LMFDB - Embedded newform 6034.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.10273.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + x + 2 $ x^4 - 2x^3 - 5x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.673533$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.326467 q^{3} +1.00000 q^{4} +0.597538 q^{5} +0.326467 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.89342 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.326467 q^{3} +1.00000 q^{4} +0.597538 q^{5} +0.326467 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.89342 q^{9} -0.597538 q^{10} -6.29588 q^{11} -0.326467 q^{12} +2.92400 q^{13} -1.00000 q^{14} -0.195076 q^{15} +1.00000 q^{16} -4.67353 q^{17} +2.89342 q^{18} +6.26530 q^{19} +0.597538 q^{20} -0.326467 q^{21} +6.29588 q^{22} +3.24049 q^{23} +0.326467 q^{24} -4.64295 q^{25} -2.92400 q^{26} +1.92400 q^{27} +1.00000 q^{28} +1.70412 q^{29} +0.195076 q^{30} -3.86861 q^{31} -1.00000 q^{32} +2.05540 q^{33} +4.67353 q^{34} +0.597538 q^{35} -2.89342 q^{36} +4.62235 q^{37} -6.26530 q^{38} -0.954590 q^{39} -0.597538 q^{40} +9.20180 q^{41} +0.326467 q^{42} +11.9884 q^{43} -6.29588 q^{44} -1.72893 q^{45} -3.24049 q^{46} +3.88092 q^{47} -0.326467 q^{48} +1.00000 q^{49} +4.64295 q^{50} +1.52575 q^{51} +2.92400 q^{52} -6.94881 q^{53} -1.92400 q^{54} -3.76203 q^{55} -1.00000 q^{56} -2.04541 q^{57} -1.70412 q^{58} -1.43305 q^{59} -0.195076 q^{60} -1.56695 q^{61} +3.86861 q^{62} -2.89342 q^{63} +1.00000 q^{64} +1.74720 q^{65} -2.05540 q^{66} -5.47846 q^{67} -4.67353 q^{68} -1.05791 q^{69} -0.597538 q^{70} +13.4752 q^{71} +2.89342 q^{72} +7.01482 q^{73} -4.62235 q^{74} +1.51577 q^{75} +6.26530 q^{76} -6.29588 q^{77} +0.954590 q^{78} -1.13391 q^{79} +0.597538 q^{80} +8.05214 q^{81} -9.20180 q^{82} -2.18258 q^{83} -0.326467 q^{84} -2.79261 q^{85} -11.9884 q^{86} -0.556338 q^{87} +6.29588 q^{88} -12.7215 q^{89} +1.72893 q^{90} +2.92400 q^{91} +3.24049 q^{92} +1.26297 q^{93} -3.88092 q^{94} +3.74375 q^{95} +0.326467 q^{96} -8.33319 q^{97} -1.00000 q^{98} +18.2166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - q^{10} - 13 q^{11} - 2 q^{12} + 11 q^{13} - 4 q^{14} + 2 q^{15} + 4 q^{16} - 18 q^{17} - 2 q^{18} + q^{20} - 2 q^{21} + 13 q^{22} - 2 q^{23} + 2 q^{24} - 5 q^{25} - 11 q^{26} + 7 q^{27} + 4 q^{28} + 19 q^{29} - 2 q^{30} - 12 q^{31} - 4 q^{32} + 11 q^{33} + 18 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 16 q^{39} - q^{40} - 6 q^{41} + 2 q^{42} + 2 q^{43} - 13 q^{44} - 9 q^{45} + 2 q^{46} + 19 q^{47} - 2 q^{48} + 4 q^{49} + 5 q^{50} - 4 q^{51} + 11 q^{52} - 17 q^{53} - 7 q^{54} + 2 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 20 q^{59} + 2 q^{60} + 8 q^{61} + 12 q^{62} + 2 q^{63} + 4 q^{64} + 15 q^{65} - 11 q^{66} - 24 q^{67} - 18 q^{68} + 25 q^{69} - q^{70} + q^{71} - 2 q^{72} + 3 q^{73} - 7 q^{74} - 19 q^{75} - 13 q^{77} + 16 q^{78} + 24 q^{79} + q^{80} - 20 q^{81} + 6 q^{82} - 23 q^{83} - 2 q^{84} - 7 q^{85} - 2 q^{86} - 5 q^{87} + 13 q^{88} - 6 q^{89} + 9 q^{90} + 11 q^{91} - 2 q^{92} - 12 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} + 6 q^{97} - 4 q^{98} + 5 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - q^10 - 13 * q^11 - 2 * q^12 + 11 * q^13 - 4 * q^14 + 2 * q^15 + 4 * q^16 - 18 * q^17 - 2 * q^18 + q^20 - 2 * q^21 + 13 * q^22 - 2 * q^23 + 2 * q^24 - 5 * q^25 - 11 * q^26 + 7 * q^27 + 4 * q^28 + 19 * q^29 - 2 * q^30 - 12 * q^31 - 4 * q^32 + 11 * q^33 + 18 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 16 * q^39 - q^40 - 6 * q^41 + 2 * q^42 + 2 * q^43 - 13 * q^44 - 9 * q^45 + 2 * q^46 + 19 * q^47 - 2 * q^48 + 4 * q^49 + 5 * q^50 - 4 * q^51 + 11 * q^52 - 17 * q^53 - 7 * q^54 + 2 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 20 * q^59 + 2 * q^60 + 8 * q^61 + 12 * q^62 + 2 * q^63 + 4 * q^64 + 15 * q^65 - 11 * q^66 - 24 * q^67 - 18 * q^68 + 25 * q^69 - q^70 + q^71 - 2 * q^72 + 3 * q^73 - 7 * q^74 - 19 * q^75 - 13 * q^77 + 16 * q^78 + 24 * q^79 + q^80 - 20 * q^81 + 6 * q^82 - 23 * q^83 - 2 * q^84 - 7 * q^85 - 2 * q^86 - 5 * q^87 + 13 * q^88 - 6 * q^89 + 9 * q^90 + 11 * q^91 - 2 * q^92 - 12 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 + 6 * q^97 - 4 * q^98 + 5 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.326467	−0.188486	−0.0942428	−	0.995549i	$-0.530043\pi$
$3$	−0.326467	−0.188486	−0.0942428	+	0.995549i	$0.530043\pi$
$4$	1.00000	0.500000
$5$	0.597538	0.267227	0.133614	−	0.991034i	$-0.457342\pi$
$5$	0.597538	0.267227	0.133614	+	0.991034i	$0.457342\pi$
$6$	0.326467	0.133279
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.89342	−0.964473
$10$	−0.597538	−0.188958
$11$	−6.29588	−1.89828	−0.949140	−	0.314855i	$-0.898044\pi$
$11$	−6.29588	−1.89828	−0.949140	+	0.314855i	$0.898044\pi$
$12$	−0.326467	−0.0942428
$13$	2.92400	0.810973	0.405487	−	0.914101i	$-0.367102\pi$
$13$	2.92400	0.810973	0.405487	+	0.914101i	$0.367102\pi$
$14$	−1.00000	−0.267261
$15$	−0.195076	−0.0503685
$16$	1.00000	0.250000
$17$	−4.67353	−1.13350	−0.566749	−	0.823890i	$-0.691799\pi$
$17$	−4.67353	−1.13350	−0.566749	+	0.823890i	$0.691799\pi$
$18$	2.89342	0.681986
$19$	6.26530	1.43736	0.718679	−	0.695342i	$-0.244747\pi$
$19$	6.26530	1.43736	0.718679	+	0.695342i	$0.244747\pi$
$20$	0.597538	0.133614
$21$	−0.326467	−0.0712409
$22$	6.29588	1.34229
$23$	3.24049	0.675688	0.337844	−	0.941202i	$-0.390302\pi$
$23$	3.24049	0.675688	0.337844	+	0.941202i	$0.390302\pi$
$24$	0.326467	0.0666397
$25$	−4.64295	−0.928590
$26$	−2.92400	−0.573445
$27$	1.92400	0.370275
$28$	1.00000	0.188982
$29$	1.70412	0.316447	0.158223	−	0.987403i	$-0.449423\pi$
$29$	1.70412	0.316447	0.158223	+	0.987403i	$0.449423\pi$
$30$	0.195076	0.0356159
$31$	−3.86861	−0.694823	−0.347411	−	0.937713i	$-0.612939\pi$
$31$	−3.86861	−0.694823	−0.347411	+	0.937713i	$0.612939\pi$
$32$	−1.00000	−0.176777
$33$	2.05540	0.357798
$34$	4.67353	0.801504
$35$	0.597538	0.101002
$36$	−2.89342	−0.482237
$37$	4.62235	0.759909	0.379955	−	0.925005i	$-0.375940\pi$
$37$	4.62235	0.759909	0.379955	+	0.925005i	$0.375940\pi$
$38$	−6.26530	−1.01637
$39$	−0.954590	−0.152857
$40$	−0.597538	−0.0944791
