LMFDB - Embedded newform 490.4.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{113})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 59x^{2} + 60x + 674 $ x^4 - 2x^3 - 59x^2 + 60*x + 674
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.40086$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -4.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} -8.45857 q^{6} +8.00000 q^{8} -9.11314 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -4.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} -8.45857 q^{6} +8.00000 q^{8} -9.11314 q^{9} +10.0000 q^{10} -44.1797 q^{11} -16.9171 q^{12} +85.3214 q^{13} -21.1464 q^{15} +16.0000 q^{16} +107.863 q^{17} -18.2263 q^{18} -53.8652 q^{19} +20.0000 q^{20} -88.3595 q^{22} -96.1723 q^{23} -33.8343 q^{24} +25.0000 q^{25} +170.643 q^{26} +152.733 q^{27} +201.241 q^{29} -42.2929 q^{30} -90.4949 q^{31} +32.0000 q^{32} +186.849 q^{33} +215.725 q^{34} -36.4525 q^{36} +312.389 q^{37} -107.730 q^{38} -360.848 q^{39} +40.0000 q^{40} -56.6718 q^{41} +227.040 q^{43} -176.719 q^{44} -45.5657 q^{45} -192.345 q^{46} +201.891 q^{47} -67.6686 q^{48} +50.0000 q^{50} -456.182 q^{51} +341.285 q^{52} -48.2617 q^{53} +305.466 q^{54} -220.899 q^{55} +227.811 q^{57} +402.483 q^{58} +678.489 q^{59} -84.5857 q^{60} +318.955 q^{61} -180.990 q^{62} +64.0000 q^{64} +426.607 q^{65} +373.697 q^{66} -647.185 q^{67} +431.450 q^{68} +406.740 q^{69} +962.862 q^{71} -72.9051 q^{72} +7.40033 q^{73} +624.778 q^{74} -105.732 q^{75} -215.461 q^{76} -721.697 q^{78} +455.803 q^{79} +80.0000 q^{80} -399.896 q^{81} -113.344 q^{82} +192.243 q^{83} +539.313 q^{85} +454.080 q^{86} -851.107 q^{87} -353.438 q^{88} +263.698 q^{89} -91.1314 q^{90} -384.689 q^{92} +382.729 q^{93} +403.783 q^{94} -269.326 q^{95} -135.337 q^{96} -1507.08 q^{97} +402.616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9} + 40 q^{10} + 18 q^{11} + 40 q^{12} + 130 q^{13} + 50 q^{15} + 64 q^{16} + 110 q^{17} + 76 q^{18} + 40 q^{19} + 80 q^{20} + 36 q^{22} - 164 q^{23} + 80 q^{24} + 100 q^{25} + 260 q^{26} + 430 q^{27} + 94 q^{29} + 100 q^{30} + 180 q^{31} + 128 q^{32} + 650 q^{33} + 220 q^{34} + 152 q^{36} + 16 q^{37} + 80 q^{38} - 10 q^{39} + 160 q^{40} + 540 q^{41} - 560 q^{43} + 72 q^{44} + 190 q^{45} - 328 q^{46} + 1150 q^{47} + 160 q^{48} + 200 q^{50} - 926 q^{51} + 520 q^{52} - 244 q^{53} + 860 q^{54} + 90 q^{55} - 840 q^{57} + 188 q^{58} + 400 q^{59} + 200 q^{60} + 1540 q^{61} + 360 q^{62} + 256 q^{64} + 650 q^{65} + 1300 q^{66} - 760 q^{67} + 440 q^{68} - 1480 q^{69} + 52 q^{71} + 304 q^{72} + 800 q^{73} + 32 q^{74} + 250 q^{75} + 160 q^{76} - 20 q^{78} + 398 q^{79} + 320 q^{80} + 348 q^{81} + 1080 q^{82} - 1220 q^{83} + 550 q^{85} - 1120 q^{86} - 930 q^{87} + 144 q^{88} + 200 q^{89} + 380 q^{90} - 656 q^{92} + 1408 q^{93} + 2300 q^{94} + 200 q^{95} + 320 q^{96} - 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9 + 40 * q^10 + 18 * q^11 + 40 * q^12 + 130 * q^13 + 50 * q^15 + 64 * q^16 + 110 * q^17 + 76 * q^18 + 40 * q^19 + 80 * q^20 + 36 * q^22 - 164 * q^23 + 80 * q^24 + 100 * q^25 + 260 * q^26 + 430 * q^27 + 94 * q^29 + 100 * q^30 + 180 * q^31 + 128 * q^32 + 650 * q^33 + 220 * q^34 + 152 * q^36 + 16 * q^37 + 80 * q^38 - 10 * q^39 + 160 * q^40 + 540 * q^41 - 560 * q^43 + 72 * q^44 + 190 * q^45 - 328 * q^46 + 1150 * q^47 + 160 * q^48 + 200 * q^50 - 926 * q^51 + 520 * q^52 - 244 * q^53 + 860 * q^54 + 90 * q^55 - 840 * q^57 + 188 * q^58 + 400 * q^59 + 200 * q^60 + 1540 * q^61 + 360 * q^62 + 256 * q^64 + 650 * q^65 + 1300 * q^66 - 760 * q^67 + 440 * q^68 - 1480 * q^69 + 52 * q^71 + 304 * q^72 + 800 * q^73 + 32 * q^74 + 250 * q^75 + 160 * q^76 - 20 * q^78 + 398 * q^79 + 320 * q^80 + 348 * q^81 + 1080 * q^82 - 1220 * q^83 + 550 * q^85 - 1120 * q^86 - 930 * q^87 + 144 * q^88 + 200 * q^89 + 380 * q^90 - 656 * q^92 + 1408 * q^93 + 2300 * q^94 + 200 * q^95 + 320 * q^96 - 670 * q^97 + 2292 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−4.22929	−0.813927	−0.406963	−	0.913445i	$-0.633412\pi$
$3$	−4.22929	−0.813927	−0.406963	+	0.913445i	$0.633412\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−8.45857	−0.575533
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−9.11314	−0.337524
$10$	10.0000	0.316228
$11$	−44.1797	−1.21097	−0.605486	−	0.795856i	$-0.707021\pi$
$11$	−44.1797	−1.21097	−0.605486	+	0.795856i	$0.707021\pi$
$12$	−16.9171	−0.406963
$13$	85.3214	1.82030	0.910149	−	0.414280i	$-0.135967\pi$
$13$	85.3214	1.82030	0.910149	+	0.414280i	$0.135967\pi$
$14$	0	0
$15$	−21.1464	−0.363999
$16$	16.0000	0.250000
$17$	107.863	1.53885	0.769427	−	0.638735i	$-0.220542\pi$
$17$	107.863	1.53885	0.769427	+	0.638735i	$0.220542\pi$
$18$	−18.2263	−0.238665
$19$	−53.8652	−0.650396	−0.325198	−	0.945646i	$-0.605431\pi$
$19$	−53.8652	−0.650396	−0.325198	+	0.945646i	$0.605431\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−88.3595	−0.856286
$23$	−96.1723	−0.871883	−0.435942	−	0.899975i	$-0.643585\pi$
$23$	−96.1723	−0.871883	−0.435942	+	0.899975i	$0.643585\pi$
$24$	−33.8343	−0.287766
$25$	25.0000	0.200000
$26$	170.643	1.28715
$27$	152.733	1.08865
$28$	0	0
$29$	201.241	1.28861	0.644303	−	0.764770i	$-0.277148\pi$
$29$	201.241	1.28861	0.644303	+	0.764770i	$0.277148\pi$
$30$	−42.2929	−0.257386
$31$	−90.4949	−0.524302	−0.262151	−	0.965027i	$-0.584432\pi$
$31$	−90.4949	−0.524302	−0.262151	+	0.965027i	$0.584432\pi$
$32$	32.0000	0.176777
$33$	186.849	0.985642
$34$	215.725	1.08813
$35$	0	0
$36$	−36.4525	−0.168762
$37$	312.389	1.38801	0.694006	−	0.719970i	$-0.255844\pi$
$37$	312.389	1.38801	0.694006	+	0.719970i	$0.255844\pi$
$38$	−107.730	−0.459899
$39$	−360.848	−1.48159
$40$	40.0000	0.158114
$41$	−56.6718	−0.215869	−0.107935	−	0.994158i	$-0.534424\pi$
$41$	−56.6718	−0.215869	−0.107935	+	0.994158i	$0.534424\pi$
$42$	0	0
$43$	227.040	0.805192	0.402596	−	0.915378i	$-0.368108\pi$
