LMFDB - Embedded newform 775.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.20308.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 4x + 12 $ x^4 - x^3 - 8x^2 + 4x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.80027$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80027 q^{2} +0.342376 q^{3} +5.84153 q^{4} +0.958747 q^{6} -1.04125 q^{7} +10.7573 q^{8} -2.88278 q^{9} +O(q^{10})$	\(q+2.80027 q^{2} +0.342376 q^{3} +5.84153 q^{4} +0.958747 q^{6} -1.04125 q^{7} +10.7573 q^{8} -2.88278 q^{9} +4.64180 q^{11} +2.00000 q^{12} -2.95875 q^{13} -2.91579 q^{14} +18.4404 q^{16} -6.29942 q^{17} -8.07256 q^{18} -1.11552 q^{19} -0.356500 q^{21} +12.9983 q^{22} -3.87454 q^{23} +3.68305 q^{24} -8.28530 q^{26} -2.01412 q^{27} -6.08251 q^{28} +2.35650 q^{29} +1.00000 q^{31} +30.1234 q^{32} +1.58924 q^{33} -17.6401 q^{34} -16.8398 q^{36} -1.30112 q^{37} -3.12376 q^{38} -1.01300 q^{39} +1.92573 q^{41} -0.998298 q^{42} +4.29942 q^{43} +27.1152 q^{44} -10.8498 q^{46} +3.31525 q^{47} +6.31355 q^{48} -5.91579 q^{49} -2.15677 q^{51} -17.2836 q^{52} -5.10964 q^{53} -5.64010 q^{54} -11.2011 q^{56} -0.381928 q^{57} +6.59884 q^{58} -5.07256 q^{59} +5.31525 q^{61} +2.80027 q^{62} +3.00170 q^{63} +47.4730 q^{64} +4.45031 q^{66} +8.64180 q^{67} -36.7982 q^{68} -1.32655 q^{69} -3.88278 q^{71} -31.0110 q^{72} -12.1740 q^{73} -3.64350 q^{74} -6.51634 q^{76} -4.83329 q^{77} -2.83669 q^{78} -7.12376 q^{79} +7.95875 q^{81} +5.39258 q^{82} +7.46614 q^{83} -2.08251 q^{84} +12.0396 q^{86} +0.806810 q^{87} +49.9333 q^{88} -12.1598 q^{89} +3.08080 q^{91} -22.6332 q^{92} +0.342376 q^{93} +9.28360 q^{94} +10.3135 q^{96} +0.915792 q^{97} -16.5658 q^{98} -13.3813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9	$ 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9} - 6 q^{11} + 8 q^{12} - 16 q^{13} + 8 q^{14} + 11 q^{16} - q^{17} + q^{18} + 5 q^{19} + 2 q^{21} + 24 q^{22} - 14 q^{24} - 12 q^{26} - 5 q^{27} - 16 q^{28} + 6 q^{29} + 4 q^{31} + 29 q^{32} + 12 q^{33} - 18 q^{34} - 25 q^{36} - 9 q^{37} - 6 q^{39} + 13 q^{41} + 24 q^{42} - 7 q^{43} + 20 q^{44} - 26 q^{46} + 14 q^{47} - 2 q^{48} - 4 q^{49} + 5 q^{51} - 20 q^{52} - 11 q^{53} + 30 q^{54} - 4 q^{56} + 31 q^{57} - 22 q^{58} + 13 q^{59} + 22 q^{61} + q^{62} + 40 q^{63} + 47 q^{64} - 20 q^{66} + 10 q^{67} - 30 q^{68} + 20 q^{69} + 3 q^{71} - 19 q^{72} - 9 q^{73} - 18 q^{74} + 14 q^{76} - 8 q^{77} - 56 q^{78} - 16 q^{79} + 36 q^{81} - 6 q^{82} + 17 q^{83} + 16 q^{86} - 38 q^{87} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 10 q^{92} + q^{93} - 12 q^{94} + 14 q^{96} - 16 q^{97} - 19 q^{98} - 52 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9 - 6 * q^11 + 8 * q^12 - 16 * q^13 + 8 * q^14 + 11 * q^16 - q^17 + q^18 + 5 * q^19 + 2 * q^21 + 24 * q^22 - 14 * q^24 - 12 * q^26 - 5 * q^27 - 16 * q^28 + 6 * q^29 + 4 * q^31 + 29 * q^32 + 12 * q^33 - 18 * q^34 - 25 * q^36 - 9 * q^37 - 6 * q^39 + 13 * q^41 + 24 * q^42 - 7 * q^43 + 20 * q^44 - 26 * q^46 + 14 * q^47 - 2 * q^48 - 4 * q^49 + 5 * q^51 - 20 * q^52 - 11 * q^53 + 30 * q^54 - 4 * q^56 + 31 * q^57 - 22 * q^58 + 13 * q^59 + 22 * q^61 + q^62 + 40 * q^63 + 47 * q^64 - 20 * q^66 + 10 * q^67 - 30 * q^68 + 20 * q^69 + 3 * q^71 - 19 * q^72 - 9 * q^73 - 18 * q^74 + 14 * q^76 - 8 * q^77 - 56 * q^78 - 16 * q^79 + 36 * q^81 - 6 * q^82 + 17 * q^83 + 16 * q^86 - 38 * q^87 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 10 * q^92 + q^93 - 12 * q^94 + 14 * q^96 - 16 * q^97 - 19 * q^98 - 52 * 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 $

$2$	2.80027	1.98009	0.990046	−	0.140746i	$-0.0449500\pi$
$2$	2.80027	1.98009	0.990046	+	0.140746i	$0.0449500\pi$
$3$	0.342376	0.197671	0.0988355	−	0.995104i	$-0.468488\pi$
$3$	0.342376	0.197671	0.0988355	+	0.995104i	$0.468488\pi$
$4$	5.84153	2.92076
$5$	0	0
$5$	0	0
$6$	0.958747	0.391407
$7$	−1.04125	−0.393557	−0.196778	−	0.980448i	$-0.563048\pi$
$7$	−1.04125	−0.393557	−0.196778	+	0.980448i	$0.563048\pi$
$8$	10.7573	3.80329
$9$	−2.88278	−0.960926
$10$	0	0
$11$	4.64180	1.39955	0.699777	−	0.714361i	$-0.253283\pi$
$11$	4.64180	1.39955	0.699777	+	0.714361i	$0.253283\pi$
$12$	2.00000	0.577350
$13$	−2.95875	−0.820609	−0.410304	−	0.911949i	$-0.634578\pi$
$13$	−2.95875	−0.820609	−0.410304	+	0.911949i	$0.634578\pi$
$14$	−2.91579	−0.779278
$15$	0	0
$16$	18.4404	4.61009
$17$	−6.29942	−1.52783	−0.763917	−	0.645314i	$-0.776726\pi$
$17$	−6.29942	−1.52783	−0.763917	+	0.645314i	$0.776726\pi$
$18$	−8.07256	−1.90272
$19$	−1.11552	−0.255918	−0.127959	−	0.991779i	$-0.540843\pi$
$19$	−1.11552	−0.255918	−0.127959	+	0.991779i	$0.540843\pi$
$20$	0	0
$21$	−0.356500	−0.0777948
$22$	12.9983	2.77125
$23$	−3.87454	−0.807897	−0.403949	−	0.914782i	$-0.632363\pi$
$23$	−3.87454	−0.807897	−0.403949	+	0.914782i	$0.632363\pi$
$24$	3.68305	0.751800
$25$	0	0
$26$	−8.28530	−1.62488
$27$	−2.01412	−0.387618
$28$	−6.08251	−1.14949
$29$	2.35650	0.437591	0.218796	−	0.975771i	$-0.429787\pi$
$29$	2.35650	0.437591	0.218796	+	0.975771i	$0.429787\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	30.1234	5.32512
$33$	1.58924	0.276651
$34$	−17.6401	−3.02525
$35$	0	0
$36$	−16.8398	−2.80664
$37$	−1.30112	−0.213903	−0.106952	−	0.994264i	$-0.534109\pi$
$37$	−1.30112	−0.213903	−0.106952	+	0.994264i	$0.534109\pi$
$38$	−3.12376	−0.506741
$39$	−1.01300	−0.162211
$40$	0	0
$41$	1.92573	0.300749	0.150375	−	0.988629i	$-0.451952\pi$
$41$	1.92573	0.300749	0.150375	+	0.988629i	$0.451952\pi$
$42$	−0.998298	−0.154041
$43$	4.29942	0.655656	0.327828	−	0.944737i	$-0.393683\pi$
$43$	4.29942	0.655656	0.327828	+	0.944737i	$0.393683\pi$
$44$	27.1152	4.08777
$45$	0	0
$46$	−10.8498	−1.59971
