LMFDB - Embedded newform 4029.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64354 q^{2} +1.00000 q^{3} +0.701226 q^{4} -1.87389 q^{5} -1.64354 q^{6} +4.02619 q^{7} +2.13459 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64354 q^{2} +1.00000 q^{3} +0.701226 q^{4} -1.87389 q^{5} -1.64354 q^{6} +4.02619 q^{7} +2.13459 q^{8} +1.00000 q^{9} +3.07982 q^{10} +1.57234 q^{11} +0.701226 q^{12} +6.00260 q^{13} -6.61722 q^{14} -1.87389 q^{15} -4.91073 q^{16} -1.00000 q^{17} -1.64354 q^{18} -4.16573 q^{19} -1.31402 q^{20} +4.02619 q^{21} -2.58421 q^{22} -5.70138 q^{23} +2.13459 q^{24} -1.48853 q^{25} -9.86552 q^{26} +1.00000 q^{27} +2.82327 q^{28} -6.30134 q^{29} +3.07982 q^{30} -7.90347 q^{31} +3.80182 q^{32} +1.57234 q^{33} +1.64354 q^{34} -7.54465 q^{35} +0.701226 q^{36} +1.44929 q^{37} +6.84655 q^{38} +6.00260 q^{39} -3.99998 q^{40} -3.49955 q^{41} -6.61722 q^{42} -9.58852 q^{43} +1.10257 q^{44} -1.87389 q^{45} +9.37046 q^{46} -12.8082 q^{47} -4.91073 q^{48} +9.21024 q^{49} +2.44646 q^{50} -1.00000 q^{51} +4.20918 q^{52} +2.73831 q^{53} -1.64354 q^{54} -2.94640 q^{55} +8.59426 q^{56} -4.16573 q^{57} +10.3565 q^{58} -8.41033 q^{59} -1.31402 q^{60} -5.52302 q^{61} +12.9897 q^{62} +4.02619 q^{63} +3.57303 q^{64} -11.2482 q^{65} -2.58421 q^{66} +9.95968 q^{67} -0.701226 q^{68} -5.70138 q^{69} +12.3999 q^{70} -9.36694 q^{71} +2.13459 q^{72} -3.13560 q^{73} -2.38196 q^{74} -1.48853 q^{75} -2.92112 q^{76} +6.33056 q^{77} -9.86552 q^{78} +1.00000 q^{79} +9.20218 q^{80} +1.00000 q^{81} +5.75166 q^{82} -15.8400 q^{83} +2.82327 q^{84} +1.87389 q^{85} +15.7591 q^{86} -6.30134 q^{87} +3.35630 q^{88} +3.61125 q^{89} +3.07982 q^{90} +24.1676 q^{91} -3.99796 q^{92} -7.90347 q^{93} +21.0508 q^{94} +7.80612 q^{95} +3.80182 q^{96} +19.0229 q^{97} -15.1374 q^{98} +1.57234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * 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 $

$2$	−1.64354	−1.16216	−0.581079	−	0.813847i	$-0.697369\pi$
$2$	−1.64354	−1.16216	−0.581079	+	0.813847i	$0.697369\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.701226	0.350613
$5$	−1.87389	−0.838030	−0.419015	−	0.907979i	$-0.637624\pi$
$5$	−1.87389	−0.838030	−0.419015	+	0.907979i	$0.637624\pi$
$6$	−1.64354	−0.670973
$7$	4.02619	1.52176	0.760879	−	0.648893i	$-0.224768\pi$
$7$	4.02619	1.52176	0.760879	+	0.648893i	$0.224768\pi$
$8$	2.13459	0.754691
$9$	1.00000	0.333333
$10$	3.07982	0.973923
$11$	1.57234	0.474079	0.237040	−	0.971500i	$-0.423823\pi$
$11$	1.57234	0.474079	0.237040	+	0.971500i	$0.423823\pi$
$12$	0.701226	0.202427
$13$	6.00260	1.66482	0.832411	−	0.554159i	$-0.186960\pi$
$13$	6.00260	1.66482	0.832411	+	0.554159i	$0.186960\pi$
$14$	−6.61722	−1.76853
$15$	−1.87389	−0.483837
$16$	−4.91073	−1.22768
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.64354	−0.387386
$19$	−4.16573	−0.955684	−0.477842	−	0.878446i	$-0.658581\pi$
$19$	−4.16573	−0.955684	−0.477842	+	0.878446i	$0.658581\pi$
$20$	−1.31402	−0.293824
$21$	4.02619	0.878588
$22$	−2.58421	−0.550955
$23$	−5.70138	−1.18882	−0.594410	−	0.804162i	$-0.702615\pi$
$23$	−5.70138	−1.18882	−0.594410	+	0.804162i	$0.702615\pi$
$24$	2.13459	0.435721
$25$	−1.48853	−0.297707
$26$	−9.86552	−1.93479
$27$	1.00000	0.192450
$28$	2.82327	0.533549
$29$	−6.30134	−1.17013	−0.585065	−	0.810987i	$-0.698931\pi$
$29$	−6.30134	−1.17013	−0.585065	+	0.810987i	$0.698931\pi$
$30$	3.07982	0.562295
$31$	−7.90347	−1.41951	−0.709753	−	0.704451i	$-0.751193\pi$
$31$	−7.90347	−1.41951	−0.709753	+	0.704451i	$0.751193\pi$
$32$	3.80182	0.672073
$33$	1.57234	0.273710
$34$	1.64354	0.281865
$35$	−7.54465	−1.27528
$36$	0.701226	0.116871
$37$	1.44929	0.238261	0.119131	−	0.992879i	$-0.461989\pi$
$37$	1.44929	0.238261	0.119131	+	0.992879i	$0.461989\pi$
$38$	6.84655	1.11066
$39$	6.00260	0.961185
$40$	−3.99998	−0.632453
$41$	−3.49955	−0.546539	−0.273269	−	0.961938i	$-0.588105\pi$
$41$	−3.49955	−0.546539	−0.273269	+	0.961938i	$0.588105\pi$
$42$	−6.61722	−1.02106
$43$	−9.58852	−1.46224	−0.731118	−	0.682251i	$-0.761001\pi$
$43$	−9.58852	−1.46224	−0.731118	+	0.682251i	$0.761001\pi$
$44$	1.10257	0.166218
$45$	−1.87389	−0.279343
$46$	9.37046	1.38160
$47$	−12.8082	−1.86827	−0.934135	−	0.356921i	$-0.883827\pi$
$47$	−12.8082	−1.86827	−0.934135	+	0.356921i	$0.883827\pi$
$48$	−4.91073	−0.708803
$49$	9.21024	1.31575
$50$	2.44646	0.345982
$51$	−1.00000	−0.140028
$52$	4.20918	0.583708
$53$	2.73831	0.376136	0.188068	−	0.982156i	$-0.439778\pi$
$53$	2.73831	0.376136	0.188068	+	0.982156i	$0.439778\pi$
$54$	−1.64354	−0.223658
$55$	−2.94640	−0.397292
$56$	8.59426	1.14846
$57$	−4.16573	−0.551764
$58$	10.3565	1.35988
$59$	−8.41033	−1.09493	−0.547466	−	0.836828i	$-0.684407\pi$
$59$	−8.41033	−1.09493	−0.547466	+	0.836828i	$0.684407\pi$
$60$	−1.31402	−0.169639
$61$	−5.52302	−0.707150	−0.353575	−	0.935406i	$-0.615034\pi$
$61$	−5.52302	−0.707150	−0.353575	+	0.935406i	$0.615034\pi$
$62$	12.9897	1.64969
$63$	4.02619	0.507253
$64$	3.57303	0.446628
$65$	−11.2482	−1.39517
$66$	−2.58421	−0.318094
$67$	9.95968	1.21677	0.608384	−	0.793643i	$-0.291818\pi$
$67$	9.95968	1.21677	0.608384	+	0.793643i	$0.291818\pi$
$68$	−0.701226	−0.0850362
$69$	−5.70138	−0.686366
$70$	12.3999	1.48208
$71$	−9.36694	−1.11165	−0.555825	−	0.831299i	$-0.687598\pi$
$71$	−9.36694	−1.11165	−0.555825	+	0.831299i	$0.687598\pi$
$72$	2.13459	0.251564
$73$	−3.13560	−0.366994	−0.183497	−	0.983020i	$-0.558742\pi$
$73$	−3.13560	−0.366994	−0.183497	+	0.983020i	$0.558742\pi$
$74$	−2.38196	−0.276898
$75$	−1.48853	−0.171881
