LMFDB - Embedded newform 966.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 356x^{2} + 245x + 16751 $ x^4 - x^3 - 356x^2 + 245x + 16751
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			1.1
Root			$17.4461$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -18.4461 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -18.4461 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +36.8923 q^{10} -50.2119 q^{11} -12.0000 q^{12} +85.6292 q^{13} +14.0000 q^{14} +55.3384 q^{15} +16.0000 q^{16} -92.4861 q^{17} -18.0000 q^{18} +9.31964 q^{19} -73.7845 q^{20} +21.0000 q^{21} +100.424 q^{22} +23.0000 q^{23} +24.0000 q^{24} +215.260 q^{25} -171.258 q^{26} -27.0000 q^{27} -28.0000 q^{28} +131.196 q^{29} -110.677 q^{30} +132.843 q^{31} -32.0000 q^{32} +150.636 q^{33} +184.972 q^{34} +129.123 q^{35} +36.0000 q^{36} +143.626 q^{37} -18.6393 q^{38} -256.888 q^{39} +147.569 q^{40} -149.502 q^{41} -42.0000 q^{42} +90.3234 q^{43} -200.848 q^{44} -166.015 q^{45} -46.0000 q^{46} +501.622 q^{47} -48.0000 q^{48} +49.0000 q^{49} -430.519 q^{50} +277.458 q^{51} +342.517 q^{52} -108.952 q^{53} +54.0000 q^{54} +926.215 q^{55} +56.0000 q^{56} -27.9589 q^{57} -262.392 q^{58} +459.906 q^{59} +221.354 q^{60} -227.420 q^{61} -265.686 q^{62} -63.0000 q^{63} +64.0000 q^{64} -1579.53 q^{65} -301.271 q^{66} -941.576 q^{67} -369.944 q^{68} -69.0000 q^{69} -258.246 q^{70} +525.103 q^{71} -72.0000 q^{72} -676.099 q^{73} -287.253 q^{74} -645.779 q^{75} +37.2785 q^{76} +351.483 q^{77} +513.775 q^{78} +75.5819 q^{79} -295.138 q^{80} +81.0000 q^{81} +299.004 q^{82} +974.756 q^{83} +84.0000 q^{84} +1706.01 q^{85} -180.647 q^{86} -393.588 q^{87} +401.695 q^{88} +517.659 q^{89} +332.030 q^{90} -599.404 q^{91} +92.0000 q^{92} -398.529 q^{93} -1003.24 q^{94} -171.911 q^{95} +96.0000 q^{96} -1282.52 q^{97} -98.0000 q^{98} -451.907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} - 5 q^{5} + 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 - 5 * q^5 + 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} - 5 q^{5} + 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 10 q^{10} - 41 q^{11} - 48 q^{12} + 23 q^{13} + 56 q^{14} + 15 q^{15} + 64 q^{16} + 18 q^{17} - 72 q^{18} + 15 q^{19} - 20 q^{20} + 84 q^{21} + 82 q^{22} + 92 q^{23} + 96 q^{24} + 219 q^{25} - 46 q^{26} - 108 q^{27} - 112 q^{28} - 46 q^{29} - 30 q^{30} + 142 q^{31} - 128 q^{32} + 123 q^{33} - 36 q^{34} + 35 q^{35} + 144 q^{36} - 142 q^{37} - 30 q^{38} - 69 q^{39} + 40 q^{40} - 621 q^{41} - 168 q^{42} + 185 q^{43} - 164 q^{44} - 45 q^{45} - 184 q^{46} + 669 q^{47} - 192 q^{48} + 196 q^{49} - 438 q^{50} - 54 q^{51} + 92 q^{52} + 422 q^{53} + 216 q^{54} + 1435 q^{55} + 224 q^{56} - 45 q^{57} + 92 q^{58} + 270 q^{59} + 60 q^{60} + 272 q^{61} - 284 q^{62} - 252 q^{63} + 256 q^{64} - 1992 q^{65} - 246 q^{66} - 67 q^{67} + 72 q^{68} - 276 q^{69} - 70 q^{70} + 611 q^{71} - 288 q^{72} - 236 q^{73} + 284 q^{74} - 657 q^{75} + 60 q^{76} + 287 q^{77} + 138 q^{78} + 558 q^{79} - 80 q^{80} + 324 q^{81} + 1242 q^{82} + 468 q^{83} + 336 q^{84} + 1045 q^{85} - 370 q^{86} + 138 q^{87} + 328 q^{88} - 1519 q^{89} + 90 q^{90} - 161 q^{91} + 368 q^{92} - 426 q^{93} - 1338 q^{94} + 23 q^{95} + 384 q^{96} + 600 q^{97} - 392 q^{98} - 369 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 - 5 * q^5 + 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 + 10 * q^10 - 41 * q^11 - 48 * q^12 + 23 * q^13 + 56 * q^14 + 15 * q^15 + 64 * q^16 + 18 * q^17 - 72 * q^18 + 15 * q^19 - 20 * q^20 + 84 * q^21 + 82 * q^22 + 92 * q^23 + 96 * q^24 + 219 * q^25 - 46 * q^26 - 108 * q^27 - 112 * q^28 - 46 * q^29 - 30 * q^30 + 142 * q^31 - 128 * q^32 + 123 * q^33 - 36 * q^34 + 35 * q^35 + 144 * q^36 - 142 * q^37 - 30 * q^38 - 69 * q^39 + 40 * q^40 - 621 * q^41 - 168 * q^42 + 185 * q^43 - 164 * q^44 - 45 * q^45 - 184 * q^46 + 669 * q^47 - 192 * q^48 + 196 * q^49 - 438 * q^50 - 54 * q^51 + 92 * q^52 + 422 * q^53 + 216 * q^54 + 1435 * q^55 + 224 * q^56 - 45 * q^57 + 92 * q^58 + 270 * q^59 + 60 * q^60 + 272 * q^61 - 284 * q^62 - 252 * q^63 + 256 * q^64 - 1992 * q^65 - 246 * q^66 - 67 * q^67 + 72 * q^68 - 276 * q^69 - 70 * q^70 + 611 * q^71 - 288 * q^72 - 236 * q^73 + 284 * q^74 - 657 * q^75 + 60 * q^76 + 287 * q^77 + 138 * q^78 + 558 * q^79 - 80 * q^80 + 324 * q^81 + 1242 * q^82 + 468 * q^83 + 336 * q^84 + 1045 * q^85 - 370 * q^86 + 138 * q^87 + 328 * q^88 - 1519 * q^89 + 90 * q^90 - 161 * q^91 + 368 * q^92 - 426 * q^93 - 1338 * q^94 + 23 * q^95 + 384 * q^96 + 600 * q^97 - 392 * q^98 - 369 * 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
$5$	−18.4461	−1.64987	−0.824936	−	0.565226i	$-0.808789\pi$
$5$	−18.4461	−1.64987	−0.824936	+	0.565226i	$0.808789\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	36.8923	1.16664
$11$	−50.2119	−1.37631	−0.688157	−	0.725562i	$-0.741580\pi$
$11$	−50.2119	−1.37631	−0.688157	+	0.725562i	$0.741580\pi$
$12$	−12.0000	−0.288675
$13$	85.6292	1.82687	0.913433	−	0.406989i	$-0.133421\pi$
$13$	85.6292	1.82687	0.913433	+	0.406989i	$0.133421\pi$
$14$	14.0000	0.267261
$15$	55.3384	0.952554
$16$	16.0000	0.250000
$17$	−92.4861	−1.31948	−0.659740	−	0.751494i	$-0.729334\pi$
$17$	−92.4861	−1.31948	−0.659740	+	0.751494i	$0.729334\pi$
$18$	−18.0000	−0.235702
$19$	9.31964	0.112530	0.0562650	−	0.998416i	$-0.482081\pi$
$19$	9.31964	0.112530	0.0562650	+	0.998416i	$0.482081\pi$
$20$	−73.7845	−0.824936
$21$	21.0000	0.218218
$22$	100.424	0.973201
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	24.0000	0.204124
$25$	215.260	1.72208
$26$	−171.258	−1.29179
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	131.196	0.840086	0.420043	−	0.907504i	$-0.362015\pi$
$29$	131.196	0.840086	0.420043	+	0.907504i	$0.362015\pi$
$30$	−110.677	−0.673557
$31$	132.843	0.769655	0.384828	−	0.922988i	$-0.374261\pi$
$31$	132.843	0.769655	0.384828	+	0.922988i	$0.374261\pi$
$32$	−32.0000	−0.176777
$33$	150.636	0.794615
$34$	184.972	0.933014
$35$	129.123	0.623593
$36$	36.0000	0.166667
$37$	143.626	0.638163	0.319082	−	0.947727i	$-0.396626\pi$
$37$	143.626	0.638163	0.319082	+	0.947727i	$0.396626\pi$
$38$	−18.6393	−0.0795708
$39$	−256.888	−1.05474
