LMFDB - Embedded newform 4034.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.93683 q^{3} +1.00000 q^{4} +0.0231797 q^{5} +2.93683 q^{6} -4.16598 q^{7} -1.00000 q^{8} +5.62497 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.93683 q^{3} +1.00000 q^{4} +0.0231797 q^{5} +2.93683 q^{6} -4.16598 q^{7} -1.00000 q^{8} +5.62497 q^{9} -0.0231797 q^{10} -0.577287 q^{11} -2.93683 q^{12} +4.15217 q^{13} +4.16598 q^{14} -0.0680749 q^{15} +1.00000 q^{16} +5.01247 q^{17} -5.62497 q^{18} -4.30029 q^{19} +0.0231797 q^{20} +12.2348 q^{21} +0.577287 q^{22} -7.61875 q^{23} +2.93683 q^{24} -4.99946 q^{25} -4.15217 q^{26} -7.70910 q^{27} -4.16598 q^{28} -6.64323 q^{29} +0.0680749 q^{30} -1.79571 q^{31} -1.00000 q^{32} +1.69539 q^{33} -5.01247 q^{34} -0.0965662 q^{35} +5.62497 q^{36} +4.49134 q^{37} +4.30029 q^{38} -12.1942 q^{39} -0.0231797 q^{40} +6.87499 q^{41} -12.2348 q^{42} +7.16461 q^{43} -0.577287 q^{44} +0.130385 q^{45} +7.61875 q^{46} +9.86016 q^{47} -2.93683 q^{48} +10.3554 q^{49} +4.99946 q^{50} -14.7208 q^{51} +4.15217 q^{52} +4.43946 q^{53} +7.70910 q^{54} -0.0133814 q^{55} +4.16598 q^{56} +12.6292 q^{57} +6.64323 q^{58} -1.52438 q^{59} -0.0680749 q^{60} -6.77934 q^{61} +1.79571 q^{62} -23.4335 q^{63} +1.00000 q^{64} +0.0962462 q^{65} -1.69539 q^{66} +3.52538 q^{67} +5.01247 q^{68} +22.3750 q^{69} +0.0965662 q^{70} -9.52005 q^{71} -5.62497 q^{72} +3.90438 q^{73} -4.49134 q^{74} +14.6826 q^{75} -4.30029 q^{76} +2.40497 q^{77} +12.1942 q^{78} +11.2247 q^{79} +0.0231797 q^{80} +5.76539 q^{81} -6.87499 q^{82} +13.2835 q^{83} +12.2348 q^{84} +0.116188 q^{85} -7.16461 q^{86} +19.5101 q^{87} +0.577287 q^{88} -5.75217 q^{89} -0.130385 q^{90} -17.2979 q^{91} -7.61875 q^{92} +5.27369 q^{93} -9.86016 q^{94} -0.0996796 q^{95} +2.93683 q^{96} +6.17466 q^{97} -10.3554 q^{98} -3.24722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.93683	−1.69558	−0.847790	−	0.530332i	$-0.822067\pi$
$3$	−2.93683	−1.69558	−0.847790	+	0.530332i	$0.822067\pi$
$4$	1.00000	0.500000
$5$	0.0231797	0.0103663	0.00518314	−	0.999987i	$-0.498350\pi$
$5$	0.0231797	0.0103663	0.00518314	+	0.999987i	$0.498350\pi$
$6$	2.93683	1.19896
$7$	−4.16598	−1.57459	−0.787296	−	0.616575i	$-0.788520\pi$
$7$	−4.16598	−1.57459	−0.787296	+	0.616575i	$0.788520\pi$
$8$	−1.00000	−0.353553
$9$	5.62497	1.87499
$10$	−0.0231797	−0.00733007
$11$	−0.577287	−0.174059	−0.0870293	−	0.996206i	$-0.527737\pi$
$11$	−0.577287	−0.174059	−0.0870293	+	0.996206i	$0.527737\pi$
$12$	−2.93683	−0.847790
$13$	4.15217	1.15161	0.575803	−	0.817588i	$-0.304690\pi$
$13$	4.15217	1.15161	0.575803	+	0.817588i	$0.304690\pi$
$14$	4.16598	1.11341
$15$	−0.0680749	−0.0175769
$16$	1.00000	0.250000
$17$	5.01247	1.21570	0.607852	−	0.794050i	$-0.292031\pi$
$17$	5.01247	1.21570	0.607852	+	0.794050i	$0.292031\pi$
$18$	−5.62497	−1.32582
$19$	−4.30029	−0.986555	−0.493278	−	0.869872i	$-0.664201\pi$
$19$	−4.30029	−0.986555	−0.493278	+	0.869872i	$0.664201\pi$
$20$	0.0231797	0.00518314
$21$	12.2348	2.66985
$22$	0.577287	0.123078
$23$	−7.61875	−1.58862	−0.794309	−	0.607514i	$-0.792167\pi$
$23$	−7.61875	−1.58862	−0.794309	+	0.607514i	$0.792167\pi$
$24$	2.93683	0.599478
$25$	−4.99946	−0.999893
$26$	−4.15217	−0.814308
$27$	−7.70910	−1.48362
$28$	−4.16598	−0.787296
$29$	−6.64323	−1.23362	−0.616809	−	0.787113i	$-0.711575\pi$
$29$	−6.64323	−1.23362	−0.616809	+	0.787113i	$0.711575\pi$
$30$	0.0680749	0.0124287
$31$	−1.79571	−0.322519	−0.161259	−	0.986912i	$-0.551556\pi$
$31$	−1.79571	−0.322519	−0.161259	+	0.986912i	$0.551556\pi$
$32$	−1.00000	−0.176777
$33$	1.69539	0.295130
$34$	−5.01247	−0.859632
$35$	−0.0965662	−0.0163227
$36$	5.62497	0.937495
$37$	4.49134	0.738372	0.369186	−	0.929356i	$-0.379637\pi$
$37$	4.49134	0.738372	0.369186	+	0.929356i	$0.379637\pi$
$38$	4.30029	0.697600
$39$	−12.1942	−1.95264
$40$	−0.0231797	−0.00366503
$41$	6.87499	1.07369	0.536846	−	0.843680i	$-0.319615\pi$
$41$	6.87499	1.07369	0.536846	+	0.843680i	$0.319615\pi$
$42$	−12.2348	−1.88787
$43$	7.16461	1.09259	0.546297	−	0.837592i	$-0.316037\pi$
$43$	7.16461	1.09259	0.546297	+	0.837592i	$0.316037\pi$
$44$	−0.577287	−0.0870293
$45$	0.130385	0.0194367
$46$	7.61875	1.12332
$47$	9.86016	1.43825	0.719126	−	0.694880i	$-0.244542\pi$
$47$	9.86016	1.43825	0.719126	+	0.694880i	$0.244542\pi$
$48$	−2.93683	−0.423895
$49$	10.3554	1.47934
$50$	4.99946	0.707031
$51$	−14.7208	−2.06132
$52$	4.15217	0.575803
$53$	4.43946	0.609807	0.304904	−	0.952383i	$-0.401376\pi$
$53$	4.43946	0.609807	0.304904	+	0.952383i	$0.401376\pi$
$54$	7.70910	1.04908
$55$	−0.0133814	−0.00180434
$56$	4.16598	0.556703
$57$	12.6292	1.67278
$58$	6.64323	0.872299
$59$	−1.52438	−0.198457	−0.0992284	−	0.995065i	$-0.531637\pi$
$59$	−1.52438	−0.198457	−0.0992284	+	0.995065i	$0.531637\pi$
$60$	−0.0680749	−0.00878843
$61$	−6.77934	−0.868006	−0.434003	−	0.900912i	$-0.642899\pi$
$61$	−6.77934	−0.868006	−0.434003	+	0.900912i	$0.642899\pi$
$62$	1.79571	0.228055
$63$	−23.4335	−2.95235
$64$	1.00000	0.125000
$65$	0.0962462	0.0119379
$66$	−1.69539	−0.208689
$67$	3.52538	0.430694	0.215347	−	0.976538i	$-0.430912\pi$
$67$	3.52538	0.430694	0.215347	+	0.976538i	$0.430912\pi$
$68$	5.01247	0.607852
$69$	22.3750	2.69363
$70$	0.0965662	0.0115419
$71$	−9.52005	−1.12982	−0.564911	−	0.825152i	$-0.691089\pi$
$71$	−9.52005	−1.12982	−0.564911	+	0.825152i	$0.691089\pi$
$72$	−5.62497	−0.662909
$73$	3.90438	0.456973	0.228487	−	0.973547i	$-0.426622\pi$
$73$	3.90438	0.456973	0.228487	+	0.973547i	$0.426622\pi$
$74$	−4.49134	−0.522108
$75$	14.6826	1.69540
$76$	−4.30029	−0.493278
$77$	2.40497	0.274071
$78$	12.1942	1.38072
