LMFDB - Embedded newform 7595.2.a.bf.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.10593 q^{2} -2.59668 q^{3} -0.776930 q^{4} +1.00000 q^{5} +2.87173 q^{6} +3.07108 q^{8} +3.74273 q^{9} +O(q^{10})$	\(q-1.10593 q^{2} -2.59668 q^{3} -0.776930 q^{4} +1.00000 q^{5} +2.87173 q^{6} +3.07108 q^{8} +3.74273 q^{9} -1.10593 q^{10} -3.23817 q^{11} +2.01744 q^{12} +0.861323 q^{13} -2.59668 q^{15} -1.84252 q^{16} -7.44353 q^{17} -4.13918 q^{18} +8.00551 q^{19} -0.776930 q^{20} +3.58118 q^{22} -3.22193 q^{23} -7.97459 q^{24} +1.00000 q^{25} -0.952559 q^{26} -1.92864 q^{27} +9.01362 q^{29} +2.87173 q^{30} -1.00000 q^{31} -4.10446 q^{32} +8.40849 q^{33} +8.23199 q^{34} -2.90784 q^{36} -6.55975 q^{37} -8.85350 q^{38} -2.23658 q^{39} +3.07108 q^{40} -2.78912 q^{41} +2.12495 q^{43} +2.51583 q^{44} +3.74273 q^{45} +3.56321 q^{46} -0.279367 q^{47} +4.78443 q^{48} -1.10593 q^{50} +19.3284 q^{51} -0.669187 q^{52} +8.19252 q^{53} +2.13293 q^{54} -3.23817 q^{55} -20.7877 q^{57} -9.96839 q^{58} +5.43423 q^{59} +2.01744 q^{60} -10.8166 q^{61} +1.10593 q^{62} +8.22427 q^{64} +0.861323 q^{65} -9.29917 q^{66} +1.55287 q^{67} +5.78310 q^{68} +8.36631 q^{69} -5.27291 q^{71} +11.4942 q^{72} -1.10731 q^{73} +7.25459 q^{74} -2.59668 q^{75} -6.21972 q^{76} +2.47349 q^{78} -15.4667 q^{79} -1.84252 q^{80} -6.22015 q^{81} +3.08456 q^{82} -14.0767 q^{83} -7.44353 q^{85} -2.35004 q^{86} -23.4055 q^{87} -9.94468 q^{88} -15.7815 q^{89} -4.13918 q^{90} +2.50321 q^{92} +2.59668 q^{93} +0.308959 q^{94} +8.00551 q^{95} +10.6580 q^{96} +1.34170 q^{97} -12.1196 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.10593	−0.782007	−0.391004	−	0.920389i	$-0.627872\pi$
$2$	−1.10593	−0.782007	−0.391004	+	0.920389i	$0.627872\pi$
$3$	−2.59668	−1.49919	−0.749596	−	0.661895i	$-0.769752\pi$
$3$	−2.59668	−1.49919	−0.749596	+	0.661895i	$0.769752\pi$
$4$	−0.776930	−0.388465
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.87173	1.17238
$7$	0	0
$7$	0	0
$8$	3.07108	1.08579
$9$	3.74273	1.24758
$10$	−1.10593	−0.349724
$11$	−3.23817	−0.976346	−0.488173	−	0.872747i	$-0.662337\pi$
$11$	−3.23817	−0.976346	−0.488173	+	0.872747i	$0.662337\pi$
$12$	2.01744	0.582383
$13$	0.861323	0.238888	0.119444	−	0.992841i	$-0.461889\pi$
$13$	0.861323	0.238888	0.119444	+	0.992841i	$0.461889\pi$
$14$	0	0
$15$	−2.59668	−0.670459
$16$	−1.84252	−0.460630
$17$	−7.44353	−1.80532	−0.902661	−	0.430353i	$-0.858389\pi$
$17$	−7.44353	−1.80532	−0.902661	+	0.430353i	$0.858389\pi$
$18$	−4.13918	−0.975615
$19$	8.00551	1.83659	0.918295	−	0.395896i	$-0.129566\pi$
$19$	8.00551	1.83659	0.918295	+	0.395896i	$0.129566\pi$
$20$	−0.776930	−0.173727
$21$	0	0
$22$	3.58118	0.763510
$23$	−3.22193	−0.671818	−0.335909	−	0.941894i	$-0.609044\pi$
$23$	−3.22193	−0.671818	−0.335909	+	0.941894i	$0.609044\pi$
$24$	−7.97459	−1.62781
$25$	1.00000	0.200000
$26$	−0.952559	−0.186812
$27$	−1.92864	−0.371167
$28$	0	0
$29$	9.01362	1.67379	0.836894	−	0.547365i	$-0.184369\pi$
$29$	9.01362	1.67379	0.836894	+	0.547365i	$0.184369\pi$
$30$	2.87173	0.524304
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.10446	−0.725573
$33$	8.40849	1.46373
$34$	8.23199	1.41177
$35$	0	0
$36$	−2.90784	−0.484640
$37$	−6.55975	−1.07842	−0.539208	−	0.842173i	$-0.681276\pi$
$37$	−6.55975	−1.07842	−0.539208	+	0.842173i	$0.681276\pi$
$38$	−8.85350	−1.43623
$39$	−2.23658	−0.358139
$40$	3.07108	0.485580
$41$	−2.78912	−0.435588	−0.217794	−	0.975995i	$-0.569886\pi$
$41$	−2.78912	−0.435588	−0.217794	+	0.975995i	$0.569886\pi$
$42$	0	0
$43$	2.12495	0.324052	0.162026	−	0.986786i	$-0.448197\pi$
$43$	2.12495	0.324052	0.162026	+	0.986786i	$0.448197\pi$
$44$	2.51583	0.379276
$45$	3.74273	0.557934
$46$	3.56321	0.525367
$47$	−0.279367	−0.0407498	−0.0203749	−	0.999792i	$-0.506486\pi$
$47$	−0.279367	−0.0407498	−0.0203749	+	0.999792i	$0.506486\pi$
$48$	4.78443	0.690574
$49$	0	0
$50$	−1.10593	−0.156401
$51$	19.3284	2.70652
$52$	−0.669187	−0.0927996
$53$	8.19252	1.12533	0.562665	−	0.826685i	$-0.309776\pi$
$53$	8.19252	1.12533	0.562665	+	0.826685i	$0.309776\pi$
$54$	2.13293	0.290255
$55$	−3.23817	−0.436635
$56$	0	0
$57$	−20.7877	−2.75340
$58$	−9.96839	−1.30891
$59$	5.43423	0.707477	0.353739	−	0.935344i	$-0.384910\pi$
$59$	5.43423	0.707477	0.353739	+	0.935344i	$0.384910\pi$
$60$	2.01744	0.260450
$61$	−10.8166	−1.38493	−0.692463	−	0.721454i	$-0.743474\pi$
$61$	−10.8166	−1.38493	−0.692463	+	0.721454i	$0.743474\pi$
$62$	1.10593	0.140453
$63$	0	0
$64$	8.22427	1.02803
$65$	0.861323	0.106834
$66$	−9.29917	−1.14465
$67$	1.55287	0.189713	0.0948563	−	0.995491i	$-0.469761\pi$
$67$	1.55287	0.189713	0.0948563	+	0.995491i	$0.469761\pi$
$68$	5.78310	0.701304
$69$	8.36631	1.00718
$70$	0	0
$71$	−5.27291	−0.625779	−0.312890	−	0.949790i	$-0.601297\pi$
$71$	−5.27291	−0.625779	−0.312890	+	0.949790i	$0.601297\pi$
$72$	11.4942	1.35461
$73$	−1.10731	−0.129601	−0.0648005	−	0.997898i	$-0.520641\pi$
$73$	−1.10731	−0.129601	−0.0648005	+	0.997898i	$0.520641\pi$
$74$	7.25459	0.843329
$75$	−2.59668	−0.299838
$76$	−6.21972	−0.713451
$77$	0	0
$78$	2.47349	0.280067
$79$	−15.4667	−1.74014	−0.870071	−	0.492926i	$-0.835927\pi$
$79$	−15.4667	−1.74014	−0.870071	+	0.492926i	$0.835927\pi$
$80$	−1.84252	−0.206000
$81$	−6.22015	−0.691128
$82$	3.08456	0.340633
