LMFDB - Embedded newform 775.2.a.g.1.1

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			1.1
Root			$-2.27244$ 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)

$f(q)$	$=$	$q-2.27244 q^{2} +0.632112 q^{3} +3.16400 q^{4} -1.43644 q^{6} -3.43644 q^{7} -2.64511 q^{8} -2.60043 q^{9} +O(q^{10})$	\(q-2.27244 q^{2} +0.632112 q^{3} +3.16400 q^{4} -1.43644 q^{6} -3.43644 q^{7} -2.64511 q^{8} -2.60043 q^{9} -3.10845 q^{11} +2.00000 q^{12} -0.563561 q^{13} +7.80911 q^{14} -0.317122 q^{16} +1.74056 q^{17} +5.90934 q^{18} +4.53667 q^{19} -2.17221 q^{21} +7.06377 q^{22} +9.24555 q^{23} -1.67201 q^{24} +1.28066 q^{26} -3.54010 q^{27} -10.8729 q^{28} +4.17221 q^{29} +1.00000 q^{31} +6.01087 q^{32} -1.96489 q^{33} -3.95532 q^{34} -8.22776 q^{36} +0.804326 q^{37} -10.3093 q^{38} -0.356234 q^{39} +9.97311 q^{41} +4.93623 q^{42} -3.74056 q^{43} -9.83511 q^{44} -21.0100 q^{46} +2.73578 q^{47} -0.200457 q^{48} +4.80911 q^{49} +1.10023 q^{51} -1.78311 q^{52} -10.7692 q^{53} +8.04468 q^{54} +9.08977 q^{56} +2.86768 q^{57} -9.48112 q^{58} +8.90934 q^{59} +4.73578 q^{61} -2.27244 q^{62} +8.93623 q^{63} -13.0251 q^{64} +4.46509 q^{66} +0.891553 q^{67} +5.50712 q^{68} +5.84422 q^{69} -3.60043 q^{71} +6.87844 q^{72} +8.98611 q^{73} -1.82779 q^{74} +14.3540 q^{76} +10.6820 q^{77} +0.809521 q^{78} -14.3093 q^{79} +5.56356 q^{81} -22.6633 q^{82} +14.9414 q^{83} -6.87288 q^{84} +8.50021 q^{86} +2.63731 q^{87} +8.22220 q^{88} +10.5262 q^{89} +1.93664 q^{91} +29.2529 q^{92} +0.632112 q^{93} -6.21689 q^{94} +3.79954 q^{96} -9.80911 q^{97} -10.9284 q^{98} +8.08331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.27244	−1.60686	−0.803430	−	0.595399i	$-0.796994\pi$
$2$	−2.27244	−1.60686	−0.803430	+	0.595399i	$0.796994\pi$
$3$	0.632112	0.364950	0.182475	−	0.983210i	$-0.441589\pi$
$3$	0.632112	0.364950	0.182475	+	0.983210i	$0.441589\pi$
$4$	3.16400	1.58200
$5$	0	0
$5$	0	0
$6$	−1.43644	−0.586424
$7$	−3.43644	−1.29885	−0.649426	−	0.760425i	$-0.724991\pi$
$7$	−3.43644	−1.29885	−0.649426	+	0.760425i	$0.724991\pi$
$8$	−2.64511	−0.935189
$9$	−2.60043	−0.866811
$10$	0	0
$11$	−3.10845	−0.937232	−0.468616	−	0.883402i	$-0.655247\pi$
$11$	−3.10845	−0.937232	−0.468616	+	0.883402i	$0.655247\pi$
$12$	2.00000	0.577350
$13$	−0.563561	−0.156304	−0.0781519	−	0.996941i	$-0.524902\pi$
$13$	−0.563561	−0.156304	−0.0781519	+	0.996941i	$0.524902\pi$
$14$	7.80911	2.08707
$15$	0	0
$16$	−0.317122	−0.0792805
$17$	1.74056	0.422148	0.211074	−	0.977470i	$-0.432304\pi$
$17$	1.74056	0.422148	0.211074	+	0.977470i	$0.432304\pi$
$18$	5.90934	1.39284
$19$	4.53667	1.04078	0.520391	−	0.853928i	$-0.325786\pi$
$19$	4.53667	1.04078	0.520391	+	0.853928i	$0.325786\pi$
$20$	0	0
$21$	−2.17221	−0.474016
$22$	7.06377	1.50600
$23$	9.24555	1.92783	0.963915	−	0.266210i	$-0.0857715\pi$
$23$	9.24555	1.92783	0.963915	+	0.266210i	$0.0857715\pi$
$24$	−1.67201	−0.341297
$25$	0	0
$26$	1.28066	0.251158
$27$	−3.54010	−0.681293
$28$	−10.8729	−2.05478
$29$	4.17221	0.774761	0.387380	−	0.921920i	$-0.373380\pi$
$29$	4.17221	0.774761	0.387380	+	0.921920i	$0.373380\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	6.01087	1.06258
$33$	−1.96489	−0.342043
$34$	−3.95532	−0.678332
$35$	0	0
$36$	−8.22776	−1.37129
$37$	0.804326	0.132230	0.0661152	−	0.997812i	$-0.478940\pi$
$37$	0.804326	0.132230	0.0661152	+	0.997812i	$0.478940\pi$
$38$	−10.3093	−1.67239
$39$	−0.356234	−0.0570431
$40$	0	0
$41$	9.97311	1.55754	0.778769	−	0.627311i	$-0.215845\pi$
$41$	9.97311	1.55754	0.778769	+	0.627311i	$0.215845\pi$
$42$	4.93623	0.761677
$43$	−3.74056	−0.570430	−0.285215	−	0.958464i	$-0.592065\pi$
$43$	−3.74056	−0.570430	−0.285215	+	0.958464i	$0.592065\pi$
$44$	−9.83511	−1.48270
$45$	0	0
$46$	−21.0100	−3.09775
$47$	2.73578	0.399054	0.199527	−	0.979892i	$-0.436059\pi$
$47$	2.73578	0.399054	0.199527	+	0.979892i	$0.436059\pi$
$48$	−0.200457	−0.0289334
$49$	4.80911	0.687016
$50$	0	0
$51$	1.10023	0.154063
$52$	−1.78311	−0.247272
$53$	−10.7692	−1.47927	−0.739633	−	0.673011i	$-0.765001\pi$
$53$	−10.7692	−1.47927	−0.739633	+	0.673011i	$0.765001\pi$
$54$	8.04468	1.09474
$55$	0	0
$56$	9.08977	1.21467
$57$	2.86768	0.379834
$58$	−9.48112	−1.24493
$59$	8.90934	1.15990	0.579949	−	0.814653i	$-0.303073\pi$
$59$	8.90934	1.15990	0.579949	+	0.814653i	$0.303073\pi$
$60$	0	0
$61$	4.73578	0.606354	0.303177	−	0.952934i	$-0.401953\pi$
$61$	4.73578	0.606354	0.303177	+	0.952934i	$0.401953\pi$
$62$	−2.27244	−0.288601
$63$	8.93623	1.12586
$64$	−13.0251	−1.62814
$65$	0	0
$66$	4.46509	0.549615
$67$	0.891553	0.108921	0.0544603	−	0.998516i	$-0.482656\pi$
$67$	0.891553	0.108921	0.0544603	+	0.998516i	$0.482656\pi$
$68$	5.50712	0.667837
$69$	5.84422	0.703562
$70$	0	0
$71$	−3.60043	−0.427293	−0.213646	−	0.976911i	$-0.568534\pi$
$71$	−3.60043	−0.427293	−0.213646	+	0.976911i	$0.568534\pi$
$72$	6.87844	0.810632
$73$	8.98611	1.05174	0.525872	−	0.850564i	$-0.323739\pi$
$73$	8.98611	1.05174	0.525872	+	0.850564i	$0.323739\pi$
$74$	−1.82779	−0.212476
$75$	0	0
$76$	14.3540	1.64652
$77$	10.6820	1.21733
$78$	0.809521	0.0916603
$79$	−14.3093	−1.60992	−0.804962	−	0.593327i	$-0.797814\pi$
$79$	−14.3093	−1.60992	−0.804962	+	0.593327i	$0.797814\pi$
$80$	0	0
