LMFDB - Embedded newform 950.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.993.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 3 $ x^3 - x^2 - 6*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.480031$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +0.960061 q^{11} +0.519969 q^{12} +2.24960 q^{13} +4.76957 q^{14} +1.00000 q^{16} -0.249601 q^{17} -2.72963 q^{18} +1.00000 q^{19} +2.48003 q^{21} +0.960061 q^{22} -9.01917 q^{23} +0.519969 q^{24} +2.24960 q^{26} -2.97923 q^{27} +4.76957 q^{28} +6.24960 q^{29} +2.96006 q^{31} +1.00000 q^{32} +0.499202 q^{33} -0.249601 q^{34} -2.72963 q^{36} -0.0399387 q^{37} +1.00000 q^{38} +1.16972 q^{39} +2.48003 q^{42} -4.96006 q^{43} +0.960061 q^{44} -9.01917 q^{46} +9.49920 q^{47} +0.519969 q^{48} +15.7488 q^{49} -0.129785 q^{51} +2.24960 q^{52} -6.84945 q^{53} -2.97923 q^{54} +4.76957 q^{56} +0.519969 q^{57} +6.24960 q^{58} -14.5583 q^{59} +7.53914 q^{61} +2.96006 q^{62} -13.0192 q^{63} +1.00000 q^{64} +0.499202 q^{66} +5.72963 q^{67} -0.249601 q^{68} -4.68969 q^{69} -9.61902 q^{71} -2.72963 q^{72} -12.0591 q^{73} -0.0399387 q^{74} +1.00000 q^{76} +4.57908 q^{77} +1.16972 q^{78} +6.07988 q^{79} +6.63979 q^{81} +7.45926 q^{83} +2.48003 q^{84} -4.96006 q^{86} +3.24960 q^{87} +0.960061 q^{88} +4.07988 q^{89} +10.7296 q^{91} -9.01917 q^{92} +1.53914 q^{93} +9.49920 q^{94} +0.519969 q^{96} -18.4193 q^{97} +15.7488 q^{98} -2.62061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} + 3 q^{16} + 12 q^{17} + 5 q^{18} + 3 q^{19} + 7 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24} - 6 q^{26} + 17 q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{31} + 3 q^{32} - 24 q^{33} + 12 q^{34} + 5 q^{36} - q^{37} + 3 q^{38} - 11 q^{39} + 7 q^{42} - 14 q^{43} + 2 q^{44} - 2 q^{46} + 3 q^{47} + 2 q^{48} + 9 q^{49} + 15 q^{51} - 6 q^{52} - 10 q^{53} + 17 q^{54} + 2 q^{56} + 2 q^{57} + 6 q^{58} + 6 q^{59} - 2 q^{61} + 8 q^{62} - 14 q^{63} + 3 q^{64} - 24 q^{66} + 4 q^{67} + 12 q^{68} - 6 q^{71} + 5 q^{72} - 12 q^{73} - q^{74} + 3 q^{76} - 10 q^{77} - 11 q^{78} + 20 q^{79} + 23 q^{81} - 4 q^{83} + 7 q^{84} - 14 q^{86} - 3 q^{87} + 2 q^{88} + 14 q^{89} + 19 q^{91} - 2 q^{92} - 20 q^{93} + 3 q^{94} + 2 q^{96} - 28 q^{97} + 9 q^{98} - 36 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 + 3 * q^16 + 12 * q^17 + 5 * q^18 + 3 * q^19 + 7 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 - 6 * q^26 + 17 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^31 + 3 * q^32 - 24 * q^33 + 12 * q^34 + 5 * q^36 - q^37 + 3 * q^38 - 11 * q^39 + 7 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^46 + 3 * q^47 + 2 * q^48 + 9 * q^49 + 15 * q^51 - 6 * q^52 - 10 * q^53 + 17 * q^54 + 2 * q^56 + 2 * q^57 + 6 * q^58 + 6 * q^59 - 2 * q^61 + 8 * q^62 - 14 * q^63 + 3 * q^64 - 24 * q^66 + 4 * q^67 + 12 * q^68 - 6 * q^71 + 5 * q^72 - 12 * q^73 - q^74 + 3 * q^76 - 10 * q^77 - 11 * q^78 + 20 * q^79 + 23 * q^81 - 4 * q^83 + 7 * q^84 - 14 * q^86 - 3 * q^87 + 2 * q^88 + 14 * q^89 + 19 * q^91 - 2 * q^92 - 20 * q^93 + 3 * q^94 + 2 * q^96 - 28 * q^97 + 9 * q^98 - 36 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.519969	0.300204	0.150102	−	0.988670i	$-0.452040\pi$
$3$	0.519969	0.300204	0.150102	+	0.988670i	$0.452040\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.519969	0.212277
$7$	4.76957	1.80273	0.901364	−	0.433062i	$-0.142567\pi$
$7$	4.76957	1.80273	0.901364	+	0.433062i	$0.142567\pi$
$8$	1.00000	0.353553
$9$	−2.72963	−0.909877
$10$	0	0
$11$	0.960061	0.289469	0.144735	−	0.989471i	$-0.453767\pi$
$11$	0.960061	0.289469	0.144735	+	0.989471i	$0.453767\pi$
$12$	0.519969	0.150102
$13$	2.24960	0.623927	0.311964	−	0.950094i	$-0.399013\pi$
$13$	2.24960	0.623927	0.311964	+	0.950094i	$0.399013\pi$
$14$	4.76957	1.27472
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.249601	−0.0605372	−0.0302686	−	0.999542i	$-0.509636\pi$
$17$	−0.249601	−0.0605372	−0.0302686	+	0.999542i	$0.509636\pi$
$18$	−2.72963	−0.643380
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	2.48003	0.541187
$22$	0.960061	0.204686
$23$	−9.01917	−1.88063	−0.940314	−	0.340309i	$-0.889468\pi$
$23$	−9.01917	−1.88063	−0.940314	+	0.340309i	$0.889468\pi$
$24$	0.519969	0.106138
$25$	0	0
$26$	2.24960	0.441183
$27$	−2.97923	−0.573354
$28$	4.76957	0.901364
$29$	6.24960	1.16052	0.580261	−	0.814431i	$-0.302951\pi$
$29$	6.24960	1.16052	0.580261	+	0.814431i	$0.302951\pi$
$30$	0	0
$31$	2.96006	0.531643	0.265821	−	0.964022i	$-0.414357\pi$
$31$	2.96006	0.531643	0.265821	+	0.964022i	$0.414357\pi$
$32$	1.00000	0.176777
$33$	0.499202	0.0869000
$34$	−0.249601	−0.0428063
$35$	0	0
$36$	−2.72963	−0.454939
$37$	−0.0399387	−0.00656589	−0.00328294	−	0.999995i	$-0.501045\pi$
$37$	−0.0399387	−0.00656589	−0.00328294	+	0.999995i	$0.501045\pi$
$38$	1.00000	0.162221
$39$	1.16972	0.187306
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	2.48003	0.382677
$43$	−4.96006	−0.756402	−0.378201	−	0.925723i	$-0.623457\pi$
$43$	−4.96006	−0.756402	−0.378201	+	0.925723i	$0.623457\pi$
$44$	0.960061	0.144735
$45$	0	0
$46$	−9.01917	−1.32980
$47$	9.49920	1.38560	0.692801	−	0.721129i	$-0.256377\pi$
$47$	9.49920	1.38560	0.692801	+	0.721129i	$0.256377\pi$
$48$	0.519969	0.0750511
$49$	15.7488	2.24983
$50$	0	0
$51$	−0.129785	−0.0181735
$52$	2.24960	0.311964
$53$	−6.84945	−0.940844	−0.470422	−	0.882442i	$-0.655898\pi$
$53$	−6.84945	−0.940844	−0.470422	+	0.882442i	$0.655898\pi$
$54$	−2.97923	−0.405422
$55$	0	0
$56$	4.76957	0.637361
