LMFDB - Embedded newform 8023.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76736 q^{2} +2.97864 q^{3} +5.65827 q^{4} -2.08289 q^{5} -8.24297 q^{6} -3.08270 q^{7} -10.1238 q^{8} +5.87230 q^{9} +O(q^{10})$	\(q-2.76736 q^{2} +2.97864 q^{3} +5.65827 q^{4} -2.08289 q^{5} -8.24297 q^{6} -3.08270 q^{7} -10.1238 q^{8} +5.87230 q^{9} +5.76411 q^{10} -5.85614 q^{11} +16.8540 q^{12} +1.74727 q^{13} +8.53093 q^{14} -6.20419 q^{15} +16.6995 q^{16} +1.40741 q^{17} -16.2508 q^{18} +3.30341 q^{19} -11.7856 q^{20} -9.18225 q^{21} +16.2060 q^{22} -4.33488 q^{23} -30.1550 q^{24} -0.661558 q^{25} -4.83532 q^{26} +8.55555 q^{27} -17.4428 q^{28} +9.30259 q^{29} +17.1692 q^{30} +1.60550 q^{31} -25.9660 q^{32} -17.4433 q^{33} -3.89481 q^{34} +6.42093 q^{35} +33.2271 q^{36} +8.92492 q^{37} -9.14171 q^{38} +5.20449 q^{39} +21.0867 q^{40} +1.69063 q^{41} +25.4106 q^{42} +8.58147 q^{43} -33.1356 q^{44} -12.2314 q^{45} +11.9962 q^{46} +2.01279 q^{47} +49.7419 q^{48} +2.50303 q^{49} +1.83077 q^{50} +4.19217 q^{51} +9.88653 q^{52} -8.96198 q^{53} -23.6763 q^{54} +12.1977 q^{55} +31.2085 q^{56} +9.83966 q^{57} -25.7436 q^{58} -6.18654 q^{59} -35.1050 q^{60} -1.34332 q^{61} -4.44298 q^{62} -18.1025 q^{63} +38.4583 q^{64} -3.63938 q^{65} +48.2720 q^{66} -4.37363 q^{67} +7.96352 q^{68} -12.9120 q^{69} -17.7690 q^{70} +1.00000 q^{71} -59.4497 q^{72} -15.1194 q^{73} -24.6985 q^{74} -1.97054 q^{75} +18.6916 q^{76} +18.0527 q^{77} -14.4027 q^{78} -7.41962 q^{79} -34.7833 q^{80} +7.86701 q^{81} -4.67858 q^{82} +2.87233 q^{83} -51.9557 q^{84} -2.93149 q^{85} -23.7480 q^{86} +27.7091 q^{87} +59.2861 q^{88} +9.03006 q^{89} +33.8486 q^{90} -5.38631 q^{91} -24.5279 q^{92} +4.78219 q^{93} -5.57011 q^{94} -6.88064 q^{95} -77.3435 q^{96} -0.220805 q^{97} -6.92679 q^{98} -34.3890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.76736	−1.95682	−0.978409	−	0.206678i	$-0.933735\pi$
$2$	−2.76736	−1.95682	−0.978409	+	0.206678i	$0.933735\pi$
$3$	2.97864	1.71972	0.859859	−	0.510531i	$-0.170551\pi$
$3$	2.97864	1.71972	0.859859	+	0.510531i	$0.170551\pi$
$4$	5.65827	2.82914
$5$	−2.08289	−0.931498	−0.465749	−	0.884917i	$-0.654215\pi$
$5$	−2.08289	−0.931498	−0.465749	+	0.884917i	$0.654215\pi$
$6$	−8.24297	−3.36518
$7$	−3.08270	−1.16515	−0.582575	−	0.812777i	$-0.697955\pi$
$7$	−3.08270	−1.16515	−0.582575	+	0.812777i	$0.697955\pi$
$8$	−10.1238	−3.57929
$9$	5.87230	1.95743
$10$	5.76411	1.82277
$11$	−5.85614	−1.76569	−0.882846	−	0.469662i	$-0.844376\pi$
$11$	−5.85614	−1.76569	−0.882846	+	0.469662i	$0.844376\pi$
$12$	16.8540	4.86532
$13$	1.74727	0.484606	0.242303	−	0.970201i	$-0.422097\pi$
$13$	1.74727	0.484606	0.242303	+	0.970201i	$0.422097\pi$