$76$	−2.92112	−0.335075
$77$	6.33056	0.721434
$78$	−9.86552	−1.11705
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	9.20218	1.02884
$81$	1.00000	0.111111
$82$	5.75166	0.635165
$83$	−15.8400	−1.73866	−0.869331	−	0.494230i	$-0.835450\pi$
$83$	−15.8400	−1.73866	−0.869331	+	0.494230i	$0.835450\pi$
$84$	2.82327	0.308044
$85$	1.87389	0.203252
$86$	15.7591	1.69935
$87$	−6.30134	−0.675574
$88$	3.35630	0.357783
$89$	3.61125	0.382791	0.191396	−	0.981513i	$-0.438699\pi$
$89$	3.61125	0.382791	0.191396	+	0.981513i	$0.438699\pi$
$90$	3.07982	0.324641
$91$	24.1676	2.53346
$92$	−3.99796	−0.416816
$93$	−7.90347	−0.819552
$94$	21.0508	2.17123
$95$	7.80612	0.800891
$96$	3.80182	0.388021
$97$	19.0229	1.93148	0.965740	−	0.259512i	$-0.0835616\pi$
$97$	19.0229	1.93148	0.965740	+	0.259512i	$0.0835616\pi$
$98$	−15.1374	−1.52911
$99$	1.57234	0.158026
$100$	−1.04380	−0.104380
$101$	12.8736	1.28097	0.640487	−	0.767969i	$-0.278733\pi$
$101$	12.8736	1.28097	0.640487	+	0.767969i	$0.278733\pi$
$102$	1.64354	0.162735
$103$	2.52916	0.249205	0.124603	−	0.992207i	$-0.460234\pi$
$103$	2.52916	0.249205	0.124603	+	0.992207i	$0.460234\pi$
$104$	12.8131	1.25643
$105$	−7.54465	−0.736282
$106$	−4.50052	−0.437129
$107$	−16.7440	−1.61870	−0.809351	−	0.587325i	$-0.800181\pi$
$107$	−16.7440	−1.61870	−0.809351	+	0.587325i	$0.800181\pi$
$108$	0.701226	0.0674755
$109$	2.21954	0.212594	0.106297	−	0.994334i	$-0.466101\pi$
$109$	2.21954	0.212594	0.106297	+	0.994334i	$0.466101\pi$
$110$	4.84253	0.461717
$111$	1.44929	0.137560
$112$	−19.7716	−1.86824
$113$	−6.15563	−0.579073	−0.289537	−	0.957167i	$-0.593501\pi$
$113$	−6.15563	−0.579073	−0.289537	+	0.957167i	$0.593501\pi$
$114$	6.84655	0.641238
$115$	10.6838	0.996267
$116$	−4.41867	−0.410263
$117$	6.00260	0.554940
$118$	13.8227	1.27248
$119$	−4.02619	−0.369081
$120$	−3.99998	−0.365147
$121$	−8.52774	−0.775249
$122$	9.07731	0.821821
$123$	−3.49955	−0.315544
$124$	−5.54212	−0.497697
$125$	12.1588	1.08752
$126$	−6.61722	−0.589508
$127$	−15.7723	−1.39956	−0.699782	−	0.714356i	$-0.746720\pi$
$127$	−15.7723	−1.39956	−0.699782	+	0.714356i	$0.746720\pi$
$128$	−13.4760	−1.19113
$129$	−9.58852	−0.844222
$130$	18.4869	1.62141
$131$	11.9268	1.04205	0.521024	−	0.853542i	$-0.325550\pi$
$131$	11.9268	1.04205	0.521024	+	0.853542i	$0.325550\pi$
$132$	1.10257	0.0959663
$133$	−16.7720	−1.45432
$134$	−16.3691	−1.41408
$135$	−1.87389	−0.161279
$136$	−2.13459	−0.183039
$137$	−3.77559	−0.322571	−0.161285	−	0.986908i	$-0.551564\pi$
$137$	−3.77559	−0.322571	−0.161285	+	0.986908i	$0.551564\pi$
$138$	9.37046	0.797666
$139$	−11.3354	−0.961455	−0.480728	−	0.876870i	$-0.659627\pi$
$139$	−11.3354	−0.961455	−0.480728	+	0.876870i	$0.659627\pi$
$140$	−5.29051	−0.447130
$141$	−12.8082	−1.07865
$142$	15.3949	1.29191
$143$	9.43814	0.789257
$144$	−4.91073	−0.409228
$145$	11.8080	0.980603
$146$	5.15348	0.426505
$147$	9.21024	0.759648
$148$	1.01628	0.0835376
$149$	23.1757	1.89863	0.949313	−	0.314333i	$-0.101781\pi$
$149$	23.1757	1.89863	0.949313	+	0.314333i	$0.101781\pi$
$150$	2.44646	0.199753
$151$	−1.55409	−0.126470	−0.0632351	−	0.997999i	$-0.520142\pi$
$151$	−1.55409	−0.126470	−0.0632351	+	0.997999i	$0.520142\pi$
$152$	−8.89212	−0.721246
$153$	−1.00000	−0.0808452
$154$	−10.4045	−0.838421
$155$	14.8102	1.18959
$156$	4.20918	0.337004
$157$	2.15027	0.171610	0.0858052	−	0.996312i	$-0.472654\pi$
$157$	2.15027	0.171610	0.0858052	+	0.996312i	$0.472654\pi$
$158$	−1.64354	−0.130753
$159$	2.73831	0.217162
$160$	−7.12419	−0.563217
$161$	−22.9549	−1.80910
$162$	−1.64354	−0.129129
$163$	−20.1342	−1.57703	−0.788517	−	0.615012i	$-0.789151\pi$
$163$	−20.1342	−1.57703	−0.788517	+	0.615012i	$0.789151\pi$
$164$	−2.45398	−0.191624
$165$	−2.94640	−0.229377
$166$	26.0336	2.02060
$167$	−9.76207	−0.755412	−0.377706	−	0.925926i	$-0.623287\pi$
$167$	−9.76207	−0.755412	−0.377706	+	0.925926i	$0.623287\pi$
$168$	8.59426	0.663062
$169$	23.0312	1.77163
$170$	−3.07982	−0.236211
$171$	−4.16573	−0.318561
$172$	−6.72373	−0.512679
$173$	20.6121	1.56711	0.783556	−	0.621321i	$-0.213404\pi$
$173$	20.6121	1.56711	0.783556	+	0.621321i	$0.213404\pi$
$174$	10.3565	0.785125
$175$	−5.99312	−0.453037
$176$	−7.72136	−0.582019
$177$	−8.41033	−0.632159
$178$	−5.93523	−0.444864
$179$	2.03538	0.152131	0.0760657	−	0.997103i	$-0.475764\pi$
$179$	2.03538	0.152131	0.0760657	+	0.997103i	$0.475764\pi$
$180$	−1.31402	−0.0979414
$181$	1.70878	0.127013	0.0635065	−	0.997981i	$-0.479772\pi$
$181$	1.70878	0.127013	0.0635065	+	0.997981i	$0.479772\pi$
$182$	−39.7205	−2.94428
$183$	−5.52302	−0.408273
$184$	−12.1701	−0.897192
$185$	−2.71581	−0.199670
$186$	12.9897	0.952449
$187$	−1.57234	−0.114981
$188$	−8.98145	−0.655040
$189$	4.02619	0.292863
$190$	−12.8297	−0.930763
$191$	−3.23995	−0.234435	−0.117217	−	0.993106i	$-0.537397\pi$
$191$	−3.23995	−0.234435	−0.117217	+	0.993106i	$0.537397\pi$
$192$	3.57303	0.257861
$193$	16.0263	1.15360	0.576800	−	0.816885i	$-0.304301\pi$
$193$	16.0263	1.15360	0.576800	+	0.816885i	$0.304301\pi$
$194$	−31.2649	−2.24469
$195$	−11.2482	−0.805501
$196$	6.45847	0.461319
$197$	−20.8560	−1.48593	−0.742963	−	0.669332i	$-0.766580\pi$
$197$	−20.8560	−1.48593	−0.742963	+	0.669332i	$0.766580\pi$
$198$	−2.58421	−0.183652
$199$	−4.24910	−0.301211	−0.150605	−	0.988594i	$-0.548122\pi$
$199$	−4.24910	−0.301211	−0.150605	+	0.988594i	$0.548122\pi$
$200$	−3.17740	−0.224676
$201$	9.95968	0.702502
$202$	−21.1583	−1.48869
$203$	−25.3704	−1.78065
$204$	−0.701226	−0.0490957
$205$	6.55778	0.458016
$206$	−4.15677	−0.289616
