LMFDB - Embedded newform 7595.2.a.w.1.4

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 14x^{9} + 67x^{7} - 130x^{5} - 2x^{4} + 90x^{3} + 4x^{2} - 14x + 2 $ x^11 - 14x^9 + 67x^7 - 130x^5 - 2x^4 + 90x^3 + 4x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.08711$ of defining polynomial
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)

$f(q)$	$=$	$q-1.08711 q^{2} -0.211543 q^{3} -0.818196 q^{4} +1.00000 q^{5} +0.229970 q^{6} +3.06368 q^{8} -2.95525 q^{9} +O(q^{10})$	\(q-1.08711 q^{2} -0.211543 q^{3} -0.818196 q^{4} +1.00000 q^{5} +0.229970 q^{6} +3.06368 q^{8} -2.95525 q^{9} -1.08711 q^{10} +4.76649 q^{11} +0.173084 q^{12} -5.24166 q^{13} -0.211543 q^{15} -1.69416 q^{16} -1.89814 q^{17} +3.21268 q^{18} +7.39723 q^{19} -0.818196 q^{20} -5.18169 q^{22} -3.53038 q^{23} -0.648101 q^{24} +1.00000 q^{25} +5.69825 q^{26} +1.25979 q^{27} +5.59616 q^{29} +0.229970 q^{30} -1.00000 q^{31} -4.28563 q^{32} -1.00832 q^{33} +2.06349 q^{34} +2.41797 q^{36} -6.43341 q^{37} -8.04158 q^{38} +1.10884 q^{39} +3.06368 q^{40} +3.72972 q^{41} -8.59603 q^{43} -3.89992 q^{44} -2.95525 q^{45} +3.83791 q^{46} -5.54752 q^{47} +0.358389 q^{48} -1.08711 q^{50} +0.401539 q^{51} +4.28870 q^{52} -3.68850 q^{53} -1.36953 q^{54} +4.76649 q^{55} -1.56483 q^{57} -6.08363 q^{58} +13.0271 q^{59} +0.173084 q^{60} -8.88974 q^{61} +1.08711 q^{62} +8.04727 q^{64} -5.24166 q^{65} +1.09615 q^{66} +7.32359 q^{67} +1.55305 q^{68} +0.746829 q^{69} -9.67712 q^{71} -9.05395 q^{72} -1.22727 q^{73} +6.99381 q^{74} -0.211543 q^{75} -6.05238 q^{76} -1.20543 q^{78} +15.7558 q^{79} -1.69416 q^{80} +8.59925 q^{81} -4.05461 q^{82} -3.43221 q^{83} -1.89814 q^{85} +9.34482 q^{86} -1.18383 q^{87} +14.6030 q^{88} -0.165284 q^{89} +3.21268 q^{90} +2.88855 q^{92} +0.211543 q^{93} +6.03075 q^{94} +7.39723 q^{95} +0.906596 q^{96} +10.5741 q^{97} -14.0862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9}+O(q^{10}) $ 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9	$ 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9} - 3 q^{11} + 16 q^{12} - 5 q^{13} - q^{15} - 15 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} - 10 q^{22} - 6 q^{23} - 16 q^{24} + 11 q^{25} + 14 q^{26} - 13 q^{27} - 15 q^{29} - 8 q^{30} - 11 q^{31} - 5 q^{33} - 16 q^{34} - 12 q^{36} - 24 q^{37} - 18 q^{38} - q^{39} - 30 q^{43} - 26 q^{44} - 2 q^{45} - 12 q^{46} - q^{47} + 4 q^{48} - 7 q^{51} - 14 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{55} - 30 q^{57} - 14 q^{58} - 2 q^{59} + 16 q^{60} + 10 q^{61} - 16 q^{64} - 5 q^{65} + 4 q^{66} + 8 q^{67} - 42 q^{68} + 24 q^{69} - 8 q^{71} - 34 q^{72} - 14 q^{73} + 24 q^{74} - q^{75} + 2 q^{76} + 2 q^{78} - 21 q^{79} + 3 q^{81} + 26 q^{82} + 12 q^{83} - 15 q^{85} - 40 q^{86} - 9 q^{87} - 4 q^{88} - 8 q^{89} - 4 q^{90} - 6 q^{92} + q^{93} + 24 q^{94} + 14 q^{95} + 28 q^{96} - 13 q^{97} - 26 q^{99}+O(q^{100}) $ 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9 - 3 * q^11 + 16 * q^12 - 5 * q^13 - q^15 - 15 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 - 10 * q^22 - 6 * q^23 - 16 * q^24 + 11 * q^25 + 14 * q^26 - 13 * q^27 - 15 * q^29 - 8 * q^30 - 11 * q^31 - 5 * q^33 - 16 * q^34 - 12 * q^36 - 24 * q^37 - 18 * q^38 - q^39 - 30 * q^43 - 26 * q^44 - 2 * q^45 - 12 * q^46 - q^47 + 4 * q^48 - 7 * q^51 - 14 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^55 - 30 * q^57 - 14 * q^58 - 2 * q^59 + 16 * q^60 + 10 * q^61 - 16 * q^64 - 5 * q^65 + 4 * q^66 + 8 * q^67 - 42 * q^68 + 24 * q^69 - 8 * q^71 - 34 * q^72 - 14 * q^73 + 24 * q^74 - q^75 + 2 * q^76 + 2 * q^78 - 21 * q^79 + 3 * q^81 + 26 * q^82 + 12 * q^83 - 15 * q^85 - 40 * q^86 - 9 * q^87 - 4 * q^88 - 8 * q^89 - 4 * q^90 - 6 * q^92 + q^93 + 24 * q^94 + 14 * q^95 + 28 * q^96 - 13 * q^97 - 26 * 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 $

$2$	−1.08711	−0.768701	−0.384351	−	0.923187i	$-0.625575\pi$
$2$	−1.08711	−0.768701	−0.384351	+	0.923187i	$0.625575\pi$
$3$	−0.211543	−0.122135	−0.0610673	−	0.998134i	$-0.519450\pi$
$3$	−0.211543	−0.122135	−0.0610673	+	0.998134i	$0.519450\pi$
$4$	−0.818196	−0.409098
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.229970	0.0938850
$7$	0	0
$7$	0	0
$8$	3.06368	1.08318
$9$	−2.95525	−0.985083
$10$	−1.08711	−0.343774
$11$	4.76649	1.43715	0.718575	−	0.695449i	$-0.244795\pi$
$11$	4.76649	1.43715	0.718575	+	0.695449i	$0.244795\pi$
$12$	0.173084	0.0499650
$13$	−5.24166	−1.45377	−0.726887	−	0.686757i	$-0.759034\pi$
$13$	−5.24166	−1.45377	−0.726887	+	0.686757i	$0.759034\pi$
$14$	0	0
$15$	−0.211543	−0.0546202
$16$	−1.69416	−0.423541
$17$	−1.89814	−0.460367	−0.230183	−	0.973147i	$-0.573933\pi$
$17$	−1.89814	−0.460367	−0.230183	+	0.973147i	$0.573933\pi$
$18$	3.21268	0.757235
$19$	7.39723	1.69704	0.848520	−	0.529163i	$-0.177494\pi$
$19$	7.39723	1.69704	0.848520	+	0.529163i	$0.177494\pi$
$20$	−0.818196	−0.182954
$21$	0	0
$22$	−5.18169	−1.10474
$23$	−3.53038	−0.736136	−0.368068	−	0.929799i	$-0.619981\pi$
$23$	−3.53038	−0.736136	−0.368068	+	0.929799i	$0.619981\pi$
$24$	−0.648101	−0.132293
$25$	1.00000	0.200000
$26$	5.69825	1.11752
$27$	1.25979	0.242447
$28$	0	0
$29$	5.59616	1.03918	0.519591	−	0.854415i	$-0.326084\pi$
$29$	5.59616	1.03918	0.519591	+	0.854415i	$0.326084\pi$
$30$	0.229970	0.0419866
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.28563	−0.757599
$33$	−1.00832	−0.175526
$34$	2.06349	0.353885
$35$	0	0
$36$	2.41797	0.402996
$37$	−6.43341	−1.05765	−0.528823	−	0.848732i	$-0.677366\pi$
$37$	−6.43341	−1.05765	−0.528823	+	0.848732i	$0.677366\pi$
$38$	−8.04158	−1.30452
$39$	1.10884	0.177556
$40$	3.06368	0.484411
$41$	3.72972	0.582485	0.291242	−	0.956649i	$-0.405931\pi$
$41$	3.72972	0.582485	0.291242	+	0.956649i	$0.405931\pi$
$42$	0	0
$43$	−8.59603	−1.31088	−0.655441	−	0.755246i	$-0.727517\pi$
