LMFDB - Embedded newform 6026.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.90304 q^{3} +1.00000 q^{4} -1.99628 q^{5} +2.90304 q^{6} -0.299170 q^{7} -1.00000 q^{8} +5.42764 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.90304 q^{3} +1.00000 q^{4} -1.99628 q^{5} +2.90304 q^{6} -0.299170 q^{7} -1.00000 q^{8} +5.42764 q^{9} +1.99628 q^{10} -4.57182 q^{11} -2.90304 q^{12} +2.85877 q^{13} +0.299170 q^{14} +5.79529 q^{15} +1.00000 q^{16} +2.21261 q^{17} -5.42764 q^{18} +5.38569 q^{19} -1.99628 q^{20} +0.868502 q^{21} +4.57182 q^{22} +1.00000 q^{23} +2.90304 q^{24} -1.01486 q^{25} -2.85877 q^{26} -7.04752 q^{27} -0.299170 q^{28} -5.80165 q^{29} -5.79529 q^{30} +7.60900 q^{31} -1.00000 q^{32} +13.2722 q^{33} -2.21261 q^{34} +0.597228 q^{35} +5.42764 q^{36} -1.64867 q^{37} -5.38569 q^{38} -8.29913 q^{39} +1.99628 q^{40} +0.356204 q^{41} -0.868502 q^{42} +11.6690 q^{43} -4.57182 q^{44} -10.8351 q^{45} -1.00000 q^{46} -1.51400 q^{47} -2.90304 q^{48} -6.91050 q^{49} +1.01486 q^{50} -6.42330 q^{51} +2.85877 q^{52} +8.03418 q^{53} +7.04752 q^{54} +9.12665 q^{55} +0.299170 q^{56} -15.6349 q^{57} +5.80165 q^{58} +5.74589 q^{59} +5.79529 q^{60} +8.87265 q^{61} -7.60900 q^{62} -1.62379 q^{63} +1.00000 q^{64} -5.70692 q^{65} -13.2722 q^{66} -15.2925 q^{67} +2.21261 q^{68} -2.90304 q^{69} -0.597228 q^{70} -6.00154 q^{71} -5.42764 q^{72} +0.198540 q^{73} +1.64867 q^{74} +2.94617 q^{75} +5.38569 q^{76} +1.36775 q^{77} +8.29913 q^{78} -10.4857 q^{79} -1.99628 q^{80} +4.17633 q^{81} -0.356204 q^{82} +14.8972 q^{83} +0.868502 q^{84} -4.41700 q^{85} -11.6690 q^{86} +16.8424 q^{87} +4.57182 q^{88} -12.9109 q^{89} +10.8351 q^{90} -0.855258 q^{91} +1.00000 q^{92} -22.0892 q^{93} +1.51400 q^{94} -10.7514 q^{95} +2.90304 q^{96} -10.0001 q^{97} +6.91050 q^{98} -24.8142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.90304	−1.67607	−0.838035	−	0.545616i	$-0.816296\pi$
$3$	−2.90304	−1.67607	−0.838035	+	0.545616i	$0.816296\pi$
$4$	1.00000	0.500000
$5$	−1.99628	−0.892765	−0.446382	−	0.894842i	$-0.647288\pi$
$5$	−1.99628	−0.892765	−0.446382	+	0.894842i	$0.647288\pi$
$6$	2.90304	1.18516
$7$	−0.299170	−0.113076	−0.0565378	−	0.998400i	$-0.518006\pi$
$7$	−0.299170	−0.113076	−0.0565378	+	0.998400i	$0.518006\pi$
$8$	−1.00000	−0.353553
$9$	5.42764	1.80921
$10$	1.99628	0.631280
$11$	−4.57182	−1.37846	−0.689228	−	0.724544i	$-0.742050\pi$
$11$	−4.57182	−1.37846	−0.689228	+	0.724544i	$0.742050\pi$
$12$	−2.90304	−0.838035
$13$	2.85877	0.792881	0.396440	−	0.918061i	$-0.370245\pi$
$13$	2.85877	0.792881	0.396440	+	0.918061i	$0.370245\pi$
$14$	0.299170	0.0799565
$15$	5.79529	1.49634
$16$	1.00000	0.250000
$17$	2.21261	0.536637	0.268319	−	0.963330i	$-0.413532\pi$
$17$	2.21261	0.536637	0.268319	+	0.963330i	$0.413532\pi$
$18$	−5.42764	−1.27931
$19$	5.38569	1.23556	0.617781	−	0.786350i	$-0.288032\pi$
$19$	5.38569	1.23556	0.617781	+	0.786350i	$0.288032\pi$
$20$	−1.99628	−0.446382
$21$	0.868502	0.189523
$22$	4.57182	0.974716
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.90304	0.592580
$25$	−1.01486	−0.202971
$26$	−2.85877	−0.560651
$27$	−7.04752	−1.35630
$28$	−0.299170	−0.0565378
$29$	−5.80165	−1.07734	−0.538670	−	0.842517i	$-0.681073\pi$
$29$	−5.80165	−1.07734	−0.538670	+	0.842517i	$0.681073\pi$
$30$	−5.79529	−1.05807
$31$	7.60900	1.36662	0.683308	−	0.730130i	$-0.260540\pi$
$31$	7.60900	1.36662	0.683308	+	0.730130i	$0.260540\pi$
$32$	−1.00000	−0.176777
$33$	13.2722	2.31039
$34$	−2.21261	−0.379460
$35$	0.597228	0.100950
$36$	5.42764	0.904606
$37$	−1.64867	−0.271040	−0.135520	−	0.990775i	$-0.543270\pi$
$37$	−1.64867	−0.271040	−0.135520	+	0.990775i	$0.543270\pi$
$38$	−5.38569	−0.873675
$39$	−8.29913	−1.32892
$40$	1.99628	0.315640
$41$	0.356204	0.0556297	0.0278149	−	0.999613i	$-0.491145\pi$
$41$	0.356204	0.0556297	0.0278149	+	0.999613i	$0.491145\pi$
$42$	−0.868502	−0.134013
$43$	11.6690	1.77951	0.889756	−	0.456437i	$-0.150875\pi$
$43$	11.6690	1.77951	0.889756	+	0.456437i	$0.150875\pi$
$44$	−4.57182	−0.689228
$45$	−10.8351	−1.61520
$46$	−1.00000	−0.147442
$47$	−1.51400	−0.220840	−0.110420	−	0.993885i	$-0.535220\pi$
$47$	−1.51400	−0.220840	−0.110420	+	0.993885i	$0.535220\pi$
$48$	−2.90304	−0.419018
$49$	−6.91050	−0.987214
$50$	1.01486	0.143522
$51$	−6.42330	−0.899442
$52$	2.85877	0.396440
$53$	8.03418	1.10358	0.551790	−	0.833983i	$-0.313945\pi$
$53$	8.03418	1.10358	0.551790	+	0.833983i	$0.313945\pi$
$54$	7.04752	0.959046
$55$	9.12665	1.23064
$56$	0.299170	0.0399783
$57$	−15.6349	−2.07089
$58$	5.80165	0.761794
$59$	5.74589	0.748052	0.374026	−	0.927418i	$-0.377977\pi$
$59$	5.74589	0.748052	0.374026	+	0.927418i	$0.377977\pi$
$60$	5.79529	0.748168
$61$	8.87265	1.13603	0.568013	−	0.823020i	$-0.307712\pi$
$61$	8.87265	1.13603	0.568013	+	0.823020i	$0.307712\pi$
$62$	−7.60900	−0.966344
$63$	−1.62379	−0.204578
$64$	1.00000	0.125000
$65$	−5.70692	−0.707856
$66$	−13.2722	−1.63369
$67$	−15.2925	−1.86827	−0.934136	−	0.356916i	$-0.883828\pi$
$67$	−15.2925	−1.86827	−0.934136	+	0.356916i	$0.883828\pi$
$68$	2.21261	0.268319
$69$	−2.90304	−0.349485
$70$	−0.597228	−0.0713823
$71$	−6.00154	−0.712252	−0.356126	−	0.934438i	$-0.615903\pi$
$71$	−6.00154	−0.712252	−0.356126	+	0.934438i	$0.615903\pi$
$72$	−5.42764	−0.639653
$73$	0.198540	0.0232374	0.0116187	−	0.999933i	$-0.496302\pi$
$73$	0.198540	0.0232374	0.0116187	+	0.999933i	$0.496302\pi$
$74$	1.64867	0.191654
$75$	2.94617	0.340194
$76$	5.38569	0.617781
$77$	1.36775	0.155870
$78$	8.29913	0.939691
$79$	−10.4857	−1.17973	−0.589864	−	0.807503i	$-0.700819\pi$
