LMFDB - Embedded newform 7595.2.a.bf.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0974727 q^{2} +2.80957 q^{3} -1.99050 q^{4} +1.00000 q^{5} -0.273856 q^{6} +0.388965 q^{8} +4.89367 q^{9} +O(q^{10})$	\(q-0.0974727 q^{2} +2.80957 q^{3} -1.99050 q^{4} +1.00000 q^{5} -0.273856 q^{6} +0.388965 q^{8} +4.89367 q^{9} -0.0974727 q^{10} -3.86034 q^{11} -5.59244 q^{12} -0.924749 q^{13} +2.80957 q^{15} +3.94308 q^{16} -7.27298 q^{17} -0.477000 q^{18} -4.70903 q^{19} -1.99050 q^{20} +0.376278 q^{22} +6.17881 q^{23} +1.09282 q^{24} +1.00000 q^{25} +0.0901378 q^{26} +5.32040 q^{27} +2.91568 q^{29} -0.273856 q^{30} -1.00000 q^{31} -1.16227 q^{32} -10.8459 q^{33} +0.708917 q^{34} -9.74085 q^{36} +4.90201 q^{37} +0.459002 q^{38} -2.59814 q^{39} +0.388965 q^{40} -6.34119 q^{41} +10.5052 q^{43} +7.68401 q^{44} +4.89367 q^{45} -0.602266 q^{46} +10.4541 q^{47} +11.0784 q^{48} -0.0974727 q^{50} -20.4339 q^{51} +1.84071 q^{52} -4.94157 q^{53} -0.518594 q^{54} -3.86034 q^{55} -13.2303 q^{57} -0.284199 q^{58} +1.96054 q^{59} -5.59244 q^{60} -12.2443 q^{61} +0.0974727 q^{62} -7.77288 q^{64} -0.924749 q^{65} +1.05718 q^{66} +3.20491 q^{67} +14.4769 q^{68} +17.3598 q^{69} -3.54537 q^{71} +1.90347 q^{72} -9.64392 q^{73} -0.477813 q^{74} +2.80957 q^{75} +9.37331 q^{76} +0.253248 q^{78} -13.5210 q^{79} +3.94308 q^{80} +0.267014 q^{81} +0.618093 q^{82} -16.2427 q^{83} -7.27298 q^{85} -1.02397 q^{86} +8.19180 q^{87} -1.50154 q^{88} -0.959678 q^{89} -0.477000 q^{90} -12.2989 q^{92} -2.80957 q^{93} -1.01899 q^{94} -4.70903 q^{95} -3.26548 q^{96} -10.3808 q^{97} -18.8912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * 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 $

$2$	−0.0974727	−0.0689236	−0.0344618	−	0.999406i	$-0.510972\pi$
$2$	−0.0974727	−0.0689236	−0.0344618	+	0.999406i	$0.510972\pi$
$3$	2.80957	1.62210	0.811052	−	0.584973i	$-0.198895\pi$
$3$	2.80957	1.62210	0.811052	+	0.584973i	$0.198895\pi$
$4$	−1.99050	−0.995250
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.273856	−0.111801
$7$	0	0
$7$	0	0
$8$	0.388965	0.137520
$9$	4.89367	1.63122
$10$	−0.0974727	−0.0308236
$11$	−3.86034	−1.16394	−0.581968	−	0.813211i	$-0.697717\pi$
$11$	−3.86034	−1.16394	−0.581968	+	0.813211i	$0.697717\pi$
$12$	−5.59244	−1.61440
$13$	−0.924749	−0.256479	−0.128240	−	0.991743i	$-0.540933\pi$
$13$	−0.924749	−0.256479	−0.128240	+	0.991743i	$0.540933\pi$
$14$	0	0
$15$	2.80957	0.725427
$16$	3.94308	0.985771
$17$	−7.27298	−1.76396	−0.881979	−	0.471289i	$-0.843789\pi$
$17$	−7.27298	−1.76396	−0.881979	+	0.471289i	$0.843789\pi$
$18$	−0.477000	−0.112430
$19$	−4.70903	−1.08032	−0.540162	−	0.841561i	$-0.681637\pi$
$19$	−4.70903	−1.08032	−0.540162	+	0.841561i	$0.681637\pi$
$20$	−1.99050	−0.445089
$21$	0	0
$22$	0.376278	0.0802227
$23$	6.17881	1.28837	0.644186	−	0.764869i	$-0.277196\pi$
$23$	6.17881	1.28837	0.644186	+	0.764869i	$0.277196\pi$
$24$	1.09282	0.223072
$25$	1.00000	0.200000
$26$	0.0901378	0.0176775
$27$	5.32040	1.02391
$28$	0	0
$29$	2.91568	0.541428	0.270714	−	0.962660i	$-0.412740\pi$
$29$	2.91568	0.541428	0.270714	+	0.962660i	$0.412740\pi$
$30$	−0.273856	−0.0499991
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.16227	−0.205463
$33$	−10.8459	−1.88803
$34$	0.708917	0.121578
$35$	0	0
$36$	−9.74085	−1.62348
$37$	4.90201	0.805886	0.402943	−	0.915225i	$-0.367987\pi$
$37$	4.90201	0.805886	0.402943	+	0.915225i	$0.367987\pi$
$38$	0.459002	0.0744599
$39$	−2.59814	−0.416036
$40$	0.388965	0.0615007
$41$	−6.34119	−0.990328	−0.495164	−	0.868799i	$-0.664892\pi$
$41$	−6.34119	−0.990328	−0.495164	+	0.868799i	$0.664892\pi$
$42$	0	0
$43$	10.5052	1.60203	0.801015	−	0.598645i	$-0.204294\pi$
$43$	10.5052	1.60203	0.801015	+	0.598645i	$0.204294\pi$
$44$	7.68401	1.15841
$45$	4.89367	0.729506
$46$	−0.602266	−0.0887992
$47$	10.4541	1.52489	0.762445	−	0.647053i	$-0.223999\pi$
$47$	10.4541	1.52489	0.762445	+	0.647053i	$0.223999\pi$
$48$	11.0784	1.59902
$49$	0	0
$50$	−0.0974727	−0.0137847
$51$	−20.4339	−2.86132
$52$	1.84071	0.255261
$53$	−4.94157	−0.678777	−0.339388	−	0.940646i	$-0.610220\pi$
$53$	−4.94157	−0.678777	−0.339388	+	0.940646i	$0.610220\pi$
$54$	−0.518594	−0.0705717
$55$	−3.86034	−0.520528
$56$	0	0
$57$	−13.2303	−1.75240
$58$	−0.284199	−0.0373172
$59$	1.96054	0.255240	0.127620	−	0.991823i	$-0.459266\pi$
$59$	1.96054	0.255240	0.127620	+	0.991823i	$0.459266\pi$
$60$	−5.59244	−0.721981
$61$	−12.2443	−1.56773	−0.783863	−	0.620934i	$-0.786753\pi$
$61$	−12.2443	−1.56773	−0.783863	+	0.620934i	$0.786753\pi$
$62$	0.0974727	0.0123790
$63$	0	0
$64$	−7.77288	−0.971610
$65$	−0.924749	−0.114701
$66$	1.05718	0.130130
$67$	3.20491	0.391543	0.195771	−	0.980650i	$-0.437279\pi$
$67$	3.20491	0.391543	0.195771	+	0.980650i	$0.437279\pi$
$68$	14.4769	1.75558
$69$	17.3598	2.08987
$70$	0	0
$71$	−3.54537	−0.420758	−0.210379	−	0.977620i	$-0.567470\pi$
$71$	−3.54537	−0.420758	−0.210379	+	0.977620i	$0.567470\pi$
$72$	1.90347	0.224326
$73$	−9.64392	−1.12874	−0.564368	−	0.825524i	$-0.690880\pi$
$73$	−9.64392	−1.12874	−0.564368	+	0.825524i	$0.690880\pi$
$74$	−0.477813	−0.0555446
$75$	2.80957	0.324421
$76$	9.37331	1.07519
$77$	0	0
$78$	0.253248	0.0286747
$79$	−13.5210	−1.52123	−0.760613	−	0.649205i	$-0.775102\pi$
$79$	−13.5210	−1.52123	−0.760613	+	0.649205i	$0.775102\pi$