$43$	227.040	0.805192	0.402596	+	0.915378i	$0.368108\pi$
$44$	−176.719	−0.605486
$45$	−45.5657	−0.150945
$46$	−192.345	−0.616514
$47$	201.891	0.626572	0.313286	−	0.949659i	$-0.398570\pi$
$47$	201.891	0.626572	0.313286	+	0.949659i	$0.398570\pi$
$48$	−67.6686	−0.203482
$49$	0	0
$50$	50.0000	0.141421
$51$	−456.182	−1.25251
$52$	341.285	0.910149
$53$	−48.2617	−0.125080	−0.0625402	−	0.998042i	$-0.519920\pi$
$53$	−48.2617	−0.125080	−0.0625402	+	0.998042i	$0.519920\pi$
$54$	305.466	0.769789
$55$	−220.899	−0.541563
$56$	0	0
$57$	227.811	0.529374
$58$	402.483	0.911182
$59$	678.489	1.49715	0.748574	−	0.663051i	$-0.230739\pi$
$59$	678.489	1.49715	0.748574	+	0.663051i	$0.230739\pi$
$60$	−84.5857	−0.182000
$61$	318.955	0.669476	0.334738	−	0.942311i	$-0.391352\pi$
$61$	318.955	0.669476	0.334738	+	0.942311i	$0.391352\pi$
$62$	−180.990	−0.370737
$63$	0	0
$64$	64.0000	0.125000
$65$	426.607	0.814062
$66$	373.697	0.696954
$67$	−647.185	−1.18009	−0.590047	−	0.807369i	$-0.700891\pi$
$67$	−647.185	−1.18009	−0.590047	+	0.807369i	$0.700891\pi$
$68$	431.450	0.769427
$69$	406.740	0.709649
$70$	0	0
$71$	962.862	1.60945	0.804723	−	0.593650i	$-0.202314\pi$
$71$	962.862	1.60945	0.804723	+	0.593650i	$0.202314\pi$
$72$	−72.9051	−0.119333
$73$	7.40033	0.0118650	0.00593249	−	0.999982i	$-0.498112\pi$
$73$	7.40033	0.0118650	0.00593249	+	0.999982i	$0.498112\pi$
$74$	624.778	0.981472
$75$	−105.732	−0.162785
$76$	−215.461	−0.325198
$77$	0	0
$78$	−721.697	−1.04764
$79$	455.803	0.649137	0.324569	−	0.945862i	$-0.394781\pi$
$79$	455.803	0.649137	0.324569	+	0.945862i	$0.394781\pi$
$80$	80.0000	0.111803
$81$	−399.896	−0.548554
$82$	−113.344	−0.152643
$83$	192.243	0.254234	0.127117	−	0.991888i	$-0.459428\pi$
$83$	192.243	0.254234	0.127117	+	0.991888i	$0.459428\pi$
$84$	0	0
$85$	539.313	0.688196
$86$	454.080	0.569357
$87$	−851.107	−1.04883
$88$	−353.438	−0.428143
$89$	263.698	0.314067	0.157034	−	0.987593i	$-0.449807\pi$
$89$	263.698	0.314067	0.157034	+	0.987593i	$0.449807\pi$
$90$	−91.1314	−0.106734
$91$	0	0
$92$	−384.689	−0.435942
$93$	382.729	0.426743
$94$	403.783	0.443054
$95$	−269.326	−0.290866
$96$	−135.337	−0.143883
$97$	−1507.08	−1.57753	−0.788767	−	0.614693i	$-0.789280\pi$
$97$	−1507.08	−1.57753	−0.788767	+	0.614693i	$0.789280\pi$
$98$	0	0
$99$	402.616	0.408731
$100$	100.000	0.100000
$101$	1218.30	1.20025	0.600127	−	0.799905i	$-0.295117\pi$
$101$	1218.30	1.20025	0.600127	+	0.799905i	$0.295117\pi$
$102$	−912.363	−0.885661
$103$	1491.87	1.42717	0.713583	−	0.700571i	$-0.247071\pi$
$103$	1491.87	1.42717	0.713583	+	0.700571i	$0.247071\pi$
$104$	682.571	0.643573
$105$	0	0
$106$	−96.5234	−0.0884451
$107$	571.331	0.516193	0.258097	−	0.966119i	$-0.416905\pi$
$107$	571.331	0.516193	0.258097	+	0.966119i	$0.416905\pi$
$108$	610.931	0.544323
$109$	−699.530	−0.614705	−0.307353	−	0.951596i	$-0.599443\pi$
$109$	−699.530	−0.614705	−0.307353	+	0.951596i	$0.599443\pi$
$110$	−441.797	−0.382943
$111$	−1321.18	−1.12974
$112$	0	0
$113$	638.305	0.531387	0.265693	−	0.964058i	$-0.414399\pi$
$113$	638.305	0.531387	0.265693	+	0.964058i	$0.414399\pi$
$114$	455.623	0.374324
$115$	−480.861	−0.389918
$116$	804.965	0.644303
$117$	−777.545	−0.614394
$118$	1356.98	1.05864
$119$	0	0
$120$	−169.171	−0.128693
$121$	620.848	0.466453
$122$	637.911	0.473391
$123$	239.681	0.175702
$124$	−361.979	−0.262151
$125$	125.000	0.0894427
$126$	0	0
$127$	−2634.26	−1.84057	−0.920286	−	0.391246i	$-0.872044\pi$
$127$	−2634.26	−1.84057	−0.920286	+	0.391246i	$0.872044\pi$
$128$	128.000	0.0883883
$129$	−960.216	−0.655367
$130$	853.214	0.575629
$131$	−975.135	−0.650366	−0.325183	−	0.945651i	$-0.605426\pi$
$131$	−975.135	−0.650366	−0.325183	+	0.945651i	$0.605426\pi$
$132$	747.395	0.492821
$133$	0	0
$134$	−1294.37	−0.834452
$135$	763.664	0.486857
$136$	862.901	0.544067
$137$	−2971.89	−1.85333	−0.926665	−	0.375889i	$-0.877337\pi$
$137$	−2971.89	−1.85333	−0.926665	+	0.375889i	$0.877337\pi$
$138$	813.480	0.501797
$139$	1234.20	0.753117	0.376558	−	0.926393i	$-0.377107\pi$
$139$	1234.20	0.753117	0.376558	+	0.926393i	$0.377107\pi$
$140$	0	0
$141$	−853.857	−0.509984
$142$	1925.72	1.13805
$143$	−3769.47	−2.20433
$144$	−145.810	−0.0843809
$145$	1006.21	0.576282
$146$	14.8007	0.00838980
$147$	0	0
$148$	1249.56	0.694006
$149$	−3115.93	−1.71320	−0.856600	−	0.515982i	$-0.827427\pi$
$149$	−3115.93	−1.71320	−0.856600	+	0.515982i	$0.827427\pi$
$150$	−211.464	−0.115107
$151$	−462.784	−0.249409	−0.124705	−	0.992194i	$-0.539798\pi$
$151$	−462.784	−0.249409	−0.124705	+	0.992194i	$0.539798\pi$
$152$	−430.921	−0.229950
$153$	−982.966	−0.519399
$154$	0	0
$155$	−452.474	−0.234475
$156$	−1443.39	−0.740795
$157$	−1077.53	−0.547746	−0.273873	−	0.961766i	$-0.588305\pi$
$157$	−1077.53	−0.547746	−0.273873	+	0.961766i	$0.588305\pi$
$158$	911.606	0.459009
$159$	204.113	0.101806
$160$	160.000	0.0790569
$161$	0	0
$162$	−799.792	−0.387886
$163$	−1519.00	−0.729921	−0.364961	−	0.931023i	$-0.618918\pi$
$163$	−1519.00	−0.729921	−0.364961	+	0.931023i	$0.618918\pi$
$164$	−226.687	−0.107935
$165$	934.244	0.440793
$166$	384.487	0.179771
$167$	1929.04	0.893856	0.446928	−	0.894570i	$-0.352518\pi$
$167$	1929.04	0.893856	0.446928	+	0.894570i	$0.352518\pi$
$168$	0	0
$169$	5082.73	2.31349
$170$	1078.63	0.486628
$171$	490.881	0.219524
$172$	908.159	0.402596
$173$	−3014.26	−1.32468	−0.662341	−	0.749203i	$-0.730437\pi$
$173$	−3014.26	−1.32468	−0.662341	+	0.749203i	$0.730437\pi$
$174$	−1702.21	−0.741635
$175$	0	0
$176$	−706.876	−0.302743
$177$	−2869.52	−1.21857
$178$	527.397	0.222079
$179$	−205.608	−0.0858540	−0.0429270	−	0.999078i	$-0.513668\pi$
$179$	−205.608	−0.0858540	−0.0429270	+	0.999078i	$0.513668\pi$
$180$	−182.263	−0.0754726
$181$	−4000.24	−1.64274	−0.821369	−	0.570398i	$-0.806789\pi$
$181$	−4000.24	−1.64274	−0.821369	+	0.570398i	$0.806789\pi$
