LMFDB - Embedded newform 7935.2.a.bv.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02762 q^{2} +1.00000 q^{3} +2.11124 q^{4} -1.00000 q^{5} +2.02762 q^{6} -3.74723 q^{7} +0.225557 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.02762 q^{2} +1.00000 q^{3} +2.11124 q^{4} -1.00000 q^{5} +2.02762 q^{6} -3.74723 q^{7} +0.225557 q^{8} +1.00000 q^{9} -2.02762 q^{10} +5.54012 q^{11} +2.11124 q^{12} +3.99911 q^{13} -7.59797 q^{14} -1.00000 q^{15} -3.76514 q^{16} -5.08479 q^{17} +2.02762 q^{18} -1.91795 q^{19} -2.11124 q^{20} -3.74723 q^{21} +11.2333 q^{22} +0.225557 q^{24} +1.00000 q^{25} +8.10867 q^{26} +1.00000 q^{27} -7.91132 q^{28} +5.51494 q^{29} -2.02762 q^{30} +0.180727 q^{31} -8.08539 q^{32} +5.54012 q^{33} -10.3100 q^{34} +3.74723 q^{35} +2.11124 q^{36} +4.47520 q^{37} -3.88888 q^{38} +3.99911 q^{39} -0.225557 q^{40} +11.6419 q^{41} -7.59797 q^{42} +5.14813 q^{43} +11.6965 q^{44} -1.00000 q^{45} +3.81812 q^{47} -3.76514 q^{48} +7.04177 q^{49} +2.02762 q^{50} -5.08479 q^{51} +8.44309 q^{52} +2.53491 q^{53} +2.02762 q^{54} -5.54012 q^{55} -0.845214 q^{56} -1.91795 q^{57} +11.1822 q^{58} -14.2665 q^{59} -2.11124 q^{60} -6.52519 q^{61} +0.366446 q^{62} -3.74723 q^{63} -8.86381 q^{64} -3.99911 q^{65} +11.2333 q^{66} +6.37395 q^{67} -10.7352 q^{68} +7.59797 q^{70} +11.9254 q^{71} +0.225557 q^{72} +13.7895 q^{73} +9.07400 q^{74} +1.00000 q^{75} -4.04927 q^{76} -20.7601 q^{77} +8.10867 q^{78} +5.17557 q^{79} +3.76514 q^{80} +1.00000 q^{81} +23.6054 q^{82} +8.33535 q^{83} -7.91132 q^{84} +5.08479 q^{85} +10.4385 q^{86} +5.51494 q^{87} +1.24961 q^{88} -2.12827 q^{89} -2.02762 q^{90} -14.9856 q^{91} +0.180727 q^{93} +7.74169 q^{94} +1.91795 q^{95} -8.08539 q^{96} +17.8630 q^{97} +14.2780 q^{98} +5.54012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19} - 31 q^{20} - 7 q^{21} - 9 q^{22} + 33 q^{24} + 25 q^{25} + 35 q^{26} + 25 q^{27} + 5 q^{28} + 33 q^{29} - 11 q^{30} + 14 q^{31} + 77 q^{32} - 9 q^{33} - 13 q^{34} + 7 q^{35} + 31 q^{36} - 4 q^{37} + 23 q^{38} + 18 q^{39} - 33 q^{40} + 56 q^{41} - 11 q^{42} + 4 q^{43} + 18 q^{44} - 25 q^{45} + 43 q^{47} + 39 q^{48} + 40 q^{49} + 11 q^{50} + 8 q^{51} + 49 q^{52} - 2 q^{53} + 11 q^{54} + 9 q^{55} - 33 q^{56} - 11 q^{57} + 26 q^{58} + 61 q^{59} - 31 q^{60} - 21 q^{61} + 51 q^{62} - 7 q^{63} + 71 q^{64} - 18 q^{65} - 9 q^{66} - 2 q^{67} + 33 q^{68} + 11 q^{70} + 66 q^{71} + 33 q^{72} + 53 q^{73} + 47 q^{74} + 25 q^{75} + 8 q^{76} + 49 q^{77} + 35 q^{78} - 35 q^{79} - 39 q^{80} + 25 q^{81} + 35 q^{82} + 26 q^{83} + 5 q^{84} - 8 q^{85} + 33 q^{86} + 33 q^{87} - 9 q^{88} + 7 q^{89} - 11 q^{90} - 28 q^{91} + 14 q^{93} + 24 q^{94} + 11 q^{95} + 77 q^{96} + 54 q^{97} + 88 q^{98} - 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * 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 $

$2$	2.02762	1.43374	0.716872	−	0.697205i	$-0.245573\pi$
$2$	2.02762	1.43374	0.716872	+	0.697205i	$0.245573\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.11124	1.05562
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.02762	0.827772
$7$	−3.74723	−1.41632	−0.708161	−	0.706051i	$-0.750475\pi$
$7$	−3.74723	−1.41632	−0.708161	+	0.706051i	$0.750475\pi$
$8$	0.225557	0.0797464
$9$	1.00000	0.333333
$10$	−2.02762	−0.641190
$11$	5.54012	1.67041	0.835205	−	0.549939i	$-0.185349\pi$
$11$	5.54012	1.67041	0.835205	+	0.549939i	$0.185349\pi$
$12$	2.11124	0.609463
$13$	3.99911	1.10915	0.554577	−	0.832133i	$-0.312880\pi$
$13$	3.99911	1.10915	0.554577	+	0.832133i	$0.312880\pi$
$14$	−7.59797	−2.03064
$15$	−1.00000	−0.258199
$16$	−3.76514	−0.941285
$17$	−5.08479	−1.23324	−0.616621	−	0.787260i	$-0.711499\pi$
$17$	−5.08479	−1.23324	−0.616621	+	0.787260i	$0.711499\pi$
$18$	2.02762	0.477915
$19$	−1.91795	−0.440009	−0.220004	−	0.975499i	$-0.570607\pi$
$19$	−1.91795	−0.440009	−0.220004	+	0.975499i	$0.570607\pi$
$20$	−2.11124	−0.472088
$21$	−3.74723	−0.817714
$22$	11.2333	2.39494
$23$	0	0
$23$	0	0
$24$	0.225557	0.0460416
$25$	1.00000	0.200000
$26$	8.10867	1.59024
$27$	1.00000	0.192450
$28$	−7.91132	−1.49510
$29$	5.51494	1.02410	0.512049	−	0.858956i	$-0.328887\pi$
$29$	5.51494	1.02410	0.512049	+	0.858956i	$0.328887\pi$
$30$	−2.02762	−0.370191
$31$	0.180727	0.0324595	0.0162298	−	0.999868i	$-0.494834\pi$
$31$	0.180727	0.0324595	0.0162298	+	0.999868i	$0.494834\pi$
$32$	−8.08539	−1.42931
$33$	5.54012	0.964412
$34$	−10.3100	−1.76815
$35$	3.74723	0.633398
$36$	2.11124	0.351874
$37$	4.47520	0.735718	0.367859	−	0.929882i	$-0.380091\pi$
$37$	4.47520	0.735718	0.367859	+	0.929882i	$0.380091\pi$
$38$	−3.88888	−0.630860
$39$	3.99911	0.640370
$40$	−0.225557	−0.0356637
$41$	11.6419	1.81817	0.909083	−	0.416615i	$-0.136784\pi$
$41$	11.6419	1.81817	0.909083	+	0.416615i	$0.136784\pi$
$42$	−7.59797	−1.17239
$43$	5.14813	0.785083	0.392541	−	0.919734i	$-0.371596\pi$
$43$	5.14813	0.785083	0.392541	+	0.919734i	$0.371596\pi$
$44$	11.6965	1.76332
$45$	−1.00000	−0.149071
$46$	0	0
$47$	3.81812	0.556930	0.278465	−	0.960446i	$-0.410174\pi$
$47$	3.81812	0.556930	0.278465	+	0.960446i	$0.410174\pi$
$48$	−3.76514	−0.543451
$49$	7.04177	1.00597
$50$	2.02762	0.286749
$51$	−5.08479	−0.712013
$52$	8.44309	1.17085
$53$	2.53491	0.348197	0.174099	−	0.984728i	$-0.444299\pi$
$53$	2.53491	0.348197	0.174099	+	0.984728i	$0.444299\pi$
$54$	2.02762	0.275924
$55$	−5.54012	−0.747030
$56$	−0.845214	−0.112947
$57$	−1.91795	−0.254039
$58$	11.1822	1.46829
$59$	−14.2665	−1.85734	−0.928671	−	0.370905i	$-0.879048\pi$
$59$	−14.2665	−1.85734	−0.928671	+	0.370905i	$0.879048\pi$
$60$	−2.11124	−0.272560
$61$	−6.52519	−0.835465	−0.417733	−	0.908570i	$-0.637175\pi$
$61$	−6.52519	−0.835465	−0.417733	+	0.908570i	$0.637175\pi$
$62$	0.366446	0.0465386
$63$	−3.74723	−0.472107