$41$	9.20180	1.43708	0.718540	−	0.695486i	$-0.244811\pi$
$41$	9.20180	1.43708	0.718540	+	0.695486i	$0.244811\pi$
$42$	0.326467	0.0503749
$43$	11.9884	1.82822	0.914111	−	0.405465i	$-0.132890\pi$
$43$	11.9884	1.82822	0.914111	+	0.405465i	$0.132890\pi$
$44$	−6.29588	−0.949140
$45$	−1.72893	−0.257733
$46$	−3.24049	−0.477784
$47$	3.88092	0.566090	0.283045	−	0.959107i	$-0.408655\pi$
$47$	3.88092	0.566090	0.283045	+	0.959107i	$0.408655\pi$
$48$	−0.326467	−0.0471214
$49$	1.00000	0.142857
$50$	4.64295	0.656612
$51$	1.52575	0.213648
$52$	2.92400	0.405487
$53$	−6.94881	−0.954493	−0.477247	−	0.878769i	$-0.658365\pi$
$53$	−6.94881	−0.954493	−0.477247	+	0.878769i	$0.658365\pi$
$54$	−1.92400	−0.261824
$55$	−3.76203	−0.507272
$56$	−1.00000	−0.133631
$57$	−2.04541	−0.270921
$58$	−1.70412	−0.223762
$59$	−1.43305	−0.186567	−0.0932834	−	0.995640i	$-0.529736\pi$
$59$	−1.43305	−0.186567	−0.0932834	+	0.995640i	$0.529736\pi$
$60$	−0.195076	−0.0251842
$61$	−1.56695	−0.200628	−0.100314	−	0.994956i	$-0.531985\pi$
$61$	−1.56695	−0.200628	−0.100314	+	0.994956i	$0.531985\pi$
$62$	3.86861	0.491314
$63$	−2.89342	−0.364537
$64$	1.00000	0.125000
$65$	1.74720	0.216714
$66$	−2.05540	−0.253002
$67$	−5.47846	−0.669300	−0.334650	−	0.942342i	$-0.608618\pi$
$67$	−5.47846	−0.669300	−0.334650	+	0.942342i	$0.608618\pi$
$68$	−4.67353	−0.566749
$69$	−1.05791	−0.127357
$70$	−0.597538	−0.0714195
$71$	13.4752	1.59921	0.799606	−	0.600525i	$-0.205042\pi$
$71$	13.4752	1.59921	0.799606	+	0.600525i	$0.205042\pi$
$72$	2.89342	0.340993
$73$	7.01482	0.821023	0.410512	−	0.911855i	$-0.365350\pi$
$73$	7.01482	0.821023	0.410512	+	0.911855i	$0.365350\pi$
$74$	−4.62235	−0.537337
$75$	1.51577	0.175026
$76$	6.26530	0.718679
$77$	−6.29588	−0.717482
$78$	0.954590	0.108086
$79$	−1.13391	−0.127574	−0.0637872	−	0.997964i	$-0.520318\pi$
$79$	−1.13391	−0.127574	−0.0637872	+	0.997964i	$0.520318\pi$
$80$	0.597538	0.0668068
$81$	8.05214	0.894682
$82$	−9.20180	−1.01617
$83$	−2.18258	−0.239569	−0.119784	−	0.992800i	$-0.538220\pi$
$83$	−2.18258	−0.239569	−0.119784	+	0.992800i	$0.538220\pi$
$84$	−0.326467	−0.0356204
$85$	−2.79261	−0.302902
$86$	−11.9884	−1.29275
$87$	−0.556338	−0.0596457
$88$	6.29588	0.671143
$89$	−12.7215	−1.34847	−0.674236	−	0.738516i	$-0.735527\pi$
$89$	−12.7215	−1.34847	−0.674236	+	0.738516i	$0.735527\pi$
$90$	1.72893	0.182245
$91$	2.92400	0.306519
$92$	3.24049	0.337844
$93$	1.26297	0.130964
$94$	−3.88092	−0.400286
$95$	3.74375	0.384101
$96$	0.326467	0.0333199
$97$	−8.33319	−0.846107	−0.423054	−	0.906105i	$-0.639042\pi$
$97$	−8.33319	−0.846107	−0.423054	+	0.906105i	$0.639042\pi$
$98$	−1.00000	−0.101015
$99$	18.2166	1.83084
$100$	−4.64295	−0.464295
$101$	−11.9265	−1.18673	−0.593367	−	0.804932i	$-0.702202\pi$
$101$	−11.9265	−1.18673	−0.593367	+	0.804932i	$0.702202\pi$
$102$	−1.52575	−0.151072
$103$	−12.3719	−1.21904	−0.609519	−	0.792772i	$-0.708637\pi$
$103$	−12.3719	−1.21904	−0.609519	+	0.792772i	$0.708637\pi$
$104$	−2.92400	−0.286722
$105$	−0.195076	−0.0190375
$106$	6.94881	0.674929
$107$	−14.2984	−1.38228	−0.691139	−	0.722722i	$-0.742891\pi$
$107$	−14.2984	−1.38228	−0.691139	+	0.722722i	$0.742891\pi$
$108$	1.92400	0.185137
$109$	−6.46037	−0.618791	−0.309396	−	0.950933i	$-0.600127\pi$
$109$	−6.46037	−0.618791	−0.309396	+	0.950933i	$0.600127\pi$
$110$	3.76203	0.358695
$111$	−1.50904	−0.143232
$112$	1.00000	0.0944911
$113$	−18.4198	−1.73279	−0.866395	−	0.499360i	$-0.833569\pi$
$113$	−18.4198	−1.73279	−0.866395	+	0.499360i	$0.833569\pi$
$114$	2.04541	0.191570
$115$	1.93631	0.180562
$116$	1.70412	0.158223
$117$	−8.46037	−0.782162
$118$	1.43305	0.131923
$119$	−4.67353	−0.428422
$120$	0.195076	0.0178079
$121$	28.6381	2.60347
$122$	1.56695	0.141865
$123$	−3.00408	−0.270869
$124$	−3.86861	−0.347411
$125$	−5.76203	−0.515372
$126$	2.89342	0.257766
$127$	4.67353	0.414709	0.207355	−	0.978266i	$-0.433515\pi$
$127$	4.67353	0.414709	0.207355	+	0.978266i	$0.433515\pi$
$128$	−1.00000	−0.0883883
$129$	−3.91383	−0.344593
$130$	−1.74720	−0.153240
$131$	−5.10100	−0.445676	−0.222838	−	0.974855i	$-0.571532\pi$
$131$	−5.10100	−0.445676	−0.222838	+	0.974855i	$0.571532\pi$
$132$	2.05540	0.178899
$133$	6.26530	0.543270
$134$	5.47846	0.473267
$135$	1.14967	0.0989475
$136$	4.67353	0.400752
$137$	−7.80744	−0.667035	−0.333517	−	0.942744i	$-0.608236\pi$
$137$	−7.80744	−0.667035	−0.333517	+	0.942744i	$0.608236\pi$
$138$	1.05791	0.0900553
$139$	−21.5473	−1.82762	−0.913809	−	0.406144i	$-0.866873\pi$
$139$	−21.5473	−1.82762	−0.913809	+	0.406144i	$0.866873\pi$
$140$	0.597538	0.0505012
$141$	−1.26699	−0.106700
$142$	−13.4752	−1.13081
$143$	−18.4092	−1.53945
$144$	−2.89342	−0.241118
$145$	1.01828	0.0845632
$146$	−7.01482	−0.580551
$147$	−0.326467	−0.0269265
$148$	4.62235	0.379955
$149$	13.8819	1.13725	0.568624	−	0.822598i	$-0.307476\pi$
$149$	13.8819	1.13725	0.568624	+	0.822598i	$0.307476\pi$
$150$	−1.51577	−0.123762
$151$	−15.5802	−1.26790	−0.633950	−	0.773374i	$-0.718567\pi$
$151$	−15.5802	−1.26790	−0.633950	+	0.773374i	$0.718567\pi$
$152$	−6.26530	−0.508183
$153$	13.5225	1.09323
$154$	6.29588	0.507337
$155$	−2.31164	−0.185676
$156$	−0.954590	−0.0764284
$157$	8.57926	0.684700	0.342350	−	0.939573i	$-0.388777\pi$
$157$	8.57926	0.684700	0.342350	+	0.939573i	$0.388777\pi$
$158$	1.13391	0.0902087
$159$	2.26856	0.179908
$160$	−0.597538	−0.0472395
$161$	3.24049	0.255386
$162$	−8.05214	−0.632635
$163$	−8.38670	−0.656897	−0.328449	−	0.944522i	$-0.606526\pi$
$163$	−8.38670	−0.656897	−0.328449	+	0.944522i	$0.606526\pi$
$164$	9.20180	0.718540
$165$	1.22818	0.0956134
$166$	2.18258	0.169401
$167$	−13.8241	−1.06974	−0.534872	−	0.844933i	$-0.679640\pi$
$167$	−13.8241	−1.06974	−0.534872	+	0.844933i	$0.679640\pi$
$168$	0.326467	0.0251874
$169$	−4.45020	−0.342323
$170$	2.79261	0.214184
$171$	−18.1281	−1.38629
$172$	11.9884	0.914111
$173$	−21.5350	−1.63728	−0.818638	−	0.574310i	$-0.805270\pi$
$173$	−21.5350	−1.63728	−0.818638	+	0.574310i	$0.805270\pi$
$174$	0.556338	0.0421759
$175$	−4.64295	−0.350974
$176$	−6.29588	−0.474570
$177$	0.467842	0.0351652
$178$	12.7215	0.953514
$179$	−7.64716	−0.571575	−0.285788	−	0.958293i	$-0.592255\pi$
