LMFDB - Embedded newform 8027.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +O(q^{10})$	\(q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +7.85221 q^{10} -4.45205 q^{11} -10.1125 q^{12} -3.16946 q^{13} -0.602164 q^{14} +6.13213 q^{15} +10.3808 q^{16} +0.815402 q^{17} -3.21353 q^{18} +2.49505 q^{19} -14.6895 q^{20} -0.470256 q^{21} +11.7131 q^{22} +1.00000 q^{23} +15.7942 q^{24} +3.90763 q^{25} +8.33867 q^{26} +3.65426 q^{27} +1.12650 q^{28} -0.608467 q^{29} -16.1333 q^{30} -3.75357 q^{31} -11.9369 q^{32} +9.14725 q^{33} -2.14527 q^{34} -0.683102 q^{35} +6.01172 q^{36} +8.00206 q^{37} -6.56433 q^{38} +6.51203 q^{39} +22.9429 q^{40} +10.8290 q^{41} +1.23721 q^{42} -0.440332 q^{43} -21.9123 q^{44} -3.64546 q^{45} -2.63094 q^{46} -10.5002 q^{47} -21.3285 q^{48} -6.94761 q^{49} -10.2807 q^{50} -1.67534 q^{51} -15.5996 q^{52} +0.700230 q^{53} -9.61413 q^{54} +13.2874 q^{55} -1.75943 q^{56} -5.12637 q^{57} +1.60084 q^{58} -12.5183 q^{59} +30.1813 q^{60} +8.02118 q^{61} +9.87540 q^{62} +0.279560 q^{63} +10.6437 q^{64} +9.45948 q^{65} -24.0659 q^{66} +15.0315 q^{67} +4.01328 q^{68} -2.05461 q^{69} +1.79720 q^{70} -16.7994 q^{71} -9.38940 q^{72} +3.78320 q^{73} -21.0529 q^{74} -8.02868 q^{75} +12.2802 q^{76} -1.01898 q^{77} -17.1327 q^{78} -3.19883 q^{79} -30.9822 q^{80} -11.1724 q^{81} -28.4905 q^{82} -6.21259 q^{83} -2.31452 q^{84} -2.43362 q^{85} +1.15849 q^{86} +1.25017 q^{87} +34.2237 q^{88} +0.573084 q^{89} +9.59099 q^{90} -0.725421 q^{91} +4.92184 q^{92} +7.71213 q^{93} +27.6254 q^{94} -7.44665 q^{95} +24.5257 q^{96} -8.68164 q^{97} +18.2787 q^{98} -5.43791 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.63094	−1.86035	−0.930177	−	0.367111i	$-0.880347\pi$
$2$	−2.63094	−1.86035	−0.930177	+	0.367111i	$0.880347\pi$
$3$	−2.05461	−1.18623	−0.593116	−	0.805117i	$-0.702102\pi$
$3$	−2.05461	−1.18623	−0.593116	+	0.805117i	$0.702102\pi$
$4$	4.92184	2.46092
$5$	−2.98457	−1.33474	−0.667369	−	0.744727i	$-0.732580\pi$
$5$	−2.98457	−1.33474	−0.667369	+	0.744727i	$0.732580\pi$
$6$	5.40556	2.20681
$7$	0.228878	0.0865078	0.0432539	−	0.999064i	$-0.486228\pi$
$7$	0.228878	0.0865078	0.0432539	+	0.999064i	$0.486228\pi$
$8$	−7.68717	−2.71783
$9$	1.22144	0.407146
$10$	7.85221	2.48309
$11$	−4.45205	−1.34234	−0.671172	−	0.741301i	$-0.734209\pi$
$11$	−4.45205	−1.34234	−0.671172	+	0.741301i	$0.734209\pi$
$12$	−10.1125	−2.91922
$13$	−3.16946	−0.879051	−0.439526	−	0.898230i	$-0.644853\pi$
$13$	−3.16946	−0.879051	−0.439526	+	0.898230i	$0.644853\pi$
$14$	−0.602164	−0.160935
$15$	6.13213	1.58331
$16$	10.3808	2.59520
$17$	0.815402	0.197764	0.0988820	−	0.995099i	$-0.468473\pi$
$17$	0.815402	0.197764	0.0988820	+	0.995099i	$0.468473\pi$
$18$	−3.21353	−0.757436
$19$	2.49505	0.572405	0.286202	−	0.958169i	$-0.407607\pi$
$19$	2.49505	0.572405	0.286202	+	0.958169i	$0.407607\pi$
$20$	−14.6895	−3.28468
$21$	−0.470256	−0.102618
$22$	11.7131	2.49724
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	15.7942	3.22397
$25$	3.90763	0.781527
$26$	8.33867	1.63535
$27$	3.65426	0.703262
$28$	1.12650	0.212889
$29$	−0.608467	−0.112990	−0.0564948	−	0.998403i	$-0.517992\pi$
$29$	−0.608467	−0.112990	−0.0564948	+	0.998403i	$0.517992\pi$
$30$	−16.1333	−2.94552
$31$	−3.75357	−0.674160	−0.337080	−	0.941476i	$-0.609439\pi$
$31$	−3.75357	−0.674160	−0.337080	+	0.941476i	$0.609439\pi$
$32$	−11.9369	−2.11017
$33$	9.14725	1.59233
$34$	−2.14527	−0.367911
$35$	−0.683102	−0.115465
$36$	6.01172	1.00195
$37$	8.00206	1.31553	0.657766	−	0.753223i	$-0.271502\pi$
$37$	8.00206	1.31553	0.657766	+	0.753223i	$0.271502\pi$
$38$	−6.56433	−1.06488
$39$	6.51203	1.04276
$40$	22.9429	3.62759
$41$	10.8290	1.69121	0.845603	−	0.533812i	$-0.179241\pi$
$41$	10.8290	1.69121	0.845603	+	0.533812i	$0.179241\pi$
$42$	1.23721	0.190906
$43$	−0.440332	−0.0671500	−0.0335750	−	0.999436i	$-0.510689\pi$
$43$	−0.440332	−0.0671500	−0.0335750	+	0.999436i	$0.510689\pi$
$44$	−21.9123	−3.30340
$45$	−3.64546	−0.543434
$46$	−2.63094	−0.387911
$47$	−10.5002	−1.53161	−0.765806	−	0.643071i	$-0.777660\pi$
$47$	−10.5002	−1.53161	−0.765806	+	0.643071i	$0.777660\pi$
$48$	−21.3285	−3.07851
$49$	−6.94761	−0.992516
$50$	−10.2807	−1.45392
$51$	−1.67534	−0.234594
$52$	−15.5996	−2.16327
$53$	0.700230	0.0961839	0.0480920	−	0.998843i	$-0.484686\pi$
$53$	0.700230	0.0961839	0.0480920	+	0.998843i	$0.484686\pi$
$54$	−9.61413	−1.30832
$55$	13.2874	1.79168
$56$	−1.75943	−0.235113
$57$	−5.12637	−0.679005
$58$	1.60084	0.210201
$59$	−12.5183	−1.62974	−0.814872	−	0.579641i	$-0.803193\pi$
$59$	−12.5183	−1.62974	−0.814872	+	0.579641i	$0.803193\pi$
$60$	30.1813	3.89639
$61$	8.02118	1.02701	0.513503	−	0.858088i	$-0.328347\pi$
$61$	8.02118	1.02701	0.513503	+	0.858088i	$0.328347\pi$
$62$	9.87540	1.25418
$63$	0.279560	0.0352213
$64$	10.6437	1.33046
$65$	9.45948	1.17330
$66$	−24.0659	−2.96230
$67$	15.0315	1.83640	0.918198	−	0.396122i	$-0.129644\pi$
$67$	15.0315	1.83640	0.918198	+	0.396122i	$0.129644\pi$
$68$	4.01328	0.486681
$69$	−2.05461	−0.247346
$70$	1.79720	0.214806
$71$	−16.7994	−1.99372	−0.996858	−	0.0792058i	$-0.974762\pi$
$71$	−16.7994	−1.99372	−0.996858	+	0.0792058i	$0.974762\pi$
$72$	−9.38940	−1.10655
$73$	3.78320	0.442791	0.221395	−	0.975184i	$-0.428939\pi$
$73$	3.78320	0.442791	0.221395	+	0.975184i	$0.428939\pi$
$74$	−21.0529	−2.44735
$75$	−8.02868	−0.927072
$76$	12.2802	1.40864
$77$	−1.01898	−0.116123
$78$	−17.1327	−1.93990
$79$	−3.19883	−0.359896	−0.179948	−	0.983676i	$-0.557593\pi$