$83$	−14.0767	−1.54512	−0.772561	−	0.634941i	$-0.781025\pi$
$83$	−14.0767	−1.54512	−0.772561	+	0.634941i	$0.781025\pi$
$84$	0	0
$85$	−7.44353	−0.807364
$86$	−2.35004	−0.253411
$87$	−23.4055	−2.50933
$88$	−9.94468	−1.06011
$89$	−15.7815	−1.67283	−0.836417	−	0.548093i	$-0.815354\pi$
$89$	−15.7815	−1.67283	−0.836417	+	0.548093i	$0.815354\pi$
$90$	−4.13918	−0.436308
$91$	0	0
$92$	2.50321	0.260978
$93$	2.59668	0.269263
$94$	0.308959	0.0318666
$95$	8.00551	0.821348
$96$	10.6580	1.08777
$97$	1.34170	0.136229	0.0681143	−	0.997678i	$-0.478302\pi$
$97$	1.34170	0.136229	0.0681143	+	0.997678i	$0.478302\pi$
$98$	0	0
$99$	−12.1196	−1.21807
$100$	−0.776930	−0.0776930
$101$	16.4818	1.64000	0.820000	−	0.572364i	$-0.193974\pi$
$101$	16.4818	1.64000	0.820000	+	0.572364i	$0.193974\pi$
$102$	−21.3758	−2.11652
$103$	−3.68787	−0.363376	−0.181688	−	0.983356i	$-0.558156\pi$
$103$	−3.68787	−0.363376	−0.181688	+	0.983356i	$0.558156\pi$
$104$	2.64519	0.259382
$105$	0	0
$106$	−9.06032	−0.880016
$107$	18.2375	1.76309	0.881545	−	0.472100i	$-0.156504\pi$
$107$	18.2375	1.76309	0.881545	+	0.472100i	$0.156504\pi$
$108$	1.49842	0.144185
$109$	7.66305	0.733987	0.366994	−	0.930223i	$-0.380387\pi$
$109$	7.66305	0.733987	0.366994	+	0.930223i	$0.380387\pi$
$110$	3.58118	0.341452
$111$	17.0335	1.61675
$112$	0	0
$113$	14.5260	1.36649	0.683244	−	0.730191i	$-0.260569\pi$
$113$	14.5260	1.36649	0.683244	+	0.730191i	$0.260569\pi$
$114$	22.9897	2.15318
$115$	−3.22193	−0.300446
$116$	−7.00295	−0.650207
$117$	3.22370	0.298031
$118$	−6.00986	−0.553252
$119$	0	0
$120$	−7.97459	−0.727978
$121$	−0.514226	−0.0467479
$122$	11.9624	1.08302
$123$	7.24245	0.653030
$124$	0.776930	0.0697703
$125$	1.00000	0.0894427
$126$	0	0
$127$	3.62974	0.322087	0.161043	−	0.986947i	$-0.448514\pi$
$127$	3.62974	0.322087	0.161043	+	0.986947i	$0.448514\pi$
$128$	−0.886505	−0.0783567
$129$	−5.51782	−0.485817
$130$	−0.952559	−0.0835450
$131$	21.5075	1.87912	0.939560	−	0.342383i	$-0.111234\pi$
$131$	21.5075	1.87912	0.939560	+	0.342383i	$0.111234\pi$
$132$	−6.53281	−0.568608
$133$	0	0
$134$	−1.71735	−0.148357
$135$	−1.92864	−0.165991
$136$	−22.8596	−1.96020
$137$	4.90609	0.419156	0.209578	−	0.977792i	$-0.432791\pi$
$137$	4.90609	0.419156	0.209578	+	0.977792i	$0.432791\pi$
$138$	−9.25251	−0.787626
$139$	2.21438	0.187821	0.0939107	−	0.995581i	$-0.470063\pi$
$139$	2.21438	0.187821	0.0939107	+	0.995581i	$0.470063\pi$
$140$	0	0
$141$	0.725425	0.0610918
$142$	5.83144	0.489364
$143$	−2.78911	−0.233237
$144$	−6.89607	−0.574672
$145$	9.01362	0.748541
$146$	1.22460	0.101349
$147$	0	0
$148$	5.09646	0.418927
$149$	22.8920	1.87539	0.937693	−	0.347466i	$-0.112958\pi$
$149$	22.8920	1.87539	0.937693	+	0.347466i	$0.112958\pi$
$150$	2.87173	0.234476
$151$	5.12377	0.416966	0.208483	−	0.978026i	$-0.433147\pi$
$151$	5.12377	0.416966	0.208483	+	0.978026i	$0.433147\pi$
$152$	24.5855	1.99415
$153$	−27.8591	−2.25228
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	1.73766	0.139124
$157$	−24.5104	−1.95614	−0.978070	−	0.208278i	$-0.933214\pi$
$157$	−24.5104	−1.95614	−0.978070	+	0.208278i	$0.933214\pi$
$158$	17.1050	1.36080
$159$	−21.2733	−1.68709
$160$	−4.10446	−0.324486
$161$	0	0
$162$	6.87902	0.540467
$163$	11.4948	0.900345	0.450172	−	0.892942i	$-0.351363\pi$
$163$	11.4948	0.900345	0.450172	+	0.892942i	$0.351363\pi$
$164$	2.16695	0.169211
$165$	8.40849	0.654600
$166$	15.5678	1.20830
$167$	10.7961	0.835424	0.417712	−	0.908580i	$-0.362832\pi$
$167$	10.7961	0.835424	0.417712	+	0.908580i	$0.362832\pi$
$168$	0	0
$169$	−12.2581	−0.942932
$170$	8.23199	0.631365
$171$	29.9625	2.29129
$172$	−1.65094	−0.125883
$173$	−22.2685	−1.69305	−0.846523	−	0.532352i	$-0.821308\pi$
$173$	−22.2685	−1.69305	−0.846523	+	0.532352i	$0.821308\pi$
$174$	25.8847	1.96231
$175$	0	0
$176$	5.96641	0.449735
$177$	−14.1110	−1.06064
$178$	17.4531	1.30817
$179$	12.6438	0.945043	0.472521	−	0.881319i	$-0.343344\pi$
$179$	12.6438	0.945043	0.472521	+	0.881319i	$0.343344\pi$
$180$	−2.90784	−0.216738
$181$	9.28574	0.690204	0.345102	−	0.938565i	$-0.387844\pi$
$181$	9.28574	0.690204	0.345102	+	0.938565i	$0.387844\pi$
$182$	0	0
$183$	28.0872	2.07627
$184$	−9.89478	−0.729453
$185$	−6.55975	−0.482282
$186$	−2.87173	−0.210566
$187$	24.1034	1.76262
$188$	0.217048	0.0158299
$189$	0	0
$190$	−8.85350	−0.642300
$191$	7.94109	0.574597	0.287299	−	0.957841i	$-0.407243\pi$
$191$	7.94109	0.574597	0.287299	+	0.957841i	$0.407243\pi$
$192$	−21.3558	−1.54122
$193$	−11.8908	−0.855921	−0.427960	−	0.903798i	$-0.640768\pi$
$193$	−11.8908	−0.855921	−0.427960	+	0.903798i	$0.640768\pi$
$194$	−1.48382	−0.106532
$195$	−2.23658	−0.160165
$196$	0	0
$197$	−4.98303	−0.355026	−0.177513	−	0.984118i	$-0.556805\pi$
$197$	−4.98303	−0.355026	−0.177513	+	0.984118i	$0.556805\pi$
$198$	13.4034	0.952538
$199$	12.4075	0.879542	0.439771	−	0.898110i	$-0.355060\pi$
$199$	12.4075	0.879542	0.439771	+	0.898110i	$0.355060\pi$
$200$	3.07108	0.217158
$201$	−4.03229	−0.284416
$202$	−18.2276	−1.28249
$203$	0	0
$204$	−15.0168	−1.05139
$205$	−2.78912	−0.194801
$206$	4.07851	0.284163
$207$	−12.0588	−0.838146
$208$	−1.58701	−0.110039
$209$	−25.9233	−1.79315
$210$	0	0
$211$	10.4068	0.716436	0.358218	−	0.933638i	$-0.383384\pi$
$211$	10.4068	0.716436	0.358218	+	0.933638i	$0.383384\pi$
