LMFDB - Embedded newform 950.2.a.i.1.3

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.12489$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -2.12489 q^{6} -4.12489 q^{7} -1.00000 q^{8} +1.51514 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -2.12489 q^{6} -4.12489 q^{7} -1.00000 q^{8} +1.51514 q^{9} -2.64002 q^{11} +2.12489 q^{12} -2.51514 q^{13} +4.12489 q^{14} +1.00000 q^{16} +0.515138 q^{17} -1.51514 q^{18} +1.00000 q^{19} -8.76491 q^{21} +2.64002 q^{22} -3.09461 q^{23} -2.12489 q^{24} +2.51514 q^{26} -3.15516 q^{27} -4.12489 q^{28} -7.79518 q^{29} +3.67030 q^{31} -1.00000 q^{32} -5.60975 q^{33} -0.515138 q^{34} +1.51514 q^{36} -10.2498 q^{37} -1.00000 q^{38} -5.34438 q^{39} +8.88979 q^{41} +8.76491 q^{42} -8.64002 q^{43} -2.64002 q^{44} +3.09461 q^{46} +4.96972 q^{47} +2.12489 q^{48} +10.0147 q^{49} +1.09461 q^{51} -2.51514 q^{52} -5.48486 q^{53} +3.15516 q^{54} +4.12489 q^{56} +2.12489 q^{57} +7.79518 q^{58} +3.15516 q^{59} -12.6400 q^{61} -3.67030 q^{62} -6.24977 q^{63} +1.00000 q^{64} +5.60975 q^{66} +7.40493 q^{67} +0.515138 q^{68} -6.57569 q^{69} +11.1396 q^{71} -1.51514 q^{72} +2.70436 q^{73} +10.2498 q^{74} +1.00000 q^{76} +10.8898 q^{77} +5.34438 q^{78} +16.7493 q^{79} -11.2498 q^{81} -8.88979 q^{82} -3.28005 q^{83} -8.76491 q^{84} +8.64002 q^{86} -16.5639 q^{87} +2.64002 q^{88} -7.60975 q^{89} +10.3747 q^{91} -3.09461 q^{92} +7.79897 q^{93} -4.96972 q^{94} -2.12489 q^{96} -3.93945 q^{97} -10.0147 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 4 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 - 4 * q^7 - 3 * q^8 + 5 * q^9	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} - 3 q^{8} + 5 q^{9} - 2 q^{12} - 8 q^{13} + 4 q^{14} + 3 q^{16} + 2 q^{17} - 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} - 2 q^{27} - 4 q^{28} - 8 q^{29} + 4 q^{31} - 3 q^{32} - 8 q^{33} - 2 q^{34} + 5 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 2 q^{41} + 10 q^{42} - 18 q^{43} + 14 q^{47} - 2 q^{48} - 3 q^{49} - 6 q^{51} - 8 q^{52} - 16 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} + 8 q^{58} + 2 q^{59} - 30 q^{61} - 4 q^{62} - 2 q^{63} + 3 q^{64} + 8 q^{66} - 2 q^{67} + 2 q^{68} - 22 q^{69} - 8 q^{71} - 5 q^{72} - 10 q^{73} + 14 q^{74} + 3 q^{76} + 8 q^{77} - 10 q^{78} - 17 q^{81} - 2 q^{82} + 6 q^{83} - 10 q^{84} + 18 q^{86} - 6 q^{87} - 14 q^{89} + 6 q^{91} - 4 q^{93} - 14 q^{94} + 2 q^{96} - 10 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 - 3 * q^8 + 5 * q^9 - 2 * q^12 - 8 * q^13 + 4 * q^14 + 3 * q^16 + 2 * q^17 - 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 - 2 * q^27 - 4 * q^28 - 8 * q^29 + 4 * q^31 - 3 * q^32 - 8 * q^33 - 2 * q^34 + 5 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 2 * q^41 + 10 * q^42 - 18 * q^43 + 14 * q^47 - 2 * q^48 - 3 * q^49 - 6 * q^51 - 8 * q^52 - 16 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 + 8 * q^58 + 2 * q^59 - 30 * q^61 - 4 * q^62 - 2 * q^63 + 3 * q^64 + 8 * q^66 - 2 * q^67 + 2 * q^68 - 22 * q^69 - 8 * q^71 - 5 * q^72 - 10 * q^73 + 14 * q^74 + 3 * q^76 + 8 * q^77 - 10 * q^78 - 17 * q^81 - 2 * q^82 + 6 * q^83 - 10 * q^84 + 18 * q^86 - 6 * q^87 - 14 * q^89 + 6 * q^91 - 4 * q^93 - 14 * q^94 + 2 * q^96 - 10 * q^97 + 3 * q^98 - 12 * 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
$3$	2.12489	1.22680	0.613402	−	0.789771i	$-0.289801\pi$
$3$	2.12489	1.22680	0.613402	+	0.789771i	$0.289801\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.12489	−0.867481
$7$	−4.12489	−1.55906	−0.779530	−	0.626365i	$-0.784542\pi$
$7$	−4.12489	−1.55906	−0.779530	+	0.626365i	$0.784542\pi$
$8$	−1.00000	−0.353553
$9$	1.51514	0.505046
$10$	0	0
$11$	−2.64002	−0.795997	−0.397999	−	0.917386i	$-0.630295\pi$
$11$	−2.64002	−0.795997	−0.397999	+	0.917386i	$0.630295\pi$
$12$	2.12489	0.613402
$13$	−2.51514	−0.697574	−0.348787	−	0.937202i	$-0.613406\pi$
$13$	−2.51514	−0.697574	−0.348787	+	0.937202i	$0.613406\pi$
$14$	4.12489	1.10242
$15$	0	0
$16$	1.00000	0.250000
$17$	0.515138	0.124939	0.0624697	−	0.998047i	$-0.480102\pi$
$17$	0.515138	0.124939	0.0624697	+	0.998047i	$0.480102\pi$
$18$	−1.51514	−0.357121
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−8.76491	−1.91266
$22$	2.64002	0.562855
$23$	−3.09461	−0.645271	−0.322635	−	0.946523i	$-0.604569\pi$
$23$	−3.09461	−0.645271	−0.322635	+	0.946523i	$0.604569\pi$
$24$	−2.12489	−0.433740
$25$	0	0
$26$	2.51514	0.493259
$27$	−3.15516	−0.607211
$28$	−4.12489	−0.779530
$29$	−7.79518	−1.44753	−0.723765	−	0.690047i	$-0.757590\pi$
$29$	−7.79518	−1.44753	−0.723765	+	0.690047i	$0.757590\pi$
$30$	0	0
$31$	3.67030	0.659205	0.329603	−	0.944120i	$-0.393085\pi$
$31$	3.67030	0.659205	0.329603	+	0.944120i	$0.393085\pi$
$32$	−1.00000	−0.176777
$33$	−5.60975	−0.976532
$34$	−0.515138	−0.0883454
$35$	0	0
$36$	1.51514	0.252523
$37$	−10.2498	−1.68505	−0.842526	−	0.538656i	$-0.818932\pi$
$37$	−10.2498	−1.68505	−0.842526	+	0.538656i	$0.818932\pi$
$38$	−1.00000	−0.162221
$39$	−5.34438	−0.855786
$40$	0	0
$41$	8.88979	1.38835	0.694176	−	0.719805i	$-0.255769\pi$
$41$	8.88979	1.38835	0.694176	+	0.719805i	$0.255769\pi$
$42$	8.76491	1.35245
$43$	−8.64002	−1.31759	−0.658796	−	0.752322i	$-0.728934\pi$
$43$	−8.64002	−1.31759	−0.658796	+	0.752322i	$0.728934\pi$
$44$	−2.64002	−0.397999
$45$	0	0
$46$	3.09461	0.456275
$47$	4.96972	0.724909	0.362454	−	0.932002i	$-0.381939\pi$
$47$	4.96972	0.724909	0.362454	+	0.932002i	$0.381939\pi$
$48$	2.12489	0.306701
$49$	10.0147	1.43067
$50$	0	0
$51$	1.09461	0.153276
$52$	−2.51514	−0.348787
$53$	−5.48486	−0.753404	−0.376702	−	0.926335i	$-0.622942\pi$