$81$	5.56356	0.618173
$82$	−22.6633	−2.50274
$83$	14.9414	1.64003	0.820017	−	0.572339i	$-0.193964\pi$
$83$	14.9414	1.64003	0.820017	+	0.572339i	$0.193964\pi$
$84$	−6.87288	−0.749892
$85$	0	0
$86$	8.50021	0.916601
$87$	2.63731	0.282749
$88$	8.22220	0.876489
$89$	10.5262	1.11578	0.557888	−	0.829916i	$-0.311612\pi$
$89$	10.5262	1.11578	0.557888	+	0.829916i	$0.311612\pi$
$90$	0	0
$91$	1.93664	0.203015
$92$	29.2529	3.04982
$93$	0.632112	0.0655470
$94$	−6.21689	−0.641224
$95$	0	0
$96$	3.79954	0.387789
$97$	−9.80911	−0.995964	−0.497982	−	0.867187i	$-0.665925\pi$
$97$	−9.80911	−0.995964	−0.497982	+	0.867187i	$0.665925\pi$
$98$	−10.9284	−1.10394
$99$	8.08331	0.812403
$100$	0	0
$101$	7.47290	0.743581	0.371791	−	0.928317i	$-0.378744\pi$
$101$	7.47290	0.743581	0.371791	+	0.928317i	$0.378744\pi$
$102$	−2.50021	−0.247557
$103$	11.0638	1.09015	0.545073	−	0.838389i	$-0.316502\pi$
$103$	11.0638	1.09015	0.545073	+	0.838389i	$0.316502\pi$
$104$	1.49068	0.146174
$105$	0	0
$106$	24.4724	2.37697
$107$	−15.0100	−1.45107	−0.725535	−	0.688186i	$-0.758407\pi$
$107$	−15.0100	−1.45107	−0.725535	+	0.688186i	$0.758407\pi$
$108$	−11.2009	−1.07780
$109$	8.33621	0.798464	0.399232	−	0.916850i	$-0.369277\pi$
$109$	8.33621	0.798464	0.399232	+	0.916850i	$0.369277\pi$
$110$	0	0
$111$	0.508424	0.0482575
$112$	1.08977	0.102974
$113$	19.7904	1.86173	0.930864	−	0.365367i	$-0.119056\pi$
$113$	19.7904	1.86173	0.930864	+	0.365367i	$0.119056\pi$
$114$	−6.51664	−0.610340
$115$	0	0
$116$	13.2009	1.22567
$117$	1.46550	0.135486
$118$	−20.2460	−1.86379
$119$	−5.98132	−0.548307
$120$	0	0
$121$	−1.33756	−0.121596
$122$	−10.7618	−0.974326
$123$	6.30412	0.568423
$124$	3.16400	0.284135
$125$	0	0
$126$	−20.3071	−1.80910
$127$	6.18178	0.548544	0.274272	−	0.961652i	$-0.411563\pi$
$127$	6.18178	0.548544	0.274272	+	0.961652i	$0.411563\pi$
$128$	17.5771	1.55361
$129$	−2.36445	−0.208178
$130$	0	0
$131$	−20.6364	−1.80301	−0.901506	−	0.432767i	$-0.857537\pi$
$131$	−20.6364	−1.80301	−0.901506	+	0.432767i	$0.857537\pi$
$132$	−6.21689	−0.541111
$133$	−15.5900	−1.35182
$134$	−2.02600	−0.175020
$135$	0	0
$136$	−4.60398	−0.394788
$137$	5.55878	0.474918	0.237459	−	0.971398i	$-0.423685\pi$
$137$	5.55878	0.474918	0.237459	+	0.971398i	$0.423685\pi$
$138$	−13.2807	−1.13052
$139$	−11.8702	−1.00682	−0.503410	−	0.864048i	$-0.667921\pi$
$139$	−11.8702	−1.00682	−0.503410	+	0.864048i	$0.667921\pi$
$140$	0	0
$141$	1.72932	0.145635
$142$	8.18178	0.686600
$143$	1.75180	0.146493
$144$	0.824655	0.0687213
$145$	0	0
$146$	−20.4204	−1.69001
$147$	3.03990	0.250726
$148$	2.54489	0.209188
$149$	1.41865	0.116221	0.0581103	−	0.998310i	$-0.481492\pi$
$149$	1.41865	0.116221	0.0581103	+	0.998310i	$0.481492\pi$
$150$	0	0
$151$	13.8069	1.12359	0.561794	−	0.827277i	$-0.310112\pi$
$151$	13.8069	1.12359	0.561794	+	0.827277i	$0.310112\pi$
$152$	−12.0000	−0.973329
$153$	−4.52621	−0.365922
$154$	−24.2742	−1.95607
$155$	0	0
$156$	−1.12712	−0.0902421
$157$	−3.82779	−0.305491	−0.152745	−	0.988266i	$-0.548811\pi$
$157$	−3.82779	−0.305491	−0.152745	+	0.988266i	$0.548811\pi$
$158$	32.5171	2.58692
$159$	−6.80735	−0.539858
$160$	0	0
$161$	−31.7718	−2.50397
$162$	−12.6429	−0.993318
$163$	−10.0260	−0.785297	−0.392649	−	0.919689i	$-0.628441\pi$
$163$	−10.0260	−0.785297	−0.392649	+	0.919689i	$0.628441\pi$
$164$	31.5549	2.46402
$165$	0	0
$166$	−33.9535	−2.63531
$167$	−7.26942	−0.562525	−0.281262	−	0.959631i	$-0.590753\pi$
$167$	−7.26942	−0.562525	−0.281262	+	0.959631i	$0.590753\pi$
$168$	5.74575	0.443295
$169$	−12.6824	−0.975569
$170$	0	0
$171$	−11.7973	−0.902162
$172$	−11.8351	−0.902419
$173$	16.1349	1.22671	0.613355	−	0.789807i	$-0.289819\pi$
$173$	16.1349	1.22671	0.613355	+	0.789807i	$0.289819\pi$
$174$	−5.99313	−0.454338
$175$	0	0
$176$	0.985757	0.0743043
$177$	5.63170	0.423305
$178$	−23.9202	−1.79290
$179$	−7.29934	−0.545578	−0.272789	−	0.962074i	$-0.587946\pi$
$179$	−7.29934	−0.545578	−0.272789	+	0.962074i	$0.587946\pi$
$180$	0	0
$181$	19.2104	1.42790	0.713950	−	0.700196i	$-0.246904\pi$
$181$	19.2104	1.42790	0.713950	+	0.700196i	$0.246904\pi$
$182$	−4.40091	−0.326217
$183$	2.99354	0.221289
$184$	−24.4555	−1.80289
$185$	0	0
$186$	−1.43644	−0.105325
$187$	−5.41044	−0.395650
$188$	8.65598	0.631302
$189$	12.1653	0.884899
$190$	0	0
$191$	−4.46509	−0.323083	−0.161541	−	0.986866i	$-0.551647\pi$
$191$	−4.46509	−0.323083	−0.161541	+	0.986866i	$0.551647\pi$
$192$	−8.23333	−0.594189
$193$	6.34443	0.456682	0.228341	−	0.973581i	$-0.426670\pi$
$193$	6.34443	0.456682	0.228341	+	0.973581i	$0.426670\pi$
$194$	22.2906	1.60037
$195$	0	0
$196$	15.2160	1.08686
$197$	7.43644	0.529824	0.264912	−	0.964273i	$-0.414657\pi$
$197$	7.43644	0.529824	0.264912	+	0.964273i	$0.414657\pi$
$198$	−18.3689	−1.30542
$199$	−4.29975	−0.304801	−0.152401	−	0.988319i	$-0.548700\pi$
$199$	−4.29975	−0.304801	−0.152401	+	0.988319i	$0.548700\pi$
$200$	0	0
$201$	0.563561	0.0397506
$202$	−16.9817	−1.19483
$203$	−14.3376	−1.00630
$204$	3.48112	0.243727
$205$	0	0
$206$	−25.1418	−1.75171
$207$	−24.0424	−1.67107
$208$	0.178718	0.0123919
$209$	−14.1020	−0.975455
$210$	0	0
$211$	−4.53532	−0.312224	−0.156112	−	0.987739i	$-0.549896\pi$
$211$	−4.53532	−0.312224	−0.156112	+	0.987739i	$0.549896\pi$
