LMFDB - Embedded newform 4001.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, 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("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66682 q^{2} +0.260886 q^{3} +5.11190 q^{4} -1.12952 q^{5} -0.695735 q^{6} -1.67133 q^{7} -8.29887 q^{8} -2.93194 q^{9} +O(q^{10})$	\(q-2.66682 q^{2} +0.260886 q^{3} +5.11190 q^{4} -1.12952 q^{5} -0.695735 q^{6} -1.67133 q^{7} -8.29887 q^{8} -2.93194 q^{9} +3.01221 q^{10} +4.71305 q^{11} +1.33362 q^{12} -4.92080 q^{13} +4.45712 q^{14} -0.294675 q^{15} +11.9077 q^{16} -3.62116 q^{17} +7.81894 q^{18} -4.61861 q^{19} -5.77398 q^{20} -0.436026 q^{21} -12.5688 q^{22} -5.48210 q^{23} -2.16506 q^{24} -3.72419 q^{25} +13.1229 q^{26} -1.54756 q^{27} -8.54367 q^{28} +2.38742 q^{29} +0.785844 q^{30} +6.32942 q^{31} -15.1580 q^{32} +1.22957 q^{33} +9.65697 q^{34} +1.88779 q^{35} -14.9878 q^{36} +1.40769 q^{37} +12.3170 q^{38} -1.28377 q^{39} +9.37371 q^{40} -5.95370 q^{41} +1.16280 q^{42} +0.539714 q^{43} +24.0927 q^{44} +3.31167 q^{45} +14.6197 q^{46} -6.16466 q^{47} +3.10656 q^{48} -4.20666 q^{49} +9.93173 q^{50} -0.944710 q^{51} -25.1546 q^{52} -10.6448 q^{53} +4.12706 q^{54} -5.32347 q^{55} +13.8701 q^{56} -1.20493 q^{57} -6.36680 q^{58} -4.98420 q^{59} -1.50635 q^{60} +9.33444 q^{61} -16.8794 q^{62} +4.90023 q^{63} +16.6081 q^{64} +5.55812 q^{65} -3.27904 q^{66} +13.2191 q^{67} -18.5110 q^{68} -1.43020 q^{69} -5.03439 q^{70} -4.18398 q^{71} +24.3318 q^{72} +5.46343 q^{73} -3.75406 q^{74} -0.971590 q^{75} -23.6099 q^{76} -7.87706 q^{77} +3.42357 q^{78} -11.6527 q^{79} -13.4500 q^{80} +8.39208 q^{81} +15.8774 q^{82} -8.72403 q^{83} -2.22892 q^{84} +4.09016 q^{85} -1.43932 q^{86} +0.622844 q^{87} -39.1130 q^{88} -5.76793 q^{89} -8.83162 q^{90} +8.22427 q^{91} -28.0240 q^{92} +1.65126 q^{93} +16.4400 q^{94} +5.21680 q^{95} -3.95451 q^{96} -3.07817 q^{97} +11.2184 q^{98} -13.8184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	−2.66682	−1.88572	−0.942861	−	0.333185i	$-0.891877\pi$
$2$	−2.66682	−1.88572	−0.942861	+	0.333185i	$0.891877\pi$
$3$	0.260886	0.150623	0.0753113	−	0.997160i	$-0.476005\pi$
$3$	0.260886	0.150623	0.0753113	+	0.997160i	$0.476005\pi$
$4$	5.11190	2.55595
$5$	−1.12952	−0.505135	−0.252568	−	0.967579i	$-0.581275\pi$
$5$	−1.12952	−0.505135	−0.252568	+	0.967579i	$0.581275\pi$
$6$	−0.695735	−0.284033
$7$	−1.67133	−0.631703	−0.315851	−	0.948809i	$-0.602290\pi$
$7$	−1.67133	−0.631703	−0.315851	+	0.948809i	$0.602290\pi$
$8$	−8.29887	−2.93409
$9$	−2.93194	−0.977313
$10$	3.01221	0.952545
$11$	4.71305	1.42104	0.710520	−	0.703677i	$-0.248460\pi$
$11$	4.71305	1.42104	0.710520	+	0.703677i	$0.248460\pi$
$12$	1.33362	0.384984
$13$	−4.92080	−1.36478	−0.682392	−	0.730987i	$-0.739060\pi$
$13$	−4.92080	−1.36478	−0.682392	+	0.730987i	$0.739060\pi$
$14$	4.45712	1.19122
$15$	−0.294675	−0.0760848
$16$	11.9077	2.97694
$17$	−3.62116	−0.878261	−0.439130	−	0.898423i	$-0.644713\pi$
$17$	−3.62116	−0.878261	−0.439130	+	0.898423i	$0.644713\pi$
$18$	7.81894	1.84294
$19$	−4.61861	−1.05958	−0.529791	−	0.848128i	$-0.677730\pi$
$19$	−4.61861	−1.05958	−0.529791	+	0.848128i	$0.677730\pi$
$20$	−5.77398	−1.29110
$21$	−0.436026	−0.0951487
$22$	−12.5688	−2.67969
$23$	−5.48210	−1.14310	−0.571548	−	0.820568i	$-0.693657\pi$
$23$	−5.48210	−1.14310	−0.571548	+	0.820568i	$0.693657\pi$
$24$	−2.16506	−0.441941
$25$	−3.72419	−0.744839
$26$	13.1229	2.57360
$27$	−1.54756	−0.297828
$28$	−8.54367	−1.61460
$29$	2.38742	0.443332	0.221666	−	0.975123i	$-0.428850\pi$
$29$	2.38742	0.443332	0.221666	+	0.975123i	$0.428850\pi$
$30$	0.785844	0.143475
$31$	6.32942	1.13680	0.568398	−	0.822753i	$-0.307563\pi$
$31$	6.32942	1.13680	0.568398	+	0.822753i	$0.307563\pi$
$32$	−15.1580	−2.67958
$33$	1.22957	0.214041
$34$	9.65697	1.65616
$35$	1.88779	0.319095
$36$	−14.9878	−2.49796
$37$	1.40769	0.231423	0.115712	−	0.993283i	$-0.463085\pi$
$37$	1.40769	0.231423	0.115712	+	0.993283i	$0.463085\pi$
$38$	12.3170	1.99808
$39$	−1.28377	−0.205567
$40$	9.37371	1.48211
$41$	−5.95370	−0.929812	−0.464906	−	0.885360i	$-0.653912\pi$
$41$	−5.95370	−0.929812	−0.464906	+	0.885360i	$0.653912\pi$
$42$	1.16280	0.179424
$43$	0.539714	0.0823056	0.0411528	−	0.999153i	$-0.486897\pi$
$43$	0.539714	0.0823056	0.0411528	+	0.999153i	$0.486897\pi$
$44$	24.0927	3.63211
$45$	3.31167	0.493675
$46$	14.6197	2.15556
$47$	−6.16466	−0.899208	−0.449604	−	0.893228i	$-0.648435\pi$
$47$	−6.16466	−0.899208	−0.449604	+	0.893228i	$0.648435\pi$
$48$	3.10656	0.448394
$49$	−4.20666	−0.600952
$50$	9.93173	1.40456
$51$	−0.944710	−0.132286
$52$	−25.1546	−3.48832
$53$	−10.6448	−1.46217	−0.731087	−	0.682284i	$-0.760987\pi$
$53$	−10.6448	−1.46217	−0.731087	+	0.682284i	$0.760987\pi$
$54$	4.12706	0.561621
$55$	−5.32347	−0.717817
$56$	13.8701	1.85347
$57$	−1.20493	−0.159597
$58$	−6.36680	−0.836002
$59$	−4.98420	−0.648887	−0.324444	−	0.945905i	$-0.605177\pi$
$59$	−4.98420	−0.648887	−0.324444	+	0.945905i	$0.605177\pi$
$60$	−1.50635	−0.194469
$61$	9.33444	1.19515	0.597576	−	0.801812i	$-0.296131\pi$
$61$	9.33444	1.19515	0.597576	+	0.801812i	$0.296131\pi$
$62$	−16.8794	−2.14368
$63$	4.90023	0.617371
$64$	16.6081	2.07601
$65$	5.55812	0.689400
$66$	−3.27904	−0.403621
$67$	13.2191	1.61497	0.807483	−	0.589891i	$-0.200829\pi$
$67$	13.2191	1.61497	0.807483	+	0.589891i	$0.200829\pi$
$68$	−18.5110	−2.24479
$69$	−1.43020	−0.172176
$70$	−5.03439	−0.601725
$71$	−4.18398	−0.496548	−0.248274	−	0.968690i	$-0.579863\pi$
$71$	−4.18398	−0.496548	−0.248274	+	0.968690i	$0.579863\pi$
$72$	24.3318	2.86753