$182$	0	0
$183$	−1348.95	−0.544904
$184$	−769.378	−0.308257
$185$	1561.94	0.620738
$186$	765.457	0.301753
$187$	−4765.34	−1.86351
$188$	807.566	0.313286
$189$	0	0
$190$	−538.652	−0.205673
$191$	−4267.51	−1.61668	−0.808342	−	0.588714i	$-0.799635\pi$
$191$	−4267.51	−1.61668	−0.808342	+	0.588714i	$0.799635\pi$
$192$	−270.674	−0.101741
$193$	2847.75	1.06210	0.531051	−	0.847340i	$-0.321797\pi$
$193$	2847.75	1.06210	0.531051	+	0.847340i	$0.321797\pi$
$194$	−3014.16	−1.11548
$195$	−1804.24	−0.662587
$196$	0	0
$197$	657.857	0.237921	0.118960	−	0.992899i	$-0.462044\pi$
$197$	657.857	0.237921	0.118960	+	0.992899i	$0.462044\pi$
$198$	805.232	0.289017
$199$	−1706.03	−0.607725	−0.303862	−	0.952716i	$-0.598276\pi$
$199$	−1706.03	−0.607725	−0.303862	+	0.952716i	$0.598276\pi$
$200$	200.000	0.0707107
$201$	2737.13	0.960509
$202$	2436.61	0.848708
$203$	0	0
$204$	−1824.73	−0.626257
$205$	−283.359	−0.0965397
$206$	2983.74	1.00916
$207$	876.431	0.294281
$208$	1365.14	0.455075
$209$	2379.75	0.787611
$210$	0	0
$211$	3062.04	0.999051	0.499526	−	0.866299i	$-0.333508\pi$
$211$	3062.04	0.999051	0.499526	+	0.866299i	$0.333508\pi$
$212$	−193.047	−0.0625402
$213$	−4072.22	−1.30997
$214$	1142.66	0.365004
$215$	1135.20	0.360093
$216$	1221.86	0.384894
$217$	0	0
$218$	−1399.06	−0.434662
$219$	−31.2981	−0.00965722
$220$	−883.595	−0.270782
$221$	9202.98	2.80117
$222$	−2642.36	−0.798846
$223$	3333.98	1.00116	0.500582	−	0.865689i	$-0.333119\pi$
$223$	3333.98	1.00116	0.500582	+	0.865689i	$0.333119\pi$
$224$	0	0
$225$	−227.828	−0.0675047
$226$	1276.61	0.375747
$227$	−589.443	−0.172347	−0.0861733	−	0.996280i	$-0.527464\pi$
$227$	−589.443	−0.172347	−0.0861733	+	0.996280i	$0.527464\pi$
$228$	911.245	0.264687
$229$	1485.79	0.428749	0.214374	−	0.976752i	$-0.431229\pi$
$229$	1485.79	0.428749	0.214374	+	0.976752i	$0.431229\pi$
$230$	−961.723	−0.275714
$231$	0	0
$232$	1609.93	0.455591
$233$	6589.75	1.85283	0.926414	−	0.376507i	$-0.122875\pi$
$233$	6589.75	1.85283	0.926414	+	0.376507i	$0.122875\pi$
$234$	−1555.09	−0.434442
$235$	1009.46	0.280212
$236$	2713.95	0.748574
$237$	−1927.72	−0.528350
$238$	0	0
$239$	−5043.16	−1.36492	−0.682458	−	0.730925i	$-0.739089\pi$
$239$	−5043.16	−1.36492	−0.682458	+	0.730925i	$0.739089\pi$
$240$	−338.343	−0.0909998
$241$	4195.47	1.12139	0.560693	−	0.828024i	$-0.310535\pi$
$241$	4195.47	1.12139	0.560693	+	0.828024i	$0.310535\pi$
$242$	1241.70	0.329832
$243$	−2432.51	−0.642163
$244$	1275.82	0.334738
$245$	0	0
$246$	479.362	0.124240
$247$	−4595.85	−1.18391
$248$	−723.959	−0.185369
$249$	−813.052	−0.206928
$250$	250.000	0.0632456
$251$	−5240.56	−1.31785	−0.658927	−	0.752207i	$-0.728989\pi$
$251$	−5240.56	−1.31785	−0.658927	+	0.752207i	$0.728989\pi$
$252$	0	0
$253$	4248.87	1.05583
$254$	−5268.52	−1.30148
$255$	−2280.91	−0.560141
$256$	256.000	0.0625000
$257$	2230.51	0.541383	0.270691	−	0.962666i	$-0.412748\pi$
$257$	2230.51	0.541383	0.270691	+	0.962666i	$0.412748\pi$
$258$	−1920.43	−0.463414
$259$	0	0
$260$	1706.43	0.407031
$261$	−1833.94	−0.434935
$262$	−1950.27	−0.459878
$263$	5021.76	1.17740	0.588698	−	0.808353i	$-0.299641\pi$
$263$	5021.76	1.17740	0.588698	+	0.808353i	$0.299641\pi$
$264$	1494.79	0.348477
$265$	−241.309	−0.0559376
$266$	0	0
$267$	−1115.26	−0.255628
$268$	−2588.74	−0.590047
$269$	2867.24	0.649883	0.324941	−	0.945734i	$-0.394655\pi$
$269$	2867.24	0.649883	0.324941	+	0.945734i	$0.394655\pi$
$270$	1527.33	0.344260
$271$	−8290.05	−1.85824	−0.929122	−	0.369772i	$-0.879436\pi$
$271$	−8290.05	−1.85824	−0.929122	+	0.369772i	$0.879436\pi$
$272$	1725.80	0.384713
$273$	0	0
$274$	−5943.79	−1.31050
$275$	−1104.49	−0.242194
$276$	1626.96	0.354824
$277$	−8275.67	−1.79508	−0.897539	−	0.440935i	$-0.854647\pi$
$277$	−8275.67	−1.79508	−0.897539	+	0.440935i	$0.854647\pi$
$278$	2468.39	0.532534
$279$	824.692	0.176964
$280$	0	0
$281$	−195.235	−0.0414475	−0.0207237	−	0.999785i	$-0.506597\pi$
$281$	−195.235	−0.0414475	−0.0207237	+	0.999785i	$0.506597\pi$
$282$	−1707.71	−0.360613
$283$	853.167	0.179207	0.0896034	−	0.995978i	$-0.471440\pi$
$283$	853.167	0.179207	0.0896034	+	0.995978i	$0.471440\pi$
$284$	3851.45	0.804723
$285$	1139.06	0.236743
$286$	−7538.95	−1.55870
$287$	0	0
$288$	−291.620	−0.0596663
$289$	6721.33	1.36807
$290$	2012.41	0.407493
$291$	6373.87	1.28400
$292$	29.6013	0.00593249
$293$	5178.51	1.03253	0.516266	−	0.856428i	$-0.327322\pi$
$293$	5178.51	1.03253	0.516266	+	0.856428i	$0.327322\pi$
$294$	0	0
$295$	3392.44	0.669545
$296$	2499.11	0.490736
$297$	−6747.69	−1.31832
$298$	−6231.85	−1.21141
$299$	−8205.55	−1.58709
$300$	−422.929	−0.0813927
$301$	0	0
$302$	−925.567	−0.176359
$303$	−5152.55	−0.976918
$304$	−861.843	−0.162599
$305$	1594.78	0.299399
$306$	−1965.93	−0.367271
$307$	7413.65	1.37824	0.689120	−	0.724648i	$-0.257997\pi$
$307$	7413.65	1.37824	0.689120	+	0.724648i	$0.257997\pi$
$308$	0	0
$309$	−6309.54	−1.16161
$310$	−904.949	−0.165799
$311$	598.848	0.109188	0.0545941	−	0.998509i	$-0.482614\pi$
$311$	598.848	0.109188	0.0545941	+	0.998509i	$0.482614\pi$
$312$	−2886.79	−0.523821
$313$	−117.140	−0.0211538	−0.0105769	−	0.999944i	$-0.503367\pi$
$313$	−117.140	−0.0211538	−0.0105769	+	0.999944i	$0.503367\pi$
$314$	−2155.06	−0.387315
$315$	0	0
$316$	1823.21	0.324569
$317$	−1485.97	−0.263281	−0.131641	−	0.991298i	$-0.542024\pi$
$317$	−1485.97	−0.263281	−0.131641	+	0.991298i	$0.542024\pi$
$318$	408.225	0.0719879
$319$	−8890.78	−1.56047
$320$	320.000	0.0559017
$321$	−2416.32	−0.420143
$322$	0	0
$323$	−5810.04	−1.00086
$324$	−1599.58	−0.274277
$325$	2133.03	0.364060
$326$	−3038.00	−0.516132
$327$	2958.51	0.500325
$328$	−453.374	−0.0763213
$329$	0	0
$330$	1868.49	0.311687
$331$	11080.1	1.83993	0.919963	−	0.392005i	$-0.128219\pi$
$331$	11080.1	1.83993	0.919963	+	0.392005i	$0.128219\pi$
$332$	768.974	0.127117
$333$	−2846.84	−0.468487
$334$	3858.09	0.632052