$53$	−5.48486	−0.753404	−0.376702	+	0.926335i	$0.622942\pi$
$54$	3.15516	0.429363
$55$	0	0
$56$	4.12489	0.551211
$57$	2.12489	0.281448
$58$	7.79518	1.02356
$59$	3.15516	0.410767	0.205384	−	0.978682i	$-0.434156\pi$
$59$	3.15516	0.410767	0.205384	+	0.978682i	$0.434156\pi$
$60$	0	0
$61$	−12.6400	−1.61839	−0.809195	−	0.587541i	$-0.800096\pi$
$61$	−12.6400	−1.61839	−0.809195	+	0.587541i	$0.800096\pi$
$62$	−3.67030	−0.466129
$63$	−6.24977	−0.787397
$64$	1.00000	0.125000
$65$	0	0
$66$	5.60975	0.690512
$67$	7.40493	0.904656	0.452328	−	0.891852i	$-0.350594\pi$
$67$	7.40493	0.904656	0.452328	+	0.891852i	$0.350594\pi$
$68$	0.515138	0.0624697
$69$	−6.57569	−0.791620
$70$	0	0
$71$	11.1396	1.32202	0.661012	−	0.750376i	$-0.270127\pi$
$71$	11.1396	1.32202	0.661012	+	0.750376i	$0.270127\pi$
$72$	−1.51514	−0.178561
$73$	2.70436	0.316521	0.158261	−	0.987397i	$-0.449411\pi$
$73$	2.70436	0.316521	0.158261	+	0.987397i	$0.449411\pi$
$74$	10.2498	1.19151
$75$	0	0
$76$	1.00000	0.114708
$77$	10.8898	1.24101
$78$	5.34438	0.605132
$79$	16.7493	1.88444	0.942222	−	0.334988i	$-0.108732\pi$
$79$	16.7493	1.88444	0.942222	+	0.334988i	$0.108732\pi$
$80$	0	0
$81$	−11.2498	−1.24997
$82$	−8.88979	−0.981714
$83$	−3.28005	−0.360032	−0.180016	−	0.983664i	$-0.557615\pi$
$83$	−3.28005	−0.360032	−0.180016	+	0.983664i	$0.557615\pi$
$84$	−8.76491	−0.956330
$85$	0	0
$86$	8.64002	0.931678
$87$	−16.5639	−1.77583
$88$	2.64002	0.281427
$89$	−7.60975	−0.806632	−0.403316	−	0.915061i	$-0.632142\pi$
$89$	−7.60975	−0.806632	−0.403316	+	0.915061i	$0.632142\pi$
$90$	0	0
$91$	10.3747	1.08756
$92$	−3.09461	−0.322635
$93$	7.79897	0.808715
$94$	−4.96972	−0.512588
$95$	0	0
$96$	−2.12489	−0.216870
$97$	−3.93945	−0.399990	−0.199995	−	0.979797i	$-0.564093\pi$
$97$	−3.93945	−0.399990	−0.199995	+	0.979797i	$0.564093\pi$
$98$	−10.0147	−1.01164
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−13.7990	−1.37305	−0.686524	−	0.727107i	$-0.740864\pi$
$101$	−13.7990	−1.37305	−0.686524	+	0.727107i	$0.740864\pi$
$102$	−1.09461	−0.108382
$103$	−4.57947	−0.451229	−0.225614	−	0.974217i	$-0.572439\pi$
$103$	−4.57947	−0.451229	−0.225614	+	0.974217i	$0.572439\pi$
$104$	2.51514	0.246630
$105$	0	0
$106$	5.48486	0.532737
$107$	10.3747	1.00296	0.501478	−	0.865170i	$-0.332790\pi$
$107$	10.3747	1.00296	0.501478	+	0.865170i	$0.332790\pi$
$108$	−3.15516	−0.303606
$109$	3.01468	0.288754	0.144377	−	0.989523i	$-0.453882\pi$
$109$	3.01468	0.288754	0.144377	+	0.989523i	$0.453882\pi$
$110$	0	0
$111$	−21.7796	−2.06723
$112$	−4.12489	−0.389765
$113$	19.2001	1.80620	0.903098	−	0.429435i	$-0.141287\pi$
$113$	19.2001	1.80620	0.903098	+	0.429435i	$0.141287\pi$
$114$	−2.12489	−0.199014
$115$	0	0
$116$	−7.79518	−0.723765
$117$	−3.81078	−0.352307
$118$	−3.15516	−0.290456
$119$	−2.12489	−0.194788
$120$	0	0
$121$	−4.03028	−0.366389
$122$	12.6400	1.14437
$123$	18.8898	1.70324
$124$	3.67030	0.329603
$125$	0	0
$126$	6.24977	0.556774
$127$	−14.3103	−1.26984	−0.634918	−	0.772580i	$-0.718966\pi$
$127$	−14.3103	−1.26984	−0.634918	+	0.772580i	$0.718966\pi$
$128$	−1.00000	−0.0883883
$129$	−18.3591	−1.61643
$130$	0	0
$131$	−6.56009	−0.573158	−0.286579	−	0.958057i	$-0.592518\pi$
$131$	−6.56009	−0.573158	−0.286579	+	0.958057i	$0.592518\pi$
$132$	−5.60975	−0.488266
$133$	−4.12489	−0.357673
$134$	−7.40493	−0.639689
$135$	0	0
$136$	−0.515138	−0.0441727
$137$	6.45459	0.551452	0.275726	−	0.961236i	$-0.411082\pi$
$137$	6.45459	0.551452	0.275726	+	0.961236i	$0.411082\pi$
$138$	6.57569	0.559760
$139$	−23.0596	−1.95589	−0.977946	−	0.208856i	$-0.933026\pi$
$139$	−23.0596	−1.95589	−0.977946	+	0.208856i	$0.933026\pi$
$140$	0	0
$141$	10.5601	0.889320
$142$	−11.1396	−0.934812
$143$	6.64002	0.555267
$144$	1.51514	0.126262
$145$	0	0
$146$	−2.70436	−0.223814
$147$	21.2800	1.75515
$148$	−10.2498	−0.842526
$149$	16.0294	1.31318	0.656588	−	0.754249i	$-0.271999\pi$
$149$	16.0294	1.31318	0.656588	+	0.754249i	$0.271999\pi$
$150$	0	0
$151$	−14.3103	−1.16456	−0.582279	−	0.812989i	$-0.697839\pi$
$151$	−14.3103	−1.16456	−0.582279	+	0.812989i	$0.697839\pi$
$152$	−1.00000	−0.0811107
$153$	0.780505	0.0631001
$154$	−10.8898	−0.877525
$155$	0	0
$156$	−5.34438	−0.427893
$157$	18.0294	1.43890	0.719450	−	0.694544i	$-0.244394\pi$
$157$	18.0294	1.43890	0.719450	+	0.694544i	$0.244394\pi$
$158$	−16.7493	−1.33250
$159$	−11.6547	−0.924278
$160$	0	0
$161$	12.7649	1.00602
$162$	11.2498	0.883865
$163$	−2.70058	−0.211525	−0.105763	−	0.994391i	$-0.533728\pi$
$163$	−2.70058	−0.211525	−0.105763	+	0.994391i	$0.533728\pi$
$164$	8.88979	0.694176
$165$	0	0
$166$	3.28005	0.254581
$167$	−8.95035	−0.692599	−0.346299	−	0.938124i	$-0.612562\pi$
$167$	−8.95035	−0.692599	−0.346299	+	0.938124i	$0.612562\pi$
$168$	8.76491	0.676227
$169$	−6.67408	−0.513391
$170$	0	0
$171$	1.51514	0.115866
$172$	−8.64002	−0.658796
$173$	−0.310323	−0.0235934	−0.0117967	−	0.999930i	$-0.503755\pi$
$173$	−0.310323	−0.0235934	−0.0117967	+	0.999930i	$0.503755\pi$
$174$	16.5639	1.25570
$175$	0	0
$176$	−2.64002	−0.198999
$177$	6.70436	0.503930
$178$	7.60975	0.570375
$179$	−1.52982	−0.114344	−0.0571720	−	0.998364i	$-0.518208\pi$
$179$	−1.52982	−0.114344	−0.0571720	+	0.998364i	$0.518208\pi$
$180$	0	0
$181$	−14.7493	−1.09631	−0.548154	−	0.836377i	$-0.684669\pi$
$181$	−14.7493	−1.09631	−0.548154	+	0.836377i	$0.684669\pi$
$182$	−10.3747	−0.769021
$183$	−26.8586	−1.98544
$184$	3.09461	0.228138
$185$	0	0
$186$	−7.79897	−0.571848
$187$	−1.35998	−0.0994513
$188$	4.96972	0.362454
$189$	13.0147	0.946679
$190$	0	0
$191$	18.1249	1.31147	0.655735	−	0.754991i	$-0.272359\pi$
$191$	18.1249	1.31147	0.655735	+	0.754991i	$0.272359\pi$