$79$	11.2247	1.26288	0.631438	−	0.775426i	$-0.282465\pi$
$79$	11.2247	1.26288	0.631438	+	0.775426i	$0.282465\pi$
$80$	0.0231797	0.00259157
$81$	5.76539	0.640599
$82$	−6.87499	−0.759215
$83$	13.2835	1.45806	0.729028	−	0.684484i	$-0.239972\pi$
$83$	13.2835	1.45806	0.729028	+	0.684484i	$0.239972\pi$
$84$	12.2348	1.33492
$85$	0.116188	0.0126023
$86$	−7.16461	−0.772580
$87$	19.5101	2.09170
$88$	0.577287	0.0615390
$89$	−5.75217	−0.609729	−0.304864	−	0.952396i	$-0.598611\pi$
$89$	−5.75217	−0.609729	−0.304864	+	0.952396i	$0.598611\pi$
$90$	−0.130385	−0.0137438
$91$	−17.2979	−1.81331
$92$	−7.61875	−0.794309
$93$	5.27369	0.546856
$94$	−9.86016	−1.01700
$95$	−0.0996796	−0.0102269
$96$	2.93683	0.299739
$97$	6.17466	0.626942	0.313471	−	0.949598i	$-0.398508\pi$
$97$	6.17466	0.626942	0.313471	+	0.949598i	$0.398508\pi$
$98$	−10.3554	−1.04605
$99$	−3.24722	−0.326358
$100$	−4.99946	−0.499946
$101$	8.81269	0.876896	0.438448	−	0.898757i	$-0.355528\pi$
$101$	8.81269	0.876896	0.438448	+	0.898757i	$0.355528\pi$
$102$	14.7208	1.45758
$103$	10.6579	1.05016	0.525078	−	0.851054i	$-0.324036\pi$
$103$	10.6579	1.05016	0.525078	+	0.851054i	$0.324036\pi$
$104$	−4.15217	−0.407154
$105$	0.283599	0.0276764
$106$	−4.43946	−0.431199
$107$	−11.3875	−1.10087	−0.550436	−	0.834878i	$-0.685538\pi$
$107$	−11.3875	−1.10087	−0.550436	+	0.834878i	$0.685538\pi$
$108$	−7.70910	−0.741808
$109$	−0.224948	−0.0215461	−0.0107731	−	0.999942i	$-0.503429\pi$
$109$	−0.224948	−0.0215461	−0.0107731	+	0.999942i	$0.503429\pi$
$110$	0.0133814	0.00127586
$111$	−13.1903	−1.25197
$112$	−4.16598	−0.393648
$113$	11.1335	1.04735	0.523675	−	0.851918i	$-0.324560\pi$
$113$	11.1335	1.04735	0.523675	+	0.851918i	$0.324560\pi$
$114$	−12.6292	−1.18284
$115$	−0.176600	−0.0164681
$116$	−6.64323	−0.616809
$117$	23.3559	2.15925
$118$	1.52438	0.140330
$119$	−20.8819	−1.91424
$120$	0.0680749	0.00621436
$121$	−10.6667	−0.969704
$122$	6.77934	0.613773
$123$	−20.1907	−1.82053
$124$	−1.79571	−0.161259
$125$	−0.231785	−0.0207314
$126$	23.4335	2.08762
$127$	−1.26298	−0.112071	−0.0560356	−	0.998429i	$-0.517846\pi$
$127$	−1.26298	−0.112071	−0.0560356	+	0.998429i	$0.517846\pi$
$128$	−1.00000	−0.0883883
$129$	−21.0413	−1.85258
$130$	−0.0962462	−0.00844135
$131$	2.51278	0.219542	0.109771	−	0.993957i	$-0.464988\pi$
$131$	2.51278	0.219542	0.109771	+	0.993957i	$0.464988\pi$
$132$	1.69539	0.147565
$133$	17.9149	1.55342
$134$	−3.52538	−0.304547
$135$	−0.178695	−0.0153796
$136$	−5.01247	−0.429816
$137$	4.99721	0.426940	0.213470	−	0.976950i	$-0.431523\pi$
$137$	4.99721	0.426940	0.213470	+	0.976950i	$0.431523\pi$
$138$	−22.3750	−1.90468
$139$	16.9877	1.44088	0.720440	−	0.693517i	$-0.243940\pi$
$139$	16.9877	1.44088	0.720440	+	0.693517i	$0.243940\pi$
$140$	−0.0965662	−0.00816133
$141$	−28.9576	−2.43867
$142$	9.52005	0.798905
$143$	−2.39700	−0.200447
$144$	5.62497	0.468748
$145$	−0.153988	−0.0127880
$146$	−3.90438	−0.323129
$147$	−30.4120	−2.50834
$148$	4.49134	0.369186
$149$	−16.6256	−1.36202	−0.681012	−	0.732272i	$-0.738460\pi$
$149$	−16.6256	−1.36202	−0.681012	+	0.732272i	$0.738460\pi$
$150$	−14.6826	−1.19883
$151$	−21.9815	−1.78883	−0.894416	−	0.447236i	$-0.852408\pi$
$151$	−21.9815	−1.78883	−0.894416	+	0.447236i	$0.852408\pi$
$152$	4.30029	0.348800
$153$	28.1950	2.27943
$154$	−2.40497	−0.193798
$155$	−0.0416240	−0.00334332
$156$	−12.1942	−0.976320
$157$	−9.43642	−0.753109	−0.376554	−	0.926395i	$-0.622891\pi$
$157$	−9.43642	−0.753109	−0.376554	+	0.926395i	$0.622891\pi$
$158$	−11.2247	−0.892988
$159$	−13.0379	−1.03398
$160$	−0.0231797	−0.00183252
$161$	31.7395	2.50143
$162$	−5.76539	−0.452972
$163$	−0.815100	−0.0638435	−0.0319218	−	0.999490i	$-0.510163\pi$
$163$	−0.815100	−0.0638435	−0.0319218	+	0.999490i	$0.510163\pi$
$164$	6.87499	0.536846
$165$	0.0392988	0.00305940
$166$	−13.2835	−1.03100
$167$	10.4443	0.808201	0.404100	−	0.914715i	$-0.367585\pi$
$167$	10.4443	0.808201	0.404100	+	0.914715i	$0.367585\pi$
$168$	−12.2348	−0.943934
$169$	4.24055	0.326196
$170$	−0.116188	−0.00891119
$171$	−24.1890	−1.84978
$172$	7.16461	0.546297
$173$	−10.7042	−0.813827	−0.406914	−	0.913467i	$-0.633395\pi$
$173$	−10.7042	−0.813827	−0.406914	+	0.913467i	$0.633395\pi$
$174$	−19.5101	−1.47905
$175$	20.8277	1.57442
$176$	−0.577287	−0.0435147
$177$	4.47683	0.336499
$178$	5.75217	0.431143
$179$	21.0300	1.57186	0.785928	−	0.618318i	$-0.212186\pi$
$179$	21.0300	1.57186	0.785928	+	0.618318i	$0.212186\pi$
$180$	0.130385	0.00971834
$181$	−8.76954	−0.651835	−0.325917	−	0.945398i	$-0.605673\pi$
$181$	−8.76954	−0.651835	−0.325917	+	0.945398i	$0.605673\pi$
$182$	17.2979	1.28220
$183$	19.9098	1.47177
$184$	7.61875	0.561661
$185$	0.104108	0.00765417
$186$	−5.27369	−0.386685
$187$	−2.89364	−0.211604
$188$	9.86016	0.719126
$189$	32.1159	2.33609
$190$	0.0996796	0.00723152
$191$	23.2752	1.68413	0.842067	−	0.539372i	$-0.181338\pi$
$191$	23.2752	1.68413	0.842067	+	0.539372i	$0.181338\pi$
$192$	−2.93683	−0.211947
$193$	6.29418	0.453065	0.226533	−	0.974004i	$-0.427261\pi$
$193$	6.29418	0.453065	0.226533	+	0.974004i	$0.427261\pi$
$194$	−6.17466	−0.443315
$195$	−0.282659	−0.0202416
$196$	10.3554	0.739671
$197$	−21.7296	−1.54817	−0.774084	−	0.633082i	$-0.781789\pi$
$197$	−21.7296	−1.54817	−0.774084	+	0.633082i	$0.781789\pi$
$198$	3.24722	0.230770
$199$	−13.0108	−0.922314	−0.461157	−	0.887319i	$-0.652566\pi$
$199$	−13.0108	−0.922314	−0.461157	+	0.887319i	$0.652566\pi$
$200$	4.99946	0.353515
$201$	−10.3535	−0.730276
$202$	−8.81269	−0.620059
$203$	27.6756	1.94245
$204$	−14.7208	−1.03066
$205$	0.159360	0.0111302
$206$	−10.6579	−0.742573
