LMFDB - Embedded newform 490.4.a.x.1.2

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:	$1$
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			1.2
Root			$7.22929$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -6.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} -12.8017 q^{6} +8.00000 q^{8} +13.9710 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -6.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} -12.8017 q^{6} +8.00000 q^{8} +13.9710 q^{9} -10.0000 q^{10} +39.0376 q^{11} -25.6034 q^{12} +21.7356 q^{13} +32.0043 q^{15} +16.0000 q^{16} -12.1913 q^{17} +27.9420 q^{18} -86.5931 q^{19} -20.0000 q^{20} +78.0752 q^{22} -7.04090 q^{23} -51.2069 q^{24} +25.0000 q^{25} +43.4711 q^{26} +83.3968 q^{27} +57.8908 q^{29} +64.0086 q^{30} -241.306 q^{31} +32.0000 q^{32} -249.874 q^{33} -24.3825 q^{34} +55.8840 q^{36} -396.313 q^{37} -173.186 q^{38} -139.126 q^{39} -40.0000 q^{40} -26.8585 q^{41} +44.5035 q^{43} +156.150 q^{44} -69.8550 q^{45} -14.0818 q^{46} -501.802 q^{47} -102.414 q^{48} +50.0000 q^{50} +78.0345 q^{51} +86.9423 q^{52} -717.205 q^{53} +166.794 q^{54} -195.188 q^{55} +554.270 q^{57} +115.782 q^{58} +455.861 q^{59} +128.017 q^{60} -533.069 q^{61} -482.612 q^{62} +64.0000 q^{64} -108.678 q^{65} -499.748 q^{66} -814.688 q^{67} -48.7650 q^{68} +45.0678 q^{69} -258.040 q^{71} +111.768 q^{72} +839.180 q^{73} -792.626 q^{74} -160.021 q^{75} -346.372 q^{76} -278.253 q^{78} +1001.85 q^{79} -80.0000 q^{80} -911.028 q^{81} -53.7170 q^{82} +130.492 q^{83} +60.9563 q^{85} +89.0070 q^{86} -370.551 q^{87} +312.301 q^{88} +1129.61 q^{89} -139.710 q^{90} -28.1636 q^{92} +1544.57 q^{93} -1003.60 q^{94} +432.966 q^{95} -204.827 q^{96} -1486.04 q^{97} +545.394 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−6.40086	−1.23185	−0.615923	−	0.787806i	$-0.711217\pi$
$3$	−6.40086	−1.23185	−0.615923	+	0.787806i	$0.711217\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−12.8017	−0.871047
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	13.9710	0.517444
$10$	−10.0000	−0.316228
$11$	39.0376	1.07003	0.535013	−	0.844844i	$-0.320307\pi$
$11$	39.0376	1.07003	0.535013	+	0.844844i	$0.320307\pi$
$12$	−25.6034	−0.615923
$13$	21.7356	0.463720	0.231860	−	0.972749i	$-0.425519\pi$
$13$	21.7356	0.463720	0.231860	+	0.972749i	$0.425519\pi$
$14$	0	0
$15$	32.0043	0.550898
$16$	16.0000	0.250000
$17$	−12.1913	−0.173930	−0.0869651	−	0.996211i	$-0.527717\pi$
$17$	−12.1913	−0.173930	−0.0869651	+	0.996211i	$0.527717\pi$
$18$	27.9420	0.365888
$19$	−86.5931	−1.04557	−0.522785	−	0.852465i	$-0.675107\pi$
$19$	−86.5931	−1.04557	−0.522785	+	0.852465i	$0.675107\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	78.0752	0.756622
$23$	−7.04090	−0.0638317	−0.0319159	−	0.999491i	$-0.510161\pi$
$23$	−7.04090	−0.0638317	−0.0319159	+	0.999491i	$0.510161\pi$
$24$	−51.2069	−0.435523
$25$	25.0000	0.200000
$26$	43.4711	0.327900
$27$	83.3968	0.594434
$28$	0	0
$29$	57.8908	0.370691	0.185346	−	0.982673i	$-0.440660\pi$
$29$	57.8908	0.370691	0.185346	+	0.982673i	$0.440660\pi$
$30$	64.0086	0.389544
$31$	−241.306	−1.39806	−0.699030	−	0.715093i	$-0.746385\pi$
$31$	−241.306	−1.39806	−0.699030	+	0.715093i	$0.746385\pi$
$32$	32.0000	0.176777
$33$	−249.874	−1.31811
$34$	−24.3825	−0.122987
$35$	0	0
$36$	55.8840	0.258722
$37$	−396.313	−1.76090	−0.880452	−	0.474136i	$-0.842761\pi$
$37$	−396.313	−1.76090	−0.880452	+	0.474136i	$0.842761\pi$
$38$	−173.186	−0.739329
$39$	−139.126	−0.571232
$40$	−40.0000	−0.158114
$41$	−26.8585	−0.102307	−0.0511535	−	0.998691i	$-0.516290\pi$
$41$	−26.8585	−0.102307	−0.0511535	+	0.998691i	$0.516290\pi$
$42$	0	0
$43$	44.5035	0.157831	0.0789153	−	0.996881i	$-0.474854\pi$
$43$	44.5035	0.157831	0.0789153	+	0.996881i	$0.474854\pi$
$44$	156.150	0.535013
$45$	−69.8550	−0.231408
$46$	−14.0818	−0.0451359
$47$	−501.802	−1.55735	−0.778674	−	0.627429i	$-0.784107\pi$
$47$	−501.802	−1.55735	−0.778674	+	0.627429i	$0.784107\pi$
$48$	−102.414	−0.307961
$49$	0	0
$50$	50.0000	0.141421
$51$	78.0345	0.214255
$52$	86.9423	0.231860
$53$	−717.205	−1.85879	−0.929394	−	0.369090i	$-0.879670\pi$
$53$	−717.205	−1.85879	−0.929394	+	0.369090i	$0.879670\pi$
$54$	166.794	0.420328
$55$	−195.188	−0.478530
$56$	0	0
$57$	554.270	1.28798
$58$	115.782	0.262118
$59$	455.861	1.00590	0.502950	−	0.864316i	$-0.332248\pi$
$59$	455.861	1.00590	0.502950	+	0.864316i	$0.332248\pi$
$60$	128.017	0.275449
$61$	−533.069	−1.11889	−0.559447	−	0.828866i	$-0.688986\pi$
$61$	−533.069	−1.11889	−0.559447	+	0.828866i	$0.688986\pi$
$62$	−482.612	−0.988577
$63$	0	0
$64$	64.0000	0.125000
$65$	−108.678	−0.207382
$66$	−499.748	−0.932042
$67$	−814.688	−1.48552	−0.742761	−	0.669556i	$-0.766484\pi$
$67$	−814.688	−1.48552	−0.742761	+	0.669556i	$0.766484\pi$
$68$	−48.7650	−0.0869651
$69$	45.0678	0.0786309
$70$	0	0
$71$	−258.040	−0.431320	−0.215660	−	0.976469i	$-0.569190\pi$
$71$	−258.040	−0.431320	−0.215660	+	0.976469i	$0.569190\pi$
$72$	111.768	0.182944
$73$	839.180	1.34546	0.672730	−	0.739888i	$-0.265121\pi$
$73$	839.180	1.34546	0.672730	+	0.739888i	$0.265121\pi$
$74$	−792.626	−1.24515
$75$	−160.021	−0.246369
$76$	−346.372	−0.522785
$77$	0	0
$78$	−278.253	−0.403922
$79$	1001.85	1.42679	0.713396	−	0.700761i	$-0.247156\pi$
$79$	1001.85	1.42679	0.713396	+	0.700761i	$0.247156\pi$
$80$	−80.0000	−0.111803
