LMFDB - Embedded newform 6005.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17289 q^{2} -1.65848 q^{3} +2.72145 q^{4} +1.00000 q^{5} +3.60369 q^{6} +5.14399 q^{7} -1.56762 q^{8} -0.249442 q^{9} +O(q^{10})$	\(q-2.17289 q^{2} -1.65848 q^{3} +2.72145 q^{4} +1.00000 q^{5} +3.60369 q^{6} +5.14399 q^{7} -1.56762 q^{8} -0.249442 q^{9} -2.17289 q^{10} -4.72148 q^{11} -4.51347 q^{12} -3.09354 q^{13} -11.1773 q^{14} -1.65848 q^{15} -2.03662 q^{16} +5.03310 q^{17} +0.542010 q^{18} -5.75916 q^{19} +2.72145 q^{20} -8.53120 q^{21} +10.2593 q^{22} -3.51984 q^{23} +2.59987 q^{24} +1.00000 q^{25} +6.72193 q^{26} +5.38914 q^{27} +13.9991 q^{28} +3.59928 q^{29} +3.60369 q^{30} +2.03502 q^{31} +7.56060 q^{32} +7.83049 q^{33} -10.9364 q^{34} +5.14399 q^{35} -0.678843 q^{36} -9.96323 q^{37} +12.5140 q^{38} +5.13058 q^{39} -1.56762 q^{40} +4.95970 q^{41} +18.5374 q^{42} +9.71877 q^{43} -12.8493 q^{44} -0.249442 q^{45} +7.64822 q^{46} -9.65028 q^{47} +3.37770 q^{48} +19.4606 q^{49} -2.17289 q^{50} -8.34730 q^{51} -8.41891 q^{52} +5.78572 q^{53} -11.7100 q^{54} -4.72148 q^{55} -8.06384 q^{56} +9.55146 q^{57} -7.82084 q^{58} +9.50615 q^{59} -4.51347 q^{60} -7.91802 q^{61} -4.42187 q^{62} -1.28313 q^{63} -12.3551 q^{64} -3.09354 q^{65} -17.0148 q^{66} -14.9513 q^{67} +13.6973 q^{68} +5.83758 q^{69} -11.1773 q^{70} +5.32791 q^{71} +0.391031 q^{72} +5.92421 q^{73} +21.6490 q^{74} -1.65848 q^{75} -15.6733 q^{76} -24.2872 q^{77} -11.1482 q^{78} +2.59705 q^{79} -2.03662 q^{80} -8.18945 q^{81} -10.7769 q^{82} +0.237227 q^{83} -23.2172 q^{84} +5.03310 q^{85} -21.1178 q^{86} -5.96934 q^{87} +7.40151 q^{88} -6.45695 q^{89} +0.542010 q^{90} -15.9131 q^{91} -9.57905 q^{92} -3.37504 q^{93} +20.9690 q^{94} -5.75916 q^{95} -12.5391 q^{96} +12.7558 q^{97} -42.2858 q^{98} +1.17774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.17289	−1.53646	−0.768232	−	0.640171i	$-0.778863\pi$
$2$	−2.17289	−1.53646	−0.768232	+	0.640171i	$0.778863\pi$
$3$	−1.65848	−0.957524	−0.478762	−	0.877945i	$-0.658914\pi$
$3$	−1.65848	−0.957524	−0.478762	+	0.877945i	$0.658914\pi$
$4$	2.72145	1.36072
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.60369	1.47120
$7$	5.14399	1.94424	0.972122	−	0.234474i	$-0.0753368\pi$
$7$	5.14399	1.94424	0.972122	+	0.234474i	$0.0753368\pi$
$8$	−1.56762	−0.554239
$9$	−0.249442	−0.0831473
$10$	−2.17289	−0.687128
$11$	−4.72148	−1.42358	−0.711790	−	0.702392i	$-0.752115\pi$
$11$	−4.72148	−1.42358	−0.711790	+	0.702392i	$0.752115\pi$
$12$	−4.51347	−1.30293
$13$	−3.09354	−0.857994	−0.428997	−	0.903306i	$-0.641133\pi$
$13$	−3.09354	−0.857994	−0.428997	+	0.903306i	$0.641133\pi$
$14$	−11.1773	−2.98726
$15$	−1.65848	−0.428218
$16$	−2.03662	−0.509155
$17$	5.03310	1.22071	0.610353	−	0.792129i	$-0.291028\pi$
$17$	5.03310	1.22071	0.610353	+	0.792129i	$0.291028\pi$
$18$	0.542010	0.127753
$19$	−5.75916	−1.32124	−0.660621	−	0.750719i	$-0.729707\pi$
$19$	−5.75916	−1.32124	−0.660621	+	0.750719i	$0.729707\pi$
$20$	2.72145	0.608534
$21$	−8.53120	−1.86166
$22$	10.2593	2.18728
$23$	−3.51984	−0.733937	−0.366968	−	0.930233i	$-0.619604\pi$
$23$	−3.51984	−0.733937	−0.366968	+	0.930233i	$0.619604\pi$
$24$	2.59987	0.530697
$25$	1.00000	0.200000
$26$	6.72193	1.31828
$27$	5.38914	1.03714
$28$	13.9991	2.64558
$29$	3.59928	0.668370	0.334185	−	0.942507i	$-0.391539\pi$
$29$	3.59928	0.668370	0.334185	+	0.942507i	$0.391539\pi$
$30$	3.60369	0.657942
$31$	2.03502	0.365500	0.182750	−	0.983159i	$-0.441500\pi$
$31$	2.03502	0.365500	0.182750	+	0.983159i	$0.441500\pi$
$32$	7.56060	1.33654
$33$	7.83049	1.36311
$34$	−10.9364	−1.87557
$35$	5.14399	0.869493
$36$	−0.678843	−0.113141
$37$	−9.96323	−1.63794	−0.818972	−	0.573833i	$-0.805456\pi$
$37$	−9.96323	−1.63794	−0.818972	+	0.573833i	$0.805456\pi$
$38$	12.5140	2.03004
$39$	5.13058	0.821550
$40$	−1.56762	−0.247863
$41$	4.95970	0.774574	0.387287	−	0.921959i	$-0.373412\pi$
$41$	4.95970	0.774574	0.387287	+	0.921959i	$0.373412\pi$
$42$	18.5374	2.86038
$43$	9.71877	1.48210	0.741049	−	0.671451i	$-0.234329\pi$
$43$	9.71877	1.48210	0.741049	+	0.671451i	$0.234329\pi$
$44$	−12.8493	−1.93710
$45$	−0.249442	−0.0371846
$46$	7.64822	1.12767
$47$	−9.65028	−1.40764	−0.703819	−	0.710379i	$-0.748523\pi$
$47$	−9.65028	−1.40764	−0.703819	+	0.710379i	$0.748523\pi$
$48$	3.37770	0.487529
$49$	19.4606	2.78009
$50$	−2.17289	−0.307293
$51$	−8.34730	−1.16886
$52$	−8.41891	−1.16749
$53$	5.78572	0.794729	0.397365	−	0.917661i	$-0.369925\pi$
$53$	5.78572	0.794729	0.397365	+	0.917661i	$0.369925\pi$
$54$	−11.7100	−1.59353
$55$	−4.72148	−0.636644
$56$	−8.06384	−1.07758
$57$	9.55146	1.26512
$58$	−7.82084	−1.02693
$59$	9.50615	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$59$	9.50615	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$60$	−4.51347	−0.582686
$61$	−7.91802	−1.01380	−0.506900	−	0.862005i	$-0.669208\pi$
$61$	−7.91802	−1.01380	−0.506900	+	0.862005i	$0.669208\pi$
$62$	−4.42187	−0.561577
$63$	−1.28313	−0.161659
$64$	−12.3551	−1.54439
$65$	−3.09354	−0.383707
$66$	−17.0148	−2.09437
$67$	−14.9513	−1.82659	−0.913295	−	0.407299i	$-0.866471\pi$
$67$	−14.9513	−1.82659	−0.913295	+	0.407299i	$0.866471\pi$
$68$	13.6973	1.66104
$69$	5.83758	0.702762
$70$	−11.1773	−1.33594
$71$	5.32791	0.632307	0.316153	−	0.948708i	$-0.397609\pi$
$71$	5.32791	0.632307	0.316153	+	0.948708i	$0.397609\pi$
$72$	0.391031	0.0460835
$73$	5.92421	0.693376	0.346688	−	0.937980i	$-0.387306\pi$
$73$	5.92421	0.693376	0.346688	+	0.937980i	$0.387306\pi$
$74$	21.6490	2.51664
$75$	−1.65848	−0.191505
