LMFDB - Embedded newform 775.2.a.e.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
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			$2.27841$ 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)

$f(q)$	$=$	$q+2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -4.99239 q^{6} -1.38995 q^{7} +1.75561 q^{8} +2.19117 q^{9} +O(q^{10})$	\(q+2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -4.99239 q^{6} -1.38995 q^{7} +1.75561 q^{8} +2.19117 q^{9} -4.99239 q^{11} -6.38234 q^{12} -2.43556 q^{13} -3.04561 q^{14} -1.75561 q^{16} -4.71397 q^{17} +4.80122 q^{18} +5.74800 q^{19} +3.16688 q^{21} -10.9392 q^{22} +1.38995 q^{23} -4.00000 q^{24} -5.33672 q^{26} +1.84285 q^{27} -3.89355 q^{28} -5.16688 q^{29} -1.00000 q^{31} -7.35805 q^{32} +11.3747 q^{33} -10.3291 q^{34} +6.13794 q^{36} +4.31641 q^{37} +12.5948 q^{38} +5.54922 q^{39} -10.0091 q^{41} +6.93916 q^{42} -2.15715 q^{43} -13.9848 q^{44} +3.04561 q^{46} +8.20785 q^{47} +4.00000 q^{48} -5.06804 q^{49} +10.7404 q^{51} -6.82254 q^{52} -13.3921 q^{53} +4.03800 q^{54} -2.44020 q^{56} -13.0963 q^{57} -11.3215 q^{58} +0.672342 q^{59} +1.44317 q^{61} -2.19117 q^{62} -3.04561 q^{63} -12.6115 q^{64} +24.9239 q^{66} +14.9772 q^{67} -13.2049 q^{68} -3.16688 q^{69} -2.80883 q^{71} +3.84683 q^{72} -2.85046 q^{73} +9.45799 q^{74} +16.1014 q^{76} +6.93916 q^{77} +12.1593 q^{78} +6.85258 q^{79} -10.7723 q^{81} -21.9316 q^{82} +14.5243 q^{83} +8.87112 q^{84} -4.72667 q^{86} +11.7723 q^{87} -8.76467 q^{88} +8.15462 q^{89} +3.38531 q^{91} +3.89355 q^{92} +2.27841 q^{93} +17.9848 q^{94} +16.7647 q^{96} +15.7951 q^{97} -11.1049 q^{98} -10.9392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9	$ 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{11} - 6 q^{12} - 10 q^{13} - 16 q^{14} + 3 q^{16} - 11 q^{17} + 13 q^{18} - 3 q^{19} - 8 q^{22} + 2 q^{23} - 16 q^{24} + 2 q^{26} - q^{27} + 24 q^{28} - 8 q^{29} - 4 q^{31} - 7 q^{32} + 10 q^{33} - 2 q^{34} - 5 q^{36} - 3 q^{37} + 22 q^{38} - 10 q^{39} - 11 q^{41} - 8 q^{42} - 17 q^{43} - 24 q^{44} + 16 q^{46} + 10 q^{47} + 16 q^{48} + 16 q^{49} + q^{51} - 22 q^{52} - 13 q^{53} + 4 q^{54} - 24 q^{56} - 25 q^{57} + 10 q^{58} - 3 q^{59} + 22 q^{61} + q^{62} - 16 q^{63} - 9 q^{64} + 32 q^{66} + 12 q^{67} - 28 q^{68} - 21 q^{71} + 13 q^{72} - 19 q^{73} - 2 q^{74} + 2 q^{76} - 8 q^{77} + 20 q^{78} - 2 q^{79} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 36 q^{84} + 8 q^{86} + 24 q^{87} + 4 q^{88} - 10 q^{89} - 4 q^{91} - 24 q^{92} + q^{93} + 40 q^{94} + 28 q^{96} - 4 q^{97} - 37 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^11 - 6 * q^12 - 10 * q^13 - 16 * q^14 + 3 * q^16 - 11 * q^17 + 13 * q^18 - 3 * q^19 - 8 * q^22 + 2 * q^23 - 16 * q^24 + 2 * q^26 - q^27 + 24 * q^28 - 8 * q^29 - 4 * q^31 - 7 * q^32 + 10 * q^33 - 2 * q^34 - 5 * q^36 - 3 * q^37 + 22 * q^38 - 10 * q^39 - 11 * q^41 - 8 * q^42 - 17 * q^43 - 24 * q^44 + 16 * q^46 + 10 * q^47 + 16 * q^48 + 16 * q^49 + q^51 - 22 * q^52 - 13 * q^53 + 4 * q^54 - 24 * q^56 - 25 * q^57 + 10 * q^58 - 3 * q^59 + 22 * q^61 + q^62 - 16 * q^63 - 9 * q^64 + 32 * q^66 + 12 * q^67 - 28 * q^68 - 21 * q^71 + 13 * q^72 - 19 * q^73 - 2 * q^74 + 2 * q^76 - 8 * q^77 + 20 * q^78 - 2 * q^79 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 36 * q^84 + 8 * q^86 + 24 * q^87 + 4 * q^88 - 10 * q^89 - 4 * q^91 - 24 * q^92 + q^93 + 40 * q^94 + 28 * q^96 - 4 * q^97 - 37 * q^98 - 8 * 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 $

$2$	2.19117	1.54939	0.774695	−	0.632335i	$-0.217903\pi$
$2$	2.19117	1.54939	0.774695	+	0.632335i	$0.217903\pi$
$3$	−2.27841	−1.31544	−0.657721	−	0.753261i	$-0.728480\pi$
$3$	−2.27841	−1.31544	−0.657721	+	0.753261i	$0.728480\pi$
$4$	2.80122	1.40061
$5$	0	0
$5$	0	0
$6$	−4.99239	−2.03813
$7$	−1.38995	−0.525351	−0.262676	−	0.964884i	$-0.584605\pi$
$7$	−1.38995	−0.525351	−0.262676	+	0.964884i	$0.584605\pi$
$8$	1.75561	0.620701
$9$	2.19117	0.730390
$10$	0	0
$11$	−4.99239	−1.50526	−0.752631	−	0.658443i	$-0.771215\pi$
$11$	−4.99239	−1.50526	−0.752631	+	0.658443i	$0.771215\pi$
$12$	−6.38234	−1.84242
$13$	−2.43556	−0.675503	−0.337752	−	0.941235i	$-0.609666\pi$
$13$	−2.43556	−0.675503	−0.337752	+	0.941235i	$0.609666\pi$
$14$	−3.04561	−0.813974
$15$	0	0
$16$	−1.75561	−0.438902
$17$	−4.71397	−1.14331	−0.571653	−	0.820495i	$-0.693698\pi$
$17$	−4.71397	−1.14331	−0.571653	+	0.820495i	$0.693698\pi$
$18$	4.80122	1.13166
$19$	5.74800	1.31868	0.659340	−	0.751845i	$-0.270836\pi$
$19$	5.74800	1.31868	0.659340	+	0.751845i	$0.270836\pi$
$20$	0	0
$21$	3.16688	0.691070
$22$	−10.9392	−2.33224
$23$	1.38995	0.289824	0.144912	−	0.989445i	$-0.453710\pi$
$23$	1.38995	0.289824	0.144912	+	0.989445i	$0.453710\pi$
$24$	−4.00000	−0.816497
$25$	0	0
$26$	−5.33672	−1.04662
$27$	1.84285	0.354657
$28$	−3.89355	−0.735812
$29$	−5.16688	−0.959465	−0.479733	−	0.877415i	$-0.659266\pi$
$29$	−5.16688	−0.959465	−0.479733	+	0.877415i	$0.659266\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−7.35805	−1.30073
$33$	11.3747	1.98009
$34$	−10.3291	−1.77143
$35$	0	0
$36$	6.13794	1.02299
$37$	4.31641	0.709614	0.354807	−	0.934940i	$-0.384547\pi$
$37$	4.31641	0.709614	0.354807	+	0.934940i	$0.384547\pi$
$38$	12.5948	2.04315
$39$	5.54922	0.888586
$40$	0	0
$41$	−10.0091	−1.56315	−0.781577	−	0.623809i	$-0.785584\pi$
$41$	−10.0091	−1.56315	−0.781577	+	0.623809i	$0.785584\pi$
$42$	6.93916	1.07074
$43$	−2.15715	−0.328962	−0.164481	−	0.986380i	$-0.552595\pi$
$43$	−2.15715	−0.328962	−0.164481	+	0.986380i	$0.552595\pi$
$44$	−13.9848	−2.10828
$45$	0	0
$46$	3.04561	0.449051
$47$	8.20785	1.19724	0.598619	−	0.801034i	$-0.295716\pi$
