LMFDB - Embedded newform 294.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -3.89949 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -3.89949 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +7.79899 q^{10} -61.3970 q^{11} -12.0000 q^{12} +53.6985 q^{13} +11.6985 q^{15} +16.0000 q^{16} +32.1005 q^{17} -18.0000 q^{18} -55.7990 q^{19} -15.5980 q^{20} +122.794 q^{22} -94.6030 q^{23} +24.0000 q^{24} -109.794 q^{25} -107.397 q^{26} -27.0000 q^{27} +138.191 q^{29} -23.3970 q^{30} +132.603 q^{31} -32.0000 q^{32} +184.191 q^{33} -64.2010 q^{34} +36.0000 q^{36} +149.206 q^{37} +111.598 q^{38} -161.095 q^{39} +31.1960 q^{40} +427.497 q^{41} +437.588 q^{43} -245.588 q^{44} -35.0955 q^{45} +189.206 q^{46} +57.0051 q^{47} -48.0000 q^{48} +219.588 q^{50} -96.3015 q^{51} +214.794 q^{52} -263.588 q^{53} +54.0000 q^{54} +239.417 q^{55} +167.397 q^{57} -276.382 q^{58} +451.799 q^{59} +46.7939 q^{60} +579.307 q^{61} -265.206 q^{62} +64.0000 q^{64} -209.397 q^{65} -368.382 q^{66} +309.588 q^{67} +128.402 q^{68} +283.809 q^{69} -1058.98 q^{71} -72.0000 q^{72} +1193.66 q^{73} -298.412 q^{74} +329.382 q^{75} -223.196 q^{76} +322.191 q^{78} +1319.56 q^{79} -62.3919 q^{80} +81.0000 q^{81} -854.995 q^{82} +1190.33 q^{83} -125.176 q^{85} -875.176 q^{86} -414.573 q^{87} +491.176 q^{88} -233.085 q^{89} +70.1909 q^{90} -378.412 q^{92} -397.809 q^{93} -114.010 q^{94} +217.588 q^{95} +96.0000 q^{96} -1609.44 q^{97} -552.573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 48 q^{13} - 36 q^{15} + 32 q^{16} + 84 q^{17} - 36 q^{18} - 72 q^{19} + 48 q^{20} + 8 q^{22} - 308 q^{23} + 48 q^{24} + 18 q^{25} - 96 q^{26} - 54 q^{27} - 80 q^{29} + 72 q^{30} + 384 q^{31} - 64 q^{32} + 12 q^{33} - 168 q^{34} + 72 q^{36} + 536 q^{37} + 144 q^{38} - 144 q^{39} - 96 q^{40} + 756 q^{41} + 400 q^{43} - 16 q^{44} + 108 q^{45} + 616 q^{46} + 312 q^{47} - 96 q^{48} - 36 q^{50} - 252 q^{51} + 192 q^{52} - 52 q^{53} + 108 q^{54} + 1152 q^{55} + 216 q^{57} + 160 q^{58} + 864 q^{59} - 144 q^{60} + 1416 q^{61} - 768 q^{62} + 128 q^{64} - 300 q^{65} - 24 q^{66} + 144 q^{67} + 336 q^{68} + 924 q^{69} - 1524 q^{71} - 144 q^{72} + 744 q^{73} - 1072 q^{74} - 54 q^{75} - 288 q^{76} + 288 q^{78} + 976 q^{79} + 192 q^{80} + 162 q^{81} - 1512 q^{82} - 312 q^{83} + 700 q^{85} - 800 q^{86} + 240 q^{87} + 32 q^{88} + 108 q^{89} - 216 q^{90} - 1232 q^{92} - 1152 q^{93} - 624 q^{94} - 40 q^{95} + 192 q^{96} - 744 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 48 * q^13 - 36 * q^15 + 32 * q^16 + 84 * q^17 - 36 * q^18 - 72 * q^19 + 48 * q^20 + 8 * q^22 - 308 * q^23 + 48 * q^24 + 18 * q^25 - 96 * q^26 - 54 * q^27 - 80 * q^29 + 72 * q^30 + 384 * q^31 - 64 * q^32 + 12 * q^33 - 168 * q^34 + 72 * q^36 + 536 * q^37 + 144 * q^38 - 144 * q^39 - 96 * q^40 + 756 * q^41 + 400 * q^43 - 16 * q^44 + 108 * q^45 + 616 * q^46 + 312 * q^47 - 96 * q^48 - 36 * q^50 - 252 * q^51 + 192 * q^52 - 52 * q^53 + 108 * q^54 + 1152 * q^55 + 216 * q^57 + 160 * q^58 + 864 * q^59 - 144 * q^60 + 1416 * q^61 - 768 * q^62 + 128 * q^64 - 300 * q^65 - 24 * q^66 + 144 * q^67 + 336 * q^68 + 924 * q^69 - 1524 * q^71 - 144 * q^72 + 744 * q^73 - 1072 * q^74 - 54 * q^75 - 288 * q^76 + 288 * q^78 + 976 * q^79 + 192 * q^80 + 162 * q^81 - 1512 * q^82 - 312 * q^83 + 700 * q^85 - 800 * q^86 + 240 * q^87 + 32 * q^88 + 108 * q^89 - 216 * q^90 - 1232 * q^92 - 1152 * q^93 - 624 * q^94 - 40 * q^95 + 192 * q^96 - 744 * q^97 - 36 * 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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−3.89949	−0.348781	−0.174391	−	0.984677i	$-0.555796\pi$
$5$	−3.89949	−0.348781	−0.174391	+	0.984677i	$0.555796\pi$
$6$	6.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	7.79899	0.246626
$11$	−61.3970	−1.68290	−0.841449	−	0.540336i	$-0.818297\pi$
$11$	−61.3970	−1.68290	−0.841449	+	0.540336i	$0.818297\pi$
$12$	−12.0000	−0.288675
$13$	53.6985	1.14564	0.572818	−	0.819682i	$-0.305850\pi$
$13$	53.6985	1.14564	0.572818	+	0.819682i	$0.305850\pi$
$14$	0	0
$15$	11.6985	0.201369
$16$	16.0000	0.250000
$17$	32.1005	0.457972	0.228986	−	0.973430i	$-0.426459\pi$
$17$	32.1005	0.457972	0.228986	+	0.973430i	$0.426459\pi$
$18$	−18.0000	−0.235702
$19$	−55.7990	−0.673746	−0.336873	−	0.941550i	$-0.609369\pi$
$19$	−55.7990	−0.673746	−0.336873	+	0.941550i	$0.609369\pi$
$20$	−15.5980	−0.174391
$21$	0	0
$22$	122.794	1.18999
$23$	−94.6030	−0.857656	−0.428828	−	0.903386i	$-0.641073\pi$
$23$	−94.6030	−0.857656	−0.428828	+	0.903386i	$0.641073\pi$
$24$	24.0000	0.204124
$25$	−109.794	−0.878352
$26$	−107.397	−0.810088
$27$	−27.0000	−0.192450
$28$	0	0
$29$	138.191	0.884876	0.442438	−	0.896799i	$-0.354114\pi$
$29$	138.191	0.884876	0.442438	+	0.896799i	$0.354114\pi$
$30$	−23.3970	−0.142389
$31$	132.603	0.768265	0.384132	−	0.923278i	$-0.374501\pi$
$31$	132.603	0.768265	0.384132	+	0.923278i	$0.374501\pi$
$32$	−32.0000	−0.176777
$33$	184.191	0.971622
$34$	−64.2010	−0.323835
$35$	0	0
$36$	36.0000	0.166667
$37$	149.206	0.662955	0.331477	−	0.943463i	$-0.392453\pi$
$37$	149.206	0.662955	0.331477	+	0.943463i	$0.392453\pi$
$38$	111.598	0.476410
$39$	−161.095	−0.661434
$40$	31.1960	0.123313
$41$	427.497	1.62839	0.814194	−	0.580593i	$-0.197179\pi$
$41$	427.497	1.62839	0.814194	+	0.580593i	$0.197179\pi$
$42$	0	0
$43$	437.588	1.55190	0.775948	−	0.630797i	$-0.217272\pi$
$43$	437.588	1.55190	0.775948	+	0.630797i	$0.217272\pi$
$44$	−245.588	−0.841449
$45$	−35.0955	−0.116260
$46$	189.206	0.606455
$47$	57.0051	0.176916	0.0884579	−	0.996080i	$-0.471806\pi$
$47$	57.0051	0.176916	0.0884579	+	0.996080i	$0.471806\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	219.588	0.621088
$51$	−96.3015	−0.264410
$52$	214.794	0.572818
$53$	−263.588	−0.683143	−0.341572	−	0.939856i	$-0.610959\pi$