$73$	5.46343	0.639446	0.319723	−	0.947511i	$-0.396410\pi$
$73$	5.46343	0.639446	0.319723	+	0.947511i	$0.396410\pi$
$74$	−3.75406	−0.436400
$75$	−0.971590	−0.112190
$76$	−23.6099	−2.70824
$77$	−7.87706	−0.897674
$78$	3.42357	0.387643
$79$	−11.6527	−1.31103	−0.655517	−	0.755181i	$-0.727549\pi$
$79$	−11.6527	−1.31103	−0.655517	+	0.755181i	$0.727549\pi$
$80$	−13.4500	−1.50375
$81$	8.39208	0.932453
$82$	15.8774	1.75337
$83$	−8.72403	−0.957587	−0.478793	−	0.877928i	$-0.658926\pi$
$83$	−8.72403	−0.957587	−0.478793	+	0.877928i	$0.658926\pi$
$84$	−2.22892	−0.243195
$85$	4.09016	0.443640
$86$	−1.43932	−0.155206
$87$	0.622844	0.0667759
$88$	−39.1130	−4.16946
$89$	−5.76793	−0.611399	−0.305700	−	0.952128i	$-0.598890\pi$
$89$	−5.76793	−0.611399	−0.305700	+	0.952128i	$0.598890\pi$
$90$	−8.83162	−0.930934
$91$	8.22427	0.862137
$92$	−28.0240	−2.92170
$93$	1.65126	0.171227
$94$	16.4400	1.69566
$95$	5.21680	0.535232
$96$	−3.95451	−0.403606
$97$	−3.07817	−0.312541	−0.156271	−	0.987714i	$-0.549947\pi$
$97$	−3.07817	−0.312541	−0.156271	+	0.987714i	$0.549947\pi$
$98$	11.2184	1.13323
$99$	−13.8184	−1.38880
$100$	−19.0377	−1.90377
$101$	14.2154	1.41449	0.707245	−	0.706969i	$-0.249938\pi$
$101$	14.2154	1.41449	0.707245	+	0.706969i	$0.249938\pi$
$102$	2.51937	0.249455
$103$	1.37888	0.135865	0.0679323	−	0.997690i	$-0.478360\pi$
$103$	1.37888	0.135865	0.0679323	+	0.997690i	$0.478360\pi$
$104$	40.8370	4.00440
$105$	0.492499	0.0480630
$106$	28.3877	2.75725
$107$	7.53616	0.728548	0.364274	−	0.931292i	$-0.381317\pi$
$107$	7.53616	0.728548	0.364274	+	0.931292i	$0.381317\pi$
$108$	−7.91098	−0.761234
$109$	16.8259	1.61163	0.805815	−	0.592168i	$-0.201728\pi$
$109$	16.8259	1.61163	0.805815	+	0.592168i	$0.201728\pi$
$110$	14.1967	1.35360
$111$	0.367248	0.0348576
$112$	−19.9017	−1.88054
$113$	9.52539	0.896073	0.448037	−	0.894015i	$-0.352123\pi$
$113$	9.52539	0.896073	0.448037	+	0.894015i	$0.352123\pi$
$114$	3.21333	0.300956
$115$	6.19212	0.577418
$116$	12.2042	1.13314
$117$	14.4275	1.33382
$118$	13.2919	1.22362
$119$	6.05215	0.554799
$120$	2.44547	0.223240
$121$	11.2129	1.01935
$122$	−24.8932	−2.25373
$123$	−1.55324	−0.140051
$124$	32.3554	2.90560
$125$	9.85412	0.881379
$126$	−13.0680	−1.16419
$127$	−12.9624	−1.15023	−0.575115	−	0.818072i	$-0.695043\pi$
$127$	−12.9624	−1.15023	−0.575115	+	0.818072i	$0.695043\pi$
$128$	−13.9748	−1.23521
$129$	0.140804	0.0123971
$130$	−14.8225	−1.30002
$131$	6.37591	0.557066	0.278533	−	0.960427i	$-0.410152\pi$
$131$	6.37591	0.557066	0.278533	+	0.960427i	$0.410152\pi$
$132$	6.28544	0.547077
$133$	7.71921	0.669341
$134$	−35.2528	−3.04538
$135$	1.74799	0.150443
$136$	30.0515	2.57690
$137$	−16.6790	−1.42498	−0.712492	−	0.701680i	$-0.752434\pi$
$137$	−16.6790	−1.42498	−0.712492	+	0.701680i	$0.752434\pi$
$138$	3.81409	0.324677
$139$	−10.6121	−0.900105	−0.450052	−	0.893002i	$-0.648595\pi$
$139$	−10.6121	−0.900105	−0.450052	+	0.893002i	$0.648595\pi$
$140$	9.65021	0.815592
$141$	−1.60827	−0.135441
$142$	11.1579	0.936351
$143$	−23.1920	−1.93941
$144$	−34.9128	−2.90940
$145$	−2.69663	−0.223943
$146$	−14.5700	−1.20582
$147$	−1.09746	−0.0905169
$148$	7.19599	0.591507
$149$	−2.26753	−0.185763	−0.0928816	−	0.995677i	$-0.529608\pi$
$149$	−2.26753	−0.185763	−0.0928816	+	0.995677i	$0.529608\pi$
$150$	2.59105	0.211558
$151$	13.4740	1.09650	0.548251	−	0.836314i	$-0.315294\pi$
$151$	13.4740	1.09650	0.548251	+	0.836314i	$0.315294\pi$
$152$	38.3292	3.10891
$153$	10.6170	0.858335
$154$	21.0067	1.69276
$155$	−7.14918	−0.574236
$156$	−6.56249	−0.525420
$157$	21.7612	1.73673	0.868367	−	0.495922i	$-0.165170\pi$
$157$	21.7612	1.73673	0.868367	+	0.495922i	$0.165170\pi$
$158$	31.0756	2.47225
$159$	−2.77708	−0.220236
$160$	17.1212	1.35355
$161$	9.16239	0.722097
$162$	−22.3801	−1.75835
$163$	16.1598	1.26573	0.632866	−	0.774261i	$-0.281878\pi$
$163$	16.1598	1.26573	0.632866	+	0.774261i	$0.281878\pi$
$164$	−30.4347	−2.37655
$165$	−1.38882	−0.108119
$166$	23.2654	1.80574
$167$	−10.0123	−0.774777	−0.387388	−	0.921917i	$-0.626623\pi$
$167$	−10.0123	−0.774777	−0.387388	+	0.921917i	$0.626623\pi$
$168$	3.61852	0.279175
$169$	11.2142	0.862634
$170$	−10.9077	−0.836583
$171$	13.5415	1.03554
$172$	2.75897	0.210369
$173$	−22.6588	−1.72272	−0.861359	−	0.507997i	$-0.830386\pi$
$173$	−22.6588	−1.72272	−0.861359	+	0.507997i	$0.830386\pi$
$174$	−1.66101	−0.125921
$175$	6.22435	0.470516
$176$	56.1218	4.23034
$177$	−1.30031	−0.0977371
$178$	15.3820	1.15293
$179$	−5.19038	−0.387947	−0.193973	−	0.981007i	$-0.562138\pi$
$179$	−5.19038	−0.387947	−0.193973	+	0.981007i	$0.562138\pi$
$180$	16.9289	1.26181
$181$	3.56788	0.265199	0.132599	−	0.991170i	$-0.457668\pi$
$181$	3.56788	0.265199	0.132599	+	0.991170i	$0.457668\pi$
$182$	−21.9326	−1.62575
$183$	2.43522	0.180017
$184$	45.4952	3.35395
$185$	−1.59001	−0.116900
$186$	−4.40360	−0.322887
$187$	−17.0667	−1.24804
$188$	−31.5131	−2.29833
$189$	2.58648	0.188139
$190$	−13.9122	−1.00930
$191$	−18.6055	−1.34624	−0.673122	−	0.739532i	$-0.735047\pi$
$191$	−18.6055	−1.34624	−0.673122	+	0.739532i	$0.735047\pi$
$192$	4.33283	0.312695
$193$	−13.7093	−0.986815	−0.493408	−	0.869798i	$-0.664249\pi$
$193$	−13.7093	−0.986815	−0.493408	+	0.869798i	$0.664249\pi$
$194$	8.20892	0.589366
$195$	1.45004	0.103839
$196$	−21.5040	−1.53600
$197$	4.22117	0.300746	0.150373	−	0.988629i	$-0.451953\pi$
$197$	4.22117	0.300746	0.150373	+	0.988629i	$0.451953\pi$
$198$	36.8511	2.61889
$199$	7.62114	0.540248	0.270124	−	0.962826i	$-0.412935\pi$
$199$	7.62114	0.540248	0.270124	+	0.962826i	$0.412935\pi$
