LMFDB - Embedded newform 8023.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34076 q^{2} -0.698142 q^{3} +3.47917 q^{4} +4.27326 q^{5} +1.63419 q^{6} -0.686172 q^{7} -3.46239 q^{8} -2.51260 q^{9} +O(q^{10})$	\(q-2.34076 q^{2} -0.698142 q^{3} +3.47917 q^{4} +4.27326 q^{5} +1.63419 q^{6} -0.686172 q^{7} -3.46239 q^{8} -2.51260 q^{9} -10.0027 q^{10} -1.00658 q^{11} -2.42896 q^{12} -3.40667 q^{13} +1.60617 q^{14} -2.98334 q^{15} +1.14630 q^{16} -6.21732 q^{17} +5.88140 q^{18} -3.26457 q^{19} +14.8674 q^{20} +0.479046 q^{21} +2.35615 q^{22} +0.141905 q^{23} +2.41724 q^{24} +13.2608 q^{25} +7.97421 q^{26} +3.84858 q^{27} -2.38731 q^{28} -0.745396 q^{29} +6.98330 q^{30} -2.29424 q^{31} +4.24157 q^{32} +0.702732 q^{33} +14.5533 q^{34} -2.93219 q^{35} -8.74176 q^{36} -0.422375 q^{37} +7.64159 q^{38} +2.37834 q^{39} -14.7957 q^{40} +6.86998 q^{41} -1.12133 q^{42} +2.08427 q^{43} -3.50205 q^{44} -10.7370 q^{45} -0.332166 q^{46} -11.1097 q^{47} -0.800280 q^{48} -6.52917 q^{49} -31.0403 q^{50} +4.34057 q^{51} -11.8524 q^{52} +10.1878 q^{53} -9.00861 q^{54} -4.30136 q^{55} +2.37580 q^{56} +2.27913 q^{57} +1.74480 q^{58} -9.60509 q^{59} -10.3796 q^{60} +10.0815 q^{61} +5.37026 q^{62} +1.72407 q^{63} -12.2211 q^{64} -14.5576 q^{65} -1.64493 q^{66} +0.269680 q^{67} -21.6311 q^{68} -0.0990698 q^{69} +6.86357 q^{70} -1.00000 q^{71} +8.69960 q^{72} +7.27738 q^{73} +0.988680 q^{74} -9.25791 q^{75} -11.3580 q^{76} +0.690684 q^{77} -5.56713 q^{78} +3.19526 q^{79} +4.89844 q^{80} +4.85094 q^{81} -16.0810 q^{82} +3.76864 q^{83} +1.66668 q^{84} -26.5683 q^{85} -4.87879 q^{86} +0.520392 q^{87} +3.48516 q^{88} -10.5455 q^{89} +25.1328 q^{90} +2.33756 q^{91} +0.493712 q^{92} +1.60170 q^{93} +26.0051 q^{94} -13.9504 q^{95} -2.96122 q^{96} -15.4133 q^{97} +15.2832 q^{98} +2.52912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.34076	−1.65517	−0.827585	−	0.561341i	$-0.810286\pi$
$2$	−2.34076	−1.65517	−0.827585	+	0.561341i	$0.810286\pi$
$3$	−0.698142	−0.403072	−0.201536	−	0.979481i	$-0.564593\pi$
$3$	−0.698142	−0.403072	−0.201536	+	0.979481i	$0.564593\pi$
$4$	3.47917	1.73959
$5$	4.27326	1.91106	0.955531	−	0.294892i	$-0.0952835\pi$
$5$	4.27326	1.91106	0.955531	+	0.294892i	$0.0952835\pi$
$6$	1.63419	0.667153
$7$	−0.686172	−0.259349	−0.129674	−	0.991557i	$-0.541393\pi$
$7$	−0.686172	−0.259349	−0.129674	+	0.991557i	$0.541393\pi$
$8$	−3.46239	−1.22414
$9$	−2.51260	−0.837533
$10$	−10.0027	−3.16313
$11$	−1.00658	−0.303494	−0.151747	−	0.988419i	$-0.548490\pi$
$11$	−1.00658	−0.303494	−0.151747	+	0.988419i	$0.548490\pi$
$12$	−2.42896	−0.701179
$13$	−3.40667	−0.944841	−0.472420	−	0.881373i	$-0.656620\pi$
$13$	−3.40667	−0.944841	−0.472420	+	0.881373i	$0.656620\pi$
$14$	1.60617	0.429266
$15$	−2.98334	−0.770296
$16$	1.14630	0.286575
$17$	−6.21732	−1.50792	−0.753961	−	0.656919i	$-0.771859\pi$
$17$	−6.21732	−1.50792	−0.753961	+	0.656919i	$0.771859\pi$
$18$	5.88140	1.38626
$19$	−3.26457	−0.748944	−0.374472	−	0.927238i	$-0.622176\pi$
$19$	−3.26457	−0.748944	−0.374472	+	0.927238i	$0.622176\pi$
$20$	14.8674	3.32446
$21$	0.479046	0.104536
$22$	2.35615	0.502334
$23$	0.141905	0.0295892	0.0147946	−	0.999891i	$-0.495291\pi$
$23$	0.141905	0.0295892	0.0147946	+	0.999891i	$0.495291\pi$
$24$	2.41724	0.493418
$25$	13.2608	2.65216
$26$	7.97421	1.56387
$27$	3.84858	0.740659
$28$	−2.38731	−0.451159
$29$	−0.745396	−0.138417	−0.0692083	−	0.997602i	$-0.522047\pi$
$29$	−0.745396	−0.138417	−0.0692083	+	0.997602i	$0.522047\pi$
$30$	6.98330	1.27497
$31$	−2.29424	−0.412057	−0.206028	−	0.978546i	$-0.566054\pi$
$31$	−2.29424	−0.412057	−0.206028	+	0.978546i	$0.566054\pi$
$32$	4.24157	0.749811
$33$	0.702732	0.122330
$34$	14.5533	2.49587
$35$	−2.93219	−0.495631
$36$	−8.74176	−1.45696
$37$	−0.422375	−0.0694380	−0.0347190	−	0.999397i	$-0.511054\pi$
$37$	−0.422375	−0.0694380	−0.0347190	+	0.999397i	$0.511054\pi$
$38$	7.64159	1.23963
$39$	2.37834	0.380839
$40$	−14.7957	−2.33941
$41$	6.86998	1.07291	0.536455	−	0.843929i	$-0.319763\pi$
$41$	6.86998	1.07291	0.536455	+	0.843929i	$0.319763\pi$
$42$	−1.12133	−0.173025
$43$	2.08427	0.317848	0.158924	−	0.987291i	$-0.449197\pi$
$43$	2.08427	0.317848	0.158924	+	0.987291i	$0.449197\pi$
$44$	−3.50205	−0.527954
$45$	−10.7370	−1.60058
$46$	−0.332166	−0.0489752
$47$	−11.1097	−1.62051	−0.810256	−	0.586075i	$-0.800672\pi$
$47$	−11.1097	−1.62051	−0.810256	+	0.586075i	$0.800672\pi$
$48$	−0.800280	−0.115510
$49$	−6.52917	−0.932738
$50$	−31.0403	−4.38977
$51$	4.34057	0.607802
$52$	−11.8524	−1.64363
$53$	10.1878	1.39940	0.699698	−	0.714439i	$-0.253318\pi$
$53$	10.1878	1.39940	0.699698	+	0.714439i	$0.253318\pi$
$54$	−9.00861	−1.22592
$55$	−4.30136	−0.579995
$56$	2.37580	0.317479
$57$	2.27913	0.301879
$58$	1.74480	0.229103
$59$	−9.60509	−1.25048	−0.625238	−	0.780434i	$-0.714998\pi$
$59$	−9.60509	−1.25048	−0.625238	+	0.780434i	$0.714998\pi$
$60$	−10.3796	−1.34000
$61$	10.0815	1.29081	0.645404	−	0.763842i	$-0.276689\pi$
$61$	10.0815	1.29081	0.645404	+	0.763842i	$0.276689\pi$
$62$	5.37026	0.682024
$63$	1.72407	0.217213
$64$	−12.2211	−1.52764
$65$	−14.5576	−1.80565
$66$	−1.64493	−0.202477
$67$	0.269680	0.0329466	0.0164733	−	0.999864i	$-0.494756\pi$
$67$	0.269680	0.0329466	0.0164733	+	0.999864i	$0.494756\pi$
$68$	−21.6311	−2.62316
$69$	−0.0990698	−0.0119266
$70$	6.86357	0.820354
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	8.69960	1.02526
$73$	7.27738	0.851753	0.425877	−	0.904781i	$-0.359966\pi$
$73$	7.27738	0.851753	0.425877	+	0.904781i	$0.359966\pi$
$74$	0.988680	0.114932
$75$	−9.25791	−1.06901