$81$	−911.028	−1.24970
$82$	−53.7170	−0.0723420
$83$	130.492	0.172571	0.0862853	−	0.996270i	$-0.472500\pi$
$83$	130.492	0.172571	0.0862853	+	0.996270i	$0.472500\pi$
$84$	0	0
$85$	60.9563	0.0777840
$86$	89.0070	0.111603
$87$	−370.551	−0.456634
$88$	312.301	0.378311
$89$	1129.61	1.34537	0.672686	−	0.739929i	$-0.265141\pi$
$89$	1129.61	1.34537	0.672686	+	0.739929i	$0.265141\pi$
$90$	−139.710	−0.163630
$91$	0	0
$92$	−28.1636	−0.0319159
$93$	1544.57	1.72219
$94$	−1003.60	−1.10121
$95$	432.966	0.467593
$96$	−204.827	−0.217762
$97$	−1486.04	−1.55551	−0.777753	−	0.628571i	$-0.783640\pi$
$97$	−1486.04	−1.55551	−0.777753	+	0.628571i	$0.783640\pi$
$98$	0	0
$99$	545.394	0.553679
$100$	100.000	0.100000
$101$	−718.739	−0.708092	−0.354046	−	0.935228i	$-0.615194\pi$
$101$	−718.739	−0.708092	−0.354046	+	0.935228i	$0.615194\pi$
$102$	156.069	0.151501
$103$	−681.710	−0.652145	−0.326072	−	0.945345i	$-0.605725\pi$
$103$	−681.710	−0.652145	−0.326072	+	0.945345i	$0.605725\pi$
$104$	173.885	0.163950
$105$	0	0
$106$	−1434.41	−1.31436
$107$	−1545.16	−1.39604	−0.698019	−	0.716079i	$-0.745935\pi$
$107$	−1545.16	−1.39604	−0.698019	+	0.716079i	$0.745935\pi$
$108$	333.587	0.297217
$109$	−1489.24	−1.30865	−0.654326	−	0.756213i	$-0.727047\pi$
$109$	−1489.24	−1.30865	−0.654326	+	0.756213i	$0.727047\pi$
$110$	−390.376	−0.338372
$111$	2536.74	2.16916
$112$	0	0
$113$	−120.838	−0.100597	−0.0502987	−	0.998734i	$-0.516017\pi$
$113$	−120.838	−0.100597	−0.0502987	+	0.998734i	$0.516017\pi$
$114$	1108.54	0.910740
$115$	35.2045	0.0285464
$116$	231.563	0.185346
$117$	303.668	0.239949
$118$	911.723	0.711279
$119$	0	0
$120$	256.034	0.194772
$121$	192.934	0.144954
$122$	−1066.14	−0.791177
$123$	171.917	0.126027
$124$	−965.224	−0.699030
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1224.87	0.855826	0.427913	−	0.903820i	$-0.359249\pi$
$127$	1224.87	0.855826	0.427913	+	0.903820i	$0.359249\pi$
$128$	128.000	0.0883883
$129$	−284.861	−0.194423
$130$	−217.356	−0.146641
$131$	−566.183	−0.377615	−0.188808	−	0.982014i	$-0.560462\pi$
$131$	−566.183	−0.377615	−0.188808	+	0.982014i	$0.560462\pi$
$132$	−999.497	−0.659053
$133$	0	0
$134$	−1629.38	−1.05042
$135$	−416.984	−0.265839
$136$	−97.5300	−0.0614936
$137$	−188.674	−0.117661	−0.0588303	−	0.998268i	$-0.518737\pi$
$137$	−188.674	−0.117661	−0.0588303	+	0.998268i	$0.518737\pi$
$138$	90.1357	0.0556004
$139$	2870.44	1.75157	0.875783	−	0.482704i	$-0.160345\pi$
$139$	2870.44	1.75157	0.875783	+	0.482704i	$0.160345\pi$
$140$	0	0
$141$	3211.96	1.91841
$142$	−516.080	−0.304989
$143$	848.504	0.496192
$144$	223.536	0.129361
$145$	−289.454	−0.165778
$146$	1678.36	0.951384
$147$	0	0
$148$	−1585.25	−0.880452
$149$	748.698	0.411649	0.205825	−	0.978589i	$-0.434012\pi$
$149$	748.698	0.411649	0.205825	+	0.978589i	$0.434012\pi$
$150$	−320.043	−0.174209
$151$	1249.30	0.673286	0.336643	−	0.941632i	$-0.390708\pi$
$151$	1249.30	0.673286	0.336643	+	0.941632i	$0.390708\pi$
$152$	−692.745	−0.369665
$153$	−170.324	−0.0899992
$154$	0	0
$155$	1206.53	0.625231
$156$	−556.505	−0.285616
$157$	1402.37	0.712875	0.356437	−	0.934319i	$-0.383991\pi$
$157$	1402.37	0.712875	0.356437	+	0.934319i	$0.383991\pi$
$158$	2003.69	1.00889
$159$	4590.73	2.28974
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−1822.06	−0.883668
$163$	2389.58	1.14826	0.574130	−	0.818764i	$-0.305340\pi$
$163$	2389.58	1.14826	0.574130	+	0.818764i	$0.305340\pi$
$164$	−107.434	−0.0511535
$165$	1249.37	0.589475
$166$	260.984	0.122026
$167$	−1305.80	−0.605067	−0.302533	−	0.953139i	$-0.597832\pi$
$167$	−1305.80	−0.605067	−0.302533	+	0.953139i	$0.597832\pi$
$168$	0	0
$169$	−1724.57	−0.784964
$170$	121.913	0.0550016
$171$	−1209.79	−0.541024
$172$	178.014	0.0789153
$173$	−1291.65	−0.567644	−0.283822	−	0.958877i	$-0.591602\pi$
$173$	−1291.65	−0.567644	−0.283822	+	0.958877i	$0.591602\pi$
$174$	−741.101	−0.322889
$175$	0	0
$176$	624.601	0.267506
$177$	−2917.90	−1.23911
$178$	2259.21	0.951321
$179$	3572.94	1.49192	0.745961	−	0.665990i	$-0.231991\pi$
$179$	3572.94	1.49192	0.745961	+	0.665990i	$0.231991\pi$
$180$	−279.420	−0.115704
$181$	2093.88	0.859872	0.429936	−	0.902859i	$-0.358536\pi$
$181$	2093.88	0.859872	0.429936	+	0.902859i	$0.358536\pi$
$182$	0	0
$183$	3412.10	1.37830
$184$	−56.3272	−0.0225679
$185$	1981.56	0.787500
$186$	3089.13	1.21778
$187$	−475.917	−0.186110
$188$	−2007.21	−0.778674
$189$	0	0
$190$	865.931	0.330638
$191$	−3775.19	−1.43017	−0.715087	−	0.699035i	$-0.753613\pi$
$191$	−3775.19	−1.43017	−0.715087	+	0.699035i	$0.753613\pi$
$192$	−409.655	−0.153981
$193$	−2085.15	−0.777682	−0.388841	−	0.921305i	$-0.627124\pi$
$193$	−2085.15	−0.777682	−0.388841	+	0.921305i	$0.627124\pi$
$194$	−2972.07	−1.09991
$195$	695.632	0.255463
$196$	0	0
$197$	−3706.99	−1.34067	−0.670335	−	0.742059i	$-0.733850\pi$
$197$	−3706.99	−1.34067	−0.670335	+	0.742059i	$0.733850\pi$
$198$	1090.79	0.391510
$199$	3111.31	1.10832	0.554159	−	0.832411i	$-0.313040\pi$
$199$	3111.31	1.10832	0.554159	+	0.832411i	$0.313040\pi$
$200$	200.000	0.0707107
$201$	5214.70	1.82993
$202$	−1437.48	−0.500696
$203$	0	0
$204$	312.138	0.107128
$205$	134.292	0.0457531
$206$	−1363.42	−0.461136
$207$	−98.3685	−0.0330294
$208$	347.769	0.115930
$209$	−3380.39	−1.11879
$210$	0	0
$211$	3056.36	0.997196	0.498598	−	0.866833i	$-0.333848\pi$