$40$	147.569	0.583318
$41$	−149.502	−0.569470	−0.284735	−	0.958606i	$-0.591906\pi$
$41$	−149.502	−0.569470	−0.284735	+	0.958606i	$0.591906\pi$
$42$	−42.0000	−0.154303
$43$	90.3234	0.320330	0.160165	−	0.987090i	$-0.448797\pi$
$43$	90.3234	0.320330	0.160165	+	0.987090i	$0.448797\pi$
$44$	−200.848	−0.688157
$45$	−166.015	−0.549957
$46$	−46.0000	−0.147442
$47$	501.622	1.55679	0.778394	−	0.627776i	$-0.216035\pi$
$47$	501.622	1.55679	0.778394	+	0.627776i	$0.216035\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−430.519	−1.21769
$51$	277.458	0.761802
$52$	342.517	0.913433
$53$	−108.952	−0.282372	−0.141186	−	0.989983i	$-0.545092\pi$
$53$	−108.952	−0.282372	−0.141186	+	0.989983i	$0.545092\pi$
$54$	54.0000	0.136083
$55$	926.215	2.27074
$56$	56.0000	0.133631
$57$	−27.9589	−0.0649693
$58$	−262.392	−0.594031
$59$	459.906	1.01482	0.507412	−	0.861704i	$-0.330602\pi$
$59$	459.906	1.01482	0.507412	+	0.861704i	$0.330602\pi$
$60$	221.354	0.476277
$61$	−227.420	−0.477346	−0.238673	−	0.971100i	$-0.576712\pi$
$61$	−227.420	−0.477346	−0.238673	+	0.971100i	$0.576712\pi$
$62$	−265.686	−0.544228
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−1579.53	−3.01410
$66$	−301.271	−0.561878
$67$	−941.576	−1.71689	−0.858446	−	0.512904i	$-0.828570\pi$
$67$	−941.576	−1.71689	−0.858446	+	0.512904i	$0.828570\pi$
$68$	−369.944	−0.659740
$69$	−69.0000	−0.120386
$70$	−258.246	−0.440947
$71$	525.103	0.877722	0.438861	−	0.898555i	$-0.355382\pi$
$71$	525.103	0.877722	0.438861	+	0.898555i	$0.355382\pi$
$72$	−72.0000	−0.117851
$73$	−676.099	−1.08399	−0.541996	−	0.840381i	$-0.682331\pi$
$73$	−676.099	−1.08399	−0.541996	+	0.840381i	$0.682331\pi$
$74$	−287.253	−0.451250
$75$	−645.779	−0.994242
$76$	37.2785	0.0562650
$77$	351.483	0.520198
$78$	513.775	0.745815
$79$	75.5819	0.107641	0.0538205	−	0.998551i	$-0.482860\pi$
$79$	75.5819	0.107641	0.0538205	+	0.998551i	$0.482860\pi$
$80$	−295.138	−0.412468
$81$	81.0000	0.111111
$82$	299.004	0.402676
$83$	974.756	1.28908	0.644538	−	0.764572i	$-0.277050\pi$
$83$	974.756	1.28908	0.644538	+	0.764572i	$0.277050\pi$
$84$	84.0000	0.109109
$85$	1706.01	2.17697
$86$	−180.647	−0.226508
$87$	−393.588	−0.485024
$88$	401.695	0.486601
$89$	517.659	0.616536	0.308268	−	0.951300i	$-0.400251\pi$
$89$	517.659	0.616536	0.308268	+	0.951300i	$0.400251\pi$
$90$	332.030	0.388879
$91$	−599.404	−0.690491
$92$	92.0000	0.104257
$93$	−398.529	−0.444361
$94$	−1003.24	−1.10082
$95$	−171.911	−0.185660
$96$	96.0000	0.102062
$97$	−1282.52	−1.34248	−0.671238	−	0.741242i	$-0.734237\pi$
$97$	−1282.52	−1.34248	−0.671238	+	0.741242i	$0.734237\pi$
$98$	−98.0000	−0.101015
$99$	−451.907	−0.458771
$100$	861.039	0.861039
$101$	−796.027	−0.784234	−0.392117	−	0.919915i	$-0.628257\pi$
$101$	−796.027	−0.784234	−0.392117	+	0.919915i	$0.628257\pi$
$102$	−554.916	−0.538676
$103$	1262.41	1.20766	0.603831	−	0.797112i	$-0.293640\pi$
$103$	1262.41	1.20766	0.603831	+	0.797112i	$0.293640\pi$
$104$	−685.033	−0.645895
$105$	−387.369	−0.360032
$106$	217.904	0.199667
$107$	−1776.42	−1.60498	−0.802490	−	0.596666i	$-0.796492\pi$
$107$	−1776.42	−1.60498	−0.802490	+	0.596666i	$0.796492\pi$
$108$	−108.000	−0.0962250
$109$	877.509	0.771102	0.385551	−	0.922687i	$-0.374011\pi$
$109$	877.509	0.771102	0.385551	+	0.922687i	$0.374011\pi$
$110$	−1852.43	−1.60566
$111$	−430.879	−0.368444
$112$	−112.000	−0.0944911
$113$	1512.26	1.25895	0.629474	−	0.777021i	$-0.283270\pi$
$113$	1512.26	1.25895	0.629474	+	0.777021i	$0.283270\pi$
$114$	55.9178	0.0459402
$115$	−424.261	−0.344022
$116$	524.784	0.420043
$117$	770.663	0.608955
$118$	−919.811	−0.717589
$119$	647.403	0.498717
$120$	−442.707	−0.336779
$121$	1190.23	0.894241
$122$	454.839	0.337534
$123$	448.506	0.328784
$124$	531.372	0.384828
$125$	−1664.94	−1.19134
$126$	126.000	0.0890871
$127$	−1602.79	−1.11988	−0.559939	−	0.828534i	$-0.689176\pi$
$127$	−1602.79	−1.11988	−0.559939	+	0.828534i	$0.689176\pi$
$128$	−128.000	−0.0883883
$129$	−270.970	−0.184943
$130$	3159.05	2.13129
$131$	372.002	0.248107	0.124053	−	0.992276i	$-0.460411\pi$
$131$	372.002	0.248107	0.124053	+	0.992276i	$0.460411\pi$
$132$	602.543	0.397308
$133$	−65.2375	−0.0425324
$134$	1883.15	1.21403
$135$	498.046	0.317518
$136$	739.889	0.466507
$137$	−725.410	−0.452379	−0.226190	−	0.974083i	$-0.572627\pi$
$137$	−725.410	−0.452379	−0.226190	+	0.974083i	$0.572627\pi$
$138$	138.000	0.0851257
$139$	−2186.14	−1.33400	−0.666999	−	0.745059i	$-0.732421\pi$
$139$	−2186.14	−1.33400	−0.666999	+	0.745059i	$0.732421\pi$
$140$	516.492	0.311797
$141$	−1504.87	−0.898812
$142$	−1050.21	−0.620643
$143$	−4299.60	−2.51434
$144$	144.000	0.0833333
$145$	−2420.06	−1.38603
$146$	1352.20	0.766498
$147$	−147.000	−0.0824786
$148$	574.506	0.319082
$149$	−1617.42	−0.889292	−0.444646	−	0.895706i	$-0.646670\pi$
$149$	−1617.42	−0.889292	−0.444646	+	0.895706i	$0.646670\pi$
$150$	1291.56	0.703035
$151$	−2047.98	−1.10372	−0.551862	−	0.833935i	$-0.686083\pi$
$151$	−2047.98	−1.10372	−0.551862	+	0.833935i	$0.686083\pi$
$152$	−74.5571	−0.0397854
$153$	−832.375	−0.439827
$154$	−702.967	−0.367835
$155$	−2450.44	−1.26983
$156$	−1027.55	−0.527371
$157$	1236.47	0.628544	0.314272	−	0.949333i	$-0.398240\pi$
$157$	1236.47	0.628544	0.314272	+	0.949333i	$0.398240\pi$
$158$	−151.164	−0.0761136
$159$	326.856	0.163028
$160$	590.276	0.291659
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	1832.08	0.880364	0.440182	−	0.897909i	$-0.354914\pi$
$163$	1832.08	0.880364	0.440182	+	0.897909i	$0.354914\pi$
$164$	−598.008	−0.284735
$165$	−2778.65	−1.31101
$166$	−1949.51	−0.911514
$167$	914.876	0.423923	0.211962	−	0.977278i	$-0.432015\pi$
$167$	914.876	0.423923	0.211962	+	0.977278i	$0.432015\pi$
$168$	−168.000	−0.0771517
$169$	5135.36	2.33744
$170$	−3412.02	−1.53935
$171$	83.8767	0.0375100
$172$	361.294	0.160165
$173$	644.919	0.283424	0.141712	−	0.989908i	$-0.454739\pi$
$173$	644.919	0.283424	0.141712	+	0.989908i	$0.454739\pi$
$174$	787.176	0.342964
$175$	−1506.82	−0.650884
$176$	−803.390	−0.344079
$177$	−1379.72	−0.585909
$178$	−1035.32	−0.435957
$179$	−1161.30	−0.484915	−0.242458	−	0.970162i	$-0.577954\pi$
$179$	−1161.30	−0.484915	−0.242458	+	0.970162i	$0.577954\pi$
