LMFDB - Embedded newform 1150.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.13448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 2 $ x^4 - 7*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.546295$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.706585 q^{3} +1.00000 q^{4} +0.706585 q^{6} -2.40815 q^{7} +1.00000 q^{8} -2.50074 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.706585 q^{3} +1.00000 q^{4} +0.706585 q^{6} -2.40815 q^{7} +1.00000 q^{8} -2.50074 q^{9} +4.95444 q^{11} +0.706585 q^{12} +4.40815 q^{13} -2.40815 q^{14} +1.00000 q^{16} -0.200825 q^{17} -2.50074 q^{18} +6.65600 q^{19} -1.70156 q^{21} +4.95444 q^{22} +1.00000 q^{23} +0.706585 q^{24} +4.40815 q^{26} -3.88674 q^{27} -2.40815 q^{28} +1.67942 q^{29} -1.82132 q^{31} +1.00000 q^{32} +3.50074 q^{33} -0.200825 q^{34} -2.50074 q^{36} +8.47732 q^{37} +6.65600 q^{38} +3.11473 q^{39} +11.0171 q^{41} -1.70156 q^{42} -2.06268 q^{43} +4.95444 q^{44} +1.00000 q^{46} -0.505760 q^{47} +0.706585 q^{48} -1.20083 q^{49} -0.141900 q^{51} +4.40815 q^{52} -5.84621 q^{53} -3.88674 q^{54} -2.40815 q^{56} +4.70304 q^{57} +1.67942 q^{58} -4.41464 q^{59} -6.67815 q^{61} -1.82132 q^{62} +6.02214 q^{63} +1.00000 q^{64} +3.50074 q^{66} -12.6625 q^{67} -0.200825 q^{68} +0.706585 q^{69} +3.61400 q^{71} -2.50074 q^{72} -14.4589 q^{73} +8.47732 q^{74} +6.65600 q^{76} -11.9310 q^{77} +3.11473 q^{78} +9.95317 q^{79} +4.75590 q^{81} +11.0171 q^{82} -13.3037 q^{83} -1.70156 q^{84} -2.06268 q^{86} +1.18665 q^{87} +4.95444 q^{88} -5.04576 q^{89} -10.6155 q^{91} +1.00000 q^{92} -1.28692 q^{93} -0.505760 q^{94} +0.706585 q^{96} -3.79917 q^{97} -1.20083 q^{98} -12.3898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9} + 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{14} + 4 q^{16} - 5 q^{17} + 7 q^{18} - q^{19} + 6 q^{21} + 5 q^{22} + 4 q^{23} + 3 q^{24} + 5 q^{26} + 6 q^{27} + 3 q^{28} + 2 q^{29} + 5 q^{31} + 4 q^{32} - 3 q^{33} - 5 q^{34} + 7 q^{36} - 6 q^{37} - q^{38} + 23 q^{41} + 6 q^{42} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 2 q^{47} + 3 q^{48} - 9 q^{49} + 7 q^{51} + 5 q^{52} + 6 q^{54} + 3 q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 9 q^{61} + 5 q^{62} + 16 q^{63} + 4 q^{64} - 3 q^{66} - 2 q^{67} - 5 q^{68} + 3 q^{69} + 19 q^{71} + 7 q^{72} - 8 q^{73} - 6 q^{74} - q^{76} - 10 q^{77} - 6 q^{79} + 16 q^{81} + 23 q^{82} - 14 q^{83} + 6 q^{84} - 2 q^{86} - 38 q^{87} + 5 q^{88} + 30 q^{89} - 13 q^{91} + 4 q^{92} - 26 q^{93} + 2 q^{94} + 3 q^{96} - 11 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9 + 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^14 + 4 * q^16 - 5 * q^17 + 7 * q^18 - q^19 + 6 * q^21 + 5 * q^22 + 4 * q^23 + 3 * q^24 + 5 * q^26 + 6 * q^27 + 3 * q^28 + 2 * q^29 + 5 * q^31 + 4 * q^32 - 3 * q^33 - 5 * q^34 + 7 * q^36 - 6 * q^37 - q^38 + 23 * q^41 + 6 * q^42 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 2 * q^47 + 3 * q^48 - 9 * q^49 + 7 * q^51 + 5 * q^52 + 6 * q^54 + 3 * q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 9 * q^61 + 5 * q^62 + 16 * q^63 + 4 * q^64 - 3 * q^66 - 2 * q^67 - 5 * q^68 + 3 * q^69 + 19 * q^71 + 7 * q^72 - 8 * q^73 - 6 * q^74 - q^76 - 10 * q^77 - 6 * q^79 + 16 * q^81 + 23 * q^82 - 14 * q^83 + 6 * q^84 - 2 * q^86 - 38 * q^87 + 5 * q^88 + 30 * q^89 - 13 * q^91 + 4 * q^92 - 26 * q^93 + 2 * q^94 + 3 * q^96 - 11 * q^97 - 9 * q^98 - 27 * 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
$3$	0.706585	0.407947	0.203974	−	0.978976i	$-0.434614\pi$
$3$	0.706585	0.407947	0.203974	+	0.978976i	$0.434614\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.706585	0.288462
$7$	−2.40815	−0.910194	−0.455097	−	0.890442i	$-0.650395\pi$
$7$	−2.40815	−0.910194	−0.455097	+	0.890442i	$0.650395\pi$
$8$	1.00000	0.353553
$9$	−2.50074	−0.833579
$10$	0	0
$11$	4.95444	1.49382	0.746910	−	0.664925i	$-0.231536\pi$
$11$	4.95444	1.49382	0.746910	+	0.664925i	$0.231536\pi$
$12$	0.706585	0.203974
$13$	4.40815	1.22260	0.611300	−	0.791399i	$-0.290647\pi$
$13$	4.40815	1.22260	0.611300	+	0.791399i	$0.290647\pi$
$14$	−2.40815	−0.643605
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.200825	−0.0487073	−0.0243536	−	0.999703i	$-0.507753\pi$
$17$	−0.200825	−0.0487073	−0.0243536	+	0.999703i	$0.507753\pi$
$18$	−2.50074	−0.589429
$19$	6.65600	1.52699	0.763496	−	0.645812i	$-0.223481\pi$
$19$	6.65600	1.52699	0.763496	+	0.645812i	$0.223481\pi$
$20$	0	0
$21$	−1.70156	−0.371311
$22$	4.95444	1.05629
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.706585	0.144231
$25$	0	0
$26$	4.40815	0.864509
$27$	−3.88674	−0.748004
$28$	−2.40815	−0.455097
$29$	1.67942	0.311860	0.155930	−	0.987768i	$-0.450163\pi$
$29$	1.67942	0.311860	0.155930	+	0.987768i	$0.450163\pi$
$30$	0	0
$31$	−1.82132	−0.327118	−0.163559	−	0.986534i	$-0.552297\pi$
$31$	−1.82132	−0.327118	−0.163559	+	0.986534i	$0.552297\pi$
$32$	1.00000	0.176777
$33$	3.50074	0.609400
$34$	−0.200825	−0.0344412
$35$	0	0
$36$	−2.50074	−0.416789
$37$	8.47732	1.39366	0.696832	−	0.717235i	$-0.254592\pi$
$37$	8.47732	1.39366	0.696832	+	0.717235i	$0.254592\pi$
$38$	6.65600	1.07975
$39$	3.11473	0.498756
$40$	0	0
$41$	11.0171	1.72059	0.860293	−	0.509801i	$-0.170281\pi$
$41$	11.0171	1.72059	0.860293	+	0.509801i	$0.170281\pi$
$42$	−1.70156	−0.262557
$43$	−2.06268	−0.314555	−0.157278	−	0.987554i	$-0.550272\pi$
$43$	−2.06268	−0.314555	−0.157278	+	0.987554i	$0.550272\pi$
$44$	4.95444	0.746910
$45$	0	0
$46$	1.00000	0.147442
$47$	−0.505760	−0.0737727	−0.0368864	−	0.999319i	$-0.511744\pi$
$47$	−0.505760	−0.0737727	−0.0368864	+	0.999319i	$0.511744\pi$
$48$	0.706585	0.101987
$49$	−1.20083	−0.171546
