LMFDB - Embedded newform 7935.2.a.bu.1.10

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			1.10
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)

$f(q)$	$=$	$q-0.688592 q^{2} -1.00000 q^{3} -1.52584 q^{4} +1.00000 q^{5} +0.688592 q^{6} -4.50249 q^{7} +2.42787 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.688592 q^{2} -1.00000 q^{3} -1.52584 q^{4} +1.00000 q^{5} +0.688592 q^{6} -4.50249 q^{7} +2.42787 q^{8} +1.00000 q^{9} -0.688592 q^{10} +3.56611 q^{11} +1.52584 q^{12} +5.74244 q^{13} +3.10038 q^{14} -1.00000 q^{15} +1.37987 q^{16} -2.76227 q^{17} -0.688592 q^{18} +7.62351 q^{19} -1.52584 q^{20} +4.50249 q^{21} -2.45559 q^{22} -2.42787 q^{24} +1.00000 q^{25} -3.95420 q^{26} -1.00000 q^{27} +6.87008 q^{28} +5.43801 q^{29} +0.688592 q^{30} +9.51642 q^{31} -5.80590 q^{32} -3.56611 q^{33} +1.90208 q^{34} -4.50249 q^{35} -1.52584 q^{36} +2.18422 q^{37} -5.24949 q^{38} -5.74244 q^{39} +2.42787 q^{40} +8.47498 q^{41} -3.10038 q^{42} -1.86818 q^{43} -5.44131 q^{44} +1.00000 q^{45} -0.179563 q^{47} -1.37987 q^{48} +13.2724 q^{49} -0.688592 q^{50} +2.76227 q^{51} -8.76204 q^{52} +2.00838 q^{53} +0.688592 q^{54} +3.56611 q^{55} -10.9314 q^{56} -7.62351 q^{57} -3.74457 q^{58} +12.2480 q^{59} +1.52584 q^{60} -5.61248 q^{61} -6.55293 q^{62} -4.50249 q^{63} +1.23816 q^{64} +5.74244 q^{65} +2.45559 q^{66} -3.37431 q^{67} +4.21479 q^{68} +3.10038 q^{70} -7.57061 q^{71} +2.42787 q^{72} +5.52203 q^{73} -1.50404 q^{74} -1.00000 q^{75} -11.6323 q^{76} -16.0564 q^{77} +3.95420 q^{78} +7.08024 q^{79} +1.37987 q^{80} +1.00000 q^{81} -5.83581 q^{82} +6.20176 q^{83} -6.87008 q^{84} -2.76227 q^{85} +1.28642 q^{86} -5.43801 q^{87} +8.65804 q^{88} +9.76552 q^{89} -0.688592 q^{90} -25.8553 q^{91} -9.51642 q^{93} +0.123646 q^{94} +7.62351 q^{95} +5.80590 q^{96} -2.89439 q^{97} -9.13929 q^{98} +3.56611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * 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 $

$2$	−0.688592	−0.486908	−0.243454	−	0.969912i	$-0.578281\pi$
$2$	−0.688592	−0.486908	−0.243454	+	0.969912i	$0.578281\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.52584	−0.762920
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.688592	0.281117
$7$	−4.50249	−1.70178	−0.850891	−	0.525342i	$-0.823937\pi$
$7$	−4.50249	−1.70178	−0.850891	+	0.525342i	$0.823937\pi$
$8$	2.42787	0.858380
$9$	1.00000	0.333333
$10$	−0.688592	−0.217752
$11$	3.56611	1.07522	0.537611	−	0.843193i	$-0.319327\pi$
$11$	3.56611	1.07522	0.537611	+	0.843193i	$0.319327\pi$
$12$	1.52584	0.440472
$13$	5.74244	1.59267	0.796333	−	0.604859i	$-0.206771\pi$
$13$	5.74244	1.59267	0.796333	+	0.604859i	$0.206771\pi$
$14$	3.10038	0.828612
$15$	−1.00000	−0.258199
$16$	1.37987	0.344968
$17$	−2.76227	−0.669950	−0.334975	−	0.942227i	$-0.608728\pi$
$17$	−2.76227	−0.669950	−0.334975	+	0.942227i	$0.608728\pi$
$18$	−0.688592	−0.162303
$19$	7.62351	1.74895	0.874477	−	0.485067i	$-0.161205\pi$
$19$	7.62351	1.74895	0.874477	+	0.485067i	$0.161205\pi$
$20$	−1.52584	−0.341188
$21$	4.50249	0.982524
$22$	−2.45559	−0.523535
$23$	0	0
$23$	0	0
$24$	−2.42787	−0.495586
$25$	1.00000	0.200000
$26$	−3.95420	−0.775482
$27$	−1.00000	−0.192450
$28$	6.87008	1.29832
$29$	5.43801	1.00981	0.504906	−	0.863174i	$-0.331527\pi$
$29$	5.43801	1.00981	0.504906	+	0.863174i	$0.331527\pi$
$30$	0.688592	0.125719
$31$	9.51642	1.70920	0.854599	−	0.519288i	$-0.173803\pi$
$31$	9.51642	1.70920	0.854599	+	0.519288i	$0.173803\pi$
$32$	−5.80590	−1.02635
$33$	−3.56611	−0.620780
$34$	1.90208	0.326204
$35$	−4.50249	−0.761060
$36$	−1.52584	−0.254307
$37$	2.18422	0.359084	0.179542	−	0.983750i	$-0.442538\pi$
$37$	2.18422	0.359084	0.179542	+	0.983750i	$0.442538\pi$
$38$	−5.24949	−0.851580
$39$	−5.74244	−0.919526
$40$	2.42787	0.383879
$41$	8.47498	1.32357	0.661785	−	0.749694i	$-0.269799\pi$
$41$	8.47498	1.32357	0.661785	+	0.749694i	$0.269799\pi$
$42$	−3.10038	−0.478399
$43$	−1.86818	−0.284895	−0.142448	−	0.989802i	$-0.545497\pi$
$43$	−1.86818	−0.284895	−0.142448	+	0.989802i	$0.545497\pi$
$44$	−5.44131	−0.820309
$45$	1.00000	0.149071
$46$	0	0
$47$	−0.179563	−0.0261920	−0.0130960	−	0.999914i	$-0.504169\pi$
$47$	−0.179563	−0.0261920	−0.0130960	+	0.999914i	$0.504169\pi$
$48$	−1.37987	−0.199167
$49$	13.2724	1.89606
$50$	−0.688592	−0.0973816
$51$	2.76227	0.386796
$52$	−8.76204	−1.21508
$53$	2.00838	0.275873	0.137936	−	0.990441i	$-0.455953\pi$
$53$	2.00838	0.275873	0.137936	+	0.990441i	$0.455953\pi$
$54$	0.688592	0.0937055
$55$	3.56611	0.480854
$56$	−10.9314	−1.46078
$57$	−7.62351	−1.00976
$58$	−3.74457	−0.491686
$59$	12.2480	1.59455	0.797275	−	0.603616i	$-0.206274\pi$
$59$	12.2480	1.59455	0.797275	+	0.603616i	$0.206274\pi$
$60$	1.52584	0.196985
$61$	−5.61248	−0.718604	−0.359302	−	0.933221i	$-0.616985\pi$
$61$	−5.61248	−0.718604	−0.359302	+	0.933221i	$0.616985\pi$
$62$	−6.55293	−0.832223
$63$	−4.50249	−0.567261
$64$	1.23816	0.154769
$65$	5.74244	0.712261
$66$	2.45559	0.302263
$67$	−3.37431	−0.412238	−0.206119	−	0.978527i	$-0.566083\pi$
$67$	−3.37431	−0.412238	−0.206119	+	0.978527i	$0.566083\pi$
$68$	4.21479	0.511118
$69$	0	0
$70$	3.10038	0.370566
$71$	−7.57061	−0.898467	−0.449233	−	0.893415i	$-0.648303\pi$
$71$	−7.57061	−0.898467	−0.449233	+	0.893415i	$0.648303\pi$
$72$	2.42787	0.286127
$73$	5.52203	0.646304	0.323152	−	0.946347i	$-0.395257\pi$
$73$	5.52203	0.646304	0.323152	+	0.946347i	$0.395257\pi$
$74$	−1.50404	−0.174841
$75$	−1.00000	−0.115470
$76$	−11.6323	−1.33431
$77$	−16.0564	−1.82979
$78$	3.95420	0.447725
