LMFDB - Embedded newform 8029.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49220 q^{2} -0.243085 q^{3} +4.21105 q^{4} +3.85659 q^{5} +0.605816 q^{6} +1.00000 q^{7} -5.51038 q^{8} -2.94091 q^{9} +O(q^{10})$	\(q-2.49220 q^{2} -0.243085 q^{3} +4.21105 q^{4} +3.85659 q^{5} +0.605816 q^{6} +1.00000 q^{7} -5.51038 q^{8} -2.94091 q^{9} -9.61139 q^{10} +3.57961 q^{11} -1.02364 q^{12} +6.80354 q^{13} -2.49220 q^{14} -0.937480 q^{15} +5.31085 q^{16} -7.57117 q^{17} +7.32933 q^{18} -1.74777 q^{19} +16.2403 q^{20} -0.243085 q^{21} -8.92110 q^{22} +7.17864 q^{23} +1.33949 q^{24} +9.87329 q^{25} -16.9558 q^{26} +1.44415 q^{27} +4.21105 q^{28} +6.29458 q^{29} +2.33639 q^{30} +1.00000 q^{31} -2.21493 q^{32} -0.870150 q^{33} +18.8689 q^{34} +3.85659 q^{35} -12.3843 q^{36} +1.00000 q^{37} +4.35580 q^{38} -1.65384 q^{39} -21.2513 q^{40} -4.41951 q^{41} +0.605816 q^{42} +3.96354 q^{43} +15.0739 q^{44} -11.3419 q^{45} -17.8906 q^{46} -3.54103 q^{47} -1.29099 q^{48} +1.00000 q^{49} -24.6062 q^{50} +1.84044 q^{51} +28.6500 q^{52} +9.23655 q^{53} -3.59910 q^{54} +13.8051 q^{55} -5.51038 q^{56} +0.424858 q^{57} -15.6873 q^{58} +7.64038 q^{59} -3.94778 q^{60} +2.15290 q^{61} -2.49220 q^{62} -2.94091 q^{63} -5.10165 q^{64} +26.2385 q^{65} +2.16859 q^{66} -5.55357 q^{67} -31.8826 q^{68} -1.74502 q^{69} -9.61139 q^{70} +3.47932 q^{71} +16.2055 q^{72} -6.92780 q^{73} -2.49220 q^{74} -2.40005 q^{75} -7.35997 q^{76} +3.57961 q^{77} +4.12170 q^{78} -12.0772 q^{79} +20.4818 q^{80} +8.47168 q^{81} +11.0143 q^{82} +8.84652 q^{83} -1.02364 q^{84} -29.1989 q^{85} -9.87793 q^{86} -1.53012 q^{87} -19.7250 q^{88} -5.40799 q^{89} +28.2662 q^{90} +6.80354 q^{91} +30.2296 q^{92} -0.243085 q^{93} +8.82495 q^{94} -6.74045 q^{95} +0.538417 q^{96} +9.91025 q^{97} -2.49220 q^{98} -10.5273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.49220	−1.76225	−0.881125	−	0.472883i	$-0.843213\pi$
$2$	−2.49220	−1.76225	−0.881125	+	0.472883i	$0.843213\pi$
$3$	−0.243085	−0.140345	−0.0701726	−	0.997535i	$-0.522355\pi$
$3$	−0.243085	−0.140345	−0.0701726	+	0.997535i	$0.522355\pi$
$4$	4.21105	2.10553
$5$	3.85659	1.72472	0.862360	−	0.506296i	$-0.168986\pi$
$5$	3.85659	1.72472	0.862360	+	0.506296i	$0.168986\pi$
$6$	0.605816	0.247324
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.51038	−1.94821
$9$	−2.94091	−0.980303
$10$	−9.61139	−3.03939
$11$	3.57961	1.07929	0.539647	−	0.841892i	$-0.318558\pi$
$11$	3.57961	1.07929	0.539647	+	0.841892i	$0.318558\pi$
$12$	−1.02364	−0.295501
$13$	6.80354	1.88696	0.943481	−	0.331427i	$-0.107530\pi$
$13$	6.80354	1.88696	0.943481	+	0.331427i	$0.107530\pi$
$14$	−2.49220	−0.666068
$15$	−0.937480	−0.242056
$16$	5.31085	1.32771
$17$	−7.57117	−1.83628	−0.918140	−	0.396257i	$-0.870309\pi$
$17$	−7.57117	−1.83628	−0.918140	+	0.396257i	$0.870309\pi$
$18$	7.32933	1.72754
$19$	−1.74777	−0.400967	−0.200483	−	0.979697i	$-0.564251\pi$
$19$	−1.74777	−0.400967	−0.200483	+	0.979697i	$0.564251\pi$
$20$	16.2403	3.63144
$21$	−0.243085	−0.0530455
$22$	−8.92110	−1.90198
$23$	7.17864	1.49685	0.748425	−	0.663219i	$-0.230810\pi$
$23$	7.17864	1.49685	0.748425	+	0.663219i	$0.230810\pi$
$24$	1.33949	0.273422
$25$	9.87329	1.97466
$26$	−16.9558	−3.32530
$27$	1.44415	0.277926
$28$	4.21105	0.795814
$29$	6.29458	1.16887	0.584437	−	0.811439i	$-0.301315\pi$
$29$	6.29458	1.16887	0.584437	+	0.811439i	$0.301315\pi$
$30$	2.33639	0.426564
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−2.21493	−0.391548
$33$	−0.870150	−0.151474
$34$	18.8689	3.23598
$35$	3.85659	0.651883
$36$	−12.3843	−2.06405
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	4.35580	0.706604
$39$	−1.65384	−0.264826
$40$	−21.2513	−3.36012
$41$	−4.41951	−0.690212	−0.345106	−	0.938564i	$-0.612157\pi$
$41$	−4.41951	−0.690212	−0.345106	+	0.938564i	$0.612157\pi$
$42$	0.605816	0.0934795
$43$	3.96354	0.604434	0.302217	−	0.953239i	$-0.402273\pi$
$43$	3.96354	0.604434	0.302217	+	0.953239i	$0.402273\pi$
$44$	15.0739	2.27248
$45$	−11.3419	−1.69075
$46$	−17.8906	−2.63782
$47$	−3.54103	−0.516513	−0.258256	−	0.966076i	$-0.583148\pi$
$47$	−3.54103	−0.516513	−0.258256	+	0.966076i	$0.583148\pi$
$48$	−1.29099	−0.186338
$49$	1.00000	0.142857
$50$	−24.6062	−3.47984
$51$	1.84044	0.257713
$52$	28.6500	3.97305
$53$	9.23655	1.26874	0.634369	−	0.773031i	$-0.281260\pi$
$53$	9.23655	1.26874	0.634369	+	0.773031i	$0.281260\pi$
$54$	−3.59910	−0.489776
$55$	13.8051	1.86148
$56$	−5.51038	−0.736355
$57$	0.424858	0.0562738
$58$	−15.6873	−2.05985
$59$	7.64038	0.994693	0.497347	−	0.867552i	$-0.334308\pi$
$59$	7.64038	0.994693	0.497347	+	0.867552i	$0.334308\pi$
$60$	−3.94778	−0.509656
$61$	2.15290	0.275650	0.137825	−	0.990457i	$-0.455989\pi$
$61$	2.15290	0.275650	0.137825	+	0.990457i	$0.455989\pi$
$62$	−2.49220	−0.316509
$63$	−2.94091	−0.370520
$64$	−5.10165	−0.637706
$65$	26.2385	3.25448
$66$	2.16859	0.266935
$67$	−5.55357	−0.678477	−0.339238	−	0.940700i	$-0.610169\pi$
$67$	−5.55357	−0.678477	−0.339238	+	0.940700i	$0.610169\pi$
$68$	−31.8826	−3.86633
$69$	−1.74502	−0.210076
$70$	−9.61139	−1.14878
$71$	3.47932	0.412919	0.206459	−	0.978455i	$-0.433806\pi$
$71$	3.47932	0.412919	0.206459	+	0.978455i	$0.433806\pi$
$72$	16.2055	1.90984
$73$	−6.92780	−0.810837	−0.405419	−	0.914131i	$-0.632874\pi$
$73$	−6.92780	−0.810837	−0.405419	+	0.914131i	$0.632874\pi$
$74$	−2.49220	−0.289712
$75$	−2.40005	−0.277134
$76$	−7.35997	−0.844246
$77$	3.57961	0.407934
$78$	4.12170	0.466690
$79$	−12.0772	−1.35879	−0.679397	−	0.733771i	$-0.737758\pi$
