LMFDB - Embedded newform 8029.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18873 q^{2} +2.37642 q^{3} +2.79052 q^{4} +1.52040 q^{5} -5.20134 q^{6} +1.00000 q^{7} -1.73024 q^{8} +2.64738 q^{9} +O(q^{10})$	\(q-2.18873 q^{2} +2.37642 q^{3} +2.79052 q^{4} +1.52040 q^{5} -5.20134 q^{6} +1.00000 q^{7} -1.73024 q^{8} +2.64738 q^{9} -3.32774 q^{10} -1.53549 q^{11} +6.63146 q^{12} +1.88370 q^{13} -2.18873 q^{14} +3.61311 q^{15} -1.79403 q^{16} +7.14122 q^{17} -5.79439 q^{18} +5.03531 q^{19} +4.24271 q^{20} +2.37642 q^{21} +3.36076 q^{22} +2.12905 q^{23} -4.11177 q^{24} -2.68838 q^{25} -4.12291 q^{26} -0.837972 q^{27} +2.79052 q^{28} +7.09236 q^{29} -7.90811 q^{30} +1.00000 q^{31} +7.38711 q^{32} -3.64897 q^{33} -15.6302 q^{34} +1.52040 q^{35} +7.38758 q^{36} +1.00000 q^{37} -11.0209 q^{38} +4.47647 q^{39} -2.63065 q^{40} -6.54979 q^{41} -5.20134 q^{42} +9.47004 q^{43} -4.28481 q^{44} +4.02508 q^{45} -4.65990 q^{46} +4.73965 q^{47} -4.26337 q^{48} +1.00000 q^{49} +5.88413 q^{50} +16.9706 q^{51} +5.25651 q^{52} +1.55309 q^{53} +1.83409 q^{54} -2.33456 q^{55} -1.73024 q^{56} +11.9660 q^{57} -15.5232 q^{58} -4.72967 q^{59} +10.0825 q^{60} +5.34659 q^{61} -2.18873 q^{62} +2.64738 q^{63} -12.5803 q^{64} +2.86398 q^{65} +7.98659 q^{66} +4.03148 q^{67} +19.9277 q^{68} +5.05952 q^{69} -3.32774 q^{70} -7.11567 q^{71} -4.58060 q^{72} +6.14236 q^{73} -2.18873 q^{74} -6.38873 q^{75} +14.0511 q^{76} -1.53549 q^{77} -9.79777 q^{78} -4.91478 q^{79} -2.72764 q^{80} -9.93352 q^{81} +14.3357 q^{82} -0.351634 q^{83} +6.63146 q^{84} +10.8575 q^{85} -20.7273 q^{86} +16.8544 q^{87} +2.65676 q^{88} -10.0248 q^{89} -8.80980 q^{90} +1.88370 q^{91} +5.94116 q^{92} +2.37642 q^{93} -10.3738 q^{94} +7.65569 q^{95} +17.5549 q^{96} -0.992631 q^{97} -2.18873 q^{98} -4.06502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−2.18873	−1.54766	−0.773832	−	0.633391i	$-0.781662\pi$
$2$	−2.18873	−1.54766	−0.773832	+	0.633391i	$0.781662\pi$
$3$	2.37642	1.37203	0.686014	−	0.727588i	$-0.259359\pi$
$3$	2.37642	1.37203	0.686014	+	0.727588i	$0.259359\pi$
$4$	2.79052	1.39526
$5$	1.52040	0.679944	0.339972	−	0.940436i	$-0.389582\pi$
$5$	1.52040	0.679944	0.339972	+	0.940436i	$0.389582\pi$
$6$	−5.20134	−2.12344
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.73024	−0.611731
$9$	2.64738	0.882460
$10$	−3.32774	−1.05232
$11$	−1.53549	−0.462967	−0.231484	−	0.972839i	$-0.574358\pi$
$11$	−1.53549	−0.462967	−0.231484	+	0.972839i	$0.574358\pi$
$12$	6.63146	1.91434
$13$	1.88370	0.522445	0.261222	−	0.965279i	$-0.415874\pi$
$13$	1.88370	0.522445	0.261222	+	0.965279i	$0.415874\pi$
$14$	−2.18873	−0.584962
$15$	3.61311	0.932902
$16$	−1.79403	−0.448507
$17$	7.14122	1.73200	0.866001	−	0.500043i	$-0.166682\pi$
$17$	7.14122	1.73200	0.866001	+	0.500043i	$0.166682\pi$
$18$	−5.79439	−1.36575
$19$	5.03531	1.15518	0.577590	−	0.816327i	$-0.303993\pi$
$19$	5.03531	1.15518	0.577590	+	0.816327i	$0.303993\pi$
$20$	4.24271	0.948699
$21$	2.37642	0.518578
$22$	3.36076	0.716517
$23$	2.12905	0.443937	0.221969	−	0.975054i	$-0.428752\pi$
$23$	2.12905	0.443937	0.221969	+	0.975054i	$0.428752\pi$
$24$	−4.11177	−0.839312
$25$	−2.68838	−0.537677
$26$	−4.12291	−0.808569
$27$	−0.837972	−0.161268
$28$	2.79052	0.527359
$29$	7.09236	1.31702	0.658509	−	0.752573i	$-0.271187\pi$
$29$	7.09236	1.31702	0.658509	+	0.752573i	$0.271187\pi$
$30$	−7.90811	−1.44382
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.38711	1.30587
$33$	−3.64897	−0.635204
$34$	−15.6302	−2.68055
$35$	1.52040	0.256995
$36$	7.38758	1.23126
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−11.0209	−1.78783
$39$	4.47647	0.716809
$40$	−2.63065	−0.415943
$41$	−6.54979	−1.02291	−0.511453	−	0.859311i	$-0.670893\pi$
$41$	−6.54979	−1.02291	−0.511453	+	0.859311i	$0.670893\pi$
$42$	−5.20134	−0.802584
$43$	9.47004	1.44417	0.722084	−	0.691805i	$-0.243184\pi$
$43$	9.47004	1.44417	0.722084	+	0.691805i	$0.243184\pi$
$44$	−4.28481	−0.645960
$45$	4.02508	0.600023
$46$	−4.65990	−0.687065
$47$	4.73965	0.691349	0.345675	−	0.938354i	$-0.387650\pi$
$47$	4.73965	0.691349	0.345675	+	0.938354i	$0.387650\pi$
$48$	−4.26337	−0.615365
$49$	1.00000	0.142857
$50$	5.88413	0.832142
$51$	16.9706	2.37635
$52$	5.25651	0.728947
$53$	1.55309	0.213334	0.106667	−	0.994295i	$-0.465982\pi$
$53$	1.55309	0.213334	0.106667	+	0.994295i	$0.465982\pi$
$54$	1.83409	0.249588
$55$	−2.33456	−0.314792
$56$	−1.73024	−0.231213
$57$	11.9660	1.58494
$58$	−15.5232	−2.03830
$59$	−4.72967	−0.615751	−0.307876	−	0.951427i	$-0.599618\pi$
$59$	−4.72967	−0.615751	−0.307876	+	0.951427i	$0.599618\pi$
$60$	10.0825	1.30164
$61$	5.34659	0.684561	0.342280	−	0.939598i	$-0.388801\pi$
$61$	5.34659	0.684561	0.342280	+	0.939598i	$0.388801\pi$
$62$	−2.18873	−0.277969
$63$	2.64738	0.333539
$64$	−12.5803	−1.57254
$65$	2.86398	0.355233
$66$	7.98659	0.983081
$67$	4.03148	0.492524	0.246262	−	0.969203i	$-0.420798\pi$
$67$	4.03148	0.492524	0.246262	+	0.969203i	$0.420798\pi$
$68$	19.9277	2.41659
$69$	5.05952	0.609094
$70$	−3.32774	−0.397741
$71$	−7.11567	−0.844474	−0.422237	−	0.906485i	$-0.638755\pi$
$71$	−7.11567	−0.844474	−0.422237	+	0.906485i	$0.638755\pi$
$72$	−4.58060	−0.539828
$73$	6.14236	0.718909	0.359454	−	0.933163i	$-0.382963\pi$
$73$	6.14236	0.718909	0.359454	+	0.933163i	$0.382963\pi$
$74$	−2.18873	−0.254434
$75$	−6.38873	−0.737707
$76$	14.0511	1.61178
$77$	−1.53549	−0.174985
$78$	−9.79777	−1.10938
$79$	−4.91478	−0.552956	−0.276478	−	0.961020i	$-0.589167\pi$
$79$	−4.91478	−0.552956	−0.276478	+	0.961020i	$0.589167\pi$