$79$	−10.4857	−1.17973	−0.589864	+	0.807503i	$0.700819\pi$
$80$	−1.99628	−0.223191
$81$	4.17633	0.464036
$82$	−0.356204	−0.0393362
$83$	14.8972	1.63518	0.817592	−	0.575798i	$-0.195308\pi$
$83$	14.8972	1.63518	0.817592	+	0.575798i	$0.195308\pi$
$84$	0.868502	0.0947613
$85$	−4.41700	−0.479091
$86$	−11.6690	−1.25830
$87$	16.8424	1.80570
$88$	4.57182	0.487358
$89$	−12.9109	−1.36856	−0.684279	−	0.729221i	$-0.739883\pi$
$89$	−12.9109	−1.36856	−0.684279	+	0.729221i	$0.739883\pi$
$90$	10.8351	1.14212
$91$	−0.855258	−0.0896554
$92$	1.00000	0.104257
$93$	−22.0892	−2.29055
$94$	1.51400	0.156157
$95$	−10.7514	−1.10307
$96$	2.90304	0.296290
$97$	−10.0001	−1.01535	−0.507676	−	0.861548i	$-0.669495\pi$
$97$	−10.0001	−1.01535	−0.507676	+	0.861548i	$0.669495\pi$
$98$	6.91050	0.698066
$99$	−24.8142	−2.49392
$100$	−1.01486	−0.101486
$101$	5.33273	0.530626	0.265313	−	0.964162i	$-0.414525\pi$
$101$	5.33273	0.530626	0.265313	+	0.964162i	$0.414525\pi$
$102$	6.42330	0.636002
$103$	1.32892	0.130942	0.0654711	−	0.997854i	$-0.479145\pi$
$103$	1.32892	0.130942	0.0654711	+	0.997854i	$0.479145\pi$
$104$	−2.85877	−0.280326
$105$	−1.73377	−0.169199
$106$	−8.03418	−0.780349
$107$	−12.8521	−1.24246	−0.621232	−	0.783627i	$-0.713367\pi$
$107$	−12.8521	−1.24246	−0.621232	+	0.783627i	$0.713367\pi$
$108$	−7.04752	−0.678148
$109$	9.37414	0.897880	0.448940	−	0.893562i	$-0.351802\pi$
$109$	9.37414	0.897880	0.448940	+	0.893562i	$0.351802\pi$
$110$	−9.12665	−0.870192
$111$	4.78616	0.454282
$112$	−0.299170	−0.0282689
$113$	−17.6472	−1.66011	−0.830053	−	0.557684i	$-0.811690\pi$
$113$	−17.6472	−1.66011	−0.830053	+	0.557684i	$0.811690\pi$
$114$	15.6349	1.46434
$115$	−1.99628	−0.186154
$116$	−5.80165	−0.538670
$117$	15.5164	1.43449
$118$	−5.74589	−0.528952
$119$	−0.661947	−0.0606806
$120$	−5.79529	−0.529035
$121$	9.90157	0.900143
$122$	−8.87265	−0.803292
$123$	−1.03407	−0.0932394
$124$	7.60900	0.683308
$125$	12.0074	1.07397
$126$	1.62379	0.144658
$127$	12.7744	1.13354	0.566771	−	0.823875i	$-0.308192\pi$
$127$	12.7744	1.13354	0.566771	+	0.823875i	$0.308192\pi$
$128$	−1.00000	−0.0883883
$129$	−33.8757	−2.98259
$130$	5.70692	0.500530
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	13.2722	1.15520
$133$	−1.61124	−0.139712
$134$	15.2925	1.32107
$135$	14.0688	1.21085
$136$	−2.21261	−0.189730
$137$	−18.7911	−1.60543	−0.802714	−	0.596364i	$-0.796612\pi$
$137$	−18.7911	−1.60543	−0.802714	+	0.596364i	$0.796612\pi$
$138$	2.90304	0.247123
$139$	9.10316	0.772120	0.386060	−	0.922474i	$-0.373836\pi$
$139$	9.10316	0.772120	0.386060	+	0.922474i	$0.373836\pi$
$140$	0.597228	0.0504749
$141$	4.39521	0.370143
$142$	6.00154	0.503638
$143$	−13.0698	−1.09295
$144$	5.42764	0.452303
$145$	11.5817	0.961811
$146$	−0.198540	−0.0164313
$147$	20.0614	1.65464
$148$	−1.64867	−0.135520
$149$	−2.93469	−0.240419	−0.120209	−	0.992749i	$-0.538357\pi$
$149$	−2.93469	−0.240419	−0.120209	+	0.992749i	$0.538357\pi$
$150$	−2.94617	−0.240554
$151$	23.7356	1.93158	0.965789	−	0.259327i	$-0.0835008\pi$
$151$	23.7356	1.93158	0.965789	+	0.259327i	$0.0835008\pi$
$152$	−5.38569	−0.436837
$153$	12.0093	0.970891
$154$	−1.36775	−0.110217
$155$	−15.1897	−1.22007
$156$	−8.29913	−0.664462
$157$	−6.72628	−0.536815	−0.268408	−	0.963305i	$-0.586497\pi$
$157$	−6.72628	−0.536815	−0.268408	+	0.963305i	$0.586497\pi$
$158$	10.4857	0.834194
$159$	−23.3235	−1.84968
$160$	1.99628	0.157820
$161$	−0.299170	−0.0235779
$162$	−4.17633	−0.328123
$163$	−4.36727	−0.342071	−0.171035	−	0.985265i	$-0.554711\pi$
$163$	−4.36727	−0.342071	−0.171035	+	0.985265i	$0.554711\pi$
$164$	0.356204	0.0278149
$165$	−26.4950	−2.06264
$166$	−14.8972	−1.15625
$167$	−14.5530	−1.12614	−0.563071	−	0.826408i	$-0.690380\pi$
$167$	−14.5530	−1.12614	−0.563071	+	0.826408i	$0.690380\pi$
$168$	−0.868502	−0.0670064
$169$	−4.82743	−0.371340
$170$	4.41700	0.338768
$171$	29.2316	2.23539
$172$	11.6690	0.889756
$173$	−9.89027	−0.751943	−0.375972	−	0.926631i	$-0.622691\pi$
$173$	−9.89027	−0.751943	−0.375972	+	0.926631i	$0.622691\pi$
$174$	−16.8424	−1.27682
$175$	0.303614	0.0229511
$176$	−4.57182	−0.344614
$177$	−16.6806	−1.25379
$178$	12.9109	0.967716
$179$	11.0242	0.823988	0.411994	−	0.911187i	$-0.364832\pi$
$179$	11.0242	0.823988	0.411994	+	0.911187i	$0.364832\pi$
$180$	−10.8351	−0.807600
$181$	−0.332497	−0.0247143	−0.0123572	−	0.999924i	$-0.503934\pi$
$181$	−0.332497	−0.0247143	−0.0123572	+	0.999924i	$0.503934\pi$
$182$	0.855258	0.0633960
$183$	−25.7576	−1.90406
$184$	−1.00000	−0.0737210
$185$	3.29121	0.241975
$186$	22.0892	1.61966
$187$	−10.1157	−0.739731
$188$	−1.51400	−0.110420
$189$	2.10841	0.153364
$190$	10.7514	0.779986
$191$	5.92893	0.429002	0.214501	−	0.976724i	$-0.431187\pi$
$191$	5.92893	0.429002	0.214501	+	0.976724i	$0.431187\pi$
$192$	−2.90304	−0.209509
$193$	−21.5083	−1.54820	−0.774102	−	0.633060i	$-0.781798\pi$
$193$	−21.5083	−1.54820	−0.774102	+	0.633060i	$0.781798\pi$
$194$	10.0001	0.717962
$195$	16.5674	1.18642
$196$	−6.91050	−0.493607
$197$	−1.17066	−0.0834058	−0.0417029	−	0.999130i	$-0.513278\pi$
$197$	−1.17066	−0.0834058	−0.0417029	+	0.999130i	$0.513278\pi$
$198$	24.8142	1.76347
$199$	10.9424	0.775684	0.387842	−	0.921726i	$-0.373221\pi$
$199$	10.9424	0.775684	0.387842	+	0.921726i	$0.373221\pi$
$200$	1.01486	0.0717612
$201$	44.3946	3.13136
$202$	−5.33273	−0.375210
$203$	1.73568	0.121821
$204$	−6.42330	−0.449721
$205$	−0.711084	−0.0496643
$206$	−1.32892	−0.0925901
$207$	5.42764	0.377247
$208$	2.85877	0.198220
$209$	−24.6224	−1.70317
$210$	1.73377	0.119642