$53$	−263.588	−0.683143	−0.341572	+	0.939856i	$0.610959\pi$
$54$	54.0000	0.136083
$55$	239.417	0.586964
$56$	0	0
$57$	167.397	0.388987
$58$	−276.382	−0.625702
$59$	451.799	0.996936	0.498468	−	0.866908i	$-0.333896\pi$
$59$	451.799	0.996936	0.498468	+	0.866908i	$0.333896\pi$
$60$	46.7939	0.100685
$61$	579.307	1.21594	0.607972	−	0.793958i	$-0.291983\pi$
$61$	579.307	1.21594	0.607972	+	0.793958i	$0.291983\pi$
$62$	−265.206	−0.543245
$63$	0	0
$64$	64.0000	0.125000
$65$	−209.397	−0.399577
$66$	−368.382	−0.687040
$67$	309.588	0.564510	0.282255	−	0.959339i	$-0.408918\pi$
$67$	309.588	0.564510	0.282255	+	0.959339i	$0.408918\pi$
$68$	128.402	0.228986
$69$	283.809	0.495168
$70$	0	0
$71$	−1058.98	−1.77012	−0.885059	−	0.465479i	$-0.845882\pi$
$71$	−1058.98	−1.77012	−0.885059	+	0.465479i	$0.845882\pi$
$72$	−72.0000	−0.117851
$73$	1193.66	1.91380	0.956898	−	0.290424i	$-0.0937964\pi$
$73$	1193.66	1.91380	0.956898	+	0.290424i	$0.0937964\pi$
$74$	−298.412	−0.468780
$75$	329.382	0.507116
$76$	−223.196	−0.336873
$77$	0	0
$78$	322.191	0.467704
$79$	1319.56	1.87926	0.939632	−	0.342187i	$-0.111168\pi$
$79$	1319.56	1.87926	0.939632	+	0.342187i	$0.111168\pi$
$80$	−62.3919	−0.0871954
$81$	81.0000	0.111111
$82$	−854.995	−1.15144
$83$	1190.33	1.57417	0.787083	−	0.616847i	$-0.211590\pi$
$83$	1190.33	1.57417	0.787083	+	0.616847i	$0.211590\pi$
$84$	0	0
$85$	−125.176	−0.159732
$86$	−875.176	−1.09736
$87$	−414.573	−0.510883
$88$	491.176	0.594994
$89$	−233.085	−0.277607	−0.138803	−	0.990320i	$-0.544326\pi$
$89$	−233.085	−0.277607	−0.138803	+	0.990320i	$0.544326\pi$
$90$	70.1909	0.0822086
$91$	0	0
$92$	−378.412	−0.428828
$93$	−397.809	−0.443558
$94$	−114.010	−0.125098
$95$	217.588	0.234990
$96$	96.0000	0.102062
$97$	−1609.44	−1.68468	−0.842338	−	0.538950i	$-0.818821\pi$
$97$	−1609.44	−1.68468	−0.842338	+	0.538950i	$0.818821\pi$
$98$	0	0
$99$	−552.573	−0.560966
$100$	−439.176	−0.439176
$101$	−1479.26	−1.45734	−0.728671	−	0.684864i	$-0.759861\pi$
$101$	−1479.26	−1.45734	−0.728671	+	0.684864i	$0.759861\pi$
$102$	192.603	0.186966
$103$	−1145.35	−1.09567	−0.547837	−	0.836585i	$-0.684548\pi$
$103$	−1145.35	−1.09567	−0.547837	+	0.836585i	$0.684548\pi$
$104$	−429.588	−0.405044
$105$	0	0
$106$	527.176	0.483055
$107$	436.955	0.394785	0.197392	−	0.980325i	$-0.436753\pi$
$107$	436.955	0.394785	0.197392	+	0.980325i	$0.436753\pi$
$108$	−108.000	−0.0962250
$109$	−166.352	−0.146180	−0.0730898	−	0.997325i	$-0.523286\pi$
$109$	−166.352	−0.146180	−0.0730898	+	0.997325i	$0.523286\pi$
$110$	−478.834	−0.415046
$111$	−447.618	−0.382757
$112$	0	0
$113$	490.824	0.408609	0.204305	−	0.978907i	$-0.434507\pi$
$113$	490.824	0.408609	0.204305	+	0.978907i	$0.434507\pi$
$114$	−334.794	−0.275055
$115$	368.904	0.299135
$116$	552.764	0.442438
$117$	483.286	0.381879
$118$	−903.598	−0.704940
$119$	0	0
$120$	−93.5879	−0.0711947
$121$	2438.59	1.83215
$122$	−1158.61	−0.859802
$123$	−1282.49	−0.940150
$124$	530.412	0.384132
$125$	915.578	0.655134
$126$	0	0
$127$	−2616.70	−1.82831	−0.914153	−	0.405369i	$-0.867143\pi$
$127$	−2616.70	−1.82831	−0.914153	+	0.405369i	$0.867143\pi$
$128$	−128.000	−0.0883883
$129$	−1312.76	−0.895988
$130$	418.794	0.282544
$131$	177.588	0.118442	0.0592211	−	0.998245i	$-0.481138\pi$
$131$	177.588	0.118442	0.0592211	+	0.998245i	$0.481138\pi$
$132$	736.764	0.485811
$133$	0	0
$134$	−619.176	−0.399169
$135$	105.286	0.0671230
$136$	−256.804	−0.161917
$137$	27.0152	0.0168472	0.00842358	−	0.999965i	$-0.497319\pi$
$137$	27.0152	0.0168472	0.00842358	+	0.999965i	$0.497319\pi$
$138$	−567.618	−0.350137
$139$	−922.754	−0.563071	−0.281536	−	0.959551i	$-0.590844\pi$
$139$	−922.754	−0.563071	−0.281536	+	0.959551i	$0.590844\pi$
$140$	0	0
$141$	−171.015	−0.102142
$142$	2117.97	1.25166
$143$	−3296.92	−1.92799
$144$	144.000	0.0833333
$145$	−538.875	−0.308628
$146$	−2387.32	−1.35326
$147$	0	0
$148$	596.824	0.331477
$149$	746.703	0.410552	0.205276	−	0.978704i	$-0.434191\pi$
$149$	746.703	0.410552	0.205276	+	0.978704i	$0.434191\pi$
$150$	−658.764	−0.358586
$151$	2073.15	1.11729	0.558643	−	0.829408i	$-0.311322\pi$
$151$	2073.15	1.11729	0.558643	+	0.829408i	$0.311322\pi$
$152$	446.392	0.238205
$153$	288.905	0.152657
$154$	0	0
$155$	−517.085	−0.267956
$156$	−644.382	−0.330717
$157$	1566.22	0.796166	0.398083	−	0.917349i	$-0.369676\pi$
$157$	1566.22	0.796166	0.398083	+	0.917349i	$0.369676\pi$
$158$	−2639.12	−1.32884
$159$	790.764	0.394413
$160$	124.784	0.0616564
$161$	0	0
$162$	−162.000	−0.0785674
$163$	98.7333	0.0474441	0.0237221	−	0.999719i	$-0.492448\pi$
$163$	98.7333	0.0474441	0.0237221	+	0.999719i	$0.492448\pi$
$164$	1709.99	0.814194
$165$	−718.252	−0.338884
$166$	−2380.66	−1.11310
$167$	−2231.36	−1.03394	−0.516969	−	0.856004i	$-0.672940\pi$
$167$	−2231.36	−1.03394	−0.516969	+	0.856004i	$0.672940\pi$
$168$	0	0
$169$	686.527	0.312484
$170$	250.352	0.112948
$171$	−502.191	−0.224582
$172$	1750.35	0.775948
$173$	2100.84	0.923261	0.461631	−	0.887072i	$-0.347265\pi$
$173$	2100.84	0.923261	0.461631	+	0.887072i	$0.347265\pi$
$174$	829.145	0.361249
$175$	0	0
$176$	−982.352	−0.420725
$177$	−1355.40	−0.575581
$178$	466.171	0.196298
$179$	1722.54	0.719267	0.359634	−	0.933094i	$-0.382902\pi$
$179$	1722.54	0.719267	0.359634	+	0.933094i	$0.382902\pi$
$180$	−140.382	−0.0581302
$181$	1655.00	0.679644	0.339822	−	0.940490i	$-0.389633\pi$
$181$	1655.00	0.679644	0.339822	+	0.940490i	$0.389633\pi$
$182$	0	0
$183$	−1737.92	−0.702026
$184$	756.824	0.303227
$185$	−581.828	−0.231226
$186$	795.618	0.313643
$187$	−1970.87	−0.770720
$188$	228.020	0.0884579
$189$	0	0
$190$	−435.176	−0.166163
$191$	−1007.69	−0.381747	−0.190874	−	0.981615i	$-0.561132\pi$
$191$	−1007.69	−0.381747	−0.190874	+	0.981615i	$0.561132\pi$
$192$	−192.000	−0.0721688
$193$	−7.64849	−0.00285259	−0.00142630	−	0.999999i	$-0.500454\pi$