$80$	−2.72764	−0.304960
$81$	−9.93352	−1.10372
$82$	14.3357	1.58311
$83$	−0.351634	−0.0385969	−0.0192984	−	0.999814i	$-0.506143\pi$
$83$	−0.351634	−0.0385969	−0.0192984	+	0.999814i	$0.506143\pi$
$84$	6.63146	0.723551
$85$	10.8575	1.17766
$86$	−20.7273	−2.23509
$87$	16.8544	1.80699
$88$	2.65676	0.283211
$89$	−10.0248	−1.06263	−0.531314	−	0.847175i	$-0.678302\pi$
$89$	−10.0248	−1.06263	−0.531314	+	0.847175i	$0.678302\pi$
$90$	−8.80980	−0.928634
$91$	1.88370	0.197466
$92$	5.94116	0.619408
$93$	2.37642	0.246423
$94$	−10.3738	−1.06998
$95$	7.65569	0.785457
$96$	17.5549	1.79169
$97$	−0.992631	−0.100786	−0.0503932	−	0.998729i	$-0.516047\pi$
$97$	−0.992631	−0.100786	−0.0503932	+	0.998729i	$0.516047\pi$
$98$	−2.18873	−0.221095
$99$	−4.06502	−0.408550
$100$	−7.50199	−0.750199
$101$	0.656575	0.0653317	0.0326658	−	0.999466i	$-0.489600\pi$
$101$	0.656575	0.0653317	0.0326658	+	0.999466i	$0.489600\pi$
$102$	−37.1439	−3.67780
$103$	0.374460	0.0368966	0.0184483	−	0.999830i	$-0.494127\pi$
$103$	0.374460	0.0368966	0.0184483	+	0.999830i	$0.494127\pi$
$104$	−3.25925	−0.319596
$105$	3.61311	0.352604
$106$	−3.39929	−0.330169
$107$	−3.61354	−0.349334	−0.174667	−	0.984628i	$-0.555885\pi$
$107$	−3.61354	−0.349334	−0.174667	+	0.984628i	$0.555885\pi$
$108$	−2.33838	−0.225011
$109$	−9.15519	−0.876909	−0.438454	−	0.898753i	$-0.644474\pi$
$109$	−9.15519	−0.876909	−0.438454	+	0.898753i	$0.644474\pi$
$110$	5.10971	0.487191
$111$	2.37642	0.225560
$112$	−1.79403	−0.169520
$113$	−10.3619	−0.974761	−0.487381	−	0.873190i	$-0.662048\pi$
$113$	−10.3619	−0.974761	−0.487381	+	0.873190i	$0.662048\pi$
$114$	−26.1903	−2.45295
$115$	3.23701	0.301852
$116$	19.7914	1.83758
$117$	4.98688	0.461037
$118$	10.3520	0.952975
$119$	7.14122	0.654635
$120$	−6.25154	−0.570685
$121$	−8.64228	−0.785661
$122$	−11.7022	−1.05947
$123$	−15.5651	−1.40346
$124$	2.79052	0.250596
$125$	−11.6894	−1.04553
$126$	−5.79439	−0.516205
$127$	−12.5002	−1.10922	−0.554609	−	0.832111i	$-0.687132\pi$
$127$	−12.5002	−1.10922	−0.554609	+	0.832111i	$0.687132\pi$
$128$	12.7606	1.12789
$129$	22.5048	1.98144
$130$	−6.26847	−0.549781
$131$	6.09480	0.532505	0.266253	−	0.963903i	$-0.414214\pi$
$131$	6.09480	0.532505	0.266253	+	0.963903i	$0.414214\pi$
$132$	−10.1825	−0.886275
$133$	5.03531	0.436617
$134$	−8.82380	−0.762261
$135$	−1.27405	−0.109653
$136$	−12.3560	−1.05952
$137$	1.94847	0.166469	0.0832345	−	0.996530i	$-0.473475\pi$
$137$	1.94847	0.166469	0.0832345	+	0.996530i	$0.473475\pi$
$138$	−11.0739	−0.942673
$139$	−11.2508	−0.954282	−0.477141	−	0.878827i	$-0.658327\pi$
$139$	−11.2508	−0.954282	−0.477141	+	0.878827i	$0.658327\pi$
$140$	4.24271	0.358575
$141$	11.2634	0.948550
$142$	15.5742	1.30696
$143$	−2.89240	−0.241875
$144$	−4.74948	−0.395790
$145$	10.7832	0.895498
$146$	−13.4439	−1.11263
$147$	2.37642	0.196004
$148$	2.79052	0.229380
$149$	12.4286	1.01819	0.509094	−	0.860711i	$-0.329981\pi$
$149$	12.4286	1.01819	0.509094	+	0.860711i	$0.329981\pi$
$150$	13.9832	1.14172
$151$	−7.76083	−0.631567	−0.315784	−	0.948831i	$-0.602267\pi$
$151$	−7.76083	−0.631567	−0.315784	+	0.948831i	$0.602267\pi$
$152$	−8.71228	−0.706659
$153$	18.9055	1.52842
$154$	3.36076	0.270818
$155$	1.52040	0.122121
$156$	12.4917	1.00014
$157$	11.3338	0.904536	0.452268	−	0.891882i	$-0.350615\pi$
$157$	11.3338	0.904536	0.452268	+	0.891882i	$0.350615\pi$
$158$	10.7571	0.855790
$159$	3.69080	0.292700
$160$	11.2314	0.887918
$161$	2.12905	0.167792
$162$	21.7417	1.70819
$163$	14.3331	1.12265	0.561327	−	0.827594i	$-0.310291\pi$
$163$	14.3331	1.12265	0.561327	+	0.827594i	$0.310291\pi$
$164$	−18.2773	−1.42722
$165$	−5.54789	−0.431903
$166$	0.769631	0.0597350
$167$	18.1444	1.40405	0.702027	−	0.712151i	$-0.252279\pi$
$167$	18.1444	1.40405	0.702027	+	0.712151i	$0.252279\pi$
$168$	−4.11177	−0.317230
$169$	−9.45167	−0.727051
$170$	−23.7641	−1.82263
$171$	13.3304	1.01940
$172$	26.4264	2.01499
$173$	4.01685	0.305396	0.152698	−	0.988273i	$-0.451204\pi$
$173$	4.01685	0.305396	0.152698	+	0.988273i	$0.451204\pi$
$174$	−36.8897	−2.79660
$175$	−2.68838	−0.203223
$176$	2.75471	0.207644
$177$	−11.2397	−0.844828
$178$	21.9416	1.64459
$179$	−8.78607	−0.656702	−0.328351	−	0.944556i	$-0.606493\pi$
$179$	−8.78607	−0.656702	−0.328351	+	0.944556i	$0.606493\pi$
$180$	11.2321	0.837189
$181$	25.9237	1.92689	0.963446	−	0.267904i	$-0.0863309\pi$
$181$	25.9237	1.92689	0.963446	+	0.267904i	$0.0863309\pi$
$182$	−4.12291	−0.305610
$183$	12.7058	0.939237
$184$	−3.68376	−0.271570
$185$	1.52040	0.111782
$186$	−5.20134	−0.381381
$187$	−10.9653	−0.801860
$188$	13.2261	0.964613
$189$	−0.837972	−0.0609535
$190$	−16.7562	−1.21562
$191$	−9.59971	−0.694611	−0.347305	−	0.937752i	$-0.612903\pi$
$191$	−9.59971	−0.694611	−0.347305	+	0.937752i	$0.612903\pi$
$192$	−29.8961	−2.15757
$193$	5.88880	0.423885	0.211943	−	0.977282i	$-0.432021\pi$
$193$	5.88880	0.423885	0.211943	+	0.977282i	$0.432021\pi$
$194$	2.17260	0.155983
$195$	6.80603	0.487390
$196$	2.79052	0.199323
$197$	−6.86446	−0.489072	−0.244536	−	0.969640i	$-0.578636\pi$
$197$	−6.86446	−0.489072	−0.244536	+	0.969640i	$0.578636\pi$
$198$	8.89722	0.632298
$199$	−15.0398	−1.06614	−0.533072	−	0.846070i	$-0.678963\pi$
$199$	−15.0398	−1.06614	−0.533072	+	0.846070i	$0.678963\pi$
$200$	4.65154	0.328913
$201$	9.58050	0.675756
$202$	−1.43706	−0.101111
$203$	7.09236	0.497786
$204$	47.3567	3.31563
$205$	−9.95831	−0.695518
$206$	−0.819591	−0.0571036
$207$	5.63640	0.391757
$208$	−3.37942	−0.234320
$209$	−7.73166	−0.534810