$212$	−34.0737	−2.34019
$213$	−2.27588	−0.155941
$214$	34.1093	2.33166
$215$	0	0
$216$	9.36397	0.637138
$217$	−3.43644	−0.233281
$218$	−18.9436	−1.28302
$219$	5.68023	0.383834
$220$	0	0
$221$	−0.980912	−0.0659833
$222$	−1.15537	−0.0775431
$223$	−19.5214	−1.30725	−0.653626	−	0.756818i	$-0.726753\pi$
$223$	−19.5214	−1.30725	−0.653626	+	0.756818i	$0.726753\pi$
$224$	−20.6560	−1.38014
$225$	0	0
$226$	−44.9726	−2.99153
$227$	25.3193	1.68050	0.840250	−	0.542199i	$-0.182408\pi$
$227$	25.3193	1.68050	0.840250	+	0.542199i	$0.182408\pi$
$228$	9.07333	0.600896
$229$	−19.0642	−1.25980	−0.629900	−	0.776676i	$-0.716904\pi$
$229$	−19.0642	−1.25980	−0.629900	+	0.776676i	$0.716904\pi$
$230$	0	0
$231$	6.75221	0.444263
$232$	−11.0360	−0.724548
$233$	8.36310	0.547885	0.273943	−	0.961746i	$-0.411672\pi$
$233$	8.36310	0.547885	0.273943	+	0.961746i	$0.411672\pi$
$234$	−3.33028	−0.217707
$235$	0	0
$236$	28.1891	1.83495
$237$	−9.04509	−0.587542
$238$	13.5922	0.881052
$239$	26.9084	1.74056	0.870281	−	0.492555i	$-0.163937\pi$
$239$	26.9084	1.74056	0.870281	+	0.492555i	$0.163937\pi$
$240$	0	0
$241$	18.5262	1.19338	0.596689	−	0.802473i	$-0.296483\pi$
$241$	18.5262	1.19338	0.596689	+	0.802473i	$0.296483\pi$
$242$	3.03952	0.195388
$243$	14.1371	0.906895
$244$	14.9840	0.959251
$245$	0	0
$246$	−14.3258	−0.913377
$247$	−2.55669	−0.162678
$248$	−2.64511	−0.167965
$249$	9.44466	0.598531
$250$	0	0
$251$	17.0733	1.07766	0.538830	−	0.842415i	$-0.318867\pi$
$251$	17.0733	1.07766	0.538830	+	0.842415i	$0.318867\pi$
$252$	28.2742	1.78111
$253$	−28.7393	−1.80682
$254$	−14.0477	−0.881434
$255$	0	0
$256$	−13.8927	−0.868293
$257$	−21.6793	−1.35232	−0.676160	−	0.736755i	$-0.736357\pi$
$257$	−21.6793	−1.35232	−0.676160	+	0.736755i	$0.736357\pi$
$258$	5.37308	0.334514
$259$	−2.76402	−0.171748
$260$	0	0
$261$	−10.8496	−0.671571
$262$	46.8951	2.89719
$263$	−14.7059	−0.906802	−0.453401	−	0.891307i	$-0.649789\pi$
$263$	−14.7059	−0.906802	−0.453401	+	0.891307i	$0.649789\pi$
$264$	5.19735	0.319875
$265$	0	0
$266$	35.4273	2.17219
$267$	6.65374	0.407203
$268$	2.82087	0.172312
$269$	14.4204	0.879228	0.439614	−	0.898187i	$-0.355115\pi$
$269$	14.4204	0.879228	0.439614	+	0.898187i	$0.355115\pi$
$270$	0	0
$271$	8.37267	0.508604	0.254302	−	0.967125i	$-0.418154\pi$
$271$	8.37267	0.508604	0.254302	+	0.967125i	$0.418154\pi$
$272$	−0.551970	−0.0334681
$273$	1.22418	0.0740905
$274$	−12.6320	−0.763127
$275$	0	0
$276$	18.4911	1.11303
$277$	−7.73832	−0.464951	−0.232475	−	0.972602i	$-0.574682\pi$
$277$	−7.73832	−0.464951	−0.232475	+	0.972602i	$0.574682\pi$
$278$	26.9744	1.61782
$279$	−2.60043	−0.155684
$280$	0	0
$281$	30.5158	1.82042	0.910209	−	0.414150i	$-0.135921\pi$
$281$	30.5158	1.82042	0.910209	+	0.414150i	$0.135921\pi$
$282$	−3.92977	−0.234015
$283$	28.8824	1.71688	0.858442	−	0.512911i	$-0.171433\pi$
$283$	28.8824	1.71688	0.858442	+	0.512911i	$0.171433\pi$
$284$	−11.3918	−0.675977
$285$	0	0
$286$	−3.98087	−0.235394
$287$	−34.2720	−2.02301
$288$	−15.6309	−0.921058
$289$	−13.9705	−0.821791
$290$	0	0
$291$	−6.20046	−0.363477
$292$	28.4320	1.66386
$293$	−6.06112	−0.354094	−0.177047	−	0.984202i	$-0.556654\pi$
$293$	−6.06112	−0.354094	−0.177047	+	0.984202i	$0.556654\pi$
$294$	−6.90799	−0.402882
$295$	0	0
$296$	−2.12753	−0.123660
$297$	11.0042	0.638530
$298$	−3.22381	−0.186750
$299$	−5.21043	−0.301327
$300$	0	0
$301$	12.8542	0.740904
$302$	−31.3753	−1.80545
$303$	4.72371	0.271370
$304$	−1.43868	−0.0825138
$305$	0	0
$306$	10.2856	0.587986
$307$	−2.69110	−0.153589	−0.0767945	−	0.997047i	$-0.524469\pi$
$307$	−2.69110	−0.153589	−0.0767945	+	0.997047i	$0.524469\pi$
$308$	33.7978	1.92581
$309$	6.99354	0.397849
$310$	0	0
$311$	−12.3175	−0.698463	−0.349232	−	0.937036i	$-0.613557\pi$
$311$	−12.3175	−0.698463	−0.349232	+	0.937036i	$0.613557\pi$
$312$	0.942280	0.0533461
$313$	−21.0190	−1.18806	−0.594032	−	0.804442i	$-0.702465\pi$
$313$	−21.0190	−1.18806	−0.594032	+	0.804442i	$0.702465\pi$
$314$	8.69842	0.490880
$315$	0	0
$316$	−45.2746	−2.54690
$317$	−21.7553	−1.22190	−0.610950	−	0.791669i	$-0.709212\pi$
$317$	−21.7553	−1.22190	−0.610950	+	0.791669i	$0.709212\pi$
$318$	15.4693	0.867476
$319$	−12.9691	−0.726131
$320$	0	0
$321$	−9.48799	−0.529568
$322$	72.1995	4.02352
$323$	7.89634	0.439364
$324$	17.6031	0.977949
$325$	0	0
$326$	22.7835	1.26186
$327$	5.26942	0.291400
$328$	−26.3800	−1.45659
$329$	−9.40133	−0.518312
$330$	0	0
$331$	15.7718	0.866894	0.433447	−	0.901179i	$-0.357297\pi$
$331$	15.7718	0.866894	0.433447	+	0.901179i	$0.357297\pi$
$332$	47.2746	2.59453
$333$	−2.09160	−0.114619
$334$	16.5193	0.903898
$335$	0	0
$336$	0.688857	0.0375802
$337$	28.4225	1.54827	0.774137	−	0.633018i	$-0.218184\pi$
$337$	28.4225	1.54827	0.774137	+	0.633018i	$0.218184\pi$
$338$	28.8200	1.56760
$339$	12.5098	0.679438
$340$	0	0
$341$	−3.10845	−0.168332
$342$	26.8087	1.44965
$343$	7.52886	0.406520
$344$	9.89420	0.533460
$345$	0	0
$346$	−36.6655	−1.97115
$347$	11.3731	0.610539	0.305270	−	0.952266i	$-0.401253\pi$
$347$	11.3731	0.610539	0.305270	+	0.952266i	$0.401253\pi$
$348$	8.34443	0.447308
$349$	26.0789	1.39597	0.697986	−	0.716112i	$-0.254080\pi$
$349$	26.0789	1.39597	0.697986	+	0.716112i	$0.254080\pi$