$64$	−8.86381	−1.10798
$65$	−3.99911	−0.496029
$66$	11.2333	1.38272
$67$	6.37395	0.778701	0.389351	−	0.921090i	$-0.372699\pi$
$67$	6.37395	0.778701	0.389351	+	0.921090i	$0.372699\pi$
$68$	−10.7352	−1.30184
$69$	0	0
$70$	7.59797	0.908131
$71$	11.9254	1.41529	0.707643	−	0.706570i	$-0.249758\pi$
$71$	11.9254	1.41529	0.707643	+	0.706570i	$0.249758\pi$
$72$	0.225557	0.0265821
$73$	13.7895	1.61394	0.806972	−	0.590590i	$-0.201105\pi$
$73$	13.7895	1.61394	0.806972	+	0.590590i	$0.201105\pi$
$74$	9.07400	1.05483
$75$	1.00000	0.115470
$76$	−4.04927	−0.464483
$77$	−20.7601	−2.36584
$78$	8.10867	0.918127
$79$	5.17557	0.582297	0.291148	−	0.956678i	$-0.405963\pi$
$79$	5.17557	0.582297	0.291148	+	0.956678i	$0.405963\pi$
$80$	3.76514	0.420956
$81$	1.00000	0.111111
$82$	23.6054	2.60678
$83$	8.33535	0.914924	0.457462	−	0.889229i	$-0.348759\pi$
$83$	8.33535	0.914924	0.457462	+	0.889229i	$0.348759\pi$
$84$	−7.91132	−0.863196
$85$	5.08479	0.551523
$86$	10.4385	1.12561
$87$	5.51494	0.591263
$88$	1.24961	0.133209
$89$	−2.12827	−0.225596	−0.112798	−	0.993618i	$-0.535981\pi$
$89$	−2.12827	−0.225596	−0.112798	+	0.993618i	$0.535981\pi$
$90$	−2.02762	−0.213730
$91$	−14.9856	−1.57092
$92$	0	0
$93$	0.180727	0.0187405
$94$	7.74169	0.798494
$95$	1.91795	0.196778
$96$	−8.08539	−0.825211
$97$	17.8630	1.81372	0.906858	−	0.421437i	$-0.138474\pi$
$97$	17.8630	1.81372	0.906858	+	0.421437i	$0.138474\pi$
$98$	14.2780	1.44230
$99$	5.54012	0.556803
$100$	2.11124	0.211124
$101$	7.81909	0.778029	0.389014	−	0.921232i	$-0.372816\pi$
$101$	7.81909	0.778029	0.389014	+	0.921232i	$0.372816\pi$
$102$	−10.3100	−1.02084
$103$	−0.654104	−0.0644508	−0.0322254	−	0.999481i	$-0.510259\pi$
$103$	−0.654104	−0.0644508	−0.0322254	+	0.999481i	$0.510259\pi$
$104$	0.902027	0.0884510
$105$	3.74723	0.365693
$106$	5.13984	0.499226
$107$	−9.19476	−0.888891	−0.444445	−	0.895806i	$-0.646599\pi$
$107$	−9.19476	−0.888891	−0.444445	+	0.895806i	$0.646599\pi$
$108$	2.11124	0.203154
$109$	−6.48841	−0.621477	−0.310739	−	0.950495i	$-0.600576\pi$
$109$	−6.48841	−0.621477	−0.310739	+	0.950495i	$0.600576\pi$
$110$	−11.2333	−1.07105
$111$	4.47520	0.424767
$112$	14.1089	1.33316
$113$	−3.94364	−0.370986	−0.185493	−	0.982646i	$-0.559388\pi$
$113$	−3.94364	−0.370986	−0.185493	+	0.982646i	$0.559388\pi$
$114$	−3.88888	−0.364227
$115$	0	0
$116$	11.6434	1.08106
$117$	3.99911	0.369718
$118$	−28.9271	−2.66295
$119$	19.0539	1.74667
$120$	−0.225557	−0.0205904
$121$	19.6930	1.79027
$122$	−13.2306	−1.19784
$123$	11.6419	1.04972
$124$	0.381558	0.0342649
$125$	−1.00000	−0.0894427
$126$	−7.59797	−0.676881
$127$	−12.4294	−1.10293	−0.551464	−	0.834199i	$-0.685931\pi$
$127$	−12.4294	−1.10293	−0.551464	+	0.834199i	$0.685931\pi$
$128$	−1.80166	−0.159246
$129$	5.14813	0.453268
$130$	−8.10867	−0.711178
$131$	7.58137	0.662388	0.331194	−	0.943563i	$-0.392549\pi$
$131$	7.58137	0.662388	0.331194	+	0.943563i	$0.392549\pi$
$132$	11.6965	1.01805
$133$	7.18703	0.623194
$134$	12.9239	1.11646
$135$	−1.00000	−0.0860663
$136$	−1.14691	−0.0983466
$137$	11.5462	0.986458	0.493229	−	0.869900i	$-0.335816\pi$
$137$	11.5462	0.986458	0.493229	+	0.869900i	$0.335816\pi$
$138$	0	0
$139$	−9.56690	−0.811454	−0.405727	−	0.913994i	$-0.632982\pi$
$139$	−9.56690	−0.811454	−0.405727	+	0.913994i	$0.632982\pi$
$140$	7.91132	0.668629
$141$	3.81812	0.321543
$142$	24.1802	2.02916
$143$	22.1556	1.85274
$144$	−3.76514	−0.313762
$145$	−5.51494	−0.457991
$146$	27.9599	2.31398
$147$	7.04177	0.580795
$148$	9.44822	0.776639
$149$	−19.2208	−1.57463	−0.787316	−	0.616550i	$-0.788530\pi$
$149$	−19.2208	−1.57463	−0.787316	+	0.616550i	$0.788530\pi$
$150$	2.02762	0.165554
$151$	−2.96179	−0.241027	−0.120514	−	0.992712i	$-0.538454\pi$
$151$	−2.96179	−0.241027	−0.120514	+	0.992712i	$0.538454\pi$
$152$	−0.432608	−0.0350891
$153$	−5.08479	−0.411081
$154$	−42.0937	−3.39201
$155$	−0.180727	−0.0145163
$156$	8.44309	0.675988
$157$	−5.85555	−0.467324	−0.233662	−	0.972318i	$-0.575071\pi$
$157$	−5.85555	−0.467324	−0.233662	+	0.972318i	$0.575071\pi$
$158$	10.4941	0.834865
$159$	2.53491	0.201032
$160$	8.08539	0.639206
$161$	0	0
$162$	2.02762	0.159305
$163$	2.35945	0.184806	0.0924032	−	0.995722i	$-0.470545\pi$
$163$	2.35945	0.184806	0.0924032	+	0.995722i	$0.470545\pi$
$164$	24.5790	1.91929
$165$	−5.54012	−0.431298
$166$	16.9009	1.31177
$167$	24.0128	1.85817	0.929085	−	0.369866i	$-0.120597\pi$
$167$	24.0128	1.85817	0.929085	+	0.369866i	$0.120597\pi$
$168$	−0.845214	−0.0652097
$169$	2.99288	0.230222
$170$	10.3100	0.790742
$171$	−1.91795	−0.146670
$172$	10.8690	0.828750
$173$	6.66865	0.507008	0.253504	−	0.967334i	$-0.418417\pi$
$173$	6.66865	0.507008	0.253504	+	0.967334i	$0.418417\pi$
$174$	11.1822	0.847720
$175$	−3.74723	−0.283264
$176$	−20.8593	−1.57233
$177$	−14.2665	−1.07234
$178$	−4.31533	−0.323447
$179$	−20.6930	−1.54666	−0.773332	−	0.634001i	$-0.781411\pi$
$179$	−20.6930	−1.54666	−0.773332	+	0.634001i	$0.781411\pi$
$180$	−2.11124	−0.157363
$181$	16.6541	1.23789	0.618945	−	0.785434i	$-0.287560\pi$
$181$	16.6541	1.23789	0.618945	+	0.785434i	$0.287560\pi$
$182$	−30.3851	−2.25229
$183$	−6.52519	−0.482356
$184$	0	0
$185$	−4.47520	−0.329023
$186$	0.366446	0.0268691
$187$	−28.1703	−2.06002
$188$	8.06097	0.587907
$189$	−3.74723	−0.272571
$190$	3.88888	0.282129
$191$	−13.4289	−0.971678	−0.485839	−	0.874048i	$-0.661486\pi$
$191$	−13.4289	−0.971678	−0.485839	+	0.874048i	$0.661486\pi$
$192$	−8.86381	−0.639690
$193$	−5.00489	−0.360260	−0.180130	−	0.983643i	$-0.557652\pi$
$193$	−5.00489	−0.360260	−0.180130	+	0.983643i	$0.557652\pi$
$194$	36.2194	2.60040
$195$	−3.99911	−0.286382
$196$	14.8669	1.06192
$197$	−11.9382	−0.850560	−0.425280	−	0.905062i	$-0.639824\pi$