$47$	8.20785	1.19724	0.598619	+	0.801034i	$0.295716\pi$
$48$	4.00000	0.577350
$49$	−5.06804	−0.724006
$50$	0	0
$51$	10.7404	1.50395
$52$	−6.82254	−0.946116
$53$	−13.3921	−1.83954	−0.919771	−	0.392455i	$-0.871626\pi$
$53$	−13.3921	−1.83954	−0.919771	+	0.392455i	$0.871626\pi$
$54$	4.03800	0.549502
$55$	0	0
$56$	−2.44020	−0.326086
$57$	−13.0963	−1.73465
$58$	−11.3215	−1.48659
$59$	0.672342	0.0875315	0.0437657	−	0.999042i	$-0.486064\pi$
$59$	0.672342	0.0875315	0.0437657	+	0.999042i	$0.486064\pi$
$60$	0	0
$61$	1.44317	0.184779	0.0923897	−	0.995723i	$-0.470549\pi$
$61$	1.44317	0.184779	0.0923897	+	0.995723i	$0.470549\pi$
$62$	−2.19117	−0.278279
$63$	−3.04561	−0.383711
$64$	−12.6115	−1.57644
$65$	0	0
$66$	24.9239	3.06793
$67$	14.9772	1.82975	0.914876	−	0.403735i	$-0.132288\pi$
$67$	14.9772	1.82975	0.914876	+	0.403735i	$0.132288\pi$
$68$	−13.2049	−1.60133
$69$	−3.16688	−0.381247
$70$	0	0
$71$	−2.80883	−0.333347	−0.166673	−	0.986012i	$-0.553303\pi$
$71$	−2.80883	−0.333347	−0.166673	+	0.986012i	$0.553303\pi$
$72$	3.84683	0.453353
$73$	−2.85046	−0.333622	−0.166811	−	0.985989i	$-0.553347\pi$
$73$	−2.85046	−0.333622	−0.166811	+	0.985989i	$0.553347\pi$
$74$	9.45799	1.09947
$75$	0	0
$76$	16.1014	1.84696
$77$	6.93916	0.790791
$78$	12.1593	1.37677
$79$	6.85258	0.770976	0.385488	−	0.922713i	$-0.374033\pi$
$79$	6.85258	0.770976	0.385488	+	0.922713i	$0.374033\pi$
$80$	0	0
$81$	−10.7723	−1.19692
$82$	−21.9316	−2.42193
$83$	14.5243	1.59424	0.797122	−	0.603818i	$-0.206355\pi$
$83$	14.5243	1.59424	0.797122	+	0.603818i	$0.206355\pi$
$84$	8.87112	0.967919
$85$	0	0
$86$	−4.72667	−0.509690
$87$	11.7723	1.26212
$88$	−8.76467	−0.934317
$89$	8.15462	0.864388	0.432194	−	0.901781i	$-0.357740\pi$
$89$	8.15462	0.864388	0.432194	+	0.901781i	$0.357740\pi$
$90$	0	0
$91$	3.38531	0.354876
$92$	3.89355	0.405931
$93$	2.27841	0.236260
$94$	17.9848	1.85499
$95$	0	0
$96$	16.7647	1.71104
$97$	15.7951	1.60375	0.801873	−	0.597495i	$-0.203837\pi$
$97$	15.7951	1.60375	0.801873	+	0.597495i	$0.203837\pi$
$98$	−11.1049	−1.12177
$99$	−10.9392	−1.09943
$100$	0	0
$101$	16.4294	1.63479	0.817393	−	0.576080i	$-0.195418\pi$
$101$	16.4294	1.63479	0.817393	+	0.576080i	$0.195418\pi$
$102$	23.5340	2.33021
$103$	−3.04561	−0.300093	−0.150047	−	0.988679i	$-0.547942\pi$
$103$	−3.04561	−0.300093	−0.150047	+	0.988679i	$0.547942\pi$
$104$	−4.27589	−0.419285
$105$	0	0
$106$	−29.3443	−2.85017
$107$	−12.5264	−1.21097	−0.605485	−	0.795856i	$-0.707021\pi$
$107$	−12.5264	−1.21097	−0.605485	+	0.795856i	$0.707021\pi$
$108$	5.16223	0.496736
$109$	−8.27014	−0.792136	−0.396068	−	0.918221i	$-0.629625\pi$
$109$	−8.27014	−0.792136	−0.396068	+	0.918221i	$0.629625\pi$
$110$	0	0
$111$	−9.83458	−0.933457
$112$	2.44020	0.230578
$113$	−1.61302	−0.151740	−0.0758700	−	0.997118i	$-0.524173\pi$
$113$	−1.61302	−0.151740	−0.0758700	+	0.997118i	$0.524173\pi$
$114$	−28.6962	−2.68765
$115$	0	0
$116$	−14.4736	−1.34384
$117$	−5.33672	−0.493380
$118$	1.47321	0.135620
$119$	6.55218	0.600638
$120$	0	0
$121$	13.9239	1.26581
$122$	3.16223	0.286295
$123$	22.8048	2.05624
$124$	−2.80122	−0.251557
$125$	0	0
$126$	−6.67345	−0.594518
$127$	−3.64044	−0.323037	−0.161518	−	0.986870i	$-0.551639\pi$
$127$	−3.64044	−0.323037	−0.161518	+	0.986870i	$0.551639\pi$
$128$	−12.9178	−1.14179
$129$	4.91487	0.432731
$130$	0	0
$131$	−8.32005	−0.726926	−0.363463	−	0.931609i	$-0.618406\pi$
$131$	−8.32005	−0.726926	−0.363463	+	0.931609i	$0.618406\pi$
$132$	31.8631	2.77333
$133$	−7.98942	−0.692771
$134$	32.8175	2.83500
$135$	0	0
$136$	−8.27589	−0.709652
$137$	−22.6303	−1.93344	−0.966719	−	0.255842i	$-0.917647\pi$
$137$	−22.6303	−1.93344	−0.966719	+	0.255842i	$0.917647\pi$
$138$	−6.93916	−0.590701
$139$	−17.3595	−1.47241	−0.736207	−	0.676757i	$-0.763385\pi$
$139$	−17.3595	−1.47241	−0.736207	+	0.676757i	$0.763385\pi$
$140$	0	0
$141$	−18.7009	−1.57490
$142$	−6.15462	−0.516485
$143$	12.1593	1.01681
$144$	−3.84683	−0.320569
$145$	0	0
$146$	−6.24585	−0.516910
$147$	11.5471	0.952388
$148$	12.0912	0.993893
$149$	12.8997	1.05678	0.528390	−	0.849002i	$-0.322796\pi$
$149$	12.8997	1.05678	0.528390	+	0.849002i	$0.322796\pi$
$150$	0	0
$151$	−6.34434	−0.516295	−0.258147	−	0.966106i	$-0.583112\pi$
$151$	−6.34434	−0.516295	−0.258147	+	0.966106i	$0.583112\pi$
$152$	10.0912	0.818506
$153$	−10.3291	−0.835059
$154$	15.2049	1.22524
$155$	0	0
$156$	15.5446	1.24456
$157$	−12.0228	−0.959522	−0.479761	−	0.877399i	$-0.659277\pi$
$157$	−12.0228	−0.959522	−0.479761	+	0.877399i	$0.659277\pi$
$158$	15.0152	1.19454
$159$	30.5127	2.41981
$160$	0	0
$161$	−1.93196	−0.152260
$162$	−23.6039	−1.85450
$163$	−0.256427	−0.0200850	−0.0100425	−	0.999950i	$-0.503197\pi$
$163$	−0.256427	−0.0200850	−0.0100425	+	0.999950i	$0.503197\pi$
$164$	−28.0376	−2.18937
$165$	0	0
$166$	31.8251	2.47011
$167$	−5.70172	−0.441212	−0.220606	−	0.975363i	$-0.570804\pi$
$167$	−5.70172	−0.441212	−0.220606	+	0.975363i	$0.570804\pi$
$168$	5.55980	0.428948
$169$	−7.06804	−0.543696
$170$	0	0
$171$	12.5948	0.963151
$172$	−6.04264	−0.460747
$173$	−13.8556	−1.05342	−0.526709	−	0.850046i	$-0.676574\pi$
$173$	−13.8556	−1.05342	−0.526709	+	0.850046i	$0.676574\pi$
$174$	25.7951	1.95552
$175$	0	0
$176$	8.76467	0.660662
$177$	−1.53187	−0.115143
$178$	17.8682	1.33927
$179$	10.8939	0.814248	0.407124	−	0.913373i	$-0.366532\pi$
$179$	10.8939	0.814248	0.407124	+	0.913373i	$0.366532\pi$
$180$	0	0
$181$	14.5082	1.07839	0.539195	−	0.842181i	$-0.318729\pi$
$181$	14.5082	1.07839	0.539195	+	0.842181i	$0.318729\pi$
$182$	7.41777	0.549842
$183$	−3.28814	−0.243067
$184$	2.44020	0.179894
$185$	0	0
$186$	4.99239	0.366060