$50$	0	0
$51$	−0.141900	−0.0198700
$52$	4.40815	0.611300
$53$	−5.84621	−0.803038	−0.401519	−	0.915851i	$-0.631518\pi$
$53$	−5.84621	−0.803038	−0.401519	+	0.915851i	$0.631518\pi$
$54$	−3.88674	−0.528918
$55$	0	0
$56$	−2.40815	−0.321802
$57$	4.70304	0.622932
$58$	1.67942	0.220518
$59$	−4.41464	−0.574738	−0.287369	−	0.957820i	$-0.592781\pi$
$59$	−4.41464	−0.574738	−0.287369	+	0.957820i	$0.592781\pi$
$60$	0	0
$61$	−6.67815	−0.855049	−0.427525	−	0.904004i	$-0.640614\pi$
$61$	−6.67815	−0.855049	−0.427525	+	0.904004i	$0.640614\pi$
$62$	−1.82132	−0.231308
$63$	6.02214	0.758719
$64$	1.00000	0.125000
$65$	0	0
$66$	3.50074	0.430911
$67$	−12.6625	−1.54697	−0.773485	−	0.633814i	$-0.781488\pi$
$67$	−12.6625	−1.54697	−0.773485	+	0.633814i	$0.781488\pi$
$68$	−0.200825	−0.0243536
$69$	0.706585	0.0850629
$70$	0	0
$71$	3.61400	0.428902	0.214451	−	0.976735i	$-0.431204\pi$
$71$	3.61400	0.428902	0.214451	+	0.976735i	$0.431204\pi$
$72$	−2.50074	−0.294715
$73$	−14.4589	−1.69229	−0.846145	−	0.532953i	$-0.821082\pi$
$73$	−14.4589	−1.69229	−0.846145	+	0.532953i	$0.821082\pi$
$74$	8.47732	0.985469
$75$	0	0
$76$	6.65600	0.763496
$77$	−11.9310	−1.35967
$78$	3.11473	0.352674
$79$	9.95317	1.11982	0.559910	−	0.828554i	$-0.310836\pi$
$79$	9.95317	1.11982	0.559910	+	0.828554i	$0.310836\pi$
$80$	0	0
$81$	4.75590	0.528433
$82$	11.0171	1.21664
$83$	−13.3037	−1.46027	−0.730133	−	0.683305i	$-0.760542\pi$
$83$	−13.3037	−1.46027	−0.730133	+	0.683305i	$0.760542\pi$
$84$	−1.70156	−0.185656
$85$	0	0
$86$	−2.06268	−0.222424
$87$	1.18665	0.127223
$88$	4.95444	0.528145
$89$	−5.04576	−0.534850	−0.267425	−	0.963579i	$-0.586173\pi$
$89$	−5.04576	−0.534850	−0.267425	+	0.963579i	$0.586173\pi$
$90$	0	0
$91$	−10.6155	−1.11280
$92$	1.00000	0.104257
$93$	−1.28692	−0.133447
$94$	−0.505760	−0.0521652
$95$	0	0
$96$	0.706585	0.0721156
$97$	−3.79917	−0.385748	−0.192874	−	0.981224i	$-0.561781\pi$
$97$	−3.79917	−0.385748	−0.192874	+	0.981224i	$0.561781\pi$
$98$	−1.20083	−0.121302
$99$	−12.3898	−1.24522
$100$	0	0
$101$	13.2410	1.31753	0.658764	−	0.752350i	$-0.271080\pi$
$101$	13.2410	1.31753	0.658764	+	0.752350i	$0.271080\pi$
$102$	−0.141900	−0.0140502
$103$	10.4202	1.02674	0.513369	−	0.858168i	$-0.328397\pi$
$103$	10.4202	1.02674	0.513369	+	0.858168i	$0.328397\pi$
$104$	4.40815	0.432254
$105$	0	0
$106$	−5.84621	−0.567834
$107$	−9.98161	−0.964959	−0.482479	−	0.875907i	$-0.660264\pi$
$107$	−9.98161	−0.964959	−0.482479	+	0.875907i	$0.660264\pi$
$108$	−3.88674	−0.374002
$109$	−13.8739	−1.32888	−0.664442	−	0.747340i	$-0.731331\pi$
$109$	−13.8739	−1.32888	−0.664442	+	0.747340i	$0.731331\pi$
$110$	0	0
$111$	5.98995	0.568541
$112$	−2.40815	−0.227549
$113$	−18.4957	−1.73993	−0.869965	−	0.493113i	$-0.835859\pi$
$113$	−18.4957	−1.73993	−0.869965	+	0.493113i	$0.835859\pi$
$114$	4.70304	0.440480
$115$	0	0
$116$	1.67942	0.155930
$117$	−11.0236	−1.01913
$118$	−4.41464	−0.406401
$119$	0.483617	0.0443331
$120$	0	0
$121$	13.5465	1.23150
$122$	−6.67815	−0.604611
$123$	7.78454	0.701908
$124$	−1.82132	−0.163559
$125$	0	0
$126$	6.02214	0.536495
$127$	18.1384	1.60952	0.804759	−	0.593601i	$-0.202294\pi$
$127$	18.1384	1.60952	0.804759	+	0.593601i	$0.202294\pi$
$128$	1.00000	0.0883883
$129$	−1.45746	−0.128322
$130$	0	0
$131$	−1.98995	−0.173863	−0.0869315	−	0.996214i	$-0.527706\pi$
$131$	−1.98995	−0.173863	−0.0869315	+	0.996214i	$0.527706\pi$
$132$	3.50074	0.304700
$133$	−16.0286	−1.38986
$134$	−12.6625	−1.09387
$135$	0	0
$136$	−0.200825	−0.0172206
$137$	1.14337	0.0976850	0.0488425	−	0.998806i	$-0.484447\pi$
$137$	1.14337	0.0976850	0.0488425	+	0.998806i	$0.484447\pi$
$138$	0.706585	0.0601486
$139$	22.4489	1.90409	0.952045	−	0.305959i	$-0.0989769\pi$
$139$	22.4489	1.90409	0.952045	+	0.305959i	$0.0989769\pi$
$140$	0	0
$141$	−0.357363	−0.0300954
$142$	3.61400	0.303280
$143$	21.8399	1.82635
$144$	−2.50074	−0.208395
$145$	0	0
$146$	−14.4589	−1.19663
$147$	−0.848486	−0.0699819
$148$	8.47732	0.696832
$149$	8.20458	0.672145	0.336073	−	0.941836i	$-0.390901\pi$
$149$	8.20458	0.672145	0.336073	+	0.941836i	$0.390901\pi$
$150$	0	0
$151$	10.5244	0.856460	0.428230	−	0.903670i	$-0.359137\pi$
$151$	10.5244	0.856460	0.428230	+	0.903670i	$0.359137\pi$
$152$	6.65600	0.539873
$153$	0.502211	0.0406013
$154$	−11.9310	−0.961430
$155$	0	0
$156$	3.11473	0.249378
$157$	−1.02991	−0.0821959	−0.0410979	−	0.999155i	$-0.513086\pi$
$157$	−1.02991	−0.0821959	−0.0410979	+	0.999155i	$0.513086\pi$
$158$	9.95317	0.791832
$159$	−4.13084	−0.327597
$160$	0	0
$161$	−2.40815	−0.189789
$162$	4.75590	0.373658
$163$	11.1802	0.875697	0.437849	−	0.899049i	$-0.355741\pi$
$163$	11.1802	0.875697	0.437849	+	0.899049i	$0.355741\pi$
$164$	11.0171	0.860293
$165$	0	0
$166$	−13.3037	−1.03256
$167$	−3.49424	−0.270392	−0.135196	−	0.990819i	$-0.543166\pi$
$167$	−3.49424	−0.270392	−0.135196	+	0.990819i	$0.543166\pi$
$168$	−1.70156	−0.131278
$169$	6.43177	0.494751
$170$	0	0
$171$	−16.6449	−1.27287
$172$	−2.06268	−0.157278
$173$	−8.61547	−0.655022	−0.327511	−	0.944847i	$-0.606210\pi$
$173$	−8.61547	−0.655022	−0.327511	+	0.944847i	$0.606210\pi$
$174$	1.18665	0.0899599
$175$	0	0
$176$	4.95444	0.373455
$177$	−3.11932	−0.234463
$178$	−5.04576	−0.378196
$179$	−3.36634	−0.251612	−0.125806	−	0.992055i	$-0.540152\pi$
$179$	−3.36634	−0.251612	−0.125806	+	0.992055i	$0.540152\pi$
$180$	0	0
$181$	−15.8970	−1.18161	−0.590807	−	0.806813i	$-0.701191\pi$
$181$	−15.8970	−1.18161	−0.590807	+	0.806813i	$0.701191\pi$
$182$	−10.6155	−0.786871
$183$	−4.71868	−0.348815
$184$	1.00000	0.0737210
$185$	0	0
$186$	−1.28692	−0.0943614
$187$	−0.994977	−0.0727599
$188$	−0.505760	−0.0368864
$189$	9.35985	0.680829