$335$	−3235.93	−0.527754
$336$	0	0
$337$	−9909.41	−1.60178	−0.800890	−	0.598811i	$-0.795640\pi$
$337$	−9909.41	−1.60178	−0.800890	+	0.598811i	$0.795640\pi$
$338$	10165.5	1.63588
$339$	−2699.58	−0.432510
$340$	2157.25	0.344098
$341$	3998.04	0.634915
$342$	981.761	0.155227
$343$	0	0
$344$	1816.32	0.284678
$345$	2033.70	0.317365
$346$	−6028.52	−0.936691
$347$	4361.14	0.674692	0.337346	−	0.941381i	$-0.390471\pi$
$347$	4361.14	0.674692	0.337346	+	0.941381i	$0.390471\pi$
$348$	−3404.43	−0.524415
$349$	−3457.97	−0.530375	−0.265187	−	0.964197i	$-0.585434\pi$
$349$	−3457.97	−0.530375	−0.265187	+	0.964197i	$0.585434\pi$
$350$	0	0
$351$	13031.4	1.98166
$352$	−1413.75	−0.214072
$353$	6027.69	0.908842	0.454421	−	0.890787i	$-0.349846\pi$
$353$	6027.69	0.908842	0.454421	+	0.890787i	$0.349846\pi$
$354$	−5739.05	−0.861658
$355$	4814.31	0.719767
$356$	1054.79	0.157034
$357$	0	0
$358$	−411.216	−0.0607080
$359$	4169.30	0.612945	0.306472	−	0.951880i	$-0.400851\pi$
$359$	4169.30	0.612945	0.306472	+	0.951880i	$0.400851\pi$
$360$	−364.525	−0.0533672
$361$	−3957.54	−0.576985
$362$	−8000.48	−1.16159
$363$	−2625.75	−0.379658
$364$	0	0
$365$	37.0016	0.00530618
$366$	−2697.91	−0.385306
$367$	929.431	0.132196	0.0660980	−	0.997813i	$-0.478945\pi$
$367$	929.431	0.132196	0.0660980	+	0.997813i	$0.478945\pi$
$368$	−1538.76	−0.217971
$369$	516.457	0.0728610
$370$	3123.89	0.438928
$371$	0	0
$372$	1530.91	0.213372
$373$	554.749	0.0770075	0.0385038	−	0.999258i	$-0.487741\pi$
$373$	554.749	0.0770075	0.0385038	+	0.999258i	$0.487741\pi$
$374$	−9530.68	−1.31770
$375$	−528.661	−0.0727998
$376$	1615.13	0.221527
$377$	17170.2	2.34565
$378$	0	0
$379$	3294.03	0.446446	0.223223	−	0.974767i	$-0.428342\pi$
$379$	3294.03	0.446446	0.223223	+	0.974767i	$0.428342\pi$
$380$	−1077.30	−0.145433
$381$	11141.0	1.49809
$382$	−8535.03	−1.14317
$383$	−7142.26	−0.952879	−0.476439	−	0.879207i	$-0.658073\pi$
$383$	−7142.26	−0.952879	−0.476439	+	0.879207i	$0.658073\pi$
$384$	−541.349	−0.0719416
$385$	0	0
$386$	5695.50	0.751020
$387$	−2069.04	−0.271771
$388$	−6028.32	−0.788767
$389$	−13408.4	−1.74765	−0.873823	−	0.486243i	$-0.838367\pi$
$389$	−13408.4	−1.74765	−0.873823	+	0.486243i	$0.838367\pi$
$390$	−3608.48	−0.468520
$391$	−10373.4	−1.34170
$392$	0	0
$393$	4124.12	0.529350
$394$	1315.71	0.168235
$395$	2279.01	0.290303
$396$	1610.46	0.204366
$397$	6201.69	0.784015	0.392008	−	0.919962i	$-0.371781\pi$
$397$	6201.69	0.784015	0.392008	+	0.919962i	$0.371781\pi$
$398$	−3412.06	−0.429726
$399$	0	0
$400$	400.000	0.0500000
$401$	27.1223	0.00337762	0.00168881	−	0.999999i	$-0.499462\pi$
$401$	27.1223	0.00337762	0.00168881	+	0.999999i	$0.499462\pi$
$402$	5474.26	0.679183
$403$	−7721.14	−0.954386
$404$	4873.21	0.600127
$405$	−1999.48	−0.245321
$406$	0	0
$407$	−13801.3	−1.68084
$408$	−3649.45	−0.442831
$409$	1635.91	0.197777	0.0988883	−	0.995099i	$-0.468471\pi$
$409$	1635.91	0.197777	0.0988883	+	0.995099i	$0.468471\pi$
$410$	−566.718	−0.0682639
$411$	12569.0	1.50847
$412$	5967.47	0.713583
$413$	0	0
$414$	1752.86	0.208088
$415$	961.217	0.113697
$416$	2730.28	0.321786
$417$	−5219.77	−0.612982
$418$	4759.50	0.556925
$419$	6677.68	0.778582	0.389291	−	0.921115i	$-0.372720\pi$
$419$	6677.68	0.778582	0.389291	+	0.921115i	$0.372720\pi$
$420$	0	0
$421$	4670.08	0.540632	0.270316	−	0.962772i	$-0.412872\pi$
$421$	4670.08	0.540632	0.270316	+	0.962772i	$0.412872\pi$
$422$	6124.09	0.706436
$423$	−1839.86	−0.211483
$424$	−386.094	−0.0442226
$425$	2696.56	0.307771
$426$	−8144.44	−0.926290
$427$	0	0
$428$	2285.32	0.258097
$429$	15942.2	1.79416
$430$	2270.40	0.254624
$431$	13246.6	1.48043	0.740215	−	0.672370i	$-0.234724\pi$
$431$	13246.6	1.48043	0.740215	+	0.672370i	$0.234724\pi$
$432$	2443.72	0.272161
$433$	−8331.65	−0.924696	−0.462348	−	0.886699i	$-0.652993\pi$
$433$	−8331.65	−0.924696	−0.462348	+	0.886699i	$0.652993\pi$
$434$	0	0
$435$	−4255.53	−0.469051
$436$	−2798.12	−0.307353
$437$	5180.34	0.567069
$438$	−62.5962	−0.00682868
$439$	−5305.24	−0.576777	−0.288388	−	0.957513i	$-0.593119\pi$
$439$	−5305.24	−0.576777	−0.288388	+	0.957513i	$0.593119\pi$
$440$	−1767.19	−0.191471
$441$	0	0
$442$	18406.0	1.98073
$443$	7059.26	0.757101	0.378550	−	0.925581i	$-0.376423\pi$
$443$	7059.26	0.757101	0.378550	+	0.925581i	$0.376423\pi$
$444$	−5284.73	−0.564870
$445$	1318.49	0.140455
$446$	6667.95	0.707930
$447$	13178.1	1.39442
$448$	0	0
$449$	−106.882	−0.0112341	−0.00561703	−	0.999984i	$-0.501788\pi$
$449$	−106.882	−0.0112341	−0.00561703	+	0.999984i	$0.501788\pi$
$450$	−455.657	−0.0477330
$451$	2503.74	0.261412
$452$	2553.22	0.265693
$453$	1957.24	0.203001
$454$	−1178.89	−0.121867
$455$	0	0
$456$	1822.49	0.187162
$457$	1113.07	0.113933	0.0569663	−	0.998376i	$-0.481857\pi$
$457$	1113.07	0.113933	0.0569663	+	0.998376i	$0.481857\pi$
$458$	2971.57	0.303171
$459$	16474.2	1.67527
$460$	−1923.45	−0.194959
$461$	−2021.78	−0.204259	−0.102130	−	0.994771i	$-0.532566\pi$
$461$	−2021.78	−0.204259	−0.102130	+	0.994771i	$0.532566\pi$
$462$	0	0
$463$	−6679.44	−0.670453	−0.335227	−	0.942138i	$-0.608813\pi$
$463$	−6679.44	−0.670453	−0.335227	+	0.942138i	$0.608813\pi$
$464$	3219.86	0.322151
$465$	1913.64	0.190845
$466$	13179.5	1.31015
$467$	12554.0	1.24396	0.621981	−	0.783032i	$-0.286328\pi$
$467$	12554.0	1.24396	0.621981	+	0.783032i	$0.286328\pi$
$468$	−3110.18	−0.307197
$469$	0	0
$470$	2018.91	0.198140
$471$	4557.18	0.445825
$472$	5427.91	0.529322
$473$	−10030.6	−0.975064
$474$	−3855.44	−0.373600
$475$	−1346.63	−0.130079
$476$	0	0
$477$	439.816	0.0422176
$478$	−10086.3	−0.965141
$479$	20219.6	1.92872	0.964358	−	0.264601i	$-0.0852402\pi$
$479$	20219.6	1.92872	0.964358	+	0.264601i	$0.0852402\pi$
$480$	−676.686	−0.0643465
$481$	26653.4	2.52660
$482$	8390.94	0.792939
$483$	0	0
$484$	2483.39	0.233226
$485$	−7535.40	−0.705494
$486$	−4865.02	−0.454078