$187$	23.5340	1.72098
$188$	22.9920	1.67686
$189$	−2.56147	−0.186320
$190$	0	0
$191$	−17.6219	−1.27508	−0.637538	−	0.770419i	$-0.720047\pi$
$191$	−17.6219	−1.27508	−0.637538	+	0.770419i	$0.720047\pi$
$192$	28.7342	2.07371
$193$	−19.1897	−1.38130	−0.690651	−	0.723188i	$-0.742676\pi$
$193$	−19.1897	−1.38130	−0.690651	+	0.723188i	$0.742676\pi$
$194$	34.6096	2.48483
$195$	0	0
$196$	−14.1967	−1.01405
$197$	−3.13352	−0.223254	−0.111627	−	0.993750i	$-0.535606\pi$
$197$	−3.13352	−0.223254	−0.111627	+	0.993750i	$0.535606\pi$
$198$	−23.9696	−1.70344
$199$	−4.03800	−0.286246	−0.143123	−	0.989705i	$-0.545714\pi$
$199$	−4.03800	−0.286246	−0.143123	+	0.989705i	$0.545714\pi$
$200$	0	0
$201$	−34.1242	−2.40693
$202$	35.9996	2.53292
$203$	7.18170	0.504056
$204$	30.0862	2.10645
$205$	0	0
$206$	−6.67345	−0.464961
$207$	3.04561	0.211685
$208$	4.27589	0.296480
$209$	−28.6962	−1.98496
$210$	0	0
$211$	1.82551	0.125673	0.0628366	−	0.998024i	$-0.479985\pi$
$211$	1.82551	0.125673	0.0628366	+	0.998024i	$0.479985\pi$
$212$	−37.5141	−2.57648
$213$	6.39968	0.438499
$214$	−27.4474	−1.87627
$215$	0	0
$216$	3.23533	0.220136
$217$	1.38995	0.0943559
$218$	−18.1213	−1.22733
$219$	6.49454	0.438860
$220$	0	0
$221$	11.4812	0.772307
$222$	−21.5492	−1.44629
$223$	−24.7714	−1.65882	−0.829409	−	0.558642i	$-0.811323\pi$
$223$	−24.7714	−1.65882	−0.829409	+	0.558642i	$0.811323\pi$
$224$	10.2273	0.683341
$225$	0	0
$226$	−3.53440	−0.235105
$227$	3.51586	0.233356	0.116678	−	0.993170i	$-0.462775\pi$
$227$	3.51586	0.233356	0.116678	+	0.993170i	$0.462775\pi$
$228$	−36.6856	−2.42957
$229$	23.5978	1.55939	0.779693	−	0.626162i	$-0.215375\pi$
$229$	23.5978	1.55939	0.779693	+	0.626162i	$0.215375\pi$
$230$	0	0
$231$	−15.8103	−1.04024
$232$	−9.07101	−0.595541
$233$	−1.87873	−0.123080	−0.0615400	−	0.998105i	$-0.519601\pi$
$233$	−1.87873	−0.123080	−0.0615400	+	0.998105i	$0.519601\pi$
$234$	−11.6937	−0.764439
$235$	0	0
$236$	1.88338	0.122597
$237$	−15.6130	−1.01417
$238$	14.3569	0.930622
$239$	2.30634	0.149184	0.0745922	−	0.997214i	$-0.476234\pi$
$239$	2.30634	0.149184	0.0745922	+	0.997214i	$0.476234\pi$
$240$	0	0
$241$	−6.35230	−0.409187	−0.204594	−	0.978847i	$-0.565587\pi$
$241$	−6.35230	−0.409187	−0.204594	+	0.978847i	$0.565587\pi$
$242$	30.5097	1.96124
$243$	19.0152	1.21982
$244$	4.04264	0.258804
$245$	0	0
$246$	49.9691	3.18592
$247$	−13.9996	−0.890773
$248$	−1.75561	−0.111481
$249$	−33.0923	−2.09714
$250$	0	0
$251$	−20.8893	−1.31852	−0.659259	−	0.751916i	$-0.729130\pi$
$251$	−20.8893	−1.31852	−0.659259	+	0.751916i	$0.729130\pi$
$252$	−8.53143	−0.537430
$253$	−6.93916	−0.436262
$254$	−7.97682	−0.500510
$255$	0	0
$256$	−3.08216	−0.192635
$257$	8.52679	0.531886	0.265943	−	0.963989i	$-0.414317\pi$
$257$	8.52679	0.531886	0.265943	+	0.963989i	$0.414317\pi$
$258$	10.7693	0.670468
$259$	−5.99959	−0.372797
$260$	0	0
$261$	−11.3215	−0.700783
$262$	−18.2306	−1.12629
$263$	−28.4225	−1.75260	−0.876302	−	0.481762i	$-0.839997\pi$
$263$	−28.4225	−1.75260	−0.876302	+	0.481762i	$0.839997\pi$
$264$	19.9696	1.22904
$265$	0	0
$266$	−17.5062	−1.07337
$267$	−18.5796	−1.13705
$268$	41.9543	2.56277
$269$	−19.2349	−1.17277	−0.586387	−	0.810031i	$-0.699450\pi$
$269$	−19.2349	−1.17277	−0.586387	+	0.810031i	$0.699450\pi$
$270$	0	0
$271$	−13.7917	−0.837789	−0.418895	−	0.908035i	$-0.637582\pi$
$271$	−13.7917	−0.837789	−0.418895	+	0.908035i	$0.637582\pi$
$272$	8.27589	0.501799
$273$	−7.71313	−0.466820
$274$	−49.5868	−2.99565
$275$	0	0
$276$	−8.87112	−0.533979
$277$	−13.3392	−0.801478	−0.400739	−	0.916192i	$-0.631247\pi$
$277$	−13.3392	−0.801478	−0.400739	+	0.916192i	$0.631247\pi$
$278$	−38.0376	−2.28134
$279$	−2.19117	−0.131182
$280$	0	0
$281$	17.2288	1.02778	0.513891	−	0.857856i	$-0.328204\pi$
$281$	17.2288	1.02778	0.513891	+	0.857856i	$0.328204\pi$
$282$	−40.9768	−2.44013
$283$	0.556827	0.0330999	0.0165500	−	0.999863i	$-0.494732\pi$
$283$	0.556827	0.0330999	0.0165500	+	0.999863i	$0.494732\pi$
$284$	−7.86815	−0.466889
$285$	0	0
$286$	26.6430	1.57543
$287$	13.9121	0.821205
$288$	−16.1227	−0.950040
$289$	5.22156	0.307150
$290$	0	0
$291$	−35.9877	−2.10964
$292$	−7.98478	−0.467274
$293$	−10.6781	−0.623821	−0.311910	−	0.950112i	$-0.600969\pi$
$293$	−10.6781	−0.623821	−0.311910	+	0.950112i	$0.600969\pi$
$294$	25.3016	1.47562
$295$	0	0
$296$	7.57793	0.440458
$297$	−9.20024	−0.533852
$298$	28.2653	1.63737
$299$	−3.38531	−0.195777
$300$	0	0
$301$	2.99832	0.172821
$302$	−13.9015	−0.799942
$303$	−37.4330	−2.15047
$304$	−10.0912	−0.578771
$305$	0	0
$306$	−22.6328	−1.29383
$307$	8.41238	0.480120	0.240060	−	0.970758i	$-0.422833\pi$
$307$	8.41238	0.480120	0.240060	+	0.970758i	$0.422833\pi$
$308$	19.4381	1.10759
$309$	6.93916	0.394755
$310$	0	0
$311$	23.9026	1.35539	0.677697	−	0.735342i	$-0.262978\pi$
$311$	23.9026	1.35539	0.677697	+	0.735342i	$0.262978\pi$
$312$	9.74224	0.551546
$313$	−4.17197	−0.235813	−0.117907	−	0.993025i	$-0.537618\pi$
$313$	−4.17197	−0.235813	−0.117907	+	0.993025i	$0.537618\pi$
$314$	−26.3439	−1.48667
$315$	0	0
$316$	19.1956	1.07984
$317$	16.9573	0.952417	0.476208	−	0.879332i	$-0.342011\pi$
$317$	16.9573	0.952417	0.476208	+	0.879332i	$0.342011\pi$
$318$	66.8584	3.74923
$319$	25.7951	1.44425
$320$	0	0
$321$	28.5403	1.59296
$322$	−4.23325	−0.235910
$323$	−27.0959	−1.50766
$324$	−30.1755	−1.67642
$325$	0	0
$326$	−0.561876	−0.0311194
$327$	18.8428	1.04201
$328$	−17.5720	−0.970251
$329$	−11.4085	−0.628970
$330$	0	0
$331$	21.8711	1.20214	0.601071	−	0.799195i	$-0.294741\pi$
$331$	21.8711	1.20214	0.601071	+	0.799195i	$0.294741\pi$
$332$	40.6856	2.23291
$333$	9.45799	0.518295
$334$	−12.4934	−0.683610