$57$	0.519969	0.0688716
$58$	6.24960	0.820613
$59$	−14.5583	−1.89533	−0.947665	−	0.319265i	$-0.896564\pi$
$59$	−14.5583	−1.89533	−0.947665	+	0.319265i	$0.896564\pi$
$60$	0	0
$61$	7.53914	0.965288	0.482644	−	0.875817i	$-0.339676\pi$
$61$	7.53914	0.965288	0.482644	+	0.875817i	$0.339676\pi$
$62$	2.96006	0.375928
$63$	−13.0192	−1.64026
$64$	1.00000	0.125000
$65$	0	0
$66$	0.499202	0.0614476
$67$	5.72963	0.699986	0.349993	−	0.936752i	$-0.386184\pi$
$67$	5.72963	0.699986	0.349993	+	0.936752i	$0.386184\pi$
$68$	−0.249601	−0.0302686
$69$	−4.68969	−0.564573
$70$	0	0
$71$	−9.61902	−1.14157	−0.570784	−	0.821100i	$-0.693361\pi$
$71$	−9.61902	−1.14157	−0.570784	+	0.821100i	$0.693361\pi$
$72$	−2.72963	−0.321690
$73$	−12.0591	−1.41141	−0.705706	−	0.708505i	$-0.749370\pi$
$73$	−12.0591	−1.41141	−0.705706	+	0.708505i	$0.749370\pi$
$74$	−0.0399387	−0.00464278
$75$	0	0
$76$	1.00000	0.114708
$77$	4.57908	0.521835
$78$	1.16972	0.132445
$79$	6.07988	0.684040	0.342020	−	0.939693i	$-0.388889\pi$
$79$	6.07988	0.684040	0.342020	+	0.939693i	$0.388889\pi$
$80$	0	0
$81$	6.63979	0.737754
$82$	0	0
$83$	7.45926	0.818761	0.409380	−	0.912364i	$-0.365745\pi$
$83$	7.45926	0.818761	0.409380	+	0.912364i	$0.365745\pi$
$84$	2.48003	0.270594
$85$	0	0
$86$	−4.96006	−0.534857
$87$	3.24960	0.348394
$88$	0.960061	0.102343
$89$	4.07988	0.432466	0.216233	−	0.976342i	$-0.430623\pi$
$89$	4.07988	0.432466	0.216233	+	0.976342i	$0.430623\pi$
$90$	0	0
$91$	10.7296	1.12477
$92$	−9.01917	−0.940314
$93$	1.53914	0.159602
$94$	9.49920	0.979768
$95$	0	0
$96$	0.519969	0.0530692
$97$	−18.4193	−1.87020	−0.935100	−	0.354385i	$-0.884690\pi$
$97$	−18.4193	−1.87020	−0.935100	+	0.354385i	$0.884690\pi$
$98$	15.7488	1.59087
$99$	−2.62061	−0.263382
$100$	0	0
$101$	5.53914	0.551165	0.275583	−	0.961277i	$-0.411129\pi$
$101$	5.53914	0.551165	0.275583	+	0.961277i	$0.411129\pi$
$102$	−0.129785	−0.0128506
$103$	6.57908	0.648256	0.324128	−	0.946013i	$-0.394929\pi$
$103$	6.57908	0.648256	0.324128	+	0.946013i	$0.394929\pi$
$104$	2.24960	0.220592
$105$	0	0
$106$	−6.84945	−0.665277
$107$	−14.9086	−1.44126	−0.720632	−	0.693317i	$-0.756148\pi$
$107$	−14.9086	−1.44126	−0.720632	+	0.693317i	$0.756148\pi$
$108$	−2.97923	−0.286677
$109$	4.76957	0.456842	0.228421	−	0.973562i	$-0.426644\pi$
$109$	4.76957	0.456842	0.228421	+	0.973562i	$0.426644\pi$
$110$	0	0
$111$	−0.0207669	−0.00197111
$112$	4.76957	0.450682
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0.519969	0.0486996
$115$	0	0
$116$	6.24960	0.580261
$117$	−6.14058	−0.567697
$118$	−14.5583	−1.34020
$119$	−1.19049	−0.109132
$120$	0	0
$121$	−10.0783	−0.916207
$122$	7.53914	0.682562
$123$	0	0
$124$	2.96006	0.265821
$125$	0	0
$126$	−13.0192	−1.15984
$127$	−17.9585	−1.59356	−0.796778	−	0.604272i	$-0.793464\pi$
$127$	−17.9585	−1.59356	−0.796778	+	0.604272i	$0.793464\pi$
$128$	1.00000	0.0883883
$129$	−2.57908	−0.227075
$130$	0	0
$131$	−6.96006	−0.608103	−0.304052	−	0.952656i	$-0.598340\pi$
$131$	−6.96006	−0.608103	−0.304052	+	0.952656i	$0.598340\pi$
$132$	0.499202	0.0434500
$133$	4.76957	0.413574
$134$	5.72963	0.494965
$135$	0	0
$136$	−0.249601	−0.0214031
$137$	−7.80951	−0.667211	−0.333606	−	0.942713i	$-0.608265\pi$
$137$	−7.80951	−0.667211	−0.333606	+	0.942713i	$0.608265\pi$
$138$	−4.68969	−0.399213
$139$	−16.0383	−1.36035	−0.680177	−	0.733048i	$-0.738097\pi$
$139$	−16.0383	−1.36035	−0.680177	+	0.733048i	$0.738097\pi$
$140$	0	0
$141$	4.93929	0.415964
$142$	−9.61902	−0.807210
$143$	2.15975	0.180608
$144$	−2.72963	−0.227469
$145$	0	0
$146$	−12.0591	−0.998019
$147$	8.18890	0.675409
$148$	−0.0399387	−0.00328294
$149$	−8.41932	−0.689738	−0.344869	−	0.938651i	$-0.612077\pi$
$149$	−8.41932	−0.689738	−0.344869	+	0.938651i	$0.612077\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	1.00000	0.0811107
$153$	0.681319	0.0550814
$154$	4.57908	0.368993
$155$	0	0
$156$	1.16972	0.0936529
$157$	−4.96006	−0.395856	−0.197928	−	0.980217i	$-0.563421\pi$
$157$	−4.96006	−0.395856	−0.197928	+	0.980217i	$0.563421\pi$
$158$	6.07988	0.483689
$159$	−3.56150	−0.282446
$160$	0	0
$161$	−43.0176	−3.39026
$162$	6.63979	0.521671
$163$	21.4593	1.68082	0.840410	−	0.541952i	$-0.182314\pi$
$163$	21.4593	1.68082	0.840410	+	0.541952i	$0.182314\pi$
$164$	0	0
$165$	0	0
$166$	7.45926	0.578951
$167$	11.0399	0.854296	0.427148	−	0.904182i	$-0.359518\pi$
$167$	11.0399	0.854296	0.427148	+	0.904182i	$0.359518\pi$
$168$	2.48003	0.191339
$169$	−7.93929	−0.610715
$170$	0	0
$171$	−2.72963	−0.208740
$172$	−4.96006	−0.378201
$173$	−16.9585	−1.28933	−0.644664	−	0.764466i	$-0.723003\pi$
$173$	−16.9585	−1.28933	−0.644664	+	0.764466i	$0.723003\pi$
$174$	3.24960	0.246352
$175$	0	0
$176$	0.960061	0.0723673
$177$	−7.56988	−0.568987
$178$	4.07988	0.305800
$179$	2.53914	0.189784	0.0948922	−	0.995488i	$-0.469749\pi$
$179$	2.53914	0.189784	0.0948922	+	0.995488i	$0.469749\pi$
$180$	0	0
$181$	−3.88018	−0.288412	−0.144206	−	0.989548i	$-0.546063\pi$
$181$	−3.88018	−0.288412	−0.144206	+	0.989548i	$0.546063\pi$
$182$	10.7296	0.795333
$183$	3.92012	0.289784
$184$	−9.01917	−0.664902
$185$	0	0
$186$	1.53914	0.112855
$187$	−0.239632	−0.0175237
$188$	9.49920	0.692801
$189$	−14.2097	−1.03360
$190$	0	0
$191$	2.05911	0.148992	0.0744960	−	0.997221i	$-0.476265\pi$
$191$	2.05911	0.148992	0.0744960	+	0.997221i	$0.476265\pi$
$192$	0.519969	0.0375256
$193$	8.46086	0.609026	0.304513	−	0.952508i	$-0.401506\pi$
$193$	8.46086	0.609026	0.304513	+	0.952508i	$0.401506\pi$
$194$	−18.4193	−1.32243
$195$	0	0