$487$	−8543.68	−0.794971	−0.397486	−	0.917608i	$-0.630117\pi$
$487$	−8543.68	−0.794971	−0.397486	+	0.917608i	$0.630117\pi$
$488$	2551.64	0.236696
$489$	6424.28	0.594102
$490$	0	0
$491$	−21590.0	−1.98441	−0.992204	−	0.124626i	$-0.960227\pi$
$491$	−21590.0	−1.98441	−0.992204	+	0.124626i	$0.960227\pi$
$492$	958.724	0.0878509
$493$	21706.4	1.98298
$494$	−9191.70	−0.837154
$495$	2013.08	0.182790
$496$	−1447.92	−0.131075
$497$	0	0
$498$	−1626.10	−0.146320
$499$	−17066.7	−1.53108	−0.765542	−	0.643386i	$-0.777529\pi$
$499$	−17066.7	−1.53108	−0.765542	+	0.643386i	$0.777529\pi$
$500$	500.000	0.0447214
$501$	−8158.48	−0.727533
$502$	−10481.1	−0.931863
$503$	3407.00	0.302009	0.151005	−	0.988533i	$-0.451749\pi$
$503$	3407.00	0.302009	0.151005	+	0.988533i	$0.451749\pi$
$504$	0	0
$505$	6091.51	0.536770
$506$	8497.73	0.746582
$507$	−21496.3	−1.88301
$508$	−10537.0	−0.920286
$509$	−144.406	−0.0125750	−0.00628750	−	0.999980i	$-0.502001\pi$
$509$	−144.406	−0.0125750	−0.00628750	+	0.999980i	$0.502001\pi$
$510$	−4561.82	−0.396080
$511$	0	0
$512$	512.000	0.0441942
$513$	−8226.98	−0.708051
$514$	4461.02	0.382815
$515$	7459.34	0.638248
$516$	−3840.87	−0.327683
$517$	−8919.51	−0.758761
$518$	0	0
$519$	12748.2	1.07819
$520$	3412.85	0.287815
$521$	−2449.68	−0.205993	−0.102997	−	0.994682i	$-0.532843\pi$
$521$	−2449.68	−0.205993	−0.102997	+	0.994682i	$0.532843\pi$
$522$	−3667.88	−0.307545
$523$	1787.73	0.149469	0.0747343	−	0.997203i	$-0.476189\pi$
$523$	1787.73	0.149469	0.0747343	+	0.997203i	$0.476189\pi$
$524$	−3900.54	−0.325183
$525$	0	0
$526$	10043.5	0.832545
$527$	−9761.01	−0.806824
$528$	2989.58	0.246411
$529$	−2917.89	−0.239820
$530$	−482.617	−0.0395539
$531$	−6183.16	−0.505323
$532$	0	0
$533$	−4835.31	−0.392947
$534$	−2230.51	−0.180756
$535$	2856.66	0.230849
$536$	−5177.48	−0.417226
$537$	869.576	0.0698789
$538$	5734.47	0.459537
$539$	0	0
$540$	3054.66	0.243429
$541$	4772.36	0.379260	0.189630	−	0.981856i	$-0.439271\pi$
$541$	4772.36	0.379260	0.189630	+	0.981856i	$0.439271\pi$
$542$	−16580.1	−1.31398
$543$	16918.2	1.33707
$544$	3451.60	0.272033
$545$	−3497.65	−0.274904
$546$	0	0
$547$	6439.81	0.503375	0.251688	−	0.967808i	$-0.419014\pi$
$547$	6439.81	0.503375	0.251688	+	0.967808i	$0.419014\pi$
$548$	−11887.6	−0.926665
$549$	−2906.68	−0.225964
$550$	−2208.99	−0.171257
$551$	−10839.9	−0.838104
$552$	3253.92	0.250899
$553$	0	0
$554$	−16551.3	−1.26931
$555$	−6605.91	−0.505235
$556$	4936.79	0.376558
$557$	−8048.88	−0.612284	−0.306142	−	0.951986i	$-0.599038\pi$
$557$	−8048.88	−0.612284	−0.306142	+	0.951986i	$0.599038\pi$
$558$	1649.38	0.125133
$559$	19371.3	1.46569
$560$	0	0
$561$	20154.0	1.51676
$562$	−390.470	−0.0293078
$563$	12461.4	0.932833	0.466416	−	0.884565i	$-0.345545\pi$
$563$	12461.4	0.932833	0.466416	+	0.884565i	$0.345545\pi$
$564$	−3415.43	−0.254992
$565$	3191.53	0.237643
$566$	1706.33	0.126718
$567$	0	0
$568$	7702.90	0.569025
$569$	10740.9	0.791357	0.395679	−	0.918389i	$-0.370509\pi$
$569$	10740.9	0.791357	0.395679	+	0.918389i	$0.370509\pi$
$570$	2278.11	0.167403
$571$	24938.0	1.82771	0.913854	−	0.406043i	$-0.133092\pi$
$571$	24938.0	1.82771	0.913854	+	0.406043i	$0.133092\pi$
$572$	−15077.9	−1.10217
$573$	18048.5	1.31586
$574$	0	0
$575$	−2404.31	−0.174377
$576$	−583.241	−0.0421904
$577$	−14660.7	−1.05777	−0.528884	−	0.848694i	$-0.677390\pi$
$577$	−14660.7	−1.05777	−0.528884	+	0.848694i	$0.677390\pi$
$578$	13442.7	0.967372
$579$	−12044.0	−0.864473
$580$	4024.83	0.288141
$581$	0	0
$582$	12747.7	0.907923
$583$	2132.19	0.151469
$584$	59.2026	0.00419490
$585$	−3887.73	−0.274765
$586$	10357.0	0.730110
$587$	−22649.5	−1.59258	−0.796291	−	0.604914i	$-0.793207\pi$
$587$	−22649.5	−1.59258	−0.796291	+	0.604914i	$0.793207\pi$
$588$	0	0
$589$	4874.52	0.341004
$590$	6784.89	0.473440
$591$	−2782.27	−0.193650
$592$	4998.22	0.347003
$593$	13064.2	0.904690	0.452345	−	0.891843i	$-0.350588\pi$
$593$	13064.2	0.904690	0.452345	+	0.891843i	$0.350588\pi$
$594$	−13495.4	−0.932193
$595$	0	0
$596$	−12463.7	−0.856600
$597$	7215.29	0.494643
$598$	−16411.1	−1.12224
$599$	18044.6	1.23086	0.615428	−	0.788193i	$-0.288983\pi$
$599$	18044.6	1.23086	0.615428	+	0.788193i	$0.288983\pi$
$600$	−845.857	−0.0575533
$601$	20263.8	1.37534	0.687668	−	0.726025i	$-0.258634\pi$
$601$	20263.8	1.37534	0.687668	+	0.726025i	$0.258634\pi$
$602$	0	0
$603$	5897.89	0.398309
$604$	−1851.13	−0.124705
$605$	3104.24	0.208604
$606$	−10305.1	−0.690786
$607$	−3783.81	−0.253015	−0.126508	−	0.991966i	$-0.540377\pi$
$607$	−3783.81	−0.253015	−0.126508	+	0.991966i	$0.540377\pi$
$608$	−1723.69	−0.114975
$609$	0	0
$610$	3189.55	0.211707
$611$	17225.7	1.14055
$612$	−3931.86	−0.259700
$613$	−12913.8	−0.850869	−0.425434	−	0.904989i	$-0.639879\pi$
$613$	−12913.8	−0.850869	−0.425434	+	0.904989i	$0.639879\pi$
$614$	14827.3	0.974562
$615$	1198.41	0.0785762
$616$	0	0
$617$	−29332.1	−1.91388	−0.956942	−	0.290279i	$-0.906252\pi$
$617$	−29332.1	−1.91388	−0.956942	+	0.290279i	$0.906252\pi$
$618$	−12619.1	−0.821381
$619$	−20636.6	−1.33999	−0.669995	−	0.742365i	$-0.733704\pi$
$619$	−20636.6	−1.33999	−0.669995	+	0.742365i	$0.733704\pi$
$620$	−1809.90	−0.117237
$621$	−14688.7	−0.949172
$622$	1197.70	0.0772077
$623$	0	0
$624$	−5773.58	−0.370397
$625$	625.000	0.0400000
$626$	−234.280	−0.0149580
$627$	−10064.6	−0.641057
$628$	−4310.12	−0.273873
$629$	33695.1	2.13595
$630$	0	0
$631$	−10164.7	−0.641284	−0.320642	−	0.947201i	$-0.603899\pi$
$631$	−10164.7	−0.641284	−0.320642	+	0.947201i	$0.603899\pi$
$632$	3646.42	0.229505
$633$	−12950.3	−0.813154
$634$	−2971.93	−0.186168
$635$	−13171.3	−0.823129
$636$	816.451	0.0509031
$637$	0	0
$638$	−17781.6	−1.10342
$639$	−8774.70	−0.543226
$640$	640.000	0.0395285
$641$	22929.6	1.41290	0.706448	−	0.707765i	$-0.250296\pi$
$641$	22929.6	1.41290	0.706448	+	0.707765i	$0.250296\pi$
$642$	−4832.65	−0.297086