$43$	−8.59603	−1.31088	−0.655441	+	0.755246i	$0.727517\pi$
$44$	−3.89992	−0.587935
$45$	−2.95525	−0.440543
$46$	3.83791	0.565869
$47$	−5.54752	−0.809189	−0.404595	−	0.914496i	$-0.632587\pi$
$47$	−5.54752	−0.809189	−0.404595	+	0.914496i	$0.632587\pi$
$48$	0.358389	0.0517290
$49$	0	0
$50$	−1.08711	−0.153740
$51$	0.401539	0.0562267
$52$	4.28870	0.594736
$53$	−3.68850	−0.506654	−0.253327	−	0.967381i	$-0.581525\pi$
$53$	−3.68850	−0.506654	−0.253327	+	0.967381i	$0.581525\pi$
$54$	−1.36953	−0.186370
$55$	4.76649	0.642713
$56$	0	0
$57$	−1.56483	−0.207267
$58$	−6.08363	−0.798820
$59$	13.0271	1.69598	0.847991	−	0.530011i	$-0.177812\pi$
$59$	13.0271	1.69598	0.847991	+	0.530011i	$0.177812\pi$
$60$	0.173084	0.0223450
$61$	−8.88974	−1.13822	−0.569108	−	0.822263i	$-0.692711\pi$
$61$	−8.88974	−1.13822	−0.569108	+	0.822263i	$0.692711\pi$
$62$	1.08711	0.138063
$63$	0	0
$64$	8.04727	1.00591
$65$	−5.24166	−0.650148
$66$	1.09615	0.134927
$67$	7.32359	0.894718	0.447359	−	0.894354i	$-0.352365\pi$
$67$	7.32359	0.894718	0.447359	+	0.894354i	$0.352365\pi$
$68$	1.55305	0.188335
$69$	0.746829	0.0899076
$70$	0	0
$71$	−9.67712	−1.14846	−0.574232	−	0.818693i	$-0.694699\pi$
$71$	−9.67712	−1.14846	−0.574232	+	0.818693i	$0.694699\pi$
$72$	−9.05395	−1.06702
$73$	−1.22727	−0.143641	−0.0718203	−	0.997418i	$-0.522881\pi$
$73$	−1.22727	−0.143641	−0.0718203	+	0.997418i	$0.522881\pi$
$74$	6.99381	0.813014
$75$	−0.211543	−0.0244269
$76$	−6.05238	−0.694256
$77$	0	0
$78$	−1.20543	−0.136488
$79$	15.7558	1.77266	0.886332	−	0.463051i	$-0.153245\pi$
$79$	15.7558	1.77266	0.886332	+	0.463051i	$0.153245\pi$
$80$	−1.69416	−0.189413
$81$	8.59925	0.955472
$82$	−4.05461	−0.447757
$83$	−3.43221	−0.376734	−0.188367	−	0.982099i	$-0.560319\pi$
$83$	−3.43221	−0.376734	−0.188367	+	0.982099i	$0.560319\pi$
$84$	0	0
$85$	−1.89814	−0.205882
$86$	9.34482	1.00768
$87$	−1.18383	−0.126920
$88$	14.6030	1.55669
$89$	−0.165284	−0.0175201	−0.00876004	−	0.999962i	$-0.502788\pi$
$89$	−0.165284	−0.0175201	−0.00876004	+	0.999962i	$0.502788\pi$
$90$	3.21268	0.338646
$91$	0	0
$92$	2.88855	0.301152
$93$	0.211543	0.0219360
$94$	6.03075	0.622025
$95$	7.39723	0.758939
$96$	0.906596	0.0925290
$97$	10.5741	1.07364	0.536820	−	0.843697i	$-0.319625\pi$
$97$	10.5741	1.07364	0.536820	+	0.843697i	$0.319625\pi$
$98$	0	0
$99$	−14.0862	−1.41571
$100$	−0.818196	−0.0818196
$101$	10.7198	1.06666	0.533329	−	0.845908i	$-0.320941\pi$
$101$	10.7198	1.06666	0.533329	+	0.845908i	$0.320941\pi$
$102$	−0.436516	−0.0432216
$103$	−5.54226	−0.546095	−0.273047	−	0.962001i	$-0.588032\pi$
$103$	−5.54226	−0.546095	−0.273047	+	0.962001i	$0.588032\pi$
$104$	−16.0588	−1.57469
$105$	0	0
$106$	4.00979	0.389466
$107$	−12.6086	−1.21892	−0.609462	−	0.792815i	$-0.708615\pi$
$107$	−12.6086	−1.21892	−0.609462	+	0.792815i	$0.708615\pi$
$108$	−1.03076	−0.0991847
$109$	−2.68574	−0.257247	−0.128624	−	0.991693i	$-0.541056\pi$
$109$	−2.68574	−0.257247	−0.128624	+	0.991693i	$0.541056\pi$
$110$	−5.18169	−0.494054
$111$	1.36094	0.129175
$112$	0	0
$113$	−3.64421	−0.342818	−0.171409	−	0.985200i	$-0.554832\pi$
$113$	−3.64421	−0.342818	−0.171409	+	0.985200i	$0.554832\pi$
$114$	1.70114	0.159327
$115$	−3.53038	−0.329210
$116$	−4.57876	−0.425127
$117$	15.4904	1.43209
$118$	−14.1618	−1.30370
$119$	0	0
$120$	−0.648101	−0.0591633
$121$	11.7194	1.06540
$122$	9.66411	0.874948
$123$	−0.788997	−0.0711415
$124$	0.818196	0.0734762
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.8201	−1.04886	−0.524432	−	0.851452i	$-0.675722\pi$
$127$	−11.8201	−1.04886	−0.524432	+	0.851452i	$0.675722\pi$
$128$	−0.176991	−0.0156440
$129$	1.81843	0.160104
$130$	5.69825	0.499769
$131$	−20.5905	−1.79900	−0.899499	−	0.436924i	$-0.856068\pi$
$131$	−20.5905	−1.79900	−0.899499	+	0.436924i	$0.856068\pi$
$132$	0.825002	0.0718072
$133$	0	0
$134$	−7.96153	−0.687771
$135$	1.25979	0.108426
$136$	−5.81531	−0.498658
$137$	9.41956	0.804767	0.402384	−	0.915471i	$-0.368182\pi$
$137$	9.41956	0.804767	0.402384	+	0.915471i	$0.368182\pi$
$138$	−0.811883	−0.0691121
$139$	−19.1542	−1.62464	−0.812319	−	0.583213i	$-0.801795\pi$
$139$	−19.1542	−1.62464	−0.812319	+	0.583213i	$0.801795\pi$
$140$	0	0
$141$	1.17354	0.0988299
$142$	10.5201	0.882825
$143$	−24.9843	−2.08929
$144$	5.00667	0.417223
$145$	5.59616	0.464736
$146$	1.33417	0.110417
$147$	0	0
$148$	5.26379	0.432681
$149$	−23.7924	−1.94915	−0.974575	−	0.224059i	$-0.928069\pi$
$149$	−23.7924	−1.94915	−0.974575	+	0.224059i	$0.928069\pi$
$150$	0.229970	0.0187770
$151$	14.9785	1.21893	0.609466	−	0.792813i	$-0.291384\pi$
$151$	14.9785	1.21893	0.609466	+	0.792813i	$0.291384\pi$
$152$	22.6628	1.83819
$153$	5.60948	0.453500
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	−0.907246	−0.0726378
$157$	23.1172	1.84496	0.922478	−	0.386049i	$-0.126160\pi$
$157$	23.1172	1.84496	0.922478	+	0.386049i	$0.126160\pi$
$158$	−17.1282	−1.36265
$159$	0.780276	0.0618799
$160$	−4.28563	−0.338809
$161$	0	0
$162$	−9.34831	−0.734473
$163$	4.09857	0.321025	0.160512	−	0.987034i	$-0.448685\pi$
$163$	4.09857	0.321025	0.160512	+	0.987034i	$0.448685\pi$
$164$	−3.05164	−0.238293
$165$	−1.00832	−0.0784975
$166$	3.73118	0.289596
$167$	4.38413	0.339254	0.169627	−	0.985508i	$-0.445744\pi$
$167$	4.38413	0.339254	0.169627	+	0.985508i	$0.445744\pi$
$168$	0	0
$169$	14.4750	1.11346
$170$	2.06349	0.158262
$171$	−21.8606	−1.67173
$172$	7.03324	0.536280
$173$	−17.4775	−1.32879	−0.664394	−	0.747382i	$-0.731310\pi$
$173$	−17.4775	−1.32879	−0.664394	+	0.747382i	$0.731310\pi$
$174$	1.28695	0.0975635
$175$	0	0
$176$	−8.07521	−0.608692
$177$	−2.75579	−0.207138
$178$	0.179682	0.0134677
$179$	−14.8271	−1.10823	−0.554115	−	0.832440i	$-0.686943\pi$
$179$	−14.8271	−1.10823	−0.554115	+	0.832440i	$0.686943\pi$
$180$	2.41797	0.180225