$179$	−7.64716	−0.571575	−0.285788	+	0.958293i	$0.592255\pi$
$180$	−1.72893	−0.128867
$181$	23.6166	1.75541	0.877703	−	0.479205i	$-0.159075\pi$
$181$	23.6166	1.75541	0.877703	+	0.479205i	$0.159075\pi$
$182$	−2.92400	−0.216742
$183$	0.511558	0.0378154
$184$	−3.24049	−0.238892
$185$	2.76203	0.203068
$186$	−1.26297	−0.0926056
$187$	29.4240	2.15170
$188$	3.88092	0.283045
$189$	1.92400	0.139951
$190$	−3.74375	−0.271600
$191$	−13.8380	−1.00128	−0.500642	−	0.865654i	$-0.666903\pi$
$191$	−13.8380	−1.00128	−0.500642	+	0.865654i	$0.666903\pi$
$192$	−0.326467	−0.0235607
$193$	12.8084	0.921968	0.460984	−	0.887408i	$-0.347497\pi$
$193$	12.8084	0.921968	0.460984	+	0.887408i	$0.347497\pi$
$194$	8.33319	0.598288
$195$	−0.570404	−0.0408475
$196$	1.00000	0.0714286
$197$	−8.03543	−0.572500	−0.286250	−	0.958155i	$-0.592409\pi$
$197$	−8.03543	−0.572500	−0.286250	+	0.958155i	$0.592409\pi$
$198$	−18.2166	−1.29460
$199$	8.58944	0.608889	0.304445	−	0.952530i	$-0.401529\pi$
$199$	8.58944	0.608889	0.304445	+	0.952530i	$0.401529\pi$
$200$	4.64295	0.328306
$201$	1.78853	0.126153
$202$	11.9265	0.839147
$203$	1.70412	0.119606
$204$	1.52575	0.106824
$205$	5.49843	0.384027
$206$	12.3719	0.861989
$207$	−9.37609	−0.651683
$208$	2.92400	0.202743
$209$	−39.4456	−2.72851
$210$	0.195076	0.0134615
$211$	−25.2232	−1.73643	−0.868217	−	0.496185i	$-0.834734\pi$
$211$	−25.2232	−1.73643	−0.868217	+	0.496185i	$0.834734\pi$
$212$	−6.94881	−0.477247
$213$	−4.39920	−0.301428
$214$	14.2984	0.977418
$215$	7.16356	0.488550
$216$	−1.92400	−0.130912
$217$	−3.86861	−0.262618
$218$	6.46037	0.437552
$219$	−2.29011	−0.154751
$220$	−3.76203	−0.253636
$221$	−13.6654	−0.919237
$222$	1.50904	0.101280
$223$	2.10426	0.140911	0.0704557	−	0.997515i	$-0.477555\pi$
$223$	2.10426	0.140911	0.0704557	+	0.997515i	$0.477555\pi$
$224$	−1.00000	−0.0668153
$225$	13.4340	0.895600
$226$	18.4198	1.22527
$227$	−0.739544	−0.0490852	−0.0245426	−	0.999699i	$-0.507813\pi$
$227$	−0.739544	−0.0490852	−0.0245426	+	0.999699i	$0.507813\pi$
$228$	−2.04541	−0.135461
$229$	−1.09019	−0.0720418	−0.0360209	−	0.999351i	$-0.511468\pi$
$229$	−1.09019	−0.0720418	−0.0360209	+	0.999351i	$0.511468\pi$
$230$	−1.93631	−0.127677
$231$	2.05540	0.135235
$232$	−1.70412	−0.111881
$233$	−0.987499	−0.0646932	−0.0323466	−	0.999477i	$-0.510298\pi$
$233$	−0.987499	−0.0646932	−0.0323466	+	0.999477i	$0.510298\pi$
$234$	8.46037	0.553072
$235$	2.31900	0.151275
$236$	−1.43305	−0.0932834
$237$	0.370182	0.0240459
$238$	4.67353	0.302940
$239$	22.3242	1.44403	0.722015	−	0.691878i	$-0.243216\pi$
$239$	22.3242	1.44403	0.722015	+	0.691878i	$0.243216\pi$
$240$	−0.195076	−0.0125921
$241$	−27.9234	−1.79870	−0.899352	−	0.437226i	$-0.855961\pi$
$241$	−27.9234	−1.79870	−0.899352	+	0.437226i	$0.855961\pi$
$242$	−28.6381	−1.84093
$243$	−8.40077	−0.538909
$244$	−1.56695	−0.100314
$245$	0.597538	0.0381753
$246$	3.00408	0.191533
$247$	18.3198	1.16566
$248$	3.86861	0.245657
$249$	0.712538	0.0451553
$250$	5.76203	0.364423
$251$	−2.65356	−0.167491	−0.0837457	−	0.996487i	$-0.526688\pi$
$251$	−2.65356	−0.167491	−0.0837457	+	0.996487i	$0.526688\pi$
$252$	−2.89342	−0.182268
$253$	−20.4017	−1.28264
$254$	−4.67353	−0.293244
$255$	0.911695	0.0570926
$256$	1.00000	0.0625000
$257$	4.49096	0.280138	0.140069	−	0.990142i	$-0.455268\pi$
$257$	4.49096	0.280138	0.140069	+	0.990142i	$0.455268\pi$
$258$	3.91383	0.243664
$259$	4.62235	0.287219
$260$	1.74720	0.108357
$261$	−4.93073	−0.305205
$262$	5.10100	0.315141
$263$	−10.8844	−0.671160	−0.335580	−	0.942012i	$-0.608932\pi$
$263$	−10.8844	−0.671160	−0.335580	+	0.942012i	$0.608932\pi$
$264$	−2.05540	−0.126501
$265$	−4.15218	−0.255066
$266$	−6.26530	−0.384150
$267$	4.15313	0.254168
$268$	−5.47846	−0.334650
$269$	10.7093	0.652956	0.326478	−	0.945205i	$-0.394138\pi$
$269$	10.7093	0.652956	0.326478	+	0.945205i	$0.394138\pi$
$270$	−1.14967	−0.0699665
$271$	19.1818	1.16521	0.582607	−	0.812754i	$-0.302033\pi$
$271$	19.1818	1.16521	0.582607	+	0.812754i	$0.302033\pi$
$272$	−4.67353	−0.283375
$273$	−0.954590	−0.0577744
$274$	7.80744	0.471665
$275$	29.2315	1.76272
$276$	−1.05791	−0.0636787
$277$	29.6214	1.77978	0.889889	−	0.456177i	$-0.150782\pi$
$277$	29.6214	1.77978	0.889889	+	0.456177i	$0.150782\pi$
$278$	21.5473	1.29232
$279$	11.1935	0.670138
$280$	−0.597538	−0.0357097
$281$	30.1745	1.80006	0.900030	−	0.435829i	$-0.143545\pi$
$281$	30.1745	1.80006	0.900030	+	0.435829i	$0.143545\pi$
$282$	1.26699	0.0754482
$283$	−21.2489	−1.26312	−0.631558	−	0.775328i	$-0.717584\pi$
$283$	−21.2489	−1.26312	−0.631558	+	0.775328i	$0.717584\pi$
$284$	13.4752	0.799606
$285$	−1.22221	−0.0723975
$286$	18.4092	1.08856
$287$	9.20180	0.543165
$288$	2.89342	0.170496
$289$	4.84191	0.284818
$290$	−1.01828	−0.0597952
$291$	2.72051	0.159479
$292$	7.01482	0.410512
$293$	−32.5106	−1.89929	−0.949645	−	0.313327i	$-0.898557\pi$
$293$	−32.5106	−1.89929	−0.949645	+	0.313327i	$0.898557\pi$
$294$	0.326467	0.0190399
$295$	−0.856300	−0.0498557
$296$	−4.62235	−0.268669
$297$	−12.1133	−0.702885
$298$	−13.8819	−0.804155
$299$	9.47520	0.547965
$300$	1.51577	0.0875129
$301$	11.9884	0.691003
$302$	15.5802	0.896540
$303$	3.89361	0.223682
$304$	6.26530	0.359339
$305$	−0.936314	−0.0536132
$306$	−13.5225	−0.773029
$307$	−20.8132	−1.18787	−0.593936	−	0.804512i	$-0.702427\pi$
$307$	−20.8132	−1.18787	−0.593936	+	0.804512i	$0.702427\pi$
$308$	−6.29588	−0.358741
$309$	4.03900	0.229771
$310$	2.31164	0.131292
$311$	29.5994	1.67843	0.839215	−	0.543800i	$-0.183015\pi$
$311$	29.5994	1.67843	0.839215	+	0.543800i	$0.183015\pi$
$312$	0.954590	0.0540430
$313$	9.44850	0.534061	0.267030	−	0.963688i	$-0.413958\pi$
$313$	9.44850	0.534061	0.267030	+	0.963688i	$0.413958\pi$
$314$	−8.57926	−0.484156
$315$	−1.72893	−0.0974141
$316$	−1.13391	−0.0637872
$317$	34.0983	1.91515	0.957576	−	0.288182i	$-0.0930507\pi$
$317$	34.0983	1.91515	0.957576	+	0.288182i	$0.0930507\pi$
$318$	−2.26856	−0.127214
$319$	−10.7289	−0.600705
$320$	0.597538	0.0334034
$321$	4.66795	0.260540
$322$	−3.24049	−0.180585
$323$	−29.2811	−1.62924
$324$	8.05214	0.447341
$325$	−13.5760	−0.753061
$326$	8.38670	0.464496