$80$	3.94308	0.440850
$81$	0.267014	0.0296683
$82$	0.618093	0.0682570
$83$	−16.2427	−1.78287	−0.891435	−	0.453148i	$-0.850301\pi$
$83$	−16.2427	−1.78287	−0.891435	+	0.453148i	$0.850301\pi$
$84$	0	0
$85$	−7.27298	−0.788866
$86$	−1.02397	−0.110418
$87$	8.19180	0.878253
$88$	−1.50154	−0.160064
$89$	−0.959678	−0.101726	−0.0508628	−	0.998706i	$-0.516197\pi$
$89$	−0.959678	−0.101726	−0.0508628	+	0.998706i	$0.516197\pi$
$90$	−0.477000	−0.0502802
$91$	0	0
$92$	−12.2989	−1.28225
$93$	−2.80957	−0.291339
$94$	−1.01899	−0.105101
$95$	−4.70903	−0.483136
$96$	−3.26548	−0.333282
$97$	−10.3808	−1.05401	−0.527006	−	0.849861i	$-0.676686\pi$
$97$	−10.3808	−1.05401	−0.527006	+	0.849861i	$0.676686\pi$
$98$	0	0
$99$	−18.8912	−1.89864
$100$	−1.99050	−0.199050
$101$	−10.4015	−1.03498	−0.517492	−	0.855688i	$-0.673134\pi$
$101$	−10.4015	−1.03498	−0.517492	+	0.855688i	$0.673134\pi$
$102$	1.99175	0.197213
$103$	−1.70159	−0.167663	−0.0838315	−	0.996480i	$-0.526716\pi$
$103$	−1.70159	−0.167663	−0.0838315	+	0.996480i	$0.526716\pi$
$104$	−0.359695	−0.0352710
$105$	0	0
$106$	0.481668	0.0467838
$107$	−8.91663	−0.862003	−0.431001	−	0.902351i	$-0.641840\pi$
$107$	−8.91663	−0.862003	−0.431001	+	0.902351i	$0.641840\pi$
$108$	−10.5903	−1.01905
$109$	15.7535	1.50891	0.754456	−	0.656350i	$-0.227901\pi$
$109$	15.7535	1.50891	0.754456	+	0.656350i	$0.227901\pi$
$110$	0.376278	0.0358767
$111$	13.7725	1.30723
$112$	0	0
$113$	−4.35280	−0.409477	−0.204738	−	0.978817i	$-0.565634\pi$
$113$	−4.35280	−0.409477	−0.204738	+	0.978817i	$0.565634\pi$
$114$	1.28960	0.120782
$115$	6.17881	0.576177
$116$	−5.80366	−0.538856
$117$	−4.52542	−0.418375
$118$	−0.191099	−0.0175921
$119$	0	0
$120$	1.09282	0.0997606
$121$	3.90223	0.354749
$122$	1.19349	0.108053
$123$	−17.8160	−1.60642
$124$	1.99050	0.178752
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.5459	−1.02453	−0.512267	−	0.858826i	$-0.671194\pi$
$127$	−11.5459	−1.02453	−0.512267	+	0.858826i	$0.671194\pi$
$128$	3.08219	0.272430
$129$	29.5151	2.59866
$130$	0.0901378	0.00790561
$131$	−14.4064	−1.25869	−0.629347	−	0.777124i	$-0.716678\pi$
$131$	−14.4064	−1.25869	−0.629347	+	0.777124i	$0.716678\pi$
$132$	21.5887	1.87906
$133$	0	0
$134$	−0.312392	−0.0269865
$135$	5.32040	0.457907
$136$	−2.82893	−0.242579
$137$	−9.85880	−0.842294	−0.421147	−	0.906992i	$-0.638372\pi$
$137$	−9.85880	−0.842294	−0.421147	+	0.906992i	$0.638372\pi$
$138$	−1.69211	−0.144042
$139$	−19.7786	−1.67760	−0.838799	−	0.544441i	$-0.816742\pi$
$139$	−19.7786	−1.67760	−0.838799	+	0.544441i	$0.816742\pi$
$140$	0	0
$141$	29.3716	2.47353
$142$	0.345577	0.0290002
$143$	3.56985	0.298526
$144$	19.2962	1.60801
$145$	2.91568	0.242134
$146$	0.940019	0.0777965
$147$	0	0
$148$	−9.75745	−0.802058
$149$	1.16136	0.0951427	0.0475714	−	0.998868i	$-0.484852\pi$
$149$	1.16136	0.0951427	0.0475714	+	0.998868i	$0.484852\pi$
$150$	−0.273856	−0.0223603
$151$	−7.82218	−0.636560	−0.318280	−	0.947997i	$-0.603105\pi$
$151$	−7.82218	−0.636560	−0.318280	+	0.947997i	$0.603105\pi$
$152$	−1.83165	−0.148566
$153$	−35.5916	−2.87741
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	5.17160	0.414060
$157$	5.81523	0.464106	0.232053	−	0.972703i	$-0.425456\pi$
$157$	5.81523	0.464106	0.232053	+	0.972703i	$0.425456\pi$
$158$	1.31792	0.104848
$159$	−13.8837	−1.10105
$160$	−1.16227	−0.0918857
$161$	0	0
$162$	−0.0260266	−0.00204484
$163$	−12.0531	−0.944072	−0.472036	−	0.881579i	$-0.656481\pi$
$163$	−12.0531	−0.944072	−0.472036	+	0.881579i	$0.656481\pi$
$164$	12.6221	0.985624
$165$	−10.8459	−0.844351
$166$	1.58322	0.122882
$167$	−12.4950	−0.966895	−0.483447	−	0.875373i	$-0.660616\pi$
$167$	−12.4950	−0.966895	−0.483447	+	0.875373i	$0.660616\pi$
$168$	0	0
$169$	−12.1448	−0.934218
$170$	0.708917	0.0543715
$171$	−23.0444	−1.76225
$172$	−20.9106	−1.59442
$173$	12.8157	0.974359	0.487180	−	0.873302i	$-0.338026\pi$
$173$	12.8157	0.974359	0.487180	+	0.873302i	$0.338026\pi$
$174$	−0.798477	−0.0605324
$175$	0	0
$176$	−15.2217	−1.14738
$177$	5.50826	0.414026
$178$	0.0935424	0.00701130
$179$	−11.2156	−0.838295	−0.419148	−	0.907918i	$-0.637671\pi$
$179$	−11.2156	−0.838295	−0.419148	+	0.907918i	$0.637671\pi$
$180$	−9.74085	−0.726040
$181$	3.63064	0.269863	0.134932	−	0.990855i	$-0.456919\pi$
$181$	3.63064	0.269863	0.134932	+	0.990855i	$0.456919\pi$
$182$	0	0
$183$	−34.4013	−2.54301
$184$	2.40334	0.177177
$185$	4.90201	0.360403
$186$	0.273856	0.0200801
$187$	28.0762	2.05313
$188$	−20.8089	−1.51765
$189$	0	0
$190$	0.459002	0.0332995
$191$	7.71346	0.558127	0.279063	−	0.960273i	$-0.409976\pi$
$191$	7.71346	0.558127	0.279063	+	0.960273i	$0.409976\pi$
$192$	−21.8384	−1.57605
$193$	−11.4401	−0.823473	−0.411737	−	0.911303i	$-0.635078\pi$
$193$	−11.4401	−0.823473	−0.411737	+	0.911303i	$0.635078\pi$
$194$	1.01185	0.0726464
$195$	−2.59814	−0.186057
$196$	0	0
$197$	15.4117	1.09804	0.549020	−	0.835809i	$-0.315001\pi$
$197$	15.4117	1.09804	0.549020	+	0.835809i	$0.315001\pi$
$198$	1.84138	0.130861
$199$	5.55621	0.393869	0.196935	−	0.980417i	$-0.436901\pi$
$199$	5.55621	0.393869	0.196935	+	0.980417i	$0.436901\pi$
$200$	0.388965	0.0275040
$201$	9.00443	0.635123
$202$	1.01386	0.0713349
$203$	0	0
$204$	40.6737	2.84773
$205$	−6.34119	−0.442888
$206$	0.165859	0.0115559
$207$	30.2371	2.10162
$208$	−3.64636	−0.252830