$211$	18.7082	1.28793	0.643963	−	0.765057i	$-0.277289\pi$
$211$	18.7082	1.28793	0.643963	+	0.765057i	$0.277289\pi$
$212$	8.03418	0.551790
$213$	17.4227	1.19378
$214$	12.8521	0.878554
$215$	−23.2947	−1.58869
$216$	7.04752	0.479523
$217$	−2.27638	−0.154531
$218$	−9.37414	−0.634897
$219$	−0.576370	−0.0389474
$220$	9.12665	0.615319
$221$	6.32535	0.425489
$222$	−4.78616	−0.321226
$223$	6.79180	0.454812	0.227406	−	0.973800i	$-0.426975\pi$
$223$	6.79180	0.454812	0.227406	+	0.973800i	$0.426975\pi$
$224$	0.299170	0.0199891
$225$	−5.50827	−0.367218
$226$	17.6472	1.17387
$227$	−16.1918	−1.07469	−0.537343	−	0.843364i	$-0.680572\pi$
$227$	−16.1918	−1.07469	−0.537343	+	0.843364i	$0.680572\pi$
$228$	−15.6349	−1.03544
$229$	−4.80204	−0.317328	−0.158664	−	0.987333i	$-0.550719\pi$
$229$	−4.80204	−0.317328	−0.158664	+	0.987333i	$0.550719\pi$
$230$	1.99628	0.131631
$231$	−3.97064	−0.261249
$232$	5.80165	0.380897
$233$	7.59441	0.497526	0.248763	−	0.968564i	$-0.419976\pi$
$233$	7.59441	0.497526	0.248763	+	0.968564i	$0.419976\pi$
$234$	−15.5164	−1.01434
$235$	3.02238	0.197158
$236$	5.74589	0.374026
$237$	30.4403	1.97731
$238$	0.661947	0.0429077
$239$	13.2132	0.854690	0.427345	−	0.904089i	$-0.359449\pi$
$239$	13.2132	0.854690	0.427345	+	0.904089i	$0.359449\pi$
$240$	5.79529	0.374084
$241$	−3.33042	−0.214531	−0.107266	−	0.994230i	$-0.534210\pi$
$241$	−3.33042	−0.214531	−0.107266	+	0.994230i	$0.534210\pi$
$242$	−9.90157	−0.636497
$243$	9.01853	0.578539
$244$	8.87265	0.568013
$245$	13.7953	0.881350
$246$	1.03407	0.0659302
$247$	15.3965	0.979653
$248$	−7.60900	−0.483172
$249$	−43.2473	−2.74068
$250$	−12.0074	−0.759412
$251$	27.4721	1.73402	0.867011	−	0.498289i	$-0.166038\pi$
$251$	27.4721	1.73402	0.867011	+	0.498289i	$0.166038\pi$
$252$	−1.62379	−0.102289
$253$	−4.57182	−0.287428
$254$	−12.7744	−0.801535
$255$	12.8227	0.802990
$256$	1.00000	0.0625000
$257$	−2.89521	−0.180598	−0.0902991	−	0.995915i	$-0.528782\pi$
$257$	−2.89521	−0.180598	−0.0902991	+	0.995915i	$0.528782\pi$
$258$	33.8757	2.10901
$259$	0.493233	0.0306480
$260$	−5.70692	−0.353928
$261$	−31.4893	−1.94914
$262$	1.00000	0.0617802
$263$	−17.6122	−1.08601	−0.543007	−	0.839728i	$-0.682714\pi$
$263$	−17.6122	−1.08601	−0.543007	+	0.839728i	$0.682714\pi$
$264$	−13.2722	−0.816846
$265$	−16.0385	−0.985237
$266$	1.61124	0.0987912
$267$	37.4810	2.29380
$268$	−15.2925	−0.934136
$269$	−3.99005	−0.243278	−0.121639	−	0.992574i	$-0.538815\pi$
$269$	−3.99005	−0.243278	−0.121639	+	0.992574i	$0.538815\pi$
$270$	−14.0688	−0.856203
$271$	−21.4377	−1.30225	−0.651123	−	0.758972i	$-0.725702\pi$
$271$	−21.4377	−1.30225	−0.651123	+	0.758972i	$0.725702\pi$
$272$	2.21261	0.134159
$273$	2.48285	0.150269
$274$	18.7911	1.13521
$275$	4.63974	0.279787
$276$	−2.90304	−0.174742
$277$	4.59290	0.275961	0.137980	−	0.990435i	$-0.455939\pi$
$277$	4.59290	0.275961	0.137980	+	0.990435i	$0.455939\pi$
$278$	−9.10316	−0.545971
$279$	41.2989	2.47250
$280$	−0.597228	−0.0356912
$281$	−28.9041	−1.72428	−0.862138	−	0.506674i	$-0.830875\pi$
$281$	−28.9041	−1.72428	−0.862138	+	0.506674i	$0.830875\pi$
$282$	−4.39521	−0.261731
$283$	−30.8096	−1.83144	−0.915719	−	0.401819i	$-0.868378\pi$
$283$	−30.8096	−1.83144	−0.915719	+	0.401819i	$0.868378\pi$
$284$	−6.00154	−0.356126
$285$	31.2116	1.84882
$286$	13.0698	0.772833
$287$	−0.106566	−0.00629037
$288$	−5.42764	−0.319827
$289$	−12.1043	−0.712020
$290$	−11.5817	−0.680103
$291$	29.0305	1.70180
$292$	0.198540	0.0116187
$293$	3.12648	0.182651	0.0913255	−	0.995821i	$-0.470890\pi$
$293$	3.12648	0.182651	0.0913255	+	0.995821i	$0.470890\pi$
$294$	−20.0614	−1.17001
$295$	−11.4704	−0.667834
$296$	1.64867	0.0958271
$297$	32.2200	1.86960
$298$	2.93469	0.170002
$299$	2.85877	0.165327
$300$	2.94617	0.170097
$301$	−3.49102	−0.201219
$302$	−23.7356	−1.36583
$303$	−15.4811	−0.889367
$304$	5.38569	0.308891
$305$	−17.7123	−1.01420
$306$	−12.0093	−0.686524
$307$	7.23198	0.412751	0.206375	−	0.978473i	$-0.433833\pi$
$307$	7.23198	0.412751	0.206375	+	0.978473i	$0.433833\pi$
$308$	1.36775	0.0779349
$309$	−3.85790	−0.219468
$310$	15.1897	0.862718
$311$	−27.5409	−1.56170	−0.780851	−	0.624717i	$-0.785214\pi$
$311$	−27.5409	−1.56170	−0.780851	+	0.624717i	$0.785214\pi$
$312$	8.29913	0.469845
$313$	26.3852	1.49138	0.745691	−	0.666292i	$-0.232120\pi$
$313$	26.3852	1.49138	0.745691	+	0.666292i	$0.232120\pi$
$314$	6.72628	0.379586
$315$	3.24153	0.182640
$316$	−10.4857	−0.589864
$317$	33.8908	1.90350	0.951749	−	0.306878i	$-0.0992843\pi$
$317$	33.8908	1.90350	0.951749	+	0.306878i	$0.0992843\pi$
$318$	23.3235	1.30792
$319$	26.5241	1.48507
$320$	−1.99628	−0.111596
$321$	37.3103	2.08246
$322$	0.299170	0.0166721
$323$	11.9165	0.663049
$324$	4.17633	0.232018
$325$	−2.90124	−0.160932
$326$	4.36727	0.241880
$327$	−27.2135	−1.50491
$328$	−0.356204	−0.0196681
$329$	0.452944	0.0249716
$330$	26.4950	1.45850
$331$	7.02599	0.386183	0.193092	−	0.981181i	$-0.438149\pi$
$331$	7.02599	0.386183	0.193092	+	0.981181i	$0.438149\pi$
$332$	14.8972	0.817592
$333$	−8.94839	−0.490369
$334$	14.5530	0.796303
$335$	30.5281	1.66793
$336$	0.868502	0.0473807
$337$	−12.4748	−0.679547	−0.339774	−	0.940507i	$-0.610350\pi$
$337$	−12.4748	−0.679547	−0.339774	+	0.940507i	$0.610350\pi$
$338$	4.82743	0.262577
$339$	51.2304	2.78246
$340$	−4.41700	−0.239545
$341$	−34.7870	−1.88382
$342$	−29.2316	−1.58066
$343$	4.16160	0.224705
$344$	−11.6690	−0.629152
$345$	5.79529	0.312008
$346$	9.89027	0.531704
$347$	0.208098	0.0111713	0.00558564	−	0.999984i	$-0.498222\pi$