$181$	−2.96385	−0.220301	−0.110151	−	0.993915i	$-0.535133\pi$
$181$	−2.96385	−0.220301	−0.110151	+	0.993915i	$0.535133\pi$
$182$	0	0
$183$	1.88057	0.139015
$184$	−10.8160	−0.797364
$185$	−6.43341	−0.472994
$186$	−0.229970	−0.0168622
$187$	−9.04747	−0.661616
$188$	4.53896	0.331038
$189$	0	0
$190$	−8.04158	−0.583398
$191$	5.86955	0.424705	0.212353	−	0.977193i	$-0.431887\pi$
$191$	5.86955	0.424705	0.212353	+	0.977193i	$0.431887\pi$
$192$	−1.70234	−0.122856
$193$	11.8750	0.854783	0.427391	−	0.904067i	$-0.359433\pi$
$193$	11.8750	0.854783	0.427391	+	0.904067i	$0.359433\pi$
$194$	−11.4952	−0.825309
$195$	1.10884	0.0794055
$196$	0	0
$197$	16.2164	1.15537	0.577686	−	0.816259i	$-0.303956\pi$
$197$	16.2164	1.15537	0.577686	+	0.816259i	$0.303956\pi$
$198$	15.3132	1.08826
$199$	−6.93497	−0.491607	−0.245804	−	0.969320i	$-0.579052\pi$
$199$	−6.93497	−0.491607	−0.245804	+	0.969320i	$0.579052\pi$
$200$	3.06368	0.216635
$201$	−1.54925	−0.109276
$202$	−11.6536	−0.819942
$203$	0	0
$204$	−0.328538	−0.0230022
$205$	3.72972	0.260495
$206$	6.02503	0.419784
$207$	10.4332	0.725155
$208$	8.88022	0.615733
$209$	35.2588	2.43890
$210$	0	0
$211$	−8.46445	−0.582717	−0.291358	−	0.956614i	$-0.594107\pi$
$211$	−8.46445	−0.582717	−0.291358	+	0.956614i	$0.594107\pi$
$212$	3.01791	0.207271
$213$	2.04713	0.140267
$214$	13.7070	0.936989
$215$	−8.59603	−0.586245
$216$	3.85961	0.262613
$217$	0	0
$218$	2.91969	0.197746
$219$	0.259620	0.0175435
$220$	−3.89992	−0.262933
$221$	9.94941	0.669270
$222$	−1.47949	−0.0992971
$223$	−18.8795	−1.26427	−0.632133	−	0.774860i	$-0.717820\pi$
$223$	−18.8795	−1.26427	−0.632133	+	0.774860i	$0.717820\pi$
$224$	0	0
$225$	−2.95525	−0.197017
$226$	3.96165	0.263525
$227$	4.49146	0.298109	0.149054	−	0.988829i	$-0.452377\pi$
$227$	4.49146	0.298109	0.149054	+	0.988829i	$0.452377\pi$
$228$	1.28034	0.0847926
$229$	22.7805	1.50538	0.752689	−	0.658377i	$-0.228757\pi$
$229$	22.7805	1.50538	0.752689	+	0.658377i	$0.228757\pi$
$230$	3.83791	0.253064
$231$	0	0
$232$	17.1449	1.12562
$233$	−10.5922	−0.693917	−0.346959	−	0.937880i	$-0.612786\pi$
$233$	−10.5922	−0.693917	−0.346959	+	0.937880i	$0.612786\pi$
$234$	−16.8397	−1.10085
$235$	−5.54752	−0.361880
$236$	−10.6587	−0.693823
$237$	−3.33303	−0.216503
$238$	0	0
$239$	17.2829	1.11794	0.558970	−	0.829188i	$-0.311197\pi$
$239$	17.2829	1.11794	0.558970	+	0.829188i	$0.311197\pi$
$240$	0.358389	0.0231339
$241$	3.19162	0.205590	0.102795	−	0.994703i	$-0.467221\pi$
$241$	3.19162	0.205590	0.102795	+	0.994703i	$0.467221\pi$
$242$	−12.7403	−0.818975
$243$	−5.59849	−0.359143
$244$	7.27355	0.465642
$245$	0	0
$246$	0.857725	0.0546866
$247$	−38.7737	−2.46711
$248$	−3.06368	−0.194544
$249$	0.726060	0.0460122
$250$	−1.08711	−0.0687547
$251$	−8.82377	−0.556951	−0.278476	−	0.960443i	$-0.589829\pi$
$251$	−8.82377	−0.556951	−0.278476	+	0.960443i	$0.589829\pi$
$252$	0	0
$253$	−16.8275	−1.05794
$254$	12.8497	0.806264
$255$	0.401539	0.0251453
$256$	−15.9021	−0.993883
$257$	21.6287	1.34916	0.674581	−	0.738201i	$-0.264325\pi$
$257$	21.6287	1.34916	0.674581	+	0.738201i	$0.264325\pi$
$258$	−1.97683	−0.123072
$259$	0	0
$260$	4.28870	0.265974
$261$	−16.5381	−1.02368
$262$	22.3841	1.38289
$263$	−26.7437	−1.64909	−0.824544	−	0.565798i	$-0.808568\pi$
$263$	−26.7437	−1.64909	−0.824544	+	0.565798i	$0.808568\pi$
$264$	−3.08917	−0.190125
$265$	−3.68850	−0.226582
$266$	0	0
$267$	0.0349647	0.00213981
$268$	−5.99213	−0.366028
$269$	1.46729	0.0894621	0.0447310	−	0.998999i	$-0.485757\pi$
$269$	1.46729	0.0894621	0.0447310	+	0.998999i	$0.485757\pi$
$270$	−1.36953	−0.0833470
$271$	10.0564	0.610885	0.305443	−	0.952210i	$-0.401196\pi$
$271$	10.0564	0.610885	0.305443	+	0.952210i	$0.401196\pi$
$272$	3.21576	0.194984
$273$	0	0
$274$	−10.2401	−0.618626
$275$	4.76649	0.287430
$276$	−0.611052	−0.0367810
$277$	−25.4485	−1.52905	−0.764525	−	0.644594i	$-0.777027\pi$
$277$	−25.4485	−1.52905	−0.764525	+	0.644594i	$0.777027\pi$
$278$	20.8227	1.24886
$279$	2.95525	0.176926
$280$	0	0
$281$	−4.10486	−0.244875	−0.122438	−	0.992476i	$-0.539071\pi$
$281$	−4.10486	−0.244875	−0.122438	+	0.992476i	$0.539071\pi$
$282$	−1.27577	−0.0759707
$283$	27.5693	1.63883	0.819413	−	0.573204i	$-0.194300\pi$
$283$	27.5693	1.63883	0.819413	+	0.573204i	$0.194300\pi$
$284$	7.91778	0.469834
$285$	−1.56483	−0.0926927
$286$	27.1606	1.60604
$287$	0	0
$288$	12.6651	0.746298
$289$	−13.3971	−0.788062
$290$	−6.08363	−0.357243
$291$	−2.23689	−0.131129
$292$	1.00414	0.0587631
$293$	−3.86999	−0.226087	−0.113044	−	0.993590i	$-0.536060\pi$
$293$	−3.86999	−0.226087	−0.113044	+	0.993590i	$0.536060\pi$
$294$	0	0
$295$	13.0271	0.758466
$296$	−19.7099	−1.14562
$297$	6.00479	0.348433
$298$	25.8649	1.49832
$299$	18.5051	1.07018
$300$	0.173084	0.00999300
$301$	0	0
$302$	−16.2832	−0.936994
$303$	−2.26770	−0.130276
$304$	−12.5321	−0.718766
$305$	−8.88974	−0.509025
$306$	−6.09811	−0.348606
$307$	27.0794	1.54551	0.772753	−	0.634707i	$-0.218879\pi$
$307$	27.0794	1.54551	0.772753	+	0.634707i	$0.218879\pi$
$308$	0	0
$309$	1.17243	0.0666970
$310$	1.08711	0.0617436
$311$	22.4647	1.27385	0.636927	−	0.770924i	$-0.280205\pi$
$311$	22.4647	1.27385	0.636927	+	0.770924i	$0.280205\pi$
$312$	3.39713	0.192324
$313$	3.83548	0.216794	0.108397	−	0.994108i	$-0.465428\pi$
$313$	3.83548	0.216794	0.108397	+	0.994108i	$0.465428\pi$
$314$	−25.1309	−1.41822
$315$	0	0
$316$	−12.8913	−0.725193
$317$	26.4713	1.48678	0.743388	−	0.668860i	$-0.233218\pi$
$317$	26.4713	1.48678	0.743388	+	0.668860i	$0.233218\pi$
$318$	−0.848245	−0.0475672
$319$	26.6740	1.49346
$320$	8.04727	0.449856
$321$	2.66727	0.148873
$322$	0	0
$323$	−14.0410	−0.781261
$324$	−7.03587	−0.390882
$325$	−5.24166	−0.290755
$326$	−4.45559	−0.246772
$327$	0.568150	0.0314188
$328$	11.4267	0.630933
