LMFDB - Embedded newform 490.4.a.q.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:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.24264 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.48528 q^{6} -8.00000 q^{8} -16.4853 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.24264 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.48528 q^{6} -8.00000 q^{8} -16.4853 q^{9} -10.0000 q^{10} -24.3137 q^{11} +12.9706 q^{12} +63.7279 q^{13} +16.2132 q^{15} +16.0000 q^{16} -117.042 q^{17} +32.9706 q^{18} +4.62742 q^{19} +20.0000 q^{20} +48.6274 q^{22} -164.836 q^{23} -25.9411 q^{24} +25.0000 q^{25} -127.456 q^{26} -141.007 q^{27} -124.823 q^{29} -32.4264 q^{30} +89.8061 q^{31} -32.0000 q^{32} -78.8406 q^{33} +234.083 q^{34} -65.9411 q^{36} -212.600 q^{37} -9.25483 q^{38} +206.647 q^{39} -40.0000 q^{40} +271.061 q^{41} +99.7746 q^{43} -97.2548 q^{44} -82.4264 q^{45} +329.671 q^{46} -204.439 q^{47} +51.8823 q^{48} -50.0000 q^{50} -379.524 q^{51} +254.912 q^{52} +425.026 q^{53} +282.014 q^{54} -121.569 q^{55} +15.0051 q^{57} +249.647 q^{58} -572.434 q^{59} +64.8528 q^{60} -308.818 q^{61} -179.612 q^{62} +64.0000 q^{64} +318.640 q^{65} +157.681 q^{66} +617.291 q^{67} -468.167 q^{68} -534.503 q^{69} -196.093 q^{71} +131.882 q^{72} -469.740 q^{73} +425.200 q^{74} +81.0660 q^{75} +18.5097 q^{76} -413.294 q^{78} -1224.24 q^{79} +80.0000 q^{80} -12.1329 q^{81} -542.122 q^{82} -267.687 q^{83} -585.208 q^{85} -199.549 q^{86} -404.757 q^{87} +194.510 q^{88} -589.677 q^{89} +164.853 q^{90} -659.342 q^{92} +291.209 q^{93} +408.877 q^{94} +23.1371 q^{95} -103.765 q^{96} -1223.38 q^{97} +400.818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 - 16 * q^9	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} - 16 q^{9} - 20 q^{10} - 26 q^{11} - 8 q^{12} + 102 q^{13} - 10 q^{15} + 32 q^{16} - 186 q^{17} + 32 q^{18} - 36 q^{19} + 40 q^{20} + 52 q^{22} - 44 q^{23} + 16 q^{24} + 50 q^{25} - 204 q^{26} - 2 q^{27} - 46 q^{29} + 20 q^{30} - 140 q^{31} - 64 q^{32} - 70 q^{33} + 372 q^{34} - 64 q^{36} + 132 q^{37} + 72 q^{38} + 6 q^{39} - 80 q^{40} + 132 q^{41} + 324 q^{43} - 104 q^{44} - 80 q^{45} + 88 q^{46} - 242 q^{47} - 32 q^{48} - 100 q^{50} - 18 q^{51} + 408 q^{52} + 208 q^{53} + 4 q^{54} - 130 q^{55} + 228 q^{57} + 92 q^{58} - 780 q^{59} - 40 q^{60} - 216 q^{61} + 280 q^{62} + 128 q^{64} + 510 q^{65} + 140 q^{66} - 256 q^{67} - 744 q^{68} - 1168 q^{69} - 692 q^{71} + 128 q^{72} - 832 q^{73} - 264 q^{74} - 50 q^{75} - 144 q^{76} - 12 q^{78} - 1962 q^{79} + 160 q^{80} - 754 q^{81} - 264 q^{82} - 1712 q^{83} - 930 q^{85} - 648 q^{86} - 818 q^{87} + 208 q^{88} - 1960 q^{89} + 160 q^{90} - 176 q^{92} + 1496 q^{93} + 484 q^{94} - 180 q^{95} + 64 q^{96} - 102 q^{97} + 400 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 - 16 * q^9 - 20 * q^10 - 26 * q^11 - 8 * q^12 + 102 * q^13 - 10 * q^15 + 32 * q^16 - 186 * q^17 + 32 * q^18 - 36 * q^19 + 40 * q^20 + 52 * q^22 - 44 * q^23 + 16 * q^24 + 50 * q^25 - 204 * q^26 - 2 * q^27 - 46 * q^29 + 20 * q^30 - 140 * q^31 - 64 * q^32 - 70 * q^33 + 372 * q^34 - 64 * q^36 + 132 * q^37 + 72 * q^38 + 6 * q^39 - 80 * q^40 + 132 * q^41 + 324 * q^43 - 104 * q^44 - 80 * q^45 + 88 * q^46 - 242 * q^47 - 32 * q^48 - 100 * q^50 - 18 * q^51 + 408 * q^52 + 208 * q^53 + 4 * q^54 - 130 * q^55 + 228 * q^57 + 92 * q^58 - 780 * q^59 - 40 * q^60 - 216 * q^61 + 280 * q^62 + 128 * q^64 + 510 * q^65 + 140 * q^66 - 256 * q^67 - 744 * q^68 - 1168 * q^69 - 692 * q^71 + 128 * q^72 - 832 * q^73 - 264 * q^74 - 50 * q^75 - 144 * q^76 - 12 * q^78 - 1962 * q^79 + 160 * q^80 - 754 * q^81 - 264 * q^82 - 1712 * q^83 - 930 * q^85 - 648 * q^86 - 818 * q^87 + 208 * q^88 - 1960 * q^89 + 160 * q^90 - 176 * q^92 + 1496 * q^93 + 484 * q^94 - 180 * q^95 + 64 * q^96 - 102 * q^97 + 400 * 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
$3$	3.24264	0.624046	0.312023	−	0.950074i	$-0.398993\pi$
$3$	3.24264	0.624046	0.312023	+	0.950074i	$0.398993\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−6.48528	−0.441268
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	−16.4853	−0.610566
$10$	−10.0000	−0.316228
$11$	−24.3137	−0.666442	−0.333221	−	0.942849i	$-0.608135\pi$
$11$	−24.3137	−0.666442	−0.333221	+	0.942849i	$0.608135\pi$
$12$	12.9706	0.312023
$13$	63.7279	1.35961	0.679806	−	0.733392i	$-0.262064\pi$
$13$	63.7279	1.35961	0.679806	+	0.733392i	$0.262064\pi$
$14$	0	0
$15$	16.2132	0.279082
$16$	16.0000	0.250000
$17$	−117.042	−1.66981	−0.834905	−	0.550394i	$-0.814477\pi$
$17$	−117.042	−1.66981	−0.834905	+	0.550394i	$0.814477\pi$
$18$	32.9706	0.431735
$19$	4.62742	0.0558738	0.0279369	−	0.999610i	$-0.491106\pi$
$19$	4.62742	0.0558738	0.0279369	+	0.999610i	$0.491106\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	48.6274	0.471245
$23$	−164.836	−1.49437	−0.747187	−	0.664614i	$-0.768596\pi$
$23$	−164.836	−1.49437	−0.747187	+	0.664614i	$0.768596\pi$
$24$	−25.9411	−0.220634
$25$	25.0000	0.200000
$26$	−127.456	−0.961390
$27$	−141.007	−1.00507
$28$	0	0
$29$	−124.823	−0.799280	−0.399640	−	0.916672i	$-0.630865\pi$
$29$	−124.823	−0.799280	−0.399640	+	0.916672i	$0.630865\pi$
$30$	−32.4264	−0.197341
$31$	89.8061	0.520312	0.260156	−	0.965567i	$-0.416226\pi$
$31$	89.8061	0.520312	0.260156	+	0.965567i	$0.416226\pi$
$32$	−32.0000	−0.176777
$33$	−78.8406	−0.415891
$34$	234.083	1.18073
$35$	0	0
$36$	−65.9411	−0.305283
$37$	−212.600	−0.944628	−0.472314	−	0.881430i	$-0.656581\pi$
$37$	−212.600	−0.944628	−0.472314	+	0.881430i	$0.656581\pi$
$38$	−9.25483	−0.0395087
$39$	206.647	0.848461
$40$	−40.0000	−0.158114
$41$	271.061	1.03250	0.516251	−	0.856437i	$-0.327327\pi$
$41$	271.061	1.03250	0.516251	+	0.856437i	$0.327327\pi$
$42$	0	0
$43$	99.7746	0.353848	0.176924	−	0.984224i	$-0.443385\pi$
$43$	99.7746	0.353848	0.176924	+	0.984224i	$0.443385\pi$