$211$	3056.36	0.997196	0.498598	+	0.866833i	$0.333848\pi$
$212$	−2868.82	−0.929394
$213$	1651.68	0.531319
$214$	−3090.32	−0.987148
$215$	−222.517	−0.0705840
$216$	667.174	0.210164
$217$	0	0
$218$	−2978.47	−0.925356
$219$	−5371.48	−1.65740
$220$	−780.752	−0.239265
$221$	−264.984	−0.0806549
$222$	5073.48	1.53383
$223$	−1436.74	−0.431440	−0.215720	−	0.976455i	$-0.569210\pi$
$223$	−1436.74	−0.431440	−0.215720	+	0.976455i	$0.569210\pi$
$224$	0	0
$225$	349.275	0.103489
$226$	−241.676	−0.0711331
$227$	2625.95	0.767800	0.383900	−	0.923375i	$-0.374581\pi$
$227$	2625.95	0.767800	0.383900	+	0.923375i	$0.374581\pi$
$228$	2217.08	0.643990
$229$	2234.06	0.644677	0.322339	−	0.946624i	$-0.395531\pi$
$229$	2234.06	0.644677	0.322339	+	0.946624i	$0.395531\pi$
$230$	70.4090	0.0201854
$231$	0	0
$232$	463.126	0.131059
$233$	−2605.90	−0.732696	−0.366348	−	0.930478i	$-0.619392\pi$
$233$	−2605.90	−0.732696	−0.366348	+	0.930478i	$0.619392\pi$
$234$	607.335	0.169670
$235$	2509.01	0.696467
$236$	1823.45	0.502950
$237$	−6412.68	−1.75759
$238$	0	0
$239$	−5069.53	−1.37205	−0.686026	−	0.727577i	$-0.740646\pi$
$239$	−5069.53	−1.37205	−0.686026	+	0.727577i	$0.740646\pi$
$240$	512.069	0.137725
$241$	−2388.45	−0.638397	−0.319198	−	0.947688i	$-0.603414\pi$
$241$	−2388.45	−0.638397	−0.319198	+	0.947688i	$0.603414\pi$
$242$	385.867	0.102498
$243$	3579.65	0.944998
$244$	−2132.28	−0.559447
$245$	0	0
$246$	343.835	0.0891142
$247$	−1882.15	−0.484852
$248$	−1930.45	−0.494289
$249$	−835.261	−0.212580
$250$	−250.000	−0.0632456
$251$	3597.48	0.904664	0.452332	−	0.891850i	$-0.350592\pi$
$251$	3597.48	0.904664	0.452332	+	0.891850i	$0.350592\pi$
$252$	0	0
$253$	−274.860	−0.0683016
$254$	2449.75	0.605160
$255$	−390.173	−0.0958179
$256$	256.000	0.0625000
$257$	403.446	0.0979233	0.0489617	−	0.998801i	$-0.484409\pi$
$257$	403.446	0.0979233	0.0489617	+	0.998801i	$0.484409\pi$
$258$	−569.721	−0.137478
$259$	0	0
$260$	−434.711	−0.103691
$261$	808.792	0.191812
$262$	−1132.37	−0.267014
$263$	5001.24	1.17258	0.586292	−	0.810100i	$-0.300587\pi$
$263$	5001.24	1.17258	0.586292	+	0.810100i	$0.300587\pi$
$264$	−1998.99	−0.466021
$265$	3586.03	0.831275
$266$	0	0
$267$	−7230.45	−1.65729
$268$	−3258.75	−0.742761
$269$	4281.35	0.970403	0.485202	−	0.874402i	$-0.338746\pi$
$269$	4281.35	0.970403	0.485202	+	0.874402i	$0.338746\pi$
$270$	−833.968	−0.187977
$271$	−7153.78	−1.60355	−0.801773	−	0.597629i	$-0.796110\pi$
$271$	−7153.78	−1.60355	−0.801773	+	0.597629i	$0.796110\pi$
$272$	−195.060	−0.0434826
$273$	0	0
$274$	−377.348	−0.0831986
$275$	975.940	0.214005
$276$	180.271	0.0393154
$277$	−7515.68	−1.63023	−0.815115	−	0.579300i	$-0.803326\pi$
$277$	−7515.68	−1.63023	−0.815115	+	0.579300i	$0.803326\pi$
$278$	5740.89	1.23854
$279$	−3371.29	−0.723418
$280$	0	0
$281$	−2058.64	−0.437040	−0.218520	−	0.975833i	$-0.570123\pi$
$281$	−2058.64	−0.437040	−0.218520	+	0.975833i	$0.570123\pi$
$282$	6423.93	1.35652
$283$	2340.36	0.491589	0.245795	−	0.969322i	$-0.420951\pi$
$283$	2340.36	0.491589	0.245795	+	0.969322i	$0.420951\pi$
$284$	−1032.16	−0.215660
$285$	−2771.35	−0.576002
$286$	1697.01	0.350861
$287$	0	0
$288$	447.072	0.0914721
$289$	−4764.37	−0.969748
$290$	−578.908	−0.117223
$291$	9511.90	1.91614
$292$	3356.72	0.672730
$293$	−3603.30	−0.718455	−0.359227	−	0.933250i	$-0.616960\pi$
$293$	−3603.30	−0.718455	−0.359227	+	0.933250i	$0.616960\pi$
$294$	0	0
$295$	−2279.31	−0.449852
$296$	−3170.50	−0.622573
$297$	3255.61	0.636059
$298$	1497.40	0.291080
$299$	−153.038	−0.0296001
$300$	−640.086	−0.123185
$301$	0	0
$302$	2498.59	0.476085
$303$	4600.55	0.872260
$304$	−1385.49	−0.261392
$305$	2665.35	0.500384
$306$	−340.648	−0.0636391
$307$	8695.23	1.61649	0.808246	−	0.588845i	$-0.200417\pi$
$307$	8695.23	1.61649	0.808246	+	0.588845i	$0.200417\pi$
$308$	0	0
$309$	4363.53	0.803342
$310$	2413.06	0.442105
$311$	−7727.30	−1.40892	−0.704462	−	0.709742i	$-0.748812\pi$
$311$	−7727.30	−1.40892	−0.704462	+	0.709742i	$0.748812\pi$
$312$	−1113.01	−0.201961
$313$	−6982.02	−1.26085	−0.630427	−	0.776249i	$-0.717120\pi$
$313$	−6982.02	−1.26085	−0.630427	+	0.776249i	$0.717120\pi$
$314$	2804.74	0.504078
$315$	0	0
$316$	4007.39	0.713396
$317$	7357.43	1.30358	0.651789	−	0.758400i	$-0.274019\pi$
$317$	7357.43	1.30358	0.651789	+	0.758400i	$0.274019\pi$
$318$	9181.46	1.61909
$319$	2259.92	0.396649
$320$	−320.000	−0.0559017
$321$	9890.34	1.71970
$322$	0	0
$323$	1055.68	0.181856
$324$	−3644.11	−0.624848
$325$	543.389	0.0927440
$326$	4779.16	0.811943
$327$	9532.39	1.61206
$328$	−214.868	−0.0361710
$329$	0	0
$330$	2498.74	0.416822
$331$	3486.19	0.578907	0.289454	−	0.957192i	$-0.406526\pi$
$331$	3486.19	0.578907	0.289454	+	0.957192i	$0.406526\pi$
$332$	521.968	0.0862853
$333$	−5536.89	−0.911170
$334$	−2611.61	−0.427847
$335$	4073.44	0.664346
$336$	0	0
$337$	−511.769	−0.0827236	−0.0413618	−	0.999144i	$-0.513170\pi$
$337$	−511.769	−0.0827236	−0.0413618	+	0.999144i	$0.513170\pi$
$338$	−3449.13	−0.555053
$339$	773.468	0.123920
$340$	243.825	0.0388920
$341$	−9420.01	−1.49596
$342$	−2419.58	−0.382562
$343$	0	0
$344$	356.028	0.0558016
$345$	−225.339	−0.0351648
$346$	−2583.30	−0.401385
$347$	−7089.88	−1.09684	−0.548422	−	0.836202i	$-0.684771\pi$
$347$	−7089.88	−1.09684	−0.548422	+	0.836202i	$0.684771\pi$
$348$	−1482.20	−0.228317