$209$	18.1785	1.25743
$210$	0	0
$211$	4.93131	0.339485	0.169743	−	0.985488i	$-0.445706\pi$
$211$	4.93131	0.339485	0.169743	+	0.985488i	$0.445706\pi$
$212$	9.83619	0.675552
$213$	−9.96095	−0.682513
$214$	0.869128	0.0594124
$215$	10.5052	0.716449
$216$	2.06945	0.140808
$217$	0	0
$218$	−1.53554	−0.104000
$219$	−27.0952	−1.83093
$220$	7.68401	0.518056
$221$	6.72568	0.452418
$222$	−1.34245	−0.0900991
$223$	9.52305	0.637710	0.318855	−	0.947803i	$-0.396702\pi$
$223$	9.52305	0.637710	0.318855	+	0.947803i	$0.396702\pi$
$224$	0	0
$225$	4.89367	0.326245
$226$	0.424279	0.0282226
$227$	28.2626	1.87586	0.937928	−	0.346830i	$-0.112742\pi$
$227$	28.2626	1.87586	0.937928	+	0.346830i	$0.112742\pi$
$228$	26.3350	1.74408
$229$	10.7296	0.709033	0.354516	−	0.935050i	$-0.384645\pi$
$229$	10.7296	0.709033	0.354516	+	0.935050i	$0.384645\pi$
$230$	−0.602266	−0.0397122
$231$	0	0
$232$	1.13410	0.0744571
$233$	19.1907	1.25722	0.628611	−	0.777720i	$-0.283624\pi$
$233$	19.1907	1.25722	0.628611	+	0.777720i	$0.283624\pi$
$234$	0.441105	0.0288359
$235$	10.4541	0.681951
$236$	−3.90245	−0.254028
$237$	−37.9880	−2.46759
$238$	0	0
$239$	−1.91153	−0.123646	−0.0618232	−	0.998087i	$-0.519691\pi$
$239$	−1.91153	−0.123646	−0.0618232	+	0.998087i	$0.519691\pi$
$240$	11.0784	0.715105
$241$	−30.4570	−1.96191	−0.980954	−	0.194238i	$-0.937777\pi$
$241$	−30.4570	−1.96191	−0.980954	+	0.194238i	$0.937777\pi$
$242$	−0.380361	−0.0244506
$243$	−15.2110	−0.975787
$244$	24.3723	1.56028
$245$	0	0
$246$	1.73658	0.110720
$247$	4.35467	0.277081
$248$	−0.388965	−0.0246993
$249$	−45.6350	−2.89200
$250$	−0.0974727	−0.00616472
$251$	−15.5507	−0.981550	−0.490775	−	0.871286i	$-0.663286\pi$
$251$	−15.5507	−0.981550	−0.490775	+	0.871286i	$0.663286\pi$
$252$	0	0
$253$	−23.8523	−1.49958
$254$	1.12541	0.0706146
$255$	−20.4339	−1.27962
$256$	15.2453	0.952833
$257$	4.44860	0.277496	0.138748	−	0.990328i	$-0.455692\pi$
$257$	4.44860	0.277496	0.138748	+	0.990328i	$0.455692\pi$
$258$	−2.87692	−0.179109
$259$	0	0
$260$	1.84071	0.114156
$261$	14.2684	0.883190
$262$	1.40423	0.0867538
$263$	23.7415	1.46396	0.731982	−	0.681324i	$-0.238596\pi$
$263$	23.7415	1.46396	0.731982	+	0.681324i	$0.238596\pi$
$264$	−4.21867	−0.259641
$265$	−4.94157	−0.303558
$266$	0	0
$267$	−2.69628	−0.165010
$268$	−6.37938	−0.389683
$269$	15.9841	0.974569	0.487285	−	0.873243i	$-0.337987\pi$
$269$	15.9841	0.974569	0.487285	+	0.873243i	$0.337987\pi$
$270$	−0.518594	−0.0315606
$271$	−7.78144	−0.472689	−0.236344	−	0.971669i	$-0.575949\pi$
$271$	−7.78144	−0.472689	−0.236344	+	0.971669i	$0.575949\pi$
$272$	−28.6780	−1.73886
$273$	0	0
$274$	0.960964	0.0580540
$275$	−3.86034	−0.232787
$276$	−34.5547	−2.07995
$277$	27.7000	1.66433	0.832166	−	0.554527i	$-0.187101\pi$
$277$	27.7000	1.66433	0.832166	+	0.554527i	$0.187101\pi$
$278$	1.92787	0.115626
$279$	−4.89367	−0.292977
$280$	0	0
$281$	6.18161	0.368764	0.184382	−	0.982855i	$-0.440972\pi$
$281$	6.18161	0.368764	0.184382	+	0.982855i	$0.440972\pi$
$282$	−2.86293	−0.170485
$283$	−25.6437	−1.52436	−0.762179	−	0.647367i	$-0.775870\pi$
$283$	−25.6437	−1.52436	−0.762179	+	0.647367i	$0.775870\pi$
$284$	7.05705	0.418759
$285$	−13.2303	−0.783697
$286$	−0.347963	−0.0205755
$287$	0	0
$288$	−5.68778	−0.335156
$289$	35.8963	2.11155
$290$	−0.284199	−0.0166888
$291$	−29.1656	−1.70972
$292$	19.1962	1.12337
$293$	23.2172	1.35636	0.678182	−	0.734894i	$-0.262768\pi$
$293$	23.2172	1.35636	0.678182	+	0.734894i	$0.262768\pi$
$294$	0	0
$295$	1.96054	0.114147
$296$	1.90671	0.110825
$297$	−20.5386	−1.19177
$298$	−0.113201	−0.00655758
$299$	−5.71385	−0.330440
$300$	−5.59244	−0.322880
$301$	0	0
$302$	0.762449	0.0438740
$303$	−29.2236	−1.67885
$304$	−18.5681	−1.06495
$305$	−12.2443	−0.701108
$306$	3.46921	0.198322
$307$	2.89328	0.165128	0.0825641	−	0.996586i	$-0.473689\pi$
$307$	2.89328	0.165128	0.0825641	+	0.996586i	$0.473689\pi$
$308$	0	0
$309$	−4.78075	−0.271967
$310$	0.0974727	0.00553608
$311$	7.75299	0.439632	0.219816	−	0.975541i	$-0.429454\pi$
$311$	7.75299	0.439632	0.219816	+	0.975541i	$0.429454\pi$
$312$	−1.01059	−0.0572132
$313$	16.3498	0.924145	0.462072	−	0.886842i	$-0.347106\pi$
$313$	16.3498	0.924145	0.462072	+	0.886842i	$0.347106\pi$
$314$	−0.566826	−0.0319879
$315$	0	0
$316$	26.9134	1.51400
$317$	5.42800	0.304867	0.152434	−	0.988314i	$-0.451289\pi$
$317$	5.42800	0.304867	0.152434	+	0.988314i	$0.451289\pi$
$318$	1.35328	0.0758882
$319$	−11.2555	−0.630188
$320$	−7.77288	−0.434517
$321$	−25.0519	−1.39826
$322$	0	0
$323$	34.2487	1.90565
$324$	−0.531492	−0.0295273
$325$	−0.924749	−0.0512958
$326$	1.17485	0.0650689
$327$	44.2606	2.44761
$328$	−2.46650	−0.136190
$329$	0	0
$330$	1.05718	0.0581958
$331$	−2.92524	−0.160786	−0.0803929	−	0.996763i	$-0.525617\pi$
$331$	−2.92524	−0.160786	−0.0803929	+	0.996763i	$0.525617\pi$
$332$	32.3311	1.77440
$333$	23.9888	1.31458
$334$	1.21793	0.0666419
$335$	3.20491	0.175103
$336$	0	0
$337$	−14.6868	−0.800040	−0.400020	−	0.916506i	$-0.630997\pi$
$337$	−14.6868	−0.800040	−0.400020	+	0.916506i	$0.630997\pi$
$338$	1.18379	0.0643897
$339$	−12.2295	−0.664214
$340$	14.4769	0.785118
$341$	3.86034	0.209049
$342$	2.24620	0.121461
$343$	0	0
$344$	4.08616	0.220311
$345$	17.3598	0.934620
$346$	−1.24918	−0.0671564
$347$	−19.7682	−1.06121	−0.530607	−	0.847618i	$-0.678036\pi$
