LMFDB - Embedded newform 7595.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$11$
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			1.8
Root			$-0.864774$ 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)

$f(q)$	$=$	$q+0.864774 q^{2} -1.32988 q^{3} -1.25217 q^{4} +1.00000 q^{5} -1.15005 q^{6} -2.81239 q^{8} -1.23142 q^{9} +O(q^{10})$	\(q+0.864774 q^{2} -1.32988 q^{3} -1.25217 q^{4} +1.00000 q^{5} -1.15005 q^{6} -2.81239 q^{8} -1.23142 q^{9} +0.864774 q^{10} -1.34420 q^{11} +1.66523 q^{12} -1.56879 q^{13} -1.32988 q^{15} +0.0722536 q^{16} -5.43257 q^{17} -1.06490 q^{18} +4.70505 q^{19} -1.25217 q^{20} -1.16243 q^{22} +5.43013 q^{23} +3.74014 q^{24} +1.00000 q^{25} -1.35665 q^{26} +5.62728 q^{27} +4.29656 q^{29} -1.15005 q^{30} -1.00000 q^{31} +5.68726 q^{32} +1.78763 q^{33} -4.69795 q^{34} +1.54194 q^{36} +3.56785 q^{37} +4.06880 q^{38} +2.08631 q^{39} -2.81239 q^{40} +1.95020 q^{41} +3.22712 q^{43} +1.68317 q^{44} -1.23142 q^{45} +4.69583 q^{46} +1.99726 q^{47} -0.0960887 q^{48} +0.864774 q^{50} +7.22467 q^{51} +1.96439 q^{52} -0.188780 q^{53} +4.86632 q^{54} -1.34420 q^{55} -6.25715 q^{57} +3.71556 q^{58} -7.39435 q^{59} +1.66523 q^{60} +13.9359 q^{61} -0.864774 q^{62} +4.77368 q^{64} -1.56879 q^{65} +1.54590 q^{66} -10.6068 q^{67} +6.80248 q^{68} -7.22142 q^{69} -15.6435 q^{71} +3.46323 q^{72} -2.23598 q^{73} +3.08538 q^{74} -1.32988 q^{75} -5.89150 q^{76} +1.80418 q^{78} -10.7173 q^{79} +0.0722536 q^{80} -3.78935 q^{81} +1.68649 q^{82} +15.1538 q^{83} -5.43257 q^{85} +2.79073 q^{86} -5.71392 q^{87} +3.78043 q^{88} -8.30518 q^{89} -1.06490 q^{90} -6.79942 q^{92} +1.32988 q^{93} +1.72718 q^{94} +4.70505 q^{95} -7.56337 q^{96} +9.17159 q^{97} +1.65528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.864774	0.611487	0.305744	−	0.952114i	$-0.401095\pi$
$2$	0.864774	0.611487	0.305744	+	0.952114i	$0.401095\pi$
$3$	−1.32988	−0.767807	−0.383903	−	0.923373i	$-0.625420\pi$
$3$	−1.32988	−0.767807	−0.383903	+	0.923373i	$0.625420\pi$
$4$	−1.25217	−0.626083
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.15005	−0.469504
$7$	0	0
$7$	0	0
$8$	−2.81239	−0.994329
$9$	−1.23142	−0.410473
$10$	0.864774	0.273465
$11$	−1.34420	−0.405293	−0.202647	−	0.979252i	$-0.564954\pi$
$11$	−1.34420	−0.405293	−0.202647	+	0.979252i	$0.564954\pi$
$12$	1.66523	0.480711
$13$	−1.56879	−0.435105	−0.217553	−	0.976049i	$-0.569807\pi$
$13$	−1.56879	−0.435105	−0.217553	+	0.976049i	$0.569807\pi$
$14$	0	0
$15$	−1.32988	−0.343374
$16$	0.0722536	0.0180634
$17$	−5.43257	−1.31759	−0.658796	−	0.752321i	$-0.728934\pi$
$17$	−5.43257	−1.31759	−0.658796	+	0.752321i	$0.728934\pi$
$18$	−1.06490	−0.250999
$19$	4.70505	1.07941	0.539706	−	0.841854i	$-0.318535\pi$
$19$	4.70505	1.07941	0.539706	+	0.841854i	$0.318535\pi$
$20$	−1.25217	−0.279993
$21$	0	0
$22$	−1.16243	−0.247832
$23$	5.43013	1.13226	0.566130	−	0.824316i	$-0.308440\pi$
$23$	5.43013	1.13226	0.566130	+	0.824316i	$0.308440\pi$
$24$	3.74014	0.763453
$25$	1.00000	0.200000
$26$	−1.35665	−0.266061
$27$	5.62728	1.08297
$28$	0	0
$29$	4.29656	0.797852	0.398926	−	0.916983i	$-0.369383\pi$
$29$	4.29656	0.797852	0.398926	+	0.916983i	$0.369383\pi$
$30$	−1.15005	−0.209969
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	5.68726	1.00537
$33$	1.78763	0.311187
$34$	−4.69795	−0.805691
$35$	0	0
$36$	1.54194	0.256990
$37$	3.56785	0.586550	0.293275	−	0.956028i	$-0.405255\pi$
$37$	3.56785	0.586550	0.293275	+	0.956028i	$0.405255\pi$
$38$	4.06880	0.660047
$39$	2.08631	0.334077
$40$	−2.81239	−0.444678
$41$	1.95020	0.304571	0.152285	−	0.988337i	$-0.451337\pi$
$41$	1.95020	0.304571	0.152285	+	0.988337i	$0.451337\pi$
$42$	0	0
$43$	3.22712	0.492132	0.246066	−	0.969253i	$-0.420862\pi$
$43$	3.22712	0.492132	0.246066	+	0.969253i	$0.420862\pi$
$44$	1.68317	0.253747
$45$	−1.23142	−0.183569
$46$	4.69583	0.692362
$47$	1.99726	0.291330	0.145665	−	0.989334i	$-0.453468\pi$
$47$	1.99726	0.291330	0.145665	+	0.989334i	$0.453468\pi$
$48$	−0.0960887	−0.0138692
$49$	0	0
$50$	0.864774	0.122297
$51$	7.22467	1.01166
$52$	1.96439	0.272412
$53$	−0.188780	−0.0259310	−0.0129655	−	0.999916i	$-0.504127\pi$
$53$	−0.188780	−0.0259310	−0.0129655	+	0.999916i	$0.504127\pi$
$54$	4.86632	0.662223
$55$	−1.34420	−0.181253
$56$	0	0
$57$	−6.25715	−0.828780
$58$	3.71556	0.487876
$59$	−7.39435	−0.962663	−0.481331	−	0.876539i	$-0.659847\pi$
$59$	−7.39435	−0.962663	−0.481331	+	0.876539i	$0.659847\pi$
$60$	1.66523	0.214980
$61$	13.9359	1.78431	0.892156	−	0.451727i	$-0.149192\pi$
$61$	13.9359	1.78431	0.892156	+	0.451727i	$0.149192\pi$
$62$	−0.864774	−0.109826
$63$	0	0
$64$	4.77368	0.596711
$65$	−1.56879	−0.194585
$66$	1.54590	0.190287
$67$	−10.6068	−1.29583	−0.647913	−	0.761715i	$-0.724358\pi$
$67$	−10.6068	−1.29583	−0.647913	+	0.761715i	$0.724358\pi$
$68$	6.80248	0.824922
$69$	−7.22142	−0.869357
$70$	0	0
$71$	−15.6435	−1.85654	−0.928270	−	0.371907i	$-0.878704\pi$
$71$	−15.6435	−1.85654	−0.928270	+	0.371907i	$0.878704\pi$
$72$	3.46323	0.408145
$73$	−2.23598	−0.261701	−0.130851	−	0.991402i	$-0.541771\pi$
$73$	−2.23598	−0.261701	−0.130851	+	0.991402i	$0.541771\pi$
$74$	3.08538	0.358668
$75$	−1.32988	−0.153561
$76$	−5.89150	−0.675802
$77$	0	0
$78$	1.80418	0.204284
$79$	−10.7173	−1.20579	−0.602896	−	0.797819i	$-0.705987\pi$