$79$	7.08024	0.796589	0.398295	−	0.917257i	$-0.369602\pi$
$79$	7.08024	0.796589	0.398295	+	0.917257i	$0.369602\pi$
$80$	1.37987	0.154274
$81$	1.00000	0.111111
$82$	−5.83581	−0.644457
$83$	6.20176	0.680731	0.340366	−	0.940293i	$-0.389449\pi$
$83$	6.20176	0.680731	0.340366	+	0.940293i	$0.389449\pi$
$84$	−6.87008	−0.749588
$85$	−2.76227	−0.299611
$86$	1.28642	0.138718
$87$	−5.43801	−0.583015
$88$	8.65804	0.922950
$89$	9.76552	1.03514	0.517572	−	0.855640i	$-0.326836\pi$
$89$	9.76552	1.03514	0.517572	+	0.855640i	$0.326836\pi$
$90$	−0.688592	−0.0725840
$91$	−25.8553	−2.71037
$92$	0	0
$93$	−9.51642	−0.986806
$94$	0.123646	0.0127531
$95$	7.62351	0.782156
$96$	5.80590	0.592562
$97$	−2.89439	−0.293881	−0.146941	−	0.989145i	$-0.546943\pi$
$97$	−2.89439	−0.293881	−0.146941	+	0.989145i	$0.546943\pi$
$98$	−9.13929	−0.923208
$99$	3.56611	0.358407
$100$	−1.52584	−0.152584
$101$	4.05771	0.403758	0.201879	−	0.979411i	$-0.435295\pi$
$101$	4.05771	0.403758	0.201879	+	0.979411i	$0.435295\pi$
$102$	−1.90208	−0.188334
$103$	−4.15739	−0.409640	−0.204820	−	0.978800i	$-0.565661\pi$
$103$	−4.15739	−0.409640	−0.204820	+	0.978800i	$0.565661\pi$
$104$	13.9419	1.36711
$105$	4.50249	0.439398
$106$	−1.38296	−0.134325
$107$	4.55274	0.440130	0.220065	−	0.975485i	$-0.429373\pi$
$107$	4.55274	0.440130	0.220065	+	0.975485i	$0.429373\pi$
$108$	1.52584	0.146824
$109$	−17.4594	−1.67231	−0.836154	−	0.548494i	$-0.815201\pi$
$109$	−17.4594	−1.67231	−0.836154	+	0.548494i	$0.815201\pi$
$110$	−2.45559	−0.234132
$111$	−2.18422	−0.207317
$112$	−6.21286	−0.587060
$113$	−13.9488	−1.31219	−0.656095	−	0.754679i	$-0.727793\pi$
$113$	−13.9488	−1.31219	−0.656095	+	0.754679i	$0.727793\pi$
$114$	5.24949	0.491660
$115$	0	0
$116$	−8.29753	−0.770406
$117$	5.74244	0.530888
$118$	−8.43386	−0.776399
$119$	12.4371	1.14011
$120$	−2.42787	−0.221633
$121$	1.71713	0.156103
$122$	3.86471	0.349894
$123$	−8.47498	−0.764163
$124$	−14.5205	−1.30398
$125$	1.00000	0.0894427
$126$	3.10038	0.276204
$127$	−7.86557	−0.697956	−0.348978	−	0.937131i	$-0.613471\pi$
$127$	−7.86557	−0.697956	−0.348978	+	0.937131i	$0.613471\pi$
$128$	10.7592	0.950990
$129$	1.86818	0.164484
$130$	−3.95420	−0.346806
$131$	−13.3812	−1.16912	−0.584561	−	0.811350i	$-0.698733\pi$
$131$	−13.3812	−1.16912	−0.584561	+	0.811350i	$0.698733\pi$
$132$	5.44131	0.473606
$133$	−34.3248	−2.97634
$134$	2.32353	0.200722
$135$	−1.00000	−0.0860663
$136$	−6.70643	−0.575072
$137$	11.6333	0.993903	0.496951	−	0.867778i	$-0.334453\pi$
$137$	11.6333	0.993903	0.496951	+	0.867778i	$0.334453\pi$
$138$	0	0
$139$	−10.3224	−0.875535	−0.437767	−	0.899088i	$-0.644231\pi$
$139$	−10.3224	−0.875535	−0.437767	+	0.899088i	$0.644231\pi$
$140$	6.87008	0.580628
$141$	0.179563	0.0151219
$142$	5.21307	0.437471
$143$	20.4781	1.71247
$144$	1.37987	0.114989
$145$	5.43801	0.451602
$146$	−3.80242	−0.314691
$147$	−13.2724	−1.09469
$148$	−3.33278	−0.273953
$149$	6.81582	0.558374	0.279187	−	0.960237i	$-0.409935\pi$
$149$	6.81582	0.558374	0.279187	+	0.960237i	$0.409935\pi$
$150$	0.688592	0.0562233
$151$	2.80665	0.228402	0.114201	−	0.993458i	$-0.463569\pi$
$151$	2.80665	0.228402	0.114201	+	0.993458i	$0.463569\pi$
$152$	18.5089	1.50127
$153$	−2.76227	−0.223317
$154$	11.0563	0.890941
$155$	9.51642	0.764377
$156$	8.76204	0.701525
$157$	6.44075	0.514028	0.257014	−	0.966408i	$-0.417261\pi$
$157$	6.44075	0.514028	0.257014	+	0.966408i	$0.417261\pi$
$158$	−4.87540	−0.387866
$159$	−2.00838	−0.159275
$160$	−5.80590	−0.458997
$161$	0	0
$162$	−0.688592	−0.0541009
$163$	1.56292	0.122417	0.0612087	−	0.998125i	$-0.480504\pi$
$163$	1.56292	0.122417	0.0612087	+	0.998125i	$0.480504\pi$
$164$	−12.9315	−1.00978
$165$	−3.56611	−0.277621
$166$	−4.27048	−0.331454
$167$	−17.0739	−1.32122	−0.660610	−	0.750729i	$-0.729702\pi$
$167$	−17.0739	−1.32122	−0.660610	+	0.750729i	$0.729702\pi$
$168$	10.9314	0.843380
$169$	19.9756	1.53658
$170$	1.90208	0.145883
$171$	7.62351	0.582985
$172$	2.85055	0.217352
$173$	−15.0431	−1.14371	−0.571855	−	0.820355i	$-0.693776\pi$
$173$	−15.0431	−1.14371	−0.571855	+	0.820355i	$0.693776\pi$
$174$	3.74457	0.283875
$175$	−4.50249	−0.340356
$176$	4.92077	0.370917
$177$	−12.2480	−0.920614
$178$	−6.72446	−0.504020
$179$	−18.5814	−1.38884	−0.694419	−	0.719571i	$-0.744338\pi$
$179$	−18.5814	−1.38884	−0.694419	+	0.719571i	$0.744338\pi$
$180$	−1.52584	−0.113729
$181$	6.57148	0.488454	0.244227	−	0.969718i	$-0.421466\pi$
$181$	6.57148	0.488454	0.244227	+	0.969718i	$0.421466\pi$
$182$	17.8037	1.31970
$183$	5.61248	0.414886
$184$	0	0
$185$	2.18422	0.160587
$186$	6.55293	0.480484
$187$	−9.85057	−0.720345
$188$	0.273985	0.0199824
$189$	4.50249	0.327508
$190$	−5.24949	−0.380838
$191$	−8.83669	−0.639401	−0.319700	−	0.947519i	$-0.603582\pi$
$191$	−8.83669	−0.639401	−0.319700	+	0.947519i	$0.603582\pi$
$192$	−1.23816	−0.0893562
$193$	26.2613	1.89033	0.945165	−	0.326593i	$-0.105901\pi$
$193$	26.2613	1.89033	0.945165	+	0.326593i	$0.105901\pi$
$194$	1.99306	0.143093
$195$	−5.74244	−0.411224
$196$	−20.2516	−1.44654
$197$	−9.68390	−0.689950	−0.344975	−	0.938612i	$-0.612113\pi$
$197$	−9.68390	−0.689950	−0.344975	+	0.938612i	$0.612113\pi$
$198$	−2.45559	−0.174512
$199$	−14.8544	−1.05300	−0.526502	−	0.850174i	$-0.676497\pi$
$199$	−14.8544	−1.05300	−0.526502	+	0.850174i	$0.676497\pi$
$200$	2.42787	0.171676
$201$	3.37431	0.238006
$202$	−2.79411	−0.196593
$203$	−24.4846	−1.71848
$204$	−4.21479	−0.295094
$205$	8.47498	0.591918
$206$	2.86275	0.199457
$207$	0	0
$208$	7.92382	0.549418