$180$	−664.061	−0.274979
$181$	−4052.00	−1.66399	−0.831997	−	0.554781i	$-0.812802\pi$
$181$	−4052.00	−1.66399	−0.831997	+	0.554781i	$0.812802\pi$
$182$	1198.81	0.488251
$183$	682.259	0.275596
$184$	−184.000	−0.0737210
$185$	−2649.35	−1.05289
$186$	797.058	0.314210
$187$	4643.90	1.81602
$188$	2006.49	0.778394
$189$	189.000	0.0727393
$190$	343.822	0.131282
$191$	2138.09	0.809981	0.404991	−	0.914321i	$-0.367275\pi$
$191$	2138.09	0.809981	0.404991	+	0.914321i	$0.367275\pi$
$192$	−192.000	−0.0721688
$193$	−4351.39	−1.62290	−0.811451	−	0.584421i	$-0.801322\pi$
$193$	−4351.39	−1.62290	−0.811451	+	0.584421i	$0.801322\pi$
$194$	2565.04	0.949274
$195$	4738.58	1.74019
$196$	196.000	0.0714286
$197$	−2427.28	−0.877852	−0.438926	−	0.898523i	$-0.644641\pi$
$197$	−2427.28	−0.877852	−0.438926	+	0.898523i	$0.644641\pi$
$198$	903.814	0.324400
$199$	−322.121	−0.114747	−0.0573733	−	0.998353i	$-0.518273\pi$
$199$	−322.121	−0.114747	−0.0573733	+	0.998353i	$0.518273\pi$
$200$	−1722.08	−0.608846
$201$	2824.73	0.991248
$202$	1592.05	0.554537
$203$	−918.373	−0.317523
$204$	1109.83	0.380901
$205$	2757.73	0.939553
$206$	−2524.83	−0.853947
$207$	207.000	0.0695048
$208$	1370.07	0.456717
$209$	−467.957	−0.154877
$210$	774.737	0.254581
$211$	−5371.05	−1.75241	−0.876204	−	0.481940i	$-0.839932\pi$
$211$	−5371.05	−1.75241	−0.876204	+	0.481940i	$0.839932\pi$
$212$	−435.808	−0.141186
$213$	−1575.31	−0.506753
$214$	3552.84	1.13489
$215$	−1666.12	−0.528504
$216$	216.000	0.0680414
$217$	−929.901	−0.290902
$218$	−1755.02	−0.545252
$219$	2028.30	0.625843
$220$	3704.86	1.13537
$221$	−7919.51	−2.41051
$222$	861.759	0.260529
$223$	3799.33	1.14091	0.570453	−	0.821330i	$-0.306768\pi$
$223$	3799.33	1.14091	0.570453	+	0.821330i	$0.306768\pi$
$224$	224.000	0.0668153
$225$	1937.34	0.574026
$226$	−3024.51	−0.890211
$227$	−325.894	−0.0952879	−0.0476439	−	0.998864i	$-0.515171\pi$
$227$	−325.894	−0.0952879	−0.0476439	+	0.998864i	$0.515171\pi$
$228$	−111.836	−0.0324846
$229$	4040.26	1.16589	0.582943	−	0.812513i	$-0.301901\pi$
$229$	4040.26	1.16589	0.582943	+	0.812513i	$0.301901\pi$
$230$	848.522	0.243260
$231$	−1054.45	−0.300336
$232$	−1049.57	−0.297015
$233$	1234.39	0.347072	0.173536	−	0.984828i	$-0.444481\pi$
$233$	1234.39	0.347072	0.173536	+	0.984828i	$0.444481\pi$
$234$	−1541.33	−0.430596
$235$	−9252.98	−2.56850
$236$	1839.62	0.507412
$237$	−226.746	−0.0621465
$238$	−1294.81	−0.352646
$239$	11.2720	0.00305075	0.00152537	−	0.999999i	$-0.499514\pi$
$239$	11.2720	0.00305075	0.00152537	+	0.999999i	$0.499514\pi$
$240$	885.414	0.238139
$241$	−4216.46	−1.12700	−0.563499	−	0.826117i	$-0.690545\pi$
$241$	−4216.46	−1.12700	−0.563499	+	0.826117i	$0.690545\pi$
$242$	−2380.47	−0.632324
$243$	−243.000	−0.0641500
$244$	−909.678	−0.238673
$245$	−903.860	−0.235696
$246$	−897.011	−0.232485
$247$	798.033	0.205577
$248$	−1062.74	−0.272114
$249$	−2924.27	−0.744248
$250$	3329.88	0.842402
$251$	−2458.91	−0.618346	−0.309173	−	0.951006i	$-0.600052\pi$
$251$	−2458.91	−0.618346	−0.309173	+	0.951006i	$0.600052\pi$
$252$	−252.000	−0.0629941
$253$	−1154.87	−0.286981
$254$	3205.58	0.791874
$255$	−5118.03	−1.25688
$256$	256.000	0.0625000
$257$	−6220.90	−1.50992	−0.754959	−	0.655772i	$-0.772343\pi$
$257$	−6220.90	−1.50992	−0.754959	+	0.655772i	$0.772343\pi$
$258$	541.941	0.130774
$259$	−1005.39	−0.241203
$260$	−6318.11	−1.50705
$261$	1180.76	0.280029
$262$	−744.005	−0.175438
$263$	−396.213	−0.0928955	−0.0464477	−	0.998921i	$-0.514790\pi$
$263$	−396.213	−0.0928955	−0.0464477	+	0.998921i	$0.514790\pi$
$264$	−1205.09	−0.280939
$265$	2009.74	0.465878
$266$	130.475	0.0300749
$267$	−1552.98	−0.355957
$268$	−3766.30	−0.858446
$269$	4443.06	1.00706	0.503528	−	0.863979i	$-0.332035\pi$
$269$	4443.06	1.00706	0.503528	+	0.863979i	$0.332035\pi$
$270$	−996.091	−0.224519
$271$	1372.99	0.307761	0.153880	−	0.988089i	$-0.450823\pi$
$271$	1372.99	0.307761	0.153880	+	0.988089i	$0.450823\pi$
$272$	−1479.78	−0.329870
$273$	1798.21	0.398655
$274$	1450.82	0.319881
$275$	−10808.6	−2.37012
$276$	−276.000	−0.0601929
$277$	1330.64	0.288629	0.144315	−	0.989532i	$-0.453902\pi$
$277$	1330.64	0.288629	0.144315	+	0.989532i	$0.453902\pi$
$278$	4372.27	0.943279
$279$	1195.59	0.256552
$280$	−1032.98	−0.220473
$281$	−8079.24	−1.71519	−0.857593	−	0.514329i	$-0.828041\pi$
$281$	−8079.24	−1.71519	−0.857593	+	0.514329i	$0.828041\pi$
$282$	3009.73	0.635556
$283$	−4962.07	−1.04228	−0.521139	−	0.853472i	$-0.674493\pi$
$283$	−4962.07	−1.04228	−0.521139	+	0.853472i	$0.674493\pi$
$284$	2100.41	0.438861
$285$	515.734	0.107191
$286$	8599.21	1.77791
$287$	1046.51	0.215239
$288$	−288.000	−0.0589256
$289$	3640.67	0.741029
$290$	4840.12	0.980075
$291$	3847.56	0.775079
$292$	−2704.40	−0.541996
$293$	7289.78	1.45349	0.726746	−	0.686906i	$-0.241032\pi$
$293$	7289.78	1.45349	0.726746	+	0.686906i	$0.241032\pi$
$294$	294.000	0.0583212
$295$	−8483.48	−1.67433
$296$	−1149.01	−0.225625
$297$	1355.72	0.264872
$298$	3234.85	0.628824
$299$	1969.47	0.380928
$300$	−2583.12	−0.497121
$301$	−632.264	−0.121073
$302$	4095.97	0.780451
$303$	2388.08	0.452778
$304$	149.114	0.0281325
$305$	4195.01	0.787559
$306$	1664.75	0.311005
$307$	8988.45	1.67100	0.835501	−	0.549489i	$-0.185177\pi$
$307$	8988.45	1.67100	0.835501	+	0.549489i	$0.185177\pi$
$308$	1405.93	0.260099
$309$	−3787.24	−0.697244
$310$	4900.88	0.897907
$311$	5200.32	0.948178	0.474089	−	0.880477i	$-0.342778\pi$
$311$	5200.32	0.948178	0.474089	+	0.880477i	$0.342778\pi$
$312$	2055.10	0.372907
$313$	1399.80	0.252784	0.126392	−	0.991980i	$-0.459660\pi$
$313$	1399.80	0.252784	0.126392	+	0.991980i	$0.459660\pi$
$314$	−2472.95	−0.444448
$315$	1162.11	0.207864
$316$	302.328	0.0538205
$317$	−500.145	−0.0886149	−0.0443075	−	0.999018i	$-0.514108\pi$
$317$	−500.145	−0.0886149	−0.0443075	+	0.999018i	$0.514108\pi$
$318$	−653.713	−0.115278
$319$	−6587.60	−1.15622
$320$	−1180.55	−0.206234
$321$	5329.25	0.926635
$322$	322.000	0.0557278
$323$	−861.937	−0.148481
$324$	324.000	0.0555556
$325$	18432.5	3.14601
$326$	−3664.15	−0.622512
$327$	−2632.53	−0.445196
$328$	1196.02	0.201338
$329$	−3511.35	−0.588411
$330$	5557.29	0.927027