$327$	2.10910	0.116633
$328$	−9.20180	−0.508084
$329$	3.88092	0.213962
$330$	−1.22818	−0.0676089
$331$	27.5537	1.51449	0.757244	−	0.653132i	$-0.226545\pi$
$331$	27.5537	1.51449	0.757244	+	0.653132i	$0.226545\pi$
$332$	−2.18258	−0.119784
$333$	−13.3744	−0.732912
$334$	13.8241	0.756424
$335$	−3.27359	−0.178855
$336$	−0.326467	−0.0178102
$337$	−8.60251	−0.468608	−0.234304	−	0.972163i	$-0.575281\pi$
$337$	−8.60251	−0.468608	−0.234304	+	0.972163i	$0.575281\pi$
$338$	4.45020	0.242059
$339$	6.01345	0.326606
$340$	−2.79261	−0.151451
$341$	24.3563	1.31897
$342$	18.1281	0.980257
$343$	1.00000	0.0539949
$344$	−11.9884	−0.646374
$345$	−0.632142	−0.0340334
$346$	21.5350	1.15773
$347$	13.7272	0.736917	0.368458	−	0.929644i	$-0.379886\pi$
$347$	13.7272	0.736917	0.368458	+	0.929644i	$0.379886\pi$
$348$	−0.556338	−0.0298228
$349$	−31.5887	−1.69090	−0.845452	−	0.534051i	$-0.820669\pi$
$349$	−31.5887	−1.69090	−0.845452	+	0.534051i	$0.820669\pi$
$350$	4.64295	0.248176
$351$	5.62580	0.300283
$352$	6.29588	0.335572
$353$	1.91728	0.102046	0.0510232	−	0.998697i	$-0.483752\pi$
$353$	1.91728	0.102046	0.0510232	+	0.998697i	$0.483752\pi$
$354$	−0.467842	−0.0248655
$355$	8.05194	0.427353
$356$	−12.7215	−0.674236
$357$	1.52575	0.0807514
$358$	7.64716	0.404165
$359$	−32.0234	−1.69013	−0.845066	−	0.534662i	$-0.820439\pi$
$359$	−32.0234	−1.69013	−0.845066	+	0.534662i	$0.820439\pi$
$360$	1.72893	0.0911225
$361$	20.2539	1.06600
$362$	−23.6166	−1.24126
$363$	−9.34939	−0.490716
$364$	2.92400	0.153259
$365$	4.19163	0.219400
$366$	−0.511558	−0.0267396
$367$	3.10218	0.161932	0.0809662	−	0.996717i	$-0.474199\pi$
$367$	3.10218	0.161932	0.0809662	+	0.996717i	$0.474199\pi$
$368$	3.24049	0.168922
$369$	−26.6247	−1.38603
$370$	−2.76203	−0.143591
$371$	−6.94881	−0.360764
$372$	1.26297	0.0654820
$373$	11.9861	0.620618	0.310309	−	0.950636i	$-0.399567\pi$
$373$	11.9861	0.620618	0.310309	+	0.950636i	$0.399567\pi$
$374$	−29.4240	−1.52148
$375$	1.88111	0.0971401
$376$	−3.88092	−0.200143
$377$	4.98285	0.256630
$378$	−1.92400	−0.0989601
$379$	20.0197	1.02834	0.514171	−	0.857688i	$-0.328100\pi$
$379$	20.0197	1.02834	0.514171	+	0.857688i	$0.328100\pi$
$380$	3.74375	0.192050
$381$	−1.52575	−0.0781667
$382$	13.8380	0.708015
$383$	−10.8589	−0.554866	−0.277433	−	0.960745i	$-0.589484\pi$
$383$	−10.8589	−0.554866	−0.277433	+	0.960745i	$0.589484\pi$
$384$	0.326467	0.0166599
$385$	−3.76203	−0.191731
$386$	−12.8084	−0.651930
$387$	−34.6876	−1.76327
$388$	−8.33319	−0.423054
$389$	−24.3950	−1.23688	−0.618438	−	0.785834i	$-0.712234\pi$
$389$	−24.3950	−1.23688	−0.618438	+	0.785834i	$0.712234\pi$
$390$	0.570404	0.0288835
$391$	−15.1445	−0.765891
$392$	−1.00000	−0.0505076
$393$	1.66531	0.0840035
$394$	8.03543	0.404819
$395$	−0.677552	−0.0340913
$396$	18.2166	0.915420
$397$	−23.4761	−1.17823	−0.589117	−	0.808048i	$-0.700524\pi$
$397$	−23.4761	−1.17823	−0.589117	+	0.808048i	$0.700524\pi$
$398$	−8.58944	−0.430550
$399$	−2.04541	−0.102399
$400$	−4.64295	−0.232147
$401$	−17.7609	−0.886937	−0.443469	−	0.896290i	$-0.646252\pi$
$401$	−17.7609	−0.886937	−0.443469	+	0.896290i	$0.646252\pi$
$402$	−1.78853	−0.0892039
$403$	−11.3118	−0.563483
$404$	−11.9265	−0.593367
$405$	4.81146	0.239083
$406$	−1.70412	−0.0845740
$407$	−29.1018	−1.44252
$408$	−1.52575	−0.0755360
$409$	−11.7157	−0.579303	−0.289652	−	0.957132i	$-0.593539\pi$
$409$	−11.7157	−0.579303	−0.289652	+	0.957132i	$0.593539\pi$
$410$	−5.49843	−0.271548
$411$	2.54887	0.125726
$412$	−12.3719	−0.609519
$413$	−1.43305	−0.0705156
$414$	9.37609	0.460810
$415$	−1.30417	−0.0640193
$416$	−2.92400	−0.143361
$417$	7.03448	0.344480
$418$	39.4456	1.92935
$419$	2.76951	0.135300	0.0676498	−	0.997709i	$-0.478450\pi$
$419$	2.76951	0.135300	0.0676498	+	0.997709i	$0.478450\pi$
$420$	−0.195076	−0.00951875
$421$	7.50735	0.365886	0.182943	−	0.983124i	$-0.441438\pi$
$421$	7.50735	0.365886	0.182943	+	0.983124i	$0.441438\pi$
$422$	25.2232	1.22784
$423$	−11.2291	−0.545979
$424$	6.94881	0.337464
$425$	21.6990	1.05255
$426$	4.39920	0.213142
$427$	−1.56695	−0.0758302
$428$	−14.2984	−0.691139
$429$	6.00999	0.290165
$430$	−7.16356	−0.345457
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	1.92400	0.0925687
$433$	23.3976	1.12442	0.562209	−	0.826995i	$-0.309952\pi$
$433$	23.3976	1.12442	0.562209	+	0.826995i	$0.309952\pi$
$434$	3.86861	0.185699
$435$	−0.332433	−0.0159389
$436$	−6.46037	−0.309396
$437$	20.3026	0.971205
$438$	2.29011	0.109426
$439$	−27.5893	−1.31676	−0.658382	−	0.752684i	$-0.728759\pi$
$439$	−27.5893	−1.31676	−0.658382	+	0.752684i	$0.728759\pi$
$440$	3.76203	0.179348
$441$	−2.89342	−0.137782
$442$	13.6654	0.649998
$443$	−34.8365	−1.65513	−0.827565	−	0.561370i	$-0.810275\pi$
$443$	−34.8365	−1.65513	−0.827565	+	0.561370i	$0.810275\pi$
$444$	−1.50904	−0.0716160
$445$	−7.60156	−0.360348
$446$	−2.10426	−0.0996394
$447$	−4.53197	−0.214355
$448$	1.00000	0.0472456
$449$	6.75625	0.318847	0.159424	−	0.987210i	$-0.449036\pi$
$449$	6.75625	0.318847	0.159424	+	0.987210i	$0.449036\pi$
$450$	−13.4340	−0.633285
$451$	−57.9335	−2.72798
$452$	−18.4198	−0.866395
$453$	5.08642	0.238981
$454$	0.739544	0.0347085
$455$	1.74720	0.0819102
$456$	2.04541	0.0957851
$457$	−12.8628	−0.601698	−0.300849	−	0.953672i	$-0.597270\pi$
$457$	−12.8628	−0.601698	−0.300849	+	0.953672i	$0.597270\pi$
$458$	1.09019	0.0509412
$459$	−8.99190	−0.419706
$460$	1.93631	0.0902811
$461$	14.1703	0.659976	0.329988	−	0.943985i	$-0.392955\pi$
$461$	14.1703	0.659976	0.329988	+	0.943985i	$0.392955\pi$
$462$	−2.05540	−0.0956256
$463$	−2.30882	−0.107300	−0.0536500	−	0.998560i	$-0.517086\pi$
$463$	−2.30882	−0.107300	−0.0536500	+	0.998560i	$0.517086\pi$
$464$	1.70412	0.0791117
$465$	0.754674	0.0349972
$466$	0.987499	0.0457450
$467$	−36.2178	−1.67596	−0.837979	−	0.545702i	$-0.816263\pi$
$467$	−36.2178	−1.67596	−0.837979	+	0.545702i	$0.816263\pi$
$468$	−8.46037	−0.391081
$469$	−5.47846	−0.252972
$470$	−2.31900	−0.106967
$471$	−2.80084	−0.129056
$472$	1.43305	0.0659613
$473$	−75.4779	−3.47048
$474$	−0.370182	−0.0170030
$475$	−29.0894	−1.33472
$476$	−4.67353	−0.214211
$477$	20.1058	0.920583
$478$	−22.3242	−1.02108