$76$	−15.6733	−1.79785
$77$	−24.2872	−2.76779
$78$	−11.1482	−1.26228
$79$	2.59705	0.292191	0.146095	−	0.989271i	$-0.453329\pi$
$79$	2.59705	0.292191	0.146095	+	0.989271i	$0.453329\pi$
$80$	−2.03662	−0.227701
$81$	−8.18945	−0.909939
$82$	−10.7769	−1.19011
$83$	0.237227	0.0260390	0.0130195	−	0.999915i	$-0.495856\pi$
$83$	0.237227	0.0260390	0.0130195	+	0.999915i	$0.495856\pi$
$84$	−23.2172	−2.53321
$85$	5.03310	0.545916
$86$	−21.1178	−2.27719
$87$	−5.96934	−0.639981
$88$	7.40151	0.789003
$89$	−6.45695	−0.684435	−0.342218	−	0.939621i	$-0.611178\pi$
$89$	−6.45695	−0.684435	−0.342218	+	0.939621i	$0.611178\pi$
$90$	0.542010	0.0571329
$91$	−15.9131	−1.66815
$92$	−9.57905	−0.998685
$93$	−3.37504	−0.349975
$94$	20.9690	2.16279
$95$	−5.75916	−0.590878
$96$	−12.5391	−1.27977
$97$	12.7558	1.29516	0.647579	−	0.761998i	$-0.275781\pi$
$97$	12.7558	1.29516	0.647579	+	0.761998i	$0.275781\pi$
$98$	−42.2858	−4.27151
$99$	1.17774	0.118367
$100$	2.72145	0.272145
$101$	−3.69184	−0.367352	−0.183676	−	0.982987i	$-0.558800\pi$
$101$	−3.69184	−0.367352	−0.183676	+	0.982987i	$0.558800\pi$
$102$	18.1378	1.79591
$103$	−12.0921	−1.19147	−0.595737	−	0.803180i	$-0.703140\pi$
$103$	−12.0921	−1.19147	−0.595737	+	0.803180i	$0.703140\pi$
$104$	4.84951	0.475534
$105$	−8.53120	−0.832560
$106$	−12.5717	−1.22107
$107$	6.91033	0.668046	0.334023	−	0.942565i	$-0.391594\pi$
$107$	6.91033	0.668046	0.334023	+	0.942565i	$0.391594\pi$
$108$	14.6662	1.41126
$109$	−3.43251	−0.328775	−0.164387	−	0.986396i	$-0.552565\pi$
$109$	−3.43251	−0.328775	−0.164387	+	0.986396i	$0.552565\pi$
$110$	10.2593	0.978182
$111$	16.5238	1.56837
$112$	−10.4764	−0.989923
$113$	8.14635	0.766344	0.383172	−	0.923677i	$-0.374832\pi$
$113$	8.14635	0.766344	0.383172	+	0.923677i	$0.374832\pi$
$114$	−20.7543	−1.94381
$115$	−3.51984	−0.328227
$116$	9.79526	0.909467
$117$	0.771660	0.0713400
$118$	−20.6558	−1.90152
$119$	25.8902	2.37335
$120$	2.59987	0.237335
$121$	11.2924	1.02658
$122$	17.2050	1.55767
$123$	−8.22556	−0.741674
$124$	5.53819	0.497344
$125$	1.00000	0.0894427
$126$	2.78809	0.248383
$127$	−14.0491	−1.24666	−0.623328	−	0.781960i	$-0.714220\pi$
$127$	−14.0491	−1.24666	−0.623328	+	0.781960i	$0.714220\pi$
$128$	11.7251	1.03636
$129$	−16.1184	−1.41914
$130$	6.72193	0.589552
$131$	−3.34577	−0.292321	−0.146161	−	0.989261i	$-0.546692\pi$
$131$	−3.34577	−0.292321	−0.146161	+	0.989261i	$0.546692\pi$
$132$	21.3102	1.85482
$133$	−29.6251	−2.56882
$134$	32.4875	2.80649
$135$	5.38914	0.463823
$136$	−7.89001	−0.676562
$137$	−19.8801	−1.69847	−0.849235	−	0.528015i	$-0.822936\pi$
$137$	−19.8801	−1.69847	−0.849235	+	0.528015i	$0.822936\pi$
$138$	−12.6844	−1.07977
$139$	16.0548	1.36175	0.680876	−	0.732399i	$-0.261599\pi$
$139$	16.0548	1.36175	0.680876	+	0.732399i	$0.261599\pi$
$140$	13.9991	1.18314
$141$	16.0048	1.34785
$142$	−11.5770	−0.971517
$143$	14.6061	1.22142
$144$	0.508019	0.0423349
$145$	3.59928	0.298904
$146$	−12.8727	−1.06535
$147$	−32.2751	−2.66200
$148$	−27.1144	−2.22879
$149$	−5.70280	−0.467191	−0.233596	−	0.972334i	$-0.575049\pi$
$149$	−5.70280	−0.467191	−0.233596	+	0.972334i	$0.575049\pi$
$150$	3.60369	0.294240
$151$	−24.0793	−1.95955	−0.979773	−	0.200110i	$-0.935870\pi$
$151$	−24.0793	−1.95955	−0.979773	+	0.200110i	$0.935870\pi$
$152$	9.02820	0.732284
$153$	−1.25547	−0.101498
$154$	52.7735	4.25261
$155$	2.03502	0.163456
$156$	13.9626	1.11790
$157$	5.16061	0.411861	0.205931	−	0.978567i	$-0.433978\pi$
$157$	5.16061	0.411861	0.205931	+	0.978567i	$0.433978\pi$
$158$	−5.64309	−0.448940
$159$	−9.59550	−0.760972
$160$	7.56060	0.597718
$161$	−18.1060	−1.42695
$162$	17.7948	1.39809
$163$	−17.1081	−1.34001	−0.670006	−	0.742356i	$-0.733708\pi$
$163$	−17.1081	−1.34001	−0.670006	+	0.742356i	$0.733708\pi$
$164$	13.4975	1.05398
$165$	7.83049	0.609602
$166$	−0.515467	−0.0400080
$167$	−2.21141	−0.171124	−0.0855620	−	0.996333i	$-0.527269\pi$
$167$	−2.21141	−0.171124	−0.0855620	+	0.996333i	$0.527269\pi$
$168$	13.3737	1.03180
$169$	−3.42999	−0.263846
$170$	−10.9364	−0.838781
$171$	1.43658	0.109858
$172$	26.4491	2.01673
$173$	1.27672	0.0970670	0.0485335	−	0.998822i	$-0.484545\pi$
$173$	1.27672	0.0970670	0.0485335	+	0.998822i	$0.484545\pi$
$174$	12.9707	0.983308
$175$	5.14399	0.388849
$176$	9.61587	0.724824
$177$	−15.7658	−1.18503
$178$	14.0302	1.05161
$179$	6.71905	0.502205	0.251103	−	0.967960i	$-0.419207\pi$
$179$	6.71905	0.502205	0.251103	+	0.967960i	$0.419207\pi$
$180$	−0.678843	−0.0505980
$181$	9.38367	0.697482	0.348741	−	0.937219i	$-0.386609\pi$
$181$	9.38367	0.697482	0.348741	+	0.937219i	$0.386609\pi$
$182$	34.5775	2.56306
$183$	13.1319	0.970737
$184$	5.51778	0.406776
$185$	−9.96323	−0.732511
$186$	7.33358	0.537724
$187$	−23.7637	−1.73777
$188$	−26.2627	−1.91541
$189$	27.7217	2.01645
$190$	12.5140	0.907862
$191$	18.7228	1.35473	0.677366	−	0.735647i	$-0.263122\pi$
$191$	18.7228	1.35473	0.677366	+	0.735647i	$0.263122\pi$
$192$	20.4907	1.47879
$193$	19.0949	1.37448	0.687242	−	0.726428i	$-0.258821\pi$
$193$	19.0949	1.37448	0.687242	+	0.726428i	$0.258821\pi$
$194$	−27.7170	−1.98997
$195$	5.13058	0.367409
$196$	52.9610	3.78293
$197$	8.76876	0.624748	0.312374	−	0.949959i	$-0.398876\pi$
$197$	8.76876	0.624748	0.312374	+	0.949959i	$0.398876\pi$
$198$	−2.55909	−0.181867
$199$	−20.8518	−1.47815	−0.739073	−	0.673625i	$-0.764736\pi$
$199$	−20.8518	−1.47815	−0.739073	+	0.673625i	$0.764736\pi$
$200$	−1.56762	−0.110848
$201$	24.7964	1.74900
$202$	8.02196	0.564423
$203$	18.5147	1.29948
$204$	−22.7167	−1.59049
$205$	4.95970	0.346400