$196$	15.7488	1.12491
$197$	−13.9201	−0.991768	−0.495884	−	0.868389i	$-0.665156\pi$
$197$	−13.9201	−0.991768	−0.495884	+	0.868389i	$0.665156\pi$
$198$	−2.62061	−0.186239
$199$	−9.15055	−0.648665	−0.324333	−	0.945943i	$-0.605140\pi$
$199$	−9.15055	−0.648665	−0.324333	+	0.945943i	$0.605140\pi$
$200$	0	0
$201$	2.97923	0.210139
$202$	5.53914	0.389733
$203$	29.8079	2.09211
$204$	−0.129785	−0.00908677
$205$	0	0
$206$	6.57908	0.458386
$207$	24.6190	1.71114
$208$	2.24960	0.155982
$209$	0.960061	0.0664088
$210$	0	0
$211$	16.5200	1.13728	0.568641	−	0.822586i	$-0.307469\pi$
$211$	16.5200	1.13728	0.568641	+	0.822586i	$0.307469\pi$
$212$	−6.84945	−0.470422
$213$	−5.00160	−0.342704
$214$	−14.9086	−1.01913
$215$	0	0
$216$	−2.97923	−0.202711
$217$	14.1182	0.958407
$218$	4.76957	0.323036
$219$	−6.27037	−0.423712
$220$	0	0
$221$	−0.561503	−0.0377708
$222$	−0.0207669	−0.00139378
$223$	−9.03994	−0.605359	−0.302680	−	0.953092i	$-0.597881\pi$
$223$	−9.03994	−0.605359	−0.302680	+	0.953092i	$0.597881\pi$
$224$	4.76957	0.318680
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−0.350246	−0.0232466	−0.0116233	−	0.999932i	$-0.503700\pi$
$227$	−0.350246	−0.0232466	−0.0116233	+	0.999932i	$0.503700\pi$
$228$	0.519969	0.0344358
$229$	−8.07988	−0.533933	−0.266967	−	0.963706i	$-0.586021\pi$
$229$	−8.07988	−0.533933	−0.266967	+	0.963706i	$0.586021\pi$
$230$	0	0
$231$	2.38098	0.156657
$232$	6.24960	0.410306
$233$	4.92012	0.322328	0.161164	−	0.986928i	$-0.448475\pi$
$233$	4.92012	0.322328	0.161164	+	0.986928i	$0.448475\pi$
$234$	−6.14058	−0.401422
$235$	0	0
$236$	−14.5583	−0.947665
$237$	3.16135	0.205352
$238$	−1.19049	−0.0771680
$239$	2.98083	0.192814	0.0964069	−	0.995342i	$-0.469265\pi$
$239$	2.98083	0.192814	0.0964069	+	0.995342i	$0.469265\pi$
$240$	0	0
$241$	20.0383	1.29078	0.645392	−	0.763852i	$-0.276694\pi$
$241$	20.0383	1.29078	0.645392	+	0.763852i	$0.276694\pi$
$242$	−10.0783	−0.647857
$243$	12.3902	0.794831
$244$	7.53914	0.482644
$245$	0	0
$246$	0	0
$247$	2.24960	0.143139
$248$	2.96006	0.187964
$249$	3.87859	0.245796
$250$	0	0
$251$	−14.8802	−0.939229	−0.469614	−	0.882872i	$-0.655607\pi$
$251$	−14.8802	−0.939229	−0.469614	+	0.882872i	$0.655607\pi$
$252$	−13.0192	−0.820131
$253$	−8.65896	−0.544384
$254$	−17.9585	−1.12681
$255$	0	0
$256$	1.00000	0.0625000
$257$	11.0399	0.688652	0.344326	−	0.938850i	$-0.388107\pi$
$257$	11.0399	0.688652	0.344326	+	0.938850i	$0.388107\pi$
$258$	−2.57908	−0.160567
$259$	−0.190491	−0.0118365
$260$	0	0
$261$	−17.0591	−1.05593
$262$	−6.96006	−0.429994
$263$	3.84025	0.236800	0.118400	−	0.992966i	$-0.462224\pi$
$263$	3.84025	0.236800	0.118400	+	0.992966i	$0.462224\pi$
$264$	0.499202	0.0307238
$265$	0	0
$266$	4.76957	0.292441
$267$	2.12141	0.129828
$268$	5.72963	0.349993
$269$	23.1981	1.41441	0.707207	−	0.707007i	$-0.249955\pi$
$269$	23.1981	1.41441	0.707207	+	0.707007i	$0.249955\pi$
$270$	0	0
$271$	23.9792	1.45663	0.728317	−	0.685240i	$-0.240303\pi$
$271$	23.9792	1.45663	0.728317	+	0.685240i	$0.240303\pi$
$272$	−0.249601	−0.0151343
$273$	5.57908	0.337661
$274$	−7.80951	−0.471790
$275$	0	0
$276$	−4.68969	−0.282286
$277$	−24.6590	−1.48161	−0.740807	−	0.671718i	$-0.765556\pi$
$277$	−24.6590	−1.48161	−0.740807	+	0.671718i	$0.765556\pi$
$278$	−16.0383	−0.961916
$279$	−8.07988	−0.483730
$280$	0	0
$281$	−18.9984	−1.13335	−0.566675	−	0.823941i	$-0.691770\pi$
$281$	−18.9984	−1.13335	−0.566675	+	0.823941i	$0.691770\pi$
$282$	4.93929	0.294131
$283$	−29.0367	−1.72606	−0.863028	−	0.505156i	$-0.831435\pi$
$283$	−29.0367	−1.72606	−0.863028	+	0.505156i	$0.831435\pi$
$284$	−9.61902	−0.570784
$285$	0	0
$286$	2.15975	0.127709
$287$	0	0
$288$	−2.72963	−0.160845
$289$	−16.9377	−0.996335
$290$	0	0
$291$	−9.57748	−0.561442
$292$	−12.0591	−0.705706
$293$	−6.24960	−0.365106	−0.182553	−	0.983196i	$-0.558436\pi$
$293$	−6.24960	−0.365106	−0.182553	+	0.983196i	$0.558436\pi$
$294$	8.18890	0.477586
$295$	0	0
$296$	−0.0399387	−0.00232139
$297$	−2.86025	−0.165968
$298$	−8.41932	−0.487718
$299$	−20.2895	−1.17337
$300$	0	0
$301$	−23.6574	−1.36359
$302$	20.0000	1.15087
$303$	2.88018	0.165462
$304$	1.00000	0.0573539
$305$	0	0
$306$	0.681319	0.0389484
$307$	−12.5391	−0.715647	−0.357823	−	0.933789i	$-0.616481\pi$
$307$	−12.5391	−0.715647	−0.357823	+	0.933789i	$0.616481\pi$
$308$	4.57908	0.260917
$309$	3.42092	0.194609
$310$	0	0
$311$	7.84785	0.445011	0.222505	−	0.974931i	$-0.428576\pi$
$311$	7.84785	0.445011	0.222505	+	0.974931i	$0.428576\pi$
$312$	1.16972	0.0662226
$313$	−10.9884	−0.621103	−0.310552	−	0.950557i	$-0.600514\pi$
$313$	−10.9884	−0.621103	−0.310552	+	0.950557i	$0.600514\pi$
$314$	−4.96006	−0.279912
$315$	0	0
$316$	6.07988	0.342020
$317$	21.5567	1.21075	0.605373	−	0.795942i	$-0.293024\pi$
$317$	21.5567	1.21075	0.605373	+	0.795942i	$0.293024\pi$
$318$	−3.56150	−0.199719
$319$	6.00000	0.335936
$320$	0	0
$321$	−7.75199	−0.432674
$322$	−43.0176	−2.39728
$323$	−0.249601	−0.0138882
$324$	6.63979	0.368877
$325$	0	0
$326$	21.4593	1.18852
$327$	2.48003	0.137146
$328$	0	0
$329$	45.3071	2.49786
$330$	0	0
$331$	33.4876	1.84065	0.920324	−	0.391158i	$-0.127925\pi$
$331$	33.4876	1.84065	0.920324	+	0.391158i	$0.127925\pi$
$332$	7.45926	0.409380
$333$	0.109018	0.00597415
$334$	11.0399	0.604079
$335$	0	0
$336$	2.48003	0.135297
$337$	−5.69890	−0.310439	−0.155219	−	0.987880i	$-0.549608\pi$
$337$	−5.69890	−0.310439	−0.155219	+	0.987880i	$0.549608\pi$
$338$	−7.93929	−0.431841
$339$	−3.11982	−0.169445
$340$	0	0
$341$	2.84184	0.153894
