LMFDB - Embedded newform 7595.2.a.bf.1.15

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			1.15
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)

$f(q)$	$=$	$q+1.17555 q^{2} +1.97842 q^{3} -0.618087 q^{4} +1.00000 q^{5} +2.32573 q^{6} -3.07769 q^{8} +0.914144 q^{9} +O(q^{10})$	\(q+1.17555 q^{2} +1.97842 q^{3} -0.618087 q^{4} +1.00000 q^{5} +2.32573 q^{6} -3.07769 q^{8} +0.914144 q^{9} +1.17555 q^{10} -1.65573 q^{11} -1.22284 q^{12} -1.30021 q^{13} +1.97842 q^{15} -2.38179 q^{16} +6.16753 q^{17} +1.07462 q^{18} -4.07265 q^{19} -0.618087 q^{20} -1.94640 q^{22} +1.54760 q^{23} -6.08896 q^{24} +1.00000 q^{25} -1.52846 q^{26} -4.12670 q^{27} -8.46106 q^{29} +2.32573 q^{30} -1.00000 q^{31} +3.35546 q^{32} -3.27574 q^{33} +7.25022 q^{34} -0.565021 q^{36} -9.27633 q^{37} -4.78759 q^{38} -2.57237 q^{39} -3.07769 q^{40} +8.82188 q^{41} -9.80094 q^{43} +1.02339 q^{44} +0.914144 q^{45} +1.81927 q^{46} +2.93309 q^{47} -4.71219 q^{48} +1.17555 q^{50} +12.2020 q^{51} +0.803645 q^{52} -9.10351 q^{53} -4.85113 q^{54} -1.65573 q^{55} -8.05741 q^{57} -9.94638 q^{58} -2.02287 q^{59} -1.22284 q^{60} +6.50835 q^{61} -1.17555 q^{62} +8.70809 q^{64} -1.30021 q^{65} -3.85079 q^{66} -12.1136 q^{67} -3.81207 q^{68} +3.06179 q^{69} +5.41795 q^{71} -2.81345 q^{72} +9.65732 q^{73} -10.9048 q^{74} +1.97842 q^{75} +2.51725 q^{76} -3.02394 q^{78} -7.54468 q^{79} -2.38179 q^{80} -10.9068 q^{81} +10.3705 q^{82} -10.3727 q^{83} +6.16753 q^{85} -11.5215 q^{86} -16.7395 q^{87} +5.09583 q^{88} -13.1371 q^{89} +1.07462 q^{90} -0.956550 q^{92} -1.97842 q^{93} +3.44799 q^{94} -4.07265 q^{95} +6.63851 q^{96} -1.20544 q^{97} -1.51358 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.17555	0.831238	0.415619	−	0.909539i	$-0.363565\pi$
$2$	1.17555	0.831238	0.415619	+	0.909539i	$0.363565\pi$
$3$	1.97842	1.14224	0.571121	−	0.820866i	$-0.306509\pi$
$3$	1.97842	1.14224	0.571121	+	0.820866i	$0.306509\pi$
$4$	−0.618087	−0.309044
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.32573	0.949474
$7$	0	0
$7$	0	0
$8$	−3.07769	−1.08813
$9$	0.914144	0.304715
$10$	1.17555	0.371741
$11$	−1.65573	−0.499223	−0.249611	−	0.968346i	$-0.580303\pi$
$11$	−1.65573	−0.499223	−0.249611	+	0.968346i	$0.580303\pi$
$12$	−1.22284	−0.353002
$13$	−1.30021	−0.360614	−0.180307	−	0.983610i	$-0.557709\pi$
$13$	−1.30021	−0.360614	−0.180307	+	0.983610i	$0.557709\pi$
$14$	0	0
$15$	1.97842	0.510826
$16$	−2.38179	−0.595448
$17$	6.16753	1.49584	0.747922	−	0.663786i	$-0.231051\pi$
$17$	6.16753	1.49584	0.747922	+	0.663786i	$0.231051\pi$
$18$	1.07462	0.253290
$19$	−4.07265	−0.934330	−0.467165	−	0.884170i	$-0.654725\pi$
$19$	−4.07265	−0.934330	−0.467165	+	0.884170i	$0.654725\pi$
$20$	−0.618087	−0.138209
$21$	0	0
$22$	−1.94640	−0.414973
$23$	1.54760	0.322696	0.161348	−	0.986898i	$-0.448416\pi$
$23$	1.54760	0.322696	0.161348	+	0.986898i	$0.448416\pi$
$24$	−6.08896	−1.24290
$25$	1.00000	0.200000
$26$	−1.52846	−0.299756
$27$	−4.12670	−0.794183
$28$	0	0
$29$	−8.46106	−1.57118	−0.785590	−	0.618748i	$-0.787640\pi$
$29$	−8.46106	−1.57118	−0.785590	+	0.618748i	$0.787640\pi$
$30$	2.32573	0.424618
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	3.35546	0.593167
$33$	−3.27574	−0.570233
$34$	7.25022	1.24340
$35$	0	0
$36$	−0.565021	−0.0941701
$37$	−9.27633	−1.52502	−0.762510	−	0.646977i	$-0.776033\pi$
$37$	−9.27633	−1.52502	−0.762510	+	0.646977i	$0.776033\pi$
$38$	−4.78759	−0.776650
$39$	−2.57237	−0.411908
$40$	−3.07769	−0.486625
$41$	8.82188	1.37775	0.688873	−	0.724882i	$-0.258106\pi$
$41$	8.82188	1.37775	0.688873	+	0.724882i	$0.258106\pi$
$42$	0	0
$43$	−9.80094	−1.49463	−0.747315	−	0.664470i	$-0.768657\pi$
$43$	−9.80094	−1.49463	−0.747315	+	0.664470i	$0.768657\pi$
$44$	1.02339	0.154282
$45$	0.914144	0.136273
$46$	1.81927	0.268237
$47$	2.93309	0.427835	0.213917	−	0.976852i	$-0.431378\pi$
$47$	2.93309	0.427835	0.213917	+	0.976852i	$0.431378\pi$
$48$	−4.71219	−0.680146
$49$	0	0
$50$	1.17555	0.166248
$51$	12.2020	1.70862
$52$	0.803645	0.111445
$53$	−9.10351	−1.25046	−0.625232	−	0.780439i	$-0.714996\pi$
$53$	−9.10351	−1.25046	−0.625232	+	0.780439i	$0.714996\pi$
$54$	−4.85113	−0.660155
$55$	−1.65573	−0.223259
$56$	0	0
$57$	−8.05741	−1.06723
$58$	−9.94638	−1.30602
$59$	−2.02287	−0.263355	−0.131678	−	0.991293i	$-0.542036\pi$
$59$	−2.02287	−0.263355	−0.131678	+	0.991293i	$0.542036\pi$
$60$	−1.22284	−0.157867
$61$	6.50835	0.833309	0.416654	−	0.909065i	$-0.363203\pi$
$61$	6.50835	0.833309	0.416654	+	0.909065i	$0.363203\pi$
$62$	−1.17555	−0.149295
$63$	0	0
$64$	8.70809	1.08851
$65$	−1.30021	−0.161271
$66$	−3.85079	−0.473999
$67$	−12.1136	−1.47991	−0.739956	−	0.672656i	$-0.765154\pi$
$67$	−12.1136	−1.47991	−0.739956	+	0.672656i	$0.765154\pi$
$68$	−3.81207	−0.462281
$69$	3.06179	0.368597
$70$	0	0
$71$	5.41795	0.642993	0.321496	−	0.946911i	$-0.395814\pi$
$71$	5.41795	0.642993	0.321496	+	0.946911i	$0.395814\pi$
$72$	−2.81345	−0.331568
$73$	9.65732	1.13030	0.565152	−	0.824987i	$-0.308818\pi$
$73$	9.65732	1.13030	0.565152	+	0.824987i	$0.308818\pi$
$74$	−10.9048	−1.26765
$75$	1.97842	0.228448
$76$	2.51725	0.288749
$77$	0	0
$78$	−3.02394	−0.342394
$79$	−7.54468	−0.848843	−0.424422	−	0.905465i	$-0.639523\pi$
$79$	−7.54468	−0.848843	−0.424422	+	0.905465i	$0.639523\pi$
