LMFDB - Embedded newform 5225.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5225,2,Mod(1,5225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5225, 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("5225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5225 = 5^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5225.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:	$41.7218350561$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 $ x^7 - x^6 - 14x^5 + 10x^4 + 59x^3 - 27x^2 - 66*x + 30
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.55401$ of defining polynomial
Character	$\chi$	$=$	5225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55401 q^{2} +2.99825 q^{3} +4.52299 q^{4} -7.65758 q^{6} -4.42321 q^{7} -6.44376 q^{8} +5.98952 q^{9} +O(q^{10})$	\(q-2.55401 q^{2} +2.99825 q^{3} +4.52299 q^{4} -7.65758 q^{6} -4.42321 q^{7} -6.44376 q^{8} +5.98952 q^{9} -1.00000 q^{11} +13.5611 q^{12} +5.89690 q^{13} +11.2969 q^{14} +7.41147 q^{16} +2.93922 q^{17} -15.2973 q^{18} +1.00000 q^{19} -13.2619 q^{21} +2.55401 q^{22} +0.372904 q^{23} -19.3200 q^{24} -15.0608 q^{26} +8.96335 q^{27} -20.0061 q^{28} -3.47526 q^{29} +6.37391 q^{31} -6.04149 q^{32} -2.99825 q^{33} -7.50681 q^{34} +27.0906 q^{36} -0.926528 q^{37} -2.55401 q^{38} +17.6804 q^{39} -6.67861 q^{41} +33.8711 q^{42} -2.12805 q^{43} -4.52299 q^{44} -0.952402 q^{46} +1.72093 q^{47} +22.2215 q^{48} +12.5648 q^{49} +8.81252 q^{51} +26.6716 q^{52} +1.44022 q^{53} -22.8925 q^{54} +28.5021 q^{56} +2.99825 q^{57} +8.87587 q^{58} +7.71718 q^{59} +4.16881 q^{61} -16.2791 q^{62} -26.4929 q^{63} +0.607107 q^{64} +7.65758 q^{66} +11.3778 q^{67} +13.2941 q^{68} +1.11806 q^{69} +2.40794 q^{71} -38.5950 q^{72} -14.4653 q^{73} +2.36637 q^{74} +4.52299 q^{76} +4.42321 q^{77} -45.1560 q^{78} +1.67368 q^{79} +8.90583 q^{81} +17.0573 q^{82} +6.47897 q^{83} -59.9835 q^{84} +5.43508 q^{86} -10.4197 q^{87} +6.44376 q^{88} -4.95706 q^{89} -26.0832 q^{91} +1.68664 q^{92} +19.1106 q^{93} -4.39529 q^{94} -18.1139 q^{96} -8.24006 q^{97} -32.0906 q^{98} -5.98952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 15 * q^4 - 2 * q^6 - 10 * q^7 + 9 * q^8 + 11 * q^9	$ 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9} - 7 q^{11} + 16 q^{12} + 4 q^{13} + 6 q^{14} + 27 q^{16} - 2 q^{17} - 9 q^{18} + 7 q^{19} - 14 q^{21} - q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{26} + 4 q^{27} - 26 q^{28} - 18 q^{29} + 24 q^{31} + 49 q^{32} + 2 q^{33} - 6 q^{34} + 29 q^{36} + q^{38} + 24 q^{39} - 12 q^{41} + 44 q^{42} - 2 q^{43} - 15 q^{44} - 4 q^{46} - 8 q^{47} + 72 q^{48} + 17 q^{49} - 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} + 26 q^{56} - 2 q^{57} + 8 q^{58} - 10 q^{59} + 14 q^{61} - 14 q^{62} + 55 q^{64} + 2 q^{66} - 8 q^{67} + 18 q^{68} - 6 q^{69} + 10 q^{71} - 53 q^{72} + 6 q^{73} + 26 q^{74} + 15 q^{76} + 10 q^{77} - 22 q^{78} + 52 q^{79} - q^{81} - 24 q^{82} + 10 q^{83} - 6 q^{84} + 8 q^{86} - 6 q^{87} - 9 q^{88} + 12 q^{91} - 2 q^{93} + 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) $ 7 * q + q^2 - 2 * q^3 + 15 * q^4 - 2 * q^6 - 10 * q^7 + 9 * q^8 + 11 * q^9 - 7 * q^11 + 16 * q^12 + 4 * q^13 + 6 * q^14 + 27 * q^16 - 2 * q^17 - 9 * q^18 + 7 * q^19 - 14 * q^21 - q^22 - 10 * q^23 - 2 * q^24 - 8 * q^26 + 4 * q^27 - 26 * q^28 - 18 * q^29 + 24 * q^31 + 49 * q^32 + 2 * q^33 - 6 * q^34 + 29 * q^36 + q^38 + 24 * q^39 - 12 * q^41 + 44 * q^42 - 2 * q^43 - 15 * q^44 - 4 * q^46 - 8 * q^47 + 72 * q^48 + 17 * q^49 - 24 * q^51 + 60 * q^52 - 2 * q^53 - 52 * q^54 + 26 * q^56 - 2 * q^57 + 8 * q^58 - 10 * q^59 + 14 * q^61 - 14 * q^62 + 55 * q^64 + 2 * q^66 - 8 * q^67 + 18 * q^68 - 6 * q^69 + 10 * q^71 - 53 * q^72 + 6 * q^73 + 26 * q^74 + 15 * q^76 + 10 * q^77 - 22 * q^78 + 52 * q^79 - q^81 - 24 * q^82 + 10 * q^83 - 6 * q^84 + 8 * q^86 - 6 * q^87 - 9 * q^88 + 12 * q^91 - 2 * q^93 + 24 * q^94 + 6 * q^96 + 24 * q^97 - 19 * q^98 - 11 * 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 $

$2$	−2.55401	−1.80596	−0.902981	−	0.429681i	$-0.858626\pi$
$2$	−2.55401	−1.80596	−0.902981	+	0.429681i	$0.858626\pi$
$3$	2.99825	1.73104	0.865521	−	0.500872i	$-0.166987\pi$
$3$	2.99825	1.73104	0.865521	+	0.500872i	$0.166987\pi$
$4$	4.52299	2.26150
$5$	0	0
$5$	0	0
$6$	−7.65758	−3.12620
$7$	−4.42321	−1.67182	−0.835908	−	0.548869i	$-0.815058\pi$
$7$	−4.42321	−1.67182	−0.835908	+	0.548869i	$0.815058\pi$
$8$	−6.44376	−2.27821
$9$	5.98952	1.99651
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	13.5611	3.91475
$13$	5.89690	1.63551	0.817753	−	0.575570i	$-0.195220\pi$
$13$	5.89690	1.63551	0.817753	+	0.575570i	$0.195220\pi$
$14$	11.2969	3.01924
$15$	0	0
$16$	7.41147	1.85287
$17$	2.93922	0.712865	0.356433	−	0.934321i	$-0.383993\pi$
$17$	2.93922	0.712865	0.356433	+	0.934321i	$0.383993\pi$
$18$	−15.2973	−3.60562
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−13.2619	−2.89398
$22$	2.55401	0.544518
$23$	0.372904	0.0777558	0.0388779	−	0.999244i	$-0.487622\pi$
$23$	0.372904	0.0777558	0.0388779	+	0.999244i	$0.487622\pi$
$24$	−19.3200	−3.94368
$25$	0	0
$26$	−15.0608	−2.95366
$27$	8.96335	1.72500
$28$	−20.0061	−3.78081
$29$	−3.47526	−0.645340	−0.322670	−	0.946512i	$-0.604580\pi$
$29$	−3.47526	−0.645340	−0.322670	+	0.946512i	$0.604580\pi$
$30$	0	0
$31$	6.37391	1.14479	0.572394	−	0.819979i	$-0.306015\pi$
$31$	6.37391	1.14479	0.572394	+	0.819979i	$0.306015\pi$
$32$	−6.04149	−1.06799
$33$	−2.99825	−0.521929
$34$	−7.50681	−1.28741
$35$	0	0
$36$	27.0906	4.51509
$37$	−0.926528	−0.152320	−0.0761601	−	0.997096i	$-0.524266\pi$
$37$	−0.926528	−0.152320	−0.0761601	+	0.997096i	$0.524266\pi$
$38$	−2.55401	−0.414316