$193$	−7.64849	−0.00285259	−0.00142630	+	0.999999i	$0.500454\pi$
$194$	3218.87	1.19125
$195$	628.191	0.230696
$196$	0	0
$197$	2689.88	0.972822	0.486411	−	0.873730i	$-0.338306\pi$
$197$	2689.88	0.972822	0.486411	+	0.873730i	$0.338306\pi$
$198$	1105.15	0.396663
$199$	867.497	0.309021	0.154511	−	0.987991i	$-0.450620\pi$
$199$	867.497	0.309021	0.154511	+	0.987991i	$0.450620\pi$
$200$	878.352	0.310544
$201$	−928.764	−0.325920
$202$	2958.51	1.03050
$203$	0	0
$204$	−385.206	−0.132205
$205$	−1667.02	−0.567951
$206$	2290.69	0.774758
$207$	−851.427	−0.285885
$208$	859.176	0.286409
$209$	3425.89	1.13385
$210$	0	0
$211$	162.030	0.0528655	0.0264328	−	0.999651i	$-0.491585\pi$
$211$	162.030	0.0528655	0.0264328	+	0.999651i	$0.491585\pi$
$212$	−1054.35	−0.341572
$213$	3176.95	1.02198
$214$	−873.909	−0.279155
$215$	−1706.37	−0.541272
$216$	216.000	0.0680414
$217$	0	0
$218$	332.703	0.103365
$219$	−3580.97	−1.10493
$220$	957.669	0.293482
$221$	1723.75	0.524669
$222$	895.236	0.270650
$223$	−4577.85	−1.37469	−0.687344	−	0.726332i	$-0.741223\pi$
$223$	−4577.85	−1.37469	−0.687344	+	0.726332i	$0.741223\pi$
$224$	0	0
$225$	−988.145	−0.292784
$226$	−981.648	−0.288930
$227$	−2218.19	−0.648575	−0.324287	−	0.945959i	$-0.605125\pi$
$227$	−2218.19	−0.648575	−0.324287	+	0.945959i	$0.605125\pi$
$228$	669.588	0.194494
$229$	785.217	0.226588	0.113294	−	0.993562i	$-0.463860\pi$
$229$	785.217	0.226588	0.113294	+	0.993562i	$0.463860\pi$
$230$	−737.808	−0.211520
$231$	0	0
$232$	−1105.53	−0.312851
$233$	−5369.12	−1.50963	−0.754813	−	0.655940i	$-0.772273\pi$
$233$	−5369.12	−1.50963	−0.754813	+	0.655940i	$0.772273\pi$
$234$	−966.573	−0.270029
$235$	−222.291	−0.0617049
$236$	1807.20	0.498468
$237$	−3958.67	−1.08499
$238$	0	0
$239$	3713.28	1.00499	0.502493	−	0.864581i	$-0.332416\pi$
$239$	3713.28	1.00499	0.502493	+	0.864581i	$0.332416\pi$
$240$	187.176	0.0503423
$241$	6998.62	1.87063	0.935313	−	0.353821i	$-0.115118\pi$
$241$	6998.62	1.87063	0.935313	+	0.353821i	$0.115118\pi$
$242$	−4877.18	−1.29552
$243$	−243.000	−0.0641500
$244$	2317.23	0.607972
$245$	0	0
$246$	2564.98	0.664786
$247$	−2996.32	−0.771868
$248$	−1060.82	−0.271623
$249$	−3570.99	−0.908846
$250$	−1831.16	−0.463250
$251$	3722.75	0.936168	0.468084	−	0.883684i	$-0.344945\pi$
$251$	3722.75	0.936168	0.468084	+	0.883684i	$0.344945\pi$
$252$	0	0
$253$	5808.34	1.44335
$254$	5233.41	1.29281
$255$	375.527	0.0922213
$256$	256.000	0.0625000
$257$	1230.15	0.298578	0.149289	−	0.988794i	$-0.452301\pi$
$257$	1230.15	0.298578	0.149289	+	0.988794i	$0.452301\pi$
$258$	2625.53	0.633559
$259$	0	0
$260$	−837.588	−0.199788
$261$	1243.72	0.294959
$262$	−355.176	−0.0837513
$263$	2388.63	0.560036	0.280018	−	0.959995i	$-0.409660\pi$
$263$	2388.63	0.560036	0.280018	+	0.959995i	$0.409660\pi$
$264$	−1473.53	−0.343520
$265$	1027.86	0.238268
$266$	0	0
$267$	699.256	0.160276
$268$	1238.35	0.282255
$269$	6702.31	1.51913	0.759567	−	0.650429i	$-0.225411\pi$
$269$	6702.31	1.51913	0.759567	+	0.650429i	$0.225411\pi$
$270$	−210.573	−0.0474631
$271$	4950.37	1.10964	0.554822	−	0.831969i	$-0.312786\pi$
$271$	4950.37	1.10964	0.554822	+	0.831969i	$0.312786\pi$
$272$	513.608	0.114493
$273$	0	0
$274$	−54.0303	−0.0119127
$275$	6741.02	1.47818
$276$	1135.24	0.247584
$277$	−3705.18	−0.803691	−0.401846	−	0.915707i	$-0.631631\pi$
$277$	−3705.18	−0.803691	−0.401846	+	0.915707i	$0.631631\pi$
$278$	1845.51	0.398152
$279$	1193.43	0.256088
$280$	0	0
$281$	9324.74	1.97960	0.989800	−	0.142465i	$-0.0455029\pi$
$281$	9324.74	1.97960	0.989800	+	0.142465i	$0.0455029\pi$
$282$	342.030	0.0722256
$283$	−5569.49	−1.16986	−0.584932	−	0.811082i	$-0.698879\pi$
$283$	−5569.49	−1.16986	−0.584932	+	0.811082i	$0.698879\pi$
$284$	−4235.94	−0.885059
$285$	−652.764	−0.135672
$286$	6593.85	1.36330
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−3882.56	−0.790262
$290$	1077.75	0.218233
$291$	4828.31	0.972648
$292$	4774.63	0.956898
$293$	−1665.31	−0.332042	−0.166021	−	0.986122i	$-0.553092\pi$
$293$	−1665.31	−0.332042	−0.166021	+	0.986122i	$0.553092\pi$
$294$	0	0
$295$	−1761.79	−0.347713
$296$	−1193.65	−0.234390
$297$	1657.72	0.323874
$298$	−1493.41	−0.290304
$299$	−5080.04	−0.982563
$300$	1317.53	0.253558
$301$	0	0
$302$	−4146.29	−0.790040
$303$	4437.77	0.841396
$304$	−892.784	−0.168436
$305$	−2259.00	−0.424099
$306$	−577.809	−0.107945
$307$	−5303.32	−0.985916	−0.492958	−	0.870053i	$-0.664084\pi$
$307$	−5303.32	−0.985916	−0.492958	+	0.870053i	$0.664084\pi$
$308$	0	0
$309$	3436.04	0.632587
$310$	1034.17	0.189474
$311$	1125.99	0.205302	0.102651	−	0.994717i	$-0.467267\pi$
$311$	1125.99	0.205302	0.102651	+	0.994717i	$0.467267\pi$
$312$	1288.76	0.233852
$313$	−8299.51	−1.49877	−0.749386	−	0.662133i	$-0.769651\pi$
$313$	−8299.51	−1.49877	−0.749386	+	0.662133i	$0.769651\pi$
$314$	−3132.44	−0.562974
$315$	0	0
$316$	5278.23	0.939632
$317$	−4278.76	−0.758105	−0.379053	−	0.925375i	$-0.623750\pi$
$317$	−4278.76	−0.758105	−0.379053	+	0.925375i	$0.623750\pi$
$318$	−1581.53	−0.278892
$319$	−8484.50	−1.48916
$320$	−249.568	−0.0435977
$321$	−1310.86	−0.227929
$322$	0	0
$323$	−1791.18	−0.308556
$324$	324.000	0.0555556
$325$	−5895.77	−1.00627
$326$	−197.467	−0.0335481
$327$	499.055	0.0843969
$328$	−3419.98	−0.575722
$329$	0	0
$330$	1436.50	0.239627
$331$	−1707.12	−0.283479	−0.141739	−	0.989904i	$-0.545270\pi$
$331$	−1707.12	−0.283479	−0.141739	+	0.989904i	$0.545270\pi$
$332$	4761.33	0.787083
$333$	1342.85	0.220985
$334$	4462.71	0.731104
$335$	−1207.24	−0.196891
$336$	0	0
$337$	1710.67	0.276517	0.138259	−	0.990396i	$-0.455849\pi$
$337$	1710.67	0.276517	0.138259	+	0.990396i	$0.455849\pi$
$338$	−1373.05	−0.220960
$339$	−1472.47	−0.235911
$340$	−500.703	−0.0798660
$341$	−8141.42	−1.29291
$342$	1004.38	0.158803
$343$	0	0
$344$	−3500.70	−0.548678