$342$	−2.72963	−0.147602
$343$	41.7280	2.25310
$344$	−4.96006	−0.267429
$345$	0	0
$346$	−16.9585	−0.911693
$347$	0.239632	0.0128641	0.00643207	−	0.999979i	$-0.497953\pi$
$347$	0.239632	0.0128641	0.00643207	+	0.999979i	$0.497953\pi$
$348$	3.24960	0.174197
$349$	−17.2380	−0.922731	−0.461365	−	0.887210i	$-0.652640\pi$
$349$	−17.2380	−0.922731	−0.461365	+	0.887210i	$0.652640\pi$
$350$	0	0
$351$	−6.70209	−0.357731
$352$	0.960061	0.0511714
$353$	34.7280	1.84839	0.924193	−	0.381925i	$-0.124739\pi$
$353$	34.7280	1.84839	0.924193	+	0.381925i	$0.124739\pi$
$354$	−7.56988	−0.402334
$355$	0	0
$356$	4.07988	0.216233
$357$	−0.619019	−0.0327619
$358$	2.53914	0.134198
$359$	26.6689	1.40753	0.703766	−	0.710432i	$-0.251500\pi$
$359$	26.6689	1.40753	0.703766	+	0.710432i	$0.251500\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−3.88018	−0.203938
$363$	−5.24040	−0.275050
$364$	10.7296	0.562386
$365$	0	0
$366$	3.92012	0.204908
$367$	15.2380	0.795419	0.397710	−	0.917511i	$-0.369805\pi$
$367$	15.2380	0.795419	0.397710	+	0.917511i	$0.369805\pi$
$368$	−9.01917	−0.470157
$369$	0	0
$370$	0	0
$371$	−32.6689	−1.69609
$372$	1.53914	0.0798008
$373$	26.6382	1.37927	0.689637	−	0.724156i	$-0.257770\pi$
$373$	26.6382	1.37927	0.689637	+	0.724156i	$0.257770\pi$
$374$	−0.239632	−0.0123911
$375$	0	0
$376$	9.49920	0.489884
$377$	14.0591	0.724081
$378$	−14.2097	−0.730866
$379$	11.9693	0.614820	0.307410	−	0.951577i	$-0.400538\pi$
$379$	11.9693	0.614820	0.307410	+	0.951577i	$0.400538\pi$
$380$	0	0
$381$	−9.33785	−0.478393
$382$	2.05911	0.105353
$383$	9.84025	0.502813	0.251407	−	0.967882i	$-0.419107\pi$
$383$	9.84025	0.502813	0.251407	+	0.967882i	$0.419107\pi$
$384$	0.519969	0.0265346
$385$	0	0
$386$	8.46086	0.430646
$387$	13.5391	0.688233
$388$	−18.4193	−0.935100
$389$	−8.65896	−0.439027	−0.219513	−	0.975610i	$-0.570447\pi$
$389$	−8.65896	−0.439027	−0.219513	+	0.975610i	$0.570447\pi$
$390$	0	0
$391$	2.25120	0.113848
$392$	15.7488	0.795435
$393$	−3.61902	−0.182555
$394$	−13.9201	−0.701286
$395$	0	0
$396$	−2.62061	−0.131691
$397$	−28.9984	−1.45539	−0.727694	−	0.685902i	$-0.759408\pi$
$397$	−28.9984	−1.45539	−0.727694	+	0.685902i	$0.759408\pi$
$398$	−9.15055	−0.458676
$399$	2.48003	0.124157
$400$	0	0
$401$	22.6174	1.12946	0.564730	−	0.825276i	$-0.308980\pi$
$401$	22.6174	1.12946	0.564730	+	0.825276i	$0.308980\pi$
$402$	2.97923	0.148591
$403$	6.65896	0.331706
$404$	5.53914	0.275583
$405$	0	0
$406$	29.8079	1.47934
$407$	−0.0383436	−0.00190062
$408$	−0.129785	−0.00642531
$409$	5.34104	0.264098	0.132049	−	0.991243i	$-0.457844\pi$
$409$	5.34104	0.264098	0.132049	+	0.991243i	$0.457844\pi$
$410$	0	0
$411$	−4.06071	−0.200300
$412$	6.57908	0.324128
$413$	−69.4369	−3.41677
$414$	24.6190	1.20996
$415$	0	0
$416$	2.24960	0.110296
$417$	−8.33945	−0.408384
$418$	0.960061	0.0469581
$419$	−22.1566	−1.08242	−0.541210	−	0.840888i	$-0.682033\pi$
$419$	−22.1566	−1.08242	−0.541210	+	0.840888i	$0.682033\pi$
$420$	0	0
$421$	29.2787	1.42696	0.713479	−	0.700676i	$-0.247118\pi$
$421$	29.2787	1.42696	0.713479	+	0.700676i	$0.247118\pi$
$422$	16.5200	0.804180
$423$	−25.9293	−1.26073
$424$	−6.84945	−0.332639
$425$	0	0
$426$	−5.00160	−0.242328
$427$	35.9585	1.74015
$428$	−14.9086	−0.720632
$429$	1.12301	0.0542193
$430$	0	0
$431$	21.3794	1.02981	0.514904	−	0.857248i	$-0.327827\pi$
$431$	21.3794	1.02981	0.514904	+	0.857248i	$0.327827\pi$
$432$	−2.97923	−0.143338
$433$	36.1182	1.73573	0.867865	−	0.496799i	$-0.165491\pi$
$433$	36.1182	1.73573	0.867865	+	0.496799i	$0.165491\pi$
$434$	14.1182	0.677696
$435$	0	0
$436$	4.76957	0.228421
$437$	−9.01917	−0.431445
$438$	−6.27037	−0.299610
$439$	20.9984	1.00220	0.501100	−	0.865390i	$-0.332929\pi$
$439$	20.9984	1.00220	0.501100	+	0.865390i	$0.332929\pi$
$440$	0	0
$441$	−42.9884	−2.04707
$442$	−0.561503	−0.0267080
$443$	31.4976	1.49650	0.748248	−	0.663419i	$-0.230895\pi$
$443$	31.4976	1.49650	0.748248	+	0.663419i	$0.230895\pi$
$444$	−0.0207669	−0.000985555 0
$445$	0	0
$446$	−9.03994	−0.428054
$447$	−4.37779	−0.207062
$448$	4.76957	0.225341
$449$	18.9601	0.894781	0.447390	−	0.894339i	$-0.352353\pi$
$449$	18.9601	0.894781	0.447390	+	0.894339i	$0.352353\pi$
$450$	0	0
$451$	0	0
$452$	−6.00000	−0.282216
$453$	10.3994	0.488606
$454$	−0.350246	−0.0164378
$455$	0	0
$456$	0.519969	0.0243498
$457$	6.32948	0.296081	0.148040	−	0.988981i	$-0.452703\pi$
$457$	6.32948	0.296081	0.148040	+	0.988981i	$0.452703\pi$
$458$	−8.07988	−0.377548
$459$	0.743620	0.0347092
$460$	0	0
$461$	−6.49920	−0.302698	−0.151349	−	0.988480i	$-0.548362\pi$
$461$	−6.49920	−0.302698	−0.151349	+	0.988480i	$0.548362\pi$
$462$	2.38098	0.110773
$463$	−28.4177	−1.32068	−0.660342	−	0.750965i	$-0.729589\pi$
$463$	−28.4177	−1.32068	−0.660342	+	0.750965i	$0.729589\pi$
$464$	6.24960	0.290130
$465$	0	0
$466$	4.92012	0.227920
$467$	−17.5775	−0.813389	−0.406694	−	0.913564i	$-0.633319\pi$
$467$	−17.5775	−0.813389	−0.406694	+	0.913564i	$0.633319\pi$
$468$	−6.14058	−0.283849
$469$	27.3279	1.26188
$470$	0	0
$471$	−2.57908	−0.118838
$472$	−14.5583	−0.670101
$473$	−4.76196	−0.218955
$474$	3.16135	0.145206
$475$	0	0
$476$	−1.19049	−0.0545660
$477$	18.6965	0.856053
$478$	2.98083	0.136340
$479$	22.7372	1.03889	0.519446	−	0.854504i	$-0.326139\pi$
$479$	22.7372	1.03889	0.519446	+	0.854504i	$0.326139\pi$
$480$	0	0
$481$	−0.0898462	−0.00409664
$482$	20.0383	0.912722
$483$	−22.3678	−1.01777
$484$	−10.0783	−0.458104
$485$	0	0
$486$	12.3902	0.562030
$487$	22.1981	1.00589	0.502946	−	0.864318i	$-0.332249\pi$