$39$	17.6804	2.83113
$40$	0	0
$41$	−6.67861	−1.04302	−0.521512	−	0.853244i	$-0.674632\pi$
$41$	−6.67861	−1.04302	−0.521512	+	0.853244i	$0.674632\pi$
$42$	33.8711	5.22642
$43$	−2.12805	−0.324525	−0.162263	−	0.986748i	$-0.551879\pi$
$43$	−2.12805	−0.324525	−0.162263	+	0.986748i	$0.551879\pi$
$44$	−4.52299	−0.681867
$45$	0	0
$46$	−0.952402	−0.140424
$47$	1.72093	0.251024	0.125512	−	0.992092i	$-0.459943\pi$
$47$	1.72093	0.251024	0.125512	+	0.992092i	$0.459943\pi$
$48$	22.2215	3.20739
$49$	12.5648	1.79497
$50$	0	0
$51$	8.81252	1.23400
$52$	26.6716	3.69869
$53$	1.44022	0.197830	0.0989150	−	0.995096i	$-0.468463\pi$
$53$	1.44022	0.197830	0.0989150	+	0.995096i	$0.468463\pi$
$54$	−22.8925	−3.11528
$55$	0	0
$56$	28.5021	3.80875
$57$	2.99825	0.397128
$58$	8.87587	1.16546
$59$	7.71718	1.00469	0.502346	−	0.864667i	$-0.332470\pi$
$59$	7.71718	1.00469	0.502346	+	0.864667i	$0.332470\pi$
$60$	0	0
$61$	4.16881	0.533762	0.266881	−	0.963730i	$-0.414007\pi$
$61$	4.16881	0.533762	0.266881	+	0.963730i	$0.414007\pi$
$62$	−16.2791	−2.06744
$63$	−26.4929	−3.33779
$64$	0.607107	0.0758884
$65$	0	0
$66$	7.65758	0.942583
$67$	11.3778	1.39002	0.695012	−	0.718998i	$-0.255399\pi$
$67$	11.3778	1.39002	0.695012	+	0.718998i	$0.255399\pi$
$68$	13.2941	1.61214
$69$	1.11806	0.134599
$70$	0	0
$71$	2.40794	0.285770	0.142885	−	0.989739i	$-0.454362\pi$
$71$	2.40794	0.285770	0.142885	+	0.989739i	$0.454362\pi$
$72$	−38.5950	−4.54847
$73$	−14.4653	−1.69303	−0.846515	−	0.532365i	$-0.821303\pi$
$73$	−14.4653	−1.69303	−0.846515	+	0.532365i	$0.821303\pi$
$74$	2.36637	0.275084
$75$	0	0
$76$	4.52299	0.518823
$77$	4.42321	0.504072
$78$	−45.1560	−5.11291
$79$	1.67368	0.188304	0.0941521	−	0.995558i	$-0.469986\pi$
$79$	1.67368	0.188304	0.0941521	+	0.995558i	$0.469986\pi$
$80$	0	0
$81$	8.90583	0.989537
$82$	17.0573	1.88366
$83$	6.47897	0.711159	0.355580	−	0.934646i	$-0.384283\pi$
$83$	6.47897	0.711159	0.355580	+	0.934646i	$0.384283\pi$
$84$	−59.9835	−6.54473
$85$	0	0
$86$	5.43508	0.586080
$87$	−10.4197	−1.11711
$88$	6.44376	0.686907
$89$	−4.95706	−0.525448	−0.262724	−	0.964871i	$-0.584621\pi$
$89$	−4.95706	−0.525448	−0.262724	+	0.964871i	$0.584621\pi$
$90$	0	0
$91$	−26.0832	−2.73426
$92$	1.68664	0.175845
$93$	19.1106	1.98168
$94$	−4.39529	−0.453339
$95$	0	0
$96$	−18.1139	−1.84874
$97$	−8.24006	−0.836651	−0.418325	−	0.908297i	$-0.637383\pi$
$97$	−8.24006	−0.836651	−0.418325	+	0.908297i	$0.637383\pi$
$98$	−32.0906	−3.24164
$99$	−5.98952	−0.601970
$100$	0	0
$101$	3.51207	0.349464	0.174732	−	0.984616i	$-0.444094\pi$
$101$	3.51207	0.349464	0.174732	+	0.984616i	$0.444094\pi$
$102$	−22.5073	−2.22856
$103$	2.43194	0.239626	0.119813	−	0.992796i	$-0.461770\pi$
$103$	2.43194	0.239626	0.119813	+	0.992796i	$0.461770\pi$
$104$	−37.9982	−3.72603
$105$	0	0
$106$	−3.67835	−0.357273
$107$	−16.9865	−1.64214	−0.821072	−	0.570825i	$-0.806624\pi$
$107$	−16.9865	−1.64214	−0.821072	+	0.570825i	$0.806624\pi$
$108$	40.5412	3.90108
$109$	3.83586	0.367409	0.183704	−	0.982982i	$-0.441191\pi$
$109$	3.83586	0.367409	0.183704	+	0.982982i	$0.441191\pi$
$110$	0	0
$111$	−2.77797	−0.263673
$112$	−32.7825	−3.09765
$113$	10.7909	1.01512	0.507562	−	0.861615i	$-0.330547\pi$
$113$	10.7909	1.01512	0.507562	+	0.861615i	$0.330547\pi$
$114$	−7.65758	−0.717198
$115$	0	0
$116$	−15.7186	−1.45943
$117$	35.3196	3.26530
$118$	−19.7098	−1.81443
$119$	−13.0008	−1.19178
$120$	0	0
$121$	1.00000	0.0909091
$122$	−10.6472	−0.963953
$123$	−20.0242	−1.80552
$124$	28.8291	2.58893
$125$	0	0
$126$	67.6633	6.02793
$127$	12.0969	1.07342	0.536712	−	0.843765i	$-0.319666\pi$
$127$	12.0969	1.07342	0.536712	+	0.843765i	$0.319666\pi$
$128$	10.5324	0.930942
$129$	−6.38045	−0.561767
$130$	0	0
$131$	−7.99822	−0.698807	−0.349404	−	0.936972i	$-0.613616\pi$
$131$	−7.99822	−0.698807	−0.349404	+	0.936972i	$0.613616\pi$
$132$	−13.5611	−1.18034
$133$	−4.42321	−0.383541
$134$	−29.0592	−2.51033
$135$	0	0
$136$	−18.9396	−1.62406
$137$	−15.9191	−1.36006	−0.680030	−	0.733184i	$-0.738033\pi$
$137$	−15.9191	−1.36006	−0.680030	+	0.733184i	$0.738033\pi$
$138$	−2.85554	−0.243080
$139$	14.7278	1.24920	0.624599	−	0.780946i	$-0.285263\pi$
$139$	14.7278	1.24920	0.624599	+	0.780946i	$0.285263\pi$
$140$	0	0
$141$	5.15979	0.434533
$142$	−6.14992	−0.516090
$143$	−5.89690	−0.493124
$144$	44.3912	3.69926
$145$	0	0
$146$	36.9445	3.05755
$147$	37.6724	3.10717
$148$	−4.19068	−0.344472
$149$	7.35723	0.602727	0.301364	−	0.953509i	$-0.402558\pi$
$149$	7.35723	0.602727	0.301364	+	0.953509i	$0.402558\pi$
$150$	0	0
$151$	10.5197	0.856083	0.428042	−	0.903759i	$-0.359204\pi$
$151$	10.5197	0.856083	0.428042	+	0.903759i	$0.359204\pi$
$152$	−6.44376	−0.522658
$153$	17.6045	1.42324
$154$	−11.2969	−0.910334
$155$	0	0
$156$	79.9683	6.40259
$157$	16.1669	1.29026	0.645131	−	0.764072i	$-0.276803\pi$
$157$	16.1669	1.29026	0.645131	+	0.764072i	$0.276803\pi$
$158$	−4.27461	−0.340070
$159$	4.31816	0.342452
$160$	0	0
$161$	−1.64943	−0.129993
$162$	−22.7456	−1.78706
$163$	−13.6643	−1.07027	−0.535136	−	0.844766i	$-0.679740\pi$
$163$	−13.6643	−1.07027	−0.535136	+	0.844766i	$0.679740\pi$
$164$	−30.2073	−2.35879
$165$	0	0
$166$	−16.5474	−1.28433
$167$	−10.3060	−0.797501	−0.398750	−	0.917060i	$-0.630556\pi$
$167$	−10.3060	−0.797501	−0.398750	+	0.917060i	$0.630556\pi$
$168$	85.4565	6.59311
$169$	21.7734	1.67488
$170$	0	0
$171$	5.98952	0.458030
$172$	−9.62517	−0.733912
$173$	25.3276	1.92562	0.962811	−	0.270174i	$-0.0870813\pi$
$173$	25.3276	1.92562	0.962811	+	0.270174i	$0.0870813\pi$
$174$	26.6121	2.01746
$175$	0	0
$176$	−7.41147	−0.558661
$177$	23.1381	1.73916
$178$	12.6604	0.948938