$349$	−3617.39	−0.554827	−0.277413	−	0.960751i	$-0.589477\pi$
$349$	−3617.39	−0.554827	−0.277413	+	0.960751i	$0.589477\pi$
$350$	0	0
$351$	1812.68	0.275651
$352$	1249.20	0.189156
$353$	−10100.4	−1.52292	−0.761462	−	0.648210i	$-0.775518\pi$
$353$	−10100.4	−1.52292	−0.761462	+	0.648210i	$0.775518\pi$
$354$	−5835.81	−0.876186
$355$	1290.20	0.192892
$356$	4518.42	0.672686
$357$	0	0
$358$	7145.88	1.05495
$359$	2309.44	0.339520	0.169760	−	0.985485i	$-0.445701\pi$
$359$	2309.44	0.339520	0.169760	+	0.985485i	$0.445701\pi$
$360$	−558.840	−0.0818152
$361$	639.365	0.0932155
$362$	4187.76	0.608022
$363$	−1234.94	−0.178561
$364$	0	0
$365$	−4195.90	−0.601708
$366$	6824.20	0.974608
$367$	4837.72	0.688084	0.344042	−	0.938954i	$-0.388204\pi$
$367$	4837.72	0.688084	0.344042	+	0.938954i	$0.388204\pi$
$368$	−112.654	−0.0159579
$369$	−375.240	−0.0529382
$370$	3963.13	0.556847
$371$	0	0
$372$	6178.26	0.861097
$373$	5183.25	0.719514	0.359757	−	0.933046i	$-0.382860\pi$
$373$	5183.25	0.719514	0.359757	+	0.933046i	$0.382860\pi$
$374$	−951.835	−0.131599
$375$	800.107	0.110180
$376$	−4014.42	−0.550606
$377$	1258.29	0.171897
$378$	0	0
$379$	4586.89	0.621670	0.310835	−	0.950464i	$-0.399391\pi$
$379$	4586.89	0.621670	0.310835	+	0.950464i	$0.399391\pi$
$380$	1731.86	0.233796
$381$	−7840.24	−1.05425
$382$	−7550.39	−1.01129
$383$	3048.42	0.406702	0.203351	−	0.979106i	$-0.434817\pi$
$383$	3048.42	0.406702	0.203351	+	0.979106i	$0.434817\pi$
$384$	−819.310	−0.108881
$385$	0	0
$386$	−4170.31	−0.549904
$387$	621.758	0.0816686
$388$	−5944.14	−0.777753
$389$	1860.09	0.242443	0.121222	−	0.992625i	$-0.461319\pi$
$389$	1860.09	0.242443	0.121222	+	0.992625i	$0.461319\pi$
$390$	1391.26	0.180639
$391$	85.8375	0.0111023
$392$	0	0
$393$	3624.06	0.465164
$394$	−7413.98	−0.947997
$395$	−5009.24	−0.638081
$396$	2181.58	0.276839
$397$	−7662.83	−0.968731	−0.484366	−	0.874866i	$-0.660950\pi$
$397$	−7662.83	−0.968731	−0.484366	+	0.874866i	$0.660950\pi$
$398$	6222.63	0.783699
$399$	0	0
$400$	400.000	0.0500000
$401$	15288.4	1.90391	0.951953	−	0.306244i	$-0.0990725\pi$
$401$	15288.4	1.90391	0.951953	+	0.306244i	$0.0990725\pi$
$402$	10429.4	1.29396
$403$	−5244.92	−0.648308
$404$	−2874.96	−0.354046
$405$	4555.14	0.558881
$406$	0	0
$407$	−15471.1	−1.88421
$408$	624.276	0.0757507
$409$	−11839.5	−1.43136	−0.715680	−	0.698429i	$-0.753883\pi$
$409$	−11839.5	−1.43136	−0.715680	+	0.698429i	$0.753883\pi$
$410$	268.585	0.0323523
$411$	1207.68	0.144940
$412$	−2726.84	−0.326072
$413$	0	0
$414$	−196.737	−0.0233553
$415$	−652.460	−0.0771759
$416$	695.538	0.0819749
$417$	−18373.3	−2.15766
$418$	−6760.77	−0.791101
$419$	−15801.0	−1.84232	−0.921159	−	0.389186i	$-0.872756\pi$
$419$	−15801.0	−1.84232	−0.921159	+	0.389186i	$0.872756\pi$
$420$	0	0
$421$	11849.4	1.37174	0.685872	−	0.727722i	$-0.259421\pi$
$421$	11849.4	1.37174	0.685872	+	0.727722i	$0.259421\pi$
$422$	6112.72	0.705124
$423$	−7010.68	−0.805841
$424$	−5737.64	−0.657181
$425$	−304.781	−0.0347860
$426$	3303.35	0.375700
$427$	0	0
$428$	−6180.63	−0.698019
$429$	−5431.16	−0.611232
$430$	−445.035	−0.0499104
$431$	12310.0	1.37576	0.687878	−	0.725827i	$-0.258542\pi$
$431$	12310.0	1.37576	0.687878	+	0.725827i	$0.258542\pi$
$432$	1334.35	0.148609
$433$	−5808.02	−0.644608	−0.322304	−	0.946636i	$-0.604457\pi$
$433$	−5808.02	−0.644608	−0.322304	+	0.946636i	$0.604457\pi$
$434$	0	0
$435$	1852.75	0.204213
$436$	−5956.95	−0.654326
$437$	609.694	0.0667405
$438$	−10743.0	−1.17196
$439$	6560.51	0.713248	0.356624	−	0.934248i	$-0.383928\pi$
$439$	6560.51	0.713248	0.356624	+	0.934248i	$0.383928\pi$
$440$	−1561.50	−0.169186
$441$	0	0
$442$	−529.968	−0.0570317
$443$	−4489.59	−0.481506	−0.240753	−	0.970586i	$-0.577394\pi$
$443$	−4489.59	−0.481506	−0.240753	+	0.970586i	$0.577394\pi$
$444$	10147.0	1.08458
$445$	−5648.03	−0.601668
$446$	−2873.47	−0.305074
$447$	−4792.31	−0.507089
$448$	0	0
$449$	−1729.91	−0.181825	−0.0909124	−	0.995859i	$-0.528978\pi$
$449$	−1729.91	−0.181825	−0.0909124	+	0.995859i	$0.528978\pi$
$450$	698.550	0.0731777
$451$	−1048.49	−0.109471
$452$	−483.353	−0.0502987
$453$	−7996.57	−0.829385
$454$	5251.90	0.542916
$455$	0	0
$456$	4434.16	0.455370
$457$	872.004	0.0892574	0.0446287	−	0.999004i	$-0.485790\pi$
$457$	872.004	0.0892574	0.0446287	+	0.999004i	$0.485790\pi$
$458$	4468.13	0.455856
$459$	−1016.71	−0.103390
$460$	140.818	0.0142732
$461$	−5678.34	−0.573680	−0.286840	−	0.957978i	$-0.592605\pi$
$461$	−5678.34	−0.573680	−0.286840	+	0.957978i	$0.592605\pi$
$462$	0	0
$463$	−3938.80	−0.395360	−0.197680	−	0.980267i	$-0.563341\pi$
$463$	−3938.80	−0.395360	−0.197680	+	0.980267i	$0.563341\pi$
$464$	926.252	0.0926728
$465$	−7722.83	−0.770189
$466$	−5211.80	−0.518094
$467$	867.873	0.0859965	0.0429983	−	0.999075i	$-0.486309\pi$
$467$	867.873	0.0859965	0.0429983	+	0.999075i	$0.486309\pi$
$468$	1214.67	0.119975
$469$	0	0
$470$	5018.02	0.492477
$471$	−8976.37	−0.878152
$472$	3646.89	0.355639
$473$	1737.31	0.168883
$474$	−12825.4	−1.24280
$475$	−2164.83	−0.209114
$476$	0	0
$477$	−10020.1	−0.961819
$478$	−10139.1	−0.970187
$479$	375.683	0.0358359	0.0179180	−	0.999839i	$-0.494296\pi$
$479$	375.683	0.0358359	0.0179180	+	0.999839i	$0.494296\pi$
$480$	1024.14	0.0973860
$481$	−8614.08	−0.816566
$482$	−4776.90	−0.451415
$483$	0	0
$484$	771.735	0.0724770
$485$	7430.18	0.695643
$486$	7159.30	0.668215