$347$	0.208098	0.0111713	0.00558564	+	0.999984i	$0.498222\pi$
$348$	16.8424	0.902849
$349$	−16.2698	−0.870903	−0.435452	−	0.900212i	$-0.643411\pi$
$349$	−16.2698	−0.870903	−0.435452	+	0.900212i	$0.643411\pi$
$350$	−0.303614	−0.0162289
$351$	−20.1473	−1.07538
$352$	4.57182	0.243679
$353$	30.1541	1.60494	0.802470	−	0.596692i	$-0.203519\pi$
$353$	30.1541	1.60494	0.802470	+	0.596692i	$0.203519\pi$
$354$	16.6806	0.886561
$355$	11.9808	0.635873
$356$	−12.9109	−0.684279
$357$	1.92166	0.101705
$358$	−11.0242	−0.582648
$359$	21.5630	1.13805	0.569025	−	0.822320i	$-0.307321\pi$
$359$	21.5630	1.13805	0.569025	+	0.822320i	$0.307321\pi$
$360$	10.8351	0.571060
$361$	10.0057	0.526614
$362$	0.332497	0.0174757
$363$	−28.7446	−1.50870
$364$	−0.855258	−0.0448277
$365$	−0.396342	−0.0207455
$366$	25.7576	1.34637
$367$	−22.1719	−1.15737	−0.578683	−	0.815553i	$-0.696433\pi$
$367$	−22.1719	−1.15737	−0.578683	+	0.815553i	$0.696433\pi$
$368$	1.00000	0.0521286
$369$	1.93335	0.100646
$370$	−3.29121	−0.171102
$371$	−2.40358	−0.124788
$372$	−22.0892	−1.14527
$373$	−32.7808	−1.69733	−0.848663	−	0.528934i	$-0.822592\pi$
$373$	−32.7808	−1.69733	−0.848663	+	0.528934i	$0.822592\pi$
$374$	10.1157	0.523069
$375$	−34.8578	−1.80005
$376$	1.51400	0.0780787
$377$	−16.5856	−0.854202
$378$	−2.10841	−0.108445
$379$	20.1438	1.03472	0.517358	−	0.855769i	$-0.326916\pi$
$379$	20.1438	1.03472	0.517358	+	0.855769i	$0.326916\pi$
$380$	−10.7514	−0.551533
$381$	−37.0845	−1.89990
$382$	−5.92893	−0.303350
$383$	18.5215	0.946404	0.473202	−	0.880954i	$-0.343098\pi$
$383$	18.5215	0.946404	0.473202	+	0.880954i	$0.343098\pi$
$384$	2.90304	0.148145
$385$	−2.73042	−0.139155
$386$	21.5083	1.09475
$387$	63.3353	3.21951
$388$	−10.0001	−0.507676
$389$	28.3962	1.43974	0.719871	−	0.694108i	$-0.244201\pi$
$389$	28.3962	1.43974	0.719871	+	0.694108i	$0.244201\pi$
$390$	−16.5674	−0.838923
$391$	2.21261	0.111897
$392$	6.91050	0.349033
$393$	2.90304	0.146439
$394$	1.17066	0.0589768
$395$	20.9323	1.05322
$396$	−24.8142	−1.24696
$397$	−19.3763	−0.972467	−0.486233	−	0.873829i	$-0.661630\pi$
$397$	−19.3763	−0.972467	−0.486233	+	0.873829i	$0.661630\pi$
$398$	−10.9424	−0.548492
$399$	4.67748	0.234167
$400$	−1.01486	−0.0507428
$401$	34.6486	1.73027	0.865134	−	0.501541i	$-0.167234\pi$
$401$	34.6486	1.73027	0.865134	+	0.501541i	$0.167234\pi$
$402$	−44.3946	−2.21420
$403$	21.7524	1.08356
$404$	5.33273	0.265313
$405$	−8.33713	−0.414275
$406$	−1.73568	−0.0861403
$407$	7.53744	0.373617
$408$	6.42330	0.318001
$409$	11.5284	0.570043	0.285021	−	0.958521i	$-0.407999\pi$
$409$	11.5284	0.570043	0.285021	+	0.958521i	$0.407999\pi$
$410$	0.711084	0.0351179
$411$	54.5512	2.69081
$412$	1.32892	0.0654711
$413$	−1.71900	−0.0845864
$414$	−5.42764	−0.266754
$415$	−29.7391	−1.45983
$416$	−2.85877	−0.140163
$417$	−26.4268	−1.29413
$418$	24.6224	1.20432
$419$	24.2659	1.18547	0.592734	−	0.805398i	$-0.298049\pi$
$419$	24.2659	1.18547	0.592734	+	0.805398i	$0.298049\pi$
$420$	−1.73377	−0.0845995
$421$	35.7685	1.74325	0.871625	−	0.490173i	$-0.163066\pi$
$421$	35.7685	1.74325	0.871625	+	0.490173i	$0.163066\pi$
$422$	−18.7082	−0.910701
$423$	−8.21745	−0.399546
$424$	−8.03418	−0.390174
$425$	−2.24548	−0.108922
$426$	−17.4227	−0.844133
$427$	−2.65443	−0.128457
$428$	−12.8521	−0.621232
$429$	37.9421	1.83186
$430$	23.2947	1.12337
$431$	−20.8793	−1.00572	−0.502860	−	0.864368i	$-0.667719\pi$
$431$	−20.8793	−1.00572	−0.502860	+	0.864368i	$0.667719\pi$
$432$	−7.04752	−0.339074
$433$	33.5188	1.61081	0.805406	−	0.592724i	$-0.201947\pi$
$433$	33.5188	1.61081	0.805406	+	0.592724i	$0.201947\pi$
$434$	2.27638	0.109270
$435$	−33.6222	−1.61206
$436$	9.37414	0.448940
$437$	5.38569	0.257633
$438$	0.576370	0.0275400
$439$	16.7535	0.799602	0.399801	−	0.916602i	$-0.369079\pi$
$439$	16.7535	0.799602	0.399801	+	0.916602i	$0.369079\pi$
$440$	−9.12665	−0.435096
$441$	−37.5077	−1.78608
$442$	−6.32535	−0.300866
$443$	−8.24002	−0.391495	−0.195748	−	0.980654i	$-0.562713\pi$
$443$	−8.24002	−0.391495	−0.195748	+	0.980654i	$0.562713\pi$
$444$	4.78616	0.227141
$445$	25.7739	1.22180
$446$	−6.79180	−0.321601
$447$	8.51951	0.402959
$448$	−0.299170	−0.0141344
$449$	39.5374	1.86588	0.932942	−	0.360028i	$-0.117233\pi$
$449$	39.5374	1.86588	0.932942	+	0.360028i	$0.117233\pi$
$450$	5.50827	0.259662
$451$	−1.62850	−0.0766832
$452$	−17.6472	−0.830053
$453$	−68.9055	−3.23746
$454$	16.1918	0.759917
$455$	1.70734	0.0800412
$456$	15.6349	0.732170
$457$	20.7700	0.971579	0.485790	−	0.874076i	$-0.338532\pi$
$457$	20.7700	0.971579	0.485790	+	0.874076i	$0.338532\pi$
$458$	4.80204	0.224385
$459$	−15.5934	−0.727839
$460$	−1.99628	−0.0930772
$461$	35.8749	1.67086	0.835430	−	0.549597i	$-0.185219\pi$
$461$	35.8749	1.67086	0.835430	+	0.549597i	$0.185219\pi$
$462$	3.97064	0.184731
$463$	−2.81429	−0.130791	−0.0653955	−	0.997859i	$-0.520831\pi$
$463$	−2.81429	−0.130791	−0.0653955	+	0.997859i	$0.520831\pi$
$464$	−5.80165	−0.269335
$465$	44.0963	2.04492
$466$	−7.59441	−0.351804
$467$	−16.0502	−0.742714	−0.371357	−	0.928490i	$-0.621107\pi$
$467$	−16.0502	−0.742714	−0.371357	+	0.928490i	$0.621107\pi$
$468$	15.5164	0.717245
$469$	4.57505	0.211256
$470$	−3.02238	−0.139412
$471$	19.5266	0.899740
$472$	−5.74589	−0.264476
$473$	−53.3488	−2.45298
$474$	−30.4403	−1.39817
$475$	−5.46570	−0.250784
$476$	−0.661947	−0.0303403
$477$	43.6066	1.99661
$478$	−13.2132	−0.604357
$479$	32.7343	1.49567	0.747833	−	0.663886i	$-0.231094\pi$
$479$	32.7343	1.49567	0.747833	+	0.663886i	$0.231094\pi$
$480$	−5.79529	−0.264517
$481$	−4.71318	−0.214902