$335$	0	0
$336$	−5.55980	−0.303312
$337$	7.78499	0.424075	0.212038	−	0.977262i	$-0.431990\pi$
$337$	7.78499	0.424075	0.212038	+	0.977262i	$0.431990\pi$
$338$	−15.4873	−0.842397
$339$	3.67513	0.199605
$340$	0	0
$341$	4.99239	0.270353
$342$	27.5974	1.49230
$343$	16.7740	0.905709
$344$	−3.78710	−0.204187
$345$	0	0
$346$	−30.3598	−1.63216
$347$	11.2683	0.604913	0.302456	−	0.953163i	$-0.402193\pi$
$347$	11.2683	0.604913	0.302456	+	0.953163i	$0.402193\pi$
$348$	32.9768	1.76774
$349$	−0.943993	−0.0505308	−0.0252654	−	0.999681i	$-0.508043\pi$
$349$	−0.943993	−0.0505308	−0.0252654	+	0.999681i	$0.508043\pi$
$350$	0	0
$351$	−4.48838	−0.239572
$352$	36.7342	1.95794
$353$	25.4275	1.35337	0.676686	−	0.736272i	$-0.263416\pi$
$353$	25.4275	1.35337	0.676686	+	0.736272i	$0.263416\pi$
$354$	−3.35659	−0.178401
$355$	0	0
$356$	22.8429	1.21067
$357$	−14.9286	−0.790104
$358$	23.8704	1.26159
$359$	−2.08194	−0.109880	−0.0549402	−	0.998490i	$-0.517497\pi$
$359$	−2.08194	−0.109880	−0.0549402	+	0.998490i	$0.517497\pi$
$360$	0	0
$361$	14.0395	0.738919
$362$	31.7900	1.67085
$363$	−31.7245	−1.66510
$364$	9.48298	0.497043
$365$	0	0
$366$	−7.20488	−0.376605
$367$	−6.58939	−0.343964	−0.171982	−	0.985100i	$-0.555017\pi$
$367$	−6.58939	−0.343964	−0.171982	+	0.985100i	$0.555017\pi$
$368$	−2.44020	−0.127204
$369$	−21.9316	−1.14171
$370$	0	0
$371$	18.6143	0.966406
$372$	6.38234	0.330909
$373$	13.6404	0.706275	0.353138	−	0.935571i	$-0.385115\pi$
$373$	13.6404	0.706275	0.353138	+	0.935571i	$0.385115\pi$
$374$	51.5669	2.66646
$375$	0	0
$376$	14.4098	0.743127
$377$	12.5842	0.648122
$378$	−5.61261	−0.288682
$379$	−30.5160	−1.56750	−0.783750	−	0.621076i	$-0.786696\pi$
$379$	−30.5160	−1.56750	−0.783750	+	0.621076i	$0.786696\pi$
$380$	0	0
$381$	8.29443	0.424936
$382$	−38.6126	−1.97559
$383$	31.9366	1.63188	0.815942	−	0.578134i	$-0.196219\pi$
$383$	31.9366	1.63188	0.815942	+	0.578134i	$0.196219\pi$
$384$	29.4322	1.50196
$385$	0	0
$386$	−42.0478	−2.14018
$387$	−4.72667	−0.240270
$388$	44.2454	2.24622
$389$	−2.52941	−0.128246	−0.0641230	−	0.997942i	$-0.520425\pi$
$389$	−2.52941	−0.128246	−0.0641230	+	0.997942i	$0.520425\pi$
$390$	0	0
$391$	−6.55218	−0.331358
$392$	−8.89749	−0.449391
$393$	18.9565	0.956229
$394$	−6.86607	−0.345908
$395$	0	0
$396$	−30.6430	−1.53987
$397$	−9.47786	−0.475680	−0.237840	−	0.971304i	$-0.576439\pi$
$397$	−9.47786	−0.475680	−0.237840	+	0.971304i	$0.576439\pi$
$398$	−8.84794	−0.443507
$399$	18.2032	0.911300
$400$	0	0
$401$	−18.6781	−0.932739	−0.466370	−	0.884590i	$-0.654438\pi$
$401$	−18.6781	−0.932739	−0.466370	+	0.884590i	$0.654438\pi$
$402$	−74.7718	−3.72928
$403$	2.43556	0.121324
$404$	46.0224	2.28970
$405$	0	0
$406$	15.7363	0.780980
$407$	−21.5492	−1.06815
$408$	18.8559	0.933506
$409$	19.1424	0.946529	0.473265	−	0.880920i	$-0.343075\pi$
$409$	19.1424	0.946529	0.473265	+	0.880920i	$0.343075\pi$
$410$	0	0
$411$	51.5612	2.54333
$412$	−8.53143	−0.420313
$413$	−0.934521	−0.0459848
$414$	6.67345	0.327982
$415$	0	0
$416$	17.9210	0.878648
$417$	39.5521	1.93688
$418$	−62.8783	−3.07548
$419$	26.3733	1.28842	0.644209	−	0.764849i	$-0.277187\pi$
$419$	26.3733	1.28842	0.644209	+	0.764849i	$0.277187\pi$
$420$	0	0
$421$	19.5550	0.953051	0.476525	−	0.879161i	$-0.341896\pi$
$421$	19.5550	0.953051	0.476525	+	0.879161i	$0.341896\pi$
$422$	4.00000	0.194717
$423$	17.9848	0.874450
$424$	−23.5112	−1.14181
$425$	0	0
$426$	14.0228	0.679406
$427$	−2.00594	−0.0970741
$428$	−35.0891	−1.69610
$429$	−27.7038	−1.33755
$430$	0	0
$431$	−28.5460	−1.37501	−0.687507	−	0.726178i	$-0.741295\pi$
$431$	−28.5460	−1.37501	−0.687507	+	0.726178i	$0.741295\pi$
$432$	−3.23533	−0.155660
$433$	4.79976	0.230662	0.115331	−	0.993327i	$-0.463207\pi$
$433$	4.79976	0.230662	0.115331	+	0.993327i	$0.463207\pi$
$434$	3.04561	0.146194
$435$	0	0
$436$	−23.1665	−1.10947
$437$	7.98942	0.382186
$438$	14.2306	0.679966
$439$	−34.5275	−1.64791	−0.823954	−	0.566657i	$-0.808236\pi$
$439$	−34.5275	−1.64791	−0.823954	+	0.566657i	$0.808236\pi$
$440$	0	0
$441$	−11.1049	−0.528806
$442$	25.1572	1.19661
$443$	−31.5488	−1.49893	−0.749465	−	0.662044i	$-0.769689\pi$
$443$	−31.5488	−1.49893	−0.749465	+	0.662044i	$0.769689\pi$
$444$	−27.5488	−1.30741
$445$	0	0
$446$	−54.2784	−2.57016
$447$	−29.3907	−1.39013
$448$	17.5293	0.828184
$449$	−24.1513	−1.13977	−0.569885	−	0.821724i	$-0.693012\pi$
$449$	−24.1513	−1.13977	−0.569885	+	0.821724i	$0.693012\pi$
$450$	0	0
$451$	49.9691	2.35296
$452$	−4.51842	−0.212529
$453$	14.4550	0.679156
$454$	7.70384	0.361559
$455$	0	0
$456$	−22.9920	−1.07670
$457$	−12.8665	−0.601868	−0.300934	−	0.953645i	$-0.597298\pi$
$457$	−12.8665	−0.601868	−0.300934	+	0.953645i	$0.597298\pi$
$458$	51.7067	2.41610
$459$	−8.68716	−0.405482
$460$	0	0
$461$	30.5716	1.42386	0.711932	−	0.702249i	$-0.247821\pi$
$461$	30.5716	1.42386	0.711932	+	0.702249i	$0.247821\pi$
$462$	−34.6430	−1.61174
$463$	−11.3747	−0.528628	−0.264314	−	0.964437i	$-0.585146\pi$
$463$	−11.3747	−0.528628	−0.264314	+	0.964437i	$0.585146\pi$
$464$	9.07101	0.421111
$465$	0	0
$466$	−4.11662	−0.190699
$467$	−17.8090	−0.824100	−0.412050	−	0.911161i	$-0.635187\pi$
$467$	−17.8090	−0.824100	−0.412050	+	0.911161i	$0.635187\pi$
$468$	−14.9493	−0.691033
$469$	−20.8175	−0.961263
$470$	0	0
$471$	27.3929	1.26220
$472$	1.18037	0.0543309
$473$	10.7693	0.495174
$474$	−34.2108	−1.57135
$475$	0	0
$476$	18.3541	0.841259
$477$	−29.3443	−1.34358
$478$	5.05357	0.231145
$479$	−5.72835	−0.261735	−0.130867	−	0.991400i	$-0.541776\pi$
$479$	−5.72835	−0.261735	−0.130867	+	0.991400i	$0.541776\pi$
$480$	0	0
$481$	−10.5129	−0.479347
$482$	−13.9190	−0.633991