$212$	−6.36501	−0.437151
$213$	13.6920	0.938163
$214$	−20.1694	−1.37875
$215$	2.12495	0.144921
$216$	−5.92300	−0.403009
$217$	0	0
$218$	−8.47476	−0.573984
$219$	2.87533	0.194297
$220$	2.51583	0.169617
$221$	−6.41128	−0.431270
$222$	−18.8378	−1.26431
$223$	−26.7846	−1.79363	−0.896813	−	0.442409i	$-0.854124\pi$
$223$	−26.7846	−1.79363	−0.896813	+	0.442409i	$0.854124\pi$
$224$	0	0
$225$	3.74273	0.249516
$226$	−16.0646	−1.06860
$227$	15.7151	1.04305	0.521523	−	0.853237i	$-0.325364\pi$
$227$	15.7151	1.04305	0.521523	+	0.853237i	$0.325364\pi$
$228$	16.1506	1.06960
$229$	−9.79685	−0.647394	−0.323697	−	0.946161i	$-0.604926\pi$
$229$	−9.79685	−0.647394	−0.323697	+	0.946161i	$0.604926\pi$
$230$	3.56321	0.234951
$231$	0	0
$232$	27.6815	1.81738
$233$	−6.96957	−0.456592	−0.228296	−	0.973592i	$-0.573315\pi$
$233$	−6.96957	−0.456592	−0.228296	+	0.973592i	$0.573315\pi$
$234$	−3.56517	−0.233063
$235$	−0.279367	−0.0182239
$236$	−4.22202	−0.274830
$237$	40.1621	2.60881
$238$	0	0
$239$	−2.92163	−0.188984	−0.0944921	−	0.995526i	$-0.530123\pi$
$239$	−2.92163	−0.188984	−0.0944921	+	0.995526i	$0.530123\pi$
$240$	4.78443	0.308834
$241$	16.5181	1.06402	0.532012	−	0.846737i	$-0.321436\pi$
$241$	16.5181	1.06402	0.532012	+	0.846737i	$0.321436\pi$
$242$	0.568696	0.0365572
$243$	21.9376	1.40730
$244$	8.40374	0.537995
$245$	0	0
$246$	−8.00961	−0.510674
$247$	6.89534	0.438740
$248$	−3.07108	−0.195014
$249$	36.5527	2.31644
$250$	−1.10593	−0.0699448
$251$	8.01263	0.505753	0.252876	−	0.967499i	$-0.418623\pi$
$251$	8.01263	0.505753	0.252876	+	0.967499i	$0.418623\pi$
$252$	0	0
$253$	10.4332	0.655927
$254$	−4.01422	−0.251874
$255$	19.3284	1.21039
$256$	−15.4681	−0.966758
$257$	−8.84829	−0.551941	−0.275971	−	0.961166i	$-0.588999\pi$
$257$	−8.84829	−0.551941	−0.275971	+	0.961166i	$0.588999\pi$
$258$	6.10229	0.379912
$259$	0	0
$260$	−0.669187	−0.0415012
$261$	33.7356	2.08818
$262$	−23.7857	−1.46949
$263$	11.8686	0.731850	0.365925	−	0.930644i	$-0.380753\pi$
$263$	11.8686	0.731850	0.365925	+	0.930644i	$0.380753\pi$
$264$	25.8231	1.58930
$265$	8.19252	0.503263
$266$	0	0
$267$	40.9794	2.50790
$268$	−1.20647	−0.0736967
$269$	−2.73916	−0.167010	−0.0835049	−	0.996507i	$-0.526611\pi$
$269$	−2.73916	−0.167010	−0.0835049	+	0.996507i	$0.526611\pi$
$270$	2.13293	0.129806
$271$	14.4968	0.880617	0.440308	−	0.897847i	$-0.354869\pi$
$271$	14.4968	0.880617	0.440308	+	0.897847i	$0.354869\pi$
$272$	13.7149	0.831586
$273$	0	0
$274$	−5.42577	−0.327783
$275$	−3.23817	−0.195269
$276$	−6.50003	−0.391256
$277$	18.9073	1.13603	0.568014	−	0.823019i	$-0.307712\pi$
$277$	18.9073	1.13603	0.568014	+	0.823019i	$0.307712\pi$
$278$	−2.44894	−0.146878
$279$	−3.74273	−0.224072
$280$	0	0
$281$	−8.14896	−0.486126	−0.243063	−	0.970010i	$-0.578152\pi$
$281$	−8.14896	−0.486126	−0.243063	+	0.970010i	$0.578152\pi$
$282$	−0.802266	−0.0477742
$283$	9.13347	0.542928	0.271464	−	0.962449i	$-0.412492\pi$
$283$	9.13347	0.542928	0.271464	+	0.962449i	$0.412492\pi$
$284$	4.09668	0.243093
$285$	−20.7877	−1.23136
$286$	3.08455	0.182393
$287$	0	0
$288$	−15.3619	−0.905209
$289$	38.4061	2.25918
$290$	−9.96839	−0.585364
$291$	−3.48395	−0.204233
$292$	0.860302	0.0503454
$293$	−5.34708	−0.312380	−0.156190	−	0.987727i	$-0.549921\pi$
$293$	−5.34708	−0.312380	−0.156190	+	0.987727i	$0.549921\pi$
$294$	0	0
$295$	5.43423	0.316393
$296$	−20.1455	−1.17093
$297$	6.24527	0.362387
$298$	−25.3168	−1.46656
$299$	−2.77512	−0.160489
$300$	2.01744	0.116477
$301$	0	0
$302$	−5.66651	−0.326071
$303$	−42.7979	−2.45867
$304$	−14.7503	−0.845990
$305$	−10.8166	−0.619357
$306$	30.8101	1.76130
$307$	−21.5653	−1.23079	−0.615397	−	0.788217i	$-0.711004\pi$
$307$	−21.5653	−1.23079	−0.615397	+	0.788217i	$0.711004\pi$
$308$	0	0
$309$	9.57620	0.544771
$310$	1.10593	0.0628123
$311$	−5.36834	−0.304410	−0.152205	−	0.988349i	$-0.548637\pi$
$311$	−5.36834	−0.304410	−0.152205	+	0.988349i	$0.548637\pi$
$312$	−6.86870	−0.388864
$313$	−14.6897	−0.830313	−0.415157	−	0.909750i	$-0.636273\pi$
$313$	−14.6897	−0.830313	−0.415157	+	0.909750i	$0.636273\pi$
$314$	27.1066	1.52972
$315$	0	0
$316$	12.0166	0.675984
$317$	22.8565	1.28375	0.641875	−	0.766810i	$-0.278157\pi$
$317$	22.8565	1.28375	0.641875	+	0.766810i	$0.278157\pi$
$318$	23.5267	1.31931
$319$	−29.1877	−1.63420
$320$	8.22427	0.459751
$321$	−47.3570	−2.64321
$322$	0	0
$323$	−59.5893	−3.31564
$324$	4.83262	0.268479
$325$	0.861323	0.0477776
$326$	−12.7124	−0.704076
$327$	−19.8985	−1.10039
$328$	−8.56561	−0.472957
$329$	0	0
$330$	−9.29917	−0.511902
$331$	−2.02562	−0.111338	−0.0556690	−	0.998449i	$-0.517729\pi$
$331$	−2.02562	−0.111338	−0.0556690	+	0.998449i	$0.517729\pi$
$332$	10.9366	0.600225
$333$	−24.5514	−1.34541
$334$	−11.9396	−0.653307
$335$	1.55287	0.0848421
$336$	0	0
$337$	−10.7878	−0.587652	−0.293826	−	0.955859i	$-0.594929\pi$
$337$	−10.7878	−0.587652	−0.293826	+	0.955859i	$0.594929\pi$
$338$	13.5566	0.737380
$339$	−37.7192	−2.04863
$340$	5.78310	0.313632
$341$	3.23817	0.175357
$342$	−33.1363	−1.79181
$343$	0	0
$344$	6.52589	0.351853
$345$	8.36631	0.450427
$346$	24.6273	1.32397
$347$	−10.4179	−0.559262	−0.279631	−	0.960107i	$-0.590212\pi$
$347$	−10.4179	−0.559262	−0.279631	+	0.960107i	$0.590212\pi$
$348$	18.1844	0.974786
$349$	−4.95408	−0.265186	−0.132593	−	0.991171i	$-0.542330\pi$