$79$	−10.7173	−1.20579	−0.602896	+	0.797819i	$0.705987\pi$
$80$	0.0722536	0.00807820
$81$	−3.78935	−0.421039
$82$	1.68649	0.186241
$83$	15.1538	1.66335	0.831673	−	0.555266i	$-0.187383\pi$
$83$	15.1538	1.66335	0.831673	+	0.555266i	$0.187383\pi$
$84$	0	0
$85$	−5.43257	−0.589245
$86$	2.79073	0.300932
$87$	−5.71392	−0.612596
$88$	3.78043	0.402995
$89$	−8.30518	−0.880348	−0.440174	−	0.897913i	$-0.645083\pi$
$89$	−8.30518	−0.880348	−0.440174	+	0.897913i	$0.645083\pi$
$90$	−1.06490	−0.112250
$91$	0	0
$92$	−6.79942	−0.708889
$93$	1.32988	0.137902
$94$	1.72718	0.178145
$95$	4.70505	0.482728
$96$	−7.56337	−0.771934
$97$	9.17159	0.931234	0.465617	−	0.884986i	$-0.345832\pi$
$97$	9.17159	0.931234	0.465617	+	0.884986i	$0.345832\pi$
$98$	0	0
$99$	1.65528	0.166362
$100$	−1.25217	−0.125217
$101$	17.2363	1.71508	0.857538	−	0.514421i	$-0.171993\pi$
$101$	17.2363	1.71508	0.857538	+	0.514421i	$0.171993\pi$
$102$	6.24771	0.618615
$103$	−12.4747	−1.22916	−0.614582	−	0.788853i	$-0.710675\pi$
$103$	−12.4747	−1.22916	−0.614582	+	0.788853i	$0.710675\pi$
$104$	4.41206	0.432638
$105$	0	0
$106$	−0.163252	−0.0158565
$107$	−16.7311	−1.61746	−0.808730	−	0.588181i	$-0.799844\pi$
$107$	−16.7311	−1.61746	−0.808730	+	0.588181i	$0.799844\pi$
$108$	−7.04629	−0.678030
$109$	−2.35101	−0.225186	−0.112593	−	0.993641i	$-0.535916\pi$
$109$	−2.35101	−0.225186	−0.112593	+	0.993641i	$0.535916\pi$
$110$	−1.16243	−0.110834
$111$	−4.74481	−0.450357
$112$	0	0
$113$	−10.8821	−1.02370	−0.511850	−	0.859075i	$-0.671040\pi$
$113$	−10.8821	−1.02370	−0.511850	+	0.859075i	$0.671040\pi$
$114$	−5.41102	−0.506788
$115$	5.43013	0.506362
$116$	−5.38001	−0.499522
$117$	1.93184	0.178599
$118$	−6.39444	−0.588656
$119$	0	0
$120$	3.74014	0.341426
$121$	−9.19311	−0.835738
$122$	12.0514	1.09108
$123$	−2.59354	−0.233851
$124$	1.25217	0.112448
$125$	1.00000	0.0894427
$126$	0	0
$127$	−17.8657	−1.58532	−0.792661	−	0.609662i	$-0.791305\pi$
$127$	−17.8657	−1.58532	−0.792661	+	0.609662i	$0.791305\pi$
$128$	−7.24636	−0.640494
$129$	−4.29169	−0.377862
$130$	−1.35665	−0.118986
$131$	8.34025	0.728691	0.364346	−	0.931264i	$-0.381293\pi$
$131$	8.34025	0.728691	0.364346	+	0.931264i	$0.381293\pi$
$132$	−2.23841	−0.194829
$133$	0	0
$134$	−9.17247	−0.792381
$135$	5.62728	0.484319
$136$	15.2785	1.31012
$137$	−17.3193	−1.47969	−0.739843	−	0.672779i	$-0.765100\pi$
$137$	−17.3193	−1.47969	−0.739843	+	0.672779i	$0.765100\pi$
$138$	−6.24489	−0.531601
$139$	−4.06111	−0.344459	−0.172229	−	0.985057i	$-0.555097\pi$
$139$	−4.06111	−0.344459	−0.172229	+	0.985057i	$0.555097\pi$
$140$	0	0
$141$	−2.65611	−0.223685
$142$	−13.5281	−1.13525
$143$	2.10878	0.176345
$144$	−0.0889745	−0.00741454
$145$	4.29656	0.356810
$146$	−1.93361	−0.160027
$147$	0	0
$148$	−4.46754	−0.367229
$149$	11.2725	0.923477	0.461738	−	0.887016i	$-0.347226\pi$
$149$	11.2725	0.923477	0.461738	+	0.887016i	$0.347226\pi$
$150$	−1.15005	−0.0939008
$151$	19.7273	1.60538	0.802691	−	0.596395i	$-0.203401\pi$
$151$	19.7273	1.60538	0.802691	+	0.596395i	$0.203401\pi$
$152$	−13.2324	−1.07329
$153$	6.68977	0.540836
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	−2.61240	−0.209160
$157$	−4.89924	−0.391002	−0.195501	−	0.980704i	$-0.562633\pi$
$157$	−4.89924	−0.391002	−0.195501	+	0.980704i	$0.562633\pi$
$158$	−9.26806	−0.737327
$159$	0.251055	0.0199100
$160$	5.68726	0.449617
$161$	0	0
$162$	−3.27693	−0.257460
$163$	22.5480	1.76610	0.883048	−	0.469284i	$-0.155488\pi$
$163$	22.5480	1.76610	0.883048	+	0.469284i	$0.155488\pi$
$164$	−2.44198	−0.190687
$165$	1.78763	0.139167
$166$	13.1046	1.01712
$167$	−13.1173	−1.01505	−0.507523	−	0.861638i	$-0.669439\pi$
$167$	−13.1173	−1.01505	−0.507523	+	0.861638i	$0.669439\pi$
$168$	0	0
$169$	−10.5389	−0.810684
$170$	−4.69795	−0.360316
$171$	−5.79389	−0.443069
$172$	−4.04090	−0.308115
$173$	9.17974	0.697923	0.348962	−	0.937137i	$-0.386534\pi$
$173$	9.17974	0.697923	0.348962	+	0.937137i	$0.386534\pi$
$174$	−4.94124	−0.374595
$175$	0	0
$176$	−0.0971237	−0.00732097
$177$	9.83360	0.739139
$178$	−7.18210	−0.538322
$179$	24.7134	1.84717	0.923584	−	0.383396i	$-0.125246\pi$
$179$	24.7134	1.84717	0.923584	+	0.383396i	$0.125246\pi$
$180$	1.54194	0.114930
$181$	−18.5078	−1.37567	−0.687835	−	0.725867i	$-0.741439\pi$
$181$	−18.5078	−1.37567	−0.687835	+	0.725867i	$0.741439\pi$
$182$	0	0
$183$	−18.5331	−1.37001
$184$	−15.2716	−1.12584
$185$	3.56785	0.262313
$186$	1.15005	0.0843254
$187$	7.30249	0.534011
$188$	−2.50090	−0.182397
$189$	0	0
$190$	4.06880	0.295182
$191$	−7.64748	−0.553352	−0.276676	−	0.960963i	$-0.589233\pi$
$191$	−7.64748	−0.553352	−0.276676	+	0.960963i	$0.589233\pi$
$192$	−6.34843	−0.458158
$193$	−10.5268	−0.757736	−0.378868	−	0.925451i	$-0.623687\pi$
$193$	−10.5268	−0.757736	−0.378868	+	0.925451i	$0.623687\pi$
$194$	7.93135	0.569438
$195$	2.08631	0.149404
$196$	0	0
$197$	−13.2375	−0.943136	−0.471568	−	0.881830i	$-0.656312\pi$
$197$	−13.2375	−0.943136	−0.471568	+	0.881830i	$0.656312\pi$
$198$	1.43144	0.101728
$199$	−4.72696	−0.335085	−0.167543	−	0.985865i	$-0.553583\pi$
$199$	−4.72696	−0.335085	−0.167543	+	0.985865i	$0.553583\pi$
$200$	−2.81239	−0.198866
$201$	14.1058	0.994944
$202$	14.9055	1.04875
$203$	0	0
$204$	−9.04649	−0.633381
$205$	1.95020	0.136208
$206$	−10.7878	−0.751619
$207$	−6.68676	−0.464762
$208$	−0.113351	−0.00785948