$331$	−5283.40	−0.877347	−0.438673	−	0.898647i	$-0.644551\pi$
$331$	−5283.40	−0.877347	−0.438673	+	0.898647i	$0.644551\pi$
$332$	3899.02	0.644538
$333$	1292.64	0.212721
$334$	−1829.75	−0.299759
$335$	17368.4	2.83265
$336$	336.000	0.0545545
$337$	−3651.41	−0.590223	−0.295112	−	0.955463i	$-0.595357\pi$
$337$	−3651.41	−0.590223	−0.295112	+	0.955463i	$0.595357\pi$
$338$	−10270.7	−1.65282
$339$	−4536.77	−0.726854
$340$	6824.04	1.08849
$341$	−6670.30	−1.05929
$342$	−167.753	−0.0265236
$343$	−343.000	−0.0539949
$344$	−722.587	−0.113254
$345$	1272.78	0.198621
$346$	−1289.84	−0.200411
$347$	−7019.35	−1.08593	−0.542966	−	0.839755i	$-0.682699\pi$
$347$	−7019.35	−1.08593	−0.542966	+	0.839755i	$0.682699\pi$
$348$	−1574.35	−0.242512
$349$	1655.77	0.253958	0.126979	−	0.991905i	$-0.459472\pi$
$349$	1655.77	0.253958	0.126979	+	0.991905i	$0.459472\pi$
$350$	3013.64	0.460245
$351$	−2311.99	−0.351581
$352$	1606.78	0.243300
$353$	11798.7	1.77898	0.889491	−	0.456952i	$-0.151059\pi$
$353$	11798.7	1.77898	0.889491	+	0.456952i	$0.151059\pi$
$354$	2759.43	0.414300
$355$	−9686.12	−1.44813
$356$	2070.63	0.308268
$357$	−1942.21	−0.287934
$358$	2322.60	0.342887
$359$	4512.53	0.663405	0.331702	−	0.943384i	$-0.392377\pi$
$359$	4512.53	0.663405	0.331702	+	0.943384i	$0.392377\pi$
$360$	1328.12	0.194439
$361$	−6772.14	−0.987337
$362$	8104.00	1.17662
$363$	−3570.70	−0.516290
$364$	−2397.62	−0.345245
$365$	12471.4	1.78845
$366$	−1364.52	−0.194876
$367$	6680.24	0.950152	0.475076	−	0.879945i	$-0.342421\pi$
$367$	6680.24	0.950152	0.475076	+	0.879945i	$0.342421\pi$
$368$	368.000	0.0521286
$369$	−1345.52	−0.189823
$370$	5298.70	0.744504
$371$	762.665	0.106727
$372$	−1594.12	−0.222180
$373$	9481.08	1.31612	0.658058	−	0.752967i	$-0.271378\pi$
$373$	9481.08	1.31612	0.658058	+	0.752967i	$0.271378\pi$
$374$	−9287.80	−1.28412
$375$	4994.83	0.687818
$376$	−4012.97	−0.550408
$377$	11234.2	1.53473
$378$	−378.000	−0.0514344
$379$	8960.90	1.21449	0.607243	−	0.794516i	$-0.292275\pi$
$379$	8960.90	1.21449	0.607243	+	0.794516i	$0.292275\pi$
$380$	−687.645	−0.0928301
$381$	4808.37	0.646562
$382$	−4276.17	−0.572743
$383$	8020.60	1.07006	0.535031	−	0.844833i	$-0.320300\pi$
$383$	8020.60	1.07006	0.535031	+	0.844833i	$0.320300\pi$
$384$	384.000	0.0510310
$385$	−6483.51	−0.858260
$386$	8702.78	1.14756
$387$	812.911	0.106777
$388$	−5130.08	−0.671238
$389$	−589.650	−0.0768547	−0.0384273	−	0.999261i	$-0.512235\pi$
$389$	−589.650	−0.0768547	−0.0384273	+	0.999261i	$0.512235\pi$
$390$	−9477.16	−1.23050
$391$	−2127.18	−0.275131
$392$	−392.000	−0.0505076
$393$	−1116.01	−0.143245
$394$	4854.57	0.620735
$395$	−1394.19	−0.177594
$396$	−1807.63	−0.229386
$397$	−9710.03	−1.22754	−0.613769	−	0.789486i	$-0.710347\pi$
$397$	−9710.03	−1.22754	−0.613769	+	0.789486i	$0.710347\pi$
$398$	644.242	0.0811381
$399$	195.712	0.0245561
$400$	3444.16	0.430519
$401$	−3038.63	−0.378409	−0.189205	−	0.981938i	$-0.560591\pi$
$401$	−3038.63	−0.378409	−0.189205	+	0.981938i	$0.560591\pi$
$402$	−5649.45	−0.700918
$403$	11375.2	1.40606
$404$	−3184.11	−0.392117
$405$	−1494.14	−0.183319
$406$	1836.75	0.224522
$407$	−7211.76	−0.878313
$408$	−2219.67	−0.269338
$409$	−1940.14	−0.234557	−0.117279	−	0.993099i	$-0.537417\pi$
$409$	−1940.14	−0.234557	−0.117279	+	0.993099i	$0.537417\pi$
$410$	−5515.46	−0.664364
$411$	2176.23	0.261181
$412$	5049.65	0.603831
$413$	−3219.34	−0.383567
$414$	−414.000	−0.0491473
$415$	−17980.5	−2.12681
$416$	−2740.13	−0.322947
$417$	6558.41	0.770184
$418$	935.913	0.109514
$419$	1393.05	0.162422	0.0812109	−	0.996697i	$-0.474121\pi$
$419$	1393.05	0.162422	0.0812109	+	0.996697i	$0.474121\pi$
$420$	−1549.47	−0.180016
$421$	11749.1	1.36013	0.680067	−	0.733150i	$-0.261951\pi$
$421$	11749.1	1.36013	0.680067	+	0.733150i	$0.261951\pi$
$422$	10742.1	1.23914
$423$	4514.60	0.518929
$424$	871.617	0.0998336
$425$	−19908.5	−2.27225
$426$	3150.62	0.358328
$427$	1591.94	0.180420
$428$	−7105.67	−0.802490
$429$	12898.8	1.45166
$430$	3332.24	0.373709
$431$	9060.09	1.01255	0.506275	−	0.862372i	$-0.331022\pi$
$431$	9060.09	1.01255	0.506275	+	0.862372i	$0.331022\pi$
$432$	−432.000	−0.0481125
$433$	14162.9	1.57188	0.785942	−	0.618300i	$-0.212178\pi$
$433$	14162.9	1.57188	0.785942	+	0.618300i	$0.212178\pi$
$434$	1859.80	0.205699
$435$	7260.18	0.800227
$436$	3510.04	0.385551
$437$	214.352	0.0234641
$438$	−4056.59	−0.442538
$439$	9782.80	1.06357	0.531785	−	0.846879i	$-0.321521\pi$
$439$	9782.80	1.06357	0.531785	+	0.846879i	$0.321521\pi$
$440$	−7409.72	−0.802829
$441$	441.000	0.0476190
$442$	15839.0	1.70449
$443$	4945.49	0.530400	0.265200	−	0.964193i	$-0.414562\pi$
$443$	4945.49	0.530400	0.265200	+	0.964193i	$0.414562\pi$
$444$	−1723.52	−0.184222
$445$	−9548.80	−1.01721
$446$	−7598.66	−0.806742
$447$	4852.27	0.513433
$448$	−448.000	−0.0472456
$449$	−6433.74	−0.676230	−0.338115	−	0.941105i	$-0.609789\pi$
$449$	−6433.74	−0.676230	−0.338115	+	0.941105i	$0.609789\pi$
$450$	−3874.67	−0.405898
$451$	7506.77	0.783770
$452$	6049.03	0.629474
$453$	6143.95	0.637236
$454$	651.788	0.0673787
$455$	11056.7	1.13922
$456$	223.671	0.0229701
$457$	−4428.80	−0.453327	−0.226664	−	0.973973i	$-0.572782\pi$
$457$	−4428.80	−0.453327	−0.226664	+	0.973973i	$0.572782\pi$
$458$	−8080.52	−0.824406
$459$	2497.12	0.253934
$460$	−1697.04	−0.172011
$461$	−13035.1	−1.31693	−0.658466	−	0.752611i	$-0.728794\pi$
$461$	−13035.1	−1.31693	−0.658466	+	0.752611i	$0.728794\pi$
$462$	2108.90	0.212370
$463$	−8486.33	−0.851821	−0.425911	−	0.904765i	$-0.640046\pi$
$463$	−8486.33	−0.851821	−0.425911	+	0.904765i	$0.640046\pi$
$464$	2099.14	0.210022
$465$	7351.32	0.733138
$466$	−2468.79	−0.245417
$467$	−19432.5	−1.92554	−0.962771	−	0.270317i	$-0.912872\pi$
$467$	−19432.5	−1.92554	−0.962771	+	0.270317i	$0.912872\pi$
$468$	3082.65	0.304478
$469$	6591.03	0.648924
$470$	18506.0	1.81620
$471$	−3709.42	−0.362890
$472$	−3679.25	−0.358794
$473$	−4535.31	−0.440875
$474$	453.492	0.0439442
$475$	2006.14	0.193786
$476$	2589.61	0.249358
$477$	−980.569	−0.0941240
$478$	−22.5441	−0.00215720
$479$	−18607.3	−1.77493	−0.887464	−	0.460877i	$-0.847535\pi$
$479$	−18607.3	−1.77493	−0.887464	+	0.460877i	$0.847535\pi$
$480$	−1770.83	−0.168389