$80$	−2.38179	−0.266293
$81$	−10.9068	−1.21186
$82$	10.3705	1.14523
$83$	−10.3727	−1.13855	−0.569277	−	0.822145i	$-0.692777\pi$
$83$	−10.3727	−1.13855	−0.569277	+	0.822145i	$0.692777\pi$
$84$	0	0
$85$	6.16753	0.668962
$86$	−11.5215	−1.24239
$87$	−16.7395	−1.79467
$88$	5.09583	0.543218
$89$	−13.1371	−1.39253	−0.696265	−	0.717785i	$-0.745156\pi$
$89$	−13.1371	−1.39253	−0.696265	+	0.717785i	$0.745156\pi$
$90$	1.07462	0.113275
$91$	0	0
$92$	−0.956550	−0.0997272
$93$	−1.97842	−0.205153
$94$	3.44799	0.355633
$95$	−4.07265	−0.417845
$96$	6.63851	0.677540
$97$	−1.20544	−0.122394	−0.0611969	−	0.998126i	$-0.519492\pi$
$97$	−1.20544	−0.122394	−0.0611969	+	0.998126i	$0.519492\pi$
$98$	0	0
$99$	−1.51358	−0.152120
$100$	−0.618087	−0.0618087
$101$	−13.1779	−1.31125	−0.655627	−	0.755085i	$-0.727596\pi$
$101$	−13.1779	−1.31125	−0.655627	+	0.755085i	$0.727596\pi$
$102$	14.3440	1.42027
$103$	−3.81828	−0.376226	−0.188113	−	0.982147i	$-0.560237\pi$
$103$	−3.81828	−0.376226	−0.188113	+	0.982147i	$0.560237\pi$
$104$	4.00165	0.392394
$105$	0	0
$106$	−10.7016	−1.03943
$107$	6.17668	0.597122	0.298561	−	0.954391i	$-0.403493\pi$
$107$	6.17668	0.597122	0.298561	+	0.954391i	$0.403493\pi$
$108$	2.55066	0.245437
$109$	6.34403	0.607648	0.303824	−	0.952728i	$-0.401737\pi$
$109$	6.34403	0.607648	0.303824	+	0.952728i	$0.401737\pi$
$110$	−1.94640	−0.185581
$111$	−18.3525	−1.74194
$112$	0	0
$113$	0.114955	0.0108141	0.00540703	−	0.999985i	$-0.498279\pi$
$113$	0.114955	0.0108141	0.00540703	+	0.999985i	$0.498279\pi$
$114$	−9.47187	−0.887122
$115$	1.54760	0.144314
$116$	5.22967	0.485563
$117$	−1.18858	−0.109884
$118$	−2.37798	−0.218911
$119$	0	0
$120$	−6.08896	−0.555843
$121$	−8.25854	−0.750777
$122$	7.65087	0.692678
$123$	17.4534	1.57372
$124$	0.618087	0.0555059
$125$	1.00000	0.0894427
$126$	0	0
$127$	19.4706	1.72774	0.863868	−	0.503719i	$-0.168035\pi$
$127$	19.4706	1.72774	0.863868	+	0.503719i	$0.168035\pi$
$128$	3.52586	0.311645
$129$	−19.3904	−1.70723
$130$	−1.52846	−0.134055
$131$	10.4971	0.917132	0.458566	−	0.888660i	$-0.348363\pi$
$131$	10.4971	0.917132	0.458566	+	0.888660i	$0.348363\pi$
$132$	2.02469	0.176227
$133$	0	0
$134$	−14.2401	−1.23016
$135$	−4.12670	−0.355170
$136$	−18.9817	−1.62767
$137$	−15.0902	−1.28924	−0.644622	−	0.764501i	$-0.722985\pi$
$137$	−15.0902	−1.28924	−0.644622	+	0.764501i	$0.722985\pi$
$138$	3.59929	0.306392
$139$	1.08175	0.0917525	0.0458763	−	0.998947i	$-0.485392\pi$
$139$	1.08175	0.0917525	0.0458763	+	0.998947i	$0.485392\pi$
$140$	0	0
$141$	5.80288	0.488691
$142$	6.36906	0.534480
$143$	2.15281	0.180027
$144$	−2.17730	−0.181442
$145$	−8.46106	−0.702653
$146$	11.3526	0.939551
$147$	0	0
$148$	5.73358	0.471298
$149$	14.4948	1.18746	0.593729	−	0.804665i	$-0.297655\pi$
$149$	14.4948	1.18746	0.593729	+	0.804665i	$0.297655\pi$
$150$	2.32573	0.189895
$151$	−13.0258	−1.06002	−0.530011	−	0.847991i	$-0.677812\pi$
$151$	−13.0258	−1.06002	−0.530011	+	0.847991i	$0.677812\pi$
$152$	12.5343	1.01667
$153$	5.63801	0.455806
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	1.58995	0.127298
$157$	7.23752	0.577617	0.288809	−	0.957387i	$-0.406741\pi$
$157$	7.23752	0.577617	0.288809	+	0.957387i	$0.406741\pi$
$158$	−8.86914	−0.705591
$159$	−18.0106	−1.42833
$160$	3.35546	0.265272
$161$	0	0
$162$	−12.8214	−1.00735
$163$	22.9598	1.79835	0.899177	−	0.437585i	$-0.144166\pi$
$163$	22.9598	1.79835	0.899177	+	0.437585i	$0.144166\pi$
$164$	−5.45269	−0.425783
$165$	−3.27574	−0.255016
$166$	−12.1936	−0.946410
$167$	1.30868	0.101268	0.0506342	−	0.998717i	$-0.483876\pi$
$167$	1.30868	0.101268	0.0506342	+	0.998717i	$0.483876\pi$
$168$	0	0
$169$	−11.3094	−0.869958
$170$	7.25022	0.556067
$171$	−3.72299	−0.284704
$172$	6.05784	0.461906
$173$	−17.1899	−1.30692	−0.653461	−	0.756961i	$-0.726683\pi$
$173$	−17.1899	−1.30692	−0.653461	+	0.756961i	$0.726683\pi$
$174$	−19.6781	−1.49179
$175$	0	0
$176$	3.94362	0.297261
$177$	−4.00208	−0.300815
$178$	−15.4433	−1.15752
$179$	−13.1775	−0.984934	−0.492467	−	0.870331i	$-0.663905\pi$
$179$	−13.1775	−0.984934	−0.492467	+	0.870331i	$0.663905\pi$
$180$	−0.565021	−0.0421142
$181$	−18.1966	−1.35254	−0.676272	−	0.736652i	$-0.736406\pi$
$181$	−18.1966	−1.35254	−0.676272	+	0.736652i	$0.736406\pi$
$182$	0	0
$183$	12.8762	0.951839
$184$	−4.76302	−0.351134
$185$	−9.27633	−0.682009
$186$	−2.32573	−0.170531
$187$	−10.2118	−0.746760
$188$	−1.81290	−0.132220
$189$	0	0
$190$	−4.78759	−0.347328
$191$	−1.93747	−0.140190	−0.0700952	−	0.997540i	$-0.522330\pi$
$191$	−1.93747	−0.140190	−0.0700952	+	0.997540i	$0.522330\pi$
$192$	17.2283	1.24334
$193$	23.8243	1.71491	0.857455	−	0.514559i	$-0.172044\pi$
$193$	23.8243	1.71491	0.857455	+	0.514559i	$0.172044\pi$
$194$	−1.41705	−0.101738
$195$	−2.57237	−0.184211
$196$	0	0
$197$	−18.8975	−1.34639	−0.673196	−	0.739464i	$-0.735079\pi$
$197$	−18.8975	−1.34639	−0.673196	+	0.739464i	$0.735079\pi$
$198$	−1.77929	−0.126448
$199$	23.1351	1.64000	0.820001	−	0.572363i	$-0.193973\pi$
$199$	23.1351	1.64000	0.820001	+	0.572363i	$0.193973\pi$
$200$	−3.07769	−0.217625
$201$	−23.9658	−1.69042
$202$	−15.4913	−1.08996
$203$	0	0
$204$	−7.54187	−0.528037
$205$	8.82188	0.616146
$206$	−4.48857	−0.312734
$207$	1.41473	0.0983303
$208$	3.09684	0.214727
$209$	6.74322	0.466439
$210$	0	0