$349$	−4.95408	−0.265186	−0.132593	+	0.991171i	$0.542330\pi$
$350$	0	0
$351$	−1.66118	−0.0886673
$352$	13.2910	0.708411
$353$	1.35427	0.0720805	0.0360402	−	0.999350i	$-0.488526\pi$
$353$	1.35427	0.0720805	0.0360402	+	0.999350i	$0.488526\pi$
$354$	15.6057	0.829431
$355$	−5.27291	−0.279857
$356$	12.2611	0.649837
$357$	0	0
$358$	−13.9831	−0.739030
$359$	−19.4825	−1.02825	−0.514123	−	0.857717i	$-0.671882\pi$
$359$	−19.4825	−1.02825	−0.514123	+	0.857717i	$0.671882\pi$
$360$	11.4942	0.605799
$361$	45.0883	2.37307
$362$	−10.2693	−0.539744
$363$	1.33528	0.0700840
$364$	0	0
$365$	−1.10731	−0.0579593
$366$	−31.0624	−1.62366
$367$	−18.2034	−0.950209	−0.475104	−	0.879929i	$-0.657590\pi$
$367$	−18.2034	−0.950209	−0.475104	+	0.879929i	$0.657590\pi$
$368$	5.93647	0.309460
$369$	−10.4389	−0.543430
$370$	7.25459	0.377148
$371$	0	0
$372$	−2.01744	−0.104599
$373$	4.73188	0.245007	0.122504	−	0.992468i	$-0.460908\pi$
$373$	4.73188	0.245007	0.122504	+	0.992468i	$0.460908\pi$
$374$	−26.6566	−1.37838
$375$	−2.59668	−0.134092
$376$	−0.857956	−0.0442457
$377$	7.76364	0.399848
$378$	0	0
$379$	9.13778	0.469376	0.234688	−	0.972071i	$-0.424593\pi$
$379$	9.13778	0.469376	0.234688	+	0.972071i	$0.424593\pi$
$380$	−6.21972	−0.319065
$381$	−9.42525	−0.482870
$382$	−8.78226	−0.449339
$383$	−19.8695	−1.01528	−0.507642	−	0.861568i	$-0.669483\pi$
$383$	−19.8695	−1.01528	−0.507642	+	0.861568i	$0.669483\pi$
$384$	2.30197	0.117472
$385$	0	0
$386$	13.1504	0.669336
$387$	7.95313	0.404280
$388$	−1.04240	−0.0529200
$389$	20.6758	1.04831	0.524153	−	0.851624i	$-0.324382\pi$
$389$	20.6758	1.04831	0.524153	+	0.851624i	$0.324382\pi$
$390$	2.47349	0.125250
$391$	23.9825	1.21285
$392$	0	0
$393$	−55.8481	−2.81716
$394$	5.51085	0.277633
$395$	−15.4667	−0.778216
$396$	9.41609	0.473176
$397$	−25.7545	−1.29258	−0.646292	−	0.763090i	$-0.723681\pi$
$397$	−25.7545	−1.29258	−0.646292	+	0.763090i	$0.723681\pi$
$398$	−13.7217	−0.687808
$399$	0	0
$400$	−1.84252	−0.0921261
$401$	1.60245	0.0800224	0.0400112	−	0.999199i	$-0.487261\pi$
$401$	1.60245	0.0800224	0.0400112	+	0.999199i	$0.487261\pi$
$402$	4.45941	0.222415
$403$	−0.861323	−0.0429056
$404$	−12.8052	−0.637082
$405$	−6.22015	−0.309082
$406$	0	0
$407$	21.2416	1.05291
$408$	59.3591	2.93871
$409$	−14.6018	−0.722012	−0.361006	−	0.932564i	$-0.617567\pi$
$409$	−14.6018	−0.722012	−0.361006	+	0.932564i	$0.617567\pi$
$410$	3.08456	0.152336
$411$	−12.7395	−0.628395
$412$	2.86521	0.141159
$413$	0	0
$414$	13.3361	0.655436
$415$	−14.0767	−0.691000
$416$	−3.53527	−0.173331
$417$	−5.75003	−0.281580
$418$	28.6692	1.40226
$419$	16.1652	0.789723	0.394862	−	0.918741i	$-0.370793\pi$
$419$	16.1652	0.789723	0.394862	+	0.918741i	$0.370793\pi$
$420$	0	0
$421$	−12.8522	−0.626378	−0.313189	−	0.949691i	$-0.601397\pi$
$421$	−12.8522	−0.626378	−0.313189	+	0.949691i	$0.601397\pi$
$422$	−11.5092	−0.560258
$423$	−1.04559	−0.0508385
$424$	25.1599	1.22187
$425$	−7.44353	−0.361064
$426$	−15.1424	−0.733650
$427$	0	0
$428$	−14.1693	−0.684898
$429$	7.24243	0.349668
$430$	−2.35004	−0.113329
$431$	−2.43032	−0.117064	−0.0585322	−	0.998286i	$-0.518642\pi$
$431$	−2.43032	−0.117064	−0.0585322	+	0.998286i	$0.518642\pi$
$432$	3.55356	0.170971
$433$	−9.27703	−0.445826	−0.222913	−	0.974838i	$-0.571557\pi$
$433$	−9.27703	−0.445826	−0.222913	+	0.974838i	$0.571557\pi$
$434$	0	0
$435$	−23.4055	−1.12221
$436$	−5.95365	−0.285128
$437$	−25.7932	−1.23386
$438$	−3.17990	−0.151941
$439$	−37.3722	−1.78368	−0.891839	−	0.452354i	$-0.850584\pi$
$439$	−37.3722	−1.78368	−0.891839	+	0.452354i	$0.850584\pi$
$440$	−9.94468	−0.474094
$441$	0	0
$442$	7.09040	0.337256
$443$	−25.7217	−1.22208	−0.611038	−	0.791601i	$-0.709248\pi$
$443$	−25.7217	−1.22208	−0.611038	+	0.791601i	$0.709248\pi$
$444$	−13.2339	−0.628052
$445$	−15.7815	−0.748114
$446$	29.6217	1.40263
$447$	−59.4431	−2.81156
$448$	0	0
$449$	21.8817	1.03266	0.516331	−	0.856389i	$-0.327297\pi$
$449$	21.8817	1.03266	0.516331	+	0.856389i	$0.327297\pi$
$450$	−4.13918	−0.195123
$451$	9.03167	0.425285
$452$	−11.2856	−0.530832
$453$	−13.3048	−0.625113
$454$	−17.3797	−0.815669
$455$	0	0
$456$	−63.8407	−2.98962
$457$	17.0265	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$457$	17.0265	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$458$	10.8346	0.506267
$459$	14.3559	0.670075
$460$	2.50321	0.116713
$461$	−10.3780	−0.483350	−0.241675	−	0.970357i	$-0.577697\pi$
$461$	−10.3780	−0.483350	−0.241675	+	0.970357i	$0.577697\pi$
$462$	0	0
$463$	−17.3935	−0.808342	−0.404171	−	0.914683i	$-0.632440\pi$
$463$	−17.3935	−0.808342	−0.404171	+	0.914683i	$0.632440\pi$
$464$	−16.6078	−0.770997
$465$	2.59668	0.120418
$466$	7.70783	0.357058
$467$	15.9385	0.737544	0.368772	−	0.929520i	$-0.379778\pi$
$467$	15.9385	0.737544	0.368772	+	0.929520i	$0.379778\pi$
$468$	−2.50459	−0.115775
$469$	0	0
$470$	0.308959	0.0142512
$471$	63.6455	2.93263
$472$	16.6889	0.768171
$473$	−6.88097	−0.316387
$474$	−44.4163	−2.04011
$475$	8.00551	0.367318
$476$	0	0
$477$	30.6624	1.40394
$478$	3.23110	0.147787
$479$	25.0147	1.14295	0.571476	−	0.820619i	$-0.306371\pi$
$479$	25.0147	1.14295	0.571476	+	0.820619i	$0.306371\pi$
$480$	10.6580	0.486467
$481$	−5.65006	−0.257621
$482$	−18.2678	−0.832075
$483$	0	0