$329$	0	0
$330$	1.09615	0.0603411
$331$	−28.1726	−1.54850	−0.774252	−	0.632877i	$-0.781874\pi$
$331$	−28.1726	−1.54850	−0.774252	+	0.632877i	$0.781874\pi$
$332$	2.80822	0.154121
$333$	19.0123	1.04187
$334$	−4.76603	−0.260785
$335$	7.32359	0.400130
$336$	0	0
$337$	−1.02289	−0.0557205	−0.0278602	−	0.999612i	$-0.508869\pi$
$337$	−1.02289	−0.0557205	−0.0278602	+	0.999612i	$0.508869\pi$
$338$	−15.7359	−0.855918
$339$	0.770908	0.0418700
$340$	1.55305	0.0842261
$341$	−4.76649	−0.258120
$342$	23.7649	1.28506
$343$	0	0
$344$	−26.3355	−1.41992
$345$	0.746829	0.0402079
$346$	18.9999	1.02144
$347$	20.3800	1.09406	0.547029	−	0.837114i	$-0.315759\pi$
$347$	20.3800	1.09406	0.547029	+	0.837114i	$0.315759\pi$
$348$	0.968605	0.0519227
$349$	−4.55388	−0.243764	−0.121882	−	0.992545i	$-0.538893\pi$
$349$	−4.55388	−0.243764	−0.121882	+	0.992545i	$0.538893\pi$
$350$	0	0
$351$	−6.60340	−0.352463
$352$	−20.4274	−1.08878
$353$	−10.9462	−0.582610	−0.291305	−	0.956630i	$-0.594089\pi$
$353$	−10.9462	−0.582610	−0.291305	+	0.956630i	$0.594089\pi$
$354$	2.99584	0.159227
$355$	−9.67712	−0.513608
$356$	0.135235	0.00716743
$357$	0	0
$358$	16.1187	0.851898
$359$	−14.1489	−0.746751	−0.373376	−	0.927680i	$-0.621800\pi$
$359$	−14.1489	−0.746751	−0.373376	+	0.927680i	$0.621800\pi$
$360$	−9.05395	−0.477185
$361$	35.7189	1.87994
$362$	3.22203	0.169346
$363$	−2.47916	−0.130122
$364$	0	0
$365$	−1.22727	−0.0642381
$366$	−2.04438	−0.106861
$367$	−32.3508	−1.68870	−0.844350	−	0.535793i	$-0.820013\pi$
$367$	−32.3508	−1.68870	−0.844350	+	0.535793i	$0.820013\pi$
$368$	5.98104	0.311784
$369$	−11.0223	−0.573796
$370$	6.99381	0.363591
$371$	0	0
$372$	−0.173084	−0.00897398
$373$	−32.6181	−1.68890	−0.844451	−	0.535632i	$-0.820073\pi$
$373$	−32.6181	−1.68890	−0.844451	+	0.535632i	$0.820073\pi$
$374$	9.83558	0.508585
$375$	−0.211543	−0.0109240
$376$	−16.9958	−0.876494
$377$	−29.3332	−1.51073
$378$	0	0
$379$	−23.0740	−1.18523	−0.592615	−	0.805485i	$-0.701905\pi$
$379$	−23.0740	−1.18523	−0.592615	+	0.805485i	$0.701905\pi$
$380$	−6.05238	−0.310481
$381$	2.50046	0.128103
$382$	−6.38083	−0.326472
$383$	−32.7736	−1.67465	−0.837327	−	0.546702i	$-0.815883\pi$
$383$	−32.7736	−1.67465	−0.837327	+	0.546702i	$0.815883\pi$
$384$	0.0374413	0.00191067
$385$	0	0
$386$	−12.9094	−0.657073
$387$	25.4034	1.29133
$388$	−8.65172	−0.439224
$389$	−26.5050	−1.34386	−0.671928	−	0.740617i	$-0.734533\pi$
$389$	−26.5050	−1.34386	−0.671928	+	0.740617i	$0.734533\pi$
$390$	−1.20543	−0.0610391
$391$	6.70117	0.338893
$392$	0	0
$393$	4.35577	0.219720
$394$	−17.6290	−0.888136
$395$	15.7558	0.792759
$396$	11.5252	0.579165
$397$	20.0291	1.00523	0.502616	−	0.864510i	$-0.332371\pi$
$397$	20.0291	1.00523	0.502616	+	0.864510i	$0.332371\pi$
$398$	7.53907	0.377899
$399$	0	0
$400$	−1.69416	−0.0847081
$401$	−34.7186	−1.73376	−0.866881	−	0.498514i	$-0.833879\pi$
$401$	−34.7186	−1.73376	−0.866881	+	0.498514i	$0.833879\pi$
$402$	1.68421	0.0840006
$403$	5.24166	0.261106
$404$	−8.77089	−0.436368
$405$	8.59925	0.427300
$406$	0	0
$407$	−30.6648	−1.52000
$408$	1.23019	0.0609034
$409$	−0.449745	−0.0222385	−0.0111192	−	0.999938i	$-0.503539\pi$
$409$	−0.449745	−0.0222385	−0.0111192	+	0.999938i	$0.503539\pi$
$410$	−4.05461	−0.200243
$411$	−1.99264	−0.0982899
$412$	4.53465	0.223406
$413$	0	0
$414$	−11.3420	−0.557428
$415$	−3.43221	−0.168480
$416$	22.4638	1.10138
$417$	4.05194	0.198424
$418$	−38.3301	−1.87479
$419$	18.8435	0.920565	0.460283	−	0.887772i	$-0.347748\pi$
$419$	18.8435	0.920565	0.460283	+	0.887772i	$0.347748\pi$
$420$	0	0
$421$	12.4930	0.608870	0.304435	−	0.952533i	$-0.401532\pi$
$421$	12.4930	0.608870	0.304435	+	0.952533i	$0.401532\pi$
$422$	9.20177	0.447935
$423$	16.3943	0.797119
$424$	−11.3004	−0.548795
$425$	−1.89814	−0.0920734
$426$	−2.22545	−0.107823
$427$	0	0
$428$	10.3163	0.498659
$429$	5.28526	0.255175
$430$	9.34482	0.450647
$431$	−14.9959	−0.722327	−0.361164	−	0.932502i	$-0.617620\pi$
$431$	−14.9959	−0.722327	−0.361164	+	0.932502i	$0.617620\pi$
$432$	−2.13429	−0.102686
$433$	−4.66175	−0.224029	−0.112015	−	0.993707i	$-0.535730\pi$
$433$	−4.66175	−0.224029	−0.112015	+	0.993707i	$0.535730\pi$
$434$	0	0
$435$	−1.18383	−0.0567603
$436$	2.19746	0.105239
$437$	−26.1150	−1.24925
$438$	−0.282235	−0.0134857
$439$	15.3709	0.733615	0.366808	−	0.930297i	$-0.380451\pi$
$439$	15.3709	0.733615	0.366808	+	0.930297i	$0.380451\pi$
$440$	14.6030	0.696171
$441$	0	0
$442$	−10.8161	−0.514469
$443$	5.30286	0.251947	0.125973	−	0.992034i	$-0.459795\pi$
$443$	5.30286	0.251947	0.125973	+	0.992034i	$0.459795\pi$
$444$	−1.11352	−0.0528453
$445$	−0.165284	−0.00783522
$446$	20.5241	0.971843
$447$	5.03313	0.238059
$448$	0	0
$449$	−29.8084	−1.40675	−0.703373	−	0.710821i	$-0.748324\pi$
$449$	−29.8084	−1.40675	−0.703373	+	0.710821i	$0.748324\pi$
$450$	3.21268	0.151447
$451$	17.7777	0.837118
$452$	2.98168	0.140246
$453$	−3.16859	−0.148874
$454$	−4.88270	−0.229157
$455$	0	0
$456$	−4.79415	−0.224507
$457$	−10.5919	−0.495469	−0.247735	−	0.968828i	$-0.579686\pi$
$457$	−10.5919	−0.495469	−0.247735	+	0.968828i	$0.579686\pi$
$458$	−24.7649	−1.15719
$459$	−2.39126	−0.111615
$460$	2.88855	0.134679
$461$	−30.3556	−1.41380	−0.706900	−	0.707314i	$-0.749907\pi$
$461$	−30.3556	−1.41380	−0.706900	+	0.707314i	$0.749907\pi$
$462$	0	0
$463$	−6.58972	−0.306250	−0.153125	−	0.988207i	$-0.548934\pi$
$463$	−6.58972	−0.306250	−0.153125	+	0.988207i	$0.548934\pi$
$464$	−9.48081	−0.440136
$465$	0.211543	0.00981008
$466$	11.5148	0.533415
$467$	−7.31702	−0.338591	−0.169296	−	0.985565i	$-0.554149\pi$
$467$	−7.31702	−0.338591	−0.169296	+	0.985565i	$0.554149\pi$
$468$	−12.6742	−0.585865
$469$	0	0
$470$	6.03075	0.278178
$471$	−4.89030	−0.225333
$472$	39.9109	1.83705
$473$	−40.9729	−1.88394
$474$	3.62336	0.166426