$200$	30.9066	2.18543
$201$	3.44867	0.243250
$202$	−37.9100	−2.66734
$203$	−3.99016	−0.280054
$204$	−4.82927	−0.338116
$205$	6.72480	0.469681
$206$	−3.67721	−0.256203
$207$	16.0732	1.11716
$208$	−58.5956	−4.06287
$209$	−21.7678	−1.50571
$210$	−1.31340	−0.0906334
$211$	−8.10951	−0.558281	−0.279141	−	0.960250i	$-0.590050\pi$
$211$	−8.10951	−0.558281	−0.279141	+	0.960250i	$0.590050\pi$
$212$	−54.4151	−3.73724
$213$	−1.09154	−0.0747913
$214$	−20.0976	−1.37384
$215$	−0.609616	−0.0415755
$216$	12.8430	0.873855
$217$	−10.5785	−0.718117
$218$	−44.8716	−3.03909
$219$	1.42533	0.0963151
$220$	−27.2131	−1.83470
$221$	17.8190	1.19864
$222$	−0.979382	−0.0657318
$223$	−6.05764	−0.405650	−0.202825	−	0.979215i	$-0.565012\pi$
$223$	−6.05764	−0.405650	−0.202825	+	0.979215i	$0.565012\pi$
$224$	25.3340	1.69270
$225$	10.9191	0.727940
$226$	−25.4025	−1.68975
$227$	8.96990	0.595353	0.297677	−	0.954667i	$-0.403788\pi$
$227$	8.96990	0.595353	0.297677	+	0.954667i	$0.403788\pi$
$228$	−6.15949	−0.407922
$229$	−11.4410	−0.756041	−0.378020	−	0.925797i	$-0.623395\pi$
$229$	−11.4410	−0.756041	−0.378020	+	0.925797i	$0.623395\pi$
$230$	−16.5132	−1.08885
$231$	−2.05501	−0.135210
$232$	−19.8129	−1.30078
$233$	−1.35862	−0.0890059	−0.0445029	−	0.999009i	$-0.514170\pi$
$233$	−1.35862	−0.0890059	−0.0445029	+	0.999009i	$0.514170\pi$
$234$	−38.4754	−2.51522
$235$	6.96308	0.454221
$236$	−25.4787	−1.65852
$237$	−3.04003	−0.197471
$238$	−16.1400	−1.04620
$239$	−7.56005	−0.489019	−0.244509	−	0.969647i	$-0.578627\pi$
$239$	−7.56005	−0.489019	−0.244509	+	0.969647i	$0.578627\pi$
$240$	−3.50891	−0.226499
$241$	12.1547	0.782956	0.391478	−	0.920188i	$-0.371964\pi$
$241$	12.1547	0.782956	0.391478	+	0.920188i	$0.371964\pi$
$242$	−29.9027	−1.92222
$243$	6.83206	0.438277
$244$	47.7167	3.05475
$245$	4.75149	0.303562
$246$	4.14220	0.264097
$247$	22.7272	1.44610
$248$	−52.5270	−3.33547
$249$	−2.27598	−0.144234
$250$	−26.2791	−1.66204
$251$	10.7689	0.679730	0.339865	−	0.940474i	$-0.389619\pi$
$251$	10.7689	0.679730	0.339865	+	0.940474i	$0.389619\pi$
$252$	25.0495	1.57797
$253$	−25.8374	−1.62438
$254$	34.5684	2.16902
$255$	1.06707	0.0668223
$256$	4.05187	0.253242
$257$	21.4851	1.34020	0.670102	−	0.742269i	$-0.266250\pi$
$257$	21.4851	1.34020	0.670102	+	0.742269i	$0.266250\pi$
$258$	−0.375498	−0.0233775
$259$	−2.35272	−0.146191
$260$	28.4126	1.76207
$261$	−6.99976	−0.433274
$262$	−17.0034	−1.05047
$263$	−19.7410	−1.21728	−0.608642	−	0.793445i	$-0.708285\pi$
$263$	−19.7410	−1.21728	−0.608642	+	0.793445i	$0.708285\pi$
$264$	−10.2040	−0.628015
$265$	12.0235	0.738595
$266$	−20.5857	−1.26219
$267$	−1.50477	−0.0920906
$268$	67.5746	4.12778
$269$	17.3366	1.05703	0.528515	−	0.848924i	$-0.322749\pi$
$269$	17.3366	1.05703	0.528515	+	0.848924i	$0.322749\pi$
$270$	−4.66158	−0.283695
$271$	−8.66725	−0.526498	−0.263249	−	0.964728i	$-0.584794\pi$
$271$	−8.66725	−0.526498	−0.263249	+	0.964728i	$0.584794\pi$
$272$	−43.1198	−2.61452
$273$	2.14560	0.129857
$274$	44.4799	2.68713
$275$	−17.5523	−1.05844
$276$	−7.31106	−0.440074
$277$	−25.6778	−1.54283	−0.771416	−	0.636331i	$-0.780451\pi$
$277$	−25.6778	−1.54283	−0.771416	+	0.636331i	$0.780451\pi$
$278$	28.3005	1.69735
$279$	−18.5575	−1.11101
$280$	−15.6665	−0.936255
$281$	−19.3374	−1.15358	−0.576788	−	0.816894i	$-0.695694\pi$
$281$	−19.3374	−1.15358	−0.576788	+	0.816894i	$0.695694\pi$
$282$	4.28897	0.255404
$283$	−4.65791	−0.276884	−0.138442	−	0.990371i	$-0.544209\pi$
$283$	−4.65791	−0.276884	−0.138442	+	0.990371i	$0.544209\pi$
$284$	−21.3881	−1.26915
$285$	1.36099	0.0806181
$286$	61.8487	3.65719
$287$	9.95059	0.587365
$288$	44.4423	2.61879
$289$	−3.88719	−0.228658
$290$	7.19141	0.422294
$291$	−0.803053	−0.0470758
$292$	27.9285	1.63439
$293$	20.7068	1.20970	0.604852	−	0.796338i	$-0.293232\pi$
$293$	20.7068	1.20970	0.604852	+	0.796338i	$0.293232\pi$
$294$	2.92672	0.170690
$295$	5.62973	0.327776
$296$	−11.6823	−0.679018
$297$	−7.29373	−0.423225
$298$	6.04708	0.350298
$299$	26.9763	1.56008
$300$	−4.96667	−0.286751
$301$	−0.902040	−0.0519927
$302$	−35.9328	−2.06770
$303$	3.70861	0.213054
$304$	−54.9972	−3.15431
$305$	−10.5434	−0.603713
$306$	−28.3136	−1.61858
$307$	−14.9485	−0.853156	−0.426578	−	0.904451i	$-0.640281\pi$
$307$	−14.9485	−0.853156	−0.426578	+	0.904451i	$0.640281\pi$
$308$	−40.2668	−2.29441
$309$	0.359729	0.0204643
$310$	19.0655	1.08285
$311$	17.0450	0.966536	0.483268	−	0.875472i	$-0.339450\pi$
$311$	17.0450	0.966536	0.483268	+	0.875472i	$0.339450\pi$
$312$	10.6538	0.603153
$313$	33.1705	1.87491	0.937453	−	0.348112i	$-0.113177\pi$
$313$	33.1705	1.87491	0.937453	+	0.348112i	$0.113177\pi$
$314$	−58.0331	−3.27500
$315$	−5.53489	−0.311856
$316$	−59.5676	−3.35094
$317$	−6.54642	−0.367683	−0.183842	−	0.982956i	$-0.558853\pi$
$317$	−6.54642	−0.367683	−0.183842	+	0.982956i	$0.558853\pi$
$318$	7.40595	0.415305
$319$	11.2520	0.629993
$320$	−18.7591	−1.04867
$321$	1.96608	0.109736
$322$	−24.4344	−1.36168
$323$	16.7247	0.930589
$324$	42.8995	2.38330
$325$	18.3260	1.01654
$326$	−43.0951	−2.38682
$327$	4.38964	0.242748
$328$	49.4090	2.72815
$329$	10.3032	0.568032
$330$	3.70372	0.203883
$331$	25.7064	1.41295	0.706476	−	0.707737i	$-0.250284\pi$
$331$	25.7064	1.41295	0.706476	+	0.707737i	$0.250284\pi$
$332$	−44.5964	−2.44755
$333$	−4.12727	−0.226173
$334$	26.7010	1.46101
$335$	−14.9312	−0.815776
$336$	−5.19209	−0.283252
$337$	11.3264	0.616990	0.308495	−	0.951226i	$-0.400175\pi$
$337$	11.3264	0.616990	0.308495	+	0.951226i	$0.400175\pi$
$338$	−29.9063	−1.62669
$339$	2.48504	0.134969