$44$	−97.2548	−0.333221
$45$	−82.4264	−0.273053
$46$	329.671	1.05668
$47$	−204.439	−0.634477	−0.317239	−	0.948346i	$-0.602756\pi$
$47$	−204.439	−0.634477	−0.317239	+	0.948346i	$0.602756\pi$
$48$	51.8823	0.156012
$49$	0	0
$50$	−50.0000	−0.141421
$51$	−379.524	−1.04204
$52$	254.912	0.679806
$53$	425.026	1.10154	0.550772	−	0.834655i	$-0.314333\pi$
$53$	425.026	1.10154	0.550772	+	0.834655i	$0.314333\pi$
$54$	282.014	0.710690
$55$	−121.569	−0.298042
$56$	0	0
$57$	15.0051	0.0348679
$58$	249.647	0.565176
$59$	−572.434	−1.26313	−0.631564	−	0.775324i	$-0.717587\pi$
$59$	−572.434	−1.26313	−0.631564	+	0.775324i	$0.717587\pi$
$60$	64.8528	0.139541
$61$	−308.818	−0.648199	−0.324099	−	0.946023i	$-0.605061\pi$
$61$	−308.818	−0.648199	−0.324099	+	0.946023i	$0.605061\pi$
$62$	−179.612	−0.367916
$63$	0	0
$64$	64.0000	0.125000
$65$	318.640	0.608037
$66$	157.681	0.294079
$67$	617.291	1.12558	0.562791	−	0.826599i	$-0.309727\pi$
$67$	617.291	1.12558	0.562791	+	0.826599i	$0.309727\pi$
$68$	−468.167	−0.834905
$69$	−534.503	−0.932559
$70$	0	0
$71$	−196.093	−0.327775	−0.163887	−	0.986479i	$-0.552403\pi$
$71$	−196.093	−0.327775	−0.163887	+	0.986479i	$0.552403\pi$
$72$	131.882	0.215868
$73$	−469.740	−0.753136	−0.376568	−	0.926389i	$-0.622896\pi$
$73$	−469.740	−0.753136	−0.376568	+	0.926389i	$0.622896\pi$
$74$	425.200	0.667953
$75$	81.0660	0.124809
$76$	18.5097	0.0279369
$77$	0	0
$78$	−413.294	−0.599952
$79$	−1224.24	−1.74352	−0.871761	−	0.489931i	$-0.837022\pi$
$79$	−1224.24	−1.74352	−0.871761	+	0.489931i	$0.837022\pi$
$80$	80.0000	0.111803
$81$	−12.1329	−0.0166432
$82$	−542.122	−0.730090
$83$	−267.687	−0.354006	−0.177003	−	0.984210i	$-0.556640\pi$
$83$	−267.687	−0.354006	−0.177003	+	0.984210i	$0.556640\pi$
$84$	0	0
$85$	−585.208	−0.746762
$86$	−199.549	−0.250209
$87$	−404.757	−0.498788
$88$	194.510	0.235623
$89$	−589.677	−0.702311	−0.351155	−	0.936317i	$-0.614211\pi$
$89$	−589.677	−0.702311	−0.351155	+	0.936317i	$0.614211\pi$
$90$	164.853	0.193078
$91$	0	0
$92$	−659.342	−0.747187
$93$	291.209	0.324699
$94$	408.877	0.448643
$95$	23.1371	0.0249875
$96$	−103.765	−0.110317
$97$	−1223.38	−1.28057	−0.640287	−	0.768136i	$-0.721185\pi$
$97$	−1223.38	−1.28057	−0.640287	+	0.768136i	$0.721185\pi$
$98$	0	0
$99$	400.818	0.406907
$100$	100.000	0.100000
$101$	−750.270	−0.739155	−0.369577	−	0.929200i	$-0.620498\pi$
$101$	−750.270	−0.739155	−0.369577	+	0.929200i	$0.620498\pi$
$102$	759.048	0.736833
$103$	108.114	0.103425	0.0517125	−	0.998662i	$-0.483532\pi$
$103$	108.114	0.103425	0.0517125	+	0.998662i	$0.483532\pi$
$104$	−509.823	−0.480695
$105$	0	0
$106$	−850.053	−0.778910
$107$	1287.10	1.16289	0.581443	−	0.813587i	$-0.302488\pi$
$107$	1287.10	1.16289	0.581443	+	0.813587i	$0.302488\pi$
$108$	−564.029	−0.502534
$109$	−74.6063	−0.0655596	−0.0327798	−	0.999463i	$-0.510436\pi$
$109$	−74.6063	−0.0655596	−0.0327798	+	0.999463i	$0.510436\pi$
$110$	243.137	0.210747
$111$	−689.386	−0.589492
$112$	0	0
$113$	2228.55	1.85526	0.927628	−	0.373506i	$-0.121844\pi$
$113$	2228.55	1.85526	0.927628	+	0.373506i	$0.121844\pi$
$114$	−30.0101	−0.0246553
$115$	−824.178	−0.668304
$116$	−499.294	−0.399640
$117$	−1050.57	−0.830132
$118$	1144.87	0.893166
$119$	0	0
$120$	−129.706	−0.0986704
$121$	−739.844	−0.555855
$122$	617.637	0.458346
$123$	878.953	0.644330
$124$	359.225	0.260156
$125$	125.000	0.0894427
$126$	0	0
$127$	−74.9105	−0.0523404	−0.0261702	−	0.999658i	$-0.508331\pi$
$127$	−74.9105	−0.0523404	−0.0261702	+	0.999658i	$0.508331\pi$
$128$	−128.000	−0.0883883
$129$	323.533	0.220818
$130$	−637.279	−0.429947
$131$	−2698.76	−1.79994	−0.899969	−	0.435954i	$-0.856411\pi$
$131$	−2698.76	−1.79994	−0.899969	+	0.435954i	$0.856411\pi$
$132$	−315.362	−0.207945
$133$	0	0
$134$	−1234.58	−0.795907
$135$	−705.036	−0.449480
$136$	936.333	0.590367
$137$	−2607.88	−1.62632	−0.813161	−	0.582039i	$-0.802255\pi$
$137$	−2607.88	−1.62632	−0.813161	+	0.582039i	$0.802255\pi$
$138$	1069.01	0.659419
$139$	371.106	0.226452	0.113226	−	0.993569i	$-0.463882\pi$
$139$	371.106	0.226452	0.113226	+	0.993569i	$0.463882\pi$
$140$	0	0
$141$	−662.921	−0.395943
$142$	392.187	0.231772
$143$	−1549.46	−0.906102
$144$	−263.765	−0.152641
$145$	−624.117	−0.357449
$146$	939.480	0.532548
$147$	0	0
$148$	−850.400	−0.472314
$149$	−271.035	−0.149021	−0.0745103	−	0.997220i	$-0.523739\pi$
$149$	−271.035	−0.149021	−0.0745103	+	0.997220i	$0.523739\pi$
$150$	−162.132	−0.0882535
$151$	−3404.22	−1.83465	−0.917324	−	0.398141i	$-0.869655\pi$
$151$	−3404.22	−1.83465	−0.917324	+	0.398141i	$0.869655\pi$
$152$	−37.0193	−0.0197544
$153$	1929.46	1.01953
$154$	0	0
$155$	449.031	0.232690
$156$	826.587	0.424230
$157$	1104.18	0.561294	0.280647	−	0.959811i	$-0.409451\pi$
$157$	1104.18	0.561294	0.280647	+	0.959811i	$0.409451\pi$
$158$	2448.49	1.23286
$159$	1378.21	0.687415
$160$	−160.000	−0.0790569
$161$	0	0
$162$	24.2658	0.0117685
$163$	3485.12	1.67470	0.837349	−	0.546668i	$-0.184104\pi$
$163$	3485.12	1.67470	0.837349	+	0.546668i	$0.184104\pi$
$164$	1084.24	0.516251
$165$	−394.203	−0.185992
$166$	535.374	0.250320
$167$	−3276.75	−1.51834	−0.759169	−	0.650894i	$-0.774394\pi$
$167$	−3276.75	−1.51834	−0.759169	+	0.650894i	$0.774394\pi$
$168$	0	0
$169$	1864.25	0.848543
$170$	1170.42	0.528040
$171$	−76.2843	−0.0341146
$172$	399.098	0.176924
$173$	1713.08	0.752849	0.376425	−	0.926447i	$-0.377153\pi$
$173$	1713.08	0.752849	0.376425	+	0.926447i	$0.377153\pi$
$174$	809.515	0.352696
$175$	0	0
$176$	−389.019	−0.166610
$177$	−1856.20	−0.788250
$178$	1179.35	0.496609
$179$	3298.96	1.37752	0.688760	−	0.724989i	$-0.258155\pi$
$179$	3298.96	1.37752	0.688760	+	0.724989i	$0.258155\pi$
$180$	−329.706	−0.136527
$181$	3898.52	1.60096	0.800482	−	0.599357i	$-0.204577\pi$
$181$	3898.52	1.60096	0.800482	+	0.599357i	$0.204577\pi$
$182$	0	0
$183$	−1001.39	−0.404506