$475$	7.39723	0.339408
$476$	0	0
$477$	10.9004	0.499096
$478$	−18.7884	−0.859362
$479$	−38.2298	−1.74677	−0.873383	−	0.487034i	$-0.838079\pi$
$479$	−38.2298	−1.74677	−0.873383	+	0.487034i	$0.838079\pi$
$480$	0.906596	0.0413802
$481$	33.7217	1.53758
$482$	−3.46963	−0.158038
$483$	0	0
$484$	−9.58877	−0.435853
$485$	10.5741	0.480147
$486$	6.08616	0.276074
$487$	−36.5218	−1.65496	−0.827480	−	0.561495i	$-0.810227\pi$
$487$	−36.5218	−1.65496	−0.827480	+	0.561495i	$0.810227\pi$
$488$	−27.2354	−1.23289
$489$	−0.867024	−0.0392082
$490$	0	0
$491$	−3.30037	−0.148944	−0.0744718	−	0.997223i	$-0.523727\pi$
$491$	−3.30037	−0.148944	−0.0744718	+	0.997223i	$0.523727\pi$
$492$	0.645554	0.0291038
$493$	−10.6223	−0.478405
$494$	42.1512	1.89647
$495$	−14.0862	−0.633126
$496$	1.69416	0.0760702
$497$	0	0
$498$	−0.789306	−0.0353696
$499$	7.56406	0.338614	0.169307	−	0.985563i	$-0.445847\pi$
$499$	7.56406	0.338614	0.169307	+	0.985563i	$0.445847\pi$
$500$	−0.818196	−0.0365908
$501$	−0.927433	−0.0414347
$502$	9.59239	0.428129
$503$	−22.2525	−0.992190	−0.496095	−	0.868268i	$-0.665233\pi$
$503$	−22.2525	−0.992190	−0.496095	+	0.868268i	$0.665233\pi$
$504$	0	0
$505$	10.7198	0.477024
$506$	18.2933	0.813238
$507$	−3.06208	−0.135992
$508$	9.67116	0.429088
$509$	2.30928	0.102357	0.0511785	−	0.998690i	$-0.483702\pi$
$509$	2.30928	0.102357	0.0511785	+	0.998690i	$0.483702\pi$
$510$	−0.436516	−0.0193293
$511$	0	0
$512$	17.6413	0.779643
$513$	9.31897	0.411443
$514$	−23.5127	−1.03710
$515$	−5.54226	−0.244221
$516$	−1.48783	−0.0654983
$517$	−26.4422	−1.16293
$518$	0	0
$519$	3.69724	0.162291
$520$	−16.0588	−0.704224
$521$	−22.6616	−0.992821	−0.496411	−	0.868088i	$-0.665349\pi$
$521$	−22.6616	−0.992821	−0.496411	+	0.868088i	$0.665349\pi$
$522$	17.9787	0.786904
$523$	−6.08924	−0.266264	−0.133132	−	0.991098i	$-0.542503\pi$
$523$	−6.08924	−0.266264	−0.133132	+	0.991098i	$0.542503\pi$
$524$	16.8470	0.735966
$525$	0	0
$526$	29.0733	1.26766
$527$	1.89814	0.0826843
$528$	1.70826	0.0743423
$529$	−10.5364	−0.458104
$530$	4.00979	0.174174
$531$	−38.4983	−1.67068
$532$	0	0
$533$	−19.5499	−0.846801
$534$	−0.0380104	−0.00164487
$535$	−12.6086	−0.545119
$536$	22.4371	0.969137
$537$	3.13657	0.135353
$538$	−1.59510	−0.0687696
$539$	0	0
$540$	−1.03076	−0.0443567
$541$	−20.4167	−0.877782	−0.438891	−	0.898540i	$-0.644629\pi$
$541$	−20.4167	−0.877782	−0.438891	+	0.898540i	$0.644629\pi$
$542$	−10.9324	−0.469589
$543$	0.626983	0.0269064
$544$	8.13473	0.348774
$545$	−2.68574	−0.115044
$546$	0	0
$547$	14.7180	0.629298	0.314649	−	0.949208i	$-0.398113\pi$
$547$	14.7180	0.629298	0.314649	+	0.949208i	$0.398113\pi$
$548$	−7.70705	−0.329229
$549$	26.2714	1.12124
$550$	−5.18169	−0.220948
$551$	41.3961	1.76353
$552$	2.28805	0.0973857
$553$	0	0
$554$	27.6652	1.17538
$555$	1.36094	0.0577688
$556$	15.6719	0.664637
$557$	21.0020	0.889884	0.444942	−	0.895559i	$-0.353224\pi$
$557$	21.0020	0.889884	0.444942	+	0.895559i	$0.353224\pi$
$558$	−3.21268	−0.136003
$559$	45.0575	1.90573
$560$	0	0
$561$	1.91393	0.0808062
$562$	4.46243	0.188236
$563$	35.8416	1.51055	0.755273	−	0.655411i	$-0.227504\pi$
$563$	35.8416	1.51055	0.755273	+	0.655411i	$0.227504\pi$
$564$	−0.960186	−0.0404311
$565$	−3.64421	−0.153313
$566$	−29.9708	−1.25977
$567$	0	0
$568$	−29.6476	−1.24399
$569$	5.12670	0.214923	0.107461	−	0.994209i	$-0.465728\pi$
$569$	5.12670	0.214923	0.107461	+	0.994209i	$0.465728\pi$
$570$	1.70114	0.0712530
$571$	−21.1250	−0.884053	−0.442027	−	0.897002i	$-0.645740\pi$
$571$	−21.1250	−0.884053	−0.442027	+	0.897002i	$0.645740\pi$
$572$	20.4421	0.854725
$573$	−1.24166	−0.0518712
$574$	0	0
$575$	−3.53038	−0.147227
$576$	−23.7817	−0.990903
$577$	27.9316	1.16281	0.581404	−	0.813615i	$-0.302504\pi$
$577$	27.9316	1.16281	0.581404	+	0.813615i	$0.302504\pi$
$578$	14.5640	0.605785
$579$	−2.51208	−0.104399
$580$	−4.57876	−0.190123
$581$	0	0
$582$	2.43174	0.100799
$583$	−17.5812	−0.728138
$584$	−3.75996	−0.155588
$585$	15.4904	0.640449
$586$	4.20710	0.173794
$587$	7.58963	0.313257	0.156629	−	0.987658i	$-0.449937\pi$
$587$	7.58963	0.313257	0.156629	+	0.987658i	$0.449937\pi$
$588$	0	0
$589$	−7.39723	−0.304797
$590$	−14.1618	−0.583034
$591$	−3.43047	−0.141111
$592$	10.8992	0.447956
$593$	−35.1823	−1.44476	−0.722381	−	0.691495i	$-0.756952\pi$
$593$	−35.1823	−1.44476	−0.722381	+	0.691495i	$0.756952\pi$
$594$	−6.52785	−0.267841
$595$	0	0
$596$	19.4669	0.797394
$597$	1.46705	0.0600422
$598$	−20.1170	−0.822645
$599$	−11.0619	−0.451976	−0.225988	−	0.974130i	$-0.572561\pi$
$599$	−11.0619	−0.451976	−0.225988	+	0.974130i	$0.572561\pi$
$600$	−0.648101	−0.0264586
$601$	−19.5892	−0.799061	−0.399531	−	0.916720i	$-0.630827\pi$
$601$	−19.5892	−0.799061	−0.399531	+	0.916720i	$0.630827\pi$
$602$	0	0
$603$	−21.6430	−0.881372
$604$	−12.2553	−0.498662
$605$	11.7194	0.476461
$606$	2.46523	0.100143
$607$	−33.4922	−1.35941	−0.679704	−	0.733487i	$-0.737892\pi$
$607$	−33.4922	−1.35941	−0.679704	+	0.733487i	$0.737892\pi$
$608$	−31.7018	−1.28568
$609$	0	0
$610$	9.66411	0.391288
$611$	29.0782	1.17638
$612$	−4.58966	−0.185526
$613$	5.15438	0.208184	0.104092	−	0.994568i	$-0.466806\pi$
$613$	5.15438	0.208184	0.104092	+	0.994568i	$0.466806\pi$
$614$	−29.4383	−1.18803
$615$	−0.788997	−0.0318154
$616$	0	0
$617$	−22.7767	−0.916957	−0.458478	−	0.888706i	$-0.651605\pi$
$617$	−22.7767	−0.916957	−0.458478	+	0.888706i	$0.651605\pi$
$618$	−1.27455	−0.0512701
$619$	−21.6801	−0.871396	−0.435698	−	0.900093i	$-0.643498\pi$
$619$	−21.6801	−0.871396	−0.435698	+	0.900093i	$0.643498\pi$
$620$	0.818196	0.0328595
$621$	−4.44755	−0.178474
$622$	−24.4215	−0.979214
$623$	0	0
$624$	−1.87855	−0.0752022
$625$	1.00000	0.0400000
$626$	−4.16958	−0.166650
$627$	−7.45876	−0.297874
$628$	−18.9144	−0.754768
$629$	12.2115	0.486905
$630$	0	0