$197$	−11.9382	−0.850560	−0.425280	+	0.905062i	$0.639824\pi$
$198$	11.2333	0.798313
$199$	21.2282	1.50482	0.752412	−	0.658693i	$-0.228890\pi$
$199$	21.2282	1.50482	0.752412	+	0.658693i	$0.228890\pi$
$200$	0.225557	0.0159493
$201$	6.37395	0.449583
$202$	15.8541	1.11549
$203$	−20.6658	−1.45045
$204$	−10.7352	−0.751615
$205$	−11.6419	−0.813109
$206$	−1.32628	−0.0924060
$207$	0	0
$208$	−15.0572	−1.04403
$209$	−10.6257	−0.734995
$210$	7.59797	0.524310
$211$	−4.40100	−0.302978	−0.151489	−	0.988459i	$-0.548407\pi$
$211$	−4.40100	−0.302978	−0.151489	+	0.988459i	$0.548407\pi$
$212$	5.35182	0.367564
$213$	11.9254	0.817116
$214$	−18.6435	−1.27444
$215$	−5.14813	−0.351100
$216$	0.225557	0.0153472
$217$	−0.677226	−0.0459731
$218$	−13.1560	−0.891039
$219$	13.7895	0.931811
$220$	−11.6965	−0.788581
$221$	−20.3346	−1.36785
$222$	9.07400	0.609007
$223$	−2.58548	−0.173136	−0.0865682	−	0.996246i	$-0.527590\pi$
$223$	−2.58548	−0.173136	−0.0865682	+	0.996246i	$0.527590\pi$
$224$	30.2978	2.02436
$225$	1.00000	0.0666667
$226$	−7.99620	−0.531899
$227$	−0.945689	−0.0627676	−0.0313838	−	0.999507i	$-0.509991\pi$
$227$	−0.945689	−0.0627676	−0.0313838	+	0.999507i	$0.509991\pi$
$228$	−4.04927	−0.268169
$229$	5.56690	0.367871	0.183936	−	0.982938i	$-0.441116\pi$
$229$	5.56690	0.367871	0.183936	+	0.982938i	$0.441116\pi$
$230$	0	0
$231$	−20.7601	−1.36592
$232$	1.24393	0.0816681
$233$	26.2039	1.71667	0.858337	−	0.513086i	$-0.171498\pi$
$233$	26.2039	1.71667	0.858337	+	0.513086i	$0.171498\pi$
$234$	8.10867	0.530081
$235$	−3.81812	−0.249066
$236$	−30.1201	−1.96065
$237$	5.17557	0.336189
$238$	38.6340	2.50427
$239$	−23.7072	−1.53349	−0.766746	−	0.641951i	$-0.778125\pi$
$239$	−23.7072	−1.53349	−0.766746	+	0.641951i	$0.778125\pi$
$240$	3.76514	0.243039
$241$	22.5768	1.45430	0.727149	−	0.686480i	$-0.240845\pi$
$241$	22.5768	1.45430	0.727149	+	0.686480i	$0.240845\pi$
$242$	39.9299	2.56679
$243$	1.00000	0.0641500
$244$	−13.7763	−0.881935
$245$	−7.04177	−0.449882
$246$	23.6054	1.50503
$247$	−7.67011	−0.488037
$248$	0.0407642	0.00258853
$249$	8.33535	0.528231
$250$	−2.02762	−0.128238
$251$	27.5129	1.73660	0.868299	−	0.496041i	$-0.165214\pi$
$251$	27.5129	1.73660	0.868299	+	0.496041i	$0.165214\pi$
$252$	−7.91132	−0.498366
$253$	0	0
$254$	−25.2020	−1.58132
$255$	5.08479	0.318422
$256$	14.0745	0.879658
$257$	14.6307	0.912639	0.456320	−	0.889816i	$-0.349167\pi$
$257$	14.6307	0.912639	0.456320	+	0.889816i	$0.349167\pi$
$258$	10.4385	0.649870
$259$	−16.7696	−1.04201
$260$	−8.44309	−0.523618
$261$	5.51494	0.341366
$262$	15.3721	0.949694
$263$	−0.128839	−0.00794457	−0.00397228	−	0.999992i	$-0.501264\pi$
$263$	−0.128839	−0.00794457	−0.00397228	+	0.999992i	$0.501264\pi$
$264$	1.24961	0.0769084
$265$	−2.53491	−0.155719
$266$	14.5726	0.893501
$267$	−2.12827	−0.130248
$268$	13.4569	0.822014
$269$	−9.12102	−0.556118	−0.278059	−	0.960564i	$-0.589691\pi$
$269$	−9.12102	−0.556118	−0.278059	+	0.960564i	$0.589691\pi$
$270$	−2.02762	−0.123397
$271$	−14.3703	−0.872936	−0.436468	−	0.899720i	$-0.643771\pi$
$271$	−14.3703	−0.872936	−0.436468	+	0.899720i	$0.643771\pi$
$272$	19.1449	1.16083
$273$	−14.9856	−0.906970
$274$	23.4113	1.41433
$275$	5.54012	0.334082
$276$	0	0
$277$	14.3468	0.862016	0.431008	−	0.902348i	$-0.358158\pi$
$277$	14.3468	0.862016	0.431008	+	0.902348i	$0.358158\pi$
$278$	−19.3980	−1.16342
$279$	0.180727	0.0108198
$280$	0.845214	0.0505112
$281$	−7.85936	−0.468850	−0.234425	−	0.972134i	$-0.575321\pi$
$281$	−7.85936	−0.468850	−0.234425	+	0.972134i	$0.575321\pi$
$282$	7.74169	0.461011
$283$	4.67600	0.277959	0.138980	−	0.990295i	$-0.455618\pi$
$283$	4.67600	0.277959	0.138980	+	0.990295i	$0.455618\pi$
$284$	25.1774	1.49401
$285$	1.91795	0.113610
$286$	44.9231	2.65636
$287$	−43.6251	−2.57511
$288$	−8.08539	−0.476436
$289$	8.85506	0.520886
$290$	−11.1822	−0.656641
$291$	17.8630	1.04715
$292$	29.1131	1.70371
$293$	−23.3022	−1.36133	−0.680665	−	0.732595i	$-0.738309\pi$
$293$	−23.3022	−1.36133	−0.680665	+	0.732595i	$0.738309\pi$
$294$	14.2780	0.832712
$295$	14.2665	0.830629
$296$	1.00941	0.0586708
$297$	5.54012	0.321471
$298$	−38.9725	−2.25762
$299$	0	0
$300$	2.11124	0.121893
$301$	−19.2913	−1.11193
$302$	−6.00539	−0.345571
$303$	7.81909	0.449195
$304$	7.22137	0.414174
$305$	6.52519	0.373631
$306$	−10.3100	−0.589384
$307$	−6.20849	−0.354337	−0.177169	−	0.984180i	$-0.556694\pi$
$307$	−6.20849	−0.354337	−0.177169	+	0.984180i	$0.556694\pi$
$308$	−43.8297	−2.49743
$309$	−0.654104	−0.0372107
$310$	−0.366446	−0.0208127
$311$	−0.808340	−0.0458368	−0.0229184	−	0.999737i	$-0.507296\pi$
$311$	−0.808340	−0.0458368	−0.0229184	+	0.999737i	$0.507296\pi$
$312$	0.902027	0.0510672
$313$	2.53203	0.143119	0.0715594	−	0.997436i	$-0.477202\pi$
$313$	2.53203	0.143119	0.0715594	+	0.997436i	$0.477202\pi$
$314$	−11.8728	−0.670023
$315$	3.74723	0.211133
$316$	10.9269	0.614685
$317$	−16.5538	−0.929753	−0.464877	−	0.885375i	$-0.653901\pi$
$317$	−16.5538	−0.929753	−0.464877	+	0.885375i	$0.653901\pi$
$318$	5.13984	0.288228
$319$	30.5534	1.71066
$320$	8.86381	0.495502
$321$	−9.19476	−0.513201
$322$	0	0
$323$	9.75239	0.542637
$324$	2.11124	0.117291
$325$	3.99911	0.221831
$326$	4.78407	0.264965
$327$	−6.48841	−0.358810
$328$	2.62592	0.144992
$329$	−14.3074	−0.788791
$330$	−11.2333	−0.618371
$331$	−10.5541	−0.580106	−0.290053	−	0.957011i	$-0.593673\pi$
$331$	−10.5541	−0.580106	−0.290053	+	0.957011i	$0.593673\pi$
$332$	17.5979	0.965813
$333$	4.47520	0.245239
$334$	48.6889	2.66414
$335$	−6.37395	−0.348246
$336$	14.1089	0.769702
$337$	9.01095	0.490858	0.245429	−	0.969415i	$-0.421071\pi$
$337$	9.01095	0.490858	0.245429	+	0.969415i	$0.421071\pi$
$338$	6.06843	0.330079
$339$	−3.94364	−0.214189
$340$	10.7352	0.582199
$341$	1.00125	0.0542207