$206$	26.2749	1.83066
$207$	0.877995	0.0610249
$208$	6.30038	0.436852
$209$	27.1918	1.88089
$210$	18.5374	1.27920
$211$	1.08214	0.0744975	0.0372488	−	0.999306i	$-0.488141\pi$
$211$	1.08214	0.0744975	0.0372488	+	0.999306i	$0.488141\pi$
$212$	15.7455	1.08141
$213$	−8.83624	−0.605449
$214$	−15.0154	−1.02643
$215$	9.71877	0.662814
$216$	−8.44814	−0.574823
$217$	10.4681	0.710621
$218$	7.45847	0.505151
$219$	−9.82519	−0.663925
$220$	−12.8493	−0.866297
$221$	−15.5701	−1.04736
$222$	−35.9044	−2.40975
$223$	8.21560	0.550157	0.275079	−	0.961422i	$-0.411296\pi$
$223$	8.21560	0.550157	0.275079	+	0.961422i	$0.411296\pi$
$224$	38.8916	2.59856
$225$	−0.249442	−0.0166295
$226$	−17.7011	−1.17746
$227$	−17.1639	−1.13921	−0.569603	−	0.821920i	$-0.692903\pi$
$227$	−17.1639	−1.13921	−0.569603	+	0.821920i	$0.692903\pi$
$228$	25.9938	1.72148
$229$	6.10273	0.403280	0.201640	−	0.979460i	$-0.435373\pi$
$229$	6.10273	0.403280	0.201640	+	0.979460i	$0.435373\pi$
$230$	7.64822	0.504308
$231$	40.2799	2.65022
$232$	−5.64232	−0.370437
$233$	6.41393	0.420191	0.210095	−	0.977681i	$-0.432623\pi$
$233$	6.41393	0.420191	0.210095	+	0.977681i	$0.432623\pi$
$234$	−1.67673	−0.109611
$235$	−9.65028	−0.629515
$236$	25.8705	1.68402
$237$	−4.30715	−0.279780
$238$	−56.2566	−3.64657
$239$	10.4259	0.674396	0.337198	−	0.941434i	$-0.390521\pi$
$239$	10.4259	0.674396	0.337198	+	0.941434i	$0.390521\pi$
$240$	3.37770	0.218029
$241$	−0.803209	−0.0517392	−0.0258696	−	0.999665i	$-0.508235\pi$
$241$	−0.803209	−0.0517392	−0.0258696	+	0.999665i	$0.508235\pi$
$242$	−24.5371	−1.57730
$243$	−2.58536	−0.165851
$244$	−21.5485	−1.37950
$245$	19.4606	1.24329
$246$	17.8732	1.13956
$247$	17.8162	1.13362
$248$	−3.19014	−0.202574
$249$	−0.393436	−0.0249330
$250$	−2.17289	−0.137426
$251$	−11.9585	−0.754817	−0.377408	−	0.926047i	$-0.623185\pi$
$251$	−11.9585	−0.754817	−0.377408	+	0.926047i	$0.623185\pi$
$252$	−3.49196	−0.219973
$253$	16.6188	1.04482
$254$	30.5272	1.91544
$255$	−8.34730	−0.522728
$256$	−0.767060	−0.0479412
$257$	−5.68756	−0.354780	−0.177390	−	0.984141i	$-0.556765\pi$
$257$	−5.68756	−0.354780	−0.177390	+	0.984141i	$0.556765\pi$
$258$	35.0235	2.18047
$259$	−51.2507	−3.18456
$260$	−8.41891	−0.522119
$261$	−0.897813	−0.0555732
$262$	7.26999	0.449141
$263$	23.6425	1.45786	0.728929	−	0.684589i	$-0.240018\pi$
$263$	23.6425	1.45786	0.728929	+	0.684589i	$0.240018\pi$
$264$	−12.2753	−0.755490
$265$	5.78572	0.355414
$266$	64.3720	3.94690
$267$	10.7087	0.655363
$268$	−40.6891	−2.48548
$269$	5.37592	0.327776	0.163888	−	0.986479i	$-0.447596\pi$
$269$	5.37592	0.327776	0.163888	+	0.986479i	$0.447596\pi$
$270$	−11.7100	−0.712648
$271$	−24.2600	−1.47369	−0.736845	−	0.676062i	$-0.763685\pi$
$271$	−24.2600	−1.47369	−0.736845	+	0.676062i	$0.763685\pi$
$272$	−10.2505	−0.621529
$273$	26.3916	1.59730
$274$	43.1972	2.60964
$275$	−4.72148	−0.284716
$276$	15.8867	0.956265
$277$	−18.1497	−1.09051	−0.545254	−	0.838271i	$-0.683567\pi$
$277$	−18.1497	−1.09051	−0.545254	+	0.838271i	$0.683567\pi$
$278$	−34.8853	−2.09228
$279$	−0.507619	−0.0303903
$280$	−8.06384	−0.481906
$281$	9.78941	0.583987	0.291994	−	0.956420i	$-0.405681\pi$
$281$	9.78941	0.583987	0.291994	+	0.956420i	$0.405681\pi$
$282$	−34.7767	−2.07092
$283$	−33.2401	−1.97592	−0.987961	−	0.154705i	$-0.950557\pi$
$283$	−33.2401	−1.97592	−0.987961	+	0.154705i	$0.950557\pi$
$284$	14.4996	0.860395
$285$	9.55146	0.565780
$286$	−31.7374	−1.87667
$287$	25.5126	1.50596
$288$	−1.88593	−0.111130
$289$	8.33210	0.490124
$290$	−7.82084	−0.459256
$291$	−21.1553	−1.24015
$292$	16.1224	0.943493
$293$	−20.6916	−1.20882	−0.604408	−	0.796675i	$-0.706590\pi$
$293$	−20.6916	−1.20882	−0.604408	+	0.796675i	$0.706590\pi$
$294$	70.1301	4.09007
$295$	9.50615	0.553469
$296$	15.6186	0.907812
$297$	−25.4447	−1.47645
$298$	12.3915	0.717823
$299$	10.8888	0.629714
$300$	−4.51347	−0.260585
$301$	49.9932	2.88156
$302$	52.3217	3.01077
$303$	6.12285	0.351748
$304$	11.7292	0.672718
$305$	−7.91802	−0.453385
$306$	2.72799	0.155949
$307$	−20.1134	−1.14793	−0.573967	−	0.818879i	$-0.694596\pi$
$307$	−20.1134	−1.14793	−0.573967	+	0.818879i	$0.694596\pi$
$308$	−66.0964	−3.76619
$309$	20.0546	1.14087
$310$	−4.42187	−0.251145
$311$	13.7016	0.776945	0.388473	−	0.921460i	$-0.373003\pi$
$311$	13.7016	0.776945	0.388473	+	0.921460i	$0.373003\pi$
$312$	−8.04282	−0.455335
$313$	−17.0568	−0.964109	−0.482054	−	0.876141i	$-0.660109\pi$
$313$	−17.0568	−0.964109	−0.482054	+	0.876141i	$0.660109\pi$
$314$	−11.2134	−0.632810
$315$	−1.28313	−0.0722960
$316$	7.06772	0.397590
$317$	−16.7215	−0.939172	−0.469586	−	0.882887i	$-0.655597\pi$
$317$	−16.7215	−0.939172	−0.469586	+	0.882887i	$0.655597\pi$
$318$	20.8500	1.16921
$319$	−16.9940	−0.951479
$320$	−12.3551	−0.690671
$321$	−11.4606	−0.639671
$322$	39.3423	2.19246
$323$	−28.9864	−1.61285
$324$	−22.2872	−1.23818
$325$	−3.09354	−0.171599
$326$	37.1740	2.05888
$327$	5.69275	0.314810
$328$	−7.77494	−0.429299
$329$	−49.6409	−2.73679
$330$	−17.0148	−0.936633
$331$	27.9233	1.53480	0.767401	−	0.641167i	$-0.221549\pi$
$331$	27.9233	1.53480	0.767401	+	0.641167i	$0.221549\pi$
$332$	0.645600	0.0354319
$333$	2.48525	0.136191
$334$	4.80515	0.262926
$335$	−14.9513	−0.816876
$336$	17.3748	0.947875
$337$	−35.4756	−1.93248	−0.966238	−	0.257650i	$-0.917052\pi$
$337$	−35.4756	−1.93248	−0.966238	+	0.257650i	$0.917052\pi$
$338$	7.45299	0.405389
$339$	−13.5106	−0.733793
$340$	13.6973	0.742841
$341$	−9.60829	−0.520318
$342$	−3.12152	−0.168793
$343$	64.0973	3.46093
$344$	−15.2354	−0.821436
