261543i	$0.0842314\pi$
$684$	6.01235	0.229888
$685$	0.0733114	0.00280108
$686$	11.1988	0.427573
$687$	−20.6717	−0.788676
$688$	0.590366	0.0225075
$689$	1.19749	0.0456208
$690$	−0.0517756	−0.00197106
$691$	−3.48967	−0.132753	−0.0663767	−	0.997795i	$-0.521144\pi$
$691$	−3.48967	−0.132753	−0.0663767	+	0.997795i	$0.521144\pi$
$692$	−16.7358	−0.636200
$693$	4.48454	0.170353
$694$	−11.0844	−0.420758
$695$	−0.129089	−0.00489663
$696$	−25.9839	−0.984917
$697$	4.52189	0.171279
$698$	−10.2988	−0.389815
$699$	−4.34930	−0.164506
$700$	17.6218	0.666041
$701$	6.44907	0.243578	0.121789	−	0.992556i	$-0.461137\pi$
$701$	6.44907	0.243578	0.121789	+	0.992556i	$0.461137\pi$
$702$	−0.950625	−0.0358790
$703$	50.1285	1.89063
$704$	8.73217	0.329106
$705$	−0.0938663	−0.00353521
$706$	9.79249	0.368545
$707$	−5.01444	−0.188587
$708$	−5.17951	−0.194658
$709$	−6.67922	−0.250843	−0.125422	−	0.992104i	$-0.540028\pi$
$709$	−6.67922	−0.250843	−0.125422	+	0.992104i	$0.540028\pi$
$710$	−0.127715	−0.00479307
$711$	−6.74186	−0.252839
$712$	12.9292	0.484541
$713$	7.06634	0.264636
$714$	1.32971	0.0497633
$715$	−0.0229187	−0.000857109 0
$716$	−4.67042	−0.174542
$717$	11.0044	0.410966
$718$	30.9598	1.15541
$719$	−12.3997	−0.462432	−0.231216	−	0.972902i	$-0.574270\pi$
$719$	−12.3997	−0.462432	−0.231216	+	0.972902i	$0.574270\pi$
$720$	0.00994810	0.000370744 0
$721$	−3.21492	−0.119730
$722$	−10.5291	−0.391854
$723$	−17.4809	−0.650122
$724$	26.0263	0.967260
$725$	44.1364	1.63918
$726$	8.60716	0.319442
$727$	−15.0358	−0.557646	−0.278823	−	0.960343i	$-0.589944\pi$
$727$	−15.0358	−0.557646	−0.278823	+	0.960343i	$0.589944\pi$
$728$	9.46289	0.350718
$729$	1.00000	0.0370370
$730$	−0.0105400	−0.000390104 0
$731$	0.424230	0.0156907
$732$	7.00742	0.259002
$733$	43.2674	1.59812	0.799058	−	0.601253i	$-0.205332\pi$
$733$	43.2674	1.59812	0.799058	+	0.601253i	$0.205332\pi$
$734$	1.34260	0.0495562
$735$	−0.0548057	−0.00202154
$736$	17.6065	0.648986
$737$	−3.78462	−0.139408
$738$	9.87984	0.363682
$739$	−32.4591	−1.19403	−0.597013	−	0.802232i	$-0.703646\pi$
$739$	−32.4591	−1.19403	−0.597013	+	0.802232i	$0.703646\pi$
$740$	−0.164645	−0.00605248
$741$	−5.48416	−0.201466
$742$	−3.65975	−0.134354
$743$	−5.54026	−0.203252	−0.101626	−	0.994823i	$-0.532405\pi$
$743$	−5.54026	−0.203252	−0.101626	+	0.994823i	$0.532405\pi$
$744$	−6.27442	−0.230031
$745$	−0.0415094	−0.00152079
$746$	−19.8219	−0.725730
$747$	11.7076	0.428359
$748$	0.665366	0.0243282
$749$	−25.2227	−0.921617
$750$	−0.156185	−0.00570306
$751$	41.7540	1.52362	0.761812	−	0.647798i	$-0.224310\pi$
$751$	41.7540	1.52362	0.761812	+	0.647798i	$0.224310\pi$
$752$	−3.45913	−0.126142
$753$	−29.2508	−1.06596
$754$	8.39189	0.305615
$755$	0.109844	0.00399764
$756$	−3.52455	−0.128187
$757$	−41.2407	−1.49892	−0.749460	−	0.662050i	$-0.769687\pi$
$757$	−41.2407	−1.49892	−0.749460	+	0.662050i	$0.769687\pi$