$47$	3.31525	0.483579	0.241789	−	0.970329i	$-0.422266\pi$
$47$	3.31525	0.483579	0.241789	+	0.970329i	$0.422266\pi$
$48$	6.31355	0.911282
$49$	−5.91579	−0.845113
$50$	0	0
$51$	−2.15677	−0.302009
$52$	−17.2836	−2.39680
$53$	−5.10964	−0.701862	−0.350931	−	0.936401i	$-0.614135\pi$
$53$	−5.10964	−0.701862	−0.350931	+	0.936401i	$0.614135\pi$
$54$	−5.64010	−0.767520
$55$	0	0
$56$	−11.2011	−1.49681
$57$	−0.381928	−0.0505875
$58$	6.59884	0.866471
$59$	−5.07256	−0.660392	−0.330196	−	0.943912i	$-0.607115\pi$
$59$	−5.07256	−0.660392	−0.330196	+	0.943912i	$0.607115\pi$
$60$	0	0
$61$	5.31525	0.680548	0.340274	−	0.940326i	$-0.389480\pi$
$61$	5.31525	0.680548	0.340274	+	0.940326i	$0.389480\pi$
$62$	2.80027	0.355635
$63$	3.00170	0.378179
$64$	47.4730	5.93413
$65$	0	0
$66$	4.45031	0.547795
$67$	8.64180	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$67$	8.64180	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$68$	−36.7982	−4.46244
$69$	−1.32655	−0.159698
$70$	0	0
$71$	−3.88278	−0.460801	−0.230401	−	0.973096i	$-0.574004\pi$
$71$	−3.88278	−0.460801	−0.230401	+	0.973096i	$0.574004\pi$
$72$	−31.0110	−3.65468
$73$	−12.1740	−1.42485	−0.712427	−	0.701746i	$-0.752404\pi$
$73$	−12.1740	−1.42485	−0.712427	+	0.701746i	$0.752404\pi$
$74$	−3.64350	−0.423548
$75$	0	0
$76$	−6.51634	−0.747475
$77$	−4.83329	−0.550804
$78$	−2.83669	−0.321192
$79$	−7.12376	−0.801486	−0.400743	−	0.916191i	$-0.631248\pi$
$79$	−7.12376	−0.801486	−0.400743	+	0.916191i	$0.631248\pi$
$80$	0	0
$81$	7.95875	0.884305
$82$	5.39258	0.595511
$83$	7.46614	0.819515	0.409757	−	0.912195i	$-0.365613\pi$
$83$	7.46614	0.819515	0.409757	+	0.912195i	$0.365613\pi$
$84$	−2.08251	−0.227220
$85$	0	0
$86$	12.0396	1.29826
$87$	0.806810	0.0864991
$88$	49.9333	5.32291
$89$	−12.1598	−1.28894	−0.644470	−	0.764630i	$-0.722922\pi$
$89$	−12.1598	−1.28894	−0.644470	+	0.764630i	$0.722922\pi$
$90$	0	0
$91$	3.08080	0.322956
$92$	−22.6332	−2.35968
$93$	0.342376	0.0355028
$94$	9.28360	0.957530
$95$	0	0
$96$	10.3135	1.05262
$97$	0.915792	0.0929846	0.0464923	−	0.998919i	$-0.485196\pi$
$97$	0.915792	0.0929846	0.0464923	+	0.998919i	$0.485196\pi$
$98$	−16.5658	−1.67340
$99$	−13.3813	−1.34487
$100$	0	0
$101$	−4.11382	−0.409340	−0.204670	−	0.978831i	$-0.565612\pi$
$101$	−4.11382	−0.409340	−0.204670	+	0.978831i	$0.565612\pi$
$102$	−6.03955	−0.598005
$103$	16.9983	1.67489	0.837446	−	0.546520i	$-0.184048\pi$
$103$	16.9983	1.67489	0.837446	+	0.546520i	$0.184048\pi$
$104$	−31.8282	−3.12101
$105$	0	0
$106$	−14.3084	−1.38975
$107$	−4.84976	−0.468844	−0.234422	−	0.972135i	$-0.575320\pi$
$107$	−4.84976	−0.468844	−0.234422	+	0.972135i	$0.575320\pi$
$108$	−11.7656	−1.13214
$109$	9.19803	0.881011	0.440506	−	0.897750i	$-0.354799\pi$
$109$	9.19803	0.881011	0.440506	+	0.897750i	$0.354799\pi$
$110$	0	0
$111$	−0.445474	−0.0422825
$112$	−19.2011	−1.81433
$113$	−3.47508	−0.326908	−0.163454	−	0.986551i	$-0.552264\pi$
$113$	−3.47508	−0.326908	−0.163454	+	0.986551i	$0.552264\pi$
$114$	−1.06950	−0.100168
$115$	0	0
$116$	13.7656	1.27810
$117$	8.52941	0.788544
$118$	−14.2046	−1.30764
$119$	6.55929	0.601289
$120$	0	0
$121$	10.5463	0.958753
$122$	14.8841	1.34755
$123$	0.659325	0.0594494
$124$	5.84153	0.524584
$125$	0	0
$126$	8.40558	0.748829
$127$	−12.8728	−1.14228	−0.571140	−	0.820853i	$-0.693499\pi$
$127$	−12.8728	−1.14228	−0.571140	+	0.820853i	$0.693499\pi$
$128$	72.6906	6.42500
$129$	1.47202	0.129604
$130$	0	0
$131$	15.4668	1.35134	0.675672	−	0.737202i	$-0.263853\pi$
$131$	15.4668	1.35134	0.675672	+	0.737202i	$0.263853\pi$
$132$	9.28360	0.808033
$133$	1.16154	0.100718
$134$	24.1994	2.09051
$135$	0	0
$136$	−67.7649	−5.81079
$137$	16.5734	1.41596	0.707981	−	0.706231i	$-0.249606\pi$
$137$	16.5734	1.41596	0.707981	+	0.706231i	$0.249606\pi$
$138$	−3.71470	−0.316216
$139$	21.5259	1.82581	0.912903	−	0.408176i	$-0.133835\pi$
$139$	21.5259	1.82581	0.912903	+	0.408176i	$0.133835\pi$
$140$	0	0
$141$	1.13506	0.0955895
$142$	−10.8728	−0.912428
$143$	−13.7339	−1.14849
$144$	−53.1595	−4.42996
$145$	0	0
$146$	−34.0904	−2.82134
$147$	−2.02543	−0.167054
$148$	−7.60054	−0.624761
$149$	20.7556	1.70037	0.850183	−	0.526487i	$-0.176491\pi$
$149$	20.7556	1.70037	0.850183	+	0.526487i	$0.176491\pi$
$150$	0	0
$151$	−18.4451	−1.50104	−0.750522	−	0.660846i	$-0.770198\pi$
$151$	−18.4451	−1.50104	−0.750522	+	0.660846i	$0.770198\pi$
$152$	−12.0000	−0.973329
$153$	18.1598	1.46814
$154$	−13.5345	−1.09064
$155$	0	0
$156$	−5.91749	−0.473779
$157$	−5.64350	−0.450400	−0.225200	−	0.974313i	$-0.572304\pi$
$157$	−5.64350	−0.450400	−0.225200	+	0.974313i	$0.572304\pi$
$158$	−19.9485	−1.58701
$159$	−1.74942	−0.138738
$160$	0	0
$161$	4.03438	0.317953
$162$	22.2867	1.75101
$163$	16.1994	1.26883	0.634417	−	0.772991i	$-0.281240\pi$
$163$	16.1994	1.26883	0.634417	+	0.772991i	$0.281240\pi$
$164$	11.2492	0.878417
$165$	0	0
$166$	20.9072	1.62271
$167$	−5.14919	−0.398456	−0.199228	−	0.979953i	$-0.563843\pi$
$167$	−5.14919	−0.398456	−0.199228	+	0.979953i	$0.563843\pi$
$168$	−3.83499	−0.295876
$169$	−4.24582	−0.326601
$170$	0	0
$171$	3.21580	0.245918
$172$	25.1152	1.91501
$173$	−10.7621	−0.818226	−0.409113	−	0.912484i	$-0.634162\pi$
$173$	−10.7621	−0.818226	−0.409113	+	0.912484i	$0.634162\pi$
$174$	2.25929	0.171276
$175$	0	0
$176$	85.5965	6.45208
$177$	−1.73673	−0.130540
$178$	−34.0509	−2.55222
$179$	−10.2740	−0.767914	−0.383957	−	0.923351i	$-0.625439\pi$
$179$	−10.2740	−0.767914	−0.383957	+	0.923351i	$0.625439\pi$
$180$	0	0
$181$	2.53622	0.188516	0.0942578	−	0.995548i	$-0.469952\pi$
$181$	2.53622	0.188516	0.0942578	+	0.995548i	$0.469952\pi$
$182$	8.62709	0.639483
$183$	1.81981	0.134525
$184$	−41.6796	−3.07266