$211$	27.0949	1.86529	0.932645	−	0.360796i	$-0.117495\pi$
$211$	27.0949	1.86529	0.932645	+	0.360796i	$0.117495\pi$
$212$	5.62676	0.386448
$213$	10.7190	0.734453
$214$	7.26098	0.496350
$215$	−9.80094	−0.668419
$216$	12.7007	0.864172
$217$	0	0
$218$	7.45771	0.505100
$219$	19.1062	1.29108
$220$	1.02339	0.0689968
$221$	−8.01909	−0.539423
$222$	−21.5742	−1.44797
$223$	−26.1990	−1.75442	−0.877208	−	0.480111i	$-0.840596\pi$
$223$	−26.1990	−1.75442	−0.877208	+	0.480111i	$0.840596\pi$
$224$	0	0
$225$	0.914144	0.0609429
$226$	0.135135	0.00898905
$227$	−12.3164	−0.817466	−0.408733	−	0.912654i	$-0.634029\pi$
$227$	−12.3164	−0.817466	−0.408733	+	0.912654i	$0.634029\pi$
$228$	4.98018	0.329820
$229$	10.1502	0.670745	0.335372	−	0.942086i	$-0.391138\pi$
$229$	10.1502	0.670745	0.335372	+	0.942086i	$0.391138\pi$
$230$	1.81927	0.119959
$231$	0	0
$232$	26.0405	1.70964
$233$	−18.5008	−1.21203	−0.606015	−	0.795453i	$-0.707233\pi$
$233$	−18.5008	−1.21203	−0.606015	+	0.795453i	$0.707233\pi$
$234$	−1.39723	−0.0913401
$235$	2.93309	0.191334
$236$	1.25031	0.0813882
$237$	−14.9266	−0.969584
$238$	0	0
$239$	−15.6918	−1.01502	−0.507509	−	0.861646i	$-0.669434\pi$
$239$	−15.6918	−1.01502	−0.507509	+	0.861646i	$0.669434\pi$
$240$	−4.71219	−0.304170
$241$	−15.7702	−1.01585	−0.507925	−	0.861401i	$-0.669587\pi$
$241$	−15.7702	−1.01585	−0.507925	+	0.861401i	$0.669587\pi$
$242$	−9.70831	−0.624074
$243$	−9.19808	−0.590057
$244$	−4.02273	−0.257529
$245$	0	0
$246$	20.5173	1.30813
$247$	5.29531	0.336932
$248$	3.07769	0.195433
$249$	−20.5216	−1.30050
$250$	1.17555	0.0743482
$251$	−12.3495	−0.779496	−0.389748	−	0.920922i	$-0.627438\pi$
$251$	−12.3495	−0.779496	−0.389748	+	0.920922i	$0.627438\pi$
$252$	0	0
$253$	−2.56241	−0.161097
$254$	22.8886	1.43616
$255$	12.2020	0.764116
$256$	−13.2714	−0.829461
$257$	21.9996	1.37230	0.686150	−	0.727460i	$-0.259299\pi$
$257$	21.9996	1.37230	0.686150	+	0.727460i	$0.259299\pi$
$258$	−22.7943	−1.41911
$259$	0	0
$260$	0.803645	0.0498399
$261$	−7.73463	−0.478761
$262$	12.3398	0.762355
$263$	−13.2280	−0.815676	−0.407838	−	0.913054i	$-0.633717\pi$
$263$	−13.2280	−0.815676	−0.407838	+	0.913054i	$0.633717\pi$
$264$	10.0817	0.620485
$265$	−9.10351	−0.559224
$266$	0	0
$267$	−25.9907	−1.59060
$268$	7.48726	0.457357
$269$	−7.84389	−0.478250	−0.239125	−	0.970989i	$-0.576861\pi$
$269$	−7.84389	−0.478250	−0.239125	+	0.970989i	$0.576861\pi$
$270$	−4.85113	−0.295230
$271$	−6.40056	−0.388807	−0.194403	−	0.980922i	$-0.562277\pi$
$271$	−6.40056	−0.388807	−0.194403	+	0.980922i	$0.562277\pi$
$272$	−14.6898	−0.890698
$273$	0	0
$274$	−17.7393	−1.07167
$275$	−1.65573	−0.0998445
$276$	−1.89246	−0.113912
$277$	−20.6729	−1.24212	−0.621058	−	0.783764i	$-0.713297\pi$
$277$	−20.6729	−1.24212	−0.621058	+	0.783764i	$0.713297\pi$
$278$	1.27164	0.0762682
$279$	−0.914144	−0.0547284
$280$	0	0
$281$	13.6448	0.813983	0.406992	−	0.913432i	$-0.366578\pi$
$281$	13.6448	0.813983	0.406992	+	0.913432i	$0.366578\pi$
$282$	6.82156	0.406218
$283$	3.80758	0.226337	0.113169	−	0.993576i	$-0.463900\pi$
$283$	3.80758	0.226337	0.113169	+	0.993576i	$0.463900\pi$
$284$	−3.34877	−0.198713
$285$	−8.05741	−0.477280
$286$	2.53073	0.149645
$287$	0	0
$288$	3.06737	0.180747
$289$	21.0384	1.23755
$290$	−9.94638	−0.584071
$291$	−2.38487	−0.139803
$292$	−5.96907	−0.349313
$293$	17.5068	1.02276	0.511378	−	0.859356i	$-0.329135\pi$
$293$	17.5068	1.02276	0.511378	+	0.859356i	$0.329135\pi$
$294$	0	0
$295$	−2.02287	−0.117776
$296$	28.5496	1.65941
$297$	6.83272	0.396474
$298$	17.0393	0.987059
$299$	−2.01220	−0.116369
$300$	−1.22284	−0.0706005
$301$	0	0
$302$	−15.3124	−0.881130
$303$	−26.0715	−1.49777
$304$	9.70021	0.556345
$305$	6.50835	0.372667
$306$	6.62775	0.378883
$307$	17.2477	0.984380	0.492190	−	0.870488i	$-0.336196\pi$
$307$	17.2477	0.984380	0.492190	+	0.870488i	$0.336196\pi$
$308$	0	0
$309$	−7.55416	−0.429741
$310$	−1.17555	−0.0667666
$311$	−5.24289	−0.297297	−0.148648	−	0.988890i	$-0.547492\pi$
$311$	−5.24289	−0.297297	−0.148648	+	0.988890i	$0.547492\pi$
$312$	7.91693	0.448208
$313$	3.07722	0.173935	0.0869674	−	0.996211i	$-0.472282\pi$
$313$	3.07722	0.173935	0.0869674	+	0.996211i	$0.472282\pi$
$314$	8.50805	0.480137
$315$	0	0
$316$	4.66327	0.262330
$317$	0.511669	0.0287382	0.0143691	−	0.999897i	$-0.495426\pi$
$317$	0.511669	0.0287382	0.0143691	+	0.999897i	$0.495426\pi$
$318$	−21.1723	−1.18728
$319$	14.0093	0.784368
$320$	8.70809	0.486797
$321$	12.2201	0.682057
$322$	0	0
$323$	−25.1182	−1.39761
$324$	6.74134	0.374519
$325$	−1.30021	−0.0721228
$326$	26.9904	1.49486
$327$	12.5512	0.694081
$328$	−27.1510	−1.49916
$329$	0	0
$330$	−3.85079	−0.211979
$331$	10.8358	0.595589	0.297794	−	0.954630i	$-0.403749\pi$
$331$	10.8358	0.595589	0.297794	+	0.954630i	$0.403749\pi$
$332$	6.41125	0.351863
$333$	−8.47990	−0.464696
$334$	1.53841	0.0841782
$335$	−12.1136	−0.661837
$336$	0	0
$337$	9.94751	0.541876	0.270938	−	0.962597i	$-0.412666\pi$
$337$	9.94751	0.541876	0.270938	+	0.962597i	$0.412666\pi$
$338$	−13.2948	−0.723142
$339$	0.227429	0.0123523
$340$	−3.81207	−0.206738
$341$	1.65573	0.0896630
$342$	−4.37655	−0.236657
$343$	0	0
$344$	30.1642	1.62635
$345$	3.06179	0.164842
$346$	−20.2075	−1.08636
$347$	−6.31613	−0.339068	−0.169534	−	0.985524i	$-0.554226\pi$