$345$	5.83758	0.314285
$346$	−2.77416	−0.149140
$347$	−6.93998	−0.372557	−0.186279	−	0.982497i	$-0.559643\pi$
$347$	−6.93998	−0.372557	−0.186279	+	0.982497i	$0.559643\pi$
$348$	−16.2452	−0.870837
$349$	15.9961	0.856252	0.428126	−	0.903719i	$-0.359174\pi$
$349$	15.9961	0.856252	0.428126	+	0.903719i	$0.359174\pi$
$350$	−11.1773	−0.597453
$351$	−16.6715	−0.889860
$352$	−35.6972	−1.90267
$353$	7.69660	0.409649	0.204824	−	0.978799i	$-0.434338\pi$
$353$	7.69660	0.409649	0.204824	+	0.978799i	$0.434338\pi$
$354$	34.2573	1.82075
$355$	5.32791	0.282776
$356$	−17.5722	−0.931327
$357$	−42.9384	−2.27254
$358$	−14.5997	−0.771620
$359$	8.96066	0.472926	0.236463	−	0.971641i	$-0.424012\pi$
$359$	8.96066	0.472926	0.236463	+	0.971641i	$0.424012\pi$
$360$	0.391031	0.0206092
$361$	14.1679	0.745681
$362$	−20.3897	−1.07166
$363$	−18.7282	−0.982976
$364$	−43.3068	−2.26989
$365$	5.92421	0.310087
$366$	−28.5341	−1.49150
$367$	9.68694	0.505654	0.252827	−	0.967511i	$-0.418640\pi$
$367$	9.68694	0.505654	0.252827	+	0.967511i	$0.418640\pi$
$368$	7.16858	0.373688
$369$	−1.23716	−0.0644038
$370$	21.6490	1.12548
$371$	29.7617	1.54515
$372$	−9.18498	−0.476219
$373$	−33.7237	−1.74615	−0.873074	−	0.487587i	$-0.837877\pi$
$373$	−33.7237	−1.74615	−0.873074	+	0.487587i	$0.837877\pi$
$374$	51.6359	2.67003
$375$	−1.65848	−0.0856436
$376$	15.1280	0.780168
$377$	−11.1345	−0.573458
$378$	−60.2361	−3.09821
$379$	−2.61046	−0.134091	−0.0670453	−	0.997750i	$-0.521357\pi$
$379$	−2.61046	−0.134091	−0.0670453	+	0.997750i	$0.521357\pi$
$380$	−15.6733	−0.804021
$381$	23.3002	1.19370
$382$	−40.6825	−2.08150
$383$	5.91116	0.302046	0.151023	−	0.988530i	$-0.451743\pi$
$383$	5.91116	0.302046	0.151023	+	0.988530i	$0.451743\pi$
$384$	−19.4458	−0.992339
$385$	−24.2872	−1.23779
$386$	−41.4912	−2.11185
$387$	−2.42427	−0.123233
$388$	34.7143	1.76235
$389$	−15.0644	−0.763795	−0.381898	−	0.924205i	$-0.624729\pi$
$389$	−15.0644	−0.763795	−0.381898	+	0.924205i	$0.624729\pi$
$390$	−11.1482	−0.564510
$391$	−17.7157	−0.895921
$392$	−30.5069	−1.54083
$393$	5.54890	0.279905
$394$	−19.0535	−0.959903
$395$	2.59705	0.130672
$396$	3.20515	0.161065
$397$	−19.2634	−0.966802	−0.483401	−	0.875399i	$-0.660599\pi$
$397$	−19.2634	−0.966802	−0.483401	+	0.875399i	$0.660599\pi$
$398$	45.3087	2.27112
$399$	49.1326	2.45971
$400$	−2.03662	−0.101831
$401$	−29.7000	−1.48315	−0.741573	−	0.670872i	$-0.765920\pi$
$401$	−29.7000	−1.48315	−0.741573	+	0.670872i	$0.765920\pi$
$402$	−53.8798	−2.68728
$403$	−6.29541	−0.313597
$404$	−10.0472	−0.499864
$405$	−8.18945	−0.406937
$406$	−40.2303	−1.99660
$407$	47.0412	2.33174
$408$	13.0854	0.647825
$409$	−22.7027	−1.12258	−0.561288	−	0.827621i	$-0.689694\pi$
$409$	−22.7027	−1.12258	−0.561288	+	0.827621i	$0.689694\pi$
$410$	−10.7769	−0.532232
$411$	32.9707	1.62633
$412$	−32.9081	−1.62127
$413$	48.8995	2.40619
$414$	−1.90779	−0.0937626
$415$	0.237227	0.0116450
$416$	−23.3890	−1.14674
$417$	−26.6266	−1.30391
$418$	−59.0847	−2.88993
$419$	18.1219	0.885312	0.442656	−	0.896692i	$-0.354036\pi$
$419$	18.1219	0.885312	0.442656	+	0.896692i	$0.354036\pi$
$420$	−23.2172	−1.13288
$421$	−7.18078	−0.349970	−0.174985	−	0.984571i	$-0.555988\pi$
$421$	−7.18078	−0.349970	−0.174985	+	0.984571i	$0.555988\pi$
$422$	−2.35137	−0.114463
$423$	2.40719	0.117041
$424$	−9.06982	−0.440470
$425$	5.03310	0.244141
$426$	19.2002	0.930251
$427$	−40.7302	−1.97107
$428$	18.8061	0.909026
$429$	−24.2239	−1.16954
$430$	−21.1178	−1.01839
$431$	−4.74168	−0.228399	−0.114199	−	0.993458i	$-0.536430\pi$
$431$	−4.74168	−0.228399	−0.114199	+	0.993458i	$0.536430\pi$
$432$	−10.9756	−0.528065
$433$	−28.5394	−1.37152	−0.685759	−	0.727829i	$-0.740530\pi$
$433$	−28.5394	−1.37152	−0.685759	+	0.727829i	$0.740530\pi$
$434$	−22.7460	−1.09184
$435$	−5.96934	−0.286208
$436$	−9.34140	−0.447372
$437$	20.2713	0.969708
$438$	21.3490	1.02010
$439$	−33.2252	−1.58575	−0.792877	−	0.609382i	$-0.791418\pi$
$439$	−33.2252	−1.58575	−0.792877	+	0.609382i	$0.791418\pi$
$440$	7.40151	0.352853
$441$	−4.85430	−0.231157
$442$	33.8321	1.60923
$443$	22.0024	1.04537	0.522683	−	0.852527i	$-0.324931\pi$
$443$	22.0024	1.04537	0.522683	+	0.852527i	$0.324931\pi$
$444$	44.9687	2.13412
$445$	−6.45695	−0.306089
$446$	−17.8516	−0.845297
$447$	9.45798	0.447347
$448$	−63.5545	−3.00267
$449$	17.6182	0.831456	0.415728	−	0.909489i	$-0.363527\pi$
$449$	17.6182	0.831456	0.415728	+	0.909489i	$0.363527\pi$
$450$	0.542010	0.0255506
$451$	−23.4171	−1.10267
$452$	22.1699	1.04278
$453$	39.9351	1.87631
$454$	37.2952	1.75035
$455$	−15.9131	−0.746020
$456$	−14.9731	−0.701179
$457$	30.6871	1.43548	0.717740	−	0.696311i	$-0.245177\pi$
$457$	30.6871	1.43548	0.717740	+	0.696311i	$0.245177\pi$
$458$	−13.2606	−0.619625
$459$	27.1241	1.26604
$460$	−9.57905	−0.446625
$461$	−10.9502	−0.510000	−0.255000	−	0.966941i	$-0.582075\pi$
$461$	−10.9502	−0.510000	−0.255000	+	0.966941i	$0.582075\pi$
$462$	−87.5238	−4.07198
$463$	−5.33059	−0.247733	−0.123867	−	0.992299i	$-0.539530\pi$
$463$	−5.33059	−0.247733	−0.123867	+	0.992299i	$0.539530\pi$
$464$	−7.33038	−0.340304
$465$	−3.37504	−0.156514
$466$	−13.9368	−0.645608
$467$	−33.8169	−1.56486	−0.782429	−	0.622740i	$-0.786020\pi$
$467$	−33.8169	−1.56486	−0.782429	+	0.622740i	$0.786020\pi$
$468$	2.10003	0.0970739
$469$	−76.9092	−3.55134
$470$	20.9690	0.967228
$471$	−8.55877	−0.394367
$472$	−14.9021	−0.685923
$473$	−45.8870	−2.10989
$474$	9.35896	0.429871
$475$	−5.75916	−0.264248
$476$	70.4588	3.22947
$477$	−1.44320	−0.0660796
$478$	−22.6544	−1.03619