$479$	8.74438	0.399541	0.199771	−	0.979843i	$-0.435980\pi$
$479$	8.74438	0.399541	0.199771	+	0.979843i	$0.435980\pi$
$480$	0.195076	0.00890397
$481$	13.5158	0.616266
$482$	27.9234	1.27188
$483$	−1.05791	−0.0481366
$484$	28.6381	1.30173
$485$	−4.97940	−0.226103
$486$	8.40077	0.381067
$487$	18.4944	0.838062	0.419031	−	0.907972i	$-0.362370\pi$
$487$	18.4944	0.838062	0.419031	+	0.907972i	$0.362370\pi$
$488$	1.56695	0.0709326
$489$	2.73798	0.123816
$490$	−0.597538	−0.0269940
$491$	−30.9092	−1.39491	−0.697456	−	0.716627i	$-0.745685\pi$
$491$	−30.9092	−1.39491	−0.697456	+	0.716627i	$0.745685\pi$
$492$	−3.00408	−0.135434
$493$	−7.96426	−0.358692
$494$	−18.3198	−0.824245
$495$	10.8851	0.489250
$496$	−3.86861	−0.173706
$497$	13.4752	0.604445
$498$	−0.712538	−0.0319296
$499$	−35.6216	−1.59464	−0.797321	−	0.603555i	$-0.793750\pi$
$499$	−35.6216	−1.59464	−0.797321	+	0.603555i	$0.793750\pi$
$500$	−5.76203	−0.257686
$501$	4.51312	0.201631
$502$	2.65356	0.118434
$503$	−5.83488	−0.260164	−0.130082	−	0.991503i	$-0.541524\pi$
$503$	−5.83488	−0.260164	−0.130082	+	0.991503i	$0.541524\pi$
$504$	2.89342	0.128883
$505$	−7.12655	−0.317127
$506$	20.4017	0.906967
$507$	1.45284	0.0645229
$508$	4.67353	0.207355
$509$	28.9564	1.28347	0.641734	−	0.766927i	$-0.278215\pi$
$509$	28.9564	1.28347	0.641734	+	0.766927i	$0.278215\pi$
$510$	−0.911695	−0.0403705
$511$	7.01482	0.310318
$512$	−1.00000	−0.0441942
$513$	12.0545	0.532217
$514$	−4.49096	−0.198088
$515$	−7.39267	−0.325760
$516$	−3.91383	−0.172297
$517$	−24.4338	−1.07460
$518$	−4.62235	−0.203094
$519$	7.03046	0.308603
$520$	−1.74720	−0.0766200
$521$	19.2493	0.843329	0.421665	−	0.906752i	$-0.361446\pi$
$521$	19.2493	0.843329	0.421665	+	0.906752i	$0.361446\pi$
$522$	4.93073	0.215812
$523$	−31.7943	−1.39027	−0.695134	−	0.718880i	$-0.744655\pi$
$523$	−31.7943	−1.39027	−0.695134	+	0.718880i	$0.744655\pi$
$524$	−5.10100	−0.222838
$525$	1.51577	0.0661535
$526$	10.8844	0.474582
$527$	18.0801	0.787580
$528$	2.05540	0.0894496
$529$	−12.4992	−0.543446
$530$	4.15218	0.180359
$531$	4.14641	0.179939
$532$	6.26530	0.271635
$533$	26.9061	1.16543
$534$	−4.15313	−0.179724
$535$	−8.54384	−0.369382
$536$	5.47846	0.236633
$537$	2.49654	0.107734
$538$	−10.7093	−0.461710
$539$	−6.29588	−0.271183
$540$	1.14967	0.0494738
$541$	9.50597	0.408694	0.204347	−	0.978899i	$-0.434493\pi$
$541$	9.50597	0.408694	0.204347	+	0.978899i	$0.434493\pi$
$542$	−19.1818	−0.823930
$543$	−7.71002	−0.330869
$544$	4.67353	0.200376
$545$	−3.86032	−0.165358
$546$	0.954590	0.0408527
$547$	−33.4348	−1.42957	−0.714785	−	0.699344i	$-0.753475\pi$
$547$	−33.4348	−1.42957	−0.714785	+	0.699344i	$0.753475\pi$
$548$	−7.80744	−0.333517
$549$	4.53385	0.193500
$550$	−29.2315	−1.24643
$551$	10.6768	0.454847
$552$	1.05791	0.0450277
$553$	−1.13391	−0.0482186
$554$	−29.6214	−1.25849
$555$	−0.901710	−0.0382755
$556$	−21.5473	−0.913809
$557$	40.3204	1.70843	0.854215	−	0.519920i	$-0.174038\pi$
$557$	40.3204	1.70843	0.854215	+	0.519920i	$0.174038\pi$
$558$	−11.1935	−0.473859
$559$	35.0543	1.48264
$560$	0.597538	0.0252506
$561$	−9.60596	−0.405564
$562$	−30.1745	−1.27283
$563$	8.40749	0.354334	0.177167	−	0.984181i	$-0.443307\pi$
$563$	8.40749	0.354334	0.177167	+	0.984181i	$0.443307\pi$
$564$	−1.26699	−0.0533499
$565$	−11.0065	−0.463048
$566$	21.2489	0.893158
$567$	8.05214	0.338158
$568$	−13.4752	−0.565407
$569$	−1.48360	−0.0621958	−0.0310979	−	0.999516i	$-0.509900\pi$
$569$	−1.48360	−0.0621958	−0.0310979	+	0.999516i	$0.509900\pi$
$570$	1.22221	0.0511928
$571$	1.70507	0.0713549	0.0356774	−	0.999363i	$-0.488641\pi$
$571$	1.70507	0.0713549	0.0356774	+	0.999363i	$0.488641\pi$
$572$	−18.4092	−0.769727
$573$	4.51765	0.188728
$574$	−9.20180	−0.384076
$575$	−15.0454	−0.627437
$576$	−2.89342	−0.120559
$577$	17.7745	0.739963	0.369982	−	0.929039i	$-0.379364\pi$
$577$	17.7745	0.739963	0.369982	+	0.929039i	$0.379364\pi$
$578$	−4.84191	−0.201397
$579$	−4.18151	−0.173778
$580$	1.01828	0.0422816
$581$	−2.18258	−0.0905485
$582$	−2.72051	−0.112769
$583$	43.7489	1.81189
$584$	−7.01482	−0.290276
$585$	−5.05540	−0.209015
$586$	32.5106	1.34300
$587$	−30.1494	−1.24440	−0.622199	−	0.782859i	$-0.713760\pi$
$587$	−30.1494	−1.24440	−0.622199	+	0.782859i	$0.713760\pi$
$588$	−0.326467	−0.0134633
$589$	−24.2380	−0.998709
$590$	0.856300	0.0352533
$591$	2.62330	0.107908
$592$	4.62235	0.189977
$593$	8.05865	0.330929	0.165465	−	0.986216i	$-0.447088\pi$
$593$	8.05865	0.330929	0.165465	+	0.986216i	$0.447088\pi$
$594$	12.1133	0.497015
$595$	−2.79261	−0.114486
$596$	13.8819	0.568624
$597$	−2.80416	−0.114767
$598$	−9.47520	−0.387470
$599$	−11.6149	−0.474571	−0.237286	−	0.971440i	$-0.576258\pi$
$599$	−11.6149	−0.474571	−0.237286	+	0.971440i	$0.576258\pi$
$600$	−1.51577	−0.0618810
$601$	−45.3184	−1.84858	−0.924288	−	0.381697i	$-0.875340\pi$
$601$	−45.3184	−1.84858	−0.924288	+	0.381697i	$0.875340\pi$
$602$	−11.9884	−0.488613
$603$	15.8515	0.645522
$604$	−15.5802	−0.633950
$605$	17.1124	0.695717
$606$	−3.89361	−0.158167
$607$	6.98982	0.283708	0.141854	−	0.989888i	$-0.454694\pi$
$607$	6.98982	0.283708	0.141854	+	0.989888i	$0.454694\pi$
$608$	−6.26530	−0.254091
$609$	−0.556338	−0.0225439
$610$	0.936314	0.0379103
$611$	11.3478	0.459084
$612$	13.5225	0.546614
$613$	−20.4786	−0.827125	−0.413562	−	0.910476i	$-0.635716\pi$
$613$	−20.4786	−0.827125	−0.413562	+	0.910476i	$0.635716\pi$
$614$	20.8132	0.839953
$615$	−1.79505	−0.0723835
$616$	6.29588	0.253668
$617$	−10.6050	−0.426942	−0.213471	−	0.976949i	$-0.568477\pi$
$617$	−10.6050	−0.426942	−0.213471	+	0.976949i	$0.568477\pi$
$618$	−4.03900	−0.162473
$619$	46.1239	1.85388	0.926939	−	0.375213i	$-0.122430\pi$
$619$	46.1239	1.85388	0.926939	+	0.375213i	$0.122430\pi$
$620$	−2.31164	−0.0928378
$621$	6.23471	0.250190
$622$	−29.5994	−1.18683
$623$	−12.7215	−0.509674
$624$	−0.954590	−0.0382142
$625$	19.7717	0.790868
$626$	−9.44850	−0.377638
$627$	12.8777	0.514284
$628$	8.57926	0.342350
$629$	−21.6027	−0.861356
$630$	1.72893	0.0688822
$631$	0.0288285	0.00114765	0.000573823	−	1.00000i	$-0.499817\pi$
$631$	0.0288285	0.00114765	0.000573823		1.00000i	$0.499817\pi$