$481$	12298.6	1.16584
$482$	8432.93	0.796907
$483$	483.000	0.0455016
$484$	4760.94	0.447120
$485$	23657.5	2.21491
$486$	486.000	0.0453609
$487$	19674.9	1.83071	0.915355	−	0.402648i	$-0.131910\pi$
$487$	19674.9	1.83071	0.915355	+	0.402648i	$0.131910\pi$
$488$	1819.36	0.168767
$489$	−5496.23	−0.508279
$490$	1807.72	0.166662
$491$	5260.15	0.483477	0.241738	−	0.970341i	$-0.422282\pi$
$491$	5260.15	0.483477	0.241738	+	0.970341i	$0.422282\pi$
$492$	1794.02	0.164392
$493$	−12133.8	−1.10848
$494$	−1596.07	−0.145365
$495$	8335.94	0.756914
$496$	2125.49	0.192414
$497$	−3675.72	−0.331748
$498$	5848.53	0.526263
$499$	−3032.76	−0.272074	−0.136037	−	0.990704i	$-0.543437\pi$
$499$	−3032.76	−0.272074	−0.136037	+	0.990704i	$0.543437\pi$
$500$	−6659.77	−0.595668
$501$	−2744.63	−0.244752
$502$	4917.81	0.437236
$503$	12086.8	1.07142	0.535709	−	0.844402i	$-0.320044\pi$
$503$	12086.8	1.07142	0.535709	+	0.844402i	$0.320044\pi$
$504$	504.000	0.0445435
$505$	14683.6	1.29389
$506$	2309.75	0.202926
$507$	−15406.1	−1.34952
$508$	−6411.16	−0.559939
$509$	2176.93	0.189569	0.0947844	−	0.995498i	$-0.469784\pi$
$509$	2176.93	0.189569	0.0947844	+	0.995498i	$0.469784\pi$
$510$	10236.1	0.888746
$511$	4732.69	0.409710
$512$	−512.000	−0.0441942
$513$	−251.630	−0.0216564
$514$	12441.8	1.06767
$515$	−23286.6	−1.99249
$516$	−1083.88	−0.0924713
$517$	−25187.4	−2.14263
$518$	2010.77	0.170556
$519$	−1934.76	−0.163635
$520$	12636.2	1.06564
$521$	1334.02	0.112177	0.0560886	−	0.998426i	$-0.482137\pi$
$521$	1334.02	0.112177	0.0560886	+	0.998426i	$0.482137\pi$
$522$	−2361.53	−0.198010
$523$	−7969.25	−0.666293	−0.333146	−	0.942875i	$-0.608110\pi$
$523$	−7969.25	−0.666293	−0.333146	+	0.942875i	$0.608110\pi$
$524$	1488.01	0.124053
$525$	4520.45	0.375788
$526$	792.425	0.0656870
$527$	−12286.1	−1.01554
$528$	2410.17	0.198654
$529$	529.000	0.0434783
$530$	−4019.49	−0.329425
$531$	4139.15	0.338275
$532$	−260.950	−0.0212662
$533$	−12801.7	−1.04035
$534$	3105.95	0.251700
$535$	32768.0	2.64801
$536$	7532.61	0.607013
$537$	3483.91	0.279966
$538$	−8886.12	−0.712096
$539$	−2460.38	−0.196616
$540$	1992.18	0.158759
$541$	−17358.1	−1.37945	−0.689727	−	0.724069i	$-0.742270\pi$
$541$	−17358.1	−1.37945	−0.689727	+	0.724069i	$0.742270\pi$
$542$	−2745.98	−0.217620
$543$	12156.0	0.960707
$544$	2959.55	0.233253
$545$	−16186.6	−1.27222
$546$	−3596.43	−0.281892
$547$	23754.7	1.85681	0.928405	−	0.371569i	$-0.121180\pi$
$547$	23754.7	1.85681	0.928405	+	0.371569i	$0.121180\pi$
$548$	−2901.64	−0.226190
$549$	−2046.78	−0.159115
$550$	21617.2	1.67593
$551$	1222.70	0.0945349
$552$	552.000	0.0425628
$553$	−529.074	−0.0406844
$554$	−2661.28	−0.204092
$555$	7948.06	0.607885
$556$	−8744.55	−0.666999
$557$	−15596.8	−1.18646	−0.593231	−	0.805032i	$-0.702148\pi$
$557$	−15596.8	−1.18646	−0.593231	+	0.805032i	$0.702148\pi$
$558$	−2391.17	−0.181409
$559$	7734.32	0.585200
$560$	2065.97	0.155898
$561$	−13931.7	−1.04848
$562$	16158.5	1.21282
$563$	173.534	0.0129904	0.00649519	−	0.999979i	$-0.497933\pi$
$563$	173.534	0.0129904	0.00649519	+	0.999979i	$0.497933\pi$
$564$	−6019.46	−0.449406
$565$	−27895.3	−2.07710
$566$	9924.14	0.737001
$567$	−567.000	−0.0419961
$568$	−4200.82	−0.310322
$569$	−21885.6	−1.61247	−0.806233	−	0.591599i	$-0.798497\pi$
$569$	−21885.6	−1.61247	−0.806233	+	0.591599i	$0.798497\pi$
$570$	−1031.47	−0.0757955
$571$	−18530.5	−1.35811	−0.679053	−	0.734090i	$-0.737609\pi$
$571$	−18530.5	−1.35811	−0.679053	+	0.734090i	$0.737609\pi$
$572$	−17198.4	−1.25717
$573$	−6414.26	−0.467643
$574$	−2093.03	−0.152197
$575$	4950.97	0.359078
$576$	576.000	0.0416667
$577$	21137.3	1.52506	0.762529	−	0.646954i	$-0.223957\pi$
$577$	21137.3	1.52506	0.762529	+	0.646954i	$0.223957\pi$
$578$	−7281.35	−0.523986
$579$	13054.2	0.936983
$580$	−9680.24	−0.693017
$581$	−6823.29	−0.487225
$582$	−7695.12	−0.548063
$583$	5470.69	0.388633
$584$	5408.79	0.383249
$585$	−14215.7	−1.00470
$586$	−14579.6	−1.02777
$587$	9989.15	0.702379	0.351190	−	0.936304i	$-0.385777\pi$
$587$	9989.15	0.702379	0.351190	+	0.936304i	$0.385777\pi$
$588$	−588.000	−0.0412393
$589$	1238.05	0.0866093
$590$	16967.0	1.18393
$591$	7281.85	0.506828
$592$	2298.02	0.159541
$593$	3766.57	0.260834	0.130417	−	0.991459i	$-0.458368\pi$
$593$	3766.57	0.260834	0.130417	+	0.991459i	$0.458368\pi$
$594$	−2711.44	−0.187293
$595$	−11942.1	−0.822819
$596$	−6469.69	−0.444646
$597$	966.363	0.0662490
$598$	−3938.94	−0.269357
$599$	599.618	0.0409011	0.0204505	−	0.999791i	$-0.493490\pi$
$599$	599.618	0.0409011	0.0204505	+	0.999791i	$0.493490\pi$
$600$	5166.23	0.351518
$601$	3176.49	0.215593	0.107797	−	0.994173i	$-0.465620\pi$
$601$	3176.49	0.215593	0.107797	+	0.994173i	$0.465620\pi$
$602$	1264.53	0.0856118
$603$	−8474.18	−0.572297
$604$	−8191.93	−0.551862
$605$	−21955.2	−1.47538
$606$	−4776.16	−0.320162
$607$	−26223.1	−1.75348	−0.876742	−	0.480961i	$-0.840288\pi$
$607$	−26223.1	−1.75348	−0.876742	+	0.480961i	$0.840288\pi$
$608$	−298.228	−0.0198927
$609$	2755.12	0.183322
$610$	−8390.02	−0.556889
$611$	42953.5	2.84404
$612$	−3329.50	−0.219913
$613$	−22434.6	−1.47818	−0.739091	−	0.673606i	$-0.764745\pi$
$613$	−22434.6	−1.47818	−0.739091	+	0.673606i	$0.764745\pi$
$614$	−17976.9	−1.18158
$615$	−8273.19	−0.542451
$616$	−2811.87	−0.183918
$617$	617.258	0.0402753	0.0201376	−	0.999797i	$-0.493590\pi$
$617$	617.258	0.0402753	0.0201376	+	0.999797i	$0.493590\pi$
$618$	7574.48	0.493026
$619$	28161.7	1.82862	0.914309	−	0.405018i	$-0.132735\pi$
$619$	28161.7	1.82862	0.914309	+	0.405018i	$0.132735\pi$
$620$	−9801.76	−0.634916
$621$	−621.000	−0.0401286
$622$	−10400.6	−0.670463
$623$	−3623.61	−0.233029
$624$	−4110.20	−0.263685
$625$	3804.28	0.243474
$626$	−2799.60	−0.178745
$627$	1403.87	0.0894181
$628$	4945.90	0.314272
$629$	−13283.4	−0.842044
$630$	−2324.21	−0.146982
$631$	−9783.70	−0.617247	−0.308623	−	0.951184i	$-0.599868\pi$
$631$	−9783.70	−0.617247	−0.308623	+	0.951184i	$0.599868\pi$
$632$	−604.656	−0.0380568
$633$	16113.1	1.01175
$634$	1000.29	0.0626602
$635$	29565.3	1.84766
$636$	1307.43	0.0815138
$637$	4195.83	0.260981
$638$	13175.2	0.817573
$639$	4725.93	0.292574
$640$	2361.10	0.145829