$179$	22.8968	1.71139	0.855695	−	0.517481i	$-0.173130\pi$
$179$	22.8968	1.71139	0.855695	+	0.517481i	$0.173130\pi$
$180$	0	0
$181$	8.05994	0.599091	0.299545	−	0.954082i	$-0.403165\pi$
$181$	8.05994	0.599091	0.299545	+	0.954082i	$0.403165\pi$
$182$	66.6169	4.93798
$183$	12.4992	0.923964
$184$	−2.40290	−0.177144
$185$	0	0
$186$	−48.8087	−3.57883
$187$	−2.93922	−0.214937
$188$	7.78376	0.567689
$189$	−39.6468	−2.88388
$190$	0	0
$191$	−17.2143	−1.24559	−0.622793	−	0.782387i	$-0.714002\pi$
$191$	−17.2143	−1.24559	−0.622793	+	0.782387i	$0.714002\pi$
$192$	1.82026	0.131366
$193$	8.31588	0.598590	0.299295	−	0.954161i	$-0.403249\pi$
$193$	8.31588	0.598590	0.299295	+	0.954161i	$0.403249\pi$
$194$	21.0452	1.51096
$195$	0	0
$196$	56.8304	4.05932
$197$	−4.38913	−0.312713	−0.156356	−	0.987701i	$-0.549975\pi$
$197$	−4.38913	−0.312713	−0.156356	+	0.987701i	$0.549975\pi$
$198$	15.2973	1.08713
$199$	19.8924	1.41014	0.705068	−	0.709140i	$-0.250917\pi$
$199$	19.8924	1.41014	0.705068	+	0.709140i	$0.250917\pi$
$200$	0	0
$201$	34.1136	2.40619
$202$	−8.96988	−0.631119
$203$	15.3718	1.07889
$204$	39.8590	2.79069
$205$	0	0
$206$	−6.21121	−0.432755
$207$	2.23352	0.155240
$208$	43.7047	3.03038
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	20.8162	1.43304	0.716522	−	0.697564i	$-0.245733\pi$
$211$	20.8162	1.43304	0.716522	+	0.697564i	$0.245733\pi$
$212$	6.51412	0.447391
$213$	7.21962	0.494680
$214$	43.3837	2.96565
$215$	0	0
$216$	−57.7577	−3.92991
$217$	−28.1931	−1.91387
$218$	−9.79684	−0.663525
$219$	−43.3705	−2.93071
$220$	0	0
$221$	17.3323	1.16590
$222$	7.09496	0.476183
$223$	−11.4967	−0.769874	−0.384937	−	0.922943i	$-0.625777\pi$
$223$	−11.4967	−0.769874	−0.384937	+	0.922943i	$0.625777\pi$
$224$	26.7228	1.78549
$225$	0	0
$226$	−27.5601	−1.83327
$227$	17.5175	1.16268	0.581339	−	0.813662i	$-0.302529\pi$
$227$	17.5175	1.16268	0.581339	+	0.813662i	$0.302529\pi$
$228$	13.5611	0.898104
$229$	−6.64251	−0.438949	−0.219475	−	0.975618i	$-0.570434\pi$
$229$	−6.64251	−0.438949	−0.219475	+	0.975618i	$0.570434\pi$
$230$	0	0
$231$	13.2619	0.872569
$232$	22.3937	1.47022
$233$	12.5323	0.821020	0.410510	−	0.911856i	$-0.365351\pi$
$233$	12.5323	0.821020	0.410510	+	0.911856i	$0.365351\pi$
$234$	−90.2068	−5.89701
$235$	0	0
$236$	34.9048	2.27211
$237$	5.01813	0.325962
$238$	33.2042	2.15231
$239$	−27.3445	−1.76877	−0.884386	−	0.466757i	$-0.845422\pi$
$239$	−27.3445	−1.76877	−0.884386	+	0.466757i	$0.845422\pi$
$240$	0	0
$241$	23.5681	1.51816	0.759079	−	0.650999i	$-0.225650\pi$
$241$	23.5681	1.51816	0.759079	+	0.650999i	$0.225650\pi$
$242$	−2.55401	−0.164178
$243$	−0.188120	−0.0120679
$244$	18.8555	1.20710
$245$	0	0
$246$	51.1420	3.26070
$247$	5.89690	0.375211
$248$	−41.0719	−2.60807
$249$	19.4256	1.23105
$250$	0	0
$251$	−2.04497	−0.129078	−0.0645388	−	0.997915i	$-0.520558\pi$
$251$	−2.04497	−0.129078	−0.0645388	+	0.997915i	$0.520558\pi$
$252$	−119.827	−7.54841
$253$	−0.372904	−0.0234443
$254$	−30.8956	−1.93856
$255$	0	0
$256$	−28.1141	−1.75713
$257$	−21.0705	−1.31434	−0.657171	−	0.753741i	$-0.728247\pi$
$257$	−21.0705	−1.31434	−0.657171	+	0.753741i	$0.728247\pi$
$258$	16.2958	1.01453
$259$	4.09823	0.254651
$260$	0	0
$261$	−20.8152	−1.28843
$262$	20.4276	1.26202
$263$	21.5153	1.32669	0.663345	−	0.748313i	$-0.269136\pi$
$263$	21.5153	1.32669	0.663345	+	0.748313i	$0.269136\pi$
$264$	19.3200	1.18906
$265$	0	0
$266$	11.2969	0.692660
$267$	−14.8625	−0.909572
$268$	51.4618	3.14353
$269$	8.56257	0.522069	0.261034	−	0.965329i	$-0.415936\pi$
$269$	8.56257	0.522069	0.261034	+	0.965329i	$0.415936\pi$
$270$	0	0
$271$	−12.5375	−0.761602	−0.380801	−	0.924657i	$-0.624352\pi$
$271$	−12.5375	−0.761602	−0.380801	+	0.924657i	$0.624352\pi$
$272$	21.7839	1.32084
$273$	−78.2041	−4.73313
$274$	40.6576	2.45622
$275$	0	0
$276$	5.05698	0.304394
$277$	−11.2455	−0.675679	−0.337840	−	0.941204i	$-0.609696\pi$
$277$	−11.2455	−0.675679	−0.337840	+	0.941204i	$0.609696\pi$
$278$	−37.6151	−2.25600
$279$	38.1767	2.28558
$280$	0	0
$281$	−20.3272	−1.21262	−0.606310	−	0.795228i	$-0.707351\pi$
$281$	−20.3272	−1.21262	−0.606310	+	0.795228i	$0.707351\pi$
$282$	−13.1782	−0.784749
$283$	26.7277	1.58880	0.794400	−	0.607395i	$-0.207786\pi$
$283$	26.7277	1.58880	0.794400	+	0.607395i	$0.207786\pi$
$284$	10.8911	0.646268
$285$	0	0
$286$	15.0608	0.890562
$287$	29.5409	1.74374
$288$	−36.1856	−2.13226
$289$	−8.36099	−0.491823
$290$	0	0
$291$	−24.7058	−1.44828
$292$	−65.4262	−3.82878
$293$	9.95580	0.581624	0.290812	−	0.956780i	$-0.406075\pi$
$293$	9.95580	0.581624	0.290812	+	0.956780i	$0.406075\pi$
$294$	−96.2159	−5.61142
$295$	0	0
$296$	5.97032	0.347018
$297$	−8.96335	−0.520106
$298$	−18.7905	−1.08850
$299$	2.19898	0.127170
$300$	0	0
$301$	9.41283	0.542547
$302$	−26.8675	−1.54605
$303$	10.5301	0.604937
$304$	7.41147	0.425077
$305$	0	0
$306$	−44.9622	−2.57032
$307$	−3.58808	−0.204783	−0.102391	−	0.994744i	$-0.532649\pi$
$307$	−3.58808	−0.204783	−0.102391	+	0.994744i	$0.532649\pi$
$308$	20.0061	1.13996
$309$	7.29157	0.414803
$310$	0	0
$311$	−13.8469	−0.785187	−0.392594	−	0.919712i	$-0.628422\pi$
$311$	−13.8469	−0.785187	−0.392594	+	0.919712i	$0.628422\pi$
$312$	−113.928	−6.44992
$313$	15.3982	0.870360	0.435180	−	0.900344i	$-0.356685\pi$
$313$	15.3982	0.870360	0.435180	+	0.900344i	$0.356685\pi$
$314$	−41.2906	−2.33016
$315$	0	0
$316$	7.57006	0.425849
$317$	5.96359	0.334949	0.167474	−	0.985876i	$-0.446439\pi$
$317$	5.96359	0.334949	0.167474	+	0.985876i	$0.446439\pi$
$318$	−11.0286	−0.618455
$319$	3.47526	0.194577
$320$	0	0
$321$	−50.9297	−2.84262
$322$	4.21267	0.234763
$323$	2.93922	0.163542
$324$	40.2810	2.23783
$325$	0	0
$326$	34.8989	1.93287