$350$	0	0
$351$	1.99507	0.106489
$352$	−18.6845	−0.995886
$353$	1.21954	0.0649098	0.0324549	−	0.999473i	$-0.489667\pi$
$353$	1.21954	0.0649098	0.0324549	+	0.999473i	$0.489667\pi$
$354$	−12.7977	−0.680191
$355$	0	0
$356$	33.3049	1.76516
$357$	−3.78087	−0.200105
$358$	16.5873	0.876667
$359$	−33.0524	−1.74444	−0.872220	−	0.489114i	$-0.837320\pi$
$359$	−33.0524	−1.74444	−0.872220	+	0.489114i	$0.837320\pi$
$360$	0	0
$361$	1.58135	0.0832288
$362$	−43.6546	−2.29444
$363$	−0.845487	−0.0443765
$364$	6.12753	0.321170
$365$	0	0
$366$	−6.80265	−0.355580
$367$	12.8468	0.670596	0.335298	−	0.942112i	$-0.391163\pi$
$367$	12.8468	0.670596	0.335298	+	0.942112i	$0.391163\pi$
$368$	−2.93197	−0.152839
$369$	−25.9344	−1.35009
$370$	0	0
$371$	37.0077	1.92135
$372$	2.00000	0.103695
$373$	0.933993	0.0483603	0.0241802	−	0.999708i	$-0.492302\pi$
$373$	0.933993	0.0483603	0.0241802	+	0.999708i	$0.492302\pi$
$374$	12.2949	0.635754
$375$	0	0
$376$	−7.23644	−0.373191
$377$	−2.35130	−0.121098
$378$	−27.6450	−1.42191
$379$	7.57219	0.388957	0.194479	−	0.980907i	$-0.437698\pi$
$379$	7.57219	0.388957	0.194479	+	0.980907i	$0.437698\pi$
$380$	0	0
$381$	3.90758	0.200191
$382$	10.1467	0.519149
$383$	−20.3145	−1.03802	−0.519011	−	0.854767i	$-0.673700\pi$
$383$	−20.3145	−1.03802	−0.519011	+	0.854767i	$0.673700\pi$
$384$	11.1107	0.566990
$385$	0	0
$386$	−14.4174	−0.733824
$387$	9.72708	0.494455
$388$	−31.0360	−1.57561
$389$	−21.0455	−1.06705	−0.533526	−	0.845784i	$-0.679133\pi$
$389$	−21.0455	−1.06705	−0.533526	+	0.845784i	$0.679133\pi$
$390$	0	0
$391$	16.0924	0.813829
$392$	−12.7206	−0.642489
$393$	−13.0445	−0.658009
$394$	−16.8989	−0.851353
$395$	0	0
$396$	25.5756	1.28522
$397$	16.6507	0.835674	0.417837	−	0.908522i	$-0.362788\pi$
$397$	16.6507	0.835674	0.417837	+	0.908522i	$0.362788\pi$
$398$	9.77093	0.489773
$399$	−9.85461	−0.493348
$400$	0	0
$401$	−34.5904	−1.72736	−0.863681	−	0.504039i	$-0.831847\pi$
$401$	−34.5904	−1.72736	−0.863681	+	0.504039i	$0.831847\pi$
$402$	−1.28066	−0.0638736
$403$	−0.563561	−0.0280730
$404$	23.6442	1.17634
$405$	0	0
$406$	32.5813	1.61698
$407$	−2.50021	−0.123931
$408$	−2.91023	−0.144078
$409$	21.5735	1.06674	0.533371	−	0.845881i	$-0.320925\pi$
$409$	21.5735	1.06674	0.533371	+	0.845881i	$0.320925\pi$
$410$	0	0
$411$	3.51377	0.173322
$412$	35.0057	1.72461
$413$	−30.6164	−1.50653
$414$	54.6351	2.68517
$415$	0	0
$416$	−3.38749	−0.166086
$417$	−7.50331	−0.367439
$418$	32.0460	1.56742
$419$	4.80511	0.234745	0.117373	−	0.993088i	$-0.462553\pi$
$419$	4.80511	0.234745	0.117373	+	0.993088i	$0.462553\pi$
$420$	0	0
$421$	−1.16358	−0.0567096	−0.0283548	−	0.999598i	$-0.509027\pi$
$421$	−1.16358	−0.0567096	−0.0283548	+	0.999598i	$0.509027\pi$
$422$	10.3063	0.501701
$423$	−7.11421	−0.345904
$424$	28.4858	1.38339
$425$	0	0
$426$	5.17180	0.250575
$427$	−16.2742	−0.787564
$428$	−47.4915	−2.29559
$429$	1.10733	0.0534626
$430$	0	0
$431$	−5.86507	−0.282510	−0.141255	−	0.989973i	$-0.545114\pi$
$431$	−5.86507	−0.282510	−0.141255	+	0.989973i	$0.545114\pi$
$432$	1.12264	0.0540133
$433$	12.1444	0.583624	0.291812	−	0.956476i	$-0.405742\pi$
$433$	12.1444	0.583624	0.291812	+	0.956476i	$0.405742\pi$
$434$	7.80911	0.374849
$435$	0	0
$436$	26.3757	1.26317
$437$	41.9440	2.00645
$438$	−12.9080	−0.616768
$439$	−17.1002	−0.816149	−0.408075	−	0.912949i	$-0.633800\pi$
$439$	−17.1002	−0.816149	−0.408075	+	0.912949i	$0.633800\pi$
$440$	0	0
$441$	−12.5058	−0.595513
$442$	2.22907	0.106026
$443$	−21.9722	−1.04393	−0.521966	−	0.852966i	$-0.674801\pi$
$443$	−21.9722	−1.04393	−0.521966	+	0.852966i	$0.674801\pi$
$444$	1.60865	0.0763433
$445$	0	0
$446$	44.3613	2.10057
$447$	0.896748	0.0424147
$448$	44.7600	2.11471
$449$	24.2169	1.14287	0.571433	−	0.820649i	$-0.306388\pi$
$449$	24.2169	1.14287	0.571433	+	0.820649i	$0.306388\pi$
$450$	0	0
$451$	−31.0009	−1.45977
$452$	62.6168	2.94525
$453$	8.72749	0.410053
$454$	−57.5366	−2.70033
$455$	0	0
$456$	−7.58535	−0.355216
$457$	30.9844	1.44939	0.724695	−	0.689069i	$-0.241981\pi$
$457$	30.9844	1.44939	0.724695	+	0.689069i	$0.241981\pi$
$458$	43.3224	2.02432
$459$	−6.16176	−0.287606
$460$	0	0
$461$	−20.0291	−0.932847	−0.466423	−	0.884562i	$-0.654458\pi$
$461$	−20.0291	−0.932847	−0.466423	+	0.884562i	$0.654458\pi$
$462$	−15.3440	−0.713868
$463$	−21.3349	−0.991517	−0.495759	−	0.868460i	$-0.665110\pi$
$463$	−21.3349	−0.991517	−0.495759	+	0.868460i	$0.665110\pi$
$464$	−1.32310	−0.0614234
$465$	0	0
$466$	−19.0047	−0.880375
$467$	−5.90534	−0.273267	−0.136633	−	0.990622i	$-0.543628\pi$
$467$	−5.90534	−0.273267	−0.136633	+	0.990622i	$0.543628\pi$
$468$	4.63685	0.214338
$469$	−3.06377	−0.141472
$470$	0	0
$471$	−2.41959	−0.111489
$472$	−23.5662	−1.08472
$473$	11.6273	0.534625
$474$	20.5545	0.944097
$475$	0	0
$476$	−18.9249	−0.867421
$477$	28.0046	1.28224
$478$	−61.1479	−2.79684
$479$	−13.2433	−0.605102	−0.302551	−	0.953133i	$-0.597838\pi$
$479$	−13.2433	−0.605102	−0.302551	+	0.953133i	$0.597838\pi$
$480$	0	0
$481$	−0.453287	−0.0206681
$482$	−42.0997	−1.91759
$483$	−20.0833	−0.913822
$484$	−4.23203	−0.192365
$485$	0	0
$486$	−32.1258	−1.45725
$487$	−10.8803	−0.493034	−0.246517	−	0.969138i	$-0.579286\pi$
$487$	−10.8803	−0.493034	−0.246517	+	0.969138i	$0.579286\pi$