$487$	−9238.87	−0.859657	−0.429829	−	0.902910i	$-0.641426\pi$
$487$	−9238.87	−0.859657	−0.429829	+	0.902910i	$0.641426\pi$
$488$	−4264.55	−0.395589
$489$	−15295.4	−1.41448
$490$	0	0
$491$	3147.80	0.289324	0.144662	−	0.989481i	$-0.453790\pi$
$491$	3147.80	0.289324	0.144662	+	0.989481i	$0.453790\pi$
$492$	687.670	0.0630133
$493$	−705.761	−0.0644744
$494$	−3764.30	−0.342842
$495$	−2726.97	−0.247613
$496$	−3860.90	−0.349515
$497$	0	0
$498$	−1670.52	−0.150317
$499$	17740.4	1.59152	0.795760	−	0.605613i	$-0.207072\pi$
$499$	17740.4	1.59152	0.795760	+	0.605613i	$0.207072\pi$
$500$	−500.000	−0.0447214
$501$	8358.27	0.745349
$502$	7194.95	0.639694
$503$	−17681.9	−1.56739	−0.783697	−	0.621144i	$-0.786668\pi$
$503$	−17681.9	−1.56739	−0.783697	+	0.621144i	$0.786668\pi$
$504$	0	0
$505$	3593.70	0.316668
$506$	−549.720	−0.0482965
$507$	11038.7	0.966954
$508$	4899.49	0.427913
$509$	−4329.81	−0.377044	−0.188522	−	0.982069i	$-0.560370\pi$
$509$	−4329.81	−0.377044	−0.188522	+	0.982069i	$0.560370\pi$
$510$	−780.345	−0.0677535
$511$	0	0
$512$	512.000	0.0441942
$513$	−7221.59	−0.621522
$514$	806.893	0.0692422
$515$	3408.55	0.291648
$516$	−1139.44	−0.0972115
$517$	−19589.1	−1.66640
$518$	0	0
$519$	8267.67	0.699250
$520$	−869.423	−0.0733206
$521$	−12535.5	−1.05411	−0.527056	−	0.849831i	$-0.676704\pi$
$521$	−12535.5	−1.05411	−0.527056	+	0.849831i	$0.676704\pi$
$522$	1617.58	0.135632
$523$	16183.4	1.35306	0.676531	−	0.736414i	$-0.263482\pi$
$523$	16183.4	1.35306	0.676531	+	0.736414i	$0.263482\pi$
$524$	−2264.73	−0.188808
$525$	0	0
$526$	10002.5	0.829141
$527$	2941.82	0.243165
$528$	−3997.99	−0.329527
$529$	−12117.4	−0.995926
$530$	7172.05	0.587800
$531$	6368.84	0.520497
$532$	0	0
$533$	−583.784	−0.0474419
$534$	−14460.9	−1.17188
$535$	7725.79	0.624327
$536$	−6517.51	−0.525212
$537$	−22869.9	−1.83782
$538$	8562.70	0.686179
$539$	0	0
$540$	−1667.94	−0.132920
$541$	21538.3	1.71165	0.855825	−	0.517266i	$-0.173050\pi$
$541$	21538.3	1.71165	0.855825	+	0.517266i	$0.173050\pi$
$542$	−14307.6	−1.13388
$543$	−13402.6	−1.05923
$544$	−390.120	−0.0307468
$545$	7446.18	0.585247
$546$	0	0
$547$	−16729.1	−1.30765	−0.653825	−	0.756646i	$-0.726837\pi$
$547$	−16729.1	−1.30765	−0.653825	+	0.756646i	$0.726837\pi$
$548$	−754.696	−0.0588303
$549$	−7447.51	−0.578965
$550$	1951.88	0.151324
$551$	−5012.94	−0.387583
$552$	360.543	0.0278002
$553$	0	0
$554$	−15031.4	−1.15275
$555$	−12683.7	−0.970079
$556$	11481.8	0.875783
$557$	22282.1	1.69502	0.847508	−	0.530782i	$-0.178102\pi$
$557$	22282.1	1.69502	0.847508	+	0.530782i	$0.178102\pi$
$558$	−6742.57	−0.511534
$559$	967.308	0.0731892
$560$	0	0
$561$	3046.28	0.229259
$562$	−4117.28	−0.309034
$563$	−4879.61	−0.365277	−0.182639	−	0.983180i	$-0.558464\pi$
$563$	−4879.61	−0.365277	−0.182639	+	0.983180i	$0.558464\pi$
$564$	12847.9	0.959206
$565$	604.191	0.0449885
$566$	4680.71	0.347606
$567$	0	0
$568$	−2064.32	−0.152495
$569$	16450.3	1.21201	0.606003	−	0.795462i	$-0.292772\pi$
$569$	16450.3	1.21201	0.606003	+	0.795462i	$0.292772\pi$
$570$	−5542.70	−0.407295
$571$	14022.0	1.02767	0.513836	−	0.857888i	$-0.328224\pi$
$571$	14022.0	1.02767	0.513836	+	0.857888i	$0.328224\pi$
$572$	3394.02	0.248096
$573$	24164.5	1.76175
$574$	0	0
$575$	−176.023	−0.0127663
$576$	894.144	0.0646806
$577$	−9448.86	−0.681735	−0.340868	−	0.940111i	$-0.610721\pi$
$577$	−9448.86	−0.681735	−0.340868	+	0.940111i	$0.610721\pi$
$578$	−9528.75	−0.685716
$579$	13346.8	0.957985
$580$	−1157.82	−0.0828891
$581$	0	0
$582$	19023.8	1.35492
$583$	−27998.0	−1.98895
$584$	6713.44	0.475692
$585$	−1518.34	−0.107309
$586$	−7206.61	−0.508024
$587$	−4636.89	−0.326039	−0.163020	−	0.986623i	$-0.552123\pi$
$587$	−4636.89	−0.326039	−0.163020	+	0.986623i	$0.552123\pi$
$588$	0	0
$589$	20895.4	1.46177
$590$	−4558.61	−0.318093
$591$	23727.9	1.65150
$592$	−6341.00	−0.440226
$593$	18366.4	1.27187	0.635933	−	0.771745i	$-0.280616\pi$
$593$	18366.4	1.27187	0.635933	+	0.771745i	$0.280616\pi$
$594$	6511.22	0.449762
$595$	0	0
$596$	2994.79	0.205825
$597$	−19915.1	−1.36528
$598$	−306.076	−0.0209304
$599$	698.580	0.0476514	0.0238257	−	0.999716i	$-0.492415\pi$
$599$	698.580	0.0476514	0.0238257	+	0.999716i	$0.492415\pi$
$600$	−1280.17	−0.0871047
$601$	26216.7	1.77937	0.889684	−	0.456577i	$-0.150925\pi$
$601$	26216.7	1.77937	0.889684	+	0.456577i	$0.150925\pi$
$602$	0	0
$603$	−11382.0	−0.768675
$604$	4997.18	0.336643
$605$	−964.668	−0.0648254
$606$	9201.10	0.616781
$607$	2183.68	0.146018	0.0730090	−	0.997331i	$-0.476740\pi$
$607$	2183.68	0.146018	0.0730090	+	0.997331i	$0.476740\pi$
$608$	−2770.98	−0.184832
$609$	0	0
$610$	5330.69	0.353825
$611$	−10906.9	−0.722173
$612$	−681.296	−0.0449996
$613$	11721.1	0.772288	0.386144	−	0.922439i	$-0.373807\pi$
$613$	11721.1	0.772288	0.386144	+	0.922439i	$0.373807\pi$
$614$	17390.5	1.14303
$615$	−859.587	−0.0563608
$616$	0	0
$617$	10891.6	0.710662	0.355331	−	0.934741i	$-0.384368\pi$
$617$	10891.6	0.710662	0.355331	+	0.934741i	$0.384368\pi$
$618$	8727.06	0.568049
$619$	2566.63	0.166658	0.0833292	−	0.996522i	$-0.473445\pi$
$619$	2566.63	0.166658	0.0833292	+	0.996522i	$0.473445\pi$
$620$	4826.12	0.312616
$621$	−587.189	−0.0379438
$622$	−15454.6	−0.996259
$623$	0	0
$624$	−2226.02	−0.142808
$625$	625.000	0.0400000
$626$	−13964.0	−0.891558
$627$	21637.4	1.37817