$192$	2.12489	0.153350
$193$	4.56009	0.328243	0.164121	−	0.986440i	$-0.447521\pi$
$193$	4.56009	0.328243	0.164121	+	0.986440i	$0.447521\pi$
$194$	3.93945	0.282836
$195$	0	0
$196$	10.0147	0.715334
$197$	2.14048	0.152503	0.0762515	−	0.997089i	$-0.475705\pi$
$197$	2.14048	0.152503	0.0762515	+	0.997089i	$0.475705\pi$
$198$	4.00000	0.284268
$199$	16.5639	1.17418	0.587091	−	0.809521i	$-0.300273\pi$
$199$	16.5639	1.17418	0.587091	+	0.809521i	$0.300273\pi$
$200$	0	0
$201$	15.7346	1.10984
$202$	13.7990	0.970892
$203$	32.1542	2.25679
$204$	1.09461	0.0766380
$205$	0	0
$206$	4.57947	0.319067
$207$	−4.68876	−0.325891
$208$	−2.51514	−0.174393
$209$	−2.64002	−0.182614
$210$	0	0
$211$	−15.2838	−1.05218	−0.526091	−	0.850428i	$-0.676343\pi$
$211$	−15.2838	−1.05218	−0.526091	+	0.850428i	$0.676343\pi$
$212$	−5.48486	−0.376702
$213$	23.6703	1.62186
$214$	−10.3747	−0.709197
$215$	0	0
$216$	3.15516	0.214682
$217$	−15.1396	−1.02774
$218$	−3.01468	−0.204180
$219$	5.74645	0.388309
$220$	0	0
$221$	−1.29564	−0.0871544
$222$	21.7796	1.46175
$223$	3.75023	0.251134	0.125567	−	0.992085i	$-0.459925\pi$
$223$	3.75023	0.251134	0.125567	+	0.992085i	$0.459925\pi$
$224$	4.12489	0.275606
$225$	0	0
$226$	−19.2001	−1.27717
$227$	24.1542	1.60317	0.801587	−	0.597878i	$-0.203989\pi$
$227$	24.1542	1.60317	0.801587	+	0.597878i	$0.203989\pi$
$228$	2.12489	0.140724
$229$	−13.0596	−0.863005	−0.431503	−	0.902112i	$-0.642016\pi$
$229$	−13.0596	−0.863005	−0.431503	+	0.902112i	$0.642016\pi$
$230$	0	0
$231$	23.1396	1.52247
$232$	7.79518	0.511779
$233$	6.43899	0.421832	0.210916	−	0.977504i	$-0.432355\pi$
$233$	6.43899	0.421832	0.210916	+	0.977504i	$0.432355\pi$
$234$	3.81078	0.249119
$235$	0	0
$236$	3.15516	0.205384
$237$	35.5904	2.31184
$238$	2.12489	0.137736
$239$	22.8742	1.47961	0.739804	−	0.672822i	$-0.234918\pi$
$239$	22.8742	1.47961	0.739804	+	0.672822i	$0.234918\pi$
$240$	0	0
$241$	4.96972	0.320128	0.160064	−	0.987107i	$-0.448830\pi$
$241$	4.96972	0.320128	0.160064	+	0.987107i	$0.448830\pi$
$242$	4.03028	0.259076
$243$	−14.4390	−0.926262
$244$	−12.6400	−0.809195
$245$	0	0
$246$	−18.8898	−1.20437
$247$	−2.51514	−0.160034
$248$	−3.67030	−0.233064
$249$	−6.96972	−0.441688
$250$	0	0
$251$	15.9201	1.00487	0.502433	−	0.864616i	$-0.332438\pi$
$251$	15.9201	1.00487	0.502433	+	0.864616i	$0.332438\pi$
$252$	−6.24977	−0.393699
$253$	8.16984	0.513634
$254$	14.3103	0.897910
$255$	0	0
$256$	1.00000	0.0625000
$257$	1.04965	0.0654756	0.0327378	−	0.999464i	$-0.489577\pi$
$257$	1.04965	0.0654756	0.0327378	+	0.999464i	$0.489577\pi$
$258$	18.3591	1.14299
$259$	42.2791	2.62710
$260$	0	0
$261$	−11.8108	−0.731069
$262$	6.56009	0.405284
$263$	11.9394	0.736218	0.368109	−	0.929783i	$-0.380005\pi$
$263$	11.9394	0.736218	0.368109	+	0.929783i	$0.380005\pi$
$264$	5.60975	0.345256
$265$	0	0
$266$	4.12489	0.252913
$267$	−16.1698	−0.989578
$268$	7.40493	0.452328
$269$	−15.9394	−0.971845	−0.485923	−	0.874002i	$-0.661516\pi$
$269$	−15.9394	−0.971845	−0.485923	+	0.874002i	$0.661516\pi$
$270$	0	0
$271$	1.46548	0.0890218	0.0445109	−	0.999009i	$-0.485827\pi$
$271$	1.46548	0.0890218	0.0445109	+	0.999009i	$0.485827\pi$
$272$	0.515138	0.0312348
$273$	22.0450	1.33422
$274$	−6.45459	−0.389936
$275$	0	0
$276$	−6.57569	−0.395810
$277$	−32.4995	−1.95271	−0.976354	−	0.216177i	$-0.930641\pi$
$277$	−32.4995	−1.95271	−0.976354	+	0.216177i	$0.930641\pi$
$278$	23.0596	1.38303
$279$	5.56101	0.332929
$280$	0	0
$281$	1.04965	0.0626171	0.0313085	−	0.999510i	$-0.490033\pi$
$281$	1.04965	0.0626171	0.0313085	+	0.999510i	$0.490033\pi$
$282$	−10.5601	−0.628844
$283$	9.34060	0.555241	0.277620	−	0.960691i	$-0.410454\pi$
$283$	9.34060	0.555241	0.277620	+	0.960691i	$0.410454\pi$
$284$	11.1396	0.661012
$285$	0	0
$286$	−6.64002	−0.392633
$287$	−36.6694	−2.16453
$288$	−1.51514	−0.0892804
$289$	−16.7346	−0.984390
$290$	0	0
$291$	−8.37088	−0.490709
$292$	2.70436	0.158261
$293$	−25.5748	−1.49409	−0.747047	−	0.664771i	$-0.768529\pi$
$293$	−25.5748	−1.49409	−0.747047	+	0.664771i	$0.768529\pi$
$294$	−21.2800	−1.24108
$295$	0	0
$296$	10.2498	0.595756
$297$	8.32970	0.483338
$298$	−16.0294	−0.928556
$299$	7.78337	0.450124
$300$	0	0
$301$	35.6391	2.05420
$302$	14.3103	0.823467
$303$	−29.3212	−1.68446
$304$	1.00000	0.0573539
$305$	0	0
$306$	−0.780505	−0.0446185
$307$	−9.43991	−0.538764	−0.269382	−	0.963033i	$-0.586819\pi$
$307$	−9.43991	−0.538764	−0.269382	+	0.963033i	$0.586819\pi$
$308$	10.8898	0.620504
$309$	−9.73085	−0.553569
$310$	0	0
$311$	−17.4655	−0.990377	−0.495188	−	0.868786i	$-0.664901\pi$
$311$	−17.4655	−0.990377	−0.495188	+	0.868786i	$0.664901\pi$
$312$	5.34438	0.302566
$313$	10.4546	0.590928	0.295464	−	0.955354i	$-0.404526\pi$
$313$	10.4546	0.590928	0.295464	+	0.955354i	$0.404526\pi$
$314$	−18.0294	−1.01746
$315$	0	0
$316$	16.7493	0.942222
$317$	−4.33348	−0.243393	−0.121696	−	0.992567i	$-0.538833\pi$
$317$	−4.33348	−0.243393	−0.121696	+	0.992567i	$0.538833\pi$
$318$	11.6547	0.653563
$319$	20.5795	1.15223
$320$	0	0
$321$	22.0450	1.23043
$322$	−12.7649	−0.711361
$323$	0.515138	0.0286630
$324$	−11.2498	−0.624987
$325$	0	0
$326$	2.70058	0.149571
$327$	6.40585	0.354244
$328$	−8.88979	−0.490857
$329$	−20.4995	−1.13018
$330$	0	0
$331$	−4.56387	−0.250853	−0.125427	−	0.992103i	$-0.540030\pi$
$331$	−4.56387	−0.250853	−0.125427	+	0.992103i	$0.540030\pi$
$332$	−3.28005	−0.180016
$333$	−15.5298	−0.851029
$334$	8.95035	0.489741
$335$	0	0
$336$	−8.76491	−0.478165
$337$	−13.0109	−0.708749	−0.354374	−	0.935104i	$-0.615306\pi$
$337$	−13.0109	−0.708749	−0.354374	+	0.935104i	$0.615306\pi$
$338$	6.67408	0.363022
$339$	40.7980	2.21585