$79$	−3.19883	−0.359896	−0.179948	+	0.983676i	$0.557593\pi$
$80$	−30.9822	−3.46391
$81$	−11.1724	−1.24138
$82$	−28.4905	−3.14624
$83$	−6.21259	−0.681921	−0.340960	−	0.940078i	$-0.610752\pi$
$83$	−6.21259	−0.681921	−0.340960	+	0.940078i	$0.610752\pi$
$84$	−2.31452	−0.252535
$85$	−2.43362	−0.263963
$86$	1.15849	0.124923
$87$	1.25017	0.134032
$88$	34.2237	3.64826
$89$	0.573084	0.0607468	0.0303734	−	0.999539i	$-0.490330\pi$
$89$	0.573084	0.0607468	0.0303734	+	0.999539i	$0.490330\pi$
$90$	9.59099	1.01098
$91$	−0.725421	−0.0760448
$92$	4.92184	0.513137
$93$	7.71213	0.799711
$94$	27.6254	2.84934
$95$	−7.44665	−0.764010
$96$	24.5257	2.50315
$97$	−8.68164	−0.881487	−0.440743	−	0.897633i	$-0.645285\pi$
$97$	−8.68164	−0.881487	−0.440743	+	0.897633i	$0.645285\pi$
$98$	18.2787	1.84643
$99$	−5.43791	−0.546530
$100$	19.2327	1.92327
$101$	−2.87422	−0.285996	−0.142998	−	0.989723i	$-0.545674\pi$
$101$	−2.87422	−0.285996	−0.142998	+	0.989723i	$0.545674\pi$
$102$	4.40771	0.436428
$103$	−4.19722	−0.413564	−0.206782	−	0.978387i	$-0.566299\pi$
$103$	−4.19722	−0.413564	−0.206782	+	0.978387i	$0.566299\pi$
$104$	24.3642	2.38911
$105$	1.40351	0.136969
$106$	−1.84226	−0.178936
$107$	−4.71951	−0.456252	−0.228126	−	0.973632i	$-0.573260\pi$
$107$	−4.71951	−0.456252	−0.228126	+	0.973632i	$0.573260\pi$
$108$	17.9857	1.73067
$109$	−10.5394	−1.00949	−0.504745	−	0.863269i	$-0.668413\pi$
$109$	−10.5394	−1.00949	−0.504745	+	0.863269i	$0.668413\pi$
$110$	−34.9585	−3.33316
$111$	−16.4412	−1.56052
$112$	2.37594	0.224505
$113$	−11.7957	−1.10964	−0.554822	−	0.831969i	$-0.687214\pi$
$113$	−11.7957	−1.10964	−0.554822	+	0.831969i	$0.687214\pi$
$114$	13.4872	1.26319
$115$	−2.98457	−0.278312
$116$	−2.99478	−0.278058
$117$	−3.87131	−0.357902
$118$	32.9349	3.03190
$119$	0.186628	0.0171081
$120$	−47.1387	−4.30316
$121$	8.82078	0.801889
$122$	−21.1032	−1.91060
$123$	−22.2494	−2.00616
$124$	−18.4744	−1.65905
$125$	3.26024	0.291604
$126$	−0.735506	−0.0655241
$127$	−9.67470	−0.858491	−0.429245	−	0.903188i	$-0.641220\pi$
$127$	−9.67470	−0.858491	−0.429245	+	0.903188i	$0.641220\pi$
$128$	−4.12899	−0.364954
$129$	0.904712	0.0796555
$130$	−24.8873	−2.18276
$131$	10.9994	0.961019	0.480510	−	0.876989i	$-0.340452\pi$
$131$	10.9994	0.961019	0.480510	+	0.876989i	$0.340452\pi$
$132$	45.0213	3.91860
$133$	0.571063	0.0495175
$134$	−39.5471	−3.41635
$135$	−10.9064	−0.938671
$136$	−6.26813	−0.537488
$137$	15.6571	1.33767	0.668837	−	0.743409i	$-0.266792\pi$
$137$	15.6571	1.33767	0.668837	+	0.743409i	$0.266792\pi$
$138$	5.40556	0.460152
$139$	−17.2793	−1.46561	−0.732807	−	0.680437i	$-0.761790\pi$
$139$	−17.2793	−1.46561	−0.732807	+	0.680437i	$0.761790\pi$
$140$	−3.36212	−0.284151
$141$	21.5739	1.81685
$142$	44.1981	3.70902
$143$	14.1106	1.17999
$144$	12.6795	1.05663
$145$	1.81601	0.150811
$146$	−9.95338	−0.823747
$147$	14.2747	1.17735
$148$	39.3848	3.23741
$149$	−8.30005	−0.679967	−0.339983	−	0.940431i	$-0.610421\pi$
$149$	−8.30005	−0.679967	−0.339983	+	0.940431i	$0.610421\pi$
$150$	21.1230	1.72468
$151$	8.26813	0.672851	0.336425	−	0.941710i	$-0.390782\pi$
$151$	8.26813	0.672851	0.336425	+	0.941710i	$0.390782\pi$
$152$	−19.1799	−1.55570
$153$	0.995963	0.0805189
$154$	2.68087	0.216030
$155$	11.2028	0.899828
$156$	32.0511	2.56614
$157$	21.4572	1.71247	0.856235	−	0.516587i	$-0.172798\pi$
$157$	21.4572	1.71247	0.856235	+	0.516587i	$0.172798\pi$
$158$	8.41591	0.669534
$159$	−1.43870	−0.114096
$160$	35.6265	2.81652
$161$	0.228878	0.0180381
$162$	29.3939	2.30940
$163$	−5.12274	−0.401244	−0.200622	−	0.979669i	$-0.564296\pi$
$163$	−5.12274	−0.401244	−0.200622	+	0.979669i	$0.564296\pi$
$164$	53.2986	4.16192
$165$	−27.3006	−2.12535
$166$	16.3449	1.26861
$167$	22.3880	1.73244	0.866220	−	0.499663i	$-0.166543\pi$
$167$	22.3880	1.73244	0.866220	+	0.499663i	$0.166543\pi$
$168$	3.61494	0.278899
$169$	−2.95449	−0.227269
$170$	6.40271	0.491065
$171$	3.04755	0.233052
$172$	−2.16724	−0.165251
$173$	−0.230581	−0.0175308	−0.00876538	−	0.999962i	$-0.502790\pi$
$173$	−0.230581	−0.0175308	−0.00876538	+	0.999962i	$0.502790\pi$
$174$	−3.28911	−0.249347
$175$	0.894372	0.0676082
$176$	−46.2159	−3.48365
$177$	25.7203	1.93325
$178$	−1.50775	−0.113010
$179$	−13.1701	−0.984379	−0.492190	−	0.870488i	$-0.663803\pi$
$179$	−13.1701	−0.984379	−0.492190	+	0.870488i	$0.663803\pi$
$180$	−17.9424	−1.33735
$181$	−22.5609	−1.67694	−0.838470	−	0.544948i	$-0.816549\pi$
$181$	−22.5609	−1.67694	−0.838470	+	0.544948i	$0.816549\pi$
$182$	1.90854	0.141470
$183$	−16.4804	−1.21827
$184$	−7.68717	−0.566706
$185$	−23.8827	−1.75589
$186$	−20.2901	−1.48775
$187$	−3.63021	−0.265468
$188$	−51.6803	−3.76917
$189$	0.836380	0.0608377
$190$	19.5917	1.42133
$191$	−11.5402	−0.835021	−0.417511	−	0.908672i	$-0.637097\pi$
$191$	−11.5402	−0.835021	−0.417511	+	0.908672i	$0.637097\pi$
$192$	−21.8686	−1.57823
$193$	−1.13217	−0.0814954	−0.0407477	−	0.999169i	$-0.512974\pi$
$193$	−1.13217	−0.0814954	−0.0407477	+	0.999169i	$0.512974\pi$
$194$	22.8408	1.63988
$195$	−19.4356	−1.39181
$196$	−34.1950	−2.44250
$197$	3.69105	0.262977	0.131488	−	0.991318i	$-0.458024\pi$
$197$	3.69105	0.262977	0.131488	+	0.991318i	$0.458024\pi$
$198$	14.3068	1.01674
$199$	−3.35641	−0.237930	−0.118965	−	0.992898i	$-0.537958\pi$
$199$	−3.35641	−0.237930	−0.118965	+	0.992898i	$0.537958\pi$
$200$	−30.0387	−2.12405
$201$	−30.8840	−2.17839
$202$	7.56191	0.532054
$203$	−0.139265	−0.00977447
$204$	−8.24573	−0.577317
$205$	−32.3199	−2.25732