$482$	3.33042	0.151696
$483$	0.868502	0.0395182
$484$	9.90157	0.450071
$485$	19.9629	0.906470
$486$	−9.01853	−0.409089
$487$	11.4435	0.518556	0.259278	−	0.965803i	$-0.416515\pi$
$487$	11.4435	0.518556	0.259278	+	0.965803i	$0.416515\pi$
$488$	−8.87265	−0.401646
$489$	12.6783	0.573334
$490$	−13.7953	−0.623208
$491$	19.9055	0.898322	0.449161	−	0.893451i	$-0.351723\pi$
$491$	19.9055	0.898322	0.449161	+	0.893451i	$0.351723\pi$
$492$	−1.03407	−0.0466197
$493$	−12.8368	−0.578141
$494$	−15.3965	−0.692720
$495$	49.5361	2.22648
$496$	7.60900	0.341654
$497$	1.79548	0.0805383
$498$	43.2473	1.93796
$499$	−20.4136	−0.913838	−0.456919	−	0.889508i	$-0.651047\pi$
$499$	−20.4136	−0.913838	−0.456919	+	0.889508i	$0.651047\pi$
$500$	12.0074	0.536985
$501$	42.2478	1.88749
$502$	−27.4721	−1.22614
$503$	34.2828	1.52859	0.764296	−	0.644865i	$-0.223086\pi$
$503$	34.2828	1.52859	0.764296	+	0.644865i	$0.223086\pi$
$504$	1.62379	0.0723291
$505$	−10.6456	−0.473725
$506$	4.57182	0.203242
$507$	14.0142	0.622393
$508$	12.7744	0.566771
$509$	9.42388	0.417706	0.208853	−	0.977947i	$-0.433027\pi$
$509$	9.42388	0.417706	0.208853	+	0.977947i	$0.433027\pi$
$510$	−12.8227	−0.567800
$511$	−0.0593972	−0.00262758
$512$	−1.00000	−0.0441942
$513$	−37.9558	−1.67579
$514$	2.89521	0.127702
$515$	−2.65289	−0.116901
$516$	−33.8757	−1.49129
$517$	6.92175	0.304418
$518$	−0.493233	−0.0216714
$519$	28.7118	1.26031
$520$	5.70692	0.250265
$521$	−4.53780	−0.198805	−0.0994024	−	0.995047i	$-0.531693\pi$
$521$	−4.53780	−0.198805	−0.0994024	+	0.995047i	$0.531693\pi$
$522$	31.4893	1.37825
$523$	25.8100	1.12859	0.564297	−	0.825572i	$-0.309147\pi$
$523$	25.8100	1.12859	0.564297	+	0.825572i	$0.309147\pi$
$524$	−1.00000	−0.0436852
$525$	−0.881404	−0.0384676
$526$	17.6122	0.767928
$527$	16.8358	0.733378
$528$	13.2722	0.577598
$529$	1.00000	0.0434783
$530$	16.0385	0.696668
$531$	31.1866	1.35338
$532$	−1.61124	−0.0698560
$533$	1.01831	0.0441077
$534$	−37.4810	−1.62196
$535$	25.6565	1.10923
$536$	15.2925	0.660534
$537$	−32.0037	−1.38106
$538$	3.99005	0.172023
$539$	31.5936	1.36083
$540$	14.0688	0.605427
$541$	30.1378	1.29573	0.647863	−	0.761757i	$-0.275663\pi$
$541$	30.1378	1.29573	0.647863	+	0.761757i	$0.275663\pi$
$542$	21.4377	0.920828
$543$	0.965253	0.0414230
$544$	−2.21261	−0.0948650
$545$	−18.7134	−0.801596
$546$	−2.48285	−0.106256
$547$	−8.26070	−0.353202	−0.176601	−	0.984283i	$-0.556510\pi$
$547$	−8.26070	−0.353202	−0.176601	+	0.984283i	$0.556510\pi$
$548$	−18.7911	−0.802714
$549$	48.1575	2.05531
$550$	−4.63974	−0.197839
$551$	−31.2459	−1.33112
$552$	2.90304	0.123562
$553$	3.13699	0.133398
$554$	−4.59290	−0.195134
$555$	−9.55452	−0.405567
$556$	9.10316	0.386060
$557$	20.8001	0.881330	0.440665	−	0.897672i	$-0.354743\pi$
$557$	20.8001	0.881330	0.440665	+	0.897672i	$0.354743\pi$
$558$	−41.2989	−1.74832
$559$	33.3591	1.41094
$560$	0.597228	0.0252375
$561$	29.3662	1.23984
$562$	28.9041	1.21925
$563$	−17.3955	−0.733135	−0.366567	−	0.930392i	$-0.619467\pi$
$563$	−17.3955	−0.733135	−0.366567	+	0.930392i	$0.619467\pi$
$564$	4.39521	0.185072
$565$	35.2287	1.48208
$566$	30.8096	1.29502
$567$	−1.24943	−0.0524712
$568$	6.00154	0.251819
$569$	19.9602	0.836777	0.418388	−	0.908268i	$-0.362595\pi$
$569$	19.9602	0.836777	0.418388	+	0.908268i	$0.362595\pi$
$570$	−31.2116	−1.30731
$571$	−0.659794	−0.0276115	−0.0138058	−	0.999905i	$-0.504395\pi$
$571$	−0.659794	−0.0276115	−0.0138058	+	0.999905i	$0.504395\pi$
$572$	−13.0698	−0.546476
$573$	−17.2119	−0.719037
$574$	0.106566	0.00444796
$575$	−1.01486	−0.0423224
$576$	5.42764	0.226152
$577$	40.3024	1.67781	0.838905	−	0.544279i	$-0.183197\pi$
$577$	40.3024	1.67781	0.838905	+	0.544279i	$0.183197\pi$
$578$	12.1043	0.503474
$579$	62.4396	2.59490
$580$	11.5817	0.480905
$581$	−4.45680	−0.184899
$582$	−29.0305	−1.20335
$583$	−36.7309	−1.52124
$584$	−0.198540	−0.00821565
$585$	−30.9751	−1.28066
$586$	−3.12648	−0.129154
$587$	28.7232	1.18553	0.592766	−	0.805374i	$-0.298036\pi$
$587$	28.7232	1.18553	0.592766	+	0.805374i	$0.298036\pi$
$588$	20.0614	0.827320
$589$	40.9797	1.68854
$590$	11.4704	0.472230
$591$	3.39846	0.139794
$592$	−1.64867	−0.0677600
$593$	−13.9715	−0.573741	−0.286871	−	0.957969i	$-0.592615\pi$
$593$	−13.9715	−0.573741	−0.286871	+	0.957969i	$0.592615\pi$
$594$	−32.2200	−1.32200
$595$	1.32143	0.0541735
$596$	−2.93469	−0.120209
$597$	−31.7661	−1.30010
$598$	−2.85877	−0.116904
$599$	−30.5853	−1.24968	−0.624840	−	0.780753i	$-0.714836\pi$
$599$	−30.5853	−1.24968	−0.624840	+	0.780753i	$0.714836\pi$
$600$	−2.94617	−0.120277
$601$	−6.53355	−0.266509	−0.133255	−	0.991082i	$-0.542543\pi$
$601$	−6.53355	−0.266509	−0.133255	+	0.991082i	$0.542543\pi$
$602$	3.49102	0.142284
$603$	−83.0020	−3.38010
$604$	23.7356	0.965789
$605$	−19.7663	−0.803616
$606$	15.4811	0.628878
$607$	−37.8749	−1.53729	−0.768647	−	0.639673i	$-0.779070\pi$
$607$	−37.8749	−1.53729	−0.768647	+	0.639673i	$0.779070\pi$
$608$	−5.38569	−0.218419
$609$	−5.03874	−0.204180
$610$	17.7123	0.717150
$611$	−4.32819	−0.175100
$612$	12.0093	0.485445
$613$	−10.3294	−0.417199	−0.208600	−	0.978001i	$-0.566891\pi$
$613$	−10.3294	−0.417199	−0.208600	+	0.978001i	$0.566891\pi$
$614$	−7.23198	−0.291859
$615$	2.06431	0.0832408
$616$	−1.36775	−0.0551083
$617$	−10.8722	−0.437698	−0.218849	−	0.975759i	$-0.570230\pi$
$617$	−10.8722	−0.437698	−0.218849	+	0.975759i	$0.570230\pi$
$618$	3.85790	0.155187
$619$	22.6457	0.910206	0.455103	−	0.890439i	$-0.349602\pi$
$619$	22.6457	0.910206	0.455103	+	0.890439i	$0.349602\pi$