$487$	22.1981	1.00589	0.502946	+	0.864318i	$0.332249\pi$
$488$	7.53914	0.341281
$489$	11.1582	0.504589
$490$	0	0
$491$	−24.9984	−1.12816	−0.564081	−	0.825719i	$-0.690769\pi$
$491$	−24.9984	−1.12816	−0.564081	+	0.825719i	$0.690769\pi$
$492$	0	0
$493$	−1.55991	−0.0702547
$494$	2.24960	0.101214
$495$	0	0
$496$	2.96006	0.132911
$497$	−45.8786	−2.05794
$498$	3.87859	0.173804
$499$	11.6574	0.521855	0.260928	−	0.965358i	$-0.415972\pi$
$499$	11.6574	0.521855	0.260928	+	0.965358i	$0.415972\pi$
$500$	0	0
$501$	5.74043	0.256463
$502$	−14.8802	−0.664135
$503$	−11.7504	−0.523924	−0.261962	−	0.965078i	$-0.584370\pi$
$503$	−11.7504	−0.523924	−0.261962	+	0.965078i	$0.584370\pi$
$504$	−13.0192	−0.579920
$505$	0	0
$506$	−8.65896	−0.384938
$507$	−4.12819	−0.183339
$508$	−17.9585	−0.796778
$509$	29.9569	1.32781	0.663907	−	0.747815i	$-0.268897\pi$
$509$	29.9569	1.32781	0.663907	+	0.747815i	$0.268897\pi$
$510$	0	0
$511$	−57.5168	−2.54439
$512$	1.00000	0.0441942
$513$	−2.97923	−0.131536
$514$	11.0399	0.486951
$515$	0	0
$516$	−2.57908	−0.113538
$517$	9.11982	0.401089
$518$	−0.190491	−0.00836968
$519$	−8.81788	−0.387062
$520$	0	0
$521$	−15.1198	−0.662411	−0.331206	−	0.943559i	$-0.607455\pi$
$521$	−15.1198	−0.662411	−0.331206	+	0.943559i	$0.607455\pi$
$522$	−17.0591	−0.746657
$523$	−15.6498	−0.684316	−0.342158	−	0.939642i	$-0.611158\pi$
$523$	−15.6498	−0.684316	−0.342158	+	0.939642i	$0.611158\pi$
$524$	−6.96006	−0.304052
$525$	0	0
$526$	3.84025	0.167443
$527$	−0.738835	−0.0321842
$528$	0.499202	0.0217250
$529$	58.3455	2.53676
$530$	0	0
$531$	39.7388	1.72452
$532$	4.76957	0.206787
$533$	0	0
$534$	2.12141	0.0918024
$535$	0	0
$536$	5.72963	0.247482
$537$	1.32028	0.0569741
$538$	23.1981	1.00014
$539$	15.1198	0.651257
$540$	0	0
$541$	−27.2995	−1.17370	−0.586849	−	0.809697i	$-0.699632\pi$
$541$	−27.2995	−1.17370	−0.586849	+	0.809697i	$0.699632\pi$
$542$	23.9792	1.03000
$543$	−2.01758	−0.0865825
$544$	−0.249601	−0.0107016
$545$	0	0
$546$	5.57908	0.238763
$547$	33.9968	1.45360	0.726799	−	0.686850i	$-0.241007\pi$
$547$	33.9968	1.45360	0.726799	+	0.686850i	$0.241007\pi$
$548$	−7.80951	−0.333606
$549$	−20.5791	−0.878294
$550$	0	0
$551$	6.24960	0.266242
$552$	−4.68969	−0.199607
$553$	28.9984	1.23314
$554$	−24.6590	−1.04766
$555$	0	0
$556$	−16.0383	−0.680177
$557$	−33.8786	−1.43548	−0.717741	−	0.696310i	$-0.754824\pi$
$557$	−33.8786	−1.43548	−0.717741	+	0.696310i	$0.754824\pi$
$558$	−8.07988	−0.342048
$559$	−11.1582	−0.471940
$560$	0	0
$561$	−0.124602	−0.00526068
$562$	−18.9984	−0.801399
$563$	−32.2995	−1.36126	−0.680631	−	0.732626i	$-0.738294\pi$
$563$	−32.2995	−1.36126	−0.680631	+	0.732626i	$0.738294\pi$
$564$	4.93929	0.207982
$565$	0	0
$566$	−29.0367	−1.22051
$567$	31.6689	1.32997
$568$	−9.61902	−0.403605
$569$	−6.73883	−0.282507	−0.141253	−	0.989973i	$-0.545113\pi$
$569$	−6.73883	−0.282507	−0.141253	+	0.989973i	$0.545113\pi$
$570$	0	0
$571$	34.4193	1.44040	0.720202	−	0.693764i	$-0.244049\pi$
$571$	34.4193	1.44040	0.720202	+	0.693764i	$0.244049\pi$
$572$	2.15975	0.0903039
$573$	1.07067	0.0447281
$574$	0	0
$575$	0	0
$576$	−2.72963	−0.113735
$577$	−28.1773	−1.17304	−0.586519	−	0.809936i	$-0.699502\pi$
$577$	−28.1773	−1.17304	−0.586519	+	0.809936i	$0.699502\pi$
$578$	−16.9377	−0.704515
$579$	4.39939	0.182832
$580$	0	0
$581$	35.5775	1.47600
$582$	−9.57748	−0.397000
$583$	−6.57589	−0.272346
$584$	−12.0591	−0.499010
$585$	0	0
$586$	−6.24960	−0.258169
$587$	34.6174	1.42881	0.714407	−	0.699730i	$-0.246697\pi$
$587$	34.6174	1.42881	0.714407	+	0.699730i	$0.246697\pi$
$588$	8.18890	0.337704
$589$	2.96006	0.121967
$590$	0	0
$591$	−7.23804	−0.297733
$592$	−0.0399387	−0.00164147
$593$	3.99840	0.164195	0.0820974	−	0.996624i	$-0.473838\pi$
$593$	3.99840	0.164195	0.0820974	+	0.996624i	$0.473838\pi$
$594$	−2.86025	−0.117357
$595$	0	0
$596$	−8.41932	−0.344869
$597$	−4.75801	−0.194732
$598$	−20.2895	−0.829701
$599$	−42.5759	−1.73960	−0.869802	−	0.493401i	$-0.835753\pi$
$599$	−42.5759	−1.73960	−0.869802	+	0.493401i	$0.835753\pi$
$600$	0	0
$601$	−18.4577	−0.752904	−0.376452	−	0.926436i	$-0.622856\pi$
$601$	−18.4577	−0.752904	−0.376452	+	0.926436i	$0.622856\pi$
$602$	−23.6574	−0.964202
$603$	−15.6398	−0.636901
$604$	20.0000	0.813788
$605$	0	0
$606$	2.88018	0.116999
$607$	12.5791	0.510569	0.255285	−	0.966866i	$-0.417831\pi$
$607$	12.5791	0.510569	0.255285	+	0.966866i	$0.417831\pi$
$608$	1.00000	0.0405554
$609$	15.4992	0.628059
$610$	0	0
$611$	21.3694	0.864514
$612$	0.681319	0.0275407
$613$	26.5759	1.07339	0.536695	−	0.843776i	$-0.319673\pi$
$613$	26.5759	1.07339	0.536695	+	0.843776i	$0.319673\pi$
$614$	−12.5391	−0.506039
$615$	0	0
$616$	4.57908	0.184496
$617$	37.8386	1.52333	0.761663	−	0.647973i	$-0.224383\pi$
$617$	37.8386	1.52333	0.761663	+	0.647973i	$0.224383\pi$
$618$	3.42092	0.137610
$619$	30.1566	1.21209	0.606047	−	0.795429i	$-0.292754\pi$
$619$	30.1566	1.21209	0.606047	+	0.795429i	$0.292754\pi$
$620$	0	0
$621$	26.8702	1.07826
$622$	7.84785	0.314670
$623$	19.4593	0.779619
$624$	1.16972	0.0468264
$625$	0	0
$626$	−10.9884	−0.439186
$627$	0.499202	0.0199362
$628$	−4.96006	−0.197928
$629$	0.00996876	0.000397480 0
$630$	0	0
$631$	−25.4992	−1.01511	−0.507554	−	0.861620i	$-0.669450\pi$
$631$	−25.4992	−1.01511	−0.507554	+	0.861620i	$0.669450\pi$
$632$	6.07988	0.241845
$633$	8.58988	0.341417
$634$	21.5567	0.856127
$635$	0	0
$636$	−3.56150	−0.141223
$637$	35.4285	1.40373
$638$	6.00000	0.237542
$639$	26.2564	1.03869
$640$	0	0