$210$	−7.90811	−0.545712
$211$	−15.6719	−1.07890	−0.539448	−	0.842019i	$-0.681367\pi$
$211$	−15.6719	−1.07890	−0.539448	+	0.842019i	$0.681367\pi$
$212$	4.33394	0.297656
$213$	−16.9098	−1.15864
$214$	7.90905	0.540652
$215$	14.3983	0.981953
$216$	1.44989	0.0986525
$217$	1.00000	0.0678844
$218$	20.0382	1.35716
$219$	14.5968	0.986363
$220$	−6.51463	−0.439216
$221$	13.4519	0.904875
$222$	−5.20134	−0.349091
$223$	−2.65028	−0.177476	−0.0887378	−	0.996055i	$-0.528283\pi$
$223$	−2.65028	−0.177476	−0.0887378	+	0.996055i	$0.528283\pi$
$224$	7.38711	0.493572
$225$	−7.11717	−0.474478
$226$	22.6793	1.50860
$227$	18.1985	1.20787	0.603937	−	0.797032i	$-0.293598\pi$
$227$	18.1985	1.20787	0.603937	+	0.797032i	$0.293598\pi$
$228$	33.3914	2.21140
$229$	−26.2107	−1.73205	−0.866027	−	0.499997i	$-0.833334\pi$
$229$	−26.2107	−1.73205	−0.866027	+	0.499997i	$0.833334\pi$
$230$	−7.08492	−0.467166
$231$	−3.64897	−0.240084
$232$	−12.2715	−0.805661
$233$	6.57230	0.430566	0.215283	−	0.976552i	$-0.430933\pi$
$233$	6.57230	0.430566	0.215283	+	0.976552i	$0.430933\pi$
$234$	−10.9149	−0.713530
$235$	7.20617	0.470079
$236$	−13.1983	−0.859134
$237$	−11.6796	−0.758671
$238$	−15.6302	−1.01315
$239$	28.4178	1.83819	0.919097	−	0.394031i	$-0.128920\pi$
$239$	28.4178	1.83819	0.919097	+	0.394031i	$0.128920\pi$
$240$	−6.48203	−0.418413
$241$	−1.11762	−0.0719921	−0.0359960	−	0.999352i	$-0.511460\pi$
$241$	−1.11762	−0.0719921	−0.0359960	+	0.999352i	$0.511460\pi$
$242$	18.9156	1.21594
$243$	−21.0923	−1.35307
$244$	14.9198	0.955141
$245$	1.52040	0.0971348
$246$	34.0677	2.17208
$247$	9.48502	0.603518
$248$	−1.73024	−0.109870
$249$	−0.835632	−0.0529560
$250$	25.5849	1.61813
$251$	10.4803	0.661513	0.330756	−	0.943716i	$-0.392696\pi$
$251$	10.4803	0.661513	0.330756	+	0.943716i	$0.392696\pi$
$252$	7.38758	0.465374
$253$	−3.26913	−0.205528
$254$	27.3596	1.71670
$255$	25.8020	1.61579
$256$	−2.76890	−0.173056
$257$	8.78726	0.548134	0.274067	−	0.961711i	$-0.411631\pi$
$257$	8.78726	0.548134	0.274067	+	0.961711i	$0.411631\pi$
$258$	−49.2569	−3.06660
$259$	1.00000	0.0621370
$260$	7.99200	0.495643
$261$	18.7762	1.16222
$262$	−13.3399	−0.824139
$263$	−6.74832	−0.416119	−0.208059	−	0.978116i	$-0.566715\pi$
$263$	−6.74832	−0.416119	−0.208059	+	0.978116i	$0.566715\pi$
$264$	6.31358	0.388574
$265$	2.36132	0.145055
$266$	−11.0209	−0.675736
$267$	−23.8232	−1.45796
$268$	11.2499	0.687199
$269$	−19.7863	−1.20639	−0.603196	−	0.797593i	$-0.706107\pi$
$269$	−19.7863	−1.20639	−0.603196	+	0.797593i	$0.706107\pi$
$270$	2.78855	0.169706
$271$	24.3030	1.47630	0.738152	−	0.674635i	$-0.235699\pi$
$271$	24.3030	1.47630	0.738152	+	0.674635i	$0.235699\pi$
$272$	−12.8116	−0.776816
$273$	4.47647	0.270928
$274$	−4.26467	−0.257638
$275$	4.12798	0.248927
$276$	14.1187	0.849845
$277$	−20.0658	−1.20564	−0.602818	−	0.797879i	$-0.705956\pi$
$277$	−20.0658	−1.20564	−0.602818	+	0.797879i	$0.705956\pi$
$278$	24.6250	1.47691
$279$	2.64738	0.158495
$280$	−2.63065	−0.157212
$281$	9.55424	0.569958	0.284979	−	0.958534i	$-0.408013\pi$
$281$	9.55424	0.569958	0.284979	+	0.958534i	$0.408013\pi$
$282$	−24.6525	−1.46804
$283$	−25.8647	−1.53749	−0.768747	−	0.639553i	$-0.779120\pi$
$283$	−25.8647	−1.53749	−0.768747	+	0.639553i	$0.779120\pi$
$284$	−19.8564	−1.17826
$285$	18.1931	1.07767
$286$	6.33068	0.374341
$287$	−6.54979	−0.386622
$288$	19.5565	1.15238
$289$	33.9971	1.99983
$290$	−23.6015	−1.38593
$291$	−2.35891	−0.138282
$292$	17.1404	1.00307
$293$	25.1173	1.46737	0.733685	−	0.679489i	$-0.237799\pi$
$293$	25.1173	1.46737	0.733685	+	0.679489i	$0.237799\pi$
$294$	−5.20134	−0.303348
$295$	−7.19100	−0.418676
$296$	−1.73024	−0.100568
$297$	1.28670	0.0746617
$298$	−27.2027	−1.57581
$299$	4.01049	0.231933
$300$	−17.8279	−1.02929
$301$	9.47004	0.545844
$302$	16.9863	0.977453
$303$	1.56030	0.0896368
$304$	−9.03350	−0.518107
$305$	8.12896	0.465463
$306$	−41.3791	−2.36548
$307$	1.72841	0.0986456	0.0493228	−	0.998783i	$-0.484294\pi$
$307$	1.72841	0.0986456	0.0493228	+	0.998783i	$0.484294\pi$
$308$	−4.28481	−0.244150
$309$	0.889875	0.0506232
$310$	−3.32774	−0.189003
$311$	25.5466	1.44862	0.724309	−	0.689476i	$-0.242159\pi$
$311$	25.5466	1.44862	0.724309	+	0.689476i	$0.242159\pi$
$312$	−7.74535	−0.438494
$313$	6.76872	0.382591	0.191295	−	0.981532i	$-0.438731\pi$
$313$	6.76872	0.382591	0.191295	+	0.981532i	$0.438731\pi$
$314$	−24.8066	−1.39992
$315$	4.02508	0.226787
$316$	−13.7148	−0.771518
$317$	23.7926	1.33633	0.668163	−	0.744015i	$-0.267081\pi$
$317$	23.7926	1.33633	0.668163	+	0.744015i	$0.267081\pi$
$318$	−8.07816	−0.453001
$319$	−10.8902	−0.609736
$320$	−19.1271	−1.06924
$321$	−8.58730	−0.479296
$322$	−4.65990	−0.259686
$323$	35.9583	2.00077
$324$	−27.7197	−1.53998
$325$	−5.06411	−0.280906
$326$	−31.3712	−1.73749
$327$	−21.7566	−1.20314
$328$	11.3327	0.625743
$329$	4.73965	0.261305
$330$	12.1428	0.668440
$331$	−15.3570	−0.844100	−0.422050	−	0.906573i	$-0.638689\pi$
$331$	−15.3570	−0.844100	−0.422050	+	0.906573i	$0.638689\pi$
$332$	−0.981244	−0.0538527
$333$	2.64738	0.145076
$334$	−39.7131	−2.17300
$335$	6.12946	0.334888
$336$	−4.26337	−0.232586
$337$	14.3835	0.783519	0.391760	−	0.920068i	$-0.371866\pi$
$337$	14.3835	0.783519	0.391760	+	0.920068i	$0.371866\pi$
$338$	20.6871	1.12523
$339$	−24.6241	−1.33740
$340$	30.2982	1.64315
$341$	−1.53549	−0.0831514
$342$	−29.1766	−1.57769
$343$	1.00000	0.0539949
$344$	−16.3854	−0.883443
$345$	7.69249	0.414150
$346$	−8.79179	−0.472649
$347$	22.0821	1.18543	0.592715	−	0.805412i	$-0.298056\pi$