$643$	−28818.8	−1.76750	−0.883750	−	0.467958i	$-0.844990\pi$
$643$	−28818.8	−1.76750	−0.883750	+	0.467958i	$0.844990\pi$
$644$	0	0
$645$	−4801.08	−0.293089
$646$	−11620.1	−0.707718
$647$	1560.66	0.0948312	0.0474156	−	0.998875i	$-0.484901\pi$
$647$	1560.66	0.0948312	0.0474156	+	0.998875i	$0.484901\pi$
$648$	−3199.17	−0.193943
$649$	−29975.4	−1.81300
$650$	4266.07	0.257429
$651$	0	0
$652$	−6076.00	−0.364961
$653$	−5763.44	−0.345392	−0.172696	−	0.984975i	$-0.555248\pi$
$653$	−5763.44	−0.345392	−0.172696	+	0.984975i	$0.555248\pi$
$654$	5917.03	0.353783
$655$	−4875.67	−0.290852
$656$	−906.748	−0.0539673
$657$	−67.4402	−0.00400471
$658$	0	0
$659$	−4394.10	−0.259742	−0.129871	−	0.991531i	$-0.541456\pi$
$659$	−4394.10	−0.259742	−0.129871	+	0.991531i	$0.541456\pi$
$660$	3736.97	0.220396
$661$	−22774.6	−1.34013	−0.670066	−	0.742301i	$-0.733734\pi$
$661$	−22774.6	−1.34013	−0.670066	+	0.742301i	$0.733734\pi$
$662$	22160.1	1.30102
$663$	−38922.0	−2.27995
$664$	1537.95	0.0898854
$665$	0	0
$666$	−5693.69	−0.331270
$667$	−19353.8	−1.12351
$668$	7716.18	0.446928
$669$	−14100.3	−0.814874
$670$	−6471.85	−0.373178
$671$	−14091.4	−0.810717
$672$	0	0
$673$	−4388.52	−0.251359	−0.125680	−	0.992071i	$-0.540111\pi$
$673$	−4388.52	−0.251359	−0.125680	+	0.992071i	$0.540111\pi$
$674$	−19818.8	−1.13263
$675$	3818.32	0.217729
$676$	20330.9	1.15674
$677$	12902.7	0.732481	0.366241	−	0.930520i	$-0.380645\pi$
$677$	12902.7	0.732481	0.366241	+	0.930520i	$0.380645\pi$
$678$	−5399.15	−0.305831
$679$	0	0
$680$	4314.50	0.243314
$681$	2492.92	0.140278
$682$	7996.08	0.448952
$683$	−21600.3	−1.21012	−0.605060	−	0.796180i	$-0.706851\pi$
$683$	−21600.3	−1.21012	−0.605060	+	0.796180i	$0.706851\pi$
$684$	1963.52	0.109762
$685$	−14859.5	−0.828834
$686$	0	0
$687$	−6283.81	−0.348970
$688$	3632.64	0.201298
$689$	−4117.76	−0.227684
$690$	4067.40	0.224411
$691$	−14327.5	−0.788775	−0.394388	−	0.918944i	$-0.629043\pi$
$691$	−14327.5	−0.788775	−0.394388	+	0.918944i	$0.629043\pi$
$692$	−12057.0	−0.662341
$693$	0	0
$694$	8722.28	0.477079
$695$	6170.99	0.336804
$696$	−6808.86	−0.370818
$697$	−6112.76	−0.332191
$698$	−6915.93	−0.375031
$699$	−27869.9	−1.50807
$700$	0	0
$701$	18260.0	0.983840	0.491920	−	0.870641i	$-0.336295\pi$
$701$	18260.0	0.983840	0.491920	+	0.870641i	$0.336295\pi$
$702$	26062.7	1.40125
$703$	−16826.9	−0.902757
$704$	−2827.50	−0.151371
$705$	−4269.28	−0.228072
$706$	12055.4	0.642649
$707$	0	0
$708$	−11478.1	−0.609284
$709$	−7848.71	−0.415747	−0.207874	−	0.978156i	$-0.566654\pi$
$709$	−7848.71	−0.415747	−0.207874	+	0.978156i	$0.566654\pi$
$710$	9628.62	0.508952
$711$	−4153.79	−0.219099
$712$	2109.59	0.111039
$713$	8703.10	0.457130
$714$	0	0
$715$	−18847.4	−0.985807
$716$	−822.433	−0.0429270
$717$	21329.0	1.11094
$718$	8338.60	0.433417
$719$	13126.4	0.680850	0.340425	−	0.940272i	$-0.389429\pi$
$719$	13126.4	0.680850	0.340425	+	0.940272i	$0.389429\pi$
$720$	−729.051	−0.0377363
$721$	0	0
$722$	−7915.09	−0.407990
$723$	−17743.8	−0.912725
$724$	−16001.0	−0.821369
$725$	5031.03	0.257721
$726$	−5251.49	−0.268459
$727$	−15013.6	−0.765922	−0.382961	−	0.923765i	$-0.625096\pi$
$727$	−15013.6	−0.765922	−0.382961	+	0.923765i	$0.625096\pi$
$728$	0	0
$729$	21085.0	1.07123
$730$	74.0033	0.00375203
$731$	24489.1	1.23907
$732$	−5395.81	−0.272452
$733$	−356.053	−0.0179415	−0.00897076	−	0.999960i	$-0.502856\pi$
$733$	−356.053	−0.0179415	−0.00897076	+	0.999960i	$0.502856\pi$
$734$	1858.86	0.0934766
$735$	0	0
$736$	−3077.51	−0.154129
$737$	28592.5	1.42906
$738$	1032.91	0.0515205
$739$	35355.2	1.75989	0.879947	−	0.475071i	$-0.157578\pi$
$739$	35355.2	1.75989	0.879947	+	0.475071i	$0.157578\pi$
$740$	6247.78	0.310369
$741$	19437.2	0.963620
$742$	0	0
$743$	20934.1	1.03364	0.516822	−	0.856093i	$-0.327115\pi$
$743$	20934.1	1.03364	0.516822	+	0.856093i	$0.327115\pi$
$744$	3061.83	0.150876
$745$	−15579.6	−0.766166
$746$	1109.50	0.0544526
$747$	−1751.94	−0.0858101
$748$	−19061.4	−0.931754
$749$	0	0
$750$	−1057.32	−0.0514772
$751$	−19080.8	−0.927124	−0.463562	−	0.886065i	$-0.653429\pi$
$751$	−19080.8	−0.927124	−0.463562	+	0.886065i	$0.653429\pi$
$752$	3230.26	0.156643
$753$	22163.8	1.07264
$754$	34340.4	1.65862
$755$	−2313.92	−0.111539
$756$	0	0
$757$	−30445.4	−1.46177	−0.730884	−	0.682502i	$-0.760892\pi$
$757$	−30445.4	−1.46177	−0.730884	+	0.682502i	$0.760892\pi$
$758$	6588.06	0.315685
$759$	−17969.7	−0.859365
$760$	−2154.61	−0.102837
$761$	−6342.93	−0.302143	−0.151072	−	0.988523i	$-0.548272\pi$
$761$	−6342.93	−0.302143	−0.151072	+	0.988523i	$0.548272\pi$
$762$	22282.1	1.05931
$763$	0	0
$764$	−17070.1	−0.808342
$765$	−4914.83	−0.232282
$766$	−14284.5	−0.673787
$767$	57889.6	2.72526
$768$	−1082.70	−0.0508704
$769$	−30865.8	−1.44740	−0.723699	−	0.690116i	$-0.757559\pi$
$769$	−30865.8	−1.44740	−0.723699	+	0.690116i	$0.757559\pi$
$770$	0	0
$771$	−9433.46	−0.440646
$772$	11391.0	0.531051
$773$	25511.4	1.18704	0.593519	−	0.804820i	$-0.297738\pi$
$773$	25511.4	1.18704	0.593519	+	0.804820i	$0.297738\pi$
$774$	−4138.09	−0.192171
$775$	−2262.37	−0.104860
$776$	−12056.6	−0.557742
$777$	0	0
$778$	−26816.9	−1.23577
$779$	3052.63	0.140400
$780$	−7216.97	−0.331294
$781$	−42539.0	−1.94899
$782$	−20746.8	−0.948726
$783$	30736.1	1.40284
$784$	0	0
$785$	−5387.65	−0.244960
$786$	8248.25	0.374307
$787$	−29156.2	−1.32059	−0.660297	−	0.751005i	$-0.729570\pi$
$787$	−29156.2	−1.32059	−0.660297	+	0.751005i	$0.729570\pi$
$788$	2631.43	0.118960
$789$	−21238.5	−0.958314
$790$	4558.03	0.205275
$791$	0	0
$792$	3220.93	0.144508
$793$	27213.7	1.21865
$794$	12403.4	0.554382
$795$	1020.56	0.0455291
$796$	−6824.12	−0.303862
$797$	−34720.9	−1.54313	−0.771566	−	0.636150i	$-0.780526\pi$
$797$	−34720.9	−1.54313	−0.771566	+	0.636150i	$0.780526\pi$
$798$	0	0
$799$	21776.5	0.964203
$800$	800.000	0.0353553
$801$	−2403.12	−0.106005