$209$	−6.32455	−0.437478
$210$	0	0
$211$	6.65534	0.458172	0.229086	−	0.973406i	$-0.426426\pi$
$211$	6.65534	0.458172	0.229086	+	0.973406i	$0.426426\pi$
$212$	0.236385	0.0162350
$213$	20.8040	1.42546
$214$	−14.4686	−0.989056
$215$	3.22712	0.220088
$216$	−15.8261	−1.07683
$217$	0	0
$218$	−2.03309	−0.137698
$219$	2.97358	0.200936
$220$	1.68317	0.113479
$221$	8.52258	0.573291
$222$	−4.10319	−0.275388
$223$	−4.29700	−0.287748	−0.143874	−	0.989596i	$-0.545956\pi$
$223$	−4.29700	−0.287748	−0.143874	+	0.989596i	$0.545956\pi$
$224$	0	0
$225$	−1.23142	−0.0820946
$226$	−9.41054	−0.625980
$227$	18.6448	1.23750	0.618750	−	0.785588i	$-0.287639\pi$
$227$	18.6448	1.23750	0.618750	+	0.785588i	$0.287639\pi$
$228$	7.83499	0.518885
$229$	−20.1912	−1.33427	−0.667136	−	0.744936i	$-0.732480\pi$
$229$	−20.1912	−1.33427	−0.667136	+	0.744936i	$0.732480\pi$
$230$	4.69583	0.309634
$231$	0	0
$232$	−12.0836	−0.793328
$233$	−12.9485	−0.848284	−0.424142	−	0.905596i	$-0.639424\pi$
$233$	−12.9485	−0.848284	−0.424142	+	0.905596i	$0.639424\pi$
$234$	1.67061	0.109211
$235$	1.99726	0.130287
$236$	9.25896	0.602707
$237$	14.2528	0.925816
$238$	0	0
$239$	−25.9716	−1.67997	−0.839983	−	0.542613i	$-0.817435\pi$
$239$	−25.9716	−1.67997	−0.839983	+	0.542613i	$0.817435\pi$
$240$	−0.0960887	−0.00620250
$241$	−0.669656	−0.0431364	−0.0215682	−	0.999767i	$-0.506866\pi$
$241$	−0.669656	−0.0431364	−0.0215682	+	0.999767i	$0.506866\pi$
$242$	−7.94996	−0.511043
$243$	−11.8425	−0.759694
$244$	−17.4501	−1.11713
$245$	0	0
$246$	−2.24282	−0.142997
$247$	−7.38125	−0.469658
$248$	2.81239	0.178587
$249$	−20.1527	−1.27713
$250$	0.864774	0.0546931
$251$	13.1756	0.831635	0.415817	−	0.909448i	$-0.363496\pi$
$251$	13.1756	0.831635	0.415817	+	0.909448i	$0.363496\pi$
$252$	0	0
$253$	−7.29920	−0.458897
$254$	−15.4498	−0.969405
$255$	7.22467	0.452426
$256$	−15.8138	−0.988365
$257$	7.27098	0.453551	0.226776	−	0.973947i	$-0.427182\pi$
$257$	7.27098	0.453551	0.226776	+	0.973947i	$0.427182\pi$
$258$	−3.71134	−0.231058
$259$	0	0
$260$	1.96439	0.121826
$261$	−5.29087	−0.327497
$262$	7.21243	0.445586
$263$	12.5400	0.773249	0.386624	−	0.922237i	$-0.373641\pi$
$263$	12.5400	0.773249	0.386624	+	0.922237i	$0.373641\pi$
$264$	−5.02751	−0.309422
$265$	−0.188780	−0.0115967
$266$	0	0
$267$	11.0449	0.675937
$268$	13.2815	0.811295
$269$	16.2153	0.988665	0.494333	−	0.869273i	$-0.335412\pi$
$269$	16.2153	0.988665	0.494333	+	0.869273i	$0.335412\pi$
$270$	4.86632	0.296155
$271$	6.48745	0.394085	0.197042	−	0.980395i	$-0.436866\pi$
$271$	6.48745	0.394085	0.197042	+	0.980395i	$0.436866\pi$
$272$	−0.392523	−0.0238002
$273$	0	0
$274$	−14.9773	−0.904810
$275$	−1.34420	−0.0810586
$276$	9.04242	0.544290
$277$	16.0852	0.966465	0.483233	−	0.875492i	$-0.339463\pi$
$277$	16.0852	0.966465	0.483233	+	0.875492i	$0.339463\pi$
$278$	−3.51194	−0.210632
$279$	1.23142	0.0737231
$280$	0	0
$281$	0.412086	0.0245830	0.0122915	−	0.999924i	$-0.496087\pi$
$281$	0.412086	0.0245830	0.0122915	+	0.999924i	$0.496087\pi$
$282$	−2.29694	−0.136781
$283$	−30.7098	−1.82551	−0.912754	−	0.408509i	$-0.866049\pi$
$283$	−30.7098	−1.82551	−0.912754	+	0.408509i	$0.866049\pi$
$284$	19.5882	1.16235
$285$	−6.25715	−0.370642
$286$	1.82362	0.107833
$287$	0	0
$288$	−7.00340	−0.412679
$289$	12.5128	0.736050
$290$	3.71556	0.218185
$291$	−12.1971	−0.715008
$292$	2.79981	0.163847
$293$	6.94863	0.405944	0.202972	−	0.979185i	$-0.434940\pi$
$293$	6.94863	0.405944	0.202972	+	0.979185i	$0.434940\pi$
$294$	0	0
$295$	−7.39435	−0.430516
$296$	−10.0342	−0.583224
$297$	−7.56422	−0.438920
$298$	9.74813	0.564694
$299$	−8.51875	−0.492652
$300$	1.66523	0.0961422
$301$	0	0
$302$	17.0596	0.981671
$303$	−22.9222	−1.31685
$304$	0.339957	0.0194979
$305$	13.9359	0.797969
$306$	5.78514	0.330714
$307$	6.06107	0.345924	0.172962	−	0.984929i	$-0.444666\pi$
$307$	6.06107	0.345924	0.172962	+	0.984929i	$0.444666\pi$
$308$	0	0
$309$	16.5898	0.943761
$310$	−0.864774	−0.0491158
$311$	−15.1508	−0.859125	−0.429563	−	0.903037i	$-0.641332\pi$
$311$	−15.1508	−0.859125	−0.429563	+	0.903037i	$0.641332\pi$
$312$	−5.86751	−0.332182
$313$	26.2729	1.48503	0.742516	−	0.669829i	$-0.233632\pi$
$313$	26.2729	1.48503	0.742516	+	0.669829i	$0.233632\pi$
$314$	−4.23673	−0.239093
$315$	0	0
$316$	13.4199	0.754927
$317$	9.30770	0.522772	0.261386	−	0.965234i	$-0.415820\pi$
$317$	9.30770	0.522772	0.261386	+	0.965234i	$0.415820\pi$
$318$	0.217106	0.0121747
$319$	−5.77546	−0.323364
$320$	4.77368	0.266857
$321$	22.2504	1.24190
$322$	0	0
$323$	−25.5605	−1.42223
$324$	4.74490	0.263605
$325$	−1.56879	−0.0870210
$326$	19.4989	1.07994
$327$	3.12656	0.172899
$328$	−5.48473	−0.302844
$329$	0	0
$330$	1.54590	0.0850988
$331$	−21.9603	−1.20705	−0.603524	−	0.797345i	$-0.706237\pi$
$331$	−21.9603	−1.20705	−0.603524	+	0.797345i	$0.706237\pi$
$332$	−18.9751	−1.04139
$333$	−4.39351	−0.240763
$334$	−11.3435	−0.620688
$335$	−10.6068	−0.579511
$336$	0	0
$337$	−3.00804	−0.163858	−0.0819291	−	0.996638i	$-0.526108\pi$
$337$	−3.00804	−0.163858	−0.0819291	+	0.996638i	$0.526108\pi$
$338$	−9.11375	−0.495723
$339$	14.4719	0.786004
$340$	6.80248	0.368917
$341$	1.34420	0.0727928
$342$	−5.01040	−0.270931
$343$	0	0
$344$	−9.07592	−0.489341
$345$	−7.22142	−0.388788
$346$	7.93840	0.426771
$347$	−2.89077	−0.155185	−0.0775923	−	0.996985i	$-0.524723\pi$