$342$	−3.88888	−0.210287
$343$	−0.156518	−0.00845119
$344$	1.16120	0.0626075
$345$	0	0
$346$	13.5215	0.726920
$347$	9.15392	0.491408	0.245704	−	0.969345i	$-0.420981\pi$
$347$	9.15392	0.491408	0.245704	+	0.969345i	$0.420981\pi$
$348$	11.6434	0.624150
$349$	−22.8061	−1.22078	−0.610391	−	0.792100i	$-0.708988\pi$
$349$	−22.8061	−1.22078	−0.610391	+	0.792100i	$0.708988\pi$
$350$	−7.59797	−0.406128
$351$	3.99911	0.213457
$352$	−44.7941	−2.38753
$353$	7.03899	0.374647	0.187324	−	0.982298i	$-0.440019\pi$
$353$	7.03899	0.374647	0.187324	+	0.982298i	$0.440019\pi$
$354$	−28.9271	−1.53746
$355$	−11.9254	−0.632936
$356$	−4.49330	−0.238144
$357$	19.0539	1.00844
$358$	−41.9574	−2.21752
$359$	8.13938	0.429580	0.214790	−	0.976660i	$-0.431093\pi$
$359$	8.13938	0.429580	0.214790	+	0.976660i	$0.431093\pi$
$360$	−0.225557	−0.0118879
$361$	−15.3215	−0.806392
$362$	33.7682	1.77482
$363$	19.6930	1.03361
$364$	−31.6382	−1.65829
$365$	−13.7895	−0.721777
$366$	−13.2306	−0.691575
$367$	−5.89080	−0.307497	−0.153749	−	0.988110i	$-0.549135\pi$
$367$	−5.89080	−0.307497	−0.153749	+	0.988110i	$0.549135\pi$
$368$	0	0
$369$	11.6419	0.606055
$370$	−9.07400	−0.471735
$371$	−9.49892	−0.493159
$372$	0.381558	0.0197829
$373$	16.7345	0.866482	0.433241	−	0.901278i	$-0.357370\pi$
$373$	16.7345	0.866482	0.433241	+	0.901278i	$0.357370\pi$
$374$	−57.1188	−2.95354
$375$	−1.00000	−0.0516398
$376$	0.861202	0.0444131
$377$	22.0548	1.13588
$378$	−7.59797	−0.390797
$379$	−16.4659	−0.845796	−0.422898	−	0.906177i	$-0.638987\pi$
$379$	−16.4659	−0.845796	−0.422898	+	0.906177i	$0.638987\pi$
$380$	4.04927	0.207723
$381$	−12.4294	−0.636776
$382$	−27.2286	−1.39314
$383$	5.03802	0.257431	0.128715	−	0.991682i	$-0.458915\pi$
$383$	5.03802	0.257431	0.128715	+	0.991682i	$0.458915\pi$
$384$	−1.80166	−0.0919408
$385$	20.7601	1.05803
$386$	−10.1480	−0.516520
$387$	5.14813	0.261694
$388$	37.7132	1.91460
$389$	−7.19488	−0.364795	−0.182398	−	0.983225i	$-0.558386\pi$
$389$	−7.19488	−0.364795	−0.182398	+	0.983225i	$0.558386\pi$
$390$	−8.10867	−0.410599
$391$	0	0
$392$	1.58832	0.0802222
$393$	7.58137	0.382430
$394$	−24.2061	−1.21949
$395$	−5.17557	−0.260411
$396$	11.6965	0.587773
$397$	27.9630	1.40342	0.701711	−	0.712461i	$-0.252420\pi$
$397$	27.9630	1.40342	0.701711	+	0.712461i	$0.252420\pi$
$398$	43.0426	2.15753
$399$	7.18703	0.359801
$400$	−3.76514	−0.188257
$401$	−29.8538	−1.49083	−0.745415	−	0.666601i	$-0.767749\pi$
$401$	−29.8538	−1.49083	−0.745415	+	0.666601i	$0.767749\pi$
$402$	12.9239	0.644587
$403$	0.722747	0.0360026
$404$	16.5080	0.821304
$405$	−1.00000	−0.0496904
$406$	−41.9023	−2.07958
$407$	24.7931	1.22895
$408$	−1.14691	−0.0567804
$409$	−5.19480	−0.256866	−0.128433	−	0.991718i	$-0.540995\pi$
$409$	−5.19480	−0.256866	−0.128433	+	0.991718i	$0.540995\pi$
$410$	−23.6054	−1.16579
$411$	11.5462	0.569532
$412$	−1.38097	−0.0680356
$413$	53.4600	2.63059
$414$	0	0
$415$	−8.33535	−0.409166
$416$	−32.3344	−1.58532
$417$	−9.56690	−0.468493
$418$	−21.5449	−1.05380
$419$	−3.88691	−0.189888	−0.0949440	−	0.995483i	$-0.530267\pi$
$419$	−3.88691	−0.189888	−0.0949440	+	0.995483i	$0.530267\pi$
$420$	7.91132	0.386033
$421$	−5.65313	−0.275517	−0.137758	−	0.990466i	$-0.543990\pi$
$421$	−5.65313	−0.275517	−0.137758	+	0.990466i	$0.543990\pi$
$422$	−8.92356	−0.434392
$423$	3.81812	0.185643
$424$	0.571767	0.0277675
$425$	−5.08479	−0.246648
$426$	24.1802	1.17154
$427$	24.4514	1.18329
$428$	−19.4124	−0.938332
$429$	22.1556	1.06968
$430$	−10.4385	−0.503387
$431$	27.1135	1.30601	0.653006	−	0.757353i	$-0.273508\pi$
$431$	27.1135	1.30601	0.653006	+	0.757353i	$0.273508\pi$
$432$	−3.76514	−0.181150
$433$	31.2260	1.50063	0.750313	−	0.661082i	$-0.229903\pi$
$433$	31.2260	1.50063	0.750313	+	0.661082i	$0.229903\pi$
$434$	−1.37316	−0.0659137
$435$	−5.51494	−0.264421
$436$	−13.6986	−0.656045
$437$	0	0
$438$	27.9599	1.33598
$439$	20.9748	1.00107	0.500535	−	0.865716i	$-0.333137\pi$
$439$	20.9748	1.00107	0.500535	+	0.865716i	$0.333137\pi$
$440$	−1.24961	−0.0595730
$441$	7.04177	0.335322
$442$	−41.2309	−1.96115
$443$	−7.16129	−0.340243	−0.170122	−	0.985423i	$-0.554416\pi$
$443$	−7.16129	−0.340243	−0.170122	+	0.985423i	$0.554416\pi$
$444$	9.44822	0.448393
$445$	2.12827	0.100890
$446$	−5.24237	−0.248233
$447$	−19.2208	−0.909114
$448$	33.2148	1.56925
$449$	13.0654	0.616594	0.308297	−	0.951290i	$-0.400241\pi$
$449$	13.0654	0.616594	0.308297	+	0.951290i	$0.400241\pi$
$450$	2.02762	0.0955829
$451$	64.4978	3.03708
$452$	−8.32598	−0.391621
$453$	−2.96179	−0.139157
$454$	−1.91750	−0.0899926
$455$	14.9856	0.702536
$456$	−0.432608	−0.0202587
$457$	−16.7402	−0.783074	−0.391537	−	0.920162i	$-0.628057\pi$
$457$	−16.7402	−0.783074	−0.391537	+	0.920162i	$0.628057\pi$
$458$	11.2876	0.527433
$459$	−5.08479	−0.237338
$460$	0	0
$461$	−35.5665	−1.65650	−0.828249	−	0.560361i	$-0.810663\pi$
$461$	−35.5665	−1.65650	−0.828249	+	0.560361i	$0.810663\pi$
$462$	−42.0937	−1.95838
$463$	−23.0733	−1.07231	−0.536153	−	0.844121i	$-0.680123\pi$
$463$	−23.0733	−1.07231	−0.536153	+	0.844121i	$0.680123\pi$
$464$	−20.7645	−0.963968
$465$	−0.180727	−0.00838101
$466$	53.1316	2.46127
$467$	4.16052	0.192526	0.0962628	−	0.995356i	$-0.469311\pi$
$467$	4.16052	0.192526	0.0962628	+	0.995356i	$0.469311\pi$
$468$	8.44309	0.390282
$469$	−23.8847	−1.10289
$470$	−7.74169	−0.357097
$471$	−5.85555	−0.269810
$472$	−3.21791	−0.148116
$473$	28.5213	1.31141
$474$	10.4941	0.482009
$475$	−1.91795	−0.0880018
$476$	40.2274	1.84382
$477$	2.53491	0.116066
$478$	−48.0692	−2.19863
$479$	−18.9143	−0.864214	−0.432107	−	0.901822i	$-0.642230\pi$
$479$	−18.9143	−0.864214	−0.432107	+	0.901822i	$0.642230\pi$
$480$	8.08539	0.369046
$481$	17.8968	0.816024
$482$	45.7771	2.08509
$483$	0	0
$484$	41.5766	1.88985