$641$	−22897.9	−1.41094	−0.705469	−	0.708741i	$-0.749263\pi$
$641$	−22897.9	−1.41094	−0.705469	+	0.708741i	$0.749263\pi$
$642$	−10658.5	−0.655230
$643$	972.177	0.0596250	0.0298125	−	0.999556i	$-0.490509\pi$
$643$	972.177	0.0596250	0.0298125	+	0.999556i	$0.490509\pi$
$644$	−644.000	−0.0394055
$645$	4998.35	0.305132
$646$	1723.87	0.104992
$647$	−13275.5	−0.806665	−0.403333	−	0.915053i	$-0.632148\pi$
$647$	−13275.5	−0.806665	−0.403333	+	0.915053i	$0.632148\pi$
$648$	−648.000	−0.0392837
$649$	−23092.7	−1.39672
$650$	−36865.0	−2.22456
$651$	2789.70	0.167953
$652$	7328.31	0.440182
$653$	−31487.6	−1.88699	−0.943494	−	0.331389i	$-0.892483\pi$
$653$	−31487.6	−1.88699	−0.943494	+	0.331389i	$0.892483\pi$
$654$	5265.05	0.314801
$655$	−6862.00	−0.409345
$656$	−2392.03	−0.142368
$657$	−6084.89	−0.361331
$658$	7022.70	0.416069
$659$	−25349.7	−1.49846	−0.749230	−	0.662310i	$-0.769576\pi$
$659$	−25349.7	−1.49846	−0.749230	+	0.662310i	$0.769576\pi$
$660$	−11114.6	−0.655507
$661$	23595.2	1.38842	0.694211	−	0.719771i	$-0.255753\pi$
$661$	23595.2	1.38842	0.694211	+	0.719771i	$0.255753\pi$
$662$	10566.8	0.620378
$663$	23758.5	1.39171
$664$	−7798.04	−0.455757
$665$	1203.38	0.0701730
$666$	−2585.28	−0.150417
$667$	3017.51	0.175170
$668$	3659.50	0.211962
$669$	−11398.0	−0.658702
$670$	−34736.9	−2.00299
$671$	11419.2	0.656978
$672$	−672.000	−0.0385758
$673$	15514.6	0.888625	0.444313	−	0.895872i	$-0.353448\pi$
$673$	15514.6	0.888625	0.444313	+	0.895872i	$0.353448\pi$
$674$	7302.83	0.417351
$675$	−5812.01	−0.331414
$676$	20541.4	1.16872
$677$	−9081.54	−0.515557	−0.257778	−	0.966204i	$-0.582990\pi$
$677$	−9081.54	−0.515557	−0.257778	+	0.966204i	$0.582990\pi$
$678$	9073.54	0.513964
$679$	8977.64	0.507408
$680$	−13648.1	−0.769676
$681$	977.682	0.0550145
$682$	13340.6	0.749029
$683$	9084.61	0.508950	0.254475	−	0.967079i	$-0.418097\pi$
$683$	9084.61	0.508950	0.254475	+	0.967079i	$0.418097\pi$
$684$	335.507	0.0187550
$685$	13381.0	0.746368
$686$	686.000	0.0381802
$687$	−12120.8	−0.673125
$688$	1445.17	0.0800825
$689$	−9329.48	−0.515856
$690$	−2545.57	−0.140446
$691$	−3450.21	−0.189945	−0.0949725	−	0.995480i	$-0.530276\pi$
$691$	−3450.21	−0.189945	−0.0949725	+	0.995480i	$0.530276\pi$
$692$	2579.68	0.141712
$693$	3163.35	0.173399
$694$	14038.7	0.767870
$695$	40325.8	2.20093
$696$	3148.71	0.171482
$697$	13826.8	0.751405
$698$	−3311.54	−0.179575
$699$	−3703.18	−0.200382
$700$	−6027.27	−0.325442
$701$	−22762.2	−1.22642	−0.613208	−	0.789922i	$-0.710121\pi$
$701$	−22762.2	−1.22642	−0.613208	+	0.789922i	$0.710121\pi$
$702$	4623.98	0.248605
$703$	1338.55	0.0718126
$704$	−3213.56	−0.172039
$705$	27758.9	1.48292
$706$	−23597.4	−1.25793
$707$	5572.19	0.296413
$708$	−5518.87	−0.292954
$709$	−16228.9	−0.859648	−0.429824	−	0.902913i	$-0.641424\pi$
$709$	−16228.9	−0.859648	−0.429824	+	0.902913i	$0.641424\pi$
$710$	19372.2	1.02398
$711$	680.237	0.0358803
$712$	−4141.27	−0.217978
$713$	3055.39	0.160484
$714$	3884.42	0.203600
$715$	79311.0	4.14834
$716$	−4645.21	−0.242458
$717$	−33.8161	−0.00176135
$718$	−9025.06	−0.469098
$719$	−12540.0	−0.650436	−0.325218	−	0.945639i	$-0.605438\pi$
$719$	−12540.0	−0.650436	−0.325218	+	0.945639i	$0.605438\pi$
$720$	−2656.24	−0.137489
$721$	−8836.89	−0.456454
$722$	13544.3	0.698153
$723$	12649.4	0.650672
$724$	−16208.0	−0.831997
$725$	28241.2	1.44669
$726$	7141.41	0.365072
$727$	25968.4	1.32478	0.662390	−	0.749159i	$-0.269542\pi$
$727$	25968.4	1.32478	0.662390	+	0.749159i	$0.269542\pi$
$728$	4795.23	0.244125
$729$	729.000	0.0370370
$730$	−24942.8	−1.26462
$731$	−8353.66	−0.422669
$732$	2729.03	0.137798
$733$	−22974.5	−1.15769	−0.578843	−	0.815439i	$-0.696496\pi$
$733$	−22974.5	−1.15769	−0.578843	+	0.815439i	$0.696496\pi$
$734$	−13360.5	−0.671859
$735$	2711.58	0.136079
$736$	−736.000	−0.0368605
$737$	47278.3	2.36298
$738$	2691.03	0.134225
$739$	−30801.6	−1.53323	−0.766614	−	0.642108i	$-0.778060\pi$
$739$	−30801.6	−1.53323	−0.766614	+	0.642108i	$0.778060\pi$
$740$	−10597.4	−0.526444
$741$	−2394.10	−0.118690
$742$	−1525.33	−0.0754671
$743$	32697.5	1.61448	0.807239	−	0.590225i	$-0.200961\pi$
$743$	32697.5	1.61448	0.807239	+	0.590225i	$0.200961\pi$
$744$	3188.23	0.157105
$745$	29835.2	1.46722
$746$	−18962.2	−0.930635
$747$	8772.80	0.429692
$748$	18575.6	0.908010
$749$	12434.9	0.606625
$750$	−9989.65	−0.486361
$751$	−7453.24	−0.362147	−0.181074	−	0.983470i	$-0.557957\pi$
$751$	−7453.24	−0.362147	−0.181074	+	0.983470i	$0.557957\pi$
$752$	8025.95	0.389197
$753$	7376.72	0.357002
$754$	−22468.4	−1.08521
$755$	37777.4	1.82100
$756$	756.000	0.0363696
$757$	−34121.2	−1.63825	−0.819125	−	0.573615i	$-0.805541\pi$
$757$	−34121.2	−1.63825	−0.819125	+	0.573615i	$0.805541\pi$
$758$	−17921.8	−0.858772
$759$	3464.62	0.165689
$760$	1375.29	0.0656408
$761$	−20434.8	−0.973405	−0.486702	−	0.873568i	$-0.661800\pi$
$761$	−20434.8	−0.973405	−0.486702	+	0.873568i	$0.661800\pi$
$762$	−9616.74	−0.457189
$763$	−6142.56	−0.291449
$764$	8552.34	0.404991
$765$	15354.1	0.725658
$766$	−16041.2	−0.756648
$767$	39381.3	1.85395
$768$	−768.000	−0.0360844
$769$	−35899.0	−1.68342	−0.841711	−	0.539928i	$-0.818451\pi$
$769$	−35899.0	−1.68342	−0.841711	+	0.539928i	$0.818451\pi$
$770$	12967.0	0.606881
$771$	18662.7	0.871752
$772$	−17405.6	−0.811451
$773$	39556.0	1.84053	0.920266	−	0.391294i	$-0.127972\pi$
$773$	39556.0	1.84053	0.920266	+	0.391294i	$0.127972\pi$
$774$	−1625.82	−0.0755025
$775$	28595.7	1.32541
$776$	10260.2	0.474637
$777$	3016.16	0.139259
$778$	1179.30	0.0543444
$779$	−1393.30	−0.0640825
$780$	18954.3	0.870094
$781$	−26366.4	−1.20802
$782$	4254.36	0.194547
$783$	−3542.29	−0.161675
$784$	784.000	0.0357143
$785$	−22808.2	−1.03702
$786$	2232.01	0.101289
$787$	−27082.1	−1.22665	−0.613325	−	0.789831i	$-0.710168\pi$
$787$	−27082.1	−1.22665	−0.613325	+	0.789831i	$0.710168\pi$
$788$	−9709.13	−0.438926
$789$	1188.64	0.0536332
$790$	2788.39	0.125578
$791$	−10585.8	−0.475838
$792$	3615.26	0.162200
$793$	−19473.7	−0.872047
$794$	19420.1	0.868000
$795$	−6029.23	−0.268975
$796$	−1288.48	−0.0573733
$797$	−10282.3	−0.456986	−0.228493	−	0.973546i	$-0.573380\pi$
$797$	−10282.3	−0.456986	−0.228493	+	0.973546i	$0.573380\pi$