$340$	0	0
$341$	−9.68968	−0.524725
$342$	−1.51514	−0.0819293
$343$	−12.4352	−0.671438
$344$	8.64002	0.465839
$345$	0	0
$346$	0.310323	0.0166831
$347$	−13.2195	−0.709660	−0.354830	−	0.934931i	$-0.615461\pi$
$347$	−13.2195	−0.709660	−0.354830	+	0.934931i	$0.615461\pi$
$348$	−16.5639	−0.887917
$349$	−20.4390	−1.09407	−0.547037	−	0.837108i	$-0.684244\pi$
$349$	−20.4390	−1.09407	−0.547037	+	0.837108i	$0.684244\pi$
$350$	0	0
$351$	7.93567	0.423575
$352$	2.64002	0.140714
$353$	−10.7044	−0.569735	−0.284868	−	0.958567i	$-0.591950\pi$
$353$	−10.7044	−0.569735	−0.284868	+	0.958567i	$0.591950\pi$
$354$	−6.70436	−0.356333
$355$	0	0
$356$	−7.60975	−0.403316
$357$	−4.51514	−0.238966
$358$	1.52982	0.0808534
$359$	−4.31410	−0.227690	−0.113845	−	0.993499i	$-0.536317\pi$
$359$	−4.31410	−0.227690	−0.113845	+	0.993499i	$0.536317\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.7493	0.775207
$363$	−8.56387	−0.449487
$364$	10.3747	0.543780
$365$	0	0
$366$	26.8586	1.40392
$367$	12.8099	0.668669	0.334335	−	0.942454i	$-0.391488\pi$
$367$	12.8099	0.668669	0.334335	+	0.942454i	$0.391488\pi$
$368$	−3.09461	−0.161318
$369$	13.4693	0.701182
$370$	0	0
$371$	22.6244	1.17460
$372$	7.79897	0.404358
$373$	−0.704357	−0.0364702	−0.0182351	−	0.999834i	$-0.505805\pi$
$373$	−0.704357	−0.0364702	−0.0182351	+	0.999834i	$0.505805\pi$
$374$	1.35998	0.0703227
$375$	0	0
$376$	−4.96972	−0.256294
$377$	19.6060	1.00976
$378$	−13.0147	−0.669403
$379$	6.12489	0.314614	0.157307	−	0.987550i	$-0.449719\pi$
$379$	6.12489	0.314614	0.157307	+	0.987550i	$0.449719\pi$
$380$	0	0
$381$	−30.4078	−1.55784
$382$	−18.1249	−0.927350
$383$	−18.6400	−0.952461	−0.476230	−	0.879321i	$-0.657997\pi$
$383$	−18.6400	−0.952461	−0.476230	+	0.879321i	$0.657997\pi$
$384$	−2.12489	−0.108435
$385$	0	0
$386$	−4.56009	−0.232103
$387$	−13.0908	−0.665444
$388$	−3.93945	−0.199995
$389$	13.9201	0.705776	0.352888	−	0.935666i	$-0.385200\pi$
$389$	13.9201	0.705776	0.352888	+	0.935666i	$0.385200\pi$
$390$	0	0
$391$	−1.59415	−0.0806197
$392$	−10.0147	−0.505818
$393$	−13.9394	−0.703152
$394$	−2.14048	−0.107836
$395$	0	0
$396$	−4.00000	−0.201008
$397$	28.3784	1.42427	0.712136	−	0.702041i	$-0.247728\pi$
$397$	28.3784	1.42427	0.712136	+	0.702041i	$0.247728\pi$
$398$	−16.5639	−0.830272
$399$	−8.76491	−0.438794
$400$	0	0
$401$	5.54920	0.277114	0.138557	−	0.990354i	$-0.455754\pi$
$401$	5.54920	0.277114	0.138557	+	0.990354i	$0.455754\pi$
$402$	−15.7346	−0.784772
$403$	−9.23131	−0.459844
$404$	−13.7990	−0.686524
$405$	0	0
$406$	−32.1542	−1.59579
$407$	27.0596	1.34130
$408$	−1.09461	−0.0541912
$409$	−5.01090	−0.247773	−0.123886	−	0.992296i	$-0.539536\pi$
$409$	−5.01090	−0.247773	−0.123886	+	0.992296i	$0.539536\pi$
$410$	0	0
$411$	13.7153	0.676524
$412$	−4.57947	−0.225614
$413$	−13.0147	−0.640411
$414$	4.68876	0.230440
$415$	0	0
$416$	2.51514	0.123315
$417$	−48.9991	−2.39950
$418$	2.64002	0.129128
$419$	−15.8889	−0.776222	−0.388111	−	0.921613i	$-0.626872\pi$
$419$	−15.8889	−0.776222	−0.388111	+	0.921613i	$0.626872\pi$
$420$	0	0
$421$	−2.38647	−0.116310	−0.0581548	−	0.998308i	$-0.518522\pi$
$421$	−2.38647	−0.116310	−0.0581548	+	0.998308i	$0.518522\pi$
$422$	15.2838	0.744005
$423$	7.52982	0.366112
$424$	5.48486	0.266368
$425$	0	0
$426$	−23.6703	−1.14683
$427$	52.1386	2.52317
$428$	10.3747	0.501478
$429$	14.1093	0.681203
$430$	0	0
$431$	−2.35906	−0.113632	−0.0568160	−	0.998385i	$-0.518095\pi$
$431$	−2.35906	−0.113632	−0.0568160	+	0.998385i	$0.518095\pi$
$432$	−3.15516	−0.151803
$433$	0.640023	0.0307576	0.0153788	−	0.999882i	$-0.495105\pi$
$433$	0.640023	0.0307576	0.0153788	+	0.999882i	$0.495105\pi$
$434$	15.1396	0.726722
$435$	0	0
$436$	3.01468	0.144377
$437$	−3.09461	−0.148035
$438$	−5.74645	−0.274576
$439$	−25.4499	−1.21466	−0.607328	−	0.794451i	$-0.707759\pi$
$439$	−25.4499	−1.21466	−0.607328	+	0.794451i	$0.707759\pi$
$440$	0	0
$441$	15.1736	0.722553
$442$	1.29564	0.0616275
$443$	35.6685	1.69466	0.847330	−	0.531067i	$-0.178209\pi$
$443$	35.6685	1.69466	0.847330	+	0.531067i	$0.178209\pi$
$444$	−21.7796	−1.03361
$445$	0	0
$446$	−3.75023	−0.177578
$447$	34.0606	1.61101
$448$	−4.12489	−0.194883
$449$	−11.4399	−0.539883	−0.269941	−	0.962877i	$-0.587004\pi$
$449$	−11.4399	−0.539883	−0.269941	+	0.962877i	$0.587004\pi$
$450$	0	0
$451$	−23.4693	−1.10512
$452$	19.2001	0.903098
$453$	−30.4078	−1.42868
$454$	−24.1542	−1.13361
$455$	0	0
$456$	−2.12489	−0.0995069
$457$	−19.4849	−0.911463	−0.455732	−	0.890117i	$-0.650622\pi$
$457$	−19.4849	−0.911463	−0.455732	+	0.890117i	$0.650622\pi$
$458$	13.0596	0.610237
$459$	−1.62534	−0.0758645
$460$	0	0
$461$	−29.3893	−1.36880	−0.684399	−	0.729108i	$-0.739935\pi$
$461$	−29.3893	−1.36880	−0.684399	+	0.729108i	$0.739935\pi$
$462$	−23.1396	−1.07655
$463$	−12.1892	−0.566481	−0.283241	−	0.959049i	$-0.591409\pi$
$463$	−12.1892	−0.566481	−0.283241	+	0.959049i	$0.591409\pi$
$464$	−7.79518	−0.361882
$465$	0	0
$466$	−6.43899	−0.298280
$467$	17.8889	0.827799	0.413899	−	0.910323i	$-0.364167\pi$
$467$	17.8889	0.827799	0.413899	+	0.910323i	$0.364167\pi$
$468$	−3.81078	−0.176153
$469$	−30.5445	−1.41041
$470$	0	0
$471$	38.3103	1.76525
$472$	−3.15516	−0.145228
$473$	22.8099	1.04880
$474$	−35.5904	−1.63472
$475$	0	0
$476$	−2.12489	−0.0973940
$477$	−8.31032	−0.380504
$478$	−22.8742	−1.04624
$479$	−1.15894	−0.0529534	−0.0264767	−	0.999649i	$-0.508429\pi$
$479$	−1.15894	−0.0529534	−0.0264767	+	0.999649i	$0.508429\pi$
$480$	0	0
$481$	25.7796	1.17545
$482$	−4.96972	−0.226365
$483$	27.1240	1.23418
$484$	−4.03028	−0.183194
$485$	0	0
$486$	14.4390	0.654966
$487$	−30.6888	−1.39064	−0.695320	−	0.718700i	$-0.744737\pi$