$184$	1318.68	0.528341
$185$	−1063.00	−0.422450
$186$	−582.418	−0.229597
$187$	2845.72	1.11283
$188$	−817.754	−0.317239
$189$	0	0
$190$	−46.2742	−0.0176688
$191$	−2677.70	−1.01441	−0.507203	−	0.861827i	$-0.669321\pi$
$191$	−2677.70	−1.01441	−0.507203	+	0.861827i	$0.669321\pi$
$192$	207.529	0.0780058
$193$	−2682.80	−1.00058	−0.500290	−	0.865858i	$-0.666773\pi$
$193$	−2682.80	−1.00058	−0.500290	+	0.865858i	$0.666773\pi$
$194$	2446.77	0.905503
$195$	1033.23	0.379443
$196$	0	0
$197$	3001.92	1.08567	0.542837	−	0.839838i	$-0.317350\pi$
$197$	3001.92	1.08567	0.542837	+	0.839838i	$0.317350\pi$
$198$	−801.637	−0.287726
$199$	2886.12	1.02810	0.514049	−	0.857761i	$-0.328145\pi$
$199$	2886.12	1.02810	0.514049	+	0.857761i	$0.328145\pi$
$200$	−200.000	−0.0707107
$201$	2001.65	0.702416
$202$	1500.54	0.522662
$203$	0	0
$204$	−1518.10	−0.521019
$205$	1355.30	0.461749
$206$	−216.228	−0.0731326
$207$	2717.36	0.912414
$208$	1019.65	0.339903
$209$	−112.510	−0.0372366
$210$	0	0
$211$	4152.02	1.35468	0.677338	−	0.735672i	$-0.263133\pi$
$211$	4152.02	1.35468	0.677338	+	0.735672i	$0.263133\pi$
$212$	1700.11	0.550772
$213$	−635.860	−0.204547
$214$	−2574.21	−0.822285
$215$	498.873	0.158246
$216$	1128.06	0.355345
$217$	0	0
$218$	149.213	0.0463576
$219$	−1523.20	−0.469992
$220$	−486.274	−0.149021
$221$	−7458.82	−2.27029
$222$	1378.77	0.416834
$223$	−2095.59	−0.629286	−0.314643	−	0.949210i	$-0.601885\pi$
$223$	−2095.59	−0.629286	−0.314643	+	0.949210i	$0.601885\pi$
$224$	0	0
$225$	−412.132	−0.122113
$226$	−4457.09	−1.31186
$227$	4453.95	1.30229	0.651143	−	0.758955i	$-0.274290\pi$
$227$	4453.95	1.30229	0.651143	+	0.758955i	$0.274290\pi$
$228$	60.0202	0.0174339
$229$	1004.93	0.289989	0.144995	−	0.989432i	$-0.453684\pi$
$229$	1004.93	0.289989	0.144995	+	0.989432i	$0.453684\pi$
$230$	1648.36	0.472562
$231$	0	0
$232$	998.587	0.282588
$233$	411.693	0.115755	0.0578775	−	0.998324i	$-0.481567\pi$
$233$	411.693	0.115755	0.0578775	+	0.998324i	$0.481567\pi$
$234$	2101.15	0.586992
$235$	−1022.19	−0.283747
$236$	−2289.73	−0.631564
$237$	−3969.79	−1.08804
$238$	0	0
$239$	4958.48	1.34200	0.670998	−	0.741459i	$-0.265866\pi$
$239$	4958.48	1.34200	0.670998	+	0.741459i	$0.265866\pi$
$240$	259.411	0.0697705
$241$	3373.18	0.901601	0.450801	−	0.892625i	$-0.351139\pi$
$241$	3373.18	0.901601	0.450801	+	0.892625i	$0.351139\pi$
$242$	1479.69	0.393049
$243$	3767.85	0.994682
$244$	−1235.27	−0.324099
$245$	0	0
$246$	−1757.91	−0.455610
$247$	294.896	0.0759666
$248$	−718.449	−0.183958
$249$	−868.013	−0.220916
$250$	−250.000	−0.0632456
$251$	766.800	0.192829	0.0964143	−	0.995341i	$-0.469263\pi$
$251$	766.800	0.192829	0.0964143	+	0.995341i	$0.469263\pi$
$252$	0	0
$253$	4007.76	0.995913
$254$	149.821	0.0370102
$255$	−1897.62	−0.466014
$256$	256.000	0.0625000
$257$	6761.96	1.64124	0.820621	−	0.571472i	$-0.193628\pi$
$257$	6761.96	1.64124	0.820621	+	0.571472i	$0.193628\pi$
$258$	−647.066	−0.156142
$259$	0	0
$260$	1274.56	0.304018
$261$	2057.75	0.488013
$262$	5397.52	1.27275
$263$	−1820.07	−0.426731	−0.213366	−	0.976972i	$-0.568443\pi$
$263$	−1820.07	−0.426731	−0.213366	+	0.976972i	$0.568443\pi$
$264$	630.725	0.147040
$265$	2125.13	0.492626
$266$	0	0
$267$	−1912.11	−0.438274
$268$	2469.16	0.562791
$269$	−5727.76	−1.29824	−0.649122	−	0.760684i	$-0.724864\pi$
$269$	−5727.76	−1.29824	−0.649122	+	0.760684i	$0.724864\pi$
$270$	1410.07	0.317830
$271$	−1201.85	−0.269399	−0.134699	−	0.990887i	$-0.543007\pi$
$271$	−1201.85	−0.269399	−0.134699	+	0.990887i	$0.543007\pi$
$272$	−1872.67	−0.417452
$273$	0	0
$274$	5215.76	1.14998
$275$	−607.843	−0.133288
$276$	−2138.01	−0.466279
$277$	3701.06	0.802798	0.401399	−	0.915903i	$-0.368524\pi$
$277$	3701.06	0.802798	0.401399	+	0.915903i	$0.368524\pi$
$278$	−742.211	−0.160125
$279$	−1480.48	−0.317685
$280$	0	0
$281$	−8844.94	−1.87774	−0.938870	−	0.344272i	$-0.888126\pi$
$281$	−8844.94	−1.87774	−0.938870	+	0.344272i	$0.888126\pi$
$282$	1325.84	0.279974
$283$	−607.698	−0.127646	−0.0638231	−	0.997961i	$-0.520329\pi$
$283$	−607.698	−0.127646	−0.0638231	+	0.997961i	$0.520329\pi$
$284$	−784.373	−0.163887
$285$	75.0253	0.0155934
$286$	3098.92	0.640711
$287$	0	0
$288$	527.529	0.107934
$289$	8785.74	1.78826
$290$	1248.23	0.252755
$291$	−3966.99	−0.799138
$292$	−1878.96	−0.376568
$293$	4088.98	0.815293	0.407646	−	0.913140i	$-0.366350\pi$
$293$	4088.98	0.815293	0.407646	+	0.913140i	$0.366350\pi$
$294$	0	0
$295$	−2862.17	−0.564888
$296$	1700.80	0.333976
$297$	3428.41	0.669819
$298$	542.071	0.105374
$299$	−10504.6	−2.03177
$300$	324.264	0.0624046
$301$	0	0
$302$	6808.45	1.29729
$303$	−2432.86	−0.461267
$304$	74.0387	0.0139685
$305$	−1544.09	−0.289883
$306$	−3858.93	−0.720916
$307$	−3404.74	−0.632961	−0.316480	−	0.948599i	$-0.602501\pi$
$307$	−3404.74	−0.632961	−0.316480	+	0.948599i	$0.602501\pi$
$308$	0	0
$309$	350.575	0.0645420
$310$	−898.061	−0.164537
$311$	−8205.86	−1.49618	−0.748089	−	0.663598i	$-0.769029\pi$
$311$	−8205.86	−1.49618	−0.748089	+	0.663598i	$0.769029\pi$
$312$	−1653.17	−0.299976
$313$	4987.57	0.900683	0.450342	−	0.892856i	$-0.351302\pi$
$313$	4987.57	0.900683	0.450342	+	0.892856i	$0.351302\pi$
$314$	−2208.36	−0.396894
$315$	0	0
$316$	−4896.98	−0.871761
$317$	−3497.97	−0.619766	−0.309883	−	0.950775i	$-0.600290\pi$
$317$	−3497.97	−0.619766	−0.309883	+	0.950775i	$0.600290\pi$
$318$	−2756.42	−0.486076
$319$	3034.92	0.532674
$320$	320.000	0.0559017
$321$	4173.61	0.725696
$322$	0	0
$323$	−541.600	−0.0932986
$324$	−48.5316	−0.00832161
$325$	1593.20	0.271922
$326$	−6970.24	−1.18419
$327$	−241.922	−0.0409122
$328$	−2168.49	−0.365045
$329$	0	0
$330$	788.406	0.131516
$331$	−2037.86	−0.338401	−0.169201	−	0.985582i	$-0.554119\pi$
$331$	−2037.86	−0.338401	−0.169201	+	0.985582i	$0.554119\pi$
$332$	−1070.75	−0.177003
$333$	3504.77	0.576758
$334$	6553.50	1.07363