$14$	8.53093	2.27999
$15$	−6.20419	−1.60191
$16$	16.6995	4.17488
$17$	1.40741	0.341348	0.170674	−	0.985328i	$-0.445406\pi$
$17$	1.40741	0.341348	0.170674	+	0.985328i	$0.445406\pi$
$18$	−16.2508	−3.83034
$19$	3.30341	0.757853	0.378927	−	0.925427i	$-0.376293\pi$
$19$	3.30341	0.757853	0.378927	+	0.925427i	$0.376293\pi$
$20$	−11.7856	−2.63534
$21$	−9.18225	−2.00373
$22$	16.2060	3.45514
$23$	−4.33488	−0.903884	−0.451942	−	0.892047i	$-0.649269\pi$
$23$	−4.33488	−0.903884	−0.451942	+	0.892047i	$0.649269\pi$
$24$	−30.1550	−6.15537
$25$	−0.661558	−0.132312
$26$	−4.83532	−0.948285
$27$	8.55555	1.64652
$28$	−17.4428	−3.29637
$29$	9.30259	1.72745	0.863724	−	0.503965i	$-0.168126\pi$
$29$	9.30259	1.72745	0.863724	+	0.503965i	$0.168126\pi$
$30$	17.1692	3.13466
$31$	1.60550	0.288355	0.144178	−	0.989552i	$-0.453946\pi$
$31$	1.60550	0.288355	0.144178	+	0.989552i	$0.453946\pi$
$32$	−25.9660	−4.59019
$33$	−17.4433	−3.03649
$34$	−3.89481	−0.667955
$35$	6.42093	1.08534
$36$	33.2271	5.53785
$37$	8.92492	1.46725	0.733624	−	0.679556i	$-0.237827\pi$
$37$	8.92492	1.46725	0.733624	+	0.679556i	$0.237827\pi$
$38$	−9.14171	−1.48298
$39$	5.20449	0.833385
$40$	21.0867	3.33410
$41$	1.69063	0.264032	0.132016	−	0.991248i	$-0.457855\pi$
$41$	1.69063	0.264032	0.132016	+	0.991248i	$0.457855\pi$
$42$	25.4106	3.92094
$43$	8.58147	1.30866	0.654331	−	0.756208i	$-0.272950\pi$
$43$	8.58147	1.30866	0.654331	+	0.756208i	$0.272950\pi$
$44$	−33.1356	−4.99539
$45$	−12.2314	−1.82335
$46$	11.9962	1.76874
$47$	2.01279	0.293596	0.146798	−	0.989167i	$-0.453103\pi$
$47$	2.01279	0.293596	0.146798	+	0.989167i	$0.453103\pi$
$48$	49.7419	7.17962
$49$	2.50303	0.357576
$50$	1.83077	0.258910
$51$	4.19217	0.587022
$52$	9.88653	1.37102
$53$	−8.96198	−1.23102	−0.615511	−	0.788128i	$-0.711050\pi$
$53$	−8.96198	−1.23102	−0.615511	+	0.788128i	$0.711050\pi$
$54$	−23.6763	−3.22193
$55$	12.1977	1.64474
$56$	31.2085	4.17041
$57$	9.83966	1.30329
$58$	−25.7436	−3.38030
$59$	−6.18654	−0.805419	−0.402710	−	0.915328i	$-0.631932\pi$
$59$	−6.18654	−0.805419	−0.402710	+	0.915328i	$0.631932\pi$
$60$	−35.1050	−4.53204
$61$	−1.34332	−0.171994	−0.0859970	−	0.996295i	$-0.527408\pi$
$61$	−1.34332	−0.171994	−0.0859970	+	0.996295i	$0.527408\pi$
$62$	−4.44298	−0.564259
$63$	−18.1025	−2.28070
$64$	38.4583	4.80729
$65$	−3.63938	−0.451409
$66$	48.2720	5.94187
$67$	−4.37363	−0.534324	−0.267162	−	0.963652i	$-0.586086\pi$
$67$	−4.37363	−0.534324	−0.267162	+	0.963652i	$0.586086\pi$
$68$	7.96352	0.965719
$69$	−12.9120	−1.55443
$70$	−17.7690	−2.12380
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−59.4497	−7.00622