$487$	−30.6888	−1.39064	−0.695320	+	0.718700i	$0.744737\pi$
$488$	12.6400	0.572187
$489$	−5.73841	−0.259500
$490$	0	0
$491$	3.67030	0.165638	0.0828192	−	0.996565i	$-0.473608\pi$
$491$	3.67030	0.165638	0.0828192	+	0.996565i	$0.473608\pi$
$492$	18.8898	0.851618
$493$	−4.01560	−0.180853
$494$	2.51514	0.113161
$495$	0	0
$496$	3.67030	0.164801
$497$	−45.9494	−2.06111
$498$	6.96972	0.312321
$499$	31.3893	1.40518	0.702590	−	0.711595i	$-0.252027\pi$
$499$	31.3893	1.40518	0.702590	+	0.711595i	$0.252027\pi$
$500$	0	0
$501$	−19.0185	−0.849682
$502$	−15.9201	−0.710548
$503$	18.1542	0.809458	0.404729	−	0.914437i	$-0.367366\pi$
$503$	18.1542	0.809458	0.404729	+	0.914437i	$0.367366\pi$
$504$	6.24977	0.278387
$505$	0	0
$506$	−8.16984	−0.363194
$507$	−14.1817	−0.629829
$508$	−14.3103	−0.634918
$509$	11.5298	0.511050	0.255525	−	0.966802i	$-0.417752\pi$
$509$	11.5298	0.511050	0.255525	+	0.966802i	$0.417752\pi$
$510$	0	0
$511$	−11.1552	−0.493475
$512$	−1.00000	−0.0441942
$513$	−3.15516	−0.139304
$514$	−1.04965	−0.0462982
$515$	0	0
$516$	−18.3591	−0.808213
$517$	−13.1202	−0.577025
$518$	−42.2791	−1.85764
$519$	−0.659401	−0.0289445
$520$	0	0
$521$	−42.5895	−1.86588	−0.932939	−	0.360035i	$-0.882765\pi$
$521$	−42.5895	−1.86588	−0.932939	+	0.360035i	$0.882765\pi$
$522$	11.8108	0.516944
$523$	−1.21571	−0.0531594	−0.0265797	−	0.999647i	$-0.508462\pi$
$523$	−1.21571	−0.0531594	−0.0265797	+	0.999647i	$0.508462\pi$
$524$	−6.56009	−0.286579
$525$	0	0
$526$	−11.9394	−0.520585
$527$	1.89071	0.0823607
$528$	−5.60975	−0.244133
$529$	−13.4234	−0.583626
$530$	0	0
$531$	4.78051	0.207456
$532$	−4.12489	−0.178836
$533$	−22.3591	−0.968478
$534$	16.1698	0.699737
$535$	0	0
$536$	−7.40493	−0.319844
$537$	−3.25069	−0.140278
$538$	15.9394	0.687198
$539$	−26.4390	−1.13881
$540$	0	0
$541$	−1.92007	−0.0825503	−0.0412751	−	0.999148i	$-0.513142\pi$
$541$	−1.92007	−0.0825503	−0.0412751	+	0.999148i	$0.513142\pi$
$542$	−1.46548	−0.0629480
$543$	−31.3406	−1.34495
$544$	−0.515138	−0.0220864
$545$	0	0
$546$	−22.0450	−0.943437
$547$	−10.9697	−0.469032	−0.234516	−	0.972112i	$-0.575350\pi$
$547$	−10.9697	−0.469032	−0.234516	+	0.972112i	$0.575350\pi$
$548$	6.45459	0.275726
$549$	−19.1514	−0.817361
$550$	0	0
$551$	−7.79518	−0.332086
$552$	6.57569	0.279880
$553$	−69.0890	−2.93796
$554$	32.4995	1.38077
$555$	0	0
$556$	−23.0596	−0.977946
$557$	−23.5005	−0.995746	−0.497873	−	0.867250i	$-0.665886\pi$
$557$	−23.5005	−0.995746	−0.497873	+	0.867250i	$0.665886\pi$
$558$	−5.56101	−0.235416
$559$	21.7309	0.919117
$560$	0	0
$561$	−2.88979	−0.122007
$562$	−1.04965	−0.0442770
$563$	7.87890	0.332056	0.166028	−	0.986121i	$-0.446906\pi$
$563$	7.87890	0.332056	0.166028	+	0.986121i	$0.446906\pi$
$564$	10.5601	0.444660
$565$	0	0
$566$	−9.34060	−0.392615
$567$	46.4040	1.94879
$568$	−11.1396	−0.467406
$569$	−1.09083	−0.0457299	−0.0228650	−	0.999739i	$-0.507279\pi$
$569$	−1.09083	−0.0457299	−0.0228650	+	0.999739i	$0.507279\pi$
$570$	0	0
$571$	21.4886	0.899272	0.449636	−	0.893212i	$-0.351554\pi$
$571$	21.4886	0.899272	0.449636	+	0.893212i	$0.351554\pi$
$572$	6.64002	0.277633
$573$	38.5133	1.60892
$574$	36.6694	1.53055
$575$	0	0
$576$	1.51514	0.0631308
$577$	16.1055	0.670481	0.335241	−	0.942133i	$-0.391182\pi$
$577$	16.1055	0.670481	0.335241	+	0.942133i	$0.391182\pi$
$578$	16.7346	0.696069
$579$	9.68968	0.402689
$580$	0	0
$581$	13.5298	0.561311
$582$	8.37088	0.346984
$583$	14.4802	0.599707
$584$	−2.70436	−0.111907
$585$	0	0
$586$	25.5748	1.05648
$587$	−0.480164	−0.0198185	−0.00990925	−	0.999951i	$-0.503154\pi$
$587$	−0.480164	−0.0198185	−0.00990925	+	0.999951i	$0.503154\pi$
$588$	21.2800	0.877574
$589$	3.67030	0.151232
$590$	0	0
$591$	4.54828	0.187091
$592$	−10.2498	−0.421263
$593$	−40.4683	−1.66184	−0.830918	−	0.556395i	$-0.812184\pi$
$593$	−40.4683	−1.66184	−0.830918	+	0.556395i	$0.812184\pi$
$594$	−8.32970	−0.341772
$595$	0	0
$596$	16.0294	0.656588
$597$	35.1963	1.44049
$598$	−7.78337	−0.318286
$599$	−36.1698	−1.47786	−0.738930	−	0.673782i	$-0.764669\pi$
$599$	−36.1698	−1.47786	−0.738930	+	0.673782i	$0.764669\pi$
$600$	0	0
$601$	24.3903	0.994899	0.497450	−	0.867493i	$-0.334270\pi$
$601$	24.3903	0.994899	0.497450	+	0.867493i	$0.334270\pi$
$602$	−35.6391	−1.45254
$603$	11.2195	0.456893
$604$	−14.3103	−0.582279
$605$	0	0
$606$	29.3212	1.19109
$607$	−21.6897	−0.880357	−0.440178	−	0.897910i	$-0.645085\pi$
$607$	−21.6897	−0.880357	−0.440178	+	0.897910i	$0.645085\pi$
$608$	−1.00000	−0.0405554
$609$	68.3241	2.76863
$610$	0	0
$611$	−12.4995	−0.505677
$612$	0.780505	0.0315501
$613$	26.2304	1.05944	0.529718	−	0.848174i	$-0.322298\pi$
$613$	26.2304	1.05944	0.529718	+	0.848174i	$0.322298\pi$
$614$	9.43991	0.380964
$615$	0	0
$616$	−10.8898	−0.438762
$617$	22.7200	0.914671	0.457335	−	0.889294i	$-0.348804\pi$
$617$	22.7200	0.914671	0.457335	+	0.889294i	$0.348804\pi$
$618$	9.73085	0.391432
$619$	−32.9192	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$619$	−32.9192	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$620$	0	0
$621$	9.76399	0.391816
$622$	17.4655	0.700302
$623$	31.3893	1.25759
$624$	−5.34438	−0.213946
$625$	0	0
$626$	−10.4546	−0.417849
$627$	−5.60975	−0.224032
$628$	18.0294	0.719450
$629$	−5.28005	−0.210529
$630$	0	0
$631$	17.2876	0.688209	0.344104	−	0.938931i	$-0.388183\pi$
$631$	17.2876	0.688209	0.344104	+	0.938931i	$0.388183\pi$
$632$	−16.7493	−0.666252
$633$	−32.4764	−1.29082
$634$	4.33348	0.172105
$635$	0	0
$636$	−11.6547	−0.462139
$637$	−25.1883	−0.997997
$638$	−20.5795	−0.814749
$639$	16.8780	0.667683
$640$	0	0
$641$	−9.29942	−0.367305	−0.183653	−	0.982991i	$-0.558792\pi$