$335$	3086.45	0.503376
$336$	0	0
$337$	2485.67	0.401789	0.200895	−	0.979613i	$-0.435615\pi$
$337$	2485.67	0.401789	0.200895	+	0.979613i	$0.435615\pi$
$338$	−3728.50	−0.600010
$339$	7226.37	1.15777
$340$	−2340.83	−0.373381
$341$	−2183.52	−0.346757
$342$	152.569	0.0241227
$343$	0	0
$344$	−798.197	−0.125104
$345$	−2672.51	−0.417053
$346$	−3426.16	−0.532345
$347$	9528.26	1.47407	0.737037	−	0.675852i	$-0.236224\pi$
$347$	9528.26	1.47407	0.737037	+	0.675852i	$0.236224\pi$
$348$	−1619.03	−0.249394
$349$	−4483.13	−0.687611	−0.343806	−	0.939041i	$-0.611716\pi$
$349$	−4483.13	−0.687611	−0.343806	+	0.939041i	$0.611716\pi$
$350$	0	0
$351$	−8986.09	−1.36650
$352$	778.039	0.117811
$353$	3883.60	0.585562	0.292781	−	0.956180i	$-0.405419\pi$
$353$	3883.60	0.585562	0.292781	+	0.956180i	$0.405419\pi$
$354$	3712.39	0.557377
$355$	−980.467	−0.146585
$356$	−2358.71	−0.351155
$357$	0	0
$358$	−6597.93	−0.974054
$359$	4434.66	0.651956	0.325978	−	0.945377i	$-0.394306\pi$
$359$	4434.66	0.651956	0.325978	+	0.945377i	$0.394306\pi$
$360$	659.411	0.0965390
$361$	−6837.59	−0.996878
$362$	−7797.03	−1.13205
$363$	−2399.05	−0.346880
$364$	0	0
$365$	−2348.70	−0.336813
$366$	2002.77	0.286029
$367$	−5831.80	−0.829475	−0.414737	−	0.909941i	$-0.636127\pi$
$367$	−5831.80	−0.829475	−0.414737	+	0.909941i	$0.636127\pi$
$368$	−2637.37	−0.373593
$369$	−4468.52	−0.630411
$370$	2126.00	0.298718
$371$	0	0
$372$	1164.84	0.162349
$373$	11041.6	1.53274	0.766370	−	0.642399i	$-0.222061\pi$
$373$	11041.6	1.53274	0.766370	+	0.642399i	$0.222061\pi$
$374$	−5691.43	−0.786890
$375$	405.330	0.0558164
$376$	1635.51	0.224322
$377$	−7954.73	−1.08671
$378$	0	0
$379$	−12987.9	−1.76027	−0.880134	−	0.474725i	$-0.842548\pi$
$379$	−12987.9	−1.76027	−0.880134	+	0.474725i	$0.842548\pi$
$380$	92.5483	0.0124938
$381$	−242.908	−0.0326628
$382$	5355.40	0.717294
$383$	−11469.8	−1.53024	−0.765118	−	0.643890i	$-0.777319\pi$
$383$	−11469.8	−1.53024	−0.765118	+	0.643890i	$0.777319\pi$
$384$	−415.058	−0.0551584
$385$	0	0
$386$	5365.60	0.707517
$387$	−1644.81	−0.216048
$388$	−4893.53	−0.640287
$389$	898.523	0.117113	0.0585565	−	0.998284i	$-0.481350\pi$
$389$	898.523	0.117113	0.0585565	+	0.998284i	$0.481350\pi$
$390$	−2066.47	−0.268307
$391$	19292.6	2.49532
$392$	0	0
$393$	−8751.11	−1.12324
$394$	−6003.84	−0.767688
$395$	−6121.22	−0.779727
$396$	1603.27	0.203453
$397$	13563.5	1.71470	0.857348	−	0.514738i	$-0.172111\pi$
$397$	13563.5	1.71470	0.857348	+	0.514738i	$0.172111\pi$
$398$	−5772.24	−0.726975
$399$	0	0
$400$	400.000	0.0500000
$401$	−2635.72	−0.328234	−0.164117	−	0.986441i	$-0.552477\pi$
$401$	−2635.72	−0.328234	−0.164117	+	0.986441i	$0.552477\pi$
$402$	−4003.30	−0.496683
$403$	5723.16	0.707421
$404$	−3001.08	−0.369577
$405$	−60.6645	−0.00744307
$406$	0	0
$407$	5169.10	0.629540
$408$	3036.19	0.368416
$409$	12894.9	1.55895	0.779474	−	0.626435i	$-0.215487\pi$
$409$	12894.9	1.55895	0.779474	+	0.626435i	$0.215487\pi$
$410$	−2710.61	−0.326506
$411$	−8456.41	−1.01490
$412$	432.456	0.0517125
$413$	0	0
$414$	−5434.72	−0.645174
$415$	−1338.44	−0.158316
$416$	−2039.29	−0.240348
$417$	1203.36	0.141316
$418$	225.019	0.0263303
$419$	−11846.7	−1.38127	−0.690633	−	0.723205i	$-0.742668\pi$
$419$	−11846.7	−1.38127	−0.690633	+	0.723205i	$0.742668\pi$
$420$	0	0
$421$	−8050.80	−0.932000	−0.466000	−	0.884785i	$-0.654305\pi$
$421$	−8050.80	−0.932000	−0.466000	+	0.884785i	$0.654305\pi$
$422$	−8304.04	−0.957901
$423$	3370.23	0.387390
$424$	−3400.21	−0.389455
$425$	−2926.04	−0.333962
$426$	1271.72	0.144636
$427$	0	0
$428$	5148.41	0.581443
$429$	−5024.35	−0.565450
$430$	−997.746	−0.111897
$431$	16812.8	1.87899	0.939494	−	0.342566i	$-0.111296\pi$
$431$	16812.8	1.87899	0.939494	+	0.342566i	$0.111296\pi$
$432$	−2256.11	−0.251267
$433$	−8707.65	−0.966427	−0.483214	−	0.875503i	$-0.660531\pi$
$433$	−8707.65	−0.966427	−0.483214	+	0.875503i	$0.660531\pi$
$434$	0	0
$435$	−2023.79	−0.223065
$436$	−298.425	−0.0327798
$437$	−762.763	−0.0834963
$438$	3046.40	0.332334
$439$	−6131.90	−0.666650	−0.333325	−	0.942812i	$-0.608171\pi$
$439$	−6131.90	−0.666650	−0.333325	+	0.942812i	$0.608171\pi$
$440$	972.548	0.105374
$441$	0	0
$442$	14917.6	1.60534
$443$	−10336.6	−1.10859	−0.554297	−	0.832319i	$-0.687013\pi$
$443$	−10336.6	−1.10859	−0.554297	+	0.832319i	$0.687013\pi$
$444$	−2757.54	−0.294746
$445$	−2948.39	−0.314083
$446$	4191.17	0.444972
$447$	−878.870	−0.0929958
$448$	0	0
$449$	15534.7	1.63280	0.816401	−	0.577485i	$-0.195966\pi$
$449$	15534.7	1.63280	0.816401	+	0.577485i	$0.195966\pi$
$450$	824.264	0.0863471
$451$	−6590.50	−0.688103
$452$	8914.18	0.927628
$453$	−11038.7	−1.14491
$454$	−8907.90	−0.920855
$455$	0	0
$456$	−120.040	−0.0123276
$457$	459.342	0.0470178	0.0235089	−	0.999724i	$-0.492516\pi$
$457$	459.342	0.0470178	0.0235089	+	0.999724i	$0.492516\pi$
$458$	−2009.86	−0.205053
$459$	16503.7	1.67827
$460$	−3296.71	−0.334152
$461$	8306.54	0.839207	0.419603	−	0.907708i	$-0.362169\pi$
$461$	8306.54	0.839207	0.419603	+	0.907708i	$0.362169\pi$
$462$	0	0
$463$	935.895	0.0939411	0.0469706	−	0.998896i	$-0.485043\pi$
$463$	935.895	0.0939411	0.0469706	+	0.998896i	$0.485043\pi$
$464$	−1997.17	−0.199820
$465$	1456.05	0.145210
$466$	−823.386	−0.0818511
$467$	5081.17	0.503487	0.251743	−	0.967794i	$-0.418996\pi$
$467$	5081.17	0.503487	0.251743	+	0.967794i	$0.418996\pi$
$468$	−4202.29	−0.415066
$469$	0	0
$470$	2044.39	0.200639
$471$	3580.46	0.350273
$472$	4579.47	0.446583
$473$	−2425.89	−0.235819
$474$	7939.57	0.769360
$475$	115.685	0.0111748
$476$	0	0
$477$	−7006.68	−0.672566
$478$	−9916.95	−0.948935
$479$	−6898.70	−0.658058	−0.329029	−	0.944320i	$-0.606721\pi$
$479$	−6898.70	−0.658058	−0.329029	+	0.944320i	$0.606721\pi$
$480$	−518.823	−0.0493352
$481$	−13548.6	−1.28433
$482$	−6746.37	−0.637528
$483$	0	0
$484$	−2959.37	−0.277928
$485$	−6116.92	−0.572690