$340$	20.9085	1.13392
$341$	29.8309	1.61543
$342$	−36.1126	−1.95275
$343$	18.7300	1.01133
$344$	−4.47902	−0.241492
$345$	1.61544	0.0869722
$346$	60.4269	3.24857
$347$	0.892326	0.0479026	0.0239513	−	0.999713i	$-0.492375\pi$
$347$	0.892326	0.0479026	0.0239513	+	0.999713i	$0.492375\pi$
$348$	3.18392	0.170676
$349$	0.270006	0.0144531	0.00722655	−	0.999974i	$-0.497700\pi$
$349$	0.270006	0.0144531	0.00722655	+	0.999974i	$0.497700\pi$
$350$	−16.5992	−0.887264
$351$	7.61523	0.406471
$352$	−71.4405	−3.80779
$353$	0.902861	0.0480545	0.0240272	−	0.999711i	$-0.492351\pi$
$353$	0.902861	0.0480545	0.0240272	+	0.999711i	$0.492351\pi$
$354$	3.46768	0.184305
$355$	4.72588	0.250824
$356$	−29.4851	−1.56271
$357$	1.57892	0.0835653
$358$	13.8418	0.731561
$359$	−12.9215	−0.681972	−0.340986	−	0.940068i	$-0.610761\pi$
$359$	−12.9215	−0.681972	−0.340986	+	0.940068i	$0.610761\pi$
$360$	−27.4831	−1.44849
$361$	2.33157	0.122714
$362$	−9.51489	−0.500091
$363$	2.92528	0.153537
$364$	42.0416	2.20358
$365$	−6.17104	−0.323007
$366$	−6.49429	−0.339462
$367$	16.9765	0.886168	0.443084	−	0.896480i	$-0.353884\pi$
$367$	16.9765	0.886168	0.443084	+	0.896480i	$0.353884\pi$
$368$	−65.2794	−3.40292
$369$	17.4559	0.908717
$370$	4.24027	0.220441
$371$	17.7909	0.923659
$372$	8.44106	0.437649
$373$	23.3625	1.20966	0.604831	−	0.796354i	$-0.293241\pi$
$373$	23.3625	1.20966	0.604831	+	0.796354i	$0.293241\pi$
$374$	45.5138	2.35346
$375$	2.57080	0.132756
$376$	51.1597	2.63836
$377$	−11.7480	−0.605053
$378$	−6.89766	−0.354778
$379$	33.5300	1.72232	0.861160	−	0.508335i	$-0.169739\pi$
$379$	33.5300	1.72232	0.861160	+	0.508335i	$0.169739\pi$
$380$	26.6678	1.36803
$381$	−3.38172	−0.173251
$382$	49.6173	2.53864
$383$	8.92843	0.456221	0.228111	−	0.973635i	$-0.426745\pi$
$383$	8.92843	0.456221	0.228111	+	0.973635i	$0.426745\pi$
$384$	−3.64582	−0.186050
$385$	8.89727	0.453447
$386$	36.5601	1.86086
$387$	−1.58241	−0.0804384
$388$	−15.7353	−0.798840
$389$	28.7435	1.45735	0.728676	−	0.684859i	$-0.240136\pi$
$389$	28.7435	1.45735	0.728676	+	0.684859i	$0.240136\pi$
$390$	−3.86698	−0.195812
$391$	19.8516	1.00394
$392$	34.9105	1.76325
$393$	1.66339	0.0839067
$394$	−11.2571	−0.567124
$395$	13.1619	0.662249
$396$	−70.6382	−3.54970
$397$	34.6846	1.74077	0.870384	−	0.492374i	$-0.163871\pi$
$397$	34.6846	1.74077	0.870384	+	0.492374i	$0.163871\pi$
$398$	−20.3242	−1.01876
$399$	2.01384	0.100818
$400$	−44.3467	−2.21734
$401$	−31.8152	−1.58878	−0.794388	−	0.607410i	$-0.792209\pi$
$401$	−31.8152	−1.58878	−0.794388	+	0.607410i	$0.792209\pi$
$402$	−9.19697	−0.458703
$403$	−31.1458	−1.55148
$404$	72.6680	3.61537
$405$	−9.47899	−0.471015
$406$	10.6410	0.528105
$407$	6.63454	0.328862
$408$	7.84003	0.388139
$409$	−6.28662	−0.310853	−0.155427	−	0.987847i	$-0.549675\pi$
$409$	−6.28662	−0.310853	−0.155427	+	0.987847i	$0.549675\pi$
$410$	−17.9338	−0.885688
$411$	−4.35132	−0.214635
$412$	7.04868	0.347263
$413$	8.33023	0.409904
$414$	−42.8642	−2.10666
$415$	9.85394	0.483711
$416$	74.5895	3.65705
$417$	−2.76854	−0.135576
$418$	58.0506	2.83935
$419$	−18.7466	−0.915832	−0.457916	−	0.888995i	$-0.651404\pi$
$419$	−18.7466	−0.915832	−0.457916	+	0.888995i	$0.651404\pi$
$420$	2.51761	0.122847
$421$	−26.0445	−1.26933	−0.634665	−	0.772787i	$-0.718862\pi$
$421$	−26.0445	−1.26933	−0.634665	+	0.772787i	$0.718862\pi$
$422$	21.6266	1.05276
$423$	18.0744	0.878807
$424$	88.3397	4.29015
$425$	13.4859	0.654162
$426$	2.91094	0.141036
$427$	−15.6009	−0.754981
$428$	38.5241	1.86213
$429$	−6.05046	−0.292119
$430$	1.62573	0.0783998
$431$	−24.0034	−1.15620	−0.578102	−	0.815965i	$-0.696206\pi$
$431$	−24.0034	−1.15620	−0.578102	+	0.815965i	$0.696206\pi$
$432$	−18.4279	−0.886615
$433$	21.0399	1.01111	0.505557	−	0.862793i	$-0.331287\pi$
$433$	21.0399	1.01111	0.505557	+	0.862793i	$0.331287\pi$
$434$	28.2110	1.35417
$435$	−0.703512	−0.0337308
$436$	86.0124	4.11925
$437$	25.3197	1.21120
$438$	−3.80110	−0.181624
$439$	−3.38447	−0.161532	−0.0807660	−	0.996733i	$-0.525737\pi$
$439$	−3.38447	−0.161532	−0.0807660	+	0.996733i	$0.525737\pi$
$440$	44.1788	2.10614
$441$	12.3337	0.587318
$442$	−47.5200	−2.26029
$443$	−37.7219	−1.79222	−0.896111	−	0.443829i	$-0.853620\pi$
$443$	−37.7219	−1.79222	−0.896111	+	0.443829i	$0.853620\pi$
$444$	1.87733	0.0890943
$445$	6.51497	0.308839
$446$	16.1546	0.764943
$447$	−0.591567	−0.0279801
$448$	−27.7576	−1.31142
$449$	9.43598	0.445311	0.222656	−	0.974897i	$-0.428527\pi$
$449$	9.43598	0.445311	0.222656	+	0.974897i	$0.428527\pi$
$450$	−29.1192	−1.37269
$451$	−28.0601	−1.32130
$452$	48.6929	2.29032
$453$	3.51519	0.165158
$454$	−23.9211	−1.12267
$455$	−9.28944	−0.435496
$456$	9.99956	0.468272
$457$	−5.49719	−0.257148	−0.128574	−	0.991700i	$-0.541040\pi$
$457$	−5.49719	−0.257148	−0.128574	+	0.991700i	$0.541040\pi$
$458$	30.5110	1.42568
$459$	5.60396	0.261571
$460$	31.6535	1.47585
$461$	5.08850	0.236995	0.118497	−	0.992954i	$-0.462192\pi$
$461$	5.08850	0.236995	0.118497	+	0.992954i	$0.462192\pi$
$462$	5.48034	0.254969
$463$	30.7145	1.42742	0.713712	−	0.700439i	$-0.247013\pi$
$463$	30.7145	1.42742	0.713712	+	0.700439i	$0.247013\pi$
$464$	28.4288	1.31977
$465$	−1.86512	−0.0864929
$466$	3.62318	0.167840
$467$	30.0865	1.39224	0.696120	−	0.717926i	$-0.254908\pi$
$467$	30.0865	1.39224	0.696120	+	0.717926i	$0.254908\pi$
$468$	73.7518	3.40918
$469$	−22.0934	−1.02018
$470$	−18.5693	−0.856536
$471$	5.67720	0.261591
$472$	41.3632	1.90390
$473$	2.54370	0.116960
$474$	8.10720	0.372376
$475$	17.2006	0.789218
$476$	30.9380	1.41804
$477$	31.2099	1.42900