$207$	−42.8552	−2.97864
$208$	4.15217	0.287902
$209$	2.48251	0.171718
$210$	−0.283599	−0.0195702
$211$	−17.7150	−1.21955	−0.609776	−	0.792574i	$-0.708741\pi$
$211$	−17.7150	−1.21955	−0.609776	+	0.792574i	$0.708741\pi$
$212$	4.43946	0.304904
$213$	27.9588	1.91570
$214$	11.3875	0.778434
$215$	0.166074	0.0113261
$216$	7.70910	0.524538
$217$	7.48088	0.507835
$218$	0.224948	0.0152354
$219$	−11.4665	−0.774835
$220$	−0.0133814	−0.000902170 0
$221$	20.8127	1.40001
$222$	13.1903	0.885275
$223$	2.87088	0.192248	0.0961241	−	0.995369i	$-0.469355\pi$
$223$	2.87088	0.192248	0.0961241	+	0.995369i	$0.469355\pi$
$224$	4.16598	0.278351
$225$	−28.1218	−1.87479
$226$	−11.1335	−0.740589
$227$	2.08872	0.138633	0.0693165	−	0.997595i	$-0.477918\pi$
$227$	2.08872	0.138633	0.0693165	+	0.997595i	$0.477918\pi$
$228$	12.6292	0.836392
$229$	7.97105	0.526742	0.263371	−	0.964695i	$-0.415166\pi$
$229$	7.97105	0.526742	0.263371	+	0.964695i	$0.415166\pi$
$230$	0.176600	0.0116447
$231$	−7.06298	−0.464710
$232$	6.64323	0.436150
$233$	−15.0854	−0.988276	−0.494138	−	0.869383i	$-0.664516\pi$
$233$	−15.0854	−0.988276	−0.494138	+	0.869383i	$0.664516\pi$
$234$	−23.3559	−1.52682
$235$	0.228556	0.0149093
$236$	−1.52438	−0.0992284
$237$	−32.9650	−2.14131
$238$	20.8819	1.35357
$239$	−19.7591	−1.27811	−0.639056	−	0.769160i	$-0.720675\pi$
$239$	−19.7591	−1.27811	−0.639056	+	0.769160i	$0.720675\pi$
$240$	−0.0680749	−0.00439421
$241$	−4.50913	−0.290459	−0.145229	−	0.989398i	$-0.546392\pi$
$241$	−4.50913	−0.290459	−0.145229	+	0.989398i	$0.546392\pi$
$242$	10.6667	0.685684
$243$	6.19531	0.397429
$244$	−6.77934	−0.434003
$245$	0.240035	0.0153353
$246$	20.1907	1.28731
$247$	−17.8556	−1.13612
$248$	1.79571	0.114028
$249$	−39.0115	−2.47225
$250$	0.231785	0.0146593
$251$	−10.3254	−0.651731	−0.325866	−	0.945416i	$-0.605656\pi$
$251$	−10.3254	−0.651731	−0.325866	+	0.945416i	$0.605656\pi$
$252$	−23.4335	−1.47617
$253$	4.39821	0.276513
$254$	1.26298	0.0792463
$255$	−0.341224	−0.0213682
$256$	1.00000	0.0625000
$257$	−3.87343	−0.241618	−0.120809	−	0.992676i	$-0.538549\pi$
$257$	−3.87343	−0.241618	−0.120809	+	0.992676i	$0.538549\pi$
$258$	21.0413	1.30997
$259$	−18.7108	−1.16263
$260$	0.0962462	0.00596894
$261$	−37.3680	−2.31302
$262$	−2.51278	−0.155240
$263$	7.06229	0.435479	0.217740	−	0.976007i	$-0.430132\pi$
$263$	7.06229	0.435479	0.217740	+	0.976007i	$0.430132\pi$
$264$	−1.69539	−0.104344
$265$	0.102905	0.00632143
$266$	−17.9149	−1.09844
$267$	16.8931	1.03384
$268$	3.52538	0.215347
$269$	−17.6481	−1.07602	−0.538012	−	0.842937i	$-0.680825\pi$
$269$	−17.6481	−1.07602	−0.538012	+	0.842937i	$0.680825\pi$
$270$	0.178695	0.0108750
$271$	10.8492	0.659040	0.329520	−	0.944149i	$-0.393113\pi$
$271$	10.8492	0.659040	0.329520	+	0.944149i	$0.393113\pi$
$272$	5.01247	0.303926
$273$	50.8009	3.07461
$274$	−4.99721	−0.301893
$275$	2.88613	0.174040
$276$	22.3750	1.34681
$277$	1.76608	0.106113	0.0530566	−	0.998592i	$-0.483104\pi$
$277$	1.76608	0.106113	0.0530566	+	0.998592i	$0.483104\pi$
$278$	−16.9877	−1.01886
$279$	−10.1008	−0.604719
$280$	0.0965662	0.00577093
$281$	3.18278	0.189869	0.0949343	−	0.995484i	$-0.469736\pi$
$281$	3.18278	0.189869	0.0949343	+	0.995484i	$0.469736\pi$
$282$	28.9576	1.72440
$283$	−3.93228	−0.233750	−0.116875	−	0.993147i	$-0.537288\pi$
$283$	−3.93228	−0.233750	−0.116875	+	0.993147i	$0.537288\pi$
$284$	−9.52005	−0.564911
$285$	0.292742	0.0173405
$286$	2.39700	0.141737
$287$	−28.6411	−1.69063
$288$	−5.62497	−0.331455
$289$	8.12490	0.477935
$290$	0.153988	0.00904250
$291$	−18.1339	−1.06303
$292$	3.90438	0.228487
$293$	14.4126	0.841991	0.420996	−	0.907063i	$-0.361681\pi$
$293$	14.4126	0.841991	0.420996	+	0.907063i	$0.361681\pi$
$294$	30.4120	1.77367
$295$	−0.0353346	−0.00205726
$296$	−4.49134	−0.261054
$297$	4.45036	0.258236
$298$	16.6256	0.963097
$299$	−31.6344	−1.82946
$300$	14.6826	0.847699
$301$	−29.8476	−1.72039
$302$	21.9815	1.26490
$303$	−25.8814	−1.48685
$304$	−4.30029	−0.246639
$305$	−0.157143	−0.00899799
$306$	−28.1950	−1.61180
$307$	−10.9201	−0.623245	−0.311623	−	0.950206i	$-0.600872\pi$
$307$	−10.9201	−0.623245	−0.311623	+	0.950206i	$0.600872\pi$
$308$	2.40497	0.137036
$309$	−31.3005	−1.78062
$310$	0.0416240	0.00236408
$311$	−9.00775	−0.510783	−0.255391	−	0.966838i	$-0.582204\pi$
$311$	−9.00775	−0.510783	−0.255391	+	0.966838i	$0.582204\pi$
$312$	12.1942	0.690362
$313$	−32.1656	−1.81811	−0.909055	−	0.416676i	$-0.863195\pi$
$313$	−32.1656	−1.81811	−0.909055	+	0.416676i	$0.863195\pi$
$314$	9.43642	0.532528
$315$	−0.543182	−0.0306049
$316$	11.2247	0.631438
$317$	18.4867	1.03831	0.519157	−	0.854679i	$-0.326246\pi$
$317$	18.4867	1.03831	0.519157	+	0.854679i	$0.326246\pi$
$318$	13.0379	0.731132
$319$	3.83505	0.214722
$320$	0.0231797	0.00129579
$321$	33.4432	1.86662
$322$	−31.7395	−1.76878
$323$	−21.5551	−1.19936
$324$	5.76539	0.320300
$325$	−20.7586	−1.15148
$326$	0.815100	0.0451442
$327$	0.660635	0.0365332
$328$	−6.87499	−0.379608
$329$	−41.0772	−2.26466
$330$	−0.0392988	−0.00216333
$331$	−2.57834	−0.141718	−0.0708592	−	0.997486i	$-0.522574\pi$
$331$	−2.57834	−0.141718	−0.0708592	+	0.997486i	$0.522574\pi$
$332$	13.2835	0.729028
$333$	25.2637	1.38444
$334$	−10.4443	−0.571484
$335$	0.0817174	0.00446470
$336$	12.2348	0.667462
$337$	15.3049	0.833710	0.416855	−	0.908973i	$-0.363132\pi$
$337$	15.3049	0.833710	0.416855	+	0.908973i	$0.363132\pi$
$338$	−4.24055	−0.230656
$339$	−32.6972	−1.77587
$340$	0.116188	0.00630116
$341$	1.03664	0.0561371
$342$	24.1890	1.30799
$343$	−13.9785	−0.754768
$344$	−7.16461	−0.386290
$345$	0.518645	0.0279229
$346$	10.7042	0.575463