$207$	−5.70138	−0.396274
$208$	−29.4772	−2.04387
$209$	−6.54996	−0.453070
$210$	12.3999	0.855677
$211$	3.50248	0.241121	0.120560	−	0.992706i	$-0.461531\pi$
$211$	3.50248	0.241121	0.120560	+	0.992706i	$0.461531\pi$
$212$	1.92017	0.131878
$213$	−9.36694	−0.641812
$214$	27.5194	1.88119
$215$	17.9678	1.22540
$216$	2.13459	0.145240
$217$	−31.8209	−2.16014
$218$	−3.64791	−0.247068
$219$	−3.13560	−0.211884
$220$	−2.06609	−0.139296
$221$	−6.00260	−0.403779
$222$	−2.38196	−0.159867
$223$	−14.3138	−0.958520	−0.479260	−	0.877673i	$-0.659095\pi$
$223$	−14.3138	−0.958520	−0.479260	+	0.877673i	$0.659095\pi$
$224$	15.3069	1.02273
$225$	−1.48853	−0.0992355
$226$	10.1170	0.672975
$227$	0.970562	0.0644184	0.0322092	−	0.999481i	$-0.489746\pi$
$227$	0.970562	0.0644184	0.0322092	+	0.999481i	$0.489746\pi$
$228$	−2.92112	−0.193456
$229$	−18.9590	−1.25284	−0.626422	−	0.779484i	$-0.715481\pi$
$229$	−18.9590	−1.25284	−0.626422	+	0.779484i	$0.715481\pi$
$230$	−17.5592	−1.15782
$231$	6.33056	0.416520
$232$	−13.4508	−0.883086
$233$	8.24911	0.540417	0.270208	−	0.962802i	$-0.412907\pi$
$233$	8.24911	0.540417	0.270208	+	0.962802i	$0.412907\pi$
$234$	−9.86552	−0.644929
$235$	24.0012	1.56566
$236$	−5.89755	−0.383898
$237$	1.00000	0.0649570
$238$	6.61722	0.428930
$239$	−5.92494	−0.383252	−0.191626	−	0.981468i	$-0.561376\pi$
$239$	−5.92494	−0.383252	−0.191626	+	0.981468i	$0.561376\pi$
$240$	9.20218	0.593998
$241$	30.9870	1.99605	0.998024	−	0.0628267i	$-0.0200115\pi$
$241$	30.9870	1.99605	0.998024	+	0.0628267i	$0.0200115\pi$
$242$	14.0157	0.900962
$243$	1.00000	0.0641500
$244$	−3.87289	−0.247936
$245$	−17.2590	−1.10264
$246$	5.75166	0.366713
$247$	−25.0052	−1.59104
$248$	−16.8707	−1.07129
$249$	−15.8400	−1.00382
$250$	−19.9835	−1.26387
$251$	2.20770	0.139348	0.0696742	−	0.997570i	$-0.477804\pi$
$251$	2.20770	0.139348	0.0696742	+	0.997570i	$0.477804\pi$
$252$	2.82327	0.177850
$253$	−8.96453	−0.563595
$254$	25.9224	1.62652
$255$	1.87389	0.117348
$256$	15.0024	0.937649
$257$	−18.3513	−1.14472	−0.572360	−	0.820002i	$-0.693972\pi$
$257$	−18.3513	−1.14472	−0.572360	+	0.820002i	$0.693972\pi$
$258$	15.7591	0.981121
$259$	5.83511	0.362576
$260$	−7.88755	−0.489165
$261$	−6.30134	−0.390043
$262$	−19.6022	−1.21103
$263$	−3.94964	−0.243545	−0.121773	−	0.992558i	$-0.538858\pi$
$263$	−3.94964	−0.243545	−0.121773	+	0.992558i	$0.538858\pi$
$264$	3.35630	0.206566
$265$	−5.13129	−0.315213
$266$	27.5655	1.69015
$267$	3.61125	0.221005
$268$	6.98399	0.426615
$269$	−30.6003	−1.86573	−0.932867	−	0.360222i	$-0.882701\pi$
$269$	−30.6003	−1.86573	−0.932867	+	0.360222i	$0.882701\pi$
$270$	3.07982	0.187432
$271$	12.3028	0.747339	0.373670	−	0.927562i	$-0.378099\pi$
$271$	12.3028	0.747339	0.373670	+	0.927562i	$0.378099\pi$
$272$	4.91073	0.297757
$273$	24.1676	1.46269
$274$	6.20534	0.374878
$275$	−2.34048	−0.141136
$276$	−3.99796	−0.240649
$277$	15.7153	0.944238	0.472119	−	0.881535i	$-0.343489\pi$
$277$	15.7153	0.944238	0.472119	+	0.881535i	$0.343489\pi$
$278$	18.6302	1.11736
$279$	−7.90347	−0.473168
$280$	−16.1047	−0.962441
$281$	−7.37271	−0.439819	−0.219910	−	0.975520i	$-0.570576\pi$
$281$	−7.37271	−0.439819	−0.219910	+	0.975520i	$0.570576\pi$
$282$	21.0508	1.25356
$283$	18.8184	1.11864	0.559319	−	0.828952i	$-0.311063\pi$
$283$	18.8184	1.11864	0.559319	+	0.828952i	$0.311063\pi$
$284$	−6.56834	−0.389759
$285$	7.80612	0.462395
$286$	−15.5120	−0.917242
$287$	−14.0899	−0.831700
$288$	3.80182	0.224024
$289$	1.00000	0.0588235
$290$	−19.4070	−1.13962
$291$	19.0229	1.11514
$292$	−2.19876	−0.128673
$293$	29.3202	1.71291	0.856453	−	0.516225i	$-0.172663\pi$
$293$	29.3202	1.71291	0.856453	+	0.516225i	$0.172663\pi$
$294$	−15.1374	−0.882832
$295$	15.7600	0.917585
$296$	3.09363	0.179814
$297$	1.57234	0.0912366
$298$	−38.0902	−2.20650
$299$	−34.2231	−1.97917
$300$	−1.04380	−0.0602637
$301$	−38.6053	−2.22517
$302$	2.55421	0.146978
$303$	12.8736	0.739570
$304$	20.4568	1.17328
$305$	10.3495	0.592613
$306$	1.64354	0.0939550
$307$	−6.78361	−0.387161	−0.193580	−	0.981084i	$-0.562010\pi$
$307$	−6.78361	−0.387161	−0.193580	+	0.981084i	$0.562010\pi$
$308$	4.43915	0.252944
$309$	2.52916	0.143879
$310$	−24.3412	−1.38249
$311$	9.89737	0.561228	0.280614	−	0.959821i	$-0.409462\pi$
$311$	9.89737	0.561228	0.280614	+	0.959821i	$0.409462\pi$
$312$	12.8131	0.725397
$313$	13.1007	0.740495	0.370248	−	0.928933i	$-0.379273\pi$
$313$	13.1007	0.740495	0.370248	+	0.928933i	$0.379273\pi$
$314$	−3.53406	−0.199438
$315$	−7.54465	−0.425093
$316$	0.701226	0.0394471
$317$	0.478643	0.0268833	0.0134416	−	0.999910i	$-0.495721\pi$
$317$	0.478643	0.0268833	0.0134416	+	0.999910i	$0.495721\pi$
$318$	−4.50052	−0.252377
$319$	−9.90787	−0.554734
$320$	−6.69546	−0.374288
$321$	−16.7440	−0.934558
$322$	37.7273	2.10246
$323$	4.16573	0.231787
$324$	0.701226	0.0389570
$325$	−8.93506	−0.495628
$326$	33.0914	1.83277
$327$	2.21954	0.122741
$328$	−7.47011	−0.412468
$329$	−51.5683	−2.84306
$330$	4.84253	0.266572
$331$	23.1152	1.27053	0.635263	−	0.772296i	$-0.280892\pi$
$331$	23.1152	1.27053	0.635263	+	0.772296i	$0.280892\pi$
$332$	−11.1074	−0.609598
$333$	1.44929	0.0794205
$334$	16.0444	0.877909
$335$	−18.6634	−1.01969
$336$	−19.7716	−1.07863
$337$	22.5577	1.22879	0.614397	−	0.788997i	$-0.289399\pi$
$337$	22.5577	1.22879	0.614397	+	0.788997i	$0.289399\pi$
$338$	−37.8527	−2.05892
$339$	−6.15563	−0.334328
$340$	1.31402	0.0712628
$341$	−12.4270	−0.672958
$342$	6.84655	0.370219
$343$	8.89887	0.480494
$344$	−20.4675	−1.10354
$345$	10.6838	0.575195