$206$	11.0426	0.769376
$207$	1.22144	0.0848958
$208$	−32.9016	−2.28131
$209$	−11.1081	−0.768364
$210$	−3.69255	−0.254810
$211$	25.5631	1.75984	0.879920	−	0.475122i	$-0.157596\pi$
$211$	25.5631	1.75984	0.879920	+	0.475122i	$0.157596\pi$
$212$	3.44642	0.236701
$213$	34.5162	2.36501
$214$	12.4167	0.848790
$215$	1.31420	0.0896277
$216$	−28.0909	−1.91134
$217$	−0.859109	−0.0583201
$218$	27.7285	1.87801
$219$	−7.77303	−0.525252
$220$	65.3986	4.40918
$221$	−2.58439	−0.173845
$222$	43.2557	2.90313
$223$	−23.6936	−1.58664	−0.793321	−	0.608804i	$-0.791650\pi$
$223$	−23.6936	−1.58664	−0.793321	+	0.608804i	$0.791650\pi$
$224$	−2.73210	−0.182546
$225$	4.77293	0.318196
$226$	31.0337	2.06433
$227$	−6.21504	−0.412506	−0.206253	−	0.978499i	$-0.566127\pi$
$227$	−6.21504	−0.412506	−0.206253	+	0.978499i	$0.566127\pi$
$228$	−25.2312	−1.67097
$229$	−17.7950	−1.17593	−0.587964	−	0.808887i	$-0.700070\pi$
$229$	−17.7950	−1.17593	−0.587964	+	0.808887i	$0.700070\pi$
$230$	7.85221	0.517759
$231$	2.09361	0.137749
$232$	4.67739	0.307086
$233$	−17.0964	−1.12002	−0.560012	−	0.828485i	$-0.689203\pi$
$233$	−17.0964	−1.12002	−0.560012	+	0.828485i	$0.689203\pi$
$234$	10.1852	0.665825
$235$	31.3386	2.04430
$236$	−61.6130	−4.01067
$237$	6.57235	0.426920
$238$	−0.491006	−0.0318272
$239$	−6.87581	−0.444759	−0.222380	−	0.974960i	$-0.571382\pi$
$239$	−6.87581	−0.444759	−0.222380	+	0.974960i	$0.571382\pi$
$240$	63.6564	4.10900
$241$	−20.7952	−1.33953	−0.669767	−	0.742571i	$-0.733606\pi$
$241$	−20.7952	−1.33953	−0.669767	+	0.742571i	$0.733606\pi$
$242$	−23.2069	−1.49180
$243$	11.9922	0.769300
$244$	39.4789	2.52738
$245$	20.7356	1.32475
$246$	58.5369	3.73217
$247$	−7.90798	−0.503173
$248$	28.8543	1.83225
$249$	12.7645	0.808916
$250$	−8.57748	−0.542488
$251$	−6.31715	−0.398735	−0.199368	−	0.979925i	$-0.563889\pi$
$251$	−6.31715	−0.398735	−0.199368	+	0.979925i	$0.563889\pi$
$252$	1.37595	0.0866768
$253$	−4.45205	−0.279898
$254$	25.4535	1.59710
$255$	5.00015	0.313122
$256$	−10.4242	−0.651512
$257$	−30.5067	−1.90295	−0.951477	−	0.307719i	$-0.900434\pi$
$257$	−30.5067	−1.90295	−0.951477	+	0.307719i	$0.900434\pi$
$258$	−2.38024	−0.148187
$259$	1.83150	0.113804
$260$	46.5580	2.88740
$261$	−0.743205	−0.0460032
$262$	−28.9387	−1.78784
$263$	5.22419	0.322137	0.161069	−	0.986943i	$-0.448506\pi$
$263$	5.22419	0.322137	0.161069	+	0.986943i	$0.448506\pi$
$264$	−70.3165	−4.32768
$265$	−2.08988	−0.128380
$266$	−1.50243	−0.0921200
$267$	−1.17747	−0.0720597
$268$	73.9828	4.51922
$269$	−15.4095	−0.939534	−0.469767	−	0.882790i	$-0.655662\pi$
$269$	−15.4095	−0.939534	−0.469767	+	0.882790i	$0.655662\pi$
$270$	28.6940	1.74626
$271$	22.6210	1.37413	0.687063	−	0.726598i	$-0.258900\pi$
$271$	22.6210	1.37413	0.687063	+	0.726598i	$0.258900\pi$
$272$	8.46453	0.513237
$273$	1.49046	0.0902067
$274$	−41.1928	−2.48855
$275$	−17.3970	−1.04908
$276$	−10.1125	−0.608699
$277$	−9.40141	−0.564876	−0.282438	−	0.959286i	$-0.591143\pi$
$277$	−9.40141	−0.564876	−0.282438	+	0.959286i	$0.591143\pi$
$278$	45.4608	2.72656
$279$	−4.58475	−0.274482
$280$	5.25112	0.313814
$281$	7.07424	0.422014	0.211007	−	0.977485i	$-0.432326\pi$
$281$	7.07424	0.422014	0.211007	+	0.977485i	$0.432326\pi$
$282$	−56.7595	−3.37998
$283$	−1.32472	−0.0787466	−0.0393733	−	0.999225i	$-0.512536\pi$
$283$	−1.32472	−0.0787466	−0.0393733	+	0.999225i	$0.512536\pi$
$284$	−82.6837	−4.90637
$285$	15.3000	0.906293
$286$	−37.1242	−2.19520
$287$	2.47852	0.146303
$288$	−14.5802	−0.859146
$289$	−16.3351	−0.960889
$290$	−4.77781	−0.280563
$291$	17.8374	1.04565
$292$	18.6203	1.08967
$293$	31.7535	1.85506	0.927529	−	0.373751i	$-0.121929\pi$
$293$	31.7535	1.85506	0.927529	+	0.373751i	$0.121929\pi$
$294$	−37.5558	−2.19030
$295$	37.3617	2.17528
$296$	−61.5132	−3.57538
$297$	−16.2690	−0.944020
$298$	21.8369	1.26498
$299$	−3.16946	−0.183295
$300$	−39.5159	−2.28145
$301$	−0.100782	−0.00580900
$302$	−21.7529	−1.25174
$303$	5.90542	0.339258
$304$	25.9007	1.48550
$305$	−23.9397	−1.37079
$306$	−2.62032	−0.149794
$307$	−4.30086	−0.245463	−0.122732	−	0.992440i	$-0.539165\pi$
$307$	−4.30086	−0.245463	−0.122732	+	0.992440i	$0.539165\pi$
$308$	−5.01524	−0.285770
$309$	8.62366	0.490583
$310$	−29.4738	−1.67400
$311$	−13.9944	−0.793547	−0.396774	−	0.917916i	$-0.629870\pi$
$311$	−13.9944	−0.793547	−0.396774	+	0.917916i	$0.629870\pi$
$312$	−50.0591	−2.83404
$313$	9.97013	0.563545	0.281773	−	0.959481i	$-0.409078\pi$
$313$	9.97013	0.563545	0.281773	+	0.959481i	$0.409078\pi$
$314$	−56.4525	−3.18580
$315$	−0.834367	−0.0470112
$316$	−15.7441	−0.885675
$317$	−22.8673	−1.28435	−0.642177	−	0.766556i	$-0.721969\pi$
$317$	−22.8673	−1.28435	−0.642177	+	0.766556i	$0.721969\pi$
$318$	3.78514	0.212260
$319$	2.70893	0.151671
$320$	−31.7667	−1.77581
$321$	9.69677	0.541221
$322$	−0.602164	−0.0335573
$323$	2.03447	0.113201
$324$	−54.9887	−3.05493
$325$	−12.3851	−0.687002
$326$	13.4776	0.746456
$327$	21.6544	1.19749
$328$	−83.2444	−4.59640
$329$	−2.40327	−0.132496
$330$	71.8261	3.95390
$331$	26.6590	1.46531	0.732655	−	0.680600i	$-0.238281\pi$
$331$	26.6590	1.46531	0.732655	+	0.680600i	$0.238281\pi$
$332$	−30.5774	−1.67815
$333$	9.77403	0.535613
$334$	−58.9016	−3.22295
$335$	−44.8626	−2.45111
$336$	−4.88163	−0.266315
$337$	−19.7403	−1.07532	−0.537660	−	0.843161i	$-0.680692\pi$
$337$	−19.7403	−1.07532	−0.537660	+	0.843161i	$0.680692\pi$
$338$	7.77309	0.422801
$339$	24.2356	1.31629
$340$	−11.9779	−0.649592
$341$	16.7111	0.904956
$342$	−8.01793	−0.433560