$347$	22.0821	1.18543	0.592715	+	0.805412i	$0.298056\pi$
$348$	47.0327	2.52122
$349$	−17.7939	−0.952485	−0.476242	−	0.879314i	$-0.658002\pi$
$349$	−17.7939	−0.952485	−0.476242	+	0.879314i	$0.658002\pi$
$350$	5.88413	0.314520
$351$	−1.57849	−0.0842535
$352$	−11.3428	−0.604575
$353$	14.2254	0.757141	0.378571	−	0.925572i	$-0.376416\pi$
$353$	14.2254	0.757141	0.378571	+	0.925572i	$0.376416\pi$
$354$	24.6006	1.30751
$355$	−10.8187	−0.574195
$356$	−27.9745	−1.48264
$357$	16.9706	0.898177
$358$	19.2303	1.01635
$359$	0.333216	0.0175864	0.00879322	−	0.999961i	$-0.497201\pi$
$359$	0.333216	0.0175864	0.00879322	+	0.999961i	$0.497201\pi$
$360$	−6.96434	−0.367053
$361$	6.35435	0.334439
$362$	−56.7398	−2.98218
$363$	−20.5377	−1.07795
$364$	5.25651	0.275516
$365$	9.33885	0.488818
$366$	−27.8094	−1.45362
$367$	−18.8354	−0.983202	−0.491601	−	0.870821i	$-0.663588\pi$
$367$	−18.8354	−0.983202	−0.491601	+	0.870821i	$0.663588\pi$
$368$	−3.81958	−0.199109
$369$	−17.3398	−0.902674
$370$	−3.32774	−0.173001
$371$	1.55309	0.0806325
$372$	6.63146	0.343825
$373$	13.6950	0.709102	0.354551	−	0.935037i	$-0.384634\pi$
$373$	13.6950	0.709102	0.354551	+	0.935037i	$0.384634\pi$
$374$	24.0000	1.24101
$375$	−27.7790	−1.43450
$376$	−8.20072	−0.422920
$377$	13.3599	0.688069
$378$	1.83409	0.0943355
$379$	20.9605	1.07667	0.538334	−	0.842732i	$-0.319054\pi$
$379$	20.9605	1.07667	0.538334	+	0.842732i	$0.319054\pi$
$380$	21.3634	1.09592
$381$	−29.7059	−1.52188
$382$	21.0111	1.07502
$383$	27.3311	1.39655	0.698277	−	0.715828i	$-0.253951\pi$
$383$	27.3311	1.39655	0.698277	+	0.715828i	$0.253951\pi$
$384$	30.3246	1.54750
$385$	−2.33456	−0.118980
$386$	−12.8890	−0.656032
$387$	25.0708	1.27442
$388$	−2.76996	−0.140623
$389$	−33.0618	−1.67630	−0.838150	−	0.545441i	$-0.816362\pi$
$389$	−33.0618	−1.67630	−0.838150	+	0.545441i	$0.816362\pi$
$390$	−14.8965	−0.754315
$391$	15.2040	0.768900
$392$	−1.73024	−0.0873902
$393$	14.4838	0.730612
$394$	15.0244	0.756919
$395$	−7.47244	−0.375979
$396$	−11.3435	−0.570034
$397$	−13.4929	−0.677191	−0.338595	−	0.940932i	$-0.609952\pi$
$397$	−13.4929	−0.677191	−0.338595	+	0.940932i	$0.609952\pi$
$398$	32.9181	1.65003
$399$	11.9660	0.599050
$400$	4.82304	0.241152
$401$	−18.1024	−0.903993	−0.451997	−	0.892020i	$-0.649288\pi$
$401$	−18.1024	−0.903993	−0.451997	+	0.892020i	$0.649288\pi$
$402$	−20.9691	−1.04584
$403$	1.88370	0.0938339
$404$	1.83219	0.0911547
$405$	−15.1029	−0.750470
$406$	−15.5232	−0.770405
$407$	−1.53549	−0.0761113
$408$	−29.3631	−1.45369
$409$	−19.6638	−0.972312	−0.486156	−	0.873872i	$-0.661601\pi$
$409$	−19.6638	−0.972312	−0.486156	+	0.873872i	$0.661601\pi$
$410$	21.7960	1.07643
$411$	4.63038	0.228400
$412$	1.04494	0.0514805
$413$	−4.72967	−0.232732
$414$	−12.3365	−0.606308
$415$	−0.534625	−0.0262437
$416$	13.9151	0.682245
$417$	−26.7367	−1.30930
$418$	16.9225	0.827706
$419$	−26.7572	−1.30717	−0.653587	−	0.756852i	$-0.726737\pi$
$419$	−26.7572	−1.30717	−0.653587	+	0.756852i	$0.726737\pi$
$420$	10.0825	0.491974
$421$	38.5964	1.88107	0.940536	−	0.339695i	$-0.110324\pi$
$421$	38.5964	1.88107	0.940536	+	0.339695i	$0.110324\pi$
$422$	34.3015	1.66977
$423$	12.5477	0.610088
$424$	−2.68722	−0.130503
$425$	−19.1983	−0.931257
$426$	37.0110	1.79319
$427$	5.34659	0.258740
$428$	−10.0837	−0.487412
$429$	−6.87357	−0.331859
$430$	−31.5138	−1.51973
$431$	−23.3895	−1.12663	−0.563316	−	0.826242i	$-0.690475\pi$
$431$	−23.3895	−1.12663	−0.563316	+	0.826242i	$0.690475\pi$
$432$	1.50335	0.0723298
$433$	−13.0643	−0.627832	−0.313916	−	0.949451i	$-0.601641\pi$
$433$	−13.0643	−0.627832	−0.313916	+	0.949451i	$0.601641\pi$
$434$	−2.18873	−0.105062
$435$	25.6255	1.22865
$436$	−25.5478	−1.22352
$437$	10.7204	0.512827
$438$	−31.9485	−1.52656
$439$	−36.6256	−1.74804	−0.874022	−	0.485886i	$-0.838497\pi$
$439$	−36.6256	−1.74804	−0.874022	+	0.485886i	$0.838497\pi$
$440$	4.03934	0.192568
$441$	2.64738	0.126066
$442$	−29.4426	−1.40044
$443$	−18.6520	−0.886182	−0.443091	−	0.896477i	$-0.646118\pi$
$443$	−18.6520	−0.886182	−0.443091	+	0.896477i	$0.646118\pi$
$444$	6.63146	0.314715
$445$	−15.2417	−0.722527
$446$	5.80073	0.274673
$447$	29.5355	1.39698
$448$	−12.5803	−0.594364
$449$	38.7343	1.82798	0.913992	−	0.405732i	$-0.132983\pi$
$449$	38.7343	1.82798	0.913992	+	0.405732i	$0.132983\pi$
$450$	15.5775	0.734332
$451$	10.0571	0.473572
$452$	−28.9150	−1.36005
$453$	−18.4430	−0.866528
$454$	−39.8314	−1.86938
$455$	2.86398	0.134265
$456$	−20.7041	−0.969556
$457$	−11.3730	−0.532007	−0.266004	−	0.963972i	$-0.585703\pi$
$457$	−11.3730	−0.532007	−0.266004	+	0.963972i	$0.585703\pi$
$458$	57.3681	2.68064
$459$	−5.98415	−0.279316
$460$	9.03294	0.421163
$461$	3.49019	0.162554	0.0812771	−	0.996692i	$-0.474100\pi$
$461$	3.49019	0.162554	0.0812771	+	0.996692i	$0.474100\pi$
$462$	7.98659	0.371570
$463$	20.3851	0.947376	0.473688	−	0.880693i	$-0.342922\pi$
$463$	20.3851	0.947376	0.473688	+	0.880693i	$0.342922\pi$
$464$	−12.7239	−0.590692
$465$	3.61311	0.167554
$466$	−14.3850	−0.666371
$467$	−7.84719	−0.363125	−0.181562	−	0.983379i	$-0.558115\pi$
$467$	−7.84719	−0.363125	−0.181562	+	0.983379i	$0.558115\pi$
$468$	13.9160	0.643267
$469$	4.03148	0.186156
$470$	−15.7723	−0.727523
$471$	26.9339	1.24105
$472$	8.18346	0.376674
$473$	−14.5411	−0.668602
$474$	25.5634	1.17417
$475$	−13.5368	−0.621113
$476$	19.9277	0.913387
$477$	4.11163	0.188258
$478$	−62.1988	−2.84491
$479$	29.3480	1.34095	0.670473	−	0.741934i	$-0.266091\pi$
$479$	29.3480	1.34095	0.670473	+	0.741934i	$0.266091\pi$