$190$	0	0
$191$	−6.74527	−0.488071	−0.244035	−	0.969766i	$-0.578471\pi$
$191$	−6.74527	−0.488071	−0.244035	+	0.969766i	$0.578471\pi$
$192$	0.706585	0.0509934
$193$	4.81630	0.346685	0.173342	−	0.984862i	$-0.444543\pi$
$193$	4.81630	0.346685	0.173342	+	0.984862i	$0.444543\pi$
$194$	−3.79917	−0.272765
$195$	0	0
$196$	−1.20083	−0.0857732
$197$	−12.8349	−0.914448	−0.457224	−	0.889352i	$-0.651156\pi$
$197$	−12.8349	−0.914448	−0.457224	+	0.889352i	$0.651156\pi$
$198$	−12.3898	−0.880502
$199$	−12.4957	−0.885798	−0.442899	−	0.896572i	$-0.646050\pi$
$199$	−12.4957	−0.885798	−0.442899	+	0.896572i	$0.646050\pi$
$200$	0	0
$201$	−8.94714	−0.631083
$202$	13.2410	0.931633
$203$	−4.04429	−0.283853
$204$	−0.141900	−0.00993500
$205$	0	0
$206$	10.4202	0.726013
$207$	−2.50074	−0.173813
$208$	4.40815	0.305650
$209$	32.9768	2.28105
$210$	0	0
$211$	−16.0130	−1.10238	−0.551190	−	0.834380i	$-0.685826\pi$
$211$	−16.0130	−1.10238	−0.551190	+	0.834380i	$0.685826\pi$
$212$	−5.84621	−0.401519
$213$	2.55360	0.174970
$214$	−9.98161	−0.682329
$215$	0	0
$216$	−3.88674	−0.264459
$217$	4.38600	0.297741
$218$	−13.8739	−0.939662
$219$	−10.2165	−0.690365
$220$	0	0
$221$	−0.885267	−0.0595495
$222$	5.98995	0.402019
$223$	−18.2094	−1.21939	−0.609695	−	0.792636i	$-0.708708\pi$
$223$	−18.2094	−1.21939	−0.609695	+	0.792636i	$0.708708\pi$
$224$	−2.40815	−0.160901
$225$	0	0
$226$	−18.4957	−1.23032
$227$	19.5331	1.29646	0.648230	−	0.761445i	$-0.275510\pi$
$227$	19.5331	1.29646	0.648230	+	0.761445i	$0.275510\pi$
$228$	4.70304	0.311466
$229$	−22.3419	−1.47640	−0.738198	−	0.674584i	$-0.764323\pi$
$229$	−22.3419	−1.47640	−0.738198	+	0.674584i	$0.764323\pi$
$230$	0	0
$231$	−8.43029	−0.554672
$232$	1.67942	0.110259
$233$	−6.42469	−0.420896	−0.210448	−	0.977605i	$-0.567492\pi$
$233$	−6.42469	−0.420896	−0.210448	+	0.977605i	$0.567492\pi$
$234$	−11.0236	−0.720636
$235$	0	0
$236$	−4.41464	−0.287369
$237$	7.03277	0.456827
$238$	0.483617	0.0313482
$239$	−9.52848	−0.616346	−0.308173	−	0.951330i	$-0.599718\pi$
$239$	−9.52848	−0.616346	−0.308173	+	0.951330i	$0.599718\pi$
$240$	0	0
$241$	−13.4842	−0.868593	−0.434297	−	0.900770i	$-0.643003\pi$
$241$	−13.4842	−0.868593	−0.434297	+	0.900770i	$0.643003\pi$
$242$	13.5465	0.870802
$243$	15.0207	0.963576
$244$	−6.67815	−0.427525
$245$	0	0
$246$	7.78454	0.496324
$247$	29.3406	1.86690
$248$	−1.82132	−0.115654
$249$	−9.40018	−0.595712
$250$	0	0
$251$	−10.1402	−0.640044	−0.320022	−	0.947410i	$-0.603690\pi$
$251$	−10.1402	−0.640044	−0.320022	+	0.947410i	$0.603690\pi$
$252$	6.02214	0.379359
$253$	4.95444	0.311483
$254$	18.1384	1.13810
$255$	0	0
$256$	1.00000	0.0625000
$257$	8.76196	0.546556	0.273278	−	0.961935i	$-0.411892\pi$
$257$	8.76196	0.546556	0.273278	+	0.961935i	$0.411892\pi$
$258$	−1.45746	−0.0907374
$259$	−20.4146	−1.26850
$260$	0	0
$261$	−4.19978	−0.259960
$262$	−1.98995	−0.122940
$263$	15.7448	0.970868	0.485434	−	0.874273i	$-0.338662\pi$
$263$	15.7448	0.970868	0.485434	+	0.874273i	$0.338662\pi$
$264$	3.50074	0.215455
$265$	0	0
$266$	−16.0286	−0.982779
$267$	−3.56526	−0.218190
$268$	−12.6625	−0.773485
$269$	23.5515	1.43596	0.717981	−	0.696063i	$-0.245067\pi$
$269$	23.5515	1.43596	0.717981	+	0.696063i	$0.245067\pi$
$270$	0	0
$271$	−1.62863	−0.0989325	−0.0494662	−	0.998776i	$-0.515752\pi$
$271$	−1.62863	−0.0989325	−0.0494662	+	0.998776i	$0.515752\pi$
$272$	−0.200825	−0.0121768
$273$	−7.50074	−0.453965
$274$	1.14337	0.0690738
$275$	0	0
$276$	0.706585	0.0425314
$277$	−21.9063	−1.31622	−0.658112	−	0.752920i	$-0.728645\pi$
$277$	−21.9063	−1.31622	−0.658112	+	0.752920i	$0.728645\pi$
$278$	22.4489	1.34639
$279$	4.55464	0.272679
$280$	0	0
$281$	−5.64264	−0.336612	−0.168306	−	0.985735i	$-0.553830\pi$
$281$	−5.64264	−0.336612	−0.168306	+	0.985735i	$0.553830\pi$
$282$	−0.357363	−0.0212807
$283$	6.15674	0.365980	0.182990	−	0.983115i	$-0.441422\pi$
$283$	6.15674	0.365980	0.182990	+	0.983115i	$0.441422\pi$
$284$	3.61400	0.214451
$285$	0	0
$286$	21.8399	1.29142
$287$	−26.5309	−1.56607
$288$	−2.50074	−0.147357
$289$	−16.9597	−0.997628
$290$	0	0
$291$	−2.68444	−0.157365
$292$	−14.4589	−0.846145
$293$	21.4888	1.25539	0.627696	−	0.778459i	$-0.283998\pi$
$293$	21.4888	1.25539	0.627696	+	0.778459i	$0.283998\pi$
$294$	−0.848486	−0.0494847
$295$	0	0
$296$	8.47732	0.492734
$297$	−19.2566	−1.11738
$298$	8.20458	0.475278
$299$	4.40815	0.254930
$300$	0	0
$301$	4.96723	0.286307
$302$	10.5244	0.605609
$303$	9.35589	0.537482
$304$	6.65600	0.381748
$305$	0	0
$306$	0.502211	0.0287095
$307$	4.09672	0.233812	0.116906	−	0.993143i	$-0.462702\pi$
$307$	4.09672	0.233812	0.116906	+	0.993143i	$0.462702\pi$
$308$	−11.9310	−0.679833
$309$	7.36279	0.418855
$310$	0	0
$311$	24.0105	1.36151	0.680754	−	0.732512i	$-0.261652\pi$
$311$	24.0105	1.36151	0.680754	+	0.732512i	$0.261652\pi$
$312$	3.11473	0.176337
$313$	−10.8696	−0.614387	−0.307194	−	0.951647i	$-0.599390\pi$
$313$	−10.8696	−0.614387	−0.307194	+	0.951647i	$0.599390\pi$
$314$	−1.02991	−0.0581213
$315$	0	0
$316$	9.95317	0.559910
$317$	22.1661	1.24497	0.622486	−	0.782631i	$-0.286123\pi$
$317$	22.1661	1.24497	0.622486	+	0.782631i	$0.286123\pi$
$318$	−4.13084	−0.231646
$319$	8.32058	0.465863
$320$	0	0
$321$	−7.05286	−0.393652
$322$	−2.40815	−0.134201
$323$	−1.33669	−0.0743756
$324$	4.75590	0.264216
$325$	0	0
$326$	11.1802	0.619212
$327$	−9.80313	−0.542114
$328$	11.0171	0.608319
$329$	1.21795	0.0671475
$330$	0	0
$331$	−9.39308	−0.516290	−0.258145	−	0.966106i	$-0.583111\pi$
$331$	−9.39308	−0.516290	−0.258145	+	0.966106i	$0.583111\pi$
$332$	−13.3037	−0.730133
$333$	−21.1996	−1.16173
$334$	−3.49424	−0.191196
$335$	0	0
$336$	−1.70156	−0.0928278