$632$	1.13391	0.0451044
$633$	8.23452	0.327293
$634$	−34.0983	−1.35422
$635$	2.79261	0.110822
$636$	2.26856	0.0899541
$637$	2.92400	0.115853
$638$	10.7289	0.424762
$639$	−38.9894	−1.54240
$640$	−0.597538	−0.0236198
$641$	−34.9163	−1.37911	−0.689556	−	0.724232i	$-0.742194\pi$
$641$	−34.9163	−1.37911	−0.689556	+	0.724232i	$0.742194\pi$
$642$	−4.66795	−0.184229
$643$	8.37302	0.330200	0.165100	−	0.986277i	$-0.447205\pi$
$643$	8.37302	0.330200	0.165100	+	0.986277i	$0.447205\pi$
$644$	3.24049	0.127693
$645$	−2.33866	−0.0920847
$646$	29.2811	1.15205
$647$	3.19916	0.125772	0.0628859	−	0.998021i	$-0.479970\pi$
$647$	3.19916	0.125772	0.0628859	+	0.998021i	$0.479970\pi$
$648$	−8.05214	−0.316318
$649$	9.02229	0.354156
$650$	13.5760	0.532495
$651$	1.26297	0.0494998
$652$	−8.38670	−0.328449
$653$	17.8349	0.697933	0.348967	−	0.937135i	$-0.386533\pi$
$653$	17.8349	0.697933	0.348967	+	0.937135i	$0.386533\pi$
$654$	−2.10910	−0.0824722
$655$	−3.04804	−0.119097
$656$	9.20180	0.359270
$657$	−20.2968	−0.791855
$658$	−3.88092	−0.151294
$659$	7.61469	0.296626	0.148313	−	0.988940i	$-0.452616\pi$
$659$	7.61469	0.296626	0.148313	+	0.988940i	$0.452616\pi$
$660$	1.22818	0.0478067
$661$	5.52311	0.214824	0.107412	−	0.994215i	$-0.465744\pi$
$661$	5.52311	0.214824	0.107412	+	0.994215i	$0.465744\pi$
$662$	−27.5537	−1.07091
$663$	4.46131	0.173263
$664$	2.18258	0.0847004
$665$	3.74375	0.145177
$666$	13.3744	0.518247
$667$	5.52217	0.213819
$668$	−13.8241	−0.534872
$669$	−0.686969	−0.0265598
$670$	3.27359	0.126470
$671$	9.86535	0.380848
$672$	0.326467	0.0125937
$673$	31.4530	1.21243	0.606213	−	0.795303i	$-0.292688\pi$
$673$	31.4530	1.21243	0.606213	+	0.795303i	$0.292688\pi$
$674$	8.60251	0.331356
$675$	−8.93305	−0.343833
$676$	−4.45020	−0.171161
$677$	−11.4337	−0.439432	−0.219716	−	0.975564i	$-0.570513\pi$
$677$	−11.4337	−0.439432	−0.219716	+	0.975564i	$0.570513\pi$
$678$	−6.01345	−0.230945
$679$	−8.33319	−0.319799
$680$	2.79261	0.107092
$681$	0.241436	0.00925186
$682$	−24.3563	−0.932651
$683$	40.9777	1.56797	0.783984	−	0.620780i	$-0.213184\pi$
$683$	40.9777	1.56797	0.783984	+	0.620780i	$0.213184\pi$
$684$	−18.1281	−0.693146
$685$	−4.66524	−0.178250
$686$	−1.00000	−0.0381802
$687$	0.355911	0.0135788
$688$	11.9884	0.457055
$689$	−20.3184	−0.774068
$690$	0.632142	0.0240652
$691$	−48.4259	−1.84221	−0.921104	−	0.389317i	$-0.872711\pi$
$691$	−48.4259	−1.84221	−0.921104	+	0.389317i	$0.872711\pi$
$692$	−21.5350	−0.818638
$693$	18.2166	0.691992
$694$	−13.7272	−0.521079
$695$	−12.8753	−0.488389
$696$	0.556338	0.0210879
$697$	−43.0049	−1.62893
$698$	31.5887	1.19565
$699$	0.322386	0.0121937
$700$	−4.64295	−0.175487
$701$	−7.43463	−0.280802	−0.140401	−	0.990095i	$-0.544839\pi$
$701$	−7.43463	−0.280802	−0.140401	+	0.990095i	$0.544839\pi$
$702$	−5.62580	−0.212332
$703$	28.9604	1.09226
$704$	−6.29588	−0.237285
$705$	−0.757075	−0.0285131
$706$	−1.91728	−0.0721578
$707$	−11.9265	−0.448543
$708$	0.467842	0.0175826
$709$	−16.1891	−0.607995	−0.303997	−	0.952673i	$-0.598321\pi$
$709$	−16.1891	−0.607995	−0.303997	+	0.952673i	$0.598321\pi$
$710$	−8.05194	−0.302184
$711$	3.28087	0.123042
$712$	12.7215	0.476757
$713$	−12.5362	−0.469484
$714$	−1.52575	−0.0570999
$715$	−11.0002	−0.411384
$716$	−7.64716	−0.285788
$717$	−7.28809	−0.272179
$718$	32.0234	1.19510
$719$	−3.12405	−0.116507	−0.0582537	−	0.998302i	$-0.518553\pi$
$719$	−3.12405	−0.116507	−0.0582537	+	0.998302i	$0.518553\pi$
$720$	−1.72893	−0.0644334
$721$	−12.3719	−0.460753
$722$	−20.2539	−0.753773
$723$	9.11605	0.339030
$724$	23.6166	0.877703
$725$	−7.91213	−0.293849
$726$	9.34939	0.346988
$727$	16.8341	0.624344	0.312172	−	0.950026i	$-0.398943\pi$
$727$	16.8341	0.624344	0.312172	+	0.950026i	$0.398943\pi$
$728$	−2.92400	−0.108371
$729$	−21.4138	−0.793105
$730$	−4.19163	−0.155139
$731$	−56.0284	−2.07229
$732$	0.511558	0.0189077
$733$	30.4615	1.12512	0.562560	−	0.826757i	$-0.309817\pi$
$733$	30.4615	1.12512	0.562560	+	0.826757i	$0.309817\pi$
$734$	−3.10218	−0.114504
$735$	−0.195076	−0.00719550
$736$	−3.24049	−0.119446
$737$	34.4917	1.27052
$738$	26.6247	0.980068
$739$	−2.03460	−0.0748441	−0.0374221	−	0.999300i	$-0.511915\pi$
$739$	−2.03460	−0.0748441	−0.0374221	+	0.999300i	$0.511915\pi$
$740$	2.76203	0.101534
$741$	−5.98079	−0.219710
$742$	6.94881	0.255099
$743$	18.4908	0.678361	0.339180	−	0.940721i	$-0.389850\pi$
$743$	18.4908	0.678361	0.339180	+	0.940721i	$0.389850\pi$
$744$	−1.26297	−0.0463028
$745$	8.29495	0.303903
$746$	−11.9861	−0.438843
$747$	6.31511	0.231058
$748$	29.4240	1.07585
$749$	−14.2984	−0.522452
$750$	−1.88111	−0.0686884
$751$	6.54246	0.238738	0.119369	−	0.992850i	$-0.461913\pi$
$751$	6.54246	0.238738	0.119369	+	0.992850i	$0.461913\pi$
$752$	3.88092	0.141523
$753$	0.866300	0.0315697
$754$	−4.98285	−0.181465
$755$	−9.30977	−0.338817
$756$	1.92400	0.0699754
$757$	46.7037	1.69747	0.848737	−	0.528815i	$-0.177363\pi$
$757$	46.7037	1.69747	0.848737	+	0.528815i	$0.177363\pi$
$758$	−20.0197	−0.727147
$759$	6.66048	0.241760
$760$	−3.74375	−0.135800
$761$	32.6293	1.18281	0.591406	−	0.806374i	$-0.298573\pi$
$761$	32.6293	1.18281	0.591406	+	0.806374i	$0.298573\pi$
$762$	1.52575	0.0552722
$763$	−6.46037	−0.233881
$764$	−13.8380	−0.500642
$765$	8.08021	0.292140
$766$	10.8589	0.392350
$767$	−4.19024	−0.151301
$768$	−0.326467	−0.0117803
$769$	22.0240	0.794206	0.397103	−	0.917774i	$-0.370016\pi$
$769$	22.0240	0.794206	0.397103	+	0.917774i	$0.370016\pi$
$770$	3.76203	0.135574
$771$	−1.46615	−0.0528020
$772$	12.8084	0.460984
$773$	34.9517	1.25712	0.628562	−	0.777760i	$-0.283644\pi$
$773$	34.9517	1.25712	0.628562	+	0.777760i	$0.283644\pi$
$774$	34.6876	1.24682
$775$	17.9618	0.645205
$776$	8.33319	0.299144
$777$	−1.50904	−0.0541366
$778$	24.3950	0.874603
$779$	57.6520	2.06560
$780$	−0.570404	−0.0204237
$781$	−84.8382	−3.03575
$782$	15.1445	0.541567
$783$	3.27873	0.117172
$784$	1.00000	0.0357143
$785$	5.12644	0.182970
$786$	−1.66531	−0.0593995
$787$	50.4667	1.79894	0.899471	−	0.436980i	$-0.143952\pi$
$787$	50.4667	1.79894	0.899471	+	0.436980i	$0.143952\pi$
$788$	−8.03543	−0.286250
$789$	3.55339	0.126504
$790$	0.677552	0.0241062