$346$	−33.8769	−1.82123
$347$	24.9094	1.33721	0.668603	−	0.743619i	$-0.266892\pi$
$347$	24.9094	1.33721	0.668603	+	0.743619i	$0.266892\pi$
$348$	−4.41867	−0.236865
$349$	−10.1007	−0.540676	−0.270338	−	0.962765i	$-0.587136\pi$
$349$	−10.1007	−0.540676	−0.270338	+	0.962765i	$0.587136\pi$
$350$	9.84994	0.526502
$351$	6.00260	0.320395
$352$	5.97776	0.318616
$353$	−5.70496	−0.303644	−0.151822	−	0.988408i	$-0.548514\pi$
$353$	−5.70496	−0.303644	−0.151822	+	0.988408i	$0.548514\pi$
$354$	13.8227	0.734670
$355$	17.5526	0.931596
$356$	2.53230	0.134212
$357$	−4.02619	−0.213089
$358$	−3.34523	−0.176801
$359$	23.4935	1.23994	0.619970	−	0.784626i	$-0.287145\pi$
$359$	23.4935	1.23994	0.619970	+	0.784626i	$0.287145\pi$
$360$	−3.99998	−0.210818
$361$	−1.64669	−0.0866679
$362$	−2.80846	−0.147609
$363$	−8.52774	−0.447590
$364$	16.9470	0.888263
$365$	5.87576	0.307551
$366$	9.07731	0.474479
$367$	7.23189	0.377502	0.188751	−	0.982025i	$-0.439556\pi$
$367$	7.23189	0.377502	0.188751	+	0.982025i	$0.439556\pi$
$368$	27.9980	1.45950
$369$	−3.49955	−0.182180
$370$	4.46354	0.232048
$371$	11.0250	0.572388
$372$	−5.54212	−0.287346
$373$	11.9006	0.616187	0.308094	−	0.951356i	$-0.400309\pi$
$373$	11.9006	0.616187	0.308094	+	0.951356i	$0.400309\pi$
$374$	2.58421	0.133626
$375$	12.1588	0.627878
$376$	−27.3402	−1.40997
$377$	−37.8244	−1.94806
$378$	−6.61722	−0.340353
$379$	18.4314	0.946756	0.473378	−	0.880859i	$-0.343034\pi$
$379$	18.4314	0.946756	0.473378	+	0.880859i	$0.343034\pi$
$380$	5.47386	0.280803
$381$	−15.7723	−0.808039
$382$	5.32499	0.272450
$383$	30.0986	1.53796	0.768982	−	0.639270i	$-0.220763\pi$
$383$	30.0986	1.53796	0.768982	+	0.639270i	$0.220763\pi$
$384$	−13.4760	−0.687697
$385$	−11.8628	−0.604583
$386$	−26.3399	−1.34067
$387$	−9.58852	−0.487412
$388$	13.3393	0.677202
$389$	15.6748	0.794743	0.397371	−	0.917658i	$-0.369923\pi$
$389$	15.6748	0.794743	0.397371	+	0.917658i	$0.369923\pi$
$390$	18.4869	0.936121
$391$	5.70138	0.288331
$392$	19.6601	0.992984
$393$	11.9268	0.601627
$394$	34.2777	1.72688
$395$	−1.87389	−0.0942857
$396$	1.10257	0.0554061
$397$	−10.7369	−0.538870	−0.269435	−	0.963019i	$-0.586837\pi$
$397$	−10.7369	−0.538870	−0.269435	+	0.963019i	$0.586837\pi$
$398$	6.98357	0.350055
$399$	−16.7720	−0.839652
$400$	7.30979	0.365489
$401$	27.3969	1.36813	0.684067	−	0.729419i	$-0.260210\pi$
$401$	27.3969	1.36813	0.684067	+	0.729419i	$0.260210\pi$
$402$	−16.3691	−0.816418
$403$	−47.4414	−2.36322
$404$	9.02732	0.449126
$405$	−1.87389	−0.0931144
$406$	41.6973	2.06940
$407$	2.27878	0.112955
$408$	−2.13459	−0.105678
$409$	12.7387	0.629890	0.314945	−	0.949110i	$-0.398014\pi$
$409$	12.7387	0.629890	0.314945	+	0.949110i	$0.398014\pi$
$410$	−10.7780	−0.532287
$411$	−3.77559	−0.186236
$412$	1.77351	0.0873746
$413$	−33.8616	−1.66622
$414$	9.37046	0.460533
$415$	29.6824	1.45705
$416$	22.8208	1.11888
$417$	−11.3354	−0.555096
$418$	10.7651	0.526539
$419$	1.67545	0.0818512	0.0409256	−	0.999162i	$-0.486969\pi$
$419$	1.67545	0.0818512	0.0409256	+	0.999162i	$0.486969\pi$
$420$	−5.29051	−0.258150
$421$	−9.69373	−0.472444	−0.236222	−	0.971699i	$-0.575909\pi$
$421$	−9.69373	−0.472444	−0.236222	+	0.971699i	$0.575909\pi$
$422$	−5.75647	−0.280221
$423$	−12.8082	−0.622756
$424$	5.84516	0.283866
$425$	1.48853	0.0722044
$426$	15.3949	0.745887
$427$	−22.2368	−1.07611
$428$	−11.7413	−0.567538
$429$	9.43814	0.455678
$430$	−29.5309	−1.42411
$431$	27.4054	1.32007	0.660035	−	0.751235i	$-0.270542\pi$
$431$	27.4054	1.32007	0.660035	+	0.751235i	$0.270542\pi$
$432$	−4.91073	−0.236268
$433$	−17.1276	−0.823099	−0.411550	−	0.911387i	$-0.635012\pi$
$433$	−17.1276	−0.823099	−0.411550	+	0.911387i	$0.635012\pi$
$434$	52.2990	2.51043
$435$	11.8080	0.566151
$436$	1.55640	0.0745381
$437$	23.7504	1.13614
$438$	5.15348	0.246243
$439$	6.60979	0.315468	0.157734	−	0.987482i	$-0.449581\pi$
$439$	6.60979	0.315468	0.157734	+	0.987482i	$0.449581\pi$
$440$	−6.28935	−0.299833
$441$	9.21024	0.438583
$442$	9.86552	0.469255
$443$	−21.2857	−1.01131	−0.505656	−	0.862735i	$-0.668750\pi$
$443$	−21.2857	−1.01131	−0.505656	+	0.862735i	$0.668750\pi$
$444$	1.01628	0.0482304
$445$	−6.76708	−0.320790
$446$	23.5252	1.11395
$447$	23.1757	1.09617
$448$	14.3857	0.679660
$449$	−23.1691	−1.09342	−0.546710	−	0.837322i	$-0.684120\pi$
$449$	−23.1691	−1.09342	−0.546710	+	0.837322i	$0.684120\pi$
$450$	2.44646	0.115327
$451$	−5.50250	−0.259103
$452$	−4.31649	−0.203031
$453$	−1.55409	−0.0730176
$454$	−1.59516	−0.0748645
$455$	−45.2875	−2.12311
$456$	−8.89212	−0.416411
$457$	23.0205	1.07686	0.538428	−	0.842672i	$-0.319018\pi$
$457$	23.0205	1.07686	0.538428	+	0.842672i	$0.319018\pi$
$458$	31.1598	1.45600
$459$	−1.00000	−0.0466760
$460$	7.49174	0.349304
$461$	0.728801	0.0339436	0.0169718	−	0.999856i	$-0.494597\pi$
$461$	0.728801	0.0339436	0.0169718	+	0.999856i	$0.494597\pi$
$462$	−10.4045	−0.484063
$463$	−31.0227	−1.44175	−0.720873	−	0.693067i	$-0.756259\pi$
$463$	−31.0227	−1.44175	−0.720873	+	0.693067i	$0.756259\pi$
$464$	30.9442	1.43655
$465$	14.8102	0.686809
$466$	−13.5577	−0.628050
$467$	3.22729	0.149341	0.0746706	−	0.997208i	$-0.476209\pi$
$467$	3.22729	0.149341	0.0746706	+	0.997208i	$0.476209\pi$
$468$	4.20918	0.194569
$469$	40.0996	1.85163
$470$	−39.4469	−1.81955
$471$	2.15027	0.0990793
$472$	−17.9526	−0.826335
$473$	−15.0764	−0.693216
$474$	−1.64354	−0.0754903
$475$	6.20083	0.284513
$476$	−2.82327	−0.129405
$477$	2.73831	0.125379
$478$	9.73788	0.445400
$479$	−0.649215	−0.0296634	−0.0148317	−	0.999890i	$-0.504721\pi$