$641$	39.1965	1.54817	0.774084	−	0.633082i	$-0.218211\pi$
$641$	39.1965	1.54817	0.774084	+	0.633082i	$0.218211\pi$
$642$	−7.75199	−0.305947
$643$	36.3778	1.43460	0.717300	−	0.696764i	$-0.245378\pi$
$643$	36.3778	1.43460	0.717300	+	0.696764i	$0.245378\pi$
$644$	−43.0176	−1.69513
$645$	0	0
$646$	−0.249601	−0.00982043
$647$	10.6897	0.420255	0.210128	−	0.977674i	$-0.432612\pi$
$647$	10.6897	0.420255	0.210128	+	0.977674i	$0.432612\pi$
$648$	6.63979	0.260835
$649$	−13.9769	−0.548640
$650$	0	0
$651$	7.34104	0.287718
$652$	21.4593	0.840410
$653$	−36.0383	−1.41029	−0.705145	−	0.709063i	$-0.749118\pi$
$653$	−36.0383	−1.41029	−0.705145	+	0.709063i	$0.749118\pi$
$654$	2.48003	0.0969769
$655$	0	0
$656$	0	0
$657$	32.9169	1.28421
$658$	45.3071	1.76626
$659$	17.1889	0.669584	0.334792	−	0.942292i	$-0.391334\pi$
$659$	17.1889	0.669584	0.334792	+	0.942292i	$0.391334\pi$
$660$	0	0
$661$	48.9054	1.90220	0.951099	−	0.308886i	$-0.0999560\pi$
$661$	48.9054	1.90220	0.951099	+	0.308886i	$0.0999560\pi$
$662$	33.4876	1.30153
$663$	−0.291964	−0.0113390
$664$	7.45926	0.289476
$665$	0	0
$666$	0.109018	0.00422436
$667$	−56.3662	−2.18251
$668$	11.0399	0.427148
$669$	−4.70049	−0.181731
$670$	0	0
$671$	7.23804	0.279421
$672$	2.48003	0.0956693
$673$	6.57908	0.253605	0.126802	−	0.991928i	$-0.459529\pi$
$673$	6.57908	0.253605	0.126802	+	0.991928i	$0.459529\pi$
$674$	−5.69890	−0.219513
$675$	0	0
$676$	−7.93929	−0.305357
$677$	−38.3087	−1.47232	−0.736162	−	0.676806i	$-0.763364\pi$
$677$	−38.3087	−1.47232	−0.736162	+	0.676806i	$0.763364\pi$
$678$	−3.11982	−0.119816
$679$	−87.8523	−3.37146
$680$	0	0
$681$	−0.182117	−0.00697874
$682$	2.84184	0.108820
$683$	7.54074	0.288538	0.144269	−	0.989538i	$-0.453917\pi$
$683$	7.54074	0.288538	0.144269	+	0.989538i	$0.453917\pi$
$684$	−2.72963	−0.104370
$685$	0	0
$686$	41.7280	1.59318
$687$	−4.20129	−0.160289
$688$	−4.96006	−0.189101
$689$	−15.4085	−0.587018
$690$	0	0
$691$	28.4193	1.08112	0.540561	−	0.841305i	$-0.318212\pi$
$691$	28.4193	1.08112	0.540561	+	0.841305i	$0.318212\pi$
$692$	−16.9585	−0.644664
$693$	−12.4992	−0.474805
$694$	0.239632	0.00909632
$695$	0	0
$696$	3.24960	0.123176
$697$	0	0
$698$	−17.2380	−0.652469
$699$	2.55831	0.0967643
$700$	0	0
$701$	−24.2596	−0.916271	−0.458136	−	0.888882i	$-0.651483\pi$
$701$	−24.2596	−0.916271	−0.458136	+	0.888882i	$0.651483\pi$
$702$	−6.70209	−0.252954
$703$	−0.0399387	−0.00150632
$704$	0.960061	0.0361837
$705$	0	0
$706$	34.7280	1.30701
$707$	26.4193	0.993601
$708$	−7.56988	−0.284493
$709$	21.7372	0.816359	0.408180	−	0.912902i	$-0.366164\pi$
$709$	21.7372	0.816359	0.408180	+	0.912902i	$0.366164\pi$
$710$	0	0
$711$	−16.5958	−0.622392
$712$	4.07988	0.152900
$713$	−26.6973	−0.999822
$714$	−0.619019	−0.0231662
$715$	0	0
$716$	2.53914	0.0948922
$717$	1.54994	0.0578835
$718$	26.6689	0.995275
$719$	−48.9361	−1.82501	−0.912504	−	0.409067i	$-0.865854\pi$
$719$	−48.9361	−1.82501	−0.912504	+	0.409067i	$0.865854\pi$
$720$	0	0
$721$	31.3794	1.16863
$722$	1.00000	0.0372161
$723$	10.4193	0.387499
$724$	−3.88018	−0.144206
$725$	0	0
$726$	−5.24040	−0.194489
$727$	4.29874	0.159432	0.0797158	−	0.996818i	$-0.474599\pi$
$727$	4.29874	0.159432	0.0797158	+	0.996818i	$0.474599\pi$
$728$	10.7296	0.397667
$729$	−13.4768	−0.499142
$730$	0	0
$731$	1.23804	0.0457905
$732$	3.92012	0.144892
$733$	12.0415	0.444764	0.222382	−	0.974960i	$-0.428617\pi$
$733$	12.0415	0.444764	0.222382	+	0.974960i	$0.428617\pi$
$734$	15.2380	0.562446
$735$	0	0
$736$	−9.01917	−0.332451
$737$	5.50080	0.202624
$738$	0	0
$739$	6.61742	0.243426	0.121713	−	0.992565i	$-0.461161\pi$
$739$	6.61742	0.243426	0.121713	+	0.992565i	$0.461161\pi$
$740$	0	0
$741$	1.16972	0.0429709
$742$	−32.6689	−1.19931
$743$	47.6158	1.74686	0.873428	−	0.486954i	$-0.161892\pi$
$743$	47.6158	1.74686	0.873428	+	0.486954i	$0.161892\pi$
$744$	1.53914	0.0564277
$745$	0	0
$746$	26.6382	0.975293
$747$	−20.3610	−0.744972
$748$	−0.239632	−0.00876183
$749$	−71.1074	−2.59821
$750$	0	0
$751$	−25.6574	−0.936250	−0.468125	−	0.883662i	$-0.655070\pi$
$751$	−25.6574	−0.936250	−0.468125	+	0.883662i	$0.655070\pi$
$752$	9.49920	0.346400
$753$	−7.73724	−0.281961
$754$	14.0591	0.512003
$755$	0	0
$756$	−14.2097	−0.516800
$757$	−8.83865	−0.321246	−0.160623	−	0.987016i	$-0.551350\pi$
$757$	−8.83865	−0.321246	−0.160623	+	0.987016i	$0.551350\pi$
$758$	11.9693	0.434743
$759$	−4.50239	−0.163426
$760$	0	0
$761$	−9.40776	−0.341031	−0.170516	−	0.985355i	$-0.554543\pi$
$761$	−9.40776	−0.341031	−0.170516	+	0.985355i	$0.554543\pi$
$762$	−9.33785	−0.338275
$763$	22.7488	0.823562
$764$	2.05911	0.0744960
$765$	0	0
$766$	9.84025	0.355543
$767$	−32.7504	−1.18255
$768$	0.519969	0.0187628
$769$	7.32788	0.264250	0.132125	−	0.991233i	$-0.457820\pi$
$769$	7.32788	0.264250	0.132125	+	0.991233i	$0.457820\pi$
$770$	0	0
$771$	5.74043	0.206737
$772$	8.46086	0.304513
$773$	−54.4369	−1.95796	−0.978980	−	0.203958i	$-0.934619\pi$
$773$	−54.4369	−1.95796	−0.978980	+	0.203958i	$0.934619\pi$
$774$	13.5391	0.486654
$775$	0	0
$776$	−18.4193	−0.661215
$777$	−0.0990493	−0.00355337
$778$	−8.65896	−0.310439
$779$	0	0
$780$	0	0
$781$	−9.23485	−0.330449
$782$	2.25120	0.0805026
$783$	−18.6190	−0.665389
$784$	15.7488	0.562457
$785$	0	0
$786$	−3.61902	−0.129086
$787$	27.6705	0.986348	0.493174	−	0.869931i	$-0.335837\pi$
$787$	27.6705	0.986348	0.493174	+	0.869931i	$0.335837\pi$
$788$	−13.9201	−0.495884
$789$	1.99681	0.0710883
$790$	0	0
$791$	−28.6174	−1.01752
$792$	−2.62061	−0.0931195
$793$	16.9601	0.602269