$209$	27.1863	1.88051
$210$	−3.10038	−0.213947
$211$	20.6464	1.42136	0.710679	−	0.703516i	$-0.248388\pi$
$211$	20.6464	1.42136	0.710679	+	0.703516i	$0.248388\pi$
$212$	−3.06447	−0.210469
$213$	7.57061	0.518730
$214$	−3.13498	−0.214303
$215$	−1.86818	−0.127409
$216$	−2.42787	−0.165195
$217$	−42.8476	−2.90868
$218$	12.0224	0.814261
$219$	−5.52203	−0.373144
$220$	−5.44131	−0.366853
$221$	−15.8622	−1.06701
$222$	1.50404	0.100945
$223$	2.92606	0.195944	0.0979718	−	0.995189i	$-0.468764\pi$
$223$	2.92606	0.195944	0.0979718	+	0.995189i	$0.468764\pi$
$224$	26.1410	1.74662
$225$	1.00000	0.0666667
$226$	9.60501	0.638916
$227$	13.3749	0.887721	0.443861	−	0.896096i	$-0.353608\pi$
$227$	13.3749	0.887721	0.443861	+	0.896096i	$0.353608\pi$
$228$	11.6323	0.770366
$229$	6.86883	0.453905	0.226953	−	0.973906i	$-0.427124\pi$
$229$	6.86883	0.453905	0.226953	+	0.973906i	$0.427124\pi$
$230$	0	0
$231$	16.0564	1.05643
$232$	13.2028	0.866803
$233$	24.8843	1.63022	0.815112	−	0.579303i	$-0.196675\pi$
$233$	24.8843	1.63022	0.815112	+	0.579303i	$0.196675\pi$
$234$	−3.95420	−0.258494
$235$	−0.179563	−0.0117134
$236$	−18.6885	−1.21651
$237$	−7.08024	−0.459911
$238$	−8.56410	−0.555128
$239$	−8.35182	−0.540234	−0.270117	−	0.962827i	$-0.587062\pi$
$239$	−8.35182	−0.540234	−0.270117	+	0.962827i	$0.587062\pi$
$240$	−1.37987	−0.0890703
$241$	−16.1183	−1.03827	−0.519134	−	0.854693i	$-0.673745\pi$
$241$	−16.1183	−1.03827	−0.519134	+	0.854693i	$0.673745\pi$
$242$	−1.18240	−0.0760077
$243$	−1.00000	−0.0641500
$244$	8.56375	0.548238
$245$	13.2724	0.847944
$246$	5.83581	0.372077
$247$	43.7775	2.78550
$248$	23.1046	1.46714
$249$	−6.20176	−0.393020
$250$	−0.688592	−0.0435504
$251$	−16.5330	−1.04356	−0.521778	−	0.853082i	$-0.674731\pi$
$251$	−16.5330	−1.04356	−0.521778	+	0.853082i	$0.674731\pi$
$252$	6.87008	0.432775
$253$	0	0
$254$	5.41617	0.339841
$255$	2.76227	0.172980
$256$	−9.88503	−0.617814
$257$	0.718986	0.0448491	0.0224246	−	0.999749i	$-0.492861\pi$
$257$	0.718986	0.0448491	0.0224246	+	0.999749i	$0.492861\pi$
$258$	−1.28642	−0.0800888
$259$	−9.83445	−0.611083
$260$	−8.76204	−0.543399
$261$	5.43801	0.336604
$262$	9.21420	0.569255
$263$	19.7883	1.22020	0.610098	−	0.792326i	$-0.291130\pi$
$263$	19.7883	1.22020	0.610098	+	0.792326i	$0.291130\pi$
$264$	−8.65804	−0.532865
$265$	2.00838	0.123374
$266$	23.6358	1.44920
$267$	−9.76552	−0.597640
$268$	5.14867	0.314505
$269$	11.4922	0.700690	0.350345	−	0.936621i	$-0.386064\pi$
$269$	11.4922	0.700690	0.350345	+	0.936621i	$0.386064\pi$
$270$	0.688592	0.0419064
$271$	−13.1326	−0.797747	−0.398873	−	0.917006i	$-0.630599\pi$
$271$	−13.1326	−0.797747	−0.398873	+	0.917006i	$0.630599\pi$
$272$	−3.81158	−0.231111
$273$	25.8553	1.56483
$274$	−8.01062	−0.483940
$275$	3.56611	0.215044
$276$	0	0
$277$	1.66350	0.0999503	0.0499751	−	0.998750i	$-0.484086\pi$
$277$	1.66350	0.0999503	0.0499751	+	0.998750i	$0.484086\pi$
$278$	7.10793	0.426305
$279$	9.51642	0.569733
$280$	−10.9314	−0.653279
$281$	21.5412	1.28504	0.642520	−	0.766269i	$-0.277889\pi$
$281$	21.5412	1.28504	0.642520	+	0.766269i	$0.277889\pi$
$282$	−0.123646	−0.00736300
$283$	17.4733	1.03868	0.519339	−	0.854569i	$-0.326178\pi$
$283$	17.4733	1.03868	0.519339	+	0.854569i	$0.326178\pi$
$284$	11.5516	0.685458
$285$	−7.62351	−0.451578
$286$	−14.1011	−0.833815
$287$	−38.1585	−2.25243
$288$	−5.80590	−0.342116
$289$	−9.36985	−0.551167
$290$	−3.74457	−0.219889
$291$	2.89439	0.169672
$292$	−8.42573	−0.493079
$293$	−13.5956	−0.794263	−0.397131	−	0.917762i	$-0.629994\pi$
$293$	−13.5956	−0.794263	−0.397131	+	0.917762i	$0.629994\pi$
$294$	9.13929	0.533014
$295$	12.2480	0.713104
$296$	5.30300	0.308231
$297$	−3.56611	−0.206927
$298$	−4.69332	−0.271877
$299$	0	0
$300$	1.52584	0.0880945
$301$	8.41148	0.484829
$302$	−1.93264	−0.111211
$303$	−4.05771	−0.233110
$304$	10.5195	0.603333
$305$	−5.61248	−0.321370
$306$	1.90208	0.108735
$307$	−25.0091	−1.42734	−0.713672	−	0.700480i	$-0.752969\pi$
$307$	−25.0091	−1.42734	−0.713672	+	0.700480i	$0.752969\pi$
$308$	24.4995	1.39599
$309$	4.15739	0.236506
$310$	−6.55293	−0.372181
$311$	−0.692158	−0.0392487	−0.0196243	−	0.999807i	$-0.506247\pi$
$311$	−0.692158	−0.0392487	−0.0196243	+	0.999807i	$0.506247\pi$
$312$	−13.9419	−0.789303
$313$	6.75489	0.381809	0.190905	−	0.981609i	$-0.438858\pi$
$313$	6.75489	0.381809	0.190905	+	0.981609i	$0.438858\pi$
$314$	−4.43505	−0.250284
$315$	−4.50249	−0.253687
$316$	−10.8033	−0.607734
$317$	26.2307	1.47326	0.736632	−	0.676294i	$-0.236415\pi$
$317$	26.2307	1.47326	0.736632	+	0.676294i	$0.236415\pi$
$318$	1.38296	0.0775524
$319$	19.3925	1.08577
$320$	1.23816	0.0692150
$321$	−4.55274	−0.254109
$322$	0	0
$323$	−21.0582	−1.17171
$324$	−1.52584	−0.0847689
$325$	5.74244	0.318533
$326$	−1.07622	−0.0596061
$327$	17.4594	0.965508
$328$	20.5761	1.13613
$329$	0.808482	0.0445730
$330$	2.45559	0.135176
$331$	10.7493	0.590834	0.295417	−	0.955368i	$-0.404541\pi$
$331$	10.7493	0.590834	0.295417	+	0.955368i	$0.404541\pi$
$332$	−9.46289	−0.519344
$333$	2.18422	0.119695
$334$	11.7570	0.643313
$335$	−3.37431	−0.184359
$336$	6.21286	0.338939
$337$	6.48062	0.353022	0.176511	−	0.984299i	$-0.443519\pi$
$337$	6.48062	0.353022	0.176511	+	0.984299i	$0.443519\pi$
$338$	−13.7550	−0.748174
$339$	13.9488	0.757593
$340$	4.21479	0.228579
$341$	33.9366	1.83777
$342$	−5.24949	−0.283860
$343$	−28.2416	−1.52490
$344$	−4.53570	−0.244548
$345$	0	0
$346$	10.3586	0.556881
$347$	26.3389	1.41394	0.706972	−	0.707242i	$-0.250061\pi$