$479$	−0.649215	−0.0296634	−0.0148317	+	0.999890i	$0.504721\pi$
$480$	−7.12419	−0.325173
$481$	8.69949	0.396663
$482$	−50.9284	−2.31973
$483$	−22.9549	−1.04448
$484$	−5.97987	−0.271812
$485$	−35.6468	−1.61864
$486$	−1.64354	−0.0745525
$487$	−26.1850	−1.18656	−0.593278	−	0.804998i	$-0.702166\pi$
$487$	−26.1850	−1.18656	−0.593278	+	0.804998i	$0.702166\pi$
$488$	−11.7894	−0.533680
$489$	−20.1342	−0.910502
$490$	28.3659	1.28144
$491$	33.5319	1.51327	0.756637	−	0.653835i	$-0.226841\pi$
$491$	33.5319	1.51327	0.756637	+	0.653835i	$0.226841\pi$
$492$	−2.45398	−0.110634
$493$	6.30134	0.283798
$494$	41.0971	1.84905
$495$	−2.94640	−0.132431
$496$	38.8119	1.74270
$497$	−37.7131	−1.69166
$498$	26.0336	1.16659
$499$	−25.2548	−1.13056	−0.565280	−	0.824899i	$-0.691232\pi$
$499$	−25.2548	−1.13056	−0.565280	+	0.824899i	$0.691232\pi$
$500$	8.52607	0.381298
$501$	−9.76207	−0.436137
$502$	−3.62844	−0.161945
$503$	0.579446	0.0258362	0.0129181	−	0.999917i	$-0.495888\pi$
$503$	0.579446	0.0258362	0.0129181	+	0.999917i	$0.495888\pi$
$504$	8.59426	0.382819
$505$	−24.1238	−1.07349
$506$	14.7336	0.654987
$507$	23.0312	1.02285
$508$	−11.0599	−0.490706
$509$	−17.9919	−0.797475	−0.398738	−	0.917065i	$-0.630552\pi$
$509$	−17.9919	−0.797475	−0.398738	+	0.917065i	$0.630552\pi$
$510$	−3.07982	−0.136377
$511$	−12.6245	−0.558476
$512$	2.29507	0.101429
$513$	−4.16573	−0.183921
$514$	30.1610	1.33035
$515$	−4.73936	−0.208841
$516$	−6.72373	−0.295996
$517$	−20.1389	−0.885708
$518$	−9.59025	−0.421371
$519$	20.6121	0.904773
$520$	−24.0103	−1.05292
$521$	6.90448	0.302491	0.151245	−	0.988496i	$-0.451672\pi$
$521$	6.90448	0.302491	0.151245	+	0.988496i	$0.451672\pi$
$522$	10.3565	0.453292
$523$	−33.1632	−1.45013	−0.725063	−	0.688683i	$-0.758189\pi$
$523$	−33.1632	−1.45013	−0.725063	+	0.688683i	$0.758189\pi$
$524$	8.36338	0.365356
$525$	−5.99312	−0.261561
$526$	6.49139	0.283038
$527$	7.90347	0.344281
$528$	−7.72136	−0.336029
$529$	9.50578	0.413295
$530$	8.43349	0.366327
$531$	−8.41033	−0.364977
$532$	−11.7610	−0.509904
$533$	−21.0064	−0.909889
$534$	−5.93523	−0.256843
$535$	31.3764	1.35652
$536$	21.2598	0.918284
$537$	2.03538	0.0878331
$538$	50.2928	2.16828
$539$	14.4817	0.623769
$540$	−1.31402	−0.0565465
$541$	−5.45880	−0.234692	−0.117346	−	0.993091i	$-0.537439\pi$
$541$	−5.45880	−0.234692	−0.117346	+	0.993091i	$0.537439\pi$
$542$	−20.2201	−0.868527
$543$	1.70878	0.0733309
$544$	−3.80182	−0.163002
$545$	−4.15918	−0.178160
$546$	−39.7205	−1.69988
$547$	0.0487135	0.00208284	0.00104142	−	0.999999i	$-0.499669\pi$
$547$	0.0487135	0.00208284	0.00104142	+	0.999999i	$0.499669\pi$
$548$	−2.64754	−0.113098
$549$	−5.52302	−0.235717
$550$	3.84668	0.164023
$551$	26.2497	1.11827
$552$	−12.1701	−0.517994
$553$	4.02619	0.171211
$554$	−25.8287	−1.09735
$555$	−2.71581	−0.115280
$556$	−7.94867	−0.337099
$557$	−16.2572	−0.688841	−0.344420	−	0.938816i	$-0.611925\pi$
$557$	−16.2572	−0.688841	−0.344420	+	0.938816i	$0.611925\pi$
$558$	12.9897	0.549897
$559$	−57.5561	−2.43436
$560$	37.0498	1.56564
$561$	−1.57234	−0.0663844
$562$	12.1174	0.511140
$563$	34.2140	1.44195	0.720973	−	0.692963i	$-0.243695\pi$
$563$	34.2140	1.44195	0.720973	+	0.692963i	$0.243695\pi$
$564$	−8.98145	−0.378187
$565$	11.5350	0.485280
$566$	−30.9288	−1.30004
$567$	4.02619	0.169084
$568$	−19.9945	−0.838952
$569$	−15.0473	−0.630817	−0.315408	−	0.948956i	$-0.602141\pi$
$569$	−15.0473	−0.630817	−0.315408	+	0.948956i	$0.602141\pi$
$570$	−12.8297	−0.537376
$571$	−10.8884	−0.455666	−0.227833	−	0.973700i	$-0.573164\pi$
$571$	−10.8884	−0.455666	−0.227833	+	0.973700i	$0.573164\pi$
$572$	6.61828	0.276724
$573$	−3.23995	−0.135351
$574$	23.1573	0.966567
$575$	8.48670	0.353920
$576$	3.57303	0.148876
$577$	−24.1308	−1.00458	−0.502289	−	0.864700i	$-0.667509\pi$
$577$	−24.1308	−1.00458	−0.502289	+	0.864700i	$0.667509\pi$
$578$	−1.64354	−0.0683623
$579$	16.0263	0.666032
$580$	8.28010	0.343812
$581$	−63.7748	−2.64582
$582$	−31.2649	−1.29597
$583$	4.30556	0.178318
$584$	−6.69320	−0.276967
$585$	−11.2482	−0.465056
$586$	−48.1890	−1.99067
$587$	−14.2990	−0.590184	−0.295092	−	0.955469i	$-0.595350\pi$
$587$	−14.2990	−0.590184	−0.295092	+	0.955469i	$0.595350\pi$
$588$	6.45847	0.266343
$589$	32.9237	1.35660
$590$	−25.9023	−1.06638
$591$	−20.8560	−0.857900
$592$	−7.11707	−0.292510
$593$	−35.4311	−1.45498	−0.727490	−	0.686118i	$-0.759313\pi$
$593$	−35.4311	−1.45498	−0.727490	+	0.686118i	$0.759313\pi$
$594$	−2.58421	−0.106031
$595$	7.54465	0.309300
$596$	16.2514	0.665683
$597$	−4.24910	−0.173904
$598$	56.2471	2.30012
$599$	−12.0587	−0.492705	−0.246353	−	0.969180i	$-0.579232\pi$
$599$	−12.0587	−0.492705	−0.246353	+	0.969180i	$0.579232\pi$
$600$	−3.17740	−0.129717
$601$	−14.6145	−0.596137	−0.298068	−	0.954544i	$-0.596342\pi$
$601$	−14.6145	−0.596137	−0.298068	+	0.954544i	$0.596342\pi$
$602$	63.4493	2.58600
$603$	9.95968	0.405589
$604$	−1.08977	−0.0443421
$605$	15.9801	0.649681
$606$	−21.1583	−0.859498
$607$	25.4032	1.03108	0.515541	−	0.856865i	$-0.327591\pi$
$607$	25.4032	1.03108	0.515541	+	0.856865i	$0.327591\pi$
$608$	−15.8373	−0.642289
$609$	−25.3704	−1.02806
$610$	−17.0099	−0.688710
$611$	−76.8825	−3.11033
$612$	−0.701226	−0.0283454
$613$	15.7210	0.634967	0.317484	−	0.948264i	$-0.397162\pi$
$613$	15.7210	0.634967	0.317484	+	0.948264i	$0.397162\pi$
$614$	11.1491	0.449942
$615$	6.55778	0.264435
$616$	13.5131	0.544460
$617$	−3.37944	−0.136051	−0.0680256	−	0.997684i	$-0.521670\pi$
$617$	−3.37944	−0.136051	−0.0680256	+	0.997684i	$0.521670\pi$
$618$	−4.15677	−0.167210