$79$	−12.0772	−1.35879	−0.679397	+	0.733771i	$0.737758\pi$
$80$	20.4818	2.28993
$81$	8.47168	0.941298
$82$	11.0143	1.21633
$83$	8.84652	0.971032	0.485516	−	0.874228i	$-0.338632\pi$
$83$	8.84652	0.971032	0.485516	+	0.874228i	$0.338632\pi$
$84$	−1.02364	−0.111689
$85$	−29.1989	−3.16707
$86$	−9.87793	−1.06516
$87$	−1.53012	−0.164046
$88$	−19.7250	−2.10269
$89$	−5.40799	−0.573246	−0.286623	−	0.958043i	$-0.592533\pi$
$89$	−5.40799	−0.573246	−0.286623	+	0.958043i	$0.592533\pi$
$90$	28.2662	2.97952
$91$	6.80354	0.713205
$92$	30.2296	3.15166
$93$	−0.243085	−0.0252068
$94$	8.82495	0.910224
$95$	−6.74045	−0.691556
$96$	0.538417	0.0549519
$97$	9.91025	1.00623	0.503117	−	0.864219i	$-0.332187\pi$
$97$	9.91025	1.00623	0.503117	+	0.864219i	$0.332187\pi$
$98$	−2.49220	−0.251750
$99$	−10.5273	−1.05803
$100$	41.5769	4.15769
$101$	−10.7248	−1.06716	−0.533581	−	0.845749i	$-0.679154\pi$
$101$	−10.7248	−1.06716	−0.533581	+	0.845749i	$0.679154\pi$
$102$	−4.58674	−0.454155
$103$	−6.91285	−0.681144	−0.340572	−	0.940218i	$-0.610621\pi$
$103$	−6.91285	−0.681144	−0.340572	+	0.940218i	$0.610621\pi$
$104$	−37.4901	−3.67620
$105$	−0.937480	−0.0914887
$106$	−23.0193	−2.23583
$107$	−14.6564	−1.41689	−0.708445	−	0.705766i	$-0.750603\pi$
$107$	−14.6564	−1.41689	−0.708445	+	0.705766i	$0.750603\pi$
$108$	6.08138	0.585181
$109$	5.66779	0.542876	0.271438	−	0.962456i	$-0.412501\pi$
$109$	5.66779	0.542876	0.271438	+	0.962456i	$0.412501\pi$
$110$	−34.4050	−3.28039
$111$	−0.243085	−0.0230726
$112$	5.31085	0.501828
$113$	0.711675	0.0669488	0.0334744	−	0.999440i	$-0.489343\pi$
$113$	0.711675	0.0669488	0.0334744	+	0.999440i	$0.489343\pi$
$114$	−1.05883	−0.0991686
$115$	27.6851	2.58165
$116$	26.5068	2.46110
$117$	−20.0086	−1.84979
$118$	−19.0414	−1.75290
$119$	−7.57117	−0.694048
$120$	5.16587	0.471577
$121$	1.81361	0.164874
$122$	−5.36545	−0.485765
$123$	1.07432	0.0968679
$124$	4.21105	0.378164
$125$	18.7943	1.68101
$126$	7.32933	0.652949
$127$	−14.6705	−1.30179	−0.650897	−	0.759166i	$-0.725607\pi$
$127$	−14.6705	−1.30179	−0.650897	+	0.759166i	$0.725607\pi$
$128$	17.1442	1.51535
$129$	−0.963478	−0.0848295
$130$	−65.3914	−5.73521
$131$	18.1701	1.58753	0.793764	−	0.608226i	$-0.208119\pi$
$131$	18.1701	1.58753	0.793764	+	0.608226i	$0.208119\pi$
$132$	−3.66425	−0.318932
$133$	−1.74777	−0.151551
$134$	13.8406	1.19565
$135$	5.56948	0.479345
$136$	41.7200	3.57746
$137$	2.26496	0.193508	0.0967542	−	0.995308i	$-0.469154\pi$
$137$	2.26496	0.193508	0.0967542	+	0.995308i	$0.469154\pi$
$138$	4.34894	0.370206
$139$	1.66020	0.140817	0.0704084	−	0.997518i	$-0.477570\pi$
$139$	1.66020	0.140817	0.0704084	+	0.997518i	$0.477570\pi$
$140$	16.2403	1.37256
$141$	0.860772	0.0724901
$142$	−8.67114	−0.727666
$143$	24.3540	2.03659
$144$	−15.6187	−1.30156
$145$	24.2756	2.01598
$146$	17.2654	1.42890
$147$	−0.243085	−0.0200493
$148$	4.21105	0.346146
$149$	−12.8697	−1.05433	−0.527163	−	0.849764i	$-0.676744\pi$
$149$	−12.8697	−1.05433	−0.527163	+	0.849764i	$0.676744\pi$
$150$	5.98140	0.488380
$151$	2.93156	0.238567	0.119283	−	0.992860i	$-0.461940\pi$
$151$	2.93156	0.238567	0.119283	+	0.992860i	$0.461940\pi$
$152$	9.63090	0.781169
$153$	22.2661	1.80011
$154$	−8.92110	−0.718882
$155$	3.85659	0.309769
$156$	−6.96440	−0.557598
$157$	23.8167	1.90078	0.950390	−	0.311062i	$-0.100685\pi$
$157$	23.8167	1.90078	0.950390	+	0.311062i	$0.100685\pi$
$158$	30.0988	2.39453
$159$	−2.24527	−0.178061
$160$	−8.54208	−0.675311
$161$	7.17864	0.565756
$162$	−21.1131	−1.65880
$163$	17.0337	1.33418	0.667091	−	0.744976i	$-0.267539\pi$
$163$	17.0337	1.33418	0.667091	+	0.744976i	$0.267539\pi$
$164$	−18.6108	−1.45326
$165$	−3.35581	−0.261250
$166$	−22.0473	−1.71120
$167$	−4.80867	−0.372106	−0.186053	−	0.982540i	$-0.559570\pi$
$167$	−4.80867	−0.372106	−0.186053	+	0.982540i	$0.559570\pi$
$168$	1.33949	0.103344
$169$	33.2881	2.56063
$170$	72.7695	5.58117
$171$	5.14005	0.393069
$172$	16.6907	1.27265
$173$	23.2920	1.77086	0.885429	−	0.464775i	$-0.153865\pi$
$173$	23.2920	1.77086	0.885429	+	0.464775i	$0.153865\pi$
$174$	3.81336	0.289090
$175$	9.87329	0.746351
$176$	19.0108	1.43299
$177$	−1.85726	−0.139601
$178$	13.4778	1.01020
$179$	1.85005	0.138279	0.0691396	−	0.997607i	$-0.477975\pi$
$179$	1.85005	0.138279	0.0691396	+	0.997607i	$0.477975\pi$
$180$	−47.7613	−3.55991
$181$	−12.9767	−0.964550	−0.482275	−	0.876020i	$-0.660189\pi$
$181$	−12.9767	−0.964550	−0.482275	+	0.876020i	$0.660189\pi$
$182$	−16.9558	−1.25684
$183$	−0.523338	−0.0386863
$184$	−39.5570	−2.91618
$185$	3.85659	0.283542
$186$	0.605816	0.0444206
$187$	−27.1019	−1.98188
$188$	−14.9115	−1.08753
$189$	1.44415	0.105046
$190$	16.7985	1.21869
$191$	12.2193	0.884159	0.442080	−	0.896976i	$-0.354241\pi$
$191$	12.2193	0.884159	0.442080	+	0.896976i	$0.354241\pi$
$192$	1.24014	0.0894991
$193$	−5.70625	−0.410745	−0.205372	−	0.978684i	$-0.565841\pi$
$193$	−5.70625	−0.410745	−0.205372	+	0.978684i	$0.565841\pi$
$194$	−24.6983	−1.77323
$195$	−6.37818	−0.456751
$196$	4.21105	0.300789
$197$	−3.65407	−0.260342	−0.130171	−	0.991492i	$-0.541553\pi$
$197$	−3.65407	−0.260342	−0.130171	+	0.991492i	$0.541553\pi$
$198$	26.2361	1.86452
$199$	−23.8300	−1.68927	−0.844633	−	0.535346i	$-0.820181\pi$
$199$	−23.8300	−1.68927	−0.844633	+	0.535346i	$0.820181\pi$
$200$	−54.4056	−3.84705
$201$	1.34999	0.0952210
$202$	26.7284	1.88061
$203$	6.29458	0.441793
$204$	7.75019	0.542622
$205$	−17.0442	−1.19042
$206$	17.2282	1.20035
$207$	−21.1117	−1.46737
$208$	36.1326	2.50534