$345$	−1106.71	−0.172705
$346$	−4201.69	−0.652844
$347$	8910.30	1.37847	0.689236	−	0.724537i	$-0.257946\pi$
$347$	8910.30	1.37847	0.689236	+	0.724537i	$0.257946\pi$
$348$	−1658.29	−0.255442
$349$	5378.68	0.824969	0.412485	−	0.910965i	$-0.364661\pi$
$349$	5378.68	0.824969	0.412485	+	0.910965i	$0.364661\pi$
$350$	0	0
$351$	−1449.86	−0.220478
$352$	1964.70	0.297497
$353$	−4252.56	−0.641193	−0.320596	−	0.947216i	$-0.603883\pi$
$353$	−4252.56	−0.641193	−0.320596	+	0.947216i	$0.603883\pi$
$354$	2710.79	0.406997
$355$	4129.51	0.617384
$356$	−932.341	−0.138803
$357$	0	0
$358$	−3445.08	−0.508599
$359$	4903.89	0.720940	0.360470	−	0.932771i	$-0.382616\pi$
$359$	4903.89	0.720940	0.360470	+	0.932771i	$0.382616\pi$
$360$	280.764	0.0411043
$361$	−3745.47	−0.546067
$362$	−3310.01	−0.480581
$363$	−7315.76	−1.05779
$364$	0	0
$365$	−4654.66	−0.667497
$366$	3475.84	0.496407
$367$	−4041.57	−0.574845	−0.287423	−	0.957804i	$-0.592798\pi$
$367$	−4041.57	−0.574845	−0.287423	+	0.957804i	$0.592798\pi$
$368$	−1513.65	−0.214414
$369$	3847.48	0.542796
$370$	1163.66	0.163502
$371$	0	0
$372$	−1591.24	−0.221779
$373$	−7451.35	−1.03436	−0.517180	−	0.855877i	$-0.673018\pi$
$373$	−7451.35	−1.03436	−0.517180	+	0.855877i	$0.673018\pi$
$374$	3941.75	0.544981
$375$	−2746.73	−0.378242
$376$	−456.040	−0.0625492
$377$	7420.64	1.01375
$378$	0	0
$379$	−12564.4	−1.70288	−0.851438	−	0.524456i	$-0.824269\pi$
$379$	−12564.4	−1.70288	−0.851438	+	0.524456i	$0.824269\pi$
$380$	870.352	0.117495
$381$	7850.11	1.05557
$382$	2015.38	0.269936
$383$	−4289.93	−0.572337	−0.286169	−	0.958179i	$-0.592382\pi$
$383$	−4289.93	−0.572337	−0.286169	+	0.958179i	$0.592382\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	15.2970	0.00201709
$387$	3938.29	0.517299
$388$	−6437.75	−0.842338
$389$	5662.77	0.738082	0.369041	−	0.929413i	$-0.379686\pi$
$389$	5662.77	0.738082	0.369041	+	0.929413i	$0.379686\pi$
$390$	−1256.38	−0.163127
$391$	−3036.81	−0.392782
$392$	0	0
$393$	−532.764	−0.0683826
$394$	−5379.76	−0.687889
$395$	−5145.61	−0.655452
$396$	−2210.29	−0.280483
$397$	14561.4	1.84084	0.920421	−	0.390928i	$-0.127846\pi$
$397$	14561.4	1.84084	0.920421	+	0.390928i	$0.127846\pi$
$398$	−1734.99	−0.218511
$399$	0	0
$400$	−1756.70	−0.219588
$401$	−3742.19	−0.466025	−0.233013	−	0.972474i	$-0.574858\pi$
$401$	−3742.19	−0.466025	−0.233013	+	0.972474i	$0.574858\pi$
$402$	1857.53	0.230460
$403$	7120.58	0.880152
$404$	−5917.02	−0.728671
$405$	−315.859	−0.0387535
$406$	0	0
$407$	−9160.80	−1.11569
$408$	770.412	0.0934830
$409$	−3517.17	−0.425215	−0.212608	−	0.977138i	$-0.568196\pi$
$409$	−3517.17	−0.425215	−0.212608	+	0.977138i	$0.568196\pi$
$410$	3334.05	0.401602
$411$	−81.0455	−0.00972671
$412$	−4581.39	−0.547837
$413$	0	0
$414$	1702.85	0.202152
$415$	−4641.69	−0.549040
$416$	−1718.35	−0.202522
$417$	2768.26	0.325089
$418$	−6851.78	−0.801750
$419$	−7579.52	−0.883732	−0.441866	−	0.897081i	$-0.645683\pi$
$419$	−7579.52	−0.883732	−0.441866	+	0.897081i	$0.645683\pi$
$420$	0	0
$421$	−4980.87	−0.576610	−0.288305	−	0.957539i	$-0.593092\pi$
$421$	−4980.87	−0.576610	−0.288305	+	0.957539i	$0.593092\pi$
$422$	−324.061	−0.0373816
$423$	513.045	0.0589719
$424$	2108.70	0.241528
$425$	−3524.44	−0.402260
$426$	−6353.91	−0.722648
$427$	0	0
$428$	1747.82	0.197392
$429$	9890.77	1.11313
$430$	3412.74	0.382737
$431$	14203.3	1.58736	0.793678	−	0.608339i	$-0.208164\pi$
$431$	14203.3	1.58736	0.793678	+	0.608339i	$0.208164\pi$
$432$	−432.000	−0.0481125
$433$	3874.82	0.430051	0.215026	−	0.976608i	$-0.431017\pi$
$433$	3874.82	0.430051	0.215026	+	0.976608i	$0.431017\pi$
$434$	0	0
$435$	1616.62	0.178187
$436$	−665.406	−0.0730898
$437$	5278.75	0.577842
$438$	7161.95	0.781304
$439$	7763.82	0.844070	0.422035	−	0.906579i	$-0.361316\pi$
$439$	7763.82	0.844070	0.422035	+	0.906579i	$0.361316\pi$
$440$	−1915.34	−0.207523
$441$	0	0
$442$	−3447.50	−0.370997
$443$	9662.24	1.03627	0.518134	−	0.855299i	$-0.326627\pi$
$443$	9662.24	1.03627	0.518134	+	0.855299i	$0.326627\pi$
$444$	−1790.47	−0.191379
$445$	908.915	0.0968241
$446$	9155.70	0.972051
$447$	−2240.11	−0.237032
$448$	0	0
$449$	−10942.6	−1.15014	−0.575069	−	0.818105i	$-0.695025\pi$
$449$	−10942.6	−1.15014	−0.575069	+	0.818105i	$0.695025\pi$
$450$	1976.29	0.207029
$451$	−26247.0	−2.74041
$452$	1963.30	0.204305
$453$	−6219.44	−0.645065
$454$	4436.38	0.458612
$455$	0	0
$456$	−1339.18	−0.137528
$457$	13618.3	1.39396	0.696979	−	0.717091i	$-0.254527\pi$
$457$	13618.3	1.39396	0.696979	+	0.717091i	$0.254527\pi$
$458$	−1570.43	−0.160222
$459$	−866.714	−0.0881367
$460$	1475.62	0.149567
$461$	11955.8	1.20789	0.603947	−	0.797025i	$-0.293594\pi$
$461$	11955.8	1.20789	0.603947	+	0.797025i	$0.293594\pi$
$462$	0	0
$463$	648.503	0.0650939	0.0325470	−	0.999470i	$-0.489638\pi$
$463$	648.503	0.0650939	0.0325470	+	0.999470i	$0.489638\pi$
$464$	2211.05	0.221219
$465$	1551.25	0.154705
$466$	10738.2	1.06747
$467$	2784.74	0.275937	0.137969	−	0.990437i	$-0.455943\pi$
$467$	2784.74	0.275937	0.137969	+	0.990437i	$0.455943\pi$
$468$	1933.15	0.190939
$469$	0	0
$470$	444.582	0.0436320
$471$	−4698.66	−0.459667
$472$	−3614.39	−0.352470
$473$	−26866.6	−2.61168
$474$	7917.35	0.767206
$475$	6126.39	0.591785
$476$	0	0
$477$	−2372.29	−0.227714
$478$	−7426.55	−0.710633
$479$	11113.4	1.06009	0.530046	−	0.847969i	$-0.322175\pi$
$479$	11113.4	1.06009	0.530046	+	0.847969i	$0.322175\pi$
$480$	−374.352	−0.0355974
$481$	8012.14	0.759505
$482$	−13997.2	−1.32273
$483$	0	0
$484$	9754.35	0.916074
$485$	6275.99	0.587584
$486$	486.000	0.0453609
$487$	−3786.27	−0.352305	−0.176152	−	0.984363i	$-0.556365\pi$
$487$	−3786.27	−0.352305	−0.176152	+	0.984363i	$0.556365\pi$
$488$	−4634.45	−0.429901
$489$	−296.200	−0.0273919
$490$	0	0
$491$	−9582.12	−0.880723	−0.440361	−	0.897821i	$-0.645150\pi$