$479$	−16.2798	−0.743842	−0.371921	−	0.928264i	$-0.621301\pi$
$479$	−16.2798	−0.743842	−0.371921	+	0.928264i	$0.621301\pi$
$480$	−12.5391	−0.572329
$481$	30.8217	1.40535
$482$	1.74528	0.0794955
$483$	30.0285	1.36634
$484$	30.7316	1.39689
$485$	12.7558	0.579213
$486$	5.61770	0.254824
$487$	21.6481	0.980970	0.490485	−	0.871450i	$-0.336820\pi$
$487$	21.6481	0.980970	0.490485	+	0.871450i	$0.336820\pi$
$488$	12.4125	0.561887
$489$	28.3735	1.28309
$490$	−42.2858	−1.91028
$491$	−2.08714	−0.0941912	−0.0470956	−	0.998890i	$-0.514997\pi$
$491$	−2.08714	−0.0941912	−0.0470956	+	0.998890i	$0.514997\pi$
$492$	−22.3854	−1.00921
$493$	18.1156	0.815884
$494$	−38.7127	−1.74176
$495$	1.17774	0.0529353
$496$	−4.14456	−0.186096
$497$	27.4067	1.22936
$498$	0.854892	0.0383086
$499$	14.2056	0.635932	0.317966	−	0.948102i	$-0.397000\pi$
$499$	14.2056	0.635932	0.317966	+	0.948102i	$0.397000\pi$
$500$	2.72145	0.121707
$501$	3.66758	0.163855
$502$	25.9846	1.15975
$503$	−21.5456	−0.960669	−0.480334	−	0.877085i	$-0.659485\pi$
$503$	−21.5456	−0.960669	−0.480334	+	0.877085i	$0.659485\pi$
$504$	2.01146	0.0895975
$505$	−3.69184	−0.164285
$506$	−36.1109	−1.60533
$507$	5.68858	0.252639
$508$	−38.2339	−1.69635
$509$	26.3397	1.16749	0.583743	−	0.811939i	$-0.301588\pi$
$509$	26.3397	1.16749	0.583743	+	0.811939i	$0.301588\pi$
$510$	18.1378	0.803153
$511$	30.4741	1.34809
$512$	−21.7834	−0.962699
$513$	−31.0369	−1.37031
$514$	12.3584	0.545107
$515$	−12.0921	−0.532843
$516$	−43.8653	−1.93106
$517$	45.5636	2.00389
$518$	111.362	4.89297
$519$	−2.11741	−0.0929440
$520$	4.84951	0.212665
$521$	13.9791	0.612435	0.306217	−	0.951962i	$-0.400937\pi$
$521$	13.9791	0.612435	0.306217	+	0.951962i	$0.400937\pi$
$522$	1.95085	0.0853863
$523$	−2.74889	−0.120201	−0.0601004	−	0.998192i	$-0.519142\pi$
$523$	−2.74889	−0.120201	−0.0601004	+	0.998192i	$0.519142\pi$
$524$	−9.10534	−0.397769
$525$	−8.53120	−0.372332
$526$	−51.3725	−2.23995
$527$	10.2424	0.446168
$528$	−15.9477	−0.694036
$529$	−10.6107	−0.461337
$530$	−12.5717	−0.546081
$531$	−2.37123	−0.102903
$532$	−80.6230	−3.49545
$533$	−15.3430	−0.664581
$534$	−23.2689	−1.00694
$535$	6.91033	0.298759
$536$	23.4380	1.01237
$537$	−11.1434	−0.480874
$538$	−11.6813	−0.503616
$539$	−91.8829	−3.95768
$540$	14.6662	0.631135
$541$	12.8122	0.550839	0.275420	−	0.961324i	$-0.411183\pi$
$541$	12.8122	0.550839	0.275420	+	0.961324i	$0.411183\pi$
$542$	52.7143	2.26427
$543$	−15.5626	−0.667856
$544$	38.0533	1.63152
$545$	−3.43251	−0.147033
$546$	−57.3461	−2.45419
$547$	−36.0381	−1.54088	−0.770440	−	0.637513i	$-0.779963\pi$
$547$	−36.0381	−1.54088	−0.770440	+	0.637513i	$0.779963\pi$
$548$	−54.1026	−2.31115
$549$	1.97509	0.0842947
$550$	10.2593	0.437456
$551$	−20.7289	−0.883079
$552$	−9.15113	−0.389498
$553$	13.3592	0.568090
$554$	39.4372	1.67553
$555$	16.5238	0.701397
$556$	43.6923	1.85297
$557$	10.0873	0.427414	0.213707	−	0.976898i	$-0.431446\pi$
$557$	10.0873	0.427414	0.213707	+	0.976898i	$0.431446\pi$
$558$	1.10300	0.0466937
$559$	−30.0654	−1.27163
$560$	−10.4764	−0.442707
$561$	39.4116	1.66396
$562$	−21.2713	−0.897276
$563$	−20.9985	−0.884980	−0.442490	−	0.896773i	$-0.645905\pi$
$563$	−20.9985	−0.884980	−0.442490	+	0.896773i	$0.645905\pi$
$564$	43.5562	1.83405
$565$	8.14635	0.342720
$566$	72.2271	3.03593
$567$	−42.1264	−1.76914
$568$	−8.35216	−0.350449
$569$	−4.70847	−0.197389	−0.0986947	−	0.995118i	$-0.531467\pi$
$569$	−4.70847	−0.197389	−0.0986947	+	0.995118i	$0.531467\pi$
$570$	−20.7543	−0.869300
$571$	24.2959	1.01675	0.508375	−	0.861136i	$-0.330246\pi$
$571$	24.2959	1.01675	0.508375	+	0.861136i	$0.330246\pi$
$572$	39.7497	1.66202
$573$	−31.0513	−1.29719
$574$	−55.4361	−2.31386
$575$	−3.51984	−0.146787
$576$	3.08188	0.128412
$577$	23.1272	0.962798	0.481399	−	0.876502i	$-0.340129\pi$
$577$	23.1272	0.962798	0.481399	+	0.876502i	$0.340129\pi$
$578$	−18.1047	−0.753057
$579$	−31.6686	−1.31610
$580$	9.79526	0.406726
$581$	1.22029	0.0506262
$582$	45.9681	1.90544
$583$	−27.3171	−1.13136
$584$	−9.28693	−0.384296
$585$	0.771660	0.0319042
$586$	44.9605	1.85730
$587$	9.80329	0.404625	0.202313	−	0.979321i	$-0.435154\pi$
$587$	9.80329	0.404625	0.202313	+	0.979321i	$0.435154\pi$
$588$	−87.8348	−3.62225
$589$	−11.7200	−0.482914
$590$	−20.6558	−0.850386
$591$	−14.5428	−0.598211
$592$	20.2913	0.833968
$593$	30.3923	1.24806	0.624031	−	0.781400i	$-0.285494\pi$
$593$	30.3923	1.24806	0.624031	+	0.781400i	$0.285494\pi$
$594$	55.2885	2.26852
$595$	25.8902	1.06140
$596$	−15.5199	−0.635718
$597$	34.5823	1.41536
$598$	−23.6601	−0.967533
$599$	−42.0499	−1.71811	−0.859056	−	0.511882i	$-0.828949\pi$
$599$	−42.0499	−1.71811	−0.859056	+	0.511882i	$0.828949\pi$
$600$	2.59987	0.106139
$601$	14.6082	0.595882	0.297941	−	0.954584i	$-0.403700\pi$
$601$	14.6082	0.595882	0.297941	+	0.954584i	$0.403700\pi$
$602$	−108.630	−4.42742
$603$	3.72948	0.151876
$604$	−65.5306	−2.66640
$605$	11.2924	0.459101
$606$	−13.3043	−0.540449
$607$	27.3753	1.11113	0.555565	−	0.831473i	$-0.312502\pi$
$607$	27.3753	1.11113	0.555565	+	0.831473i	$0.312502\pi$
$608$	−43.5427	−1.76589
$609$	−30.7062	−1.24428
$610$	17.2050	0.696610
$611$	29.8536	1.20775
$612$	−3.41669	−0.138111
$613$	46.9962	1.89816	0.949080	−	0.315034i	$-0.102016\pi$
$613$	46.9962	1.89816	0.949080	+	0.315034i	$0.102016\pi$
$614$	43.7042	1.76376
$615$	−8.22556	−0.331687
$616$	38.0733	1.53402
$617$	29.4541	1.18578	0.592888	−	0.805285i	$-0.297988\pi$
$617$	29.4541	1.18578	0.592888	+	0.805285i	$0.297988\pi$
$618$	−43.5764	−1.75290