$327$	11.5009	0.636000
$328$	43.0354	2.37623
$329$	−7.61204	−0.419665
$330$	0	0
$331$	−5.58507	−0.306983	−0.153492	−	0.988150i	$-0.549052\pi$
$331$	−5.58507	−0.306983	−0.153492	+	0.988150i	$0.549052\pi$
$332$	29.3043	1.60828
$333$	−5.54946	−0.304109
$334$	26.3216	1.44026
$335$	0	0
$336$	−98.2902	−5.36217
$337$	29.0465	1.58227	0.791133	−	0.611645i	$-0.209492\pi$
$337$	29.0465	1.58227	0.791133	+	0.611645i	$0.209492\pi$
$338$	−55.6097	−3.02477
$339$	32.3539	1.75722
$340$	0	0
$341$	−6.37391	−0.345166
$342$	−15.2973	−0.827185
$343$	−24.6142	−1.32904
$344$	13.7127	0.739337
$345$	0	0
$346$	−64.6871	−3.47760
$347$	6.25081	0.335561	0.167781	−	0.985824i	$-0.446340\pi$
$347$	6.25081	0.335561	0.167781	+	0.985824i	$0.446340\pi$
$348$	−47.1283	−2.52634
$349$	7.81752	0.418462	0.209231	−	0.977866i	$-0.432904\pi$
$349$	7.81752	0.418462	0.209231	+	0.977866i	$0.432904\pi$
$350$	0	0
$351$	52.8560	2.82124
$352$	6.04149	0.322012
$353$	−10.0965	−0.537380	−0.268690	−	0.963227i	$-0.586591\pi$
$353$	−10.0965	−0.537380	−0.268690	+	0.963227i	$0.586591\pi$
$354$	−59.0950	−3.14086
$355$	0	0
$356$	−22.4208	−1.18830
$357$	−38.9796	−2.06302
$358$	−58.4788	−3.09070
$359$	29.3266	1.54780	0.773899	−	0.633309i	$-0.218304\pi$
$359$	29.3266	1.54780	0.773899	+	0.633309i	$0.218304\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−20.5852	−1.08193
$363$	2.99825	0.157368
$364$	−117.974	−6.18353
$365$	0	0
$366$	−31.9230	−1.66864
$367$	13.7848	0.719558	0.359779	−	0.933037i	$-0.382852\pi$
$367$	13.7848	0.719558	0.359779	+	0.933037i	$0.382852\pi$
$368$	2.76377	0.144071
$369$	−40.0017	−2.08241
$370$	0	0
$371$	−6.37041	−0.330735
$372$	86.4370	4.48155
$373$	−16.4169	−0.850036	−0.425018	−	0.905185i	$-0.639732\pi$
$373$	−16.4169	−0.850036	−0.425018	+	0.905185i	$0.639732\pi$
$374$	7.50681	0.388168
$375$	0	0
$376$	−11.0893	−0.571885
$377$	−20.4933	−1.05546
$378$	101.258	5.20817
$379$	6.93533	0.356244	0.178122	−	0.984008i	$-0.442998\pi$
$379$	6.93533	0.356244	0.178122	+	0.984008i	$0.442998\pi$
$380$	0	0
$381$	36.2695	1.85814
$382$	43.9657	2.24948
$383$	−1.47147	−0.0751884	−0.0375942	−	0.999293i	$-0.511969\pi$
$383$	−1.47147	−0.0751884	−0.0375942	+	0.999293i	$0.511969\pi$
$384$	31.5788	1.61150
$385$	0	0
$386$	−21.2389	−1.08103
$387$	−12.7460	−0.647917
$388$	−37.2697	−1.89208
$389$	6.79609	0.344575	0.172288	−	0.985047i	$-0.444884\pi$
$389$	6.79609	0.344575	0.172288	+	0.985047i	$0.444884\pi$
$390$	0	0
$391$	1.09605	0.0554294
$392$	−80.9644	−4.08932
$393$	−23.9807	−1.20967
$394$	11.2099	0.564747
$395$	0	0
$396$	−27.0906	−1.36135
$397$	12.3808	0.621373	0.310687	−	0.950512i	$-0.399441\pi$
$397$	12.3808	0.621373	0.310687	+	0.950512i	$0.399441\pi$
$398$	−50.8055	−2.54665
$399$	−13.2619	−0.663926
$400$	0	0
$401$	−0.0361352	−0.00180451	−0.000902254	−	1.00000i	$-0.500287\pi$
$401$	−0.0361352	−0.00180451	−0.000902254		1.00000i	$0.500287\pi$
$402$	−87.1267	−4.34549
$403$	37.5863	1.87231
$404$	15.8851	0.790312
$405$	0	0
$406$	−39.2598	−1.94843
$407$	0.926528	0.0459263
$408$	−56.7858	−2.81131
$409$	−9.94955	−0.491973	−0.245987	−	0.969273i	$-0.579112\pi$
$409$	−9.94955	−0.491973	−0.245987	+	0.969273i	$0.579112\pi$
$410$	0	0
$411$	−47.7295	−2.35432
$412$	10.9996	0.541913
$413$	−34.1347	−1.67966
$414$	−5.70444	−0.280358
$415$	0	0
$416$	−35.6260	−1.74671
$417$	44.1577	2.16241
$418$	2.55401	0.124921
$419$	27.2560	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$419$	27.2560	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$420$	0	0
$421$	16.5342	0.805828	0.402914	−	0.915238i	$-0.367997\pi$
$421$	16.5342	0.805828	0.402914	+	0.915238i	$0.367997\pi$
$422$	−53.1648	−2.58802
$423$	10.3076	0.501171
$424$	−9.28045	−0.450699
$425$	0	0
$426$	−18.4390	−0.893374
$427$	−18.4395	−0.892351
$428$	−76.8296	−3.71370
$429$	−17.6804	−0.853618
$430$	0	0
$431$	33.9550	1.63556	0.817778	−	0.575533i	$-0.195206\pi$
$431$	33.9550	1.63556	0.817778	+	0.575533i	$0.195206\pi$
$432$	66.4316	3.19619
$433$	3.55114	0.170657	0.0853285	−	0.996353i	$-0.472806\pi$
$433$	3.55114	0.170657	0.0853285	+	0.996353i	$0.472806\pi$
$434$	72.0057	3.45638
$435$	0	0
$436$	17.3496	0.830893
$437$	0.372904	0.0178384
$438$	110.769	5.29274
$439$	6.28232	0.299839	0.149919	−	0.988698i	$-0.452099\pi$
$439$	6.28232	0.299839	0.149919	+	0.988698i	$0.452099\pi$
$440$	0	0
$441$	75.2571	3.58367
$442$	−44.2669	−2.10556
$443$	−26.3969	−1.25415	−0.627077	−	0.778957i	$-0.715749\pi$
$443$	−26.3969	−1.25415	−0.627077	+	0.778957i	$0.715749\pi$
$444$	−12.5647	−0.596295
$445$	0	0
$446$	29.3627	1.39036
$447$	22.0588	1.04335
$448$	−2.68536	−0.126872
$449$	−0.649120	−0.0306339	−0.0153169	−	0.999883i	$-0.504876\pi$
$449$	−0.649120	−0.0306339	−0.0153169	+	0.999883i	$0.504876\pi$
$450$	0	0
$451$	6.67861	0.314484
$452$	48.8072	2.29570
$453$	31.5408	1.48192
$454$	−44.7400	−2.09975
$455$	0	0
$456$	−19.3200	−0.904743
$457$	4.74769	0.222087	0.111044	−	0.993816i	$-0.464581\pi$
$457$	4.74769	0.222087	0.111044	+	0.993816i	$0.464581\pi$
$458$	16.9651	0.792725
$459$	26.3453	1.22969
$460$	0	0
$461$	13.9711	0.650701	0.325350	−	0.945594i	$-0.394518\pi$
$461$	13.9711	0.650701	0.325350	+	0.945594i	$0.394518\pi$
$462$	−33.8711	−1.57583
$463$	14.7822	0.686985	0.343492	−	0.939155i	$-0.388390\pi$
$463$	14.7822	0.686985	0.343492	+	0.939155i	$0.388390\pi$
$464$	−25.7568	−1.19573
$465$	0	0
$466$	−32.0077	−1.48273
$467$	22.5444	1.04323	0.521615	−	0.853181i	$-0.325330\pi$
$467$	22.5444	1.04323	0.521615	+	0.853181i	$0.325330\pi$
$468$	159.750	7.38446
$469$	−50.3265	−2.32386
$470$	0	0
$471$	48.4726	2.23350
$472$	−49.7277	−2.28890
$473$	2.12805	0.0978480
$474$	−12.8164	−0.588676
$475$	0	0
$476$	−58.8024	−2.69520