$641$	−9.29942	−0.367305	−0.183653	+	0.982991i	$0.558792\pi$
$642$	−22.0450	−0.870045
$643$	3.40115	0.134128	0.0670642	−	0.997749i	$-0.478637\pi$
$643$	3.40115	0.134128	0.0670642	+	0.997749i	$0.478637\pi$
$644$	12.7649	0.503008
$645$	0	0
$646$	−0.515138	−0.0202678
$647$	−14.9348	−0.587146	−0.293573	−	0.955937i	$-0.594844\pi$
$647$	−14.9348	−0.587146	−0.293573	+	0.955937i	$0.594844\pi$
$648$	11.2498	0.441933
$649$	−8.32970	−0.326969
$650$	0	0
$651$	−32.1698	−1.26084
$652$	−2.70058	−0.105763
$653$	−21.1202	−0.826497	−0.413248	−	0.910618i	$-0.635606\pi$
$653$	−21.1202	−0.826497	−0.413248	+	0.910618i	$0.635606\pi$
$654$	−6.40585	−0.250489
$655$	0	0
$656$	8.88979	0.347088
$657$	4.09747	0.159858
$658$	20.4995	0.799155
$659$	27.6547	1.07727	0.538637	−	0.842538i	$-0.318939\pi$
$659$	27.6547	1.07727	0.538637	+	0.842538i	$0.318939\pi$
$660$	0	0
$661$	10.2342	0.398063	0.199032	−	0.979993i	$-0.436220\pi$
$661$	10.2342	0.398063	0.199032	+	0.979993i	$0.436220\pi$
$662$	4.56387	0.177380
$663$	−2.75309	−0.106921
$664$	3.28005	0.127291
$665$	0	0
$666$	15.5298	0.601768
$667$	24.1231	0.934048
$668$	−8.95035	−0.346299
$669$	7.96881	0.308092
$670$	0	0
$671$	33.3700	1.28823
$672$	8.76491	0.338114
$673$	13.4693	0.519202	0.259601	−	0.965716i	$-0.416409\pi$
$673$	13.4693	0.519202	0.259601	+	0.965716i	$0.416409\pi$
$674$	13.0109	0.501161
$675$	0	0
$676$	−6.67408	−0.256695
$677$	−15.1433	−0.582006	−0.291003	−	0.956722i	$-0.593989\pi$
$677$	−15.1433	−0.582006	−0.291003	+	0.956722i	$0.593989\pi$
$678$	−40.7980	−1.56684
$679$	16.2498	0.623609
$680$	0	0
$681$	51.3250	1.96678
$682$	9.68968	0.371037
$683$	−15.8789	−0.607589	−0.303795	−	0.952738i	$-0.598254\pi$
$683$	−15.8789	−0.607589	−0.303795	+	0.952738i	$0.598254\pi$
$684$	1.51514	0.0579328
$685$	0	0
$686$	12.4352	0.474778
$687$	−27.7502	−1.05874
$688$	−8.64002	−0.329398
$689$	13.7952	0.525555
$690$	0	0
$691$	27.3094	1.03890	0.519449	−	0.854501i	$-0.326137\pi$
$691$	27.3094	1.03890	0.519449	+	0.854501i	$0.326137\pi$
$692$	−0.310323	−0.0117967
$693$	16.4995	0.626766
$694$	13.2195	0.501805
$695$	0	0
$696$	16.5639	0.627852
$697$	4.57947	0.173460
$698$	20.4390	0.773627
$699$	13.6821	0.517505
$700$	0	0
$701$	−20.9697	−0.792016	−0.396008	−	0.918247i	$-0.629605\pi$
$701$	−20.9697	−0.792016	−0.396008	+	0.918247i	$0.629605\pi$
$702$	−7.93567	−0.299512
$703$	−10.2498	−0.386577
$704$	−2.64002	−0.0994996
$705$	0	0
$706$	10.7044	0.402864
$707$	56.9192	2.14067
$708$	6.70436	0.251965
$709$	37.5592	1.41056	0.705282	−	0.708927i	$-0.250820\pi$
$709$	37.5592	1.41056	0.705282	+	0.708927i	$0.250820\pi$
$710$	0	0
$711$	25.3775	0.951731
$712$	7.60975	0.285187
$713$	−11.3581	−0.425366
$714$	4.51514	0.168975
$715$	0	0
$716$	−1.52982	−0.0571720
$717$	48.6050	1.81519
$718$	4.31410	0.161001
$719$	3.94323	0.147058	0.0735288	−	0.997293i	$-0.476574\pi$
$719$	3.94323	0.147058	0.0735288	+	0.997293i	$0.476574\pi$
$720$	0	0
$721$	18.8898	0.703493
$722$	−1.00000	−0.0372161
$723$	10.5601	0.392734
$724$	−14.7493	−0.548154
$725$	0	0
$726$	8.56387	0.317835
$727$	−33.2139	−1.23183	−0.615917	−	0.787811i	$-0.711214\pi$
$727$	−33.2139	−1.23183	−0.615917	+	0.787811i	$0.711214\pi$
$728$	−10.3747	−0.384510
$729$	3.06811	0.113634
$730$	0	0
$731$	−4.45080	−0.164619
$732$	−26.8586	−0.992722
$733$	8.62065	0.318411	0.159205	−	0.987245i	$-0.449107\pi$
$733$	8.62065	0.318411	0.159205	+	0.987245i	$0.449107\pi$
$734$	−12.8099	−0.472821
$735$	0	0
$736$	3.09461	0.114069
$737$	−19.5492	−0.720104
$738$	−13.4693	−0.495811
$739$	−45.1689	−1.66157	−0.830783	−	0.556597i	$-0.812107\pi$
$739$	−45.1689	−1.66157	−0.830783	+	0.556597i	$0.812107\pi$
$740$	0	0
$741$	−5.34438	−0.196331
$742$	−22.6244	−0.830569
$743$	24.7905	0.909475	0.454737	−	0.890626i	$-0.349733\pi$
$743$	24.7905	0.909475	0.454737	+	0.890626i	$0.349733\pi$
$744$	−7.79897	−0.285924
$745$	0	0
$746$	0.704357	0.0257883
$747$	−4.96972	−0.181833
$748$	−1.35998	−0.0497257
$749$	−42.7943	−1.56367
$750$	0	0
$751$	−6.76869	−0.246993	−0.123497	−	0.992345i	$-0.539411\pi$
$751$	−6.76869	−0.246993	−0.123497	+	0.992345i	$0.539411\pi$
$752$	4.96972	0.181227
$753$	33.8283	1.23277
$754$	−19.6060	−0.714007
$755$	0	0
$756$	13.0147	0.473339
$757$	−45.2101	−1.64319	−0.821595	−	0.570072i	$-0.806915\pi$
$757$	−45.2101	−1.64319	−0.821595	+	0.570072i	$0.806915\pi$
$758$	−6.12489	−0.222466
$759$	17.3600	0.630127
$760$	0	0
$761$	19.8851	0.720834	0.360417	−	0.932791i	$-0.382634\pi$
$761$	19.8851	0.720834	0.360417	+	0.932791i	$0.382634\pi$
$762$	30.4078	1.10156
$763$	−12.4352	−0.450185
$764$	18.1249	0.655735
$765$	0	0
$766$	18.6400	0.673491
$767$	−7.93567	−0.286540
$768$	2.12489	0.0766752
$769$	8.07615	0.291233	0.145617	−	0.989341i	$-0.453483\pi$
$769$	8.07615	0.291233	0.145617	+	0.989341i	$0.453483\pi$
$770$	0	0
$771$	2.23039	0.0803257
$772$	4.56009	0.164121
$773$	−45.9456	−1.65255	−0.826275	−	0.563267i	$-0.809544\pi$
$773$	−45.9456	−1.65255	−0.826275	+	0.563267i	$0.809544\pi$
$774$	13.0908	0.470540
$775$	0	0
$776$	3.93945	0.141418
$777$	89.8383	3.22293
$778$	−13.9201	−0.499059
$779$	8.88979	0.318510
$780$	0	0
$781$	−29.4087	−1.05233
$782$	1.59415	0.0570067
$783$	24.5951	0.878956
$784$	10.0147	0.357667
$785$	0	0
$786$	13.9394	0.497204
$787$	17.8439	0.636067	0.318034	−	0.948079i	$-0.396978\pi$
$787$	17.8439	0.636067	0.318034	+	0.948079i	$0.396978\pi$
$788$	2.14048	0.0762515
$789$	25.3700	0.903194
$790$	0	0
$791$	−79.1983	−2.81597
$792$	4.00000	0.142134
$793$	31.7914	1.12895
$794$	−28.3784	−1.00711
$795$	0	0
$796$	16.5639	0.587091
$797$	37.3326	1.32239	0.661194	−	0.750215i	$-0.270050\pi$