$347$	−2.89077	−0.155185	−0.0775923	+	0.996985i	$0.524723\pi$
$348$	7.15477	0.383536
$349$	16.6736	0.892518	0.446259	−	0.894904i	$-0.352756\pi$
$349$	16.6736	0.892518	0.446259	+	0.894904i	$0.352756\pi$
$350$	0	0
$351$	−8.82804	−0.471206
$352$	−7.64484	−0.407471
$353$	−23.1466	−1.23197	−0.615985	−	0.787758i	$-0.711242\pi$
$353$	−23.1466	−1.23197	−0.615985	+	0.787758i	$0.711242\pi$
$354$	8.50384	0.451974
$355$	−15.6435	−0.830270
$356$	10.3995	0.551171
$357$	0	0
$358$	21.3715	1.12952
$359$	26.3578	1.39111	0.695556	−	0.718472i	$-0.255158\pi$
$359$	26.3578	1.39111	0.695556	+	0.718472i	$0.255158\pi$
$360$	3.46323	0.182528
$361$	3.13748	0.165131
$362$	−16.0050	−0.841205
$363$	12.2257	0.641685
$364$	0	0
$365$	−2.23598	−0.117036
$366$	−16.0269	−0.837742
$367$	11.1408	0.581545	0.290773	−	0.956792i	$-0.406088\pi$
$367$	11.1408	0.581545	0.290773	+	0.956792i	$0.406088\pi$
$368$	0.392346	0.0204525
$369$	−2.40152	−0.125018
$370$	3.08538	0.160401
$371$	0	0
$372$	−1.66523	−0.0863382
$373$	−31.1044	−1.61053	−0.805263	−	0.592917i	$-0.797976\pi$
$373$	−31.1044	−1.61053	−0.805263	+	0.592917i	$0.797976\pi$
$374$	6.31500	0.326541
$375$	−1.32988	−0.0686747
$376$	−5.61707	−0.289678
$377$	−6.74042	−0.347149
$378$	0	0
$379$	−20.6232	−1.05934	−0.529671	−	0.848203i	$-0.677685\pi$
$379$	−20.6232	−1.05934	−0.529671	+	0.848203i	$0.677685\pi$
$380$	−5.89150	−0.302228
$381$	23.7592	1.21722
$382$	−6.61334	−0.338368
$383$	−32.9933	−1.68588	−0.842940	−	0.538007i	$-0.819177\pi$
$383$	−32.9933	−1.68588	−0.842940	+	0.538007i	$0.819177\pi$
$384$	9.63679	0.491775
$385$	0	0
$386$	−9.10331	−0.463346
$387$	−3.97394	−0.202007
$388$	−11.4844	−0.583030
$389$	−29.5852	−1.50003	−0.750014	−	0.661422i	$-0.769953\pi$
$389$	−29.5852	−1.50003	−0.750014	+	0.661422i	$0.769953\pi$
$390$	1.80418	0.0913584
$391$	−29.4996	−1.49186
$392$	0	0
$393$	−11.0915	−0.559494
$394$	−11.4475	−0.576716
$395$	−10.7173	−0.539247
$396$	−2.07269	−0.104156
$397$	−19.0976	−0.958479	−0.479239	−	0.877684i	$-0.659087\pi$
$397$	−19.0976	−0.958479	−0.479239	+	0.877684i	$0.659087\pi$
$398$	−4.08775	−0.204900
$399$	0	0
$400$	0.0722536	0.00361268
$401$	16.0454	0.801270	0.400635	−	0.916238i	$-0.368790\pi$
$401$	16.0454	0.801270	0.400635	+	0.916238i	$0.368790\pi$
$402$	12.1983	0.608395
$403$	1.56879	0.0781472
$404$	−21.5827	−1.07378
$405$	−3.78935	−0.188294
$406$	0	0
$407$	−4.79592	−0.237725
$408$	−20.3186	−1.00592
$409$	−35.4211	−1.75146	−0.875731	−	0.482800i	$-0.839620\pi$
$409$	−35.4211	−1.75146	−0.875731	+	0.482800i	$0.839620\pi$
$410$	1.68649	0.0832896
$411$	23.0326	1.13611
$412$	15.6203	0.769559
$413$	0	0
$414$	−5.78253	−0.284196
$415$	15.1538	0.743871
$416$	−8.92213	−0.437444
$417$	5.40079	0.264478
$418$	−5.46930	−0.267512
$419$	−30.1731	−1.47405	−0.737026	−	0.675864i	$-0.763771\pi$
$419$	−30.1731	−1.47405	−0.737026	+	0.675864i	$0.763771\pi$
$420$	0	0
$421$	34.6669	1.68956	0.844780	−	0.535114i	$-0.179731\pi$
$421$	34.6669	1.68956	0.844780	+	0.535114i	$0.179731\pi$
$422$	5.75536	0.280167
$423$	−2.45946	−0.119583
$424$	0.530924	0.0257839
$425$	−5.43257	−0.263518
$426$	17.9907	0.871653
$427$	0	0
$428$	20.9502	1.01266
$429$	−2.80442	−0.135399
$430$	2.79073	0.134581
$431$	29.4707	1.41955	0.709776	−	0.704428i	$-0.248796\pi$
$431$	29.4707	1.41955	0.709776	+	0.704428i	$0.248796\pi$
$432$	0.406591	0.0195621
$433$	2.94205	0.141386	0.0706929	−	0.997498i	$-0.477479\pi$
$433$	2.94205	0.141386	0.0706929	+	0.997498i	$0.477479\pi$
$434$	0	0
$435$	−5.71392	−0.273961
$436$	2.94385	0.140985
$437$	25.5490	1.22217
$438$	2.57147	0.122870
$439$	−1.78357	−0.0851253	−0.0425626	−	0.999094i	$-0.513552\pi$
$439$	−1.78357	−0.0851253	−0.0425626	+	0.999094i	$0.513552\pi$
$440$	3.78043	0.180225
$441$	0	0
$442$	7.37011	0.350560
$443$	11.8621	0.563583	0.281792	−	0.959476i	$-0.409071\pi$
$443$	11.8621	0.563583	0.281792	+	0.959476i	$0.409071\pi$
$444$	5.94129	0.281961
$445$	−8.30518	−0.393703
$446$	−3.71593	−0.175954
$447$	−14.9910	−0.709052
$448$	0	0
$449$	−31.7752	−1.49957	−0.749783	−	0.661684i	$-0.769842\pi$
$449$	−31.7752	−1.49957	−0.749783	+	0.661684i	$0.769842\pi$
$450$	−1.06490	−0.0501998
$451$	−2.62147	−0.123440
$452$	13.6262	0.640921
$453$	−26.2349	−1.23262
$454$	16.1235	0.756715
$455$	0	0
$456$	17.5975	0.824080
$457$	−26.0033	−1.21638	−0.608192	−	0.793790i	$-0.708105\pi$
$457$	−26.0033	−1.21638	−0.608192	+	0.793790i	$0.708105\pi$
$458$	−17.4608	−0.815890
$459$	−30.5706	−1.42691
$460$	−6.79942	−0.317025
$461$	19.7816	0.921320	0.460660	−	0.887577i	$-0.347613\pi$
$461$	19.7816	0.921320	0.460660	+	0.887577i	$0.347613\pi$
$462$	0	0
$463$	−1.36841	−0.0635956	−0.0317978	−	0.999494i	$-0.510123\pi$
$463$	−1.36841	−0.0635956	−0.0317978	+	0.999494i	$0.510123\pi$
$464$	0.310442	0.0144119
$465$	1.32988	0.0616717
$466$	−11.1975	−0.518715
$467$	−11.6624	−0.539670	−0.269835	−	0.962907i	$-0.586969\pi$
$467$	−11.6624	−0.539670	−0.269835	+	0.962907i	$0.586969\pi$
$468$	−2.41899	−0.111818
$469$	0	0
$470$	1.72718	0.0796687
$471$	6.51540	0.300214
$472$	20.7958	0.957204
$473$	−4.33792	−0.199458
$474$	12.3254	0.566125
$475$	4.70505	0.215882
$476$	0	0
$477$	0.232468	0.0106440
$478$	−22.4596	−1.02728
$479$	−19.8055	−0.904935	−0.452468	−	0.891781i	$-0.649456\pi$
$479$	−19.8055	−0.904935	−0.452468	+	0.891781i	$0.649456\pi$