$76$	−11.3580	−1.30285
$77$	0.690684	0.0787107
$78$	−5.56713	−0.630354
$79$	3.19526	0.359495	0.179748	−	0.983713i	$-0.442472\pi$
$79$	3.19526	0.359495	0.179748	+	0.983713i	$0.442472\pi$
$80$	4.89844	0.547662
$81$	4.85094	0.538993
$82$	−16.0810	−1.77585
$83$	3.76864	0.413662	0.206831	−	0.978377i	$-0.433685\pi$
$83$	3.76864	0.413662	0.206831	+	0.978377i	$0.433685\pi$
$84$	1.66668	0.181850
$85$	−26.5683	−2.88173
$86$	−4.87879	−0.526093
$87$	0.520392	0.0557919
$88$	3.48516	0.371519
$89$	−10.5455	−1.11782	−0.558910	−	0.829228i	$-0.688780\pi$
$89$	−10.5455	−1.11782	−0.558910	+	0.829228i	$0.688780\pi$
$90$	25.1328	2.64923
$91$	2.33756	0.245043
$92$	0.493712	0.0514730
$93$	1.60170	0.166089
$94$	26.0051	2.68222
$95$	−13.9504	−1.43128
$96$	−2.96122	−0.302228
$97$	−15.4133	−1.56498	−0.782492	−	0.622661i	$-0.786052\pi$
$97$	−15.4133	−1.56498	−0.782492	+	0.622661i	$0.786052\pi$
$98$	15.2832	1.54384
$99$	2.52912	0.254186
$100$	46.1365	4.61365
$101$	−7.32569	−0.728934	−0.364467	−	0.931216i	$-0.618749\pi$
$101$	−7.32569	−0.728934	−0.364467	+	0.931216i	$0.618749\pi$
$102$	−10.1603	−1.00602
$103$	1.48092	0.145920	0.0729598	−	0.997335i	$-0.476756\pi$
$103$	1.48092	0.145920	0.0729598	+	0.997335i	$0.476756\pi$
$104$	11.7952	1.15662
$105$	2.04709	0.199775
$106$	−23.8471	−2.31624
$107$	−5.52583	−0.534202	−0.267101	−	0.963669i	$-0.586066\pi$
$107$	−5.52583	−0.534202	−0.267101	+	0.963669i	$0.586066\pi$
$108$	13.3899	1.28844
$109$	7.39795	0.708595	0.354297	−	0.935133i	$-0.384720\pi$
$109$	7.39795	0.708595	0.354297	+	0.935133i	$0.384720\pi$
$110$	10.0685	0.959991
$111$	0.294878	0.0279885
$112$	−0.786559	−0.0743228
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−5.33491	−0.499660
$115$	0.606397	0.0565468
$116$	−2.59336	−0.240788
$117$	8.55960	0.791335
$118$	22.4832	2.06975
$119$	4.26615	0.391078
$120$	10.3295	0.942951
$121$	−9.98681	−0.907891
$122$	−23.5985	−2.13651
$123$	−4.79622	−0.432461
$124$	−7.98204	−0.716808
$125$	35.3005	3.15737
$126$	−4.03565	−0.359524
$127$	2.15382	0.191120	0.0955601	−	0.995424i	$-0.469536\pi$
$127$	2.15382	0.191120	0.0955601	+	0.995424i	$0.469536\pi$
$128$	20.1236	1.77869
$129$	−1.45512	−0.128116
$130$	34.0759	2.98866
$131$	19.3227	1.68823	0.844115	−	0.536163i	$-0.180127\pi$
$131$	19.3227	1.68823	0.844115	+	0.536163i	$0.180127\pi$
$132$	2.44493	0.212804
$133$	2.24006	0.194238
$134$	−0.631256	−0.0545322
$135$	16.4460	1.41544
$136$	21.5268	1.84591
$137$	3.76755	0.321884	0.160942	−	0.986964i	$-0.448547\pi$
$137$	3.76755	0.321884	0.160942	+	0.986964i	$0.448547\pi$
$138$	0.231899	0.0197405
$139$	−9.50659	−0.806338	−0.403169	−	0.915126i	$-0.632091\pi$
$139$	−9.50659	−0.806338	−0.403169	+	0.915126i	$0.632091\pi$
$140$	−10.2016	−0.862193
$141$	7.75613	0.653184
$142$	2.34076	0.196432
$143$	3.42907	0.286753
$144$	−2.88019	−0.240016
$145$	−3.18527	−0.264523
$146$	−17.0346	−1.40980
$147$	4.55829	0.375961
$148$	−1.46952	−0.120793
$149$	15.5649	1.27512	0.637561	−	0.770400i	$-0.279943\pi$
$149$	15.5649	1.27512	0.637561	+	0.770400i	$0.279943\pi$
$150$	21.6706	1.76939
$151$	16.9658	1.38066	0.690330	−	0.723494i	$-0.257465\pi$
$151$	16.9658	1.38066	0.690330	+	0.723494i	$0.257465\pi$
$152$	11.3032	0.916813
$153$	15.6216	1.26293
$154$	−1.61673	−0.130280
$155$	−9.80387	−0.787466
$156$	8.27466	0.662503
$157$	20.6986	1.65193	0.825965	−	0.563721i	$-0.190631\pi$
$157$	20.6986	1.65193	0.825965	+	0.563721i	$0.190631\pi$
$158$	−7.47936	−0.595026
$159$	−7.11250	−0.564058
$160$	18.1254	1.43294
$161$	−0.0973712	−0.00767392
$162$	−11.3549	−0.892126
$163$	21.2685	1.66588	0.832941	−	0.553362i	$-0.186656\pi$
$163$	21.2685	1.66588	0.832941	+	0.553362i	$0.186656\pi$
$164$	23.9019	1.86642
$165$	3.00296	0.233780
$166$	−8.82150	−0.684681
$167$	9.43926	0.730432	0.365216	−	0.930923i	$-0.380995\pi$
$167$	9.43926	0.730432	0.365216	+	0.930923i	$0.380995\pi$
$168$	−1.65864	−0.127967
$169$	−1.39458	−0.107276
$170$	62.1900	4.76976
$171$	8.20255	0.627265
$172$	7.25154	0.552925
$173$	−9.37358	−0.712660	−0.356330	−	0.934360i	$-0.615972\pi$
$173$	−9.37358	−0.712660	−0.356330	+	0.934360i	$0.615972\pi$
$174$	−1.21812	−0.0923451
$175$	−9.09918	−0.687833
$176$	−1.15384	−0.0869737
$177$	6.70572	0.504033
$178$	24.6845	1.85018
$179$	0.666370	0.0498068	0.0249034	−	0.999690i	$-0.492072\pi$
$179$	0.666370	0.0498068	0.0249034	+	0.999690i	$0.492072\pi$
$180$	−37.3559	−2.78434
$181$	−8.58984	−0.638478	−0.319239	−	0.947674i	$-0.603427\pi$
$181$	−8.58984	−0.638478	−0.319239	+	0.947674i	$0.603427\pi$
$182$	−5.47168	−0.405588
$183$	−7.03834	−0.520289
$184$	−0.491331	−0.0362214
$185$	−1.80492	−0.132700
$186$	−3.74921	−0.274905
$187$	6.25820	0.457645
$188$	−38.6525	−2.81902
$189$	−2.64079	−0.192089
$190$	32.6545	2.36901
$191$	−21.8633	−1.58197	−0.790986	−	0.611834i	$-0.790432\pi$
$191$	−21.8633	−1.58197	−0.790986	+	0.611834i	$0.790432\pi$
$192$	8.53208	0.615749
$193$	8.04259	0.578918	0.289459	−	0.957190i	$-0.406525\pi$
$193$	8.04259	0.578918	0.289459	+	0.957190i	$0.406525\pi$
$194$	36.0789	2.59031
$195$	10.1633	0.727807
$196$	−22.7161	−1.62258
$197$	−7.64569	−0.544733	−0.272366	−	0.962194i	$-0.587806\pi$
$197$	−7.64569	−0.544733	−0.272366	+	0.962194i	$0.587806\pi$
$198$	−5.92007	−0.420721
$199$	−0.0951452	−0.00674466	−0.00337233	−	0.999994i	$-0.501073\pi$
$199$	−0.0951452	−0.00674466	−0.00337233	+	0.999994i	$0.501073\pi$
$200$	−45.9140	−3.24661
$201$	−0.188275	−0.0132799
$202$	17.1477	1.20651
$203$	0.511470	0.0358981
$204$	15.1016	1.05732
$205$	29.3572	2.05040
$206$	−3.46649	−0.241522
$207$	−0.356550	−0.0247819