$491$	−9582.12	−0.880723	−0.440361	+	0.897821i	$0.645150\pi$
$492$	−5129.97	−0.470075
$493$	4436.00	0.405248
$494$	5992.64	0.545793
$495$	2154.75	0.195655
$496$	2121.65	0.192066
$497$	0	0
$498$	7141.99	0.642651
$499$	5581.55	0.500730	0.250365	−	0.968152i	$-0.419449\pi$
$499$	5581.55	0.500730	0.250365	+	0.968152i	$0.419449\pi$
$500$	3662.31	0.327567
$501$	6694.07	0.596944
$502$	−7445.51	−0.661970
$503$	−14116.3	−1.25132	−0.625661	−	0.780095i	$-0.715171\pi$
$503$	−14116.3	−1.25132	−0.625661	+	0.780095i	$0.715171\pi$
$504$	0	0
$505$	5768.35	0.508294
$506$	−11616.7	−1.02060
$507$	−2059.58	−0.180413
$508$	−10466.8	−0.914153
$509$	16787.6	1.46188	0.730941	−	0.682441i	$-0.239081\pi$
$509$	16787.6	1.46188	0.730941	+	0.682441i	$0.239081\pi$
$510$	−751.055	−0.0652103
$511$	0	0
$512$	−512.000	−0.0441942
$513$	1506.57	0.129662
$514$	−2460.30	−0.211127
$515$	4466.27	0.382150
$516$	−5251.05	−0.447994
$517$	−3499.94	−0.297731
$518$	0	0
$519$	−6302.53	−0.533045
$520$	1675.18	0.141272
$521$	−5598.61	−0.470786	−0.235393	−	0.971900i	$-0.575638\pi$
$521$	−5598.61	−0.470786	−0.235393	+	0.971900i	$0.575638\pi$
$522$	−2487.44	−0.208567
$523$	−13270.7	−1.10954	−0.554769	−	0.832004i	$-0.687193\pi$
$523$	−13270.7	−1.10954	−0.554769	+	0.832004i	$0.687193\pi$
$524$	710.352	0.0592211
$525$	0	0
$526$	−4777.27	−0.396005
$527$	4256.62	0.351843
$528$	2947.05	0.242905
$529$	−3217.27	−0.264426
$530$	−2055.72	−0.168481
$531$	4066.19	0.332312
$532$	0	0
$533$	22956.0	1.86554
$534$	−1398.51	−0.113332
$535$	−1703.90	−0.137694
$536$	−2476.70	−0.199584
$537$	−5167.63	−0.415269
$538$	−13404.6	−1.07419
$539$	0	0
$540$	421.145	0.0335615
$541$	−23017.5	−1.82921	−0.914603	−	0.404353i	$-0.867497\pi$
$541$	−23017.5	−1.82921	−0.914603	+	0.404353i	$0.867497\pi$
$542$	−9900.74	−0.784637
$543$	−4965.01	−0.392393
$544$	−1027.22	−0.0809587
$545$	648.687	0.0509848
$546$	0	0
$547$	4475.84	0.349859	0.174930	−	0.984581i	$-0.444030\pi$
$547$	4475.84	0.349859	0.174930	+	0.984581i	$0.444030\pi$
$548$	108.061	0.00842358
$549$	5213.76	0.405315
$550$	−13482.0	−1.04523
$551$	−7710.91	−0.596181
$552$	−2270.47	−0.175068
$553$	0	0
$554$	7410.35	0.568295
$555$	1745.48	0.133499
$556$	−3691.01	−0.281536
$557$	1541.70	0.117278	0.0586390	−	0.998279i	$-0.481324\pi$
$557$	1541.70	0.117278	0.0586390	+	0.998279i	$0.481324\pi$
$558$	−2386.85	−0.181082
$559$	23497.8	1.77791
$560$	0	0
$561$	5912.62	0.444975
$562$	−18649.5	−1.39979
$563$	13079.7	0.979115	0.489557	−	0.871971i	$-0.337158\pi$
$563$	13079.7	0.979115	0.489557	+	0.871971i	$0.337158\pi$
$564$	−684.061	−0.0510712
$565$	−1913.97	−0.142515
$566$	11139.0	0.827219
$567$	0	0
$568$	8471.88	0.625831
$569$	11411.2	0.840740	0.420370	−	0.907353i	$-0.361900\pi$
$569$	11411.2	0.840740	0.420370	+	0.907353i	$0.361900\pi$
$570$	1305.53	0.0959342
$571$	2311.74	0.169428	0.0847139	−	0.996405i	$-0.473002\pi$
$571$	2311.74	0.169428	0.0847139	+	0.996405i	$0.473002\pi$
$572$	−13187.7	−0.963995
$573$	3023.06	0.220402
$574$	0	0
$575$	10386.8	0.753324
$576$	576.000	0.0416667
$577$	25097.0	1.81075	0.905373	−	0.424617i	$-0.139591\pi$
$577$	25097.0	1.81075	0.905373	+	0.424617i	$0.139591\pi$
$578$	7765.12	0.558800
$579$	22.9455	0.00164694
$580$	−2155.50	−0.154314
$581$	0	0
$582$	−9656.62	−0.687766
$583$	16183.5	1.14966
$584$	−9549.26	−0.676629
$585$	−1884.57	−0.133192
$586$	3330.61	0.234789
$587$	19789.1	1.39145	0.695726	−	0.718307i	$-0.255083\pi$
$587$	19789.1	1.39145	0.695726	+	0.718307i	$0.255083\pi$
$588$	0	0
$589$	−7399.12	−0.517615
$590$	3523.58	0.245870
$591$	−8069.64	−0.561659
$592$	2387.30	0.165739
$593$	−2774.13	−0.192108	−0.0960540	−	0.995376i	$-0.530622\pi$
$593$	−2774.13	−0.192108	−0.0960540	+	0.995376i	$0.530622\pi$
$594$	−3315.44	−0.229013
$595$	0	0
$596$	2986.81	0.205276
$597$	−2602.49	−0.178414
$598$	10160.1	0.694777
$599$	−26190.3	−1.78649	−0.893245	−	0.449570i	$-0.851577\pi$
$599$	−26190.3	−1.78649	−0.893245	+	0.449570i	$0.851577\pi$
$600$	−2635.05	−0.179293
$601$	−11038.6	−0.749211	−0.374605	−	0.927184i	$-0.622222\pi$
$601$	−11038.6	−0.749211	−0.374605	+	0.927184i	$0.622222\pi$
$602$	0	0
$603$	2786.29	0.188170
$604$	8292.58	0.558643
$605$	−9509.26	−0.639019
$606$	−8875.54	−0.594957
$607$	−1854.39	−0.123999	−0.0619996	−	0.998076i	$-0.519748\pi$
$607$	−1854.39	−0.123999	−0.0619996	+	0.998076i	$0.519748\pi$
$608$	1785.57	0.119103
$609$	0	0
$610$	4518.01	0.299883
$611$	3061.08	0.202681
$612$	1155.62	0.0763286
$613$	−14856.8	−0.978894	−0.489447	−	0.872033i	$-0.662801\pi$
$613$	−14856.8	−0.978894	−0.489447	+	0.872033i	$0.662801\pi$
$614$	10606.6	0.697148
$615$	5001.07	0.327907
$616$	0	0
$617$	7600.00	0.495890	0.247945	−	0.968774i	$-0.420245\pi$
$617$	7600.00	0.495890	0.247945	+	0.968774i	$0.420245\pi$
$618$	−6872.08	−0.447307
$619$	22685.3	1.47302	0.736509	−	0.676427i	$-0.236473\pi$
$619$	22685.3	1.47302	0.736509	+	0.676427i	$0.236473\pi$
$620$	−2068.34	−0.133978
$621$	2554.28	0.165056
$622$	−2251.98	−0.145171
$623$	0	0
$624$	−2577.53	−0.165358
$625$	10154.0	0.649853
$626$	16599.0	1.05979
$627$	−10277.7	−0.654626
$628$	6264.88	0.398083
$629$	4789.59	0.303614
$630$	0	0
$631$	−12024.1	−0.758595	−0.379297	−	0.925275i	$-0.623834\pi$
$631$	−12024.1	−0.758595	−0.379297	+	0.925275i	$0.623834\pi$
$632$	−10556.5	−0.664420
$633$	−486.091	−0.0305219
$634$	8557.53	0.536061
$635$	10203.8	0.637679
$636$	3163.05	0.197206
$637$	0	0
$638$	16969.0	1.05299
$639$	−9530.86	−0.590039
$640$	499.135	0.0308282
$641$	11320.6	0.697559	0.348779	−	0.937205i	$-0.386596\pi$
$641$	11320.6	0.697559	0.348779	+	0.937205i	$0.386596\pi$
$642$	2621.73	0.161170
$643$	16843.6	1.03304	0.516521	−	0.856275i	$-0.327227\pi$
$643$	16843.6	1.03304	0.516521	+	0.856275i	$0.327227\pi$
$644$	0	0
$645$	5119.12	0.312504
$646$	3582.35	0.218182