$209$	−6.25635	−0.432761
$210$	2.33639	0.161226
$211$	0.157690	0.0108558	0.00542792	−	0.999985i	$-0.498272\pi$
$211$	0.157690	0.0108558	0.00542792	+	0.999985i	$0.498272\pi$
$212$	38.8956	2.67136
$213$	−0.845770	−0.0579512
$214$	36.5267	2.49691
$215$	15.2858	1.04248
$216$	−7.95779	−0.541459
$217$	1.00000	0.0678844
$218$	−14.1253	−0.956683
$219$	1.68405	0.113797
$220$	58.1339	3.91939
$221$	−51.5108	−3.46499
$222$	0.605816	0.0406597
$223$	−2.72430	−0.182433	−0.0912165	−	0.995831i	$-0.529076\pi$
$223$	−2.72430	−0.182433	−0.0912165	+	0.995831i	$0.529076\pi$
$224$	−2.21493	−0.147991
$225$	−29.0365	−1.93576
$226$	−1.77364	−0.117980
$227$	16.0760	1.06700	0.533500	−	0.845800i	$-0.320876\pi$
$227$	16.0760	1.06700	0.533500	+	0.845800i	$0.320876\pi$
$228$	1.78910	0.118486
$229$	5.81791	0.384458	0.192229	−	0.981350i	$-0.438428\pi$
$229$	5.81791	0.384458	0.192229	+	0.981350i	$0.438428\pi$
$230$	−68.9967	−4.54951
$231$	−0.870150	−0.0572517
$232$	−34.6855	−2.27722
$233$	−27.3332	−1.79066	−0.895329	−	0.445404i	$-0.853060\pi$
$233$	−27.3332	−1.79066	−0.895329	+	0.445404i	$0.853060\pi$
$234$	49.8654	3.25980
$235$	−13.6563	−0.890840
$236$	32.1740	2.09435
$237$	2.93579	0.190700
$238$	18.8689	1.22309
$239$	2.10934	0.136442	0.0682209	−	0.997670i	$-0.478268\pi$
$239$	2.10934	0.136442	0.0682209	+	0.997670i	$0.478268\pi$
$240$	−4.97881	−0.321381
$241$	14.7616	0.950877	0.475439	−	0.879749i	$-0.342289\pi$
$241$	14.7616	0.950877	0.475439	+	0.879749i	$0.342289\pi$
$242$	−4.51987	−0.290548
$243$	−6.39178	−0.410033
$244$	9.06597	0.580389
$245$	3.85659	0.246389
$246$	−2.67741	−0.170706
$247$	−11.8911	−0.756609
$248$	−5.51038	−0.349909
$249$	−2.15046	−0.136280
$250$	−46.8391	−2.96237
$251$	28.0362	1.76963	0.884816	−	0.465941i	$-0.154284\pi$
$251$	28.0362	1.76963	0.884816	+	0.465941i	$0.154284\pi$
$252$	−12.3843	−0.780139
$253$	25.6967	1.61554
$254$	36.5617	2.29409
$255$	7.09783	0.444483
$256$	−32.5234	−2.03271
$257$	−29.1436	−1.81793	−0.908964	−	0.416875i	$-0.863125\pi$
$257$	−29.1436	−1.81793	−0.908964	+	0.416875i	$0.863125\pi$
$258$	2.40118	0.149491
$259$	1.00000	0.0621370
$260$	110.492	6.85239
$261$	−18.5118	−1.14585
$262$	−45.2834	−2.79762
$263$	−12.0339	−0.742042	−0.371021	−	0.928625i	$-0.620992\pi$
$263$	−12.0339	−0.742042	−0.371021	+	0.928625i	$0.620992\pi$
$264$	4.79486	0.295103
$265$	35.6216	2.18822
$266$	4.35580	0.267071
$267$	1.31460	0.0804524
$268$	−23.3864	−1.42855
$269$	23.9958	1.46305	0.731525	−	0.681814i	$-0.238809\pi$
$269$	23.9958	1.46305	0.731525	+	0.681814i	$0.238809\pi$
$270$	−13.8803	−0.844726
$271$	14.5481	0.883736	0.441868	−	0.897080i	$-0.354316\pi$
$271$	14.5481	0.883736	0.441868	+	0.897080i	$0.354316\pi$
$272$	−40.2094	−2.43805
$273$	−1.65384	−0.100095
$274$	−5.64472	−0.341010
$275$	35.3425	2.13124
$276$	−7.34838	−0.442320
$277$	−6.61554	−0.397489	−0.198745	−	0.980051i	$-0.563686\pi$
$277$	−6.61554	−0.397489	−0.198745	+	0.980051i	$0.563686\pi$
$278$	−4.13756	−0.248154
$279$	−2.94091	−0.176068
$280$	−21.2513	−1.27001
$281$	22.7328	1.35612	0.678062	−	0.735005i	$-0.262820\pi$
$281$	22.7328	1.35612	0.678062	+	0.735005i	$0.262820\pi$
$282$	−2.14522	−0.127746
$283$	11.7230	0.696862	0.348431	−	0.937334i	$-0.386715\pi$
$283$	11.7230	0.696862	0.348431	+	0.937334i	$0.386715\pi$
$284$	14.6516	0.869411
$285$	1.63850	0.0970566
$286$	−60.6950	−3.58897
$287$	−4.41951	−0.260875
$288$	6.51391	0.383836
$289$	40.3227	2.37192
$290$	−60.4997	−3.55266
$291$	−2.40903	−0.141220
$292$	−29.1733	−1.70724
$293$	7.50297	0.438328	0.219164	−	0.975688i	$-0.429667\pi$
$293$	7.50297	0.438328	0.219164	+	0.975688i	$0.429667\pi$
$294$	0.605816	0.0353319
$295$	29.4658	1.71557
$296$	−5.51038	−0.320284
$297$	5.16948	0.299964
$298$	32.0738	1.85799
$299$	48.8402	2.82450
$300$	−10.1067	−0.583513
$301$	3.96354	0.228455
$302$	−7.30602	−0.420414
$303$	2.60705	0.149771
$304$	−9.28216	−0.532369
$305$	8.30285	0.475420
$306$	−55.4916	−3.17225
$307$	−25.7656	−1.47052	−0.735261	−	0.677784i	$-0.762940\pi$
$307$	−25.7656	−1.47052	−0.735261	+	0.677784i	$0.762940\pi$
$308$	15.0739	0.858916
$309$	1.68041	0.0955953
$310$	−9.61139	−0.545890
$311$	−14.3371	−0.812981	−0.406490	−	0.913655i	$-0.633248\pi$
$311$	−14.3371	−0.812981	−0.406490	+	0.913655i	$0.633248\pi$
$312$	9.11328	0.515938
$313$	4.83546	0.273316	0.136658	−	0.990618i	$-0.456364\pi$
$313$	4.83546	0.273316	0.136658	+	0.990618i	$0.456364\pi$
$314$	−59.3559	−3.34965
$315$	−11.3419	−0.639043
$316$	−50.8578	−2.86097
$317$	−1.87093	−0.105082	−0.0525409	−	0.998619i	$-0.516732\pi$
$317$	−1.87093	−0.105082	−0.0525409	+	0.998619i	$0.516732\pi$
$318$	5.59565	0.313789
$319$	22.5322	1.26156
$320$	−19.6750	−1.09986
$321$	3.56276	0.198854
$322$	−17.8906	−0.997004
$323$	13.2327	0.736288
$324$	35.6747	1.98193
$325$	67.1733	3.72611
$326$	−42.4513	−2.35116
$327$	−1.37776	−0.0761901
$328$	24.3532	1.34468
$329$	−3.54103	−0.195223
$330$	8.36335	0.460387
$331$	−19.1290	−1.05142	−0.525712	−	0.850663i	$-0.676201\pi$
$331$	−19.1290	−1.05142	−0.525712	+	0.850663i	$0.676201\pi$
$332$	37.2531	2.04453
$333$	−2.94091	−0.161161
$334$	11.9842	0.655744
$335$	−21.4178	−1.17018
$336$	−1.29099	−0.0704292
$337$	−23.1140	−1.25910	−0.629551	−	0.776959i	$-0.716761\pi$
$337$	−23.1140	−1.25910	−0.629551	+	0.776959i	$0.716761\pi$
$338$	−82.9606	−4.51246
$339$	−0.172998	−0.00939594
$340$	−122.958	−6.66834
$341$	3.57961	0.193847
$342$	−12.8100	−0.692686
$343$	1.00000	0.0539949
$344$	−21.8406	−1.17757
$345$	−6.72983	−0.362322
$346$	−58.0483	−3.12069