$631$	−16.2065	−0.645172	−0.322586	−	0.946540i	$-0.604552\pi$
$631$	−16.2065	−0.645172	−0.322586	+	0.946540i	$0.604552\pi$
$632$	48.2707	1.92011
$633$	1.79060	0.0711698
$634$	−28.7772	−1.14289
$635$	−11.8201	−0.469066
$636$	−0.638419	−0.0253150
$637$	0	0
$638$	−28.9976	−1.14802
$639$	28.5983	1.13133
$640$	−0.176991	−0.00699620
$641$	−34.4042	−1.35888	−0.679442	−	0.733730i	$-0.737778\pi$
$641$	−34.4042	−1.35888	−0.679442	+	0.733730i	$0.737778\pi$
$642$	−2.89962	−0.114439
$643$	41.4330	1.63396	0.816979	−	0.576667i	$-0.195647\pi$
$643$	41.4330	1.63396	0.816979	+	0.576667i	$0.195647\pi$
$644$	0	0
$645$	1.81843	0.0716007
$646$	15.2641	0.600557
$647$	−9.03373	−0.355152	−0.177576	−	0.984107i	$-0.556826\pi$
$647$	−9.03373	−0.355152	−0.177576	+	0.984107i	$0.556826\pi$
$648$	26.3454	1.03494
$649$	62.0934	2.43738
$650$	5.69825	0.223504
$651$	0	0
$652$	−3.35343	−0.131331
$653$	−1.87109	−0.0732216	−0.0366108	−	0.999330i	$-0.511656\pi$
$653$	−1.87109	−0.0732216	−0.0366108	+	0.999330i	$0.511656\pi$
$654$	−0.617641	−0.0241517
$655$	−20.5905	−0.804536
$656$	−6.31875	−0.246706
$657$	3.62688	0.141498
$658$	0	0
$659$	−28.7629	−1.12044	−0.560221	−	0.828343i	$-0.689284\pi$
$659$	−28.7629	−1.12044	−0.560221	+	0.828343i	$0.689284\pi$
$660$	0.825002	0.0321132
$661$	−33.4727	−1.30194	−0.650968	−	0.759105i	$-0.725637\pi$
$661$	−33.4727	−1.30194	−0.650968	+	0.759105i	$0.725637\pi$
$662$	30.6266	1.19034
$663$	−2.10473	−0.0817409
$664$	−10.5152	−0.408069
$665$	0	0
$666$	−20.6685	−0.800886
$667$	−19.7566	−0.764979
$668$	−3.58708	−0.138788
$669$	3.99383	0.154410
$670$	−7.96153	−0.307581
$671$	−42.3729	−1.63579
$672$	0	0
$673$	−43.3555	−1.67123	−0.835616	−	0.549313i	$-0.814889\pi$
$673$	−43.3555	−1.67123	−0.835616	+	0.549313i	$0.814889\pi$
$674$	1.11199	0.0428324
$675$	1.25979	0.0484894
$676$	−11.8434	−0.455514
$677$	−39.3617	−1.51279	−0.756397	−	0.654112i	$-0.773042\pi$
$677$	−39.3617	−1.51279	−0.756397	+	0.654112i	$0.773042\pi$
$678$	−0.838060	−0.0321855
$679$	0	0
$680$	−5.81531	−0.223007
$681$	−0.950138	−0.0364094
$682$	5.18169	0.198417
$683$	−10.8276	−0.414308	−0.207154	−	0.978308i	$-0.566420\pi$
$683$	−10.8276	−0.414308	−0.207154	+	0.978308i	$0.566420\pi$
$684$	17.8863	0.683900
$685$	9.41956	0.359903
$686$	0	0
$687$	−4.81906	−0.183859
$688$	14.5631	0.555212
$689$	19.3338	0.736560
$690$	−0.811883	−0.0309079
$691$	12.4102	0.472108	0.236054	−	0.971740i	$-0.424146\pi$
$691$	12.4102	0.472108	0.236054	+	0.971740i	$0.424146\pi$
$692$	14.3000	0.543605
$693$	0	0
$694$	−22.1553	−0.841004
$695$	−19.1542	−0.726561
$696$	−3.62688	−0.137477
$697$	−7.07954	−0.268157
$698$	4.95056	0.187381
$699$	2.24070	0.0847512
$700$	0	0
$701$	14.6397	0.552934	0.276467	−	0.961023i	$-0.410836\pi$
$701$	14.6397	0.552934	0.276467	+	0.961023i	$0.410836\pi$
$702$	7.17861	0.270939
$703$	−47.5894	−1.79487
$704$	38.3572	1.44564
$705$	1.17354	0.0441981
$706$	11.8998	0.447853
$707$	0	0
$708$	2.25478	0.0847397
$709$	3.00528	0.112866	0.0564329	−	0.998406i	$-0.482027\pi$
$709$	3.00528	0.112866	0.0564329	+	0.998406i	$0.482027\pi$
$710$	10.5201	0.394812
$711$	−46.5623	−1.74622
$712$	−0.506378	−0.0189773
$713$	3.53038	0.132214
$714$	0	0
$715$	−24.9843	−0.934360
$716$	12.1315	0.453375
$717$	−3.65609	−0.136539
$718$	15.3814	0.574029
$719$	23.1910	0.864878	0.432439	−	0.901663i	$-0.357653\pi$
$719$	23.1910	0.864878	0.432439	+	0.901663i	$0.357653\pi$
$720$	5.00667	0.186588
$721$	0	0
$722$	−38.8303	−1.44512
$723$	−0.675165	−0.0251097
$724$	2.42501	0.0901249
$725$	5.59616	0.207836
$726$	2.69511	0.100025
$727$	−44.1700	−1.63817	−0.819087	−	0.573669i	$-0.805520\pi$
$727$	−44.1700	−1.63817	−0.819087	+	0.573669i	$0.805520\pi$
$728$	0	0
$729$	−24.6134	−0.911608
$730$	1.33417	0.0493799
$731$	16.3165	0.603487
$732$	−1.53867	−0.0568709
$733$	−25.1926	−0.930511	−0.465256	−	0.885176i	$-0.654038\pi$
$733$	−25.1926	−0.930511	−0.465256	+	0.885176i	$0.654038\pi$
$734$	35.1688	1.29811
$735$	0	0
$736$	15.1299	0.557696
$737$	34.9078	1.28584
$738$	11.9824	0.441078
$739$	13.1271	0.482888	0.241444	−	0.970415i	$-0.422379\pi$
$739$	13.1271	0.482888	0.241444	+	0.970415i	$0.422379\pi$
$740$	5.26379	0.193501
$741$	8.20232	0.301320
$742$	0	0
$743$	24.4994	0.898797	0.449398	−	0.893332i	$-0.351638\pi$
$743$	24.4994	0.898797	0.449398	+	0.893332i	$0.351638\pi$
$744$	0.648101	0.0237606
$745$	−23.7924	−0.871687
$746$	35.4594	1.29826
$747$	10.1430	0.371114
$748$	7.40260	0.270666
$749$	0	0
$750$	0.229970	0.00839733
$751$	−16.9698	−0.619236	−0.309618	−	0.950861i	$-0.600201\pi$
$751$	−16.9698	−0.619236	−0.309618	+	0.950861i	$0.600201\pi$
$752$	9.39840	0.342725
$753$	1.86661	0.0680230
$754$	31.8883	1.16130
$755$	14.9785	0.545123
$756$	0	0
$757$	−0.0285706	−0.00103842	−0.000519208	−	1.00000i	$-0.500165\pi$
$757$	−0.0285706	−0.00103842	−0.000519208		1.00000i	$0.500165\pi$
$758$	25.0839	0.911089
$759$	3.55975	0.129211
$760$	22.6628	0.822065
$761$	30.5995	1.10923	0.554616	−	0.832106i	$-0.312865\pi$
$761$	30.5995	1.10923	0.554616	+	0.832106i	$0.312865\pi$
$762$	−2.71827	−0.0984726
$763$	0	0
$764$	−4.80244	−0.173746
$765$	5.60948	0.202811
$766$	35.6285	1.28731
$767$	−68.2835	−2.46557
$768$	3.36399	0.121387
$769$	16.8431	0.607379	0.303689	−	0.952771i	$-0.401781\pi$
$769$	16.8431	0.607379	0.303689	+	0.952771i	$0.401781\pi$
$770$	0	0
$771$	−4.57540	−0.164779
$772$	−9.71610	−0.349690
$773$	15.7220	0.565480	0.282740	−	0.959197i	$-0.408757\pi$
$773$	15.7220	0.565480	0.282740	+	0.959197i	$0.408757\pi$
$774$	−27.6163	−0.992646
$775$	−1.00000	−0.0359211
$776$	32.3958	1.16294
$777$	0	0
$778$	28.8138	1.03302
$779$	27.5896	0.988499
$780$	−0.907246	−0.0324846
$781$	−46.1259	−1.65051
$782$	−7.28489	−0.260507
$783$	7.05000	0.251947
$784$	0	0
$785$	23.1172	0.825090
$786$	−4.73520	−0.168899