$485$	−17.8630	−0.811118
$486$	2.02762	0.0919747
$487$	37.8426	1.71481	0.857407	−	0.514639i	$-0.172074\pi$
$487$	37.8426	1.71481	0.857407	+	0.514639i	$0.172074\pi$
$488$	−1.47180	−0.0666253
$489$	2.35945	0.106698
$490$	−14.2780	−0.645016
$491$	−28.8454	−1.30177	−0.650887	−	0.759175i	$-0.725603\pi$
$491$	−28.8454	−1.30177	−0.650887	+	0.759175i	$0.725603\pi$
$492$	24.5790	1.10811
$493$	−28.0423	−1.26296
$494$	−15.5521	−0.699721
$495$	−5.54012	−0.249010
$496$	−0.680462	−0.0305537
$497$	−44.6873	−2.00450
$498$	16.9009	0.757349
$499$	−22.2778	−0.997292	−0.498646	−	0.866806i	$-0.666169\pi$
$499$	−22.2778	−0.997292	−0.498646	+	0.866806i	$0.666169\pi$
$500$	−2.11124	−0.0944176
$501$	24.0128	1.07281
$502$	55.7857	2.48984
$503$	18.1602	0.809724	0.404862	−	0.914378i	$-0.367320\pi$
$503$	18.1602	0.809724	0.404862	+	0.914378i	$0.367320\pi$
$504$	−0.845214	−0.0376488
$505$	−7.81909	−0.347945
$506$	0	0
$507$	2.99288	0.132919
$508$	−26.2414	−1.16427
$509$	9.07552	0.402265	0.201133	−	0.979564i	$-0.435538\pi$
$509$	9.07552	0.402265	0.201133	+	0.979564i	$0.435538\pi$
$510$	10.3100	0.456535
$511$	−51.6726	−2.28586
$512$	32.1411	1.42045
$513$	−1.91795	−0.0846798
$514$	29.6655	1.30849
$515$	0.654104	0.0288233
$516$	10.8690	0.478479
$517$	21.1528	0.930301
$518$	−34.0024	−1.49398
$519$	6.66865	0.292721
$520$	−0.902027	−0.0395565
$521$	8.40779	0.368352	0.184176	−	0.982893i	$-0.441038\pi$
$521$	8.40779	0.368352	0.184176	+	0.982893i	$0.441038\pi$
$522$	11.1822	0.489431
$523$	41.8032	1.82793	0.913964	−	0.405796i	$-0.133006\pi$
$523$	41.8032	1.82793	0.913964	+	0.405796i	$0.133006\pi$
$524$	16.0061	0.699230
$525$	−3.74723	−0.163543
$526$	−0.261237	−0.0113905
$527$	−0.918958	−0.0400304
$528$	−20.8593	−0.907787
$529$	0	0
$530$	−5.13984	−0.223260
$531$	−14.2665	−0.619114
$532$	15.1736	0.657857
$533$	46.5574	2.01663
$534$	−4.31533	−0.186742
$535$	9.19476	0.397524
$536$	1.43769	0.0620986
$537$	−20.6930	−0.892967
$538$	−18.4940	−0.797331
$539$	39.0123	1.68038
$540$	−2.11124	−0.0908534
$541$	−23.5678	−1.01326	−0.506630	−	0.862164i	$-0.669109\pi$
$541$	−23.5678	−1.01326	−0.506630	+	0.862164i	$0.669109\pi$
$542$	−29.1376	−1.25157
$543$	16.6541	0.714697
$544$	41.1125	1.76268
$545$	6.48841	0.277933
$546$	−30.3851	−1.30036
$547$	−23.2971	−0.996112	−0.498056	−	0.867145i	$-0.665953\pi$
$547$	−23.2971	−0.996112	−0.498056	+	0.867145i	$0.665953\pi$
$548$	24.3768	1.04133
$549$	−6.52519	−0.278488
$550$	11.2333	0.478988
$551$	−10.5774	−0.450612
$552$	0	0
$553$	−19.3941	−0.824720
$554$	29.0899	1.23591
$555$	−4.47520	−0.189962
$556$	−20.1980	−0.856588
$557$	34.4138	1.45816	0.729081	−	0.684428i	$-0.239948\pi$
$557$	34.4138	1.45816	0.729081	+	0.684428i	$0.239948\pi$
$558$	0.366446	0.0155129
$559$	20.5879	0.870777
$560$	−14.1089	−0.596208
$561$	−28.1703	−1.18935
$562$	−15.9358	−0.672211
$563$	18.4372	0.777036	0.388518	−	0.921441i	$-0.372987\pi$
$563$	18.4372	0.777036	0.388518	+	0.921441i	$0.372987\pi$
$564$	8.06097	0.339428
$565$	3.94364	0.165910
$566$	9.48115	0.398522
$567$	−3.74723	−0.157369
$568$	2.68986	0.112864
$569$	5.22040	0.218850	0.109425	−	0.993995i	$-0.465099\pi$
$569$	5.22040	0.218850	0.109425	+	0.993995i	$0.465099\pi$
$570$	3.88888	0.162887
$571$	−21.1363	−0.884527	−0.442263	−	0.896885i	$-0.645824\pi$
$571$	−21.1363	−0.884527	−0.442263	+	0.896885i	$0.645824\pi$
$572$	46.7758	1.95579
$573$	−13.4289	−0.560998
$574$	−88.4551	−3.69205
$575$	0	0
$576$	−8.86381	−0.369325
$577$	−12.8794	−0.536176	−0.268088	−	0.963394i	$-0.586392\pi$
$577$	−12.8794	−0.536176	−0.268088	+	0.963394i	$0.586392\pi$
$578$	17.9547	0.746817
$579$	−5.00489	−0.207996
$580$	−11.6434	−0.483465
$581$	−31.2345	−1.29583
$582$	36.2194	1.50134
$583$	14.0437	0.581632
$584$	3.11032	0.128706
$585$	−3.99911	−0.165343
$586$	−47.2480	−1.95180
$587$	−26.6211	−1.09877	−0.549386	−	0.835569i	$-0.685138\pi$
$587$	−26.6211	−1.09877	−0.549386	+	0.835569i	$0.685138\pi$
$588$	14.8669	0.613100
$589$	−0.346626	−0.0142825
$590$	28.9271	1.19091
$591$	−11.9382	−0.491071
$592$	−16.8497	−0.692520
$593$	−17.9338	−0.736452	−0.368226	−	0.929736i	$-0.620035\pi$
$593$	−17.9338	−0.736452	−0.368226	+	0.929736i	$0.620035\pi$
$594$	11.2333	0.460906
$595$	−19.0539	−0.781133
$596$	−40.5798	−1.66221
$597$	21.2282	0.868811
$598$	0	0
$599$	29.0377	1.18645	0.593224	−	0.805038i	$-0.297855\pi$
$599$	29.0377	1.18645	0.593224	+	0.805038i	$0.297855\pi$
$600$	0.225557	0.00920832
$601$	−25.7902	−1.05200	−0.526002	−	0.850484i	$-0.676309\pi$
$601$	−25.7902	−1.05200	−0.526002	+	0.850484i	$0.676309\pi$
$602$	−39.1153	−1.59422
$603$	6.37395	0.259567
$604$	−6.25306	−0.254433
$605$	−19.6930	−0.800633
$606$	15.8541	0.644031
$607$	14.5374	0.590056	0.295028	−	0.955489i	$-0.404671\pi$
$607$	14.5374	0.590056	0.295028	+	0.955489i	$0.404671\pi$
$608$	15.5074	0.628908
$609$	−20.6658	−0.837419
$610$	13.2306	0.535692
$611$	15.2691	0.617720
$612$	−10.7352	−0.433945
$613$	10.9973	0.444177	0.222089	−	0.975026i	$-0.428713\pi$
$613$	10.9973	0.444177	0.222089	+	0.975026i	$0.428713\pi$
$614$	−12.5885	−0.508029
$615$	−11.6419	−0.469449
$616$	−4.68259	−0.188667
$617$	−0.549907	−0.0221384	−0.0110692	−	0.999939i	$-0.503524\pi$
$617$	−0.549907	−0.0221384	−0.0110692	+	0.999939i	$0.503524\pi$
$618$	−1.32628	−0.0533506
$619$	−25.8590	−1.03936	−0.519680	−	0.854361i	$-0.673949\pi$
$619$	−25.8590	−1.03936	−0.519680	+	0.854361i	$0.673949\pi$
$620$	−0.381558	−0.0153238
$621$	0	0
$622$	−1.63901	−0.0657182
$623$	7.97513	0.319517
$624$	−15.0572	−0.602771
$625$	1.00000	0.0400000
$626$	5.13399	0.205196
$627$	−10.6257	−0.424350
$628$	−12.3625	−0.493317
$629$	−22.7554	−0.907318
$630$	7.59797	0.302710
$631$	−46.0671	−1.83390	−0.916951	−	0.398999i	$-0.869358\pi$