$477$	8.62625	0.394969
$478$	69.8384	3.19433
$479$	−21.7949	−0.995835	−0.497918	−	0.867224i	$-0.665902\pi$
$479$	−21.7949	−0.995835	−0.497918	+	0.867224i	$0.665902\pi$
$480$	0	0
$481$	−5.46364	−0.249121
$482$	−60.1934	−2.74173
$483$	−4.94542	−0.225024
$484$	4.52299	0.205591
$485$	0	0
$486$	0.480462	0.0217942
$487$	5.40569	0.244955	0.122478	−	0.992471i	$-0.460916\pi$
$487$	5.40569	0.244955	0.122478	+	0.992471i	$0.460916\pi$
$488$	−26.8628	−1.21602
$489$	−40.9691	−1.85269
$490$	0	0
$491$	−41.4597	−1.87105	−0.935524	−	0.353263i	$-0.885072\pi$
$491$	−41.4597	−1.87105	−0.935524	+	0.353263i	$0.885072\pi$
$492$	−90.5692	−4.08317
$493$	−10.2146	−0.460040
$494$	−15.0608	−0.677616
$495$	0	0
$496$	47.2400	2.12114
$497$	−10.6508	−0.477755
$498$	−49.6133	−2.22322
$499$	18.0596	0.808459	0.404229	−	0.914658i	$-0.367540\pi$
$499$	18.0596	0.808459	0.404229	+	0.914658i	$0.367540\pi$
$500$	0	0
$501$	−30.8999	−1.38051
$502$	5.22289	0.233109
$503$	−33.5764	−1.49710	−0.748549	−	0.663080i	$-0.769249\pi$
$503$	−33.5764	−1.49710	−0.748549	+	0.663080i	$0.769249\pi$
$504$	170.714	7.60420
$505$	0	0
$506$	0.952402	0.0423394
$507$	65.2823	2.89929
$508$	54.7141	2.42755
$509$	−19.8963	−0.881889	−0.440944	−	0.897534i	$-0.645356\pi$
$509$	−19.8963	−0.881889	−0.440944	+	0.897534i	$0.645356\pi$
$510$	0	0
$511$	63.9829	2.83044
$512$	50.7391	2.24237
$513$	8.96335	0.395742
$514$	53.8144	2.37365
$515$	0	0
$516$	−28.8587	−1.27043
$517$	−1.72093	−0.0756865
$518$	−10.4669	−0.459891
$519$	75.9386	3.33334
$520$	0	0
$521$	−22.1379	−0.969878	−0.484939	−	0.874548i	$-0.661158\pi$
$521$	−22.1379	−0.969878	−0.484939	+	0.874548i	$0.661158\pi$
$522$	53.1622	2.32685
$523$	−16.0313	−0.701001	−0.350500	−	0.936563i	$-0.613988\pi$
$523$	−16.0313	−0.701001	−0.350500	+	0.936563i	$0.613988\pi$
$524$	−36.1759	−1.58035
$525$	0	0
$526$	−54.9504	−2.39595
$527$	18.7343	0.816079
$528$	−22.2215	−0.967065
$529$	−22.8609	−0.993954
$530$	0	0
$531$	46.2223	2.00588
$532$	−20.0061	−0.867376
$533$	−39.3831	−1.70587
$534$	37.9591	1.64265
$535$	0	0
$536$	−73.3160	−3.16677
$537$	68.6505	2.96249
$538$	−21.8689	−0.942836
$539$	−12.5648	−0.541204
$540$	0	0
$541$	−30.5422	−1.31311	−0.656556	−	0.754278i	$-0.727987\pi$
$541$	−30.5422	−1.31311	−0.656556	+	0.754278i	$0.727987\pi$
$542$	32.0211	1.37542
$543$	24.1657	1.03705
$544$	−17.7572	−0.761336
$545$	0	0
$546$	199.734	8.54785
$547$	−0.0830197	−0.00354967	−0.00177483	−	0.999998i	$-0.500565\pi$
$547$	−0.0830197	−0.00354967	−0.00177483	+	0.999998i	$0.500565\pi$
$548$	−72.0019	−3.07577
$549$	24.9692	1.06566
$550$	0	0
$551$	−3.47526	−0.148051
$552$	−7.20451	−0.306644
$553$	−7.40305	−0.314810
$554$	28.7213	1.22025
$555$	0	0
$556$	66.6138	2.82505
$557$	6.33324	0.268348	0.134174	−	0.990958i	$-0.457162\pi$
$557$	6.33324	0.268348	0.134174	+	0.990958i	$0.457162\pi$
$558$	−97.5038	−4.12767
$559$	−12.5489	−0.530763
$560$	0	0
$561$	−8.81252	−0.372065
$562$	51.9160	2.18995
$563$	26.4539	1.11490	0.557451	−	0.830210i	$-0.311780\pi$
$563$	26.4539	1.11490	0.557451	+	0.830210i	$0.311780\pi$
$564$	23.3377	0.982694
$565$	0	0
$566$	−68.2630	−2.86931
$567$	−39.3924	−1.65432
$568$	−15.5162	−0.651045
$569$	−23.9553	−1.00426	−0.502128	−	0.864793i	$-0.667450\pi$
$569$	−23.9553	−1.00426	−0.502128	+	0.864793i	$0.667450\pi$
$570$	0	0
$571$	8.33187	0.348678	0.174339	−	0.984686i	$-0.444221\pi$
$571$	8.33187	0.348678	0.174339	+	0.984686i	$0.444221\pi$
$572$	−26.6716	−1.11520
$573$	−51.6130	−2.15616
$574$	−75.4479	−3.14913
$575$	0	0
$576$	3.63629	0.151512
$577$	−21.7197	−0.904203	−0.452101	−	0.891967i	$-0.649326\pi$
$577$	−21.7197	−0.904203	−0.452101	+	0.891967i	$0.649326\pi$
$578$	21.3541	0.888214
$579$	24.9331	1.03618
$580$	0	0
$581$	−28.6578	−1.18893
$582$	63.0989	2.61553
$583$	−1.44022	−0.0596480
$584$	93.2106	3.85708
$585$	0	0
$586$	−25.4273	−1.05039
$587$	−38.3274	−1.58194	−0.790971	−	0.611853i	$-0.790424\pi$
$587$	−38.3274	−1.58194	−0.790971	+	0.611853i	$0.790424\pi$
$588$	170.392	7.02685
$589$	6.37391	0.262632
$590$	0	0
$591$	−13.1597	−0.541319
$592$	−6.86693	−0.282229
$593$	−25.1482	−1.03271	−0.516357	−	0.856373i	$-0.672712\pi$
$593$	−25.1482	−1.03271	−0.516357	+	0.856373i	$0.672712\pi$
$594$	22.8925	0.939292
$595$	0	0
$596$	33.2767	1.36307
$597$	59.6425	2.44100
$598$	−5.61622	−0.229664
$599$	−5.97251	−0.244030	−0.122015	−	0.992528i	$-0.538936\pi$
$599$	−5.97251	−0.244030	−0.122015	+	0.992528i	$0.538936\pi$
$600$	0	0
$601$	−1.61426	−0.0658469	−0.0329234	−	0.999458i	$-0.510482\pi$
$601$	−1.61426	−0.0658469	−0.0329234	+	0.999458i	$0.510482\pi$
$602$	−24.0405	−0.979818
$603$	68.1478	2.77519
$604$	47.5806	1.93603
$605$	0	0
$606$	−26.8940	−1.09249
$607$	43.1541	1.75157	0.875786	−	0.482700i	$-0.160344\pi$
$607$	43.1541	1.75157	0.875786	+	0.482700i	$0.160344\pi$
$608$	−6.04149	−0.245015
$609$	46.0886	1.86760
$610$	0	0
$611$	10.1482	0.410551
$612$	79.6251	3.21865
$613$	15.2118	0.614400	0.307200	−	0.951645i	$-0.400608\pi$
$613$	15.2118	0.614400	0.307200	+	0.951645i	$0.400608\pi$
$614$	9.16402	0.369830
$615$	0	0
$616$	−28.5021	−1.14838
$617$	10.1846	0.410016	0.205008	−	0.978760i	$-0.434278\pi$
$617$	10.1846	0.410016	0.205008	+	0.978760i	$0.434278\pi$
$618$	−18.6228	−0.749118
$619$	23.7636	0.955139	0.477569	−	0.878594i	$-0.341518\pi$
$619$	23.7636	0.955139	0.477569	+	0.878594i	$0.341518\pi$
$620$	0	0
$621$	3.34247	0.134129
$622$	35.3653	1.41802
$623$	21.9261	0.878452
$624$	131.038	5.24571
$625$	0	0
$626$	−39.3273	−1.57184
$627$	−2.99825	−0.119739
$628$	73.1229	2.91792
$629$	−2.72327	−0.108584
$630$	0	0
$631$	36.1097	1.43751	0.718753	−	0.695266i	$-0.244713\pi$
$631$	36.1097	1.43751	0.718753	+	0.695266i	$0.244713\pi$