$480$	−7.56337	−0.345219
$481$	−5.59721	−0.255211
$482$	−0.579101	−0.0263773
$483$	0	0
$484$	11.5113	0.523241
$485$	9.17159	0.416460
$486$	−10.2410	−0.464543
$487$	−5.85211	−0.265184	−0.132592	−	0.991171i	$-0.542330\pi$
$487$	−5.85211	−0.265184	−0.132592	+	0.991171i	$0.542330\pi$
$488$	−39.1932	−1.77419
$489$	−29.9861	−1.35602
$490$	0	0
$491$	−22.8376	−1.03065	−0.515323	−	0.856996i	$-0.672328\pi$
$491$	−22.8376	−1.03065	−0.515323	+	0.856996i	$0.672328\pi$
$492$	3.24754	0.146410
$493$	−23.3414	−1.05124
$494$	−6.38311	−0.287190
$495$	1.65528	0.0743993
$496$	−0.0722536	−0.00324428
$497$	0	0
$498$	−17.4276	−0.780948
$499$	−24.4562	−1.09481	−0.547404	−	0.836868i	$-0.684384\pi$
$499$	−24.4562	−1.09481	−0.547404	+	0.836868i	$0.684384\pi$
$500$	−1.25217	−0.0559986
$501$	17.4444	0.779359
$502$	11.3939	0.508534
$503$	39.2653	1.75075	0.875376	−	0.483443i	$-0.160614\pi$
$503$	39.2653	1.75075	0.875376	+	0.483443i	$0.160614\pi$
$504$	0	0
$505$	17.2363	0.767005
$506$	−6.31216	−0.280610
$507$	14.0155	0.622448
$508$	22.3708	0.992544
$509$	18.5480	0.822125	0.411062	−	0.911607i	$-0.365158\pi$
$509$	18.5480	0.822125	0.411062	+	0.911607i	$0.365158\pi$
$510$	6.24771	0.276653
$511$	0	0
$512$	0.817335	0.0361215
$513$	26.4766	1.16897
$514$	6.28775	0.277341
$515$	−12.4747	−0.549699
$516$	5.37391	0.236573
$517$	−2.68472	−0.118074
$518$	0	0
$519$	−12.2080	−0.535870
$520$	4.41206	0.193481
$521$	11.3658	0.497943	0.248971	−	0.968511i	$-0.419907\pi$
$521$	11.3658	0.497943	0.248971	+	0.968511i	$0.419907\pi$
$522$	−4.57541	−0.200260
$523$	8.45749	0.369820	0.184910	−	0.982755i	$-0.440801\pi$
$523$	8.45749	0.369820	0.184910	+	0.982755i	$0.440801\pi$
$524$	−10.4434	−0.456221
$525$	0	0
$526$	10.8442	0.472832
$527$	5.43257	0.236647
$528$	0.129163	0.00562109
$529$	6.48628	0.282012
$530$	−0.163252	−0.00709123
$531$	9.10554	0.395147
$532$	0	0
$533$	−3.05947	−0.132520
$534$	9.55134	0.413327
$535$	−16.7311	−0.723350
$536$	29.8304	1.28848
$537$	−32.8659	−1.41827
$538$	14.0226	0.604556
$539$	0	0
$540$	−7.04629	−0.303224
$541$	−20.4847	−0.880708	−0.440354	−	0.897824i	$-0.645147\pi$
$541$	−20.4847	−0.880708	−0.440354	+	0.897824i	$0.645147\pi$
$542$	5.61018	0.240978
$543$	24.6131	1.05625
$544$	−30.8964	−1.32467
$545$	−2.35101	−0.100706
$546$	0	0
$547$	1.63349	0.0698430	0.0349215	−	0.999390i	$-0.488882\pi$
$547$	1.63349	0.0698430	0.0349215	+	0.999390i	$0.488882\pi$
$548$	21.6866	0.926407
$549$	−17.1610	−0.732412
$550$	−1.16243	−0.0495663
$551$	20.2155	0.861211
$552$	20.3094	0.864427
$553$	0	0
$554$	13.9100	0.590981
$555$	−4.74481	−0.201406
$556$	5.08518	0.215660
$557$	−16.8478	−0.713864	−0.356932	−	0.934130i	$-0.616177\pi$
$557$	−16.8478	−0.713864	−0.356932	+	0.934130i	$0.616177\pi$
$558$	1.06490	0.0450808
$559$	−5.06269	−0.214129
$560$	0	0
$561$	−9.71144	−0.410017
$562$	0.356361	0.0150322
$563$	−7.55061	−0.318220	−0.159110	−	0.987261i	$-0.550862\pi$
$563$	−7.55061	−0.318220	−0.159110	+	0.987261i	$0.550862\pi$
$564$	3.32590	0.140046
$565$	−10.8821	−0.457813
$566$	−26.5570	−1.11628
$567$	0	0
$568$	43.9955	1.84601
$569$	−15.6195	−0.654804	−0.327402	−	0.944885i	$-0.606173\pi$
$569$	−15.6195	−0.654804	−0.327402	+	0.944885i	$0.606173\pi$
$570$	−5.41102	−0.226643
$571$	−20.3348	−0.850985	−0.425493	−	0.904962i	$-0.639899\pi$
$571$	−20.3348	−0.850985	−0.425493	+	0.904962i	$0.639899\pi$
$572$	−2.64054	−0.110407
$573$	10.1702	0.424867
$574$	0	0
$575$	5.43013	0.226452
$576$	−5.87841	−0.244934
$577$	−25.2276	−1.05024	−0.525120	−	0.851028i	$-0.675980\pi$
$577$	−25.2276	−1.05024	−0.525120	+	0.851028i	$0.675980\pi$
$578$	10.8208	0.450085
$579$	13.9994	0.581795
$580$	−5.38001	−0.223393
$581$	0	0
$582$	−10.5477	−0.437218
$583$	0.253760	0.0105096
$584$	6.28843	0.260217
$585$	1.93184	0.0798718
$586$	6.00900	0.248229
$587$	10.9015	0.449951	0.224976	−	0.974364i	$-0.427770\pi$
$587$	10.9015	0.449951	0.224976	+	0.974364i	$0.427770\pi$
$588$	0	0
$589$	−4.70505	−0.193868
$590$	−6.39444	−0.263255
$591$	17.6043	0.724146
$592$	0.257790	0.0105951
$593$	9.66178	0.396762	0.198381	−	0.980125i	$-0.436432\pi$
$593$	9.66178	0.396762	0.198381	+	0.980125i	$0.436432\pi$
$594$	−6.54134	−0.268394
$595$	0	0
$596$	−14.1150	−0.578173
$597$	6.28629	0.257281
$598$	−7.36679	−0.301250
$599$	7.46685	0.305087	0.152544	−	0.988297i	$-0.451254\pi$
$599$	7.46685	0.305087	0.152544	+	0.988297i	$0.451254\pi$
$600$	3.74014	0.152691
$601$	20.4524	0.834269	0.417135	−	0.908845i	$-0.363034\pi$
$601$	20.4524	0.834269	0.417135	+	0.908845i	$0.363034\pi$
$602$	0	0
$603$	13.0614	0.531901
$604$	−24.7018	−1.00510
$605$	−9.19311	−0.373753
$606$	−19.8225	−0.805235
$607$	24.6315	0.999760	0.499880	−	0.866095i	$-0.333377\pi$
$607$	24.6315	0.999760	0.499880	+	0.866095i	$0.333377\pi$
$608$	26.7588	1.08521
$609$	0	0
$610$	12.0514	0.487948
$611$	−3.13329	−0.126759
$612$	−8.37671	−0.338608
$613$	−49.2690	−1.98996	−0.994978	−	0.100092i	$-0.968086\pi$
$613$	−49.2690	−1.98996	−0.994978	+	0.100092i	$0.968086\pi$
$614$	5.24146	0.211528
$615$	−2.59354	−0.104582
$616$	0	0
$617$	−20.1692	−0.811983	−0.405991	−	0.913877i	$-0.633074\pi$
$617$	−20.1692	−0.811983	−0.405991	+	0.913877i	$0.633074\pi$
$618$	14.3464	0.577098
$619$	−19.2565	−0.773984	−0.386992	−	0.922083i	$-0.626486\pi$
$619$	−19.2565	−0.773984	−0.386992	+	0.922083i	$0.626486\pi$