$347$	−20.5214	−1.10165	−0.550823	−	0.834622i	$-0.685686\pi$
$347$	−20.5214	−1.10165	−0.550823	+	0.834622i	$0.685686\pi$
$348$	−6.44341	−0.345403
$349$	28.9992	1.55229	0.776144	−	0.630555i	$-0.217173\pi$
$349$	28.9992	1.55229	0.776144	+	0.630555i	$0.217173\pi$
$350$	−24.6062	−1.31526
$351$	9.82531	0.524436
$352$	−7.92859	−0.422595
$353$	−31.0663	−1.65349	−0.826747	−	0.562573i	$-0.809811\pi$
$353$	−31.0663	−1.65349	−0.826747	+	0.562573i	$0.809811\pi$
$354$	4.62867	0.246011
$355$	13.4183	0.712169
$356$	−22.7733	−1.20698
$357$	1.84044	0.0974064
$358$	−4.61069	−0.243682
$359$	−10.7733	−0.568592	−0.284296	−	0.958737i	$-0.591760\pi$
$359$	−10.7733	−0.568592	−0.284296	+	0.958737i	$0.591760\pi$
$360$	62.4981	3.29394
$361$	−15.9453	−0.839225
$362$	32.3405	1.69978
$363$	−0.440861	−0.0231392
$364$	28.6500	1.50167
$365$	−26.7177	−1.39847
$366$	1.30426	0.0681749
$367$	−24.4924	−1.27849	−0.639246	−	0.769002i	$-0.720753\pi$
$367$	−24.4924	−1.27849	−0.639246	+	0.769002i	$0.720753\pi$
$368$	38.1247	1.98739
$369$	12.9974	0.676617
$370$	−9.61139	−0.499672
$371$	9.23655	0.479538
$372$	−1.02364	−0.0530735
$373$	1.12795	0.0584029	0.0292015	−	0.999574i	$-0.490704\pi$
$373$	1.12795	0.0584029	0.0292015	+	0.999574i	$0.490704\pi$
$374$	67.5432	3.49258
$375$	−4.56862	−0.235922
$376$	19.5124	1.00628
$377$	42.8254	2.20562
$378$	−3.59910	−0.185118
$379$	17.9698	0.923045	0.461522	−	0.887129i	$-0.347303\pi$
$379$	17.9698	0.923045	0.461522	+	0.887129i	$0.347303\pi$
$380$	−28.3844	−1.45609
$381$	3.56617	0.182701
$382$	−30.4530	−1.55811
$383$	12.4631	0.636834	0.318417	−	0.947951i	$-0.396849\pi$
$383$	12.4631	0.636834	0.318417	+	0.947951i	$0.396849\pi$
$384$	−4.16750	−0.212672
$385$	13.8051	0.703573
$386$	14.2211	0.723835
$387$	−11.6564	−0.592529
$388$	41.7326	2.11865
$389$	5.04372	0.255727	0.127863	−	0.991792i	$-0.459188\pi$
$389$	5.04372	0.255727	0.127863	+	0.991792i	$0.459188\pi$
$390$	15.8957	0.804910
$391$	−54.3508	−2.74864
$392$	−5.51038	−0.278316
$393$	−4.41688	−0.222802
$394$	9.10666	0.458787
$395$	−46.5769	−2.34354
$396$	−44.3310	−2.22772
$397$	−19.5886	−0.983123	−0.491561	−	0.870843i	$-0.663574\pi$
$397$	−19.5886	−0.983123	−0.491561	+	0.870843i	$0.663574\pi$
$398$	59.3891	2.97691
$399$	0.424858	0.0212695
$400$	52.4356	2.62178
$401$	−11.1581	−0.557211	−0.278605	−	0.960406i	$-0.589872\pi$
$401$	−11.1581	−0.557211	−0.278605	+	0.960406i	$0.589872\pi$
$402$	−3.36444	−0.167803
$403$	6.80354	0.338908
$404$	−45.1629	−2.24694
$405$	32.6718	1.62347
$406$	−15.6873	−0.778550
$407$	3.57961	0.177435
$408$	−10.1415	−0.502080
$409$	−36.5148	−1.80554	−0.902769	−	0.430125i	$-0.858469\pi$
$409$	−36.5148	−1.80554	−0.902769	+	0.430125i	$0.858469\pi$
$410$	42.4776	2.09782
$411$	−0.550578	−0.0271580
$412$	−29.1104	−1.43417
$413$	7.64038	0.375959
$414$	52.6146	2.58587
$415$	34.1174	1.67476
$416$	−15.0694	−0.738836
$417$	−0.403571	−0.0197630
$418$	15.5921	0.762633
$419$	16.9552	0.828315	0.414157	−	0.910205i	$-0.364076\pi$
$419$	16.9552	0.828315	0.414157	+	0.910205i	$0.364076\pi$
$420$	−3.94778	−0.192632
$421$	−39.3932	−1.91991	−0.959954	−	0.280156i	$-0.909614\pi$
$421$	−39.3932	−1.91991	−0.959954	+	0.280156i	$0.909614\pi$
$422$	−0.392995	−0.0191307
$423$	10.4139	0.506339
$424$	−50.8968	−2.47177
$425$	−74.7524	−3.62603
$426$	2.10783	0.102125
$427$	2.15290	0.104186
$428$	−61.7189	−2.98330
$429$	−5.92010	−0.285825
$430$	−38.0951	−1.83711
$431$	5.18866	0.249929	0.124964	−	0.992161i	$-0.460118\pi$
$431$	5.18866	0.249929	0.124964	+	0.992161i	$0.460118\pi$
$432$	7.66965	0.369006
$433$	−33.8722	−1.62779	−0.813896	−	0.581010i	$-0.802658\pi$
$433$	−33.8722	−1.62779	−0.813896	+	0.581010i	$0.802658\pi$
$434$	−2.49220	−0.119629
$435$	−5.90105	−0.282934
$436$	23.8674	1.14304
$437$	−12.5466	−0.600188
$438$	−4.19697	−0.200539
$439$	5.76426	0.275113	0.137557	−	0.990494i	$-0.456075\pi$
$439$	5.76426	0.275113	0.137557	+	0.990494i	$0.456075\pi$
$440$	−76.0713	−3.62655
$441$	−2.94091	−0.140043
$442$	128.375	6.10618
$443$	0.722019	0.0343042	0.0171521	−	0.999853i	$-0.494540\pi$
$443$	0.722019	0.0343042	0.0171521	+	0.999853i	$0.494540\pi$
$444$	−1.02364	−0.0485800
$445$	−20.8564	−0.988689
$446$	6.78951	0.321492
$447$	3.12843	0.147970
$448$	−5.10165	−0.241030
$449$	6.43896	0.303873	0.151937	−	0.988390i	$-0.451449\pi$
$449$	6.43896	0.303873	0.151937	+	0.988390i	$0.451449\pi$
$450$	72.3646	3.41130
$451$	−15.8201	−0.744941
$452$	2.99690	0.140962
$453$	−0.712618	−0.0334817
$454$	−40.0645	−1.88032
$455$	26.2385	1.23008
$456$	−2.34113	−0.109633
$457$	−7.50698	−0.351162	−0.175581	−	0.984465i	$-0.556180\pi$
$457$	−7.50698	−0.351162	−0.175581	+	0.984465i	$0.556180\pi$
$458$	−14.4994	−0.677511
$459$	−10.9339	−0.510350
$460$	116.583	5.43572
$461$	19.4982	0.908121	0.454061	−	0.890971i	$-0.349975\pi$
$461$	19.4982	0.908121	0.454061	+	0.890971i	$0.349975\pi$
$462$	2.16859	0.100892
$463$	8.47234	0.393743	0.196872	−	0.980429i	$-0.436922\pi$
$463$	8.47234	0.393743	0.196872	+	0.980429i	$0.436922\pi$
$464$	33.4296	1.55193
$465$	−0.937480	−0.0434746
$466$	68.1198	3.15559
$467$	−20.7597	−0.960646	−0.480323	−	0.877092i	$-0.659481\pi$
$467$	−20.7597	−0.960646	−0.480323	+	0.877092i	$0.659481\pi$
$468$	−84.2572	−3.89479
$469$	−5.55357	−0.256440
$470$	34.0342	1.56988
$471$	−5.78949	−0.266765
$472$	−42.1014	−1.93787
$473$	14.1879	0.652362
$474$	−7.31658	−0.336062
$475$	−17.2563	−0.791773
$476$	−31.8826	−1.46134
$477$	−27.1638	−1.24375
$478$	−5.25689	−0.240444
$479$	−18.7419	−0.856338	−0.428169	−	0.903699i	$-0.640841\pi$