$347$	26.3389	1.41394	0.706972	+	0.707242i	$0.250061\pi$
$348$	8.29753	0.444794
$349$	19.8326	1.06162	0.530809	−	0.847492i	$-0.321888\pi$
$349$	19.8326	1.06162	0.530809	+	0.847492i	$0.321888\pi$
$350$	3.10038	0.165722
$351$	−5.74244	−0.306509
$352$	−20.7045	−1.10355
$353$	−4.86454	−0.258913	−0.129457	−	0.991585i	$-0.541323\pi$
$353$	−4.86454	−0.258913	−0.129457	+	0.991585i	$0.541323\pi$
$354$	8.43386	0.448254
$355$	−7.57061	−0.401806
$356$	−14.9006	−0.789732
$357$	−12.4371	−0.658242
$358$	12.7950	0.676236
$359$	−24.7416	−1.30581	−0.652906	−	0.757439i	$-0.726450\pi$
$359$	−24.7416	−1.30581	−0.652906	+	0.757439i	$0.726450\pi$
$360$	2.42787	0.127960
$361$	39.1179	2.05884
$362$	−4.52507	−0.237832
$363$	−1.71713	−0.0901259
$364$	39.4510	2.06780
$365$	5.52203	0.289036
$366$	−3.86471	−0.202012
$367$	−21.4031	−1.11723	−0.558617	−	0.829425i	$-0.688668\pi$
$367$	−21.4031	−1.11723	−0.558617	+	0.829425i	$0.688668\pi$
$368$	0	0
$369$	8.47498	0.441190
$370$	−1.50404	−0.0781913
$371$	−9.04273	−0.469475
$372$	14.5205	0.752855
$373$	−3.14480	−0.162832	−0.0814158	−	0.996680i	$-0.525944\pi$
$373$	−3.14480	−0.162832	−0.0814158	+	0.996680i	$0.525944\pi$
$374$	6.78302	0.350742
$375$	−1.00000	−0.0516398
$376$	−0.435955	−0.0224827
$377$	31.2274	1.60829
$378$	−3.10038	−0.159466
$379$	10.7027	0.549759	0.274879	−	0.961479i	$-0.411362\pi$
$379$	10.7027	0.549759	0.274879	+	0.961479i	$0.411362\pi$
$380$	−11.6323	−0.596723
$381$	7.86557	0.402965
$382$	6.08488	0.311329
$383$	−17.4465	−0.891474	−0.445737	−	0.895164i	$-0.647058\pi$
$383$	−17.4465	−0.891474	−0.445737	+	0.895164i	$0.647058\pi$
$384$	−10.7592	−0.549054
$385$	−16.0564	−0.818308
$386$	−18.0833	−0.920417
$387$	−1.86818	−0.0949651
$388$	4.41638	0.224208
$389$	9.82475	0.498135	0.249067	−	0.968486i	$-0.419876\pi$
$389$	9.82475	0.498135	0.249067	+	0.968486i	$0.419876\pi$
$390$	3.95420	0.200229
$391$	0	0
$392$	32.2237	1.62754
$393$	13.3812	0.674993
$394$	6.66826	0.335942
$395$	7.08024	0.356246
$396$	−5.44131	−0.273436
$397$	26.4127	1.32562	0.662808	−	0.748789i	$-0.269364\pi$
$397$	26.4127	1.32562	0.662808	+	0.748789i	$0.269364\pi$
$398$	10.2287	0.512716
$399$	34.3248	1.71839
$400$	1.37987	0.0689936
$401$	−16.1356	−0.805771	−0.402886	−	0.915250i	$-0.631993\pi$
$401$	−16.1356	−0.805771	−0.402886	+	0.915250i	$0.631993\pi$
$402$	−2.32353	−0.115887
$403$	54.6474	2.72218
$404$	−6.19143	−0.308035
$405$	1.00000	0.0496904
$406$	16.8599	0.836742
$407$	7.78918	0.386095
$408$	6.70643	0.332018
$409$	−10.0135	−0.495138	−0.247569	−	0.968870i	$-0.579632\pi$
$409$	−10.0135	−0.495138	−0.247569	+	0.968870i	$0.579632\pi$
$410$	−5.83581	−0.288210
$411$	−11.6333	−0.573830
$412$	6.34351	0.312522
$413$	−55.1464	−2.71358
$414$	0	0
$415$	6.20176	0.304432
$416$	−33.3400	−1.63463
$417$	10.3224	0.505490
$418$	−18.7203	−0.915638
$419$	20.5197	1.00245	0.501226	−	0.865316i	$-0.332882\pi$
$419$	20.5197	1.00245	0.501226	+	0.865316i	$0.332882\pi$
$420$	−6.87008	−0.335226
$421$	9.21321	0.449025	0.224512	−	0.974471i	$-0.427921\pi$
$421$	9.21321	0.449025	0.224512	+	0.974471i	$0.427921\pi$
$422$	−14.2170	−0.692071
$423$	−0.179563	−0.00873066
$424$	4.87609	0.236804
$425$	−2.76227	−0.133990
$426$	−5.21307	−0.252574
$427$	25.2701	1.22291
$428$	−6.94676	−0.335784
$429$	−20.4781	−0.988694
$430$	1.28642	0.0620365
$431$	0.986048	0.0474963	0.0237481	−	0.999718i	$-0.492440\pi$
$431$	0.986048	0.0474963	0.0237481	+	0.999718i	$0.492440\pi$
$432$	−1.37987	−0.0663891
$433$	2.00316	0.0962656	0.0481328	−	0.998841i	$-0.484673\pi$
$433$	2.00316	0.0962656	0.0481328	+	0.998841i	$0.484673\pi$
$434$	29.5045	1.41626
$435$	−5.43801	−0.260732
$436$	26.6403	1.27584
$437$	0	0
$438$	3.80242	0.181687
$439$	−0.674919	−0.0322121	−0.0161061	−	0.999870i	$-0.505127\pi$
$439$	−0.674919	−0.0322121	−0.0161061	+	0.999870i	$0.505127\pi$
$440$	8.65804	0.412756
$441$	13.2724	0.632020
$442$	10.9226	0.519534
$443$	−15.5270	−0.737709	−0.368854	−	0.929487i	$-0.620250\pi$
$443$	−15.5270	−0.737709	−0.368854	+	0.929487i	$0.620250\pi$
$444$	3.33278	0.158167
$445$	9.76552	0.462930
$446$	−2.01486	−0.0954066
$447$	−6.81582	−0.322377
$448$	−5.57479	−0.263384
$449$	−0.0259632	−0.00122528	−0.000612639	−	1.00000i	$-0.500195\pi$
$449$	−0.0259632	−0.00122528	−0.000612639		1.00000i	$0.500195\pi$
$450$	−0.688592	−0.0324605
$451$	30.2227	1.42313
$452$	21.2836	1.00110
$453$	−2.80665	−0.131868
$454$	−9.20983	−0.432239
$455$	−25.8553	−1.21211
$456$	−18.5089	−0.866757
$457$	−25.5521	−1.19528	−0.597638	−	0.801766i	$-0.703894\pi$
$457$	−25.5521	−1.19528	−0.597638	+	0.801766i	$0.703894\pi$
$458$	−4.72983	−0.221010
$459$	2.76227	0.128932
$460$	0	0
$461$	−12.2974	−0.572745	−0.286373	−	0.958118i	$-0.592450\pi$
$461$	−12.2974	−0.572745	−0.286373	+	0.958118i	$0.592450\pi$
$462$	−11.0563	−0.514385
$463$	−2.55258	−0.118629	−0.0593143	−	0.998239i	$-0.518891\pi$
$463$	−2.55258	−0.118629	−0.0593143	+	0.998239i	$0.518891\pi$
$464$	7.50375	0.348353
$465$	−9.51642	−0.441313
$466$	−17.1351	−0.793769
$467$	30.0231	1.38930	0.694652	−	0.719346i	$-0.255558\pi$
$467$	30.0231	1.38930	0.694652	+	0.719346i	$0.255558\pi$
$468$	−8.76204	−0.405026
$469$	15.1928	0.701539
$470$	0.123646	0.00570336
$471$	−6.44075	−0.296774
$472$	29.7364	1.36873
$473$	−6.66214	−0.306326
$474$	4.87540	0.223935
$475$	7.62351	0.349791
$476$	−18.9771	−0.869812
$477$	2.00838	0.0919576
$478$	5.75100	0.263044
$479$	−21.7578	−0.994138	−0.497069	−	0.867711i	$-0.665590\pi$
$479$	−21.7578	−0.994138	−0.497069	+	0.867711i	$0.665590\pi$
$480$	5.80590	0.265002