$758$	−17.0158	−0.618042
$759$	−4.62405	−0.167842
$760$	0.265219	0.00962052
$761$	−21.2549	−0.770489	−0.385245	−	0.922814i	$-0.625883\pi$
$761$	−21.2549	−0.770489	−0.385245	+	0.922814i	$0.625883\pi$
$762$	−2.52976	−0.0916434
$763$	14.3353	0.518973
$764$	−7.05857	−0.255370
$765$	0.00714859	0.000258458 0
$766$	−8.91884	−0.322251
$767$	4.72448	0.170591
$768$	−16.9610	−0.612027
$769$	−36.2250	−1.30631	−0.653154	−	0.757225i	$-0.726555\pi$
$769$	−36.2250	−1.30631	−0.653154	+	0.757225i	$0.726555\pi$
$770$	0.0700436	0.00252419
$771$	−9.57585	−0.344866
$772$	6.00093	0.215978
$773$	16.8058	0.604463	0.302231	−	0.953235i	$-0.402269\pi$
$773$	16.8058	0.604463	0.302231	+	0.953235i	$0.402269\pi$
$774$	0.926898	0.0333166
$775$	10.6578	0.382838
$776$	19.5018	0.700074
$777$	−29.3862	−1.05423
$778$	−25.8488	−0.926726
$779$	56.9968	2.04212
$780$	0.0180125	0.000644953 0
$781$	−11.4062	−0.408146
$782$	−1.37108	−0.0490298
$783$	−8.82776	−0.315478
$784$	−2.01969	−0.0721316
$785$	0.400608	0.0142983
$786$	5.53763	0.197521
$787$	12.5946	0.448950	0.224475	−	0.974480i	$-0.427933\pi$
$787$	12.5946	0.448950	0.224475	+	0.974480i	$0.427933\pi$
$788$	−13.1918	−0.469940
$789$	6.91080	0.246031
$790$	−0.105300	−0.00374642
$791$	−9.42918	−0.335263
$792$	4.10584	0.145895
$793$	−6.39181	−0.226980
$794$	8.57684	0.304381
$795$	−0.0196750	−0.000697799 0
$796$	−10.0522	−0.356291
$797$	−23.2174	−0.822401	−0.411201	−	0.911545i	$-0.634890\pi$
$797$	−23.2174	−0.822401	−0.411201	+	0.911545i	$0.634890\pi$
$798$	16.7606	0.593318
$799$	−2.48569	−0.0879375
$800$	26.5550	0.938860
$801$	4.39255	0.155203
$802$	−7.66629	−0.270706
$803$	−0.941324	−0.0332186
$804$	2.97446	0.104901
$805$	0.175100	0.00617146
$806$	2.02642	0.0713775
$807$	12.5944	0.443343
$808$	−4.59100	−0.161511
$809$	−31.7364	−1.11579	−0.557897	−	0.829910i	$-0.688392\pi$
$809$	−31.7364	−1.11579	−0.557897	+	0.829910i	$0.688392\pi$
$810$	0.0156189	0.000548792 0
$811$	−38.2533	−1.34325	−0.671627	−	0.740890i	$-0.734404\pi$
$811$	−38.2533	−1.34325	−0.671627	+	0.740890i	$0.734404\pi$
$812$	31.1139	1.09188
$813$	−17.5377	−0.615074
$814$	12.1208	0.424834
$815$	−0.359796	−0.0126031
$816$	0.263438	0.00922216
$817$	5.34727	0.187077
$818$	29.4174	1.02855
$819$	3.21492	0.112338
$820$	−0.187204	−0.00653746
$821$	−15.2767	−0.533162	−0.266581	−	0.963813i	$-0.585894\pi$
$821$	−15.2767	−0.533162	−0.266581	+	0.963813i	$0.585894\pi$
$822$	4.24170	0.147946
$823$	52.1045	1.81625	0.908124	−	0.418700i	$-0.137514\pi$
$823$	52.1045	1.81625	0.908124	+	0.418700i	$0.137514\pi$
$824$	−2.94343	−0.102539
$825$	−6.97420	−0.242811
$826$	−14.4389	−0.502393
$827$	−10.4427	−0.363127	−0.181564	−	0.983379i	$-0.558116\pi$
$827$	−10.4427	−0.363127	−0.181564	+	0.983379i	$0.558116\pi$
$828$	3.63420	0.126297
$829$	5.84434	0.202982	0.101491	−	0.994836i	$-0.467639\pi$
$829$	5.84434	0.202982	0.101491	+	0.994836i	$0.467639\pi$