$185$	0	0
$186$	0.958747	0.0702987
$187$	−29.2406	−2.13829
$188$	19.3661	1.41242
$189$	2.09721	0.152550
$190$	0	0
$191$	−4.45031	−0.322013	−0.161007	−	0.986953i	$-0.551474\pi$
$191$	−4.45031	−0.322013	−0.161007	+	0.986953i	$0.551474\pi$
$192$	16.2536	1.17301
$193$	2.71300	0.195286	0.0976430	−	0.995222i	$-0.468870\pi$
$193$	2.71300	0.195286	0.0976430	+	0.995222i	$0.468870\pi$
$194$	2.56447	0.184118
$195$	0	0
$196$	−34.5573	−2.46838
$197$	5.04125	0.359174	0.179587	−	0.983742i	$-0.442524\pi$
$197$	5.04125	0.359174	0.179587	+	0.983742i	$0.442524\pi$
$198$	−37.4712	−2.66296
$199$	−14.3531	−1.01746	−0.508732	−	0.860925i	$-0.669886\pi$
$199$	−14.3531	−1.01746	−0.508732	+	0.860925i	$0.669886\pi$
$200$	0	0
$201$	2.95875	0.208694
$202$	−11.5198	−0.810531
$203$	−2.45371	−0.172217
$204$	−12.5988	−0.882095
$205$	0	0
$206$	47.5999	3.31644
$207$	11.1694	0.776330
$208$	−54.5604	−3.78308
$209$	−5.17802	−0.358171
$210$	0	0
$211$	−11.6288	−0.800559	−0.400280	−	0.916393i	$-0.631087\pi$
$211$	−11.6288	−0.800559	−0.400280	+	0.916393i	$0.631087\pi$
$212$	−29.8481	−2.04997
$213$	−1.32937	−0.0910870
$214$	−13.5807	−0.928355
$215$	0	0
$216$	−21.6666	−1.47422
$217$	−1.04125	−0.0706849
$218$	25.7570	1.74448
$219$	−4.16808	−0.281652
$220$	0	0
$221$	18.6384	1.25375
$222$	−1.24745	−0.0837232
$223$	−5.45483	−0.365283	−0.182641	−	0.983180i	$-0.558465\pi$
$223$	−5.45483	−0.365283	−0.182641	+	0.983180i	$0.558465\pi$
$224$	−31.3661	−2.09574
$225$	0	0
$226$	−9.73118	−0.647309
$227$	7.97352	0.529221	0.264611	−	0.964355i	$-0.414757\pi$
$227$	7.97352	0.529221	0.264611	+	0.964355i	$0.414757\pi$
$228$	−2.23104	−0.147754
$229$	22.0197	1.45510	0.727550	−	0.686054i	$-0.240659\pi$
$229$	22.0197	1.45510	0.727550	+	0.686054i	$0.240659\pi$
$230$	0	0
$231$	−1.65480	−0.108878
$232$	25.3496	1.66428
$233$	17.2723	1.13155	0.565773	−	0.824561i	$-0.308578\pi$
$233$	17.2723	1.13155	0.565773	+	0.824561i	$0.308578\pi$
$234$	23.8847	1.56139
$235$	0	0
$236$	−29.6315	−1.92885
$237$	−2.43901	−0.158430
$238$	18.3678	1.19061
$239$	−21.3462	−1.38077	−0.690386	−	0.723441i	$-0.742559\pi$
$239$	−21.3462	−1.38077	−0.690386	+	0.723441i	$0.742559\pi$
$240$	0	0
$241$	−4.15984	−0.267959	−0.133979	−	0.990984i	$-0.542776\pi$
$241$	−4.15984	−0.267959	−0.133979	+	0.990984i	$0.542776\pi$
$242$	29.5325	1.89842
$243$	8.76726	0.562420
$244$	31.0492	1.98772
$245$	0	0
$246$	1.84629	0.117715
$247$	3.30054	0.210008
$248$	10.7573	0.683090
$249$	2.55623	0.161994
$250$	0	0
$251$	5.76896	0.364134	0.182067	−	0.983286i	$-0.441721\pi$
$251$	5.76896	0.364134	0.182067	+	0.983286i	$0.441721\pi$
$252$	17.5345	1.10457
$253$	−17.9848	−1.13070
$254$	−36.0475	−2.26182
$255$	0	0
$256$	108.607	6.78796
$257$	22.4417	1.39988	0.699938	−	0.714203i	$-0.253211\pi$
$257$	22.4417	1.39988	0.699938	+	0.714203i	$0.253211\pi$
$258$	4.12206	0.256628
$259$	1.35480	0.0841831
$260$	0	0
$261$	−6.79327	−0.420493
$262$	43.3114	2.67579
$263$	−10.1904	−0.628369	−0.314185	−	0.949362i	$-0.601731\pi$
$263$	−10.1904	−0.628369	−0.314185	+	0.949362i	$0.601731\pi$
$264$	17.0960	1.05218
$265$	0	0
$266$	3.25262	0.199431
$267$	−4.16324	−0.254786
$268$	50.4813	3.08364
$269$	28.0904	1.71270	0.856351	−	0.516394i	$-0.172726\pi$
$269$	28.0904	1.71270	0.856351	+	0.516394i	$0.172726\pi$
$270$	0	0
$271$	0.0429548	0.00260932	0.00130466	−	0.999999i	$-0.499585\pi$
$271$	0.0429548	0.00260932	0.00130466	+	0.999999i	$0.499585\pi$
$272$	−116.164	−7.04346
$273$	1.05479	0.0638391
$274$	46.4101	2.80374
$275$	0	0
$276$	−7.74908	−0.466440
$277$	21.8288	1.31156	0.655782	−	0.754951i	$-0.272339\pi$
$277$	21.8288	1.31156	0.655782	+	0.754951i	$0.272339\pi$
$278$	60.2785	3.61526
$279$	−2.88278	−0.172587
$280$	0	0
$281$	−9.20415	−0.549074	−0.274537	−	0.961577i	$-0.588525\pi$
$281$	−9.20415	−0.549074	−0.274537	+	0.961577i	$0.588525\pi$
$282$	3.17848	0.189276
$283$	6.85317	0.407379	0.203689	−	0.979036i	$-0.434707\pi$
$283$	6.85317	0.407379	0.203689	+	0.979036i	$0.434707\pi$
$284$	−22.6813	−1.34589
$285$	0	0
$286$	−38.4587	−2.27411
$287$	−2.00518	−0.118362
$288$	−86.8391	−5.11705
$289$	22.6827	1.33428
$290$	0	0
$291$	0.313546	0.0183804
$292$	−71.1145	−4.16166
$293$	16.6101	0.970375	0.485188	−	0.874410i	$-0.338751\pi$
$293$	16.6101	0.970375	0.485188	+	0.874410i	$0.338751\pi$
$294$	−5.67175	−0.330783
$295$	0	0
$296$	−13.9966	−0.813536
$297$	−9.34916	−0.542493
$298$	58.1214	3.36688
$299$	11.4638	0.662968
$300$	0	0
$301$	−4.47679	−0.258038
$302$	−51.6514	−2.97220
$303$	−1.40847	−0.0809147
$304$	−20.5706	−1.17980
$305$	0	0
$306$	50.8525	2.90704
$307$	−16.9553	−0.967693	−0.483846	−	0.875153i	$-0.660761\pi$
$307$	−16.9553	−0.967693	−0.483846	+	0.875153i	$0.660761\pi$
$308$	−28.2338	−1.60877
$309$	5.81981	0.331078
$310$	0	0
$311$	−0.638734	−0.0362193	−0.0181096	−	0.999836i	$-0.505765\pi$
$311$	−0.638734	−0.0362193	−0.0181096	+	0.999836i	$0.505765\pi$
$312$	−10.8972	−0.616933
$313$	18.1141	1.02387	0.511934	−	0.859025i	$-0.328929\pi$
$313$	18.1141	1.02387	0.511934	+	0.859025i	$0.328929\pi$
$314$	−15.8033	−0.891834
$315$	0	0
$316$	−41.6136	−2.34095
$317$	5.06433	0.284441	0.142220	−	0.989835i	$-0.454576\pi$
$317$	5.06433	0.284441	0.142220	+	0.989835i	$0.454576\pi$
$318$	−4.89885	−0.274714
$319$	10.9384	0.612433
$320$	0	0
$321$	−1.66044	−0.0926770
$322$	11.2974	0.629577
$323$	7.02713	0.391000
$324$	46.4912	2.58285
$325$	0	0
$326$	45.3627	2.51241
$327$	3.14919	0.174150
$328$	20.7157	1.14383
$329$	−3.45201	−0.190316
$330$	0	0
$331$	−20.0344	−1.10119	−0.550594	−	0.834773i	$-0.685599\pi$
$331$	−20.0344	−1.10119	−0.550594	+	0.834773i	$0.685599\pi$
$332$	43.6136	2.39361
$333$	3.75085	0.205545
$334$	−14.4191	−0.788979