$479$	−18.7419	−0.856338	−0.428169	+	0.903699i	$0.640841\pi$
$480$	2.07645	0.0947767
$481$	6.80354	0.310215
$482$	−36.7888	−1.67568
$483$	−1.74502	−0.0794012
$484$	7.63720	0.347145
$485$	38.2198	1.73547
$486$	15.9296	0.722581
$487$	9.86692	0.447113	0.223556	−	0.974691i	$-0.428233\pi$
$487$	9.86692	0.447113	0.223556	+	0.974691i	$0.428233\pi$
$488$	−11.8633	−0.537026
$489$	−4.14064	−0.187246
$490$	−9.61139	−0.434198
$491$	25.8214	1.16530	0.582651	−	0.812723i	$-0.302016\pi$
$491$	25.8214	1.16530	0.582651	+	0.812723i	$0.302016\pi$
$492$	4.52401	0.203958
$493$	−47.6574	−2.14638
$494$	29.6349	1.33334
$495$	−40.5995	−1.82481
$496$	5.31085	0.238464
$497$	3.47932	0.156069
$498$	5.35937	0.240159
$499$	10.6186	0.475356	0.237678	−	0.971344i	$-0.423614\pi$
$499$	10.6186	0.475356	0.237678	+	0.971344i	$0.423614\pi$
$500$	79.1438	3.53942
$501$	1.16892	0.0522233
$502$	−69.8719	−3.11853
$503$	24.0358	1.07170	0.535851	−	0.844312i	$-0.319991\pi$
$503$	24.0358	1.07170	0.535851	+	0.844312i	$0.319991\pi$
$504$	16.2055	0.721851
$505$	−41.3613	−1.84056
$506$	−64.0414	−2.84699
$507$	−8.09185	−0.359372
$508$	−61.7781	−2.74096
$509$	−16.3768	−0.725889	−0.362944	−	0.931811i	$-0.618229\pi$
$509$	−16.3768	−0.725889	−0.362944	+	0.931811i	$0.618229\pi$
$510$	−17.6892	−0.783290
$511$	−6.92780	−0.306468
$512$	46.7664	2.06680
$513$	−2.52404	−0.111439
$514$	72.6316	3.20364
$515$	−26.6600	−1.17478
$516$	−4.05726	−0.178611
$517$	−12.6755	−0.557468
$518$	−2.49220	−0.109501
$519$	−5.66194	−0.248532
$520$	−144.584	−6.34042
$521$	19.2030	0.841300	0.420650	−	0.907223i	$-0.361802\pi$
$521$	19.2030	0.841300	0.420650	+	0.907223i	$0.361802\pi$
$522$	46.1351	2.01928
$523$	39.2979	1.71838	0.859188	−	0.511660i	$-0.170969\pi$
$523$	39.2979	1.71838	0.859188	+	0.511660i	$0.170969\pi$
$524$	76.5151	3.34258
$525$	−2.40005	−0.104747
$526$	29.9908	1.30766
$527$	−7.57117	−0.329806
$528$	−4.62124	−0.201113
$529$	28.5329	1.24056
$530$	−88.7760	−3.85618
$531$	−22.4697	−0.975101
$532$	−7.35997	−0.319095
$533$	−30.0683	−1.30240
$534$	−3.27625	−0.141777
$535$	−56.5238	−2.44374
$536$	30.6023	1.32182
$537$	−0.449719	−0.0194068
$538$	−59.8023	−2.57826
$539$	3.57961	0.154185
$540$	23.4534	1.00927
$541$	−6.74114	−0.289824	−0.144912	−	0.989445i	$-0.546290\pi$
$541$	−6.74114	−0.289824	−0.144912	+	0.989445i	$0.546290\pi$
$542$	−36.2568	−1.55736
$543$	3.15444	0.135370
$544$	16.7696	0.718992
$545$	21.8583	0.936309
$546$	4.12170	0.176392
$547$	2.49138	0.106524	0.0532618	−	0.998581i	$-0.483038\pi$
$547$	2.49138	0.106524	0.0532618	+	0.998581i	$0.483038\pi$
$548$	9.53786	0.407437
$549$	−6.33148	−0.270221
$550$	−88.0806	−3.75577
$551$	−11.0015	−0.468680
$552$	9.61573	0.409273
$553$	−12.0772	−0.513576
$554$	16.4872	0.700476
$555$	−0.937480	−0.0397938
$556$	6.99121	0.296493
$557$	24.6662	1.04514	0.522570	−	0.852596i	$-0.324973\pi$
$557$	24.6662	1.04514	0.522570	+	0.852596i	$0.324973\pi$
$558$	7.32933	0.310275
$559$	26.9661	1.14054
$560$	20.4818	0.865513
$561$	6.58806	0.278148
$562$	−56.6546	−2.38983
$563$	30.7636	1.29653	0.648265	−	0.761415i	$-0.275495\pi$
$563$	30.7636	1.29653	0.648265	+	0.761415i	$0.275495\pi$
$564$	3.62476	0.152630
$565$	2.74464	0.115468
$566$	−29.2161	−1.22805
$567$	8.47168	0.355777
$568$	−19.1723	−0.804453
$569$	−18.5937	−0.779490	−0.389745	−	0.920923i	$-0.627437\pi$
$569$	−18.5937	−0.779490	−0.389745	+	0.920923i	$0.627437\pi$
$570$	−4.08348	−0.171038
$571$	−32.1706	−1.34630	−0.673149	−	0.739507i	$-0.735059\pi$
$571$	−32.1706	−1.34630	−0.673149	+	0.739507i	$0.735059\pi$
$572$	102.556	4.28808
$573$	−2.97034	−0.124088
$574$	11.0143	0.459728
$575$	70.8768	2.95577
$576$	15.0035	0.625145
$577$	−11.6502	−0.485004	−0.242502	−	0.970151i	$-0.577968\pi$
$577$	−11.6502	−0.485004	−0.242502	+	0.970151i	$0.577968\pi$
$578$	−100.492	−4.17992
$579$	1.38711	0.0576461
$580$	102.226	4.24470
$581$	8.84652	0.367015
$582$	6.00379	0.248865
$583$	33.0632	1.36934
$584$	38.1748	1.57968
$585$	−77.1650	−3.19038
$586$	−18.6989	−0.772444
$587$	9.37700	0.387030	0.193515	−	0.981097i	$-0.438011\pi$
$587$	9.37700	0.387030	0.193515	+	0.981097i	$0.438011\pi$
$588$	−1.02364	−0.0422144
$589$	−1.74777	−0.0720158
$590$	−73.4347	−3.02326
$591$	0.888250	0.0365377
$592$	5.31085	0.218274
$593$	15.9875	0.656527	0.328263	−	0.944586i	$-0.393537\pi$
$593$	15.9875	0.656527	0.328263	+	0.944586i	$0.393537\pi$
$594$	−12.8834	−0.528611
$595$	−29.1989	−1.19704
$596$	−54.1949	−2.21991
$597$	5.79273	0.237081
$598$	−121.719	−4.97748
$599$	0.273517	0.0111756	0.00558780	−	0.999984i	$-0.498221\pi$
$599$	0.273517	0.0111756	0.00558780	+	0.999984i	$0.498221\pi$
$600$	13.2252	0.539916
$601$	1.16061	0.0473425	0.0236712	−	0.999720i	$-0.492465\pi$
$601$	1.16061	0.0473425	0.0236712	+	0.999720i	$0.492465\pi$
$602$	−9.87793	−0.402594
$603$	16.3325	0.665113
$604$	12.3449	0.502308
$605$	6.99435	0.284361
$606$	−6.49729	−0.263934
$607$	12.2814	0.498486	0.249243	−	0.968441i	$-0.419818\pi$
$607$	12.2814	0.498486	0.249243	+	0.968441i	$0.419818\pi$
$608$	3.87120	0.156998
$609$	−1.53012	−0.0620036
$610$	−20.6923	−0.837809
$611$	−24.0915	−0.974640
$612$	93.7639	3.79018
$613$	18.6604	0.753688	0.376844	−	0.926277i	$-0.377009\pi$
$613$	18.6604	0.753688	0.376844	+	0.926277i	$0.377009\pi$
$614$	64.2130	2.59143
$615$	4.14320	0.167070
$616$	−19.7250	−0.794743
$617$	21.1964	0.853333	0.426667	−	0.904409i	$-0.359688\pi$
$617$	21.1964	0.853333	0.426667	+	0.904409i	$0.359688\pi$
$618$	−4.18792	−0.168463
$619$	−46.6396	−1.87460	−0.937302	−	0.348519i	$-0.886685\pi$