$347$	1.47659	0.0792677	0.0396338	−	0.999214i	$-0.487381\pi$
$347$	1.47659	0.0792677	0.0396338	+	0.999214i	$0.487381\pi$
$348$	19.5101	1.04585
$349$	−6.04925	−0.323809	−0.161905	−	0.986806i	$-0.551764\pi$
$349$	−6.04925	−0.323809	−0.161905	+	0.986806i	$0.551764\pi$
$350$	−20.8277	−1.11329
$351$	−32.0095	−1.70854
$352$	0.577287	0.0307695
$353$	−19.1525	−1.01939	−0.509693	−	0.860357i	$-0.670241\pi$
$353$	−19.1525	−1.01939	−0.509693	+	0.860357i	$0.670241\pi$
$354$	−4.47683	−0.237941
$355$	−0.220672	−0.0117120
$356$	−5.75217	−0.304864
$357$	61.3265	3.24574
$358$	−21.0300	−1.11147
$359$	32.5771	1.71935	0.859677	−	0.510838i	$-0.170665\pi$
$359$	32.5771	1.71935	0.859677	+	0.510838i	$0.170665\pi$
$360$	−0.130385	−0.00687190
$361$	−0.507464	−0.0267086
$362$	8.76954	0.460917
$363$	31.3264	1.64421
$364$	−17.2979	−0.906655
$365$	0.0905024	0.00473711
$366$	−19.9098	−1.04070
$367$	−34.9836	−1.82613	−0.913064	−	0.407816i	$-0.866291\pi$
$367$	−34.9836	−1.82613	−0.913064	+	0.407816i	$0.866291\pi$
$368$	−7.61875	−0.397155
$369$	38.6716	2.01316
$370$	−0.104108	−0.00541231
$371$	−18.4947	−0.960198
$372$	5.27369	0.273428
$373$	−29.0916	−1.50631	−0.753153	−	0.657846i	$-0.771468\pi$
$373$	−29.0916	−1.50631	−0.753153	+	0.657846i	$0.771468\pi$
$374$	2.89364	0.149626
$375$	0.680712	0.0351518
$376$	−9.86016	−0.508499
$377$	−27.5839	−1.42064
$378$	−32.1159	−1.65187
$379$	33.2176	1.70627	0.853137	−	0.521688i	$-0.174697\pi$
$379$	33.2176	1.70627	0.853137	+	0.521688i	$0.174697\pi$
$380$	−0.0996796	−0.00511345
$381$	3.70915	0.190026
$382$	−23.2752	−1.19086
$383$	−12.9076	−0.659548	−0.329774	−	0.944060i	$-0.606973\pi$
$383$	−12.9076	−0.659548	−0.329774	+	0.944060i	$0.606973\pi$
$384$	2.93683	0.149869
$385$	0.0557464	0.00284110
$386$	−6.29418	−0.320365
$387$	40.3008	2.04860
$388$	6.17466	0.313471
$389$	20.1573	1.02201	0.511007	−	0.859576i	$-0.329272\pi$
$389$	20.1573	1.02201	0.511007	+	0.859576i	$0.329272\pi$
$390$	0.282659	0.0143130
$391$	−38.1888	−1.93129
$392$	−10.3554	−0.523026
$393$	−7.37960	−0.372252
$394$	21.7296	1.09472
$395$	0.260185	0.0130913
$396$	−3.24722	−0.163179
$397$	−39.2556	−1.97018	−0.985091	−	0.172033i	$-0.944967\pi$
$397$	−39.2556	−1.97018	−0.985091	+	0.172033i	$0.944967\pi$
$398$	13.0108	0.652175
$399$	−52.6131	−2.63395
$400$	−4.99946	−0.249973
$401$	−37.6142	−1.87836	−0.939181	−	0.343422i	$-0.888414\pi$
$401$	−37.6142	−1.87836	−0.939181	+	0.343422i	$0.888414\pi$
$402$	10.3535	0.516383
$403$	−7.45609	−0.371414
$404$	8.81269	0.438448
$405$	0.133640	0.00664063
$406$	−27.6756	−1.37352
$407$	−2.59279	−0.128520
$408$	14.7208	0.728788
$409$	−7.57524	−0.374572	−0.187286	−	0.982305i	$-0.559969\pi$
$409$	−7.57524	−0.374572	−0.187286	+	0.982305i	$0.559969\pi$
$410$	−0.159360	−0.00787024
$411$	−14.6760	−0.723912
$412$	10.6579	0.525078
$413$	6.35052	0.312489
$414$	42.8552	2.10622
$415$	0.307908	0.0151146
$416$	−4.15217	−0.203577
$417$	−49.8901	−2.44313
$418$	−2.48251	−0.121423
$419$	17.4627	0.853107	0.426553	−	0.904462i	$-0.359728\pi$
$419$	17.4627	0.853107	0.426553	+	0.904462i	$0.359728\pi$
$420$	0.283599	0.0138382
$421$	11.8366	0.576879	0.288440	−	0.957498i	$-0.406864\pi$
$421$	11.8366	0.576879	0.288440	+	0.957498i	$0.406864\pi$
$422$	17.7150	0.862354
$423$	55.4631	2.69671
$424$	−4.43946	−0.215599
$425$	−25.0597	−1.21557
$426$	−27.9588	−1.35461
$427$	28.2426	1.36676
$428$	−11.3875	−0.550436
$429$	7.03957	0.339874
$430$	−0.166074	−0.00800878
$431$	23.9206	1.15222	0.576108	−	0.817374i	$-0.304571\pi$
$431$	23.9206	1.15222	0.576108	+	0.817374i	$0.304571\pi$
$432$	−7.70910	−0.370904
$433$	−11.4726	−0.551339	−0.275669	−	0.961253i	$-0.588899\pi$
$433$	−11.4726	−0.551339	−0.275669	+	0.961253i	$0.588899\pi$
$434$	−7.48088	−0.359094
$435$	0.452237	0.0216831
$436$	−0.224948	−0.0107731
$437$	32.7629	1.56726
$438$	11.4665	0.547891
$439$	−15.2169	−0.726264	−0.363132	−	0.931738i	$-0.618293\pi$
$439$	−15.2169	−0.726264	−0.363132	+	0.931738i	$0.618293\pi$
$440$	0.0133814	0.000637931 0
$441$	58.2488	2.77375
$442$	−20.8127	−0.989958
$443$	29.1287	1.38394	0.691972	−	0.721924i	$-0.256742\pi$
$443$	29.1287	1.38394	0.691972	+	0.721924i	$0.256742\pi$
$444$	−13.1903	−0.625984
$445$	−0.133334	−0.00632062
$446$	−2.87088	−0.135940
$447$	48.8267	2.30942
$448$	−4.16598	−0.196824
$449$	−18.7684	−0.885737	−0.442869	−	0.896586i	$-0.646039\pi$
$449$	−18.7684	−0.885737	−0.442869	+	0.896586i	$0.646039\pi$
$450$	28.1218	1.32568
$451$	−3.96884	−0.186886
$452$	11.1335	0.523675
$453$	64.5560	3.03311
$454$	−2.08872	−0.0980284
$455$	−0.400960	−0.0187973
$456$	−12.6292	−0.591418
$457$	−27.1487	−1.26996	−0.634982	−	0.772527i	$-0.718992\pi$
$457$	−27.1487	−1.26996	−0.634982	+	0.772527i	$0.718992\pi$
$458$	−7.97105	−0.372463
$459$	−38.6417	−1.80364
$460$	−0.176600	−0.00823403
$461$	11.8403	0.551459	0.275729	−	0.961235i	$-0.411081\pi$
$461$	11.8403	0.551459	0.275729	+	0.961235i	$0.411081\pi$
$462$	7.06298	0.328600
$463$	−28.1461	−1.30806	−0.654030	−	0.756469i	$-0.726923\pi$
$463$	−28.1461	−1.30806	−0.654030	+	0.756469i	$0.726923\pi$
$464$	−6.64323	−0.308404
$465$	0.122243	0.00566886
$466$	15.0854	0.698817
$467$	14.2690	0.660293	0.330146	−	0.943930i	$-0.392902\pi$
$467$	14.2690	0.660293	0.330146	+	0.943930i	$0.392902\pi$
$468$	23.3559	1.07963
$469$	−14.6867	−0.678168
$470$	−0.228556	−0.0105425
$471$	27.7132	1.27696
$472$	1.52438	0.0701651
$473$	−4.13604	−0.190175
$474$	32.9650	1.51413
$475$	21.4992	0.986449
$476$	−20.8819	−0.957119
$477$	24.9719	1.14338
$478$	19.7591	0.903762
$479$	−0.804060	−0.0367385	−0.0183692	−	0.999831i	$-0.505847\pi$