$647$	7719.32	0.469054	0.234527	−	0.972110i	$-0.424646\pi$
$647$	7719.32	0.469054	0.234527	+	0.972110i	$0.424646\pi$
$648$	−648.000	−0.0392837
$649$	−27739.1	−1.67774
$650$	11791.5	0.711542
$651$	0	0
$652$	394.933	0.0237221
$653$	−30803.2	−1.84597	−0.922987	−	0.384832i	$-0.874259\pi$
$653$	−30803.2	−1.84597	−0.922987	+	0.384832i	$0.874259\pi$
$654$	−998.109	−0.0596776
$655$	−692.503	−0.0413104
$656$	6839.96	0.407097
$657$	10742.9	0.637932
$658$	0	0
$659$	9760.68	0.576968	0.288484	−	0.957485i	$-0.406849\pi$
$659$	9760.68	0.576968	0.288484	+	0.957485i	$0.406849\pi$
$660$	−2873.01	−0.169442
$661$	18071.1	1.06336	0.531682	−	0.846944i	$-0.321560\pi$
$661$	18071.1	1.06336	0.531682	+	0.846944i	$0.321560\pi$
$662$	3414.23	0.200450
$663$	−5171.25	−0.302918
$664$	−9522.65	−0.556552
$665$	0	0
$666$	−2685.71	−0.156260
$667$	−13073.3	−0.758920
$668$	−8925.43	−0.516969
$669$	13733.5	0.793676
$670$	2414.47	0.139223
$671$	−35567.7	−2.04631
$672$	0	0
$673$	26591.1	1.52305	0.761524	−	0.648137i	$-0.224451\pi$
$673$	26591.1	1.52305	0.761524	+	0.648137i	$0.224451\pi$
$674$	−3421.35	−0.195527
$675$	2964.44	0.169039
$676$	2746.11	0.156242
$677$	33080.3	1.87796	0.938979	−	0.343975i	$-0.111773\pi$
$677$	33080.3	1.87796	0.938979	+	0.343975i	$0.111773\pi$
$678$	2944.95	0.166814
$679$	0	0
$680$	1001.41	0.0564738
$681$	6654.57	0.374455
$682$	16282.8	0.914227
$683$	−10466.1	−0.586344	−0.293172	−	0.956060i	$-0.594711\pi$
$683$	−10466.1	−0.586344	−0.293172	+	0.956060i	$0.594711\pi$
$684$	−2008.76	−0.112291
$685$	−105.345	−0.00587597
$686$	0	0
$687$	−2355.65	−0.130820
$688$	7001.41	0.387974
$689$	−14154.3	−0.782634
$690$	2213.42	0.122121
$691$	13269.9	0.730551	0.365275	−	0.930900i	$-0.380975\pi$
$691$	13269.9	0.730551	0.365275	+	0.930900i	$0.380975\pi$
$692$	8403.38	0.461631
$693$	0	0
$694$	−17820.6	−0.974727
$695$	3598.27	0.196389
$696$	3316.58	0.180625
$697$	13722.9	0.745755
$698$	−10757.4	−0.583341
$699$	16107.4	0.871583
$700$	0	0
$701$	−15169.9	−0.817344	−0.408672	−	0.912681i	$-0.634008\pi$
$701$	−15169.9	−0.817344	−0.408672	+	0.912681i	$0.634008\pi$
$702$	2899.72	0.155901
$703$	−8325.55	−0.446663
$704$	−3929.41	−0.210362
$705$	666.873	0.0356254
$706$	8505.13	0.453392
$707$	0	0
$708$	−5421.59	−0.287791
$709$	26317.7	1.39405	0.697026	−	0.717046i	$-0.254506\pi$
$709$	26317.7	1.39405	0.697026	+	0.717046i	$0.254506\pi$
$710$	−8259.01	−0.436557
$711$	11876.0	0.626421
$712$	1864.68	0.0981488
$713$	−12544.6	−0.658907
$714$	0	0
$715$	12856.3	0.672447
$716$	6890.17	0.359634
$717$	−11139.8	−0.580229
$718$	−9807.78	−0.509781
$719$	23013.1	1.19366	0.596831	−	0.802367i	$-0.296426\pi$
$719$	23013.1	1.19366	0.596831	+	0.802367i	$0.296426\pi$
$720$	−561.527	−0.0290651
$721$	0	0
$722$	7490.95	0.386128
$723$	−20995.9	−1.08001
$724$	6620.02	0.339822
$725$	−15172.5	−0.777232
$726$	14631.5	0.747971
$727$	−16265.4	−0.829780	−0.414890	−	0.909872i	$-0.636180\pi$
$727$	−16265.4	−0.829780	−0.414890	+	0.909872i	$0.636180\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	9309.33	0.471991
$731$	14046.8	0.710724
$732$	−6951.68	−0.351013
$733$	−866.444	−0.0436601	−0.0218300	−	0.999762i	$-0.506949\pi$
$733$	−866.444	−0.0436601	−0.0218300	+	0.999762i	$0.506949\pi$
$734$	8083.14	0.406477
$735$	0	0
$736$	3027.30	0.151614
$737$	−19007.8	−0.950013
$738$	−7694.95	−0.383815
$739$	10990.1	0.547058	0.273529	−	0.961864i	$-0.411809\pi$
$739$	10990.1	0.547058	0.273529	+	0.961864i	$0.411809\pi$
$740$	−2327.31	−0.115613
$741$	8988.96	0.445638
$742$	0	0
$743$	−22416.4	−1.10683	−0.553417	−	0.832905i	$-0.686676\pi$
$743$	−22416.4	−1.10683	−0.553417	+	0.832905i	$0.686676\pi$
$744$	3182.47	0.156821
$745$	−2911.76	−0.143193
$746$	14902.7	0.731403
$747$	10713.0	0.524722
$748$	−7883.49	−0.385360
$749$	0	0
$750$	5493.47	0.267457
$751$	−19717.9	−0.958080	−0.479040	−	0.877793i	$-0.659015\pi$
$751$	−19717.9	−0.958080	−0.479040	+	0.877793i	$0.659015\pi$
$752$	912.081	0.0442289
$753$	−11168.3	−0.540497
$754$	−14841.3	−0.716827
$755$	−8084.22	−0.389689
$756$	0	0
$757$	839.321	0.0402981	0.0201490	−	0.999797i	$-0.493586\pi$
$757$	839.321	0.0402981	0.0201490	+	0.999797i	$0.493586\pi$
$758$	25128.8	1.20411
$759$	−17425.0	−0.833318
$760$	−1740.70	−0.0830815
$761$	18364.5	0.874786	0.437393	−	0.899270i	$-0.355902\pi$
$761$	18364.5	0.874786	0.437393	+	0.899270i	$0.355902\pi$
$762$	−15700.2	−0.746403
$763$	0	0
$764$	−4030.75	−0.190874
$765$	−1126.58	−0.0532440
$766$	8579.86	0.404704
$767$	24260.9	1.14213
$768$	−768.000	−0.0360844
$769$	−14890.8	−0.698277	−0.349138	−	0.937071i	$-0.613526\pi$
$769$	−14890.8	−0.698277	−0.349138	+	0.937071i	$0.613526\pi$
$770$	0	0
$771$	−3690.45	−0.172384
$772$	−30.5939	−0.00142630
$773$	−16606.2	−0.772683	−0.386341	−	0.922356i	$-0.626261\pi$
$773$	−16606.2	−0.772683	−0.386341	+	0.922356i	$0.626261\pi$
$774$	−7876.58	−0.365785
$775$	−14559.0	−0.674807
$776$	12875.5	0.595623
$777$	0	0
$778$	−11325.5	−0.521903
$779$	−23853.9	−1.09712
$780$	2512.76	0.115348
$781$	65018.5	2.97893
$782$	6073.61	0.277739
$783$	−3731.15	−0.170294
$784$	0	0
$785$	−6107.47	−0.277688
$786$	1065.53	0.0483538
$787$	3156.20	0.142956	0.0714781	−	0.997442i	$-0.477228\pi$
$787$	3156.20	0.142956	0.0714781	+	0.997442i	$0.477228\pi$
$788$	10759.5	0.486411
$789$	−7165.90	−0.323337
$790$	10291.2	0.463475
$791$	0	0
$792$	4420.58	0.198331
$793$	31107.9	1.39303
$794$	−29122.8	−1.30167
$795$	−3083.58	−0.137564
$796$	3469.99	0.154511
$797$	−13514.8	−0.600652	−0.300326	−	0.953837i	$-0.597096\pi$
$797$	−13514.8	−0.600652	−0.300326	+	0.953837i	$0.597096\pi$
$798$	0	0
$799$	1829.89	0.0810224
$800$	3513.41	0.155272
$801$	−2097.77	−0.0925356
$802$	7484.38	0.329530
$803$	−73287.0	−3.22072
$804$	−3715.05	−0.162960
$805$	0	0
$806$	−14241.2	−0.622362
$807$	−20106.9	−0.877073
$808$	11834.0	0.515248