$208$	−3.90507	−0.270768
$209$	3.28604	0.227300
$210$	−4.79175	−0.330662
$211$	10.2778	0.707554	0.353777	−	0.935330i	$-0.384897\pi$
$211$	10.2778	0.707554	0.353777	+	0.935330i	$0.384897\pi$
$212$	35.4450	2.43437
$213$	0.698142	0.0478359
$214$	12.9346	0.884194
$215$	8.90664	0.607428
$216$	−13.3253	−0.906671
$217$	1.57424	0.106866
$218$	−17.3168	−1.17284
$219$	−5.08065	−0.343318
$220$	−14.9652	−1.00895
$221$	21.1804	1.42475
$222$	−0.690239	−0.0463258
$223$	−1.98106	−0.132662	−0.0663309	−	0.997798i	$-0.521129\pi$
$223$	−1.98106	−0.132662	−0.0663309	+	0.997798i	$0.521129\pi$
$224$	−2.91045	−0.194463
$225$	−33.3190	−2.22127
$226$	−2.34076	−0.155705
$227$	−0.193368	−0.0128343	−0.00641714	−	0.999979i	$-0.502043\pi$
$227$	−0.193368	−0.0128343	−0.00641714	+	0.999979i	$0.502043\pi$
$228$	7.92950	0.525144
$229$	25.1218	1.66009	0.830046	−	0.557695i	$-0.188314\pi$
$229$	25.1218	1.66009	0.830046	+	0.557695i	$0.188314\pi$
$230$	−1.41943	−0.0935946
$231$	−0.482195	−0.0317261
$232$	2.58085	0.169441
$233$	4.70098	0.307972	0.153986	−	0.988073i	$-0.450789\pi$
$233$	4.70098	0.307972	0.153986	+	0.988073i	$0.450789\pi$
$234$	−20.0360	−1.30979
$235$	−47.4746	−3.09690
$236$	−33.4178	−2.17531
$237$	−2.23075	−0.144903
$238$	−9.98605	−0.647300
$239$	8.87332	0.573967	0.286984	−	0.957936i	$-0.407347\pi$
$239$	8.87332	0.573967	0.286984	+	0.957936i	$0.407347\pi$
$240$	−3.41981	−0.220748
$241$	−18.9834	−1.22283	−0.611415	−	0.791310i	$-0.709399\pi$
$241$	−18.9834	−1.22283	−0.611415	+	0.791310i	$0.709399\pi$
$242$	23.3768	1.50271
$243$	−14.9324	−0.957912
$244$	35.0754	2.24547
$245$	−27.9009	−1.78252
$246$	11.2268	0.715796
$247$	11.1213	0.707633
$248$	7.94355	0.504416
$249$	−2.63105	−0.166736
$250$	−82.6301	−5.22599
$251$	−8.65588	−0.546355	−0.273177	−	0.961964i	$-0.588075\pi$
$251$	−8.65588	−0.546355	−0.273177	+	0.961964i	$0.588075\pi$
$252$	5.99835	0.377861
$253$	−0.142838	−0.00898015
$254$	−5.04157	−0.316336
$255$	18.5484	1.16155
$256$	−22.6623	−1.41640
$257$	25.3980	1.58428	0.792142	−	0.610337i	$-0.208966\pi$
$257$	25.3980	1.58428	0.792142	+	0.610337i	$0.208966\pi$
$258$	3.40609	0.212054
$259$	0.289822	0.0180087
$260$	−50.6484	−3.14108
$261$	1.87288	0.115928
$262$	−45.2298	−2.79431
$263$	7.38726	0.455518	0.227759	−	0.973718i	$-0.426860\pi$
$263$	7.38726	0.455518	0.227759	+	0.973718i	$0.426860\pi$
$264$	−2.43314	−0.149749
$265$	43.5350	2.67433
$266$	−5.24344	−0.321496
$267$	7.36226	0.450563
$268$	0.938262	0.0573135
$269$	−6.31507	−0.385037	−0.192518	−	0.981293i	$-0.561665\pi$
$269$	−6.31507	−0.385037	−0.192518	+	0.981293i	$0.561665\pi$
$270$	−38.4961	−2.34280
$271$	−21.6727	−1.31652	−0.658260	−	0.752790i	$-0.728707\pi$
$271$	−21.6727	−1.31652	−0.658260	+	0.752790i	$0.728707\pi$
$272$	−7.12691	−0.432133
$273$	−1.63195	−0.0987702
$274$	−8.81895	−0.532772
$275$	−13.3480	−0.804913
$276$	−0.344681	−0.0207473
$277$	14.7092	0.883792	0.441896	−	0.897066i	$-0.354306\pi$
$277$	14.7092	0.883792	0.441896	+	0.897066i	$0.354306\pi$
$278$	22.2527	1.33463
$279$	5.76449	0.345111
$280$	10.1524	0.606723
$281$	−1.59921	−0.0954008	−0.0477004	−	0.998862i	$-0.515189\pi$
$281$	−1.59921	−0.0954008	−0.0477004	+	0.998862i	$0.515189\pi$
$282$	−18.1553	−1.08113
$283$	14.9558	0.889031	0.444515	−	0.895771i	$-0.353376\pi$
$283$	14.9558	0.889031	0.444515	+	0.895771i	$0.353376\pi$
$284$	−3.47917	−0.206451
$285$	9.73934	0.576909
$286$	−8.02665	−0.474626
$287$	−4.71399	−0.278258
$288$	−10.6574	−0.627991
$289$	21.6551	1.27383
$290$	7.45597	0.437830
$291$	10.7607	0.630802
$292$	25.3193	1.48170
$293$	28.6350	1.67288	0.836438	−	0.548062i	$-0.184634\pi$
$293$	28.6350	1.67288	0.836438	+	0.548062i	$0.184634\pi$
$294$	−10.6699	−0.622279
$295$	−41.0451	−2.38974
$296$	1.46243	0.0850019
$297$	−3.87388	−0.224785
$298$	−36.4336	−2.11054
$299$	−0.483423	−0.0279571
$300$	−32.2099	−1.85964
$301$	−1.43017	−0.0824336
$302$	−39.7130	−2.28523
$303$	5.11437	0.293813
$304$	−3.74218	−0.214628
$305$	43.0810	2.46681
$306$	−36.5665	−2.09037
$307$	−22.7468	−1.29823	−0.649115	−	0.760691i	$-0.724860\pi$
$307$	−22.7468	−1.29823	−0.649115	+	0.760691i	$0.724860\pi$
$308$	2.40301	0.136924
$309$	−1.03389	−0.0588162
$310$	22.9485	1.30339
$311$	4.89704	0.277686	0.138843	−	0.990314i	$-0.455662\pi$
$311$	4.89704	0.277686	0.138843	+	0.990314i	$0.455662\pi$
$312$	−8.23475	−0.466201
$313$	5.00294	0.282783	0.141391	−	0.989954i	$-0.454842\pi$
$313$	5.00294	0.282783	0.141391	+	0.989954i	$0.454842\pi$
$314$	−48.4506	−2.73423
$315$	7.36742	0.415107
$316$	11.1169	0.625373
$317$	−11.7915	−0.662279	−0.331140	−	0.943582i	$-0.607433\pi$
$317$	−11.7915	−0.662279	−0.331140	+	0.943582i	$0.607433\pi$
$318$	16.6487	0.933611
$319$	0.750297	0.0420086
$320$	−52.2241	−2.91941
$321$	3.85781	0.215322
$322$	0.227923	0.0127016
$323$	20.2969	1.12935
$324$	16.8773	0.937626
$325$	−45.1751	−2.50587
$326$	−49.7846	−2.75732
$327$	−5.16482	−0.285615
$328$	−23.7866	−1.31339
$329$	7.62315	0.420278
$330$	−7.02922	−0.386946
$331$	25.1382	1.38172	0.690859	−	0.722990i	$-0.257233\pi$
$331$	25.1382	1.38172	0.690859	+	0.722990i	$0.257233\pi$
$332$	13.1118	0.719601
$333$	1.06126	0.0581566
$334$	−22.0951	−1.20899
$335$	1.15241	0.0629630
$336$	0.549130	0.0299575
$337$	2.48543	0.135390	0.0676951	−	0.997706i	$-0.478435\pi$
$337$	2.48543	0.135390	0.0676951	+	0.997706i	$0.478435\pi$
$338$	3.26439	0.177559
$339$	−0.698142	−0.0379179
$340$	−92.4356	−5.01302
$341$	2.30932	0.125057
$342$	−19.2002	−1.03823
$343$	9.28334	0.501253
$344$	−7.21657	−0.389091
$345$	−0.423351	−0.0227925
$346$	21.9413	1.17957