$628$	5609.48	0.356437
$629$	4831.55	0.306274
$630$	0	0
$631$	9837.42	0.620636	0.310318	−	0.950633i	$-0.399564\pi$
$631$	9837.42	0.620636	0.310318	+	0.950633i	$0.399564\pi$
$632$	8014.78	0.504447
$633$	−19563.3	−1.22839
$634$	14714.9	0.921769
$635$	−6124.37	−0.382737
$636$	18362.9	1.14487
$637$	0	0
$638$	4519.83	0.280473
$639$	−3605.07	−0.223184
$640$	−640.000	−0.0395285
$641$	−11701.3	−0.721023	−0.360511	−	0.932755i	$-0.617398\pi$
$641$	−11701.3	−0.721023	−0.360511	+	0.932755i	$0.617398\pi$
$642$	19780.7	1.21601
$643$	17847.3	1.09460	0.547300	−	0.836937i	$-0.315656\pi$
$643$	17847.3	1.09460	0.547300	+	0.836937i	$0.315656\pi$
$644$	0	0
$645$	1424.30	0.0869486
$646$	2111.36	0.128592
$647$	6796.91	0.413005	0.206502	−	0.978446i	$-0.433792\pi$
$647$	6796.91	0.413005	0.206502	+	0.978446i	$0.433792\pi$
$648$	−7288.23	−0.441834
$649$	17795.7	1.07634
$650$	1086.78	0.0655799
$651$	0	0
$652$	9558.33	0.574130
$653$	12581.9	0.754010	0.377005	−	0.926211i	$-0.376954\pi$
$653$	12581.9	0.754010	0.377005	+	0.926211i	$0.376954\pi$
$654$	19064.8	1.13990
$655$	2830.91	0.168875
$656$	−429.736	−0.0255768
$657$	11724.2	0.696201
$658$	0	0
$659$	−25697.6	−1.51902	−0.759512	−	0.650493i	$-0.774562\pi$
$659$	−25697.6	−1.51902	−0.759512	+	0.650493i	$0.774562\pi$
$660$	4997.48	0.294738
$661$	26298.6	1.54750	0.773749	−	0.633492i	$-0.218379\pi$
$661$	26298.6	1.54750	0.773749	+	0.633492i	$0.218379\pi$
$662$	6972.38	0.409349
$663$	1696.12	0.0993545
$664$	1043.94	0.0610129
$665$	0	0
$666$	−11073.8	−0.644294
$667$	−407.603	−0.0236619
$668$	−5223.22	−0.302533
$669$	9196.35	0.531467
$670$	8146.88	0.469763
$671$	−20809.7	−1.19724
$672$	0	0
$673$	5189.30	0.297225	0.148613	−	0.988895i	$-0.452519\pi$
$673$	5189.30	0.297225	0.148613	+	0.988895i	$0.452519\pi$
$674$	−1023.54	−0.0584944
$675$	2084.92	0.118887
$676$	−6898.26	−0.392482
$677$	−28846.1	−1.63758	−0.818792	−	0.574091i	$-0.805356\pi$
$677$	−28846.1	−1.63758	−0.818792	+	0.574091i	$0.805356\pi$
$678$	1546.94	0.0876250
$679$	0	0
$680$	487.650	0.0275008
$681$	−16808.3	−0.945811
$682$	−18840.0	−1.05780
$683$	31459.5	1.76246	0.881232	−	0.472684i	$-0.156715\pi$
$683$	31459.5	1.76246	0.881232	+	0.472684i	$0.156715\pi$
$684$	−4839.17	−0.270512
$685$	943.370	0.0526194
$686$	0	0
$687$	−14299.9	−0.794143
$688$	712.056	0.0394577
$689$	−15588.9	−0.861957
$690$	−450.678	−0.0248653
$691$	6065.50	0.333925	0.166963	−	0.985963i	$-0.446604\pi$
$691$	6065.50	0.333925	0.166963	+	0.985963i	$0.446604\pi$
$692$	−5166.60	−0.283822
$693$	0	0
$694$	−14179.8	−0.775586
$695$	−14352.2	−0.783324
$696$	−2964.41	−0.161445
$697$	327.439	0.0177943
$698$	−7234.78	−0.392322
$699$	16680.0	0.902569
$700$	0	0
$701$	−30292.4	−1.63214	−0.816068	−	0.577956i	$-0.803851\pi$
$701$	−30292.4	−1.63214	−0.816068	+	0.577956i	$0.803851\pi$
$702$	3625.35	0.194915
$703$	34318.0	1.84115
$704$	2498.41	0.133753
$705$	−16059.8	−0.857940
$706$	−20200.9	−1.07687
$707$	0	0
$708$	−11671.6	−0.619557
$709$	32732.9	1.73386	0.866932	−	0.498426i	$-0.166088\pi$
$709$	32732.9	1.73386	0.866932	+	0.498426i	$0.166088\pi$
$710$	2580.40	0.136395
$711$	13996.8	0.738286
$712$	9036.85	0.475660
$713$	1699.01	0.0892406
$714$	0	0
$715$	−4242.52	−0.221904
$716$	14291.8	0.745961
$717$	32449.3	1.69016
$718$	4618.89	0.240077
$719$	23781.0	1.23349	0.616747	−	0.787161i	$-0.288450\pi$
$719$	23781.0	1.23349	0.616747	+	0.787161i	$0.288450\pi$
$720$	−1117.68	−0.0578520
$721$	0	0
$722$	1278.73	0.0659133
$723$	15288.1	0.786406
$724$	8375.52	0.429936
$725$	1447.27	0.0741382
$726$	−2469.88	−0.126262
$727$	14202.3	0.724531	0.362265	−	0.932075i	$-0.382003\pi$
$727$	14202.3	0.724531	0.362265	+	0.932075i	$0.382003\pi$
$728$	0	0
$729$	1684.93	0.0856031
$730$	−8391.80	−0.425472
$731$	−542.553	−0.0274515
$732$	13648.4	0.689152
$733$	27692.9	1.39544	0.697722	−	0.716368i	$-0.254197\pi$
$733$	27692.9	1.39544	0.697722	+	0.716368i	$0.254197\pi$
$734$	9675.44	0.486549
$735$	0	0
$736$	−225.309	−0.0112840
$737$	−31803.5	−1.58955
$738$	−750.480	−0.0374330
$739$	−23308.0	−1.16022	−0.580109	−	0.814539i	$-0.696990\pi$
$739$	−23308.0	−1.16022	−0.580109	+	0.814539i	$0.696990\pi$
$740$	7926.26	0.393750
$741$	12047.4	0.597262
$742$	0	0
$743$	−36614.8	−1.80790	−0.903949	−	0.427641i	$-0.859345\pi$
$743$	−36614.8	−1.80790	−0.903949	+	0.427641i	$0.859345\pi$
$744$	12356.5	0.608888
$745$	−3743.49	−0.184095
$746$	10366.5	0.508773
$747$	1823.10	0.0892957
$748$	−1903.67	−0.0930549
$749$	0	0
$750$	1600.21	0.0779088
$751$	−4251.49	−0.206577	−0.103288	−	0.994651i	$-0.532936\pi$
$751$	−4251.49	−0.206577	−0.103288	+	0.994651i	$0.532936\pi$
$752$	−8028.83	−0.389337
$753$	−23026.9	−1.11441
$754$	2516.58	0.121550
$755$	−6246.48	−0.301103
$756$	0	0
$757$	15481.6	0.743314	0.371657	−	0.928370i	$-0.378790\pi$
$757$	15481.6	0.743314	0.371657	+	0.928370i	$0.378790\pi$
$758$	9173.79	0.439587
$759$	1759.34	0.0841370
$760$	3463.72	0.165319
$761$	22924.3	1.09199	0.545997	−	0.837787i	$-0.316151\pi$
$761$	22924.3	1.09199	0.545997	+	0.837787i	$0.316151\pi$
$762$	−15680.5	−0.745464
$763$	0	0
$764$	−15100.8	−0.715087
$765$	851.620	0.0402489
$766$	6096.83	0.287582
$767$	9908.40	0.466456
$768$	−1638.62	−0.0769904
$769$	10601.5	0.497140	0.248570	−	0.968614i	$-0.420039\pi$
$769$	10601.5	0.497140	0.248570	+	0.968614i	$0.420039\pi$
$770$	0	0
$771$	−2582.40	−0.120626