$343$	−3.19230	−0.172368
$344$	3.38491	0.182502
$345$	6.13213	0.330143
$346$	0.606645	0.0326134
$347$	−13.8804	−0.745138	−0.372569	−	0.928004i	$-0.621523\pi$
$347$	−13.8804	−0.745138	−0.372569	+	0.928004i	$0.621523\pi$
$348$	6.15311	0.329841
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−2.35304	−0.125775
$351$	−11.5820	−0.618204
$352$	53.1437	2.83257
$353$	9.75402	0.519154	0.259577	−	0.965722i	$-0.416417\pi$
$353$	9.75402	0.519154	0.259577	+	0.965722i	$0.416417\pi$
$354$	−67.6684	−3.59654
$355$	50.1388	2.66109
$356$	2.82062	0.149493
$357$	−0.383448	−0.0202942
$358$	34.6497	1.83129
$359$	−16.4800	−0.869782	−0.434891	−	0.900483i	$-0.643213\pi$
$359$	−16.4800	−0.869782	−0.434891	+	0.900483i	$0.643213\pi$
$360$	28.0233	1.47696
$361$	−12.7747	−0.672353
$362$	59.3564	3.11970
$363$	−18.1233	−0.951226
$364$	−3.57040	−0.187140
$365$	−11.2912	−0.591010
$366$	43.3590	2.26641
$367$	−7.70470	−0.402182	−0.201091	−	0.979573i	$-0.564449\pi$
$367$	−7.70470	−0.402182	−0.201091	+	0.979573i	$0.564449\pi$
$368$	10.3808	0.541137
$369$	13.2270	0.688568
$370$	62.8339	3.26658
$371$	0.160267	0.00832066
$372$	37.9578	1.96802
$373$	12.6023	0.652525	0.326262	−	0.945279i	$-0.394211\pi$
$373$	12.6023	0.652525	0.326262	+	0.945279i	$0.394211\pi$
$374$	9.55087	0.493864
$375$	−6.69853	−0.345910
$376$	80.7169	4.16266
$377$	1.92852	0.0993236
$378$	−2.20046	−0.113180
$379$	10.9700	0.563489	0.281745	−	0.959489i	$-0.409087\pi$
$379$	10.9700	0.563489	0.281745	+	0.959489i	$0.409087\pi$
$380$	−36.6512	−1.88017
$381$	19.8778	1.01837
$382$	30.3616	1.55344
$383$	24.1547	1.23425	0.617123	−	0.786867i	$-0.288298\pi$
$383$	24.1547	1.23425	0.617123	+	0.786867i	$0.288298\pi$
$384$	8.48347	0.432920
$385$	3.04121	0.154994
$386$	2.97867	0.151610
$387$	−0.537838	−0.0273399
$388$	−42.7296	−2.16927
$389$	7.28676	0.369454	0.184727	−	0.982790i	$-0.440860\pi$
$389$	7.28676	0.369454	0.184727	+	0.982790i	$0.440860\pi$
$390$	51.1338	2.58926
$391$	0.815402	0.0412367
$392$	53.4075	2.69749
$393$	−22.5995	−1.13999
$394$	−9.71093	−0.489230
$395$	9.54711	0.480367
$396$	−26.7645	−1.34497
$397$	−10.8698	−0.545542	−0.272771	−	0.962079i	$-0.587940\pi$
$397$	−10.8698	−0.545542	−0.272771	+	0.962079i	$0.587940\pi$
$398$	8.83052	0.442634
$399$	−1.17331	−0.0587392
$400$	40.5644	2.02822
$401$	−19.8380	−0.990663	−0.495331	−	0.868704i	$-0.664953\pi$
$401$	−19.8380	−0.990663	−0.495331	+	0.868704i	$0.664953\pi$
$402$	81.2540	4.05258
$403$	11.8968	0.592622
$404$	−14.1465	−0.703813
$405$	33.3448	1.65692
$406$	0.366397	0.0181840
$407$	−35.6256	−1.76590
$408$	12.8786	0.637586
$409$	16.4458	0.813193	0.406597	−	0.913608i	$-0.366715\pi$
$409$	16.4458	0.813193	0.406597	+	0.913608i	$0.366715\pi$
$410$	85.0316	4.19941
$411$	−32.1692	−1.58679
$412$	−20.6580	−1.01775
$413$	−2.86516	−0.140986
$414$	−3.21353	−0.157936
$415$	18.5419	0.910186
$416$	37.8336	1.85494
$417$	35.5023	1.73856
$418$	29.2248	1.42943
$419$	14.1447	0.691012	0.345506	−	0.938417i	$-0.387707\pi$
$419$	14.1447	0.691012	0.345506	+	0.938417i	$0.387707\pi$
$420$	6.90785	0.337069
$421$	2.57159	0.125332	0.0626658	−	0.998035i	$-0.480040\pi$
$421$	2.57159	0.125332	0.0626658	+	0.998035i	$0.480040\pi$
$422$	−67.2551	−3.27393
$423$	−12.8254	−0.623590
$424$	−5.38278	−0.261411
$425$	3.18629	0.154558
$426$	−90.8100	−4.39976
$427$	1.83587	0.0888441
$428$	−23.2286	−1.12280
$429$	−28.9919	−1.39974
$430$	−3.45758	−0.166739
$431$	−39.6491	−1.90983	−0.954915	−	0.296879i	$-0.904054\pi$
$431$	−39.6491	−1.90983	−0.954915	+	0.296879i	$0.904054\pi$
$432$	37.9341	1.82511
$433$	−30.4796	−1.46476	−0.732379	−	0.680897i	$-0.761590\pi$
$433$	−30.4796	−1.46476	−0.732379	+	0.680897i	$0.761590\pi$
$434$	2.26026	0.108496
$435$	−3.73120	−0.178897
$436$	−51.8731	−2.48427
$437$	2.49505	0.119355
$438$	20.4503	0.977155
$439$	−15.9366	−0.760615	−0.380307	−	0.924860i	$-0.624182\pi$
$439$	−15.9366	−0.760615	−0.380307	+	0.924860i	$0.624182\pi$
$440$	−102.143	−4.86947
$441$	−8.48608	−0.404099
$442$	6.79937	0.323413
$443$	−2.43015	−0.115460	−0.0577298	−	0.998332i	$-0.518386\pi$
$443$	−2.43015	−0.115460	−0.0577298	+	0.998332i	$0.518386\pi$
$444$	−80.9207	−3.84032
$445$	−1.71041	−0.0810810
$446$	62.3364	2.95172
$447$	17.0534	0.806598
$448$	2.43610	0.115095
$449$	−19.9848	−0.943143	−0.471571	−	0.881828i	$-0.656313\pi$
$449$	−19.9848	−0.943143	−0.471571	+	0.881828i	$0.656313\pi$
$450$	−12.5573	−0.591957
$451$	−48.2113	−2.27018
$452$	−58.0564	−2.73074
$453$	−16.9878	−0.798157
$454$	16.3514	0.767408
$455$	2.16507	0.101500
$456$	39.4073	1.84542
$457$	0.626530	0.0293078	0.0146539	−	0.999893i	$-0.495335\pi$
$457$	0.626530	0.0293078	0.0146539	+	0.999893i	$0.495335\pi$
$458$	46.8176	2.18764
$459$	2.97969	0.139080
$460$	−14.6895	−0.684904
$461$	19.4873	0.907616	0.453808	−	0.891099i	$-0.350065\pi$
$461$	19.4873	0.907616	0.453808	+	0.891099i	$0.350065\pi$
$462$	−5.50815	−0.256262
$463$	38.4685	1.78778	0.893892	−	0.448283i	$-0.147964\pi$
$463$	38.4685	1.78778	0.893892	+	0.448283i	$0.147964\pi$
$464$	−6.31638	−0.293230
$465$	−23.0174	−1.06740
$466$	44.9796	2.08364
$467$	−33.6159	−1.55556	−0.777778	−	0.628539i	$-0.783653\pi$
$467$	−33.6159	−1.55556	−0.777778	+	0.628539i	$0.783653\pi$
$468$	−19.0539	−0.880768
$469$	3.44039	0.158863
$470$	−82.4498	−3.80313
$471$	−44.0862	−2.03139
$472$	96.2303	4.42936
$473$	1.96038	0.0901384
$474$	−17.2915	−0.794223
$475$	9.74976	0.447350
$476$	0.918551	0.0421017
$477$	0.855287	0.0391609
$478$	18.0898	0.827410