$347$	−19.7682	−1.06121	−0.530607	+	0.847618i	$0.678036\pi$
$348$	−16.3058	−0.874081
$349$	−20.1523	−1.07873	−0.539365	−	0.842072i	$-0.681336\pi$
$349$	−20.1523	−1.07873	−0.539365	+	0.842072i	$0.681336\pi$
$350$	0	0
$351$	−4.92004	−0.262612
$352$	4.48677	0.239146
$353$	5.46159	0.290691	0.145346	−	0.989381i	$-0.453571\pi$
$353$	5.46159	0.290691	0.145346	+	0.989381i	$0.453571\pi$
$354$	−0.536905	−0.0285362
$355$	−3.54537	−0.188169
$356$	1.91024	0.101242
$357$	0	0
$358$	1.09322	0.0577784
$359$	14.1817	0.748483	0.374242	−	0.927331i	$-0.377903\pi$
$359$	14.1817	0.748483	0.374242	+	0.927331i	$0.377903\pi$
$360$	1.90347	0.100321
$361$	3.17494	0.167102
$362$	−0.353888	−0.0186000
$363$	10.9636	0.575439
$364$	0	0
$365$	−9.64392	−0.504786
$366$	3.35318	0.175274
$367$	−25.3912	−1.32541	−0.662706	−	0.748879i	$-0.730592\pi$
$367$	−25.3912	−1.32541	−0.662706	+	0.748879i	$0.730592\pi$
$368$	24.3636	1.27004
$369$	−31.0317	−1.61545
$370$	−0.477813	−0.0248403
$371$	0	0
$372$	5.59244	0.289955
$373$	4.63450	0.239965	0.119983	−	0.992776i	$-0.461716\pi$
$373$	4.63450	0.239965	0.119983	+	0.992776i	$0.461716\pi$
$374$	−2.73666	−0.141509
$375$	2.80957	0.145085
$376$	4.06628	0.209703
$377$	−2.69627	−0.138865
$378$	0	0
$379$	12.1429	0.623740	0.311870	−	0.950125i	$-0.399045\pi$
$379$	12.1429	0.623740	0.311870	+	0.950125i	$0.399045\pi$
$380$	9.37331	0.480841
$381$	−32.4390	−1.66190
$382$	−0.751852	−0.0384681
$383$	11.3784	0.581408	0.290704	−	0.956813i	$-0.406110\pi$
$383$	11.3784	0.581408	0.290704	+	0.956813i	$0.406110\pi$
$384$	8.65962	0.441909
$385$	0	0
$386$	1.11509	0.0567568
$387$	51.4091	2.61327
$388$	20.6630	1.04901
$389$	23.4387	1.18839	0.594194	−	0.804322i	$-0.297471\pi$
$389$	23.4387	1.18839	0.594194	+	0.804322i	$0.297471\pi$
$390$	0.253248	0.0128237
$391$	−44.9384	−2.27263
$392$	0	0
$393$	−40.4758	−2.04173
$394$	−1.50222	−0.0756809
$395$	−13.5210	−0.680313
$396$	37.6030	1.88962
$397$	6.75290	0.338918	0.169459	−	0.985537i	$-0.445798\pi$
$397$	6.75290	0.338918	0.169459	+	0.985537i	$0.445798\pi$
$398$	−0.541579	−0.0271469
$399$	0	0
$400$	3.94308	0.197154
$401$	−22.1596	−1.10660	−0.553300	−	0.832982i	$-0.686632\pi$
$401$	−22.1596	−1.10660	−0.553300	+	0.832982i	$0.686632\pi$
$402$	−0.877686	−0.0437750
$403$	0.924749	0.0460650
$404$	20.7041	1.03007
$405$	0.267014	0.0132681
$406$	0	0
$407$	−18.9234	−0.938000
$408$	−7.94808	−0.393489
$409$	23.1661	1.14549	0.572746	−	0.819733i	$-0.305878\pi$
$409$	23.1661	1.14549	0.572746	+	0.819733i	$0.305878\pi$
$410$	0.618093	0.0305255
$411$	−27.6990	−1.36629
$412$	3.38702	0.166867
$413$	0	0
$414$	−2.94729	−0.144851
$415$	−16.2427	−0.797324
$416$	1.07481	0.0526969
$417$	−55.5693	−2.72124
$418$	−1.77190	−0.0866666
$419$	3.22831	0.157713	0.0788567	−	0.996886i	$-0.474873\pi$
$419$	3.22831	0.157713	0.0788567	+	0.996886i	$0.474873\pi$
$420$	0	0
$421$	34.7901	1.69557	0.847783	−	0.530343i	$-0.177937\pi$
$421$	34.7901	1.69557	0.847783	+	0.530343i	$0.177937\pi$
$422$	−0.480668	−0.0233986
$423$	51.1590	2.48744
$424$	−1.92210	−0.0933453
$425$	−7.27298	−0.352791
$426$	0.970921	0.0470413
$427$	0	0
$428$	17.7485	0.857908
$429$	10.0297	0.484240
$430$	−1.02397	−0.0493803
$431$	−28.7841	−1.38648	−0.693241	−	0.720706i	$-0.743818\pi$
$431$	−28.7841	−1.38648	−0.693241	+	0.720706i	$0.743818\pi$
$432$	20.9788	1.00934
$433$	29.1461	1.40067	0.700336	−	0.713813i	$-0.253033\pi$
$433$	29.1461	1.40067	0.700336	+	0.713813i	$0.253033\pi$
$434$	0	0
$435$	8.19180	0.392767
$436$	−31.3573	−1.50174
$437$	−29.0962	−1.39186
$438$	2.64105	0.126194
$439$	−5.59587	−0.267076	−0.133538	−	0.991044i	$-0.542634\pi$
$439$	−5.59587	−0.267076	−0.133538	+	0.991044i	$0.542634\pi$
$440$	−1.50154	−0.0715830
$441$	0	0
$442$	−0.655571	−0.0311823
$443$	6.90443	0.328039	0.164020	−	0.986457i	$-0.447554\pi$
$443$	6.90443	0.328039	0.164020	+	0.986457i	$0.447554\pi$
$444$	−27.4142	−1.30102
$445$	−0.959678	−0.0454931
$446$	−0.928237	−0.0439533
$447$	3.26293	0.154331
$448$	0	0
$449$	−1.91931	−0.0905778	−0.0452889	−	0.998974i	$-0.514421\pi$
$449$	−1.91931	−0.0905778	−0.0452889	+	0.998974i	$0.514421\pi$
$450$	−0.477000	−0.0224860
$451$	24.4792	1.15268
$452$	8.66424	0.407532
$453$	−21.9769	−1.03257
$454$	−2.75483	−0.129291
$455$	0	0
$456$	−5.14613	−0.240990
$457$	16.1670	0.756260	0.378130	−	0.925753i	$-0.376567\pi$
$457$	16.1670	0.756260	0.378130	+	0.925753i	$0.376567\pi$
$458$	−1.04584	−0.0488691
$459$	−38.6952	−1.80614
$460$	−12.2989	−0.573440
$461$	−18.5189	−0.862511	−0.431255	−	0.902230i	$-0.641929\pi$
$461$	−18.5189	−0.862511	−0.431255	+	0.902230i	$0.641929\pi$
$462$	0	0
$463$	−20.4791	−0.951742	−0.475871	−	0.879515i	$-0.657867\pi$
$463$	−20.4791	−0.951742	−0.475871	+	0.879515i	$0.657867\pi$
$464$	11.4968	0.533724
$465$	−2.80957	−0.130291
$466$	−1.87057	−0.0866523
$467$	15.7337	0.728067	0.364034	−	0.931386i	$-0.381399\pi$
$467$	15.7337	0.728067	0.364034	+	0.931386i	$0.381399\pi$
$468$	9.00784	0.416388
$469$	0	0
$470$	−1.01899	−0.0470026
$471$	16.3383	0.752828
$472$	0.762580	0.0351006
$473$	−40.5537	−1.86466
$474$	3.70280	0.170075
$475$	−4.70903	−0.216065
$476$	0	0
$477$	−24.1824	−1.10724
$478$	0.186322	0.00852215
$479$	−25.3726	−1.15930	−0.579651	−	0.814865i	$-0.696811\pi$
$479$	−25.3726	−1.15930	−0.579651	+	0.814865i	$0.696811\pi$