$478$	20.1613	0.922154
$479$	−8.64566	−0.395030	−0.197515	−	0.980300i	$-0.563287\pi$
$479$	−8.64566	−0.395030	−0.197515	+	0.980300i	$0.563287\pi$
$480$	4.46669	0.203875
$481$	−6.92697	−0.315843
$482$	−32.4144	−1.47644
$483$	2.39034	0.108764
$484$	57.3191	2.60541
$485$	3.47685	0.157876
$486$	−18.2198	−0.826468
$487$	−14.3671	−0.651036	−0.325518	−	0.945536i	$-0.605539\pi$
$487$	−14.3671	−0.651036	−0.325518	+	0.945536i	$0.605539\pi$
$488$	−77.4653	−3.50669
$489$	4.21586	0.190648
$490$	−12.6714	−0.572434
$491$	−2.67645	−0.120786	−0.0603932	−	0.998175i	$-0.519235\pi$
$491$	−2.67645	−0.120786	−0.0603932	+	0.998175i	$0.519235\pi$
$492$	−7.94000	−0.357963
$493$	−8.64522	−0.389361
$494$	−60.6094	−2.72694
$495$	15.6081	0.701531
$496$	75.3690	3.38417
$497$	6.99281	0.313670
$498$	6.06961	0.271986
$499$	3.06516	0.137215	0.0686076	−	0.997644i	$-0.478144\pi$
$499$	3.06516	0.137215	0.0686076	+	0.997644i	$0.478144\pi$
$500$	50.3733	2.25276
$501$	−2.61208	−0.116699
$502$	−28.7188	−1.28178
$503$	18.7567	0.836320	0.418160	−	0.908373i	$-0.362675\pi$
$503$	18.7567	0.836320	0.418160	+	0.908373i	$0.362675\pi$
$504$	−40.6664	−1.81142
$505$	−16.0566	−0.714508
$506$	68.9036	3.06314
$507$	2.92564	0.129932
$508$	−66.2628	−2.93993
$509$	8.27642	0.366846	0.183423	−	0.983034i	$-0.441282\pi$
$509$	8.27642	0.366846	0.183423	+	0.983034i	$0.441282\pi$
$510$	−2.84567	−0.126008
$511$	−9.13119	−0.403940
$512$	17.1439	0.757662
$513$	7.14758	0.315573
$514$	−57.2968	−2.52725
$515$	−1.55746	−0.0686300
$516$	0.719776	0.0316864
$517$	−29.0544	−1.27781
$518$	6.27426	0.275675
$519$	−5.91137	−0.259480
$520$	−46.1261	−2.02276
$521$	−21.9674	−0.962409	−0.481205	−	0.876608i	$-0.659801\pi$
$521$	−21.9674	−0.962409	−0.481205	+	0.876608i	$0.659801\pi$
$522$	18.6671	0.817035
$523$	−13.2891	−0.581093	−0.290546	−	0.956861i	$-0.593837\pi$
$523$	−13.2891	−0.581093	−0.290546	+	0.956861i	$0.593837\pi$
$524$	32.5930	1.42383
$525$	1.62385	0.0708704
$526$	52.6456	2.29546
$527$	−22.9198	−0.998404
$528$	14.6414	0.637185
$529$	7.05341	0.306670
$530$	−32.0643	−1.39279
$531$	14.6134	0.634166
$532$	39.4599	1.71080
$533$	29.2970	1.26899
$534$	4.01295	0.173657
$535$	−8.51222	−0.368015
$536$	−109.703	−4.73846
$537$	−1.35410	−0.0584336
$538$	−46.2334	−1.99326
$539$	−19.8262	−0.853976
$540$	8.93558	0.384526
$541$	9.28973	0.399397	0.199698	−	0.979857i	$-0.436004\pi$
$541$	9.28973	0.399397	0.199698	+	0.979857i	$0.436004\pi$
$542$	23.1140	0.992830
$543$	0.930811	0.0399449
$544$	54.8896	2.35337
$545$	−19.0051	−0.814091
$546$	−5.72191	−0.244875
$547$	36.3891	1.55589	0.777943	−	0.628335i	$-0.216263\pi$
$547$	36.3891	1.55589	0.777943	+	0.628335i	$0.216263\pi$
$548$	−85.2615	−3.64219
$549$	−27.3680	−1.16804
$550$	46.8088	1.99593
$551$	−11.0266	−0.469747
$552$	11.8691	0.505181
$553$	19.4755	0.828183
$554$	68.4781	2.90935
$555$	−0.414812	−0.0176078
$556$	−54.2479	−2.30062
$557$	3.05969	0.129643	0.0648215	−	0.997897i	$-0.479352\pi$
$557$	3.05969	0.129643	0.0648215	+	0.997897i	$0.479352\pi$
$558$	49.4893	2.09505
$559$	−2.65582	−0.112329
$560$	22.4793	0.949926
$561$	−4.45247	−0.187983
$562$	51.5694	2.17532
$563$	8.52793	0.359410	0.179705	−	0.983721i	$-0.442486\pi$
$563$	8.52793	0.359410	0.179705	+	0.983721i	$0.442486\pi$
$564$	−8.22134	−0.346181
$565$	−10.7591	−0.452638
$566$	12.4218	0.522127
$567$	−14.0259	−0.589033
$568$	34.7223	1.45692
$569$	13.7878	0.578015	0.289007	−	0.957327i	$-0.406675\pi$
$569$	13.7878	0.578015	0.289007	+	0.957327i	$0.406675\pi$
$570$	−3.62951	−0.152023
$571$	−5.02593	−0.210328	−0.105164	−	0.994455i	$-0.533537\pi$
$571$	−5.02593	−0.210328	−0.105164	+	0.994455i	$0.533537\pi$
$572$	−118.555	−4.95704
$573$	−4.85390	−0.202775
$574$	−26.5364	−1.10761
$575$	20.4164	0.851422
$576$	−48.6940	−2.02892
$577$	45.6531	1.90056	0.950281	−	0.311393i	$-0.100796\pi$
$577$	45.6531	1.90056	0.950281	+	0.311393i	$0.100796\pi$
$578$	10.3664	0.431187
$579$	−3.57656	−0.148637
$580$	−13.7849	−0.572387
$581$	14.5807	0.604910
$582$	2.14159	0.0887719
$583$	−50.1694	−2.07781
$584$	−45.3403	−1.87619
$585$	−16.2961	−0.673759
$586$	−55.2212	−2.28117
$587$	−28.1483	−1.16180	−0.580902	−	0.813974i	$-0.697300\pi$
$587$	−28.1483	−1.16180	−0.580902	+	0.813974i	$0.697300\pi$
$588$	−5.61011	−0.231357
$589$	−29.2331	−1.20453
$590$	−15.0135	−0.618094
$591$	1.10124	0.0452992
$592$	16.7625	0.688933
$593$	−19.2788	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$593$	−19.2788	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$594$	19.4510	0.798086
$595$	−6.83600	−0.280249
$596$	−11.5914	−0.474802
$597$	1.98825	0.0813736
$598$	−71.9408	−2.94188
$599$	40.7242	1.66395	0.831973	−	0.554817i	$-0.187212\pi$
$599$	40.7242	1.66395	0.831973	+	0.554817i	$0.187212\pi$
$600$	8.06310	0.329175
$601$	−28.2427	−1.15204	−0.576021	−	0.817435i	$-0.695395\pi$
$601$	−28.2427	−1.15204	−0.576021	+	0.817435i	$0.695395\pi$
$602$	2.40557	0.0980438
$603$	−38.7575	−1.57833
$604$	68.8780	2.80261
$605$	−12.6651	−0.514911
$606$	−9.89018	−0.401761
$607$	−39.4914	−1.60290	−0.801452	−	0.598059i	$-0.795939\pi$
$607$	−39.4914	−1.60290	−0.801452	+	0.598059i	$0.795939\pi$
$608$	70.0089	2.83924
$609$	−1.04098	−0.0421825
$610$	28.1173	1.13844
$611$	30.3350	1.22722
$612$	54.2732	2.19386
$613$	−40.6178	−1.64054	−0.820269	−	0.571979i	$-0.806176\pi$
$613$	−40.6178	−1.64054	−0.820269	+	0.571979i	$0.806176\pi$
$614$	39.8649	1.60882
$615$	1.75441	0.0707445
$616$	65.3707	2.63386
$617$	37.0976	1.49349	0.746746	−	0.665109i	$-0.231615\pi$
$617$	37.0976	1.49349	0.746746	+	0.665109i	$0.231615\pi$