$479$	17.9263	0.819072	0.409536	−	0.912294i	$-0.365691\pi$
$479$	17.9263	0.819072	0.409536	+	0.912294i	$0.365691\pi$
$480$	−73.1986	−3.34105
$481$	−25.3623	−1.15642
$482$	54.7108	2.49201
$483$	−0.470256	−0.0213974
$484$	43.4144	1.97338
$485$	25.9109	1.17655
$486$	−31.5507	−1.43117
$487$	−0.128777	−0.00583546	−0.00291773	−	0.999996i	$-0.500929\pi$
$487$	−0.128777	−0.00583546	−0.00291773	+	0.999996i	$0.500929\pi$
$488$	−61.6602	−2.79122
$489$	10.5253	0.475969
$490$	−54.5541	−2.46450
$491$	−15.6854	−0.707872	−0.353936	−	0.935270i	$-0.615157\pi$
$491$	−15.6854	−0.707872	−0.353936	+	0.935270i	$0.615157\pi$
$492$	−109.508	−4.93700
$493$	−0.496145	−0.0223453
$494$	20.8054	0.936080
$495$	16.2298	0.729475
$496$	−38.9650	−1.74958
$497$	−3.84500	−0.172472
$498$	−33.5826	−1.50487
$499$	−3.37144	−0.150926	−0.0754632	−	0.997149i	$-0.524044\pi$
$499$	−3.37144	−0.150926	−0.0754632	+	0.997149i	$0.524044\pi$
$500$	16.0464	0.717615
$501$	−45.9988	−2.05507
$502$	16.6200	0.741789
$503$	−30.0034	−1.33779	−0.668894	−	0.743358i	$-0.733232\pi$
$503$	−30.0034	−1.33779	−0.668894	+	0.743358i	$0.733232\pi$
$504$	−2.14903	−0.0957254
$505$	8.57831	0.381730
$506$	11.7131	0.520710
$507$	6.07035	0.269594
$508$	−47.6173	−2.11268
$509$	−28.6795	−1.27120	−0.635598	−	0.772020i	$-0.719246\pi$
$509$	−28.6795	−1.27120	−0.635598	+	0.772020i	$0.719246\pi$
$510$	−13.1551	−0.582517
$511$	0.865893	0.0383048
$512$	35.6834	1.57700
$513$	9.11757	0.402550
$514$	80.2612	3.54017
$515$	12.5269	0.552000
$516$	4.45285	0.196026
$517$	46.7475	2.05595
$518$	−4.81856	−0.211715
$519$	0.473755	0.0207955
$520$	−72.7166	−3.18883
$521$	−40.1973	−1.76108	−0.880538	−	0.473975i	$-0.842819\pi$
$521$	−40.1973	−1.76108	−0.880538	+	0.473975i	$0.842819\pi$
$522$	1.95533	0.0855823
$523$	−17.7048	−0.774175	−0.387087	−	0.922043i	$-0.626519\pi$
$523$	−17.7048	−0.774175	−0.387087	+	0.922043i	$0.626519\pi$
$524$	54.1371	2.36499
$525$	−1.83759	−0.0801990
$526$	−13.7445	−0.599289
$527$	−3.06067	−0.133325
$528$	94.9558	4.13242
$529$	1.00000	0.0434783
$530$	5.49835	0.238833
$531$	−15.2903	−0.663544
$532$	2.81068	0.121858
$533$	−34.3222	−1.48666
$534$	3.09784	0.134057
$535$	14.0857	0.608977
$536$	−115.550	−4.99100
$537$	27.0595	1.16770
$538$	40.5415	1.74787
$539$	30.9312	1.33230
$540$	−53.6794	−2.30999
$541$	5.59650	0.240612	0.120306	−	0.992737i	$-0.461612\pi$
$541$	5.59650	0.240612	0.120306	+	0.992737i	$0.461612\pi$
$542$	−59.5144	−2.55636
$543$	46.3540	1.98924
$544$	−9.73337	−0.417315
$545$	31.4555	1.34740
$546$	−3.92131	−0.167817
$547$	−22.2762	−0.952462	−0.476231	−	0.879320i	$-0.657997\pi$
$547$	−22.2762	−0.952462	−0.476231	+	0.879320i	$0.657997\pi$
$548$	77.0616	3.29191
$549$	9.79737	0.418142
$550$	45.7704	1.95166
$551$	−1.51816	−0.0646757
$552$	15.7942	0.672244
$553$	−0.732141	−0.0311338
$554$	24.7345	1.05087
$555$	49.0697	2.08289
$556$	−85.0460	−3.60675
$557$	39.0311	1.65380	0.826900	−	0.562349i	$-0.190102\pi$
$557$	39.0311	1.65380	0.826900	+	0.562349i	$0.190102\pi$
$558$	12.0622	0.510633
$559$	1.39562	0.0590283
$560$	−7.09114	−0.299655
$561$	7.45869	0.314906
$562$	−18.6119	−0.785095
$563$	−33.2073	−1.39952	−0.699761	−	0.714377i	$-0.746710\pi$
$563$	−33.2073	−1.39952	−0.699761	+	0.714377i	$0.746710\pi$
$564$	106.183	4.47111
$565$	35.2050	1.48108
$566$	3.48526	0.146497
$567$	−2.55712	−0.107389
$568$	129.140	5.41857
$569$	32.7635	1.37352	0.686759	−	0.726885i	$-0.259033\pi$
$569$	32.7635	1.37352	0.686759	+	0.726885i	$0.259033\pi$
$570$	−40.2533	−1.68603
$571$	41.6595	1.74339	0.871697	−	0.490044i	$-0.163019\pi$
$571$	41.6595	1.74339	0.871697	+	0.490044i	$0.163019\pi$
$572$	69.4502	2.90386
$573$	23.7107	0.990529
$574$	−6.52084	−0.272175
$575$	3.90763	0.162960
$576$	13.0006	0.541690
$577$	−23.0819	−0.960914	−0.480457	−	0.877018i	$-0.659529\pi$
$577$	−23.0819	−0.960914	−0.480457	+	0.877018i	$0.659529\pi$
$578$	42.9767	1.78759
$579$	2.32617	0.0966725
$580$	8.93811	0.371135
$581$	−1.42193	−0.0589915
$582$	−46.9291	−1.94527
$583$	−3.11746	−0.129112
$584$	−29.0821	−1.20343
$585$	11.5542	0.477706
$586$	−83.5414	−3.45107
$587$	9.00552	0.371698	0.185849	−	0.982578i	$-0.440497\pi$
$587$	9.00552	0.371698	0.185849	+	0.982578i	$0.440497\pi$
$588$	70.2576	2.89737
$589$	−9.36535	−0.385892
$590$	−98.2963	−4.04679
$591$	−7.58369	−0.311951
$592$	83.0678	3.41407
$593$	−25.9986	−1.06763	−0.533816	−	0.845600i	$-0.679243\pi$
$593$	−25.9986	−1.06763	−0.533816	+	0.845600i	$0.679243\pi$
$594$	42.8026	1.75621
$595$	−0.557003	−0.0228349
$596$	−40.8515	−1.67334
$597$	6.89613	0.282240
$598$	8.33867	0.340993
$599$	18.5189	0.756661	0.378330	−	0.925671i	$-0.376498\pi$
$599$	18.5189	0.756661	0.378330	+	0.925671i	$0.376498\pi$
$600$	61.7178	2.51962
$601$	35.6404	1.45380	0.726901	−	0.686743i	$-0.240960\pi$
$601$	35.6404	1.45380	0.726901	+	0.686743i	$0.240960\pi$
$602$	0.265152	0.0108068
$603$	18.3601	0.747681
$604$	40.6944	1.65583
$605$	−26.3262	−1.07031
$606$	−15.5368	−0.631139
$607$	−44.7603	−1.81676	−0.908381	−	0.418142i	$-0.862681\pi$
$607$	−44.7603	−1.81676	−0.908381	+	0.418142i	$0.862681\pi$
$608$	−29.7832	−1.20787
$609$	0.286135	0.0115948
$610$	62.9840	2.55015
$611$	33.2800	1.34637
$612$	4.90197	0.198150
$613$	25.3292	1.02304	0.511518	−	0.859272i	$-0.329083\pi$
$613$	25.3292	1.02304	0.511518	+	0.859272i	$0.329083\pi$
$614$	11.3153	0.456649
$615$	66.4049	2.67770
$616$	7.83305	0.315603
$617$	12.2873	0.494669	0.247334	−	0.968930i	$-0.420445\pi$
$617$	12.2873	0.494669	0.247334	+	0.968930i	$0.420445\pi$