$484$	0.399518	0.0181599
$485$	1.34170	0.0609233
$486$	−24.2614	−1.10052
$487$	11.8098	0.535152	0.267576	−	0.963537i	$-0.413777\pi$
$487$	11.8098	0.535152	0.267576	+	0.963537i	$0.413777\pi$
$488$	−33.2186	−1.50374
$489$	−29.8484	−1.34979
$490$	0	0
$491$	16.6143	0.749795	0.374897	−	0.927066i	$-0.377678\pi$
$491$	16.6143	0.749795	0.374897	+	0.927066i	$0.377678\pi$
$492$	−5.62688	−0.253679
$493$	−67.0932	−3.02172
$494$	−7.62572	−0.343098
$495$	−12.1196	−0.544737
$496$	1.84252	0.0827317
$497$	0	0
$498$	−40.4246	−1.81147
$499$	0.692258	0.0309897	0.0154949	−	0.999880i	$-0.495068\pi$
$499$	0.692258	0.0309897	0.0154949	+	0.999880i	$0.495068\pi$
$500$	−0.776930	−0.0347453
$501$	−28.0339	−1.25246
$502$	−8.86137	−0.395502
$503$	1.52831	0.0681440	0.0340720	−	0.999419i	$-0.489152\pi$
$503$	1.52831	0.0681440	0.0340720	+	0.999419i	$0.489152\pi$
$504$	0	0
$505$	16.4818	0.733430
$506$	−11.5383	−0.512940
$507$	31.8304	1.41364
$508$	−2.82005	−0.125119
$509$	−38.5498	−1.70869	−0.854345	−	0.519706i	$-0.826042\pi$
$509$	−38.5498	−1.70869	−0.854345	+	0.519706i	$0.826042\pi$
$510$	−21.3758	−0.946537
$511$	0	0
$512$	18.8796	0.834369
$513$	−15.4397	−0.681681
$514$	9.78555	0.431622
$515$	−3.68787	−0.162507
$516$	4.28696	0.188723
$517$	0.904638	0.0397859
$518$	0	0
$519$	57.8242	2.53820
$520$	2.64519	0.115999
$521$	−38.5957	−1.69091	−0.845455	−	0.534047i	$-0.820671\pi$
$521$	−38.5957	−1.69091	−0.845455	+	0.534047i	$0.820671\pi$
$522$	−37.3090	−1.63297
$523$	−29.9107	−1.30790	−0.653952	−	0.756536i	$-0.726890\pi$
$523$	−29.9107	−1.30790	−0.653952	+	0.756536i	$0.726890\pi$
$524$	−16.7098	−0.729972
$525$	0	0
$526$	−13.1258	−0.572312
$527$	7.44353	0.324245
$528$	−15.4928	−0.674239
$529$	−12.6192	−0.548660
$530$	−9.06032	−0.393555
$531$	20.3389	0.882633
$532$	0	0
$533$	−2.40234	−0.104057
$534$	−45.3202	−1.96120
$535$	18.2375	0.788478
$536$	4.76897	0.205988
$537$	−32.8319	−1.41680
$538$	3.02931	0.130603
$539$	0	0
$540$	1.49842	0.0644816
$541$	−19.9067	−0.855854	−0.427927	−	0.903813i	$-0.640756\pi$
$541$	−19.9067	−0.855854	−0.427927	+	0.903813i	$0.640756\pi$
$542$	−16.0324	−0.688649
$543$	−24.1121	−1.03475
$544$	30.5517	1.30989
$545$	7.66305	0.328249
$546$	0	0
$547$	−7.25773	−0.310318	−0.155159	−	0.987890i	$-0.549589\pi$
$547$	−7.25773	−0.310318	−0.155159	+	0.987890i	$0.549589\pi$
$548$	−3.81169	−0.162827
$549$	−40.4837	−1.72780
$550$	3.58118	0.152702
$551$	72.1587	3.07406
$552$	25.6936	1.09359
$553$	0	0
$554$	−20.9100	−0.888383
$555$	17.0335	0.723034
$556$	−1.72042	−0.0729620
$557$	−10.9581	−0.464310	−0.232155	−	0.972679i	$-0.574578\pi$
$557$	−10.9581	−0.464310	−0.232155	+	0.972679i	$0.574578\pi$
$558$	4.13918	0.175226
$559$	1.83027	0.0774122
$560$	0	0
$561$	−62.5889	−2.64250
$562$	9.01215	0.380154
$563$	16.4060	0.691429	0.345715	−	0.938340i	$-0.387637\pi$
$563$	16.4060	0.691429	0.345715	+	0.938340i	$0.387637\pi$
$564$	−0.563604	−0.0237320
$565$	14.5260	0.611112
$566$	−10.1009	−0.424574
$567$	0	0
$568$	−16.1935	−0.679464
$569$	44.1475	1.85076	0.925379	−	0.379042i	$-0.123747\pi$
$569$	44.1475	1.85076	0.925379	+	0.379042i	$0.123747\pi$
$570$	22.9897	0.962932
$571$	−0.219444	−0.00918343	−0.00459171	−	0.999989i	$-0.501462\pi$
$571$	−0.219444	−0.00918343	−0.00459171	+	0.999989i	$0.501462\pi$
$572$	2.16695	0.0906045
$573$	−20.6205	−0.861432
$574$	0	0
$575$	−3.22193	−0.134364
$576$	30.7812	1.28255
$577$	5.63012	0.234385	0.117193	−	0.993109i	$-0.462611\pi$
$577$	5.63012	0.234385	0.117193	+	0.993109i	$0.462611\pi$
$578$	−42.4743	−1.76670
$579$	30.8767	1.28319
$580$	−7.00295	−0.290782
$581$	0	0
$582$	3.85299	0.159712
$583$	−26.5288	−1.09871
$584$	−3.40064	−0.140719
$585$	3.22370	0.133284
$586$	5.91347	0.244283
$587$	−4.53773	−0.187292	−0.0936460	−	0.995606i	$-0.529852\pi$
$587$	−4.53773	−0.187292	−0.0936460	+	0.995606i	$0.529852\pi$
$588$	0	0
$589$	−8.00551	−0.329861
$590$	−6.00986	−0.247422
$591$	12.9393	0.532252
$592$	12.0865	0.496751
$593$	−6.31337	−0.259259	−0.129629	−	0.991563i	$-0.541379\pi$
$593$	−6.31337	−0.259259	−0.129629	+	0.991563i	$0.541379\pi$
$594$	−6.90680	−0.283389
$595$	0	0
$596$	−17.7855	−0.728521
$597$	−32.2182	−1.31860
$598$	3.06908	0.125504
$599$	−39.9475	−1.63221	−0.816106	−	0.577902i	$-0.803872\pi$
$599$	−39.9475	−1.63221	−0.816106	+	0.577902i	$0.803872\pi$
$600$	−7.97459	−0.325561
$601$	−6.53611	−0.266613	−0.133307	−	0.991075i	$-0.542560\pi$
$601$	−6.53611	−0.266613	−0.133307	+	0.991075i	$0.542560\pi$
$602$	0	0
$603$	5.81196	0.236681
$604$	−3.98081	−0.161977
$605$	−0.514226	−0.0209063
$606$	47.3313	1.92270
$607$	−1.62721	−0.0660464	−0.0330232	−	0.999455i	$-0.510514\pi$
$607$	−1.62721	−0.0660464	−0.0330232	+	0.999455i	$0.510514\pi$
$608$	−32.8583	−1.33258
$609$	0	0
$610$	11.9624	0.484342
$611$	−0.240625	−0.00973464
$612$	21.6446	0.874931
$613$	−14.0998	−0.569485	−0.284743	−	0.958604i	$-0.591908\pi$
$613$	−14.0998	−0.569485	−0.284743	+	0.958604i	$0.591908\pi$
$614$	23.8496	0.962490
$615$	7.24245	0.292044
$616$	0	0
$617$	−10.3694	−0.417457	−0.208729	−	0.977974i	$-0.566933\pi$
$617$	−10.3694	−0.417457	−0.208729	+	0.977974i	$0.566933\pi$
$618$	−10.5906	−0.426015
$619$	14.4264	0.579844	0.289922	−	0.957050i	$-0.406371\pi$
$619$	14.4264	0.579844	0.289922	+	0.957050i	$0.406371\pi$
$620$	0.776930	0.0312022