$480$	−3.26548	−0.149048
$481$	−4.53313	−0.206693
$482$	2.96873	0.135222
$483$	0	0
$484$	−7.76739	−0.353063
$485$	−10.3808	−0.471369
$486$	1.48266	0.0672548
$487$	15.4834	0.701621	0.350810	−	0.936446i	$-0.385906\pi$
$487$	15.4834	0.701621	0.350810	+	0.936446i	$0.385906\pi$
$488$	−4.76261	−0.215593
$489$	−33.8640	−1.53138
$490$	0	0
$491$	−30.2207	−1.36384	−0.681920	−	0.731427i	$-0.738855\pi$
$491$	−30.2207	−1.36384	−0.681920	+	0.731427i	$0.738855\pi$
$492$	35.4628	1.59878
$493$	−21.2057	−0.955056
$494$	−0.424461	−0.0190974
$495$	−18.8912	−0.849098
$496$	−3.94308	−0.177050
$497$	0	0
$498$	4.44817	0.199327
$499$	−26.6921	−1.19490	−0.597450	−	0.801906i	$-0.703820\pi$
$499$	−26.6921	−1.19490	−0.597450	+	0.801906i	$0.703820\pi$
$500$	−1.99050	−0.0890178
$501$	−35.1057	−1.56841
$502$	1.51577	0.0676520
$503$	10.2336	0.456295	0.228148	−	0.973627i	$-0.426733\pi$
$503$	10.2336	0.456295	0.228148	+	0.973627i	$0.426733\pi$
$504$	0	0
$505$	−10.4015	−0.462859
$506$	2.32495	0.103357
$507$	−34.1218	−1.51540
$508$	22.9821	1.01967
$509$	−31.6583	−1.40323	−0.701615	−	0.712556i	$-0.747537\pi$
$509$	−31.6583	−1.40323	−0.701615	+	0.712556i	$0.747537\pi$
$510$	1.99175	0.0881963
$511$	0	0
$512$	−7.65038	−0.338102
$513$	−25.0539	−1.10616
$514$	−0.433617	−0.0191260
$515$	−1.70159	−0.0749812
$516$	−58.7498	−2.58632
$517$	−40.3565	−1.77487
$518$	0	0
$519$	36.0066	1.58051
$520$	−0.359695	−0.0157737
$521$	−38.2683	−1.67657	−0.838283	−	0.545236i	$-0.816440\pi$
$521$	−38.2683	−1.67657	−0.838283	+	0.545236i	$0.816440\pi$
$522$	−1.39078	−0.0608727
$523$	20.1649	0.881750	0.440875	−	0.897568i	$-0.354668\pi$
$523$	20.1649	0.881750	0.440875	+	0.897568i	$0.354668\pi$
$524$	28.6760	1.25272
$525$	0	0
$526$	−2.31415	−0.100902
$527$	7.27298	0.316816
$528$	−42.7663	−1.86116
$529$	15.1777	0.659901
$530$	0.481668	0.0209223
$531$	9.59422	0.416354
$532$	0	0
$533$	5.86401	0.253999
$534$	0.262814	0.0113731
$535$	−8.91663	−0.385499
$536$	1.24660	0.0538449
$537$	−31.5111	−1.35980
$538$	−1.55802	−0.0671708
$539$	0	0
$540$	−10.5903	−0.455732
$541$	13.8218	0.594246	0.297123	−	0.954839i	$-0.403973\pi$
$541$	13.8218	0.594246	0.297123	+	0.954839i	$0.403973\pi$
$542$	0.758478	0.0325794
$543$	10.2005	0.437746
$544$	8.45319	0.362428
$545$	15.7535	0.674806
$546$	0	0
$547$	24.0211	1.02707	0.513535	−	0.858069i	$-0.328336\pi$
$547$	24.0211	1.02707	0.513535	+	0.858069i	$0.328336\pi$
$548$	19.6239	0.838293
$549$	−59.9197	−2.55731
$550$	0.376278	0.0160445
$551$	−13.7300	−0.584918
$552$	6.75235	0.287399
$553$	0	0
$554$	−2.69999	−0.114712
$555$	13.7725	0.584612
$556$	39.3693	1.66963
$557$	0.384078	0.0162739	0.00813696	−	0.999967i	$-0.497410\pi$
$557$	0.384078	0.0162739	0.00813696	+	0.999967i	$0.497410\pi$
$558$	0.477000	0.0201930
$559$	−9.71468	−0.410887
$560$	0	0
$561$	78.8820	3.33040
$562$	−0.602539	−0.0254166
$563$	−17.8710	−0.753173	−0.376586	−	0.926382i	$-0.622902\pi$
$563$	−17.8710	−0.753173	−0.376586	+	0.926382i	$0.622902\pi$
$564$	−58.4640	−2.46178
$565$	−4.35280	−0.183124
$566$	2.49956	0.105064
$567$	0	0
$568$	−1.37902	−0.0578625
$569$	19.1043	0.800894	0.400447	−	0.916320i	$-0.368855\pi$
$569$	19.1043	0.800894	0.400447	+	0.916320i	$0.368855\pi$
$570$	1.28960	0.0540153
$571$	22.9658	0.961091	0.480545	−	0.876970i	$-0.340439\pi$
$571$	22.9658	0.961091	0.480545	+	0.876970i	$0.340439\pi$
$572$	−7.10578	−0.297107
$573$	21.6715	0.905340
$574$	0	0
$575$	6.17881	0.257674
$576$	−38.0379	−1.58491
$577$	−10.9690	−0.456646	−0.228323	−	0.973585i	$-0.573324\pi$
$577$	−10.9690	−0.456646	−0.228323	+	0.973585i	$0.573324\pi$
$578$	−3.49891	−0.145535
$579$	−32.1416	−1.33576
$580$	−5.80366	−0.240984
$581$	0	0
$582$	2.84285	0.117840
$583$	19.0761	0.790053
$584$	−3.75114	−0.155223
$585$	−4.52542	−0.187103
$586$	−2.26304	−0.0934855
$587$	41.2347	1.70194	0.850969	−	0.525215i	$-0.176015\pi$
$587$	41.2347	1.70194	0.850969	+	0.525215i	$0.176015\pi$
$588$	0	0
$589$	4.70903	0.194032
$590$	−0.191099	−0.00786741
$591$	43.3003	1.78114
$592$	19.3291	0.794419
$593$	−33.2725	−1.36634	−0.683168	−	0.730261i	$-0.739398\pi$
$593$	−33.2725	−1.36634	−0.683168	+	0.730261i	$0.739398\pi$
$594$	2.00195	0.0821410
$595$	0	0
$596$	−2.31170	−0.0946908
$597$	15.6106	0.638897
$598$	0.556945	0.0227752
$599$	11.9410	0.487897	0.243949	−	0.969788i	$-0.421557\pi$
$599$	11.9410	0.487897	0.243949	+	0.969788i	$0.421557\pi$
$600$	1.09282	0.0446143
$601$	17.8235	0.727037	0.363518	−	0.931587i	$-0.381575\pi$
$601$	17.8235	0.727037	0.363518	+	0.931587i	$0.381575\pi$
$602$	0	0
$603$	15.6838	0.638694
$604$	15.5700	0.633536
$605$	3.90223	0.158648
$606$	2.84851	0.115713
$607$	34.5933	1.40410	0.702049	−	0.712129i	$-0.252269\pi$
$607$	34.5933	1.40410	0.702049	+	0.712129i	$0.252269\pi$
$608$	5.47317	0.221967
$609$	0	0
$610$	1.19349	0.0483229
$611$	−9.66743	−0.391102
$612$	70.8450	2.86374
$613$	3.93695	0.159012	0.0795059	−	0.996834i	$-0.474666\pi$
$613$	3.93695	0.159012	0.0795059	+	0.996834i	$0.474666\pi$
$614$	−0.282016	−0.0113812
$615$	−17.8160	−0.718411
$616$	0	0
$617$	−6.75383	−0.271899	−0.135950	−	0.990716i	$-0.543409\pi$
$617$	−6.75383	−0.271899	−0.135950	+	0.990716i	$0.543409\pi$
$618$	0.465992	0.0187450
$619$	7.62619	0.306522	0.153261	−	0.988186i	$-0.451022\pi$
$619$	7.62619	0.306522	0.153261	+	0.988186i	$0.451022\pi$