$347$	−22.8003	−1.22399	−0.611993	−	0.790863i	$-0.709632\pi$
$347$	−22.8003	−1.22399	−0.611993	+	0.790863i	$0.709632\pi$
$348$	1.81053	0.0970548
$349$	−17.7499	−0.950131	−0.475065	−	0.879950i	$-0.657576\pi$
$349$	−17.7499	−0.950131	−0.475065	+	0.879950i	$0.657576\pi$
$350$	21.2990	1.13848
$351$	−13.1108	−0.699805
$352$	−4.26946	−0.227563
$353$	−12.0922	−0.643601	−0.321801	−	0.946807i	$-0.604288\pi$
$353$	−12.0922	−0.643601	−0.321801	+	0.946807i	$0.604288\pi$
$354$	−15.6965	−0.834259
$355$	−4.27326	−0.226801
$356$	−36.6896	−1.94455
$357$	−2.97838	−0.157633
$358$	−1.55981	−0.0824387
$359$	1.23504	0.0651831	0.0325915	−	0.999469i	$-0.489624\pi$
$359$	1.23504	0.0651831	0.0325915	+	0.999469i	$0.489624\pi$
$360$	37.1757	1.95933
$361$	−8.34258	−0.439083
$362$	20.1068	1.05679
$363$	6.97221	0.365946
$364$	8.13279	0.426274
$365$	31.0982	1.62775
$366$	16.4751	0.861166
$367$	13.1150	0.684598	0.342299	−	0.939591i	$-0.388794\pi$
$367$	13.1150	0.684598	0.342299	+	0.939591i	$0.388794\pi$
$368$	0.162666	0.00847953
$369$	−17.2615	−0.898598
$370$	4.22489	0.219641
$371$	−6.99055	−0.362931
$372$	5.57260	0.288926
$373$	31.4600	1.62894	0.814468	−	0.580208i	$-0.197029\pi$
$373$	31.4600	1.62894	0.814468	+	0.580208i	$0.197029\pi$
$374$	−14.6490	−0.757480
$375$	−24.6448	−1.27265
$376$	38.4661	1.98374
$377$	2.53932	0.130782
$378$	6.18145	0.317940
$379$	22.1650	1.13854	0.569271	−	0.822150i	$-0.307226\pi$
$379$	22.1650	1.13854	0.569271	+	0.822150i	$0.307226\pi$
$380$	−48.5357	−2.48983
$381$	−1.50367	−0.0770353
$382$	51.1768	2.61843
$383$	26.3376	1.34579	0.672895	−	0.739738i	$-0.265050\pi$
$383$	26.3376	1.34579	0.672895	+	0.739738i	$0.265050\pi$
$384$	−14.0491	−0.716942
$385$	2.95147	0.150421
$386$	−18.8258	−0.958208
$387$	−5.23694	−0.266208
$388$	−53.6255	−2.72242
$389$	6.16428	0.312541	0.156271	−	0.987714i	$-0.450053\pi$
$389$	6.16428	0.312541	0.156271	+	0.987714i	$0.450053\pi$
$390$	−23.7898	−1.20464
$391$	−0.882268	−0.0446182
$392$	22.6066	1.14180
$393$	−13.4900	−0.680479
$394$	17.8967	0.901625
$395$	13.6542	0.687017
$396$	8.79924	0.442179
$397$	5.11026	0.256477	0.128238	−	0.991743i	$-0.459068\pi$
$397$	5.11026	0.256477	0.128238	+	0.991743i	$0.459068\pi$
$398$	0.222712	0.0111636
$399$	−1.56388	−0.0782918
$400$	15.2008	0.760041
$401$	37.3422	1.86478	0.932389	−	0.361456i	$-0.117720\pi$
$401$	37.3422	1.86478	0.932389	+	0.361456i	$0.117720\pi$
$402$	0.440707	0.0219804
$403$	7.81571	0.389328
$404$	−25.4874	−1.26804
$405$	20.7293	1.03005
$406$	−1.19723	−0.0594175
$407$	0.425152	0.0210740
$408$	−15.0288	−0.744035
$409$	25.2549	1.24877	0.624387	−	0.781115i	$-0.285349\pi$
$409$	25.2549	1.24877	0.624387	+	0.781115i	$0.285349\pi$
$410$	−68.7183	−3.39376
$411$	−2.63029	−0.129742
$412$	5.15238	0.253840
$413$	6.59074	0.324309
$414$	0.834599	0.0410183
$415$	16.1044	0.790534
$416$	−14.4496	−0.708452
$417$	6.63695	0.325013
$418$	−7.69183	−0.376220
$419$	12.1312	0.592647	0.296324	−	0.955088i	$-0.404239\pi$
$419$	12.1312	0.592647	0.296324	+	0.955088i	$0.404239\pi$
$420$	7.12217	0.347526
$421$	11.0039	0.536298	0.268149	−	0.963377i	$-0.413588\pi$
$421$	11.0039	0.536298	0.268149	+	0.963377i	$0.413588\pi$
$422$	−24.0579	−1.17112
$423$	27.9141	1.35723
$424$	−35.2740	−1.71306
$425$	−82.4465	−3.99924
$426$	−1.63419	−0.0791765
$427$	−6.91766	−0.334769
$428$	−19.2253	−0.929290
$429$	−2.39398	−0.115582
$430$	−20.8483	−1.00540
$431$	1.05410	0.0507742	0.0253871	−	0.999678i	$-0.491918\pi$
$431$	1.05410	0.0507742	0.0253871	+	0.999678i	$0.491918\pi$
$432$	4.41162	0.212254
$433$	0.952517	0.0457750	0.0228875	−	0.999738i	$-0.492714\pi$
$433$	0.952517	0.0457750	0.0228875	+	0.999738i	$0.492714\pi$
$434$	−3.68492	−0.176882
$435$	2.22377	0.106622
$436$	25.7387	1.23266
$437$	−0.463258	−0.0221607
$438$	11.8926	0.568250
$439$	−37.8879	−1.80829	−0.904145	−	0.427226i	$-0.859491\pi$
$439$	−37.8879	−1.80829	−0.904145	+	0.427226i	$0.859491\pi$
$440$	14.8930	0.709996
$441$	16.4052	0.781199
$442$	−49.5783	−2.35820
$443$	−0.880342	−0.0418263	−0.0209131	−	0.999781i	$-0.506657\pi$
$443$	−0.880342	−0.0418263	−0.0209131	+	0.999781i	$0.506657\pi$
$444$	1.02593	0.0486885
$445$	−45.0637	−2.13622
$446$	4.63720	0.219578
$447$	−10.8665	−0.513967
$448$	8.38579	0.396191
$449$	−35.7600	−1.68762	−0.843809	−	0.536643i	$-0.819692\pi$
$449$	−35.7600	−1.68762	−0.843809	+	0.536643i	$0.819692\pi$
$450$	77.9919	3.67657
$451$	−6.91515	−0.325622
$452$	3.47917	0.163647
$453$	−11.8446	−0.556506
$454$	0.452629	0.0212429
$455$	9.98902	0.468293
$456$	−7.89126	−0.369542
$457$	−2.18645	−0.102278	−0.0511389	−	0.998692i	$-0.516285\pi$
$457$	−2.18645	−0.102278	−0.0511389	+	0.998692i	$0.516285\pi$
$458$	−58.8041	−2.74773
$459$	−23.9278	−1.11686
$460$	2.10976	0.0983681
$461$	20.6887	0.963569	0.481785	−	0.876290i	$-0.339989\pi$
$461$	20.6887	0.963569	0.481785	+	0.876290i	$0.339989\pi$
$462$	1.12871	0.0525121
$463$	−17.7352	−0.824224	−0.412112	−	0.911133i	$-0.635209\pi$
$463$	−17.7352	−0.824224	−0.412112	+	0.911133i	$0.635209\pi$
$464$	−0.854447	−0.0396667
$465$	6.84449	0.317406
$466$	−11.0039	−0.509745
$467$	0.771571	0.0357040	0.0178520	−	0.999841i	$-0.494317\pi$
$467$	0.771571	0.0357040	0.0178520	+	0.999841i	$0.494317\pi$
$468$	29.7803	1.37660
$469$	−0.185047	−0.00854466
$470$	111.127	5.12589
$471$	−14.4506	−0.665848
$472$	33.2566	1.53076
$473$	−2.09798	−0.0964651
$474$	5.22165	0.239838
$475$	−43.2907	−1.98632
$476$	14.8427	0.680313
$477$	−25.5977	−1.17204
$478$	−20.7703	−0.950013
$479$	14.4536	0.660402	0.330201	−	0.943911i	$-0.392884\pi$