$335$	0	0
$336$	−6.57400	−0.358641
$337$	4.86729	0.265138	0.132569	−	0.991174i	$-0.457677\pi$
$337$	4.86729	0.265138	0.132569	+	0.991174i	$0.457677\pi$
$338$	−11.8894	−0.646700
$339$	−1.18979	−0.0646203
$340$	0	0
$341$	4.64180	0.251367
$342$	9.00511	0.486940
$343$	13.4486	0.726157
$344$	46.2502	2.49365
$345$	0	0
$346$	−30.1368	−1.62016
$347$	10.1221	0.543381	0.271690	−	0.962385i	$-0.412417\pi$
$347$	10.1221	0.543381	0.271690	+	0.962385i	$0.412417\pi$
$348$	4.71300	0.252643
$349$	−18.3245	−0.980888	−0.490444	−	0.871473i	$-0.663165\pi$
$349$	−18.3245	−0.980888	−0.490444	+	0.871473i	$0.663165\pi$
$350$	0	0
$351$	5.95928	0.318083
$352$	139.827	7.45279
$353$	14.3248	0.762435	0.381217	−	0.924485i	$-0.375505\pi$
$353$	14.3248	0.762435	0.381217	+	0.924485i	$0.375505\pi$
$354$	−4.86331	−0.258482
$355$	0	0
$356$	−71.0320	−3.76469
$357$	2.24575	0.118857
$358$	−28.7700	−1.52054
$359$	12.3197	0.650207	0.325104	−	0.945678i	$-0.394601\pi$
$359$	12.3197	0.650207	0.325104	+	0.945678i	$0.394601\pi$
$360$	0	0
$361$	−17.7556	−0.934506
$362$	7.10210	0.373278
$363$	3.61080	0.189518
$364$	17.9966	0.943278
$365$	0	0
$366$	5.09598	0.266371
$367$	−24.4706	−1.27735	−0.638676	−	0.769475i	$-0.720518\pi$
$367$	−24.4706	−1.27735	−0.638676	+	0.769475i	$0.720518\pi$
$368$	−71.4479	−3.72448
$369$	−5.55146	−0.288998
$370$	0	0
$371$	5.32042	0.276223
$372$	2.00000	0.103695
$373$	−26.5276	−1.37355	−0.686775	−	0.726870i	$-0.740974\pi$
$373$	−26.5276	−1.37355	−0.686775	+	0.726870i	$0.740974\pi$
$374$	−81.8818	−4.23400
$375$	0	0
$376$	35.6632	1.83919
$377$	−6.97229	−0.359091
$378$	5.87277	0.302063
$379$	12.5528	0.644795	0.322398	−	0.946604i	$-0.395511\pi$
$379$	12.5528	0.644795	0.322398	+	0.946604i	$0.395511\pi$
$380$	0	0
$381$	−4.40735	−0.225796
$382$	−12.4621	−0.637615
$383$	−11.5882	−0.592129	−0.296064	−	0.955168i	$-0.595674\pi$
$383$	−11.5882	−0.592129	−0.296064	+	0.955168i	$0.595674\pi$
$384$	24.8875	1.27004
$385$	0	0
$386$	7.59714	0.386684
$387$	−12.3943	−0.630037
$388$	5.34962	0.271586
$389$	32.5790	1.65182	0.825909	−	0.563803i	$-0.190662\pi$
$389$	32.5790	1.65182	0.825909	+	0.563803i	$0.190662\pi$
$390$	0	0
$391$	24.4074	1.23433
$392$	−63.6381	−3.21421
$393$	5.29548	0.267122
$394$	14.1169	0.711198
$395$	0	0
$396$	−78.1671	−3.92804
$397$	−29.8508	−1.49817	−0.749084	−	0.662475i	$-0.769506\pi$
$397$	−29.8508	−1.49817	−0.749084	+	0.662475i	$0.769506\pi$
$398$	−40.1926	−2.01467
$399$	0.397683	0.0199091
$400$	0	0
$401$	−24.9176	−1.24432	−0.622162	−	0.782889i	$-0.713745\pi$
$401$	−24.9176	−1.24432	−0.622162	+	0.782889i	$0.713745\pi$
$402$	8.28530	0.413233
$403$	−2.95875	−0.147386
$404$	−24.0310	−1.19559
$405$	0	0
$406$	−6.87107	−0.341005
$407$	−6.03955	−0.299369
$408$	−23.2011	−1.14863
$409$	13.8085	0.682787	0.341393	−	0.939920i	$-0.389101\pi$
$409$	13.8085	0.682787	0.341393	+	0.939920i	$0.389101\pi$
$410$	0	0
$411$	5.67435	0.279895
$412$	99.2960	4.89196
$413$	5.28182	0.259902
$414$	31.2775	1.53720
$415$	0	0
$416$	−89.1276	−4.36984
$417$	7.36997	0.360909
$418$	−14.4999	−0.709211
$419$	−21.7799	−1.06402	−0.532009	−	0.846738i	$-0.678563\pi$
$419$	−21.7799	−1.06402	−0.532009	+	0.846738i	$0.678563\pi$
$420$	0	0
$421$	3.23758	0.157790	0.0788949	−	0.996883i	$-0.474861\pi$
$421$	3.23758	0.157790	0.0788949	+	0.996883i	$0.474861\pi$
$422$	−32.5638	−1.58518
$423$	−9.55712	−0.464683
$424$	−54.9660	−2.66938
$425$	0	0
$426$	−3.72260	−0.180361
$427$	−5.53452	−0.267834
$428$	−28.3300	−1.36938
$429$	−4.70216	−0.227023
$430$	0	0
$431$	−12.6466	−0.609167	−0.304583	−	0.952486i	$-0.598517\pi$
$431$	−12.6466	−0.609167	−0.304583	+	0.952486i	$0.598517\pi$
$432$	−37.1412	−1.78696
$433$	−31.9914	−1.53741	−0.768705	−	0.639604i	$-0.779098\pi$
$433$	−31.9914	−1.53741	−0.768705	+	0.639604i	$0.779098\pi$
$434$	−2.91579	−0.139963
$435$	0	0
$436$	53.7305	2.57322
$437$	4.32212	0.206755
$438$	−11.6717	−0.557698
$439$	−13.8432	−0.660701	−0.330351	−	0.943858i	$-0.607167\pi$
$439$	−13.8432	−0.660701	−0.330351	+	0.943858i	$0.607167\pi$
$440$	0	0
$441$	17.0539	0.812091
$442$	52.1926	2.48255
$443$	20.3479	0.966759	0.483379	−	0.875411i	$-0.339409\pi$
$443$	20.3479	0.966759	0.483379	+	0.875411i	$0.339409\pi$
$444$	−2.60225	−0.123497
$445$	0	0
$446$	−15.2750	−0.723293
$447$	7.10623	0.336113
$448$	−49.4314	−2.33542
$449$	8.71640	0.411353	0.205676	−	0.978620i	$-0.434061\pi$
$449$	8.71640	0.411353	0.205676	+	0.978620i	$0.434061\pi$
$450$	0	0
$451$	8.93886	0.420915
$452$	−20.2998	−0.954822
$453$	−6.31518	−0.296713
$454$	22.3280	1.04791
$455$	0	0
$456$	−4.10852	−0.192399
$457$	0.0311855	0.00145879	0.000729397	−	1.00000i	$-0.499768\pi$
$457$	0.0311855	0.00145879	0.000729397		1.00000i	$0.499768\pi$
$458$	61.6611	2.88123
$459$	12.6878	0.592217
$460$	0	0
$461$	−29.4882	−1.37340	−0.686700	−	0.726941i	$-0.740941\pi$
$461$	−29.4882	−1.37340	−0.686700	+	0.726941i	$0.740941\pi$
$462$	−4.63390	−0.215588
$463$	19.1547	0.890196	0.445098	−	0.895482i	$-0.353169\pi$
$463$	19.1547	0.890196	0.445098	+	0.895482i	$0.353169\pi$
$464$	43.4547	2.01734
$465$	0	0
$466$	48.3671	2.24056
$467$	23.9367	1.10766	0.553829	−	0.832630i	$-0.313166\pi$
$467$	23.9367	1.10766	0.553829	+	0.832630i	$0.313166\pi$
$468$	49.8248	2.30315
$469$	−8.99830	−0.415503
$470$	0	0
$471$	−1.93220	−0.0890311
$472$	−54.5672	−2.51166
$473$	19.9570	0.917626
$474$	−6.82988	−0.313707
$475$	0	0
$476$	38.3163	1.75622
$477$	14.7299	0.674438
$478$	−59.7752	−2.73406
$479$	21.4039	0.977968	0.488984	−	0.872293i	$-0.337368\pi$
$479$	21.4039	0.977968	0.488984	+	0.872293i	$0.337368\pi$
$480$	0	0
$481$	3.84969	0.175531
$482$	−11.6487	−0.530583
$483$	1.38127	0.0628502
$484$	61.6064	2.80029
$485$	0	0