$486$	−7535.70	−0.703346
$487$	13423.5	1.24903	0.624514	−	0.781014i	$-0.285297\pi$
$487$	13423.5	1.24903	0.624514	+	0.781014i	$0.285297\pi$
$488$	2470.55	0.229173
$489$	11301.0	1.04509
$490$	0	0
$491$	3756.18	0.345242	0.172621	−	0.984988i	$-0.444776\pi$
$491$	3756.18	0.345242	0.172621	+	0.984988i	$0.444776\pi$
$492$	3515.81	0.322165
$493$	14609.5	1.33465
$494$	−589.791	−0.0537165
$495$	2004.09	0.181974
$496$	1436.90	0.130078
$497$	0	0
$498$	1736.03	0.156211
$499$	5839.50	0.523871	0.261936	−	0.965085i	$-0.415639\pi$
$499$	5839.50	0.523871	0.261936	+	0.965085i	$0.415639\pi$
$500$	500.000	0.0447214
$501$	−10625.3	−0.947513
$502$	−1533.60	−0.136350
$503$	8622.79	0.764356	0.382178	−	0.924089i	$-0.375174\pi$
$503$	8622.79	0.764356	0.382178	+	0.924089i	$0.375174\pi$
$504$	0	0
$505$	−3751.35	−0.330560
$506$	−8015.53	−0.704217
$507$	6045.09	0.529530
$508$	−299.642	−0.0261702
$509$	15809.6	1.37672	0.688359	−	0.725371i	$-0.258332\pi$
$509$	15809.6	1.37672	0.688359	+	0.725371i	$0.258332\pi$
$510$	3795.24	0.329522
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−652.499	−0.0561570
$514$	−13523.9	−1.16053
$515$	540.570	0.0462531
$516$	1294.13	0.110409
$517$	4970.66	0.422842
$518$	0	0
$519$	5554.90	0.469813
$520$	−2549.12	−0.214973
$521$	−19295.3	−1.62254	−0.811269	−	0.584673i	$-0.801223\pi$
$521$	−19295.3	−1.62254	−0.811269	+	0.584673i	$0.801223\pi$
$522$	−4115.50	−0.345077
$523$	−6167.58	−0.515658	−0.257829	−	0.966191i	$-0.583007\pi$
$523$	−6167.58	−0.515658	−0.257829	+	0.966191i	$0.583007\pi$
$524$	−10795.0	−0.899969
$525$	0	0
$526$	3640.14	0.301745
$527$	−10511.1	−0.868821
$528$	−1261.45	−0.103973
$529$	15003.8	1.23315
$530$	−4250.26	−0.348339
$531$	9436.73	0.771222
$532$	0	0
$533$	17274.2	1.40380
$534$	3824.22	0.309907
$535$	6435.51	0.520059
$536$	−4938.32	−0.397954
$537$	10697.4	0.859637
$538$	11455.5	0.917997
$539$	0	0
$540$	−2820.14	−0.224740
$541$	19451.4	1.54581	0.772905	−	0.634522i	$-0.218803\pi$
$541$	19451.4	1.54581	0.772905	+	0.634522i	$0.218803\pi$
$542$	2403.70	0.190494
$543$	12641.5	0.999075
$544$	3745.33	0.295183
$545$	−373.032	−0.0293191
$546$	0	0
$547$	−25004.2	−1.95449	−0.977243	−	0.212122i	$-0.931963\pi$
$547$	−25004.2	−1.95449	−0.977243	+	0.212122i	$0.931963\pi$
$548$	−10431.5	−0.813161
$549$	5090.96	0.395768
$550$	1215.69	0.0942491
$551$	−577.610	−0.0446588
$552$	4276.02	0.329709
$553$	0	0
$554$	−7402.12	−0.567664
$555$	−3446.93	−0.263629
$556$	1484.42	0.113226
$557$	11384.2	0.866002	0.433001	−	0.901393i	$-0.357455\pi$
$557$	11384.2	0.866002	0.433001	+	0.901393i	$0.357455\pi$
$558$	2960.96	0.224637
$559$	6358.43	0.481096
$560$	0	0
$561$	9227.63	0.694458
$562$	17689.9	1.32776
$563$	5912.06	0.442564	0.221282	−	0.975210i	$-0.428976\pi$
$563$	5912.06	0.442564	0.221282	+	0.975210i	$0.428976\pi$
$564$	−2651.68	−0.197972
$565$	11142.7	0.829696
$566$	1215.40	0.0902595
$567$	0	0
$568$	1568.75	0.115886
$569$	−2145.68	−0.158087	−0.0790436	−	0.996871i	$-0.525187\pi$
$569$	−2145.68	−0.158087	−0.0790436	+	0.996871i	$0.525187\pi$
$570$	−150.051	−0.0110262
$571$	−10587.1	−0.775932	−0.387966	−	0.921674i	$-0.626822\pi$
$571$	−10587.1	−0.775932	−0.387966	+	0.921674i	$0.626822\pi$
$572$	−6197.85	−0.453051
$573$	−8682.82	−0.633037
$574$	0	0
$575$	−4120.89	−0.298875
$576$	−1055.06	−0.0763207
$577$	9283.05	0.669772	0.334886	−	0.942259i	$-0.391302\pi$
$577$	9283.05	0.669772	0.334886	+	0.942259i	$0.391302\pi$
$578$	−17571.5	−1.26449
$579$	−8699.35	−0.624409
$580$	−2496.47	−0.178724
$581$	0	0
$582$	7933.98	0.565076
$583$	−10334.0	−0.734115
$584$	3757.92	0.266274
$585$	−5252.86	−0.371246
$586$	−8177.96	−0.576499
$587$	−25588.2	−1.79921	−0.899607	−	0.436700i	$-0.856147\pi$
$587$	−25588.2	−1.79921	−0.899607	+	0.436700i	$0.856147\pi$
$588$	0	0
$589$	415.570	0.0290718
$590$	5724.34	0.399436
$591$	9734.14	0.677511
$592$	−3401.60	−0.236157
$593$	4541.25	0.314480	0.157240	−	0.987560i	$-0.449740\pi$
$593$	4541.25	0.314480	0.157240	+	0.987560i	$0.449740\pi$
$594$	−6856.81	−0.473634
$595$	0	0
$596$	−1084.14	−0.0745103
$597$	9358.65	0.641581
$598$	21009.3	1.43668
$599$	−26756.2	−1.82509	−0.912546	−	0.408973i	$-0.865887\pi$
$599$	−26756.2	−1.82509	−0.912546	+	0.408973i	$0.865887\pi$
$600$	−648.528	−0.0441268
$601$	−7557.44	−0.512936	−0.256468	−	0.966553i	$-0.582559\pi$
$601$	−7557.44	−0.512936	−0.256468	+	0.966553i	$0.582559\pi$
$602$	0	0
$603$	−10176.2	−0.687243
$604$	−13616.9	−0.917324
$605$	−3699.22	−0.248586
$606$	4865.71	0.326165
$607$	−1498.02	−0.100169	−0.0500847	−	0.998745i	$-0.515949\pi$
$607$	−1498.02	−0.100169	−0.0500847	+	0.998745i	$0.515949\pi$
$608$	−148.077	−0.00987719
$609$	0	0
$610$	3088.18	0.204979
$611$	−13028.4	−0.862642
$612$	7717.86	0.509764
$613$	−10860.5	−0.715583	−0.357791	−	0.933802i	$-0.616470\pi$
$613$	−10860.5	−0.715583	−0.357791	+	0.933802i	$0.616470\pi$
$614$	6809.48	0.447571
$615$	4394.77	0.288153
$616$	0	0
$617$	1328.60	0.0866898	0.0433449	−	0.999060i	$-0.486199\pi$
$617$	1328.60	0.0866898	0.0433449	+	0.999060i	$0.486199\pi$
$618$	−701.149	−0.0456381
$619$	−14301.7	−0.928647	−0.464323	−	0.885666i	$-0.653702\pi$
$619$	−14301.7	−0.928647	−0.464323	+	0.885666i	$0.653702\pi$
$620$	1796.12	0.116345
$621$	23243.0	1.50195
$622$	16411.7	1.05796
$623$	0	0
$624$	3306.35	0.212115
$625$	625.000	0.0400000
$626$	−9975.13	−0.636879
$627$	−364.828	−0.0232374
$628$	4416.72	0.280647
$629$	24883.1	1.57735
$630$	0	0
$631$	−25272.8	−1.59444	−0.797222	−	0.603686i	$-0.793698\pi$
$631$	−25272.8	−1.59444	−0.797222	+	0.603686i	$0.793698\pi$
$632$	9793.96	0.616428
$633$	13463.5	0.845381
$634$	6995.95	0.438241
$635$	−374.552	−0.0234073
$636$	5512.83	0.343708
$637$	0	0
$638$	−6069.84	−0.376657
$639$	3232.65	0.200128
$640$	−640.000	−0.0395285
$641$	−12803.4	−0.788930	−0.394465	−	0.918911i	$-0.629070\pi$