$73$	−15.1194	−1.76960	−0.884798	−	0.465975i	$-0.845704\pi$
$73$	−15.1194	−1.76960	−0.884798	+	0.465975i	$0.845704\pi$
$74$	−24.6985	−2.87114
$75$	−1.97054	−0.227539
$76$	18.6916	2.14407
$77$	18.0527	2.05730
$78$	−14.4027	−1.63078
$79$	−7.41962	−0.834773	−0.417386	−	0.908729i	$-0.637054\pi$
$79$	−7.41962	−0.834773	−0.417386	+	0.908729i	$0.637054\pi$
$80$	−34.7833	−3.88889
$81$	7.86701	0.874112
$82$	−4.67858	−0.516663
$83$	2.87233	0.315279	0.157640	−	0.987497i	$-0.449612\pi$
$83$	2.87233	0.315279	0.157640	+	0.987497i	$0.449612\pi$
$84$	−51.9557	−5.66883
$85$	−2.93149	−0.317965
$86$	−23.7480	−2.56081
$87$	27.7091	2.97073
$88$	59.2861	6.31992
$89$	9.03006	0.957184	0.478592	−	0.878037i	$-0.341147\pi$
$89$	9.03006	0.957184	0.478592	+	0.878037i	$0.341147\pi$
$90$	33.8486	3.56795
$91$	−5.38631	−0.564639
$92$	−24.5279	−2.55721
$93$	4.78219	0.495890
$94$	−5.57011	−0.574513
$95$	−6.88064	−0.705939
$96$	−77.3435	−7.89384
$97$	−0.220805	−0.0224193	−0.0112097	−	0.999937i	$-0.503568\pi$
$97$	−0.220805	−0.0224193	−0.0112097	+	0.999937i	$0.503568\pi$
$98$	−6.92679	−0.699711
$99$	−34.3890	−3.45622
$100$	−3.74328	−0.374328
$101$	−6.71491	−0.668159	−0.334079	−	0.942545i	$-0.608425\pi$
$101$	−6.71491	−0.668159	−0.334079	+	0.942545i	$0.608425\pi$
$102$	−11.6013	−1.14869
$103$	12.1757	1.19970	0.599852	−	0.800111i	$-0.295226\pi$
$103$	12.1757	1.19970	0.599852	+	0.800111i	$0.295226\pi$
$104$	−17.6889	−1.73454
$105$	19.1256	1.86647
$106$	24.8010	2.40889
$107$	−2.91447	−0.281752	−0.140876	−	0.990027i	$-0.544992\pi$
$107$	−2.91447	−0.281752	−0.140876	+	0.990027i	$0.544992\pi$
$108$	48.4096	4.65822
$109$	−8.78431	−0.841384	−0.420692	−	0.907203i	$-0.638213\pi$
$109$	−8.78431	−0.841384	−0.420692	+	0.907203i	$0.638213\pi$
$110$	−33.7554	−3.21845
$111$	26.5841	2.52325
$112$	−51.4796	−4.86436
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−27.2299	−2.55031
$115$	9.02908	0.841967
$116$	52.6366	4.88719
$117$	10.2605	0.948583
$118$	17.1204	1.57606
$119$	−4.33863	−0.397721
$120$	62.8097	5.73371
$121$	23.2944	2.11767
$122$	3.71744	0.336561
$123$	5.03578	0.454061
$124$	9.08433	0.815797
$125$	11.7924	1.05475
$126$	50.0962	4.46292
$127$	−17.1618	−1.52287	−0.761433	−	0.648243i	$-0.775504\pi$
$127$	−17.1618	−1.52287	−0.761433	+	0.648243i	$0.775504\pi$
$128$	−54.4959	−4.81680
$129$	25.5611	2.25053
$130$	10.0715	0.883326
$131$	−15.4703	−1.35165	−0.675824	−	0.737063i	$-0.736212\pi$
$131$	−15.4703	−1.35165	−0.675824	+	0.737063i	$0.736212\pi$
$132$	−98.6992	−8.59066
$133$	−10.1834	−0.883013
$134$	12.1034	1.04557
$135$	−17.8203	−1.53373
$136$	−14.2483	−1.22178
$137$	−2.29071	−0.195708	−0.0978542	−	0.995201i	$-0.531198\pi$