$631$	−46.0671	−1.83390	−0.916951	+	0.398999i	$0.869358\pi$
$632$	1.16738	0.0464361
$633$	−4.40100	−0.174924
$634$	−33.5648	−1.33303
$635$	12.4294	0.493244
$636$	5.35182	0.212213
$637$	28.1608	1.11577
$638$	61.9508	2.45265
$639$	11.9254	0.471762
$640$	1.80166	0.0712170
$641$	−20.2141	−0.798407	−0.399204	−	0.916862i	$-0.630713\pi$
$641$	−20.2141	−0.798407	−0.399204	+	0.916862i	$0.630713\pi$
$642$	−18.6435	−0.735799
$643$	−20.8274	−0.821352	−0.410676	−	0.911781i	$-0.634707\pi$
$643$	−20.8274	−0.821352	−0.410676	+	0.911781i	$0.634707\pi$
$644$	0	0
$645$	−5.14813	−0.202708
$646$	19.7741	0.778003
$647$	−33.0946	−1.30108	−0.650542	−	0.759470i	$-0.725458\pi$
$647$	−33.0946	−1.30108	−0.650542	+	0.759470i	$0.725458\pi$
$648$	0.225557	0.00886071
$649$	−79.0383	−3.10252
$650$	8.10867	0.318048
$651$	−0.677226	−0.0265426
$652$	4.98137	0.195086
$653$	−26.6042	−1.04110	−0.520551	−	0.853831i	$-0.674273\pi$
$653$	−26.6042	−1.04110	−0.520551	+	0.853831i	$0.674273\pi$
$654$	−13.1560	−0.514442
$655$	−7.58137	−0.296229
$656$	−43.8336	−1.71141
$657$	13.7895	0.537981
$658$	−29.0099	−1.13092
$659$	11.8240	0.460598	0.230299	−	0.973120i	$-0.426030\pi$
$659$	11.8240	0.460598	0.230299	+	0.973120i	$0.426030\pi$
$660$	−11.6965	−0.455287
$661$	6.30522	0.245245	0.122622	−	0.992453i	$-0.460870\pi$
$661$	6.30522	0.245245	0.122622	+	0.992453i	$0.460870\pi$
$662$	−21.3997	−0.831723
$663$	−20.3346	−0.789731
$664$	1.88010	0.0729619
$665$	−7.18703	−0.278701
$666$	9.07400	0.351610
$667$	0	0
$668$	50.6969	1.96152
$669$	−2.58548	−0.0999604
$670$	−12.9239	−0.499295
$671$	−36.1504	−1.39557
$672$	30.2978	1.16876
$673$	−20.3880	−0.785901	−0.392951	−	0.919560i	$-0.628546\pi$
$673$	−20.3880	−0.785901	−0.392951	+	0.919560i	$0.628546\pi$
$674$	18.2708	0.703764
$675$	1.00000	0.0384900
$676$	6.31870	0.243027
$677$	23.6428	0.908667	0.454334	−	0.890832i	$-0.349877\pi$
$677$	23.6428	0.908667	0.454334	+	0.890832i	$0.349877\pi$
$678$	−7.99620	−0.307092
$679$	−66.9369	−2.56880
$680$	1.14691	0.0439819
$681$	−0.945689	−0.0362389
$682$	2.03015	0.0777386
$683$	29.8545	1.14235	0.571176	−	0.820828i	$-0.306487\pi$
$683$	29.8545	1.14235	0.571176	+	0.820828i	$0.306487\pi$
$684$	−4.04927	−0.154828
$685$	−11.5462	−0.441157
$686$	−0.317359	−0.0121168
$687$	5.56690	0.212391
$688$	−19.3834	−0.738987
$689$	10.1374	0.386204
$690$	0	0
$691$	8.28327	0.315110	0.157555	−	0.987510i	$-0.449639\pi$
$691$	8.28327	0.315110	0.157555	+	0.987510i	$0.449639\pi$
$692$	14.0791	0.535209
$693$	−20.7601	−0.788613
$694$	18.5607	0.704553
$695$	9.56690	0.362893
$696$	1.24393	0.0471511
$697$	−59.1968	−2.24224
$698$	−46.2421	−1.75029
$699$	26.2039	0.991123
$700$	−7.91132	−0.299020
$701$	−47.9680	−1.81173	−0.905863	−	0.423571i	$-0.860776\pi$
$701$	−47.9680	−1.81173	−0.905863	+	0.423571i	$0.860776\pi$
$702$	8.10867	0.306042
$703$	−8.58322	−0.323722
$704$	−49.1066	−1.85078
$705$	−3.81812	−0.143799
$706$	14.2724	0.537148
$707$	−29.3000	−1.10194
$708$	−30.1201	−1.13198
$709$	−14.5048	−0.544741	−0.272370	−	0.962193i	$-0.587808\pi$
$709$	−14.5048	−0.544741	−0.272370	+	0.962193i	$0.587808\pi$
$710$	−24.1802	−0.907467
$711$	5.17557	0.194099
$712$	−0.480046	−0.0179905
$713$	0	0
$714$	38.6340	1.44584
$715$	−22.1556	−0.828571
$716$	−43.6878	−1.63269
$717$	−23.7072	−0.885362
$718$	16.5036	0.615908
$719$	−31.0200	−1.15685	−0.578425	−	0.815736i	$-0.696332\pi$
$719$	−31.0200	−1.15685	−0.578425	+	0.815736i	$0.696332\pi$
$720$	3.76514	0.140319
$721$	2.45108	0.0912831
$722$	−31.0661	−1.15616
$723$	22.5768	0.839639
$724$	35.1609	1.30674
$725$	5.51494	0.204820
$726$	39.9299	1.48194
$727$	−28.5945	−1.06051	−0.530256	−	0.847838i	$-0.677904\pi$
$727$	−28.5945	−1.06051	−0.530256	+	0.847838i	$0.677904\pi$
$728$	−3.38011	−0.125275
$729$	1.00000	0.0370370
$730$	−27.9599	−1.03484
$731$	−26.1772	−0.968197
$732$	−13.7763	−0.509185
$733$	−33.1696	−1.22515	−0.612574	−	0.790413i	$-0.709866\pi$
$733$	−33.1696	−1.22515	−0.612574	+	0.790413i	$0.709866\pi$
$734$	−11.9443	−0.440873
$735$	−7.04177	−0.259740
$736$	0	0
$737$	35.3124	1.30075
$738$	23.6054	0.868928
$739$	−12.4639	−0.458492	−0.229246	−	0.973369i	$-0.573626\pi$
$739$	−12.4639	−0.458492	−0.229246	+	0.973369i	$0.573626\pi$
$740$	−9.44822	−0.347324
$741$	−7.67011	−0.281769
$742$	−19.2602	−0.707064
$743$	−25.9167	−0.950791	−0.475395	−	0.879772i	$-0.657695\pi$
$743$	−25.9167	−0.950791	−0.475395	+	0.879772i	$0.657695\pi$
$744$	0.0407642	0.00149449
$745$	19.2208	0.704197
$746$	33.9313	1.24231
$747$	8.33535	0.304975
$748$	−59.4744	−2.17460
$749$	34.4549	1.25896
$750$	−2.02762	−0.0740382
$751$	−15.1200	−0.551738	−0.275869	−	0.961195i	$-0.588966\pi$
$751$	−15.1200	−0.551738	−0.275869	+	0.961195i	$0.588966\pi$
$752$	−14.3757	−0.524230
$753$	27.5129	1.00263
$754$	44.7188	1.62856
$755$	2.96179	0.107791
$756$	−7.91132	−0.287732
$757$	−31.6539	−1.15048	−0.575241	−	0.817984i	$-0.695092\pi$
$757$	−31.6539	−1.15048	−0.575241	+	0.817984i	$0.695092\pi$
$758$	−33.3866	−1.21265
$759$	0	0
$760$	0.432608	0.0156923
$761$	21.8601	0.792427	0.396213	−	0.918158i	$-0.370324\pi$
$761$	21.8601	0.792427	0.396213	+	0.918158i	$0.370324\pi$
$762$	−25.2020	−0.912973
$763$	24.3136	0.880212
$764$	−28.3516	−1.02572
$765$	5.08479	0.183841
$766$	10.2152	0.369090
$767$	−57.0534	−2.06008
$768$	14.0745	0.507871
$769$	47.5834	1.71590	0.857950	−	0.513733i	$-0.171738\pi$
$769$	47.5834	1.71590	0.857950	+	0.513733i	$0.171738\pi$
$770$	42.0937	1.51695
$771$	14.6307	0.526912
$772$	−10.5665	−0.380298
$773$	0.0836308	0.00300799	0.00150399	−	0.999999i	$-0.499521\pi$
$773$	0.0836308	0.00300799	0.00150399	+	0.999999i	$0.499521\pi$
$774$	10.4385	0.375203
$775$	0.180727	0.00649190
$776$	4.02913	0.144637
$777$	−16.7696	−0.601607
$778$	−14.5885	−0.523023