$809$	−26758.1	−1.16287	−0.581437	−	0.813591i	$-0.697509\pi$
$809$	−26758.1	−1.16287	−0.581437	+	0.813591i	$0.697509\pi$
$810$	631.718	0.0274029
$811$	−15920.7	−0.689338	−0.344669	−	0.938724i	$-0.612009\pi$
$811$	−15920.7	−0.689338	−0.344669	+	0.938724i	$0.612009\pi$
$812$	0	0
$813$	−14851.1	−0.640653
$814$	18321.6	0.788909
$815$	−385.010	−0.0165476
$816$	−1540.82	−0.0661025
$817$	−24417.0	−1.04558
$818$	7034.35	0.300673
$819$	0	0
$820$	−6668.10	−0.283976
$821$	−19306.2	−0.820696	−0.410348	−	0.911929i	$-0.634593\pi$
$821$	−19306.2	−0.820696	−0.410348	+	0.911929i	$0.634593\pi$
$822$	162.091	0.00687782
$823$	791.000	0.0335025	0.0167512	−	0.999860i	$-0.494668\pi$
$823$	791.000	0.0335025	0.0167512	+	0.999860i	$0.494668\pi$
$824$	9162.77	0.387379
$825$	−20223.0	−0.853426
$826$	0	0
$827$	29537.6	1.24199	0.620993	−	0.783816i	$-0.286730\pi$
$827$	29537.6	1.24199	0.620993	+	0.783816i	$0.286730\pi$
$828$	−3405.71	−0.142943
$829$	−5766.52	−0.241592	−0.120796	−	0.992677i	$-0.538545\pi$
$829$	−5766.52	−0.241592	−0.120796	+	0.992677i	$0.538545\pi$
$830$	9283.38	0.388230
$831$	11115.5	0.464011
$832$	3436.70	0.143205
$833$	0	0
$834$	−5536.52	−0.229873
$835$	8701.16	0.360618
$836$	13703.6	0.566923
$837$	−3580.28	−0.147853
$838$	15159.0	0.624893
$839$	29726.4	1.22321	0.611603	−	0.791165i	$-0.290525\pi$
$839$	29726.4	1.22321	0.611603	+	0.791165i	$0.290525\pi$
$840$	0	0
$841$	−5292.27	−0.216994
$842$	9961.75	0.407725
$843$	−27974.2	−1.14292
$844$	648.121	0.0264328
$845$	−2677.11	−0.108989
$846$	−1026.09	−0.0416994
$847$	0	0
$848$	−4217.41	−0.170786
$849$	16708.5	0.675421
$850$	7048.88	0.284441
$851$	−14115.3	−0.568587
$852$	12707.8	0.510989
$853$	−17829.6	−0.715677	−0.357838	−	0.933784i	$-0.616486\pi$
$853$	−17829.6	−0.715677	−0.357838	+	0.933784i	$0.616486\pi$
$854$	0	0
$855$	1958.29	0.0783300
$856$	−3495.64	−0.139578
$857$	−39682.4	−1.58171	−0.790856	−	0.612003i	$-0.790364\pi$
$857$	−39682.4	−1.58171	−0.790856	+	0.612003i	$0.790364\pi$
$858$	−19781.5	−0.787099
$859$	−2195.13	−0.0871909	−0.0435955	−	0.999049i	$-0.513881\pi$
$859$	−2195.13	−0.0871909	−0.0435955	+	0.999049i	$0.513881\pi$
$860$	−6825.49	−0.270636
$861$	0	0
$862$	−28406.6	−1.12243
$863$	31917.1	1.25894	0.629472	−	0.777023i	$-0.283271\pi$
$863$	31917.1	1.25894	0.629472	+	0.777023i	$0.283271\pi$
$864$	864.000	0.0340207
$865$	−8192.23	−0.322016
$866$	−7749.65	−0.304092
$867$	11647.7	0.456258
$868$	0	0
$869$	−81016.8	−3.16261
$870$	−3233.25	−0.125997
$871$	16624.4	0.646724
$872$	1330.81	0.0516823
$873$	−14484.9	−0.561559
$874$	−10557.5	−0.408596
$875$	0	0
$876$	−14323.9	−0.552465
$877$	28842.9	1.11055	0.555276	−	0.831666i	$-0.312613\pi$
$877$	28842.9	1.11055	0.555276	+	0.831666i	$0.312613\pi$
$878$	−15527.6	−0.596848
$879$	4995.92	0.191704
$880$	3830.67	0.146741
$881$	−15350.2	−0.587015	−0.293508	−	0.955957i	$-0.594823\pi$
$881$	−15350.2	−0.587015	−0.293508	+	0.955957i	$0.594823\pi$
$882$	0	0
$883$	6089.64	0.232087	0.116043	−	0.993244i	$-0.462979\pi$
$883$	6089.64	0.232087	0.116043	+	0.993244i	$0.462979\pi$
$884$	6894.99	0.262335
$885$	5285.36	0.200752
$886$	−19324.5	−0.732752
$887$	−384.441	−0.0145527	−0.00727637	−	0.999974i	$-0.502316\pi$
$887$	−384.441	−0.0145527	−0.00727637	+	0.999974i	$0.502316\pi$
$888$	3580.95	0.135325
$889$	0	0
$890$	−1817.83	−0.0684650
$891$	−4973.15	−0.186989
$892$	−18311.4	−0.687344
$893$	−3180.82	−0.119196
$894$	4480.22	0.167607
$895$	−6717.05	−0.250867
$896$	0	0
$897$	15240.1	0.567283
$898$	21885.2	0.813271
$899$	18324.5	0.679819
$900$	−3952.58	−0.146392
$901$	−8461.30	−0.312860
$902$	52494.1	1.93776
$903$	0	0
$904$	−3926.59	−0.144465
$905$	−6453.68	−0.237047
$906$	12438.9	0.456130
$907$	−7267.93	−0.266073	−0.133036	−	0.991111i	$-0.542473\pi$
$907$	−7267.93	−0.266073	−0.133036	+	0.991111i	$0.542473\pi$
$908$	−8872.76	−0.324287
$909$	−13313.3	−0.485780
$910$	0	0
$911$	−8535.12	−0.310408	−0.155204	−	0.987882i	$-0.549603\pi$
$911$	−8535.12	−0.310408	−0.155204	+	0.987882i	$0.549603\pi$
$912$	2678.35	0.0972468
$913$	−73082.7	−2.64916
$914$	−27236.7	−0.985678
$915$	6777.01	0.244854
$916$	3140.87	0.113294
$917$	0	0
$918$	1733.43	0.0623220
$919$	−10851.7	−0.389516	−0.194758	−	0.980851i	$-0.562392\pi$
$919$	−10851.7	−0.389516	−0.194758	+	0.980851i	$0.562392\pi$
$920$	−2951.23	−0.105760
$921$	15909.9	0.569219
$922$	−23911.7	−0.854110
$923$	−56865.9	−2.02791
$924$	0	0
$925$	−16381.9	−0.582307
$926$	−1297.01	−0.0460284
$927$	−10308.1	−0.365224
$928$	−4422.11	−0.156425
$929$	−1560.64	−0.0551161	−0.0275581	−	0.999620i	$-0.508773\pi$
$929$	−1560.64	−0.0551161	−0.0275581	+	0.999620i	$0.508773\pi$
$930$	−3102.51	−0.109393
$931$	0	0
$932$	−21476.5	−0.754813
$933$	−3377.97	−0.118531
$934$	−5569.49	−0.195117
$935$	7685.41	0.268813
$936$	−3866.29	−0.135015
$937$	11978.4	0.417627	0.208813	−	0.977956i	$-0.433040\pi$
$937$	11978.4	0.417627	0.208813	+	0.977956i	$0.433040\pi$
$938$	0	0
$939$	24898.5	0.865317
$940$	−889.164	−0.0308525
$941$	24597.7	0.852137	0.426068	−	0.904691i	$-0.359898\pi$
$941$	24597.7	0.852137	0.426068	+	0.904691i	$0.359898\pi$
$942$	9397.32	0.325033
$943$	−40442.6	−1.39660
$944$	7228.78	0.249234
$945$	0	0
$946$	53733.1	1.84674
$947$	−10834.6	−0.371783	−0.185891	−	0.982570i	$-0.559517\pi$
$947$	−10834.6	−0.371783	−0.185891	+	0.982570i	$0.559517\pi$
$948$	−15834.7	−0.542497
$949$	64097.6	2.19252
$950$	−12252.8	−0.418456
$951$	12836.3	0.437692
$952$	0	0
$953$	701.418	0.0238417	0.0119209	−	0.999929i	$-0.496205\pi$
$953$	701.418	0.0238417	0.0119209	+	0.999929i	$0.496205\pi$
$954$	4744.58	0.161018
$955$	3929.47	0.133146
$956$	14853.1	0.502493
$957$	25453.5	0.859765
$958$	−22226.8	−0.749599
$959$	0	0
$960$	748.703	0.0251711
$961$	−12207.4	−0.409769
$962$	−16024.3	−0.537051
$963$	3932.59	0.131595
$964$	27994.5	0.935313