$787$	−35.2331	−1.25592	−0.627961	−	0.778245i	$-0.716110\pi$
$787$	−35.2331	−1.25592	−0.627961	+	0.778245i	$0.716110\pi$
$788$	−13.2682	−0.472660
$789$	5.65745	0.201411
$790$	−17.1282	−0.609395
$791$	0	0
$792$	−43.1555	−1.53347
$793$	46.5970	1.65471
$794$	−21.7738	−0.772723
$795$	0.780276	0.0276735
$796$	5.67417	0.201116
$797$	−0.418101	−0.0148099	−0.00740494	−	0.999973i	$-0.502357\pi$
$797$	−0.418101	−0.0148099	−0.00740494	+	0.999973i	$0.502357\pi$
$798$	0	0
$799$	10.5300	0.372524
$800$	−4.28563	−0.151520
$801$	0.488456	0.0172587
$802$	37.7428	1.33275
$803$	−5.84975	−0.206433
$804$	1.26759	0.0447046
$805$	0	0
$806$	−5.69825	−0.200712
$807$	−0.310395	−0.0109264
$808$	32.8420	1.15538
$809$	−53.9500	−1.89678	−0.948390	−	0.317107i	$-0.897289\pi$
$809$	−53.9500	−1.89678	−0.948390	+	0.317107i	$0.897289\pi$
$810$	−9.34831	−0.328466
$811$	32.4684	1.14012	0.570061	−	0.821603i	$-0.306920\pi$
$811$	32.4684	1.14012	0.570061	+	0.821603i	$0.306920\pi$
$812$	0	0
$813$	−2.12737	−0.0746102
$814$	33.3359	1.16842
$815$	4.09857	0.143567
$816$	−0.680272	−0.0238143
$817$	−63.5868	−2.22462
$818$	0.488922	0.0170947
$819$	0	0
$820$	−3.05164	−0.106568
$821$	−0.0404587	−0.00141202	−0.000706010	−	1.00000i	$-0.500225\pi$
$821$	−0.0404587	−0.00141202	−0.000706010		1.00000i	$0.500225\pi$
$822$	2.16622	0.0755556
$823$	−19.5796	−0.682502	−0.341251	−	0.939972i	$-0.610851\pi$
$823$	−19.5796	−0.682502	−0.341251	+	0.939972i	$0.610851\pi$
$824$	−16.9797	−0.591517
$825$	−1.00832	−0.0351051
$826$	0	0
$827$	22.6781	0.788596	0.394298	−	0.918983i	$-0.370988\pi$
$827$	22.6781	0.788596	0.394298	+	0.918983i	$0.370988\pi$
$828$	−8.53637	−0.296659
$829$	16.1540	0.561052	0.280526	−	0.959846i	$-0.409491\pi$
$829$	16.1540	0.561052	0.280526	+	0.959846i	$0.409491\pi$
$830$	3.73118	0.129511
$831$	5.38345	0.186750
$832$	−42.1810	−1.46236
$833$	0	0
$834$	−4.40490	−0.152529
$835$	4.38413	0.151719
$836$	−28.8486	−0.997750
$837$	−1.25979	−0.0435448
$838$	−20.4849	−0.707640
$839$	−17.1737	−0.592901	−0.296451	−	0.955048i	$-0.595803\pi$
$839$	−17.1737	−0.592901	−0.296451	+	0.955048i	$0.595803\pi$
$840$	0	0
$841$	2.31703	0.0798977
$842$	−13.5812	−0.468040
$843$	0.868355	0.0299078
$844$	6.92558	0.238388
$845$	14.4750	0.497954
$846$	−17.8224	−0.612746
$847$	0	0
$848$	6.24891	0.214589
$849$	−5.83210	−0.200157
$850$	2.06349	0.0707770
$851$	22.7124	0.778571
$852$	−1.67495	−0.0573830
$853$	40.2344	1.37760	0.688800	−	0.724951i	$-0.258138\pi$
$853$	40.2344	1.37760	0.688800	+	0.724951i	$0.258138\pi$
$854$	0	0
$855$	−21.8606	−0.747618
$856$	−38.6289	−1.32031
$857$	−13.9134	−0.475272	−0.237636	−	0.971354i	$-0.576373\pi$
$857$	−13.9134	−0.475272	−0.237636	+	0.971354i	$0.576373\pi$
$858$	−5.74565	−0.196153
$859$	45.3398	1.54697	0.773487	−	0.633812i	$-0.218511\pi$
$859$	45.3398	1.54697	0.773487	+	0.633812i	$0.218511\pi$
$860$	7.03324	0.239832
$861$	0	0
$862$	16.3022	0.555254
$863$	1.16692	0.0397226	0.0198613	−	0.999803i	$-0.493678\pi$
$863$	1.16692	0.0397226	0.0198613	+	0.999803i	$0.493678\pi$
$864$	−5.39900	−0.183678
$865$	−17.4775	−0.594252
$866$	5.06783	0.172212
$867$	2.83406	0.0962496
$868$	0	0
$869$	75.0997	2.54758
$870$	1.28695	0.0436317
$871$	−38.3877	−1.30072
$872$	−8.22826	−0.278644
$873$	−31.2492	−1.05763
$874$	28.3899	0.960302
$875$	0	0
$876$	−0.212420	−0.00717701
$877$	1.00020	0.0337744	0.0168872	−	0.999857i	$-0.494624\pi$
$877$	1.00020	0.0337744	0.0168872	+	0.999857i	$0.494624\pi$
$878$	−16.7099	−0.563931
$879$	0.818670	0.0276130
$880$	−8.07521	−0.272215
$881$	−29.8364	−1.00521	−0.502606	−	0.864515i	$-0.667625\pi$
$881$	−29.8364	−1.00521	−0.502606	+	0.864515i	$0.667625\pi$
$882$	0	0
$883$	−14.4125	−0.485021	−0.242510	−	0.970149i	$-0.577971\pi$
$883$	−14.4125	−0.485021	−0.242510	+	0.970149i	$0.577971\pi$
$884$	−8.14057	−0.273797
$885$	−2.75579	−0.0926349
$886$	−5.76478	−0.193672
$887$	7.16070	0.240433	0.120216	−	0.992748i	$-0.461641\pi$
$887$	7.16070	0.240433	0.120216	+	0.992748i	$0.461641\pi$
$888$	4.16950	0.139919
$889$	0	0
$890$	0.179682	0.00602294
$891$	40.9882	1.37316
$892$	15.4471	0.517209
$893$	−41.0363	−1.37323
$894$	−5.47155	−0.182996
$895$	−14.8271	−0.495615
$896$	0	0
$897$	−3.91462	−0.130705
$898$	32.4050	1.08137
$899$	−5.59616	−0.186642
$900$	2.41797	0.0805991
$901$	7.00129	0.233247
$902$	−19.3262	−0.643494
$903$	0	0
$904$	−11.1647	−0.371332
$905$	−2.96385	−0.0985218
$906$	3.44461	0.114439
$907$	−5.39781	−0.179231	−0.0896157	−	0.995976i	$-0.528564\pi$
$907$	−5.39781	−0.179231	−0.0896157	+	0.995976i	$0.528564\pi$
$908$	−3.67490	−0.121956
$909$	−31.6796	−1.05075
$910$	0	0
$911$	−53.3284	−1.76685	−0.883425	−	0.468573i	$-0.844768\pi$
$911$	−53.3284	−1.76685	−0.883425	+	0.468573i	$0.844768\pi$
$912$	2.65108	0.0877861
$913$	−16.3596	−0.541423
$914$	11.5146	0.380868
$915$	1.88057	0.0621696
$916$	−18.6389	−0.615847
$917$	0	0
$918$	2.59956	0.0857984
$919$	7.34902	0.242422	0.121211	−	0.992627i	$-0.461322\pi$
$919$	7.34902	0.242422	0.121211	+	0.992627i	$0.461322\pi$
$920$	−10.8160	−0.356592
$921$	−5.72847	−0.188760
$922$	32.9998	1.08679
$923$	50.7242	1.66961
$924$	0	0
$925$	−6.43341	−0.211529
$926$	7.16374	0.235415
$927$	16.3787	0.537949
$928$	−23.9831	−0.787283
$929$	40.1384	1.31690	0.658449	−	0.752625i	$-0.271213\pi$
$929$	40.1384	1.31690	0.658449	+	0.752625i	$0.271213\pi$
$930$	−0.229970	−0.00754102
$931$	0	0
$932$	8.66648	0.283880
$933$	−4.75225	−0.155582
$934$	7.95439	0.260276
$935$	−9.04747	−0.295884
$936$	47.4577	1.55120
$937$	35.3920	1.15621	0.578104	−	0.815963i	$-0.303793\pi$
$937$	35.3920	1.15621	0.578104	+	0.815963i	$0.303793\pi$
$938$	0	0
$939$	−0.811370	−0.0264781
$940$	4.53896	0.148045
$941$	4.29528	0.140022	0.0700111	−	0.997546i	$-0.477697\pi$
$941$	4.29528	0.140022	0.0700111	+	0.997546i	$0.477697\pi$