$779$	−22.3287	−0.800009
$780$	−8.44309	−0.302311
$781$	66.0683	2.36411
$782$	0	0
$783$	5.51494	0.197088
$784$	−26.5133	−0.946902
$785$	5.85555	0.208994
$786$	15.3721	0.548306
$787$	−14.2474	−0.507866	−0.253933	−	0.967222i	$-0.581724\pi$
$787$	−14.2474	−0.507866	−0.253933	+	0.967222i	$0.581724\pi$
$788$	−25.2044	−0.897869
$789$	−0.128839	−0.00458680
$790$	−10.4941	−0.373363
$791$	14.7777	0.525436
$792$	1.24961	0.0444031
$793$	−26.0950	−0.926659
$794$	56.6983	2.01215
$795$	−2.53491	−0.0899041
$796$	44.8178	1.58852
$797$	−39.8873	−1.41288	−0.706440	−	0.707773i	$-0.749700\pi$
$797$	−39.8873	−1.41288	−0.706440	+	0.707773i	$0.749700\pi$
$798$	14.5726	0.515863
$799$	−19.4143	−0.686829
$800$	−8.08539	−0.285862
$801$	−2.12827	−0.0751988
$802$	−60.5322	−2.13747
$803$	76.3958	2.69595
$804$	13.4569	0.474590
$805$	0	0
$806$	1.46546	0.0516185
$807$	−9.12102	−0.321075
$808$	1.76365	0.0620450
$809$	49.5178	1.74095	0.870476	−	0.492211i	$-0.163811\pi$
$809$	49.5178	1.74095	0.870476	+	0.492211i	$0.163811\pi$
$810$	−2.02762	−0.0712433
$811$	−13.0664	−0.458823	−0.229411	−	0.973330i	$-0.573680\pi$
$811$	−13.0664	−0.458823	−0.229411	+	0.973330i	$0.573680\pi$
$812$	−43.6304	−1.53113
$813$	−14.3703	−0.503990
$814$	50.2711	1.76200
$815$	−2.35945	−0.0826480
$816$	19.1449	0.670207
$817$	−9.87388	−0.345443
$818$	−10.5331	−0.368281
$819$	−14.9856	−0.523639
$820$	−24.5790	−0.858335
$821$	−6.75673	−0.235811	−0.117906	−	0.993025i	$-0.537618\pi$
$821$	−6.75673	−0.235811	−0.117906	+	0.993025i	$0.537618\pi$
$822$	23.4113	0.816562
$823$	38.0859	1.32759	0.663796	−	0.747914i	$-0.268944\pi$
$823$	38.0859	1.32759	0.663796	+	0.747914i	$0.268944\pi$
$824$	−0.147538	−0.00513972
$825$	5.54012	0.192882
$826$	108.397	3.77160
$827$	−17.1488	−0.596324	−0.298162	−	0.954515i	$-0.596374\pi$
$827$	−17.1488	−0.596324	−0.298162	+	0.954515i	$0.596374\pi$
$828$	0	0
$829$	−23.7181	−0.823764	−0.411882	−	0.911237i	$-0.635128\pi$
$829$	−23.7181	−0.823764	−0.411882	+	0.911237i	$0.635128\pi$
$830$	−16.9009	−0.586640
$831$	14.3468	0.497685
$832$	−35.4474	−1.22892
$833$	−35.8059	−1.24060
$834$	−19.3980	−0.671699
$835$	−24.0128	−0.830999
$836$	−22.4334	−0.775877
$837$	0.180727	0.00624684
$838$	−7.88118	−0.272251
$839$	0.588992	0.0203343	0.0101671	−	0.999948i	$-0.496764\pi$
$839$	0.588992	0.0203343	0.0101671	+	0.999948i	$0.496764\pi$
$840$	0.845214	0.0291627
$841$	1.41453	0.0487769
$842$	−11.4624	−0.395020
$843$	−7.85936	−0.270691
$844$	−9.29159	−0.319830
$845$	−2.99288	−0.102958
$846$	7.74169	0.266165
$847$	−73.7942	−2.53560
$848$	−9.54431	−0.327753
$849$	4.67600	0.160480
$850$	−10.3100	−0.353631
$851$	0	0
$852$	25.1774	0.862565
$853$	−8.42683	−0.288529	−0.144265	−	0.989539i	$-0.546082\pi$
$853$	−8.42683	−0.288529	−0.144265	+	0.989539i	$0.546082\pi$
$854$	49.5782	1.69653
$855$	1.91795	0.0655927
$856$	−2.07394	−0.0708858
$857$	9.67493	0.330489	0.165245	−	0.986253i	$-0.447159\pi$
$857$	9.67493	0.330489	0.165245	+	0.986253i	$0.447159\pi$
$858$	44.9231	1.53365
$859$	−12.6192	−0.430560	−0.215280	−	0.976552i	$-0.569066\pi$
$859$	−12.6192	−0.430560	−0.215280	+	0.976552i	$0.569066\pi$
$860$	−10.8690	−0.370628
$861$	−43.6251	−1.48674
$862$	54.9759	1.87249
$863$	10.8519	0.369402	0.184701	−	0.982795i	$-0.440868\pi$
$863$	10.8519	0.369402	0.184701	+	0.982795i	$0.440868\pi$
$864$	−8.08539	−0.275070
$865$	−6.66865	−0.226741
$866$	63.3145	2.15151
$867$	8.85506	0.300734
$868$	−1.42979	−0.0485302
$869$	28.6733	0.972675
$870$	−11.1822	−0.379112
$871$	25.4901	0.863699
$872$	−1.46351	−0.0495606
$873$	17.8630	0.604572
$874$	0	0
$875$	3.74723	0.126680
$876$	29.1131	0.983639
$877$	−49.4246	−1.66895	−0.834475	−	0.551046i	$-0.814229\pi$
$877$	−49.4246	−1.66895	−0.834475	+	0.551046i	$0.814229\pi$
$878$	42.5288	1.43528
$879$	−23.3022	−0.785964
$880$	20.8593	0.703168
$881$	−37.4007	−1.26006	−0.630032	−	0.776570i	$-0.716958\pi$
$881$	−37.4007	−1.26006	−0.630032	+	0.776570i	$0.716958\pi$
$882$	14.2780	0.480766
$883$	36.2182	1.21884	0.609421	−	0.792847i	$-0.291402\pi$
$883$	36.2182	1.21884	0.609421	+	0.792847i	$0.291402\pi$
$884$	−42.9313	−1.44394
$885$	14.2665	0.479564
$886$	−14.5204	−0.487821
$887$	−2.74627	−0.0922106	−0.0461053	−	0.998937i	$-0.514681\pi$
$887$	−2.74627	−0.0922106	−0.0461053	+	0.998937i	$0.514681\pi$
$888$	1.00941	0.0338736
$889$	46.5758	1.56210
$890$	4.31533	0.144650
$891$	5.54012	0.185601
$892$	−5.45857	−0.182767
$893$	−7.32297	−0.245054
$894$	−38.9725	−1.30344
$895$	20.6930	0.691689
$896$	6.75126	0.225544
$897$	0	0
$898$	26.4917	0.884038
$899$	0.996698	0.0332417
$900$	2.11124	0.0703747
$901$	−12.8895	−0.429411
$902$	130.777	4.35440
$903$	−19.2913	−0.641973
$904$	−0.889515	−0.0295848
$905$	−16.6541	−0.553602
$906$	−6.00539	−0.199516
$907$	14.0813	0.467561	0.233780	−	0.972289i	$-0.424890\pi$
$907$	14.0813	0.467561	0.233780	+	0.972289i	$0.424890\pi$
$908$	−1.99658	−0.0662588
$909$	7.81909	0.259343
$910$	30.3851	1.00726
$911$	−21.1213	−0.699780	−0.349890	−	0.936791i	$-0.613781\pi$
$911$	−21.1213	−0.699780	−0.349890	+	0.936791i	$0.613781\pi$
$912$	7.22137	0.239123
$913$	46.1789	1.52830
$914$	−33.9428	−1.12273
$915$	6.52519	0.215716
$916$	11.7531	0.388333
$917$	−28.4092	−0.938154
$918$	−10.3100	−0.340281
$919$	13.1042	0.432266	0.216133	−	0.976364i	$-0.430655\pi$
$919$	13.1042	0.432266	0.216133	+	0.976364i	$0.430655\pi$
$920$	0	0
$921$	−6.20849	−0.204577
$922$	−72.1154	−2.37499
$923$	47.6911	1.56977
$924$	−43.8297	−1.44189
$925$	4.47520	0.147144
$926$	−46.7839	−1.53741
$927$	−0.654104	−0.0214836
$928$	−44.5904	−1.46375
$929$	11.3621	0.372780	0.186390	−	0.982476i	$-0.440321\pi$
$929$	11.3621	0.372780	0.186390	+	0.982476i	$0.440321\pi$
$930$	−0.366446	−0.0120162
$931$	−13.5058	−0.442634
$932$	55.3228	1.81216