$480$	26.6905	1.21825
$481$	1.88370	0.0858894
$482$	2.44616	0.111419
$483$	5.05952	0.230216
$484$	−24.1165	−1.09620
$485$	−1.50920	−0.0685291
$486$	46.1653	2.09410
$487$	20.3859	0.923775	0.461888	−	0.886938i	$-0.347172\pi$
$487$	20.3859	0.923775	0.461888	+	0.886938i	$0.347172\pi$
$488$	−9.25087	−0.418767
$489$	34.0615	1.54031
$490$	−3.32774	−0.150332
$491$	2.99245	0.135047	0.0675236	−	0.997718i	$-0.478490\pi$
$491$	2.99245	0.135047	0.0675236	+	0.997718i	$0.478490\pi$
$492$	−43.4347	−1.95819
$493$	50.6481	2.28108
$494$	−20.7601	−0.934042
$495$	−6.18046	−0.277791
$496$	−1.79403	−0.0805543
$497$	−7.11567	−0.319181
$498$	1.82897	0.0819581
$499$	−20.8631	−0.933960	−0.466980	−	0.884268i	$-0.654658\pi$
$499$	−20.8631	−0.933960	−0.466980	+	0.884268i	$0.654658\pi$
$500$	−32.6196	−1.45879
$501$	43.1187	1.92640
$502$	−22.9386	−1.02380
$503$	15.3076	0.682532	0.341266	−	0.939967i	$-0.389144\pi$
$503$	15.3076	0.682532	0.341266	+	0.939967i	$0.389144\pi$
$504$	−4.58060	−0.204036
$505$	0.998257	0.0444218
$506$	7.15523	0.318089
$507$	−22.4611	−0.997535
$508$	−34.8822	−1.54765
$509$	−13.0455	−0.578233	−0.289117	−	0.957294i	$-0.593362\pi$
$509$	−13.0455	−0.578233	−0.289117	+	0.957294i	$0.593362\pi$
$510$	−56.4736	−2.50069
$511$	6.14236	0.271722
$512$	−19.4609	−0.860058
$513$	−4.21945	−0.186293
$514$	−19.2329	−0.848327
$515$	0.569329	0.0250876
$516$	62.8002	2.76462
$517$	−7.27768	−0.320072
$518$	−2.18873	−0.0961671
$519$	9.54573	0.419011
$520$	−4.95537	−0.217307
$521$	−10.7936	−0.472878	−0.236439	−	0.971646i	$-0.575980\pi$
$521$	−10.7936	−0.472878	−0.236439	+	0.971646i	$0.575980\pi$
$522$	−41.0959	−1.79872
$523$	2.55063	0.111531	0.0557656	−	0.998444i	$-0.482240\pi$
$523$	2.55063	0.111531	0.0557656	+	0.998444i	$0.482240\pi$
$524$	17.0077	0.742984
$525$	−6.38873	−0.278827
$526$	14.7702	0.644012
$527$	7.14122	0.311077
$528$	6.54636	0.284894
$529$	−18.4672	−0.802920
$530$	−5.16829	−0.224496
$531$	−12.5213	−0.543376
$532$	14.0511	0.609194
$533$	−12.3379	−0.534412
$534$	52.1424	2.25642
$535$	−5.49403	−0.237528
$536$	−6.97541	−0.301292
$537$	−20.8794	−0.901013
$538$	43.3068	1.86709
$539$	−1.53549	−0.0661382
$540$	−3.55527	−0.152995
$541$	−17.2962	−0.743621	−0.371811	−	0.928309i	$-0.621263\pi$
$541$	−17.2962	−0.743621	−0.371811	+	0.928309i	$0.621263\pi$
$542$	−53.1927	−2.28482
$543$	61.6056	2.64375
$544$	52.7530	2.26177
$545$	−13.9196	−0.596248
$546$	−9.79777	−0.419306
$547$	11.1962	0.478714	0.239357	−	0.970932i	$-0.423063\pi$
$547$	11.1962	0.478714	0.239357	+	0.970932i	$0.423063\pi$
$548$	5.43725	0.232268
$549$	14.1545	0.604098
$550$	−9.03502	−0.385255
$551$	35.7122	1.52139
$552$	−8.75416	−0.372602
$553$	−4.91478	−0.208998
$554$	43.9185	1.86592
$555$	3.61311	0.153368
$556$	−31.3957	−1.33147
$557$	−31.9735	−1.35476	−0.677381	−	0.735632i	$-0.736885\pi$
$557$	−31.9735	−1.35476	−0.677381	+	0.735632i	$0.736885\pi$
$558$	−5.79439	−0.245296
$559$	17.8387	0.754498
$560$	−2.72764	−0.115264
$561$	−26.0581	−1.10017
$562$	−20.9116	−0.882103
$563$	−18.1131	−0.763374	−0.381687	−	0.924292i	$-0.624657\pi$
$563$	−18.1131	−0.763374	−0.381687	+	0.924292i	$0.624657\pi$
$564$	31.4308	1.32348
$565$	−15.7542	−0.662783
$566$	56.6107	2.37952
$567$	−9.93352	−0.417169
$568$	12.3118	0.516591
$569$	22.3039	0.935026	0.467513	−	0.883986i	$-0.345150\pi$
$569$	22.3039	0.935026	0.467513	+	0.883986i	$0.345150\pi$
$570$	−39.8198	−1.66787
$571$	23.1628	0.969332	0.484666	−	0.874699i	$-0.338941\pi$
$571$	23.1628	0.969332	0.484666	+	0.874699i	$0.338941\pi$
$572$	−8.07131	−0.337479
$573$	−22.8130	−0.953025
$574$	14.3357	0.598361
$575$	−5.72370	−0.238695
$576$	−33.3049	−1.38770
$577$	−28.2686	−1.17684	−0.588418	−	0.808557i	$-0.700249\pi$
$577$	−28.2686	−1.17684	−0.588418	+	0.808557i	$0.700249\pi$
$578$	−74.4103	−3.09506
$579$	13.9943	0.581582
$580$	30.0908	1.24945
$581$	−0.351634	−0.0145883
$582$	5.16301	0.214014
$583$	−2.38476	−0.0987665
$584$	−10.6277	−0.439779
$585$	7.58205	0.313479
$586$	−54.9750	−2.27100
$587$	19.2157	0.793116	0.396558	−	0.918010i	$-0.370205\pi$
$587$	19.2157	0.793116	0.396558	+	0.918010i	$0.370205\pi$
$588$	6.63146	0.273477
$589$	5.03531	0.207476
$590$	15.7391	0.647970
$591$	−16.3128	−0.671021
$592$	−1.79403	−0.0737342
$593$	−8.46645	−0.347676	−0.173838	−	0.984774i	$-0.555617\pi$
$593$	−8.46645	−0.347676	−0.173838	+	0.984774i	$0.555617\pi$
$594$	−2.81623	−0.115551
$595$	10.8575	0.445115
$596$	34.6822	1.42064
$597$	−35.7410	−1.46278
$598$	−8.77787	−0.358954
$599$	−13.8218	−0.564743	−0.282371	−	0.959305i	$-0.591121\pi$
$599$	−13.8218	−0.564743	−0.282371	+	0.959305i	$0.591121\pi$
$600$	11.0540	0.451278
$601$	−25.2846	−1.03138	−0.515690	−	0.856775i	$-0.672464\pi$
$601$	−25.2846	−1.03138	−0.515690	+	0.856775i	$0.672464\pi$
$602$	−20.7273	−0.844783
$603$	10.6729	0.434633
$604$	−21.6568	−0.881201
$605$	−13.1397	−0.534206
$606$	−3.41507	−0.138728
$607$	46.0078	1.86740	0.933699	−	0.358058i	$-0.116561\pi$
$607$	46.0078	1.86740	0.933699	+	0.358058i	$0.116561\pi$
$608$	37.1964	1.50851
$609$	16.8544	0.682976
$610$	−17.7921	−0.720380
$611$	8.92809	0.361192
$612$	52.7563	2.13255
$613$	−47.7881	−1.93014	−0.965071	−	0.261988i	$-0.915622\pi$
$613$	−47.7881	−1.93014	−0.965071	+	0.261988i	$0.915622\pi$
$614$	−3.78302	−0.152670
$615$	−23.6651	−0.954271
$616$	2.65676	0.107044
$617$	39.4613	1.58865	0.794326	−	0.607492i	$-0.207824\pi$
$617$	39.4613	1.58865	0.794326	+	0.607492i	$0.207824\pi$
$618$	−1.94769	−0.0783477
$619$	−23.7459	−0.954429	−0.477215	−	0.878787i	$-0.658354\pi$