$830$	0.182860	0.00634716
$831$	19.6368	0.681192
$832$	6.26000	0.217026
$833$	−1.45132	−0.0502853
$834$	−7.46892	−0.258628
$835$	−0.339905	−0.0117629
$836$	8.38672	0.290061
$837$	−2.13167	−0.0736812
$838$	−33.1219	−1.14418
$839$	−12.9618	−0.447492	−0.223746	−	0.974647i	$-0.571829\pi$
$839$	−12.9618	−0.447492	−0.223746	+	0.974647i	$0.571829\pi$
$840$	−0.155477	−0.00536445
$841$	48.9293	1.68722
$842$	22.6310	0.779914
$843$	25.0995	0.864471
$844$	−4.55247	−0.156702
$845$	−0.0164301	−0.000565214 0
$846$	−5.43097	−0.186721
$847$	−29.1085	−1.00018
$848$	−0.725056	−0.0248985
$849$	−2.15995	−0.0741294
$850$	−2.06793	−0.0709293
$851$	30.3004	1.03869
$852$	8.96451	0.307119
$853$	15.8724	0.543459	0.271730	−	0.962374i	$-0.412404\pi$
$853$	15.8724	0.543459	0.271730	+	0.962374i	$0.412404\pi$
$854$	19.5345	0.668458
$855$	0.0901055	0.00308154
$856$	−23.0928	−0.789294
$857$	30.6675	1.04758	0.523791	−	0.851847i	$-0.324517\pi$
$857$	30.6675	1.04758	0.523791	+	0.851847i	$0.324517\pi$
$858$	−1.32604	−0.0452703
$859$	−3.39646	−0.115886	−0.0579428	−	0.998320i	$-0.518454\pi$
$859$	−3.39646	−0.115886	−0.0579428	+	0.998320i	$0.518454\pi$
$860$	−0.0175629	−0.000598892 0
$861$	−33.4126	−1.13870
$862$	−6.76600	−0.230451
$863$	−21.6608	−0.737343	−0.368671	−	0.929560i	$-0.620187\pi$
$863$	−21.6608	−0.737343	−0.368671	+	0.929560i	$0.620187\pi$
$864$	−5.31128	−0.180693
$865$	−0.250815	−0.00852798
$866$	10.5931	0.359968
$867$	−16.8107	−0.570921
$868$	7.51317	0.255014
$869$	−9.40433	−0.319020
$870$	−0.137880	−0.00467457
$871$	−2.71316	−0.0919318
$872$	13.1248	0.444460
$873$	6.62553	0.224240
$874$	−17.2820	−0.584573
$875$	0.528201	0.0178564
$876$	0.739818	0.0249961
$877$	−31.9278	−1.07812	−0.539062	−	0.842266i	$-0.681221\pi$
$877$	−31.9278	−1.07812	−0.539062	+	0.842266i	$0.681221\pi$
$878$	−13.8057	−0.465919
$879$	13.1915	0.444940
$880$	0.0138768	0.000467785 0
$881$	−4.39036	−0.147915	−0.0739574	−	0.997261i	$-0.523563\pi$
$881$	−4.39036	−0.147915	−0.0739574	+	0.997261i	$0.523563\pi$
$882$	−3.17099	−0.106773
$883$	−1.24186	−0.0417918	−0.0208959	−	0.999782i	$-0.506652\pi$
$883$	−1.24186	−0.0417918	−0.0208959	+	0.999782i	$0.506652\pi$
$884$	0.476994	0.0160430
$885$	−0.0776239	−0.00260930
$886$	−33.7609	−1.13422
$887$	−28.4823	−0.956343	−0.478171	−	0.878267i	$-0.658700\pi$
$887$	−28.4823	−0.956343	−0.478171	+	0.878267i	$0.658700\pi$
$888$	−26.9047	−0.902863
$889$	8.55538	0.286938
$890$	0.0686068	0.00229970
$891$	1.39492	0.0467314
$892$	4.61248	0.154437
$893$	−31.3313	−1.04846
$894$	−2.40168	−0.0803241
$895$	−0.0699943	−0.00233965
$896$	15.0190	0.501748
$897$	−3.31493	−0.110682
$898$	−22.9190	−0.764817
$899$	18.8179	0.627610
$900$	5.48126	0.182709
$901$	−0.521017	−0.0173576
$902$	13.7815	0.458875
$903$	−3.13467	−0.104315
$904$	−8.63293	−0.287127
$905$	0.390050	0.0129657
$906$	6.35544	0.211145