$619$	−31.5180	−1.26682	−0.633408	−	0.773818i	$-0.718345\pi$
$619$	−31.5180	−1.26682	−0.633408	+	0.773818i	$0.718345\pi$
$620$	5.53819	0.222419
$621$	−18.9689	−0.761195
$622$	−29.7720	−1.19375
$623$	−33.2145	−1.33071
$624$	−10.4491	−0.418297
$625$	1.00000	0.0400000
$626$	37.0626	1.48132
$627$	−45.0970	−1.80100
$628$	14.0443	0.560429
$629$	−50.1459	−1.99945
$630$	2.78809	0.111080
$631$	20.0465	0.798040	0.399020	−	0.916942i	$-0.369350\pi$
$631$	20.0465	0.798040	0.399020	+	0.916942i	$0.369350\pi$
$632$	−4.07119	−0.161943
$633$	−1.79471	−0.0713332
$634$	36.3339	1.44300
$635$	−14.0491	−0.557522
$636$	−26.1136	−1.03547
$637$	−60.2022	−2.38530
$638$	36.9260	1.46191
$639$	−1.32901	−0.0525746
$640$	11.7251	0.463474
$641$	−23.8352	−0.941433	−0.470717	−	0.882284i	$-0.656005\pi$
$641$	−23.8352	−0.941433	−0.470717	+	0.882284i	$0.656005\pi$
$642$	24.9027	0.982831
$643$	−20.9241	−0.825165	−0.412583	−	0.910920i	$-0.635373\pi$
$643$	−20.9241	−0.825165	−0.412583	+	0.910920i	$0.635373\pi$
$644$	−49.2745	−1.94169
$645$	−16.1184	−0.634661
$646$	62.9843	2.47808
$647$	−3.41499	−0.134257	−0.0671286	−	0.997744i	$-0.521384\pi$
$647$	−3.41499	−0.134257	−0.0671286	+	0.997744i	$0.521384\pi$
$648$	12.8380	0.504323
$649$	−44.8831	−1.76182
$650$	6.72193	0.263656
$651$	−17.3611	−0.680437
$652$	−46.5588	−1.82338
$653$	−38.1585	−1.49326	−0.746629	−	0.665241i	$-0.768329\pi$
$653$	−38.1585	−1.49326	−0.746629	+	0.665241i	$0.768329\pi$
$654$	−12.3697	−0.483694
$655$	−3.34577	−0.130730
$656$	−10.1010	−0.394379
$657$	−1.47775	−0.0576524
$658$	107.864	4.20499
$659$	−43.1664	−1.68153	−0.840763	−	0.541404i	$-0.817893\pi$
$659$	−43.1664	−1.68153	−0.840763	+	0.541404i	$0.817893\pi$
$660$	21.3102	0.829500
$661$	−26.9350	−1.04765	−0.523825	−	0.851826i	$-0.675495\pi$
$661$	−26.9350	−1.04765	−0.523825	+	0.851826i	$0.675495\pi$
$662$	−60.6742	−2.35817
$663$	25.8227	1.00287
$664$	−0.371882	−0.0144318
$665$	−29.6251	−1.14881
$666$	−5.40017	−0.209252
$667$	−12.6689	−0.490542
$668$	−6.01823	−0.232852
$669$	−13.6254	−0.526789
$670$	32.4875	1.25510
$671$	37.3848	1.44322
$672$	−64.5010	−2.48818
$673$	−34.9664	−1.34786	−0.673928	−	0.738797i	$-0.735394\pi$
$673$	−34.9664	−1.34786	−0.673928	+	0.738797i	$0.735394\pi$
$674$	77.0844	2.96918
$675$	5.38914	0.207428
$676$	−9.33454	−0.359021
$677$	18.0394	0.693311	0.346655	−	0.937993i	$-0.387317\pi$
$677$	18.0394	0.693311	0.346655	+	0.937993i	$0.387317\pi$
$678$	29.3570	1.12745
$679$	65.6159	2.51811
$680$	−7.89001	−0.302568
$681$	28.4660	1.09082
$682$	20.8778	0.799451
$683$	2.82424	0.108066	0.0540332	−	0.998539i	$-0.482792\pi$
$683$	2.82424	0.108066	0.0540332	+	0.998539i	$0.482792\pi$
$684$	3.90957	0.149486
$685$	−19.8801	−0.759579
$686$	−139.276	−5.31759
$687$	−10.1213	−0.386150
$688$	−19.7934	−0.754618
$689$	−17.8984	−0.681873
$690$	−12.6844	−0.482888
$691$	36.7341	1.39743	0.698715	−	0.715400i	$-0.253756\pi$
$691$	36.7341	1.39743	0.698715	+	0.715400i	$0.253756\pi$
$692$	3.47452	0.132081
$693$	6.05826	0.230134
$694$	15.0798	0.572421
$695$	16.0548	0.608994
$696$	9.35768	0.354702
$697$	24.9627	0.945528
$698$	−34.7578	−1.31560
$699$	−10.6374	−0.402343
$700$	13.9991	0.529116
$701$	−41.3366	−1.56126	−0.780632	−	0.624991i	$-0.785102\pi$
$701$	−41.3366	−1.56126	−0.780632	+	0.624991i	$0.785102\pi$
$702$	36.2254	1.36724
$703$	57.3798	2.16412
$704$	58.3344	2.19856
$705$	16.0048	0.602776
$706$	−16.7239	−0.629411
$707$	−18.9908	−0.714222
$708$	−42.9057	−1.61249
$709$	51.3956	1.93020	0.965102	−	0.261874i	$-0.0843406\pi$
$709$	51.3956	1.93020	0.965102	+	0.261874i	$0.0843406\pi$
$710$	−11.5770	−0.434476
$711$	−0.647813	−0.0242949
$712$	10.1221	0.379340
$713$	−7.16293	−0.268254
$714$	93.3004	3.49168
$715$	14.6061	0.546237
$716$	18.2855	0.683362
$717$	−17.2912	−0.645751
$718$	−19.4705	−0.726634
$719$	−14.7104	−0.548605	−0.274302	−	0.961643i	$-0.588447\pi$
$719$	−14.7104	−0.548605	−0.274302	+	0.961643i	$0.588447\pi$
$720$	0.508019	0.0189327
$721$	−62.2018	−2.31652
$722$	−30.7854	−1.14571
$723$	1.33211	0.0495416
$724$	25.5371	0.949081
$725$	3.59928	0.133674
$726$	40.6943	1.51031
$727$	27.5968	1.02351	0.511754	−	0.859132i	$-0.328996\pi$
$727$	27.5968	1.02351	0.511754	+	0.859132i	$0.328996\pi$
$728$	24.9458	0.924554
$729$	28.8561	1.06875
$730$	−12.8727	−0.476438
$731$	48.9155	1.80921
$732$	35.7377	1.32090
$733$	−15.9738	−0.590007	−0.295004	−	0.955496i	$-0.595321\pi$
$733$	−15.9738	−0.590007	−0.295004	+	0.955496i	$0.595321\pi$
$734$	−21.0486	−0.776920
$735$	−32.2751	−1.19048
$736$	−26.6121	−0.980934
$737$	70.5922	2.60030
$738$	2.68820	0.0989542
$739$	−31.7848	−1.16922	−0.584612	−	0.811313i	$-0.698753\pi$
$739$	−31.7848	−1.16922	−0.584612	+	0.811313i	$0.698753\pi$
$740$	−27.1144	−0.996745
$741$	−29.5478	−1.08547
$742$	−64.6688	−2.37407
$743$	48.1710	1.76722	0.883611	−	0.468221i	$-0.155105\pi$
$743$	48.1710	1.76722	0.883611	+	0.468221i	$0.155105\pi$
$744$	5.29079	0.193970
$745$	−5.70280	−0.208934
$746$	73.2779	2.68290
$747$	−0.0591743	−0.00216507
$748$	−64.6716	−2.36463
$749$	35.5466	1.29885
$750$	3.60369	0.131588
$751$	−18.3076	−0.668052	−0.334026	−	0.942564i	$-0.608407\pi$
$751$	−18.3076	−0.668052	−0.334026	+	0.942564i	$0.608407\pi$
$752$	19.6540	0.716707
$753$	19.8330	0.722755
$754$	24.1941	0.881098
$755$	−24.0793	−0.876336
$756$	75.4430	2.74384
$757$	−18.8775	−0.686115	−0.343057	−	0.939314i	$-0.611463\pi$
$757$	−18.8775	−0.686115	−0.343057	+	0.939314i	$0.611463\pi$
$758$	5.67225	0.206025
$759$	−27.5620	−1.00044
$760$	9.02820	0.327487
$761$	30.9315	1.12126	0.560632	−	0.828065i	$-0.310558\pi$