$481$	12.5428	0.571901
$482$	11.0989	0.505541
$483$	0	0
$484$	−2.62007	−0.119094
$485$	−2.89439	−0.131428
$486$	0.688592	0.0312352
$487$	−10.0915	−0.457288	−0.228644	−	0.973510i	$-0.573429\pi$
$487$	−10.0915	−0.457288	−0.228644	+	0.973510i	$0.573429\pi$
$488$	−13.6263	−0.616836
$489$	−1.56292	−0.0706777
$490$	−9.13929	−0.412871
$491$	40.0665	1.80817	0.904087	−	0.427348i	$-0.140552\pi$
$491$	40.0665	1.80817	0.904087	+	0.427348i	$0.140552\pi$
$492$	12.9315	0.582996
$493$	−15.0213	−0.676523
$494$	−30.1449	−1.35628
$495$	3.56611	0.160285
$496$	13.1314	0.589619
$497$	34.0866	1.52899
$498$	4.27048	0.191365
$499$	−8.33551	−0.373149	−0.186574	−	0.982441i	$-0.559739\pi$
$499$	−8.33551	−0.373149	−0.186574	+	0.982441i	$0.559739\pi$
$500$	−1.52584	−0.0682377
$501$	17.0739	0.762807
$502$	11.3845	0.508116
$503$	−31.9244	−1.42344	−0.711719	−	0.702464i	$-0.752083\pi$
$503$	−31.9244	−1.42344	−0.711719	+	0.702464i	$0.752083\pi$
$504$	−10.9314	−0.486925
$505$	4.05771	0.180566
$506$	0	0
$507$	−19.9756	−0.887146
$508$	12.0016	0.532485
$509$	−21.3699	−0.947205	−0.473602	−	0.880739i	$-0.657047\pi$
$509$	−21.3699	−0.947205	−0.473602	+	0.880739i	$0.657047\pi$
$510$	−1.90208	−0.0842255
$511$	−24.8629	−1.09987
$512$	−14.7117	−0.650171
$513$	−7.62351	−0.336586
$514$	−0.495088	−0.0218374
$515$	−4.15739	−0.183196
$516$	−2.85055	−0.125488
$517$	−0.640342	−0.0281622
$518$	6.77193	0.297541
$519$	15.0431	0.660321
$520$	13.9419	0.611391
$521$	−12.0773	−0.529116	−0.264558	−	0.964370i	$-0.585226\pi$
$521$	−12.0773	−0.529116	−0.264558	+	0.964370i	$0.585226\pi$
$522$	−3.74457	−0.163895
$523$	−9.38256	−0.410271	−0.205135	−	0.978734i	$-0.565763\pi$
$523$	−9.38256	−0.410271	−0.205135	+	0.978734i	$0.565763\pi$
$524$	20.4176	0.891947
$525$	4.50249	0.196505
$526$	−13.6260	−0.594124
$527$	−26.2869	−1.14508
$528$	−4.92077	−0.214149
$529$	0	0
$530$	−1.38296	−0.0600719
$531$	12.2480	0.531517
$532$	52.3742	2.27071
$533$	48.6670	2.10800
$534$	6.72446	0.290996
$535$	4.55274	0.196832
$536$	−8.19239	−0.353857
$537$	18.5814	0.801845
$538$	−7.91342	−0.341172
$539$	47.3309	2.03869
$540$	1.52584	0.0656617
$541$	23.7397	1.02065	0.510325	−	0.859982i	$-0.329525\pi$
$541$	23.7397	1.02065	0.510325	+	0.859982i	$0.329525\pi$
$542$	9.04299	0.388429
$543$	−6.57148	−0.282009
$544$	16.0375	0.687602
$545$	−17.4594	−0.747879
$546$	−17.8037	−0.761930
$547$	23.2553	0.994327	0.497163	−	0.867657i	$-0.334375\pi$
$547$	23.2553	0.994327	0.497163	+	0.867657i	$0.334375\pi$
$548$	−17.7506	−0.758269
$549$	−5.61248	−0.239535
$550$	−2.45559	−0.104707
$551$	41.4567	1.76611
$552$	0	0
$553$	−31.8787	−1.35562
$554$	−1.14548	−0.0486666
$555$	−2.18422	−0.0927151
$556$	15.7503	0.667963
$557$	1.42358	0.0603191	0.0301595	−	0.999545i	$-0.490398\pi$
$557$	1.42358	0.0603191	0.0301595	+	0.999545i	$0.490398\pi$
$558$	−6.55293	−0.277408
$559$	−10.7279	−0.453743
$560$	−6.21286	−0.262541
$561$	9.85057	0.415891
$562$	−14.8331	−0.625697
$563$	−37.5524	−1.58264	−0.791322	−	0.611400i	$-0.790607\pi$
$563$	−37.5524	−1.58264	−0.791322	+	0.611400i	$0.790607\pi$
$564$	−0.273985	−0.0115368
$565$	−13.9488	−0.586829
$566$	−12.0319	−0.505740
$567$	−4.50249	−0.189087
$568$	−18.3804	−0.771226
$569$	−12.5933	−0.527938	−0.263969	−	0.964531i	$-0.585032\pi$
$569$	−12.5933	−0.527938	−0.263969	+	0.964531i	$0.585032\pi$
$570$	5.24949	0.219877
$571$	−19.1538	−0.801562	−0.400781	−	0.916174i	$-0.631261\pi$
$571$	−19.1538	−0.801562	−0.400781	+	0.916174i	$0.631261\pi$
$572$	−31.2464	−1.30648
$573$	8.83669	0.369158
$574$	26.2757	1.09673
$575$	0	0
$576$	1.23816	0.0515898
$577$	−5.17498	−0.215437	−0.107719	−	0.994181i	$-0.534355\pi$
$577$	−5.17498	−0.215437	−0.107719	+	0.994181i	$0.534355\pi$
$578$	6.45200	0.268368
$579$	−26.2613	−1.09138
$580$	−8.29753	−0.344536
$581$	−27.9234	−1.15846
$582$	−1.99306	−0.0826149
$583$	7.16212	0.296625
$584$	13.4067	0.554775
$585$	5.74244	0.237420
$586$	9.36182	0.386733
$587$	−5.65430	−0.233378	−0.116689	−	0.993168i	$-0.537228\pi$
$587$	−5.65430	−0.233378	−0.116689	+	0.993168i	$0.537228\pi$
$588$	20.2516	0.835162
$589$	72.5485	2.98931
$590$	−8.43386	−0.347216
$591$	9.68390	0.398343
$592$	3.01395	0.123873
$593$	2.01231	0.0826355	0.0413178	−	0.999146i	$-0.486844\pi$
$593$	2.01231	0.0826355	0.0413178	+	0.999146i	$0.486844\pi$
$594$	2.45559	0.100754
$595$	12.4371	0.509872
$596$	−10.3999	−0.425995
$597$	14.8544	0.607952
$598$	0	0
$599$	45.6878	1.86675	0.933376	−	0.358899i	$-0.116848\pi$
$599$	45.6878	1.86675	0.933376	+	0.358899i	$0.116848\pi$
$600$	−2.42787	−0.0991172
$601$	−32.9682	−1.34480	−0.672400	−	0.740188i	$-0.734737\pi$
$601$	−32.9682	−1.34480	−0.672400	+	0.740188i	$0.734737\pi$
$602$	−5.79208	−0.236067
$603$	−3.37431	−0.137413
$604$	−4.28250	−0.174252
$605$	1.71713	0.0698112
$606$	2.79411	0.113503
$607$	−9.13199	−0.370656	−0.185328	−	0.982677i	$-0.559335\pi$
$607$	−9.13199	−0.370656	−0.185328	+	0.982677i	$0.559335\pi$
$608$	−44.2614	−1.79504
$609$	24.4846	0.992165
$610$	3.86471	0.156478
$611$	−1.03113	−0.0417151
$612$	4.21479	0.170373
$613$	5.16155	0.208473	0.104237	−	0.994553i	$-0.466760\pi$
$613$	5.16155	0.208473	0.104237	+	0.994553i	$0.466760\pi$
$614$	17.2211	0.694985
$615$	−8.47498	−0.341744
$616$	−38.9827	−1.57066
$617$	−31.7948	−1.28001	−0.640005	−	0.768370i	$-0.721068\pi$
$617$	−31.7948	−1.28001	−0.640005	+	0.768370i	$0.721068\pi$
$618$	−2.86275	−0.115157
$619$	−15.3983	−0.618910	−0.309455	−	0.950914i	$-0.600147\pi$
$619$	−15.3983	−0.618910	−0.309455	+	0.950914i	$0.600147\pi$
$620$	−14.5205	−0.583159