$619$	−35.1366	−1.41226	−0.706130	−	0.708082i	$-0.749561\pi$
$619$	−35.1366	−1.41226	−0.706130	+	0.708082i	$0.749561\pi$
$620$	10.3853	0.417085
$621$	−5.70138	−0.228789
$622$	−16.2667	−0.652236
$623$	14.5396	0.582516
$624$	−29.4772	−1.18003
$625$	−15.3416	−0.613664
$626$	−21.5315	−0.860573
$627$	−6.54996	−0.261580
$628$	1.50783	0.0601688
$629$	−1.44929	−0.0577869
$630$	12.3999	0.494025
$631$	−23.3551	−0.929751	−0.464876	−	0.885376i	$-0.653901\pi$
$631$	−23.3551	−0.929751	−0.464876	+	0.885376i	$0.653901\pi$
$632$	2.13459	0.0849093
$633$	3.50248	0.139211
$634$	−0.786670	−0.0312427
$635$	29.5556	1.17288
$636$	1.92017	0.0761399
$637$	55.2854	2.19049
$638$	16.2840	0.644689
$639$	−9.36694	−0.370550
$640$	25.2526	0.998199
$641$	15.0289	0.593605	0.296803	−	0.954939i	$-0.404080\pi$
$641$	15.0289	0.593605	0.296803	+	0.954939i	$0.404080\pi$
$642$	27.5194	1.08610
$643$	−13.3379	−0.525994	−0.262997	−	0.964797i	$-0.584711\pi$
$643$	−13.3379	−0.525994	−0.262997	+	0.964797i	$0.584711\pi$
$644$	−16.0966	−0.634294
$645$	17.9678	0.707483
$646$	−6.84655	−0.269374
$647$	−17.6514	−0.693950	−0.346975	−	0.937874i	$-0.612791\pi$
$647$	−17.6514	−0.693950	−0.346975	+	0.937874i	$0.612791\pi$
$648$	2.13459	0.0838545
$649$	−13.2239	−0.519085
$650$	14.6851	0.575999
$651$	−31.8209	−1.24716
$652$	−14.1187	−0.552929
$653$	−40.3445	−1.57880	−0.789401	−	0.613878i	$-0.789609\pi$
$653$	−40.3445	−1.57880	−0.789401	+	0.613878i	$0.789609\pi$
$654$	−3.64791	−0.142644
$655$	−22.3495	−0.873267
$656$	17.1854	0.670977
$657$	−3.13560	−0.122331
$658$	84.7547	3.30408
$659$	25.7431	1.00281	0.501405	−	0.865213i	$-0.332817\pi$
$659$	25.7431	1.00281	0.501405	+	0.865213i	$0.332817\pi$
$660$	−2.06609	−0.0804226
$661$	18.0112	0.700556	0.350278	−	0.936646i	$-0.386087\pi$
$661$	18.0112	0.700556	0.350278	+	0.936646i	$0.386087\pi$
$662$	−37.9908	−1.47655
$663$	−6.00260	−0.233122
$664$	−33.8118	−1.31215
$665$	31.4290	1.21876
$666$	−2.38196	−0.0922992
$667$	35.9264	1.39107
$668$	−6.84542	−0.264857
$669$	−14.3138	−0.553402
$670$	30.6740	1.18504
$671$	−8.68408	−0.335245
$672$	15.3069	0.590475
$673$	15.1991	0.585880	0.292940	−	0.956131i	$-0.405366\pi$
$673$	15.1991	0.585880	0.292940	+	0.956131i	$0.405366\pi$
$674$	−37.0744	−1.42805
$675$	−1.48853	−0.0572937
$676$	16.1501	0.621157
$677$	−50.2969	−1.93307	−0.966533	−	0.256542i	$-0.917417\pi$
$677$	−50.2969	−1.93307	−0.966533	+	0.256542i	$0.917417\pi$
$678$	10.1170	0.388542
$679$	76.5898	2.93925
$680$	3.99998	0.153392
$681$	0.970562	0.0371920
$682$	20.4242	0.782084
$683$	−6.85002	−0.262109	−0.131054	−	0.991375i	$-0.541836\pi$
$683$	−6.85002	−0.262109	−0.131054	+	0.991375i	$0.541836\pi$
$684$	−2.92112	−0.111692
$685$	7.07505	0.270324
$686$	−14.6257	−0.558410
$687$	−18.9590	−0.723329
$688$	47.0867	1.79516
$689$	16.4370	0.626199
$690$	−17.5592	−0.668468
$691$	23.0076	0.875250	0.437625	−	0.899158i	$-0.355820\pi$
$691$	23.0076	0.875250	0.437625	+	0.899158i	$0.355820\pi$
$692$	14.4538	0.549450
$693$	6.33056	0.240478
$694$	−40.9396	−1.55405
$695$	21.2413	0.805728
$696$	−13.4508	−0.509850
$697$	3.49955	0.132555
$698$	16.6009	0.628352
$699$	8.24911	0.312010
$700$	−4.20254	−0.158841
$701$	27.8580	1.05218	0.526091	−	0.850428i	$-0.323657\pi$
$701$	27.8580	1.05218	0.526091	+	0.850428i	$0.323657\pi$
$702$	−9.86552	−0.372350
$703$	−6.03734	−0.227703
$704$	5.61802	0.211737
$705$	24.0012	0.903937
$706$	9.37633	0.352883
$707$	51.8317	1.94933
$708$	−5.89755	−0.221643
$709$	11.3916	0.427819	0.213909	−	0.976853i	$-0.431380\pi$
$709$	11.3916	0.427819	0.213909	+	0.976853i	$0.431380\pi$
$710$	−28.8484	−1.08266
$711$	1.00000	0.0375029
$712$	7.70852	0.288889
$713$	45.0607	1.68754
$714$	6.61722	0.247643
$715$	−17.6861	−0.661421
$716$	1.42726	0.0533392
$717$	−5.92494	−0.221271
$718$	−38.6125	−1.44101
$719$	22.6201	0.843587	0.421794	−	0.906692i	$-0.361401\pi$
$719$	22.6201	0.843587	0.421794	+	0.906692i	$0.361401\pi$
$720$	9.20218	0.342945
$721$	10.1829	0.379230
$722$	2.70640	0.100722
$723$	30.9870	1.15242
$724$	1.19824	0.0445324
$725$	9.37975	0.348355
$726$	14.0157	0.520171
$727$	18.0005	0.667601	0.333801	−	0.942644i	$-0.391669\pi$
$727$	18.0005	0.667601	0.333801	+	0.942644i	$0.391669\pi$
$728$	51.5879	1.91198
$729$	1.00000	0.0370370
$730$	−9.65706	−0.357424
$731$	9.58852	0.354644
$732$	−3.87289	−0.143146
$733$	−8.63138	−0.318807	−0.159404	−	0.987213i	$-0.550957\pi$
$733$	−8.63138	−0.318807	−0.159404	+	0.987213i	$0.550957\pi$
$734$	−11.8859	−0.438717
$735$	−17.2590	−0.636608
$736$	−21.6756	−0.798974
$737$	15.6600	0.576845
$738$	5.75166	0.211722
$739$	−48.9490	−1.80062	−0.900309	−	0.435251i	$-0.856660\pi$
$739$	−48.9490	−1.80062	−0.900309	+	0.435251i	$0.856660\pi$
$740$	−1.90440	−0.0700070
$741$	−25.0052	−0.918589
$742$	−18.1200	−0.665205
$743$	−25.4752	−0.934593	−0.467296	−	0.884101i	$-0.654772\pi$
$743$	−25.4752	−0.934593	−0.467296	+	0.884101i	$0.654772\pi$
$744$	−16.8707	−0.618508
$745$	−43.4287	−1.59110
$746$	−19.5590	−0.716108
$747$	−15.8400	−0.579554
$748$	−1.10257	−0.0403139
$749$	−67.4145	−2.46327
$750$	−19.9835	−0.729694
$751$	40.7882	1.48838	0.744192	−	0.667966i	$-0.232835\pi$
$751$	40.7882	1.48838	0.744192	+	0.667966i	$0.232835\pi$
$752$	62.8977	2.29364
$753$	2.20770	0.0804529
$754$	62.1660	2.26395
$755$	2.91220	0.105986
$756$	2.82327	0.102681
$757$	−10.0385	−0.364856	−0.182428	−	0.983219i	$-0.558396\pi$
$757$	−10.0385	−0.364856	−0.182428	+	0.983219i	$0.558396\pi$
$758$	−30.2927	−1.10028
$759$	−8.96453	−0.325392
$760$	16.6629	0.604425