$798$	−391.425	−0.0173638
$799$	−46393.0	−2.05415
$800$	−6888.31	−0.304423
$801$	4658.93	0.205512
$802$	6077.26	0.267576
$803$	33948.2	1.49191
$804$	11298.9	0.495624
$805$	2969.83	0.130028
$806$	−22750.5	−0.994232
$807$	−13329.2	−0.581424
$808$	6368.21	0.277269
$809$	−10479.5	−0.455428	−0.227714	−	0.973728i	$-0.573125\pi$
$809$	−10479.5	−0.455428	−0.227714	+	0.973728i	$0.573125\pi$
$810$	2988.27	0.129626
$811$	−17746.8	−0.768401	−0.384201	−	0.923250i	$-0.625523\pi$
$811$	−17746.8	−0.768401	−0.384201	+	0.923250i	$0.625523\pi$
$812$	−3673.49	−0.158761
$813$	−4118.97	−0.177686
$814$	14423.5	0.621061
$815$	−33794.7	−1.45249
$816$	4439.33	0.190451
$817$	841.782	0.0360468
$818$	3880.29	0.165857
$819$	−5394.64	−0.230164
$820$	11030.9	0.469776
$821$	4288.12	0.182286	0.0911429	−	0.995838i	$-0.470948\pi$
$821$	4288.12	0.182286	0.0911429	+	0.995838i	$0.470948\pi$
$822$	−4352.46	−0.184683
$823$	34649.4	1.46756	0.733781	−	0.679387i	$-0.237754\pi$
$823$	34649.4	1.46756	0.733781	+	0.679387i	$0.237754\pi$
$824$	−10099.3	−0.426973
$825$	32425.8	1.36839
$826$	6438.68	0.271223
$827$	26130.8	1.09874	0.549369	−	0.835580i	$-0.314868\pi$
$827$	26130.8	1.09874	0.549369	+	0.835580i	$0.314868\pi$
$828$	828.000	0.0347524
$829$	−2810.93	−0.117766	−0.0588828	−	0.998265i	$-0.518754\pi$
$829$	−2810.93	−0.117766	−0.0588828	+	0.998265i	$0.518754\pi$
$830$	35960.9	1.50388
$831$	−3991.92	−0.166640
$832$	5480.27	0.228358
$833$	−4531.82	−0.188497
$834$	−13116.8	−0.544602
$835$	−16875.9	−0.699419
$836$	−1871.83	−0.0774384
$837$	−3586.76	−0.148120
$838$	−2786.09	−0.114850
$839$	−33151.0	−1.36413	−0.682063	−	0.731294i	$-0.738917\pi$
$839$	−33151.0	−1.36413	−0.682063	+	0.731294i	$0.738917\pi$
$840$	3098.95	0.127290
$841$	−7176.59	−0.294255
$842$	−23498.2	−0.961759
$843$	24237.7	0.990263
$844$	−21484.2	−0.876204
$845$	−94727.4	−3.85648
$846$	−9029.19	−0.366939
$847$	−8331.64	−0.337991
$848$	−1743.23	−0.0705930
$849$	14886.2	0.601759
$850$	39817.0	1.60672
$851$	3303.41	0.133066
$852$	−6301.24	−0.253377
$853$	−32650.2	−1.31058	−0.655288	−	0.755379i	$-0.727453\pi$
$853$	−32650.2	−1.31058	−0.655288	+	0.755379i	$0.727453\pi$
$854$	−3183.87	−0.127576
$855$	−1547.20	−0.0618867
$856$	14211.3	0.567446
$857$	7975.17	0.317884	0.158942	−	0.987288i	$-0.449192\pi$
$857$	7975.17	0.317884	0.158942	+	0.987288i	$0.449192\pi$
$858$	−25797.6	−1.02648
$859$	−36089.9	−1.43349	−0.716746	−	0.697334i	$-0.754369\pi$
$859$	−36089.9	−1.43349	−0.716746	+	0.697334i	$0.754369\pi$
$860$	−6664.47	−0.264252
$861$	−3139.54	−0.124269
$862$	−18120.2	−0.715981
$863$	8140.95	0.321114	0.160557	−	0.987027i	$-0.448671\pi$
$863$	8140.95	0.321114	0.160557	+	0.987027i	$0.448671\pi$
$864$	864.000	0.0340207
$865$	−11896.3	−0.467613
$866$	−28325.8	−1.11149
$867$	−10922.0	−0.427833
$868$	−3719.60	−0.145451
$869$	−3795.11	−0.148148
$870$	−14520.4	−0.565846
$871$	−80626.4	−3.13653
$872$	−7020.07	−0.272626
$873$	−11542.7	−0.447492
$874$	−428.703	−0.0165917
$875$	11654.6	0.450283
$876$	8113.19	0.312921
$877$	−42661.8	−1.64263	−0.821314	−	0.570476i	$-0.806759\pi$
$877$	−42661.8	−1.64263	−0.821314	+	0.570476i	$0.806759\pi$
$878$	−19565.6	−0.752058
$879$	−21869.3	−0.839174
$880$	14819.4	0.567686
$881$	38950.1	1.48951	0.744757	−	0.667336i	$-0.232565\pi$
$881$	38950.1	1.48951	0.744757	+	0.667336i	$0.232565\pi$
$882$	−882.000	−0.0336718
$883$	−18676.4	−0.711791	−0.355896	−	0.934526i	$-0.615824\pi$
$883$	−18676.4	−0.711791	−0.355896	+	0.934526i	$0.615824\pi$
$884$	−31678.0	−1.20526
$885$	25450.4	0.966675
$886$	−9890.98	−0.375050
$887$	5588.09	0.211533	0.105767	−	0.994391i	$-0.466270\pi$
$887$	5588.09	0.211533	0.105767	+	0.994391i	$0.466270\pi$
$888$	3447.03	0.130265
$889$	11219.5	0.423274
$890$	19097.6	0.719273
$891$	−4067.16	−0.152924
$892$	15197.3	0.570453
$893$	4674.93	0.175185
$894$	−9704.54	−0.363052
$895$	21421.5	0.800048
$896$	896.000	0.0334077
$897$	−5908.41	−0.219929
$898$	12867.5	0.478167
$899$	17428.5	0.646577
$900$	7749.35	0.287013
$901$	10076.6	0.372584
$902$	−15013.5	−0.554209
$903$	1896.79	0.0699018
$904$	−12098.1	−0.445106
$905$	74743.7	2.74538
$906$	−12287.9	−0.450594
$907$	−48637.4	−1.78057	−0.890286	−	0.455403i	$-0.849495\pi$
$907$	−48637.4	−1.78057	−0.890286	+	0.455403i	$0.849495\pi$
$908$	−1303.58	−0.0476439
$909$	−7164.24	−0.261411
$910$	−22113.4	−0.805551
$911$	−29584.9	−1.07595	−0.537975	−	0.842961i	$-0.680811\pi$
$911$	−29584.9	−1.07595	−0.537975	+	0.842961i	$0.680811\pi$
$912$	−447.343	−0.0162423
$913$	−48944.3	−1.77417
$914$	8857.60	0.320551
$915$	−12585.0	−0.454698
$916$	16161.0	0.582943
$917$	−2604.02	−0.0937756
$918$	−4994.25	−0.179559
$919$	25539.7	0.916734	0.458367	−	0.888763i	$-0.348435\pi$
$919$	25539.7	0.916734	0.458367	+	0.888763i	$0.348435\pi$
$920$	3394.09	0.121630
$921$	−26965.3	−0.964754
$922$	26070.2	0.931211
$923$	44964.1	1.60348
$924$	−4217.80	−0.150168
$925$	30917.0	1.09897
$926$	16972.7	0.602329
$927$	11361.7	0.402554
$928$	−4198.27	−0.148508
$929$	−8168.39	−0.288478	−0.144239	−	0.989543i	$-0.546073\pi$
$929$	−8168.39	−0.288478	−0.144239	+	0.989543i	$0.546073\pi$
$930$	−14702.6	−0.518407
$931$	456.662	0.0160757
$932$	4937.57	0.173536
$933$	−15601.0	−0.547431
$934$	38865.0	1.36156
$935$	−85662.0	−2.99620
$936$	−6165.30	−0.215298
$937$	36961.4	1.28866	0.644332	−	0.764746i	$-0.277136\pi$
$937$	36961.4	1.28866	0.644332	+	0.764746i	$0.277136\pi$
$938$	−13182.1	−0.458859
$939$	−4199.40	−0.145945
$940$	−37011.9	−1.28425
$941$	−31983.8	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$941$	−31983.8	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$942$	7418.84	0.256602
$943$	−3438.54	−0.118743
$944$	7358.49	0.253706
$945$	−3486.32	−0.120011
$946$	9070.62	0.311746
$947$	2074.44	0.0711829	0.0355914	−	0.999366i	$-0.488668\pi$
$947$	2074.44	0.0711829	0.0355914	+	0.999366i	$0.488668\pi$
$948$	−906.983	−0.0310733
$949$	−57893.8	−1.98031
$950$	−4012.28	−0.137027
$951$	1500.43	0.0511619
$952$	−5179.22	−0.176323
$953$	3386.15	0.115098	0.0575489	−	0.998343i	$-0.481671\pi$
$953$	3386.15	0.115098	0.0575489	+	0.998343i	$0.481671\pi$
$954$	1961.14	0.0665557
$955$	−39439.4	−1.33637