$620$	−15.1897	−0.610034
$621$	−7.04752	−0.282807
$622$	27.5409	1.10429
$623$	3.86257	0.154750
$624$	−8.29913	−0.332231
$625$	−18.8958	−0.755831
$626$	−26.3852	−1.05457
$627$	71.4799	2.85463
$628$	−6.72628	−0.268408
$629$	−3.64787	−0.145450
$630$	−3.24153	−0.129146
$631$	26.9122	1.07136	0.535679	−	0.844421i	$-0.320056\pi$
$631$	26.9122	1.07136	0.535679	+	0.844421i	$0.320056\pi$
$632$	10.4857	0.417097
$633$	−54.3106	−2.15865
$634$	−33.8908	−1.34598
$635$	−25.5013	−1.01199
$636$	−23.3235	−0.924839
$637$	−19.7555	−0.782743
$638$	−26.5241	−1.05010
$639$	−32.5742	−1.28861
$640$	1.99628	0.0789100
$641$	−46.9822	−1.85569	−0.927843	−	0.372970i	$-0.878339\pi$
$641$	−46.9822	−1.85569	−0.927843	+	0.372970i	$0.878339\pi$
$642$	−37.3103	−1.47252
$643$	15.9695	0.629774	0.314887	−	0.949129i	$-0.398033\pi$
$643$	15.9695	0.629774	0.314887	+	0.949129i	$0.398033\pi$
$644$	−0.299170	−0.0117889
$645$	67.6254	2.66275
$646$	−11.9165	−0.468846
$647$	−33.2993	−1.30913	−0.654565	−	0.756006i	$-0.727148\pi$
$647$	−33.2993	−1.30913	−0.654565	+	0.756006i	$0.727148\pi$
$648$	−4.17633	−0.164062
$649$	−26.2692	−1.03116
$650$	2.90124	0.113796
$651$	6.60843	0.259005
$652$	−4.36727	−0.171035
$653$	−21.4516	−0.839467	−0.419734	−	0.907647i	$-0.637877\pi$
$653$	−21.4516	−0.839467	−0.419734	+	0.907647i	$0.637877\pi$
$654$	27.2135	1.06413
$655$	1.99628	0.0780012
$656$	0.356204	0.0139074
$657$	1.07760	0.0420413
$658$	−0.452944	−0.0176576
$659$	−22.2112	−0.865227	−0.432613	−	0.901580i	$-0.642408\pi$
$659$	−22.2112	−0.865227	−0.432613	+	0.901580i	$0.642408\pi$
$660$	−26.4950	−1.03132
$661$	−27.5229	−1.07052	−0.535258	−	0.844689i	$-0.679786\pi$
$661$	−27.5229	−1.07052	−0.535258	+	0.844689i	$0.679786\pi$
$662$	−7.02599	−0.273073
$663$	−18.3628	−0.713150
$664$	−14.8972	−0.578125
$665$	3.21648	0.124730
$666$	8.94839	0.346743
$667$	−5.80165	−0.224641
$668$	−14.5530	−0.563071
$669$	−19.7169	−0.762298
$670$	−30.5281	−1.17940
$671$	−40.5642	−1.56596
$672$	−0.868502	−0.0335032
$673$	10.2442	0.394884	0.197442	−	0.980315i	$-0.436737\pi$
$673$	10.2442	0.394884	0.197442	+	0.980315i	$0.436737\pi$
$674$	12.4748	0.480513
$675$	7.15222	0.275289
$676$	−4.82743	−0.185670
$677$	2.44748	0.0940644	0.0470322	−	0.998893i	$-0.485024\pi$
$677$	2.44748	0.0940644	0.0470322	+	0.998893i	$0.485024\pi$
$678$	−51.2304	−1.96749
$679$	2.99171	0.114811
$680$	4.41700	0.169384
$681$	47.0053	1.80125
$682$	34.7870	1.33206
$683$	6.30511	0.241258	0.120629	−	0.992698i	$-0.461509\pi$
$683$	6.30511	0.241258	0.120629	+	0.992698i	$0.461509\pi$
$684$	29.2316	1.11770
$685$	37.5123	1.43327
$686$	−4.16160	−0.158891
$687$	13.9405	0.531864
$688$	11.6690	0.444878
$689$	22.9679	0.875007
$690$	−5.79529	−0.220623
$691$	15.8959	0.604710	0.302355	−	0.953195i	$-0.402227\pi$
$691$	15.8959	0.604710	0.302355	+	0.953195i	$0.402227\pi$
$692$	−9.89027	−0.375972
$693$	7.42366	0.282001
$694$	−0.208098	−0.00789929
$695$	−18.1725	−0.689321
$696$	−16.8424	−0.638410
$697$	0.788142	0.0298530
$698$	16.2698	0.615822
$699$	−22.0469	−0.833889
$700$	0.303614	0.0114755
$701$	−10.3998	−0.392794	−0.196397	−	0.980524i	$-0.562924\pi$
$701$	−10.3998	−0.392794	−0.196397	+	0.980524i	$0.562924\pi$
$702$	20.1473	0.760409
$703$	−8.87924	−0.334887
$704$	−4.57182	−0.172307
$705$	−8.77408	−0.330451
$706$	−30.1541	−1.13486
$707$	−1.59539	−0.0600009
$708$	−16.6806	−0.626894
$709$	0.592012	0.0222335	0.0111167	−	0.999938i	$-0.496461\pi$
$709$	0.592012	0.0222335	0.0111167	+	0.999938i	$0.496461\pi$
$710$	−11.9808	−0.449630
$711$	−56.9123	−2.13438
$712$	12.9109	0.483858
$713$	7.60900	0.284959
$714$	−1.92166	−0.0719162
$715$	26.0910	0.975749
$716$	11.0242	0.411994
$717$	−38.3584	−1.43252
$718$	−21.5630	−0.804722
$719$	−7.05382	−0.263063	−0.131532	−	0.991312i	$-0.541989\pi$
$719$	−7.05382	−0.263063	−0.131532	+	0.991312i	$0.541989\pi$
$720$	−10.8351	−0.403800
$721$	−0.397572	−0.0148064
$722$	−10.0057	−0.372373
$723$	9.66834	0.359569
$724$	−0.332497	−0.0123572
$725$	5.88784	0.218669
$726$	28.7446	1.06681
$727$	34.3283	1.27317	0.636583	−	0.771208i	$-0.280347\pi$
$727$	34.3283	1.27317	0.636583	+	0.771208i	$0.280347\pi$
$728$	0.855258	0.0316980
$729$	−38.7101	−1.43371
$730$	0.396342	0.0146693
$731$	25.8191	0.954953
$732$	−25.7576	−0.952030
$733$	−34.1728	−1.26220	−0.631101	−	0.775701i	$-0.717396\pi$
$733$	−34.1728	−1.26220	−0.631101	+	0.775701i	$0.717396\pi$
$734$	22.1719	0.818381
$735$	−40.0483	−1.47720
$736$	−1.00000	−0.0368605
$737$	69.9145	2.57533
$738$	−1.93335	−0.0711675
$739$	22.2291	0.817709	0.408855	−	0.912600i	$-0.365928\pi$
$739$	22.2291	0.817709	0.408855	+	0.912600i	$0.365928\pi$
$740$	3.29121	0.120987
$741$	−44.6965	−1.64197
$742$	2.40358	0.0882384
$743$	40.0747	1.47020	0.735098	−	0.677960i	$-0.237136\pi$
$743$	40.0747	1.47020	0.735098	+	0.677960i	$0.237136\pi$
$744$	22.0892	0.809830
$745$	5.85847	0.214638
$746$	32.7808	1.20019
$747$	80.8568	2.95840
$748$	−10.1157	−0.369866
$749$	3.84497	0.140492
$750$	34.8578	1.27283
$751$	23.7212	0.865597	0.432799	−	0.901491i	$-0.357526\pi$
$751$	23.7212	0.865597	0.432799	+	0.901491i	$0.357526\pi$
$752$	−1.51400	−0.0552100
$753$	−79.7525	−2.90634
$754$	16.5856	0.604012
$755$	−47.3830	−1.72445
$756$	2.10841	0.0766820
$757$	−29.8645	−1.08544	−0.542722	−	0.839912i	$-0.682606\pi$
$757$	−29.8645	−1.08544	−0.542722	+	0.839912i	$0.682606\pi$
$758$	−20.1438	−0.731655
$759$	13.2722	0.481750
$760$	10.7514	0.389993
$761$	−27.5344	−0.998121	−0.499061	−	0.866567i	$-0.666322\pi$
$761$	−27.5344	−0.998121	−0.499061	+	0.866567i	$0.666322\pi$