$479$	−0.804060	−0.0367385	−0.0183692	+	0.999831i	$0.505847\pi$
$480$	0.0680749	0.00310718
$481$	18.6488	0.850313
$482$	4.50913	0.205385
$483$	−93.2137	−4.24137
$484$	−10.6667	−0.484852
$485$	0.143127	0.00649906
$486$	−6.19531	−0.281025
$487$	−8.15983	−0.369757	−0.184879	−	0.982761i	$-0.559189\pi$
$487$	−8.15983	−0.369757	−0.184879	+	0.982761i	$0.559189\pi$
$488$	6.77934	0.306886
$489$	2.39381	0.108252
$490$	−0.240035	−0.0108437
$491$	−35.3176	−1.59386	−0.796930	−	0.604071i	$-0.793544\pi$
$491$	−35.3176	−1.59386	−0.796930	+	0.604071i	$0.793544\pi$
$492$	−20.1907	−0.910266
$493$	−33.2990	−1.49971
$494$	17.8556	0.803360
$495$	−0.0752697	−0.00338312
$496$	−1.79571	−0.0806296
$497$	39.6603	1.77901
$498$	39.0115	1.74814
$499$	17.7472	0.794473	0.397237	−	0.917716i	$-0.369969\pi$
$499$	17.7472	0.794473	0.397237	+	0.917716i	$0.369969\pi$
$500$	−0.231785	−0.0103657
$501$	−30.6730	−1.37037
$502$	10.3254	0.460844
$503$	−38.2805	−1.70684	−0.853422	−	0.521221i	$-0.825477\pi$
$503$	−38.2805	−1.70684	−0.853422	+	0.521221i	$0.825477\pi$
$504$	23.4335	1.04381
$505$	0.204276	0.00909015
$506$	−4.39821	−0.195524
$507$	−12.4538	−0.553092
$508$	−1.26298	−0.0560356
$509$	−40.7996	−1.80841	−0.904205	−	0.427099i	$-0.859536\pi$
$509$	−40.7996	−1.80841	−0.904205	+	0.427099i	$0.859536\pi$
$510$	0.341224	0.0151096
$511$	−16.2656	−0.719547
$512$	−1.00000	−0.0441942
$513$	33.1514	1.46367
$514$	3.87343	0.170850
$515$	0.247048	0.0108862
$516$	−21.0413	−0.926290
$517$	−5.69214	−0.250340
$518$	18.7108	0.822107
$519$	31.4365	1.37991
$520$	−0.0962462	−0.00422068
$521$	29.9346	1.31146	0.655730	−	0.754995i	$-0.272361\pi$
$521$	29.9346	1.31146	0.655730	+	0.754995i	$0.272361\pi$
$522$	37.3680	1.63555
$523$	−14.3097	−0.625718	−0.312859	−	0.949800i	$-0.601287\pi$
$523$	−14.3097	−0.625718	−0.312859	+	0.949800i	$0.601287\pi$
$524$	2.51278	0.109771
$525$	−61.1673	−2.66956
$526$	−7.06229	−0.307930
$527$	−9.00094	−0.392087
$528$	1.69539	0.0737826
$529$	35.0453	1.52371
$530$	−0.102905	−0.00446993
$531$	−8.57457	−0.372105
$532$	17.9149	0.776711
$533$	28.5462	1.23647
$534$	−16.8931	−0.731038
$535$	−0.263959	−0.0114119
$536$	−3.52538	−0.152273
$537$	−61.7615	−2.66521
$538$	17.6481	0.760864
$539$	−5.97804	−0.257492
$540$	−0.178695	−0.00768979
$541$	−13.8365	−0.594876	−0.297438	−	0.954741i	$-0.596132\pi$
$541$	−13.8365	−0.594876	−0.297438	+	0.954741i	$0.596132\pi$
$542$	−10.8492	−0.466012
$543$	25.7546	1.10524
$544$	−5.01247	−0.214908
$545$	−0.00521424	−0.000223353 0
$546$	−50.8009	−2.17408
$547$	−0.154292	−0.00659706	−0.00329853	−	0.999995i	$-0.501050\pi$
$547$	−0.154292	−0.00659706	−0.00329853	+	0.999995i	$0.501050\pi$
$548$	4.99721	0.213470
$549$	−38.1336	−1.62750
$550$	−2.88613	−0.123065
$551$	28.5679	1.21703
$552$	−22.3750	−0.952342
$553$	−46.7618	−1.98852
$554$	−1.76608	−0.0750334
$555$	−0.305747	−0.0129782
$556$	16.9877	0.720440
$557$	29.0861	1.23242	0.616208	−	0.787583i	$-0.288668\pi$
$557$	29.0861	1.23242	0.616208	+	0.787583i	$0.288668\pi$
$558$	10.1008	0.427601
$559$	29.7487	1.25824
$560$	−0.0965662	−0.00408067
$561$	8.49812	0.358791
$562$	−3.18278	−0.134257
$563$	−24.8876	−1.04889	−0.524443	−	0.851445i	$-0.675726\pi$
$563$	−24.8876	−1.04889	−0.524443	+	0.851445i	$0.675726\pi$
$564$	−28.9576	−1.21934
$565$	0.258071	0.0108571
$566$	3.93228	0.165286
$567$	−24.0185	−1.00868
$568$	9.52005	0.399452
$569$	13.3640	0.560246	0.280123	−	0.959964i	$-0.409625\pi$
$569$	13.3640	0.560246	0.280123	+	0.959964i	$0.409625\pi$
$570$	−0.292742	−0.0122616
$571$	33.5801	1.40528	0.702641	−	0.711544i	$-0.252004\pi$
$571$	33.5801	1.40528	0.702641	+	0.711544i	$0.252004\pi$
$572$	−2.39700	−0.100224
$573$	−68.3553	−2.85558
$574$	28.6411	1.19545
$575$	38.0896	1.58845
$576$	5.62497	0.234374
$577$	−34.0024	−1.41554	−0.707770	−	0.706443i	$-0.750299\pi$
$577$	−34.0024	−1.41554	−0.707770	+	0.706443i	$0.750299\pi$
$578$	−8.12490	−0.337951
$579$	−18.4849	−0.768208
$580$	−0.153988	−0.00639401
$581$	−55.3389	−2.29584
$582$	18.1339	0.751676
$583$	−2.56285	−0.106142
$584$	−3.90438	−0.161564
$585$	0.541382	0.0223834
$586$	−14.4126	−0.595378
$587$	7.32035	0.302143	0.151071	−	0.988523i	$-0.451728\pi$
$587$	7.32035	0.302143	0.151071	+	0.988523i	$0.451728\pi$
$588$	−30.4120	−1.25417
$589$	7.72207	0.318182
$590$	0.0353346	0.00145470
$591$	63.8161	2.62504
$592$	4.49134	0.184593
$593$	−9.48985	−0.389702	−0.194851	−	0.980833i	$-0.562422\pi$
$593$	−9.48985	−0.389702	−0.194851	+	0.980833i	$0.562422\pi$
$594$	−4.45036	−0.182601
$595$	−0.484036	−0.0198435
$596$	−16.6256	−0.681012
$597$	38.2106	1.56386
$598$	31.6344	1.29363
$599$	−6.93790	−0.283475	−0.141737	−	0.989904i	$-0.545269\pi$
$599$	−6.93790	−0.283475	−0.141737	+	0.989904i	$0.545269\pi$
$600$	−14.6826	−0.599414
$601$	−19.8983	−0.811667	−0.405834	−	0.913947i	$-0.633019\pi$
$601$	−19.8983	−0.811667	−0.405834	+	0.913947i	$0.633019\pi$
$602$	29.8476	1.21650
$603$	19.8302	0.807548
$604$	−21.9815	−0.894416
$605$	−0.247252	−0.0100522
$606$	25.8814	1.05136
$607$	−35.3068	−1.43306	−0.716529	−	0.697557i	$-0.754270\pi$
$607$	−35.3068	−1.43306	−0.716529	+	0.697557i	$0.754270\pi$
$608$	4.30029	0.174400
$609$	−81.2785	−3.29357
$610$	0.157143	0.00636254
$611$	40.9411	1.65630
$612$	28.1950	1.13972
$613$	2.61157	0.105480	0.0527401	−	0.998608i	$-0.483205\pi$
$613$	2.61157	0.105480	0.0527401	+	0.998608i	$0.483205\pi$
$614$	10.9201	0.440701
$615$	−0.468014	−0.0188721
$616$	−2.40497	−0.0968989
$617$	−16.0554	−0.646365	−0.323183	−	0.946337i	$-0.604753\pi$
$617$	−16.0554	−0.646365	−0.323183	+	0.946337i	$0.604753\pi$
$618$	31.3005	1.25909
$619$	−5.21325	−0.209538	−0.104769	−	0.994497i	$-0.533410\pi$