$620$	1.99050	0.0799404
$621$	32.8738	1.31918
$622$	−0.755705	−0.0303010
$623$	0	0
$624$	−10.2447	−0.410116
$625$	1.00000	0.0400000
$626$	−1.59366	−0.0636954
$627$	51.0736	2.03968
$628$	−11.5752	−0.461901
$629$	−35.6523	−1.42155
$630$	0	0
$631$	38.9373	1.55007	0.775035	−	0.631919i	$-0.217732\pi$
$631$	38.9373	1.55007	0.775035	+	0.631919i	$0.217732\pi$
$632$	−5.25918	−0.209199
$633$	13.8548	0.550681
$634$	−0.529082	−0.0210125
$635$	−11.5459	−0.458185
$636$	27.6355	1.09582
$637$	0	0
$638$	1.09711	0.0434348
$639$	−17.3499	−0.686350
$640$	3.08219	0.121834
$641$	16.3232	0.644726	0.322363	−	0.946616i	$-0.395523\pi$
$641$	16.3232	0.644726	0.322363	+	0.946616i	$0.395523\pi$
$642$	2.44187	0.0963731
$643$	32.0318	1.26321	0.631605	−	0.775291i	$-0.282397\pi$
$643$	32.0318	1.26321	0.631605	+	0.775291i	$0.282397\pi$
$644$	0	0
$645$	29.5151	1.16216
$646$	−3.33831	−0.131344
$647$	−17.0755	−0.671306	−0.335653	−	0.941986i	$-0.608957\pi$
$647$	−17.0755	−0.671306	−0.335653	+	0.941986i	$0.608957\pi$
$648$	0.103859	0.00407997
$649$	−7.56834	−0.297083
$650$	0.0901378	0.00353549
$651$	0	0
$652$	23.9917	0.939587
$653$	−8.26699	−0.323512	−0.161756	−	0.986831i	$-0.551716\pi$
$653$	−8.26699	−0.323512	−0.161756	+	0.986831i	$0.551716\pi$
$654$	−4.31420	−0.168698
$655$	−14.4064	−0.562905
$656$	−25.0039	−0.976237
$657$	−47.1942	−1.84122
$658$	0	0
$659$	−36.7933	−1.43326	−0.716631	−	0.697453i	$-0.754317\pi$
$659$	−36.7933	−1.43326	−0.716631	+	0.697453i	$0.754317\pi$
$660$	21.5887	0.840340
$661$	−37.2651	−1.44944	−0.724722	−	0.689042i	$-0.758032\pi$
$661$	−37.2651	−1.44944	−0.724722	+	0.689042i	$0.758032\pi$
$662$	0.285131	0.0110819
$663$	18.8963	0.733870
$664$	−6.31785	−0.245180
$665$	0	0
$666$	−2.33826	−0.0906057
$667$	18.0154	0.697560
$668$	24.8714	0.962302
$669$	26.7556	1.03443
$670$	−0.312392	−0.0120687
$671$	47.2673	1.82473
$672$	0	0
$673$	−47.5605	−1.83332	−0.916662	−	0.399663i	$-0.869127\pi$
$673$	−47.5605	−1.83332	−0.916662	+	0.399663i	$0.869127\pi$
$674$	1.43156	0.0551416
$675$	5.32040	0.204782
$676$	24.1743	0.929780
$677$	50.7397	1.95009	0.975043	−	0.222017i	$-0.0712640\pi$
$677$	50.7397	1.95009	0.975043	+	0.222017i	$0.0712640\pi$
$678$	1.19204	0.0457800
$679$	0	0
$680$	−2.82893	−0.108485
$681$	79.4058	3.04284
$682$	−0.376278	−0.0144084
$683$	−14.3536	−0.549224	−0.274612	−	0.961555i	$-0.588549\pi$
$683$	−14.3536	−0.549224	−0.274612	+	0.961555i	$0.588549\pi$
$684$	45.8699	1.75388
$685$	−9.85880	−0.376685
$686$	0	0
$687$	30.1456	1.15013
$688$	41.4229	1.57923
$689$	4.56971	0.174092
$690$	−1.69211	−0.0644174
$691$	10.3681	0.394423	0.197211	−	0.980361i	$-0.436811\pi$
$691$	10.3681	0.394423	0.197211	+	0.980361i	$0.436811\pi$
$692$	−25.5096	−0.969731
$693$	0	0
$694$	1.92686	0.0731428
$695$	−19.7786	−0.750245
$696$	3.18632	0.120777
$697$	46.1194	1.74690
$698$	1.96430	0.0743499
$699$	53.9175	2.03935
$700$	0	0
$701$	39.4281	1.48918	0.744589	−	0.667523i	$-0.232645\pi$
$701$	39.4281	1.48918	0.744589	+	0.667523i	$0.232645\pi$
$702$	0.479569	0.0181002
$703$	−23.0837	−0.870619
$704$	30.0060	1.13089
$705$	29.3716	1.10620
$706$	−0.532356	−0.0200355
$707$	0	0
$708$	−10.9642	−0.412059
$709$	18.4512	0.692951	0.346475	−	0.938059i	$-0.387378\pi$
$709$	18.4512	0.692951	0.346475	+	0.938059i	$0.387378\pi$
$710$	0.345577	0.0129693
$711$	−66.1671	−2.48146
$712$	−0.373281	−0.0139893
$713$	−6.17881	−0.231398
$714$	0	0
$715$	3.56985	0.133505
$716$	22.3247	0.834313
$717$	−5.37056	−0.200567
$718$	−1.38233	−0.0515882
$719$	7.88704	0.294137	0.147069	−	0.989126i	$-0.453016\pi$
$719$	7.88704	0.294137	0.147069	+	0.989126i	$0.453016\pi$
$720$	19.2962	0.719126
$721$	0	0
$722$	−0.309470	−0.0115173
$723$	−85.5711	−3.18242
$724$	−7.22678	−0.268581
$725$	2.91568	0.108286
$726$	−1.06865	−0.0396614
$727$	18.6930	0.693286	0.346643	−	0.937997i	$-0.387322\pi$
$727$	18.6930	0.693286	0.346643	+	0.937997i	$0.387322\pi$
$728$	0	0
$729$	−43.5374	−1.61250
$730$	0.940019	0.0347917
$731$	−76.4042	−2.82591
$732$	68.4757	2.53093
$733$	33.5139	1.23786	0.618932	−	0.785444i	$-0.287566\pi$
$733$	33.5139	1.23786	0.618932	+	0.785444i	$0.287566\pi$
$734$	2.47495	0.0913522
$735$	0	0
$736$	−7.18147	−0.264712
$737$	−12.3721	−0.455731
$738$	3.02475	0.111342
$739$	6.19962	0.228057	0.114028	−	0.993477i	$-0.463625\pi$
$739$	6.19962	0.228057	0.114028	+	0.993477i	$0.463625\pi$
$740$	−9.75745	−0.358691
$741$	12.2347	0.449454
$742$	0	0
$743$	−11.3220	−0.415365	−0.207683	−	0.978196i	$-0.566592\pi$
$743$	−11.3220	−0.415365	−0.207683	+	0.978196i	$0.566592\pi$
$744$	−1.09282	−0.0400648
$745$	1.16136	0.0425491
$746$	−0.451737	−0.0165393
$747$	−79.4866	−2.90826
$748$	−55.8856	−2.04338
$749$	0	0
$750$	−0.273856	−0.00999982
$751$	−8.81643	−0.321716	−0.160858	−	0.986978i	$-0.551426\pi$
$751$	−8.81643	−0.321716	−0.160858	+	0.986978i	$0.551426\pi$
$752$	41.2215	1.50319
$753$	−43.6907	−1.59218
$754$	0.262813	0.00957108
$755$	−7.82218	−0.284678
$756$	0	0
$757$	−44.3945	−1.61355	−0.806773	−	0.590861i	$-0.798788\pi$
$757$	−44.3945	−1.61355	−0.806773	+	0.590861i	$0.798788\pi$
$758$	−1.18360	−0.0429904
$759$	−67.0147	−2.43248
$760$	−1.83165	−0.0664408
$761$	37.3700	1.35466	0.677330	−	0.735679i	$-0.263137\pi$
$761$	37.3700	1.35466	0.677330	+	0.735679i	$0.263137\pi$
$762$	3.16192	0.114544
$763$	0	0
$764$	−15.3536	−0.555475