$347$	−6.31613	−0.339068	−0.169534	+	0.985524i	$0.554226\pi$
$348$	10.3465	0.554630
$349$	−25.7993	−1.38100	−0.690501	−	0.723331i	$-0.742610\pi$
$349$	−25.7993	−1.38100	−0.690501	+	0.723331i	$0.742610\pi$
$350$	0	0
$351$	5.36558	0.286394
$352$	−5.55575	−0.296123
$353$	−18.8831	−1.00505	−0.502523	−	0.864564i	$-0.667595\pi$
$353$	−18.8831	−1.00505	−0.502523	+	0.864564i	$0.667595\pi$
$354$	−4.70464	−0.250049
$355$	5.41795	0.287555
$356$	8.11987	0.430352
$357$	0	0
$358$	−15.4908	−0.818715
$359$	−2.74493	−0.144872	−0.0724359	−	0.997373i	$-0.523077\pi$
$359$	−2.74493	−0.144872	−0.0724359	+	0.997373i	$0.523077\pi$
$360$	−2.81345	−0.148282
$361$	−2.41354	−0.127028
$362$	−21.3910	−1.12429
$363$	−16.3389	−0.857568
$364$	0	0
$365$	9.65732	0.505487
$366$	15.1366	0.791205
$367$	2.39631	0.125086	0.0625432	−	0.998042i	$-0.480079\pi$
$367$	2.39631	0.125086	0.0625432	+	0.998042i	$0.480079\pi$
$368$	−3.68606	−0.192149
$369$	8.06446	0.419819
$370$	−10.9048	−0.566912
$371$	0	0
$372$	1.22284	0.0634011
$373$	−3.78027	−0.195735	−0.0978674	−	0.995199i	$-0.531202\pi$
$373$	−3.78027	−0.195735	−0.0978674	+	0.995199i	$0.531202\pi$
$374$	−12.0044	−0.620735
$375$	1.97842	0.102165
$376$	−9.02713	−0.465539
$377$	11.0012	0.566589
$378$	0	0
$379$	4.89805	0.251596	0.125798	−	0.992056i	$-0.459851\pi$
$379$	4.89805	0.251596	0.125798	+	0.992056i	$0.459851\pi$
$380$	2.51725	0.129132
$381$	38.5210	1.97349
$382$	−2.27759	−0.116532
$383$	1.54393	0.0788909	0.0394455	−	0.999222i	$-0.487441\pi$
$383$	1.54393	0.0788909	0.0394455	+	0.999222i	$0.487441\pi$
$384$	6.97563	0.355973
$385$	0	0
$386$	28.0066	1.42550
$387$	−8.95947	−0.455436
$388$	0.745067	0.0378250
$389$	6.20570	0.314641	0.157321	−	0.987548i	$-0.449714\pi$
$389$	6.20570	0.314641	0.157321	+	0.987548i	$0.449714\pi$
$390$	−3.02394	−0.153123
$391$	9.54484	0.482703
$392$	0	0
$393$	20.7676	1.04759
$394$	−22.2149	−1.11917
$395$	−7.54468	−0.379614
$396$	0.935524	0.0470119
$397$	13.2149	0.663236	0.331618	−	0.943414i	$-0.392405\pi$
$397$	13.2149	0.663236	0.331618	+	0.943414i	$0.392405\pi$
$398$	27.1964	1.36323
$399$	0	0
$400$	−2.38179	−0.119090
$401$	35.7821	1.78687	0.893436	−	0.449191i	$-0.148288\pi$
$401$	35.7821	1.78687	0.893436	+	0.449191i	$0.148288\pi$
$402$	−28.1729	−1.40514
$403$	1.30021	0.0647682
$404$	8.14511	0.405235
$405$	−10.9068	−0.541962
$406$	0	0
$407$	15.3591	0.761324
$408$	−37.5538	−1.85919
$409$	−29.4299	−1.45521	−0.727607	−	0.685994i	$-0.759368\pi$
$409$	−29.4299	−1.45521	−0.727607	+	0.685994i	$0.759368\pi$
$410$	10.3705	0.512164
$411$	−29.8548	−1.47263
$412$	2.36003	0.116270
$413$	0	0
$414$	1.66308	0.0817358
$415$	−10.3727	−0.509177
$416$	−4.36281	−0.213904
$417$	2.14015	0.104804
$418$	7.92698	0.387721
$419$	19.3058	0.943150	0.471575	−	0.881826i	$-0.343686\pi$
$419$	19.3058	0.943150	0.471575	+	0.881826i	$0.343686\pi$
$420$	0	0
$421$	37.2237	1.81417	0.907086	−	0.420945i	$-0.138301\pi$
$421$	37.2237	1.81417	0.907086	+	0.420945i	$0.138301\pi$
$422$	31.8514	1.55050
$423$	2.68127	0.130368
$424$	28.0178	1.36066
$425$	6.16753	0.299169
$426$	12.6007	0.610505
$427$	0	0
$428$	−3.81773	−0.184537
$429$	4.25915	0.205634
$430$	−11.5215	−0.555615
$431$	6.78001	0.326581	0.163291	−	0.986578i	$-0.447789\pi$
$431$	6.78001	0.326581	0.163291	+	0.986578i	$0.447789\pi$
$432$	9.82894	0.472895
$433$	1.31647	0.0632655	0.0316328	−	0.999500i	$-0.489929\pi$
$433$	1.31647	0.0632655	0.0316328	+	0.999500i	$0.489929\pi$
$434$	0	0
$435$	−16.7395	−0.802599
$436$	−3.92117	−0.187790
$437$	−6.30282	−0.301505
$438$	22.4603	1.07319
$439$	−1.58476	−0.0756364	−0.0378182	−	0.999285i	$-0.512041\pi$
$439$	−1.58476	−0.0756364	−0.0378182	+	0.999285i	$0.512041\pi$
$440$	5.09583	0.242934
$441$	0	0
$442$	−9.42683	−0.448388
$443$	24.5663	1.16718	0.583590	−	0.812048i	$-0.301647\pi$
$443$	24.5663	1.16718	0.583590	+	0.812048i	$0.301647\pi$
$444$	11.3434	0.538335
$445$	−13.1371	−0.622758
$446$	−30.7982	−1.45834
$447$	28.6767	1.35636
$448$	0	0
$449$	−19.1065	−0.901690	−0.450845	−	0.892602i	$-0.648877\pi$
$449$	−19.1065	−0.901690	−0.450845	+	0.892602i	$0.648877\pi$
$450$	1.07462	0.0506581
$451$	−14.6067	−0.687802
$452$	−0.0710522	−0.00334202
$453$	−25.7704	−1.21080
$454$	−14.4785	−0.679509
$455$	0	0
$456$	24.7982	1.16128
$457$	25.1428	1.17613	0.588065	−	0.808813i	$-0.299890\pi$
$457$	25.1428	1.17613	0.588065	+	0.808813i	$0.299890\pi$
$458$	11.9321	0.557548
$459$	−25.4515	−1.18798
$460$	−0.956550	−0.0445994
$461$	−2.34259	−0.109105	−0.0545527	−	0.998511i	$-0.517373\pi$
$461$	−2.34259	−0.109105	−0.0545527	+	0.998511i	$0.517373\pi$
$462$	0	0
$463$	34.2728	1.59279	0.796397	−	0.604774i	$-0.206737\pi$
$463$	34.2728	1.59279	0.796397	+	0.604774i	$0.206737\pi$
$464$	20.1525	0.935556
$465$	−1.97842	−0.0917470
$466$	−21.7486	−1.00748
$467$	10.6927	0.494797	0.247399	−	0.968914i	$-0.420424\pi$
$467$	10.6927	0.494797	0.247399	+	0.968914i	$0.420424\pi$
$468$	0.734647	0.0339591
$469$	0	0
$470$	3.44799	0.159044
$471$	14.3189	0.659778
$472$	6.22576	0.286564
$473$	16.2278	0.746153
$474$	−17.5469	−0.805955
$475$	−4.07265	−0.186866
$476$	0	0
$477$	−8.32192	−0.381035
$478$	−18.4465	−0.843722
$479$	29.7253	1.35818	0.679091	−	0.734054i	$-0.262374\pi$
$479$	29.7253	1.35818	0.679091	+	0.734054i	$0.262374\pi$
$480$	6.63851	0.303005