$486$	24.5507	1.11364
$487$	−26.0763	−1.18163	−0.590815	−	0.806807i	$-0.701194\pi$
$487$	−26.0763	−1.18163	−0.590815	+	0.806807i	$0.701194\pi$
$488$	57.1778	2.58832
$489$	5.54629	0.250812
$490$	0	0
$491$	−11.9367	−0.538696	−0.269348	−	0.963043i	$-0.586808\pi$
$491$	−11.9367	−0.538696	−0.269348	+	0.963043i	$0.586808\pi$
$492$	3.85147	0.173638
$493$	−14.8446	−0.668567
$494$	9.24241	0.415836
$495$	0	0
$496$	18.4404	0.827997
$497$	4.04295	0.181351
$498$	7.15813	0.320764
$499$	16.5394	0.740406	0.370203	−	0.928951i	$-0.379288\pi$
$499$	16.5394	0.740406	0.370203	+	0.928951i	$0.379288\pi$
$500$	0	0
$501$	−1.76296	−0.0787632
$502$	16.1547	0.721018
$503$	−16.6418	−0.742021	−0.371011	−	0.928629i	$-0.620989\pi$
$503$	−16.6418	−0.742021	−0.371011	+	0.928629i	$0.620989\pi$
$504$	32.2903	1.43832
$505$	0	0
$506$	−50.3624	−2.23888
$507$	−1.45367	−0.0645596
$508$	−75.1970	−3.33633
$509$	−43.0388	−1.90766	−0.953831	−	0.300345i	$-0.902898\pi$
$509$	−43.0388	−1.90766	−0.953831	+	0.300345i	$0.902898\pi$
$510$	0	0
$511$	12.6762	0.560761
$512$	158.749	7.01579
$513$	2.24680	0.0991984
$514$	62.8430	2.77188
$515$	0	0
$516$	8.59884	0.378543
$517$	15.3887	0.676795
$518$	3.79381	0.166690
$519$	−3.68468	−0.161740
$520$	0	0
$521$	37.2138	1.63037	0.815184	−	0.579203i	$-0.196636\pi$
$521$	37.2138	1.63037	0.815184	+	0.579203i	$0.196636\pi$
$522$	−19.0230	−0.832614
$523$	23.4085	1.02358	0.511791	−	0.859110i	$-0.328982\pi$
$523$	23.4085	1.02358	0.511791	+	0.859110i	$0.328982\pi$
$524$	90.3500	3.94696
$525$	0	0
$526$	−28.5360	−1.24423
$527$	−6.29942	−0.274407
$528$	29.3062	1.27539
$529$	−7.98795	−0.347302
$530$	0	0
$531$	14.6231	0.634588
$532$	6.78516	0.294174
$533$	−5.69776	−0.246797
$534$	−11.6582	−0.504500
$535$	0	0
$536$	92.9626	4.01537
$537$	−3.51757	−0.151794
$538$	78.6608	3.39131
$539$	−27.4599	−1.18278
$540$	0	0
$541$	2.38298	0.102452	0.0512261	−	0.998687i	$-0.483687\pi$
$541$	2.38298	0.102452	0.0512261	+	0.998687i	$0.483687\pi$
$542$	0.120285	0.00516669
$543$	0.868341	0.0372641
$544$	−189.760	−8.13590
$545$	0	0
$546$	2.95371	0.126407
$547$	21.4400	0.916709	0.458355	−	0.888769i	$-0.348439\pi$
$547$	21.4400	0.916709	0.458355	+	0.888769i	$0.348439\pi$
$548$	96.8140	4.13569
$549$	−15.3227	−0.653956
$550$	0	0
$551$	−2.62872	−0.111987
$552$	−14.2701	−0.607377
$553$	7.41764	0.315430
$554$	61.1265	2.59702
$555$	0	0
$556$	125.744	5.33275
$557$	12.5276	0.530813	0.265407	−	0.964137i	$-0.414494\pi$
$557$	12.5276	0.530813	0.265407	+	0.964137i	$0.414494\pi$
$558$	−8.07256	−0.341739
$559$	−12.7209	−0.538037
$560$	0	0
$561$	−10.0113	−0.422678
$562$	−25.7741	−1.08722
$563$	−10.7361	−0.452472	−0.226236	−	0.974073i	$-0.572642\pi$
$563$	−10.7361	−0.452472	−0.226236	+	0.974073i	$0.572642\pi$
$564$	6.63049	0.279194
$565$	0	0
$566$	19.1907	0.806647
$567$	−8.28707	−0.348024
$568$	−41.7683	−1.75256
$569$	1.00783	0.0422504	0.0211252	−	0.999777i	$-0.493275\pi$
$569$	1.00783	0.0422504	0.0211252	+	0.999777i	$0.493275\pi$
$570$	0	0
$571$	−9.88631	−0.413729	−0.206865	−	0.978370i	$-0.566326\pi$
$571$	−9.88631	−0.413729	−0.206865	+	0.978370i	$0.566326\pi$
$572$	−80.2270	−3.35446
$573$	−1.52368	−0.0636527
$574$	−5.61504	−0.234367
$575$	0	0
$576$	−136.854	−5.70226
$577$	−22.1564	−0.922384	−0.461192	−	0.887300i	$-0.652578\pi$
$577$	−22.1564	−0.922384	−0.461192	+	0.887300i	$0.652578\pi$
$578$	63.5178	2.64199
$579$	0.928867	0.0386024
$580$	0	0
$581$	−7.77414	−0.322526
$582$	0.878013	0.0363948
$583$	−23.7179	−0.982295
$584$	−130.959	−5.41913
$585$	0	0
$586$	46.5129	1.92143
$587$	−16.7526	−0.691452	−0.345726	−	0.938336i	$-0.612367\pi$
$587$	−16.7526	−0.691452	−0.345726	+	0.938336i	$0.612367\pi$
$588$	−11.8316	−0.487926
$589$	−1.11552	−0.0459642
$590$	0	0
$591$	1.72601	0.0709984
$592$	−23.9932	−0.986114
$593$	21.0526	0.864525	0.432262	−	0.901748i	$-0.357715\pi$
$593$	21.0526	0.864525	0.432262	+	0.901748i	$0.357715\pi$
$594$	−26.1802	−1.07419
$595$	0	0
$596$	121.244	4.96637
$597$	−4.91416	−0.201123
$598$	32.1017	1.31274
$599$	−24.1994	−0.988760	−0.494380	−	0.869246i	$-0.664605\pi$
$599$	−24.1994	−0.988760	−0.494380	+	0.869246i	$0.664605\pi$
$600$	0	0
$601$	−37.0275	−1.51038	−0.755192	−	0.655504i	$-0.772456\pi$
$601$	−37.0275	−1.51038	−0.755192	+	0.655504i	$0.772456\pi$
$602$	−12.5362	−0.510938
$603$	−24.9124	−1.01451
$604$	−107.748	−4.38419
$605$	0	0
$606$	−3.94411	−0.160219
$607$	10.9011	0.442461	0.221231	−	0.975222i	$-0.428993\pi$
$607$	10.9011	0.442461	0.221231	+	0.975222i	$0.428993\pi$
$608$	−33.6033	−1.36279
$609$	−0.840093	−0.0340423
$610$	0	0
$611$	−9.80898	−0.396829
$612$	106.081	4.28808
$613$	−17.8882	−0.722497	−0.361249	−	0.932469i	$-0.617649\pi$
$613$	−17.8882	−0.722497	−0.361249	+	0.932469i	$0.617649\pi$
$614$	−47.4796	−1.91612
$615$	0	0
$616$	−51.9932	−2.09487
$617$	39.3548	1.58436	0.792182	−	0.610285i	$-0.208945\pi$
$617$	39.3548	1.58436	0.792182	+	0.610285i	$0.208945\pi$
$618$	16.2971	0.655564
$619$	19.5429	0.785495	0.392747	−	0.919646i	$-0.371525\pi$
$619$	19.5429	0.785495	0.392747	+	0.919646i	$0.371525\pi$
$620$	0	0
$621$	7.80380	0.313156
$622$	−1.78863	−0.0717175
$623$	12.6615	0.507271
$624$	−18.6802	−0.747806
$625$	0	0
$626$	50.7243	2.02735
$627$	−1.77283	−0.0708000
$628$	−32.9666	−1.31551
$629$	8.19632	0.326809
$630$	0	0
$631$	−33.4486	−1.33157	−0.665784	−	0.746145i	$-0.731903\pi$
$631$	−33.4486	−1.33157	−0.665784	+	0.746145i	$0.731903\pi$
$632$	−76.6325	−3.04828
$633$	−3.98142	−0.158247
$634$	14.1815	0.563219
$635$	0	0
$636$	−10.2193	−0.405220
$637$	17.5033	0.693507
$638$	30.6305	1.21267
$639$	11.1932	0.442796
$640$	0	0
$641$	7.13506	0.281818	0.140909	−	0.990023i	$-0.454998\pi$