$794$	−28.9984	−1.02911
$795$	0	0
$796$	−9.15055	−0.324333
$797$	−21.5906	−0.764780	−0.382390	−	0.924001i	$-0.624899\pi$
$797$	−21.5906	−0.764780	−0.382390	+	0.924001i	$0.624899\pi$
$798$	2.48003	0.0877921
$799$	−2.37101	−0.0838804
$800$	0	0
$801$	−11.1366	−0.393491
$802$	22.6174	0.798649
$803$	−11.5775	−0.408561
$804$	2.97923	0.105069
$805$	0	0
$806$	6.65896	0.234552
$807$	12.0623	0.424613
$808$	5.53914	0.194866
$809$	9.72963	0.342076	0.171038	−	0.985264i	$-0.445288\pi$
$809$	9.72963	0.342076	0.171038	+	0.985264i	$0.445288\pi$
$810$	0	0
$811$	−38.7280	−1.35993	−0.679963	−	0.733247i	$-0.738004\pi$
$811$	−38.7280	−1.35993	−0.679963	+	0.733247i	$0.738004\pi$
$812$	29.8079	1.04605
$813$	12.4685	0.437288
$814$	−0.0383436	−0.00134394
$815$	0	0
$816$	−0.129785	−0.00454338
$817$	−4.96006	−0.173531
$818$	5.34104	0.186745
$819$	−29.2879	−1.02340
$820$	0	0
$821$	−30.2780	−1.05671	−0.528354	−	0.849024i	$-0.677191\pi$
$821$	−30.2780	−1.05671	−0.528354	+	0.849024i	$0.677191\pi$
$822$	−4.06071	−0.141633
$823$	7.93770	0.276691	0.138345	−	0.990384i	$-0.455822\pi$
$823$	7.93770	0.276691	0.138345	+	0.990384i	$0.455822\pi$
$824$	6.57908	0.229193
$825$	0	0
$826$	−69.4369	−2.41602
$827$	−30.2496	−1.05188	−0.525941	−	0.850521i	$-0.676287\pi$
$827$	−30.2496	−1.05188	−0.525941	+	0.850521i	$0.676287\pi$
$828$	24.6190	0.855570
$829$	−40.6765	−1.41275	−0.706377	−	0.707836i	$-0.749672\pi$
$829$	−40.6765	−1.41275	−0.706377	+	0.707836i	$0.749672\pi$
$830$	0	0
$831$	−12.8219	−0.444787
$832$	2.24960	0.0779909
$833$	−3.93092	−0.136198
$834$	−8.33945	−0.288771
$835$	0	0
$836$	0.960061	0.0332044
$837$	−8.81871	−0.304819
$838$	−22.1566	−0.765386
$839$	45.9553	1.58655	0.793276	−	0.608862i	$-0.208374\pi$
$839$	45.9553	1.58655	0.793276	+	0.608862i	$0.208374\pi$
$840$	0	0
$841$	10.0575	0.346811
$842$	29.2787	1.00901
$843$	−9.87859	−0.340237
$844$	16.5200	0.568641
$845$	0	0
$846$	−25.9293	−0.891469
$847$	−48.0691	−1.65167
$848$	−6.84945	−0.235211
$849$	−15.0982	−0.518170
$850$	0	0
$851$	0.360214	0.0123480
$852$	−5.00160	−0.171352
$853$	−17.2196	−0.589589	−0.294794	−	0.955561i	$-0.595251\pi$
$853$	−17.2196	−0.589589	−0.294794	+	0.955561i	$0.595251\pi$
$854$	35.9585	1.23047
$855$	0	0
$856$	−14.9086	−0.509564
$857$	−17.2995	−0.590940	−0.295470	−	0.955352i	$-0.595476\pi$
$857$	−17.2995	−0.590940	−0.295470	+	0.955352i	$0.595476\pi$
$858$	1.12301	0.0383388
$859$	17.6190	0.601153	0.300577	−	0.953758i	$-0.402821\pi$
$859$	17.6190	0.601153	0.300577	+	0.953758i	$0.402821\pi$
$860$	0	0
$861$	0	0
$862$	21.3794	0.728185
$863$	4.07988	0.138881	0.0694403	−	0.997586i	$-0.477879\pi$
$863$	4.07988	0.138881	0.0694403	+	0.997586i	$0.477879\pi$
$864$	−2.97923	−0.101356
$865$	0	0
$866$	36.1182	1.22735
$867$	−8.80708	−0.299104
$868$	14.1182	0.479204
$869$	5.83705	0.198009
$870$	0	0
$871$	12.8894	0.436740
$872$	4.76957	0.161518
$873$	50.2780	1.70165
$874$	−9.01917	−0.305078
$875$	0	0
$876$	−6.27037	−0.211856
$877$	−25.2787	−0.853602	−0.426801	−	0.904345i	$-0.640360\pi$
$877$	−25.2787	−0.853602	−0.426801	+	0.904345i	$0.640360\pi$
$878$	20.9984	0.708662
$879$	−3.24960	−0.109606
$880$	0	0
$881$	−0.0814726	−0.00274488	−0.00137244	−	0.999999i	$-0.500437\pi$
$881$	−0.0814726	−0.00274488	−0.00137244	+	0.999999i	$0.500437\pi$
$882$	−42.9884	−1.44750
$883$	−19.3410	−0.650878	−0.325439	−	0.945563i	$-0.605512\pi$
$883$	−19.3410	−0.650878	−0.325439	+	0.945563i	$0.605512\pi$
$884$	−0.561503	−0.0188854
$885$	0	0
$886$	31.4976	1.05818
$887$	−5.53914	−0.185986	−0.0929931	−	0.995667i	$-0.529643\pi$
$887$	−5.53914	−0.185986	−0.0929931	+	0.995667i	$0.529643\pi$
$888$	−0.0207669	−0.000696892 0
$889$	−85.6542	−2.87275
$890$	0	0
$891$	6.37460	0.213557
$892$	−9.03994	−0.302680
$893$	9.49920	0.317879
$894$	−4.37779	−0.146415
$895$	0	0
$896$	4.76957	0.159340
$897$	−10.5499	−0.352252
$898$	18.9601	0.632705
$899$	18.4992	0.616983
$900$	0	0
$901$	1.70963	0.0569561
$902$	0	0
$903$	−12.3011	−0.409355
$904$	−6.00000	−0.199557
$905$	0	0
$906$	10.3994	0.345497
$907$	−10.8111	−0.358977	−0.179488	−	0.983760i	$-0.557444\pi$
$907$	−10.8111	−0.358977	−0.179488	+	0.983760i	$0.557444\pi$
$908$	−0.350246	−0.0116233
$909$	−15.1198	−0.501493
$910$	0	0
$911$	35.1166	1.16347	0.581733	−	0.813380i	$-0.302375\pi$
$911$	35.1166	1.16347	0.581733	+	0.813380i	$0.302375\pi$
$912$	0.519969	0.0172179
$913$	7.16135	0.237006
$914$	6.32948	0.209361
$915$	0	0
$916$	−8.07988	−0.266967
$917$	−33.1965	−1.09625
$918$	0.743620	0.0245431
$919$	30.8287	1.01694	0.508472	−	0.861078i	$-0.330210\pi$
$919$	30.8287	1.01694	0.508472	+	0.861078i	$0.330210\pi$
$920$	0	0
$921$	−6.51997	−0.214840
$922$	−6.49920	−0.214040
$923$	−21.6390	−0.712255
$924$	2.38098	0.0783285
$925$	0	0
$926$	−28.4177	−0.933865
$927$	−17.9585	−0.589833
$928$	6.24960	0.205153
$929$	−45.0575	−1.47829	−0.739145	−	0.673547i	$-0.764770\pi$
$929$	−45.0575	−1.47829	−0.739145	+	0.673547i	$0.764770\pi$
$930$	0	0
$931$	15.7488	0.516146
$932$	4.92012	0.161164
$933$	4.08064	0.133594
$934$	−17.5775	−0.575153
$935$	0	0
$936$	−6.14058	−0.200711
$937$	22.2464	0.726759	0.363379	−	0.931641i	$-0.381623\pi$
$937$	22.2464	0.726759	0.363379	+	0.931641i	$0.381623\pi$
$938$	27.3279	0.892287
$939$	−5.71365	−0.186458
$940$	0	0
$941$	−53.9277	−1.75799	−0.878997	−	0.476828i	$-0.841787\pi$
$941$	−53.9277	−1.75799	−0.878997	+	0.476828i	$0.841787\pi$
$942$	−2.57908	−0.0840310
$943$	0	0
$944$	−14.5583	−0.473833
$945$	0	0
$946$	−4.76196	−0.154825