$337$	−19.8113	−1.07919	−0.539594	−	0.841925i	$-0.681422\pi$
$337$	−19.8113	−1.07919	−0.539594	+	0.841925i	$0.681422\pi$
$338$	6.43177	0.349842
$339$	−13.0688	−0.709800
$340$	0	0
$341$	−9.02362	−0.488656
$342$	−16.6449	−0.900054
$343$	19.7488	1.06633
$344$	−2.06268	−0.111212
$345$	0	0
$346$	−8.61547	−0.463171
$347$	19.5128	1.04750	0.523752	−	0.851871i	$-0.324532\pi$
$347$	19.5128	1.04750	0.523752	+	0.851871i	$0.324532\pi$
$348$	1.18665	0.0636113
$349$	−22.7352	−1.21699	−0.608494	−	0.793558i	$-0.708226\pi$
$349$	−22.7352	−1.21699	−0.608494	+	0.793558i	$0.708226\pi$
$350$	0	0
$351$	−17.1333	−0.914509
$352$	4.95444	0.264073
$353$	24.6471	1.31183	0.655915	−	0.754835i	$-0.272283\pi$
$353$	24.6471	1.31183	0.655915	+	0.754835i	$0.272283\pi$
$354$	−3.11932	−0.165790
$355$	0	0
$356$	−5.04576	−0.267425
$357$	0.341716	0.0180856
$358$	−3.36634	−0.177917
$359$	15.2778	0.806330	0.403165	−	0.915127i	$-0.367910\pi$
$359$	15.2778	0.806330	0.403165	+	0.915127i	$0.367910\pi$
$360$	0	0
$361$	25.3024	1.33170
$362$	−15.8970	−0.835527
$363$	9.57176	0.502387
$364$	−10.6155	−0.556402
$365$	0	0
$366$	−4.71868	−0.246649
$367$	−9.59581	−0.500897	−0.250449	−	0.968130i	$-0.580578\pi$
$367$	−9.59581	−0.500897	−0.250449	+	0.968130i	$0.580578\pi$
$368$	1.00000	0.0521286
$369$	−27.5509	−1.43424
$370$	0	0
$371$	14.0785	0.730921
$372$	−1.28692	−0.0667236
$373$	17.2125	0.891232	0.445616	−	0.895224i	$-0.352985\pi$
$373$	17.2125	0.891232	0.445616	+	0.895224i	$0.352985\pi$
$374$	−0.994977	−0.0514490
$375$	0	0
$376$	−0.505760	−0.0260826
$377$	7.40312	0.381280
$378$	9.35985	0.481419
$379$	−20.7354	−1.06511	−0.532554	−	0.846396i	$-0.678768\pi$
$379$	−20.7354	−1.06511	−0.532554	+	0.846396i	$0.678768\pi$
$380$	0	0
$381$	12.8163	0.656599
$382$	−6.74527	−0.345118
$383$	−13.0115	−0.664858	−0.332429	−	0.943128i	$-0.607868\pi$
$383$	−13.0115	−0.664858	−0.332429	+	0.943128i	$0.607868\pi$
$384$	0.706585	0.0360578
$385$	0	0
$386$	4.81630	0.245143
$387$	5.15822	0.262207
$388$	−3.79917	−0.192874
$389$	6.55279	0.332240	0.166120	−	0.986106i	$-0.446876\pi$
$389$	6.55279	0.332240	0.166120	+	0.986106i	$0.446876\pi$
$390$	0	0
$391$	−0.200825	−0.0101562
$392$	−1.20083	−0.0606508
$393$	−1.40607	−0.0709270
$394$	−12.8349	−0.646612
$395$	0	0
$396$	−12.3898	−0.622609
$397$	−6.79516	−0.341039	−0.170520	−	0.985354i	$-0.554545\pi$
$397$	−6.79516	−0.341039	−0.170520	+	0.985354i	$0.554545\pi$
$398$	−12.4957	−0.626354
$399$	−11.3256	−0.566989
$400$	0	0
$401$	−30.5660	−1.52639	−0.763196	−	0.646167i	$-0.776371\pi$
$401$	−30.5660	−1.52639	−0.763196	+	0.646167i	$0.776371\pi$
$402$	−8.94714	−0.446243
$403$	−8.02864	−0.399935
$404$	13.2410	0.658764
$405$	0	0
$406$	−4.04429	−0.200715
$407$	42.0004	2.08188
$408$	−0.141900	−0.00702510
$409$	19.8610	0.982066	0.491033	−	0.871141i	$-0.336620\pi$
$409$	19.8610	0.982066	0.491033	+	0.871141i	$0.336620\pi$
$410$	0	0
$411$	0.807892	0.0398503
$412$	10.4202	0.513369
$413$	10.6311	0.523123
$414$	−2.50074	−0.122905
$415$	0	0
$416$	4.40815	0.216127
$417$	15.8621	0.776768
$418$	32.9768	1.61295
$419$	4.19057	0.204723	0.102361	−	0.994747i	$-0.467360\pi$
$419$	4.19057	0.204723	0.102361	+	0.994747i	$0.467360\pi$
$420$	0	0
$421$	−32.2306	−1.57082	−0.785411	−	0.618975i	$-0.787548\pi$
$421$	−32.2306	−1.57082	−0.785411	+	0.618975i	$0.787548\pi$
$422$	−16.0130	−0.779500
$423$	1.26477	0.0614954
$424$	−5.84621	−0.283917
$425$	0	0
$426$	2.55360	0.123722
$427$	16.0820	0.778261
$428$	−9.98161	−0.482479
$429$	15.4318	0.745053
$430$	0	0
$431$	18.7583	0.903554	0.451777	−	0.892131i	$-0.350790\pi$
$431$	18.7583	0.903554	0.451777	+	0.892131i	$0.350790\pi$
$432$	−3.88674	−0.187001
$433$	−28.3271	−1.36131	−0.680656	−	0.732603i	$-0.738305\pi$
$433$	−28.3271	−1.36131	−0.680656	+	0.732603i	$0.738305\pi$
$434$	4.38600	0.210535
$435$	0	0
$436$	−13.8739	−0.664442
$437$	6.65600	0.318400
$438$	−10.2165	−0.488162
$439$	23.7532	1.13368	0.566840	−	0.823828i	$-0.308166\pi$
$439$	23.7532	1.13368	0.566840	+	0.823828i	$0.308166\pi$
$440$	0	0
$441$	3.00295	0.142998
$442$	−0.885267	−0.0421079
$443$	−9.91284	−0.470973	−0.235487	−	0.971878i	$-0.575668\pi$
$443$	−9.91284	−0.470973	−0.235487	+	0.971878i	$0.575668\pi$
$444$	5.98995	0.284271
$445$	0	0
$446$	−18.2094	−0.862239
$447$	5.79724	0.274200
$448$	−2.40815	−0.113774
$449$	−39.3758	−1.85826	−0.929129	−	0.369755i	$-0.879442\pi$
$449$	−39.3758	−1.85826	−0.929129	+	0.369755i	$0.879442\pi$
$450$	0	0
$451$	54.5837	2.57025
$452$	−18.4957	−0.869965
$453$	7.43636	0.349390
$454$	19.5331	0.916735
$455$	0	0
$456$	4.70304	0.220240
$457$	−15.1737	−0.709794	−0.354897	−	0.934905i	$-0.615484\pi$
$457$	−15.1737	−0.709794	−0.354897	+	0.934905i	$0.615484\pi$
$458$	−22.3419	−1.04397
$459$	0.780555	0.0364332
$460$	0	0
$461$	8.44848	0.393485	0.196742	−	0.980455i	$-0.436964\pi$
$461$	8.44848	0.393485	0.196742	+	0.980455i	$0.436964\pi$
$462$	−8.43029	−0.392213
$463$	−19.8888	−0.924311	−0.462155	−	0.886799i	$-0.652924\pi$
$463$	−19.8888	−0.924311	−0.462155	+	0.886799i	$0.652924\pi$
$464$	1.67942	0.0779650
$465$	0	0
$466$	−6.42469	−0.297618
$467$	27.3066	1.26360	0.631800	−	0.775132i	$-0.282317\pi$
$467$	27.3066	1.26360	0.631800	+	0.775132i	$0.282317\pi$
$468$	−11.0236	−0.509567
$469$	30.4932	1.40804
$470$	0	0
$471$	−0.727720	−0.0335316
$472$	−4.41464	−0.203201
$473$	−10.2194	−0.469889
$474$	7.03277	0.323026
$475$	0	0
$476$	0.483617	0.0221665
$477$	14.6198	0.669396
$478$	−9.52848	−0.435823
$479$	21.0558	0.962064	0.481032	−	0.876703i	$-0.340262\pi$
$479$	21.0558	0.962064	0.481032	+	0.876703i	$0.340262\pi$
$480$	0	0
$481$	37.3693	1.70389
$482$	−13.4842	−0.614188
$483$	−1.70156	−0.0774238