$956$	45.0882	0.00152537
$957$	19762.8	0.667545
$958$	37214.7	1.25506
$959$	5077.87	0.170983
$960$	3541.66	0.119069
$961$	−12143.7	−0.407631
$962$	−24597.2	−0.824373
$963$	−15987.8	−0.534993
$964$	−16865.9	−0.563499
$965$	80266.3	2.67758
$966$	−966.000	−0.0321745
$967$	−7154.83	−0.237936	−0.118968	−	0.992898i	$-0.537959\pi$
$967$	−7154.83	−0.237936	−0.118968	+	0.992898i	$0.537959\pi$
$968$	−9521.88	−0.316162
$969$	2585.81	0.0857257
$970$	−47315.0	−1.56618
$971$	19143.1	0.632678	0.316339	−	0.948646i	$-0.397546\pi$
$971$	19143.1	0.632678	0.316339	+	0.948646i	$0.397546\pi$
$972$	−972.000	−0.0320750
$973$	15303.0	0.504204
$974$	−39349.8	−1.29451
$975$	−55297.5	−1.81635
$976$	−3638.71	−0.119336
$977$	15800.1	0.517389	0.258694	−	0.965959i	$-0.416708\pi$
$977$	15800.1	0.517389	0.258694	+	0.965959i	$0.416708\pi$
$978$	10992.5	0.359407
$979$	−25992.6	−0.848547
$980$	−3615.44	−0.117848
$981$	7897.58	0.257034
$982$	−10520.3	−0.341870
$983$	−6019.42	−0.195310	−0.0976550	−	0.995220i	$-0.531134\pi$
$983$	−6019.42	−0.195310	−0.0976550	+	0.995220i	$0.531134\pi$
$984$	−3588.05	−0.116243
$985$	44774.0	1.44834
$986$	24267.6	0.783812
$987$	10534.1	0.339719
$988$	3192.13	0.102789
$989$	2077.44	0.0667934
$990$	−16671.9	−0.535219
$991$	3999.62	0.128206	0.0641029	−	0.997943i	$-0.479581\pi$
$991$	3999.62	0.128206	0.0641029	+	0.997943i	$0.479581\pi$
$992$	−4250.98	−0.136057
$993$	15850.2	0.506536
$994$	7351.44	0.234581
$995$	5941.89	0.189317
$996$	−11697.1	−0.372124
$997$	−27106.4	−0.861051	−0.430525	−	0.902579i	$-0.641672\pi$
$997$	−27106.4	−0.861051	−0.430525	+	0.902579i	$0.641672\pi$
$998$	6065.52	0.192385
$999$	−3877.91	−0.122815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.h.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.h.1.1	✓	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -18.4461 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -18.4461 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +36.8923 q^{10} -50.2119 q^{11} -12.0000 q^{12} +85.6292 q^{13} +14.0000 q^{14} +55.3384 q^{15} +16.0000 q^{16} -92.4861 q^{17} -18.0000 q^{18} +9.31964 q^{19} -73.7845 q^{20} +21.0000 q^{21} +100.424 q^{22} +23.0000 q^{23} +24.0000 q^{24} +215.260 q^{25} -171.258 q^{26} -27.0000 q^{27} -28.0000 q^{28} +131.196 q^{29} -110.677 q^{30} +132.843 q^{31} -32.0000 q^{32} +150.636 q^{33} +184.972 q^{34} +129.123 q^{35} +36.0000 q^{36} +143.626 q^{37} -18.6393 q^{38} -256.888 q^{39} +147.569 q^{40} -149.502 q^{41} -42.0000 q^{42} +90.3234 q^{43} -200.848 q^{44} -166.015 q^{45} -46.0000 q^{46} +501.622 q^{47} -48.0000 q^{48} +49.0000 q^{49} -430.519 q^{50} +277.458 q^{51} +342.517 q^{52} -108.952 q^{53} +54.0000 q^{54} +926.215 q^{55} +56.0000 q^{56} -27.9589 q^{57} -262.392 q^{58} +459.906 q^{59} +221.354 q^{60} -227.420 q^{61} -265.686 q^{62} -63.0000 q^{63} +64.0000 q^{64} -1579.53 q^{65} -301.271 q^{66} -941.576 q^{67} -369.944 q^{68} -69.0000 q^{69} -258.246 q^{70} +525.103 q^{71} -72.0000 q^{72} -676.099 q^{73} -287.253 q^{74} -645.779 q^{75} +37.2785 q^{76} +351.483 q^{77} +513.775 q^{78} +75.5819 q^{79} -295.138 q^{80} +81.0000 q^{81} +299.004 q^{82} +974.756 q^{83} +84.0000 q^{84} +1706.01 q^{85} -180.647 q^{86} -393.588 q^{87} +401.695 q^{88} +517.659 q^{89} +332.030 q^{90} -599.404 q^{91} +92.0000 q^{92} -398.529 q^{93} -1003.24 q^{94} -171.911 q^{95} +96.0000 q^{96} -1282.52 q^{97} -98.0000 q^{98} -451.907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} - 5 q^{5} + 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 - 5 * q^5 + 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} - 5 q^{5} + 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 10 q^{10} - 41 q^{11} - 48 q^{12} + 23 q^{13} + 56 q^{14} + 15 q^{15} + 64 q^{16} + 18 q^{17} - 72 q^{18} + 15 q^{19} - 20 q^{20} + 84 q^{21} + 82 q^{22} + 92 q^{23} + 96 q^{24} + 219 q^{25} - 46 q^{26} - 108 q^{27} - 112 q^{28} - 46 q^{29} - 30 q^{30} + 142 q^{31} - 128 q^{32} + 123 q^{33} - 36 q^{34} + 35 q^{35} + 144 q^{36} - 142 q^{37} - 30 q^{38} - 69 q^{39} + 40 q^{40} - 621 q^{41} - 168 q^{42} + 185 q^{43} - 164 q^{44} - 45 q^{45} - 184 q^{46} + 669 q^{47} - 192 q^{48} + 196 q^{49} - 438 q^{50} - 54 q^{51} + 92 q^{52} + 422 q^{53} + 216 q^{54} + 1435 q^{55} + 224 q^{56} - 45 q^{57} + 92 q^{58} + 270 q^{59} + 60 q^{60} + 272 q^{61} - 284 q^{62} - 252 q^{63} + 256 q^{64} - 1992 q^{65} - 246 q^{66} - 67 q^{67} + 72 q^{68} - 276 q^{69} - 70 q^{70} + 611 q^{71} - 288 q^{72} - 236 q^{73} + 284 q^{74} - 657 q^{75} + 60 q^{76} + 287 q^{77} + 138 q^{78} + 558 q^{79} - 80 q^{80} + 324 q^{81} + 1242 q^{82} + 468 q^{83} + 336 q^{84} + 1045 q^{85} - 370 q^{86} + 138 q^{87} + 328 q^{88} - 1519 q^{89} + 90 q^{90} - 161 q^{91} + 368 q^{92} - 426 q^{93} - 1338 q^{94} + 23 q^{95} + 384 q^{96} + 600 q^{97} - 392 q^{98} - 369 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 - 5 * q^5 + 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 + 10 * q^10 - 41 * q^11 - 48 * q^12 + 23 * q^13 + 56 * q^14 + 15 * q^15 + 64 * q^16 + 18 * q^17 - 72 * q^18 + 15 * q^19 - 20 * q^20 + 84 * q^21 + 82 * q^22 + 92 * q^23 + 96 * q^24 + 219 * q^25 - 46 * q^26 - 108 * q^27 - 112 * q^28 - 46 * q^29 - 30 * q^30 + 142 * q^31 - 128 * q^32 + 123 * q^33 - 36 * q^34 + 35 * q^35 + 144 * q^36 - 142 * q^37 - 30 * q^38 - 69 * q^39 + 40 * q^40 - 621 * q^41 - 168 * q^42 + 185 * q^43 - 164 * q^44 - 45 * q^45 - 184 * q^46 + 669 * q^47 - 192 * q^48 + 196 * q^49 - 438 * q^50 - 54 * q^51 + 92 * q^52 + 422 * q^53 + 216 * q^54 + 1435 * q^55 + 224 * q^56 - 45 * q^57 + 92 * q^58 + 270 * q^59 + 60 * q^60 + 272 * q^61 - 284 * q^62 - 252 * q^63 + 256 * q^64 - 1992 * q^65 - 246 * q^66 - 67 * q^67 + 72 * q^68 - 276 * q^69 - 70 * q^70 + 611 * q^71 - 288 * q^72 - 236 * q^73 + 284 * q^74 - 657 * q^75 + 60 * q^76 + 287 * q^77 + 138 * q^78 + 558 * q^79 - 80 * q^80 + 324 * q^81 + 1242 * q^82 + 468 * q^83 + 336 * q^84 + 1045 * q^85 - 370 * q^86 + 138 * q^87 + 328 * q^88 - 1519 * q^89 + 90 * q^90 - 161 * q^91 + 368 * q^92 - 426 * q^93 - 1338 * q^94 + 23 * q^95 + 384 * q^96 + 600 * q^97 - 392 * q^98 - 369 * q^99

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