$483$	4.40180	0.200289
$484$	39.0040	1.77291
$485$	0	0
$486$	41.6654	1.88998
$487$	−2.88806	−0.130870	−0.0654352	−	0.997857i	$-0.520844\pi$
$487$	−2.88806	−0.130870	−0.0654352	+	0.997857i	$0.520844\pi$
$488$	2.53364	0.114693
$489$	0.584248	0.0264206
$490$	0	0
$491$	16.3490	0.737819	0.368910	−	0.929465i	$-0.379731\pi$
$491$	16.3490	0.737819	0.368910	+	0.929465i	$0.379731\pi$
$492$	63.8812	2.87999
$493$	24.3565	1.09696
$494$	−30.6755	−1.38015
$495$	0	0
$496$	1.75561	0.0788291
$497$	3.90413	0.175124
$498$	−72.5108	−3.24928
$499$	31.2378	1.39840	0.699199	−	0.714927i	$-0.253540\pi$
$499$	31.2378	1.39840	0.699199	+	0.714927i	$0.253540\pi$
$500$	0	0
$501$	12.9909	0.580390
$502$	−45.7719	−2.04290
$503$	12.8099	0.571167	0.285583	−	0.958354i	$-0.407813\pi$
$503$	12.8099	0.571167	0.285583	+	0.958354i	$0.407813\pi$
$504$	−5.34690	−0.238170
$505$	0	0
$506$	−15.2049	−0.675939
$507$	16.1039	0.715200
$508$	−10.1977	−0.452449
$509$	1.01093	0.0448086	0.0224043	−	0.999749i	$-0.492868\pi$
$509$	1.01093	0.0448086	0.0224043	+	0.999749i	$0.492868\pi$
$510$	0	0
$511$	3.96200	0.175269
$512$	19.0822	0.843320
$513$	10.5927	0.467680
$514$	18.6836	0.824099
$515$	0	0
$516$	13.7676	0.606087
$517$	−40.9768	−1.80216
$518$	−13.1461	−0.577608
$519$	31.5687	1.38571
$520$	0	0
$521$	−34.0725	−1.49274	−0.746371	−	0.665530i	$-0.768205\pi$
$521$	−34.0725	−1.49274	−0.746371	+	0.665530i	$0.768205\pi$
$522$	−24.8073	−1.08579
$523$	−3.49520	−0.152834	−0.0764172	−	0.997076i	$-0.524348\pi$
$523$	−3.49520	−0.152834	−0.0764172	+	0.997076i	$0.524348\pi$
$524$	−23.3063	−1.01814
$525$	0	0
$526$	−62.2784	−2.71547
$527$	4.71397	0.205344
$528$	−19.9696	−0.869063
$529$	−21.0680	−0.916002
$530$	0	0
$531$	1.47321	0.0639321
$532$	−22.3801	−0.970301
$533$	24.3777	1.05592
$534$	−40.7110	−1.76174
$535$	0	0
$536$	26.2940	1.13573
$537$	−24.8208	−1.07110
$538$	−42.1470	−1.81708
$539$	25.3016	1.08982
$540$	0	0
$541$	18.5915	0.799312	0.399656	−	0.916665i	$-0.369130\pi$
$541$	18.5915	0.799312	0.399656	+	0.916665i	$0.369130\pi$
$542$	−30.2200	−1.29806
$543$	−33.0558	−1.41856
$544$	34.6856	1.48713
$545$	0	0
$546$	−16.9008	−0.723286
$547$	37.4262	1.60023	0.800115	−	0.599847i	$-0.204772\pi$
$547$	37.4262	1.60023	0.800115	+	0.599847i	$0.204772\pi$
$548$	−63.3925	−2.70799
$549$	3.16223	0.134961
$550$	0	0
$551$	−29.6992	−1.26523
$552$	−5.55980	−0.236641
$553$	−9.52474	−0.405033
$554$	−29.2285	−1.24180
$555$	0	0
$556$	−48.6278	−2.06228
$557$	8.67942	0.367759	0.183879	−	0.982949i	$-0.441134\pi$
$557$	8.67942	0.367759	0.183879	+	0.982949i	$0.441134\pi$
$558$	−4.80122	−0.203252
$559$	5.25386	0.222215
$560$	0	0
$561$	−53.6202	−2.26385
$562$	37.7511	1.59244
$563$	−15.9011	−0.670152	−0.335076	−	0.942191i	$-0.608762\pi$
$563$	−15.9011	−0.670152	−0.335076	+	0.942191i	$0.608762\pi$
$564$	−52.3852	−2.20582
$565$	0	0
$566$	1.22010	0.0512847
$567$	14.9729	0.628804
$568$	−4.93121	−0.206909
$569$	−14.9124	−0.625162	−0.312581	−	0.949891i	$-0.601194\pi$
$569$	−14.9124	−0.625162	−0.312581	+	0.949891i	$0.601194\pi$
$570$	0	0
$571$	13.5565	0.567321	0.283661	−	0.958925i	$-0.408451\pi$
$571$	13.5565	0.567321	0.283661	+	0.958925i	$0.408451\pi$
$572$	34.0608	1.42415
$573$	40.1500	1.67729
$574$	30.4837	1.27237
$575$	0	0
$576$	−27.6339	−1.15141
$577$	5.64770	0.235117	0.117559	−	0.993066i	$-0.462493\pi$
$577$	5.64770	0.235117	0.117559	+	0.993066i	$0.462493\pi$
$578$	11.4413	0.475896
$579$	43.7220	1.81702
$580$	0	0
$581$	−20.1880	−0.837539
$582$	−78.8551	−3.26865
$583$	66.8584	2.76899
$584$	−5.00430	−0.207079
$585$	0	0
$586$	−23.3975	−0.966542
$587$	1.11697	0.0461023	0.0230511	−	0.999734i	$-0.492662\pi$
$587$	1.11697	0.0461023	0.0230511	+	0.999734i	$0.492662\pi$
$588$	32.3460	1.33392
$589$	−5.74800	−0.236842
$590$	0	0
$591$	7.13946	0.293678
$592$	−7.57793	−0.311451
$593$	−12.6249	−0.518441	−0.259221	−	0.965818i	$-0.583466\pi$
$593$	−12.6249	−0.518441	−0.259221	+	0.965818i	$0.583466\pi$
$594$	−20.1593	−0.827145
$595$	0	0
$596$	36.1348	1.48014
$597$	9.20024	0.376541
$598$	−7.41777	−0.303335
$599$	7.03633	0.287496	0.143748	−	0.989614i	$-0.454084\pi$
$599$	7.03633	0.287496	0.143748	+	0.989614i	$0.454084\pi$
$600$	0	0
$601$	−31.6687	−1.29180	−0.645898	−	0.763424i	$-0.723517\pi$
$601$	−31.6687	−1.29180	−0.645898	+	0.763424i	$0.723517\pi$
$602$	6.56983	0.267766
$603$	32.8175	1.33643
$604$	−17.7719	−0.723128
$605$	0	0
$606$	−82.0220	−3.33191
$607$	6.56874	0.266617	0.133308	−	0.991075i	$-0.457440\pi$
$607$	6.56874	0.266617	0.133308	+	0.991075i	$0.457440\pi$
$608$	−42.2940	−1.71525
$609$	−16.3629	−0.663057
$610$	0	0
$611$	−19.9907	−0.808738
$612$	−28.9341	−1.16959
$613$	−12.5728	−0.507812	−0.253906	−	0.967229i	$-0.581715\pi$
$613$	−12.5728	−0.507812	−0.253906	+	0.967229i	$0.581715\pi$
$614$	18.4329	0.743893
$615$	0	0
$616$	12.1824	0.490845
$617$	13.4993	0.543462	0.271731	−	0.962373i	$-0.412404\pi$
$617$	13.4993	0.543462	0.271731	+	0.962373i	$0.412404\pi$
$618$	15.2049	0.611630
$619$	10.2412	0.411629	0.205814	−	0.978591i	$-0.434016\pi$
$619$	10.2412	0.411629	0.205814	+	0.978591i	$0.434016\pi$
$620$	0	0
$621$	2.56147	0.102788
$622$	52.3747	2.10003
$623$	−11.3345	−0.454108
$624$	−9.74224	−0.390002
$625$	0	0
$626$	−9.14148	−0.365367
$627$	65.3819	2.61110
$628$	−33.6784	−1.34392
$629$	−20.3475	−0.811307
$630$	0	0
$631$	21.2564	0.846203	0.423101	−	0.906082i	$-0.360941\pi$
$631$	21.2564	0.846203	0.423101	+	0.906082i	$0.360941\pi$
$632$	12.0304	0.478545
$633$	−4.15927	−0.165316
$634$	37.1563	1.47567
$635$	0	0
$636$	85.4727	3.38921
$637$	12.3435	0.489068
$638$	56.5213	2.23770
$639$	−6.15462	−0.243473
$640$	0	0