$619$	−46.6396	−1.87460	−0.937302	+	0.348519i	$0.886685\pi$
$620$	16.2403	0.652226
$621$	10.3670	0.416014
$622$	35.7308	1.43268
$623$	−5.40799	−0.216667
$624$	−8.78329	−0.351613
$625$	23.1155	0.924618
$626$	−12.0509	−0.481651
$627$	1.52083	0.0607360
$628$	100.293	4.00214
$629$	−7.57117	−0.301883
$630$	28.2662	1.12615
$631$	30.4052	1.21041	0.605205	−	0.796069i	$-0.293091\pi$
$631$	30.4052	1.21041	0.605205	+	0.796069i	$0.293091\pi$
$632$	66.5500	2.64722
$633$	−0.0383322	−0.00152357
$634$	4.66272	0.185180
$635$	−56.5780	−2.24523
$636$	−9.45494	−0.374913
$637$	6.80354	0.269566
$638$	−56.1546	−2.22318
$639$	−10.2324	−0.404786
$640$	66.1181	2.61355
$641$	5.20160	0.205451	0.102725	−	0.994710i	$-0.467244\pi$
$641$	5.20160	0.205451	0.102725	+	0.994710i	$0.467244\pi$
$642$	−8.87910	−0.350430
$643$	−28.4366	−1.12143	−0.560715	−	0.828009i	$-0.689474\pi$
$643$	−28.4366	−1.12143	−0.560715	+	0.828009i	$0.689474\pi$
$644$	30.2296	1.19121
$645$	−3.71574	−0.146307
$646$	−32.9785	−1.29752
$647$	−7.65112	−0.300797	−0.150398	−	0.988625i	$-0.548056\pi$
$647$	−7.65112	−0.300797	−0.150398	+	0.988625i	$0.548056\pi$
$648$	−46.6821	−1.83385
$649$	27.3496	1.07357
$650$	−167.409	−6.56633
$651$	−0.243085	−0.00952726
$652$	71.7298	2.80915
$653$	−25.2919	−0.989748	−0.494874	−	0.868965i	$-0.664786\pi$
$653$	−25.2919	−0.989748	−0.494874	+	0.868965i	$0.664786\pi$
$654$	3.43364	0.134266
$655$	70.0746	2.73804
$656$	−23.4713	−0.916402
$657$	20.3740	0.794866
$658$	8.82495	0.344032
$659$	25.1645	0.980271	0.490135	−	0.871646i	$-0.336947\pi$
$659$	25.1645	0.980271	0.490135	+	0.871646i	$0.336947\pi$
$660$	−14.1315	−0.550068
$661$	23.9229	0.930494	0.465247	−	0.885181i	$-0.345965\pi$
$661$	23.9229	0.930494	0.465247	+	0.885181i	$0.345965\pi$
$662$	47.6732	1.85287
$663$	12.5215	0.486295
$664$	−48.7476	−1.89178
$665$	−6.74045	−0.261383
$666$	7.32933	0.284006
$667$	45.1866	1.74963
$668$	−20.2495	−0.783478
$669$	0.662238	0.0256036
$670$	53.3775	2.06215
$671$	7.70654	0.297508
$672$	0.538417	0.0207699
$673$	−15.6204	−0.602121	−0.301060	−	0.953605i	$-0.597341\pi$
$673$	−15.6204	−0.602121	−0.301060	+	0.953605i	$0.597341\pi$
$674$	57.6048	2.21885
$675$	14.2585	0.548809
$676$	140.178	5.39146
$677$	−35.8444	−1.37761	−0.688807	−	0.724945i	$-0.741865\pi$
$677$	−35.8444	−1.37761	−0.688807	+	0.724945i	$0.741865\pi$
$678$	0.431144	0.0165580
$679$	9.91025	0.380320
$680$	160.897	6.17012
$681$	−3.90783	−0.149749
$682$	−8.92110	−0.341606
$683$	29.5632	1.13120	0.565602	−	0.824678i	$-0.308644\pi$
$683$	29.5632	1.13120	0.565602	+	0.824678i	$0.308644\pi$
$684$	21.6450	0.827617
$685$	8.73502	0.333748
$686$	−2.49220	−0.0951526
$687$	−1.41425	−0.0539569
$688$	21.0498	0.802515
$689$	62.8412	2.39406
$690$	16.7721	0.638502
$691$	23.0561	0.877096	0.438548	−	0.898708i	$-0.355493\pi$
$691$	23.0561	0.877096	0.438548	+	0.898708i	$0.355493\pi$
$692$	98.0838	3.72859
$693$	−10.5273	−0.399899
$694$	51.1434	1.94138
$695$	6.40273	0.242869
$696$	8.43154	0.319597
$697$	33.4609	1.26742
$698$	−72.2716	−2.73552
$699$	6.64430	0.251311
$700$	41.5769	1.57146
$701$	−41.2129	−1.55659	−0.778295	−	0.627898i	$-0.783915\pi$
$701$	−41.2129	−1.55659	−0.778295	+	0.627898i	$0.783915\pi$
$702$	−24.4866	−0.924188
$703$	−1.74777	−0.0659186
$704$	−18.2619	−0.688272
$705$	3.31965	0.125025
$706$	77.4235	2.91387
$707$	−10.7248	−0.403349
$708$	−7.82103	−0.293932
$709$	−16.3251	−0.613102	−0.306551	−	0.951854i	$-0.599175\pi$
$709$	−16.3251	−0.613102	−0.306551	+	0.951854i	$0.599175\pi$
$710$	−33.4410	−1.25502
$711$	35.5180	1.33203
$712$	29.8001	1.11680
$713$	7.17864	0.268842
$714$	−4.58674	−0.171655
$715$	93.9235	3.51254
$716$	7.79065	0.291150
$717$	−0.512749	−0.0191490
$718$	26.8491	1.00200
$719$	17.2626	0.643787	0.321893	−	0.946776i	$-0.395681\pi$
$719$	17.2626	0.643787	0.321893	+	0.946776i	$0.395681\pi$
$720$	−60.2350	−2.24483
$721$	−6.91285	−0.257448
$722$	39.7388	1.47893
$723$	−3.58832	−0.133451
$724$	−54.6455	−2.03088
$725$	62.1483	2.30813
$726$	1.09871	0.0407771
$727$	18.5216	0.686930	0.343465	−	0.939166i	$-0.388399\pi$
$727$	18.5216	0.686930	0.343465	+	0.939166i	$0.388399\pi$
$728$	−37.4901	−1.38947
$729$	−23.8613	−0.883751
$730$	66.5858	2.46445
$731$	−30.0087	−1.10991
$732$	−2.20380	−0.0814549
$733$	26.1158	0.964609	0.482304	−	0.876004i	$-0.339800\pi$
$733$	26.1158	0.964609	0.482304	+	0.876004i	$0.339800\pi$
$734$	61.0399	2.25302
$735$	−0.937480	−0.0345795
$736$	−15.9002	−0.586089
$737$	−19.8796	−0.732275
$738$	−32.3920	−1.19237
$739$	−51.9201	−1.90991	−0.954956	−	0.296749i	$-0.904098\pi$
$739$	−51.9201	−1.90991	−0.954956	+	0.296749i	$0.904098\pi$
$740$	16.2403	0.597005
$741$	2.89054	0.106187
$742$	−23.0193	−0.845065
$743$	9.17840	0.336723	0.168361	−	0.985725i	$-0.446152\pi$
$743$	9.17840	0.336723	0.168361	+	0.985725i	$0.446152\pi$
$744$	1.33949	0.0491081
$745$	−49.6331	−1.81842
$746$	−2.81107	−0.102921
$747$	−26.0168	−0.951905
$748$	−114.127	−4.17291
$749$	−14.6564	−0.535534
$750$	11.3859	0.415754
$751$	24.0855	0.878894	0.439447	−	0.898269i	$-0.355175\pi$
$751$	24.0855	0.878894	0.439447	+	0.898269i	$0.355175\pi$
$752$	−18.8059	−0.685780
$753$	−6.81519	−0.248359
$754$	−106.729	−3.88686
$755$	11.3058	0.411461
$756$	6.08138	0.221178
$757$	24.3323	0.884374	0.442187	−	0.896923i	$-0.354203\pi$
$757$	24.3323	0.884374	0.442187	+	0.896923i	$0.354203\pi$
$758$	−44.7842	−1.62664
$759$	−6.24650	−0.226733
$760$	37.1424	1.34730
$761$	0.713711	0.0258720	0.0129360	−	0.999916i	$-0.495882\pi$