$621$	0	0
$622$	0.476615	0.0191105
$623$	−43.9692	−1.76159
$624$	−7.92382	−0.317207
$625$	1.00000	0.0400000
$626$	−4.65137	−0.185906
$627$	−27.1863	−1.08571
$628$	−9.82755	−0.392162
$629$	−6.03342	−0.240568
$630$	3.10038	0.123522
$631$	−32.1473	−1.27976	−0.639881	−	0.768474i	$-0.721017\pi$
$631$	−32.1473	−1.27976	−0.639881	+	0.768474i	$0.721017\pi$
$632$	17.1899	0.683777
$633$	−20.6464	−0.820622
$634$	−18.0623	−0.717345
$635$	−7.86557	−0.312135
$636$	3.06447	0.121514
$637$	76.2161	3.01979
$638$	−13.3535	−0.528672
$639$	−7.57061	−0.299489
$640$	10.7592	0.425295
$641$	−0.0267859	−0.00105798	−0.000528990	−	1.00000i	$-0.500168\pi$
$641$	−0.0267859	−0.00105798	−0.000528990		1.00000i	$0.500168\pi$
$642$	3.13498	0.123728
$643$	−4.96731	−0.195892	−0.0979458	−	0.995192i	$-0.531227\pi$
$643$	−4.96731	−0.195892	−0.0979458	+	0.995192i	$0.531227\pi$
$644$	0	0
$645$	1.86818	0.0735596
$646$	14.5005	0.570516
$647$	−19.8224	−0.779301	−0.389650	−	0.920963i	$-0.627404\pi$
$647$	−19.8224	−0.779301	−0.389650	+	0.920963i	$0.627404\pi$
$648$	2.42787	0.0953756
$649$	43.6776	1.71450
$650$	−3.95420	−0.155096
$651$	42.8476	1.67933
$652$	−2.38477	−0.0933947
$653$	8.51141	0.333077	0.166539	−	0.986035i	$-0.446741\pi$
$653$	8.51141	0.333077	0.166539	+	0.986035i	$0.446741\pi$
$654$	−12.0224	−0.470114
$655$	−13.3812	−0.522847
$656$	11.6944	0.456589
$657$	5.52203	0.215435
$658$	−0.556714	−0.0217030
$659$	−0.703960	−0.0274224	−0.0137112	−	0.999906i	$-0.504365\pi$
$659$	−0.703960	−0.0274224	−0.0137112	+	0.999906i	$0.504365\pi$
$660$	5.44131	0.211803
$661$	−17.4933	−0.680411	−0.340205	−	0.940351i	$-0.610497\pi$
$661$	−17.4933	−0.680411	−0.340205	+	0.940351i	$0.610497\pi$
$662$	−7.40187	−0.287682
$663$	15.8622	0.616036
$664$	15.0570	0.584326
$665$	−34.3248	−1.33106
$666$	−1.50404	−0.0582804
$667$	0	0
$668$	26.0521	1.00799
$669$	−2.92606	−0.113128
$670$	2.32353	0.0897657
$671$	−20.0147	−0.772659
$672$	−26.1410	−1.00841
$673$	39.5279	1.52369	0.761844	−	0.647761i	$-0.224294\pi$
$673$	39.5279	1.52369	0.761844	+	0.647761i	$0.224294\pi$
$674$	−4.46250	−0.171889
$675$	−1.00000	−0.0384900
$676$	−30.4795	−1.17229
$677$	−8.69695	−0.334251	−0.167125	−	0.985936i	$-0.553448\pi$
$677$	−8.69695	−0.334251	−0.167125	+	0.985936i	$0.553448\pi$
$678$	−9.60501	−0.368878
$679$	13.0320	0.500122
$680$	−6.70643	−0.257180
$681$	−13.3749	−0.512526
$682$	−23.3685	−0.894825
$683$	0.641729	0.0245551	0.0122775	−	0.999925i	$-0.496092\pi$
$683$	0.641729	0.0245551	0.0122775	+	0.999925i	$0.496092\pi$
$684$	−11.6323	−0.444771
$685$	11.6333	0.444487
$686$	19.4469	0.742487
$687$	−6.86883	−0.262062
$688$	−2.57785	−0.0982797
$689$	11.5330	0.439373
$690$	0	0
$691$	16.7072	0.635574	0.317787	−	0.948162i	$-0.397060\pi$
$691$	16.7072	0.635574	0.317787	+	0.948162i	$0.397060\pi$
$692$	22.9534	0.872559
$693$	−16.0564	−0.609931
$694$	−18.1367	−0.688461
$695$	−10.3224	−0.391551
$696$	−13.2028	−0.500449
$697$	−23.4102	−0.886725
$698$	−13.6566	−0.516910
$699$	−24.8843	−0.941210
$700$	6.87008	0.259665
$701$	11.6684	0.440708	0.220354	−	0.975420i	$-0.429279\pi$
$701$	11.6684	0.440708	0.220354	+	0.975420i	$0.429279\pi$
$702$	3.95420	0.149242
$703$	16.6515	0.628022
$704$	4.41540	0.166412
$705$	0.179563	0.00676274
$706$	3.34968	0.126067
$707$	−18.2698	−0.687107
$708$	18.6885	0.702355
$709$	8.23458	0.309256	0.154628	−	0.987973i	$-0.450582\pi$
$709$	8.23458	0.309256	0.154628	+	0.987973i	$0.450582\pi$
$710$	5.21307	0.195643
$711$	7.08024	0.265530
$712$	23.7094	0.888547
$713$	0	0
$714$	8.56410	0.320503
$715$	20.4781	0.765839
$716$	28.3522	1.05957
$717$	8.35182	0.311904
$718$	17.0369	0.635810
$719$	−37.6181	−1.40292	−0.701460	−	0.712709i	$-0.747468\pi$
$719$	−37.6181	−1.40292	−0.701460	+	0.712709i	$0.747468\pi$
$720$	1.37987	0.0514248
$721$	18.7186	0.697117
$722$	−26.9363	−1.00247
$723$	16.1183	0.599444
$724$	−10.0270	−0.372652
$725$	5.43801	0.201962
$726$	1.18240	0.0438830
$727$	20.3605	0.755128	0.377564	−	0.925984i	$-0.376762\pi$
$727$	20.3605	0.755128	0.377564	+	0.925984i	$0.376762\pi$
$728$	−62.7731	−2.32653
$729$	1.00000	0.0370370
$730$	−3.80242	−0.140734
$731$	5.16043	0.190865
$732$	−8.56375	−0.316525
$733$	−1.55236	−0.0573379	−0.0286689	−	0.999589i	$-0.509127\pi$
$733$	−1.55236	−0.0573379	−0.0286689	+	0.999589i	$0.509127\pi$
$734$	14.7380	0.543991
$735$	−13.2724	−0.489561
$736$	0	0
$737$	−12.0332	−0.443248
$738$	−5.83581	−0.214819
$739$	32.3189	1.18887	0.594434	−	0.804144i	$-0.297376\pi$
$739$	32.3189	1.18887	0.594434	+	0.804144i	$0.297376\pi$
$740$	−3.33278	−0.122515
$741$	−43.7775	−1.60821
$742$	6.22676	0.228591
$743$	−5.21934	−0.191479	−0.0957396	−	0.995406i	$-0.530522\pi$
$743$	−5.21934	−0.191479	−0.0957396	+	0.995406i	$0.530522\pi$
$744$	−23.1046	−0.847055
$745$	6.81582	0.249712
$746$	2.16549	0.0792840
$747$	6.20176	0.226910
$748$	15.0304	0.549566
$749$	−20.4987	−0.749006
$750$	0.688592	0.0251438
$751$	−37.3019	−1.36116	−0.680582	−	0.732672i	$-0.738273\pi$
$751$	−37.3019	−1.36116	−0.680582	+	0.732672i	$0.738273\pi$
$752$	−0.247774	−0.00903539
$753$	16.5330	0.602497
$754$	−21.5029	−0.783091
$755$	2.80665	0.102144
$756$	−6.87008	−0.249863
$757$	26.2915	0.955581	0.477790	−	0.878474i	$-0.341438\pi$
$757$	26.2915	0.955581	0.477790	+	0.878474i	$0.341438\pi$
$758$	−7.36977	−0.267682
$759$	0	0
$760$	18.5089	0.671387
$761$	−46.6531	−1.69117	−0.845587	−	0.533838i	$-0.820749\pi$
$761$	−46.6531	−1.69117	−0.845587	+	0.533838i	$0.820749\pi$
$762$	−5.41617	−0.196207
$763$	78.6109	2.84590