$632$	−10.7848	−0.428997
$633$	62.4122	2.48066
$634$	−15.2311	−0.604904
$635$	0	0
$636$	19.5310	0.774454
$637$	74.0933	2.93568
$638$	−8.87587	−0.351399
$639$	14.4224	0.570543
$640$	0	0
$641$	−34.7607	−1.37297	−0.686483	−	0.727146i	$-0.740846\pi$
$641$	−34.7607	−1.37297	−0.686483	+	0.727146i	$0.740846\pi$
$642$	130.075	5.13366
$643$	32.5548	1.28384	0.641919	−	0.766773i	$-0.278139\pi$
$643$	32.5548	1.28384	0.641919	+	0.766773i	$0.278139\pi$
$644$	−7.46037	−0.293980
$645$	0	0
$646$	−7.50681	−0.295351
$647$	0.726588	0.0285651	0.0142826	−	0.999898i	$-0.495454\pi$
$647$	0.726588	0.0285651	0.0142826	+	0.999898i	$0.495454\pi$
$648$	−57.3870	−2.25437
$649$	−7.71718	−0.302926
$650$	0	0
$651$	−84.5302	−3.31300
$652$	−61.8036	−2.42041
$653$	2.07531	0.0812132	0.0406066	−	0.999175i	$-0.487071\pi$
$653$	2.07531	0.0812132	0.0406066	+	0.999175i	$0.487071\pi$
$654$	−29.3734	−1.14859
$655$	0	0
$656$	−49.4983	−1.93259
$657$	−86.6400	−3.38015
$658$	19.4413	0.757900
$659$	−6.83577	−0.266284	−0.133142	−	0.991097i	$-0.542507\pi$
$659$	−6.83577	−0.266284	−0.133142	+	0.991097i	$0.542507\pi$
$660$	0	0
$661$	26.6223	1.03549	0.517744	−	0.855536i	$-0.326772\pi$
$661$	26.6223	1.03549	0.517744	+	0.855536i	$0.326772\pi$
$662$	14.2644	0.554400
$663$	51.9666	2.01821
$664$	−41.7489	−1.62017
$665$	0	0
$666$	14.1734	0.549208
$667$	−1.29594	−0.0501790
$668$	−46.6139	−1.80354
$669$	−34.4699	−1.33268
$670$	0	0
$671$	−4.16881	−0.160935
$672$	80.1216	3.09076
$673$	−26.9513	−1.03890	−0.519449	−	0.854502i	$-0.673863\pi$
$673$	−26.9513	−1.03890	−0.519449	+	0.854502i	$0.673863\pi$
$674$	−74.1853	−2.85751
$675$	0	0
$676$	98.4810	3.78773
$677$	7.83263	0.301033	0.150516	−	0.988608i	$-0.451906\pi$
$677$	7.83263	0.301033	0.150516	+	0.988608i	$0.451906\pi$
$678$	−82.6323	−3.17347
$679$	36.4475	1.39873
$680$	0	0
$681$	52.5219	2.01264
$682$	16.2791	0.623357
$683$	−3.91204	−0.149690	−0.0748451	−	0.997195i	$-0.523846\pi$
$683$	−3.91204	−0.149690	−0.0748451	+	0.997195i	$0.523846\pi$
$684$	27.0906	1.03583
$685$	0	0
$686$	62.8651	2.40020
$687$	−19.9159	−0.759840
$688$	−15.7720	−0.601302
$689$	8.49285	0.323552
$690$	0	0
$691$	−34.8112	−1.32428	−0.662140	−	0.749380i	$-0.730352\pi$
$691$	−34.8112	−1.32428	−0.662140	+	0.749380i	$0.730352\pi$
$692$	114.557	4.35479
$693$	26.4929	1.00638
$694$	−15.9647	−0.606010
$695$	0	0
$696$	67.1421	2.54502
$697$	−19.6299	−0.743536
$698$	−19.9661	−0.755726
$699$	37.5751	1.42122
$700$	0	0
$701$	−20.0313	−0.756572	−0.378286	−	0.925689i	$-0.623486\pi$
$701$	−20.0313	−0.756572	−0.378286	+	0.925689i	$0.623486\pi$
$702$	−134.995	−5.09506
$703$	−0.926528	−0.0349447
$704$	−0.607107	−0.0228812
$705$	0	0
$706$	25.7865	0.970488
$707$	−15.5346	−0.584240
$708$	104.653	3.93311
$709$	20.5264	0.770886	0.385443	−	0.922732i	$-0.374049\pi$
$709$	20.5264	0.770886	0.385443	+	0.922732i	$0.374049\pi$
$710$	0	0
$711$	10.0246	0.375951
$712$	31.9421	1.19708
$713$	2.37686	0.0890139
$714$	99.5546	3.72574
$715$	0	0
$716$	103.562	3.87030
$717$	−81.9859	−3.06182
$718$	−74.9005	−2.79526
$719$	−3.14609	−0.117329	−0.0586647	−	0.998278i	$-0.518684\pi$
$719$	−3.14609	−0.117329	−0.0586647	+	0.998278i	$0.518684\pi$
$720$	0	0
$721$	−10.7570	−0.400611
$722$	−2.55401	−0.0950506
$723$	70.6633	2.62800
$724$	36.4550	1.35484
$725$	0	0
$726$	−7.65758	−0.284200
$727$	−36.6121	−1.35787	−0.678934	−	0.734199i	$-0.737558\pi$
$727$	−36.6121	−1.35787	−0.678934	+	0.734199i	$0.737558\pi$
$728$	168.074	6.22924
$729$	−27.2815	−1.01043
$730$	0	0
$731$	−6.25482	−0.231343
$732$	56.5336	2.08954
$733$	1.44149	0.0532428	0.0266214	−	0.999646i	$-0.491525\pi$
$733$	1.44149	0.0532428	0.0266214	+	0.999646i	$0.491525\pi$
$734$	−35.2065	−1.29949
$735$	0	0
$736$	−2.25289	−0.0830428
$737$	−11.3778	−0.419108
$738$	102.165	3.76074
$739$	−27.8090	−1.02297	−0.511485	−	0.859292i	$-0.670904\pi$
$739$	−27.8090	−1.02297	−0.511485	+	0.859292i	$0.670904\pi$
$740$	0	0
$741$	17.6804	0.649506
$742$	16.2701	0.597295
$743$	−1.15020	−0.0421967	−0.0210983	−	0.999777i	$-0.506716\pi$
$743$	−1.15020	−0.0421967	−0.0210983	+	0.999777i	$0.506716\pi$
$744$	−123.144	−4.51468
$745$	0	0
$746$	41.9291	1.53513
$747$	38.8060	1.41984
$748$	−13.2941	−0.486079
$749$	75.1347	2.74536
$750$	0	0
$751$	43.4326	1.58488	0.792439	−	0.609951i	$-0.208811\pi$
$751$	43.4326	1.58488	0.792439	+	0.609951i	$0.208811\pi$
$752$	12.7546	0.465114
$753$	−6.13135	−0.223439
$754$	52.3401	1.90611
$755$	0	0
$756$	−179.322	−6.52188
$757$	22.5876	0.820962	0.410481	−	0.911869i	$-0.365361\pi$
$757$	22.5876	0.820962	0.410481	+	0.911869i	$0.365361\pi$
$758$	−17.7129	−0.643362
$759$	−1.11806	−0.0405830
$760$	0	0
$761$	23.0477	0.835479	0.417739	−	0.908567i	$-0.362823\pi$
$761$	23.0477	0.835479	0.417739	+	0.908567i	$0.362823\pi$
$762$	−92.6329	−3.35574
$763$	−16.9668	−0.614239
$764$	−77.8603	−2.81689
$765$	0	0
$766$	3.75814	0.135787
$767$	45.5075	1.64318
$768$	−84.2933	−3.04167
$769$	−26.7350	−0.964088	−0.482044	−	0.876147i	$-0.660105\pi$
$769$	−26.7350	−0.964088	−0.482044	+	0.876147i	$0.660105\pi$
$770$	0	0
$771$	−63.1747	−2.27518
$772$	37.6126	1.35371
$773$	−28.4074	−1.02174	−0.510872	−	0.859657i	$-0.670677\pi$
$773$	−28.4074	−1.02174	−0.510872	+	0.859657i	$0.670677\pi$
$774$	32.5536	1.17011
$775$	0	0
$776$	53.0969	1.90607
$777$	12.2875	0.440812
$778$	−17.3573	−0.622290
$779$	−6.67861	−0.239286
$780$	0	0
$781$	−2.40794	−0.0861630
$782$	−2.79932	−0.100103
$783$	−31.1500	−1.11321
$784$	93.1235	3.32584
$785$	0	0
$786$	61.2470	2.18461
$787$	6.60374	0.235398	0.117699	−	0.993049i	$-0.462448\pi$
$787$	6.60374	0.235398	0.117699	+	0.993049i	$0.462448\pi$
$788$	−19.8520	−0.707199