$618$	−0.959332	−0.0385900
$619$	1.45186	0.0583553	0.0291777	−	0.999574i	$-0.490711\pi$
$619$	1.45186	0.0583553	0.0291777	+	0.999574i	$0.490711\pi$
$620$	−36.5459	−1.46772
$621$	8.48388	0.340446
$622$	−45.4560	−1.82262
$623$	9.64010	0.386223
$624$	−15.2868	−0.611960
$625$	7.49057	0.299623
$626$	−88.4595	−3.53555
$627$	−5.67890	−0.226794
$628$	111.241	4.43901
$629$	−5.09749	−0.203250
$630$	14.7605	0.588074
$631$	4.60082	0.183156	0.0915778	−	0.995798i	$-0.470809\pi$
$631$	4.60082	0.183156	0.0915778	+	0.995798i	$0.470809\pi$
$632$	96.7044	3.84669
$633$	−2.11566	−0.0840898
$634$	17.4581	0.693349
$635$	14.6413	0.581022
$636$	−14.1961	−0.562914
$637$	20.7001	0.820169
$638$	−30.0071	−1.18799
$639$	12.2672	0.485282
$640$	15.7847	0.623946
$641$	1.29923	0.0513166	0.0256583	−	0.999671i	$-0.491832\pi$
$641$	1.29923	0.0513166	0.0256583	+	0.999671i	$0.491832\pi$
$642$	−5.24317	−0.206931
$643$	−15.7137	−0.619688	−0.309844	−	0.950787i	$-0.600277\pi$
$643$	−15.7137	−0.619688	−0.309844	+	0.950787i	$0.600277\pi$
$644$	46.8372	1.84564
$645$	−0.159040	−0.00626221
$646$	−44.6018	−1.75483
$647$	6.72193	0.264266	0.132133	−	0.991232i	$-0.457817\pi$
$647$	6.72193	0.264266	0.132133	+	0.991232i	$0.457817\pi$
$648$	−69.6447	−2.73590
$649$	−23.4908	−0.922094
$650$	−48.8720	−1.91692
$651$	−2.75979	−0.108165
$652$	82.6072	3.23515
$653$	36.9605	1.44638	0.723189	−	0.690650i	$-0.242676\pi$
$653$	36.9605	1.44638	0.723189	+	0.690650i	$0.242676\pi$
$654$	−11.7064	−0.457755
$655$	−7.20169	−0.281393
$656$	−70.8951	−2.76799
$657$	−16.0184	−0.624939
$658$	−27.4766	−1.07115
$659$	43.2215	1.68367	0.841836	−	0.539734i	$-0.181475\pi$
$659$	43.2215	1.68367	0.841836	+	0.539734i	$0.181475\pi$
$660$	−7.09951	−0.276348
$661$	8.86608	0.344851	0.172425	−	0.985023i	$-0.444840\pi$
$661$	8.86608	0.344851	0.172425	+	0.985023i	$0.444840\pi$
$662$	−68.5542	−2.66443
$663$	4.64873	0.180542
$664$	72.3996	2.80965
$665$	−8.71898	−0.338108
$666$	11.0067	0.426500
$667$	−13.0881	−0.506772
$668$	−51.1820	−1.98029
$669$	−1.58035	−0.0611000
$670$	39.8186	1.53833
$671$	43.9937	1.69836
$672$	6.60929	0.254959
$673$	−15.8930	−0.612631	−0.306315	−	0.951930i	$-0.599096\pi$
$673$	−15.8930	−0.612631	−0.306315	+	0.951930i	$0.599096\pi$
$674$	−30.2055	−1.16347
$675$	5.76341	0.221834
$676$	57.3261	2.20485
$677$	43.2428	1.66195	0.830977	−	0.556307i	$-0.187782\pi$
$677$	43.2428	1.66195	0.830977	+	0.556307i	$0.187782\pi$
$678$	−6.62715	−0.254514
$679$	5.14464	0.197433
$680$	−33.9437	−1.30168
$681$	2.34012	0.0896737
$682$	−79.5534	−3.04626
$683$	6.49914	0.248683	0.124341	−	0.992240i	$-0.460318\pi$
$683$	6.49914	0.248683	0.124341	+	0.992240i	$0.460318\pi$
$684$	69.2227	2.64680
$685$	18.8392	0.719810
$686$	−49.9495	−1.90708
$687$	−2.98479	−0.113877
$688$	6.42678	0.245019
$689$	52.3808	1.99555
$690$	−4.30807	−0.164006
$691$	43.1426	1.64122	0.820612	−	0.571486i	$-0.193633\pi$
$691$	43.1426	1.64122	0.820612	+	0.571486i	$0.193633\pi$
$692$	−115.830	−4.40318
$693$	23.0951	0.877308
$694$	−2.37967	−0.0903310
$695$	11.9865	0.454675
$696$	−5.16890	−0.195927
$697$	21.5593	0.816617
$698$	−0.720057	−0.0272545
$699$	−0.354444	−0.0134063
$700$	31.8183	1.20262
$701$	3.28421	0.124043	0.0620214	−	0.998075i	$-0.480245\pi$
$701$	3.28421	0.124043	0.0620214	+	0.998075i	$0.480245\pi$
$702$	−20.3084	−0.766491
$703$	−6.50159	−0.245212
$704$	78.2749	2.95010
$705$	1.81657	0.0684160
$706$	−2.40776	−0.0906174
$707$	−23.7587	−0.893537
$708$	−6.64704	−0.249811
$709$	24.8641	0.933792	0.466896	−	0.884312i	$-0.345372\pi$
$709$	24.8641	0.933792	0.466896	+	0.884312i	$0.345372\pi$
$710$	−12.6030	−0.472984
$711$	34.1651	1.28129
$712$	47.8673	1.79390
$713$	−34.6985	−1.29947
$714$	−4.21069	−0.157581
$715$	26.1957	0.979664
$716$	−26.5327	−0.991574
$717$	−1.97231	−0.0736573
$718$	34.4593	1.28601
$719$	36.9827	1.37922	0.689610	−	0.724181i	$-0.257782\pi$
$719$	36.9827	1.37922	0.689610	+	0.724181i	$0.257782\pi$
$720$	39.4345	1.46964
$721$	−2.30455	−0.0858261
$722$	−6.21786	−0.231405
$723$	3.17100	0.117931
$724$	18.2387	0.677835
$725$	−8.89120	−0.330211
$726$	−7.80119	−0.289529
$727$	46.4086	1.72120	0.860599	−	0.509283i	$-0.170089\pi$
$727$	46.4086	1.72120	0.860599	+	0.509283i	$0.170089\pi$
$728$	−68.2521	−2.52959
$729$	−23.3938	−0.866439
$730$	16.4570	0.609101
$731$	−1.95439	−0.0722858
$732$	12.4486	0.460115
$733$	15.9976	0.590886	0.295443	−	0.955360i	$-0.404533\pi$
$733$	15.9976	0.590886	0.295443	+	0.955360i	$0.404533\pi$
$734$	−45.2733	−1.67107
$735$	1.23960	0.0457233
$736$	83.0977	3.06302
$737$	62.3022	2.29493
$738$	−46.5516	−1.71359
$739$	−12.6336	−0.464734	−0.232367	−	0.972628i	$-0.574647\pi$
$739$	−12.6336	−0.464734	−0.232367	+	0.972628i	$0.574647\pi$
$740$	−8.12799	−0.298791
$741$	5.92922	0.217815
$742$	−47.4451	−1.74176
$743$	−6.28028	−0.230401	−0.115201	−	0.993342i	$-0.536751\pi$
$743$	−6.28028	−0.230401	−0.115201	+	0.993342i	$0.536751\pi$
$744$	−13.7036	−0.502397
$745$	2.56121	0.0938355
$746$	−62.3034	−2.28109
$747$	25.5783	0.935862
$748$	−87.2434	−3.18994
$749$	−12.5954	−0.460226
$750$	−6.85585	−0.250340
$751$	51.3487	1.87374	0.936871	−	0.349676i	$-0.113708\pi$
$751$	51.3487	1.87374	0.936871	+	0.349676i	$0.113708\pi$
$752$	−73.4071	−2.67688
$753$	2.80947	0.102383
$754$	31.3297	1.14096
$755$	−15.2192	−0.553882
$756$	13.2218	0.480873
$757$	−14.3881	−0.522945	−0.261473	−	0.965211i	$-0.584208\pi$
$757$	−14.3881	−0.522945	−0.261473	+	0.965211i	$0.584208\pi$
$758$	−89.4182	−3.24782
$759$	−6.74062	−0.244669
$760$	−43.2935	−1.57042
$761$	−27.5473	−0.998589	−0.499295	−	0.866432i	$-0.666408\pi$