$488$	−12.5267	−0.567056
$489$	−6.33756	−0.286594
$490$	0	0
$491$	17.9053	0.808057	0.404028	−	0.914746i	$-0.367610\pi$
$491$	17.9053	0.808057	0.404028	+	0.914746i	$0.367610\pi$
$492$	19.9462	0.899245
$493$	7.26199	0.327063
$494$	5.80993	0.261401
$495$	0	0
$496$	−0.317122	−0.0142392
$497$	12.3727	0.554990
$498$	−21.4624	−0.961755
$499$	−33.5458	−1.50171	−0.750857	−	0.660465i	$-0.770359\pi$
$499$	−33.5458	−1.50171	−0.750857	+	0.660465i	$0.770359\pi$
$500$	0	0
$501$	−4.59509	−0.205293
$502$	−38.7982	−1.73165
$503$	−8.89155	−0.396455	−0.198227	−	0.980156i	$-0.563518\pi$
$503$	−8.89155	−0.396455	−0.198227	+	0.980156i	$0.563518\pi$
$504$	−23.6374	−1.05289
$505$	0	0
$506$	65.3084	2.90331
$507$	−8.01670	−0.356034
$508$	19.5591	0.867796
$509$	37.5600	1.66482	0.832408	−	0.554164i	$-0.186962\pi$
$509$	37.5600	1.66482	0.832408	+	0.554164i	$0.186962\pi$
$510$	0	0
$511$	−30.8802	−1.36606
$512$	−3.58383	−0.158384
$513$	−16.0603	−0.709078
$514$	49.2650	2.17299
$515$	0	0
$516$	−7.48112	−0.329338
$517$	−8.50401	−0.374006
$518$	6.28107	0.275975
$519$	10.1990	0.447688
$520$	0	0
$521$	−0.568717	−0.0249160	−0.0124580	−	0.999922i	$-0.503966\pi$
$521$	−0.568717	−0.0249160	−0.0124580	+	0.999922i	$0.503966\pi$
$522$	24.6550	1.07912
$523$	17.2763	0.755439	0.377720	−	0.925920i	$-0.376708\pi$
$523$	17.2763	0.755439	0.377720	+	0.925920i	$0.376708\pi$
$524$	−65.2935	−2.85236
$525$	0	0
$526$	33.4182	1.45710
$527$	1.74056	0.0758199
$528$	0.623109	0.0271173
$529$	62.4802	2.71653
$530$	0	0
$531$	−23.1681	−1.00541
$532$	−49.3266	−2.13858
$533$	−5.62046	−0.243449
$534$	−15.1203	−0.654317
$535$	0	0
$536$	−2.35826	−0.101861
$537$	−4.61400	−0.199109
$538$	−32.7696	−1.41280
$539$	−14.9489	−0.643893
$540$	0	0
$541$	−13.1471	−0.565237	−0.282619	−	0.959232i	$-0.591203\pi$
$541$	−13.1471	−0.565237	−0.282619	+	0.959232i	$0.591203\pi$
$542$	−19.0264	−0.817255
$543$	12.1431	0.521112
$544$	10.4623	0.448566
$545$	0	0
$546$	−2.78187	−0.119053
$547$	−28.6156	−1.22351	−0.611757	−	0.791046i	$-0.709537\pi$
$547$	−28.6156	−1.22351	−0.611757	+	0.791046i	$0.709537\pi$
$548$	17.5880	0.751320
$549$	−12.3151	−0.525595
$550$	0	0
$551$	18.9279	0.806358
$552$	−15.4586	−0.657963
$553$	49.1731	2.09105
$554$	17.5849	0.747110
$555$	0	0
$556$	−37.5573	−1.59279
$557$	−14.9340	−0.632774	−0.316387	−	0.948630i	$-0.602470\pi$
$557$	−14.9340	−0.632774	−0.316387	+	0.948630i	$0.602470\pi$
$558$	5.90934	0.250162
$559$	2.10804	0.0891604
$560$	0	0
$561$	−3.42000	−0.144393
$562$	−69.3453	−2.92515
$563$	14.8473	0.625740	0.312870	−	0.949796i	$-0.398710\pi$
$563$	14.8473	0.625740	0.312870	+	0.949796i	$0.398710\pi$
$564$	5.47155	0.230394
$565$	0	0
$566$	−65.6337	−2.75879
$567$	−19.1188	−0.802916
$568$	9.52356	0.399600
$569$	−31.9157	−1.33798	−0.668988	−	0.743273i	$-0.733272\pi$
$569$	−31.9157	−1.33798	−0.668988	+	0.743273i	$0.733272\pi$
$570$	0	0
$571$	25.8573	1.08209	0.541047	−	0.840992i	$-0.318028\pi$
$571$	25.8573	1.08209	0.541047	+	0.840992i	$0.318028\pi$
$572$	5.54269	0.231752
$573$	−2.82244	−0.117909
$574$	77.8811	3.25069
$575$	0	0
$576$	33.8709	1.41129
$577$	12.3987	0.516164	0.258082	−	0.966123i	$-0.416910\pi$
$577$	12.3987	0.516164	0.258082	+	0.966123i	$0.416910\pi$
$578$	31.7471	1.32050
$579$	4.01039	0.166666
$580$	0	0
$581$	−51.3453	−2.13016
$582$	14.0902	0.584057
$583$	33.4755	1.38641
$584$	−23.7693	−0.983580
$585$	0	0
$586$	13.7735	0.568980
$587$	−16.8446	−0.695252	−0.347626	−	0.937633i	$-0.613012\pi$
$587$	−16.8446	−0.695252	−0.347626	+	0.937633i	$0.613012\pi$
$588$	9.61822	0.396649
$589$	4.53667	0.186930
$590$	0	0
$591$	4.70066	0.193359
$592$	−0.255070	−0.0104833
$593$	16.8564	0.692211	0.346106	−	0.938196i	$-0.387504\pi$
$593$	16.8564	0.692211	0.346106	+	0.938196i	$0.387504\pi$
$594$	−25.0065	−1.02603
$595$	0	0
$596$	4.48861	0.183861
$597$	−2.71792	−0.111237
$598$	11.8404	0.484191
$599$	2.02600	0.0827803	0.0413901	−	0.999143i	$-0.486821\pi$
$599$	2.02600	0.0827803	0.0413901	+	0.999143i	$0.486821\pi$
$600$	0	0
$601$	36.9800	1.50844	0.754222	−	0.656620i	$-0.228014\pi$
$601$	36.9800	1.50844	0.754222	+	0.656620i	$0.228014\pi$
$602$	−29.2104	−1.19053
$603$	−2.31843	−0.0944136
$604$	43.6849	1.77751
$605$	0	0
$606$	−10.7344	−0.436054
$607$	−5.10158	−0.207067	−0.103533	−	0.994626i	$-0.533015\pi$
$607$	−5.10158	−0.207067	−0.103533	+	0.994626i	$0.533015\pi$
$608$	27.2693	1.10592
$609$	−9.06294	−0.367249
$610$	0	0
$611$	−1.54178	−0.0623737
$612$	−14.3209	−0.578888
$613$	−22.3263	−0.901751	−0.450876	−	0.892587i	$-0.648888\pi$
$613$	−22.3263	−0.901751	−0.450876	+	0.892587i	$0.648888\pi$
$614$	6.11536	0.246796
$615$	0	0
$616$	−28.2551	−1.13843
$617$	35.2360	1.41855	0.709274	−	0.704933i	$-0.249023\pi$
$617$	35.2360	1.41855	0.709274	+	0.704933i	$0.249023\pi$
$618$	−15.8924	−0.639287
$619$	−4.21002	−0.169215	−0.0846076	−	0.996414i	$-0.526964\pi$
$619$	−4.21002	−0.169215	−0.0846076	+	0.996414i	$0.526964\pi$
$620$	0	0
$621$	−32.7302	−1.31342
$622$	27.9909	1.12233
$623$	−36.1727	−1.44923
$624$	0.112970	0.00452241
$625$	0	0
$626$	47.7644	1.90905
$627$	−8.91404	−0.355992
$628$	−12.1111	−0.483285
$629$	1.39998	0.0558208
$630$	0	0
$631$	−27.5289	−1.09591	−0.547953	−	0.836509i	$-0.684593\pi$