$481$	12.0612	0.549943
$482$	−18.5387	−0.844413
$483$	0	0
$484$	5.10450	0.232023
$485$	−1.20544	−0.0547362
$486$	−10.8128	−0.490478
$487$	37.8176	1.71368	0.856840	−	0.515583i	$-0.172425\pi$
$487$	37.8176	1.71368	0.856840	+	0.515583i	$0.172425\pi$
$488$	−20.0307	−0.906745
$489$	45.4242	2.05415
$490$	0	0
$491$	32.3484	1.45986	0.729931	−	0.683521i	$-0.239552\pi$
$491$	32.3484	1.45986	0.729931	+	0.683521i	$0.239552\pi$
$492$	−10.7877	−0.486347
$493$	−52.1838	−2.35024
$494$	6.22489	0.280071
$495$	−1.51358	−0.0680303
$496$	2.38179	0.106946
$497$	0	0
$498$	−24.1241	−1.08103
$499$	−35.1201	−1.57219	−0.786096	−	0.618104i	$-0.787901\pi$
$499$	−35.1201	−1.57219	−0.786096	+	0.618104i	$0.787901\pi$
$500$	−0.618087	−0.0276417
$501$	2.58911	0.115673
$502$	−14.5175	−0.647946
$503$	9.17085	0.408908	0.204454	−	0.978876i	$-0.434458\pi$
$503$	9.17085	0.408908	0.204454	+	0.978876i	$0.434458\pi$
$504$	0	0
$505$	−13.1779	−0.586410
$506$	−3.01223	−0.133910
$507$	−22.3748	−0.993701
$508$	−12.0345	−0.533946
$509$	25.2385	1.11868	0.559339	−	0.828939i	$-0.311055\pi$
$509$	25.2385	1.11868	0.559339	+	0.828939i	$0.311055\pi$
$510$	14.3440	0.635162
$511$	0	0
$512$	−22.6528	−1.00112
$513$	16.8066	0.742029
$514$	25.8616	1.14071
$515$	−3.81828	−0.168254
$516$	11.9849	0.527608
$517$	−4.85642	−0.213585
$518$	0	0
$519$	−34.0088	−1.49282
$520$	4.00165	0.175484
$521$	−19.2970	−0.845418	−0.422709	−	0.906265i	$-0.638921\pi$
$521$	−19.2970	−0.845418	−0.422709	+	0.906265i	$0.638921\pi$
$522$	−9.09242	−0.397965
$523$	21.9414	0.959429	0.479715	−	0.877425i	$-0.340740\pi$
$523$	21.9414	0.959429	0.479715	+	0.877425i	$0.340740\pi$
$524$	−6.48810	−0.283434
$525$	0	0
$526$	−15.5502	−0.678021
$527$	−6.16753	−0.268662
$528$	7.80213	0.339544
$529$	−20.6049	−0.895867
$530$	−10.7016	−0.464848
$531$	−1.84919	−0.0802482
$532$	0	0
$533$	−11.4703	−0.496834
$534$	−30.5533	−1.32217
$535$	6.17668	0.267041
$536$	37.2819	1.61033
$537$	−26.0707	−1.12503
$538$	−9.22087	−0.397540
$539$	0	0
$540$	2.55066	0.109763
$541$	5.43481	0.233661	0.116830	−	0.993152i	$-0.462727\pi$
$541$	5.43481	0.233661	0.116830	+	0.993152i	$0.462727\pi$
$542$	−7.52417	−0.323191
$543$	−36.0006	−1.54493
$544$	20.6949	0.887286
$545$	6.34403	0.271748
$546$	0	0
$547$	31.9148	1.36458	0.682289	−	0.731083i	$-0.260985\pi$
$547$	31.9148	1.36458	0.682289	+	0.731083i	$0.260985\pi$
$548$	9.32707	0.398433
$549$	5.94957	0.253921
$550$	−1.94640	−0.0829946
$551$	34.4589	1.46800
$552$	−9.42325	−0.401080
$553$	0	0
$554$	−24.3020	−1.03249
$555$	−18.3525	−0.779019
$556$	−0.668614	−0.0283555
$557$	−9.64899	−0.408841	−0.204420	−	0.978883i	$-0.565531\pi$
$557$	−9.64899	−0.408841	−0.204420	+	0.978883i	$0.565531\pi$
$558$	−1.07462	−0.0454923
$559$	12.7433	0.538984
$560$	0	0
$561$	−20.2032	−0.852980
$562$	16.0402	0.676614
$563$	11.3669	0.479056	0.239528	−	0.970889i	$-0.423007\pi$
$563$	11.3669	0.479056	0.239528	+	0.970889i	$0.423007\pi$
$564$	−3.58669	−0.151027
$565$	0.114955	0.00483619
$566$	4.47599	0.188140
$567$	0	0
$568$	−16.6748	−0.699658
$569$	20.9353	0.877653	0.438827	−	0.898572i	$-0.355394\pi$
$569$	20.9353	0.877653	0.438827	+	0.898572i	$0.355394\pi$
$570$	−9.47187	−0.396733
$571$	7.37397	0.308591	0.154295	−	0.988025i	$-0.450689\pi$
$571$	7.37397	0.308591	0.154295	+	0.988025i	$0.450689\pi$
$572$	−1.33062	−0.0556361
$573$	−3.83313	−0.160131
$574$	0	0
$575$	1.54760	0.0645392
$576$	7.96045	0.331685
$577$	−28.7643	−1.19747	−0.598736	−	0.800946i	$-0.704330\pi$
$577$	−28.7643	−1.19747	−0.598736	+	0.800946i	$0.704330\pi$
$578$	24.7316	1.02870
$579$	47.1344	1.95884
$580$	5.22967	0.217150
$581$	0	0
$582$	−2.80352	−0.116210
$583$	15.0730	0.624260
$584$	−29.7222	−1.22991
$585$	−1.18858	−0.0491418
$586$	20.5801	0.850154
$587$	10.1529	0.419057	0.209528	−	0.977803i	$-0.432807\pi$
$587$	10.1529	0.419057	0.209528	+	0.977803i	$0.432807\pi$
$588$	0	0
$589$	4.07265	0.167811
$590$	−2.37798	−0.0978999
$591$	−37.3872	−1.53791
$592$	22.0943	0.908070
$593$	21.0324	0.863697	0.431849	−	0.901946i	$-0.357861\pi$
$593$	21.0324	0.863697	0.431849	+	0.901946i	$0.357861\pi$
$594$	8.03219	0.329565
$595$	0	0
$596$	−8.95903	−0.366976
$597$	45.7709	1.87328
$598$	−2.36544	−0.0967301
$599$	−4.09471	−0.167305	−0.0836526	−	0.996495i	$-0.526659\pi$
$599$	−4.09471	−0.167305	−0.0836526	+	0.996495i	$0.526659\pi$
$600$	−6.08896	−0.248581
$601$	−24.2267	−0.988227	−0.494113	−	0.869397i	$-0.664507\pi$
$601$	−24.2267	−0.988227	−0.494113	+	0.869397i	$0.664507\pi$
$602$	0	0
$603$	−11.0736	−0.450951
$604$	8.05106	0.327593
$605$	−8.25854	−0.335758
$606$	−30.6483	−1.24500
$607$	34.6641	1.40697	0.703487	−	0.710709i	$-0.251626\pi$
$607$	34.6641	1.40697	0.703487	+	0.710709i	$0.251626\pi$
$608$	−13.6656	−0.554214
$609$	0	0
$610$	7.65087	0.309775
$611$	−3.81364	−0.154283
$612$	−3.48478	−0.140864
$613$	23.0847	0.932381	0.466191	−	0.884684i	$-0.345626\pi$
$613$	23.0847	0.932381	0.466191	+	0.884684i	$0.345626\pi$
$614$	20.2755	0.818254
$615$	17.4534	0.703788
$616$	0	0
$617$	−9.48678	−0.381924	−0.190962	−	0.981597i	$-0.561161\pi$
$617$	−9.48678	−0.381924	−0.190962	+	0.981597i	$0.561161\pi$
$618$	−8.88028	−0.357217
$619$	−37.4166	−1.50390	−0.751951	−	0.659219i	$-0.770887\pi$
$619$	−37.4166	−1.50390	−0.751951	+	0.659219i	$0.770887\pi$
$620$	0.618087	0.0248230