$764$	13.4834	0.487812
$765$	−2.76227	−0.0998702
$766$	12.0135	0.434066
$767$	70.3332	2.53958
$768$	9.88503	0.356695
$769$	40.3284	1.45428	0.727139	−	0.686490i	$-0.240849\pi$
$769$	40.3284	1.45428	0.727139	+	0.686490i	$0.240849\pi$
$770$	11.0563	0.398441
$771$	−0.718986	−0.0258937
$772$	−40.0706	−1.44217
$773$	38.2118	1.37438	0.687192	−	0.726476i	$-0.258843\pi$
$773$	38.2118	1.37438	0.687192	+	0.726476i	$0.258843\pi$
$774$	1.28642	0.0462393
$775$	9.51642	0.341840
$776$	−7.02720	−0.252262
$777$	9.83445	0.352809
$778$	−6.76525	−0.242546
$779$	64.6091	2.31486
$780$	8.76204	0.313731
$781$	−26.9976	−0.966051
$782$	0	0
$783$	−5.43801	−0.194338
$784$	18.3142	0.654080
$785$	6.44075	0.229880
$786$	−9.21420	−0.328660
$787$	41.3220	1.47297	0.736484	−	0.676455i	$-0.236484\pi$
$787$	41.3220	1.47297	0.736484	+	0.676455i	$0.236484\pi$
$788$	14.7761	0.526377
$789$	−19.7883	−0.704481
$790$	−4.87540	−0.173459
$791$	62.8042	2.23306
$792$	8.65804	0.307650
$793$	−32.2293	−1.14450
$794$	−18.1876	−0.645454
$795$	−2.00838	−0.0712301
$796$	22.6655	0.803358
$797$	3.63870	0.128890	0.0644448	−	0.997921i	$-0.479472\pi$
$797$	3.63870	0.128890	0.0644448	+	0.997921i	$0.479472\pi$
$798$	−23.6358	−0.836698
$799$	0.496003	0.0175473
$800$	−5.80590	−0.205270
$801$	9.76552	0.345048
$802$	11.1108	0.392337
$803$	19.6921	0.694921
$804$	−5.14867	−0.181579
$805$	0	0
$806$	−37.6298	−1.32545
$807$	−11.4922	−0.404544
$808$	9.85159	0.346578
$809$	−26.9836	−0.948692	−0.474346	−	0.880339i	$-0.657315\pi$
$809$	−26.9836	−0.948692	−0.474346	+	0.880339i	$0.657315\pi$
$810$	−0.688592	−0.0241947
$811$	42.2813	1.48470	0.742348	−	0.670014i	$-0.233712\pi$
$811$	42.2813	1.48470	0.742348	+	0.670014i	$0.233712\pi$
$812$	37.3596	1.31106
$813$	13.1326	0.460579
$814$	−5.36357	−0.187993
$815$	1.56292	0.0547467
$816$	3.81158	0.133432
$817$	−14.2421	−0.498268
$818$	6.89525	0.241087
$819$	−25.8553	−0.903456
$820$	−12.9315	−0.451587
$821$	10.8830	0.379819	0.189909	−	0.981802i	$-0.439181\pi$
$821$	10.8830	0.379819	0.189909	+	0.981802i	$0.439181\pi$
$822$	8.01062	0.279403
$823$	7.07650	0.246671	0.123336	−	0.992365i	$-0.460641\pi$
$823$	7.07650	0.246671	0.123336	+	0.992365i	$0.460641\pi$
$824$	−10.0936	−0.351627
$825$	−3.56611	−0.124156
$826$	37.9734	1.32126
$827$	−27.4763	−0.955446	−0.477723	−	0.878511i	$-0.658538\pi$
$827$	−27.4763	−0.955446	−0.477723	+	0.878511i	$0.658538\pi$
$828$	0	0
$829$	39.3770	1.36762	0.683810	−	0.729660i	$-0.260322\pi$
$829$	39.3770	1.36762	0.683810	+	0.729660i	$0.260322\pi$
$830$	−4.27048	−0.148231
$831$	−1.66350	−0.0577063
$832$	7.11003	0.246496
$833$	−36.6621	−1.27027
$834$	−7.10793	−0.246127
$835$	−17.0739	−0.590868
$836$	−41.4819	−1.43468
$837$	−9.51642	−0.328935
$838$	−14.1297	−0.488102
$839$	15.7836	0.544909	0.272455	−	0.962169i	$-0.412165\pi$
$839$	15.7836	0.544909	0.272455	+	0.962169i	$0.412165\pi$
$840$	10.9314	0.377171
$841$	0.571905	0.0197208
$842$	−6.34415	−0.218634
$843$	−21.5412	−0.741919
$844$	−31.5032	−1.08438
$845$	19.9756	0.687180
$846$	0.123646	0.00425103
$847$	−7.73136	−0.265653
$848$	2.77131	0.0951673
$849$	−17.4733	−0.599680
$850$	1.90208	0.0652408
$851$	0	0
$852$	−11.5516	−0.395750
$853$	1.94952	0.0667502	0.0333751	−	0.999443i	$-0.489374\pi$
$853$	1.94952	0.0667502	0.0333751	+	0.999443i	$0.489374\pi$
$854$	−17.4008	−0.595444
$855$	7.62351	0.260719
$856$	11.0535	0.377799
$857$	38.7052	1.32214	0.661072	−	0.750323i	$-0.270102\pi$
$857$	38.7052	1.32214	0.661072	+	0.750323i	$0.270102\pi$
$858$	14.1011	0.481403
$859$	−31.0203	−1.05840	−0.529199	−	0.848497i	$-0.677508\pi$
$859$	−31.0203	−1.05840	−0.529199	+	0.848497i	$0.677508\pi$
$860$	2.85055	0.0972029
$861$	38.1585	1.30044
$862$	−0.678985	−0.0231263
$863$	8.65664	0.294676	0.147338	−	0.989086i	$-0.452930\pi$
$863$	8.65664	0.294676	0.147338	+	0.989086i	$0.452930\pi$
$864$	5.80590	0.197521
$865$	−15.0431	−0.511482
$866$	−1.37936	−0.0468725
$867$	9.36985	0.318217
$868$	65.3786	2.21909
$869$	25.2489	0.856511
$870$	3.74457	0.126953
$871$	−19.3768	−0.656557
$872$	−42.3891	−1.43548
$873$	−2.89439	−0.0979604
$874$	0	0
$875$	−4.50249	−0.152212
$876$	8.42573	0.284679
$877$	1.11483	0.0376453	0.0188226	−	0.999823i	$-0.494008\pi$
$877$	1.11483	0.0376453	0.0188226	+	0.999823i	$0.494008\pi$
$878$	0.464744	0.0156844
$879$	13.5956	0.458568
$880$	4.92077	0.165879
$881$	8.26458	0.278441	0.139220	−	0.990261i	$-0.455540\pi$
$881$	8.26458	0.278441	0.139220	+	0.990261i	$0.455540\pi$
$882$	−9.13929	−0.307736
$883$	−30.5813	−1.02914	−0.514572	−	0.857447i	$-0.672049\pi$
$883$	−30.5813	−1.02914	−0.514572	+	0.857447i	$0.672049\pi$
$884$	24.2032	0.814040
$885$	−12.2480	−0.411711
$886$	10.6918	0.359196
$887$	23.1617	0.777694	0.388847	−	0.921302i	$-0.372874\pi$
$887$	23.1617	0.777694	0.388847	+	0.921302i	$0.372874\pi$
$888$	−5.30300	−0.177957
$889$	35.4146	1.18777
$890$	−6.72446	−0.225404
$891$	3.56611	0.119469
$892$	−4.46470	−0.149489
$893$	−1.36890	−0.0458086
$894$	4.69332	0.156968
$895$	−18.5814	−0.621107
$896$	−48.4433	−1.61838
$897$	0	0
$898$	0.0178780	0.000596598 0
$899$	51.7503	1.72597
$900$	−1.52584	−0.0508614
$901$	−5.54771	−0.184821
$902$	−20.8111	−0.692934
$903$	−8.41148	−0.279916
$904$	−33.8657	−1.12636
$905$	6.57148	0.218443
$906$	1.93264	0.0642075
$907$	45.4706	1.50983	0.754914	−	0.655824i	$-0.227679\pi$
$907$	45.4706	1.50983	0.754914	+	0.655824i	$0.227679\pi$
$908$	−20.4079	−0.677261
$909$	4.05771	0.134586
$910$	17.8037	0.590188
$911$	−5.42190	−0.179635	−0.0898177	−	0.995958i	$-0.528628\pi$