$765$	−35.5916	−1.28682
$766$	−1.10908	−0.0400728
$767$	−1.81300	−0.0654638
$768$	42.8328	1.54560
$769$	−3.50426	−0.126367	−0.0631835	−	0.998002i	$-0.520125\pi$
$769$	−3.50426	−0.126367	−0.0631835	+	0.998002i	$0.520125\pi$
$770$	0	0
$771$	12.4986	0.450127
$772$	22.7714	0.819562
$773$	10.0577	0.361749	0.180874	−	0.983506i	$-0.442107\pi$
$773$	10.0577	0.361749	0.180874	+	0.983506i	$0.442107\pi$
$774$	−5.01098	−0.180116
$775$	−1.00000	−0.0359211
$776$	−4.03777	−0.144948
$777$	0	0
$778$	−2.28463	−0.0819080
$779$	29.8609	1.06988
$780$	5.17160	0.185173
$781$	13.6863	0.489735
$782$	4.38027	0.156638
$783$	15.5126	0.554375
$784$	0	0
$785$	5.81523	0.207554
$786$	3.94529	0.140724
$787$	−5.77732	−0.205939	−0.102970	−	0.994685i	$-0.532834\pi$
$787$	−5.77732	−0.205939	−0.102970	+	0.994685i	$0.532834\pi$
$788$	−30.6770	−1.09282
$789$	66.7034	2.37470
$790$	1.31792	0.0468896
$791$	0	0
$792$	−7.34803	−0.261101
$793$	11.3229	0.402089
$794$	−0.658224	−0.0233595
$795$	−13.8837	−0.492403
$796$	−11.0596	−0.391998
$797$	7.65503	0.271155	0.135578	−	0.990767i	$-0.456711\pi$
$797$	7.65503	0.271155	0.135578	+	0.990767i	$0.456711\pi$
$798$	0	0
$799$	−76.0326	−2.68984
$800$	−1.16227	−0.0410926
$801$	−4.69635	−0.165937
$802$	2.15996	0.0762708
$803$	37.2288	1.31378
$804$	−17.9233	−0.632106
$805$	0	0
$806$	−0.0901378	−0.00317497
$807$	44.9085	1.58085
$808$	−4.04580	−0.142331
$809$	−44.0353	−1.54820	−0.774099	−	0.633064i	$-0.781797\pi$
$809$	−44.0353	−1.54820	−0.774099	+	0.633064i	$0.781797\pi$
$810$	−0.0260266	−0.000914482 0
$811$	16.3771	0.575079	0.287540	−	0.957769i	$-0.407163\pi$
$811$	16.3771	0.575079	0.287540	+	0.957769i	$0.407163\pi$
$812$	0	0
$813$	−21.8625	−0.766751
$814$	1.84452	0.0646504
$815$	−12.0531	−0.422202
$816$	−80.5728	−2.82061
$817$	−49.4693	−1.73071
$818$	−2.25807	−0.0789515
$819$	0	0
$820$	12.6221	0.440784
$821$	12.2923	0.429005	0.214502	−	0.976723i	$-0.431187\pi$
$821$	12.2923	0.429005	0.214502	+	0.976723i	$0.431187\pi$
$822$	2.69989	0.0941696
$823$	−31.0892	−1.08370	−0.541850	−	0.840475i	$-0.682276\pi$
$823$	−31.0892	−1.08370	−0.541850	+	0.840475i	$0.682276\pi$
$824$	−0.661860	−0.0230570
$825$	−10.8459	−0.377605
$826$	0	0
$827$	52.9279	1.84048	0.920242	−	0.391350i	$-0.127992\pi$
$827$	52.9279	1.84048	0.920242	+	0.391350i	$0.127992\pi$
$828$	−60.1869	−2.09164
$829$	−23.4160	−0.813273	−0.406636	−	0.913590i	$-0.633298\pi$
$829$	−23.4160	−0.813273	−0.406636	+	0.913590i	$0.633298\pi$
$830$	1.58322	0.0549545
$831$	77.8250	2.69972
$832$	7.18796	0.249198
$833$	0	0
$834$	5.41649	0.187558
$835$	−12.4950	−0.432409
$836$	−36.1842	−1.25146
$837$	−5.32040	−0.183900
$838$	−0.314672	−0.0108702
$839$	22.1600	0.765048	0.382524	−	0.923946i	$-0.375055\pi$
$839$	22.1600	0.765048	0.382524	+	0.923946i	$0.375055\pi$
$840$	0	0
$841$	−20.4988	−0.706856
$842$	−3.39109	−0.116865
$843$	17.3677	0.598174
$844$	−9.81576	−0.337872
$845$	−12.1448	−0.417795
$846$	−4.98661	−0.171443
$847$	0	0
$848$	−19.4850	−0.669119
$849$	−72.0476	−2.47267
$850$	0.708917	0.0243157
$851$	30.2886	1.03828
$852$	19.8273	0.679271
$853$	−30.9034	−1.05811	−0.529055	−	0.848587i	$-0.677454\pi$
$853$	−30.9034	−1.05811	−0.529055	+	0.848587i	$0.677454\pi$
$854$	0	0
$855$	−23.0444	−0.788103
$856$	−3.46825	−0.118542
$857$	49.9664	1.70682	0.853411	−	0.521239i	$-0.174530\pi$
$857$	49.9664	1.70682	0.853411	+	0.521239i	$0.174530\pi$
$858$	−0.977625	−0.0333756
$859$	−12.0969	−0.412740	−0.206370	−	0.978474i	$-0.566165\pi$
$859$	−12.0969	−0.412740	−0.206370	+	0.978474i	$0.566165\pi$
$860$	−20.9106	−0.713046
$861$	0	0
$862$	2.80566	0.0955613
$863$	−34.2893	−1.16722	−0.583611	−	0.812033i	$-0.698361\pi$
$863$	−34.2893	−1.16722	−0.583611	+	0.812033i	$0.698361\pi$
$864$	−6.18376	−0.210376
$865$	12.8157	0.435747
$866$	−2.84095	−0.0965394
$867$	100.853	3.42515
$868$	0	0
$869$	52.1955	1.77061
$870$	−0.798477	−0.0270709
$871$	−2.96374	−0.100423
$872$	6.12756	0.207505
$873$	−50.8003	−1.71933
$874$	2.83609	0.0959320
$875$	0	0
$876$	53.9331	1.82223
$877$	36.0858	1.21853	0.609265	−	0.792967i	$-0.291465\pi$
$877$	36.0858	1.21853	0.609265	+	0.792967i	$0.291465\pi$
$878$	0.545444	0.0184079
$879$	65.2303	2.20016
$880$	−15.2217	−0.513122
$881$	−54.3319	−1.83049	−0.915244	−	0.402900i	$-0.868002\pi$
$881$	−54.3319	−1.83049	−0.915244	+	0.402900i	$0.868002\pi$
$882$	0	0
$883$	34.7952	1.17095	0.585476	−	0.810690i	$-0.300908\pi$
$883$	34.7952	1.17095	0.585476	+	0.810690i	$0.300908\pi$
$884$	−13.3875	−0.450269
$885$	5.50826	0.185158
$886$	−0.672994	−0.0226097
$887$	−7.85395	−0.263710	−0.131855	−	0.991269i	$-0.542093\pi$
$887$	−7.85395	−0.263710	−0.131855	+	0.991269i	$0.542093\pi$
$888$	5.35703	0.179770
$889$	0	0
$890$	0.0935424	0.00313555
$891$	−1.03077	−0.0345320
$892$	−18.9556	−0.634681
$893$	−49.2287	−1.64738
$894$	−0.318047	−0.0106371
$895$	−11.2156	−0.374897
$896$	0	0
$897$	−16.0535	−0.536009
$898$	0.187080	0.00624295
$899$	−2.91568	−0.0972433
$900$	−9.74085	−0.324695
$901$	35.9400	1.19733
$902$	−2.38605	−0.0794468
$903$	0	0
$904$	−1.69308	−0.0563112
$905$	3.63064	0.120686
$906$	2.14215	0.0711683
$907$	18.6984	0.620869	0.310434	−	0.950595i	$-0.399526\pi$
$907$	18.6984	0.620869	0.310434	+	0.950595i	$0.399526\pi$
$908$	−56.2567	−1.86695
$909$	−50.9014	−1.68829
$910$	0	0