$789$	64.5083	2.29656
$790$	0	0
$791$	−47.7305	−1.69710
$792$	38.5950	1.37142
$793$	24.5831	0.872970
$794$	−31.6207	−1.12218
$795$	0	0
$796$	89.9732	3.18901
$797$	−45.9061	−1.62608	−0.813038	−	0.582210i	$-0.802188\pi$
$797$	−45.9061	−1.62608	−0.813038	+	0.582210i	$0.802188\pi$
$798$	33.8711	1.19902
$799$	5.05820	0.178946
$800$	0	0
$801$	−29.6904	−1.04906
$802$	0.0922899	0.00325887
$803$	14.4653	0.510468
$804$	154.296	5.44159
$805$	0	0
$806$	−95.9960	−3.38131
$807$	25.6727	0.903723
$808$	−22.6309	−0.796154
$809$	−19.0359	−0.669266	−0.334633	−	0.942349i	$-0.608612\pi$
$809$	−19.0359	−0.669266	−0.334633	+	0.942349i	$0.608612\pi$
$810$	0	0
$811$	−56.0480	−1.96811	−0.984056	−	0.177860i	$-0.943083\pi$
$811$	−56.0480	−1.96811	−0.984056	+	0.177860i	$0.943083\pi$
$812$	69.5266	2.43990
$813$	−37.5908	−1.31837
$814$	−2.36637	−0.0829411
$815$	0	0
$816$	65.3137	2.28644
$817$	−2.12805	−0.0744512
$818$	25.4113	0.888485
$819$	−156.226	−5.45898
$820$	0	0
$821$	3.28817	0.114758	0.0573789	−	0.998352i	$-0.481726\pi$
$821$	3.28817	0.114758	0.0573789	+	0.998352i	$0.481726\pi$
$822$	121.902	4.25181
$823$	5.84050	0.203587	0.101793	−	0.994806i	$-0.467542\pi$
$823$	5.84050	0.203587	0.101793	+	0.994806i	$0.467542\pi$
$824$	−15.6708	−0.545919
$825$	0	0
$826$	87.1806	3.03340
$827$	14.4956	0.504061	0.252030	−	0.967719i	$-0.418902\pi$
$827$	14.4956	0.504061	0.252030	+	0.967719i	$0.418902\pi$
$828$	10.1022	0.351075
$829$	−52.7194	−1.83102	−0.915511	−	0.402293i	$-0.868213\pi$
$829$	−52.7194	−1.83102	−0.915511	+	0.402293i	$0.868213\pi$
$830$	0	0
$831$	−33.7170	−1.16963
$832$	3.58005	0.124116
$833$	36.9306	1.27957
$834$	−112.780	−3.90523
$835$	0	0
$836$	−4.52299	−0.156431
$837$	57.1316	1.97476
$838$	−69.6122	−2.40471
$839$	−28.9506	−0.999485	−0.499742	−	0.866174i	$-0.666572\pi$
$839$	−28.9506	−0.999485	−0.499742	+	0.866174i	$0.666572\pi$
$840$	0	0
$841$	−16.9226	−0.583536
$842$	−42.2286	−1.45529
$843$	−60.9462	−2.09910
$844$	94.1514	3.24082
$845$	0	0
$846$	−26.3257	−0.905095
$847$	−4.42321	−0.151983
$848$	10.6742	0.366553
$849$	80.1365	2.75028
$850$	0	0
$851$	−0.345506	−0.0118438
$852$	32.6543	1.11872
$853$	17.2571	0.590873	0.295436	−	0.955362i	$-0.404535\pi$
$853$	17.2571	0.590873	0.295436	+	0.955362i	$0.404535\pi$
$854$	47.0948	1.61155
$855$	0	0
$856$	109.457	3.74115
$857$	−43.2863	−1.47863	−0.739315	−	0.673359i	$-0.764851\pi$
$857$	−43.2863	−1.47863	−0.739315	+	0.673359i	$0.764851\pi$
$858$	45.1560	1.54160
$859$	−41.5981	−1.41931	−0.709654	−	0.704550i	$-0.751149\pi$
$859$	−41.5981	−1.41931	−0.709654	+	0.704550i	$0.751149\pi$
$860$	0	0
$861$	88.5711	3.01850
$862$	−86.7217	−2.95375
$863$	31.0676	1.05755	0.528777	−	0.848761i	$-0.322651\pi$
$863$	31.0676	1.05755	0.528777	+	0.848761i	$0.322651\pi$
$864$	−54.1520	−1.84229
$865$	0	0
$866$	−9.06967	−0.308200
$867$	−25.0684	−0.851367
$868$	−127.517	−4.32822
$869$	−1.67368	−0.0567758
$870$	0	0
$871$	67.0939	2.27339
$872$	−24.7173	−0.837035
$873$	−49.3540	−1.67038
$874$	−0.952402	−0.0322155
$875$	0	0
$876$	−196.164	−6.62778
$877$	−0.708001	−0.0239075	−0.0119537	−	0.999929i	$-0.503805\pi$
$877$	−0.708001	−0.0239075	−0.0119537	+	0.999929i	$0.503805\pi$
$878$	−16.0451	−0.541497
$879$	29.8500	1.00682
$880$	0	0
$881$	−35.1566	−1.18446	−0.592229	−	0.805770i	$-0.701752\pi$
$881$	−35.1566	−1.18446	−0.592229	+	0.805770i	$0.701752\pi$
$882$	−192.208	−6.47197
$883$	1.50768	0.0507374	0.0253687	−	0.999678i	$-0.491924\pi$
$883$	1.50768	0.0507374	0.0253687	+	0.999678i	$0.491924\pi$
$884$	78.3937	2.63667
$885$	0	0
$886$	67.4180	2.26495
$887$	−46.0348	−1.54570	−0.772849	−	0.634590i	$-0.781169\pi$
$887$	−46.0348	−1.54570	−0.772849	+	0.634590i	$0.781169\pi$
$888$	17.9005	0.600703
$889$	−53.5070	−1.79457
$890$	0	0
$891$	−8.90583	−0.298357
$892$	−51.9993	−1.74107
$893$	1.72093	0.0575888
$894$	−56.3386	−1.88424
$895$	0	0
$896$	−46.5871	−1.55636
$897$	6.59309	0.220137
$898$	1.65786	0.0553236
$899$	−22.1510	−0.738777
$900$	0	0
$901$	4.23313	0.141026
$902$	−17.0573	−0.567945
$903$	28.2221	0.939171
$904$	−69.5340	−2.31267
$905$	0	0
$906$	−80.5557	−2.67628
$907$	−0.994096	−0.0330084	−0.0165042	−	0.999864i	$-0.505254\pi$
$907$	−0.994096	−0.0330084	−0.0165042	+	0.999864i	$0.505254\pi$
$908$	79.2315	2.62939
$909$	21.0356	0.697708
$910$	0	0
$911$	−6.86962	−0.227601	−0.113800	−	0.993504i	$-0.536302\pi$
$911$	−6.86962	−0.227601	−0.113800	+	0.993504i	$0.536302\pi$
$912$	22.2215	0.735826
$913$	−6.47897	−0.214423
$914$	−12.1257	−0.401081
$915$	0	0
$916$	−30.0440	−0.992682
$917$	35.3778	1.16828
$918$	−67.2862	−2.22077
$919$	12.5820	0.415043	0.207521	−	0.978230i	$-0.433460\pi$
$919$	12.5820	0.415043	0.207521	+	0.978230i	$0.433460\pi$
$920$	0	0
$921$	−10.7580	−0.354488
$922$	−35.6825	−1.17514
$923$	14.1994	0.467379
$924$	59.9835	1.97331
$925$	0	0
$926$	−37.7538	−1.24067
$927$	14.5662	0.478415
$928$	20.9957	0.689219
$929$	43.3197	1.42127	0.710636	−	0.703560i	$-0.248407\pi$
$929$	43.3197	1.42127	0.710636	+	0.703560i	$0.248407\pi$
$930$	0	0
$931$	12.5648	0.411794
$932$	56.6836	1.85673
$933$	−41.5166	−1.35919
$934$	−57.5787	−1.88403
$935$	0	0
$936$	−227.591	−7.43905
$937$	44.3170	1.44777	0.723887	−	0.689918i	$-0.242354\pi$
$937$	44.3170	1.44777	0.723887	+	0.689918i	$0.242354\pi$
$938$	128.535	4.19681
$939$	46.1678	1.50663
$940$	0	0
$941$	58.0333	1.89183	0.945916	−	0.324410i	$-0.105166\pi$
$941$	58.0333	1.89183	0.945916	+	0.324410i	$0.105166\pi$
$942$	−123.800	−4.03361
$943$	−2.49048	−0.0811012
$944$	57.1957	1.86156
$945$	0	0
$946$	−5.43508	−0.176710
$947$	−27.2005	−0.883897	−0.441949	−	0.897040i	$-0.645713\pi$
$947$	−27.2005	−0.883897	−0.441949	+	0.897040i	$0.645713\pi$