$618$	−22.6883	−0.912658
$619$	−8.52472	−0.342637	−0.171319	−	0.985216i	$-0.554803\pi$
$619$	−8.52472	−0.342637	−0.171319	+	0.985216i	$0.554803\pi$
$620$	55.1382	2.21440
$621$	3.65426	0.146640
$622$	36.8183	1.47628
$623$	0.131166	0.00525507
$624$	67.6000	2.70617
$625$	−29.2686	−1.17074
$626$	−26.2308	−1.04839
$627$	22.8229	0.911458
$628$	105.609	4.21425
$629$	6.52490	0.260165
$630$	2.19517	0.0874576
$631$	−27.3594	−1.08916	−0.544581	−	0.838708i	$-0.683311\pi$
$631$	−27.3594	−1.08916	−0.544581	+	0.838708i	$0.683311\pi$
$632$	24.5899	0.978134
$633$	−52.5224	−2.08758
$634$	60.1624	2.38935
$635$	28.8748	1.14586
$636$	−7.08105	−0.280782
$637$	22.0202	0.872473
$638$	−7.12702	−0.282162
$639$	−20.5194	−0.811734
$640$	12.3232	0.487119
$641$	46.9265	1.85348	0.926742	−	0.375699i	$-0.122597\pi$
$641$	46.9265	1.85348	0.926742	+	0.375699i	$0.122597\pi$
$642$	−25.5116	−1.00686
$643$	20.9496	0.826171	0.413086	−	0.910692i	$-0.364451\pi$
$643$	20.9496	0.826171	0.413086	+	0.910692i	$0.364451\pi$
$644$	1.12650	0.0443903
$645$	−2.70017	−0.106319
$646$	−5.35257	−0.210594
$647$	19.8076	0.778718	0.389359	−	0.921086i	$-0.372697\pi$
$647$	19.8076	0.778718	0.389359	+	0.921086i	$0.372697\pi$
$648$	85.8842	3.37385
$649$	55.7321	2.18768
$650$	32.5845	1.27807
$651$	1.76514	0.0691812
$652$	−25.2133	−0.987429
$653$	1.13530	0.0444278	0.0222139	−	0.999753i	$-0.492929\pi$
$653$	1.13530	0.0444278	0.0222139	+	0.999753i	$0.492929\pi$
$654$	−56.9713	−2.22775
$655$	−32.8283	−1.28271
$656$	112.414	4.38902
$657$	4.62095	0.180280
$658$	6.32285	0.246490
$659$	−41.2185	−1.60564	−0.802822	−	0.596218i	$-0.796669\pi$
$659$	−41.2185	−1.60564	−0.802822	+	0.596218i	$0.796669\pi$
$660$	−134.369	−5.23030
$661$	14.1319	0.549668	0.274834	−	0.961492i	$-0.411377\pi$
$661$	14.1319	0.549668	0.274834	+	0.961492i	$0.411377\pi$
$662$	−70.1381	−2.72599
$663$	5.30992	0.206220
$664$	47.7573	1.85334
$665$	−1.70438	−0.0660929
$666$	−25.7149	−0.996431
$667$	−0.608467	−0.0235599
$668$	110.190	4.26339
$669$	48.6812	1.88213
$670$	118.031	4.55993
$671$	−35.7107	−1.37860
$672$	5.61340	0.216542
$673$	9.93640	0.383020	0.191510	−	0.981491i	$-0.438662\pi$
$673$	9.93640	0.383020	0.191510	+	0.981491i	$0.438662\pi$
$674$	51.9354	2.00048
$675$	14.2795	0.549618
$676$	−14.5415	−0.559290
$677$	15.6518	0.601546	0.300773	−	0.953696i	$-0.402755\pi$
$677$	15.6518	0.601546	0.300773	+	0.953696i	$0.402755\pi$
$678$	−63.7623	−2.44877
$679$	−1.98704	−0.0762555
$680$	18.7077	0.717406
$681$	12.7695	0.489328
$682$	−43.9658	−1.68354
$683$	27.4149	1.04900	0.524501	−	0.851410i	$-0.324252\pi$
$683$	27.4149	1.04900	0.524501	+	0.851410i	$0.324252\pi$
$684$	14.9996	0.573523
$685$	−46.7296	−1.78545
$686$	8.39875	0.320666
$687$	36.5619	1.39492
$688$	−4.57100	−0.174268
$689$	−2.21935	−0.0845506
$690$	−16.1333	−0.614183
$691$	−15.2052	−0.578434	−0.289217	−	0.957264i	$-0.593395\pi$
$691$	−15.2052	−0.578434	−0.289217	+	0.957264i	$0.593395\pi$
$692$	−1.13488	−0.0431418
$693$	−1.24462	−0.0472791
$694$	36.5184	1.38622
$695$	51.5713	1.95621
$696$	−9.61023	−0.364275
$697$	8.83000	0.334460
$698$	2.63094	0.0995825
$699$	35.1265	1.32861
$700$	4.40195	0.166378
$701$	23.8884	0.902252	0.451126	−	0.892460i	$-0.351022\pi$
$701$	23.8884	0.902252	0.451126	+	0.892460i	$0.351022\pi$
$702$	30.4716	1.15008
$703$	19.9656	0.753016
$704$	−47.3861	−1.78593
$705$	−64.3886	−2.42502
$706$	−25.6622	−0.965811
$707$	−0.657847	−0.0247409
$708$	126.591	4.75758
$709$	−9.91002	−0.372178	−0.186089	−	0.982533i	$-0.559581\pi$
$709$	−9.91002	−0.372178	−0.186089	+	0.982533i	$0.559581\pi$
$710$	−131.912	−4.95057
$711$	−3.90717	−0.146530
$712$	−4.40539	−0.165099
$713$	−3.75357	−0.140572
$714$	1.00883	0.0377544
$715$	−42.1141	−1.57498
$716$	−64.8210	−2.42248
$717$	14.1271	0.527588
$718$	43.3579	1.61810
$719$	−51.1979	−1.90936	−0.954680	−	0.297633i	$-0.903803\pi$
$719$	−51.1979	−1.90936	−0.954680	+	0.297633i	$0.903803\pi$
$720$	−37.8428	−1.41032
$721$	−0.960651	−0.0357765
$722$	33.6095	1.25081
$723$	42.7260	1.58900
$724$	−111.041	−4.12681
$725$	−2.37767	−0.0883044
$726$	47.6813	1.76962
$727$	31.7496	1.17753	0.588764	−	0.808305i	$-0.299615\pi$
$727$	31.7496	1.17753	0.588764	+	0.808305i	$0.299615\pi$
$728$	5.57644	0.206676
$729$	8.87787	0.328810
$730$	29.7065	1.09949
$731$	−0.359048	−0.0132799
$732$	−81.1139	−2.99806
$733$	−3.16313	−0.116833	−0.0584165	−	0.998292i	$-0.518605\pi$
$733$	−3.16313	−0.116833	−0.0584165	+	0.998292i	$0.518605\pi$
$734$	20.2706	0.748201
$735$	−42.6037	−1.57146
$736$	−11.9369	−0.440000
$737$	−66.9212	−2.46508
$738$	−34.7993	−1.28098
$739$	−26.8997	−0.989521	−0.494760	−	0.869029i	$-0.664744\pi$
$739$	−26.8997	−0.989521	−0.494760	+	0.869029i	$0.664744\pi$
$740$	−117.547	−4.32110
$741$	16.2479	0.596880
$742$	−0.421653	−0.0154794
$743$	32.0968	1.17752	0.588760	−	0.808308i	$-0.299616\pi$
$743$	32.0968	1.17752	0.588760	+	0.808308i	$0.299616\pi$
$744$	−59.2845	−2.17347
$745$	24.7720	0.907578
$746$	−33.1560	−1.21393
$747$	−7.58830	−0.277641
$748$	−17.8673	−0.653294
$749$	−1.08019	−0.0394694
$750$	17.6234	0.643516
$751$	26.3161	0.960289	0.480145	−	0.877189i	$-0.340584\pi$
$751$	26.3161	0.960289	0.480145	+	0.877189i	$0.340584\pi$
$752$	−109.001	−3.97484
$753$	12.9793	0.472992
$754$	−5.07380	−0.184777
$755$	−24.6768	−0.898080
$756$	4.11652	0.149717
$757$	−7.12245	−0.258870	−0.129435	−	0.991588i	$-0.541316\pi$
$757$	−7.12245	−0.258870	−0.129435	+	0.991588i	$0.541316\pi$
$758$	−28.8613	−1.04829
$759$	9.14725	0.332024