$619$	−23.7459	−0.954429	−0.477215	+	0.878787i	$0.658354\pi$
$620$	4.24271	0.170391
$621$	−1.78408	−0.0715928
$622$	−55.9146	−2.24197
$623$	−10.0248	−0.401636
$624$	−8.03092	−0.321494
$625$	−4.33068	−0.173227
$626$	−14.8149	−0.592122
$627$	−18.3737	−0.733774
$628$	31.6272	1.26206
$629$	7.14122	0.284739
$630$	−8.80980	−0.350991
$631$	−38.9464	−1.55043	−0.775217	−	0.631695i	$-0.782359\pi$
$631$	−38.9464	−1.55043	−0.775217	+	0.631695i	$0.782359\pi$
$632$	8.50374	0.338261
$633$	−37.2430	−1.48028
$634$	−52.0755	−2.06818
$635$	−19.0054	−0.754206
$636$	10.2993	0.408393
$637$	1.88370	0.0746350
$638$	23.8357	0.943666
$639$	−18.8379	−0.745215
$640$	19.4013	0.766902
$641$	28.1247	1.11086	0.555429	−	0.831564i	$-0.312554\pi$
$641$	28.1247	1.11086	0.555429	+	0.831564i	$0.312554\pi$
$642$	18.7952	0.741789
$643$	−4.99956	−0.197163	−0.0985817	−	0.995129i	$-0.531431\pi$
$643$	−4.99956	−0.197163	−0.0985817	+	0.995129i	$0.531431\pi$
$644$	5.94116	0.234114
$645$	34.2163	1.34727
$646$	−78.7028	−3.09652
$647$	−13.3981	−0.526733	−0.263367	−	0.964696i	$-0.584833\pi$
$647$	−13.3981	−0.526733	−0.263367	+	0.964696i	$0.584833\pi$
$648$	17.1873	0.675182
$649$	7.26236	0.285073
$650$	11.0840	0.434748
$651$	2.37642	0.0931393
$652$	39.9968	1.56640
$653$	−8.50886	−0.332978	−0.166489	−	0.986043i	$-0.553243\pi$
$653$	−8.50886	−0.332978	−0.166489	+	0.986043i	$0.553243\pi$
$654$	47.6192	1.86206
$655$	9.26654	0.362074
$656$	11.7505	0.458781
$657$	16.2612	0.634409
$658$	−10.3738	−0.404413
$659$	40.2973	1.56976	0.784880	−	0.619648i	$-0.212725\pi$
$659$	40.2973	1.56976	0.784880	+	0.619648i	$0.212725\pi$
$660$	−15.4815	−0.602617
$661$	−26.4347	−1.02819	−0.514096	−	0.857733i	$-0.671872\pi$
$661$	−26.4347	−1.02819	−0.514096	+	0.857733i	$0.671872\pi$
$662$	33.6124	1.30638
$663$	31.9675	1.24151
$664$	0.608411	0.0236109
$665$	7.65569	0.296875
$666$	−5.79439	−0.224528
$667$	15.1000	0.584673
$668$	50.6323	1.95902
$669$	−6.29818	−0.243502
$670$	−13.4157	−0.518294
$671$	−8.20963	−0.316929
$672$	17.5549	0.677195
$673$	6.04500	0.233018	0.116509	−	0.993190i	$-0.462830\pi$
$673$	6.04500	0.233018	0.116509	+	0.993190i	$0.462830\pi$
$674$	−31.4816	−1.21262
$675$	2.25279	0.0867099
$676$	−26.3751	−1.01443
$677$	4.47981	0.172173	0.0860865	−	0.996288i	$-0.472564\pi$
$677$	4.47981	0.172173	0.0860865	+	0.996288i	$0.472564\pi$
$678$	53.8955	2.06984
$679$	−0.992631	−0.0380937
$680$	−18.7861	−0.720413
$681$	43.2472	1.65724
$682$	3.36076	0.128690
$683$	16.4687	0.630159	0.315080	−	0.949065i	$-0.397969\pi$
$683$	16.4687	0.630159	0.315080	+	0.949065i	$0.397969\pi$
$684$	37.1987	1.42233
$685$	2.96245	0.113190
$686$	−2.18873	−0.0835660
$687$	−62.2878	−2.37643
$688$	−16.9895	−0.647720
$689$	2.92556	0.111455
$690$	−16.8368	−0.640964
$691$	−33.4424	−1.27221	−0.636105	−	0.771603i	$-0.719455\pi$
$691$	−33.4424	−1.27221	−0.636105	+	0.771603i	$0.719455\pi$
$692$	11.2091	0.426107
$693$	−4.06502	−0.154417
$694$	−48.3317	−1.83465
$695$	−17.1058	−0.648858
$696$	−29.1622	−1.10539
$697$	−46.7736	−1.77167
$698$	38.9459	1.47413
$699$	15.6186	0.590748
$700$	−7.50199	−0.283549
$701$	2.63193	0.0994065	0.0497032	−	0.998764i	$-0.484172\pi$
$701$	2.63193	0.0994065	0.0497032	+	0.998764i	$0.484172\pi$
$702$	3.45488	0.130396
$703$	5.03531	0.189910
$704$	19.3169	0.728034
$705$	17.1249	0.644961
$706$	−31.1355	−1.17180
$707$	0.656575	0.0246930
$708$	−31.3646	−1.17876
$709$	−34.1246	−1.28157	−0.640787	−	0.767718i	$-0.721392\pi$
$709$	−34.1246	−1.28157	−0.640787	+	0.767718i	$0.721392\pi$
$710$	23.6791	0.888660
$711$	−13.0113	−0.487962
$712$	17.3453	0.650043
$713$	2.12905	0.0797335
$714$	−37.1439	−1.39008
$715$	−4.39761	−0.164461
$716$	−24.5177	−0.916271
$717$	67.5327	2.52205
$718$	−0.729318	−0.0272179
$719$	35.8962	1.33870	0.669352	−	0.742945i	$-0.266572\pi$
$719$	35.8962	1.33870	0.669352	+	0.742945i	$0.266572\pi$
$720$	−7.22111	−0.269115
$721$	0.374460	0.0139456
$722$	−13.9079	−0.517600
$723$	−2.65593	−0.0987751
$724$	72.3406	2.68852
$725$	−19.0670	−0.708130
$726$	44.9514	1.66830
$727$	36.0785	1.33808	0.669038	−	0.743228i	$-0.266706\pi$
$727$	36.0785	1.33808	0.669038	+	0.743228i	$0.266706\pi$
$728$	−3.25925	−0.120796
$729$	−20.3237	−0.752729
$730$	−20.4402	−0.756525
$731$	67.6277	2.50130
$732$	35.4557	1.31048
$733$	−1.54179	−0.0569472	−0.0284736	−	0.999595i	$-0.509065\pi$
$733$	−1.54179	−0.0569472	−0.0284736	+	0.999595i	$0.509065\pi$
$734$	41.2256	1.52167
$735$	3.61311	0.133272
$736$	15.7275	0.579724
$737$	−6.19029	−0.228022
$738$	37.9521	1.39704
$739$	−10.2236	−0.376080	−0.188040	−	0.982161i	$-0.560213\pi$
$739$	−10.2236	−0.376080	−0.188040	+	0.982161i	$0.560213\pi$
$740$	4.24271	0.155965
$741$	22.5404	0.828043
$742$	−3.39929	−0.124792
$743$	−45.1529	−1.65650	−0.828250	−	0.560359i	$-0.810663\pi$
$743$	−45.1529	−1.65650	−0.828250	+	0.560359i	$0.810663\pi$
$744$	−4.11177	−0.150745
$745$	18.8964	0.692310
$746$	−29.9747	−1.09745
$747$	−0.930910	−0.0340602
$748$	−30.5988	−1.11880
$749$	−3.61354	−0.132036
$750$	60.8006	2.22012
$751$	30.3196	1.10638	0.553190	−	0.833055i	$-0.313410\pi$
$751$	30.3196	1.10638	0.553190	+	0.833055i	$0.313410\pi$
$752$	−8.50308	−0.310075
$753$	24.9057	0.907614
$754$	−29.2411	−1.06490
$755$	−11.7996	−0.429430
$756$	−2.33838	−0.0850460
$757$	29.4621	1.07082	0.535409	−	0.844593i	$-0.320157\pi$
$757$	29.4621	1.07082	0.535409	+	0.844593i	$0.320157\pi$
$758$	−45.8767	−1.66632
$759$	−7.76883	−0.281991
$760$	−13.2462	−0.480488
$761$	−23.3806	−0.847546	−0.423773	−	0.905768i	$-0.639295\pi$