$479$	14.4536	0.660402	0.330201	+	0.943911i	$0.392884\pi$
$480$	−12.6541	−0.577577
$481$	1.43889	0.0656079
$482$	44.4357	2.02399
$483$	0.0679789	0.00309315
$484$	−34.7458	−1.57936
$485$	−65.8651	−2.99078
$486$	34.9532	1.58551
$487$	−28.1009	−1.27337	−0.636687	−	0.771122i	$-0.719696\pi$
$487$	−28.1009	−1.27337	−0.636687	+	0.771122i	$0.719696\pi$
$488$	−34.9062	−1.58013
$489$	−14.8485	−0.671471
$490$	65.3093	2.95037
$491$	22.3481	1.00855	0.504277	−	0.863542i	$-0.331759\pi$
$491$	22.3481	1.00855	0.504277	+	0.863542i	$0.331759\pi$
$492$	−16.6869	−0.752303
$493$	4.63437	0.208721
$494$	−26.0324	−1.17125
$495$	10.8076	0.485765
$496$	−2.62988	−0.118085
$497$	0.686172	0.0307790
$498$	6.15866	0.275976
$499$	−28.7889	−1.28877	−0.644385	−	0.764702i	$-0.722886\pi$
$499$	−28.7889	−1.28877	−0.644385	+	0.764702i	$0.722886\pi$
$500$	122.817	5.49252
$501$	−6.58994	−0.294417
$502$	20.2614	0.904310
$503$	−12.3740	−0.551731	−0.275865	−	0.961196i	$-0.588964\pi$
$503$	−12.3740	−0.551731	−0.275865	+	0.961196i	$0.588964\pi$
$504$	−5.96943	−0.265899
$505$	−31.3046	−1.39304
$506$	0.334350	0.0148637
$507$	0.973618	0.0432399
$508$	7.49350	0.332470
$509$	17.4899	0.775227	0.387614	−	0.921822i	$-0.373299\pi$
$509$	17.4899	0.775227	0.387614	+	0.921822i	$0.373299\pi$
$510$	−43.4175	−1.92256
$511$	−4.99354	−0.220901
$512$	12.8000	0.565685
$513$	−12.5639	−0.554712
$514$	−59.4507	−2.62226
$515$	6.32837	0.278861
$516$	−5.06261	−0.222869
$517$	11.1827	0.491816
$518$	−0.678404	−0.0298074
$519$	6.54409	0.287254
$520$	50.4042	2.21037
$521$	−5.89063	−0.258073	−0.129037	−	0.991640i	$-0.541188\pi$
$521$	−5.89063	−0.258073	−0.129037	+	0.991640i	$0.541188\pi$
$522$	−4.38397	−0.191881
$523$	19.8032	0.865934	0.432967	−	0.901410i	$-0.357467\pi$
$523$	19.8032	0.865934	0.432967	+	0.901410i	$0.357467\pi$
$524$	67.2269	2.93682
$525$	6.35252	0.277247
$526$	−17.2918	−0.753959
$527$	14.2640	0.621350
$528$	0.805542	0.0350567
$529$	−22.9799	−0.999124
$530$	−101.905	−4.42647
$531$	24.1337	1.04731
$532$	7.79354	0.337893
$533$	−23.4038	−1.01373
$534$	−17.2333	−0.745758
$535$	−23.6133	−1.02089
$536$	−0.933737	−0.0403313
$537$	−0.465221	−0.0200758
$538$	14.7821	0.637301
$539$	6.57210	0.283080
$540$	57.2184	2.46229
$541$	27.0252	1.16190	0.580952	−	0.813938i	$-0.302680\pi$
$541$	27.0252	1.16190	0.580952	+	0.813938i	$0.302680\pi$
$542$	50.7306	2.17907
$543$	5.99693	0.257353
$544$	−26.3712	−1.13066
$545$	31.6134	1.35417
$546$	3.82001	0.163481
$547$	5.76840	0.246639	0.123320	−	0.992367i	$-0.460646\pi$
$547$	5.76840	0.246639	0.123320	+	0.992367i	$0.460646\pi$
$548$	13.1080	0.559945
$549$	−25.3308	−1.08109
$550$	31.2444	1.33227
$551$	2.43340	0.103666
$552$	0.343019	0.0145998
$553$	−2.19250	−0.0932346
$554$	−34.4308	−1.46283
$555$	1.26009	0.0534878
$556$	−33.0751	−1.40270
$557$	31.0812	1.31695	0.658476	−	0.752602i	$-0.271202\pi$
$557$	31.0812	1.31695	0.658476	+	0.752602i	$0.271202\pi$
$558$	−13.4933	−0.571217
$559$	−7.10043	−0.300316
$560$	−3.36117	−0.142035
$561$	−4.36911	−0.184464
$562$	3.74337	0.157904
$563$	35.3187	1.48850	0.744252	−	0.667899i	$-0.232806\pi$
$563$	35.3187	1.48850	0.744252	+	0.667899i	$0.232806\pi$
$564$	26.9849	1.13627
$565$	4.27326	0.179778
$566$	−35.0080	−1.47150
$567$	−3.32858	−0.139787
$568$	3.46239	0.145279
$569$	11.0549	0.463447	0.231723	−	0.972782i	$-0.425564\pi$
$569$	11.0549	0.463447	0.231723	+	0.972782i	$0.425564\pi$
$570$	−22.7975	−0.954881
$571$	−25.1562	−1.05275	−0.526377	−	0.850251i	$-0.676450\pi$
$571$	−25.1562	−1.05275	−0.526377	+	0.850251i	$0.676450\pi$
$572$	11.9303	0.498832
$573$	15.2637	0.637650
$574$	11.0343	0.460564
$575$	1.88177	0.0784752
$576$	30.7068	1.27945
$577$	12.4176	0.516951	0.258475	−	0.966018i	$-0.416780\pi$
$577$	12.4176	0.516951	0.258475	+	0.966018i	$0.416780\pi$
$578$	−50.6895	−2.10840
$579$	−5.61487	−0.233346
$580$	−11.0821	−0.460160
$581$	−2.58594	−0.107283
$582$	−25.1882	−1.04408
$583$	−10.2547	−0.424708
$584$	−25.1972	−1.04267
$585$	36.5774	1.51229
$586$	−67.0278	−2.76889
$587$	14.4799	0.597650	0.298825	−	0.954308i	$-0.403405\pi$
$587$	14.4799	0.597650	0.298825	+	0.954308i	$0.403405\pi$
$588$	15.8591	0.654017
$589$	7.48969	0.308607
$590$	96.0768	3.95542
$591$	5.33777	0.219567
$592$	−0.484168	−0.0198992
$593$	16.9718	0.696948	0.348474	−	0.937318i	$-0.386700\pi$
$593$	16.9718	0.696948	0.348474	+	0.937318i	$0.386700\pi$
$594$	9.06784	0.372058
$595$	18.2304	0.747373
$596$	54.1528	2.21819
$597$	0.0664248	0.00271859
$598$	1.13158	0.0462737
$599$	−4.89194	−0.199879	−0.0999396	−	0.994994i	$-0.531865\pi$
$599$	−4.89194	−0.199879	−0.0999396	+	0.994994i	$0.531865\pi$
$600$	32.0545	1.30862
$601$	24.7400	1.00917	0.504583	−	0.863363i	$-0.331646\pi$
$601$	24.7400	1.00917	0.504583	+	0.863363i	$0.331646\pi$
$602$	3.34769	0.136442
$603$	−0.677597	−0.0275939
$604$	59.0271	2.40178
$605$	−42.6763	−1.73504
$606$	−11.9715	−0.486311
$607$	−45.7428	−1.85664	−0.928322	−	0.371778i	$-0.878748\pi$
$607$	−45.7428	−1.85664	−0.928322	+	0.371778i	$0.878748\pi$
$608$	−13.8469	−0.561566
$609$	−0.357079	−0.0144696
$610$	−100.842	−4.08299
$611$	37.8470	1.53113
$612$	54.3504	2.19698
$613$	−6.07101	−0.245206	−0.122603	−	0.992456i	$-0.539124\pi$
$613$	−6.07101	−0.245206	−0.122603	+	0.992456i	$0.539124\pi$
$614$	53.2449	2.14879
$615$	−20.4955	−0.826459
$616$	−2.39142	−0.0963530
$617$	44.3975	1.78738	0.893689	−	0.448688i	$-0.148108\pi$
$617$	44.3975	1.78738	0.893689	+	0.448688i	$0.148108\pi$
$618$	2.42010	0.0973507
$619$	−37.3296	−1.50040	−0.750201	−	0.661210i	$-0.770043\pi$
$619$	−37.3296	−1.50040	−0.750201	+	0.661210i	$0.770043\pi$