$772$	−8340.61	−0.388841
$773$	−2102.91	−0.0978481	−0.0489241	−	0.998803i	$-0.515579\pi$
$773$	−2102.91	−0.0978481	−0.0489241	+	0.998803i	$0.515579\pi$
$774$	1243.52	0.0577484
$775$	−6032.65	−0.279612
$776$	−11888.3	−0.549954
$777$	0	0
$778$	3720.19	0.171433
$779$	2325.76	0.106969
$780$	2782.53	0.127731
$781$	−10073.3	−0.461523
$782$	171.675	0.00785049
$783$	4827.90	0.220351
$784$	0	0
$785$	−7011.85	−0.318807
$786$	7248.11	0.328921
$787$	23532.0	1.06585	0.532926	−	0.846162i	$-0.321092\pi$
$787$	23532.0	1.06585	0.532926	+	0.846162i	$0.321092\pi$
$788$	−14828.0	−0.670335
$789$	−32012.2	−1.44444
$790$	−10018.5	−0.451191
$791$	0	0
$792$	4363.15	0.195755
$793$	−11586.6	−0.518853
$794$	−15325.7	−0.684996
$795$	−22953.7	−1.02400
$796$	12445.3	0.554159
$797$	−19448.3	−0.864360	−0.432180	−	0.901787i	$-0.642255\pi$
$797$	−19448.3	−0.864360	−0.432180	+	0.901787i	$0.642255\pi$
$798$	0	0
$799$	6117.60	0.270870
$800$	800.000	0.0353553
$801$	15781.7	0.696155
$802$	30576.8	1.34626
$803$	32759.6	1.43968
$804$	20858.8	0.914967
$805$	0	0
$806$	−10489.8	−0.458423
$807$	−27404.3	−1.19539
$808$	−5749.92	−0.250348
$809$	−35740.3	−1.55323	−0.776615	−	0.629976i	$-0.783065\pi$
$809$	−35740.3	−1.55323	−0.776615	+	0.629976i	$0.783065\pi$
$810$	9110.28	0.395188
$811$	−18334.2	−0.793836	−0.396918	−	0.917854i	$-0.629920\pi$
$811$	−18334.2	−0.793836	−0.396918	+	0.917854i	$0.629920\pi$
$812$	0	0
$813$	45790.3	1.97532
$814$	−30942.2	−1.33234
$815$	−11947.9	−0.513518
$816$	1248.55	0.0535638
$817$	−3853.69	−0.165023
$818$	−23679.0	−1.01212
$819$	0	0
$820$	537.170	0.0228766
$821$	31568.6	1.34196	0.670981	−	0.741474i	$-0.265873\pi$
$821$	31568.6	1.34196	0.670981	+	0.741474i	$0.265873\pi$
$822$	2415.35	0.102488
$823$	6075.81	0.257338	0.128669	−	0.991688i	$-0.458929\pi$
$823$	6075.81	0.257338	0.128669	+	0.991688i	$0.458929\pi$
$824$	−5453.68	−0.230568
$825$	−6246.85	−0.263621
$826$	0	0
$827$	4950.48	0.208156	0.104078	−	0.994569i	$-0.466811\pi$
$827$	4950.48	0.208156	0.104078	+	0.994569i	$0.466811\pi$
$828$	−393.474	−0.0165147
$829$	21431.4	0.897883	0.448941	−	0.893561i	$-0.351801\pi$
$829$	21431.4	0.897883	0.448941	+	0.893561i	$0.351801\pi$
$830$	−1304.92	−0.0545716
$831$	48106.8	2.00819
$832$	1391.08	0.0579650
$833$	0	0
$834$	−36746.6	−1.52570
$835$	6529.02	0.270594
$836$	−13521.5	−0.559393
$837$	−20124.2	−0.831054
$838$	−31602.1	−1.30272
$839$	6685.20	0.275088	0.137544	−	0.990496i	$-0.456079\pi$
$839$	6685.20	0.275088	0.137544	+	0.990496i	$0.456079\pi$
$840$	0	0
$841$	−21037.7	−0.862588
$842$	23698.8	0.969970
$843$	13177.1	0.538366
$844$	12225.4	0.498598
$845$	8622.83	0.351046
$846$	−14021.4	−0.569816
$847$	0	0
$848$	−11475.3	−0.464697
$849$	−14980.3	−0.605562
$850$	−609.563	−0.0245974
$851$	2790.40	0.112402
$852$	6606.71	0.265660
$853$	−8900.16	−0.357252	−0.178626	−	0.983917i	$-0.557165\pi$
$853$	−8900.16	−0.357252	−0.178626	+	0.983917i	$0.557165\pi$
$854$	0	0
$855$	6048.96	0.241953
$856$	−12361.3	−0.493574
$857$	−32667.2	−1.30209	−0.651045	−	0.759039i	$-0.725669\pi$
$857$	−32667.2	−1.30209	−0.651045	+	0.759039i	$0.725669\pi$
$858$	−10862.3	−0.432207
$859$	20830.0	0.827369	0.413684	−	0.910420i	$-0.364242\pi$
$859$	20830.0	0.827369	0.413684	+	0.910420i	$0.364242\pi$
$860$	−890.070	−0.0352920
$861$	0	0
$862$	24620.0	0.972806
$863$	3912.36	0.154320	0.0771600	−	0.997019i	$-0.475415\pi$
$863$	3912.36	0.154320	0.0771600	+	0.997019i	$0.475415\pi$
$864$	2668.70	0.105082
$865$	6458.25	0.253858
$866$	−11616.0	−0.455807
$867$	30496.1	1.19458
$868$	0	0
$869$	39109.7	1.52670
$870$	3705.51	0.144400
$871$	−17707.7	−0.688867
$872$	−11913.9	−0.462678
$873$	−20761.4	−0.804888
$874$	1219.39	0.0471927
$875$	0	0
$876$	−21485.9	−0.828700
$877$	−38307.4	−1.47497	−0.737486	−	0.675363i	$-0.763987\pi$
$877$	−38307.4	−1.47497	−0.737486	+	0.675363i	$0.763987\pi$
$878$	13121.0	0.504343
$879$	23064.2	0.885025
$880$	−3123.01	−0.119632
$881$	−33492.4	−1.28080	−0.640402	−	0.768040i	$-0.721232\pi$
$881$	−33492.4	−1.28080	−0.640402	+	0.768040i	$0.721232\pi$
$882$	0	0
$883$	5739.96	0.218760	0.109380	−	0.994000i	$-0.465114\pi$
$883$	5739.96	0.218760	0.109380	+	0.994000i	$0.465114\pi$
$884$	−1059.94	−0.0403275
$885$	14589.5	0.554148
$886$	−8979.19	−0.340476
$887$	−35932.5	−1.36020	−0.680098	−	0.733121i	$-0.738063\pi$
$887$	−35932.5	−1.36020	−0.680098	+	0.733121i	$0.738063\pi$
$888$	20293.9	0.766914
$889$	0	0
$890$	−11296.1	−0.425444
$891$	−35564.3	−1.33721
$892$	−5746.95	−0.215720
$893$	43452.6	1.62832
$894$	−9584.63	−0.358566
$895$	−17864.7	−0.667208
$896$	0	0
$897$	979.575	0.0364627
$898$	−3459.81	−0.128570
$899$	−13969.4	−0.518248
$900$	1397.10	0.0517444
$901$	8743.64	0.323299
$902$	−2096.98	−0.0774078
$903$	0	0
$904$	−966.705	−0.0355665
$905$	−10469.4	−0.384547
$906$	−15993.1	−0.586464
$907$	−9589.89	−0.351077	−0.175539	−	0.984473i	$-0.556167\pi$
$907$	−9589.89	−0.351077	−0.175539	+	0.984473i	$0.556167\pi$
$908$	10503.8	0.383900
$909$	−10041.5	−0.366398
$910$	0	0
$911$	51521.7	1.87376	0.936878	−	0.349657i	$-0.113702\pi$
$911$	51521.7	1.87376	0.936878	+	0.349657i	$0.113702\pi$
$912$	8868.32	0.321995
$913$	5094.09	0.184655
$914$	1744.01	0.0631145
$915$	−17060.5	−0.616397
$916$	8936.25	0.322339
$917$	0	0
$918$	−2033.42	−0.0731078
$919$	4203.92	0.150897	0.0754486	−	0.997150i	$-0.475961\pi$