$761$	−23.3806	−0.847546	−0.423773	+	0.905768i	$0.639295\pi$
$762$	65.0180	2.35535
$763$	−9.15519	−0.331440
$764$	−26.7882	−0.969164
$765$	28.7440	1.03924
$766$	−59.8203	−2.16139
$767$	−8.90930	−0.321696
$768$	−6.58006	−0.237438
$769$	−11.3458	−0.409140	−0.204570	−	0.978852i	$-0.565580\pi$
$769$	−11.3458	−0.409140	−0.204570	+	0.978852i	$0.565580\pi$
$770$	5.10971	0.184141
$771$	20.8822	0.752055
$772$	16.4328	0.591431
$773$	24.9469	0.897278	0.448639	−	0.893713i	$-0.351909\pi$
$773$	24.9469	0.897278	0.448639	+	0.893713i	$0.351909\pi$
$774$	−54.8731	−1.97237
$775$	−2.68838	−0.0965696
$776$	1.71749	0.0616542
$777$	2.37642	0.0852537
$778$	72.3632	2.59435
$779$	−32.9802	−1.18164
$780$	18.9924	0.680036
$781$	10.9260	0.390964
$782$	−33.2774	−1.19000
$783$	−5.94320	−0.212393
$784$	−1.79403	−0.0640725
$785$	17.2319	0.615034
$786$	−31.7011	−1.13074
$787$	9.98834	0.356046	0.178023	−	0.984026i	$-0.443030\pi$
$787$	9.98834	0.356046	0.178023	+	0.984026i	$0.443030\pi$
$788$	−19.1554	−0.682383
$789$	−16.0368	−0.570927
$790$	16.3551	0.581889
$791$	−10.3619	−0.368425
$792$	7.03345	0.249923
$793$	10.0714	0.357645
$794$	29.5323	1.04806
$795$	5.61150	0.199019
$796$	−41.9690	−1.48755
$797$	1.45776	0.0516365	0.0258183	−	0.999667i	$-0.491781\pi$
$797$	1.45776	0.0516365	0.0258183	+	0.999667i	$0.491781\pi$
$798$	−26.1903	−0.927128
$799$	33.8469	1.19742
$800$	−19.8594	−0.702135
$801$	−26.5395	−0.937727
$802$	39.6213	1.39908
$803$	−9.43152	−0.332831
$804$	26.7346	0.942856
$805$	3.23701	0.114089
$806$	−4.12291	−0.145223
$807$	−47.0206	−1.65520
$808$	−1.13603	−0.0399654
$809$	−30.8725	−1.08542	−0.542709	−	0.839921i	$-0.682601\pi$
$809$	−30.8725	−1.08542	−0.542709	+	0.839921i	$0.682601\pi$
$810$	33.0562	1.16148
$811$	−30.2081	−1.06075	−0.530375	−	0.847763i	$-0.677949\pi$
$811$	−30.2081	−1.06075	−0.530375	+	0.847763i	$0.677949\pi$
$812$	19.7914	0.694542
$813$	57.7542	2.02553
$814$	3.36076	0.117795
$815$	21.7920	0.763342
$816$	−30.4457	−1.06581
$817$	47.6846	1.66827
$818$	43.0387	1.50481
$819$	4.98688	0.174256
$820$	−27.7889	−0.970430
$821$	−26.1394	−0.912272	−0.456136	−	0.889910i	$-0.650767\pi$
$821$	−26.1394	−0.912272	−0.456136	+	0.889910i	$0.650767\pi$
$822$	−10.1346	−0.353486
$823$	30.3255	1.05708	0.528541	−	0.848908i	$-0.322739\pi$
$823$	30.3255	1.05708	0.528541	+	0.848908i	$0.322739\pi$
$824$	−0.647905	−0.0225708
$825$	9.80982	0.341534
$826$	10.3520	0.360191
$827$	−39.8873	−1.38702	−0.693508	−	0.720449i	$-0.743936\pi$
$827$	−39.8873	−1.38702	−0.693508	+	0.720449i	$0.743936\pi$
$828$	15.7285	0.546603
$829$	−23.7073	−0.823389	−0.411694	−	0.911322i	$-0.635063\pi$
$829$	−23.7073	−0.823389	−0.411694	+	0.911322i	$0.635063\pi$
$830$	1.17015	0.0406164
$831$	−47.6848	−1.65417
$832$	−23.6976	−0.821565
$833$	7.14122	0.247429
$834$	58.5193	2.02636
$835$	27.5867	0.954677
$836$	−21.5754	−0.746200
$837$	−0.837972	−0.0289645
$838$	58.5641	2.02306
$839$	−14.1872	−0.489795	−0.244897	−	0.969549i	$-0.578754\pi$
$839$	−14.1872	−0.489795	−0.244897	+	0.969549i	$0.578754\pi$
$840$	−6.25154	−0.215699
$841$	21.3016	0.734537
$842$	−84.4769	−2.91126
$843$	22.7049	0.781998
$844$	−43.7327	−1.50534
$845$	−14.3703	−0.494354
$846$	−27.4634	−0.944211
$847$	−8.64228	−0.296952
$848$	−2.78629	−0.0956817
$849$	−61.4654	−2.10949
$850$	42.0199	1.44127
$851$	2.12905	0.0729828
$852$	−47.1873	−1.61661
$853$	38.8171	1.32907	0.664536	−	0.747256i	$-0.268629\pi$
$853$	38.8171	1.32907	0.664536	+	0.747256i	$0.268629\pi$
$854$	−11.7022	−0.400442
$855$	20.2675	0.693135
$856$	6.25228	0.213699
$857$	15.6750	0.535448	0.267724	−	0.963496i	$-0.413728\pi$
$857$	15.6750	0.535448	0.267724	+	0.963496i	$0.413728\pi$
$858$	15.0444	0.513606
$859$	−14.1278	−0.482034	−0.241017	−	0.970521i	$-0.577481\pi$
$859$	−14.1278	−0.482034	−0.241017	+	0.970521i	$0.577481\pi$
$860$	40.1787	1.37008
$861$	−15.5651	−0.530456
$862$	51.1932	1.74365
$863$	27.1518	0.924259	0.462129	−	0.886813i	$-0.347086\pi$
$863$	27.1518	0.924259	0.462129	+	0.886813i	$0.347086\pi$
$864$	−6.19019	−0.210595
$865$	6.10722	0.207652
$866$	28.5943	0.971673
$867$	80.7914	2.74382
$868$	2.79052	0.0947165
$869$	7.54659	0.256001
$870$	−56.0872	−1.90153
$871$	7.59411	0.257316
$872$	15.8407	0.536432
$873$	−2.62787	−0.0889400
$874$	−23.4641	−0.793684
$875$	−11.6894	−0.395175
$876$	40.7328	1.37623
$877$	−19.2262	−0.649222	−0.324611	−	0.945848i	$-0.605233\pi$
$877$	−19.2262	−0.649222	−0.324611	+	0.945848i	$0.605233\pi$
$878$	80.1634	2.70538
$879$	59.6894	2.01327
$880$	4.18826	0.141186
$881$	−9.00813	−0.303492	−0.151746	−	0.988420i	$-0.548489\pi$
$881$	−9.00813	−0.303492	−0.151746	+	0.988420i	$0.548489\pi$
$882$	−5.79439	−0.195107
$883$	−6.73717	−0.226724	−0.113362	−	0.993554i	$-0.536162\pi$
$883$	−6.73717	−0.226724	−0.113362	+	0.993554i	$0.536162\pi$
$884$	37.5379	1.26254
$885$	−17.0888	−0.574435
$886$	40.8240	1.37151
$887$	−17.4858	−0.587117	−0.293558	−	0.955941i	$-0.594840\pi$
$887$	−17.4858	−0.587117	−0.293558	+	0.955941i	$0.594840\pi$
$888$	−4.11177	−0.137982
$889$	−12.5002	−0.419245
$890$	33.3600	1.11823
$891$	15.2528	0.510988
$892$	−7.39566	−0.247625
$893$	23.8656	0.798632
$894$	−64.6451	−2.16206
$895$	−13.3583	−0.446520
$896$	12.7606	0.426303
$897$	9.53062	0.318218
$898$	−84.7788	−2.82910
$899$	7.09236	0.236543
$900$	−19.8606	−0.662021
$901$	11.0910	0.369494
$902$	−22.0123	−0.732930
$903$	22.5048	0.748913
$904$	17.9285	0.596292
$905$	39.4144	1.31018
$906$	40.3667	1.34109
$907$	54.2067	1.79990	0.899951	−	0.435990i	$-0.143602\pi$
$907$	54.2067	1.79990	0.899951	+	0.435990i	$0.143602\pi$