$620$	−34.1094	−1.36987
$621$	0.546132	0.0219155
$622$	−11.4628	−0.459617
$623$	7.23603	0.289905
$624$	2.72629	0.109139
$625$	84.5444	3.38177
$626$	−11.7107	−0.468053
$627$	−2.29412	−0.0916183
$628$	72.0141	2.87368
$629$	2.62604	0.104707
$630$	−17.2454	−0.687073
$631$	−8.78665	−0.349791	−0.174895	−	0.984587i	$-0.555959\pi$
$631$	−8.78665	−0.349791	−0.174895	+	0.984587i	$0.555959\pi$
$632$	−11.0633	−0.440073
$633$	−7.17537	−0.285195
$634$	27.6012	1.09618
$635$	9.20382	0.365242
$636$	−24.7456	−0.981228
$637$	22.2427	0.881289
$638$	−1.75627	−0.0695313
$639$	2.51260	0.0993968
$640$	85.9934	3.39919
$641$	5.62620	0.222221	0.111111	−	0.993808i	$-0.464559\pi$
$641$	5.62620	0.222221	0.111111	+	0.993808i	$0.464559\pi$
$642$	−9.03022	−0.356394
$643$	−35.9633	−1.41825	−0.709127	−	0.705081i	$-0.750911\pi$
$643$	−35.9633	−1.41825	−0.709127	+	0.705081i	$0.750911\pi$
$644$	−0.338771	−0.0133495
$645$	−6.21810	−0.244837
$646$	−47.5102	−1.86926
$647$	33.8087	1.32916	0.664579	−	0.747218i	$-0.268611\pi$
$647$	33.8087	1.32916	0.664579	+	0.747218i	$0.268611\pi$
$648$	−16.7959	−0.659804
$649$	9.66825	0.379512
$650$	105.744	4.14763
$651$	−1.09904	−0.0430749
$652$	73.9970	2.89794
$653$	24.9246	0.975375	0.487688	−	0.873018i	$-0.337840\pi$
$653$	24.9246	0.975375	0.487688	+	0.873018i	$0.337840\pi$
$654$	12.0896	0.472741
$655$	82.5709	3.22631
$656$	7.87506	0.307469
$657$	−18.2851	−0.713371
$658$	−17.8440	−0.695631
$659$	2.98794	0.116393	0.0581967	−	0.998305i	$-0.481465\pi$
$659$	2.98794	0.116393	0.0581967	+	0.998305i	$0.481465\pi$
$660$	10.4478	0.406681
$661$	−9.34498	−0.363477	−0.181739	−	0.983347i	$-0.558173\pi$
$661$	−9.34498	−0.363477	−0.181739	+	0.983347i	$0.558173\pi$
$662$	−58.8425	−2.28698
$663$	−14.7869	−0.574276
$664$	−13.0485	−0.506381
$665$	9.57235	0.371200
$666$	−2.48415	−0.0962590
$667$	−0.105775	−0.00409564
$668$	32.8408	1.27065
$669$	1.38306	0.0534723
$670$	−2.69752	−0.104214
$671$	−10.1478	−0.391752
$672$	2.03191	0.0783825
$673$	−4.37851	−0.168779	−0.0843896	−	0.996433i	$-0.526894\pi$
$673$	−4.37851	−0.168779	−0.0843896	+	0.996433i	$0.526894\pi$
$674$	−5.81782	−0.224094
$675$	51.0351	1.96434
$676$	−4.85200	−0.186615
$677$	28.0605	1.07845	0.539227	−	0.842161i	$-0.318717\pi$
$677$	28.0605	1.07845	0.539227	+	0.842161i	$0.318717\pi$
$678$	1.63419	0.0627605
$679$	10.5762	0.405876
$680$	91.9898	3.52765
$681$	0.134998	0.00517315
$682$	−5.40557	−0.206990
$683$	44.4327	1.70017	0.850085	−	0.526645i	$-0.176550\pi$
$683$	44.4327	1.70017	0.850085	+	0.526645i	$0.176550\pi$
$684$	28.5381	1.09118
$685$	16.0997	0.615140
$686$	−21.7301	−0.829659
$687$	−17.5386	−0.669137
$688$	2.38920	0.0910874
$689$	−34.7063	−1.32221
$690$	0.990965	0.0377254
$691$	39.1485	1.48928	0.744640	−	0.667467i	$-0.232621\pi$
$691$	39.1485	1.48928	0.744640	+	0.667467i	$0.232621\pi$
$692$	−32.6123	−1.23973
$693$	−1.73541	−0.0659228
$694$	53.3702	2.02591
$695$	−40.6241	−1.54096
$696$	−1.80180	−0.0682972
$697$	−42.7129	−1.61787
$698$	41.5483	1.57263
$699$	−3.28195	−0.124135
$700$	−31.6576	−1.19655
$701$	−1.35321	−0.0511099	−0.0255550	−	0.999673i	$-0.508135\pi$
$701$	−1.35321	−0.0511099	−0.0255550	+	0.999673i	$0.508135\pi$
$702$	30.6894	1.15830
$703$	1.37887	0.0520052
$704$	12.3015	0.463629
$705$	33.1440	1.24828
$706$	28.3049	1.06527
$707$	5.02669	0.189048
$708$	23.3304	0.876808
$709$	−48.2778	−1.81311	−0.906556	−	0.422085i	$-0.861298\pi$
$709$	−48.2778	−1.81311	−0.906556	+	0.422085i	$0.861298\pi$
$710$	10.0027	0.375395
$711$	−8.02841	−0.301089
$712$	36.5127	1.36837
$713$	−0.325563	−0.0121924
$714$	6.97168	0.260909
$715$	14.6533	0.548003
$716$	2.31842	0.0866433
$717$	−6.19483	−0.231350
$718$	−2.89094	−0.107889
$719$	39.7418	1.48212	0.741059	−	0.671440i	$-0.234324\pi$
$719$	39.7418	1.48212	0.741059	+	0.671440i	$0.234324\pi$
$720$	−12.3078	−0.458685
$721$	−1.01617	−0.0378440
$722$	19.5280	0.726757
$723$	13.2531	0.492889
$724$	−29.8855	−1.11069
$725$	−9.88453	−0.367102
$726$	−16.3203	−0.605703
$727$	−4.04717	−0.150101	−0.0750507	−	0.997180i	$-0.523912\pi$
$727$	−4.04717	−0.150101	−0.0750507	+	0.997180i	$0.523912\pi$
$728$	−8.09357	−0.299968
$729$	−4.12791	−0.152885
$730$	−72.7935	−2.69421
$731$	−12.9586	−0.479291
$732$	−24.4876	−0.905088
$733$	25.9942	0.960116	0.480058	−	0.877237i	$-0.340616\pi$
$733$	25.9942	0.960116	0.480058	+	0.877237i	$0.340616\pi$
$734$	−30.6991	−1.13313
$735$	19.4788	0.718485
$736$	0.601900	0.0221863
$737$	−0.271453	−0.00999910
$738$	40.4051	1.48733
$739$	−44.3559	−1.63166	−0.815828	−	0.578294i	$-0.803719\pi$
$739$	−44.3559	−1.63166	−0.815828	+	0.578294i	$0.803719\pi$
$740$	−6.27963	−0.230844
$741$	−7.76426	−0.285227
$742$	16.3632	0.600713
$743$	−30.0822	−1.10361	−0.551805	−	0.833973i	$-0.686061\pi$
$743$	−30.0822	−1.10361	−0.551805	+	0.833973i	$0.686061\pi$
$744$	−5.54572	−0.203316
$745$	66.5127	2.43684
$746$	−73.6404	−2.69617
$747$	−9.46908	−0.346456
$748$	21.7734	0.796113
$749$	3.79167	0.138544
$750$	57.6875	2.10645
$751$	−45.2282	−1.65040	−0.825201	−	0.564840i	$-0.808938\pi$
$751$	−45.2282	−1.65040	−0.825201	+	0.564840i	$0.808938\pi$
$752$	−12.7350	−0.464398
$753$	6.04304	0.220220
$754$	−5.94395	−0.216466
$755$	72.4995	2.63853
$756$	−9.18775	−0.334155
$757$	−16.8067	−0.610851	−0.305425	−	0.952216i	$-0.598799\pi$
$757$	−16.8067	−0.610851	−0.305425	+	0.952216i	$0.598799\pi$
$758$	−51.8831	−1.88448
$759$	0.0997212	0.00361965
$760$	48.3017	1.75209
$761$	24.4259	0.885439	0.442720	−	0.896660i	$-0.354014\pi$
$761$	24.4259	0.885439	0.442720	+	0.896660i	$0.354014\pi$