$484$	13.5465	0.615750
$485$	0	0
$486$	15.0207	0.681351
$487$	22.5530	1.02197	0.510987	−	0.859589i	$-0.329280\pi$
$487$	22.5530	1.02197	0.510987	+	0.859589i	$0.329280\pi$
$488$	−6.67815	−0.302306
$489$	7.89974	0.357238
$490$	0	0
$491$	−17.1369	−0.773376	−0.386688	−	0.922211i	$-0.626381\pi$
$491$	−17.1369	−0.773376	−0.386688	+	0.922211i	$0.626381\pi$
$492$	7.78454	0.350954
$493$	−0.337269	−0.0151899
$494$	29.3406	1.32010
$495$	0	0
$496$	−1.82132	−0.0817796
$497$	−8.70304	−0.390385
$498$	−9.40018	−0.421232
$499$	−12.1254	−0.542805	−0.271403	−	0.962466i	$-0.587488\pi$
$499$	−12.1254	−0.542805	−0.271403	+	0.962466i	$0.587488\pi$
$500$	0	0
$501$	−2.46898	−0.110306
$502$	−10.1402	−0.452579
$503$	−38.5026	−1.71675	−0.858373	−	0.513025i	$-0.828525\pi$
$503$	−38.5026	−1.71675	−0.858373	+	0.513025i	$0.828525\pi$
$504$	6.02214	0.268248
$505$	0	0
$506$	4.95444	0.220252
$507$	4.54459	0.201832
$508$	18.1384	0.804759
$509$	11.8646	0.525889	0.262945	−	0.964811i	$-0.415306\pi$
$509$	11.8646	0.525889	0.262945	+	0.964811i	$0.415306\pi$
$510$	0	0
$511$	34.8192	1.54031
$512$	1.00000	0.0441942
$513$	−25.8702	−1.14220
$514$	8.76196	0.386474
$515$	0	0
$516$	−1.45746	−0.0641610
$517$	−2.50576	−0.110203
$518$	−20.4146	−0.896968
$519$	−6.08757	−0.267214
$520$	0	0
$521$	0.876118	0.0383834	0.0191917	−	0.999816i	$-0.493891\pi$
$521$	0.876118	0.0383834	0.0191917	+	0.999816i	$0.493891\pi$
$522$	−4.19978	−0.183820
$523$	35.9716	1.57293	0.786463	−	0.617637i	$-0.211910\pi$
$523$	35.9716	1.57293	0.786463	+	0.617637i	$0.211910\pi$
$524$	−1.98995	−0.0869315
$525$	0	0
$526$	15.7448	0.686508
$527$	0.365767	0.0159330
$528$	3.50074	0.152350
$529$	1.00000	0.0434783
$530$	0	0
$531$	11.0399	0.479089
$532$	−16.0286	−0.694930
$533$	48.5651	2.10359
$534$	−3.56526	−0.154284
$535$	0	0
$536$	−12.6625	−0.546937
$537$	−2.37861	−0.102645
$538$	23.5515	1.01538
$539$	−5.94942	−0.256260
$540$	0	0
$541$	−32.7051	−1.40610	−0.703051	−	0.711140i	$-0.748179\pi$
$541$	−32.7051	−1.40610	−0.703051	+	0.711140i	$0.748179\pi$
$542$	−1.62863	−0.0699558
$543$	−11.2326	−0.482036
$544$	−0.200825	−0.00861031
$545$	0	0
$546$	−7.50074	−0.321002
$547$	−17.1463	−0.733124	−0.366562	−	0.930394i	$-0.619465\pi$
$547$	−17.1463	−0.733124	−0.366562	+	0.930394i	$0.619465\pi$
$548$	1.14337	0.0488425
$549$	16.7003	0.712751
$550$	0	0
$551$	11.1782	0.476208
$552$	0.706585	0.0300743
$553$	−23.9687	−1.01925
$554$	−21.9063	−0.930711
$555$	0	0
$556$	22.4489	0.952045
$557$	5.35049	0.226708	0.113354	−	0.993555i	$-0.463841\pi$
$557$	5.35049	0.226708	0.113354	+	0.993555i	$0.463841\pi$
$558$	4.55464	0.192813
$559$	−9.09259	−0.384576
$560$	0	0
$561$	−0.703036	−0.0296822
$562$	−5.64264	−0.238020
$563$	12.7511	0.537394	0.268697	−	0.963225i	$-0.413407\pi$
$563$	12.7511	0.537394	0.268697	+	0.963225i	$0.413407\pi$
$564$	−0.357363	−0.0150477
$565$	0	0
$566$	6.15674	0.258787
$567$	−11.4529	−0.480977
$568$	3.61400	0.151640
$569$	38.8368	1.62812	0.814062	−	0.580779i	$-0.197252\pi$
$569$	38.8368	1.62812	0.814062	+	0.580779i	$0.197252\pi$
$570$	0	0
$571$	−8.80350	−0.368415	−0.184208	−	0.982887i	$-0.558972\pi$
$571$	−8.80350	−0.368415	−0.184208	+	0.982887i	$0.558972\pi$
$572$	21.8399	0.913173
$573$	−4.76611	−0.199107
$574$	−26.5309	−1.10738
$575$	0	0
$576$	−2.50074	−0.104197
$577$	16.5133	0.687456	0.343728	−	0.939069i	$-0.388310\pi$
$577$	16.5133	0.687456	0.343728	+	0.939069i	$0.388310\pi$
$578$	−16.9597	−0.705429
$579$	3.40312	0.141429
$580$	0	0
$581$	32.0372	1.32913
$582$	−2.68444	−0.111274
$583$	−28.9647	−1.19959
$584$	−14.4589	−0.598315
$585$	0	0
$586$	21.4888	0.887696
$587$	−31.0543	−1.28175	−0.640874	−	0.767646i	$-0.721428\pi$
$587$	−31.0543	−1.28175	−0.640874	+	0.767646i	$0.721428\pi$
$588$	−0.848486	−0.0349910
$589$	−12.1227	−0.499507
$590$	0	0
$591$	−9.06895	−0.373047
$592$	8.47732	0.348416
$593$	−10.6211	−0.436155	−0.218078	−	0.975931i	$-0.569979\pi$
$593$	−10.6211	−0.436155	−0.218078	+	0.975931i	$0.569979\pi$
$594$	−19.2566	−0.790109
$595$	0	0
$596$	8.20458	0.336073
$597$	−8.82929	−0.361359
$598$	4.40815	0.180263
$599$	5.31351	0.217104	0.108552	−	0.994091i	$-0.465379\pi$
$599$	5.31351	0.217104	0.108552	+	0.994091i	$0.465379\pi$
$600$	0	0
$601$	−15.6336	−0.637708	−0.318854	−	0.947804i	$-0.603298\pi$
$601$	−15.6336	−0.637708	−0.318854	+	0.947804i	$0.603298\pi$
$602$	4.96723	0.202449
$603$	31.6656	1.28952
$604$	10.5244	0.428230
$605$	0	0
$606$	9.35589	0.380057
$607$	−15.0588	−0.611216	−0.305608	−	0.952157i	$-0.598860\pi$
$607$	−15.0588	−0.611216	−0.305608	+	0.952157i	$0.598860\pi$
$608$	6.65600	0.269937
$609$	−2.85763	−0.115797
$610$	0	0
$611$	−2.22947	−0.0901945
$612$	0.502211	0.0203007
$613$	−44.1496	−1.78319	−0.891594	−	0.452836i	$-0.850412\pi$
$613$	−44.1496	−1.78319	−0.891594	+	0.452836i	$0.850412\pi$
$614$	4.09672	0.165330
$615$	0	0
$616$	−11.9310	−0.480715
$617$	−10.1871	−0.410117	−0.205058	−	0.978750i	$-0.565738\pi$
$617$	−10.1871	−0.410117	−0.205058	+	0.978750i	$0.565738\pi$
$618$	7.36279	0.296175
$619$	2.48087	0.0997147	0.0498573	−	0.998756i	$-0.484123\pi$
$619$	2.48087	0.0997147	0.0498573	+	0.998756i	$0.484123\pi$
$620$	0	0
$621$	−3.88674	−0.155970
$622$	24.0105	0.962731
$623$	12.1509	0.486817
$624$	3.11473	0.124689
$625$	0	0
$626$	−10.8696	−0.434437
$627$	23.3009	0.930549
$628$	−1.02991	−0.0410979
$629$	−1.70246	−0.0678815
$630$	0	0
$631$	14.0029	0.557449	0.278724	−	0.960371i	$-0.410088\pi$
$631$	14.0029	0.557449	0.278724	+	0.960371i	$0.410088\pi$
$632$	9.95317	0.395916
$633$	−11.3145	−0.449713
$634$	22.1661	0.880328
$635$	0	0
$636$	−4.13084	−0.163799
$637$	−5.29341	−0.209733
$638$	8.32058	0.329415