$641$	32.7676	1.29424	0.647121	−	0.762387i	$-0.275973\pi$
$641$	32.7676	1.29424	0.647121	+	0.762387i	$0.275973\pi$
$642$	62.5366	2.46812
$643$	−12.8052	−0.504988	−0.252494	−	0.967598i	$-0.581251\pi$
$643$	−12.8052	−0.504988	−0.252494	+	0.967598i	$0.581251\pi$
$644$	−5.41184	−0.213256
$645$	0	0
$646$	−59.3717	−2.33595
$647$	1.36929	0.0538324	0.0269162	−	0.999638i	$-0.491431\pi$
$647$	1.36929	0.0538324	0.0269162	+	0.999638i	$0.491431\pi$
$648$	−18.9119	−0.742930
$649$	−3.35659	−0.131758
$650$	0	0
$651$	−3.16688	−0.124120
$652$	−0.718310	−0.0281312
$653$	−24.6611	−0.965065	−0.482532	−	0.875878i	$-0.660283\pi$
$653$	−24.6611	−0.965065	−0.482532	+	0.875878i	$0.660283\pi$
$654$	41.2877	1.61448
$655$	0	0
$656$	17.5720	0.686071
$657$	−6.24585	−0.243674
$658$	−24.9979	−0.974520
$659$	−37.5553	−1.46295	−0.731473	−	0.681871i	$-0.761167\pi$
$659$	−37.5553	−1.46295	−0.731473	+	0.681871i	$0.761167\pi$
$660$	0	0
$661$	−13.2427	−0.515080	−0.257540	−	0.966268i	$-0.582912\pi$
$661$	−13.2427	−0.515080	−0.257540	+	0.966268i	$0.582912\pi$
$662$	47.9232	1.86259
$663$	−26.1589	−1.01593
$664$	25.4989	0.989549
$665$	0	0
$666$	20.7241	0.803041
$667$	−7.18170	−0.278076
$668$	−15.9718	−0.617966
$669$	56.4396	2.18208
$670$	0	0
$671$	−7.20488	−0.278141
$672$	−23.3020	−0.898896
$673$	−2.67133	−0.102972	−0.0514861	−	0.998674i	$-0.516396\pi$
$673$	−2.67133	−0.102972	−0.0514861	+	0.998674i	$0.516396\pi$
$674$	17.0582	0.657058
$675$	0	0
$676$	−19.7991	−0.761505
$677$	−37.0811	−1.42514	−0.712571	−	0.701600i	$-0.752469\pi$
$677$	−37.0811	−1.42514	−0.712571	+	0.701600i	$0.752469\pi$
$678$	8.05282	0.309267
$679$	−21.9543	−0.842530
$680$	0	0
$681$	−8.01058	−0.306966
$682$	10.9392	0.418882
$683$	−26.2074	−1.00280	−0.501400	−	0.865216i	$-0.667181\pi$
$683$	−26.2074	−1.00280	−0.501400	+	0.865216i	$0.667181\pi$
$684$	35.2809	1.34900
$685$	0	0
$686$	36.7546	1.40330
$687$	−53.7655	−2.05128
$688$	3.78710	0.144382
$689$	32.6172	1.24262
$690$	0	0
$691$	28.7324	1.09303	0.546516	−	0.837448i	$-0.315954\pi$
$691$	28.7324	1.09303	0.546516	+	0.837448i	$0.315954\pi$
$692$	−38.8124	−1.47543
$693$	15.2049	0.577586
$694$	24.6907	0.937246
$695$	0	0
$696$	20.6675	0.783400
$697$	47.1825	1.78716
$698$	−2.06845	−0.0782919
$699$	4.28053	0.161905
$700$	0	0
$701$	−50.2576	−1.89820	−0.949102	−	0.314968i	$-0.898006\pi$
$701$	−50.2576	−1.89820	−0.949102	+	0.314968i	$0.898006\pi$
$702$	−9.83480	−0.371190
$703$	24.8107	0.935754
$704$	62.9615	2.37295
$705$	0	0
$706$	55.7160	2.09690
$707$	−22.8360	−0.858837
$708$	−4.29111	−0.161270
$709$	17.5518	0.659173	0.329587	−	0.944125i	$-0.393091\pi$
$709$	17.5518	0.659173	0.329587	+	0.944125i	$0.393091\pi$
$710$	0	0
$711$	15.0152	0.563113
$712$	14.3163	0.536527
$713$	−1.38995	−0.0520540
$714$	−32.7110	−1.22418
$715$	0	0
$716$	30.5162	1.14044
$717$	−5.25479	−0.196244
$718$	−4.56188	−0.170248
$719$	−31.4309	−1.17217	−0.586087	−	0.810248i	$-0.699332\pi$
$719$	−31.4309	−1.17217	−0.586087	+	0.810248i	$0.699332\pi$
$720$	0	0
$721$	4.23325	0.157654
$722$	30.7628	1.14487
$723$	14.4732	0.538262
$724$	40.6408	1.51040
$725$	0	0
$726$	−69.5137	−2.57990
$727$	33.1665	1.23008	0.615038	−	0.788497i	$-0.289141\pi$
$727$	33.1665	1.23008	0.615038	+	0.788497i	$0.289141\pi$
$728$	5.94327	0.220272
$729$	−11.0076	−0.407687
$730$	0	0
$731$	10.1687	0.376104
$732$	−9.21082	−0.340442
$733$	18.4272	0.680624	0.340312	−	0.940313i	$-0.389467\pi$
$733$	18.4272	0.680624	0.340312	+	0.940313i	$0.389467\pi$
$734$	−14.4385	−0.532934
$735$	0	0
$736$	−10.2273	−0.376984
$737$	−74.7718	−2.75426
$738$	−48.0557	−1.76896
$739$	43.3750	1.59558	0.797788	−	0.602938i	$-0.206003\pi$
$739$	43.3750	1.59558	0.797788	+	0.602938i	$0.206003\pi$
$740$	0	0
$741$	31.8969	1.17176
$742$	40.7870	1.49734
$743$	17.6531	0.647631	0.323815	−	0.946120i	$-0.395034\pi$
$743$	17.6531	0.647631	0.323815	+	0.946120i	$0.395034\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	29.8885	1.09430
$747$	31.8251	1.16442
$748$	65.9239	2.41042
$749$	17.4110	0.636185
$750$	0	0
$751$	−28.3786	−1.03555	−0.517775	−	0.855517i	$-0.673240\pi$
$751$	−28.3786	−1.03555	−0.517775	+	0.855517i	$0.673240\pi$
$752$	−14.4098	−0.525470
$753$	47.5944	1.73444
$754$	27.5742	1.00419
$755$	0	0
$756$	−7.17524	−0.260961
$757$	18.9234	0.687784	0.343892	−	0.939009i	$-0.388255\pi$
$757$	18.9234	0.687784	0.343892	+	0.939009i	$0.388255\pi$
$758$	−66.8657	−2.42867
$759$	15.8103	0.573877
$760$	0	0
$761$	10.1107	0.366512	0.183256	−	0.983065i	$-0.441336\pi$
$761$	10.1107	0.366512	0.183256	+	0.983065i	$0.441336\pi$
$762$	18.1745	0.658392
$763$	11.4951	0.416149
$764$	−49.3628	−1.78588
$765$	0	0
$766$	69.9784	2.52842
$767$	−1.63753	−0.0591278
$768$	7.02243	0.253400
$769$	4.47770	0.161470	0.0807349	−	0.996736i	$-0.474273\pi$
$769$	4.47770	0.161470	0.0807349	+	0.996736i	$0.474273\pi$
$770$	0	0
$771$	−19.4275	−0.699666
$772$	−53.7544	−1.93466
$773$	21.3747	0.768795	0.384398	−	0.923168i	$-0.374409\pi$
$773$	21.3747	0.768795	0.384398	+	0.923168i	$0.374409\pi$
$774$	−10.3569	−0.372272
$775$	0	0
$776$	27.7299	0.995447
$777$	13.6696	0.490393
$778$	−5.54236	−0.198703
$779$	−57.5321	−2.06130
$780$	0	0
$781$	14.0228	0.501774
$782$	−14.3569	−0.513403
$783$	−9.52179	−0.340281
$784$	8.89749	0.317768
$785$	0	0
$786$	41.5369	1.48157
$787$	36.0634	1.28552	0.642761	−	0.766067i	$-0.277789\pi$
$787$	36.0634	1.28552	0.642761	+	0.766067i	$0.277789\pi$
$788$	−8.77768	−0.312692
$789$	64.7581	2.30545
$790$	0	0
$791$	2.24201	0.0797169
$792$	−19.2049	−0.682416
$793$	−3.51494	−0.124819
$794$	−20.7676	−0.737014
$795$	0	0
$796$	−11.3113	−0.400919
$797$	−16.8981	−0.598563	−0.299281	−	0.954165i	$-0.596747\pi$