$641$	−12803.4	−0.788930	−0.394465	+	0.918911i	$0.629070\pi$
$642$	−8347.22	−0.513144
$643$	11483.6	0.704309	0.352154	−	0.935942i	$-0.385449\pi$
$643$	11483.6	0.704309	0.352154	+	0.935942i	$0.385449\pi$
$644$	0	0
$645$	1617.67	0.0987528
$646$	1083.20	0.0659721
$647$	−28418.8	−1.72683	−0.863414	−	0.504496i	$-0.831678\pi$
$647$	−28418.8	−1.72683	−0.863414	+	0.504496i	$0.831678\pi$
$648$	97.0632	0.00588426
$649$	13918.0	0.841801
$650$	−3186.40	−0.192278
$651$	0	0
$652$	13940.5	0.837349
$653$	8279.99	0.496204	0.248102	−	0.968734i	$-0.420193\pi$
$653$	8279.99	0.496204	0.248102	+	0.968734i	$0.420193\pi$
$654$	483.843	0.0289293
$655$	−13493.8	−0.804957
$656$	4336.98	0.258126
$657$	7743.80	0.459839
$658$	0	0
$659$	9029.94	0.533773	0.266887	−	0.963728i	$-0.414005\pi$
$659$	9029.94	0.533773	0.266887	+	0.963728i	$0.414005\pi$
$660$	−1576.81	−0.0929960
$661$	−1301.94	−0.0766105	−0.0383053	−	0.999266i	$-0.512196\pi$
$661$	−1301.94	−0.0766105	−0.0383053	+	0.999266i	$0.512196\pi$
$662$	4075.72	0.239286
$663$	−24186.3	−1.41677
$664$	2141.50	0.125160
$665$	0	0
$666$	−7009.54	−0.407829
$667$	20575.3	1.19442
$668$	−13107.0	−0.759169
$669$	−6795.23	−0.392704
$670$	−6172.91	−0.355941
$671$	7508.52	0.431987
$672$	0	0
$673$	6881.43	0.394145	0.197073	−	0.980389i	$-0.436857\pi$
$673$	6881.43	0.394145	0.197073	+	0.980389i	$0.436857\pi$
$674$	−4971.34	−0.284108
$675$	−3525.18	−0.201014
$676$	7456.99	0.424271
$677$	17113.9	0.971553	0.485777	−	0.874083i	$-0.338537\pi$
$677$	17113.9	0.971553	0.485777	+	0.874083i	$0.338537\pi$
$678$	−14452.7	−0.818664
$679$	0	0
$680$	4681.67	0.264020
$681$	14442.6	0.812687
$682$	4367.04	0.245194
$683$	−24996.9	−1.40041	−0.700204	−	0.713942i	$-0.746908\pi$
$683$	−24996.9	−1.40041	−0.700204	+	0.713942i	$0.746908\pi$
$684$	−305.137	−0.0170573
$685$	−13039.4	−0.727313
$686$	0	0
$687$	3258.62	0.180967
$688$	1596.39	0.0884621
$689$	27086.1	1.49767
$690$	5345.03	0.294901
$691$	10367.5	0.570762	0.285381	−	0.958414i	$-0.407880\pi$
$691$	10367.5	0.570762	0.285381	+	0.958414i	$0.407880\pi$
$692$	6852.31	0.376425
$693$	0	0
$694$	−19056.5	−1.04233
$695$	1855.53	0.101272
$696$	3238.06	0.176348
$697$	−31725.4	−1.72408
$698$	8966.25	0.486214
$699$	1334.97	0.0722365
$700$	0	0
$701$	33425.5	1.80095	0.900474	−	0.434910i	$-0.143220\pi$
$701$	33425.5	1.80095	0.900474	+	0.434910i	$0.143220\pi$
$702$	17972.2	0.966263
$703$	−983.789	−0.0527800
$704$	−1556.08	−0.0833052
$705$	−3314.60	−0.177071
$706$	−7767.21	−0.414055
$707$	0	0
$708$	−7424.79	−0.394125
$709$	24659.5	1.30622	0.653108	−	0.757265i	$-0.273465\pi$
$709$	24659.5	1.30622	0.653108	+	0.757265i	$0.273465\pi$
$710$	1960.93	0.103651
$711$	20182.0	1.06454
$712$	4717.42	0.248304
$713$	−14803.2	−0.777540
$714$	0	0
$715$	−7747.31	−0.405221
$716$	13195.9	0.688760
$717$	16078.6	0.837468
$718$	−8869.32	−0.461003
$719$	−6019.08	−0.312203	−0.156101	−	0.987741i	$-0.549893\pi$
$719$	−6019.08	−0.312203	−0.156101	+	0.987741i	$0.549893\pi$
$720$	−1318.82	−0.0682634
$721$	0	0
$722$	13675.2	0.704899
$723$	10938.0	0.562641
$724$	15594.1	0.800482
$725$	−3120.58	−0.159856
$726$	4798.09	0.245281
$727$	−34300.8	−1.74986	−0.874929	−	0.484251i	$-0.839092\pi$
$727$	−34300.8	−1.74986	−0.874929	+	0.484251i	$0.839092\pi$
$728$	0	0
$729$	12545.4	0.637371
$730$	4697.40	0.238162
$731$	−11677.8	−0.590860
$732$	−4005.55	−0.202253
$733$	9451.64	0.476268	0.238134	−	0.971232i	$-0.423464\pi$
$733$	9451.64	0.476268	0.238134	+	0.971232i	$0.423464\pi$
$734$	11663.6	0.586527
$735$	0	0
$736$	5274.74	0.264170
$737$	−15008.6	−0.750135
$738$	8937.03	0.445768
$739$	5851.60	0.291278	0.145639	−	0.989338i	$-0.453476\pi$
$739$	5851.60	0.291278	0.145639	+	0.989338i	$0.453476\pi$
$740$	−4252.00	−0.211225
$741$	956.241	0.0474067
$742$	0	0
$743$	4909.31	0.242403	0.121201	−	0.992628i	$-0.461325\pi$
$743$	4909.31	0.242403	0.121201	+	0.992628i	$0.461325\pi$
$744$	−2329.67	−0.114798
$745$	−1355.18	−0.0666441
$746$	−22083.2	−1.08381
$747$	4412.90	0.216144
$748$	11382.9	0.556415
$749$	0	0
$750$	−810.660	−0.0394682
$751$	−15155.1	−0.736376	−0.368188	−	0.929751i	$-0.620022\pi$
$751$	−15155.1	−0.736376	−0.368188	+	0.929751i	$0.620022\pi$
$752$	−3271.02	−0.158619
$753$	2486.46	0.120334
$754$	15909.5	0.768420
$755$	−17021.1	−0.820480
$756$	0	0
$757$	−9211.81	−0.442284	−0.221142	−	0.975242i	$-0.570978\pi$
$757$	−9211.81	−0.442284	−0.221142	+	0.975242i	$0.570978\pi$
$758$	25975.7	1.24470
$759$	12995.7	0.621496
$760$	−185.097	−0.00883442
$761$	−1057.10	−0.0503546	−0.0251773	−	0.999683i	$-0.508015\pi$
$761$	−1057.10	−0.0503546	−0.0251773	+	0.999683i	$0.508015\pi$
$762$	485.815	0.0230961
$763$	0	0
$764$	−10710.8	−0.507203
$765$	9647.32	0.455947
$766$	22939.6	1.08204
$767$	−36480.0	−1.71736
$768$	830.116	0.0390029
$769$	−15117.5	−0.708908	−0.354454	−	0.935073i	$-0.615333\pi$
$769$	−15117.5	−0.708908	−0.354454	+	0.935073i	$0.615333\pi$
$770$	0	0
$771$	21926.6	1.02421
$772$	−10731.2	−0.500290
$773$	−15050.5	−0.700294	−0.350147	−	0.936695i	$-0.613868\pi$
$773$	−15050.5	−0.700294	−0.350147	+	0.936695i	$0.613868\pi$
$774$	3289.62	0.152769
$775$	2245.15	0.104062
$776$	9787.06	0.452751
$777$	0	0
$778$	−1797.05	−0.0828113
$779$	1254.31	0.0576899
$780$	4132.94	0.189722
$781$	4767.76	0.218443
$782$	−38585.2	−1.76446
$783$	17601.0	0.803331
$784$	0	0
$785$	5520.90	0.251018
$786$	17502.2	0.794254
$787$	−33466.2	−1.51581	−0.757905	−	0.652365i	$-0.773777\pi$
$787$	−33466.2	−1.51581	−0.757905	+	0.652365i	$0.773777\pi$
$788$	12007.7	0.542837
$789$	−5901.84	−0.266300
$790$	12242.4	0.551350
$791$	0	0
$792$	−3206.55	−0.143863
$793$	−19680.4	−0.881299
$794$	−27127.1	−1.21247
$795$	6891.04	0.307421
$796$	11544.5	0.514049
$797$	−18349.6	−0.815530	−0.407765	−	0.913087i	$-0.633692\pi$
$797$	−18349.6	−0.815530	−0.407765	+	0.913087i	$0.633692\pi$
$798$	0	0
$799$	23927.8	1.05946
$800$	−800.000	−0.0353553