$137$	−2.29071	−0.195708	−0.0978542	+	0.995201i	$0.531198\pi$
$138$	35.7323	3.04173
$139$	11.5424	0.979011	0.489506	−	0.872000i	$-0.337177\pi$
$139$	11.5424	0.979011	0.489506	+	0.872000i	$0.337177\pi$
$140$	36.3314	3.07056
$141$	5.99538	0.504902
$142$	−2.76736	−0.232232
$143$	−10.2323	−0.855664
$144$	98.0646	8.17205
$145$	−19.3763	−1.60911
$146$	41.8409	3.46278
$147$	7.45563	0.614930
$148$	50.4996	4.15105
$149$	−13.3797	−1.09611	−0.548053	−	0.836443i	$-0.684631\pi$
$149$	−13.3797	−1.09611	−0.548053	+	0.836443i	$0.684631\pi$
$150$	5.45320	0.445252
$151$	5.62209	0.457519	0.228760	−	0.973483i	$-0.426533\pi$
$151$	5.62209	0.457519	0.228760	+	0.973483i	$0.426533\pi$
$152$	−33.4429	−2.71258
$153$	8.26475	0.668165
$154$	−49.9583	−4.02576
$155$	−3.34407	−0.268603
$156$	29.4484	2.35776
$157$	3.21571	0.256642	0.128321	−	0.991733i	$-0.459041\pi$
$157$	3.21571	0.256642	0.128321	+	0.991733i	$0.459041\pi$
$158$	20.5328	1.63350
$159$	−26.6945	−2.11701
$160$	54.0845	4.27575
$161$	13.3631	1.05316
$162$	−21.7708	−1.71048
$163$	10.0602	0.787978	0.393989	−	0.919115i	$-0.371095\pi$
$163$	10.0602	0.787978	0.393989	+	0.919115i	$0.371095\pi$
$164$	9.56605	0.746983
$165$	36.3326	2.82849
$166$	−7.94877	−0.616944
$167$	1.63650	0.126636	0.0633179	−	0.997993i	$-0.479832\pi$
$167$	1.63650	0.126636	0.0633179	+	0.997993i	$0.479832\pi$
$168$	92.9589	7.17193
$169$	−9.94705	−0.765157
$170$	8.11248	0.622199
$171$	19.3986	1.48345
$172$	48.5563	3.70238
$173$	−13.4223	−1.02048	−0.510238	−	0.860033i	$-0.670443\pi$
$173$	−13.4223	−1.02048	−0.510238	+	0.860033i	$0.670443\pi$
$174$	−76.6810	−5.81317
$175$	2.03938	0.154163
$176$	−97.7947	−7.37155
$177$	−18.4275	−1.38509
$178$	−24.9894	−1.87304
$179$	20.5491	1.53591	0.767955	−	0.640503i	$-0.221274\pi$
$179$	20.5491	1.53591	0.767955	+	0.640503i	$0.221274\pi$
$180$	−69.2084	−5.15849
$181$	−7.55141	−0.561292	−0.280646	−	0.959811i	$-0.590549\pi$
$181$	−7.55141	−0.561292	−0.280646	+	0.959811i	$0.590549\pi$
$182$	14.9058	1.10489
$183$	−4.00126	−0.295782
$184$	43.8852	3.23526
$185$	−18.5897	−1.36674
$186$	−13.2340	−0.970367
$187$	−8.24200	−0.602715
$188$	11.3889	0.830622
$189$	−26.3742	−1.91844
$190$	19.0412	1.38139
$191$	20.5508	1.48700	0.743501	−	0.668735i	$-0.233164\pi$
$191$	20.5508	1.48700	0.743501	+	0.668735i	$0.233164\pi$
$192$	114.553	8.26719
$193$	9.53860	0.686604	0.343302	−	0.939225i	$-0.388455\pi$
$193$	9.53860	0.686604	0.343302	+	0.939225i	$0.388455\pi$
$194$	0.611045	0.0438705
$195$	−10.8404	−0.776297
$196$	14.1628	1.01163
$197$	12.4913	0.889970	0.444985	−	0.895538i	$-0.353209\pi$
$197$	12.4913	0.889970	0.444985	+	0.895538i	$0.353209\pi$
$198$	95.1667	6.76320