$797$	−16.8981	−0.598563	−0.299281	+	0.954165i	$0.596747\pi$
$798$	39.8863	1.41196
$799$	−38.6916	−1.36881
$800$	0	0
$801$	17.8682	0.631340
$802$	−40.9269	−1.44518
$803$	14.2306	0.502188
$804$	−95.5893	−3.37118
$805$	0	0
$806$	5.33672	0.187978
$807$	43.8251	1.54272
$808$	28.8436	1.01471
$809$	1.58984	0.0558957	0.0279478	−	0.999609i	$-0.491103\pi$
$809$	1.58984	0.0558957	0.0279478	+	0.999609i	$0.491103\pi$
$810$	0	0
$811$	17.4096	0.611334	0.305667	−	0.952139i	$-0.401121\pi$
$811$	17.4096	0.611334	0.305667	+	0.952139i	$0.401121\pi$
$812$	20.1175	0.705986
$813$	31.4233	1.10206
$814$	−47.2180	−1.65499
$815$	0	0
$816$	−18.8559	−0.660088
$817$	−12.3993	−0.433796
$818$	41.9442	1.46654
$819$	7.41777	0.259198
$820$	0	0
$821$	−4.16391	−0.145321	−0.0726607	−	0.997357i	$-0.523149\pi$
$821$	−4.16391	−0.145321	−0.0726607	+	0.997357i	$0.523149\pi$
$822$	112.979	3.94060
$823$	14.7701	0.514854	0.257427	−	0.966298i	$-0.417125\pi$
$823$	14.7701	0.514854	0.257427	+	0.966298i	$0.417125\pi$
$824$	−5.34690	−0.186268
$825$	0	0
$826$	−2.04769	−0.0712483
$827$	2.50439	0.0870863	0.0435432	−	0.999052i	$-0.486135\pi$
$827$	2.50439	0.0870863	0.0435432	+	0.999052i	$0.486135\pi$
$828$	8.53143	0.296488
$829$	33.1956	1.15293	0.576465	−	0.817122i	$-0.304432\pi$
$829$	33.1956	1.15293	0.576465	+	0.817122i	$0.304432\pi$
$830$	0	0
$831$	30.3923	1.05430
$832$	30.7161	1.06489
$833$	23.8906	0.827761
$834$	86.6654	3.00098
$835$	0	0
$836$	−80.3844	−2.78015
$837$	−1.84285	−0.0636983
$838$	57.7883	1.99626
$839$	10.5316	0.363592	0.181796	−	0.983336i	$-0.441809\pi$
$839$	10.5316	0.363592	0.181796	+	0.983336i	$0.441809\pi$
$840$	0	0
$841$	−2.30337	−0.0794265
$842$	42.8482	1.47665
$843$	−39.2543	−1.35199
$844$	5.11365	0.176019
$845$	0	0
$846$	39.4077	1.35486
$847$	−19.3536	−0.664996
$848$	23.5112	0.807378
$849$	−1.26868	−0.0435411
$850$	0	0
$851$	5.99959	0.205663
$852$	17.9269	0.614166
$853$	−38.3367	−1.31262	−0.656311	−	0.754490i	$-0.727884\pi$
$853$	−38.3367	−1.31262	−0.656311	+	0.754490i	$0.727884\pi$
$854$	−4.39534	−0.150406
$855$	0	0
$856$	−21.9914	−0.751651
$857$	−6.68112	−0.228223	−0.114111	−	0.993468i	$-0.536402\pi$
$857$	−6.68112	−0.228223	−0.114111	+	0.993468i	$0.536402\pi$
$858$	−60.7038	−2.07239
$859$	14.0300	0.478699	0.239349	−	0.970933i	$-0.423066\pi$
$859$	14.0300	0.478699	0.239349	+	0.970933i	$0.423066\pi$
$860$	0	0
$861$	−31.6975	−1.08025
$862$	−62.5492	−2.13043
$863$	6.17370	0.210155	0.105078	−	0.994464i	$-0.466491\pi$
$863$	6.17370	0.210155	0.105078	+	0.994464i	$0.466491\pi$
$864$	−13.5598	−0.461314
$865$	0	0
$866$	10.5171	0.357385
$867$	−11.8969	−0.404039
$868$	3.89355	0.132156
$869$	−34.2108	−1.16052
$870$	0	0
$871$	−36.4778	−1.23600
$872$	−14.5191	−0.491679
$873$	34.6096	1.17136
$874$	17.5062	0.592155
$875$	0	0
$876$	18.1926	0.614672
$877$	26.8323	0.906063	0.453031	−	0.891495i	$-0.350343\pi$
$877$	26.8323	0.906063	0.453031	+	0.891495i	$0.350343\pi$
$878$	−75.6555	−2.55325
$879$	24.3291	0.820601
$880$	0	0
$881$	1.34933	0.0454600	0.0227300	−	0.999742i	$-0.492764\pi$
$881$	1.34933	0.0454600	0.0227300	+	0.999742i	$0.492764\pi$
$882$	−24.3328	−0.819327
$883$	2.30160	0.0774549	0.0387274	−	0.999250i	$-0.487670\pi$
$883$	2.30160	0.0774549	0.0387274	+	0.999250i	$0.487670\pi$
$884$	32.1613	1.08170
$885$	0	0
$886$	−69.1288	−2.32243
$887$	−28.3102	−0.950562	−0.475281	−	0.879834i	$-0.657654\pi$
$887$	−28.3102	−0.950562	−0.475281	+	0.879834i	$0.657654\pi$
$888$	−17.2657	−0.579397
$889$	5.06003	0.169708
$890$	0	0
$891$	53.7794	1.80168
$892$	−69.3902	−2.32336
$893$	47.1787	1.57877
$894$	−64.4001	−2.15386
$895$	0	0
$896$	17.9551	0.599839
$897$	7.71313	0.257534
$898$	−52.9196	−1.76595
$899$	5.16688	0.172325
$900$	0	0
$901$	63.1299	2.10316
$902$	109.491	3.64565
$903$	−6.83142	−0.227336
$904$	−2.83183	−0.0941852
$905$	0	0
$906$	31.6734	1.05228
$907$	34.3106	1.13926	0.569632	−	0.821900i	$-0.307086\pi$
$907$	34.3106	1.13926	0.569632	+	0.821900i	$0.307086\pi$
$908$	9.84869	0.326840
$909$	35.9996	1.19403
$910$	0	0
$911$	50.9606	1.68840	0.844200	−	0.536028i	$-0.180076\pi$
$911$	50.9606	1.68840	0.844200	+	0.536028i	$0.180076\pi$
$912$	22.9920	0.761341
$913$	−72.5108	−2.39976
$914$	−28.1926	−0.932529
$915$	0	0
$916$	66.1026	2.18409
$917$	11.5644	0.381891
$918$	−19.0350	−0.628250
$919$	34.8768	1.15048	0.575239	−	0.817985i	$-0.304909\pi$
$919$	34.8768	1.15048	0.575239	+	0.817985i	$0.304909\pi$
$920$	0	0
$921$	−19.1669	−0.631570
$922$	66.9876	2.20612
$923$	6.84108	0.225177
$924$	−44.2881	−1.45697
$925$	0	0
$926$	−24.9239	−0.819052
$927$	−6.67345	−0.219185
$928$	38.0181	1.24801
$929$	−31.5112	−1.03385	−0.516925	−	0.856031i	$-0.672923\pi$
$929$	−31.5112	−1.03385	−0.516925	+	0.856031i	$0.672923\pi$
$930$	0	0
$931$	−29.1311	−0.954733
$932$	−5.26275	−0.172387
$933$	−54.4601	−1.78294
$934$	−39.0224	−1.27685
$935$	0	0
$936$	−9.36919	−0.306242
$937$	−32.4318	−1.05950	−0.529751	−	0.848153i	$-0.677715\pi$
$937$	−32.4318	−1.05950	−0.529751	+	0.848153i	$0.677715\pi$
$938$	−45.6146	−1.48937
$939$	9.50546	0.310199
$940$	0	0
$941$	−58.2556	−1.89908	−0.949539	−	0.313648i	$-0.898449\pi$
$941$	−58.2556	−1.89908	−0.949539	+	0.313648i	$0.898449\pi$
$942$	60.0224	1.95563
$943$	−13.9121	−0.453040
$944$	−1.18037	−0.0384177
$945$	0	0
$946$	23.5974	0.767217
$947$	−4.71660	−0.153269	−0.0766344	−	0.997059i	$-0.524417\pi$
$947$	−4.71660	−0.153269	−0.0766344	+	0.997059i	$0.524417\pi$
$948$	−43.7355	−1.42046
$949$	6.94248	0.225362
$950$	0	0
$951$	−38.6357	−1.25285
$952$	11.5031	0.372816
$953$	−45.8332	−1.48468	−0.742341	−	0.670022i	$-0.766284\pi$
$953$	−45.8332	−1.48468	−0.742341	+	0.670022i	$0.766284\pi$