$621$	6.21393	0.249357
$622$	5.93698	0.238051
$623$	0	0
$624$	4.12094	0.164970
$625$	1.00000	0.0400000
$626$	16.2458	0.649311
$627$	67.3143	2.68828
$628$	19.0428	0.759891
$629$	48.8277	1.94689
$630$	0	0
$631$	14.3410	0.570907	0.285453	−	0.958393i	$-0.407856\pi$
$631$	14.3410	0.570907	0.285453	+	0.958393i	$0.407856\pi$
$632$	−47.4995	−1.88943
$633$	−27.0232	−1.07408
$634$	−25.2776	−1.00390
$635$	3.62974	0.144042
$636$	16.5279	0.655373
$637$	0	0
$638$	32.2794	1.27795
$639$	−19.7351	−0.780708
$640$	−0.886505	−0.0350422
$641$	−29.6920	−1.17277	−0.586383	−	0.810034i	$-0.699448\pi$
$641$	−29.6920	−1.17277	−0.586383	+	0.810034i	$0.699448\pi$
$642$	52.3733	2.06701
$643$	5.74459	0.226545	0.113272	−	0.993564i	$-0.463867\pi$
$643$	5.74459	0.226545	0.113272	+	0.993564i	$0.463867\pi$
$644$	0	0
$645$	−5.51782	−0.217264
$646$	65.9013	2.59285
$647$	−17.8793	−0.702909	−0.351455	−	0.936205i	$-0.614313\pi$
$647$	−17.8793	−0.702909	−0.351455	+	0.936205i	$0.614313\pi$
$648$	−19.1025	−0.750419
$649$	−17.5970	−0.690743
$650$	−0.952559	−0.0373624
$651$	0	0
$652$	−8.93068	−0.349752
$653$	−24.3873	−0.954350	−0.477175	−	0.878808i	$-0.658339\pi$
$653$	−24.3873	−0.954350	−0.477175	+	0.878808i	$0.658339\pi$
$654$	22.0062	0.860512
$655$	21.5075	0.840368
$656$	5.13902	0.200645
$657$	−4.14437	−0.161687
$658$	0	0
$659$	−40.1951	−1.56578	−0.782889	−	0.622161i	$-0.786255\pi$
$659$	−40.1951	−1.56578	−0.782889	+	0.622161i	$0.786255\pi$
$660$	−6.53281	−0.254289
$661$	27.5971	1.07340	0.536702	−	0.843772i	$-0.319670\pi$
$661$	27.5971	1.07340	0.536702	+	0.843772i	$0.319670\pi$
$662$	2.24018	0.0870672
$663$	16.6480	0.646556
$664$	−43.2307	−1.67768
$665$	0	0
$666$	27.1520	1.05212
$667$	−29.0412	−1.12448
$668$	−8.38777	−0.324533
$669$	69.5509	2.68899
$670$	−1.71735	−0.0663471
$671$	35.0261	1.35217
$672$	0	0
$673$	15.0366	0.579619	0.289809	−	0.957084i	$-0.406408\pi$
$673$	15.0366	0.579619	0.289809	+	0.957084i	$0.406408\pi$
$674$	11.9306	0.459548
$675$	−1.92864	−0.0742333
$676$	9.52370	0.366296
$677$	−40.0877	−1.54069	−0.770347	−	0.637625i	$-0.779917\pi$
$677$	−40.0877	−1.54069	−0.770347	+	0.637625i	$0.779917\pi$
$678$	41.7146	1.60204
$679$	0	0
$680$	−22.8596	−0.876627
$681$	−40.8070	−1.56373
$682$	−3.58118	−0.137130
$683$	4.35898	0.166792	0.0833959	−	0.996516i	$-0.473423\pi$
$683$	4.35898	0.166792	0.0833959	+	0.996516i	$0.473423\pi$
$684$	−23.2788	−0.890085
$685$	4.90609	0.187452
$686$	0	0
$687$	25.4393	0.970569
$688$	−3.91527	−0.149268
$689$	7.05641	0.268828
$690$	−9.25251	−0.352237
$691$	40.6691	1.54713	0.773564	−	0.633719i	$-0.218472\pi$
$691$	40.6691	1.54713	0.773564	+	0.633719i	$0.218472\pi$
$692$	17.3011	0.657689
$693$	0	0
$694$	11.5214	0.437347
$695$	2.21438	0.0839963
$696$	−71.8800	−2.72460
$697$	20.7609	0.786376
$698$	5.47884	0.207377
$699$	18.0977	0.684519
$700$	0	0
$701$	−32.1520	−1.21437	−0.607183	−	0.794562i	$-0.707700\pi$
$701$	−32.1520	−1.21437	−0.607183	+	0.794562i	$0.707700\pi$
$702$	1.83714	0.0693385
$703$	−52.5142	−1.98061
$704$	−26.6316	−1.00372
$705$	0.725425	0.0273211
$706$	−1.49772	−0.0563675
$707$	0	0
$708$	10.9632	0.412023
$709$	−35.2772	−1.32486	−0.662432	−	0.749122i	$-0.730476\pi$
$709$	−35.2772	−1.32486	−0.662432	+	0.749122i	$0.730476\pi$
$710$	5.83144	0.218850
$711$	−57.8878	−2.17096
$712$	−48.4662	−1.81635
$713$	3.22193	0.120662
$714$	0	0
$715$	−2.78911	−0.104307
$716$	−9.82335	−0.367116
$717$	7.58652	0.283324
$718$	21.5462	0.804095
$719$	9.53413	0.355563	0.177781	−	0.984070i	$-0.443108\pi$
$719$	9.53413	0.355563	0.177781	+	0.984070i	$0.443108\pi$
$720$	−6.89607	−0.257001
$721$	0	0
$722$	−49.8642	−1.85575
$723$	−42.8922	−1.59518
$724$	−7.21437	−0.268120
$725$	9.01362	0.334757
$726$	−1.47672	−0.0548062
$727$	−25.0333	−0.928433	−0.464216	−	0.885722i	$-0.653664\pi$
$727$	−25.0333	−0.928433	−0.464216	+	0.885722i	$0.653664\pi$
$728$	0	0
$729$	−38.3045	−1.41869
$730$	1.22460	0.0453246
$731$	−15.8172	−0.585018
$732$	−21.8218	−0.806557
$733$	3.65720	0.135082	0.0675410	−	0.997717i	$-0.478485\pi$
$733$	3.65720	0.135082	0.0675410	+	0.997717i	$0.478485\pi$
$734$	20.1316	0.743070
$735$	0	0
$736$	13.2243	0.487453
$737$	−5.02845	−0.185225
$738$	11.5447	0.424966
$739$	−10.1454	−0.373204	−0.186602	−	0.982436i	$-0.559747\pi$
$739$	−10.1454	−0.373204	−0.186602	+	0.982436i	$0.559747\pi$
$740$	5.09646	0.187350
$741$	−17.9050	−0.657755
$742$	0	0
$743$	16.3395	0.599439	0.299720	−	0.954027i	$-0.403107\pi$
$743$	16.3395	0.599439	0.299720	+	0.954027i	$0.403107\pi$
$744$	7.97459	0.292363
$745$	22.8920	0.838698
$746$	−5.23311	−0.191598
$747$	−52.6854	−1.92766
$748$	−18.7267	−0.684715
$749$	0	0
$750$	2.87173	0.104861
$751$	17.6239	0.643105	0.321552	−	0.946892i	$-0.395795\pi$
$751$	17.6239	0.643105	0.321552	+	0.946892i	$0.395795\pi$
$752$	0.514739	0.0187706
$753$	−20.8062	−0.758221
$754$	−8.58601	−0.312684
$755$	5.12377	0.186473
$756$	0	0
$757$	−9.32967	−0.339092	−0.169546	−	0.985522i	$-0.554230\pi$
$757$	−9.32967	−0.339092	−0.169546	+	0.985522i	$0.554230\pi$
$758$	−10.1057	−0.367055
$759$	−27.0916	−0.983361
$760$	24.5855	0.891811
$761$	26.1123	0.946570	0.473285	−	0.880909i	$-0.343068\pi$
$761$	26.1123	0.946570	0.473285	+	0.880909i	$0.343068\pi$
$762$	10.4236	0.377608
$763$	0	0
$764$	−6.16967	−0.223211