$639$	−9.03765	−0.357524
$640$	0	0
$641$	21.3592	0.843639	0.421820	−	0.906680i	$-0.361392\pi$
$641$	21.3592	0.843639	0.421820	+	0.906680i	$0.361392\pi$
$642$	−7.05286	−0.278354
$643$	7.65098	0.301725	0.150863	−	0.988555i	$-0.451795\pi$
$643$	7.65098	0.301725	0.150863	+	0.988555i	$0.451795\pi$
$644$	−2.40815	−0.0948943
$645$	0	0
$646$	−1.33669	−0.0525915
$647$	−9.66388	−0.379926	−0.189963	−	0.981791i	$-0.560837\pi$
$647$	−9.66388	−0.379926	−0.189963	+	0.981791i	$0.560837\pi$
$648$	4.75590	0.186829
$649$	−21.8721	−0.858555
$650$	0	0
$651$	3.09909	0.121463
$652$	11.1802	0.437849
$653$	7.76698	0.303946	0.151973	−	0.988385i	$-0.451437\pi$
$653$	7.76698	0.303946	0.151973	+	0.988385i	$0.451437\pi$
$654$	−9.80313	−0.383333
$655$	0	0
$656$	11.0171	0.430146
$657$	36.1580	1.41066
$658$	1.21795	0.0474805
$659$	10.6157	0.413528	0.206764	−	0.978391i	$-0.433707\pi$
$659$	10.6157	0.413528	0.206764	+	0.978391i	$0.433707\pi$
$660$	0	0
$661$	24.7693	0.963413	0.481706	−	0.876333i	$-0.340017\pi$
$661$	24.7693	0.963413	0.481706	+	0.876333i	$0.340017\pi$
$662$	−9.39308	−0.365072
$663$	−0.625517	−0.0242931
$664$	−13.3037	−0.516282
$665$	0	0
$666$	−21.1996	−0.821466
$667$	1.67942	0.0650273
$668$	−3.49424	−0.135196
$669$	−12.8665	−0.497447
$670$	0	0
$671$	−33.0865	−1.27729
$672$	−1.70156	−0.0656392
$673$	42.4961	1.63811	0.819053	−	0.573719i	$-0.194500\pi$
$673$	42.4961	1.63811	0.819053	+	0.573719i	$0.194500\pi$
$674$	−19.8113	−0.763102
$675$	0	0
$676$	6.43177	0.247376
$677$	42.9463	1.65056	0.825280	−	0.564723i	$-0.191017\pi$
$677$	42.9463	1.65056	0.825280	+	0.564723i	$0.191017\pi$
$678$	−13.0688	−0.501904
$679$	9.14897	0.351105
$680$	0	0
$681$	13.8018	0.528887
$682$	−9.02362	−0.345532
$683$	42.2263	1.61575	0.807873	−	0.589357i	$-0.200619\pi$
$683$	42.2263	1.61575	0.807873	+	0.589357i	$0.200619\pi$
$684$	−16.6449	−0.636434
$685$	0	0
$686$	19.7488	0.754013
$687$	−15.7865	−0.602292
$688$	−2.06268	−0.0786389
$689$	−25.7709	−0.981795
$690$	0	0
$691$	47.6928	1.81432	0.907160	−	0.420785i	$-0.138245\pi$
$691$	47.6928	1.81432	0.907160	+	0.420785i	$0.138245\pi$
$692$	−8.61547	−0.327511
$693$	29.8364	1.13339
$694$	19.5128	0.740697
$695$	0	0
$696$	1.18665	0.0449800
$697$	−2.21251	−0.0838050
$698$	−22.7352	−0.860541
$699$	−4.53959	−0.171703
$700$	0	0
$701$	−4.52516	−0.170913	−0.0854565	−	0.996342i	$-0.527235\pi$
$701$	−4.52516	−0.170913	−0.0854565	+	0.996342i	$0.527235\pi$
$702$	−17.1333	−0.646656
$703$	56.4251	2.12811
$704$	4.95444	0.186728
$705$	0	0
$706$	24.6471	0.927604
$707$	−31.8863	−1.19921
$708$	−3.11932	−0.117231
$709$	−21.5986	−0.811151	−0.405575	−	0.914062i	$-0.632929\pi$
$709$	−21.5986	−0.811151	−0.405575	+	0.914062i	$0.632929\pi$
$710$	0	0
$711$	−24.8903	−0.933458
$712$	−5.04576	−0.189098
$713$	−1.82132	−0.0682089
$714$	0.341716	0.0127884
$715$	0	0
$716$	−3.36634	−0.125806
$717$	−6.73269	−0.251437
$718$	15.2778	0.570161
$719$	16.8098	0.626900	0.313450	−	0.949605i	$-0.398515\pi$
$719$	16.8098	0.626900	0.313450	+	0.949605i	$0.398515\pi$
$720$	0	0
$721$	−25.0935	−0.934530
$722$	25.3024	0.941658
$723$	−9.52773	−0.354340
$724$	−15.8970	−0.590807
$725$	0	0
$726$	9.57176	0.355241
$727$	5.65373	0.209685	0.104843	−	0.994489i	$-0.466566\pi$
$727$	5.65373	0.209685	0.104843	+	0.994489i	$0.466566\pi$
$728$	−10.6155	−0.393435
$729$	−3.65430	−0.135345
$730$	0	0
$731$	0.414238	0.0153211
$732$	−4.71868	−0.174408
$733$	−40.2821	−1.48785	−0.743927	−	0.668261i	$-0.767039\pi$
$733$	−40.2821	−1.48785	−0.743927	+	0.668261i	$0.767039\pi$
$734$	−9.59581	−0.354188
$735$	0	0
$736$	1.00000	0.0368605
$737$	−62.7356	−2.31090
$738$	−27.5509	−1.01416
$739$	1.97327	0.0725877	0.0362939	−	0.999341i	$-0.488445\pi$
$739$	1.97327	0.0725877	0.0362939	+	0.999341i	$0.488445\pi$
$740$	0	0
$741$	20.7317	0.761597
$742$	14.0785	0.516839
$743$	24.8403	0.911304	0.455652	−	0.890158i	$-0.349406\pi$
$743$	24.8403	0.911304	0.455652	+	0.890158i	$0.349406\pi$
$744$	−1.28692	−0.0471807
$745$	0	0
$746$	17.2125	0.630196
$747$	33.2690	1.21725
$748$	−0.994977	−0.0363799
$749$	24.0372	0.878300
$750$	0	0
$751$	3.61665	0.131973	0.0659867	−	0.997821i	$-0.478981\pi$
$751$	3.61665	0.131973	0.0659867	+	0.997821i	$0.478981\pi$
$752$	−0.505760	−0.0184432
$753$	−7.16492	−0.261104
$754$	7.40312	0.269606
$755$	0	0
$756$	9.35985	0.340414
$757$	22.3992	0.814113	0.407056	−	0.913403i	$-0.366555\pi$
$757$	22.3992	0.814113	0.407056	+	0.913403i	$0.366555\pi$
$758$	−20.7354	−0.753145
$759$	3.50074	0.127069
$760$	0	0
$761$	25.5137	0.924872	0.462436	−	0.886653i	$-0.346975\pi$
$761$	25.5137	0.924872	0.462436	+	0.886653i	$0.346975\pi$
$762$	12.8163	0.464285
$763$	33.4105	1.20954
$764$	−6.74527	−0.244035
$765$	0	0
$766$	−13.0115	−0.470125
$767$	−19.4604	−0.702675
$768$	0.706585	0.0254967
$769$	−13.8123	−0.498084	−0.249042	−	0.968493i	$-0.580116\pi$
$769$	−13.8123	−0.498084	−0.249042	+	0.968493i	$0.580116\pi$
$770$	0	0
$771$	6.19107	0.222966
$772$	4.81630	0.173342
$773$	−3.36423	−0.121003	−0.0605015	−	0.998168i	$-0.519270\pi$
$773$	−3.36423	−0.121003	−0.0605015	+	0.998168i	$0.519270\pi$
$774$	5.15822	0.185408
$775$	0	0
$776$	−3.79917	−0.136382
$777$	−14.4247	−0.517483
$778$	6.55279	0.234929
$779$	73.3300	2.62732
$780$	0	0
$781$	17.9053	0.640703
$782$	−0.200825	−0.00718149
$783$	−6.52746	−0.233273
$784$	−1.20083	−0.0428866
$785$	0	0
$786$	−1.40607	−0.0501529
$787$	−1.29067	−0.0460074	−0.0230037	−	0.999735i	$-0.507323\pi$
$787$	−1.29067	−0.0460074	−0.0230037	+	0.999735i	$0.507323\pi$
$788$	−12.8349	−0.457224
$789$	11.1251	0.396063
$790$	0	0
$791$	44.5404	1.58367
$792$	−12.3898	−0.440251
$793$	−29.4383	−1.04538
$794$	−6.79516	−0.241151
$795$	0	0