$761$	−27.5473	−0.998589	−0.499295	+	0.866432i	$0.666408\pi$
$762$	9.01842	0.326703
$763$	−28.1216	−1.01807
$764$	−95.1093	−3.44093
$765$	−11.9921	−0.433575
$766$	−23.8105	−0.860307
$767$	24.5262	0.885590
$768$	1.05708	0.0381439
$769$	−33.9788	−1.22531	−0.612653	−	0.790352i	$-0.709898\pi$
$769$	−33.9788	−1.22531	−0.612653	+	0.790352i	$0.709898\pi$
$770$	−23.7274	−0.855075
$771$	5.60516	0.201865
$772$	−70.0805	−2.52225
$773$	2.71623	0.0976962	0.0488481	−	0.998806i	$-0.484445\pi$
$773$	2.71623	0.0976962	0.0488481	+	0.998806i	$0.484445\pi$
$774$	4.21999	0.151684
$775$	−23.5720	−0.846730
$776$	25.5454	0.917025
$777$	−0.613791	−0.0220196
$778$	−76.6535	−2.74816
$779$	27.4978	0.985212
$780$	7.41244	0.265408
$781$	−19.7193	−0.705613
$782$	−52.9404	−1.89315
$783$	−3.69467	−0.132037
$784$	−50.0918	−1.78899
$785$	−24.5796	−0.877285
$786$	−4.43594	−0.158225
$787$	−24.2374	−0.863969	−0.431985	−	0.901881i	$-0.642187\pi$
$787$	−24.2374	−0.863969	−0.431985	+	0.901881i	$0.642187\pi$
$788$	21.5782	0.768692
$789$	−5.15015	−0.183350
$790$	−35.1004	−1.24882
$791$	−15.9201	−0.566052
$792$	114.677	4.07487
$793$	−45.9329	−1.63112
$794$	−92.4973	−3.28261
$795$	3.13675	0.111249
$796$	38.9585	1.38085
$797$	−14.9368	−0.529087	−0.264544	−	0.964374i	$-0.585221\pi$
$797$	−14.9368	−0.529087	−0.264544	+	0.964374i	$0.585221\pi$
$798$	−5.37053	−0.190115
$799$	22.3232	0.789739
$800$	56.4513	1.99586
$801$	16.9112	0.597528
$802$	84.8453	2.99599
$803$	25.7494	0.908678
$804$	17.6293	0.621736
$805$	−10.3491	−0.364757
$806$	83.0600	2.92566
$807$	4.52287	0.159212
$808$	−117.972	−4.15024
$809$	14.9015	0.523908	0.261954	−	0.965080i	$-0.415633\pi$
$809$	14.9015	0.523908	0.261954	+	0.965080i	$0.415633\pi$
$810$	25.2787	0.888203
$811$	−6.71278	−0.235717	−0.117859	−	0.993030i	$-0.537603\pi$
$811$	−6.71278	−0.235717	−0.117859	+	0.993030i	$0.537603\pi$
$812$	−20.3973	−0.715805
$813$	−2.26117	−0.0793025
$814$	−17.6931	−0.620142
$815$	−18.2527	−0.639365
$816$	−11.2494	−0.393807
$817$	−2.49273	−0.0872096
$818$	16.7653	0.586184
$819$	−24.1130	−0.842578
$820$	34.3765	1.20048
$821$	−35.5031	−1.23907	−0.619533	−	0.784971i	$-0.712678\pi$
$821$	−35.5031	−1.23907	−0.619533	+	0.784971i	$0.712678\pi$
$822$	11.6042	0.404742
$823$	−12.7052	−0.442876	−0.221438	−	0.975174i	$-0.571075\pi$
$823$	−12.7052	−0.442876	−0.221438	+	0.975174i	$0.571075\pi$
$824$	−11.4431	−0.398639
$825$	−4.57915	−0.159426
$826$	−22.2152	−0.772965
$827$	50.8723	1.76900	0.884501	−	0.466538i	$-0.154499\pi$
$827$	50.8723	1.76900	0.884501	+	0.466538i	$0.154499\pi$
$828$	82.1645	2.85541
$829$	11.0155	0.382584	0.191292	−	0.981533i	$-0.438732\pi$
$829$	11.0155	0.382584	0.191292	+	0.981533i	$0.438732\pi$
$830$	−26.2786	−0.912144
$831$	−6.69899	−0.232385
$832$	−81.7252	−2.83331
$833$	15.2330	0.527792
$834$	7.38319	0.255659
$835$	11.3091	0.391367
$836$	−111.275	−3.84851
$837$	−9.79515	−0.338570
$838$	49.9937	1.72701
$839$	−24.2472	−0.837107	−0.418553	−	0.908192i	$-0.637463\pi$
$839$	−24.2472	−0.837107	−0.418553	+	0.908192i	$0.637463\pi$
$840$	−4.08718	−0.141021
$841$	−23.3002	−0.803456
$842$	69.4558	2.39360
$843$	−5.04487	−0.173754
$844$	−41.4550	−1.42694
$845$	−12.6667	−0.435747
$846$	−48.2011	−1.65719
$847$	−18.7404	−0.643927
$848$	−126.755	−4.35280
$849$	−1.21518	−0.0417050
$850$	−35.9644	−1.23357
$851$	−7.71712	−0.264539
$852$	−5.57986	−0.191163
$853$	52.7244	1.80525	0.902625	−	0.430427i	$-0.141637\pi$
$853$	52.7244	1.80525	0.902625	+	0.430427i	$0.141637\pi$
$854$	41.6047	1.42368
$855$	−15.2953	−0.523089
$856$	−62.5416	−2.13763
$857$	2.98849	0.102085	0.0510425	−	0.998696i	$-0.483746\pi$
$857$	2.98849	0.102085	0.0510425	+	0.998696i	$0.483746\pi$
$858$	16.1355	0.550856
$859$	−44.4602	−1.51696	−0.758481	−	0.651696i	$-0.774058\pi$
$859$	−44.4602	−1.51696	−0.758481	+	0.651696i	$0.774058\pi$
$860$	−3.11630	−0.106265
$861$	2.59597	0.0884704
$862$	64.0127	2.18028
$863$	−33.7711	−1.14958	−0.574791	−	0.818300i	$-0.694917\pi$
$863$	−33.7711	−1.14958	−0.574791	+	0.818300i	$0.694917\pi$
$864$	23.4579	0.798055
$865$	25.5935	0.870205
$866$	−56.1096	−1.90668
$867$	−1.01411	−0.0344411
$868$	−54.0764	−1.83547
$869$	−54.9199	−1.86303
$870$	1.87614	0.0636070
$871$	−65.0484	−2.20408
$872$	−139.636	−4.72867
$873$	9.02502	0.305451
$874$	−67.5229	−2.28400
$875$	−16.4695	−0.556770
$876$	7.28616	0.246177
$877$	8.40463	0.283804	0.141902	−	0.989881i	$-0.454678\pi$
$877$	8.40463	0.283804	0.141902	+	0.989881i	$0.454678\pi$
$878$	9.02576	0.304605
$879$	5.40211	0.182209
$880$	−63.3905	−2.13689
$881$	19.9128	0.670881	0.335440	−	0.942061i	$-0.391115\pi$
$881$	19.9128	0.670881	0.335440	+	0.942061i	$0.391115\pi$
$882$	−32.8916	−1.10752
$883$	37.2718	1.25429	0.627147	−	0.778901i	$-0.284222\pi$
$883$	37.2718	1.25429	0.627147	+	0.778901i	$0.284222\pi$
$884$	91.0890	3.06365
$885$	1.46872	0.0493704
$886$	100.597	3.37964
$887$	14.5131	0.487302	0.243651	−	0.969863i	$-0.421655\pi$
$887$	14.5131	0.487302	0.243651	+	0.969863i	$0.421655\pi$
$888$	−3.04774	−0.102275
$889$	21.6645	0.726604
$890$	−17.3742	−0.582385
$891$	39.5523	1.32505
$892$	−30.9661	−1.03682
$893$	28.4722	0.952784
$894$	1.57760	0.0527628
$895$	5.86262	0.195966
$896$	23.3564	0.780283
$897$	7.03774	0.234983
$898$	−25.1640	−0.839734
$899$	15.1110	0.503979
$900$	55.8174	1.86058
$901$	38.5465	1.28417
$902$	74.8311	2.49160
$903$	−0.235330	−0.00783128
$904$	−79.0500	−2.62916
$905$	−4.02998	−0.133961
$906$	−9.37436	−0.311442
$907$	16.3760	0.543756	0.271878	−	0.962332i	$-0.412355\pi$
$907$	16.3760	0.543756	0.271878	+	0.962332i	$0.412355\pi$