$761$	0.713711	0.0258720	0.0129360	+	0.999916i	$0.495882\pi$
$762$	−8.88761	−0.321964
$763$	5.66779	0.205188
$764$	51.4562	1.86162
$765$	85.8714	3.10469
$766$	−31.0605	−1.12226
$767$	51.9817	1.87695
$768$	7.90596	0.285282
$769$	−20.9103	−0.754046	−0.377023	−	0.926204i	$-0.623052\pi$
$769$	−20.9103	−0.754046	−0.377023	+	0.926204i	$0.623052\pi$
$770$	−34.4050	−1.23987
$771$	7.08438	0.255138
$772$	−24.0293	−0.864834
$773$	−24.9760	−0.898324	−0.449162	−	0.893450i	$-0.648277\pi$
$773$	−24.9760	−0.898324	−0.449162	+	0.893450i	$0.648277\pi$
$774$	29.0501	1.04418
$775$	9.87329	0.354659
$776$	−54.6092	−1.96036
$777$	−0.243085	−0.00872063
$778$	−12.5700	−0.450655
$779$	7.72431	0.276752
$780$	−26.8588	−0.961701
$781$	12.4546	0.445660
$782$	135.453	4.84378
$783$	9.09030	0.324861
$784$	5.31085	0.189673
$785$	91.8513	3.27831
$786$	11.0077	0.392633
$787$	1.60243	0.0571203	0.0285601	−	0.999592i	$-0.490908\pi$
$787$	1.60243	0.0571203	0.0285601	+	0.999592i	$0.490908\pi$
$788$	−15.3875	−0.548156
$789$	2.92526	0.104142
$790$	116.079	4.12990
$791$	0.711675	0.0253043
$792$	58.0094	2.06128
$793$	14.6473	0.520142
$794$	48.8186	1.73251
$795$	−8.65908	−0.307106
$796$	−100.349	−3.55679
$797$	55.7353	1.97425	0.987123	−	0.159960i	$-0.0511366\pi$
$797$	55.7353	1.97425	0.987123	+	0.159960i	$0.0511366\pi$
$798$	−1.05883	−0.0374822
$799$	26.8098	0.948462
$800$	−21.8687	−0.773174
$801$	15.9044	0.561955
$802$	27.8083	0.981944
$803$	−24.7988	−0.875131
$804$	5.68488	0.200490
$805$	27.6851	0.975771
$806$	−16.9558	−0.597241
$807$	−5.83303	−0.205332
$808$	59.0979	2.07906
$809$	35.0362	1.23181	0.615904	−	0.787821i	$-0.288791\pi$
$809$	35.0362	1.23181	0.615904	+	0.787821i	$0.288791\pi$
$810$	−81.4246	−2.86097
$811$	−38.0785	−1.33712	−0.668558	−	0.743660i	$-0.733088\pi$
$811$	−38.0785	−1.33712	−0.668558	+	0.743660i	$0.733088\pi$
$812$	26.5068	0.930207
$813$	−3.53643	−0.124028
$814$	−8.92110	−0.312684
$815$	65.6920	2.30109
$816$	9.77430	0.342169
$817$	−6.92738	−0.242358
$818$	91.0020	3.18181
$819$	−20.0086	−0.699157
$820$	−71.7742	−2.50646
$821$	−22.4708	−0.784237	−0.392119	−	0.919915i	$-0.628258\pi$
$821$	−22.4708	−0.784237	−0.392119	+	0.919915i	$0.628258\pi$
$822$	1.37215	0.0478592
$823$	11.3334	0.395057	0.197529	−	0.980297i	$-0.436708\pi$
$823$	11.3334	0.395057	0.197529	+	0.980297i	$0.436708\pi$
$824$	38.0924	1.32701
$825$	−8.59125	−0.299109
$826$	−19.0414	−0.662533
$827$	−44.2751	−1.53959	−0.769797	−	0.638288i	$-0.779643\pi$
$827$	−44.2751	−1.53959	−0.769797	+	0.638288i	$0.779643\pi$
$828$	−88.9026	−3.08958
$829$	27.2609	0.946810	0.473405	−	0.880845i	$-0.343025\pi$
$829$	27.2609	0.946810	0.473405	+	0.880845i	$0.343025\pi$
$830$	−85.0273	−2.95134
$831$	1.60814	0.0557858
$832$	−34.7093	−1.20333
$833$	−7.57117	−0.262326
$834$	1.00578	0.0348273
$835$	−18.5451	−0.641778
$836$	−26.3458	−0.911189
$837$	1.44415	0.0499170
$838$	−42.2557	−1.45970
$839$	7.72959	0.266855	0.133428	−	0.991059i	$-0.457402\pi$
$839$	7.72959	0.266855	0.133428	+	0.991059i	$0.457402\pi$
$840$	5.16587	0.178239
$841$	10.6218	0.366268
$842$	98.1757	3.38336
$843$	−5.52600	−0.190326
$844$	0.664042	0.0228573
$845$	128.379	4.41636
$846$	−25.9534	−0.892296
$847$	1.81361	0.0623163
$848$	49.0539	1.68452
$849$	−2.84970	−0.0978014
$850$	186.298	6.38996
$851$	7.17864	0.246081
$852$	−3.56158	−0.122018
$853$	−24.5459	−0.840436	−0.420218	−	0.907423i	$-0.638046\pi$
$853$	−24.5459	−0.840436	−0.420218	+	0.907423i	$0.638046\pi$
$854$	−5.36545	−0.183602
$855$	19.8231	0.677934
$856$	80.7624	2.76040
$857$	32.9670	1.12613	0.563066	−	0.826412i	$-0.309622\pi$
$857$	32.9670	1.12613	0.563066	+	0.826412i	$0.309622\pi$
$858$	14.7541	0.503695
$859$	−14.9050	−0.508552	−0.254276	−	0.967132i	$-0.581837\pi$
$859$	−14.9050	−0.508552	−0.254276	+	0.967132i	$0.581837\pi$
$860$	64.3691	2.19497
$861$	1.07432	0.0366126
$862$	−12.9312	−0.440437
$863$	14.2210	0.484088	0.242044	−	0.970265i	$-0.422182\pi$
$863$	14.2210	0.484088	0.242044	+	0.970265i	$0.422182\pi$
$864$	−3.19869	−0.108822
$865$	89.8277	3.05423
$866$	84.4161	2.86858
$867$	−9.80185	−0.332888
$868$	4.21105	0.142932
$869$	−43.2317	−1.46654
$870$	14.7066	0.498600
$871$	−37.7839	−1.28026
$872$	−31.2317	−1.05764
$873$	−29.1451	−0.986414
$874$	31.2687	1.05768
$875$	18.7943	0.635363
$876$	7.09160	0.239603
$877$	−43.4610	−1.46757	−0.733786	−	0.679381i	$-0.762249\pi$
$877$	−43.4610	−1.46757	−0.733786	+	0.679381i	$0.762249\pi$
$878$	−14.3657	−0.484818
$879$	−1.82386	−0.0615173
$880$	73.3167	2.47151
$881$	49.3687	1.66327	0.831636	−	0.555320i	$-0.187404\pi$
$881$	49.3687	1.66327	0.831636	+	0.555320i	$0.187404\pi$
$882$	7.32933	0.246791
$883$	15.2348	0.512691	0.256345	−	0.966585i	$-0.417482\pi$
$883$	15.2348	0.512691	0.256345	+	0.966585i	$0.417482\pi$
$884$	−216.915	−7.29562
$885$	−7.16271	−0.240772
$886$	−1.79942	−0.0604525
$887$	47.5058	1.59509	0.797545	−	0.603260i	$-0.206132\pi$
$887$	47.5058	1.59509	0.797545	+	0.603260i	$0.206132\pi$
$888$	1.33949	0.0449504
$889$	−14.6705	−0.492032
$890$	51.9783	1.74232
$891$	30.3253	1.01594
$892$	−11.4722	−0.384117
$893$	6.18893	0.207104
$894$	−7.79667	−0.260760
$895$	7.13488	0.238493
$896$	17.1442	0.572747
$897$	−11.8723	−0.396405
$898$	−16.0472	−0.535501
$899$	6.29458	0.209936
$900$	−122.274	−4.07580
$901$	−69.9315	−2.32976
$902$	39.4269	1.31277
$903$	−0.963478	−0.0320625
$904$	−3.92160	−0.130430
$905$	−50.0458	−1.66358
$906$	1.77599	0.0590032
$907$	−57.9150	−1.92304	−0.961518	−	0.274741i	$-0.911408\pi$