$942$	5.31628	0.173214
$943$	−13.1673	−0.428788
$944$	−22.0700	−0.718317
$945$	0	0
$946$	44.5420	1.44818
$947$	−29.0375	−0.943591	−0.471795	−	0.881708i	$-0.656394\pi$
$947$	−29.0375	−0.943591	−0.471795	+	0.881708i	$0.656394\pi$
$948$	2.72707	0.0885711
$949$	6.43291	0.208821
$950$	−8.04158	−0.260903
$951$	−5.59982	−0.181587
$952$	0	0
$953$	33.3981	1.08187	0.540936	−	0.841064i	$-0.318070\pi$
$953$	33.3981	1.08187	0.540936	+	0.841064i	$0.318070\pi$
$954$	−11.8499	−0.383656
$955$	5.86955	0.189934
$956$	−14.1408	−0.457347
$957$	−5.64271	−0.182403
$958$	41.5600	1.34274
$959$	0	0
$960$	−1.70234	−0.0549429
$961$	1.00000	0.0322581
$962$	−36.6592	−1.18194
$963$	37.2617	1.20074
$964$	−2.61137	−0.0841066
$965$	11.8750	0.382271
$966$	0	0
$967$	−6.39457	−0.205635	−0.102818	−	0.994700i	$-0.532786\pi$
$967$	−6.39457	−0.205635	−0.102818	+	0.994700i	$0.532786\pi$
$968$	35.9045	1.15402
$969$	2.97027	0.0954190
$970$	−11.4952	−0.369090
$971$	9.60676	0.308295	0.154148	−	0.988048i	$-0.450737\pi$
$971$	9.60676	0.308295	0.154148	+	0.988048i	$0.450737\pi$
$972$	4.58066	0.146925
$973$	0	0
$974$	39.7031	1.27217
$975$	1.10884	0.0355112
$976$	15.0607	0.482080
$977$	−26.0191	−0.832425	−0.416213	−	0.909267i	$-0.636643\pi$
$977$	−26.0191	−0.832425	−0.416213	+	0.909267i	$0.636643\pi$
$978$	0.942549	0.0301394
$979$	−0.787825	−0.0251790
$980$	0	0
$981$	7.93703	0.253410
$982$	3.58786	0.114493
$983$	28.7835	0.918049	0.459025	−	0.888423i	$-0.348199\pi$
$983$	28.7835	0.918049	0.459025	+	0.888423i	$0.348199\pi$
$984$	−2.41724	−0.0770587
$985$	16.2164	0.516698
$986$	11.5476	0.367750
$987$	0	0
$988$	31.7245	1.00929
$989$	30.3473	0.964988
$990$	15.3132	0.486685
$991$	−40.7315	−1.29388	−0.646939	−	0.762542i	$-0.723951\pi$
$991$	−40.7315	−1.29388	−0.646939	+	0.762542i	$0.723951\pi$
$992$	4.28563	0.136069
$993$	5.95971	0.189126
$994$	0	0
$995$	−6.93497	−0.219853
$996$	−0.594059	−0.0188235
$997$	42.2618	1.33844	0.669222	−	0.743062i	$-0.266627\pi$
$997$	42.2618	1.33844	0.669222	+	0.743062i	$0.266627\pi$
$998$	−8.22295	−0.260293
$999$	−8.10476	−0.256423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.w.1.4	✓	11
7.6	odd	2		7595.2.a.x.1.4	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7595.2.a.w.1.4	✓	11	1.1	even	1	trivial
7595.2.a.x.1.4	yes	11	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)

\(f(q)\)	\(=\)	\(q-1.08711 q^{2} -0.211543 q^{3} -0.818196 q^{4} +1.00000 q^{5} +0.229970 q^{6} +3.06368 q^{8} -2.95525 q^{9} +O(q^{10})\)	\(q-1.08711 q^{2} -0.211543 q^{3} -0.818196 q^{4} +1.00000 q^{5} +0.229970 q^{6} +3.06368 q^{8} -2.95525 q^{9} -1.08711 q^{10} +4.76649 q^{11} +0.173084 q^{12} -5.24166 q^{13} -0.211543 q^{15} -1.69416 q^{16} -1.89814 q^{17} +3.21268 q^{18} +7.39723 q^{19} -0.818196 q^{20} -5.18169 q^{22} -3.53038 q^{23} -0.648101 q^{24} +1.00000 q^{25} +5.69825 q^{26} +1.25979 q^{27} +5.59616 q^{29} +0.229970 q^{30} -1.00000 q^{31} -4.28563 q^{32} -1.00832 q^{33} +2.06349 q^{34} +2.41797 q^{36} -6.43341 q^{37} -8.04158 q^{38} +1.10884 q^{39} +3.06368 q^{40} +3.72972 q^{41} -8.59603 q^{43} -3.89992 q^{44} -2.95525 q^{45} +3.83791 q^{46} -5.54752 q^{47} +0.358389 q^{48} -1.08711 q^{50} +0.401539 q^{51} +4.28870 q^{52} -3.68850 q^{53} -1.36953 q^{54} +4.76649 q^{55} -1.56483 q^{57} -6.08363 q^{58} +13.0271 q^{59} +0.173084 q^{60} -8.88974 q^{61} +1.08711 q^{62} +8.04727 q^{64} -5.24166 q^{65} +1.09615 q^{66} +7.32359 q^{67} +1.55305 q^{68} +0.746829 q^{69} -9.67712 q^{71} -9.05395 q^{72} -1.22727 q^{73} +6.99381 q^{74} -0.211543 q^{75} -6.05238 q^{76} -1.20543 q^{78} +15.7558 q^{79} -1.69416 q^{80} +8.59925 q^{81} -4.05461 q^{82} -3.43221 q^{83} -1.89814 q^{85} +9.34482 q^{86} -1.18383 q^{87} +14.6030 q^{88} -0.165284 q^{89} +3.21268 q^{90} +2.88855 q^{92} +0.211543 q^{93} +6.03075 q^{94} +7.39723 q^{95} +0.906596 q^{96} +10.5741 q^{97} -14.0862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9	\( 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9} - 3 q^{11} + 16 q^{12} - 5 q^{13} - q^{15} - 15 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} - 10 q^{22} - 6 q^{23} - 16 q^{24} + 11 q^{25} + 14 q^{26} - 13 q^{27} - 15 q^{29} - 8 q^{30} - 11 q^{31} - 5 q^{33} - 16 q^{34} - 12 q^{36} - 24 q^{37} - 18 q^{38} - q^{39} - 30 q^{43} - 26 q^{44} - 2 q^{45} - 12 q^{46} - q^{47} + 4 q^{48} - 7 q^{51} - 14 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{55} - 30 q^{57} - 14 q^{58} - 2 q^{59} + 16 q^{60} + 10 q^{61} - 16 q^{64} - 5 q^{65} + 4 q^{66} + 8 q^{67} - 42 q^{68} + 24 q^{69} - 8 q^{71} - 34 q^{72} - 14 q^{73} + 24 q^{74} - q^{75} + 2 q^{76} + 2 q^{78} - 21 q^{79} + 3 q^{81} + 26 q^{82} + 12 q^{83} - 15 q^{85} - 40 q^{86} - 9 q^{87} - 4 q^{88} - 8 q^{89} - 4 q^{90} - 6 q^{92} + q^{93} + 24 q^{94} + 14 q^{95} + 28 q^{96} - 13 q^{97} - 26 q^{99}+O(q^{100}) \) 11 * q - q^3 + 6 * q^4 + 11 * q^5 - 8 * q^6 - 2 * q^9 - 3 * q^11 + 16 * q^12 - 5 * q^13 - q^15 - 15 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 - 10 * q^22 - 6 * q^23 - 16 * q^24 + 11 * q^25 + 14 * q^26 - 13 * q^27 - 15 * q^29 - 8 * q^30 - 11 * q^31 - 5 * q^33 - 16 * q^34 - 12 * q^36 - 24 * q^37 - 18 * q^38 - q^39 - 30 * q^43 - 26 * q^44 - 2 * q^45 - 12 * q^46 - q^47 + 4 * q^48 - 7 * q^51 - 14 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^55 - 30 * q^57 - 14 * q^58 - 2 * q^59 + 16 * q^60 + 10 * q^61 - 16 * q^64 - 5 * q^65 + 4 * q^66 + 8 * q^67 - 42 * q^68 + 24 * q^69 - 8 * q^71 - 34 * q^72 - 14 * q^73 + 24 * q^74 - q^75 + 2 * q^76 + 2 * q^78 - 21 * q^79 + 3 * q^81 + 26 * q^82 + 12 * q^83 - 15 * q^85 - 40 * q^86 - 9 * q^87 - 4 * q^88 - 8 * q^89 - 4 * q^90 - 6 * q^92 + q^93 + 24 * q^94 + 14 * q^95 + 28 * q^96 - 13 * q^97 - 26 * q^99

Introduction

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