$641$	7.13506	0.281818	0.140909	+	0.990023i	$0.454998\pi$
$642$	−4.64970	−0.183509
$643$	−21.1141	−0.832660	−0.416330	−	0.909214i	$-0.636684\pi$
$643$	−21.1141	−0.832660	−0.416330	+	0.909214i	$0.636684\pi$
$644$	23.5669	0.928666
$645$	0	0
$646$	19.6779	0.774216
$647$	1.08185	0.0425320	0.0212660	−	0.999774i	$-0.493230\pi$
$647$	1.08185	0.0425320	0.0212660	+	0.999774i	$0.493230\pi$
$648$	85.6148	3.36327
$649$	−23.5458	−0.924254
$650$	0	0
$651$	−0.356500	−0.0139724
$652$	94.6291	3.70596
$653$	−47.5112	−1.85926	−0.929629	−	0.368497i	$-0.879873\pi$
$653$	−47.5112	−1.85926	−0.929629	+	0.368497i	$0.879873\pi$
$654$	8.81858	0.344834
$655$	0	0
$656$	35.5112	1.38648
$657$	35.0948	1.36918
$658$	−9.66657	−0.376842
$659$	−24.3048	−0.946782	−0.473391	−	0.880852i	$-0.656970\pi$
$659$	−24.3048	−0.946782	−0.473391	+	0.880852i	$0.656970\pi$
$660$	0	0
$661$	1.23308	0.0479613	0.0239806	−	0.999712i	$-0.492366\pi$
$661$	1.23308	0.0479613	0.0239806	+	0.999712i	$0.492366\pi$
$662$	−56.1017	−2.18045
$663$	6.38134	0.247831
$664$	80.3156	3.11685
$665$	0	0
$666$	10.5034	0.406999
$667$	−9.13035	−0.353529
$668$	−30.0791	−1.16380
$669$	−1.86761	−0.0722058
$670$	0	0
$671$	24.6723	0.952464
$672$	−10.7390	−0.414266
$673$	11.0242	0.424951	0.212476	−	0.977166i	$-0.431847\pi$
$673$	11.0242	0.424951	0.212476	+	0.977166i	$0.431847\pi$
$674$	13.6297	0.524998
$675$	0	0
$676$	−24.8020	−0.953925
$677$	39.3994	1.51424	0.757122	−	0.653274i	$-0.226605\pi$
$677$	39.3994	1.51424	0.757122	+	0.653274i	$0.226605\pi$
$678$	−3.33173	−0.127954
$679$	−0.953571	−0.0365947
$680$	0	0
$681$	2.72995	0.104612
$682$	12.9983	0.497731
$683$	−42.8213	−1.63851	−0.819256	−	0.573428i	$-0.805613\pi$
$683$	−42.8213	−1.63851	−0.819256	+	0.573428i	$0.805613\pi$
$684$	18.7852	0.718268
$685$	0	0
$686$	37.6598	1.43786
$687$	7.53901	0.287631
$688$	79.2829	3.02263
$689$	15.1181	0.575954
$690$	0	0
$691$	−34.1911	−1.30069	−0.650346	−	0.759638i	$-0.725376\pi$
$691$	−34.1911	−1.30069	−0.650346	+	0.759638i	$0.725376\pi$
$692$	−62.8670	−2.38984
$693$	13.9333	0.529282
$694$	28.3445	1.07594
$695$	0	0
$696$	8.67911	0.328981
$697$	−12.1310	−0.459495
$698$	−51.3136	−1.94225
$699$	5.91362	0.223674
$700$	0	0
$701$	−31.6598	−1.19577	−0.597886	−	0.801581i	$-0.703993\pi$
$701$	−31.6598	−1.19577	−0.597886	+	0.801581i	$0.703993\pi$
$702$	16.6876	0.629834
$703$	1.45143	0.0547417
$704$	220.360	8.30514
$705$	0	0
$706$	40.1135	1.50969
$707$	4.28353	0.161099
$708$	−10.1451	−0.381277
$709$	−19.8198	−0.744349	−0.372174	−	0.928163i	$-0.621388\pi$
$709$	−19.8198	−0.744349	−0.372174	+	0.928163i	$0.621388\pi$
$710$	0	0
$711$	20.5362	0.770168
$712$	−130.807	−4.90221
$713$	−3.87454	−0.145103
$714$	6.28870	0.235349
$715$	0	0
$716$	−60.0158	−2.24290
$717$	−7.30844	−0.272939
$718$	34.4984	1.28747
$719$	25.7339	0.959713	0.479856	−	0.877347i	$-0.340689\pi$
$719$	25.7339	0.959713	0.479856	+	0.877347i	$0.340689\pi$
$720$	0	0
$721$	−17.6995	−0.659165
$722$	−49.7206	−1.85041
$723$	−1.42423	−0.0529677
$724$	14.8154	0.550610
$725$	0	0
$726$	10.1112	0.375263
$727$	−24.6909	−0.915734	−0.457867	−	0.889021i	$-0.651386\pi$
$727$	−24.6909	−0.915734	−0.457867	+	0.889021i	$0.651386\pi$
$728$	33.1412	1.22829
$729$	−20.8745	−0.773131
$730$	0	0
$731$	−27.0839	−1.00173
$732$	10.6305	0.392914
$733$	−23.0265	−0.850505	−0.425252	−	0.905075i	$-0.639815\pi$
$733$	−23.0265	−0.850505	−0.425252	+	0.905075i	$0.639815\pi$
$734$	−68.5242	−2.52928
$735$	0	0
$736$	−116.714	−4.30215
$737$	40.1135	1.47760
$738$	−15.5456	−0.572242
$739$	−27.2176	−1.00121	−0.500607	−	0.865675i	$-0.666890\pi$
$739$	−27.2176	−1.00121	−0.500607	+	0.865675i	$0.666890\pi$
$740$	0	0
$741$	1.13003	0.0415126
$742$	14.8986	0.546946
$743$	23.0434	0.845380	0.422690	−	0.906274i	$-0.361086\pi$
$743$	23.0434	0.845380	0.422690	+	0.906274i	$0.361086\pi$
$744$	3.68305	0.135027
$745$	0	0
$746$	−74.2846	−2.71975
$747$	−21.5232	−0.787493
$748$	−170.810	−6.24543
$749$	5.04983	0.184517
$750$	0	0
$751$	−12.5480	−0.457883	−0.228941	−	0.973440i	$-0.573526\pi$
$751$	−12.5480	−0.457883	−0.228941	+	0.973440i	$0.573526\pi$
$752$	61.1344	2.22934
$753$	1.97516	0.0719787
$754$	−19.5243	−0.711033
$755$	0	0
$756$	12.2509	0.445562
$757$	0.441361	0.0160415	0.00802077	−	0.999968i	$-0.497447\pi$
$757$	0.441361	0.0160415	0.00802077	+	0.999968i	$0.497447\pi$
$758$	35.1513	1.27675
$759$	−6.15758	−0.223506
$760$	0	0
$761$	−23.0903	−0.837024	−0.418512	−	0.908211i	$-0.637448\pi$
$761$	−23.0903	−0.837024	−0.418512	+	0.908211i	$0.637448\pi$
$762$	−12.3418	−0.447096
$763$	−9.57747	−0.346728
$764$	−25.9966	−0.940524
$765$	0	0
$766$	−32.4501	−1.17247
$767$	15.0084	0.541923
$768$	37.1846	1.34178
$769$	−16.5906	−0.598272	−0.299136	−	0.954210i	$-0.596699\pi$
$769$	−16.5906	−0.598272	−0.299136	+	0.954210i	$0.596699\pi$
$770$	0	0
$771$	7.68352	0.276715
$772$	15.8481	0.570384
$773$	−50.6033	−1.82008	−0.910038	−	0.414525i	$-0.863948\pi$
$773$	−50.6033	−1.82008	−0.910038	+	0.414525i	$0.863948\pi$
$774$	−34.7074	−1.24753
$775$	0	0
$776$	9.85147	0.353647
$777$	0.463851	0.0166406
$778$	91.2300	3.27075
$779$	−2.14819	−0.0769670
$780$	0	0
$781$	−18.0231	−0.644916
$782$	68.3472	2.44409
$783$	−4.74628	−0.169618
$784$	−109.089	−3.89605
$785$	0	0
$786$	14.8288	0.528925
$787$	−42.9038	−1.52936	−0.764678	−	0.644413i	$-0.777102\pi$
$787$	−42.9038	−1.52936	−0.764678	+	0.644413i	$0.777102\pi$
$788$	29.4486	1.04906
$789$	−3.48897	−0.124210
$790$	0	0
$791$	3.61844	0.128657
$792$	−143.947	−5.11492
$793$	−15.7265	−0.558463
$794$	−83.5903	−2.96651
$795$	0	0
$796$	−83.8440	−2.97177
$797$	33.5707	1.18913	0.594567	−	0.804046i	$-0.297324\pi$
$797$	33.5707	1.18913	0.594567	+	0.804046i	$0.297324\pi$