$802$	54.2447	0.00238834
$803$	−326.945	−0.0143681
$804$	10948.5	0.480255
$805$	0	0
$806$	−15442.3	−0.674853
$807$	−12126.4	−0.528957
$808$	9746.42	0.424354
$809$	32900.7	1.42982	0.714912	−	0.699215i	$-0.246467\pi$
$809$	32900.7	1.42982	0.714912	+	0.699215i	$0.246467\pi$
$810$	−3998.96	−0.173468
$811$	−10882.0	−0.471168	−0.235584	−	0.971854i	$-0.575700\pi$
$811$	−10882.0	−0.471168	−0.235584	+	0.971854i	$0.575700\pi$
$812$	0	0
$813$	35061.0	1.51247
$814$	−27602.5	−1.18854
$815$	−7594.99	−0.326431
$816$	−7298.91	−0.313129
$817$	−12229.5	−0.523693
$818$	3271.82	0.139849
$819$	0	0
$820$	−1133.44	−0.0482698
$821$	−26493.2	−1.12621	−0.563105	−	0.826385i	$-0.690393\pi$
$821$	−26493.2	−1.12621	−0.563105	+	0.826385i	$0.690393\pi$
$822$	25138.0	1.06665
$823$	15941.5	0.675197	0.337599	−	0.941290i	$-0.390385\pi$
$823$	15941.5	0.675197	0.337599	+	0.941290i	$0.390385\pi$
$824$	11934.9	0.504579
$825$	4671.22	0.197128
$826$	0	0
$827$	12910.8	0.542869	0.271434	−	0.962457i	$-0.412502\pi$
$827$	12910.8	0.542869	0.271434	+	0.962457i	$0.412502\pi$
$828$	3505.72	0.147141
$829$	36604.2	1.53356	0.766778	−	0.641912i	$-0.221859\pi$
$829$	36604.2	1.53356	0.766778	+	0.641912i	$0.221859\pi$
$830$	1922.43	0.0803960
$831$	35000.2	1.46106
$832$	5460.57	0.227537
$833$	0	0
$834$	−10439.5	−0.433444
$835$	9645.22	0.399745
$836$	9519.00	0.393805
$837$	−13821.5	−0.570779
$838$	13355.4	0.550541
$839$	17281.2	0.711102	0.355551	−	0.934657i	$-0.384293\pi$
$839$	17281.2	0.711102	0.355551	+	0.934657i	$0.384293\pi$
$840$	0	0
$841$	16109.0	0.660505
$842$	9340.17	0.382284
$843$	825.704	0.0337352
$844$	12248.2	0.499526
$845$	25413.7	1.03462
$846$	−3679.73	−0.149541
$847$	0	0
$848$	−772.188	−0.0312701
$849$	−3608.29	−0.145861
$850$	5393.13	0.217627
$851$	−30043.2	−1.21018
$852$	−16288.9	−0.654986
$853$	−33389.4	−1.34025	−0.670123	−	0.742250i	$-0.733759\pi$
$853$	−33389.4	−1.34025	−0.670123	+	0.742250i	$0.733759\pi$
$854$	0	0
$855$	2454.40	0.0981741
$856$	4570.65	0.182502
$857$	3634.58	0.144872	0.0724358	−	0.997373i	$-0.476923\pi$
$857$	3634.58	0.144872	0.0724358	+	0.997373i	$0.476923\pi$
$858$	31884.4	1.26866
$859$	−45662.5	−1.81372	−0.906859	−	0.421434i	$-0.861527\pi$
$859$	−45662.5	−1.81372	−0.906859	+	0.421434i	$0.861527\pi$
$860$	4540.80	0.180046
$861$	0	0
$862$	26493.2	1.04682
$863$	−31054.7	−1.22493	−0.612465	−	0.790498i	$-0.709822\pi$
$863$	−31054.7	−1.22493	−0.612465	+	0.790498i	$0.709822\pi$
$864$	4887.45	0.192447
$865$	−15071.3	−0.592416
$866$	−16663.3	−0.653859
$867$	−28426.4	−1.11351
$868$	0	0
$869$	−20137.2	−0.786087
$870$	−8511.07	−0.331669
$871$	−55218.7	−2.14812
$872$	−5596.24	−0.217331
$873$	13734.2	0.532455
$874$	10360.7	0.400978
$875$	0	0
$876$	−125.192	−0.00482861
$877$	1974.34	0.0760191	0.0380096	−	0.999277i	$-0.487898\pi$
$877$	1974.34	0.0760191	0.0380096	+	0.999277i	$0.487898\pi$
$878$	−10610.5	−0.407843
$879$	−21901.4	−0.840405
$880$	−3534.38	−0.135391
$881$	24411.9	0.933552	0.466776	−	0.884376i	$-0.345415\pi$
$881$	24411.9	0.933552	0.466776	+	0.884376i	$0.345415\pi$
$882$	0	0
$883$	24412.8	0.930416	0.465208	−	0.885201i	$-0.345980\pi$
$883$	24412.8	0.930416	0.465208	+	0.885201i	$0.345980\pi$
$884$	36811.9	1.40059
$885$	−14347.6	−0.544960
$886$	14118.5	0.535351
$887$	25250.3	0.955832	0.477916	−	0.878406i	$-0.341392\pi$
$887$	25250.3	0.955832	0.477916	+	0.878406i	$0.341392\pi$
$888$	−10569.5	−0.399423
$889$	0	0
$890$	2636.98	0.0993167
$891$	17667.3	0.664284
$892$	13335.9	0.500582
$893$	−10874.9	−0.407520
$894$	26356.3	0.986003
$895$	−1028.04	−0.0383951
$896$	0	0
$897$	34703.6	1.29177
$898$	−213.765	−0.00794368
$899$	−18211.3	−0.675618
$900$	−911.314	−0.0337524
$901$	−5205.63	−0.192480
$902$	5007.49	0.184846
$903$	0	0
$904$	5106.44	0.187874
$905$	−20001.2	−0.734654
$906$	3914.49	0.143543
$907$	−10247.7	−0.375159	−0.187579	−	0.982249i	$-0.560064\pi$
$907$	−10247.7	−0.375159	−0.187579	+	0.982249i	$0.560064\pi$
$908$	−2357.77	−0.0861733
$909$	−11102.6	−0.405114
$910$	0	0
$911$	−16593.0	−0.603458	−0.301729	−	0.953394i	$-0.597564\pi$
$911$	−16593.0	−0.603458	−0.301729	+	0.953394i	$0.597564\pi$
$912$	3644.98	0.132344
$913$	−8493.26	−0.307871
$914$	2226.14	0.0805625
$915$	−6744.77	−0.243689
$916$	5943.14	0.214374
$917$	0	0
$918$	32948.3	1.18459
$919$	19477.7	0.699141	0.349570	−	0.936910i	$-0.386328\pi$
$919$	19477.7	0.699141	0.349570	+	0.936910i	$0.386328\pi$
$920$	−3846.89	−0.137857
$921$	−31354.5	−1.12179
$922$	−4043.55	−0.144433
$923$	82152.7	2.92967
$924$	0	0
$925$	7809.72	0.277602
$926$	−13358.9	−0.474082
$927$	−13595.6	−0.481702
$928$	6439.72	0.227795
$929$	47559.1	1.67962	0.839808	−	0.542883i	$-0.182667\pi$
$929$	47559.1	1.67962	0.839808	+	0.542883i	$0.182667\pi$
$930$	3827.29	0.134948
$931$	0	0
$932$	26359.0	0.926414
$933$	−2532.70	−0.0888712
$934$	25108.0	0.879614
$935$	−23826.7	−0.833386
$936$	−6220.36	−0.217221
$937$	−377.536	−0.0131628	−0.00658141	−	0.999978i	$-0.502095\pi$
$937$	−377.536	−0.0131628	−0.00658141	+	0.999978i	$0.502095\pi$
$938$	0	0
$939$	495.419	0.0172177
$940$	4037.83	0.140106
$941$	6264.95	0.217037	0.108518	−	0.994094i	$-0.465389\pi$
$941$	6264.95	0.217037	0.108518	+	0.994094i	$0.465389\pi$
$942$	9114.36	0.315246
$943$	5450.25	0.188213
$944$	10855.8	0.374287
$945$	0	0
$946$	−20061.1	−0.689475
$947$	−14226.9	−0.488185	−0.244092	−	0.969752i	$-0.578490\pi$
$947$	−14226.9	−0.488185	−0.244092	+	0.969752i	$0.578490\pi$
$948$	−7710.88	−0.264175
$949$	631.406	0.0215978
$950$	−2693.26	−0.0919799
$951$	6284.58	0.214292
$952$	0	0
$953$	−12681.3	−0.431048	−0.215524	−	0.976499i	$-0.569146\pi$
$953$	−12681.3	−0.431048	−0.215524	+	0.976499i	$0.569146\pi$
$954$	879.631	0.0298523
$955$	−21337.6	−0.723003
$956$	−20172.6	−0.682458
$957$	37601.7	1.27010
$958$	40439.1	1.36381
$959$	0	0
$960$	−1353.37	−0.0454999
$961$	−21601.7	−0.725108
$962$	53306.9	1.78657