$620$	1.25217	0.0502882
$621$	30.5568	1.22620
$622$	−13.1020	−0.525344
$623$	0	0
$624$	0.150743	0.00603456
$625$	1.00000	0.0400000
$626$	22.7201	0.908078
$627$	8.41089	0.335899
$628$	6.13466	0.244800
$629$	−19.3826	−0.772834
$630$	0	0
$631$	13.3706	0.532274	0.266137	−	0.963935i	$-0.414253\pi$
$631$	13.3706	0.532274	0.266137	+	0.963935i	$0.414253\pi$
$632$	30.1413	1.19896
$633$	−8.85080	−0.351788
$634$	8.04905	0.319669
$635$	−17.8657	−0.708978
$636$	−0.314363	−0.0124653
$637$	0	0
$638$	−4.99447	−0.197733
$639$	19.2637	0.762059
$640$	−7.24636	−0.286438
$641$	30.5925	1.20833	0.604165	−	0.796859i	$-0.293507\pi$
$641$	30.5925	1.20833	0.604165	+	0.796859i	$0.293507\pi$
$642$	19.2416	0.759404
$643$	3.49276	0.137741	0.0688705	−	0.997626i	$-0.478060\pi$
$643$	3.49276	0.137741	0.0688705	+	0.997626i	$0.478060\pi$
$644$	0	0
$645$	−4.29169	−0.168985
$646$	−22.1041	−0.869673
$647$	−20.5133	−0.806463	−0.403231	−	0.915098i	$-0.632113\pi$
$647$	−20.5133	−0.806463	−0.403231	+	0.915098i	$0.632113\pi$
$648$	10.6571	0.418651
$649$	9.93953	0.390161
$650$	−1.35665	−0.0532122
$651$	0	0
$652$	−28.2338	−1.10572
$653$	−14.9304	−0.584270	−0.292135	−	0.956377i	$-0.594366\pi$
$653$	−14.9304	−0.584270	−0.292135	+	0.956377i	$0.594366\pi$
$654$	2.70376	0.105726
$655$	8.34025	0.325881
$656$	0.140909	0.00550158
$657$	2.75342	0.107421
$658$	0	0
$659$	24.1999	0.942696	0.471348	−	0.881947i	$-0.343768\pi$
$659$	24.1999	0.942696	0.471348	+	0.881947i	$0.343768\pi$
$660$	−2.23841	−0.0871301
$661$	−19.0974	−0.742803	−0.371402	−	0.928472i	$-0.621123\pi$
$661$	−19.0974	−0.742803	−0.371402	+	0.928472i	$0.621123\pi$
$662$	−18.9907	−0.738095
$663$	−11.3340	−0.440177
$664$	−42.6184	−1.65391
$665$	0	0
$666$	−3.79939	−0.147224
$667$	23.3309	0.903376
$668$	16.4250	0.635503
$669$	5.71449	0.220935
$670$	−9.17247	−0.354364
$671$	−18.7327	−0.723169
$672$	0	0
$673$	−30.5410	−1.17727	−0.588635	−	0.808399i	$-0.700334\pi$
$673$	−30.5410	−1.17727	−0.588635	+	0.808399i	$0.700334\pi$
$674$	−2.60127	−0.100197
$675$	5.62728	0.216594
$676$	13.1964	0.507555
$677$	50.2587	1.93160	0.965800	−	0.259288i	$-0.0834878\pi$
$677$	50.2587	1.93160	0.965800	+	0.259288i	$0.0834878\pi$
$678$	12.5149	0.480631
$679$	0	0
$680$	15.2785	0.585904
$681$	−24.7954	−0.950160
$682$	1.16243	0.0445119
$683$	31.8283	1.21787	0.608937	−	0.793218i	$-0.291596\pi$
$683$	31.8283	1.21787	0.608937	+	0.793218i	$0.291596\pi$
$684$	7.25491	0.277398
$685$	−17.3193	−0.661736
$686$	0	0
$687$	26.8519	1.02446
$688$	0.233171	0.00888957
$689$	0.296158	0.0112827
$690$	−6.24489	−0.237739
$691$	−16.1069	−0.612735	−0.306367	−	0.951913i	$-0.599114\pi$
$691$	−16.1069	−0.612735	−0.306367	+	0.951913i	$0.599114\pi$
$692$	−11.4946	−0.436958
$693$	0	0
$694$	−2.49986	−0.0948934
$695$	−4.06111	−0.154047
$696$	16.0697	0.609122
$697$	−10.5946	−0.401300
$698$	14.4189	0.545763
$699$	17.2199	0.651318
$700$	0	0
$701$	1.09626	0.0414052	0.0207026	−	0.999786i	$-0.493410\pi$
$701$	1.09626	0.0414052	0.0207026	+	0.999786i	$0.493410\pi$
$702$	−7.63426	−0.288136
$703$	16.7869	0.633130
$704$	−6.41681	−0.241843
$705$	−2.65611	−0.100035
$706$	−20.0166	−0.753334
$707$	0	0
$708$	−12.3133	−0.462762
$709$	−17.8344	−0.669786	−0.334893	−	0.942256i	$-0.608700\pi$
$709$	−17.8344	−0.669786	−0.334893	+	0.942256i	$0.608700\pi$
$710$	−13.5281	−0.507700
$711$	13.1975	0.494945
$712$	23.3574	0.875356
$713$	−5.43013	−0.203360
$714$	0	0
$715$	2.10878	0.0788639
$716$	−30.9453	−1.15648
$717$	34.5392	1.28989
$718$	22.7935	0.850647
$719$	−6.13379	−0.228752	−0.114376	−	0.993438i	$-0.536487\pi$
$719$	−6.13379	−0.228752	−0.114376	+	0.993438i	$0.536487\pi$
$720$	−0.0889745	−0.00331588
$721$	0	0
$722$	2.71321	0.100975
$723$	0.890563	0.0331204
$724$	23.1748	0.861284
$725$	4.29656	0.159570
$726$	10.5725	0.392382
$727$	35.0523	1.30002	0.650009	−	0.759927i	$-0.274765\pi$
$727$	35.0523	1.30002	0.650009	+	0.759927i	$0.274765\pi$
$728$	0	0
$729$	27.1171	1.00434
$730$	−1.93361	−0.0715662
$731$	−17.5316	−0.648429
$732$	23.2065	0.857738
$733$	29.4351	1.08721	0.543605	−	0.839341i	$-0.317059\pi$
$733$	29.4351	1.08721	0.543605	+	0.839341i	$0.317059\pi$
$734$	9.63428	0.355608
$735$	0	0
$736$	30.8825	1.13835
$737$	14.2577	0.525189
$738$	−2.07677	−0.0764469
$739$	12.9249	0.475450	0.237725	−	0.971332i	$-0.423598\pi$
$739$	12.9249	0.475450	0.237725	+	0.971332i	$0.423598\pi$
$740$	−4.46754	−0.164230
$741$	9.81618	0.360606
$742$	0	0
$743$	32.2255	1.18224	0.591119	−	0.806584i	$-0.298686\pi$
$743$	32.2255	1.18224	0.591119	+	0.806584i	$0.298686\pi$
$744$	−3.74014	−0.137120
$745$	11.2725	0.412991
$746$	−26.8983	−0.984817
$747$	−18.6607	−0.682759
$748$	−9.14393	−0.334335
$749$	0	0
$750$	−1.15005	−0.0419937
$751$	−5.91881	−0.215980	−0.107990	−	0.994152i	$-0.534442\pi$
$751$	−5.91881	−0.215980	−0.107990	+	0.994152i	$0.534442\pi$
$752$	0.144309	0.00526241
$753$	−17.5219	−0.638535
$754$	−5.82894	−0.212277
$755$	19.7273	0.717949
$756$	0	0
$757$	−17.5388	−0.637458	−0.318729	−	0.947846i	$-0.603256\pi$
$757$	−17.5388	−0.637458	−0.318729	+	0.947846i	$0.603256\pi$
$758$	−17.8344	−0.647775
$759$	9.70707	0.352344
$760$	−13.2324	−0.479990
$761$	−30.0896	−1.09075	−0.545374	−	0.838193i	$-0.683613\pi$
$761$	−30.0896	−1.09075	−0.545374	+	0.838193i	$0.683613\pi$
$762$	20.5463	0.744315
$763$	0	0
$764$	9.57592	0.346444