$631$	−27.5289	−1.09591	−0.547953	+	0.836509i	$0.684593\pi$
$632$	37.8498	1.50558
$633$	−2.86683	−0.113946
$634$	49.4377	1.96342
$635$	0	0
$636$	−21.5384	−0.854054
$637$	−2.71023	−0.107383
$638$	29.4716	1.16679
$639$	9.36269	0.370382
$640$	0	0
$641$	7.72932	0.305290	0.152645	−	0.988281i	$-0.451221\pi$
$641$	7.72932	0.305290	0.152645	+	0.988281i	$0.451221\pi$
$642$	21.5609	0.850941
$643$	3.55572	0.140224	0.0701119	−	0.997539i	$-0.477664\pi$
$643$	3.55572	0.140224	0.0701119	+	0.997539i	$0.477664\pi$
$644$	−100.526	−3.96127
$645$	0	0
$646$	−17.9440	−0.705996
$647$	−12.3428	−0.485244	−0.242622	−	0.970121i	$-0.578007\pi$
$647$	−12.3428	−0.485244	−0.242622	+	0.970121i	$0.578007\pi$
$648$	−14.7163	−0.578109
$649$	−27.6942	−1.08709
$650$	0	0
$651$	−2.17221	−0.0851358
$652$	−31.7222	−1.24234
$653$	−8.83731	−0.345831	−0.172915	−	0.984937i	$-0.555319\pi$
$653$	−8.83731	−0.345831	−0.172915	+	0.984937i	$0.555319\pi$
$654$	−11.9745	−0.468238
$655$	0	0
$656$	−3.16269	−0.123482
$657$	−23.3678	−0.911664
$658$	21.3640	0.832854
$659$	−20.9853	−0.817472	−0.408736	−	0.912653i	$-0.634030\pi$
$659$	−20.9853	−0.817472	−0.408736	+	0.912653i	$0.634030\pi$
$660$	0	0
$661$	27.1613	1.05645	0.528227	−	0.849103i	$-0.322857\pi$
$661$	27.1613	1.05645	0.528227	+	0.849103i	$0.322857\pi$
$662$	−35.8404	−1.39298
$663$	−0.620046	−0.0240806
$664$	−39.5218	−1.53374
$665$	0	0
$666$	4.75304	0.184176
$667$	38.5744	1.49361
$668$	−23.0004	−0.889913
$669$	−12.3397	−0.477082
$670$	0	0
$671$	−14.7209	−0.568294
$672$	−13.0569	−0.503681
$673$	−16.0079	−0.617059	−0.308529	−	0.951215i	$-0.599837\pi$
$673$	−16.0079	−0.617059	−0.308529	+	0.951215i	$0.599837\pi$
$674$	−64.5886	−2.48786
$675$	0	0
$676$	−40.1271	−1.54335
$677$	5.16362	0.198454	0.0992271	−	0.995065i	$-0.468363\pi$
$677$	5.16362	0.198454	0.0992271	+	0.995065i	$0.468363\pi$
$678$	−28.4277	−1.09176
$679$	33.7084	1.29361
$680$	0	0
$681$	16.0046	0.613299
$682$	7.06377	0.270486
$683$	28.6989	1.09813	0.549066	−	0.835779i	$-0.314984\pi$
$683$	28.6989	1.09813	0.549066	+	0.835779i	$0.314984\pi$
$684$	−37.3266	−1.42722
$685$	0	0
$686$	−17.1089	−0.653221
$687$	−12.0507	−0.459764
$688$	1.18621	0.0452240
$689$	6.06911	0.231215
$690$	0	0
$691$	4.87199	0.185339	0.0926695	−	0.995697i	$-0.470460\pi$
$691$	4.87199	0.185339	0.0926695	+	0.995697i	$0.470460\pi$
$692$	51.0506	1.94065
$693$	−27.7778	−1.05519
$694$	−25.8447	−0.981051
$695$	0	0
$696$	−6.97598	−0.264424
$697$	17.3588	0.657511
$698$	−59.2628	−2.24313
$699$	5.28642	0.199951
$700$	0	0
$701$	23.1089	0.872811	0.436406	−	0.899750i	$-0.356251\pi$
$701$	23.1089	0.872811	0.436406	+	0.899750i	$0.356251\pi$
$702$	−4.53367	−0.171112
$703$	3.64896	0.137623
$704$	40.4879	1.52594
$705$	0	0
$706$	−2.77135	−0.104301
$707$	−25.6802	−0.965802
$708$	17.8187	0.669667
$709$	−20.9935	−0.788429	−0.394214	−	0.919018i	$-0.628983\pi$
$709$	−20.9935	−0.788429	−0.394214	+	0.919018i	$0.628983\pi$
$710$	0	0
$711$	37.2104	1.39550
$712$	−27.8430	−1.04346
$713$	9.24555	0.346248
$714$	8.59180	0.321540
$715$	0	0
$716$	−23.0951	−0.863103
$717$	17.0092	0.635219
$718$	75.1097	2.80307
$719$	10.2482	0.382193	0.191097	−	0.981571i	$-0.438796\pi$
$719$	10.2482	0.382193	0.191097	+	0.981571i	$0.438796\pi$
$720$	0	0
$721$	−38.0200	−1.41594
$722$	−3.59352	−0.133737
$723$	11.7106	0.435523
$724$	60.7817	2.25894
$725$	0	0
$726$	1.92132	0.0713069
$727$	13.5877	0.503941	0.251971	−	0.967735i	$-0.418921\pi$
$727$	13.5877	0.503941	0.251971	+	0.967735i	$0.418921\pi$
$728$	−5.12264	−0.189858
$729$	−7.75445	−0.287202
$730$	0	0
$731$	−6.51066	−0.240806
$732$	9.47155	0.350079
$733$	−20.1440	−0.744035	−0.372017	−	0.928226i	$-0.621334\pi$
$733$	−20.1440	−0.744035	−0.372017	+	0.928226i	$0.621334\pi$
$734$	−29.1935	−1.07755
$735$	0	0
$736$	55.5738	2.04848
$737$	−2.77135	−0.102084
$738$	58.9345	2.16941
$739$	−32.6022	−1.19929	−0.599646	−	0.800266i	$-0.704692\pi$
$739$	−32.6022	−1.19929	−0.599646	+	0.800266i	$0.704692\pi$
$740$	0	0
$741$	−1.61612	−0.0593695
$742$	−84.0980	−3.08733
$743$	−29.0404	−1.06539	−0.532694	−	0.846308i	$-0.678820\pi$
$743$	−29.0404	−1.06539	−0.532694	+	0.846308i	$0.678820\pi$
$744$	−1.67201	−0.0612988
$745$	0	0
$746$	−2.12245	−0.0777083
$747$	−38.8542	−1.42160
$748$	−17.1186	−0.625918
$749$	51.5809	1.88472
$750$	0	0
$751$	−6.59867	−0.240789	−0.120395	−	0.992726i	$-0.538416\pi$
$751$	−6.59867	−0.240789	−0.120395	+	0.992726i	$0.538416\pi$
$752$	−0.867575	−0.0316372
$753$	10.7923	0.393292
$754$	5.34319	0.194588
$755$	0	0
$756$	38.4911	1.39991
$757$	31.1970	1.13387	0.566936	−	0.823762i	$-0.308129\pi$
$757$	31.1970	1.13387	0.566936	+	0.823762i	$0.308129\pi$
$758$	−17.2074	−0.625000
$759$	−18.1665	−0.659401
$760$	0	0
$761$	5.04285	0.182803	0.0914016	−	0.995814i	$-0.470865\pi$
$761$	5.04285	0.182803	0.0914016	+	0.995814i	$0.470865\pi$
$762$	−8.87975	−0.321679
$763$	−28.6469	−1.03709
$764$	−14.1275	−0.511116
$765$	0	0
$766$	46.1636	1.66796
$767$	−5.02096	−0.181296
$768$	−8.78174	−0.316884
$769$	12.3271	0.444527	0.222263	−	0.974987i	$-0.428656\pi$
$769$	12.3271	0.444527	0.222263	+	0.974987i	$0.428656\pi$
$770$	0	0
$771$	−13.7038	−0.493529
$772$	20.0737	0.722470
$773$	−4.19395	−0.150846	−0.0754230	−	0.997152i	$-0.524031\pi$