$765$	−27.8591	−1.00725
$766$	21.9742	0.793960
$767$	4.68063	0.169008
$768$	40.1658	1.44936
$769$	−23.7046	−0.854811	−0.427405	−	0.904060i	$-0.640572\pi$
$769$	−23.7046	−0.854811	−0.427405	+	0.904060i	$0.640572\pi$
$770$	0	0
$771$	22.9762	0.827466
$772$	9.23834	0.332495
$773$	−11.6577	−0.419297	−0.209649	−	0.977777i	$-0.567232\pi$
$773$	−11.6577	−0.419297	−0.209649	+	0.977777i	$0.567232\pi$
$774$	−8.79557	−0.316150
$775$	−1.00000	−0.0359211
$776$	4.12045	0.147916
$777$	0	0
$778$	−22.8659	−0.819783
$779$	−22.3284	−0.799997
$780$	1.73766	0.0622183
$781$	17.0746	0.610977
$782$	−26.5229	−0.948456
$783$	−17.3840	−0.621254
$784$	0	0
$785$	−24.5104	−0.874812
$786$	61.7638	2.20304
$787$	9.07091	0.323343	0.161671	−	0.986845i	$-0.448312\pi$
$787$	9.07091	0.323343	0.161671	+	0.986845i	$0.448312\pi$
$788$	3.87146	0.137915
$789$	−30.8190	−1.09718
$790$	17.1050	0.608570
$791$	0	0
$792$	−37.2203	−1.32257
$793$	−9.31660	−0.330842
$794$	28.4826	1.01081
$795$	−21.2733	−0.754488
$796$	−9.63973	−0.341671
$797$	25.8832	0.916831	0.458415	−	0.888738i	$-0.348417\pi$
$797$	25.8832	0.916831	0.458415	+	0.888738i	$0.348417\pi$
$798$	0	0
$799$	2.07947	0.0735665
$800$	−4.10446	−0.145115
$801$	−59.0659	−2.08699
$802$	−1.77219	−0.0625781
$803$	3.58566	0.126535
$804$	3.13281	0.110486
$805$	0	0
$806$	0.952559	0.0335525
$807$	7.11273	0.250380
$808$	50.6168	1.78069
$809$	−37.6365	−1.32323	−0.661614	−	0.749845i	$-0.730128\pi$
$809$	−37.6365	−1.32323	−0.661614	+	0.749845i	$0.730128\pi$
$810$	6.87902	0.241704
$811$	−24.6594	−0.865908	−0.432954	−	0.901416i	$-0.642529\pi$
$811$	−24.6594	−0.865908	−0.432954	+	0.901416i	$0.642529\pi$
$812$	0	0
$813$	−37.6435	−1.32021
$814$	−23.4916	−0.823381
$815$	11.4948	0.402646
$816$	−35.6131	−1.24671
$817$	17.0113	0.595152
$818$	16.1485	0.564618
$819$	0	0
$820$	2.16695	0.0756733
$821$	−21.8477	−0.762492	−0.381246	−	0.924474i	$-0.624505\pi$
$821$	−21.8477	−0.762492	−0.381246	+	0.924474i	$0.624505\pi$
$822$	14.0890	0.491410
$823$	33.1187	1.15445	0.577223	−	0.816586i	$-0.304136\pi$
$823$	33.1187	1.15445	0.577223	+	0.816586i	$0.304136\pi$
$824$	−11.3257	−0.394550
$825$	8.40849	0.292746
$826$	0	0
$827$	3.21567	0.111820	0.0559099	−	0.998436i	$-0.482194\pi$
$827$	3.21567	0.111820	0.0559099	+	0.998436i	$0.482194\pi$
$828$	9.36885	0.325590
$829$	−43.0839	−1.49636	−0.748182	−	0.663493i	$-0.769073\pi$
$829$	−43.0839	−1.49636	−0.748182	+	0.663493i	$0.769073\pi$
$830$	15.5678	0.540367
$831$	−49.0961	−1.70313
$832$	7.08375	0.245585
$833$	0	0
$834$	6.35911	0.220198
$835$	10.7961	0.373613
$836$	20.1405	0.696575
$837$	1.92864	0.0666635
$838$	−17.8775	−0.617569
$839$	−35.9727	−1.24192	−0.620958	−	0.783844i	$-0.713256\pi$
$839$	−35.9727	−1.24192	−0.620958	+	0.783844i	$0.713256\pi$
$840$	0	0
$841$	52.2454	1.80156
$842$	14.2136	0.489832
$843$	21.1602	0.728797
$844$	−8.08538	−0.278310
$845$	−12.2581	−0.421692
$846$	1.15635	0.0397561
$847$	0	0
$848$	−15.0949	−0.518361
$849$	−23.7167	−0.813954
$850$	8.23199	0.282355
$851$	21.1350	0.724500
$852$	−10.6378	−0.364443
$853$	−12.1833	−0.417147	−0.208574	−	0.978007i	$-0.566882\pi$
$853$	−12.1833	−0.417147	−0.208574	+	0.978007i	$0.566882\pi$
$854$	0	0
$855$	29.9625	1.02470
$856$	56.0089	1.91434
$857$	−14.2989	−0.488441	−0.244221	−	0.969720i	$-0.578532\pi$
$857$	−14.2989	−0.488441	−0.244221	+	0.969720i	$0.578532\pi$
$858$	−8.00959	−0.273443
$859$	−20.1288	−0.686784	−0.343392	−	0.939192i	$-0.611576\pi$
$859$	−20.1288	−0.686784	−0.343392	+	0.939192i	$0.611576\pi$
$860$	−1.65094	−0.0562965
$861$	0	0
$862$	2.68775	0.0915452
$863$	22.6871	0.772277	0.386139	−	0.922441i	$-0.373809\pi$
$863$	22.6871	0.772277	0.386139	+	0.922441i	$0.373809\pi$
$864$	7.91602	0.269309
$865$	−22.2685	−0.757153
$866$	10.2597	0.348639
$867$	−99.7283	−3.38695
$868$	0	0
$869$	50.0840	1.69898
$870$	25.8847	0.877573
$871$	1.33752	0.0453201
$872$	23.5338	0.796956
$873$	5.02161	0.169956
$874$	28.5253	0.964884
$875$	0	0
$876$	−2.23393	−0.0754774
$877$	−25.3233	−0.855108	−0.427554	−	0.903990i	$-0.640625\pi$
$877$	−25.3233	−0.855108	−0.427554	+	0.903990i	$0.640625\pi$
$878$	41.3308	1.39485
$879$	13.8846	0.468317
$880$	5.96641	0.201128
$881$	2.63663	0.0888302	0.0444151	−	0.999013i	$-0.485858\pi$
$881$	2.63663	0.0888302	0.0444151	+	0.999013i	$0.485858\pi$
$882$	0	0
$883$	−10.5661	−0.355579	−0.177789	−	0.984069i	$-0.556895\pi$
$883$	−10.5661	−0.355579	−0.177789	+	0.984069i	$0.556895\pi$
$884$	4.98112	0.167533
$885$	−14.1110	−0.474335
$886$	28.4463	0.955673
$887$	25.4656	0.855050	0.427525	−	0.904003i	$-0.359386\pi$
$887$	25.4656	0.855050	0.427525	+	0.904003i	$0.359386\pi$
$888$	52.3113	1.75545
$889$	0	0
$890$	17.4531	0.585031
$891$	20.1419	0.674780
$892$	20.8097	0.696761
$893$	−2.23647	−0.0748407
$894$	65.7396	2.19866
$895$	12.6438	0.422636
$896$	0	0
$897$	7.20609	0.240604
$898$	−24.1995	−0.807549
$899$	−9.01362	−0.300621
$900$	−2.90784	−0.0969280
$901$	−60.9813	−2.03158
$902$	−9.98835	−0.332576
$903$	0	0
$904$	44.6103	1.48372
$905$	9.28574	0.308668
$906$	14.7141	0.488843
$907$	4.53446	0.150564	0.0752821	−	0.997162i	$-0.476014\pi$
$907$	4.53446	0.150564	0.0752821	+	0.997162i	$0.476014\pi$
$908$	−12.2095	−0.405187
$909$	61.6869	2.04603
$910$	0	0
$911$	28.0740	0.930135	0.465067	−	0.885275i	$-0.346030\pi$