$907$	−1.60961	−0.0534463	−0.0267231	−	0.999643i	$-0.508507\pi$
$907$	−1.60961	−0.0534463	−0.0267231	+	0.999643i	$0.508507\pi$
$908$	1.92448	0.0638662
$909$	−1.55974	−0.0517334
$910$	0.0502135	0.00166456
$911$	−31.0593	−1.02904	−0.514521	−	0.857478i	$-0.672030\pi$
$911$	−31.0593	−1.02904	−0.514521	+	0.857478i	$0.672030\pi$
$912$	3.32054	0.109954
$913$	16.3311	0.540481
$914$	0.880875	0.0291368
$915$	0.105018	0.00347180
$916$	22.6627	0.748795
$917$	−18.7277	−0.618443
$918$	0.413608	0.0136511
$919$	−4.65712	−0.153624	−0.0768121	−	0.997046i	$-0.524474\pi$
$919$	−4.65712	−0.153624	−0.0768121	+	0.997046i	$0.524474\pi$
$920$	0.160313	0.00528538
$921$	−7.50778	−0.247390
$922$	20.6664	0.680611
$923$	−8.17697	−0.269148
$924$	−4.91645	−0.161739
$925$	45.7005	1.50262
$926$	−14.6820	−0.482481
$927$	−1.00000	−0.0328443
$928$	46.8867	1.53913
$929$	−1.87956	−0.0616664	−0.0308332	−	0.999525i	$-0.509816\pi$
$929$	−1.87956	−0.0616664	−0.0308332	+	0.999525i	$0.509816\pi$
$930$	−0.0332943	−0.00109176
$931$	−18.2934	−0.599543
$932$	4.76818	0.156187
$933$	2.58125	0.0845063
$934$	−11.4204	−0.373685
$935$	0.00997168	0.000326109 0
$936$	2.94343	0.0962091
$937$	−10.1995	−0.333205	−0.166602	−	0.986024i	$-0.553280\pi$
$937$	−10.1995	−0.333205	−0.166602	+	0.986024i	$0.553280\pi$
$938$	8.29189	0.270740
$939$	35.0024	1.14226
$940$	0.102907	0.00335644
$941$	0.110100	0.00358914	0.00179457	−	0.999998i	$-0.499429\pi$
$941$	0.110100	0.00358914	0.00179457	+	0.999998i	$0.499429\pi$
$942$	23.1786	0.755201
$943$	34.4521	1.12191
$944$	−2.86058	−0.0931038
$945$	−0.0528215	−0.00171828
$946$	1.29294	0.0420372
$947$	−34.8443	−1.13229	−0.566144	−	0.824307i	$-0.691565\pi$
$947$	−34.8443	−1.13229	−0.566144	+	0.824307i	$0.691565\pi$
$948$	7.39118	0.240054
$949$	−0.674825	−0.0219057
$950$	−26.0655	−0.845676
$951$	1.24437	0.0403514
$952$	−4.11721	−0.133439
$953$	51.8714	1.68028	0.840139	−	0.542371i	$-0.182473\pi$
$953$	51.8714	1.68028	0.840139	+	0.542371i	$0.182473\pi$
$954$	−1.13837	−0.0368560
$955$	−0.105785	−0.00342312
$956$	−12.0642	−0.390185
$957$	−12.3140	−0.398054
$958$	6.58883	0.212875
$959$	−14.3450	−0.463224
$960$	−0.102853	−0.00331955
$961$	−26.4560	−0.853419
$962$	8.68928	0.280154
$963$	−7.84552	−0.252818
$964$	19.1645	0.617248
$965$	0.0899344	0.00289509
$966$	10.1310	0.325961
$967$	−31.8757	−1.02505	−0.512527	−	0.858671i	$-0.671291\pi$
$967$	−31.8757	−1.02505	−0.512527	+	0.858671i	$0.671291\pi$
$968$	−26.6505	−0.856578
$969$	2.38610	0.0766527
$970$	0.103484	0.00332266
$971$	36.9604	1.18612	0.593058	−	0.805160i	$-0.297920\pi$
$971$	36.9604	1.18612	0.593058	+	0.805160i	$0.297920\pi$
$972$	−1.09631	−0.0351642
$973$	25.2591	0.809770
$974$	−9.70231	−0.310882
$975$	−4.99973	−0.160120
$976$	3.87011	0.123879
$977$	30.9920	0.991523	0.495761	−	0.868459i	$-0.334889\pi$
$977$	30.9920	0.991523	0.495761	+	0.868459i	$0.334889\pi$
$978$	−20.8173	−0.665664