$765$	6.68977	0.241869
$766$	−28.5318	−1.03089
$767$	11.6002	0.418859
$768$	21.0305	0.758873
$769$	30.9668	1.11669	0.558345	−	0.829609i	$-0.311436\pi$
$769$	30.9668	1.11669	0.558345	+	0.829609i	$0.311436\pi$
$770$	0	0
$771$	−9.66953	−0.348240
$772$	13.1813	0.474406
$773$	−49.8524	−1.79307	−0.896534	−	0.442975i	$-0.853923\pi$
$773$	−49.8524	−1.79307	−0.896534	+	0.442975i	$0.853923\pi$
$774$	−3.43656	−0.123525
$775$	−1.00000	−0.0359211
$776$	−25.7941	−0.925953
$777$	0	0
$778$	−25.5845	−0.917248
$779$	9.17581	0.328757
$780$	−2.61240	−0.0935391
$781$	21.0280	0.752443
$782$	−25.5104	−0.912252
$783$	24.1780	0.864050
$784$	0	0
$785$	−4.89924	−0.174861
$786$	−9.59167	−0.342124
$787$	18.4628	0.658127	0.329064	−	0.944308i	$-0.393267\pi$
$787$	18.4628	0.658127	0.329064	+	0.944308i	$0.393267\pi$
$788$	16.5756	0.590481
$789$	−16.6767	−0.593705
$790$	−9.26806	−0.329743
$791$	0	0
$792$	−4.65529	−0.165418
$793$	−21.8626	−0.776363
$794$	−16.5151	−0.586098
$795$	0.251055	0.00890402
$796$	5.91894	0.209791
$797$	−29.2682	−1.03673	−0.518366	−	0.855159i	$-0.673459\pi$
$797$	−29.2682	−1.03673	−0.518366	+	0.855159i	$0.673459\pi$
$798$	0	0
$799$	−10.8503	−0.383854
$800$	5.68726	0.201075
$801$	10.2272	0.361359
$802$	13.8756	0.489966
$803$	3.00561	0.106066
$804$	−17.6628	−0.622917
$805$	0	0
$806$	1.35665	0.0477860
$807$	−21.5644	−0.759104
$808$	−48.4751	−1.70535
$809$	5.82283	0.204720	0.102360	−	0.994747i	$-0.467361\pi$
$809$	5.82283	0.204720	0.102360	+	0.994747i	$0.467361\pi$
$810$	−3.27693	−0.115140
$811$	49.9139	1.75271	0.876356	−	0.481663i	$-0.159967\pi$
$811$	49.9139	1.75271	0.876356	+	0.481663i	$0.159967\pi$
$812$	0	0
$813$	−8.62753	−0.302581
$814$	−4.14738	−0.145366
$815$	22.5480	0.789822
$816$	0.522009	0.0182740
$817$	15.1838	0.531213
$818$	−30.6313	−1.07100
$819$	0	0
$820$	−2.44198	−0.0852776
$821$	12.2633	0.427991	0.213995	−	0.976835i	$-0.431352\pi$
$821$	12.2633	0.427991	0.213995	+	0.976835i	$0.431352\pi$
$822$	19.9180	0.694719
$823$	−8.02719	−0.279810	−0.139905	−	0.990165i	$-0.544680\pi$
$823$	−8.02719	−0.279810	−0.139905	+	0.990165i	$0.544680\pi$
$824$	35.0836	1.22219
$825$	1.78763	0.0622373
$826$	0	0
$827$	−51.8428	−1.80275	−0.901376	−	0.433038i	$-0.857442\pi$
$827$	−51.8428	−1.80275	−0.901376	+	0.433038i	$0.857442\pi$
$828$	8.37294	0.290980
$829$	28.8317	1.00137	0.500683	−	0.865631i	$-0.333082\pi$
$829$	28.8317	1.00137	0.500683	+	0.865631i	$0.333082\pi$
$830$	13.1046	0.454868
$831$	−21.3914	−0.742058
$832$	−7.48893	−0.259632
$833$	0	0
$834$	4.67046	0.161725
$835$	−13.1173	−0.453943
$836$	7.91939	0.273898
$837$	−5.62728	−0.194507
$838$	−26.0929	−0.901365
$839$	−31.2608	−1.07924	−0.539622	−	0.841907i	$-0.681433\pi$
$839$	−31.2608	−1.07924	−0.539622	+	0.841907i	$0.681433\pi$
$840$	0	0
$841$	−10.5395	−0.363432
$842$	29.9790	1.03314
$843$	−0.548025	−0.0188750
$844$	−8.33359	−0.286854
$845$	−10.5389	−0.362549
$846$	−2.12688	−0.0731236
$847$	0	0
$848$	−0.0136401	−0.000468402 0
$849$	40.8404	1.40164
$850$	−4.69795	−0.161138
$851$	19.3739	0.664127
$852$	−26.0500	−0.892459
$853$	−0.0523093	−0.00179103	−0.000895517	−	1.00000i	$-0.500285\pi$
$853$	−0.0523093	−0.00179103	−0.000895517		1.00000i	$0.500285\pi$
$854$	0	0
$855$	−5.79389	−0.198147
$856$	47.0544	1.60829
$857$	−17.8524	−0.609827	−0.304914	−	0.952380i	$-0.598628\pi$
$857$	−17.8524	−0.609827	−0.304914	+	0.952380i	$0.598628\pi$
$858$	−2.42519	−0.0827947
$859$	19.1365	0.652929	0.326464	−	0.945209i	$-0.394143\pi$
$859$	19.1365	0.652929	0.326464	+	0.945209i	$0.394143\pi$
$860$	−4.04090	−0.137793
$861$	0	0
$862$	25.4855	0.868038
$863$	−0.466200	−0.0158696	−0.00793481	−	0.999969i	$-0.502526\pi$
$863$	−0.466200	−0.0158696	−0.00793481	+	0.999969i	$0.502526\pi$
$864$	32.0038	1.08879
$865$	9.17974	0.312121
$866$	2.54421	0.0864556
$867$	−16.6406	−0.565144
$868$	0	0
$869$	14.4063	0.488699
$870$	−4.94124	−0.167524
$871$	16.6399	0.563820
$872$	6.61194	0.223909
$873$	−11.2941	−0.382246
$874$	22.0941	0.747345
$875$	0	0
$876$	−3.72342	−0.125803
$877$	−17.8623	−0.603166	−0.301583	−	0.953440i	$-0.597515\pi$
$877$	−17.8623	−0.603166	−0.301583	+	0.953440i	$0.597515\pi$
$878$	−1.54239	−0.0520530
$879$	−9.24085	−0.311686
$880$	−0.0971237	−0.00327404
$881$	−44.1925	−1.48888	−0.744442	−	0.667687i	$-0.767285\pi$
$881$	−44.1925	−1.48888	−0.744442	+	0.667687i	$0.767285\pi$
$882$	0	0
$883$	14.1469	0.476082	0.238041	−	0.971255i	$-0.423495\pi$
$883$	14.1469	0.476082	0.238041	+	0.971255i	$0.423495\pi$
$884$	−10.6717	−0.358928
$885$	9.83360	0.330553
$886$	10.2580	0.344624
$887$	−1.05581	−0.0354507	−0.0177253	−	0.999843i	$-0.505642\pi$
$887$	−1.05581	−0.0354507	−0.0177253	+	0.999843i	$0.505642\pi$
$888$	13.3442	0.447803
$889$	0	0
$890$	−7.18210	−0.240745
$891$	5.09367	0.170644
$892$	5.38055	0.180154
$893$	9.39720	0.314465
$894$	−12.9639	−0.433576
$895$	24.7134	0.826079
$896$	0	0
$897$	11.3289	0.378261
$898$	−27.4784	−0.916965
$899$	−4.29656	−0.143298
$900$	1.54194	0.0513980
$901$	1.02556	0.0341665
$902$	−2.26698	−0.0754822
$903$	0	0
$904$	30.6046	1.01789
$905$	−18.5078	−0.615218
$906$	−22.6872	−0.753733
$907$	−24.9512	−0.828490	−0.414245	−	0.910166i	$-0.635954\pi$
$907$	−24.9512	−0.828490	−0.414245	+	0.910166i	$0.635954\pi$
$908$	−23.3464	−0.774778
$909$	−21.2251	−0.703992
$910$	0	0