$761$	−21.6243	−0.783881	−0.391941	−	0.919990i	$-0.628196\pi$
$761$	−21.6243	−0.783881	−0.391941	+	0.919990i	$0.628196\pi$
$762$	25.9224	0.939070
$763$	8.93631	0.323516
$764$	−2.27194	−0.0821959
$765$	1.87389	0.0677507
$766$	−49.4682	−1.78736
$767$	−50.4839	−1.82287
$768$	15.0024	0.541352
$769$	−23.9086	−0.862166	−0.431083	−	0.902312i	$-0.641868\pi$
$769$	−23.9086	−0.862166	−0.431083	+	0.902312i	$0.641868\pi$
$770$	19.4970	0.702622
$771$	−18.3513	−0.660904
$772$	11.2381	0.404468
$773$	−4.37392	−0.157319	−0.0786595	−	0.996902i	$-0.525064\pi$
$773$	−4.37392	−0.157319	−0.0786595	+	0.996902i	$0.525064\pi$
$774$	15.7591	0.566450
$775$	11.7646	0.422596
$776$	40.6060	1.45767
$777$	5.83511	0.209334
$778$	−25.7621	−0.923617
$779$	14.5782	0.522318
$780$	−7.88755	−0.282419
$781$	−14.7280	−0.527011
$782$	−9.37046	−0.335087
$783$	−6.30134	−0.225191
$784$	−45.2291	−1.61532
$785$	−4.02937	−0.143815
$786$	−19.6022	−0.699186
$787$	28.8509	1.02842	0.514212	−	0.857663i	$-0.328084\pi$
$787$	28.8509	1.02842	0.514212	+	0.857663i	$0.328084\pi$
$788$	−14.6248	−0.520986
$789$	−3.94964	−0.140611
$790$	3.07982	0.109575
$791$	−24.7838	−0.881210
$792$	3.35630	0.119261
$793$	−33.1525	−1.17728
$794$	17.6465	0.626252
$795$	−5.13129	−0.181988
$796$	−2.97958	−0.105608
$797$	38.1701	1.35205	0.676027	−	0.736877i	$-0.263700\pi$
$797$	38.1701	1.35205	0.676027	+	0.736877i	$0.263700\pi$
$798$	27.5655	0.975809
$799$	12.8082	0.453122
$800$	−5.65913	−0.200080
$801$	3.61125	0.127597
$802$	−45.0279	−1.58999
$803$	−4.93023	−0.173984
$804$	6.98399	0.246306
$805$	43.0149	1.51608
$806$	77.9718	2.74644
$807$	−30.6003	−1.07718
$808$	27.4799	0.966738
$809$	45.9119	1.61418	0.807089	−	0.590430i	$-0.201042\pi$
$809$	45.9119	1.61418	0.807089	+	0.590430i	$0.201042\pi$
$810$	3.07982	0.108214
$811$	33.3074	1.16958	0.584790	−	0.811185i	$-0.301177\pi$
$811$	33.3074	1.16958	0.584790	+	0.811185i	$0.301177\pi$
$812$	−17.7904	−0.624321
$813$	12.3028	0.431476
$814$	−3.74526	−0.131271
$815$	37.7294	1.32160
$816$	4.91073	0.171910
$817$	39.9432	1.39744
$818$	−20.9366	−0.732032
$819$	24.1676	0.844485
$820$	4.59849	0.160586
$821$	−15.5455	−0.542541	−0.271270	−	0.962503i	$-0.587444\pi$
$821$	−15.5455	−0.542541	−0.271270	+	0.962503i	$0.587444\pi$
$822$	6.20534	0.216436
$823$	−4.51308	−0.157316	−0.0786581	−	0.996902i	$-0.525064\pi$
$823$	−4.51308	−0.157316	−0.0786581	+	0.996902i	$0.525064\pi$
$824$	5.39870	0.188073
$825$	−2.34048	−0.0814852
$826$	55.6530	1.93641
$827$	−12.3541	−0.429593	−0.214796	−	0.976659i	$-0.568909\pi$
$827$	−12.3541	−0.429593	−0.214796	+	0.976659i	$0.568909\pi$
$828$	−3.99796	−0.138939
$829$	36.5274	1.26865	0.634325	−	0.773066i	$-0.281278\pi$
$829$	36.5274	1.26865	0.634325	+	0.773066i	$0.281278\pi$
$830$	−48.7842	−1.69332
$831$	15.7153	0.545156
$832$	21.4474	0.743556
$833$	−9.21024	−0.319116
$834$	18.6302	0.645110
$835$	18.2931	0.633058
$836$	−4.59300	−0.158852
$837$	−7.90347	−0.273184
$838$	−2.75367	−0.0951241
$839$	−20.7148	−0.715155	−0.357578	−	0.933883i	$-0.616397\pi$
$839$	−20.7148	−0.715155	−0.357578	+	0.933883i	$0.616397\pi$
$840$	−16.1047	−0.555665
$841$	10.7069	0.369203
$842$	15.9320	0.549055
$843$	−7.37271	−0.253930
$844$	2.45603	0.0845401
$845$	−43.1579	−1.48468
$846$	21.0508	0.723742
$847$	−34.3343	−1.17974
$848$	−13.4471	−0.461776
$849$	18.8184	0.645846
$850$	−2.44646	−0.0839130
$851$	−8.26294	−0.283250
$852$	−6.56834	−0.225028
$853$	−18.4710	−0.632436	−0.316218	−	0.948687i	$-0.602413\pi$
$853$	−18.4710	−0.632436	−0.316218	+	0.948687i	$0.602413\pi$
$854$	36.5470	1.25061
$855$	7.80612	0.266964
$856$	−35.7415	−1.22162
$857$	−18.0998	−0.618276	−0.309138	−	0.951017i	$-0.600041\pi$
$857$	−18.0998	−0.618276	−0.309138	+	0.951017i	$0.600041\pi$
$858$	−15.5120	−0.529570
$859$	13.2983	0.453731	0.226865	−	0.973926i	$-0.427152\pi$
$859$	13.2983	0.453731	0.226865	+	0.973926i	$0.427152\pi$
$860$	12.5995	0.429640
$861$	−14.0899	−0.480182
$862$	−45.0418	−1.53413
$863$	7.07076	0.240691	0.120346	−	0.992732i	$-0.461600\pi$
$863$	7.07076	0.240691	0.120346	+	0.992732i	$0.461600\pi$
$864$	3.80182	0.129340
$865$	−38.6249	−1.31329
$866$	28.1499	0.956572
$867$	1.00000	0.0339618
$868$	−22.3137	−0.757375
$869$	1.57234	0.0533381
$870$	−19.4070	−0.657958
$871$	59.7840	2.02570
$872$	4.73781	0.160442
$873$	19.0229	0.643827
$874$	−39.0348	−1.32037
$875$	48.9537	1.65494
$876$	−2.19876	−0.0742893
$877$	−12.9249	−0.436443	−0.218221	−	0.975899i	$-0.570025\pi$
$877$	−12.9249	−0.436443	−0.218221	+	0.975899i	$0.570025\pi$
$878$	−10.8635	−0.366624
$879$	29.3202	0.988947
$880$	14.4690	0.487749
$881$	14.4983	0.488460	0.244230	−	0.969717i	$-0.421465\pi$
$881$	14.4983	0.488460	0.244230	+	0.969717i	$0.421465\pi$
$882$	−15.1374	−0.509703
$883$	10.6230	0.357493	0.178747	−	0.983895i	$-0.442796\pi$
$883$	10.6230	0.357493	0.178747	+	0.983895i	$0.442796\pi$
$884$	−4.20918	−0.141570
$885$	15.7600	0.529768
$886$	34.9839	1.17531
$887$	16.4851	0.553517	0.276759	−	0.960939i	$-0.410740\pi$
$887$	16.4851	0.553517	0.276759	+	0.960939i	$0.410740\pi$
$888$	3.09363	0.103815
$889$	−63.5023	−2.12980
$890$	11.1220	0.372810
$891$	1.57234	0.0526755
$892$	−10.0372	−0.336070
$893$	53.3555	1.78548
$894$	−38.0902	−1.27393
$895$	−3.81408	−0.127491
$896$	−54.2572	−1.81261
$897$	−34.2231	−1.14268
$898$	38.0794	1.27073
$899$	49.8025	1.66100
$900$	−1.04380	−0.0347933
$901$	−2.73831	−0.0912263
$902$	9.04358	0.301118
$903$	−38.6053	−1.28470
$904$	−13.1397	−0.437021
$905$	−3.20208	−0.106441
$906$	2.55421	0.0848580
$907$	3.94029	0.130835	0.0654176	−	0.997858i	$-0.479162\pi$