$791$	−18.4198	−0.654933
$792$	−18.2166	−0.647300
$793$	−4.58178	−0.162704
$794$	23.4761	0.833137
$795$	1.35555	0.0480764
$796$	8.58944	0.304445
$797$	38.6872	1.37037	0.685186	−	0.728368i	$-0.259721\pi$
$797$	38.6872	1.37037	0.685186	+	0.728368i	$0.259721\pi$
$798$	2.04541	0.0724067
$799$	−18.1376	−0.641662
$800$	4.64295	0.164153
$801$	36.8085	1.30057
$802$	17.7609	0.627159
$803$	−44.1645	−1.55853
$804$	1.78853	0.0630767
$805$	1.93631	0.0682461
$806$	11.3118	0.398442
$807$	−3.49622	−0.123073
$808$	11.9265	0.419574
$809$	−27.8162	−0.977967	−0.488983	−	0.872293i	$-0.662632\pi$
$809$	−27.8162	−0.977967	−0.488983	+	0.872293i	$0.662632\pi$
$810$	−4.81146	−0.169057
$811$	−9.70425	−0.340762	−0.170381	−	0.985378i	$-0.554500\pi$
$811$	−9.70425	−0.340762	−0.170381	+	0.985378i	$0.554500\pi$
$812$	1.70412	0.0598028
$813$	−6.26223	−0.219626
$814$	29.1018	1.02002
$815$	−5.01137	−0.175541
$816$	1.52575	0.0534120
$817$	75.1112	2.62781
$818$	11.7157	0.409629
$819$	−8.46037	−0.295629
$820$	5.49843	0.192013
$821$	−16.5016	−0.575909	−0.287954	−	0.957644i	$-0.592975\pi$
$821$	−16.5016	−0.575909	−0.287954	+	0.957644i	$0.592975\pi$
$822$	−2.54887	−0.0889020
$823$	−23.9337	−0.834276	−0.417138	−	0.908843i	$-0.636967\pi$
$823$	−23.9337	−0.834276	−0.417138	+	0.908843i	$0.636967\pi$
$824$	12.3719	0.430995
$825$	−9.54309	−0.332248
$826$	1.43305	0.0498621
$827$	−15.4464	−0.537123	−0.268561	−	0.963263i	$-0.586548\pi$
$827$	−15.4464	−0.537123	−0.268561	+	0.963263i	$0.586548\pi$
$828$	−9.37609	−0.325842
$829$	−45.3512	−1.57511	−0.787555	−	0.616244i	$-0.788654\pi$
$829$	−45.3512	−1.57511	−0.787555	+	0.616244i	$0.788654\pi$
$830$	1.30417	0.0452685
$831$	−9.67040	−0.335463
$832$	2.92400	0.101372
$833$	−4.67353	−0.161928
$834$	−7.03448	−0.243584
$835$	−8.26046	−0.285865
$836$	−39.4456	−1.36425
$837$	−7.44322	−0.257275
$838$	−2.76951	−0.0956712
$839$	−18.0761	−0.624058	−0.312029	−	0.950073i	$-0.601009\pi$
$839$	−18.0761	−0.624058	−0.312029	+	0.950073i	$0.601009\pi$
$840$	0.195076	0.00673077
$841$	−26.0960	−0.899861
$842$	−7.50735	−0.258720
$843$	−9.85096	−0.339285
$844$	−25.2232	−0.868217
$845$	−2.65916	−0.0914780
$846$	11.2291	0.386065
$847$	28.6381	0.984018
$848$	−6.94881	−0.238623
$849$	6.93706	0.238079
$850$	−21.6990	−0.744269
$851$	14.9787	0.513462
$852$	−4.39920	−0.150714
$853$	−21.7332	−0.744129	−0.372064	−	0.928207i	$-0.621350\pi$
$853$	−21.7332	−0.744129	−0.372064	+	0.928207i	$0.621350\pi$
$854$	1.56695	0.0536200
$855$	−10.8322	−0.370455
$856$	14.2984	0.488709
$857$	−40.7494	−1.39197	−0.695987	−	0.718055i	$-0.745033\pi$
$857$	−40.7494	−1.39197	−0.695987	+	0.718055i	$0.745033\pi$
$858$	−6.00999	−0.205178
$859$	−15.4373	−0.526712	−0.263356	−	0.964699i	$-0.584829\pi$
$859$	−15.4373	−0.526712	−0.263356	+	0.964699i	$0.584829\pi$
$860$	7.16356	0.244275
$861$	−3.00408	−0.102379
$862$	−1.00000	−0.0340601
$863$	−35.2555	−1.20011	−0.600056	−	0.799958i	$-0.704855\pi$
$863$	−35.2555	−1.20011	−0.600056	+	0.799958i	$0.704855\pi$
$864$	−1.92400	−0.0654560
$865$	−12.8680	−0.437524
$866$	−23.3976	−0.795084
$867$	−1.58072	−0.0536842
$868$	−3.86861	−0.131309
$869$	7.13894	0.242172
$870$	0.332433	0.0112705
$871$	−16.0190	−0.542784
$872$	6.46037	0.218776
$873$	24.1114	0.816048
$874$	−20.3026	−0.686746
$875$	−5.76203	−0.194792
$876$	−2.29011	−0.0773755
$877$	−49.9094	−1.68532	−0.842660	−	0.538445i	$-0.819012\pi$
$877$	−49.9094	−1.68532	−0.842660	+	0.538445i	$0.819012\pi$
$878$	27.5893	0.931092
$879$	10.6136	0.357989
$880$	−3.76203	−0.126818
$881$	−6.41289	−0.216056	−0.108028	−	0.994148i	$-0.534454\pi$
$881$	−6.41289	−0.216056	−0.108028	+	0.994148i	$0.534454\pi$
$882$	2.89342	0.0974265
$883$	−6.35047	−0.213710	−0.106855	−	0.994275i	$-0.534078\pi$
$883$	−6.35047	−0.213710	−0.106855	+	0.994275i	$0.534078\pi$
$884$	−13.6654	−0.459618
$885$	0.279553	0.00939709
$886$	34.8365	1.17035
$887$	55.1723	1.85250	0.926252	−	0.376904i	$-0.123011\pi$
$887$	55.1723	1.85250	0.926252	+	0.376904i	$0.123011\pi$
$888$	1.50904	0.0506401
$889$	4.67353	0.156745
$890$	7.60156	0.254805
$891$	−50.6953	−1.69836
$892$	2.10426	0.0704557
$893$	24.3151	0.813674
$894$	4.53197	0.151572
$895$	−4.56947	−0.152740
$896$	−1.00000	−0.0334077
$897$	−3.09334	−0.103283
$898$	−6.75625	−0.225459
$899$	−6.59257	−0.219875
$900$	13.4340	0.447800
$901$	32.4755	1.08192
$902$	57.9335	1.92897
$903$	−3.91383	−0.130244
$904$	18.4198	0.612634
$905$	14.1118	0.469092
$906$	−5.08642	−0.168985
$907$	−42.6906	−1.41752	−0.708758	−	0.705451i	$-0.750744\pi$
$907$	−42.6906	−1.41752	−0.708758	+	0.705451i	$0.750744\pi$
$908$	−0.739544	−0.0245426
$909$	34.5084	1.14457
$910$	−1.74720	−0.0579193
$911$	−11.3984	−0.377647	−0.188824	−	0.982011i	$-0.560467\pi$
$911$	−11.3984	−0.377647	−0.188824	+	0.982011i	$0.560467\pi$
$912$	−2.04541	−0.0677303
$913$	13.7412	0.454769
$914$	12.8628	0.425465
$915$	0.305675	0.0101053
$916$	−1.09019	−0.0360209
$917$	−5.10100	−0.168450
$918$	8.99190	0.296777
$919$	−32.0123	−1.05599	−0.527995	−	0.849248i	$-0.677056\pi$
$919$	−32.0123	−1.05599	−0.527995	+	0.849248i	$0.677056\pi$
$920$	−1.93631	−0.0638384
$921$	6.79482	0.223897
$922$	−14.1703	−0.466673
$923$	39.4015	1.29692
$924$	2.05540	0.0676175
$925$	−21.4613	−0.705644
$926$	2.30882	0.0758726
$927$	35.7970	1.17573
$928$	−1.70412	−0.0559404
$929$	10.3112	0.338300	0.169150	−	0.985590i	$-0.445898\pi$
$929$	10.3112	0.338300	0.169150	+	0.985590i	$0.445898\pi$
$930$	−0.754674	−0.0247467
$931$	6.26530	0.205337
$932$	−0.987499	−0.0323466
$933$	−9.66323	−0.316360
$934$	36.2178	1.18508
$935$	17.5820	0.574992
$936$	8.46037	0.276536
$937$	−22.1636	−0.724052	−0.362026	−	0.932168i	$-0.617915\pi$
$937$	−22.1636	−0.724052	−0.362026	+	0.932168i	$0.617915\pi$
$938$	5.47846	0.178878
$939$	−3.08462	−0.100663
$940$	2.31900	0.0756373
$941$	20.2809	0.661138	0.330569	−	0.943782i	$-0.392759\pi$
$941$	20.2809	0.661138	0.330569	+	0.943782i	$0.392759\pi$
$942$	2.80084	0.0912564
$943$	29.8183	0.971018
$944$	−1.43305	−0.0466417
$945$	1.14967	0.0373986
$946$	75.4779	2.45400
$947$	−52.8580	−1.71765	−0.858827	−	0.512265i	$-0.828806\pi$
$947$	−52.8580	−1.71765	−0.858827	+	0.512265i	$0.828806\pi$