$908$	45.8533	1.52169
$909$	−41.6788	−1.38240
$910$	24.7732	0.821224
$911$	22.9496	0.760354	0.380177	−	0.924914i	$-0.375863\pi$
$911$	22.9496	0.760354	0.380177	+	0.924914i	$0.375863\pi$
$912$	−14.3480	−0.475110
$913$	−41.1168	−1.36077
$914$	14.6600	0.484909
$915$	−2.75063	−0.0909329
$916$	−58.4851	−1.93240
$917$	−10.6562	−0.351900
$918$	−14.9447	−0.493250
$919$	−50.6601	−1.67112	−0.835561	−	0.549397i	$-0.814857\pi$
$919$	−50.6601	−1.67112	−0.835561	+	0.549397i	$0.814857\pi$
$920$	−51.3876	−1.69420
$921$	−3.89985	−0.128505
$922$	−13.5701	−0.446907
$923$	20.5885	0.677680
$924$	−10.5050	−0.345590
$925$	−5.24252	−0.172373
$926$	−81.9099	−2.69173
$927$	−4.04278	−0.132782
$928$	−36.1885	−1.18795
$929$	−4.59751	−0.150839	−0.0754197	−	0.997152i	$-0.524030\pi$
$929$	−4.59751	−0.150839	−0.0754197	+	0.997152i	$0.524030\pi$
$930$	4.97393	0.163102
$931$	19.4289	0.636758
$932$	−6.94511	−0.227495
$933$	4.44682	0.145582
$934$	−80.2352	−2.62538
$935$	19.2771	0.630430
$936$	−119.732	−3.91355
$937$	−38.7376	−1.26550	−0.632751	−	0.774356i	$-0.718074\pi$
$937$	−38.7376	−1.26550	−0.632751	+	0.774356i	$0.718074\pi$
$938$	58.9190	1.92377
$939$	8.65371	0.282403
$940$	35.5946	1.16097
$941$	29.6625	0.966971	0.483485	−	0.875352i	$-0.339371\pi$
$941$	29.6625	0.966971	0.483485	+	0.875352i	$0.339371\pi$
$942$	−15.1400	−0.493289
$943$	32.6388	1.06286
$944$	−59.3505	−1.93169
$945$	−2.92147	−0.0950355
$946$	−6.78358	−0.220553
$947$	−25.2583	−0.820784	−0.410392	−	0.911909i	$-0.634608\pi$
$947$	−25.2583	−0.820784	−0.410392	+	0.911909i	$0.634608\pi$
$948$	−15.5403	−0.504727
$949$	−26.8844	−0.872706
$950$	−45.8708	−1.48825
$951$	−1.70787	−0.0553814
$952$	−50.2260	−1.62783
$953$	6.92818	0.224426	0.112213	−	0.993684i	$-0.464206\pi$
$953$	6.92818	0.224426	0.112213	+	0.993684i	$0.464206\pi$
$954$	−83.2309	−2.69470
$955$	21.0152	0.680035
$956$	−38.6462	−1.24991
$957$	2.93550	0.0948911
$958$	23.0564	0.744918
$959$	27.8761	0.900167
$960$	−4.89400	−0.157953
$961$	9.06151	0.292307
$962$	18.4730	0.595592
$963$	−22.0956	−0.712020
$964$	62.1339	2.00120
$965$	15.4849	0.498475
$966$	−6.37459	−0.205099
$967$	−50.5479	−1.62551	−0.812755	−	0.582606i	$-0.802033\pi$
$967$	−50.5479	−1.62551	−0.812755	+	0.582606i	$0.802033\pi$
$968$	−93.0541	−2.99087
$969$	4.36325	0.140168
$970$	−9.27211	−0.297710
$971$	1.28799	0.0413334	0.0206667	−	0.999786i	$-0.493421\pi$
$971$	1.28799	0.0413334	0.0206667	+	0.999786i	$0.493421\pi$
$972$	34.9248	1.12021
$973$	17.7363	0.568599
$974$	38.3144	1.22767
$975$	4.78100	0.153114
$976$	111.152	3.55789
$977$	−48.1093	−1.53915	−0.769576	−	0.638555i	$-0.779533\pi$
$977$	−48.1093	−1.53915	−0.769576	+	0.638555i	$0.779533\pi$
$978$	−11.2429	−0.359509
$979$	−27.1846	−0.868822
$980$	24.2892	0.775889
$981$	−49.3325	−1.57507
$982$	7.13759	0.227770
$983$	−35.7244	−1.13943	−0.569716	−	0.821842i	$-0.692947\pi$
$983$	−35.7244	−1.13943	−0.569716	+	0.821842i	$0.692947\pi$
$984$	12.8901	0.410922
$985$	−4.76788	−0.151917
$986$	23.0552	0.734228
$987$	2.68795	0.0855585
$988$	116.179	3.69616
$989$	−2.95877	−0.0940833
$990$	−41.6239	−1.32289
$991$	−34.1872	−1.08599	−0.542996	−	0.839736i	$-0.682710\pi$
$991$	−34.1872	−1.08599	−0.542996	+	0.839736i	$0.682710\pi$
$992$	−95.9413	−3.04614
$993$	6.70644	0.212822
$994$	−18.6485	−0.591495
$995$	−8.60820	−0.272898
$996$	−11.6346	−0.368656
$997$	4.41113	0.139702	0.0698509	−	0.997557i	$-0.477748\pi$
$997$	4.41113	0.139702	0.0698509	+	0.997557i	$0.477748\pi$
$998$	−8.17421	−0.258750
$999$	−2.17849	−0.0689244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.9	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.9	✓	184	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66682 q^{2} +0.260886 q^{3} +5.11190 q^{4} -1.12952 q^{5} -0.695735 q^{6} -1.67133 q^{7} -8.29887 q^{8} -2.93194 q^{9} +O(q^{10})\)	\(q-2.66682 q^{2} +0.260886 q^{3} +5.11190 q^{4} -1.12952 q^{5} -0.695735 q^{6} -1.67133 q^{7} -8.29887 q^{8} -2.93194 q^{9} +3.01221 q^{10} +4.71305 q^{11} +1.33362 q^{12} -4.92080 q^{13} +4.45712 q^{14} -0.294675 q^{15} +11.9077 q^{16} -3.62116 q^{17} +7.81894 q^{18} -4.61861 q^{19} -5.77398 q^{20} -0.436026 q^{21} -12.5688 q^{22} -5.48210 q^{23} -2.16506 q^{24} -3.72419 q^{25} +13.1229 q^{26} -1.54756 q^{27} -8.54367 q^{28} +2.38742 q^{29} +0.785844 q^{30} +6.32942 q^{31} -15.1580 q^{32} +1.22957 q^{33} +9.65697 q^{34} +1.88779 q^{35} -14.9878 q^{36} +1.40769 q^{37} +12.3170 q^{38} -1.28377 q^{39} +9.37371 q^{40} -5.95370 q^{41} +1.16280 q^{42} +0.539714 q^{43} +24.0927 q^{44} +3.31167 q^{45} +14.6197 q^{46} -6.16466 q^{47} +3.10656 q^{48} -4.20666 q^{49} +9.93173 q^{50} -0.944710 q^{51} -25.1546 q^{52} -10.6448 q^{53} +4.12706 q^{54} -5.32347 q^{55} +13.8701 q^{56} -1.20493 q^{57} -6.36680 q^{58} -4.98420 q^{59} -1.50635 q^{60} +9.33444 q^{61} -16.8794 q^{62} +4.90023 q^{63} +16.6081 q^{64} +5.55812 q^{65} -3.27904 q^{66} +13.2191 q^{67} -18.5110 q^{68} -1.43020 q^{69} -5.03439 q^{70} -4.18398 q^{71} +24.3318 q^{72} +5.46343 q^{73} -3.75406 q^{74} -0.971590 q^{75} -23.6099 q^{76} -7.87706 q^{77} +3.42357 q^{78} -11.6527 q^{79} -13.4500 q^{80} +8.39208 q^{81} +15.8774 q^{82} -8.72403 q^{83} -2.22892 q^{84} +4.09016 q^{85} -1.43932 q^{86} +0.622844 q^{87} -39.1130 q^{88} -5.76793 q^{89} -8.83162 q^{90} +8.22427 q^{91} -28.0240 q^{92} +1.65126 q^{93} +16.4400 q^{94} +5.21680 q^{95} -3.95451 q^{96} -3.07817 q^{97} +11.2184 q^{98} -13.8184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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