$908$	50.7832	1.68530
$909$	1.73820	0.0576526
$910$	−6.26847	−0.207798
$911$	−1.59291	−0.0527753	−0.0263877	−	0.999652i	$-0.508400\pi$
$911$	−1.59291	−0.0527753	−0.0263877	+	0.999652i	$0.508400\pi$
$912$	−21.4674	−0.710857
$913$	0.539930	0.0178691
$914$	24.8924	0.823368
$915$	19.3178	0.638628
$916$	−73.1416	−2.41667
$917$	6.09480	0.201268
$918$	13.0977	0.432287
$919$	13.8264	0.456090	0.228045	−	0.973651i	$-0.426767\pi$
$919$	13.8264	0.456090	0.228045	+	0.973651i	$0.426767\pi$
$920$	−5.60079	−0.184652
$921$	4.10743	0.135344
$922$	−7.63907	−0.251579
$923$	−13.4038	−0.441191
$924$	−10.1825	−0.334981
$925$	−2.68838	−0.0883935
$926$	−44.6174	−1.46622
$927$	0.991338	0.0325598
$928$	52.3921	1.71985
$929$	33.1493	1.08759	0.543797	−	0.839217i	$-0.316986\pi$
$929$	33.1493	1.08759	0.543797	+	0.839217i	$0.316986\pi$
$930$	−7.90811	−0.259317
$931$	5.03531	0.165026
$932$	18.3402	0.600752
$933$	60.7096	1.98754
$934$	17.1754	0.561995
$935$	−16.6716	−0.545219
$936$	−8.62848	−0.282031
$937$	4.41439	0.144212	0.0721059	−	0.997397i	$-0.477028\pi$
$937$	4.41439	0.144212	0.0721059	+	0.997397i	$0.477028\pi$
$938$	−8.82380	−0.288107
$939$	16.0853	0.524925
$940$	20.1090	0.655882
$941$	−29.9325	−0.975772	−0.487886	−	0.872907i	$-0.662232\pi$
$941$	−29.9325	−0.975772	−0.487886	+	0.872907i	$0.662232\pi$
$942$	−58.9509	−1.92073
$943$	−13.9448	−0.454106
$944$	8.48518	0.276169
$945$	−1.27405	−0.0414449
$946$	31.8266	1.03477
$947$	−38.7819	−1.26024	−0.630121	−	0.776497i	$-0.716995\pi$
$947$	−38.7819	−1.26024	−0.630121	+	0.776497i	$0.716995\pi$
$948$	−32.5922	−1.05854
$949$	11.5704	0.375590
$950$	29.6284	0.961274
$951$	56.5413	1.83348
$952$	−12.3560	−0.400461
$953$	58.1974	1.88520	0.942599	−	0.333926i	$-0.108373\pi$
$953$	58.1974	1.88520	0.942599	+	0.333926i	$0.108373\pi$
$954$	−8.99923	−0.291361
$955$	−14.5954	−0.472296
$956$	79.3005	2.56476
$957$	−25.8798	−0.836575
$958$	−64.2348	−2.07533
$959$	1.94847	0.0629193
$960$	−45.4541	−1.46702
$961$	1.00000	0.0322581
$962$	−4.12291	−0.132928
$963$	−9.56642	−0.308274
$964$	−3.11874	−0.100448
$965$	8.95334	0.288218
$966$	−11.0739	−0.356297
$967$	6.12361	0.196922	0.0984609	−	0.995141i	$-0.468608\pi$
$967$	6.12361	0.196922	0.0984609	+	0.995141i	$0.468608\pi$
$968$	14.9532	0.480614
$969$	85.4520	2.74512
$970$	3.30322	0.106060
$971$	−52.3438	−1.67979	−0.839896	−	0.542748i	$-0.817384\pi$
$971$	−52.3438	−1.67979	−0.839896	+	0.542748i	$0.817384\pi$
$972$	−58.8586	−1.88789
$973$	−11.2508	−0.360685
$974$	−44.6193	−1.42969
$975$	−12.0345	−0.385411
$976$	−9.59194	−0.307031
$977$	49.9789	1.59897	0.799483	−	0.600688i	$-0.205107\pi$
$977$	49.9789	1.59897	0.799483	+	0.600688i	$0.205107\pi$
$978$	−74.5512	−2.38389
$979$	15.3930	0.491962
$980$	4.24271	0.135528
$981$	−24.2373	−0.773837
$982$	−6.54964	−0.209008
$983$	42.3589	1.35104	0.675519	−	0.737342i	$-0.263919\pi$
$983$	42.3589	1.35104	0.675519	+	0.737342i	$0.263919\pi$
$984$	26.9313	0.858537
$985$	−10.4367	−0.332542
$986$	−110.855	−3.53034
$987$	11.2634	0.358518
$988$	26.4682	0.842065
$989$	20.1622	0.641120
$990$	13.5273	0.429927
$991$	24.4642	0.777130	0.388565	−	0.921421i	$-0.372971\pi$
$991$	24.4642	0.777130	0.388565	+	0.921421i	$0.372971\pi$
$992$	7.38711	0.234541
$993$	−36.4948	−1.15813
$994$	15.5742	0.493985
$995$	−22.8665	−0.724918
$996$	−2.33185	−0.0738875
$997$	−17.0930	−0.541342	−0.270671	−	0.962672i	$-0.587246\pi$
$997$	−17.0930	−0.541342	−0.270671	+	0.962672i	$0.587246\pi$
$998$	45.6636	1.44546
$999$	−0.837972	−0.0265123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.10	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.10	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18873 q^{2} +2.37642 q^{3} +2.79052 q^{4} +1.52040 q^{5} -5.20134 q^{6} +1.00000 q^{7} -1.73024 q^{8} +2.64738 q^{9} +O(q^{10})\)	\(q-2.18873 q^{2} +2.37642 q^{3} +2.79052 q^{4} +1.52040 q^{5} -5.20134 q^{6} +1.00000 q^{7} -1.73024 q^{8} +2.64738 q^{9} -3.32774 q^{10} -1.53549 q^{11} +6.63146 q^{12} +1.88370 q^{13} -2.18873 q^{14} +3.61311 q^{15} -1.79403 q^{16} +7.14122 q^{17} -5.79439 q^{18} +5.03531 q^{19} +4.24271 q^{20} +2.37642 q^{21} +3.36076 q^{22} +2.12905 q^{23} -4.11177 q^{24} -2.68838 q^{25} -4.12291 q^{26} -0.837972 q^{27} +2.79052 q^{28} +7.09236 q^{29} -7.90811 q^{30} +1.00000 q^{31} +7.38711 q^{32} -3.64897 q^{33} -15.6302 q^{34} +1.52040 q^{35} +7.38758 q^{36} +1.00000 q^{37} -11.0209 q^{38} +4.47647 q^{39} -2.63065 q^{40} -6.54979 q^{41} -5.20134 q^{42} +9.47004 q^{43} -4.28481 q^{44} +4.02508 q^{45} -4.65990 q^{46} +4.73965 q^{47} -4.26337 q^{48} +1.00000 q^{49} +5.88413 q^{50} +16.9706 q^{51} +5.25651 q^{52} +1.55309 q^{53} +1.83409 q^{54} -2.33456 q^{55} -1.73024 q^{56} +11.9660 q^{57} -15.5232 q^{58} -4.72967 q^{59} +10.0825 q^{60} +5.34659 q^{61} -2.18873 q^{62} +2.64738 q^{63} -12.5803 q^{64} +2.86398 q^{65} +7.98659 q^{66} +4.03148 q^{67} +19.9277 q^{68} +5.05952 q^{69} -3.32774 q^{70} -7.11567 q^{71} -4.58060 q^{72} +6.14236 q^{73} -2.18873 q^{74} -6.38873 q^{75} +14.0511 q^{76} -1.53549 q^{77} -9.79777 q^{78} -4.91478 q^{79} -2.72764 q^{80} -9.93352 q^{81} +14.3357 q^{82} -0.351634 q^{83} +6.63146 q^{84} +10.8575 q^{85} -20.7273 q^{86} +16.8544 q^{87} +2.65676 q^{88} -10.0248 q^{89} -8.80980 q^{90} +1.88370 q^{91} +5.94116 q^{92} +2.37642 q^{93} -10.3738 q^{94} +7.65569 q^{95} +17.5549 q^{96} -0.992631 q^{97} -2.18873 q^{98} -4.06502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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