$798$	1.11362	0.0394218
$799$	−20.8841	−0.738828
$800$	0	0
$801$	35.0541	1.23858
$802$	−69.7760	−2.46388
$803$	−56.5091	−1.99416
$804$	17.2836	0.609545
$805$	0	0
$806$	−8.28530	−0.291837
$807$	9.61749	0.338552
$808$	−44.2536	−1.55684
$809$	35.3774	1.24380	0.621902	−	0.783095i	$-0.286360\pi$
$809$	35.3774	1.24380	0.621902	+	0.783095i	$0.286360\pi$
$810$	0	0
$811$	54.9833	1.93072	0.965362	−	0.260916i	$-0.0840245\pi$
$811$	54.9833	1.93072	0.965362	+	0.260916i	$0.0840245\pi$
$812$	−14.3334	−0.503005
$813$	0.0147067	0.000515787 0
$814$	−16.9124	−0.592779
$815$	0	0
$816$	−39.7717	−1.39229
$817$	−4.79609	−0.167794
$818$	38.6676	1.35198
$819$	−8.88128	−0.310337
$820$	0	0
$821$	47.1995	1.64727	0.823636	−	0.567118i	$-0.191942\pi$
$821$	47.1995	1.64727	0.823636	+	0.567118i	$0.191942\pi$
$822$	15.8897	0.554217
$823$	31.1661	1.08638	0.543192	−	0.839609i	$-0.317216\pi$
$823$	31.1661	1.08638	0.543192	+	0.839609i	$0.317216\pi$
$824$	182.856	6.37009
$825$	0	0
$826$	14.7905	0.514629
$827$	−2.62427	−0.0912548	−0.0456274	−	0.998959i	$-0.514529\pi$
$827$	−2.62427	−0.0912548	−0.0456274	+	0.998959i	$0.514529\pi$
$828$	65.2466	2.26747
$829$	30.1876	1.04846	0.524230	−	0.851577i	$-0.324353\pi$
$829$	30.1876	1.04846	0.524230	+	0.851577i	$0.324353\pi$
$830$	0	0
$831$	7.47365	0.259258
$832$	−140.461	−4.86960
$833$	37.2661	1.29119
$834$	20.6379	0.714633
$835$	0	0
$836$	−30.2475	−1.04613
$837$	−2.01412	−0.0696183
$838$	−60.9897	−2.10685
$839$	−9.75555	−0.336799	−0.168399	−	0.985719i	$-0.553860\pi$
$839$	−9.75555	−0.336799	−0.168399	+	0.985719i	$0.553860\pi$
$840$	0	0
$841$	−23.4469	−0.808514
$842$	9.06610	0.312438
$843$	−3.15128	−0.108536
$844$	−67.9299	−2.33824
$845$	0	0
$846$	−26.7625	−0.920115
$847$	−10.9814	−0.377324
$848$	−94.2236	−3.23565
$849$	2.34636	0.0805270
$850$	0	0
$851$	5.04125	0.172812
$852$	−7.76556	−0.266044
$853$	−39.4547	−1.35090	−0.675452	−	0.737404i	$-0.736052\pi$
$853$	−39.4547	−1.35090	−0.675452	+	0.737404i	$0.736052\pi$
$854$	−15.4982	−0.530336
$855$	0	0
$856$	−52.1705	−1.78315
$857$	10.6006	0.362110	0.181055	−	0.983473i	$-0.442049\pi$
$857$	10.6006	0.362110	0.181055	+	0.983473i	$0.442049\pi$
$858$	−13.1673	−0.449526
$859$	−30.1660	−1.02925	−0.514625	−	0.857416i	$-0.672069\pi$
$859$	−30.1660	−1.02925	−0.514625	+	0.857416i	$0.672069\pi$
$860$	0	0
$861$	−0.686525	−0.0233967
$862$	−35.4140	−1.20621
$863$	−11.7962	−0.401546	−0.200773	−	0.979638i	$-0.564345\pi$
$863$	−11.7962	−0.401546	−0.200773	+	0.979638i	$0.564345\pi$
$864$	−60.6723	−2.06411
$865$	0	0
$866$	−89.5847	−3.04421
$867$	7.76602	0.263748
$868$	−6.08251	−0.206454
$869$	−33.0670	−1.12172
$870$	0	0
$871$	−25.5689	−0.866369
$872$	98.9461	3.35074
$873$	−2.64003	−0.0893513
$874$	12.1031	0.409394
$875$	0	0
$876$	−24.3479	−0.822640
$877$	−12.3531	−0.417134	−0.208567	−	0.978008i	$-0.566880\pi$
$877$	−12.3531	−0.417134	−0.208567	+	0.978008i	$0.566880\pi$
$878$	−38.7648	−1.30825
$879$	5.68692	0.191815
$880$	0	0
$881$	28.2740	0.952575	0.476288	−	0.879290i	$-0.341982\pi$
$881$	28.2740	0.952575	0.476288	+	0.879290i	$0.341982\pi$
$882$	47.7556	1.60802
$883$	−14.7328	−0.495798	−0.247899	−	0.968786i	$-0.579740\pi$
$883$	−14.7328	−0.495798	−0.247899	+	0.968786i	$0.579740\pi$
$884$	108.877	3.66192
$885$	0	0
$886$	56.9797	1.91427
$887$	−26.9237	−0.904009	−0.452005	−	0.892016i	$-0.649291\pi$
$887$	−26.9237	−0.904009	−0.452005	+	0.892016i	$0.649291\pi$
$888$	−4.79210	−0.160812
$889$	13.4039	0.449552
$890$	0	0
$891$	36.9429	1.23763
$892$	−31.8645	−1.06690
$893$	−3.69822	−0.123756
$894$	19.8994	0.665535
$895$	0	0
$896$	−75.6893	−2.52860
$897$	3.92493	0.131050
$898$	24.4083	0.814516
$899$	2.35650	0.0785937
$900$	0	0
$901$	32.1877	1.07233
$902$	25.0313	0.833450
$903$	−1.53275	−0.0510066
$904$	−37.3826	−1.24333
$905$	0	0
$906$	−17.6842	−0.587519
$907$	25.7869	0.856239	0.428119	−	0.903722i	$-0.359176\pi$
$907$	25.7869	0.856239	0.428119	+	0.903722i	$0.359176\pi$
$908$	46.5775	1.54573
$909$	11.8592	0.393346
$910$	0	0
$911$	24.4130	0.808839	0.404419	−	0.914574i	$-0.367474\pi$
$911$	24.4130	0.808839	0.404419	+	0.914574i	$0.367474\pi$
$912$	−7.04288	−0.233213
$913$	34.6563	1.14696
$914$	0.0873278	0.00288855
$915$	0	0
$916$	128.628	4.25000
$917$	−16.1049	−0.531831
$918$	35.5293	1.17264
$919$	−6.86800	−0.226554	−0.113277	−	0.993563i	$-0.536135\pi$
$919$	−6.86800	−0.226554	−0.113277	+	0.993563i	$0.536135\pi$
$920$	0	0
$921$	−5.80511	−0.191285
$922$	−82.5749	−2.71946
$923$	11.4882	0.378137
$924$	−9.66657	−0.318007
$925$	0	0
$926$	53.6385	1.76267
$927$	−49.0023	−1.60945
$928$	70.9858	2.33022
$929$	12.6470	0.414934	0.207467	−	0.978242i	$-0.433478\pi$
$929$	12.6470	0.414934	0.207467	+	0.978242i	$0.433478\pi$
$930$	0	0
$931$	6.59918	0.216279
$932$	100.897	3.30498
$933$	−0.218687	−0.00715950
$934$	67.0293	2.19326
$935$	0	0
$936$	91.7536	2.99906
$937$	−42.8873	−1.40107	−0.700534	−	0.713619i	$-0.747055\pi$
$937$	−42.8873	−1.40107	−0.700534	+	0.713619i	$0.747055\pi$
$938$	−25.1977	−0.822734
$939$	6.20183	0.202389
$940$	0	0
$941$	24.2254	0.789725	0.394863	−	0.918740i	$-0.370792\pi$
$941$	24.2254	0.789725	0.394863	+	0.918740i	$0.370792\pi$
$942$	−5.41069	−0.176290
$943$	−7.46133	−0.242974
$944$	−93.5400	−3.04447
$945$	0	0
$946$	55.8852	1.81698
$947$	16.2682	0.528647	0.264323	−	0.964434i	$-0.414851\pi$
$947$	16.2682	0.528647	0.264323	+	0.964434i	$0.414851\pi$
$948$	−14.2475	−0.462738
$949$	36.0197	1.16925
$950$	0	0
$951$	1.73391	0.0562257
$952$	70.5604	2.28688
$953$	−19.2891	−0.624837	−0.312418	−	0.949945i	$-0.601139\pi$
$953$	−19.2891	−0.624837	−0.312418	+	0.949945i	$0.601139\pi$
$954$	41.2479	1.33545
$955$	0	0
$956$	−124.694	−4.03291