$621$	−6.38646	−0.256280
$622$	−6.16327	−0.247125
$623$	0	0
$624$	6.12684	0.245270
$625$	1.00000	0.0400000
$626$	3.61742	0.144581
$627$	13.3409	0.532785
$628$	−4.47342	−0.178509
$629$	−57.2120	−2.28119
$630$	0	0
$631$	−32.5252	−1.29481	−0.647404	−	0.762147i	$-0.724145\pi$
$631$	−32.5252	−1.29481	−0.647404	+	0.762147i	$0.724145\pi$
$632$	23.2202	0.923649
$633$	53.6051	2.13061
$634$	0.601492	0.0238883
$635$	19.4706	0.772667
$636$	11.1321	0.441417
$637$	0	0
$638$	16.4686	0.651997
$639$	4.95279	0.195929
$640$	3.52586	0.139372
$641$	−7.50280	−0.296343	−0.148171	−	0.988962i	$-0.547339\pi$
$641$	−7.50280	−0.296343	−0.148171	+	0.988962i	$0.547339\pi$
$642$	14.3653	0.566952
$643$	14.6785	0.578862	0.289431	−	0.957199i	$-0.406534\pi$
$643$	14.6785	0.578862	0.289431	+	0.957199i	$0.406534\pi$
$644$	0	0
$645$	−19.3904	−0.763495
$646$	−29.5276	−1.16175
$647$	7.27075	0.285843	0.142921	−	0.989734i	$-0.454350\pi$
$647$	7.27075	0.285843	0.142921	+	0.989734i	$0.454350\pi$
$648$	33.5676	1.31866
$649$	3.34933	0.131473
$650$	−1.52846	−0.0599512
$651$	0	0
$652$	−14.1912	−0.555770
$653$	−25.2991	−0.990029	−0.495014	−	0.868885i	$-0.664837\pi$
$653$	−25.2991	−0.990029	−0.495014	+	0.868885i	$0.664837\pi$
$654$	14.7545	0.576946
$655$	10.4971	0.410154
$656$	−21.0119	−0.820376
$657$	8.82818	0.344420
$658$	0	0
$659$	−23.5873	−0.918832	−0.459416	−	0.888221i	$-0.651941\pi$
$659$	−23.5873	−0.918832	−0.459416	+	0.888221i	$0.651941\pi$
$660$	2.02469	0.0788110
$661$	−16.2779	−0.633139	−0.316569	−	0.948569i	$-0.602531\pi$
$661$	−16.2779	−0.633139	−0.316569	+	0.948569i	$0.602531\pi$
$662$	12.7380	0.495076
$663$	−15.8651	−0.616151
$664$	31.9240	1.23889
$665$	0	0
$666$	−9.96853	−0.386273
$667$	−13.0943	−0.507013
$668$	−0.808876	−0.0312964
$669$	−51.8326	−2.00397
$670$	−14.2401	−0.550144
$671$	−10.7761	−0.416007
$672$	0	0
$673$	−39.1697	−1.50988	−0.754941	−	0.655793i	$-0.772334\pi$
$673$	−39.1697	−1.50988	−0.754941	+	0.655793i	$0.772334\pi$
$674$	11.6938	0.450428
$675$	−4.12670	−0.158837
$676$	6.99023	0.268855
$677$	34.0996	1.31055	0.655277	−	0.755388i	$-0.272552\pi$
$677$	34.0996	1.31055	0.655277	+	0.755388i	$0.272552\pi$
$678$	0.267354	0.0102677
$679$	0	0
$680$	−18.9817	−0.727916
$681$	−24.3669	−0.933743
$682$	1.94640	0.0745313
$683$	−44.1244	−1.68837	−0.844186	−	0.536050i	$-0.819916\pi$
$683$	−44.1244	−1.68837	−0.844186	+	0.536050i	$0.819916\pi$
$684$	2.30113	0.0879859
$685$	−15.0902	−0.576568
$686$	0	0
$687$	20.0814	0.766152
$688$	23.3438	0.889975
$689$	11.8365	0.450935
$690$	3.59929	0.137022
$691$	−5.12260	−0.194873	−0.0974365	−	0.995242i	$-0.531064\pi$
$691$	−5.12260	−0.194873	−0.0974365	+	0.995242i	$0.531064\pi$
$692$	10.6248	0.403896
$693$	0	0
$694$	−7.42492	−0.281846
$695$	1.08175	0.0410330
$696$	51.5190	1.95282
$697$	54.4091	2.06089
$698$	−30.3283	−1.14794
$699$	−36.6024	−1.38443
$700$	0	0
$701$	−3.80840	−0.143841	−0.0719206	−	0.997410i	$-0.522913\pi$
$701$	−3.80840	−0.143841	−0.0719206	+	0.997410i	$0.522913\pi$
$702$	6.30750	0.238061
$703$	37.7792	1.42487
$704$	−14.4183	−0.543410
$705$	5.80288	0.218549
$706$	−22.1980	−0.835433
$707$	0	0
$708$	2.47364	0.0929650
$709$	9.77983	0.367289	0.183645	−	0.982993i	$-0.441210\pi$
$709$	9.77983	0.367289	0.183645	+	0.982993i	$0.441210\pi$
$710$	6.36906	0.239027
$711$	−6.89693	−0.258655
$712$	40.4319	1.51525
$713$	−1.54760	−0.0579579
$714$	0	0
$715$	2.15281	0.0805104
$716$	8.14486	0.304388
$717$	−31.0450	−1.15940
$718$	−3.22680	−0.120423
$719$	4.10536	0.153104	0.0765521	−	0.997066i	$-0.475609\pi$
$719$	4.10536	0.153104	0.0765521	+	0.997066i	$0.475609\pi$
$720$	−2.17730	−0.0811433
$721$	0	0
$722$	−2.83723	−0.105591
$723$	−31.2001	−1.16035
$724$	11.2471	0.417995
$725$	−8.46106	−0.314236
$726$	−19.2071	−0.712843
$727$	26.7159	0.990837	0.495418	−	0.868655i	$-0.335015\pi$
$727$	26.7159	0.990837	0.495418	+	0.868655i	$0.335015\pi$
$728$	0	0
$729$	14.5227	0.537876
$730$	11.3526	0.420180
$731$	−60.4476	−2.23573
$732$	−7.95864	−0.294160
$733$	−48.1237	−1.77749	−0.888744	−	0.458404i	$-0.848421\pi$
$733$	−48.1237	−1.77749	−0.888744	+	0.458404i	$0.848421\pi$
$734$	2.81698	0.103977
$735$	0	0
$736$	5.19290	0.191413
$737$	20.0569	0.738805
$738$	9.48016	0.348970
$739$	16.3649	0.601991	0.300995	−	0.953626i	$-0.402681\pi$
$739$	16.3649	0.601991	0.300995	+	0.953626i	$0.402681\pi$
$740$	5.73358	0.210771
$741$	10.4763	0.384858
$742$	0	0
$743$	−9.02092	−0.330945	−0.165473	−	0.986214i	$-0.552915\pi$
$743$	−9.02092	−0.330945	−0.165473	+	0.986214i	$0.552915\pi$
$744$	6.08896	0.223232
$745$	14.4948	0.531047
$746$	−4.44389	−0.162702
$747$	−9.48217	−0.346934
$748$	6.31177	0.230781
$749$	0	0
$750$	2.32573	0.0849235
$751$	−18.2497	−0.665941	−0.332970	−	0.942937i	$-0.608051\pi$
$751$	−18.2497	−0.665941	−0.332970	+	0.942937i	$0.608051\pi$
$752$	−6.98601	−0.254754
$753$	−24.4326	−0.890372
$754$	12.9324	0.470970
$755$	−13.0258	−0.474056
$756$	0	0
$757$	−14.5803	−0.529928	−0.264964	−	0.964258i	$-0.585360\pi$
$757$	−14.5803	−0.529928	−0.264964	+	0.964258i	$0.585360\pi$
$758$	5.75789	0.209136
$759$	−5.06952	−0.184012
$760$	12.5343	0.454668
$761$	38.9303	1.41122	0.705611	−	0.708599i	$-0.250673\pi$
$761$	38.9303	1.41122	0.705611	+	0.708599i	$0.250673\pi$
$762$	45.2833	1.64044
$763$	0	0
$764$	1.19753	0.0433250