$761$	30.9315	1.12126	0.560632	+	0.828065i	$0.310558\pi$
$762$	−50.6287	−1.83408
$763$	−17.6568	−0.639219
$764$	50.9530	1.84341
$765$	−1.25547	−0.0453915
$766$	−12.8443	−0.464083
$767$	−29.4077	−1.06185
$768$	1.27215	0.0459049
$769$	46.3252	1.67053	0.835265	−	0.549847i	$-0.185314\pi$
$769$	46.3252	1.67053	0.835265	+	0.549847i	$0.185314\pi$
$770$	52.7735	1.90182
$771$	9.43271	0.339711
$772$	51.9659	1.87029
$773$	29.6219	1.06543	0.532713	−	0.846296i	$-0.321173\pi$
$773$	29.6219	1.06543	0.532713	+	0.846296i	$0.321173\pi$
$774$	5.26767	0.189342
$775$	2.03502	0.0731000
$776$	−19.9963	−0.717827
$777$	84.9983	3.04930
$778$	32.7333	1.17354
$779$	−28.5637	−1.02340
$780$	13.9626	0.499941
$781$	−25.1556	−0.900140
$782$	38.4942	1.37655
$783$	19.3970	0.693193
$784$	−39.6339	−1.41550
$785$	5.16061	0.184190
$786$	−12.0571	−0.430064
$787$	−8.45185	−0.301276	−0.150638	−	0.988589i	$-0.548133\pi$
$787$	−8.45185	−0.301276	−0.150638	+	0.988589i	$0.548133\pi$
$788$	23.8637	0.850109
$789$	−39.2106	−1.39594
$790$	−5.64309	−0.200772
$791$	41.9047	1.48996
$792$	−1.84625	−0.0656035
$793$	24.4947	0.869834
$794$	41.8572	1.48546
$795$	−9.59550	−0.340317
$796$	−56.7471	−2.01135
$797$	−49.5424	−1.75488	−0.877441	−	0.479684i	$-0.840751\pi$
$797$	−49.5424	−1.75488	−0.877441	+	0.479684i	$0.840751\pi$
$798$	−106.760	−3.77925
$799$	−48.5708	−1.71831
$800$	7.56060	0.267308
$801$	1.61063	0.0569090
$802$	64.5347	2.27880
$803$	−27.9711	−0.987077
$804$	67.4821	2.37991
$805$	−18.1060	−0.638153
$806$	13.6792	0.481830
$807$	−8.91587	−0.313853
$808$	5.78742	0.203601
$809$	1.81099	0.0636710	0.0318355	−	0.999493i	$-0.489865\pi$
$809$	1.81099	0.0636710	0.0318355	+	0.999493i	$0.489865\pi$
$810$	17.7948	0.625245
$811$	−23.7035	−0.832342	−0.416171	−	0.909286i	$-0.636628\pi$
$811$	−23.7035	−0.832342	−0.416171	+	0.909286i	$0.636628\pi$
$812$	50.3867	1.76823
$813$	40.2347	1.41109
$814$	−102.215	−3.58264
$815$	−17.1081	−0.599271
$816$	17.0003	0.595129
$817$	−55.9720	−1.95821
$818$	49.3304	1.72480
$819$	3.96941	0.138702
$820$	13.4975	0.471355
$821$	−23.9705	−0.836576	−0.418288	−	0.908314i	$-0.637370\pi$
$821$	−23.9705	−0.836576	−0.418288	+	0.908314i	$0.637370\pi$
$822$	−71.6417	−2.49879
$823$	20.8609	0.727165	0.363583	−	0.931562i	$-0.381553\pi$
$823$	20.8609	0.727165	0.363583	+	0.931562i	$0.381553\pi$
$824$	18.9559	0.660361
$825$	7.83049	0.272623
$826$	−106.253	−3.69702
$827$	3.62504	0.126055	0.0630275	−	0.998012i	$-0.479924\pi$
$827$	3.62504	0.126055	0.0630275	+	0.998012i	$0.479924\pi$
$828$	2.38942	0.0830380
$829$	13.4487	0.467091	0.233546	−	0.972346i	$-0.424967\pi$
$829$	13.4487	0.467091	0.233546	+	0.972346i	$0.424967\pi$
$830$	−0.515467	−0.0178921
$831$	30.1009	1.04419
$832$	38.2210	1.32508
$833$	97.9472	3.39367
$834$	57.8566	2.00341
$835$	−2.21141	−0.0765290
$836$	74.0010	2.55938
$837$	10.9670	0.379074
$838$	−39.3768	−1.36025
$839$	1.94241	0.0670593	0.0335296	−	0.999438i	$-0.489325\pi$
$839$	1.94241	0.0670593	0.0335296	+	0.999438i	$0.489325\pi$
$840$	13.3737	0.461437
$841$	−16.0452	−0.553281
$842$	15.6030	0.537716
$843$	−16.2355	−0.559182
$844$	2.94498	0.101370
$845$	−3.42999	−0.117995
$846$	−5.23055	−0.179830
$847$	58.0879	1.99592
$848$	−11.7833	−0.404641
$849$	55.1281	1.89199
$850$	−10.9364	−0.375114
$851$	35.0689	1.20215
$852$	−24.0474	−0.823849
$853$	31.2717	1.07072	0.535362	−	0.844623i	$-0.320175\pi$
$853$	31.2717	1.07072	0.535362	+	0.844623i	$0.320175\pi$
$854$	88.5023	3.02848
$855$	1.43658	0.0491299
$856$	−10.8328	−0.370257
$857$	−13.5760	−0.463746	−0.231873	−	0.972746i	$-0.574485\pi$
$857$	−13.5760	−0.463746	−0.231873	+	0.972746i	$0.574485\pi$
$858$	52.6359	1.79696
$859$	−53.0364	−1.80958	−0.904789	−	0.425861i	$-0.859971\pi$
$859$	−53.0364	−1.80958	−0.904789	+	0.425861i	$0.859971\pi$
$860$	26.4491	0.901907
$861$	−42.3122	−1.44200
$862$	10.3032	0.350927
$863$	−26.6335	−0.906614	−0.453307	−	0.891355i	$-0.649756\pi$
$863$	−26.6335	−0.906614	−0.453307	+	0.891355i	$0.649756\pi$
$864$	40.7451	1.38618
$865$	1.27672	0.0434097
$866$	62.0130	2.10729
$867$	−13.8186	−0.469305
$868$	28.4884	0.966959
$869$	−12.2619	−0.415957
$870$	12.9707	0.439749
$871$	46.2524	1.56720
$872$	5.38088	0.182220
$873$	−3.18184	−0.107689
$874$	−44.0473	−1.48992
$875$	5.14399	0.173899
$876$	−26.7387	−0.903418
$877$	12.3589	0.417332	0.208666	−	0.977987i	$-0.433088\pi$
$877$	12.3589	0.417332	0.208666	+	0.977987i	$0.433088\pi$
$878$	72.1947	2.43645
$879$	34.3166	1.15747
$880$	9.61587	0.324151
$881$	−39.0240	−1.31475	−0.657376	−	0.753563i	$-0.728334\pi$
$881$	−39.0240	−1.31475	−0.657376	+	0.753563i	$0.728334\pi$
$882$	10.5478	0.355164
$883$	−44.8497	−1.50931	−0.754656	−	0.656121i	$-0.772196\pi$
$883$	−44.8497	−1.50931	−0.754656	+	0.656121i	$0.772196\pi$
$884$	−42.3732	−1.42517
$885$	−15.7658	−0.529960
$886$	−47.8088	−1.60617
$887$	−39.3084	−1.31985	−0.659923	−	0.751333i	$-0.729411\pi$
$887$	−39.3084	−1.31985	−0.659923	+	0.751333i	$0.729411\pi$
$888$	−25.9031	−0.869252
$889$	−72.2684	−2.42381
$890$	14.0302	0.470294
$891$	38.6663	1.29537
$892$	22.3583	0.748612
$893$	55.5775	1.85983
$894$	−20.5511	−0.687333
$895$	6.71905	0.224593
$896$	60.3136	2.01494
$897$	−18.0588	−0.602966
$898$	−38.2825	−1.27750
$899$	7.32460	0.244289
$900$	−0.678843	−0.0226281
$901$	29.1201	0.970131
$902$	50.8828	1.69421
$903$	−82.9128	−2.75916
$904$	−12.7704	−0.424738
$905$	9.38367	0.311924
$906$	−86.7745	−2.88289
$907$	−48.3209	−1.60447	−0.802234	−	0.597010i	$-0.796355\pi$
$907$	−48.3209	−1.60447	−0.802234	+	0.597010i	$0.796355\pi$