$957$	3.74505	0.121060
$958$	59.9367	1.93647
$959$	−17.2571	−0.557261
$960$	0	0
$961$	1.00000	0.0322581
$962$	10.7802	0.347567
$963$	13.9808	0.450525
$964$	−24.2998	−0.782644
$965$	0	0
$966$	3.86795	0.124449
$967$	−20.9745	−0.674496	−0.337248	−	0.941416i	$-0.609496\pi$
$967$	−20.9745	−0.674496	−0.337248	+	0.941416i	$0.609496\pi$
$968$	113.450	3.64641
$969$	2.40592	0.0772894
$970$	0	0
$971$	−16.2572	−0.521718	−0.260859	−	0.965377i	$-0.584006\pi$
$971$	−16.2572	−0.521718	−0.260859	+	0.965377i	$0.584006\pi$
$972$	51.2142	1.64270
$973$	−22.4139	−0.718558
$974$	−73.0207	−2.33973
$975$	0	0
$976$	98.0151	3.13739
$977$	−12.3649	−0.395587	−0.197794	−	0.980244i	$-0.563378\pi$
$977$	−12.3649	−0.395587	−0.197794	+	0.980244i	$0.563378\pi$
$978$	15.5311	0.496630
$979$	−56.4435	−1.80394
$980$	0	0
$981$	−26.5159	−0.846587
$982$	−33.4260	−1.06667
$983$	−39.4586	−1.25853	−0.629267	−	0.777189i	$-0.716645\pi$
$983$	−39.4586	−1.25853	−0.629267	+	0.777189i	$0.716645\pi$
$984$	7.09257	0.226103
$985$	0	0
$986$	−41.5689	−1.32382
$987$	−1.18189	−0.0376199
$988$	19.2802	0.613385
$989$	−16.6583	−0.529702
$990$	0	0
$991$	−55.5390	−1.76425	−0.882127	−	0.471011i	$-0.843889\pi$
$991$	−55.5390	−1.76425	−0.882127	+	0.471011i	$0.843889\pi$
$992$	30.1234	0.956420
$993$	−6.85930	−0.217673
$994$	11.3214	0.359092
$995$	0	0
$996$	14.9323	0.473147
$997$	−13.4120	−0.424762	−0.212381	−	0.977187i	$-0.568122\pi$
$997$	−13.4120	−0.424762	−0.212381	+	0.977187i	$0.568122\pi$
$998$	46.3149	1.46607
$999$	2.62062	0.0829129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.g.1.4		4
3.2	odd	2		6975.2.a.bj.1.1		4
5.2	odd	4		775.2.b.e.249.8		8
5.3	odd	4		775.2.b.e.249.1		8
5.4	even	2		155.2.a.d.1.1	✓	4
15.14	odd	2		1395.2.a.m.1.4		4
20.19	odd	2		2480.2.a.z.1.2		4
35.34	odd	2		7595.2.a.q.1.1		4
40.19	odd	2		9920.2.a.cd.1.3		4
40.29	even	2		9920.2.a.ch.1.2		4
155.154	odd	2		4805.2.a.j.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.d.1.1	✓	4	5.4	even	2
775.2.a.g.1.4		4	1.1	even	1	trivial
775.2.b.e.249.1		8	5.3	odd	4
775.2.b.e.249.8		8	5.2	odd	4
1395.2.a.m.1.4		4	15.14	odd	2
2480.2.a.z.1.2		4	20.19	odd	2
4805.2.a.j.1.1		4	155.154	odd	2
6975.2.a.bj.1.1		4	3.2	odd	2
7595.2.a.q.1.1		4	35.34	odd	2
9920.2.a.cd.1.3		4	40.19	odd	2
9920.2.a.ch.1.2		4	40.29	even	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+2.80027 q^{2} +0.342376 q^{3} +5.84153 q^{4} +0.958747 q^{6} -1.04125 q^{7} +10.7573 q^{8} -2.88278 q^{9} +O(q^{10})\)	\(q+2.80027 q^{2} +0.342376 q^{3} +5.84153 q^{4} +0.958747 q^{6} -1.04125 q^{7} +10.7573 q^{8} -2.88278 q^{9} +4.64180 q^{11} +2.00000 q^{12} -2.95875 q^{13} -2.91579 q^{14} +18.4404 q^{16} -6.29942 q^{17} -8.07256 q^{18} -1.11552 q^{19} -0.356500 q^{21} +12.9983 q^{22} -3.87454 q^{23} +3.68305 q^{24} -8.28530 q^{26} -2.01412 q^{27} -6.08251 q^{28} +2.35650 q^{29} +1.00000 q^{31} +30.1234 q^{32} +1.58924 q^{33} -17.6401 q^{34} -16.8398 q^{36} -1.30112 q^{37} -3.12376 q^{38} -1.01300 q^{39} +1.92573 q^{41} -0.998298 q^{42} +4.29942 q^{43} +27.1152 q^{44} -10.8498 q^{46} +3.31525 q^{47} +6.31355 q^{48} -5.91579 q^{49} -2.15677 q^{51} -17.2836 q^{52} -5.10964 q^{53} -5.64010 q^{54} -11.2011 q^{56} -0.381928 q^{57} +6.59884 q^{58} -5.07256 q^{59} +5.31525 q^{61} +2.80027 q^{62} +3.00170 q^{63} +47.4730 q^{64} +4.45031 q^{66} +8.64180 q^{67} -36.7982 q^{68} -1.32655 q^{69} -3.88278 q^{71} -31.0110 q^{72} -12.1740 q^{73} -3.64350 q^{74} -6.51634 q^{76} -4.83329 q^{77} -2.83669 q^{78} -7.12376 q^{79} +7.95875 q^{81} +5.39258 q^{82} +7.46614 q^{83} -2.08251 q^{84} +12.0396 q^{86} +0.806810 q^{87} +49.9333 q^{88} -12.1598 q^{89} +3.08080 q^{91} -22.6332 q^{92} +0.342376 q^{93} +9.28360 q^{94} +10.3135 q^{96} +0.915792 q^{97} -16.5658 q^{98} -13.3813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9	\( 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9} - 6 q^{11} + 8 q^{12} - 16 q^{13} + 8 q^{14} + 11 q^{16} - q^{17} + q^{18} + 5 q^{19} + 2 q^{21} + 24 q^{22} - 14 q^{24} - 12 q^{26} - 5 q^{27} - 16 q^{28} + 6 q^{29} + 4 q^{31} + 29 q^{32} + 12 q^{33} - 18 q^{34} - 25 q^{36} - 9 q^{37} - 6 q^{39} + 13 q^{41} + 24 q^{42} - 7 q^{43} + 20 q^{44} - 26 q^{46} + 14 q^{47} - 2 q^{48} - 4 q^{49} + 5 q^{51} - 20 q^{52} - 11 q^{53} + 30 q^{54} - 4 q^{56} + 31 q^{57} - 22 q^{58} + 13 q^{59} + 22 q^{61} + q^{62} + 40 q^{63} + 47 q^{64} - 20 q^{66} + 10 q^{67} - 30 q^{68} + 20 q^{69} + 3 q^{71} - 19 q^{72} - 9 q^{73} - 18 q^{74} + 14 q^{76} - 8 q^{77} - 56 q^{78} - 16 q^{79} + 36 q^{81} - 6 q^{82} + 17 q^{83} + 16 q^{86} - 38 q^{87} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 10 q^{92} + q^{93} - 12 q^{94} + 14 q^{96} - 16 q^{97} - 19 q^{98} - 52 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + 9 * q^4 + 8 * q^6 + 9 * q^8 + 7 * q^9 - 6 * q^11 + 8 * q^12 - 16 * q^13 + 8 * q^14 + 11 * q^16 - q^17 + q^18 + 5 * q^19 + 2 * q^21 + 24 * q^22 - 14 * q^24 - 12 * q^26 - 5 * q^27 - 16 * q^28 + 6 * q^29 + 4 * q^31 + 29 * q^32 + 12 * q^33 - 18 * q^34 - 25 * q^36 - 9 * q^37 - 6 * q^39 + 13 * q^41 + 24 * q^42 - 7 * q^43 + 20 * q^44 - 26 * q^46 + 14 * q^47 - 2 * q^48 - 4 * q^49 + 5 * q^51 - 20 * q^52 - 11 * q^53 + 30 * q^54 - 4 * q^56 + 31 * q^57 - 22 * q^58 + 13 * q^59 + 22 * q^61 + q^62 + 40 * q^63 + 47 * q^64 - 20 * q^66 + 10 * q^67 - 30 * q^68 + 20 * q^69 + 3 * q^71 - 19 * q^72 - 9 * q^73 - 18 * q^74 + 14 * q^76 - 8 * q^77 - 56 * q^78 - 16 * q^79 + 36 * q^81 - 6 * q^82 + 17 * q^83 + 16 * q^86 - 38 * q^87 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 10 * q^92 + q^93 - 12 * q^94 + 14 * q^96 - 16 * q^97 - 19 * q^98 - 52 * q^99

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