$911$	−6.17965	−0.204741	−0.102370	−	0.994746i	$-0.532643\pi$
$911$	−6.17965	−0.204741	−0.102370	+	0.994746i	$0.532643\pi$
$912$	−0.452102	−0.0149706
$913$	−20.3698	−0.674143
$914$	−22.4870	−0.743803
$915$	−18.5331	−0.612686
$916$	25.2827	0.835365
$917$	0	0
$918$	−26.4367	−0.872540
$919$	−3.64013	−0.120077	−0.0600384	−	0.998196i	$-0.519122\pi$
$919$	−3.64013	−0.120077	−0.0600384	+	0.998196i	$0.519122\pi$
$920$	−15.2716	−0.503491
$921$	−8.06050	−0.265603
$922$	17.1066	0.563376
$923$	24.5414	0.807790
$924$	0	0
$925$	3.56785	0.117310
$926$	−1.18337	−0.0388879
$927$	15.3615	0.504539
$928$	24.4357	0.802140
$929$	−14.4978	−0.475658	−0.237829	−	0.971307i	$-0.576436\pi$
$929$	−14.4978	−0.475658	−0.237829	+	0.971307i	$0.576436\pi$
$930$	1.15005	0.0377115
$931$	0	0
$932$	16.2137	0.531096
$933$	20.1488	0.659642
$934$	−10.0853	−0.330001
$935$	7.30249	0.238817
$936$	−5.43309	−0.177586
$937$	−5.84894	−0.191077	−0.0955383	−	0.995426i	$-0.530457\pi$
$937$	−5.84894	−0.191077	−0.0955383	+	0.995426i	$0.530457\pi$
$938$	0	0
$939$	−34.9398	−1.14022
$940$	−2.50090	−0.0815704
$941$	15.7557	0.513621	0.256811	−	0.966462i	$-0.417328\pi$
$941$	15.7557	0.513621	0.256811	+	0.966462i	$0.417328\pi$
$942$	5.63434	0.183577
$943$	10.5899	0.344853
$944$	−0.534269	−0.0173890
$945$	0	0
$946$	−3.75132	−0.121966
$947$	−28.3262	−0.920477	−0.460239	−	0.887795i	$-0.652236\pi$
$947$	−28.3262	−0.920477	−0.460239	+	0.887795i	$0.652236\pi$
$948$	−17.8468	−0.579638
$949$	3.50778	0.113867
$950$	4.06880	0.132009
$951$	−12.3781	−0.401388
$952$	0	0
$953$	−21.2419	−0.688093	−0.344047	−	0.938953i	$-0.611798\pi$
$953$	−21.2419	−0.688093	−0.344047	+	0.938953i	$0.611798\pi$
$954$	0.201032	0.00650865
$955$	−7.64748	−0.247467
$956$	32.5208	1.05180
$957$	7.68067	0.248281
$958$	−17.1273	−0.553357
$959$	0	0
$960$	−6.34843	−0.204895
$961$	1.00000	0.0322581
$962$	−4.84032	−0.156058
$963$	20.6030	0.663923
$964$	0.838521	0.0270069
$965$	−10.5268	−0.338870
$966$	0	0
$967$	−23.6698	−0.761169	−0.380584	−	0.924746i	$-0.624277\pi$
$967$	−23.6698	−0.761169	−0.380584	+	0.924746i	$0.624277\pi$
$968$	25.8546	0.830998
$969$	33.9924	1.09199
$970$	7.93135	0.254660
$971$	11.4013	0.365884	0.182942	−	0.983124i	$-0.441438\pi$
$971$	11.4013	0.365884	0.182942	+	0.983124i	$0.441438\pi$
$972$	14.8287	0.475632
$973$	0	0
$974$	−5.06075	−0.162157
$975$	2.08631	0.0668153
$976$	1.00692	0.0322307
$977$	−0.659812	−0.0211092	−0.0105546	−	0.999944i	$-0.503360\pi$
$977$	−0.659812	−0.0211092	−0.0105546	+	0.999944i	$0.503360\pi$
$978$	−25.9312	−0.829189
$979$	11.1639	0.356799
$980$	0	0
$981$	2.89507	0.0924326
$982$	−19.7493	−0.630226
$983$	−25.5079	−0.813575	−0.406787	−	0.913523i	$-0.633351\pi$
$983$	−25.5079	−0.813575	−0.406787	+	0.913523i	$0.633351\pi$
$984$	7.29403	0.232525
$985$	−13.2375	−0.421783
$986$	−20.1850	−0.642822
$987$	0	0
$988$	9.24255	0.294045
$989$	17.5237	0.557221
$990$	1.43144	0.0454942
$991$	−6.93060	−0.220158	−0.110079	−	0.993923i	$-0.535110\pi$
$991$	−6.93060	−0.220158	−0.110079	+	0.993923i	$0.535110\pi$
$992$	−5.68726	−0.180571
$993$	29.2046	0.926780
$994$	0	0
$995$	−4.72696	−0.149855
$996$	25.2346	0.799589
$997$	−52.7898	−1.67187	−0.835935	−	0.548828i	$-0.815074\pi$
$997$	−52.7898	−1.67187	−0.835935	+	0.548828i	$0.815074\pi$
$998$	−21.1491	−0.669462
$999$	20.0773	0.635217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.w.1.8	✓	11
7.6	odd	2		7595.2.a.x.1.8	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7595.2.a.w.1.8	✓	11	1.1	even	1	trivial
7595.2.a.x.1.8	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)

\(f(q)\)	\(=\)	\(q+0.864774 q^{2} -1.32988 q^{3} -1.25217 q^{4} +1.00000 q^{5} -1.15005 q^{6} -2.81239 q^{8} -1.23142 q^{9} +O(q^{10})\)	\(q+0.864774 q^{2} -1.32988 q^{3} -1.25217 q^{4} +1.00000 q^{5} -1.15005 q^{6} -2.81239 q^{8} -1.23142 q^{9} +0.864774 q^{10} -1.34420 q^{11} +1.66523 q^{12} -1.56879 q^{13} -1.32988 q^{15} +0.0722536 q^{16} -5.43257 q^{17} -1.06490 q^{18} +4.70505 q^{19} -1.25217 q^{20} -1.16243 q^{22} +5.43013 q^{23} +3.74014 q^{24} +1.00000 q^{25} -1.35665 q^{26} +5.62728 q^{27} +4.29656 q^{29} -1.15005 q^{30} -1.00000 q^{31} +5.68726 q^{32} +1.78763 q^{33} -4.69795 q^{34} +1.54194 q^{36} +3.56785 q^{37} +4.06880 q^{38} +2.08631 q^{39} -2.81239 q^{40} +1.95020 q^{41} +3.22712 q^{43} +1.68317 q^{44} -1.23142 q^{45} +4.69583 q^{46} +1.99726 q^{47} -0.0960887 q^{48} +0.864774 q^{50} +7.22467 q^{51} +1.96439 q^{52} -0.188780 q^{53} +4.86632 q^{54} -1.34420 q^{55} -6.25715 q^{57} +3.71556 q^{58} -7.39435 q^{59} +1.66523 q^{60} +13.9359 q^{61} -0.864774 q^{62} +4.77368 q^{64} -1.56879 q^{65} +1.54590 q^{66} -10.6068 q^{67} +6.80248 q^{68} -7.22142 q^{69} -15.6435 q^{71} +3.46323 q^{72} -2.23598 q^{73} +3.08538 q^{74} -1.32988 q^{75} -5.89150 q^{76} +1.80418 q^{78} -10.7173 q^{79} +0.0722536 q^{80} -3.78935 q^{81} +1.68649 q^{82} +15.1538 q^{83} -5.43257 q^{85} +2.79073 q^{86} -5.71392 q^{87} +3.78043 q^{88} -8.30518 q^{89} -1.06490 q^{90} -6.79942 q^{92} +1.32988 q^{93} +1.72718 q^{94} +4.70505 q^{95} -7.56337 q^{96} +9.17159 q^{97} +1.65528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{3} + 6 q^{4} + 11 q^{5} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 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

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