$762$	3.51973	0.127506
$763$	−5.07627	−0.183773
$764$	−76.0662	−2.75198
$765$	66.7553	2.41354
$766$	−61.6502	−2.22751
$767$	32.7214	1.18150
$768$	15.8215	0.570911
$769$	−14.0704	−0.507393	−0.253697	−	0.967284i	$-0.581647\pi$
$769$	−14.0704	−0.507393	−0.253697	+	0.967284i	$0.581647\pi$
$770$	−6.90870	−0.248972
$771$	−17.7314	−0.638581
$772$	27.9816	1.00708
$773$	−28.2663	−1.01667	−0.508334	−	0.861160i	$-0.669738\pi$
$773$	−28.2663	−1.01667	−0.508334	+	0.861160i	$0.669738\pi$
$774$	12.2584	0.440620
$775$	−30.4233	−1.09284
$776$	53.3669	1.91576
$777$	−0.202337	−0.00725879
$778$	−14.4291	−0.517309
$779$	−22.4275	−0.803550
$780$	35.3598	1.26608
$781$	1.00658	0.0360181
$782$	2.06518	0.0738507
$783$	−2.86871	−0.102519
$784$	−7.48438	−0.267299
$785$	88.4507	3.15694
$786$	31.5768	1.12631
$787$	40.9855	1.46098	0.730488	−	0.682925i	$-0.239292\pi$
$787$	40.9855	1.46098	0.730488	+	0.682925i	$0.239292\pi$
$788$	−26.6007	−0.947609
$789$	−5.15736	−0.183607
$790$	−31.9613	−1.13713
$791$	−0.686172	−0.0243975
$792$	−8.75681	−0.311160
$793$	−34.3445	−1.21961
$794$	−11.9619	−0.424513
$795$	−30.3936	−1.07795
$796$	−0.331027	−0.0117329
$797$	−5.11732	−0.181265	−0.0906323	−	0.995884i	$-0.528889\pi$
$797$	−5.11732	−0.181265	−0.0906323	+	0.995884i	$0.528889\pi$
$798$	3.66067	0.129586
$799$	69.0724	2.44361
$800$	56.2466	1.98862
$801$	26.4966	0.936211
$802$	−87.4092	−3.08652
$803$	−7.32523	−0.258502
$804$	−0.655040	−0.0231015
$805$	−0.416093	−0.0146653
$806$	−18.2947	−0.644404
$807$	4.40882	0.155198
$808$	25.3644	0.892318
$809$	−1.02734	−0.0361195	−0.0180597	−	0.999837i	$-0.505749\pi$
$809$	−1.02734	−0.0361195	−0.0180597	+	0.999837i	$0.505749\pi$
$810$	−48.5225	−1.70491
$811$	10.9540	0.384647	0.192324	−	0.981332i	$-0.438398\pi$
$811$	10.9540	0.384647	0.192324	+	0.981332i	$0.438398\pi$
$812$	1.77949	0.0624479
$813$	15.1306	0.530653
$814$	−0.995181	−0.0348811
$815$	90.8861	3.18360
$816$	4.97560	0.174181
$817$	−6.80425	−0.238051
$818$	−59.1158	−2.06693
$819$	−5.87336	−0.205232
$820$	102.139	3.56685
$821$	5.64225	0.196916	0.0984579	−	0.995141i	$-0.468609\pi$
$821$	5.64225	0.196916	0.0984579	+	0.995141i	$0.468609\pi$
$822$	6.15688	0.214746
$823$	0.00274382	9.56437e−5 0	4.78218e−5	−	1.00000i	$-0.499985\pi$
$823$	0.00274382	9.56437e−5 0	4.78218e−5		1.00000i	$0.499985\pi$
$824$	−5.12754	−0.178626
$825$	9.31878	0.324438
$826$	−15.4274	−0.536787
$827$	33.0947	1.15081	0.575407	−	0.817867i	$-0.304844\pi$
$827$	33.0947	1.15081	0.575407	+	0.817867i	$0.304844\pi$
$828$	−1.24050	−0.0431103
$829$	1.62677	0.0564999	0.0282500	−	0.999601i	$-0.491007\pi$
$829$	1.62677	0.0564999	0.0282500	+	0.999601i	$0.491007\pi$
$830$	−37.6966	−1.30847
$831$	−10.2691	−0.356232
$832$	41.6333	1.44338
$833$	40.5939	1.40650
$834$	−15.5355	−0.537951
$835$	40.3364	1.39590
$836$	11.4327	0.395408
$837$	−8.82954	−0.305193
$838$	−28.3962	−0.980932
$839$	18.4942	0.638492	0.319246	−	0.947672i	$-0.396570\pi$
$839$	18.4942	0.638492	0.319246	+	0.947672i	$0.396570\pi$
$840$	−7.08782	−0.244553
$841$	−28.4444	−0.980841
$842$	−25.7576	−0.887665
$843$	1.11647	0.0384534
$844$	35.7583	1.23085
$845$	−5.95943	−0.205010
$846$	−65.3404	−2.24645
$847$	6.85267	0.235460
$848$	11.6782	0.401032
$849$	−10.4413	−0.358344
$850$	192.988	6.61943
$851$	−0.0599371	−0.00205462
$852$	2.42896	0.0832147
$853$	18.2185	0.623790	0.311895	−	0.950117i	$-0.399036\pi$
$853$	18.2185	0.623790	0.311895	+	0.950117i	$0.399036\pi$
$854$	16.1926	0.554100
$855$	35.0517	1.19874
$856$	19.1326	0.653938
$857$	−6.04963	−0.206651	−0.103326	−	0.994648i	$-0.532948\pi$
$857$	−6.04963	−0.206651	−0.103326	+	0.994648i	$0.532948\pi$
$858$	5.60374	0.191308
$859$	−51.8367	−1.76865	−0.884323	−	0.466876i	$-0.845379\pi$
$859$	−51.8367	−1.76865	−0.884323	+	0.466876i	$0.845379\pi$
$860$	30.9877	1.05667
$861$	3.29103	0.112158
$862$	−2.46740	−0.0840400
$863$	2.62812	0.0894623	0.0447311	−	0.998999i	$-0.485757\pi$
$863$	2.62812	0.0894623	0.0447311	+	0.998999i	$0.485757\pi$
$864$	16.3240	0.555354
$865$	−40.0558	−1.36194
$866$	−2.22962	−0.0757655
$867$	−15.1183	−0.513446
$868$	5.47705	0.185903
$869$	−3.21627	−0.109105
$870$	−5.20533	−0.176477
$871$	−0.918710	−0.0311293
$872$	−25.6146	−0.867420
$873$	38.7274	1.31072
$874$	1.08438	0.0366796
$875$	−24.2222	−0.818860
$876$	−17.6764	−0.597232
$877$	11.6768	0.394299	0.197150	−	0.980373i	$-0.436832\pi$
$877$	11.6768	0.394299	0.197150	+	0.980373i	$0.436832\pi$
$878$	88.6866	2.99303
$879$	−19.9913	−0.674290
$880$	−4.93065	−0.166212
$881$	51.5913	1.73815	0.869077	−	0.494677i	$-0.164714\pi$
$881$	51.5913	1.73815	0.869077	+	0.494677i	$0.164714\pi$
$882$	−38.4006	−1.29302
$883$	−6.05412	−0.203737	−0.101869	−	0.994798i	$-0.532482\pi$
$883$	−6.05412	−0.203737	−0.101869	+	0.994798i	$0.532482\pi$
$884$	73.6902	2.47847
$885$	28.6553	0.963237
$886$	2.06067	0.0692296
$887$	33.1402	1.11274	0.556370	−	0.830935i	$-0.312194\pi$
$887$	33.1402	1.11274	0.556370	+	0.830935i	$0.312194\pi$
$888$	−1.02098	−0.0342619
$889$	−1.47789	−0.0495668
$890$	105.483	3.53581
$891$	−4.88284	−0.163581
$892$	−6.89246	−0.230777
$893$	36.2683	1.21367
$894$	25.4358	0.850702
$895$	2.84757	0.0951839
$896$	−13.8083	−0.461301
$897$	0.337498	0.0112687
$898$	83.7057	2.79330
$899$	1.71011	0.0570355
$900$	−115.923	−3.86409
$901$	−63.3406	−2.11018
$902$	16.1867	0.538959
$903$	0.998461	0.0332267
$904$	−3.46239	−0.115158
$905$	−36.7066	−1.22017
$906$	27.7253	0.921112
$907$	−23.8017	−0.790321	−0.395161	−	0.918612i	$-0.629311\pi$
$907$	−23.8017	−0.790321	−0.395161	+	0.918612i	$0.629311\pi$