$908$	−46.7106	−1.55015
$909$	0.920900	0.0305443
$910$	34.5775	1.14623
$911$	−30.6008	−1.01385	−0.506926	−	0.861990i	$-0.669218\pi$
$911$	−30.6008	−1.01385	−0.506926	+	0.861990i	$0.669218\pi$
$912$	−19.4527	−0.644143
$913$	−1.12006	−0.0370686
$914$	−66.6796	−2.20557
$915$	13.1319	0.434127
$916$	16.6083	0.548752
$917$	−17.2106	−0.568344
$918$	−58.9376	−1.94523
$919$	53.6270	1.76899	0.884495	−	0.466549i	$-0.154503\pi$
$919$	53.6270	1.76899	0.884495	+	0.466549i	$0.154503\pi$
$920$	5.51778	0.181916
$921$	33.3577	1.09917
$922$	23.7935	0.783597
$923$	−16.4821	−0.542516
$924$	109.620	3.60622
$925$	−9.96323	−0.327589
$926$	11.5828	0.380634
$927$	3.01629	0.0990679
$928$	27.2127	0.893302
$929$	48.7899	1.60074	0.800372	−	0.599504i	$-0.204635\pi$
$929$	48.7899	1.60074	0.800372	+	0.599504i	$0.204635\pi$
$930$	7.33358	0.240477
$931$	−112.077	−3.67317
$932$	17.4552	0.571763
$933$	−22.7238	−0.743944
$934$	73.4803	2.40435
$935$	−23.7637	−0.777156
$936$	−1.20967	−0.0395394
$937$	40.0896	1.30967	0.654834	−	0.755773i	$-0.272738\pi$
$937$	40.0896	1.30967	0.654834	+	0.755773i	$0.272738\pi$
$938$	167.115	5.45650
$939$	28.2884	0.923157
$940$	−26.2627	−0.856596
$941$	−51.2003	−1.66908	−0.834541	−	0.550946i	$-0.814267\pi$
$941$	−51.2003	−1.66908	−0.834541	+	0.550946i	$0.814267\pi$
$942$	18.5973	0.605931
$943$	−17.4573	−0.568489
$944$	−19.3604	−0.630128
$945$	27.7217	0.901786
$946$	99.7073	3.24176
$947$	−1.36140	−0.0442397	−0.0221199	−	0.999755i	$-0.507042\pi$
$947$	−1.36140	−0.0442397	−0.0221199	+	0.999755i	$0.507042\pi$
$948$	−11.7217	−0.380703
$949$	−18.3268	−0.594913
$950$	12.5140	0.406008
$951$	27.7322	0.899280
$952$	−40.5861	−1.31540
$953$	−12.5656	−0.407041	−0.203520	−	0.979071i	$-0.565238\pi$
$953$	−12.5656	−0.407041	−0.203520	+	0.979071i	$0.565238\pi$
$954$	3.13591	0.101529
$955$	18.7228	0.605854
$956$	28.3736	0.917667
$957$	28.1841	0.911064
$958$	35.3741	1.14289
$959$	−102.263	−3.30224
$960$	20.4907	0.661334
$961$	−26.8587	−0.866410
$962$	−66.9721	−2.15927
$963$	−1.72373	−0.0555463
$964$	−2.18589	−0.0704028
$965$	19.0949	0.614688
$966$	−65.2485	−2.09934
$967$	3.27273	0.105244	0.0526219	−	0.998615i	$-0.483242\pi$
$967$	3.27273	0.105244	0.0526219	+	0.998615i	$0.483242\pi$
$968$	−17.7022	−0.568971
$969$	48.0734	1.54434
$970$	−27.7170	−0.889940
$971$	−23.4955	−0.754007	−0.377003	−	0.926212i	$-0.623046\pi$
$971$	−23.4955	−0.754007	−0.377003	+	0.926212i	$0.623046\pi$
$972$	−7.03592	−0.225677
$973$	82.5858	2.64758
$974$	−47.0390	−1.50723
$975$	5.13058	0.164310
$976$	16.1260	0.516181
$977$	27.3928	0.876375	0.438187	−	0.898884i	$-0.355621\pi$
$977$	27.3928	0.876375	0.438187	+	0.898884i	$0.355621\pi$
$978$	−61.6524	−1.97143
$979$	30.4864	0.974348
$980$	52.9610	1.69178
$981$	0.856213	0.0273368
$982$	4.53512	0.144721
$983$	−28.2423	−0.900791	−0.450395	−	0.892829i	$-0.648717\pi$
$983$	−28.2423	−0.900791	−0.450395	+	0.892829i	$0.648717\pi$
$984$	12.8946	0.411064
$985$	8.76876	0.279396
$986$	−39.3631	−1.25358
$987$	82.3285	2.62055
$988$	48.4859	1.54254
$989$	−34.2085	−1.08777
$990$	−2.55909	−0.0813332
$991$	23.1669	0.735920	0.367960	−	0.929842i	$-0.380056\pi$
$991$	23.1669	0.735920	0.367960	+	0.929842i	$0.380056\pi$
$992$	15.3859	0.488504
$993$	−46.3102	−1.46961
$994$	−59.5518	−1.88887
$995$	−20.8518	−0.661047
$996$	−1.07071	−0.0339269
$997$	−32.0304	−1.01441	−0.507207	−	0.861824i	$-0.669322\pi$
$997$	−32.0304	−1.01441	−0.507207	+	0.861824i	$0.669322\pi$
$998$	−30.8673	−0.977087
$999$	−53.6932	−1.69878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.15	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.15	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17289 q^{2} -1.65848 q^{3} +2.72145 q^{4} +1.00000 q^{5} +3.60369 q^{6} +5.14399 q^{7} -1.56762 q^{8} -0.249442 q^{9} +O(q^{10})\)	\(q-2.17289 q^{2} -1.65848 q^{3} +2.72145 q^{4} +1.00000 q^{5} +3.60369 q^{6} +5.14399 q^{7} -1.56762 q^{8} -0.249442 q^{9} -2.17289 q^{10} -4.72148 q^{11} -4.51347 q^{12} -3.09354 q^{13} -11.1773 q^{14} -1.65848 q^{15} -2.03662 q^{16} +5.03310 q^{17} +0.542010 q^{18} -5.75916 q^{19} +2.72145 q^{20} -8.53120 q^{21} +10.2593 q^{22} -3.51984 q^{23} +2.59987 q^{24} +1.00000 q^{25} +6.72193 q^{26} +5.38914 q^{27} +13.9991 q^{28} +3.59928 q^{29} +3.60369 q^{30} +2.03502 q^{31} +7.56060 q^{32} +7.83049 q^{33} -10.9364 q^{34} +5.14399 q^{35} -0.678843 q^{36} -9.96323 q^{37} +12.5140 q^{38} +5.13058 q^{39} -1.56762 q^{40} +4.95970 q^{41} +18.5374 q^{42} +9.71877 q^{43} -12.8493 q^{44} -0.249442 q^{45} +7.64822 q^{46} -9.65028 q^{47} +3.37770 q^{48} +19.4606 q^{49} -2.17289 q^{50} -8.34730 q^{51} -8.41891 q^{52} +5.78572 q^{53} -11.7100 q^{54} -4.72148 q^{55} -8.06384 q^{56} +9.55146 q^{57} -7.82084 q^{58} +9.50615 q^{59} -4.51347 q^{60} -7.91802 q^{61} -4.42187 q^{62} -1.28313 q^{63} -12.3551 q^{64} -3.09354 q^{65} -17.0148 q^{66} -14.9513 q^{67} +13.6973 q^{68} +5.83758 q^{69} -11.1773 q^{70} +5.32791 q^{71} +0.391031 q^{72} +5.92421 q^{73} +21.6490 q^{74} -1.65848 q^{75} -15.6733 q^{76} -24.2872 q^{77} -11.1482 q^{78} +2.59705 q^{79} -2.03662 q^{80} -8.18945 q^{81} -10.7769 q^{82} +0.237227 q^{83} -23.2172 q^{84} +5.03310 q^{85} -21.1178 q^{86} -5.96934 q^{87} +7.40151 q^{88} -6.45695 q^{89} +0.542010 q^{90} -15.9131 q^{91} -9.57905 q^{92} -3.37504 q^{93} +20.9690 q^{94} -5.75916 q^{95} -12.5391 q^{96} +12.7558 q^{97} -42.2858 q^{98} +1.17774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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