$760$	57.2437	2.07645
$761$	24.8606	0.901196	0.450598	−	0.892727i	$-0.351211\pi$
$761$	24.8606	0.901196	0.450598	+	0.892727i	$0.351211\pi$
$762$	−52.2972	−1.89453
$763$	−2.41223	−0.0873287
$764$	−56.7991	−2.05492
$765$	−2.97252	−0.107472
$766$	−63.5494	−2.29613
$767$	39.6763	1.43263
$768$	21.4177	0.772844
$769$	−10.8611	−0.391661	−0.195831	−	0.980638i	$-0.562740\pi$
$769$	−10.8611	−0.391661	−0.195831	+	0.980638i	$0.562740\pi$
$770$	−8.00122	−0.288344
$771$	62.6795	2.25735
$772$	−5.57236	−0.200554
$773$	37.4718	1.34777	0.673884	−	0.738837i	$-0.264625\pi$
$773$	37.4718	1.34777	0.673884	+	0.738837i	$0.264625\pi$
$774$	1.41502	0.0508618
$775$	−14.6676	−0.526875
$776$	66.7372	2.39573
$777$	−3.76302	−0.134998
$778$	−19.1710	−0.687315
$779$	27.0190	0.968055
$780$	−95.6587	−3.42513
$781$	74.7916	2.67625
$782$	−2.14527	−0.0767148
$783$	−2.22350	−0.0794613
$784$	−72.1218	−2.57578
$785$	−64.0404	−2.28570
$786$	59.4578	2.12079
$787$	17.8744	0.637155	0.318577	−	0.947897i	$-0.396795\pi$
$787$	17.8744	0.637155	0.318577	+	0.947897i	$0.396795\pi$
$788$	18.1668	0.647164
$789$	−10.7337	−0.382129
$790$	−25.1178	−0.893653
$791$	−2.69977	−0.0959928
$792$	41.8021	1.48537
$793$	−25.4228	−0.902791
$794$	28.5979	1.01490
$795$	4.29390	0.152289
$796$	−16.5197	−0.585526
$797$	−35.6080	−1.26130	−0.630649	−	0.776068i	$-0.717211\pi$
$797$	−35.6080	−1.26130	−0.630649	+	0.776068i	$0.717211\pi$
$798$	3.08692	0.109276
$799$	−8.56189	−0.302898
$800$	−46.6450	−1.64915
$801$	0.699986	0.0247328
$802$	52.1926	1.84298
$803$	−16.8430	−0.594378
$804$	−152.006	−5.36084
$805$	−0.683102	−0.0240762
$806$	−31.2997	−1.10249
$807$	31.6606	1.11451
$808$	22.0947	0.777287
$809$	26.1925	0.920881	0.460440	−	0.887691i	$-0.347692\pi$
$809$	26.1925	0.920881	0.460440	+	0.887691i	$0.347692\pi$
$810$	−87.7280	−3.08245
$811$	−31.0296	−1.08960	−0.544798	−	0.838567i	$-0.683394\pi$
$811$	−31.0296	−1.08960	−0.544798	+	0.838567i	$0.683394\pi$
$812$	−0.685439	−0.0240542
$813$	−46.4774	−1.63003
$814$	93.7288	3.28519
$815$	15.2892	0.535556
$816$	−17.3913	−0.608818
$817$	−1.09865	−0.0384370
$818$	−43.2679	−1.51283
$819$	−0.886057	−0.0309613
$820$	−159.073	−5.55508
$821$	20.9002	0.729422	0.364711	−	0.931121i	$-0.381168\pi$
$821$	20.9002	0.729422	0.364711	+	0.931121i	$0.381168\pi$
$822$	84.6353	2.95199
$823$	16.2708	0.567165	0.283583	−	0.958948i	$-0.408477\pi$
$823$	16.2708	0.567165	0.283583	+	0.958948i	$0.408477\pi$
$824$	32.2647	1.12400
$825$	35.7441	1.24445
$826$	7.53807	0.262283
$827$	23.9242	0.831928	0.415964	−	0.909381i	$-0.363444\pi$
$827$	23.9242	0.831928	0.415964	+	0.909381i	$0.363444\pi$
$828$	6.01172	0.208922
$829$	−1.51181	−0.0525075	−0.0262537	−	0.999655i	$-0.508358\pi$
$829$	−1.51181	−0.0525075	−0.0262537	+	0.999655i	$0.508358\pi$
$830$	−48.7826	−1.69327
$831$	19.3163	0.670074
$832$	−33.7347	−1.16954
$833$	−5.66510	−0.196284
$834$	−93.4045	−3.23433
$835$	−66.8186	−2.31235
$836$	−54.6723	−1.89088
$837$	−13.7165	−0.474112
$838$	−37.2137	−1.28553
$839$	19.9387	0.688360	0.344180	−	0.938904i	$-0.388157\pi$
$839$	19.9387	0.688360	0.344180	+	0.938904i	$0.388157\pi$
$840$	−10.7890	−0.372257
$841$	−28.6298	−0.987233
$842$	−6.76570	−0.233161
$843$	−14.5348	−0.500606
$844$	125.818	4.33082
$845$	8.81789	0.303344
$846$	33.7427	1.16010
$847$	2.01888	0.0693697
$848$	7.26894	0.249617
$849$	2.72179	0.0934117
$850$	−8.38294	−0.287533
$851$	8.00206	0.274307
$852$	169.883	5.82010
$853$	43.3645	1.48477	0.742385	−	0.669973i	$-0.233694\pi$
$853$	43.3645	1.48477	0.742385	+	0.669973i	$0.233694\pi$
$854$	−4.83007	−0.165281
$855$	−9.09563	−0.311064
$856$	36.2797	1.24001
$857$	48.0809	1.64241	0.821206	−	0.570632i	$-0.193302\pi$
$857$	48.0809	1.64241	0.821206	+	0.570632i	$0.193302\pi$
$858$	76.2759	2.60402
$859$	−16.5351	−0.564169	−0.282084	−	0.959390i	$-0.591026\pi$
$859$	−16.5351	−0.564169	−0.282084	+	0.959390i	$0.591026\pi$
$860$	6.46828	0.220566
$861$	−5.09241	−0.173549
$862$	104.314	3.55296
$863$	0.918753	0.0312747	0.0156374	−	0.999878i	$-0.495022\pi$
$863$	0.918753	0.0312747	0.0156374	+	0.999878i	$0.495022\pi$
$864$	−43.6205	−1.48400
$865$	0.688185	0.0233990
$866$	80.1900	2.72497
$867$	33.5624	1.13984
$868$	−4.22839	−0.143521
$869$	14.2413	0.483104
$870$	9.81656	0.332812
$871$	−47.6419	−1.61429
$872$	81.0180	2.74362
$873$	−10.6041	−0.358894
$874$	−6.56433	−0.222042
$875$	0.746197	0.0252261
$876$	−38.2576	−1.29260
$877$	−14.4453	−0.487782	−0.243891	−	0.969803i	$-0.578424\pi$
$877$	−14.4453	−0.487782	−0.243891	+	0.969803i	$0.578424\pi$
$878$	41.9283	1.41501
$879$	−65.2411	−2.20053
$880$	137.934	4.64977
$881$	32.9166	1.10899	0.554494	−	0.832188i	$-0.312912\pi$
$881$	32.9166	1.10899	0.554494	+	0.832188i	$0.312912\pi$
$882$	22.3264	0.751768
$883$	49.2930	1.65884	0.829420	−	0.558625i	$-0.188671\pi$
$883$	49.2930	1.65884	0.829420	+	0.558625i	$0.188671\pi$
$884$	−12.7199	−0.427818
$885$	−76.7638	−2.58039
$886$	6.39356	0.214796
$887$	−42.2438	−1.41841	−0.709204	−	0.705003i	$-0.750946\pi$
$887$	−42.2438	−1.41841	−0.709204	+	0.705003i	$0.750946\pi$
$888$	126.386	4.24123
$889$	−2.21433	−0.0742661
$890$	4.49997	0.150839
$891$	49.7401	1.66636
$892$	−116.616	−3.90460
$893$	−26.1986	−0.876702
$894$	−44.8664	−1.50056
$895$	39.3070	1.31389
$896$	−0.945035	−0.0315714
$897$	6.51203	0.217430
$898$	52.5789	1.75458
$899$	2.28392	0.0761731
$900$	23.4916	0.783053
$901$	0.570969	0.0190217
$902$	126.841	4.22334
$903$	0.207069	0.00689082
$904$	90.6754	3.01582
$905$	67.3346	2.23828