$948$	22.6970	0.737163
$949$	−85.3002	−2.76896
$950$	0	0
$951$	17.8804	0.579810
$952$	83.7739	2.71513
$953$	7.27158	0.235550	0.117775	−	0.993040i	$-0.462424\pi$
$953$	7.27158	0.235550	0.117775	+	0.993040i	$0.462424\pi$
$954$	−22.0316	−0.713299
$955$	0	0
$956$	−123.679	−4.00007
$957$	10.4197	0.336822
$958$	55.6646	1.79844
$959$	70.4135	2.27377
$960$	0	0
$961$	9.62671	0.310539
$962$	13.9542	0.449902
$963$	−101.741	−3.27855
$964$	106.599	3.43331
$965$	0	0
$966$	12.6307	0.406385
$967$	−8.85046	−0.284612	−0.142306	−	0.989823i	$-0.545452\pi$
$967$	−8.85046	−0.284612	−0.142306	+	0.989823i	$0.545452\pi$
$968$	−6.44376	−0.207110
$969$	8.81252	0.283099
$970$	0	0
$971$	−37.1779	−1.19310	−0.596548	−	0.802577i	$-0.703462\pi$
$971$	−37.1779	−1.19310	−0.596548	+	0.802577i	$0.703462\pi$
$972$	−0.850867	−0.0272916
$973$	−65.1442	−2.08843
$974$	−13.8062	−0.442380
$975$	0	0
$976$	30.8970	0.988989
$977$	−46.5181	−1.48825	−0.744123	−	0.668043i	$-0.767132\pi$
$977$	−46.5181	−1.48825	−0.744123	+	0.668043i	$0.767132\pi$
$978$	104.636	3.34588
$979$	4.95706	0.158428
$980$	0	0
$981$	22.9750	0.733534
$982$	105.889	3.37904
$983$	−24.6218	−0.785313	−0.392656	−	0.919685i	$-0.628444\pi$
$983$	−24.6218	−0.785313	−0.392656	+	0.919685i	$0.628444\pi$
$984$	129.031	4.11336
$985$	0	0
$986$	26.0881	0.830815
$987$	−22.8228	−0.726459
$988$	26.6716	0.848538
$989$	−0.793560	−0.0252337
$990$	0	0
$991$	40.2121	1.27738	0.638690	−	0.769464i	$-0.279477\pi$
$991$	40.2121	1.27738	0.638690	+	0.769464i	$0.279477\pi$
$992$	−38.5079	−1.22263
$993$	−16.7455	−0.531401
$994$	27.2024	0.862807
$995$	0	0
$996$	87.8618	2.78401
$997$	−21.2470	−0.672900	−0.336450	−	0.941701i	$-0.609226\pi$
$997$	−21.2470	−0.672900	−0.336450	+	0.941701i	$0.609226\pi$
$998$	−46.1245	−1.46004
$999$	−8.30480	−0.262752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5225.2.a.n.1.1		7
5.4	even	2		209.2.a.d.1.7	✓	7
15.14	odd	2		1881.2.a.p.1.1		7
20.19	odd	2		3344.2.a.ba.1.7		7
55.54	odd	2		2299.2.a.q.1.1		7
95.94	odd	2		3971.2.a.i.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.d.1.7	✓	7	5.4	even	2
1881.2.a.p.1.1		7	15.14	odd	2
2299.2.a.q.1.1		7	55.54	odd	2
3344.2.a.ba.1.7		7	20.19	odd	2
3971.2.a.i.1.1		7	95.94	odd	2
5225.2.a.n.1.1		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5225.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55401 q^{2} +2.99825 q^{3} +4.52299 q^{4} -7.65758 q^{6} -4.42321 q^{7} -6.44376 q^{8} +5.98952 q^{9} +O(q^{10})\)	\(q-2.55401 q^{2} +2.99825 q^{3} +4.52299 q^{4} -7.65758 q^{6} -4.42321 q^{7} -6.44376 q^{8} +5.98952 q^{9} -1.00000 q^{11} +13.5611 q^{12} +5.89690 q^{13} +11.2969 q^{14} +7.41147 q^{16} +2.93922 q^{17} -15.2973 q^{18} +1.00000 q^{19} -13.2619 q^{21} +2.55401 q^{22} +0.372904 q^{23} -19.3200 q^{24} -15.0608 q^{26} +8.96335 q^{27} -20.0061 q^{28} -3.47526 q^{29} +6.37391 q^{31} -6.04149 q^{32} -2.99825 q^{33} -7.50681 q^{34} +27.0906 q^{36} -0.926528 q^{37} -2.55401 q^{38} +17.6804 q^{39} -6.67861 q^{41} +33.8711 q^{42} -2.12805 q^{43} -4.52299 q^{44} -0.952402 q^{46} +1.72093 q^{47} +22.2215 q^{48} +12.5648 q^{49} +8.81252 q^{51} +26.6716 q^{52} +1.44022 q^{53} -22.8925 q^{54} +28.5021 q^{56} +2.99825 q^{57} +8.87587 q^{58} +7.71718 q^{59} +4.16881 q^{61} -16.2791 q^{62} -26.4929 q^{63} +0.607107 q^{64} +7.65758 q^{66} +11.3778 q^{67} +13.2941 q^{68} +1.11806 q^{69} +2.40794 q^{71} -38.5950 q^{72} -14.4653 q^{73} +2.36637 q^{74} +4.52299 q^{76} +4.42321 q^{77} -45.1560 q^{78} +1.67368 q^{79} +8.90583 q^{81} +17.0573 q^{82} +6.47897 q^{83} -59.9835 q^{84} +5.43508 q^{86} -10.4197 q^{87} +6.44376 q^{88} -4.95706 q^{89} -26.0832 q^{91} +1.68664 q^{92} +19.1106 q^{93} -4.39529 q^{94} -18.1139 q^{96} -8.24006 q^{97} -32.0906 q^{98} -5.98952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 15 * q^4 - 2 * q^6 - 10 * q^7 + 9 * q^8 + 11 * q^9	\( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9} - 7 q^{11} + 16 q^{12} + 4 q^{13} + 6 q^{14} + 27 q^{16} - 2 q^{17} - 9 q^{18} + 7 q^{19} - 14 q^{21} - q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{26} + 4 q^{27} - 26 q^{28} - 18 q^{29} + 24 q^{31} + 49 q^{32} + 2 q^{33} - 6 q^{34} + 29 q^{36} + q^{38} + 24 q^{39} - 12 q^{41} + 44 q^{42} - 2 q^{43} - 15 q^{44} - 4 q^{46} - 8 q^{47} + 72 q^{48} + 17 q^{49} - 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} + 26 q^{56} - 2 q^{57} + 8 q^{58} - 10 q^{59} + 14 q^{61} - 14 q^{62} + 55 q^{64} + 2 q^{66} - 8 q^{67} + 18 q^{68} - 6 q^{69} + 10 q^{71} - 53 q^{72} + 6 q^{73} + 26 q^{74} + 15 q^{76} + 10 q^{77} - 22 q^{78} + 52 q^{79} - q^{81} - 24 q^{82} + 10 q^{83} - 6 q^{84} + 8 q^{86} - 6 q^{87} - 9 q^{88} + 12 q^{91} - 2 q^{93} + 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 15 * q^4 - 2 * q^6 - 10 * q^7 + 9 * q^8 + 11 * q^9 - 7 * q^11 + 16 * q^12 + 4 * q^13 + 6 * q^14 + 27 * q^16 - 2 * q^17 - 9 * q^18 + 7 * q^19 - 14 * q^21 - q^22 - 10 * q^23 - 2 * q^24 - 8 * q^26 + 4 * q^27 - 26 * q^28 - 18 * q^29 + 24 * q^31 + 49 * q^32 + 2 * q^33 - 6 * q^34 + 29 * q^36 + q^38 + 24 * q^39 - 12 * q^41 + 44 * q^42 - 2 * q^43 - 15 * q^44 - 4 * q^46 - 8 * q^47 + 72 * q^48 + 17 * q^49 - 24 * q^51 + 60 * q^52 - 2 * q^53 - 52 * q^54 + 26 * q^56 - 2 * q^57 + 8 * q^58 - 10 * q^59 + 14 * q^61 - 14 * q^62 + 55 * q^64 + 2 * q^66 - 8 * q^67 + 18 * q^68 - 6 * q^69 + 10 * q^71 - 53 * q^72 + 6 * q^73 + 26 * q^74 + 15 * q^76 + 10 * q^77 - 22 * q^78 + 52 * q^79 - q^81 - 24 * q^82 + 10 * q^83 - 6 * q^84 + 8 * q^86 - 6 * q^87 - 9 * q^88 + 12 * q^91 - 2 * q^93 + 24 * q^94 + 6 * q^96 + 24 * q^97 - 19 * q^98 - 11 * q^99

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