$762$	37.0845	1.34343
$763$	−2.80446	−0.101528
$764$	5.92893	0.214501
$765$	−23.9739	−0.866777
$766$	−18.5215	−0.669209
$767$	16.4262	0.593116
$768$	−2.90304	−0.104754
$769$	−6.84988	−0.247013	−0.123507	−	0.992344i	$-0.539414\pi$
$769$	−6.84988	−0.247013	−0.123507	+	0.992344i	$0.539414\pi$
$770$	2.73042	0.0983975
$771$	8.40491	0.302695
$772$	−21.5083	−0.774102
$773$	−11.8017	−0.424477	−0.212238	−	0.977218i	$-0.568075\pi$
$773$	−11.8017	−0.424477	−0.212238	+	0.977218i	$0.568075\pi$
$774$	−63.3353	−2.27654
$775$	−7.72204	−0.277384
$776$	10.0001	0.358981
$777$	−1.43187	−0.0513682
$778$	−28.3962	−1.01805
$779$	1.91841	0.0687340
$780$	16.5674	0.593208
$781$	27.4380	0.981808
$782$	−2.21261	−0.0791229
$783$	40.8873	1.46119
$784$	−6.91050	−0.246803
$785$	13.4275	0.479250
$786$	−2.90304	−0.103548
$787$	16.5118	0.588583	0.294291	−	0.955716i	$-0.404916\pi$
$787$	16.5118	0.588583	0.294291	+	0.955716i	$0.404916\pi$
$788$	−1.17066	−0.0417029
$789$	51.1289	1.82024
$790$	−20.9323	−0.744739
$791$	5.27950	0.187717
$792$	24.8142	0.881734
$793$	25.3649	0.900733
$794$	19.3763	0.687638
$795$	46.5604	1.65133
$796$	10.9424	0.387842
$797$	−21.3082	−0.754776	−0.377388	−	0.926055i	$-0.623178\pi$
$797$	−21.3082	−0.754776	−0.377388	+	0.926055i	$0.623178\pi$
$798$	−4.67748	−0.165581
$799$	−3.34990	−0.118511
$800$	1.01486	0.0358806
$801$	−70.0759	−2.47601
$802$	−34.6486	−1.22348
$803$	−0.907690	−0.0320317
$804$	44.3946	1.56568
$805$	0.597228	0.0210495
$806$	−21.7524	−0.766195
$807$	11.5833	0.407751
$808$	−5.33273	−0.187605
$809$	−27.6812	−0.973219	−0.486609	−	0.873620i	$-0.661767\pi$
$809$	−27.6812	−0.973219	−0.486609	+	0.873620i	$0.661767\pi$
$810$	8.33713	0.292937
$811$	−31.0862	−1.09158	−0.545792	−	0.837921i	$-0.683771\pi$
$811$	−31.0862	−1.09158	−0.545792	+	0.837921i	$0.683771\pi$
$812$	1.73568	0.0609104
$813$	62.2345	2.18266
$814$	−7.53744	−0.264187
$815$	8.71830	0.305389
$816$	−6.42330	−0.224861
$817$	62.8458	2.19870
$818$	−11.5284	−0.403081
$819$	−4.64203	−0.162206
$820$	−0.711084	−0.0248321
$821$	52.7409	1.84067	0.920336	−	0.391130i	$-0.127916\pi$
$821$	52.7409	1.84067	0.920336	+	0.391130i	$0.127916\pi$
$822$	−54.5512	−1.90269
$823$	20.6223	0.718849	0.359424	−	0.933174i	$-0.382973\pi$
$823$	20.6223	0.718849	0.359424	+	0.933174i	$0.382973\pi$
$824$	−1.32892	−0.0462950
$825$	−13.4694	−0.468943
$826$	1.71900	0.0598116
$827$	0.0646806	0.00224916	0.00112458	−	0.999999i	$-0.499642\pi$
$827$	0.0646806	0.00224916	0.00112458	+	0.999999i	$0.499642\pi$
$828$	5.42764	0.188623
$829$	−22.0909	−0.767249	−0.383625	−	0.923489i	$-0.625324\pi$
$829$	−22.0909	−0.767249	−0.383625	+	0.923489i	$0.625324\pi$
$830$	29.7391	1.03226
$831$	−13.3334	−0.462529
$832$	2.85877	0.0991101
$833$	−15.2903	−0.529776
$834$	26.4268	0.915086
$835$	29.0518	1.00538
$836$	−24.6224	−0.851585
$837$	−53.6246	−1.85354
$838$	−24.2659	−0.838252
$839$	−13.4723	−0.465117	−0.232558	−	0.972582i	$-0.574710\pi$
$839$	−13.4723	−0.465117	−0.232558	+	0.972582i	$0.574710\pi$
$840$	1.73377	0.0598209
$841$	4.65916	0.160661
$842$	−35.7685	−1.23266
$843$	83.9098	2.89001
$844$	18.7082	0.643963
$845$	9.63691	0.331520
$846$	8.21745	0.282522
$847$	−2.96225	−0.101784
$848$	8.03418	0.275895
$849$	89.4414	3.06962
$850$	2.24548	0.0770195
$851$	−1.64867	−0.0565157
$852$	17.4227	0.596892
$853$	−40.0186	−1.37021	−0.685105	−	0.728444i	$-0.740244\pi$
$853$	−40.0186	−1.37021	−0.685105	+	0.728444i	$0.740244\pi$
$854$	2.65443	0.0908327
$855$	−58.3545	−1.99568
$856$	12.8521	0.439277
$857$	2.46464	0.0841906	0.0420953	−	0.999114i	$-0.486597\pi$
$857$	2.46464	0.0841906	0.0420953	+	0.999114i	$0.486597\pi$
$858$	−37.9421	−1.29532
$859$	−44.6726	−1.52421	−0.762105	−	0.647454i	$-0.775834\pi$
$859$	−44.6726	−1.52421	−0.762105	+	0.647454i	$0.775834\pi$
$860$	−23.2947	−0.794343
$861$	0.309364	0.0105431
$862$	20.8793	0.711151
$863$	−55.2001	−1.87903	−0.939517	−	0.342502i	$-0.888726\pi$
$863$	−55.2001	−1.87903	−0.939517	+	0.342502i	$0.888726\pi$
$864$	7.04752	0.239762
$865$	19.7438	0.671308
$866$	−33.5188	−1.13902
$867$	35.1394	1.19340
$868$	−2.27638	−0.0772655
$869$	47.9386	1.62620
$870$	33.6222	1.13990
$871$	−43.7177	−1.48132
$872$	−9.37414	−0.317449
$873$	−54.2766	−1.83699
$874$	−5.38569	−0.182174
$875$	−3.59224	−0.121440
$876$	−0.576370	−0.0194737
$877$	7.89962	0.266751	0.133376	−	0.991066i	$-0.457418\pi$
$877$	7.89962	0.266751	0.133376	+	0.991066i	$0.457418\pi$
$878$	−16.7535	−0.565404
$879$	−9.07630	−0.306136
$880$	9.12665	0.307659
$881$	−52.9505	−1.78395	−0.891973	−	0.452088i	$-0.850679\pi$
$881$	−52.9505	−1.78395	−0.891973	+	0.452088i	$0.850679\pi$
$882$	37.5077	1.26295
$883$	−22.6132	−0.760993	−0.380497	−	0.924782i	$-0.624247\pi$
$883$	−22.6132	−0.760993	−0.380497	+	0.924782i	$0.624247\pi$
$884$	6.32535	0.212745
$885$	33.2991	1.11934
$886$	8.24002	0.276829
$887$	−51.8687	−1.74158	−0.870790	−	0.491656i	$-0.836392\pi$
$887$	−51.8687	−1.74158	−0.870790	+	0.491656i	$0.836392\pi$
$888$	−4.78616	−0.160613
$889$	−3.82171	−0.128176
$890$	−25.7739	−0.863943
$891$	−19.0934	−0.639654
$892$	6.79180	0.227406
$893$	−8.15395	−0.272862
$894$	−8.51951	−0.284935
$895$	−22.0074	−0.735627
$896$	0.299170	0.00999456
$897$	−8.29913	−0.277100
$898$	−39.5374	−1.31938
$899$	−44.1448	−1.47231
$900$	−5.50827	−0.183609
$901$	17.7765	0.592222
$902$	1.62850	0.0542232
$903$	10.1346	0.337258
$904$	17.6472	0.586936
$905$	0.663759	0.0220641
$906$	68.9055	2.28923
$907$	26.9059	0.893395	0.446697	−	0.894685i	$-0.352600\pi$
$907$	26.9059	0.893395	0.446697	+	0.894685i	$0.352600\pi$