$907$	−57.9150	−1.92304	−0.961518	+	0.274741i	$0.911408\pi$
$908$	67.6968	2.24660
$909$	31.5408	1.04614
$910$	−65.3914	−2.16771
$911$	47.6820	1.57977	0.789887	−	0.613252i	$-0.210139\pi$
$911$	47.6820	1.57977	0.789887	+	0.613252i	$0.210139\pi$
$912$	2.25636	0.0747154
$913$	31.6671	1.04803
$914$	18.7089	0.618835
$915$	−2.01830	−0.0667229
$916$	24.4995	0.809486
$917$	18.1701	0.600029
$918$	27.2494	0.899365
$919$	11.3980	0.375986	0.187993	−	0.982170i	$-0.439802\pi$
$919$	11.3980	0.375986	0.187993	+	0.982170i	$0.439802\pi$
$920$	−152.555	−5.02960
$921$	6.26324	0.206381
$922$	−48.5933	−1.60034
$923$	23.6717	0.779162
$924$	−3.66425	−0.120545
$925$	9.87329	0.324632
$926$	−21.1148	−0.693874
$927$	20.3301	0.667727
$928$	−13.9421	−0.457671
$929$	−35.9213	−1.17854	−0.589270	−	0.807936i	$-0.700585\pi$
$929$	−35.9213	−1.17854	−0.589270	+	0.807936i	$0.700585\pi$
$930$	2.33639	0.0766131
$931$	−1.74777	−0.0572810
$932$	−115.102	−3.77028
$933$	3.48513	0.114098
$934$	51.7374	1.69290
$935$	−104.521	−3.41819
$936$	110.255	3.60379
$937$	−51.5346	−1.68356	−0.841781	−	0.539819i	$-0.818493\pi$
$937$	−51.5346	−1.68356	−0.841781	+	0.539819i	$0.818493\pi$
$938$	13.8406	0.451911
$939$	−1.17543	−0.0383586
$940$	−57.5074	−1.87569
$941$	21.0335	0.685671	0.342836	−	0.939395i	$-0.388613\pi$
$941$	21.0335	0.685671	0.342836	+	0.939395i	$0.388613\pi$
$942$	14.4285	0.470107
$943$	−31.7261	−1.03314
$944$	40.5769	1.32067
$945$	5.56948	0.181175
$946$	−35.3591	−1.14962
$947$	9.02966	0.293424	0.146712	−	0.989179i	$-0.453131\pi$
$947$	9.02966	0.293424	0.146712	+	0.989179i	$0.453131\pi$
$948$	12.3628	0.401524
$949$	−47.1335	−1.53002
$950$	43.0061	1.39530
$951$	0.454795	0.0147477
$952$	41.7200	1.35215
$953$	−25.8578	−0.837616	−0.418808	−	0.908075i	$-0.637552\pi$
$953$	−25.8578	−0.837616	−0.418808	+	0.908075i	$0.637552\pi$
$954$	67.6977	2.19179
$955$	47.1249	1.52493
$956$	8.88253	0.287281
$957$	−5.47723	−0.177054
$958$	46.7085	1.50908
$959$	2.26496	0.0731393
$960$	4.78269	0.154361
$961$	1.00000	0.0322581
$962$	−16.9558	−0.546676
$963$	43.1032	1.38898
$964$	62.1618	2.00210
$965$	−22.0067	−0.708420
$966$	4.34894	0.139925
$967$	22.6283	0.727678	0.363839	−	0.931462i	$-0.381466\pi$
$967$	22.6283	0.727678	0.363839	+	0.931462i	$0.381466\pi$
$968$	−9.99367	−0.321209
$969$	−3.21668	−0.103334
$970$	−95.2512	−3.05833
$971$	31.4364	1.00884	0.504421	−	0.863458i	$-0.331706\pi$
$971$	31.4364	1.00884	0.504421	+	0.863458i	$0.331706\pi$
$972$	−26.9161	−0.863335
$973$	1.66020	0.0532237
$974$	−24.5903	−0.787925
$975$	−16.3288	−0.522941
$976$	11.4337	0.365984
$977$	46.3605	1.48321	0.741603	−	0.670839i	$-0.234066\pi$
$977$	46.3605	1.48321	0.741603	+	0.670839i	$0.234066\pi$
$978$	10.3193	0.329975
$979$	−19.3585	−0.618700
$980$	16.2403	0.518777
$981$	−16.6685	−0.532183
$982$	−64.3519	−2.05355
$983$	36.9141	1.17738	0.588689	−	0.808360i	$-0.299644\pi$
$983$	36.9141	1.17738	0.588689	+	0.808360i	$0.299644\pi$
$984$	−5.91989	−0.188719
$985$	−14.0922	−0.449016
$986$	118.772	3.78246
$987$	0.860772	0.0273987
$988$	−50.0738	−1.59306
$989$	28.4528	0.904748
$990$	101.182	3.21578
$991$	36.8877	1.17178	0.585889	−	0.810392i	$-0.300746\pi$
$991$	36.8877	1.17178	0.585889	+	0.810392i	$0.300746\pi$
$992$	−2.21493	−0.0703241
$993$	4.64997	0.147562
$994$	−8.67114	−0.275032
$995$	−91.9027	−2.91351
$996$	−9.05569	−0.286940
$997$	4.31890	0.136781	0.0683905	−	0.997659i	$-0.478214\pi$
$997$	4.31890	0.136781	0.0683905	+	0.997659i	$0.478214\pi$
$998$	−26.4638	−0.837696
$999$	1.44415	0.0456908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.5	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.5	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49220 q^{2} -0.243085 q^{3} +4.21105 q^{4} +3.85659 q^{5} +0.605816 q^{6} +1.00000 q^{7} -5.51038 q^{8} -2.94091 q^{9} +O(q^{10})\)	\(q-2.49220 q^{2} -0.243085 q^{3} +4.21105 q^{4} +3.85659 q^{5} +0.605816 q^{6} +1.00000 q^{7} -5.51038 q^{8} -2.94091 q^{9} -9.61139 q^{10} +3.57961 q^{11} -1.02364 q^{12} +6.80354 q^{13} -2.49220 q^{14} -0.937480 q^{15} +5.31085 q^{16} -7.57117 q^{17} +7.32933 q^{18} -1.74777 q^{19} +16.2403 q^{20} -0.243085 q^{21} -8.92110 q^{22} +7.17864 q^{23} +1.33949 q^{24} +9.87329 q^{25} -16.9558 q^{26} +1.44415 q^{27} +4.21105 q^{28} +6.29458 q^{29} +2.33639 q^{30} +1.00000 q^{31} -2.21493 q^{32} -0.870150 q^{33} +18.8689 q^{34} +3.85659 q^{35} -12.3843 q^{36} +1.00000 q^{37} +4.35580 q^{38} -1.65384 q^{39} -21.2513 q^{40} -4.41951 q^{41} +0.605816 q^{42} +3.96354 q^{43} +15.0739 q^{44} -11.3419 q^{45} -17.8906 q^{46} -3.54103 q^{47} -1.29099 q^{48} +1.00000 q^{49} -24.6062 q^{50} +1.84044 q^{51} +28.6500 q^{52} +9.23655 q^{53} -3.59910 q^{54} +13.8051 q^{55} -5.51038 q^{56} +0.424858 q^{57} -15.6873 q^{58} +7.64038 q^{59} -3.94778 q^{60} +2.15290 q^{61} -2.49220 q^{62} -2.94091 q^{63} -5.10165 q^{64} +26.2385 q^{65} +2.16859 q^{66} -5.55357 q^{67} -31.8826 q^{68} -1.74502 q^{69} -9.61139 q^{70} +3.47932 q^{71} +16.2055 q^{72} -6.92780 q^{73} -2.49220 q^{74} -2.40005 q^{75} -7.35997 q^{76} +3.57961 q^{77} +4.12170 q^{78} -12.0772 q^{79} +20.4818 q^{80} +8.47168 q^{81} +11.0143 q^{82} +8.84652 q^{83} -1.02364 q^{84} -29.1989 q^{85} -9.87793 q^{86} -1.53012 q^{87} -19.7250 q^{88} -5.40799 q^{89} +28.2662 q^{90} +6.80354 q^{91} +30.2296 q^{92} -0.243085 q^{93} +8.82495 q^{94} -6.74045 q^{95} +0.538417 q^{96} +9.91025 q^{97} -2.49220 q^{98} -10.5273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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