$965$	29.8252	0.000994931 0
$966$	0	0
$967$	42402.5	1.41011	0.705053	−	0.709154i	$-0.250923\pi$
$967$	42402.5	1.41011	0.705053	+	0.709154i	$0.250923\pi$
$968$	−19508.7	−0.647762
$969$	5373.53	0.178145
$970$	−12552.0	−0.415484
$971$	15463.4	0.511064	0.255532	−	0.966801i	$-0.417749\pi$
$971$	15463.4	0.511064	0.255532	+	0.966801i	$0.417749\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	7572.55	0.249117
$975$	17687.3	0.580971
$976$	9268.91	0.303986
$977$	−34484.1	−1.12922	−0.564609	−	0.825359i	$-0.690973\pi$
$977$	−34484.1	−1.12922	−0.564609	+	0.825359i	$0.690973\pi$
$978$	592.400	0.0193690
$979$	14310.7	0.467184
$980$	0	0
$981$	−1497.16	−0.0487266
$982$	19164.2	0.622765
$983$	7335.36	0.238008	0.119004	−	0.992894i	$-0.462030\pi$
$983$	7335.36	0.238008	0.119004	+	0.992894i	$0.462030\pi$
$984$	10259.9	0.332393
$985$	−10489.2	−0.339302
$986$	−8872.00	−0.286554
$987$	0	0
$988$	−11985.3	−0.385934
$989$	−41397.1	−1.33099
$990$	−4309.51	−0.138349
$991$	−10123.0	−0.324487	−0.162243	−	0.986751i	$-0.551873\pi$
$991$	−10123.0	−0.324487	−0.162243	+	0.986751i	$0.551873\pi$
$992$	−4243.30	−0.135811
$993$	5121.35	0.163667
$994$	0	0
$995$	−3382.80	−0.107781
$996$	−14284.0	−0.454423
$997$	56669.2	1.80013	0.900066	−	0.435755i	$-0.143518\pi$
$997$	56669.2	1.80013	0.900066	+	0.435755i	$0.143518\pi$
$998$	−11163.1	−0.354070
$999$	−4028.56	−0.127586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.a.j.1.1	✓	2
3.2	odd	2		882.4.a.bc.1.2		2
4.3	odd	2		2352.4.a.cd.1.1		2
7.2	even	3		294.4.e.o.67.2		4
7.3	odd	6		294.4.e.n.79.1		4
7.4	even	3		294.4.e.o.79.2		4
7.5	odd	6		294.4.e.n.67.1		4
7.6	odd	2		294.4.a.k.1.2	yes	2
21.2	odd	6		882.4.g.bd.361.1		4
21.5	even	6		882.4.g.y.361.2		4
21.11	odd	6		882.4.g.bd.667.1		4
21.17	even	6		882.4.g.y.667.2		4
21.20	even	2		882.4.a.bi.1.1		2
28.27	even	2		2352.4.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.j.1.1	✓	2	1.1	even	1	trivial
294.4.a.k.1.2	yes	2	7.6	odd	2
294.4.e.n.67.1		4	7.5	odd	6
294.4.e.n.79.1		4	7.3	odd	6
294.4.e.o.67.2		4	7.2	even	3
294.4.e.o.79.2		4	7.4	even	3
882.4.a.bc.1.2		2	3.2	odd	2
882.4.a.bi.1.1		2	21.20	even	2
882.4.g.y.361.2		4	21.5	even	6
882.4.g.y.667.2		4	21.17	even	6
882.4.g.bd.361.1		4	21.2	odd	6
882.4.g.bd.667.1		4	21.11	odd	6
2352.4.a.bn.1.2		2	28.27	even	2
2352.4.a.cd.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -3.89949 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -3.89949 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +7.79899 q^{10} -61.3970 q^{11} -12.0000 q^{12} +53.6985 q^{13} +11.6985 q^{15} +16.0000 q^{16} +32.1005 q^{17} -18.0000 q^{18} -55.7990 q^{19} -15.5980 q^{20} +122.794 q^{22} -94.6030 q^{23} +24.0000 q^{24} -109.794 q^{25} -107.397 q^{26} -27.0000 q^{27} +138.191 q^{29} -23.3970 q^{30} +132.603 q^{31} -32.0000 q^{32} +184.191 q^{33} -64.2010 q^{34} +36.0000 q^{36} +149.206 q^{37} +111.598 q^{38} -161.095 q^{39} +31.1960 q^{40} +427.497 q^{41} +437.588 q^{43} -245.588 q^{44} -35.0955 q^{45} +189.206 q^{46} +57.0051 q^{47} -48.0000 q^{48} +219.588 q^{50} -96.3015 q^{51} +214.794 q^{52} -263.588 q^{53} +54.0000 q^{54} +239.417 q^{55} +167.397 q^{57} -276.382 q^{58} +451.799 q^{59} +46.7939 q^{60} +579.307 q^{61} -265.206 q^{62} +64.0000 q^{64} -209.397 q^{65} -368.382 q^{66} +309.588 q^{67} +128.402 q^{68} +283.809 q^{69} -1058.98 q^{71} -72.0000 q^{72} +1193.66 q^{73} -298.412 q^{74} +329.382 q^{75} -223.196 q^{76} +322.191 q^{78} +1319.56 q^{79} -62.3919 q^{80} +81.0000 q^{81} -854.995 q^{82} +1190.33 q^{83} -125.176 q^{85} -875.176 q^{86} -414.573 q^{87} +491.176 q^{88} -233.085 q^{89} +70.1909 q^{90} -378.412 q^{92} -397.809 q^{93} -114.010 q^{94} +217.588 q^{95} +96.0000 q^{96} -1609.44 q^{97} -552.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 48 q^{13} - 36 q^{15} + 32 q^{16} + 84 q^{17} - 36 q^{18} - 72 q^{19} + 48 q^{20} + 8 q^{22} - 308 q^{23} + 48 q^{24} + 18 q^{25} - 96 q^{26} - 54 q^{27} - 80 q^{29} + 72 q^{30} + 384 q^{31} - 64 q^{32} + 12 q^{33} - 168 q^{34} + 72 q^{36} + 536 q^{37} + 144 q^{38} - 144 q^{39} - 96 q^{40} + 756 q^{41} + 400 q^{43} - 16 q^{44} + 108 q^{45} + 616 q^{46} + 312 q^{47} - 96 q^{48} - 36 q^{50} - 252 q^{51} + 192 q^{52} - 52 q^{53} + 108 q^{54} + 1152 q^{55} + 216 q^{57} + 160 q^{58} + 864 q^{59} - 144 q^{60} + 1416 q^{61} - 768 q^{62} + 128 q^{64} - 300 q^{65} - 24 q^{66} + 144 q^{67} + 336 q^{68} + 924 q^{69} - 1524 q^{71} - 144 q^{72} + 744 q^{73} - 1072 q^{74} - 54 q^{75} - 288 q^{76} + 288 q^{78} + 976 q^{79} + 192 q^{80} + 162 q^{81} - 1512 q^{82} - 312 q^{83} + 700 q^{85} - 800 q^{86} + 240 q^{87} + 32 q^{88} + 108 q^{89} - 216 q^{90} - 1232 q^{92} - 1152 q^{93} - 624 q^{94} - 40 q^{95} + 192 q^{96} - 744 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 48 * q^13 - 36 * q^15 + 32 * q^16 + 84 * q^17 - 36 * q^18 - 72 * q^19 + 48 * q^20 + 8 * q^22 - 308 * q^23 + 48 * q^24 + 18 * q^25 - 96 * q^26 - 54 * q^27 - 80 * q^29 + 72 * q^30 + 384 * q^31 - 64 * q^32 + 12 * q^33 - 168 * q^34 + 72 * q^36 + 536 * q^37 + 144 * q^38 - 144 * q^39 - 96 * q^40 + 756 * q^41 + 400 * q^43 - 16 * q^44 + 108 * q^45 + 616 * q^46 + 312 * q^47 - 96 * q^48 - 36 * q^50 - 252 * q^51 + 192 * q^52 - 52 * q^53 + 108 * q^54 + 1152 * q^55 + 216 * q^57 + 160 * q^58 + 864 * q^59 - 144 * q^60 + 1416 * q^61 - 768 * q^62 + 128 * q^64 - 300 * q^65 - 24 * q^66 + 144 * q^67 + 336 * q^68 + 924 * q^69 - 1524 * q^71 - 144 * q^72 + 744 * q^73 - 1072 * q^74 - 54 * q^75 - 288 * q^76 + 288 * q^78 + 976 * q^79 + 192 * q^80 + 162 * q^81 - 1512 * q^82 - 312 * q^83 + 700 * q^85 - 800 * q^86 + 240 * q^87 + 32 * q^88 + 108 * q^89 - 216 * q^90 - 1232 * q^92 - 1152 * q^93 - 624 * q^94 - 40 * q^95 + 192 * q^96 - 744 * q^97 - 36 * q^99

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