$619$	−5.21325	−0.209538	−0.104769	+	0.994497i	$0.533410\pi$
$620$	−0.0416240	−0.00167166
$621$	58.7337	2.35690
$622$	9.00775	0.361178
$623$	23.9634	0.960074
$624$	−12.1942	−0.488160
$625$	24.9919	0.999678
$626$	32.1656	1.28560
$627$	−7.29070	−0.291162
$628$	−9.43642	−0.376554
$629$	22.5127	0.897641
$630$	0.543182	0.0216409
$631$	11.2553	0.448067	0.224034	−	0.974581i	$-0.428077\pi$
$631$	11.2553	0.448067	0.224034	+	0.974581i	$0.428077\pi$
$632$	−11.2247	−0.446494
$633$	52.0260	2.06785
$634$	−18.4867	−0.734200
$635$	−0.0292755	−0.00116176
$636$	−13.0379	−0.516988
$637$	42.9974	1.70362
$638$	−3.83505	−0.151831
$639$	−53.5500	−2.11840
$640$	−0.0231797	−0.000916258 0
$641$	13.7748	0.544070	0.272035	−	0.962287i	$-0.412303\pi$
$641$	13.7748	0.544070	0.272035	+	0.962287i	$0.412303\pi$
$642$	−33.4432	−1.31990
$643$	45.9380	1.81162	0.905809	−	0.423686i	$-0.139264\pi$
$643$	45.9380	1.81162	0.905809	+	0.423686i	$0.139264\pi$
$644$	31.7395	1.25071
$645$	−0.487730	−0.0192044
$646$	21.5551	0.848075
$647$	28.4148	1.11710	0.558550	−	0.829471i	$-0.311358\pi$
$647$	28.4148	1.11710	0.558550	+	0.829471i	$0.311358\pi$
$648$	−5.76539	−0.226486
$649$	0.880003	0.0345431
$650$	20.7586	0.814221
$651$	−21.9701	−0.861075
$652$	−0.815100	−0.0319218
$653$	−1.73975	−0.0680818	−0.0340409	−	0.999420i	$-0.510838\pi$
$653$	−1.73975	−0.0680818	−0.0340409	+	0.999420i	$0.510838\pi$
$654$	−0.660635	−0.0258329
$655$	0.0582454	0.00227584
$656$	6.87499	0.268423
$657$	21.9620	0.856821
$658$	41.0772	1.60136
$659$	7.09310	0.276308	0.138154	−	0.990411i	$-0.455883\pi$
$659$	7.09310	0.276308	0.138154	+	0.990411i	$0.455883\pi$
$660$	0.0392988	0.00152970
$661$	−7.69796	−0.299416	−0.149708	−	0.988730i	$-0.547833\pi$
$661$	−7.69796	−0.299416	−0.149708	+	0.988730i	$0.547833\pi$
$662$	2.57834	0.100210
$663$	−61.1233	−2.37383
$664$	−13.2835	−0.515501
$665$	0.415263	0.0161032
$666$	−25.2637	−0.978947
$667$	50.6131	1.95975
$668$	10.4443	0.404100
$669$	−8.43128	−0.325972
$670$	−0.0817174	−0.00315702
$671$	3.91363	0.151084
$672$	−12.2348	−0.471967
$673$	25.7053	0.990867	0.495434	−	0.868646i	$-0.335009\pi$
$673$	25.7053	0.990867	0.495434	+	0.868646i	$0.335009\pi$
$674$	−15.3049	−0.589522
$675$	38.5413	1.48346
$676$	4.24055	0.163098
$677$	46.4405	1.78485	0.892427	−	0.451191i	$-0.149001\pi$
$677$	46.4405	1.78485	0.892427	+	0.451191i	$0.149001\pi$
$678$	32.6972	1.25573
$679$	−25.7235	−0.987178
$680$	−0.116188	−0.00445560
$681$	−6.13421	−0.235063
$682$	−1.03664	−0.0396950
$683$	−43.1269	−1.65020	−0.825102	−	0.564984i	$-0.808882\pi$
$683$	−43.1269	−1.65020	−0.825102	+	0.564984i	$0.808882\pi$
$684$	−24.1890	−0.924891
$685$	0.115834	0.00442578
$686$	13.9785	0.533701
$687$	−23.4096	−0.893133
$688$	7.16461	0.273148
$689$	18.4334	0.702258
$690$	−0.518645	−0.0197445
$691$	−19.7224	−0.750274	−0.375137	−	0.926969i	$-0.622404\pi$
$691$	−19.7224	−0.750274	−0.375137	+	0.926969i	$0.622404\pi$
$692$	−10.7042	−0.406914
$693$	13.5279	0.513881
$694$	−1.47659	−0.0560507
$695$	0.393771	0.0149366
$696$	−19.5101	−0.739527
$697$	34.4607	1.30529
$698$	6.04925	0.228968
$699$	44.3032	1.67570
$700$	20.8277	0.787212
$701$	4.37466	0.165229	0.0826143	−	0.996582i	$-0.473673\pi$
$701$	4.37466	0.165229	0.0826143	+	0.996582i	$0.473673\pi$
$702$	32.0095	1.20812
$703$	−19.3141	−0.728444
$704$	−0.577287	−0.0217573
$705$	−0.671229	−0.0252800
$706$	19.1525	0.720814
$707$	−36.7135	−1.38075
$708$	4.47683	0.168250
$709$	7.27346	0.273160	0.136580	−	0.990629i	$-0.456389\pi$
$709$	7.27346	0.273160	0.136580	+	0.990629i	$0.456389\pi$
$710$	0.220672	0.00828167
$711$	63.1385	2.36788
$712$	5.75217	0.215572
$713$	13.6810	0.512359
$714$	−61.3265	−2.29509
$715$	−0.0555617	−0.00207789
$716$	21.0300	0.785928
$717$	58.0292	2.16714
$718$	−32.5771	−1.21577
$719$	−20.1023	−0.749691	−0.374845	−	0.927087i	$-0.622304\pi$
$719$	−20.1023	−0.749691	−0.374845	+	0.927087i	$0.622304\pi$
$720$	0.130385	0.00485917
$721$	−44.4007	−1.65357
$722$	0.507464	0.0188858
$723$	13.2426	0.492496
$724$	−8.76954	−0.325917
$725$	33.2126	1.23349
$726$	−31.3264	−1.16263
$727$	−39.2572	−1.45597	−0.727984	−	0.685594i	$-0.759542\pi$
$727$	−39.2572	−1.45597	−0.727984	+	0.685594i	$0.759542\pi$
$728$	17.2979	0.641102
$729$	−35.4908	−1.31447
$730$	−0.0905024	−0.00334965
$731$	35.9124	1.32827
$732$	19.9098	0.735886
$733$	−35.0675	−1.29525	−0.647624	−	0.761960i	$-0.724237\pi$
$733$	−35.0675	−1.29525	−0.647624	+	0.761960i	$0.724237\pi$
$734$	34.9836	1.29127
$735$	−0.704942	−0.0260022
$736$	7.61875	0.280831
$737$	−2.03516	−0.0749661
$738$	−38.6716	−1.42352
$739$	−34.5983	−1.27272	−0.636360	−	0.771392i	$-0.719561\pi$
$739$	−34.5983	−1.27272	−0.636360	+	0.771392i	$0.719561\pi$
$740$	0.104108	0.00382708
$741$	52.4388	1.92639
$742$	18.4947	0.678962
$743$	8.15795	0.299286	0.149643	−	0.988740i	$-0.452188\pi$
$743$	8.15795	0.299286	0.149643	+	0.988740i	$0.452188\pi$
$744$	−5.27369	−0.193343
$745$	−0.385377	−0.0141191
$746$	29.0916	1.06512
$747$	74.7194	2.73384
$748$	−2.89364	−0.105802
$749$	47.4401	1.73342
$750$	−0.680712	−0.0248561
$751$	−8.91042	−0.325146	−0.162573	−	0.986697i	$-0.551979\pi$
$751$	−8.91042	−0.325146	−0.162573	+	0.986697i	$0.551979\pi$
$752$	9.86016	0.359563
$753$	30.3239	1.10506
$754$	27.5839	1.00455
$755$	−0.509526	−0.0185435
$756$	32.1159	1.16805
$757$	26.1238	0.949487	0.474743	−	0.880124i	$-0.342541\pi$
$757$	26.1238	0.949487	0.474743	+	0.880124i	$0.342541\pi$
$758$	−33.2176	−1.20652
$759$	−12.9168	−0.468850
$760$	0.0996796	0.00361576
$761$	35.8173	1.29837	0.649187	−	0.760628i	$-0.275109\pi$