$933$	−0.808340	−0.0264639
$934$	8.43594	0.276032
$935$	28.1703	0.921269
$936$	0.902027	0.0294837
$937$	0.956226	0.0312385	0.0156193	−	0.999878i	$-0.495028\pi$
$937$	0.956226	0.0312385	0.0156193	+	0.999878i	$0.495028\pi$
$938$	−48.4290	−1.58126
$939$	2.53203	0.0826297
$940$	−8.06097	−0.262920
$941$	−30.2967	−0.987645	−0.493823	−	0.869563i	$-0.664401\pi$
$941$	−30.2967	−0.987645	−0.493823	+	0.869563i	$0.664401\pi$
$942$	−11.8728	−0.386838
$943$	0	0
$944$	53.7154	1.74829
$945$	3.74723	0.121898
$946$	57.8303	1.88023
$947$	−17.6391	−0.573194	−0.286597	−	0.958051i	$-0.592524\pi$
$947$	−17.6391	−0.573194	−0.286597	+	0.958051i	$0.592524\pi$
$948$	10.9269	0.354889
$949$	55.1459	1.79011
$950$	−3.88888	−0.126172
$951$	−16.5538	−0.536793
$952$	4.29774	0.139290
$953$	45.1592	1.46285	0.731426	−	0.681921i	$-0.238855\pi$
$953$	45.1592	1.46285	0.731426	+	0.681921i	$0.238855\pi$
$954$	5.13984	0.166409
$955$	13.4289	0.434547
$956$	−50.0517	−1.61879
$957$	30.5534	0.987652
$958$	−38.3509	−1.23906
$959$	−43.2663	−1.39714
$960$	8.86381	0.286078
$961$	−30.9673	−0.998946
$962$	36.2879	1.16997
$963$	−9.19476	−0.296297
$964$	47.6650	1.53519
$965$	5.00489	0.161113
$966$	0	0
$967$	−21.5445	−0.692823	−0.346412	−	0.938083i	$-0.612600\pi$
$967$	−21.5445	−0.692823	−0.346412	+	0.938083i	$0.612600\pi$
$968$	4.44188	0.142768
$969$	9.75239	0.313292
$970$	−36.2194	−1.16294
$971$	−18.7924	−0.603075	−0.301538	−	0.953454i	$-0.597500\pi$
$971$	−18.7924	−0.603075	−0.301538	+	0.953454i	$0.597500\pi$
$972$	2.11124	0.0677181
$973$	35.8494	1.14928
$974$	76.7305	2.45860
$975$	3.99911	0.128074
$976$	24.5683	0.786411
$977$	56.7147	1.81446	0.907231	−	0.420632i	$-0.138192\pi$
$977$	56.7147	1.81446	0.907231	+	0.420632i	$0.138192\pi$
$978$	4.78407	0.152978
$979$	−11.7909	−0.376838
$980$	−14.8669	−0.474905
$981$	−6.48841	−0.207159
$982$	−58.4875	−1.86641
$983$	−30.5126	−0.973202	−0.486601	−	0.873624i	$-0.661763\pi$
$983$	−30.5126	−0.973202	−0.486601	+	0.873624i	$0.661763\pi$
$984$	2.62592	0.0837113
$985$	11.9382	0.380382
$986$	−56.8591	−1.81076
$987$	−14.3074	−0.455409
$988$	−16.1935	−0.515183
$989$	0	0
$990$	−11.2333	−0.357017
$991$	−42.9729	−1.36508	−0.682540	−	0.730849i	$-0.739125\pi$
$991$	−42.9729	−1.36508	−0.682540	+	0.730849i	$0.739125\pi$
$992$	−1.46125	−0.0463946
$993$	−10.5541	−0.334924
$994$	−90.6090	−2.87394
$995$	−21.2282	−0.672978
$996$	17.5979	0.557612
$997$	21.5854	0.683616	0.341808	−	0.939770i	$-0.388961\pi$
$997$	21.5854	0.683616	0.341808	+	0.939770i	$0.388961\pi$
$998$	−45.1709	−1.42986
$999$	4.47520	0.141589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bv.1.19		25
23.4	even	11		345.2.m.c.16.2	✓	50
23.6	even	11		345.2.m.c.151.2	yes	50
23.22	odd	2		7935.2.a.bw.1.19		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.2	✓	50	23.4	even	11
345.2.m.c.151.2	yes	50	23.6	even	11
7935.2.a.bv.1.19		25	1.1	even	1	trivial
7935.2.a.bw.1.19		25	23.22	odd	2

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02762 q^{2} +1.00000 q^{3} +2.11124 q^{4} -1.00000 q^{5} +2.02762 q^{6} -3.74723 q^{7} +0.225557 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.02762 q^{2} +1.00000 q^{3} +2.11124 q^{4} -1.00000 q^{5} +2.02762 q^{6} -3.74723 q^{7} +0.225557 q^{8} +1.00000 q^{9} -2.02762 q^{10} +5.54012 q^{11} +2.11124 q^{12} +3.99911 q^{13} -7.59797 q^{14} -1.00000 q^{15} -3.76514 q^{16} -5.08479 q^{17} +2.02762 q^{18} -1.91795 q^{19} -2.11124 q^{20} -3.74723 q^{21} +11.2333 q^{22} +0.225557 q^{24} +1.00000 q^{25} +8.10867 q^{26} +1.00000 q^{27} -7.91132 q^{28} +5.51494 q^{29} -2.02762 q^{30} +0.180727 q^{31} -8.08539 q^{32} +5.54012 q^{33} -10.3100 q^{34} +3.74723 q^{35} +2.11124 q^{36} +4.47520 q^{37} -3.88888 q^{38} +3.99911 q^{39} -0.225557 q^{40} +11.6419 q^{41} -7.59797 q^{42} +5.14813 q^{43} +11.6965 q^{44} -1.00000 q^{45} +3.81812 q^{47} -3.76514 q^{48} +7.04177 q^{49} +2.02762 q^{50} -5.08479 q^{51} +8.44309 q^{52} +2.53491 q^{53} +2.02762 q^{54} -5.54012 q^{55} -0.845214 q^{56} -1.91795 q^{57} +11.1822 q^{58} -14.2665 q^{59} -2.11124 q^{60} -6.52519 q^{61} +0.366446 q^{62} -3.74723 q^{63} -8.86381 q^{64} -3.99911 q^{65} +11.2333 q^{66} +6.37395 q^{67} -10.7352 q^{68} +7.59797 q^{70} +11.9254 q^{71} +0.225557 q^{72} +13.7895 q^{73} +9.07400 q^{74} +1.00000 q^{75} -4.04927 q^{76} -20.7601 q^{77} +8.10867 q^{78} +5.17557 q^{79} +3.76514 q^{80} +1.00000 q^{81} +23.6054 q^{82} +8.33535 q^{83} -7.91132 q^{84} +5.08479 q^{85} +10.4385 q^{86} +5.51494 q^{87} +1.24961 q^{88} -2.12827 q^{89} -2.02762 q^{90} -14.9856 q^{91} +0.180727 q^{93} +7.74169 q^{94} +1.91795 q^{95} -8.08539 q^{96} +17.8630 q^{97} +14.2780 q^{98} +5.54012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19} - 31 q^{20} - 7 q^{21} - 9 q^{22} + 33 q^{24} + 25 q^{25} + 35 q^{26} + 25 q^{27} + 5 q^{28} + 33 q^{29} - 11 q^{30} + 14 q^{31} + 77 q^{32} - 9 q^{33} - 13 q^{34} + 7 q^{35} + 31 q^{36} - 4 q^{37} + 23 q^{38} + 18 q^{39} - 33 q^{40} + 56 q^{41} - 11 q^{42} + 4 q^{43} + 18 q^{44} - 25 q^{45} + 43 q^{47} + 39 q^{48} + 40 q^{49} + 11 q^{50} + 8 q^{51} + 49 q^{52} - 2 q^{53} + 11 q^{54} + 9 q^{55} - 33 q^{56} - 11 q^{57} + 26 q^{58} + 61 q^{59} - 31 q^{60} - 21 q^{61} + 51 q^{62} - 7 q^{63} + 71 q^{64} - 18 q^{65} - 9 q^{66} - 2 q^{67} + 33 q^{68} + 11 q^{70} + 66 q^{71} + 33 q^{72} + 53 q^{73} + 47 q^{74} + 25 q^{75} + 8 q^{76} + 49 q^{77} + 35 q^{78} - 35 q^{79} - 39 q^{80} + 25 q^{81} + 35 q^{82} + 26 q^{83} + 5 q^{84} - 8 q^{85} + 33 q^{86} + 33 q^{87} - 9 q^{88} + 7 q^{89} - 11 q^{90} - 28 q^{91} + 14 q^{93} + 24 q^{94} + 11 q^{95} + 77 q^{96} + 54 q^{97} + 88 q^{98} - 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * q^99

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