$908$	−16.1918	−0.537343
$909$	28.9441	0.960016
$910$	−1.70734	−0.0565977
$911$	17.6047	0.583270	0.291635	−	0.956530i	$-0.405801\pi$
$911$	17.6047	0.583270	0.291635	+	0.956530i	$0.405801\pi$
$912$	−15.6349	−0.517722
$913$	−68.1075	−2.25403
$914$	−20.7700	−0.687010
$915$	51.4195	1.69988
$916$	−4.80204	−0.158664
$917$	0.299170	0.00987946
$918$	15.5934	0.514660
$919$	46.2792	1.52661	0.763304	−	0.646039i	$-0.223576\pi$
$919$	46.2792	1.52661	0.763304	+	0.646039i	$0.223576\pi$
$920$	1.99628	0.0658155
$921$	−20.9947	−0.691799
$922$	−35.8749	−1.18148
$923$	−17.1570	−0.564731
$924$	−3.97064	−0.130624
$925$	1.67316	0.0550133
$926$	2.81429	0.0924832
$927$	7.21288	0.236902
$928$	5.80165	0.190449
$929$	−13.5008	−0.442946	−0.221473	−	0.975167i	$-0.571086\pi$
$929$	−13.5008	−0.442946	−0.221473	+	0.975167i	$0.571086\pi$
$930$	−44.0963	−1.44598
$931$	−37.2178	−1.21976
$932$	7.59441	0.248763
$933$	79.9524	2.61752
$934$	16.0502	0.525178
$935$	20.1937	0.660406
$936$	−15.5164	−0.507168
$937$	−3.63818	−0.118854	−0.0594271	−	0.998233i	$-0.518927\pi$
$937$	−3.63818	−0.118854	−0.0594271	+	0.998233i	$0.518927\pi$
$938$	−4.57505	−0.149381
$939$	−76.5974	−2.49966
$940$	3.02238	0.0985790
$941$	0.128378	0.00418499	0.00209250	−	0.999998i	$-0.499334\pi$
$941$	0.128378	0.00418499	0.00209250	+	0.999998i	$0.499334\pi$
$942$	−19.5266	−0.636212
$943$	0.356204	0.0115996
$944$	5.74589	0.187013
$945$	−4.20897	−0.136918
$946$	53.3488	1.73452
$947$	−16.6341	−0.540537	−0.270268	−	0.962785i	$-0.587112\pi$
$947$	−16.6341	−0.540537	−0.270268	+	0.962785i	$0.587112\pi$
$948$	30.4403	0.988654
$949$	0.567581	0.0184244
$950$	5.46570	0.177331
$951$	−98.3864	−3.19040
$952$	0.661947	0.0214538
$953$	49.9243	1.61721	0.808603	−	0.588355i	$-0.200224\pi$
$953$	49.9243	1.61721	0.808603	+	0.588355i	$0.200224\pi$
$954$	−43.6066	−1.41182
$955$	−11.8358	−0.382998
$956$	13.2132	0.427345
$957$	−77.0006	−2.48908
$958$	−32.7343	−1.05760
$959$	5.62172	0.181535
$960$	5.79529	0.187042
$961$	26.8969	0.867641
$962$	4.71318	0.151959
$963$	−69.7567	−2.24788
$964$	−3.33042	−0.107266
$965$	42.9367	1.38218
$966$	−0.868502	−0.0279436
$967$	16.4027	0.527475	0.263738	−	0.964594i	$-0.415045\pi$
$967$	16.4027	0.527475	0.263738	+	0.964594i	$0.415045\pi$
$968$	−9.90157	−0.318249
$969$	−34.5939	−1.11132
$970$	−19.9629	−0.640971
$971$	39.0035	1.25168	0.625841	−	0.779950i	$-0.284756\pi$
$971$	39.0035	1.25168	0.625841	+	0.779950i	$0.284756\pi$
$972$	9.01853	0.289269
$973$	−2.72339	−0.0873079
$974$	−11.4435	−0.366674
$975$	8.42242	0.269733
$976$	8.87265	0.284007
$977$	30.7719	0.984482	0.492241	−	0.870459i	$-0.336178\pi$
$977$	30.7719	0.984482	0.492241	+	0.870459i	$0.336178\pi$
$978$	−12.6783	−0.405409
$979$	59.0266	1.88650
$980$	13.7953	0.440675
$981$	50.8794	1.62446
$982$	−19.9055	−0.635210
$983$	−6.75620	−0.215489	−0.107745	−	0.994179i	$-0.534363\pi$
$983$	−6.75620	−0.215489	−0.107745	+	0.994179i	$0.534363\pi$
$984$	1.03407	0.0329651
$985$	2.33696	0.0744617
$986$	12.8368	0.408807
$987$	−1.31491	−0.0418542
$988$	15.3965	0.489827
$989$	11.6690	0.371054
$990$	−49.5361	−1.57436
$991$	2.50644	0.0796196	0.0398098	−	0.999207i	$-0.487325\pi$
$991$	2.50644	0.0796196	0.0398098	+	0.999207i	$0.487325\pi$
$992$	−7.60900	−0.241586
$993$	−20.3967	−0.647270
$994$	−1.79548	−0.0569492
$995$	−21.8441	−0.692504
$996$	−43.2473	−1.37034
$997$	−12.3300	−0.390496	−0.195248	−	0.980754i	$-0.562551\pi$
$997$	−12.3300	−0.390496	−0.195248	+	0.980754i	$0.562551\pi$
$998$	20.4136	0.646181
$999$	11.6191	0.367611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.3	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.3	✓	33	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.90304 q^{3} +1.00000 q^{4} -1.99628 q^{5} +2.90304 q^{6} -0.299170 q^{7} -1.00000 q^{8} +5.42764 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.90304 q^{3} +1.00000 q^{4} -1.99628 q^{5} +2.90304 q^{6} -0.299170 q^{7} -1.00000 q^{8} +5.42764 q^{9} +1.99628 q^{10} -4.57182 q^{11} -2.90304 q^{12} +2.85877 q^{13} +0.299170 q^{14} +5.79529 q^{15} +1.00000 q^{16} +2.21261 q^{17} -5.42764 q^{18} +5.38569 q^{19} -1.99628 q^{20} +0.868502 q^{21} +4.57182 q^{22} +1.00000 q^{23} +2.90304 q^{24} -1.01486 q^{25} -2.85877 q^{26} -7.04752 q^{27} -0.299170 q^{28} -5.80165 q^{29} -5.79529 q^{30} +7.60900 q^{31} -1.00000 q^{32} +13.2722 q^{33} -2.21261 q^{34} +0.597228 q^{35} +5.42764 q^{36} -1.64867 q^{37} -5.38569 q^{38} -8.29913 q^{39} +1.99628 q^{40} +0.356204 q^{41} -0.868502 q^{42} +11.6690 q^{43} -4.57182 q^{44} -10.8351 q^{45} -1.00000 q^{46} -1.51400 q^{47} -2.90304 q^{48} -6.91050 q^{49} +1.01486 q^{50} -6.42330 q^{51} +2.85877 q^{52} +8.03418 q^{53} +7.04752 q^{54} +9.12665 q^{55} +0.299170 q^{56} -15.6349 q^{57} +5.80165 q^{58} +5.74589 q^{59} +5.79529 q^{60} +8.87265 q^{61} -7.60900 q^{62} -1.62379 q^{63} +1.00000 q^{64} -5.70692 q^{65} -13.2722 q^{66} -15.2925 q^{67} +2.21261 q^{68} -2.90304 q^{69} -0.597228 q^{70} -6.00154 q^{71} -5.42764 q^{72} +0.198540 q^{73} +1.64867 q^{74} +2.94617 q^{75} +5.38569 q^{76} +1.36775 q^{77} +8.29913 q^{78} -10.4857 q^{79} -1.99628 q^{80} +4.17633 q^{81} -0.356204 q^{82} +14.8972 q^{83} +0.868502 q^{84} -4.41700 q^{85} -11.6690 q^{86} +16.8424 q^{87} +4.57182 q^{88} -12.9109 q^{89} +10.8351 q^{90} -0.855258 q^{91} +1.00000 q^{92} -22.0892 q^{93} +1.51400 q^{94} -10.7514 q^{95} +2.90304 q^{96} -10.0001 q^{97} +6.91050 q^{98} -24.8142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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