$979$	6.12723	0.195827
$980$	0.0600842	0.00191932
$981$	4.45900	0.142365
$982$	31.4807	1.00459
$983$	27.6613	0.882258	0.441129	−	0.897444i	$-0.354578\pi$
$983$	27.6613	0.882258	0.441129	+	0.897444i	$0.354578\pi$
$984$	−30.5911	−0.975208
$985$	−0.197703	−0.00629933
$986$	−3.65123	−0.116279
$987$	18.3670	0.584628
$988$	6.01235	0.191278
$989$	3.23219	0.102778
$990$	0.0217871	0.000692438 0
$991$	28.6808	0.911074	0.455537	−	0.890217i	$-0.349447\pi$
$991$	28.6808	0.911074	0.455537	+	0.890217i	$0.349447\pi$
$992$	11.3219	0.359470
$993$	2.55054	0.0809390
$994$	24.9903	0.792645
$995$	−0.150650	−0.00477592
$996$	−12.8352	−0.406698
$997$	20.4775	0.648529	0.324264	−	0.945966i	$-0.394883\pi$
$997$	20.4775	0.648529	0.324264	+	0.945966i	$0.394883\pi$
$998$	27.2822	0.863603
$999$	−9.14059	−0.289196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.8	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.8	✓	19	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.950625 q^{2} +1.00000 q^{3} -1.09631 q^{4} -0.0164301 q^{5} -0.950625 q^{6} +3.21492 q^{7} +2.94343 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.950625 q^{2} +1.00000 q^{3} -1.09631 q^{4} -0.0164301 q^{5} -0.950625 q^{6} +3.21492 q^{7} +2.94343 q^{8} +1.00000 q^{9} +0.0156189 q^{10} +1.39492 q^{11} -1.09631 q^{12} +1.00000 q^{13} -3.05618 q^{14} -0.0164301 q^{15} -0.605479 q^{16} -0.435090 q^{17} -0.950625 q^{18} -5.48416 q^{19} +0.0180125 q^{20} +3.21492 q^{21} -1.32604 q^{22} -3.31493 q^{23} +2.94343 q^{24} -4.99973 q^{25} -0.950625 q^{26} +1.00000 q^{27} -3.52455 q^{28} -8.82776 q^{29} +0.0156189 q^{30} -2.13167 q^{31} -5.31128 q^{32} +1.39492 q^{33} +0.413608 q^{34} -0.0528215 q^{35} -1.09631 q^{36} -9.14059 q^{37} +5.21338 q^{38} +1.00000 q^{39} -0.0483610 q^{40} -10.3930 q^{41} -3.05618 q^{42} -0.975040 q^{43} -1.52926 q^{44} -0.0164301 q^{45} +3.15126 q^{46} +5.71305 q^{47} -0.605479 q^{48} +3.33568 q^{49} +4.75287 q^{50} -0.435090 q^{51} -1.09631 q^{52} +1.19749 q^{53} -0.950625 q^{54} -0.0229187 q^{55} +9.46289 q^{56} -5.48416 q^{57} +8.39189 q^{58} +4.72448 q^{59} +0.0180125 q^{60} -6.39181 q^{61} +2.02642 q^{62} +3.21492 q^{63} +6.26000 q^{64} -0.0164301 q^{65} -1.32604 q^{66} -2.71316 q^{67} +0.476994 q^{68} -3.31493 q^{69} +0.0502135 q^{70} -8.17697 q^{71} +2.94343 q^{72} -0.674825 q^{73} +8.68928 q^{74} -4.99973 q^{75} +6.01235 q^{76} +4.48454 q^{77} -0.950625 q^{78} -6.74186 q^{79} +0.00994810 q^{80} +1.00000 q^{81} +9.87984 q^{82} +11.7076 q^{83} -3.52455 q^{84} +0.00714859 q^{85} +0.926898 q^{86} -8.82776 q^{87} +4.10584 q^{88} +4.39255 q^{89} +0.0156189 q^{90} +3.21492 q^{91} +3.63420 q^{92} -2.13167 q^{93} -5.43097 q^{94} +0.0901055 q^{95} -5.31128 q^{96} +6.62553 q^{97} -3.17099 q^{98} +1.39492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

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