$911$	28.0740	0.930135	0.465067	+	0.885275i	$0.346030\pi$
$912$	38.3019	1.26830
$913$	45.5829	1.50857
$914$	−18.8301	−0.622843
$915$	28.0872	0.928536
$916$	7.61146	0.251490
$917$	0	0
$918$	−15.8765	−0.524003
$919$	37.0583	1.22244	0.611221	−	0.791460i	$-0.290679\pi$
$919$	37.0583	1.22244	0.611221	+	0.791460i	$0.290679\pi$
$920$	−9.89478	−0.326221
$921$	55.9980	1.84520
$922$	11.4772	0.377983
$923$	−4.54168	−0.149491
$924$	0	0
$925$	−6.55975	−0.215683
$926$	19.2359	0.632129
$927$	−13.8027	−0.453340
$928$	−36.9961	−1.21446
$929$	10.3849	0.340718	0.170359	−	0.985382i	$-0.445507\pi$
$929$	10.3849	0.340718	0.170359	+	0.985382i	$0.445507\pi$
$930$	−2.87173	−0.0941678
$931$	0	0
$932$	5.41487	0.177370
$933$	13.9398	0.456370
$934$	−17.6267	−0.576765
$935$	24.1034	0.788267
$936$	9.90024	0.323599
$937$	−15.7631	−0.514958	−0.257479	−	0.966284i	$-0.582892\pi$
$937$	−15.7631	−0.514958	−0.257479	+	0.966284i	$0.582892\pi$
$938$	0	0
$939$	38.1445	1.24480
$940$	0.217048	0.00707933
$941$	−13.8375	−0.451089	−0.225545	−	0.974233i	$-0.572416\pi$
$941$	−13.8375	−0.451089	−0.225545	+	0.974233i	$0.572416\pi$
$942$	−70.3871	−2.29334
$943$	8.98635	0.292636
$944$	−10.0127	−0.325885
$945$	0	0
$946$	7.60984	0.247417
$947$	20.5056	0.666343	0.333171	−	0.942866i	$-0.391881\pi$
$947$	20.5056	0.666343	0.333171	+	0.942866i	$0.391881\pi$
$948$	−31.2031	−1.01343
$949$	−0.953752	−0.0309601
$950$	−8.85350	−0.287245
$951$	−59.3510	−1.92459
$952$	0	0
$953$	−4.72428	−0.153035	−0.0765173	−	0.997068i	$-0.524380\pi$
$953$	−4.72428	−0.153035	−0.0765173	+	0.997068i	$0.524380\pi$
$954$	−33.9104	−1.09789
$955$	7.94109	0.256968
$956$	2.26990	0.0734137
$957$	75.7910	2.44997
$958$	−27.6644	−0.893797
$959$	0	0
$960$	−21.3558	−0.689255
$961$	1.00000	0.0322581
$962$	6.24855	0.201461
$963$	68.2583	2.19959
$964$	−12.8334	−0.413336
$965$	−11.8908	−0.382779
$966$	0	0
$967$	−19.6248	−0.631092	−0.315546	−	0.948910i	$-0.602188\pi$
$967$	−19.6248	−0.631092	−0.315546	+	0.948910i	$0.602188\pi$
$968$	−1.57923	−0.0507583
$969$	154.734	4.97078
$970$	−1.48382	−0.0476425
$971$	−7.26363	−0.233101	−0.116550	−	0.993185i	$-0.537184\pi$
$971$	−7.26363	−0.233101	−0.116550	+	0.993185i	$0.537184\pi$
$972$	−17.0440	−0.546686
$973$	0	0
$974$	−13.0607	−0.418492
$975$	−2.23658	−0.0716278
$976$	19.9298	0.637939
$977$	−53.2573	−1.70385	−0.851926	−	0.523663i	$-0.824565\pi$
$977$	−53.2573	−1.70385	−0.851926	+	0.523663i	$0.824565\pi$
$978$	33.0101	1.05555
$979$	51.1032	1.63327
$980$	0	0
$981$	28.6808	0.915706
$982$	−18.3742	−0.586345
$983$	35.3463	1.12737	0.563686	−	0.825989i	$-0.309383\pi$
$983$	35.3463	1.12737	0.563686	+	0.825989i	$0.309383\pi$
$984$	22.2421	0.709053
$985$	−4.98303	−0.158772
$986$	74.2000	2.36301
$987$	0	0
$988$	−5.35719	−0.170435
$989$	−6.84645	−0.217704
$990$	13.4034	0.425988
$991$	−11.0495	−0.350998	−0.175499	−	0.984480i	$-0.556154\pi$
$991$	−11.0495	−0.350998	−0.175499	+	0.984480i	$0.556154\pi$
$992$	4.10446	0.130317
$993$	5.25988	0.166917
$994$	0	0
$995$	12.4075	0.393343
$996$	−28.3989	−0.899853
$997$	−24.7075	−0.782495	−0.391248	−	0.920285i	$-0.627956\pi$
$997$	−24.7075	−0.782495	−0.391248	+	0.920285i	$0.627956\pi$
$998$	−0.765585	−0.0242342
$999$	12.6514	0.400272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.8		21
7.3	odd	6		1085.2.j.d.156.14	✓	42
7.5	odd	6		1085.2.j.d.466.14	yes	42
7.6	odd	2		7595.2.a.bg.1.8		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.14	✓	42	7.3	odd	6
1085.2.j.d.466.14	yes	42	7.5	odd	6
7595.2.a.bf.1.8		21	1.1	even	1	trivial
7595.2.a.bg.1.8		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)

\(f(q)\)	\(=\)	\(q-1.10593 q^{2} -2.59668 q^{3} -0.776930 q^{4} +1.00000 q^{5} +2.87173 q^{6} +3.07108 q^{8} +3.74273 q^{9} +O(q^{10})\)	\(q-1.10593 q^{2} -2.59668 q^{3} -0.776930 q^{4} +1.00000 q^{5} +2.87173 q^{6} +3.07108 q^{8} +3.74273 q^{9} -1.10593 q^{10} -3.23817 q^{11} +2.01744 q^{12} +0.861323 q^{13} -2.59668 q^{15} -1.84252 q^{16} -7.44353 q^{17} -4.13918 q^{18} +8.00551 q^{19} -0.776930 q^{20} +3.58118 q^{22} -3.22193 q^{23} -7.97459 q^{24} +1.00000 q^{25} -0.952559 q^{26} -1.92864 q^{27} +9.01362 q^{29} +2.87173 q^{30} -1.00000 q^{31} -4.10446 q^{32} +8.40849 q^{33} +8.23199 q^{34} -2.90784 q^{36} -6.55975 q^{37} -8.85350 q^{38} -2.23658 q^{39} +3.07108 q^{40} -2.78912 q^{41} +2.12495 q^{43} +2.51583 q^{44} +3.74273 q^{45} +3.56321 q^{46} -0.279367 q^{47} +4.78443 q^{48} -1.10593 q^{50} +19.3284 q^{51} -0.669187 q^{52} +8.19252 q^{53} +2.13293 q^{54} -3.23817 q^{55} -20.7877 q^{57} -9.96839 q^{58} +5.43423 q^{59} +2.01744 q^{60} -10.8166 q^{61} +1.10593 q^{62} +8.22427 q^{64} +0.861323 q^{65} -9.29917 q^{66} +1.55287 q^{67} +5.78310 q^{68} +8.36631 q^{69} -5.27291 q^{71} +11.4942 q^{72} -1.10731 q^{73} +7.25459 q^{74} -2.59668 q^{75} -6.21972 q^{76} +2.47349 q^{78} -15.4667 q^{79} -1.84252 q^{80} -6.22015 q^{81} +3.08456 q^{82} -14.0767 q^{83} -7.44353 q^{85} -2.35004 q^{86} -23.4055 q^{87} -9.94468 q^{88} -15.7815 q^{89} -4.13918 q^{90} +2.50321 q^{92} +2.59668 q^{93} +0.308959 q^{94} +8.00551 q^{95} +10.6580 q^{96} +1.34170 q^{97} -12.1196 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 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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