$765$	5.63801	0.203843
$766$	1.81496	0.0655771
$767$	2.63016	0.0949696
$768$	−26.2563	−0.947444
$769$	−11.6877	−0.421470	−0.210735	−	0.977543i	$-0.567586\pi$
$769$	−11.6877	−0.421470	−0.210735	+	0.977543i	$0.567586\pi$
$770$	0	0
$771$	43.5245	1.56750
$772$	−14.7255	−0.529982
$773$	−32.9342	−1.18456	−0.592281	−	0.805731i	$-0.701772\pi$
$773$	−32.9342	−1.18456	−0.592281	+	0.805731i	$0.701772\pi$
$774$	−10.5323	−0.378575
$775$	−1.00000	−0.0359211
$776$	3.70997	0.133180
$777$	0	0
$778$	7.29509	0.261542
$779$	−35.9284	−1.28727
$780$	1.58995	0.0569292
$781$	−8.97069	−0.320997
$782$	11.2204	0.401241
$783$	34.9162	1.24780
$784$	0	0
$785$	7.23752	0.258318
$786$	24.4133	0.870793
$787$	9.73161	0.346895	0.173447	−	0.984843i	$-0.444509\pi$
$787$	9.73161	0.346895	0.173447	+	0.984843i	$0.444509\pi$
$788$	11.6803	0.416094
$789$	−26.1706	−0.931699
$790$	−8.86914	−0.315550
$791$	0	0
$792$	4.65832	0.165526
$793$	−8.46223	−0.300503
$794$	15.5347	0.551307
$795$	−18.0106	−0.638769
$796$	−14.2995	−0.506832
$797$	−33.8137	−1.19774	−0.598871	−	0.800845i	$-0.704384\pi$
$797$	−33.8137	−1.19774	−0.598871	+	0.800845i	$0.704384\pi$
$798$	0	0
$799$	18.0899	0.639975
$800$	3.35546	0.118633
$801$	−12.0092	−0.424324
$802$	42.0635	1.48532
$803$	−15.9900	−0.564273
$804$	14.8129	0.522412
$805$	0	0
$806$	1.52846	0.0538378
$807$	−15.5185	−0.546277
$808$	40.5576	1.42681
$809$	−43.3230	−1.52316	−0.761578	−	0.648073i	$-0.775575\pi$
$809$	−43.3230	−1.52316	−0.761578	+	0.648073i	$0.775575\pi$
$810$	−12.8214	−0.450499
$811$	−7.26200	−0.255003	−0.127502	−	0.991838i	$-0.540696\pi$
$811$	−7.26200	−0.255003	−0.127502	+	0.991838i	$0.540696\pi$
$812$	0	0
$813$	−12.6630	−0.444111
$814$	18.0554	0.632842
$815$	22.9598	0.804248
$816$	−29.0625	−1.01739
$817$	39.9158	1.39648
$818$	−34.5963	−1.20963
$819$	0	0
$820$	−5.45269	−0.190416
$821$	−35.9450	−1.25449	−0.627245	−	0.778822i	$-0.715817\pi$
$821$	−35.9450	−1.25449	−0.627245	+	0.778822i	$0.715817\pi$
$822$	−35.0957	−1.22410
$823$	2.87246	0.100128	0.0500639	−	0.998746i	$-0.484058\pi$
$823$	2.87246	0.100128	0.0500639	+	0.998746i	$0.484058\pi$
$824$	11.7515	0.409382
$825$	−3.27574	−0.114047
$826$	0	0
$827$	−18.3297	−0.637385	−0.318692	−	0.947858i	$-0.603244\pi$
$827$	−18.3297	−0.637385	−0.318692	+	0.947858i	$0.603244\pi$
$828$	−0.874424	−0.0303883
$829$	−38.9299	−1.35209	−0.676047	−	0.736859i	$-0.736308\pi$
$829$	−38.9299	−1.35209	−0.676047	+	0.736859i	$0.736308\pi$
$830$	−12.1936	−0.423247
$831$	−40.8997	−1.41880
$832$	−11.3224	−0.392532
$833$	0	0
$834$	2.51585	0.0871166
$835$	1.30868	0.0452886
$836$	−4.16790	−0.144150
$837$	4.12670	0.142640
$838$	22.6949	0.783982
$839$	−35.4369	−1.22342	−0.611708	−	0.791083i	$-0.709517\pi$
$839$	−35.4369	−1.22342	−0.611708	+	0.791083i	$0.709517\pi$
$840$	0	0
$841$	42.5895	1.46860
$842$	43.7583	1.50801
$843$	26.9952	0.929765
$844$	−16.7470	−0.576456
$845$	−11.3094	−0.389057
$846$	3.15196	0.108366
$847$	0	0
$848$	21.6827	0.744587
$849$	7.53299	0.258531
$850$	7.25022	0.248681
$851$	−14.3560	−0.492118
$852$	−6.62527	−0.226978
$853$	−23.7903	−0.814564	−0.407282	−	0.913303i	$-0.633523\pi$
$853$	−23.7903	−0.814564	−0.407282	+	0.913303i	$0.633523\pi$
$854$	0	0
$855$	−3.72299	−0.127323
$856$	−19.0099	−0.649744
$857$	37.6826	1.28721	0.643606	−	0.765357i	$-0.277437\pi$
$857$	37.6826	1.28721	0.643606	+	0.765357i	$0.277437\pi$
$858$	5.00684	0.170931
$859$	23.5755	0.804386	0.402193	−	0.915555i	$-0.368248\pi$
$859$	23.5755	0.804386	0.402193	+	0.915555i	$0.368248\pi$
$860$	6.05784	0.206570
$861$	0	0
$862$	7.97022	0.271467
$863$	38.5510	1.31229	0.656146	−	0.754634i	$-0.272186\pi$
$863$	38.5510	1.31229	0.656146	+	0.754634i	$0.272186\pi$
$864$	−13.8470	−0.471084
$865$	−17.1899	−0.584473
$866$	1.54757	0.0525887
$867$	41.6227	1.41358
$868$	0	0
$869$	12.4920	0.423762
$870$	−19.6781	−0.667150
$871$	15.7502	0.533677
$872$	−19.5249	−0.661198
$873$	−1.10195	−0.0372952
$874$	−7.40926	−0.250622
$875$	0	0
$876$	−11.8093	−0.399000
$877$	18.7856	0.634343	0.317171	−	0.948368i	$-0.397267\pi$
$877$	18.7856	0.634343	0.317171	+	0.948368i	$0.397267\pi$
$878$	−1.86296	−0.0628719
$879$	34.6358	1.16824
$880$	3.94362	0.132939
$881$	15.3963	0.518716	0.259358	−	0.965781i	$-0.416489\pi$
$881$	15.3963	0.518716	0.259358	+	0.965781i	$0.416489\pi$
$882$	0	0
$883$	−24.5975	−0.827773	−0.413887	−	0.910328i	$-0.635829\pi$
$883$	−24.5975	−0.827773	−0.413887	+	0.910328i	$0.635829\pi$
$884$	4.95650	0.166705
$885$	−4.00208	−0.134529
$886$	28.8789	0.970205
$887$	23.2412	0.780362	0.390181	−	0.920738i	$-0.372412\pi$
$887$	23.2412	0.780362	0.390181	+	0.920738i	$0.372412\pi$
$888$	56.4832	1.89545
$889$	0	0
$890$	−15.4433	−0.517660
$891$	18.0587	0.604990
$892$	16.1933	0.542191
$893$	−11.9454	−0.399739
$894$	33.7109	1.12746
$895$	−13.1775	−0.440476
$896$	0	0
$897$	−3.98098	−0.132921
$898$	−22.4606	−0.749519
$899$	8.46106	0.282192
$900$	−0.565021	−0.0188340
$901$	−56.1462	−1.87050
$902$	−17.1709	−0.571727
$903$	0	0
$904$	−0.353796	−0.0117671
$905$	−18.1966	−0.604876
$906$	−30.2944	−1.00646
$907$	−7.95389	−0.264104	−0.132052	−	0.991243i	$-0.542157\pi$
$907$	−7.95389	−0.264104	−0.132052	+	0.991243i	$0.542157\pi$
$908$	7.61259	0.252633
$909$	−12.0465	−0.399558
$910$	0	0