$761$	35.8173	1.29837	0.649187	+	0.760628i	$0.275109\pi$
$762$	−3.70915	−0.134368
$763$	0.937130	0.0339264
$764$	23.2752	0.842067
$765$	0.653553	0.0236292
$766$	12.9076	0.466371
$767$	−6.32948	−0.228544
$768$	−2.93683	−0.105974
$769$	−0.516497	−0.0186254	−0.00931268	−	0.999957i	$-0.502964\pi$
$769$	−0.516497	−0.0186254	−0.00931268	+	0.999957i	$0.502964\pi$
$770$	−0.0557464	−0.00200896
$771$	11.3756	0.409682
$772$	6.29418	0.226533
$773$	23.6685	0.851297	0.425649	−	0.904888i	$-0.360046\pi$
$773$	23.6685	0.851297	0.425649	+	0.904888i	$0.360046\pi$
$774$	−40.3008	−1.44858
$775$	8.97757	0.322484
$776$	−6.17466	−0.221657
$777$	54.9505	1.97134
$778$	−20.1573	−0.722674
$779$	−29.5645	−1.05926
$780$	−0.282659	−0.0101208
$781$	5.49580	0.196655
$782$	38.1888	1.36563
$783$	51.2133	1.83022
$784$	10.3554	0.369835
$785$	−0.218734	−0.00780694
$786$	7.37960	0.263222
$787$	16.3955	0.584436	0.292218	−	0.956352i	$-0.405607\pi$
$787$	16.3955	0.584436	0.292218	+	0.956352i	$0.405607\pi$
$788$	−21.7296	−0.774084
$789$	−20.7407	−0.738390
$790$	−0.260185	−0.00925697
$791$	−46.3819	−1.64915
$792$	3.24722	0.115385
$793$	−28.1490	−0.999600
$794$	39.2556	1.39313
$795$	−0.302216	−0.0107185
$796$	−13.0108	−0.461157
$797$	41.6472	1.47522	0.737610	−	0.675227i	$-0.235954\pi$
$797$	41.6472	1.47522	0.737610	+	0.675227i	$0.235954\pi$
$798$	52.6131	1.86249
$799$	49.4238	1.74849
$800$	4.99946	0.176758
$801$	−32.3558	−1.14324
$802$	37.6142	1.32820
$803$	−2.25395	−0.0795402
$804$	−10.3535	−0.365138
$805$	0.735714	0.0259305
$806$	7.45609	0.262630
$807$	51.8295	1.82448
$808$	−8.81269	−0.310029
$809$	−32.3918	−1.13883	−0.569417	−	0.822049i	$-0.692831\pi$
$809$	−32.3918	−1.13883	−0.569417	+	0.822049i	$0.692831\pi$
$810$	−0.133640	−0.00469563
$811$	−3.85660	−0.135423	−0.0677117	−	0.997705i	$-0.521570\pi$
$811$	−3.85660	−0.135423	−0.0677117	+	0.997705i	$0.521570\pi$
$812$	27.6756	0.971223
$813$	−31.8622	−1.11745
$814$	2.59279	0.0908773
$815$	−0.0188938	−0.000661820 0
$816$	−14.7208	−0.515331
$817$	−30.8100	−1.07790
$818$	7.57524	0.264862
$819$	−97.3001	−3.39994
$820$	0.159360	0.00556510
$821$	−6.54261	−0.228339	−0.114169	−	0.993461i	$-0.536421\pi$
$821$	−6.54261	−0.228339	−0.114169	+	0.993461i	$0.536421\pi$
$822$	14.6760	0.511883
$823$	−24.2837	−0.846477	−0.423238	−	0.906018i	$-0.639107\pi$
$823$	−24.2837	−0.846477	−0.423238	+	0.906018i	$0.639107\pi$
$824$	−10.6579	−0.371287
$825$	−8.47606	−0.295099
$826$	−6.35052	−0.220963
$827$	−17.8895	−0.622078	−0.311039	−	0.950397i	$-0.600677\pi$
$827$	−17.8895	−0.622078	−0.311039	+	0.950397i	$0.600677\pi$
$828$	−42.8552	−1.48932
$829$	0.664216	0.0230692	0.0115346	−	0.999933i	$-0.496328\pi$
$829$	0.664216	0.0230692	0.0115346	+	0.999933i	$0.496328\pi$
$830$	−0.307908	−0.0106876
$831$	−5.18667	−0.179923
$832$	4.15217	0.143951
$833$	51.9061	1.79844
$834$	49.8901	1.72755
$835$	0.242095	0.00837804
$836$	2.48251	0.0858592
$837$	13.8433	0.478494
$838$	−17.4627	−0.603237
$839$	−45.5358	−1.57207	−0.786034	−	0.618183i	$-0.787869\pi$
$839$	−45.5358	−1.57207	−0.786034	+	0.618183i	$0.787869\pi$
$840$	−0.283599	−0.00978508
$841$	15.1326	0.521813
$842$	−11.8366	−0.407915
$843$	−9.34728	−0.321937
$844$	−17.7150	−0.609776
$845$	0.0982948	0.00338144
$846$	−55.4631	−1.90686
$847$	44.4374	1.52689
$848$	4.43946	0.152452
$849$	11.5485	0.396342
$850$	25.0597	0.859540
$851$	−34.2184	−1.17299
$852$	27.9588	0.957851
$853$	−20.2671	−0.693932	−0.346966	−	0.937878i	$-0.612788\pi$
$853$	−20.2671	−0.693932	−0.346966	+	0.937878i	$0.612788\pi$
$854$	−28.2426	−0.966442
$855$	−0.560695	−0.0191754
$856$	11.3875	0.389217
$857$	6.39449	0.218432	0.109216	−	0.994018i	$-0.465166\pi$
$857$	6.39449	0.218432	0.109216	+	0.994018i	$0.465166\pi$
$858$	−7.03957	−0.240327
$859$	−39.5565	−1.34965	−0.674825	−	0.737978i	$-0.735781\pi$
$859$	−39.5565	−1.34965	−0.674825	+	0.737978i	$0.735781\pi$
$860$	0.166074	0.00566307
$861$	84.1139	2.86660
$862$	−23.9206	−0.814739
$863$	32.0268	1.09020	0.545102	−	0.838370i	$-0.316491\pi$
$863$	32.0268	1.09020	0.545102	+	0.838370i	$0.316491\pi$
$864$	7.70910	0.262269
$865$	−0.248121	−0.00843636
$866$	11.4726	0.389855
$867$	−23.8615	−0.810378
$868$	7.48088	0.253918
$869$	−6.47987	−0.219814
$870$	−0.452237	−0.0153323
$871$	14.6380	0.495990
$872$	0.224948	0.00761771
$873$	34.7323	1.17551
$874$	−32.7629	−1.10822
$875$	0.965610	0.0326436
$876$	−11.4665	−0.387417
$877$	−36.5710	−1.23491	−0.617457	−	0.786605i	$-0.711837\pi$
$877$	−36.5710	−1.23491	−0.617457	+	0.786605i	$0.711837\pi$
$878$	15.2169	0.513546
$879$	−42.3273	−1.42766
$880$	−0.0133814	−0.000451085 0
$881$	25.8930	0.872356	0.436178	−	0.899860i	$-0.356332\pi$
$881$	25.8930	0.872356	0.436178	+	0.899860i	$0.356332\pi$
$882$	−58.2488	−1.96134
$883$	26.7146	0.899016	0.449508	−	0.893276i	$-0.351599\pi$
$883$	26.7146	0.899016	0.449508	+	0.893276i	$0.351599\pi$
$884$	20.8127	0.700006
$885$	0.103772	0.00348825
$886$	−29.1287	−0.978597
$887$	−21.5056	−0.722087	−0.361043	−	0.932549i	$-0.617579\pi$
$887$	−21.5056	−0.722087	−0.361043	+	0.932549i	$0.617579\pi$
$888$	13.1903	0.442637
$889$	5.26154	0.176466
$890$	0.133334	0.00446935
$891$	−3.32829	−0.111502
$892$	2.87088	0.0961241
$893$	−42.4016	−1.41892
$894$	−48.8267	−1.63301
$895$	0.487469	0.0162943
$896$	4.16598	0.139176
$897$	92.9048	3.10200
$898$	18.7684	0.626311
$899$	11.9293	0.397865
$900$	−28.1218	−0.937395
$901$	22.2527	0.741345
$902$	3.96884	0.132148
$903$	87.6575	2.91706
$904$	−11.1335	−0.370294
$905$	−0.203275	−0.00675710
$906$	−64.5560	−2.14473
$907$	−1.95747	−0.0649969	−0.0324984	−	0.999472i	$-0.510346\pi$
$907$	−1.95747	−0.0649969	−0.0324984	+	0.999472i	$0.510346\pi$