$908$	−0.672761	−0.0223264
$909$	18.4065	0.610506
$910$	−23.3819	−0.775104
$911$	−45.6000	−1.51080	−0.755398	−	0.655266i	$-0.772557\pi$
$911$	−45.6000	−1.51080	−0.755398	+	0.655266i	$0.772557\pi$
$912$	2.61257	0.0865108
$913$	−3.79342	−0.125544
$914$	5.11796	0.169287
$915$	−30.0767	−0.994304
$916$	87.4029	2.88787
$917$	−13.2587	−0.437840
$918$	56.0094	1.84859
$919$	48.2559	1.59181	0.795907	−	0.605419i	$-0.206994\pi$
$919$	48.2559	1.59181	0.795907	+	0.605419i	$0.206994\pi$
$920$	−2.09959	−0.0692213
$921$	15.8805	0.523280
$922$	−48.4274	−1.59487
$923$	3.40667	0.112132
$924$	−1.67764	−0.0551903
$925$	−5.60102	−0.184160
$926$	41.5139	1.36423
$927$	−3.72096	−0.122212
$928$	−3.16165	−0.103786
$929$	13.4489	0.441245	0.220622	−	0.975359i	$-0.429191\pi$
$929$	13.4489	0.441245	0.220622	+	0.975359i	$0.429191\pi$
$930$	−16.0213	−0.525360
$931$	21.3149	0.698568
$932$	16.3555	0.535743
$933$	−3.41883	−0.111927
$934$	−1.80607	−0.0590963
$935$	26.7430	0.874588
$936$	−29.6367	−0.968706
$937$	−1.27591	−0.0416822	−0.0208411	−	0.999783i	$-0.506634\pi$
$937$	−1.27591	−0.0416822	−0.0208411	+	0.999783i	$0.506634\pi$
$938$	0.433150	0.0141429
$939$	−3.49276	−0.113982
$940$	−165.172	−5.38733
$941$	−22.5964	−0.736623	−0.368312	−	0.929702i	$-0.620064\pi$
$941$	−22.5964	−0.736623	−0.368312	+	0.929702i	$0.620064\pi$
$942$	33.8254	1.10209
$943$	0.974884	0.0317466
$944$	−11.0103	−0.358355
$945$	−11.2848	−0.367094
$946$	4.91087	0.159666
$947$	−47.9259	−1.55738	−0.778690	−	0.627408i	$-0.784116\pi$
$947$	−47.9259	−1.55738	−0.778690	+	0.627408i	$0.784116\pi$
$948$	−7.76116	−0.252071
$949$	−24.7917	−0.804771
$950$	101.333	3.28769
$951$	8.23217	0.266946
$952$	−14.7711	−0.478734
$953$	−19.5934	−0.634692	−0.317346	−	0.948310i	$-0.602792\pi$
$953$	−19.5934	−0.634692	−0.317346	+	0.948310i	$0.602792\pi$
$954$	59.9182	1.93992
$955$	−93.4276	−3.02325
$956$	30.8718	0.998465
$957$	−0.523814	−0.0169325
$958$	−33.8324	−1.09308
$959$	−2.58519	−0.0834801
$960$	36.4598	1.17674
$961$	−25.7365	−0.830209
$962$	−3.36811	−0.108592
$963$	13.8842	0.447411
$964$	−66.0466	−2.12722
$965$	34.3681	1.10635
$966$	−0.159123	−0.00511968
$967$	17.9355	0.576766	0.288383	−	0.957515i	$-0.406882\pi$
$967$	17.9355	0.576766	0.288383	+	0.957515i	$0.406882\pi$
$968$	34.5783	1.11139
$969$	−14.1701	−0.455209
$970$	154.175	4.95025
$971$	0.760114	0.0243932	0.0121966	−	0.999926i	$-0.496118\pi$
$971$	0.760114	0.0243932	0.0121966	+	0.999926i	$0.496118\pi$
$972$	−51.9523	−1.66637
$973$	6.52315	0.209123
$974$	65.7776	2.10765
$975$	31.5387	1.01005
$976$	11.5565	0.369913
$977$	−26.3165	−0.841939	−0.420970	−	0.907075i	$-0.638310\pi$
$977$	−26.3165	−0.841939	−0.420970	+	0.907075i	$0.638310\pi$
$978$	34.7567	1.11140
$979$	10.6148	0.339252
$980$	−97.0719	−3.10085
$981$	−18.5881	−0.593471
$982$	−52.3116	−1.66933
$983$	−27.1149	−0.864832	−0.432416	−	0.901674i	$-0.642339\pi$
$983$	−27.1149	−0.864832	−0.432416	+	0.901674i	$0.642339\pi$
$984$	16.6064	0.529393
$985$	−32.6720	−1.04102
$986$	−10.8480	−0.345469
$987$	−5.32204	−0.169402
$988$	38.6930	1.23099
$989$	0.295768	0.00940489
$990$	−25.2980	−0.804024
$991$	−20.7234	−0.658299	−0.329150	−	0.944278i	$-0.606762\pi$
$991$	−20.7234	−0.658299	−0.329150	+	0.944278i	$0.606762\pi$
$992$	−9.73117	−0.308965
$993$	−17.5500	−0.556932
$994$	−1.60617	−0.0509445
$995$	−0.406580	−0.0128895
$996$	−9.15387	−0.290051
$997$	39.5903	1.25384	0.626918	−	0.779085i	$-0.284316\pi$
$997$	39.5903	1.25384	0.626918	+	0.779085i	$0.284316\pi$
$998$	67.3880	2.13313
$999$	−1.62554	−0.0514299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.17	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.17	✓	172	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34076 q^{2} -0.698142 q^{3} +3.47917 q^{4} +4.27326 q^{5} +1.63419 q^{6} -0.686172 q^{7} -3.46239 q^{8} -2.51260 q^{9} +O(q^{10})\)	\(q-2.34076 q^{2} -0.698142 q^{3} +3.47917 q^{4} +4.27326 q^{5} +1.63419 q^{6} -0.686172 q^{7} -3.46239 q^{8} -2.51260 q^{9} -10.0027 q^{10} -1.00658 q^{11} -2.42896 q^{12} -3.40667 q^{13} +1.60617 q^{14} -2.98334 q^{15} +1.14630 q^{16} -6.21732 q^{17} +5.88140 q^{18} -3.26457 q^{19} +14.8674 q^{20} +0.479046 q^{21} +2.35615 q^{22} +0.141905 q^{23} +2.41724 q^{24} +13.2608 q^{25} +7.97421 q^{26} +3.84858 q^{27} -2.38731 q^{28} -0.745396 q^{29} +6.98330 q^{30} -2.29424 q^{31} +4.24157 q^{32} +0.702732 q^{33} +14.5533 q^{34} -2.93219 q^{35} -8.74176 q^{36} -0.422375 q^{37} +7.64159 q^{38} +2.37834 q^{39} -14.7957 q^{40} +6.86998 q^{41} -1.12133 q^{42} +2.08427 q^{43} -3.50205 q^{44} -10.7370 q^{45} -0.332166 q^{46} -11.1097 q^{47} -0.800280 q^{48} -6.52917 q^{49} -31.0403 q^{50} +4.34057 q^{51} -11.8524 q^{52} +10.1878 q^{53} -9.00861 q^{54} -4.30136 q^{55} +2.37580 q^{56} +2.27913 q^{57} +1.74480 q^{58} -9.60509 q^{59} -10.3796 q^{60} +10.0815 q^{61} +5.37026 q^{62} +1.72407 q^{63} -12.2211 q^{64} -14.5576 q^{65} -1.64493 q^{66} +0.269680 q^{67} -21.6311 q^{68} -0.0990698 q^{69} +6.86357 q^{70} -1.00000 q^{71} +8.69960 q^{72} +7.27738 q^{73} +0.988680 q^{74} -9.25791 q^{75} -11.3580 q^{76} +0.690684 q^{77} -5.56713 q^{78} +3.19526 q^{79} +4.89844 q^{80} +4.85094 q^{81} -16.0810 q^{82} +3.76864 q^{83} +1.66668 q^{84} -26.5683 q^{85} -4.87879 q^{86} +0.520392 q^{87} +3.48516 q^{88} -10.5455 q^{89} +25.1328 q^{90} +2.33756 q^{91} +0.493712 q^{92} +1.60170 q^{93} +26.0051 q^{94} -13.9504 q^{95} -2.96122 q^{96} -15.4133 q^{97} +15.2832 q^{98} +2.52912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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