$907$	3.94029	0.130835	0.0654176	+	0.997858i	$0.479162\pi$
$908$	0.680583	0.0225860
$909$	12.8736	0.426991
$910$	74.4319	2.46739
$911$	19.9891	0.662269	0.331134	−	0.943584i	$-0.392569\pi$
$911$	19.9891	0.662269	0.331134	+	0.943584i	$0.392569\pi$
$912$	20.4568	0.677392
$913$	−24.9059	−0.824264
$914$	−37.8352	−1.25148
$915$	10.3495	0.342145
$916$	−13.2945	−0.439263
$917$	48.0196	1.58575
$918$	1.64354	0.0542449
$919$	−33.3404	−1.09980	−0.549899	−	0.835231i	$-0.685334\pi$
$919$	−33.3404	−1.09980	−0.549899	+	0.835231i	$0.685334\pi$
$920$	22.8054	0.751873
$921$	−6.78361	−0.223527
$922$	−1.19781	−0.0394479
$923$	−56.2260	−1.85070
$924$	4.43915	0.146037
$925$	−2.15731	−0.0709320
$926$	50.9870	1.67554
$927$	2.52916	0.0830683
$928$	−23.9565	−0.786412
$929$	−25.4275	−0.834250	−0.417125	−	0.908849i	$-0.636962\pi$
$929$	−25.4275	−0.834250	−0.417125	+	0.908849i	$0.636962\pi$
$930$	−24.3412	−0.798181
$931$	−38.3674	−1.25744
$932$	5.78449	0.189477
$933$	9.89737	0.324025
$934$	−5.30418	−0.173558
$935$	2.94640	0.0963576
$936$	12.8131	0.418808
$937$	54.4396	1.77846	0.889231	−	0.457458i	$-0.151240\pi$
$937$	54.4396	1.77846	0.889231	+	0.457458i	$0.151240\pi$
$938$	−65.9053	−2.15189
$939$	13.1007	0.427525
$940$	16.8303	0.548943
$941$	−19.9112	−0.649085	−0.324543	−	0.945871i	$-0.605210\pi$
$941$	−19.9112	−0.649085	−0.324543	+	0.945871i	$0.605210\pi$
$942$	−3.53406	−0.115146
$943$	19.9523	0.649737
$944$	41.3009	1.34423
$945$	−7.54465	−0.245427
$946$	24.7788	0.805627
$947$	44.7446	1.45400	0.727002	−	0.686635i	$-0.240913\pi$
$947$	44.7446	1.45400	0.727002	+	0.686635i	$0.240913\pi$
$948$	0.701226	0.0227748
$949$	−18.8217	−0.610979
$950$	−10.1913	−0.330650
$951$	0.478643	0.0155211
$952$	−8.59426	−0.278542
$953$	37.5144	1.21521	0.607606	−	0.794239i	$-0.292130\pi$
$953$	37.5144	1.21521	0.607606	+	0.794239i	$0.292130\pi$
$954$	−4.50052	−0.145710
$955$	6.07131	0.196463
$956$	−4.15472	−0.134373
$957$	−9.90787	−0.320276
$958$	1.06701	0.0344735
$959$	−15.2013	−0.490875
$960$	−6.69546	−0.216095
$961$	31.4649	1.01500
$962$	−14.2980	−0.460985
$963$	−16.7440	−0.539567
$964$	21.7289	0.699841
$965$	−30.0316	−0.966752
$966$	37.7273	1.21386
$967$	14.4473	0.464594	0.232297	−	0.972645i	$-0.425376\pi$
$967$	14.4473	0.464594	0.232297	+	0.972645i	$0.425376\pi$
$968$	−18.2032	−0.585073
$969$	4.16573	0.133823
$970$	58.5869	1.88111
$971$	−25.5922	−0.821292	−0.410646	−	0.911795i	$-0.634697\pi$
$971$	−25.5922	−0.821292	−0.410646	+	0.911795i	$0.634697\pi$
$972$	0.701226	0.0224918
$973$	−45.6385	−1.46310
$974$	43.0361	1.37897
$975$	−8.93506	−0.286151
$976$	27.1221	0.868157
$977$	31.0567	0.993592	0.496796	−	0.867867i	$-0.334510\pi$
$977$	31.0567	0.993592	0.496796	+	0.867867i	$0.334510\pi$
$978$	33.0914	1.05815
$979$	5.67812	0.181473
$980$	−12.1025	−0.386599
$981$	2.21954	0.0708645
$982$	−55.1111	−1.75867
$983$	54.7174	1.74521	0.872607	−	0.488423i	$-0.162428\pi$
$983$	54.7174	1.74521	0.872607	+	0.488423i	$0.162428\pi$
$984$	−7.47011	−0.238138
$985$	39.0818	1.24525
$986$	−10.3565	−0.329818
$987$	−51.5683	−1.64144
$988$	−17.5343	−0.557841
$989$	54.6679	1.73834
$990$	4.84253	0.153906
$991$	−30.2758	−0.961741	−0.480871	−	0.876792i	$-0.659679\pi$
$991$	−30.2758	−0.961741	−0.480871	+	0.876792i	$0.659679\pi$
$992$	−30.0476	−0.954011
$993$	23.1152	0.733539
$994$	61.9830	1.96598
$995$	7.96235	0.252424
$996$	−11.1074	−0.351951
$997$	−58.4959	−1.85259	−0.926293	−	0.376805i	$-0.877023\pi$
$997$	−58.4959	−1.85259	−0.926293	+	0.376805i	$0.877023\pi$
$998$	41.5073	1.31389
$999$	1.44929	0.0458534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.8	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64354 q^{2} +1.00000 q^{3} +0.701226 q^{4} -1.87389 q^{5} -1.64354 q^{6} +4.02619 q^{7} +2.13459 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64354 q^{2} +1.00000 q^{3} +0.701226 q^{4} -1.87389 q^{5} -1.64354 q^{6} +4.02619 q^{7} +2.13459 q^{8} +1.00000 q^{9} +3.07982 q^{10} +1.57234 q^{11} +0.701226 q^{12} +6.00260 q^{13} -6.61722 q^{14} -1.87389 q^{15} -4.91073 q^{16} -1.00000 q^{17} -1.64354 q^{18} -4.16573 q^{19} -1.31402 q^{20} +4.02619 q^{21} -2.58421 q^{22} -5.70138 q^{23} +2.13459 q^{24} -1.48853 q^{25} -9.86552 q^{26} +1.00000 q^{27} +2.82327 q^{28} -6.30134 q^{29} +3.07982 q^{30} -7.90347 q^{31} +3.80182 q^{32} +1.57234 q^{33} +1.64354 q^{34} -7.54465 q^{35} +0.701226 q^{36} +1.44929 q^{37} +6.84655 q^{38} +6.00260 q^{39} -3.99998 q^{40} -3.49955 q^{41} -6.61722 q^{42} -9.58852 q^{43} +1.10257 q^{44} -1.87389 q^{45} +9.37046 q^{46} -12.8082 q^{47} -4.91073 q^{48} +9.21024 q^{49} +2.44646 q^{50} -1.00000 q^{51} +4.20918 q^{52} +2.73831 q^{53} -1.64354 q^{54} -2.94640 q^{55} +8.59426 q^{56} -4.16573 q^{57} +10.3565 q^{58} -8.41033 q^{59} -1.31402 q^{60} -5.52302 q^{61} +12.9897 q^{62} +4.02619 q^{63} +3.57303 q^{64} -11.2482 q^{65} -2.58421 q^{66} +9.95968 q^{67} -0.701226 q^{68} -5.70138 q^{69} +12.3999 q^{70} -9.36694 q^{71} +2.13459 q^{72} -3.13560 q^{73} -2.38196 q^{74} -1.48853 q^{75} -2.92112 q^{76} +6.33056 q^{77} -9.86552 q^{78} +1.00000 q^{79} +9.20218 q^{80} +1.00000 q^{81} +5.75166 q^{82} -15.8400 q^{83} +2.82327 q^{84} +1.87389 q^{85} +15.7591 q^{86} -6.30134 q^{87} +3.35630 q^{88} +3.61125 q^{89} +3.07982 q^{90} +24.1676 q^{91} -3.99796 q^{92} -7.90347 q^{93} +21.0508 q^{94} +7.80612 q^{95} +3.80182 q^{96} +19.0229 q^{97} -15.1374 q^{98} +1.57234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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