$797$	37.3326	1.32239	0.661194	+	0.750215i	$0.270050\pi$
$798$	8.76491	0.310274
$799$	2.56009	0.0905696
$800$	0	0
$801$	−11.5298	−0.407386
$802$	−5.54920	−0.195949
$803$	−7.13957	−0.251950
$804$	15.7346	0.554918
$805$	0	0
$806$	9.23131	0.325159
$807$	−33.8695	−1.19226
$808$	13.7990	0.485446
$809$	−38.6950	−1.36044	−0.680221	−	0.733007i	$-0.738116\pi$
$809$	−38.6950	−1.36044	−0.680221	+	0.733007i	$0.738116\pi$
$810$	0	0
$811$	13.3444	0.468585	0.234292	−	0.972166i	$-0.424723\pi$
$811$	13.3444	0.468585	0.234292	+	0.972166i	$0.424723\pi$
$812$	32.1542	1.12839
$813$	3.11399	0.109212
$814$	−27.0596	−0.948440
$815$	0	0
$816$	1.09461	0.0383190
$817$	−8.64002	−0.302276
$818$	5.01090	0.175202
$819$	15.7190	0.549268
$820$	0	0
$821$	−37.3482	−1.30346	−0.651730	−	0.758451i	$-0.725956\pi$
$821$	−37.3482	−1.30346	−0.651730	+	0.758451i	$0.725956\pi$
$822$	−13.7153	−0.478374
$823$	51.5630	1.79737	0.898686	−	0.438593i	$-0.144523\pi$
$823$	51.5630	1.79737	0.898686	+	0.438593i	$0.144523\pi$
$824$	4.57947	0.159533
$825$	0	0
$826$	13.0147	0.452839
$827$	48.5639	1.68873	0.844366	−	0.535767i	$-0.179978\pi$
$827$	48.5639	1.68873	0.844366	+	0.535767i	$0.179978\pi$
$828$	−4.68876	−0.162946
$829$	0.325919	0.0113196	0.00565982	−	0.999984i	$-0.498198\pi$
$829$	0.325919	0.0113196	0.00565982	+	0.999984i	$0.498198\pi$
$830$	0	0
$831$	−69.0578	−2.39559
$832$	−2.51514	−0.0871967
$833$	5.15894	0.178747
$834$	48.9991	1.69670
$835$	0	0
$836$	−2.64002	−0.0913071
$837$	−11.5804	−0.400277
$838$	15.8889	0.548872
$839$	−17.1202	−0.591055	−0.295527	−	0.955334i	$-0.595495\pi$
$839$	−17.1202	−0.591055	−0.295527	+	0.955334i	$0.595495\pi$
$840$	0	0
$841$	31.7649	1.09534
$842$	2.38647	0.0822432
$843$	2.23039	0.0768188
$844$	−15.2838	−0.526091
$845$	0	0
$846$	−7.52982	−0.258880
$847$	16.6244	0.571222
$848$	−5.48486	−0.188351
$849$	19.8477	0.681171
$850$	0	0
$851$	31.7190	1.08731
$852$	23.6703	0.810931
$853$	24.9092	0.852874	0.426437	−	0.904517i	$-0.359769\pi$
$853$	24.9092	0.852874	0.426437	+	0.904517i	$0.359769\pi$
$854$	−52.1386	−1.78415
$855$	0	0
$856$	−10.3747	−0.354598
$857$	11.6509	0.397988	0.198994	−	0.980001i	$-0.436233\pi$
$857$	11.6509	0.397988	0.198994	+	0.980001i	$0.436233\pi$
$858$	−14.1093	−0.481683
$859$	−5.35998	−0.182880	−0.0914400	−	0.995811i	$-0.529147\pi$
$859$	−5.35998	−0.182880	−0.0914400	+	0.995811i	$0.529147\pi$
$860$	0	0
$861$	−77.9182	−2.65545
$862$	2.35906	0.0803499
$863$	41.0790	1.39835	0.699173	−	0.714953i	$-0.253552\pi$
$863$	41.0790	1.39835	0.699173	+	0.714953i	$0.253552\pi$
$864$	3.15516	0.107341
$865$	0	0
$866$	−0.640023	−0.0217489
$867$	−35.5592	−1.20765
$868$	−15.1396	−0.513870
$869$	−44.2186	−1.50001
$870$	0	0
$871$	−18.6244	−0.631065
$872$	−3.01468	−0.102090
$873$	−5.96881	−0.202014
$874$	3.09461	0.104677
$875$	0	0
$876$	5.74645	0.194154
$877$	−45.9532	−1.55173	−0.775865	−	0.630899i	$-0.782686\pi$
$877$	−45.9532	−1.55173	−0.775865	+	0.630899i	$0.782686\pi$
$878$	25.4499	0.858892
$879$	−54.3435	−1.83296
$880$	0	0
$881$	−6.90917	−0.232776	−0.116388	−	0.993204i	$-0.537132\pi$
$881$	−6.90917	−0.232776	−0.116388	+	0.993204i	$0.537132\pi$
$882$	−15.1736	−0.510922
$883$	−48.5213	−1.63287	−0.816437	−	0.577435i	$-0.804054\pi$
$883$	−48.5213	−1.63287	−0.816437	+	0.577435i	$0.804054\pi$
$884$	−1.29564	−0.0435772
$885$	0	0
$886$	−35.6685	−1.19831
$887$	−23.7990	−0.799091	−0.399546	−	0.916713i	$-0.630832\pi$
$887$	−23.7990	−0.799091	−0.399546	+	0.916713i	$0.630832\pi$
$888$	21.7796	0.730875
$889$	59.0284	1.97975
$890$	0	0
$891$	29.6997	0.994976
$892$	3.75023	0.125567
$893$	4.96972	0.166305
$894$	−34.0606	−1.13916
$895$	0	0
$896$	4.12489	0.137803
$897$	16.5388	0.552213
$898$	11.4399	0.381755
$899$	−28.6107	−0.954219
$900$	0	0
$901$	−2.82546	−0.0941298
$902$	23.4693	0.781441
$903$	75.7290	2.52010
$904$	−19.2001	−0.638586
$905$	0	0
$906$	30.4078	1.01023
$907$	−17.9726	−0.596770	−0.298385	−	0.954446i	$-0.596448\pi$
$907$	−17.9726	−0.596770	−0.298385	+	0.954446i	$0.596448\pi$
$908$	24.1542	0.801587
$909$	−20.9073	−0.693453
$910$	0	0
$911$	19.5592	0.648024	0.324012	−	0.946053i	$-0.394968\pi$
$911$	19.5592	0.648024	0.324012	+	0.946053i	$0.394968\pi$
$912$	2.12489	0.0703620
$913$	8.65940	0.286584
$914$	19.4849	0.644502
$915$	0	0
$916$	−13.0596	−0.431503
$917$	27.0596	0.893588
$918$	1.62534	0.0536443
$919$	35.4948	1.17087	0.585433	−	0.810720i	$-0.300924\pi$
$919$	35.4948	1.17087	0.585433	+	0.810720i	$0.300924\pi$
$920$	0	0
$921$	−20.0587	−0.660957
$922$	29.3893	0.967886
$923$	−28.0175	−0.922209
$924$	23.1396	0.761236
$925$	0	0
$926$	12.1892	0.400563
$927$	−6.93853	−0.227891
$928$	7.79518	0.255889
$929$	17.9532	0.589026	0.294513	−	0.955648i	$-0.404843\pi$
$929$	17.9532	0.589026	0.294513	+	0.955648i	$0.404843\pi$
$930$	0	0
$931$	10.0147	0.328218
$932$	6.43899	0.210916
$933$	−37.1122	−1.21500
$934$	−17.8889	−0.585342
$935$	0	0
$936$	3.81078	0.124559
$937$	5.66652	0.185117	0.0925585	−	0.995707i	$-0.470495\pi$
$937$	5.66652	0.185117	0.0925585	+	0.995707i	$0.470495\pi$
$938$	30.5445	0.997313
$939$	22.2148	0.724953
$940$	0	0
$941$	−24.7044	−0.805339	−0.402670	−	0.915345i	$-0.631918\pi$
$941$	−24.7044	−0.805339	−0.402670	+	0.915345i	$0.631918\pi$
$942$	−38.3103	−1.24822
$943$	−27.5104	−0.895863
$944$	3.15516	0.102692
$945$	0	0
$946$	−22.8099	−0.741613
$947$	−13.5904	−0.441628	−0.220814	−	0.975316i	$-0.570871\pi$
$947$	−13.5904	−0.441628	−0.220814	+	0.975316i	$0.570871\pi$
$948$	35.5904	1.15592
$949$	−6.80183	−0.220797
$950$	0	0
$951$	−9.20815	−0.298595
$952$	2.12489	0.0688679
$953$	−24.7375	−0.801326	−0.400663	−	0.916225i	$-0.631220\pi$