$948$	0.370182	0.0120230
$949$	20.5114	0.665828
$950$	29.0894	0.943786
$951$	−11.1320	−0.360978
$952$	4.67353	0.151470
$953$	−8.60131	−0.278624	−0.139312	−	0.990249i	$-0.544489\pi$
$953$	−8.60131	−0.278624	−0.139312	+	0.990249i	$0.544489\pi$
$954$	−20.1058	−0.650950
$955$	−8.26875	−0.267570
$956$	22.3242	0.722015
$957$	3.50264	0.113224
$958$	−8.74438	−0.282518
$959$	−7.80744	−0.252115
$960$	−0.195076	−0.00629606
$961$	−16.0339	−0.517221
$962$	−13.5158	−0.435766
$963$	41.3713	1.33317
$964$	−27.9234	−0.899352
$965$	7.65350	0.246375
$966$	1.05791	0.0340377
$967$	40.6256	1.30643	0.653216	−	0.757171i	$-0.273419\pi$
$967$	40.6256	1.30643	0.653216	+	0.757171i	$0.273419\pi$
$968$	−28.6381	−0.920464
$969$	9.55929	0.307089
$970$	4.97940	0.159879
$971$	−43.0008	−1.37996	−0.689980	−	0.723828i	$-0.742381\pi$
$971$	−43.0008	−1.37996	−0.689980	+	0.723828i	$0.742381\pi$
$972$	−8.40077	−0.269455
$973$	−21.5473	−0.690775
$974$	−18.4944	−0.592600
$975$	4.43211	0.141941
$976$	−1.56695	−0.0501569
$977$	32.2182	1.03075	0.515376	−	0.856964i	$-0.327652\pi$
$977$	32.2182	1.03075	0.515376	+	0.856964i	$0.327652\pi$
$978$	−2.73798	−0.0875509
$979$	80.0928	2.55978
$980$	0.597538	0.0190877
$981$	18.6926	0.596808
$982$	30.9092	0.986352
$983$	−7.57568	−0.241627	−0.120813	−	0.992675i	$-0.538550\pi$
$983$	−7.57568	−0.241627	−0.120813	+	0.992675i	$0.538550\pi$
$984$	3.00408	0.0957666
$985$	−4.80147	−0.152988
$986$	7.96426	0.253634
$987$	−1.26699	−0.0403288
$988$	18.3198	0.582829
$989$	38.8484	1.23531
$990$	−10.8851	−0.345952
$991$	18.3659	0.583412	0.291706	−	0.956508i	$-0.405777\pi$
$991$	18.3659	0.583412	0.291706	+	0.956508i	$0.405777\pi$
$992$	3.86861	0.122828
$993$	−8.99537	−0.285459
$994$	−13.4752	−0.427407
$995$	5.13252	0.162712
$996$	0.712538	0.0225776
$997$	39.9530	1.26532	0.632662	−	0.774428i	$-0.281962\pi$
$997$	39.9530	1.26532	0.632662	+	0.774428i	$0.281962\pi$
$998$	35.6216	1.12758
$999$	8.89342	0.281375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.j.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.j.1.3	✓	4	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.326467 q^{3} +1.00000 q^{4} +0.597538 q^{5} +0.326467 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.89342 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.326467 q^{3} +1.00000 q^{4} +0.597538 q^{5} +0.326467 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.89342 q^{9} -0.597538 q^{10} -6.29588 q^{11} -0.326467 q^{12} +2.92400 q^{13} -1.00000 q^{14} -0.195076 q^{15} +1.00000 q^{16} -4.67353 q^{17} +2.89342 q^{18} +6.26530 q^{19} +0.597538 q^{20} -0.326467 q^{21} +6.29588 q^{22} +3.24049 q^{23} +0.326467 q^{24} -4.64295 q^{25} -2.92400 q^{26} +1.92400 q^{27} +1.00000 q^{28} +1.70412 q^{29} +0.195076 q^{30} -3.86861 q^{31} -1.00000 q^{32} +2.05540 q^{33} +4.67353 q^{34} +0.597538 q^{35} -2.89342 q^{36} +4.62235 q^{37} -6.26530 q^{38} -0.954590 q^{39} -0.597538 q^{40} +9.20180 q^{41} +0.326467 q^{42} +11.9884 q^{43} -6.29588 q^{44} -1.72893 q^{45} -3.24049 q^{46} +3.88092 q^{47} -0.326467 q^{48} +1.00000 q^{49} +4.64295 q^{50} +1.52575 q^{51} +2.92400 q^{52} -6.94881 q^{53} -1.92400 q^{54} -3.76203 q^{55} -1.00000 q^{56} -2.04541 q^{57} -1.70412 q^{58} -1.43305 q^{59} -0.195076 q^{60} -1.56695 q^{61} +3.86861 q^{62} -2.89342 q^{63} +1.00000 q^{64} +1.74720 q^{65} -2.05540 q^{66} -5.47846 q^{67} -4.67353 q^{68} -1.05791 q^{69} -0.597538 q^{70} +13.4752 q^{71} +2.89342 q^{72} +7.01482 q^{73} -4.62235 q^{74} +1.51577 q^{75} +6.26530 q^{76} -6.29588 q^{77} +0.954590 q^{78} -1.13391 q^{79} +0.597538 q^{80} +8.05214 q^{81} -9.20180 q^{82} -2.18258 q^{83} -0.326467 q^{84} -2.79261 q^{85} -11.9884 q^{86} -0.556338 q^{87} +6.29588 q^{88} -12.7215 q^{89} +1.72893 q^{90} +2.92400 q^{91} +3.24049 q^{92} +1.26297 q^{93} -3.88092 q^{94} +3.74375 q^{95} +0.326467 q^{96} -8.33319 q^{97} -1.00000 q^{98} +18.2166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - q^{10} - 13 q^{11} - 2 q^{12} + 11 q^{13} - 4 q^{14} + 2 q^{15} + 4 q^{16} - 18 q^{17} - 2 q^{18} + q^{20} - 2 q^{21} + 13 q^{22} - 2 q^{23} + 2 q^{24} - 5 q^{25} - 11 q^{26} + 7 q^{27} + 4 q^{28} + 19 q^{29} - 2 q^{30} - 12 q^{31} - 4 q^{32} + 11 q^{33} + 18 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 16 q^{39} - q^{40} - 6 q^{41} + 2 q^{42} + 2 q^{43} - 13 q^{44} - 9 q^{45} + 2 q^{46} + 19 q^{47} - 2 q^{48} + 4 q^{49} + 5 q^{50} - 4 q^{51} + 11 q^{52} - 17 q^{53} - 7 q^{54} + 2 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 20 q^{59} + 2 q^{60} + 8 q^{61} + 12 q^{62} + 2 q^{63} + 4 q^{64} + 15 q^{65} - 11 q^{66} - 24 q^{67} - 18 q^{68} + 25 q^{69} - q^{70} + q^{71} - 2 q^{72} + 3 q^{73} - 7 q^{74} - 19 q^{75} - 13 q^{77} + 16 q^{78} + 24 q^{79} + q^{80} - 20 q^{81} + 6 q^{82} - 23 q^{83} - 2 q^{84} - 7 q^{85} - 2 q^{86} - 5 q^{87} + 13 q^{88} - 6 q^{89} + 9 q^{90} + 11 q^{91} - 2 q^{92} - 12 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} + 6 q^{97} - 4 q^{98} + 5 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - q^10 - 13 * q^11 - 2 * q^12 + 11 * q^13 - 4 * q^14 + 2 * q^15 + 4 * q^16 - 18 * q^17 - 2 * q^18 + q^20 - 2 * q^21 + 13 * q^22 - 2 * q^23 + 2 * q^24 - 5 * q^25 - 11 * q^26 + 7 * q^27 + 4 * q^28 + 19 * q^29 - 2 * q^30 - 12 * q^31 - 4 * q^32 + 11 * q^33 + 18 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 16 * q^39 - q^40 - 6 * q^41 + 2 * q^42 + 2 * q^43 - 13 * q^44 - 9 * q^45 + 2 * q^46 + 19 * q^47 - 2 * q^48 + 4 * q^49 + 5 * q^50 - 4 * q^51 + 11 * q^52 - 17 * q^53 - 7 * q^54 + 2 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 20 * q^59 + 2 * q^60 + 8 * q^61 + 12 * q^62 + 2 * q^63 + 4 * q^64 + 15 * q^65 - 11 * q^66 - 24 * q^67 - 18 * q^68 + 25 * q^69 - q^70 + q^71 - 2 * q^72 + 3 * q^73 - 7 * q^74 - 19 * q^75 - 13 * q^77 + 16 * q^78 + 24 * q^79 + q^80 - 20 * q^81 + 6 * q^82 - 23 * q^83 - 2 * q^84 - 7 * q^85 - 2 * q^86 - 5 * q^87 + 13 * q^88 - 6 * q^89 + 9 * q^90 + 11 * q^91 - 2 * q^92 - 12 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 + 6 * q^97 - 4 * q^98 + 5 * q^99

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