$919$	4203.92	0.150897	0.0754486	+	0.997150i	$0.475961\pi$
$920$	281.636	0.0100927
$921$	−55656.9	−1.99127
$922$	−11356.7	−0.405653
$923$	−5608.64	−0.200012
$924$	0	0
$925$	−9907.82	−0.352181
$926$	−7877.61	−0.279562
$927$	−9524.18	−0.337449
$928$	1852.50	0.0655296
$929$	−25417.5	−0.897655	−0.448828	−	0.893618i	$-0.648158\pi$
$929$	−25417.5	−0.897655	−0.448828	+	0.893618i	$0.648158\pi$
$930$	−15445.7	−0.544606
$931$	0	0
$932$	−10423.6	−0.366348
$933$	49461.4	1.73558
$934$	1735.75	0.0608087
$935$	2379.59	0.0832308
$936$	2429.34	0.0848349
$937$	41927.0	1.46179	0.730894	−	0.682491i	$-0.239103\pi$
$937$	41927.0	1.46179	0.730894	+	0.682491i	$0.239103\pi$
$938$	0	0
$939$	44690.9	1.55318
$940$	10036.0	0.348234
$941$	−10823.2	−0.374947	−0.187474	−	0.982270i	$-0.560030\pi$
$941$	−10823.2	−0.374947	−0.187474	+	0.982270i	$0.560030\pi$
$942$	−17952.7	−0.620947
$943$	189.108	0.00653044
$944$	7293.78	0.251475
$945$	0	0
$946$	3474.62	0.119418
$947$	34655.6	1.18918	0.594591	−	0.804028i	$-0.297314\pi$
$947$	34655.6	1.18918	0.594591	+	0.804028i	$0.297314\pi$
$948$	−25650.7	−0.878794
$949$	18240.1	0.623917
$950$	−4329.66	−0.147866
$951$	−47093.9	−1.60581
$952$	0	0
$953$	47201.1	1.60440	0.802201	−	0.597055i	$-0.203662\pi$
$953$	47201.1	1.60440	0.802201	+	0.597055i	$0.203662\pi$
$954$	−20040.2	−0.680109
$955$	18876.0	0.639594
$956$	−20278.1	−0.686026
$957$	−14465.4	−0.488610
$958$	751.366	0.0253398
$959$	0	0
$960$	2048.27	0.0688623
$961$	28437.6	0.954570
$962$	−17228.2	−0.577400
$963$	−21587.4	−0.722372
$964$	−9553.80	−0.319198
$965$	10425.8	0.347790
$966$	0	0
$967$	24931.6	0.829107	0.414553	−	0.910025i	$-0.363938\pi$
$967$	24931.6	0.829107	0.414553	+	0.910025i	$0.363938\pi$
$968$	1543.47	0.0512490
$969$	−6757.25	−0.224019
$970$	14860.4	0.491894
$971$	−47113.4	−1.55710	−0.778548	−	0.627585i	$-0.784043\pi$
$971$	−47113.4	−1.55710	−0.778548	+	0.627585i	$0.784043\pi$
$972$	14318.6	0.472499
$973$	0	0
$974$	−18477.7	−0.607869
$975$	−3478.16	−0.114246
$976$	−8529.11	−0.279723
$977$	34269.7	1.12220	0.561098	−	0.827749i	$-0.310379\pi$
$977$	34269.7	1.12220	0.561098	+	0.827749i	$0.310379\pi$
$978$	−30590.8	−1.00019
$979$	44097.1	1.43958
$980$	0	0
$981$	−20806.1	−0.677154
$982$	6295.60	0.204583
$983$	11156.6	0.361993	0.180997	−	0.983484i	$-0.442068\pi$
$983$	11156.6	0.361993	0.180997	+	0.983484i	$0.442068\pi$
$984$	1375.34	0.0445571
$985$	18534.9	0.599566
$986$	−1411.52	−0.0455903
$987$	0	0
$988$	−7528.60	−0.242426
$989$	−313.345	−0.0100746
$990$	−5453.94	−0.175089
$991$	−14571.0	−0.467068	−0.233534	−	0.972349i	$-0.575029\pi$
$991$	−14571.0	−0.467068	−0.233534	+	0.972349i	$0.575029\pi$
$992$	−7721.79	−0.247144
$993$	−22314.6	−0.713125
$994$	0	0
$995$	−15556.6	−0.495655
$996$	−3341.04	−0.106290
$997$	−5875.47	−0.186638	−0.0933190	−	0.995636i	$-0.529748\pi$
$997$	−5875.47	−0.186638	−0.0933190	+	0.995636i	$0.529748\pi$
$998$	35480.7	1.12537
$999$	−33051.2	−1.04674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.x.1.2	✓	4
5.4	even	2		2450.4.a.cp.1.3		4
7.2	even	3		490.4.e.ba.361.3		8
7.3	odd	6		490.4.e.z.471.2		8
7.4	even	3		490.4.e.ba.471.3		8
7.5	odd	6		490.4.e.z.361.2		8
7.6	odd	2		490.4.a.y.1.3	yes	4
35.34	odd	2		2450.4.a.cj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.x.1.2	✓	4	1.1	even	1	trivial
490.4.a.y.1.3	yes	4	7.6	odd	2
490.4.e.z.361.2		8	7.5	odd	6
490.4.e.z.471.2		8	7.3	odd	6
490.4.e.ba.361.3		8	7.2	even	3
490.4.e.ba.471.3		8	7.4	even	3
2450.4.a.cj.1.2		4	35.34	odd	2
2450.4.a.cp.1.3		4	5.4	even	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -6.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} -12.8017 q^{6} +8.00000 q^{8} +13.9710 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -6.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} -12.8017 q^{6} +8.00000 q^{8} +13.9710 q^{9} -10.0000 q^{10} +39.0376 q^{11} -25.6034 q^{12} +21.7356 q^{13} +32.0043 q^{15} +16.0000 q^{16} -12.1913 q^{17} +27.9420 q^{18} -86.5931 q^{19} -20.0000 q^{20} +78.0752 q^{22} -7.04090 q^{23} -51.2069 q^{24} +25.0000 q^{25} +43.4711 q^{26} +83.3968 q^{27} +57.8908 q^{29} +64.0086 q^{30} -241.306 q^{31} +32.0000 q^{32} -249.874 q^{33} -24.3825 q^{34} +55.8840 q^{36} -396.313 q^{37} -173.186 q^{38} -139.126 q^{39} -40.0000 q^{40} -26.8585 q^{41} +44.5035 q^{43} +156.150 q^{44} -69.8550 q^{45} -14.0818 q^{46} -501.802 q^{47} -102.414 q^{48} +50.0000 q^{50} +78.0345 q^{51} +86.9423 q^{52} -717.205 q^{53} +166.794 q^{54} -195.188 q^{55} +554.270 q^{57} +115.782 q^{58} +455.861 q^{59} +128.017 q^{60} -533.069 q^{61} -482.612 q^{62} +64.0000 q^{64} -108.678 q^{65} -499.748 q^{66} -814.688 q^{67} -48.7650 q^{68} +45.0678 q^{69} -258.040 q^{71} +111.768 q^{72} +839.180 q^{73} -792.626 q^{74} -160.021 q^{75} -346.372 q^{76} -278.253 q^{78} +1001.85 q^{79} -80.0000 q^{80} -911.028 q^{81} -53.7170 q^{82} +130.492 q^{83} +60.9563 q^{85} +89.0070 q^{86} -370.551 q^{87} +312.301 q^{88} +1129.61 q^{89} -139.710 q^{90} -28.1636 q^{92} +1544.57 q^{93} -1003.60 q^{94} +432.966 q^{95} -204.827 q^{96} -1486.04 q^{97} +545.394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 10 q^{3} + 16 q^{4} - 20 q^{5} - 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) \) 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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