$953$	−24.7375	−0.801326	−0.400663	+	0.916225i	$0.631220\pi$
$954$	8.31032	0.269057
$955$	0	0
$956$	22.8742	0.739804
$957$	43.7290	1.41356
$958$	1.15894	0.0374437
$959$	−26.6244	−0.859748
$960$	0	0
$961$	−17.5289	−0.565448
$962$	−25.7796	−0.831167
$963$	15.7190	0.506539
$964$	4.96972	0.160064
$965$	0	0
$966$	−27.1240	−0.872699
$967$	35.6897	1.14770	0.573851	−	0.818960i	$-0.305449\pi$
$967$	35.6897	1.14770	0.573851	+	0.818960i	$0.305449\pi$
$968$	4.03028	0.129538
$969$	1.09461	0.0351639
$970$	0	0
$971$	16.4995	0.529495	0.264748	−	0.964318i	$-0.414711\pi$
$971$	16.4995	0.529495	0.264748	+	0.964318i	$0.414711\pi$
$972$	−14.4390	−0.463131
$973$	95.1184	3.04935
$974$	30.6888	0.983331
$975$	0	0
$976$	−12.6400	−0.404597
$977$	−49.8501	−1.59485	−0.797423	−	0.603420i	$-0.793804\pi$
$977$	−49.8501	−1.59485	−0.797423	+	0.603420i	$0.793804\pi$
$978$	5.73841	0.183494
$979$	20.0899	0.642076
$980$	0	0
$981$	4.56766	0.145834
$982$	−3.67030	−0.117124
$983$	5.19014	0.165540	0.0827698	−	0.996569i	$-0.473623\pi$
$983$	5.19014	0.165540	0.0827698	+	0.996569i	$0.473623\pi$
$984$	−18.8898	−0.602185
$985$	0	0
$986$	4.01560	0.127883
$987$	−43.5592	−1.38650
$988$	−2.51514	−0.0800172
$989$	26.7375	0.850203
$990$	0	0
$991$	−32.4272	−1.03008	−0.515042	−	0.857165i	$-0.672224\pi$
$991$	−32.4272	−1.03008	−0.515042	+	0.857165i	$0.672224\pi$
$992$	−3.67030	−0.116532
$993$	−9.69771	−0.307748
$994$	45.9494	1.45743
$995$	0	0
$996$	−6.96972	−0.220844
$997$	−10.1992	−0.323012	−0.161506	−	0.986872i	$-0.551635\pi$
$997$	−10.1992	−0.323012	−0.161506	+	0.986872i	$0.551635\pi$
$998$	−31.3893	−0.993612
$999$	32.3397	1.02318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.i.1.3		3
3.2	odd	2		8550.2.a.cl.1.1		3
4.3	odd	2		7600.2.a.cd.1.1		3
5.2	odd	4		190.2.b.b.39.1	✓	6
5.3	odd	4		190.2.b.b.39.6	yes	6
5.4	even	2		950.2.a.n.1.1		3
15.2	even	4		1710.2.d.d.1369.4		6
15.8	even	4		1710.2.d.d.1369.1		6
15.14	odd	2		8550.2.a.ck.1.3		3
20.3	even	4		1520.2.d.j.609.2		6
20.7	even	4		1520.2.d.j.609.5		6
20.19	odd	2		7600.2.a.bi.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.1	✓	6	5.2	odd	4
190.2.b.b.39.6	yes	6	5.3	odd	4
950.2.a.i.1.3		3	1.1	even	1	trivial
950.2.a.n.1.1		3	5.4	even	2
1520.2.d.j.609.2		6	20.3	even	4
1520.2.d.j.609.5		6	20.7	even	4
1710.2.d.d.1369.1		6	15.8	even	4
1710.2.d.d.1369.4		6	15.2	even	4
7600.2.a.bi.1.3		3	20.19	odd	2
7600.2.a.cd.1.1		3	4.3	odd	2
8550.2.a.ck.1.3		3	15.14	odd	2
8550.2.a.cl.1.1		3	3.2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -2.12489 q^{6} -4.12489 q^{7} -1.00000 q^{8} +1.51514 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -2.12489 q^{6} -4.12489 q^{7} -1.00000 q^{8} +1.51514 q^{9} -2.64002 q^{11} +2.12489 q^{12} -2.51514 q^{13} +4.12489 q^{14} +1.00000 q^{16} +0.515138 q^{17} -1.51514 q^{18} +1.00000 q^{19} -8.76491 q^{21} +2.64002 q^{22} -3.09461 q^{23} -2.12489 q^{24} +2.51514 q^{26} -3.15516 q^{27} -4.12489 q^{28} -7.79518 q^{29} +3.67030 q^{31} -1.00000 q^{32} -5.60975 q^{33} -0.515138 q^{34} +1.51514 q^{36} -10.2498 q^{37} -1.00000 q^{38} -5.34438 q^{39} +8.88979 q^{41} +8.76491 q^{42} -8.64002 q^{43} -2.64002 q^{44} +3.09461 q^{46} +4.96972 q^{47} +2.12489 q^{48} +10.0147 q^{49} +1.09461 q^{51} -2.51514 q^{52} -5.48486 q^{53} +3.15516 q^{54} +4.12489 q^{56} +2.12489 q^{57} +7.79518 q^{58} +3.15516 q^{59} -12.6400 q^{61} -3.67030 q^{62} -6.24977 q^{63} +1.00000 q^{64} +5.60975 q^{66} +7.40493 q^{67} +0.515138 q^{68} -6.57569 q^{69} +11.1396 q^{71} -1.51514 q^{72} +2.70436 q^{73} +10.2498 q^{74} +1.00000 q^{76} +10.8898 q^{77} +5.34438 q^{78} +16.7493 q^{79} -11.2498 q^{81} -8.88979 q^{82} -3.28005 q^{83} -8.76491 q^{84} +8.64002 q^{86} -16.5639 q^{87} +2.64002 q^{88} -7.60975 q^{89} +10.3747 q^{91} -3.09461 q^{92} +7.79897 q^{93} -4.96972 q^{94} -2.12489 q^{96} -3.93945 q^{97} -10.0147 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 - 3 * q^8 + 5 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} - 3 q^{8} + 5 q^{9} - 2 q^{12} - 8 q^{13} + 4 q^{14} + 3 q^{16} + 2 q^{17} - 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} - 2 q^{27} - 4 q^{28} - 8 q^{29} + 4 q^{31} - 3 q^{32} - 8 q^{33} - 2 q^{34} + 5 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 2 q^{41} + 10 q^{42} - 18 q^{43} + 14 q^{47} - 2 q^{48} - 3 q^{49} - 6 q^{51} - 8 q^{52} - 16 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} + 8 q^{58} + 2 q^{59} - 30 q^{61} - 4 q^{62} - 2 q^{63} + 3 q^{64} + 8 q^{66} - 2 q^{67} + 2 q^{68} - 22 q^{69} - 8 q^{71} - 5 q^{72} - 10 q^{73} + 14 q^{74} + 3 q^{76} + 8 q^{77} - 10 q^{78} - 17 q^{81} - 2 q^{82} + 6 q^{83} - 10 q^{84} + 18 q^{86} - 6 q^{87} - 14 q^{89} + 6 q^{91} - 4 q^{93} - 14 q^{94} + 2 q^{96} - 10 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 - 3 * q^8 + 5 * q^9 - 2 * q^12 - 8 * q^13 + 4 * q^14 + 3 * q^16 + 2 * q^17 - 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 - 2 * q^27 - 4 * q^28 - 8 * q^29 + 4 * q^31 - 3 * q^32 - 8 * q^33 - 2 * q^34 + 5 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 2 * q^41 + 10 * q^42 - 18 * q^43 + 14 * q^47 - 2 * q^48 - 3 * q^49 - 6 * q^51 - 8 * q^52 - 16 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 + 8 * q^58 + 2 * q^59 - 30 * q^61 - 4 * q^62 - 2 * q^63 + 3 * q^64 + 8 * q^66 - 2 * q^67 + 2 * q^68 - 22 * q^69 - 8 * q^71 - 5 * q^72 - 10 * q^73 + 14 * q^74 + 3 * q^76 + 8 * q^77 - 10 * q^78 - 17 * q^81 - 2 * q^82 + 6 * q^83 - 10 * q^84 + 18 * q^86 - 6 * q^87 - 14 * q^89 + 6 * q^91 - 4 * q^93 - 14 * q^94 + 2 * q^96 - 10 * q^97 + 3 * q^98 - 12 * q^99

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