$773$	−4.19395	−0.150846	−0.0754230	+	0.997152i	$0.524031\pi$
$774$	−22.1042	−0.794520
$775$	0	0
$776$	25.9462	0.931415
$777$	−1.74717	−0.0626794
$778$	47.8248	1.71460
$779$	45.2447	1.62106
$780$	0	0
$781$	11.1918	0.400473
$782$	−36.5691	−1.30771
$783$	−14.7701	−0.527839
$784$	−1.52508	−0.0544670
$785$	0	0
$786$	29.6429	1.05733
$787$	23.8260	0.849305	0.424653	−	0.905356i	$-0.360396\pi$
$787$	23.8260	0.849305	0.424653	+	0.905356i	$0.360396\pi$
$788$	23.5289	0.838181
$789$	−9.29575	−0.330937
$790$	0	0
$791$	−68.0086	−2.41811
$792$	−21.3813	−0.759751
$793$	−2.66890	−0.0947755
$794$	−37.8377	−1.34281
$795$	0	0
$796$	−13.6044	−0.482195
$797$	28.9019	1.02376	0.511880	−	0.859057i	$-0.328949\pi$
$797$	28.9019	1.02376	0.511880	+	0.859057i	$0.328949\pi$
$798$	22.3940	0.792741
$799$	4.76178	0.168460
$800$	0	0
$801$	−27.3727	−0.967167
$802$	78.6047	2.77563
$803$	−27.9328	−0.985728
$804$	1.78311	0.0628853
$805$	0	0
$806$	1.28066	0.0451094
$807$	9.11532	0.320874
$808$	−19.7667	−0.695389
$809$	18.0760	0.635518	0.317759	−	0.948172i	$-0.397070\pi$
$809$	18.0760	0.635518	0.317759	+	0.948172i	$0.397070\pi$
$810$	0	0
$811$	12.4729	0.437981	0.218991	−	0.975727i	$-0.429724\pi$
$811$	12.4729	0.437981	0.218991	+	0.975727i	$0.429724\pi$
$812$	−45.3640	−1.59196
$813$	5.29247	0.185615
$814$	5.68157	0.199139
$815$	0	0
$816$	−0.348907	−0.0122142
$817$	−16.9697	−0.593694
$818$	−49.0246	−1.71411
$819$	−5.03612	−0.175976
$820$	0	0
$821$	35.4373	1.23677	0.618384	−	0.785876i	$-0.287787\pi$
$821$	35.4373	1.23677	0.618384	+	0.785876i	$0.287787\pi$
$822$	−7.98484	−0.278503
$823$	42.9296	1.49643	0.748216	−	0.663455i	$-0.230911\pi$
$823$	42.9296	1.49643	0.748216	+	0.663455i	$0.230911\pi$
$824$	−29.2649	−1.01949
$825$	0	0
$826$	69.5740	2.42079
$827$	18.5210	0.644039	0.322019	−	0.946733i	$-0.395638\pi$
$827$	18.5210	0.644039	0.322019	+	0.946733i	$0.395638\pi$
$828$	−76.0702	−2.64362
$829$	26.5858	0.923362	0.461681	−	0.887046i	$-0.347247\pi$
$829$	26.5858	0.923362	0.461681	+	0.887046i	$0.347247\pi$
$830$	0	0
$831$	−4.89149	−0.169684
$832$	7.34045	0.254484
$833$	8.37054	0.290022
$834$	17.0508	0.590423
$835$	0	0
$836$	−44.6186	−1.54317
$837$	−3.54010	−0.122364
$838$	−10.9193	−0.377202
$839$	24.0446	0.830112	0.415056	−	0.909796i	$-0.363762\pi$
$839$	24.0446	0.830112	0.415056	+	0.909796i	$0.363762\pi$
$840$	0	0
$841$	−11.5926	−0.399746
$842$	2.64418	0.0911244
$843$	19.2894	0.664361
$844$	−14.3497	−0.493938
$845$	0	0
$846$	16.1666	0.555820
$847$	4.59644	0.157935
$848$	3.41516	0.117277
$849$	18.2569	0.626577
$850$	0	0
$851$	7.43644	0.254918
$852$	−7.20087	−0.246698
$853$	5.32310	0.182260	0.0911298	−	0.995839i	$-0.470952\pi$
$853$	5.32310	0.182260	0.0911298	+	0.995839i	$0.470952\pi$
$854$	36.9822	1.26550
$855$	0	0
$856$	39.7031	1.35702
$857$	14.9184	0.509602	0.254801	−	0.966993i	$-0.417990\pi$
$857$	14.9184	0.509602	0.254801	+	0.966993i	$0.417990\pi$
$858$	−2.51635	−0.0859069
$859$	31.3782	1.07061	0.535305	−	0.844659i	$-0.320197\pi$
$859$	31.3782	1.07061	0.535305	+	0.844659i	$0.320197\pi$
$860$	0	0
$861$	−21.6637	−0.738298
$862$	13.3280	0.453955
$863$	−38.4329	−1.30827	−0.654136	−	0.756377i	$-0.726968\pi$
$863$	−38.4329	−1.30827	−0.654136	+	0.756377i	$0.726968\pi$
$864$	−21.2791	−0.723929
$865$	0	0
$866$	−27.5975	−0.937802
$867$	−8.83089	−0.299913
$868$	−10.8729	−0.369049
$869$	44.4797	1.50887
$870$	0	0
$871$	−0.502445	−0.0170247
$872$	−22.0502	−0.746715
$873$	25.5079	0.863313
$874$	−95.3153	−3.22409
$875$	0	0
$876$	17.9722	0.607225
$877$	−2.29975	−0.0776570	−0.0388285	−	0.999246i	$-0.512363\pi$
$877$	−2.29975	−0.0776570	−0.0388285	+	0.999246i	$0.512363\pi$
$878$	38.8593	1.31144
$879$	−3.83131	−0.129227
$880$	0	0
$881$	25.2993	0.852356	0.426178	−	0.904639i	$-0.359860\pi$
$881$	25.2993	0.852356	0.426178	+	0.904639i	$0.359860\pi$
$882$	28.4187	0.956906
$883$	2.93567	0.0987931	0.0493966	−	0.998779i	$-0.484270\pi$
$883$	2.93567	0.0987931	0.0493966	+	0.998779i	$0.484270\pi$
$884$	−3.10360	−0.104385
$885$	0	0
$886$	49.9306	1.67745
$887$	2.26157	0.0759362	0.0379681	−	0.999279i	$-0.487911\pi$
$887$	2.26157	0.0759362	0.0379681	+	0.999279i	$0.487911\pi$
$888$	−1.34484	−0.0451299
$889$	−21.2433	−0.712478
$890$	0	0
$891$	−17.2940	−0.579372
$892$	−61.7657	−2.06807
$893$	12.4113	0.415328
$894$	−2.03781	−0.0681545
$895$	0	0
$896$	−60.4026	−2.01791
$897$	−3.29358	−0.109969
$898$	−55.0315	−1.83643
$899$	4.17221	0.139151
$900$	0	0
$901$	−18.7445	−0.624468
$902$	70.4477	2.34565
$903$	8.12530	0.270393
$904$	−52.3479	−1.74107
$905$	0	0
$906$	−19.8327	−0.658898
$907$	−24.3904	−0.809870	−0.404935	−	0.914346i	$-0.632706\pi$
$907$	−24.3904	−0.809870	−0.404935	+	0.914346i	$0.632706\pi$
$908$	80.1101	2.65855
$909$	−19.4328	−0.644545
$910$	0	0
$911$	32.3326	1.07123	0.535614	−	0.844463i	$-0.320080\pi$
$911$	32.3326	1.07123	0.535614	+	0.844463i	$0.320080\pi$
$912$	−0.909405	−0.0301134
$913$	−46.4446	−1.53709
$914$	−70.4103	−2.32897
$915$	0	0
$916$	−60.3191	−1.99300
$917$	70.9158	2.34185
$918$	14.0022	0.462143
$919$	13.1553	0.433953	0.216977	−	0.976177i	$-0.430380\pi$
$919$	13.1553	0.433953	0.216977	+	0.976177i	$0.430380\pi$
$920$	0	0
$921$	−1.70107	−0.0560523