$908$	2.08872	0.0693165
$909$	49.5711	1.64417
$910$	0.400960	0.0132917
$911$	9.23980	0.306128	0.153064	−	0.988216i	$-0.451086\pi$
$911$	9.23980	0.306128	0.153064	+	0.988216i	$0.451086\pi$
$912$	12.6292	0.418196
$913$	−7.66841	−0.253787
$914$	27.1487	0.898000
$915$	0.461503	0.0152568
$916$	7.97105	0.263371
$917$	−10.4682	−0.345690
$918$	38.6417	1.27536
$919$	13.6276	0.449531	0.224766	−	0.974413i	$-0.427838\pi$
$919$	13.6276	0.449531	0.224766	+	0.974413i	$0.427838\pi$
$920$	0.176600	0.00582234
$921$	32.0706	1.05676
$922$	−11.8403	−0.389940
$923$	−39.5289	−1.30111
$924$	−7.06298	−0.232355
$925$	−22.4543	−0.738292
$926$	28.1461	0.924938
$927$	59.9506	1.96903
$928$	6.64323	0.218075
$929$	32.6313	1.07060	0.535298	−	0.844663i	$-0.320199\pi$
$929$	32.6313	1.07060	0.535298	+	0.844663i	$0.320199\pi$
$930$	−0.122243	−0.00400849
$931$	−44.5312	−1.45945
$932$	−15.0854	−0.494138
$933$	26.4542	0.866073
$934$	−14.2690	−0.466898
$935$	−0.0670737	−0.00219354
$936$	−23.3559	−0.763410
$937$	60.4924	1.97620	0.988101	−	0.153810i	$-0.0491542\pi$
$937$	60.4924	1.97620	0.988101	+	0.153810i	$0.0491542\pi$
$938$	14.6867	0.479537
$939$	94.4650	3.08275
$940$	0.228556	0.00745466
$941$	−6.56878	−0.214136	−0.107068	−	0.994252i	$-0.534146\pi$
$941$	−6.56878	−0.214136	−0.107068	+	0.994252i	$0.534146\pi$
$942$	−27.7132	−0.902944
$943$	−52.3788	−1.70569
$944$	−1.52438	−0.0496142
$945$	0.744438	0.0242166
$946$	4.13604	0.134474
$947$	16.1514	0.524848	0.262424	−	0.964953i	$-0.415478\pi$
$947$	16.1514	0.524848	0.262424	+	0.964953i	$0.415478\pi$
$948$	−32.9650	−1.07065
$949$	16.2117	0.526253
$950$	−21.4992	−0.697525
$951$	−54.2922	−1.76055
$952$	20.8819	0.676785
$953$	−20.4096	−0.661132	−0.330566	−	0.943783i	$-0.607240\pi$
$953$	−20.4096	−0.661132	−0.330566	+	0.943783i	$0.607240\pi$
$954$	−24.9719	−0.808494
$955$	0.539513	0.0174582
$956$	−19.7591	−0.639056
$957$	−11.2629	−0.364078
$958$	0.804060	0.0259780
$959$	−20.8183	−0.672257
$960$	−0.0680749	−0.00219711
$961$	−27.7754	−0.895982
$962$	−18.6488	−0.601262
$963$	−64.0544	−2.06412
$964$	−4.50913	−0.145229
$965$	0.145897	0.00469660
$966$	93.2137	2.99910
$967$	−42.0434	−1.35203	−0.676013	−	0.736890i	$-0.736294\pi$
$967$	−42.0434	−1.35203	−0.676013	+	0.736890i	$0.736294\pi$
$968$	10.6667	0.342842
$969$	63.3037	2.03361
$970$	−0.143127	−0.00459553
$971$	−40.1923	−1.28983	−0.644916	−	0.764253i	$-0.723108\pi$
$971$	−40.1923	−1.28983	−0.644916	+	0.764253i	$0.723108\pi$
$972$	6.19531	0.198715
$973$	−70.7705	−2.26880
$974$	8.15983	0.261458
$975$	60.9646	1.95243
$976$	−6.77934	−0.217001
$977$	−11.7995	−0.377501	−0.188750	−	0.982025i	$-0.560444\pi$
$977$	−11.7995	−0.377501	−0.188750	+	0.982025i	$0.560444\pi$
$978$	−2.39381	−0.0765456
$979$	3.32065	0.106129
$980$	0.240035	0.00766764
$981$	−1.26533	−0.0403988
$982$	35.3176	1.12703
$983$	61.4120	1.95874	0.979369	−	0.202079i	$-0.0647698\pi$
$983$	61.4120	1.95874	0.979369	+	0.202079i	$0.0647698\pi$
$984$	20.1907	0.643655
$985$	−0.503685	−0.0160488
$986$	33.2990	1.06046
$987$	120.637	3.83991
$988$	−17.8556	−0.568062
$989$	−54.5854	−1.73571
$990$	0.0752697	0.00239223
$991$	−11.7404	−0.372945	−0.186473	−	0.982460i	$-0.559706\pi$
$991$	−11.7404	−0.372945	−0.186473	+	0.982460i	$0.559706\pi$
$992$	1.79571	0.0570138
$993$	7.57215	0.240295
$994$	−39.6603	−1.25795
$995$	−0.301588	−0.00956097
$996$	−39.0115	−1.23613
$997$	−35.1350	−1.11274	−0.556368	−	0.830936i	$-0.687806\pi$
$997$	−35.1350	−1.11274	−0.556368	+	0.830936i	$0.687806\pi$
$998$	−17.7472	−0.561777
$999$	−34.6242	−1.09546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.3	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.3	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.93683 q^{3} +1.00000 q^{4} +0.0231797 q^{5} +2.93683 q^{6} -4.16598 q^{7} -1.00000 q^{8} +5.62497 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.93683 q^{3} +1.00000 q^{4} +0.0231797 q^{5} +2.93683 q^{6} -4.16598 q^{7} -1.00000 q^{8} +5.62497 q^{9} -0.0231797 q^{10} -0.577287 q^{11} -2.93683 q^{12} +4.15217 q^{13} +4.16598 q^{14} -0.0680749 q^{15} +1.00000 q^{16} +5.01247 q^{17} -5.62497 q^{18} -4.30029 q^{19} +0.0231797 q^{20} +12.2348 q^{21} +0.577287 q^{22} -7.61875 q^{23} +2.93683 q^{24} -4.99946 q^{25} -4.15217 q^{26} -7.70910 q^{27} -4.16598 q^{28} -6.64323 q^{29} +0.0680749 q^{30} -1.79571 q^{31} -1.00000 q^{32} +1.69539 q^{33} -5.01247 q^{34} -0.0965662 q^{35} +5.62497 q^{36} +4.49134 q^{37} +4.30029 q^{38} -12.1942 q^{39} -0.0231797 q^{40} +6.87499 q^{41} -12.2348 q^{42} +7.16461 q^{43} -0.577287 q^{44} +0.130385 q^{45} +7.61875 q^{46} +9.86016 q^{47} -2.93683 q^{48} +10.3554 q^{49} +4.99946 q^{50} -14.7208 q^{51} +4.15217 q^{52} +4.43946 q^{53} +7.70910 q^{54} -0.0133814 q^{55} +4.16598 q^{56} +12.6292 q^{57} +6.64323 q^{58} -1.52438 q^{59} -0.0680749 q^{60} -6.77934 q^{61} +1.79571 q^{62} -23.4335 q^{63} +1.00000 q^{64} +0.0962462 q^{65} -1.69539 q^{66} +3.52538 q^{67} +5.01247 q^{68} +22.3750 q^{69} +0.0965662 q^{70} -9.52005 q^{71} -5.62497 q^{72} +3.90438 q^{73} -4.49134 q^{74} +14.6826 q^{75} -4.30029 q^{76} +2.40497 q^{77} +12.1942 q^{78} +11.2247 q^{79} +0.0231797 q^{80} +5.76539 q^{81} -6.87499 q^{82} +13.2835 q^{83} +12.2348 q^{84} +0.116188 q^{85} -7.16461 q^{86} +19.5101 q^{87} +0.577287 q^{88} -5.75217 q^{89} -0.130385 q^{90} -17.2979 q^{91} -7.61875 q^{92} +5.27369 q^{93} -9.86016 q^{94} -0.0996796 q^{95} +2.93683 q^{96} +6.17466 q^{97} -10.3554 q^{98} -3.24722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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