$796$	−12.4957	−0.442899
$797$	22.4673	0.795832	0.397916	−	0.917422i	$-0.369734\pi$
$797$	22.4673	0.795832	0.397916	+	0.917422i	$0.369734\pi$
$798$	−11.3256	−0.400922
$799$	0.101569	0.00359327
$800$	0	0
$801$	12.6181	0.445839
$802$	−30.5660	−1.07932
$803$	−71.6359	−2.52798
$804$	−8.94714	−0.315541
$805$	0	0
$806$	−8.02864	−0.282797
$807$	16.6412	0.585797
$808$	13.2410	0.465816
$809$	−22.3547	−0.785950	−0.392975	−	0.919549i	$-0.628554\pi$
$809$	−22.3547	−0.785950	−0.392975	+	0.919549i	$0.628554\pi$
$810$	0	0
$811$	−49.6698	−1.74414	−0.872071	−	0.489380i	$-0.837223\pi$
$811$	−49.6698	−1.74414	−0.872071	+	0.489380i	$0.837223\pi$
$812$	−4.04429	−0.141927
$813$	−1.15077	−0.0403592
$814$	42.0004	1.47211
$815$	0	0
$816$	−0.141900	−0.00496750
$817$	−13.7292	−0.480324
$818$	19.8610	0.694425
$819$	26.5465	0.927610
$820$	0	0
$821$	−50.2031	−1.75210	−0.876051	−	0.482219i	$-0.839831\pi$
$821$	−50.2031	−1.75210	−0.876051	+	0.482219i	$0.839831\pi$
$822$	0.807892	0.0281785
$823$	34.2979	1.19555	0.597776	−	0.801663i	$-0.296051\pi$
$823$	34.2979	1.19555	0.597776	+	0.801663i	$0.296051\pi$
$824$	10.4202	0.363006
$825$	0	0
$826$	10.6311	0.369904
$827$	44.4915	1.54712	0.773560	−	0.633723i	$-0.218474\pi$
$827$	44.4915	1.54712	0.773560	+	0.633723i	$0.218474\pi$
$828$	−2.50074	−0.0869066
$829$	18.0055	0.625356	0.312678	−	0.949859i	$-0.398774\pi$
$829$	18.0055	0.625356	0.312678	+	0.949859i	$0.398774\pi$
$830$	0	0
$831$	−15.4787	−0.536950
$832$	4.40815	0.152825
$833$	0.241156	0.00835556
$834$	15.8621	0.549258
$835$	0	0
$836$	32.9768	1.14053
$837$	7.07899	0.244686
$838$	4.19057	0.144761
$839$	−6.47816	−0.223651	−0.111825	−	0.993728i	$-0.535670\pi$
$839$	−6.47816	−0.223651	−0.111825	+	0.993728i	$0.535670\pi$
$840$	0	0
$841$	−26.1796	−0.902743
$842$	−32.2306	−1.11074
$843$	−3.98701	−0.137320
$844$	−16.0130	−0.551190
$845$	0	0
$846$	1.26477	0.0434838
$847$	−32.6220	−1.12090
$848$	−5.84621	−0.200760
$849$	4.35026	0.149301
$850$	0	0
$851$	8.47732	0.290599
$852$	2.55360	0.0874848
$853$	45.4861	1.55742	0.778708	−	0.627387i	$-0.215876\pi$
$853$	45.4861	1.55742	0.778708	+	0.627387i	$0.215876\pi$
$854$	16.0820	0.550314
$855$	0	0
$856$	−9.98161	−0.341164
$857$	−19.4734	−0.665199	−0.332599	−	0.943068i	$-0.607926\pi$
$857$	−19.4734	−0.665199	−0.332599	+	0.943068i	$0.607926\pi$
$858$	15.4318	0.526832
$859$	−32.7724	−1.11818	−0.559090	−	0.829107i	$-0.688849\pi$
$859$	−32.7724	−1.11818	−0.559090	+	0.829107i	$0.688849\pi$
$860$	0	0
$861$	−18.7463	−0.638873
$862$	18.7583	0.638909
$863$	9.47045	0.322378	0.161189	−	0.986924i	$-0.448467\pi$
$863$	9.47045	0.322378	0.161189	+	0.986924i	$0.448467\pi$
$864$	−3.88674	−0.132230
$865$	0	0
$866$	−28.3271	−0.962593
$867$	−11.9835	−0.406980
$868$	4.38600	0.148871
$869$	49.3124	1.67281
$870$	0	0
$871$	−55.8182	−1.89133
$872$	−13.8739	−0.469831
$873$	9.50074	0.321551
$874$	6.65600	0.225143
$875$	0	0
$876$	−10.2165	−0.345183
$877$	8.59538	0.290245	0.145123	−	0.989414i	$-0.453642\pi$
$877$	8.59538	0.290245	0.145123	+	0.989414i	$0.453642\pi$
$878$	23.7532	0.801633
$879$	15.1837	0.512134
$880$	0	0
$881$	18.6633	0.628784	0.314392	−	0.949293i	$-0.398199\pi$
$881$	18.6633	0.628784	0.314392	+	0.949293i	$0.398199\pi$
$882$	3.00295	0.101115
$883$	−48.3855	−1.62830	−0.814151	−	0.580653i	$-0.802797\pi$
$883$	−48.3855	−1.62830	−0.814151	+	0.580653i	$0.802797\pi$
$884$	−0.885267	−0.0297747
$885$	0	0
$886$	−9.91284	−0.333028
$887$	21.8123	0.732385	0.366192	−	0.930539i	$-0.380661\pi$
$887$	21.8123	0.732385	0.366192	+	0.930539i	$0.380661\pi$
$888$	5.98995	0.201010
$889$	−43.6798	−1.46497
$890$	0	0
$891$	23.5628	0.789384
$892$	−18.2094	−0.609695
$893$	−3.36634	−0.112650
$894$	5.79724	0.193889
$895$	0	0
$896$	−2.40815	−0.0804506
$897$	3.11473	0.103998
$898$	−39.3758	−1.31399
$899$	−3.05876	−0.102015
$900$	0	0
$901$	1.17407	0.0391138
$902$	54.5837	1.81744
$903$	3.50977	0.116798
$904$	−18.4957	−0.615158
$905$	0	0
$906$	7.43636	0.247056
$907$	−20.7436	−0.688779	−0.344389	−	0.938827i	$-0.611914\pi$
$907$	−20.7436	−0.688779	−0.344389	+	0.938827i	$0.611914\pi$
$908$	19.5331	0.648230
$909$	−33.1122	−1.09826
$910$	0	0
$911$	−52.4263	−1.73696	−0.868480	−	0.495725i	$-0.834902\pi$
$911$	−52.4263	−1.73696	−0.868480	+	0.495725i	$0.834902\pi$
$912$	4.70304	0.155733
$913$	−65.9122	−2.18138
$914$	−15.1737	−0.501900
$915$	0	0
$916$	−22.3419	−0.738198
$917$	4.79210	0.158249
$918$	0.780555	0.0257622
$919$	10.9334	0.360660	0.180330	−	0.983606i	$-0.442284\pi$
$919$	10.9334	0.360660	0.180330	+	0.983606i	$0.442284\pi$
$920$	0	0
$921$	2.89468	0.0953829
$922$	8.44848	0.278236
$923$	15.9310	0.524376
$924$	−8.43029	−0.277336
$925$	0	0
$926$	−19.8888	−0.653586
$927$	−26.0583	−0.855867
$928$	1.67942	0.0551296
$929$	30.7620	1.00927	0.504634	−	0.863334i	$-0.331628\pi$
$929$	30.7620	1.00927	0.504634	+	0.863334i	$0.331628\pi$
$930$	0	0
$931$	−7.99270	−0.261950
$932$	−6.42469	−0.210448
$933$	16.9654	0.555424
$934$	27.3066	0.893500
$935$	0	0
$936$	−11.0236	−0.360318
$937$	−11.3523	−0.370865	−0.185432	−	0.982657i	$-0.559369\pi$
$937$	−11.3523	−0.370865	−0.185432	+	0.982657i	$0.559369\pi$
$938$	30.4932	0.995637
$939$	−7.68032	−0.250638
$940$	0	0
$941$	11.5019	0.374953	0.187476	−	0.982269i	$-0.439969\pi$
$941$	11.5019	0.374953	0.187476	+	0.982269i	$0.439969\pi$
$942$	−0.727720	−0.0237104
$943$	11.0171	0.358767
$944$	−4.41464	−0.143684
$945$	0	0
$946$	−10.2194	−0.332262
$947$	27.0735	0.879771	0.439885	−	0.898054i	$-0.355019\pi$
$947$	27.0735	0.879771	0.439885	+	0.898054i	$0.355019\pi$
$948$	7.03277	0.228414
$949$	−63.7371	−2.06899
$950$	0	0
$951$	15.6622	0.507883
$952$	0.483617	0.0156741