$911$	−5.42190	−0.179635	−0.0898177	+	0.995958i	$0.528628\pi$
$912$	−10.5195	−0.348334
$913$	22.1161	0.731937
$914$	17.5950	0.581990
$915$	5.61248	0.185543
$916$	−10.4807	−0.346294
$917$	60.2488	1.98959
$918$	−1.90208	−0.0627780
$919$	−0.194900	−0.00642916	−0.00321458	−	0.999995i	$-0.501023\pi$
$919$	−0.194900	−0.00642916	−0.00321458	+	0.999995i	$0.501023\pi$
$920$	0	0
$921$	25.0091	0.824077
$922$	8.46787	0.278874
$923$	−43.4738	−1.43096
$924$	−24.4995	−0.805973
$925$	2.18422	0.0718168
$926$	1.75769	0.0577613
$927$	−4.15739	−0.136547
$928$	−31.5725	−1.03642
$929$	−49.2488	−1.61580	−0.807901	−	0.589319i	$-0.799396\pi$
$929$	−49.2488	−1.61580	−0.807901	+	0.589319i	$0.799396\pi$
$930$	6.55293	0.214879
$931$	101.183	3.31612
$932$	−37.9695	−1.24373
$933$	0.692158	0.0226602
$934$	−20.6737	−0.676464
$935$	−9.85057	−0.322148
$936$	13.9419	0.455704
$937$	−32.5565	−1.06357	−0.531787	−	0.846878i	$-0.678479\pi$
$937$	−32.5565	−1.06357	−0.531787	+	0.846878i	$0.678479\pi$
$938$	−10.4617	−0.341585
$939$	−6.75489	−0.220438
$940$	0.273985	0.00893640
$941$	38.1017	1.24208	0.621041	−	0.783778i	$-0.286710\pi$
$941$	38.1017	1.24208	0.621041	+	0.783778i	$0.286710\pi$
$942$	4.43505	0.144502
$943$	0	0
$944$	16.9006	0.550068
$945$	4.50249	0.146466
$946$	4.58750	0.149152
$947$	−46.6566	−1.51614	−0.758069	−	0.652175i	$-0.773857\pi$
$947$	−46.6566	−1.51614	−0.758069	+	0.652175i	$0.773857\pi$
$948$	10.8033	0.350876
$949$	31.7099	1.02935
$950$	−5.24949	−0.170316
$951$	−26.2307	−0.850590
$952$	30.1956	0.978647
$953$	45.5895	1.47679	0.738394	−	0.674369i	$-0.235584\pi$
$953$	45.5895	1.47679	0.738394	+	0.674369i	$0.235584\pi$
$954$	−1.38296	−0.0447749
$955$	−8.83669	−0.285949
$956$	12.7435	0.412156
$957$	−19.3925	−0.626871
$958$	14.9822	0.484054
$959$	−52.3790	−1.69141
$960$	−1.23816	−0.0399613
$961$	59.5622	1.92136
$962$	−8.63685	−0.278463
$963$	4.55274	0.146710
$964$	24.5939	0.792116
$965$	26.2613	0.845381
$966$	0	0
$967$	−49.6160	−1.59554	−0.797771	−	0.602960i	$-0.793988\pi$
$967$	−49.6160	−1.59554	−0.797771	+	0.602960i	$0.793988\pi$
$968$	4.16896	0.133995
$969$	21.0582	0.676488
$970$	1.99306	0.0639932
$971$	38.3677	1.23128	0.615639	−	0.788029i	$-0.288898\pi$
$971$	38.3677	1.23128	0.615639	+	0.788029i	$0.288898\pi$
$972$	1.52584	0.0489414
$973$	46.4765	1.48997
$974$	6.94891	0.222657
$975$	−5.74244	−0.183905
$976$	−7.74450	−0.247895
$977$	18.7193	0.598883	0.299441	−	0.954115i	$-0.403200\pi$
$977$	18.7193	0.598883	0.299441	+	0.954115i	$0.403200\pi$
$978$	1.07622	0.0344136
$979$	34.8249	1.11301
$980$	−20.2516	−0.646914
$981$	−17.4594	−0.557436
$982$	−27.5895	−0.880415
$983$	−24.0026	−0.765564	−0.382782	−	0.923839i	$-0.625034\pi$
$983$	−24.0026	−0.765564	−0.382782	+	0.923839i	$0.625034\pi$
$984$	−20.5761	−0.655943
$985$	−9.68390	−0.308555
$986$	10.3435	0.329405
$987$	−0.808482	−0.0257343
$988$	−66.7975	−2.12511
$989$	0	0
$990$	−2.45559	−0.0780439
$991$	22.2128	0.705613	0.352807	−	0.935696i	$-0.385227\pi$
$991$	22.2128	0.705613	0.352807	+	0.935696i	$0.385227\pi$
$992$	−55.2514	−1.75423
$993$	−10.7493	−0.341118
$994$	−23.4718	−0.744480
$995$	−14.8544	−0.470917
$996$	9.46289	0.299843
$997$	11.6934	0.370333	0.185166	−	0.982707i	$-0.440718\pi$
$997$	11.6934	0.370333	0.185166	+	0.982707i	$0.440718\pi$
$998$	5.73977	0.181689
$999$	−2.18422	−0.0691058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.10		25
23.3	even	11		345.2.m.d.331.3	yes	50
23.8	even	11		345.2.m.d.271.3	✓	50
23.22	odd	2		7935.2.a.bt.1.10		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.271.3	✓	50	23.8	even	11
345.2.m.d.331.3	yes	50	23.3	even	11
7935.2.a.bt.1.10		25	23.22	odd	2
7935.2.a.bu.1.10		25	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-0.688592 q^{2} -1.00000 q^{3} -1.52584 q^{4} +1.00000 q^{5} +0.688592 q^{6} -4.50249 q^{7} +2.42787 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.688592 q^{2} -1.00000 q^{3} -1.52584 q^{4} +1.00000 q^{5} +0.688592 q^{6} -4.50249 q^{7} +2.42787 q^{8} +1.00000 q^{9} -0.688592 q^{10} +3.56611 q^{11} +1.52584 q^{12} +5.74244 q^{13} +3.10038 q^{14} -1.00000 q^{15} +1.37987 q^{16} -2.76227 q^{17} -0.688592 q^{18} +7.62351 q^{19} -1.52584 q^{20} +4.50249 q^{21} -2.45559 q^{22} -2.42787 q^{24} +1.00000 q^{25} -3.95420 q^{26} -1.00000 q^{27} +6.87008 q^{28} +5.43801 q^{29} +0.688592 q^{30} +9.51642 q^{31} -5.80590 q^{32} -3.56611 q^{33} +1.90208 q^{34} -4.50249 q^{35} -1.52584 q^{36} +2.18422 q^{37} -5.24949 q^{38} -5.74244 q^{39} +2.42787 q^{40} +8.47498 q^{41} -3.10038 q^{42} -1.86818 q^{43} -5.44131 q^{44} +1.00000 q^{45} -0.179563 q^{47} -1.37987 q^{48} +13.2724 q^{49} -0.688592 q^{50} +2.76227 q^{51} -8.76204 q^{52} +2.00838 q^{53} +0.688592 q^{54} +3.56611 q^{55} -10.9314 q^{56} -7.62351 q^{57} -3.74457 q^{58} +12.2480 q^{59} +1.52584 q^{60} -5.61248 q^{61} -6.55293 q^{62} -4.50249 q^{63} +1.23816 q^{64} +5.74244 q^{65} +2.45559 q^{66} -3.37431 q^{67} +4.21479 q^{68} +3.10038 q^{70} -7.57061 q^{71} +2.42787 q^{72} +5.52203 q^{73} -1.50404 q^{74} -1.00000 q^{75} -11.6323 q^{76} -16.0564 q^{77} +3.95420 q^{78} +7.08024 q^{79} +1.37987 q^{80} +1.00000 q^{81} -5.83581 q^{82} +6.20176 q^{83} -6.87008 q^{84} -2.76227 q^{85} +1.28642 q^{86} -5.43801 q^{87} +8.65804 q^{88} +9.76552 q^{89} -0.688592 q^{90} -25.8553 q^{91} -9.51642 q^{93} +0.123646 q^{94} +7.62351 q^{95} +5.80590 q^{96} -2.89439 q^{97} -9.13929 q^{98} +3.56611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

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