$954$	−64.2983	−2.08173
$955$	0	0
$956$	6.46055	0.208949
$957$	−58.7718	−1.89982
$958$	−12.5518	−0.405530
$959$	31.4550	1.01573
$960$	0	0
$961$	1.00000	0.0322581
$962$	−23.0355	−0.742695
$963$	−27.4474	−0.884480
$964$	−17.7942	−0.573112
$965$	0	0
$966$	9.64508	0.310325
$967$	−0.784541	−0.0252291	−0.0126146	−	0.999920i	$-0.504015\pi$
$967$	−0.784541	−0.0252291	−0.0126146	+	0.999920i	$0.504015\pi$
$968$	24.4450	0.785691
$969$	61.7357	1.98324
$970$	0	0
$971$	−28.2625	−0.906986	−0.453493	−	0.891260i	$-0.649822\pi$
$971$	−28.2625	−0.906986	−0.453493	+	0.891260i	$0.649822\pi$
$972$	53.2657	1.70850
$973$	24.1288	0.773534
$974$	−6.32823	−0.202769
$975$	0	0
$976$	−2.53364	−0.0811000
$977$	33.6354	1.07609	0.538046	−	0.842916i	$-0.319163\pi$
$977$	33.6354	1.07609	0.538046	+	0.842916i	$0.319163\pi$
$978$	1.28019	0.0409358
$979$	−40.7110	−1.30113
$980$	0	0
$981$	−18.1213	−0.578568
$982$	35.8234	1.14317
$983$	32.3523	1.03188	0.515939	−	0.856625i	$-0.327443\pi$
$983$	32.3523	1.03188	0.515939	+	0.856625i	$0.327443\pi$
$984$	40.0363	1.27631
$985$	0	0
$986$	53.3693	1.69962
$987$	25.9933	0.827374
$988$	−39.2159	−1.24763
$989$	−2.99832	−0.0953412
$990$	0	0
$991$	−16.2184	−0.515195	−0.257598	−	0.966252i	$-0.582931\pi$
$991$	−16.2184	−0.515195	−0.257598	+	0.966252i	$0.582931\pi$
$992$	7.35805	0.233618
$993$	−49.8313	−1.58135
$994$	8.55461	0.271336
$995$	0	0
$996$	−92.6987	−2.93727
$997$	−43.0862	−1.36455	−0.682277	−	0.731093i	$-0.739010\pi$
$997$	−43.0862	−1.36455	−0.682277	+	0.731093i	$0.739010\pi$
$998$	68.4474	2.16666
$999$	7.95451	0.251670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.e.1.4		4
3.2	odd	2		6975.2.a.bn.1.1		4
5.2	odd	4		775.2.b.f.249.7		8
5.3	odd	4		775.2.b.f.249.2		8
5.4	even	2		155.2.a.e.1.1	✓	4
15.14	odd	2		1395.2.a.l.1.4		4
20.19	odd	2		2480.2.a.x.1.1		4
35.34	odd	2		7595.2.a.s.1.1		4
40.19	odd	2		9920.2.a.cg.1.4		4
40.29	even	2		9920.2.a.cb.1.1		4
155.154	odd	2		4805.2.a.n.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.e.1.1	✓	4	5.4	even	2
775.2.a.e.1.4		4	1.1	even	1	trivial
775.2.b.f.249.2		8	5.3	odd	4
775.2.b.f.249.7		8	5.2	odd	4
1395.2.a.l.1.4		4	15.14	odd	2
2480.2.a.x.1.1		4	20.19	odd	2
4805.2.a.n.1.1		4	155.154	odd	2
6975.2.a.bn.1.1		4	3.2	odd	2
7595.2.a.s.1.1		4	35.34	odd	2
9920.2.a.cb.1.1		4	40.29	even	2
9920.2.a.cg.1.4		4	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -4.99239 q^{6} -1.38995 q^{7} +1.75561 q^{8} +2.19117 q^{9} +O(q^{10})\)	\(q+2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -4.99239 q^{6} -1.38995 q^{7} +1.75561 q^{8} +2.19117 q^{9} -4.99239 q^{11} -6.38234 q^{12} -2.43556 q^{13} -3.04561 q^{14} -1.75561 q^{16} -4.71397 q^{17} +4.80122 q^{18} +5.74800 q^{19} +3.16688 q^{21} -10.9392 q^{22} +1.38995 q^{23} -4.00000 q^{24} -5.33672 q^{26} +1.84285 q^{27} -3.89355 q^{28} -5.16688 q^{29} -1.00000 q^{31} -7.35805 q^{32} +11.3747 q^{33} -10.3291 q^{34} +6.13794 q^{36} +4.31641 q^{37} +12.5948 q^{38} +5.54922 q^{39} -10.0091 q^{41} +6.93916 q^{42} -2.15715 q^{43} -13.9848 q^{44} +3.04561 q^{46} +8.20785 q^{47} +4.00000 q^{48} -5.06804 q^{49} +10.7404 q^{51} -6.82254 q^{52} -13.3921 q^{53} +4.03800 q^{54} -2.44020 q^{56} -13.0963 q^{57} -11.3215 q^{58} +0.672342 q^{59} +1.44317 q^{61} -2.19117 q^{62} -3.04561 q^{63} -12.6115 q^{64} +24.9239 q^{66} +14.9772 q^{67} -13.2049 q^{68} -3.16688 q^{69} -2.80883 q^{71} +3.84683 q^{72} -2.85046 q^{73} +9.45799 q^{74} +16.1014 q^{76} +6.93916 q^{77} +12.1593 q^{78} +6.85258 q^{79} -10.7723 q^{81} -21.9316 q^{82} +14.5243 q^{83} +8.87112 q^{84} -4.72667 q^{86} +11.7723 q^{87} -8.76467 q^{88} +8.15462 q^{89} +3.38531 q^{91} +3.89355 q^{92} +2.27841 q^{93} +17.9848 q^{94} +16.7647 q^{96} +15.7951 q^{97} -11.1049 q^{98} -10.9392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9	\( 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{11} - 6 q^{12} - 10 q^{13} - 16 q^{14} + 3 q^{16} - 11 q^{17} + 13 q^{18} - 3 q^{19} - 8 q^{22} + 2 q^{23} - 16 q^{24} + 2 q^{26} - q^{27} + 24 q^{28} - 8 q^{29} - 4 q^{31} - 7 q^{32} + 10 q^{33} - 2 q^{34} - 5 q^{36} - 3 q^{37} + 22 q^{38} - 10 q^{39} - 11 q^{41} - 8 q^{42} - 17 q^{43} - 24 q^{44} + 16 q^{46} + 10 q^{47} + 16 q^{48} + 16 q^{49} + q^{51} - 22 q^{52} - 13 q^{53} + 4 q^{54} - 24 q^{56} - 25 q^{57} + 10 q^{58} - 3 q^{59} + 22 q^{61} + q^{62} - 16 q^{63} - 9 q^{64} + 32 q^{66} + 12 q^{67} - 28 q^{68} - 21 q^{71} + 13 q^{72} - 19 q^{73} - 2 q^{74} + 2 q^{76} - 8 q^{77} + 20 q^{78} - 2 q^{79} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 36 q^{84} + 8 q^{86} + 24 q^{87} + 4 q^{88} - 10 q^{89} - 4 q^{91} - 24 q^{92} + q^{93} + 40 q^{94} + 28 q^{96} - 4 q^{97} - 37 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^11 - 6 * q^12 - 10 * q^13 - 16 * q^14 + 3 * q^16 - 11 * q^17 + 13 * q^18 - 3 * q^19 - 8 * q^22 + 2 * q^23 - 16 * q^24 + 2 * q^26 - q^27 + 24 * q^28 - 8 * q^29 - 4 * q^31 - 7 * q^32 + 10 * q^33 - 2 * q^34 - 5 * q^36 - 3 * q^37 + 22 * q^38 - 10 * q^39 - 11 * q^41 - 8 * q^42 - 17 * q^43 - 24 * q^44 + 16 * q^46 + 10 * q^47 + 16 * q^48 + 16 * q^49 + q^51 - 22 * q^52 - 13 * q^53 + 4 * q^54 - 24 * q^56 - 25 * q^57 + 10 * q^58 - 3 * q^59 + 22 * q^61 + q^62 - 16 * q^63 - 9 * q^64 + 32 * q^66 + 12 * q^67 - 28 * q^68 - 21 * q^71 + 13 * q^72 - 19 * q^73 - 2 * q^74 + 2 * q^76 - 8 * q^77 + 20 * q^78 - 2 * q^79 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 36 * q^84 + 8 * q^86 + 24 * q^87 + 4 * q^88 - 10 * q^89 - 4 * q^91 - 24 * q^92 + q^93 + 40 * q^94 + 28 * q^96 - 4 * q^97 - 37 * q^98 - 8 * q^99

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