$922$	45.5149	1.49895
$923$	2.02907	0.0667875
$924$	21.3640	0.702823
$925$	0	0
$926$	48.4824	1.59323
$927$	−28.7706	−0.944950
$928$	25.0786	0.823247
$929$	37.1635	1.21930	0.609648	−	0.792672i	$-0.291311\pi$
$929$	37.1635	1.21930	0.609648	+	0.792672i	$0.291311\pi$
$930$	0	0
$931$	21.8173	0.715034
$932$	26.4608	0.866753
$933$	−7.78606	−0.254904
$934$	13.4195	0.439101
$935$	0	0
$936$	−3.87643	−0.126705
$937$	49.5180	1.61768	0.808841	−	0.588028i	$-0.200095\pi$
$937$	49.5180	1.61768	0.808841	+	0.588028i	$0.200095\pi$
$938$	6.96224	0.227325
$939$	−13.2864	−0.433584
$940$	0	0
$941$	−3.31354	−0.108018	−0.0540091	−	0.998540i	$-0.517200\pi$
$941$	−3.31354	−0.108018	−0.0540091	+	0.998540i	$0.517200\pi$
$942$	5.49838	0.179147
$943$	92.2068	3.00267
$944$	−2.82535	−0.0919573
$945$	0	0
$946$	−26.4224	−0.859068
$947$	−22.7250	−0.738463	−0.369231	−	0.929337i	$-0.620379\pi$
$947$	−22.7250	−0.738463	−0.369231	+	0.929337i	$0.620379\pi$
$948$	−28.6186	−0.929490
$949$	−5.06422	−0.164392
$950$	0	0
$951$	−13.7518	−0.445933
$952$	15.8213	0.512771
$953$	38.8212	1.25754	0.628771	−	0.777590i	$-0.283558\pi$
$953$	38.8212	1.25754	0.628771	+	0.777590i	$0.283558\pi$
$954$	−63.6389	−2.06039
$955$	0	0
$956$	85.1382	2.75357
$957$	−8.19793	−0.265001
$958$	30.0947	0.972314
$959$	−19.1024	−0.616849
$960$	0	0
$961$	1.00000	0.0322581
$962$	1.03007	0.0332108
$963$	39.0325	1.25780
$964$	58.6168	1.88792
$965$	0	0
$966$	45.6382	1.46838
$967$	18.3414	0.589819	0.294909	−	0.955525i	$-0.404711\pi$
$967$	18.3414	0.589819	0.294909	+	0.955525i	$0.404711\pi$
$968$	3.53799	0.113715
$969$	4.99137	0.160346
$970$	0	0
$971$	43.6911	1.40211	0.701057	−	0.713106i	$-0.252712\pi$
$971$	43.6911	1.40211	0.701057	+	0.713106i	$0.252712\pi$
$972$	44.7297	1.43471
$973$	40.7913	1.30771
$974$	24.7249	0.792236
$975$	0	0
$976$	−1.50182	−0.0480721
$977$	20.3120	0.649839	0.324919	−	0.945742i	$-0.394663\pi$
$977$	20.3120	0.649839	0.324919	+	0.945742i	$0.394663\pi$
$978$	14.4017	0.460517
$979$	−32.7202	−1.04574
$980$	0	0
$981$	−21.6778	−0.692118
$982$	−40.6889	−1.29843
$983$	9.48240	0.302442	0.151221	−	0.988500i	$-0.451680\pi$
$983$	9.48240	0.302442	0.151221	+	0.988500i	$0.451680\pi$
$984$	−16.6751	−0.531583
$985$	0	0
$986$	−16.5024	−0.525545
$987$	−5.94269	−0.189158
$988$	−8.08936	−0.257357
$989$	−34.5835	−1.09969
$990$	0	0
$991$	−35.9493	−1.14197	−0.570983	−	0.820962i	$-0.693438\pi$
$991$	−35.9493	−1.14197	−0.570983	+	0.820962i	$0.693438\pi$
$992$	6.01087	0.190845
$993$	9.96952	0.316373
$994$	−28.1162	−0.891791
$995$	0	0
$996$	29.8829	0.946875
$997$	−38.9329	−1.23302	−0.616508	−	0.787348i	$-0.711453\pi$
$997$	−38.9329	−1.23302	−0.616508	+	0.787348i	$0.711453\pi$
$998$	76.2308	2.41304
$999$	−2.84740	−0.0900877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.g.1.1		4
3.2	odd	2		6975.2.a.bj.1.4		4
5.2	odd	4		775.2.b.e.249.2		8
5.3	odd	4		775.2.b.e.249.7		8
5.4	even	2		155.2.a.d.1.4	✓	4
15.14	odd	2		1395.2.a.m.1.1		4
20.19	odd	2		2480.2.a.z.1.3		4
35.34	odd	2		7595.2.a.q.1.4		4
40.19	odd	2		9920.2.a.cd.1.2		4
40.29	even	2		9920.2.a.ch.1.3		4
155.154	odd	2		4805.2.a.j.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.d.1.4	✓	4	5.4	even	2
775.2.a.g.1.1		4	1.1	even	1	trivial
775.2.b.e.249.2		8	5.2	odd	4
775.2.b.e.249.7		8	5.3	odd	4
1395.2.a.m.1.1		4	15.14	odd	2
2480.2.a.z.1.3		4	20.19	odd	2
4805.2.a.j.1.4		4	155.154	odd	2
6975.2.a.bj.1.4		4	3.2	odd	2
7595.2.a.q.1.4		4	35.34	odd	2
9920.2.a.cd.1.2		4	40.19	odd	2
9920.2.a.ch.1.3		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)

\(f(q)\)	\(=\)	\(q-2.27244 q^{2} +0.632112 q^{3} +3.16400 q^{4} -1.43644 q^{6} -3.43644 q^{7} -2.64511 q^{8} -2.60043 q^{9} +O(q^{10})\)	\(q-2.27244 q^{2} +0.632112 q^{3} +3.16400 q^{4} -1.43644 q^{6} -3.43644 q^{7} -2.64511 q^{8} -2.60043 q^{9} -3.10845 q^{11} +2.00000 q^{12} -0.563561 q^{13} +7.80911 q^{14} -0.317122 q^{16} +1.74056 q^{17} +5.90934 q^{18} +4.53667 q^{19} -2.17221 q^{21} +7.06377 q^{22} +9.24555 q^{23} -1.67201 q^{24} +1.28066 q^{26} -3.54010 q^{27} -10.8729 q^{28} +4.17221 q^{29} +1.00000 q^{31} +6.01087 q^{32} -1.96489 q^{33} -3.95532 q^{34} -8.22776 q^{36} +0.804326 q^{37} -10.3093 q^{38} -0.356234 q^{39} +9.97311 q^{41} +4.93623 q^{42} -3.74056 q^{43} -9.83511 q^{44} -21.0100 q^{46} +2.73578 q^{47} -0.200457 q^{48} +4.80911 q^{49} +1.10023 q^{51} -1.78311 q^{52} -10.7692 q^{53} +8.04468 q^{54} +9.08977 q^{56} +2.86768 q^{57} -9.48112 q^{58} +8.90934 q^{59} +4.73578 q^{61} -2.27244 q^{62} +8.93623 q^{63} -13.0251 q^{64} +4.46509 q^{66} +0.891553 q^{67} +5.50712 q^{68} +5.84422 q^{69} -3.60043 q^{71} +6.87844 q^{72} +8.98611 q^{73} -1.82779 q^{74} +14.3540 q^{76} +10.6820 q^{77} +0.809521 q^{78} -14.3093 q^{79} +5.56356 q^{81} -22.6633 q^{82} +14.9414 q^{83} -6.87288 q^{84} +8.50021 q^{86} +2.63731 q^{87} +8.22220 q^{88} +10.5262 q^{89} +1.93664 q^{91} +29.2529 q^{92} +0.632112 q^{93} -6.21689 q^{94} +3.79954 q^{96} -9.80911 q^{97} -10.9284 q^{98} +8.08331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + 9 q^{4} + 8 q^{6} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 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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