$906$	44.6939	1.48485
$907$	−42.6787	−1.41712	−0.708561	−	0.705650i	$-0.750655\pi$
$907$	−42.6787	−1.41712	−0.708561	+	0.705650i	$0.750655\pi$
$908$	−30.5894	−1.01514
$909$	−3.51069	−0.116442
$910$	−5.69616	−0.188826
$911$	20.8112	0.689507	0.344753	−	0.938693i	$-0.387963\pi$
$911$	20.8112	0.689507	0.344753	+	0.938693i	$0.387963\pi$
$912$	−53.2158	−1.76215
$913$	27.6588	0.915373
$914$	−1.64836	−0.0545230
$915$	49.1869	1.62607
$916$	−87.5841	−2.89386
$917$	2.51751	0.0831356
$918$	−7.83938	−0.258738
$919$	0.198263	0.00654009	0.00327005	−	0.999995i	$-0.498959\pi$
$919$	0.198263	0.00654009	0.00327005	+	0.999995i	$0.498959\pi$
$920$	22.9429	0.756404
$921$	8.83661	0.291176
$922$	−51.2700	−1.68849
$923$	53.2450	1.75258
$924$	10.3044	0.338989
$925$	31.2691	1.02812
$926$	−101.208	−3.32591
$927$	−5.12664	−0.168381
$928$	7.26321	0.238427
$929$	13.5423	0.444309	0.222155	−	0.975011i	$-0.428691\pi$
$929$	13.5423	0.444309	0.222155	+	0.975011i	$0.428691\pi$
$930$	60.5573	1.98575
$931$	−17.3347	−0.568121
$932$	−84.1457	−2.75629
$933$	28.7530	0.941331
$934$	88.4413	2.89389
$935$	10.8346	0.354330
$936$	29.7594	0.972716
$937$	−49.2146	−1.60777	−0.803885	−	0.594785i	$-0.797237\pi$
$937$	−49.2146	−1.60777	−0.803885	+	0.594785i	$0.797237\pi$
$938$	−9.05146	−0.295541
$939$	−20.4848	−0.668495
$940$	154.243	5.03086
$941$	25.0294	0.815935	0.407968	−	0.912996i	$-0.366238\pi$
$941$	25.0294	0.815935	0.407968	+	0.912996i	$0.366238\pi$
$942$	115.988	3.77910
$943$	10.8290	0.352641
$944$	−129.950	−4.22951
$945$	−2.49623	−0.0812024
$946$	−5.15764	−0.167689
$947$	−48.9624	−1.59106	−0.795532	−	0.605912i	$-0.792808\pi$
$947$	−48.9624	−1.59106	−0.795532	+	0.605912i	$0.792808\pi$
$948$	32.3480	1.05062
$949$	−11.9907	−0.389236
$950$	−25.6510	−0.832229
$951$	46.9834	1.52354
$952$	−1.43464	−0.0464969
$953$	38.3680	1.24286	0.621431	−	0.783469i	$-0.286552\pi$
$953$	38.3680	1.24286	0.621431	+	0.783469i	$0.286552\pi$
$954$	−2.25021	−0.0728532
$955$	34.4426	1.11454
$956$	−33.8416	−1.09452
$957$	−5.56580	−0.179917
$958$	−47.1629	−1.52377
$959$	3.58356	0.115719
$960$	65.2683	2.10652
$961$	−16.9107	−0.545508
$962$	66.7265	2.15135
$963$	−5.76459	−0.185761
$964$	−102.350	−3.29648
$965$	3.37904	0.108775
$966$	1.23721	0.0398067
$967$	−25.1060	−0.807356	−0.403678	−	0.914901i	$-0.632268\pi$
$967$	−25.1060	−0.807356	−0.403678	+	0.914901i	$0.632268\pi$
$968$	−67.8068	−2.17939
$969$	−4.18005	−0.134283
$970$	−68.1700	−2.18881
$971$	−6.37105	−0.204457	−0.102228	−	0.994761i	$-0.532597\pi$
$971$	−6.37105	−0.204457	−0.102228	+	0.994761i	$0.532597\pi$
$972$	59.0237	1.89318
$973$	−3.95486	−0.126787
$974$	0.338806	0.0108560
$975$	25.4466	0.814944
$976$	83.2662	2.66529
$977$	42.7400	1.36737	0.683686	−	0.729776i	$-0.260376\pi$
$977$	42.7400	1.36737	0.683686	+	0.729776i	$0.260376\pi$
$978$	−27.6913	−0.885470
$979$	−2.55140	−0.0815431
$980$	102.057	3.26010
$981$	−12.8732	−0.411010
$982$	41.2673	1.31689
$983$	−4.74542	−0.151356	−0.0756778	−	0.997132i	$-0.524112\pi$
$983$	−4.74542	−0.151356	−0.0756778	+	0.997132i	$0.524112\pi$
$984$	171.035	5.45240
$985$	−11.0162	−0.351005
$986$	1.30533	0.0415701
$987$	4.93779	0.157171
$988$	−38.9218	−1.23827
$989$	−0.440332	−0.0140017
$990$	−42.6996	−1.35708
$991$	−27.5281	−0.874460	−0.437230	−	0.899350i	$-0.644041\pi$
$991$	−27.5281	−0.874460	−0.437230	+	0.899350i	$0.644041\pi$
$992$	44.8060	1.42259
$993$	−54.7739	−1.73820
$994$	10.1160	0.320859
$995$	10.0174	0.317574
$996$	62.8247	1.99068
$997$	−17.2609	−0.546660	−0.273330	−	0.961920i	$-0.588125\pi$
$997$	−17.2609	−0.546660	−0.273330	+	0.961920i	$0.588125\pi$
$998$	8.87005	0.280776
$999$	29.2416	0.925163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.8	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.8	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +O(q^{10})\)	\(q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +7.85221 q^{10} -4.45205 q^{11} -10.1125 q^{12} -3.16946 q^{13} -0.602164 q^{14} +6.13213 q^{15} +10.3808 q^{16} +0.815402 q^{17} -3.21353 q^{18} +2.49505 q^{19} -14.6895 q^{20} -0.470256 q^{21} +11.7131 q^{22} +1.00000 q^{23} +15.7942 q^{24} +3.90763 q^{25} +8.33867 q^{26} +3.65426 q^{27} +1.12650 q^{28} -0.608467 q^{29} -16.1333 q^{30} -3.75357 q^{31} -11.9369 q^{32} +9.14725 q^{33} -2.14527 q^{34} -0.683102 q^{35} +6.01172 q^{36} +8.00206 q^{37} -6.56433 q^{38} +6.51203 q^{39} +22.9429 q^{40} +10.8290 q^{41} +1.23721 q^{42} -0.440332 q^{43} -21.9123 q^{44} -3.64546 q^{45} -2.63094 q^{46} -10.5002 q^{47} -21.3285 q^{48} -6.94761 q^{49} -10.2807 q^{50} -1.67534 q^{51} -15.5996 q^{52} +0.700230 q^{53} -9.61413 q^{54} +13.2874 q^{55} -1.75943 q^{56} -5.12637 q^{57} +1.60084 q^{58} -12.5183 q^{59} +30.1813 q^{60} +8.02118 q^{61} +9.87540 q^{62} +0.279560 q^{63} +10.6437 q^{64} +9.45948 q^{65} -24.0659 q^{66} +15.0315 q^{67} +4.01328 q^{68} -2.05461 q^{69} +1.79720 q^{70} -16.7994 q^{71} -9.38940 q^{72} +3.78320 q^{73} -21.0529 q^{74} -8.02868 q^{75} +12.2802 q^{76} -1.01898 q^{77} -17.1327 q^{78} -3.19883 q^{79} -30.9822 q^{80} -11.1724 q^{81} -28.4905 q^{82} -6.21259 q^{83} -2.31452 q^{84} -2.43362 q^{85} +1.15849 q^{86} +1.25017 q^{87} +34.2237 q^{88} +0.573084 q^{89} +9.59099 q^{90} -0.725421 q^{91} +4.92184 q^{92} +7.71213 q^{93} +27.6254 q^{94} -7.44665 q^{95} +24.5257 q^{96} -8.68164 q^{97} +18.2787 q^{98} -5.43791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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