$911$	5.91228	0.195883	0.0979413	−	0.995192i	$-0.468774\pi$
$911$	5.91228	0.195883	0.0979413	+	0.995192i	$0.468774\pi$
$912$	19.1911	0.635480
$913$	17.1745	0.568392
$914$	29.5566	0.977644
$915$	12.8762	0.425675
$916$	−6.27372	−0.207289
$917$	0	0
$918$	−29.9195	−0.987490
$919$	18.8427	0.621563	0.310782	−	0.950481i	$-0.399409\pi$
$919$	18.8427	0.621563	0.310782	+	0.950481i	$0.399409\pi$
$920$	−4.76302	−0.157032
$921$	34.1233	1.12440
$922$	−2.75383	−0.0906925
$923$	−7.04449	−0.231872
$924$	0	0
$925$	−9.27633	−0.305004
$926$	40.2894	1.32399
$927$	−3.49046	−0.114642
$928$	−28.3908	−0.931972
$929$	22.1954	0.728206	0.364103	−	0.931359i	$-0.381376\pi$
$929$	22.1954	0.728206	0.364103	+	0.931359i	$0.381376\pi$
$930$	−2.32573	−0.0762636
$931$	0	0
$932$	11.4351	0.374570
$933$	−10.3726	−0.339585
$934$	12.5697	0.411294
$935$	−10.2118	−0.333961
$936$	3.65808	0.119568
$937$	33.5066	1.09461	0.547306	−	0.836933i	$-0.315653\pi$
$937$	33.5066	1.09461	0.547306	+	0.836933i	$0.315653\pi$
$938$	0	0
$939$	6.08803	0.198675
$940$	−1.81290	−0.0591304
$941$	53.5218	1.74476	0.872380	−	0.488828i	$-0.162575\pi$
$941$	53.5218	1.74476	0.872380	+	0.488828i	$0.162575\pi$
$942$	16.8325	0.548433
$943$	13.6527	0.444593
$944$	4.81806	0.156814
$945$	0	0
$946$	19.0765	0.620231
$947$	−16.0983	−0.523124	−0.261562	−	0.965187i	$-0.584238\pi$
$947$	−16.0983	−0.523124	−0.261562	+	0.965187i	$0.584238\pi$
$948$	9.22591	0.299644
$949$	−12.5566	−0.407603
$950$	−4.78759	−0.155330
$951$	1.01230	0.0328260
$952$	0	0
$953$	44.2061	1.43198	0.715988	−	0.698112i	$-0.245976\pi$
$953$	44.2061	1.43198	0.715988	+	0.698112i	$0.245976\pi$
$954$	−9.78282	−0.316730
$955$	−1.93747	−0.0626951
$956$	9.69891	0.313685
$957$	27.7162	0.895938
$958$	34.9435	1.12897
$959$	0	0
$960$	17.2283	0.556040
$961$	1.00000	0.0322581
$962$	14.1785	0.457134
$963$	5.64637	0.181952
$964$	9.74738	0.313942
$965$	23.8243	0.766931
$966$	0	0
$967$	2.03955	0.0655875	0.0327937	−	0.999462i	$-0.489560\pi$
$967$	2.03955	0.0655875	0.0327937	+	0.999462i	$0.489560\pi$
$968$	25.4172	0.816940
$969$	−49.6943	−1.59641
$970$	−1.41705	−0.0454988
$971$	−5.19126	−0.166595	−0.0832977	−	0.996525i	$-0.526545\pi$
$971$	−5.19126	−0.166595	−0.0832977	+	0.996525i	$0.526545\pi$
$972$	5.68521	0.182353
$973$	0	0
$974$	44.4564	1.42448
$975$	−2.57237	−0.0823816
$976$	−15.5015	−0.496192
$977$	33.9231	1.08530	0.542648	−	0.839960i	$-0.317422\pi$
$977$	33.9231	1.08530	0.542648	+	0.839960i	$0.317422\pi$
$978$	53.3983	1.70749
$979$	21.7515	0.695182
$980$	0	0
$981$	5.79936	0.185159
$982$	38.0271	1.21349
$983$	−7.72807	−0.246487	−0.123244	−	0.992376i	$-0.539330\pi$
$983$	−7.72807	−0.246487	−0.123244	+	0.992376i	$0.539330\pi$
$984$	−53.7160	−1.71240
$985$	−18.8975	−0.602125
$986$	−61.3446	−1.95361
$987$	0	0
$988$	−3.27296	−0.104127
$989$	−15.1679	−0.482311
$990$	−1.77929	−0.0565494
$991$	25.6723	0.815508	0.407754	−	0.913092i	$-0.366312\pi$
$991$	25.6723	0.815508	0.407754	+	0.913092i	$0.366312\pi$
$992$	−3.35546	−0.106536
$993$	21.4377	0.680306
$994$	0	0
$995$	23.1351	0.733431
$996$	12.6841	0.401913
$997$	−16.4831	−0.522024	−0.261012	−	0.965336i	$-0.584056\pi$
$997$	−16.4831	−0.522024	−0.261012	+	0.965336i	$0.584056\pi$
$998$	−41.2854	−1.30687
$999$	38.2806	1.21115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.15		21
7.3	odd	6		1085.2.j.d.156.7	✓	42
7.5	odd	6		1085.2.j.d.466.7	yes	42
7.6	odd	2		7595.2.a.bg.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.7	✓	42	7.3	odd	6
1085.2.j.d.466.7	yes	42	7.5	odd	6
7595.2.a.bf.1.15		21	1.1	even	1	trivial
7595.2.a.bg.1.15		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)

\(f(q)\)	\(=\)	\(q+1.17555 q^{2} +1.97842 q^{3} -0.618087 q^{4} +1.00000 q^{5} +2.32573 q^{6} -3.07769 q^{8} +0.914144 q^{9} +O(q^{10})\)	\(q+1.17555 q^{2} +1.97842 q^{3} -0.618087 q^{4} +1.00000 q^{5} +2.32573 q^{6} -3.07769 q^{8} +0.914144 q^{9} +1.17555 q^{10} -1.65573 q^{11} -1.22284 q^{12} -1.30021 q^{13} +1.97842 q^{15} -2.38179 q^{16} +6.16753 q^{17} +1.07462 q^{18} -4.07265 q^{19} -0.618087 q^{20} -1.94640 q^{22} +1.54760 q^{23} -6.08896 q^{24} +1.00000 q^{25} -1.52846 q^{26} -4.12670 q^{27} -8.46106 q^{29} +2.32573 q^{30} -1.00000 q^{31} +3.35546 q^{32} -3.27574 q^{33} +7.25022 q^{34} -0.565021 q^{36} -9.27633 q^{37} -4.78759 q^{38} -2.57237 q^{39} -3.07769 q^{40} +8.82188 q^{41} -9.80094 q^{43} +1.02339 q^{44} +0.914144 q^{45} +1.81927 q^{46} +2.93309 q^{47} -4.71219 q^{48} +1.17555 q^{50} +12.2020 q^{51} +0.803645 q^{52} -9.10351 q^{53} -4.85113 q^{54} -1.65573 q^{55} -8.05741 q^{57} -9.94638 q^{58} -2.02287 q^{59} -1.22284 q^{60} +6.50835 q^{61} -1.17555 q^{62} +8.70809 q^{64} -1.30021 q^{65} -3.85079 q^{66} -12.1136 q^{67} -3.81207 q^{68} +3.06179 q^{69} +5.41795 q^{71} -2.81345 q^{72} +9.65732 q^{73} -10.9048 q^{74} +1.97842 q^{75} +2.51725 q^{76} -3.02394 q^{78} -7.54468 q^{79} -2.38179 q^{80} -10.9068 q^{81} +10.3705 q^{82} -10.3727 q^{83} +6.16753 q^{85} -11.5215 q^{86} -16.7395 q^{87} +5.09583 q^{88} -13.1371 q^{89} +1.07462 q^{90} -0.956550 q^{92} -1.97842 q^{93} +3.44799 q^{94} -4.07265 q^{95} +6.63851 q^{96} -1.20544 q^{97} -1.51358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 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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