$801$	9720.99	0.428807
$802$	5271.44	0.232096
$803$	11421.1	0.501921
$804$	8006.61	0.351208
$805$	0	0
$806$	−11446.3	−0.500222
$807$	−18573.1	−0.810165
$808$	6002.16	0.261331
$809$	−33860.7	−1.47154	−0.735772	−	0.677229i	$-0.763181\pi$
$809$	−33860.7	−1.47154	−0.735772	+	0.677229i	$0.763181\pi$
$810$	121.329	0.00526305
$811$	−37993.5	−1.64505	−0.822524	−	0.568731i	$-0.807435\pi$
$811$	−37993.5	−1.64505	−0.822524	+	0.568731i	$0.807435\pi$
$812$	0	0
$813$	−3897.16	−0.168117
$814$	−10338.2	−0.445152
$815$	17425.6	0.748948
$816$	−6072.38	−0.260510
$817$	461.699	0.0197709
$818$	−25789.7	−1.10234
$819$	0	0
$820$	5421.22	0.230875
$821$	14338.0	0.609500	0.304750	−	0.952432i	$-0.401427\pi$
$821$	14338.0	0.609500	0.304750	+	0.952432i	$0.401427\pi$
$822$	16912.8	0.717643
$823$	29831.4	1.26350	0.631748	−	0.775174i	$-0.282338\pi$
$823$	29831.4	1.26350	0.631748	+	0.775174i	$0.282338\pi$
$824$	−864.911	−0.0365663
$825$	−1971.02	−0.0831781
$826$	0	0
$827$	−3025.94	−0.127234	−0.0636168	−	0.997974i	$-0.520264\pi$
$827$	−3025.94	−0.127234	−0.0636168	+	0.997974i	$0.520264\pi$
$828$	10869.4	0.456207
$829$	2692.48	0.112803	0.0564015	−	0.998408i	$-0.482037\pi$
$829$	2692.48	0.112803	0.0564015	+	0.998408i	$0.482037\pi$
$830$	2676.87	0.111946
$831$	12001.2	0.500984
$832$	4078.59	0.169951
$833$	0	0
$834$	−2406.72	−0.0999257
$835$	−16383.7	−0.679021
$836$	−450.039	−0.0186183
$837$	−12663.3	−0.522948
$838$	23693.5	0.976703
$839$	8331.82	0.342844	0.171422	−	0.985198i	$-0.445164\pi$
$839$	8331.82	0.342844	0.171422	+	0.985198i	$0.445164\pi$
$840$	0	0
$841$	−8808.12	−0.361152
$842$	16101.6	0.659024
$843$	−28681.0	−1.17180
$844$	16608.1	0.677338
$845$	9321.24	0.379480
$846$	−6740.46	−0.273926
$847$	0	0
$848$	6800.42	0.275386
$849$	−1970.55	−0.0796572
$850$	5852.08	0.236147
$851$	35044.1	1.41163
$852$	−2543.44	−0.102273
$853$	30357.4	1.21854	0.609271	−	0.792962i	$-0.291462\pi$
$853$	30357.4	1.21854	0.609271	+	0.792962i	$0.291462\pi$
$854$	0	0
$855$	−381.421	−0.0152565
$856$	−10296.8	−0.411143
$857$	−15910.2	−0.634166	−0.317083	−	0.948398i	$-0.602703\pi$
$857$	−15910.2	−0.634166	−0.317083	+	0.948398i	$0.602703\pi$
$858$	10048.7	0.399833
$859$	−21467.5	−0.852693	−0.426346	−	0.904560i	$-0.640200\pi$
$859$	−21467.5	−0.852693	−0.426346	+	0.904560i	$0.640200\pi$
$860$	1995.49	0.0791229
$861$	0	0
$862$	−33625.6	−1.32864
$863$	−18027.1	−0.711067	−0.355533	−	0.934664i	$-0.615701\pi$
$863$	−18027.1	−0.711067	−0.355533	+	0.934664i	$0.615701\pi$
$864$	4512.23	0.177673
$865$	8565.39	0.336685
$866$	17415.3	0.683367
$867$	28489.0	1.11596
$868$	0	0
$869$	29765.9	1.16196
$870$	4047.57	0.157731
$871$	39338.6	1.53035
$872$	596.851	0.0231788
$873$	20167.8	0.781875
$874$	1525.53	0.0590408
$875$	0	0
$876$	−6092.79	−0.234996
$877$	1054.25	0.0405923	0.0202962	−	0.999794i	$-0.493539\pi$
$877$	1054.25	0.0405923	0.0202962	+	0.999794i	$0.493539\pi$
$878$	12263.8	0.471393
$879$	13259.1	0.508781
$880$	−1945.10	−0.0745104
$881$	−23111.8	−0.883833	−0.441917	−	0.897056i	$-0.645701\pi$
$881$	−23111.8	−0.883833	−0.441917	+	0.897056i	$0.645701\pi$
$882$	0	0
$883$	15594.4	0.594329	0.297165	−	0.954826i	$-0.403959\pi$
$883$	15594.4	0.594329	0.297165	+	0.954826i	$0.403959\pi$
$884$	−29835.3	−1.13515
$885$	−9280.98	−0.352516
$886$	20673.2	0.783894
$887$	25726.0	0.973836	0.486918	−	0.873448i	$-0.338121\pi$
$887$	25726.0	0.973836	0.486918	+	0.873448i	$0.338121\pi$
$888$	5515.09	0.208417
$889$	0	0
$890$	5896.77	0.222090
$891$	294.996	0.0110917
$892$	−8382.34	−0.314643
$893$	−946.023	−0.0354507
$894$	1757.74	0.0657580
$895$	16494.8	0.616046
$896$	0	0
$897$	−34062.7	−1.26792
$898$	−31069.4	−1.15457
$899$	−11209.9	−0.415875
$900$	−1648.53	−0.0610566
$901$	−49745.8	−1.83937
$902$	13181.0	0.486562
$903$	0	0
$904$	−17828.4	−0.655932
$905$	19492.6	0.715973
$906$	22077.4	0.809571
$907$	2751.50	0.100730	0.0503650	−	0.998731i	$-0.483962\pi$
$907$	2751.50	0.100730	0.0503650	+	0.998731i	$0.483962\pi$
$908$	17815.8	0.651143
$909$	12368.4	0.451303
$910$	0	0
$911$	5517.89	0.200676	0.100338	−	0.994953i	$-0.468008\pi$
$911$	5517.89	0.200676	0.100338	+	0.994953i	$0.468008\pi$
$912$	240.081	0.00871696
$913$	6508.47	0.235924
$914$	−918.685	−0.0332466
$915$	−5006.93	−0.180901
$916$	4019.71	0.144995
$917$	0	0
$918$	−33007.4	−1.18672
$919$	−6759.48	−0.242628	−0.121314	−	0.992614i	$-0.538711\pi$
$919$	−6759.48	−0.242628	−0.121314	+	0.992614i	$0.538711\pi$
$920$	6593.42	0.236281
$921$	−11040.4	−0.394997
$922$	−16613.1	−0.593409
$923$	−12496.6	−0.445646
$924$	0	0
$925$	−5315.00	−0.188926
$926$	−1871.79	−0.0664264
$927$	−1782.29	−0.0631478
$928$	3994.35	0.141294
$929$	−52566.0	−1.85644	−0.928221	−	0.372028i	$-0.878663\pi$
$929$	−52566.0	−1.85644	−0.928221	+	0.372028i	$0.878663\pi$
$930$	−2912.09	−0.102679
$931$	0	0
$932$	1646.77	0.0578775
$933$	−26608.7	−0.933685
$934$	−10162.3	−0.356019
$935$	14228.6	0.497673
$936$	8404.58	0.293496
$937$	53135.4	1.85257	0.926285	−	0.376823i	$-0.122983\pi$
$937$	53135.4	1.85257	0.926285	+	0.376823i	$0.122983\pi$
$938$	0	0
$939$	16172.9	0.562068
$940$	−4088.77	−0.141873
$941$	−7712.77	−0.267193	−0.133597	−	0.991036i	$-0.542653\pi$
$941$	−7712.77	−0.267193	−0.133597	+	0.991036i	$0.542653\pi$
$942$	−7160.91	−0.247681
$943$	−44680.5	−1.54294
$944$	−9158.94	−0.315782
$945$	0	0
$946$	4851.78	0.166749
$947$	−11186.8	−0.383867	−0.191933	−	0.981408i	$-0.561476\pi$
$947$	−11186.8	−0.383867	−0.191933	+	0.981408i	$0.561476\pi$
$948$	−15879.1	−0.544020
$949$	−29935.6	−1.02397
$950$	−231.371	−0.00790175
$951$	−11342.7	−0.386763
$952$	0	0
$953$	27159.3	0.923164	0.461582	−	0.887098i	$-0.347282\pi$
$953$	27159.3	0.923164	0.461582	+	0.887098i	$0.347282\pi$
$954$	14013.4	0.475576
$955$	−13388.5	−0.453656
$956$	19833.9	0.670998
$957$	9841.15	0.332413
$958$	13797.4	0.465317
$959$	0	0