$947$	−4.76196	−0.154743	−0.0773715	−	0.997002i	$-0.524653\pi$
$947$	−4.76196	−0.154743	−0.0773715	+	0.997002i	$0.524653\pi$
$948$	3.16135	0.102676
$949$	−27.1282	−0.880618
$950$	0	0
$951$	11.2088	0.363471
$952$	−1.19049	−0.0385840
$953$	4.37779	0.141811	0.0709053	−	0.997483i	$-0.477411\pi$
$953$	4.37779	0.141811	0.0709053	+	0.997483i	$0.477411\pi$
$954$	18.6965	0.605321
$955$	0	0
$956$	2.98083	0.0964069
$957$	3.11982	0.100849
$958$	22.7372	0.734607
$959$	−37.2480	−1.20280
$960$	0	0
$961$	−22.2380	−0.717356
$962$	−0.0898462	−0.00289676
$963$	40.6949	1.31137
$964$	20.0383	0.645392
$965$	0	0
$966$	−22.3678	−0.719673
$967$	−13.1582	−0.423138	−0.211569	−	0.977363i	$-0.567857\pi$
$967$	−13.1582	−0.423138	−0.211569	+	0.977363i	$0.567857\pi$
$968$	−10.0783	−0.323928
$969$	−0.129785	−0.00416929
$970$	0	0
$971$	25.9201	0.831816	0.415908	−	0.909407i	$-0.363464\pi$
$971$	25.9201	0.831816	0.415908	+	0.909407i	$0.363464\pi$
$972$	12.3902	0.397415
$973$	−76.4960	−2.45235
$974$	22.1981	0.711273
$975$	0	0
$976$	7.53914	0.241322
$977$	31.2764	1.00062	0.500310	−	0.865846i	$-0.333219\pi$
$977$	31.2764	1.00062	0.500310	+	0.865846i	$0.333219\pi$
$978$	11.1582	0.356799
$979$	3.91693	0.125186
$980$	0	0
$981$	−13.0192	−0.415670
$982$	−24.9984	−0.797731
$983$	26.2364	0.836813	0.418406	−	0.908260i	$-0.362589\pi$
$983$	26.2364	0.836813	0.418406	+	0.908260i	$0.362589\pi$
$984$	0	0
$985$	0	0
$986$	−1.55991	−0.0496776
$987$	23.5583	0.749869
$988$	2.24960	0.0715693
$989$	44.7356	1.42251
$990$	0	0
$991$	39.2764	1.24766	0.623828	−	0.781562i	$-0.285577\pi$
$991$	39.2764	1.24766	0.623828	+	0.781562i	$0.285577\pi$
$992$	2.96006	0.0939820
$993$	17.4125	0.552570
$994$	−45.8786	−1.45518
$995$	0	0
$996$	3.87859	0.122898
$997$	14.4609	0.457980	0.228990	−	0.973429i	$-0.426458\pi$
$997$	14.4609	0.457980	0.228990	+	0.973429i	$0.426458\pi$
$998$	11.6574	0.369007
$999$	0.118987	0.00376458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.l.1.2	yes	3
3.2	odd	2		8550.2.a.ci.1.3		3
4.3	odd	2		7600.2.a.bk.1.2		3
5.2	odd	4		950.2.b.h.799.5		6
5.3	odd	4		950.2.b.h.799.2		6
5.4	even	2		950.2.a.j.1.2	✓	3
15.14	odd	2		8550.2.a.cp.1.1		3
20.19	odd	2		7600.2.a.bz.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.j.1.2	✓	3	5.4	even	2
950.2.a.l.1.2	yes	3	1.1	even	1	trivial
950.2.b.h.799.2		6	5.3	odd	4
950.2.b.h.799.5		6	5.2	odd	4
7600.2.a.bk.1.2		3	4.3	odd	2
7600.2.a.bz.1.2		3	20.19	odd	2
8550.2.a.ci.1.3		3	3.2	odd	2
8550.2.a.cp.1.1		3	15.14	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.519969 q^{3} +1.00000 q^{4} +0.519969 q^{6} +4.76957 q^{7} +1.00000 q^{8} -2.72963 q^{9} +0.960061 q^{11} +0.519969 q^{12} +2.24960 q^{13} +4.76957 q^{14} +1.00000 q^{16} -0.249601 q^{17} -2.72963 q^{18} +1.00000 q^{19} +2.48003 q^{21} +0.960061 q^{22} -9.01917 q^{23} +0.519969 q^{24} +2.24960 q^{26} -2.97923 q^{27} +4.76957 q^{28} +6.24960 q^{29} +2.96006 q^{31} +1.00000 q^{32} +0.499202 q^{33} -0.249601 q^{34} -2.72963 q^{36} -0.0399387 q^{37} +1.00000 q^{38} +1.16972 q^{39} +2.48003 q^{42} -4.96006 q^{43} +0.960061 q^{44} -9.01917 q^{46} +9.49920 q^{47} +0.519969 q^{48} +15.7488 q^{49} -0.129785 q^{51} +2.24960 q^{52} -6.84945 q^{53} -2.97923 q^{54} +4.76957 q^{56} +0.519969 q^{57} +6.24960 q^{58} -14.5583 q^{59} +7.53914 q^{61} +2.96006 q^{62} -13.0192 q^{63} +1.00000 q^{64} +0.499202 q^{66} +5.72963 q^{67} -0.249601 q^{68} -4.68969 q^{69} -9.61902 q^{71} -2.72963 q^{72} -12.0591 q^{73} -0.0399387 q^{74} +1.00000 q^{76} +4.57908 q^{77} +1.16972 q^{78} +6.07988 q^{79} +6.63979 q^{81} +7.45926 q^{83} +2.48003 q^{84} -4.96006 q^{86} +3.24960 q^{87} +0.960061 q^{88} +4.07988 q^{89} +10.7296 q^{91} -9.01917 q^{92} +1.53914 q^{93} +9.49920 q^{94} +0.519969 q^{96} -18.4193 q^{97} +15.7488 q^{98} -2.62061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} + 3 q^{16} + 12 q^{17} + 5 q^{18} + 3 q^{19} + 7 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24} - 6 q^{26} + 17 q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{31} + 3 q^{32} - 24 q^{33} + 12 q^{34} + 5 q^{36} - q^{37} + 3 q^{38} - 11 q^{39} + 7 q^{42} - 14 q^{43} + 2 q^{44} - 2 q^{46} + 3 q^{47} + 2 q^{48} + 9 q^{49} + 15 q^{51} - 6 q^{52} - 10 q^{53} + 17 q^{54} + 2 q^{56} + 2 q^{57} + 6 q^{58} + 6 q^{59} - 2 q^{61} + 8 q^{62} - 14 q^{63} + 3 q^{64} - 24 q^{66} + 4 q^{67} + 12 q^{68} - 6 q^{71} + 5 q^{72} - 12 q^{73} - q^{74} + 3 q^{76} - 10 q^{77} - 11 q^{78} + 20 q^{79} + 23 q^{81} - 4 q^{83} + 7 q^{84} - 14 q^{86} - 3 q^{87} + 2 q^{88} + 14 q^{89} + 19 q^{91} - 2 q^{92} - 20 q^{93} + 3 q^{94} + 2 q^{96} - 28 q^{97} + 9 q^{98} - 36 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 + 3 * q^16 + 12 * q^17 + 5 * q^18 + 3 * q^19 + 7 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 - 6 * q^26 + 17 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^31 + 3 * q^32 - 24 * q^33 + 12 * q^34 + 5 * q^36 - q^37 + 3 * q^38 - 11 * q^39 + 7 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^46 + 3 * q^47 + 2 * q^48 + 9 * q^49 + 15 * q^51 - 6 * q^52 - 10 * q^53 + 17 * q^54 + 2 * q^56 + 2 * q^57 + 6 * q^58 + 6 * q^59 - 2 * q^61 + 8 * q^62 - 14 * q^63 + 3 * q^64 - 24 * q^66 + 4 * q^67 + 12 * q^68 - 6 * q^71 + 5 * q^72 - 12 * q^73 - q^74 + 3 * q^76 - 10 * q^77 - 11 * q^78 + 20 * q^79 + 23 * q^81 - 4 * q^83 + 7 * q^84 - 14 * q^86 - 3 * q^87 + 2 * q^88 + 14 * q^89 + 19 * q^91 - 2 * q^92 - 20 * q^93 + 3 * q^94 + 2 * q^96 - 28 * q^97 + 9 * q^98 - 36 * q^99

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