$911$	−30.2456	−1.00208	−0.501040	−	0.865424i	$-0.667049\pi$
$911$	−30.2456	−1.00208	−0.501040	+	0.865424i	$0.667049\pi$
$912$	−52.1683	−1.72747
$913$	62.7025	2.07515
$914$	−1.57584	−0.0521242
$915$	−34.4013	−1.13727
$916$	−21.3573	−0.705665
$917$	0	0
$918$	3.77173	0.124486
$919$	−13.1487	−0.433736	−0.216868	−	0.976201i	$-0.569584\pi$
$919$	−13.1487	−0.433736	−0.216868	+	0.976201i	$0.569584\pi$
$920$	2.40334	0.0792358
$921$	8.12886	0.267855
$922$	1.80509	0.0594474
$923$	3.27858	0.107916
$924$	0	0
$925$	4.90201	0.161177
$926$	1.99615	0.0655975
$927$	−8.32705	−0.273496
$928$	−3.38881	−0.111243
$929$	32.8980	1.07935	0.539675	−	0.841874i	$-0.318547\pi$
$929$	32.8980	1.07935	0.539675	+	0.841874i	$0.318547\pi$
$930$	0.273856	0.00898010
$931$	0	0
$932$	−38.1990	−1.25125
$933$	21.7826	0.713129
$934$	−1.53360	−0.0501810
$935$	28.0762	0.918190
$936$	−1.76023	−0.0575349
$937$	32.7104	1.06860	0.534300	−	0.845295i	$-0.320575\pi$
$937$	32.7104	1.06860	0.534300	+	0.845295i	$0.320575\pi$
$938$	0	0
$939$	45.9358	1.49906
$940$	−20.8089	−0.678712
$941$	15.8595	0.517004	0.258502	−	0.966011i	$-0.416771\pi$
$941$	15.8595	0.517004	0.258502	+	0.966011i	$0.416771\pi$
$942$	−1.59254	−0.0518877
$943$	−39.1810	−1.27591
$944$	7.73056	0.251608
$945$	0	0
$946$	3.95288	0.128519
$947$	−27.6706	−0.899173	−0.449587	−	0.893237i	$-0.648429\pi$
$947$	−27.6706	−0.899173	−0.449587	+	0.893237i	$0.648429\pi$
$948$	75.6152	2.45587
$949$	8.91820	0.289497
$950$	0.459002	0.0148920
$951$	15.2503	0.494526
$952$	0	0
$953$	16.6351	0.538864	0.269432	−	0.963019i	$-0.413164\pi$
$953$	16.6351	0.538864	0.269432	+	0.963019i	$0.413164\pi$
$954$	2.35713	0.0763148
$955$	7.71346	0.249602
$956$	3.80489	0.123059
$957$	−31.6231	−1.02223
$958$	2.47313	0.0799033
$959$	0	0
$960$	−21.8384	−0.704832
$961$	1.00000	0.0322581
$962$	0.441857	0.0142460
$963$	−43.6350	−1.40612
$964$	60.6247	1.95259
$965$	−11.4401	−0.368269
$966$	0	0
$967$	−13.5515	−0.435786	−0.217893	−	0.975973i	$-0.569918\pi$
$967$	−13.5515	−0.435786	−0.217893	+	0.975973i	$0.569918\pi$
$968$	1.51783	0.0487850
$969$	96.2240	3.09116
$970$	1.01185	0.0324884
$971$	−6.29255	−0.201938	−0.100969	−	0.994890i	$-0.532194\pi$
$971$	−6.29255	−0.201938	−0.100969	+	0.994890i	$0.532194\pi$
$972$	30.2775	0.971151
$973$	0	0
$974$	−1.50921	−0.0483583
$975$	−2.59814	−0.0832072
$976$	−48.2804	−1.54542
$977$	−15.2657	−0.488393	−0.244196	−	0.969726i	$-0.578524\pi$
$977$	−15.2657	−0.488393	−0.244196	+	0.969726i	$0.578524\pi$
$978$	3.30082	0.105548
$979$	3.70468	0.118402
$980$	0	0
$981$	77.0925	2.46137
$982$	2.94569	0.0940007
$983$	51.7379	1.65018	0.825091	−	0.565000i	$-0.191124\pi$
$983$	51.7379	1.65018	0.825091	+	0.565000i	$0.191124\pi$
$984$	−6.92980	−0.220914
$985$	15.4117	0.491058
$986$	2.06698	0.0658259
$987$	0	0
$988$	−8.66796	−0.275765
$989$	64.9097	2.06401
$990$	1.84138	0.0585229
$991$	10.2627	0.326007	0.163003	−	0.986626i	$-0.447882\pi$
$991$	10.2627	0.326007	0.163003	+	0.986626i	$0.447882\pi$
$992$	1.16227	0.0369022
$993$	−8.21866	−0.260811
$994$	0	0
$995$	5.55621	0.176144
$996$	90.8365	2.87826
$997$	33.2660	1.05354	0.526772	−	0.850007i	$-0.323402\pi$
$997$	33.2660	1.05354	0.526772	+	0.850007i	$0.323402\pi$
$998$	2.60175	0.0823569
$999$	26.0807	0.825156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.11		21
7.3	odd	6		1085.2.j.d.156.11	✓	42
7.5	odd	6		1085.2.j.d.466.11	yes	42
7.6	odd	2		7595.2.a.bg.1.11		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.11	✓	42	7.3	odd	6
1085.2.j.d.466.11	yes	42	7.5	odd	6
7595.2.a.bf.1.11		21	1.1	even	1	trivial
7595.2.a.bg.1.11		21	7.6	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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0974727 q^{2} +2.80957 q^{3} -1.99050 q^{4} +1.00000 q^{5} -0.273856 q^{6} +0.388965 q^{8} +4.89367 q^{9} +O(q^{10})\)	\(q-0.0974727 q^{2} +2.80957 q^{3} -1.99050 q^{4} +1.00000 q^{5} -0.273856 q^{6} +0.388965 q^{8} +4.89367 q^{9} -0.0974727 q^{10} -3.86034 q^{11} -5.59244 q^{12} -0.924749 q^{13} +2.80957 q^{15} +3.94308 q^{16} -7.27298 q^{17} -0.477000 q^{18} -4.70903 q^{19} -1.99050 q^{20} +0.376278 q^{22} +6.17881 q^{23} +1.09282 q^{24} +1.00000 q^{25} +0.0901378 q^{26} +5.32040 q^{27} +2.91568 q^{29} -0.273856 q^{30} -1.00000 q^{31} -1.16227 q^{32} -10.8459 q^{33} +0.708917 q^{34} -9.74085 q^{36} +4.90201 q^{37} +0.459002 q^{38} -2.59814 q^{39} +0.388965 q^{40} -6.34119 q^{41} +10.5052 q^{43} +7.68401 q^{44} +4.89367 q^{45} -0.602266 q^{46} +10.4541 q^{47} +11.0784 q^{48} -0.0974727 q^{50} -20.4339 q^{51} +1.84071 q^{52} -4.94157 q^{53} -0.518594 q^{54} -3.86034 q^{55} -13.2303 q^{57} -0.284199 q^{58} +1.96054 q^{59} -5.59244 q^{60} -12.2443 q^{61} +0.0974727 q^{62} -7.77288 q^{64} -0.924749 q^{65} +1.05718 q^{66} +3.20491 q^{67} +14.4769 q^{68} +17.3598 q^{69} -3.54537 q^{71} +1.90347 q^{72} -9.64392 q^{73} -0.477813 q^{74} +2.80957 q^{75} +9.37331 q^{76} +0.253248 q^{78} -13.5210 q^{79} +3.94308 q^{80} +0.267014 q^{81} +0.618093 q^{82} -16.2427 q^{83} -7.27298 q^{85} -1.02397 q^{86} +8.19180 q^{87} -1.50154 q^{88} -0.959678 q^{89} -0.477000 q^{90} -12.2989 q^{92} -2.80957 q^{93} -1.01899 q^{94} -4.70903 q^{95} -3.26548 q^{96} -10.3808 q^{97} -18.8912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

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