$960$	1037.65	0.0348853
$961$	−21725.9	−0.729276
$962$	27097.1	0.908156
$963$	−21218.2	−0.710019
$964$	13492.7	0.450801
$965$	−13414.0	−0.447473
$966$	0	0
$967$	−34356.0	−1.14252	−0.571259	−	0.820770i	$-0.693545\pi$
$967$	−34356.0	−1.14252	−0.571259	+	0.820770i	$0.693545\pi$
$968$	5918.75	0.196525
$969$	−1756.22	−0.0582227
$970$	12233.8	0.404953
$971$	−1009.33	−0.0333584	−0.0166792	−	0.999861i	$-0.505309\pi$
$971$	−1009.33	−0.0333584	−0.0166792	+	0.999861i	$0.505309\pi$
$972$	15071.4	0.497341
$973$	0	0
$974$	−26847.0	−0.883196
$975$	5166.17	0.169692
$976$	−4941.09	−0.162050
$977$	7287.16	0.238625	0.119313	−	0.992857i	$-0.461931\pi$
$977$	7287.16	0.238625	0.119313	+	0.992857i	$0.461931\pi$
$978$	−22602.0	−0.738990
$979$	14337.2	0.468049
$980$	0	0
$981$	1229.91	0.0400284
$982$	−7512.36	−0.244123
$983$	−50239.5	−1.63010	−0.815052	−	0.579388i	$-0.803292\pi$
$983$	−50239.5	−1.63010	−0.815052	+	0.579388i	$0.803292\pi$
$984$	−7031.63	−0.227805
$985$	15009.6	0.485528
$986$	−29219.1	−0.943737
$987$	0	0
$988$	1179.58	0.0379833
$989$	−16446.4	−0.528782
$990$	−4008.18	−0.128675
$991$	56936.4	1.82507	0.912535	−	0.408998i	$-0.134122\pi$
$991$	56936.4	1.82507	0.912535	+	0.408998i	$0.134122\pi$
$992$	−2873.80	−0.0919790
$993$	−6608.05	−0.211178
$994$	0	0
$995$	14430.6	0.459780
$996$	−3472.05	−0.110458
$997$	−57598.8	−1.82966	−0.914831	−	0.403836i	$-0.867677\pi$
$997$	−57598.8	−1.82966	−0.914831	+	0.403836i	$0.867677\pi$
$998$	−11679.0	−0.370433
$999$	29978.1	0.949415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.q.1.2	✓	2
5.4	even	2		2450.4.a.by.1.1		2
7.2	even	3		490.4.e.w.361.1		4
7.3	odd	6		490.4.e.v.471.2		4
7.4	even	3		490.4.e.w.471.1		4
7.5	odd	6		490.4.e.v.361.2		4
7.6	odd	2		490.4.a.s.1.1	yes	2
35.34	odd	2		2450.4.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.q.1.2	✓	2	1.1	even	1	trivial
490.4.a.s.1.1	yes	2	7.6	odd	2
490.4.e.v.361.2		4	7.5	odd	6
490.4.e.v.471.2		4	7.3	odd	6
490.4.e.w.361.1		4	7.2	even	3
490.4.e.w.471.1		4	7.4	even	3
2450.4.a.bu.1.2		2	35.34	odd	2
2450.4.a.by.1.1		2	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.24264 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.48528 q^{6} -8.00000 q^{8} -16.4853 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.24264 q^{3} +4.00000 q^{4} +5.00000 q^{5} -6.48528 q^{6} -8.00000 q^{8} -16.4853 q^{9} -10.0000 q^{10} -24.3137 q^{11} +12.9706 q^{12} +63.7279 q^{13} +16.2132 q^{15} +16.0000 q^{16} -117.042 q^{17} +32.9706 q^{18} +4.62742 q^{19} +20.0000 q^{20} +48.6274 q^{22} -164.836 q^{23} -25.9411 q^{24} +25.0000 q^{25} -127.456 q^{26} -141.007 q^{27} -124.823 q^{29} -32.4264 q^{30} +89.8061 q^{31} -32.0000 q^{32} -78.8406 q^{33} +234.083 q^{34} -65.9411 q^{36} -212.600 q^{37} -9.25483 q^{38} +206.647 q^{39} -40.0000 q^{40} +271.061 q^{41} +99.7746 q^{43} -97.2548 q^{44} -82.4264 q^{45} +329.671 q^{46} -204.439 q^{47} +51.8823 q^{48} -50.0000 q^{50} -379.524 q^{51} +254.912 q^{52} +425.026 q^{53} +282.014 q^{54} -121.569 q^{55} +15.0051 q^{57} +249.647 q^{58} -572.434 q^{59} +64.8528 q^{60} -308.818 q^{61} -179.612 q^{62} +64.0000 q^{64} +318.640 q^{65} +157.681 q^{66} +617.291 q^{67} -468.167 q^{68} -534.503 q^{69} -196.093 q^{71} +131.882 q^{72} -469.740 q^{73} +425.200 q^{74} +81.0660 q^{75} +18.5097 q^{76} -413.294 q^{78} -1224.24 q^{79} +80.0000 q^{80} -12.1329 q^{81} -542.122 q^{82} -267.687 q^{83} -585.208 q^{85} -199.549 q^{86} -404.757 q^{87} +194.510 q^{88} -589.677 q^{89} +164.853 q^{90} -659.342 q^{92} +291.209 q^{93} +408.877 q^{94} +23.1371 q^{95} -103.765 q^{96} -1223.38 q^{97} +400.818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 - 16 * q^9	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} - 16 q^{9} - 20 q^{10} - 26 q^{11} - 8 q^{12} + 102 q^{13} - 10 q^{15} + 32 q^{16} - 186 q^{17} + 32 q^{18} - 36 q^{19} + 40 q^{20} + 52 q^{22} - 44 q^{23} + 16 q^{24} + 50 q^{25} - 204 q^{26} - 2 q^{27} - 46 q^{29} + 20 q^{30} - 140 q^{31} - 64 q^{32} - 70 q^{33} + 372 q^{34} - 64 q^{36} + 132 q^{37} + 72 q^{38} + 6 q^{39} - 80 q^{40} + 132 q^{41} + 324 q^{43} - 104 q^{44} - 80 q^{45} + 88 q^{46} - 242 q^{47} - 32 q^{48} - 100 q^{50} - 18 q^{51} + 408 q^{52} + 208 q^{53} + 4 q^{54} - 130 q^{55} + 228 q^{57} + 92 q^{58} - 780 q^{59} - 40 q^{60} - 216 q^{61} + 280 q^{62} + 128 q^{64} + 510 q^{65} + 140 q^{66} - 256 q^{67} - 744 q^{68} - 1168 q^{69} - 692 q^{71} + 128 q^{72} - 832 q^{73} - 264 q^{74} - 50 q^{75} - 144 q^{76} - 12 q^{78} - 1962 q^{79} + 160 q^{80} - 754 q^{81} - 264 q^{82} - 1712 q^{83} - 930 q^{85} - 648 q^{86} - 818 q^{87} + 208 q^{88} - 1960 q^{89} + 160 q^{90} - 176 q^{92} + 1496 q^{93} + 484 q^{94} - 180 q^{95} + 64 q^{96} - 102 q^{97} + 400 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 - 16 * q^9 - 20 * q^10 - 26 * q^11 - 8 * q^12 + 102 * q^13 - 10 * q^15 + 32 * q^16 - 186 * q^17 + 32 * q^18 - 36 * q^19 + 40 * q^20 + 52 * q^22 - 44 * q^23 + 16 * q^24 + 50 * q^25 - 204 * q^26 - 2 * q^27 - 46 * q^29 + 20 * q^30 - 140 * q^31 - 64 * q^32 - 70 * q^33 + 372 * q^34 - 64 * q^36 + 132 * q^37 + 72 * q^38 + 6 * q^39 - 80 * q^40 + 132 * q^41 + 324 * q^43 - 104 * q^44 - 80 * q^45 + 88 * q^46 - 242 * q^47 - 32 * q^48 - 100 * q^50 - 18 * q^51 + 408 * q^52 + 208 * q^53 + 4 * q^54 - 130 * q^55 + 228 * q^57 + 92 * q^58 - 780 * q^59 - 40 * q^60 - 216 * q^61 + 280 * q^62 + 128 * q^64 + 510 * q^65 + 140 * q^66 - 256 * q^67 - 744 * q^68 - 1168 * q^69 - 692 * q^71 + 128 * q^72 - 832 * q^73 - 264 * q^74 - 50 * q^75 - 144 * q^76 - 12 * q^78 - 1962 * q^79 + 160 * q^80 - 754 * q^81 - 264 * q^82 - 1712 * q^83 - 930 * q^85 - 648 * q^86 - 818 * q^87 + 208 * q^88 - 1960 * q^89 + 160 * q^90 - 176 * q^92 + 1496 * q^93 + 484 * q^94 - 180 * q^95 + 64 * q^96 - 102 * q^97 + 400 * q^99

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