$953$	8.05878	0.261050	0.130525	−	0.991445i	$-0.458334\pi$
$953$	8.05878	0.261050	0.130525	+	0.991445i	$0.458334\pi$
$954$	14.6198	0.473334
$955$	0	0
$956$	−9.52848	−0.308173
$957$	5.87920	0.190048
$958$	21.0558	0.680282
$959$	−2.75341	−0.0889124
$960$	0	0
$961$	−27.6828	−0.892994
$962$	37.3693	1.20483
$963$	24.9614	0.804369
$964$	−13.4842	−0.434297
$965$	0	0
$966$	−1.70156	−0.0547469
$967$	35.8257	1.15208	0.576038	−	0.817423i	$-0.304598\pi$
$967$	35.8257	1.15208	0.576038	+	0.817423i	$0.304598\pi$
$968$	13.5465	0.435401
$969$	−0.944488	−0.0303413
$970$	0	0
$971$	18.5815	0.596310	0.298155	−	0.954517i	$-0.403629\pi$
$971$	18.5815	0.596310	0.298155	+	0.954517i	$0.403629\pi$
$972$	15.0207	0.481788
$973$	−54.0602	−1.73309
$974$	22.5530	0.722645
$975$	0	0
$976$	−6.67815	−0.213762
$977$	−56.7588	−1.81588	−0.907938	−	0.419105i	$-0.862344\pi$
$977$	−56.7588	−1.81588	−0.907938	+	0.419105i	$0.862344\pi$
$978$	7.89974	0.252606
$979$	−24.9989	−0.798969
$980$	0	0
$981$	34.6951	1.10773
$982$	−17.1369	−0.546860
$983$	61.1897	1.95165	0.975824	−	0.218556i	$-0.0701347\pi$
$983$	61.1897	1.95165	0.975824	+	0.218556i	$0.0701347\pi$
$984$	7.78454	0.248162
$985$	0	0
$986$	−0.337269	−0.0107408
$987$	0.860583	0.0273926
$988$	29.3406	0.933450
$989$	−2.06268	−0.0655893
$990$	0	0
$991$	−34.9833	−1.11128	−0.555640	−	0.831423i	$-0.687527\pi$
$991$	−34.9833	−1.11128	−0.555640	+	0.831423i	$0.687527\pi$
$992$	−1.82132	−0.0578269
$993$	−6.63701	−0.210619
$994$	−8.70304	−0.276044
$995$	0	0
$996$	−9.40018	−0.297856
$997$	41.6506	1.31909	0.659543	−	0.751667i	$-0.270750\pi$
$997$	41.6506	1.31909	0.659543	+	0.751667i	$0.270750\pi$
$998$	−12.1254	−0.383821
$999$	−32.9492	−1.04247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.s.1.2		4
4.3	odd	2		9200.2.a.cj.1.3		4
5.2	odd	4		230.2.b.b.139.7	yes	8
5.3	odd	4		230.2.b.b.139.2	✓	8
5.4	even	2		1150.2.a.r.1.3		4
15.2	even	4		2070.2.d.f.829.4		8
15.8	even	4		2070.2.d.f.829.8		8
20.3	even	4		1840.2.e.e.369.4		8
20.7	even	4		1840.2.e.e.369.5		8
20.19	odd	2		9200.2.a.cr.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.2	✓	8	5.3	odd	4
230.2.b.b.139.7	yes	8	5.2	odd	4
1150.2.a.r.1.3		4	5.4	even	2
1150.2.a.s.1.2		4	1.1	even	1	trivial
1840.2.e.e.369.4		8	20.3	even	4
1840.2.e.e.369.5		8	20.7	even	4
2070.2.d.f.829.4		8	15.2	even	4
2070.2.d.f.829.8		8	15.8	even	4
9200.2.a.cj.1.3		4	4.3	odd	2
9200.2.a.cr.1.2		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.706585 q^{3} +1.00000 q^{4} +0.706585 q^{6} -2.40815 q^{7} +1.00000 q^{8} -2.50074 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.706585 q^{3} +1.00000 q^{4} +0.706585 q^{6} -2.40815 q^{7} +1.00000 q^{8} -2.50074 q^{9} +4.95444 q^{11} +0.706585 q^{12} +4.40815 q^{13} -2.40815 q^{14} +1.00000 q^{16} -0.200825 q^{17} -2.50074 q^{18} +6.65600 q^{19} -1.70156 q^{21} +4.95444 q^{22} +1.00000 q^{23} +0.706585 q^{24} +4.40815 q^{26} -3.88674 q^{27} -2.40815 q^{28} +1.67942 q^{29} -1.82132 q^{31} +1.00000 q^{32} +3.50074 q^{33} -0.200825 q^{34} -2.50074 q^{36} +8.47732 q^{37} +6.65600 q^{38} +3.11473 q^{39} +11.0171 q^{41} -1.70156 q^{42} -2.06268 q^{43} +4.95444 q^{44} +1.00000 q^{46} -0.505760 q^{47} +0.706585 q^{48} -1.20083 q^{49} -0.141900 q^{51} +4.40815 q^{52} -5.84621 q^{53} -3.88674 q^{54} -2.40815 q^{56} +4.70304 q^{57} +1.67942 q^{58} -4.41464 q^{59} -6.67815 q^{61} -1.82132 q^{62} +6.02214 q^{63} +1.00000 q^{64} +3.50074 q^{66} -12.6625 q^{67} -0.200825 q^{68} +0.706585 q^{69} +3.61400 q^{71} -2.50074 q^{72} -14.4589 q^{73} +8.47732 q^{74} +6.65600 q^{76} -11.9310 q^{77} +3.11473 q^{78} +9.95317 q^{79} +4.75590 q^{81} +11.0171 q^{82} -13.3037 q^{83} -1.70156 q^{84} -2.06268 q^{86} +1.18665 q^{87} +4.95444 q^{88} -5.04576 q^{89} -10.6155 q^{91} +1.00000 q^{92} -1.28692 q^{93} -0.505760 q^{94} +0.706585 q^{96} -3.79917 q^{97} -1.20083 q^{98} -12.3898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9} + 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{14} + 4 q^{16} - 5 q^{17} + 7 q^{18} - q^{19} + 6 q^{21} + 5 q^{22} + 4 q^{23} + 3 q^{24} + 5 q^{26} + 6 q^{27} + 3 q^{28} + 2 q^{29} + 5 q^{31} + 4 q^{32} - 3 q^{33} - 5 q^{34} + 7 q^{36} - 6 q^{37} - q^{38} + 23 q^{41} + 6 q^{42} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 2 q^{47} + 3 q^{48} - 9 q^{49} + 7 q^{51} + 5 q^{52} + 6 q^{54} + 3 q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 9 q^{61} + 5 q^{62} + 16 q^{63} + 4 q^{64} - 3 q^{66} - 2 q^{67} - 5 q^{68} + 3 q^{69} + 19 q^{71} + 7 q^{72} - 8 q^{73} - 6 q^{74} - q^{76} - 10 q^{77} - 6 q^{79} + 16 q^{81} + 23 q^{82} - 14 q^{83} + 6 q^{84} - 2 q^{86} - 38 q^{87} + 5 q^{88} + 30 q^{89} - 13 q^{91} + 4 q^{92} - 26 q^{93} + 2 q^{94} + 3 q^{96} - 11 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9 + 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^14 + 4 * q^16 - 5 * q^17 + 7 * q^18 - q^19 + 6 * q^21 + 5 * q^22 + 4 * q^23 + 3 * q^24 + 5 * q^26 + 6 * q^27 + 3 * q^28 + 2 * q^29 + 5 * q^31 + 4 * q^32 - 3 * q^33 - 5 * q^34 + 7 * q^36 - 6 * q^37 - q^38 + 23 * q^41 + 6 * q^42 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 2 * q^47 + 3 * q^48 - 9 * q^49 + 7 * q^51 + 5 * q^52 + 6 * q^54 + 3 * q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 9 * q^61 + 5 * q^62 + 16 * q^63 + 4 * q^64 - 3 * q^66 - 2 * q^67 - 5 * q^68 + 3 * q^69 + 19 * q^71 + 7 * q^72 - 8 * q^73 - 6 * q^74 - q^76 - 10 * q^77 - 6 * q^79 + 16 * q^81 + 23 * q^82 - 14 * q^83 + 6 * q^84 - 2 * q^86 - 38 * q^87 + 5 * q^88 + 30 * q^89 - 13 * q^91 + 4 * q^92 - 26 * q^93 + 2 * q^94 + 3 * q^96 - 11 * q^97 - 9 * q^98 - 27 * q^99

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