$963$	−5206.62	−0.174227
$964$	16781.9	0.560693
$965$	14238.8	0.474987
$966$	0	0
$967$	−2087.98	−0.0694362	−0.0347181	−	0.999397i	$-0.511053\pi$
$967$	−2087.98	−0.0694362	−0.0347181	+	0.999397i	$0.511053\pi$
$968$	4966.79	0.164916
$969$	24572.3	0.814630
$970$	−15070.8	−0.498860
$971$	−34385.8	−1.13645	−0.568224	−	0.822874i	$-0.692369\pi$
$971$	−34385.8	−1.13645	−0.568224	+	0.822874i	$0.692369\pi$
$972$	−9730.04	−0.321082
$973$	0	0
$974$	−17087.4	−0.562129
$975$	−9021.21	−0.296318
$976$	5103.28	0.167369
$977$	−24065.2	−0.788038	−0.394019	−	0.919102i	$-0.628916\pi$
$977$	−24065.2	−0.788038	−0.394019	+	0.919102i	$0.628916\pi$
$978$	12848.6	0.420094
$979$	−11650.1	−0.380326
$980$	0	0
$981$	6374.91	0.207477
$982$	−43180.0	−1.40319
$983$	14225.3	0.461563	0.230781	−	0.973006i	$-0.425872\pi$
$983$	14225.3	0.461563	0.230781	+	0.973006i	$0.425872\pi$
$984$	1917.45	0.0621200
$985$	3289.29	0.106401
$986$	43412.8	1.40218
$987$	0	0
$988$	−18383.4	−0.591957
$989$	−21834.9	−0.702033
$990$	4026.16	0.129252
$991$	−8066.97	−0.258583	−0.129291	−	0.991607i	$-0.541270\pi$
$991$	−8066.97	−0.258583	−0.129291	+	0.991607i	$0.541270\pi$
$992$	−2895.84	−0.0926843
$993$	−46860.8	−1.49756
$994$	0	0
$995$	−8530.15	−0.271783
$996$	−3252.21	−0.103464
$997$	−3104.79	−0.0986254	−0.0493127	−	0.998783i	$-0.515703\pi$
$997$	−3104.79	−0.0986254	−0.0493127	+	0.998783i	$0.515703\pi$
$998$	−34133.4	−1.08264
$999$	47712.0	1.51105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.y.1.1	yes	4
5.4	even	2		2450.4.a.cj.1.4		4
7.2	even	3		490.4.e.z.361.4		8
7.3	odd	6		490.4.e.ba.471.1		8
7.4	even	3		490.4.e.z.471.4		8
7.5	odd	6		490.4.e.ba.361.1		8
7.6	odd	2		490.4.a.x.1.4	✓	4
35.34	odd	2		2450.4.a.cp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.x.1.4	✓	4	7.6	odd	2
490.4.a.y.1.1	yes	4	1.1	even	1	trivial
490.4.e.z.361.4		8	7.2	even	3
490.4.e.z.471.4		8	7.4	even	3
490.4.e.ba.361.1		8	7.5	odd	6
490.4.e.ba.471.1		8	7.3	odd	6
2450.4.a.cj.1.4		4	5.4	even	2
2450.4.a.cp.1.1		4	35.34	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -4.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} -8.45857 q^{6} +8.00000 q^{8} -9.11314 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -4.22929 q^{3} +4.00000 q^{4} +5.00000 q^{5} -8.45857 q^{6} +8.00000 q^{8} -9.11314 q^{9} +10.0000 q^{10} -44.1797 q^{11} -16.9171 q^{12} +85.3214 q^{13} -21.1464 q^{15} +16.0000 q^{16} +107.863 q^{17} -18.2263 q^{18} -53.8652 q^{19} +20.0000 q^{20} -88.3595 q^{22} -96.1723 q^{23} -33.8343 q^{24} +25.0000 q^{25} +170.643 q^{26} +152.733 q^{27} +201.241 q^{29} -42.2929 q^{30} -90.4949 q^{31} +32.0000 q^{32} +186.849 q^{33} +215.725 q^{34} -36.4525 q^{36} +312.389 q^{37} -107.730 q^{38} -360.848 q^{39} +40.0000 q^{40} -56.6718 q^{41} +227.040 q^{43} -176.719 q^{44} -45.5657 q^{45} -192.345 q^{46} +201.891 q^{47} -67.6686 q^{48} +50.0000 q^{50} -456.182 q^{51} +341.285 q^{52} -48.2617 q^{53} +305.466 q^{54} -220.899 q^{55} +227.811 q^{57} +402.483 q^{58} +678.489 q^{59} -84.5857 q^{60} +318.955 q^{61} -180.990 q^{62} +64.0000 q^{64} +426.607 q^{65} +373.697 q^{66} -647.185 q^{67} +431.450 q^{68} +406.740 q^{69} +962.862 q^{71} -72.9051 q^{72} +7.40033 q^{73} +624.778 q^{74} -105.732 q^{75} -215.461 q^{76} -721.697 q^{78} +455.803 q^{79} +80.0000 q^{80} -399.896 q^{81} -113.344 q^{82} +192.243 q^{83} +539.313 q^{85} +454.080 q^{86} -851.107 q^{87} -353.438 q^{88} +263.698 q^{89} -91.1314 q^{90} -384.689 q^{92} +382.729 q^{93} +403.783 q^{94} -269.326 q^{95} -135.337 q^{96} -1507.08 q^{97} +402.616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} + 10 q^{3} + 16 q^{4} + 20 q^{5} + 20 q^{6} + 32 q^{8} + 38 q^{9} + 40 q^{10} + 18 q^{11} + 40 q^{12} + 130 q^{13} + 50 q^{15} + 64 q^{16} + 110 q^{17} + 76 q^{18} + 40 q^{19} + 80 q^{20} + 36 q^{22} - 164 q^{23} + 80 q^{24} + 100 q^{25} + 260 q^{26} + 430 q^{27} + 94 q^{29} + 100 q^{30} + 180 q^{31} + 128 q^{32} + 650 q^{33} + 220 q^{34} + 152 q^{36} + 16 q^{37} + 80 q^{38} - 10 q^{39} + 160 q^{40} + 540 q^{41} - 560 q^{43} + 72 q^{44} + 190 q^{45} - 328 q^{46} + 1150 q^{47} + 160 q^{48} + 200 q^{50} - 926 q^{51} + 520 q^{52} - 244 q^{53} + 860 q^{54} + 90 q^{55} - 840 q^{57} + 188 q^{58} + 400 q^{59} + 200 q^{60} + 1540 q^{61} + 360 q^{62} + 256 q^{64} + 650 q^{65} + 1300 q^{66} - 760 q^{67} + 440 q^{68} - 1480 q^{69} + 52 q^{71} + 304 q^{72} + 800 q^{73} + 32 q^{74} + 250 q^{75} + 160 q^{76} - 20 q^{78} + 398 q^{79} + 320 q^{80} + 348 q^{81} + 1080 q^{82} - 1220 q^{83} + 550 q^{85} - 1120 q^{86} - 930 q^{87} + 144 q^{88} + 200 q^{89} + 380 q^{90} - 656 q^{92} + 1408 q^{93} + 2300 q^{94} + 200 q^{95} + 320 q^{96} - 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 10 * q^3 + 16 * q^4 + 20 * q^5 + 20 * q^6 + 32 * q^8 + 38 * q^9 + 40 * q^10 + 18 * q^11 + 40 * q^12 + 130 * q^13 + 50 * q^15 + 64 * q^16 + 110 * q^17 + 76 * q^18 + 40 * q^19 + 80 * q^20 + 36 * q^22 - 164 * q^23 + 80 * q^24 + 100 * q^25 + 260 * q^26 + 430 * q^27 + 94 * q^29 + 100 * q^30 + 180 * q^31 + 128 * q^32 + 650 * q^33 + 220 * q^34 + 152 * q^36 + 16 * q^37 + 80 * q^38 - 10 * q^39 + 160 * q^40 + 540 * q^41 - 560 * q^43 + 72 * q^44 + 190 * q^45 - 328 * q^46 + 1150 * q^47 + 160 * q^48 + 200 * q^50 - 926 * q^51 + 520 * q^52 - 244 * q^53 + 860 * q^54 + 90 * q^55 - 840 * q^57 + 188 * q^58 + 400 * q^59 + 200 * q^60 + 1540 * q^61 + 360 * q^62 + 256 * q^64 + 650 * q^65 + 1300 * q^66 - 760 * q^67 + 440 * q^68 - 1480 * q^69 + 52 * q^71 + 304 * q^72 + 800 * q^73 + 32 * q^74 + 250 * q^75 + 160 * q^76 - 20 * q^78 + 398 * q^79 + 320 * q^80 + 348 * q^81 + 1080 * q^82 - 1220 * q^83 + 550 * q^85 - 1120 * q^86 - 930 * q^87 + 144 * q^88 + 200 * q^89 + 380 * q^90 - 656 * q^92 + 1408 * q^93 + 2300 * q^94 + 200 * q^95 + 320 * q^96 - 670 * q^97 + 2292 * q^99

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