$199$	4.42540	0.313708	0.156854	−	0.987622i	$-0.449865\pi$
$199$	4.42540	0.313708	0.156854	+	0.987622i	$0.449865\pi$
$200$	6.69745	0.473581
$201$	−13.0275	−0.918887
$202$	18.5826	1.30747
$203$	−28.6771	−2.01274
$204$	23.7205	1.66077
$205$	−3.52140	−0.245945
$206$	−33.6944	−2.34760
$207$	−25.4557	−1.76929
$208$	29.1786	2.02317
$209$	−19.3452	−1.33814
$210$	−52.9275	−3.65235
$211$	−11.9362	−0.821719	−0.410859	−	0.911699i	$-0.634771\pi$
$211$	−11.9362	−0.821719	−0.410859	+	0.911699i	$0.634771\pi$
$212$	−50.7093	−3.48273
$213$	2.97864	0.204093
$214$	8.06538	0.551338
$215$	−17.8743	−1.21902
$216$	−86.6143	−5.89336
$217$	−4.94926	−0.335978
$218$	24.3093	1.64644
$219$	−45.0353	−3.04321
$220$	69.0180	4.65319
$221$	2.45913	0.165419
$222$	−73.5678	−4.93755
$223$	9.42365	0.631054	0.315527	−	0.948917i	$-0.397819\pi$
$223$	9.42365	0.631054	0.315527	+	0.948917i	$0.397819\pi$
$224$	80.0455	5.34826
$225$	−3.88487	−0.258991
$226$	−2.76736	−0.184082
$227$	−27.5721	−1.83002	−0.915012	−	0.403427i	$-0.867819\pi$
$227$	−27.5721	−1.83002	−0.915012	+	0.403427i	$0.867819\pi$
$228$	55.6755	3.68720
$229$	25.2459	1.66830	0.834149	−	0.551539i	$-0.185959\pi$
$229$	25.2459	1.66830	0.834149	+	0.551539i	$0.185959\pi$
$230$	−24.9867	−1.64758
$231$	53.7725	3.53797
$232$	−94.1772	−6.18304
$233$	4.06392	0.266236	0.133118	−	0.991100i	$-0.457501\pi$
$233$	4.06392	0.266236	0.133118	+	0.991100i	$0.457501\pi$
$234$	−28.3945	−1.85620
$235$	−4.19243	−0.273484
$236$	−35.0051	−2.27864
$237$	−22.1004	−1.43557
$238$	12.0065	0.778268
$239$	−28.6775	−1.85499	−0.927497	−	0.373832i	$-0.878044\pi$
$239$	−28.6775	−1.85499	−0.927497	+	0.373832i	$0.878044\pi$
$240$	−103.607	−6.68780
$241$	−5.03210	−0.324146	−0.162073	−	0.986779i	$-0.551818\pi$
$241$	−5.03210	−0.324146	−0.162073	+	0.986779i	$0.551818\pi$
$242$	−64.4639	−4.14389
$243$	−2.23366	−0.143290
$244$	−7.60085	−0.486595
$245$	−5.21355	−0.333081
$246$	−13.9358	−0.888515
$247$	5.77194	0.367260
$248$	−16.2536	−1.03211
$249$	8.55564	0.542192
$250$	−32.6338	−2.06395
$251$	13.9588	0.881070	0.440535	−	0.897735i	$-0.354789\pi$
$251$	13.9588	0.881070	0.440535	+	0.897735i	$0.354789\pi$
$252$	−102.429	−6.45243
$253$	25.3856	1.59598
$254$	47.4930	2.97997
$255$	−8.73185	−0.546810
$256$	73.8930	4.61831
$257$	−27.0920	−1.68995	−0.844977	−	0.534802i	$-0.820386\pi$
$257$	−27.0920	−1.68995	−0.844977	+	0.534802i	$0.820386\pi$
$258$	−70.7368	−4.40388
$259$	−27.5128	−1.70956
$260$	−20.5926	−1.27710
$261$	54.6276	3.38137
$262$	42.8119	2.64493
$263$	−26.1951	−1.61526	−0.807629	−	0.589691i	$-0.799249\pi$
$263$	−26.1951	−1.61526	−0.807629	+	0.589691i	$0.799249\pi$
$264$	176.592	10.8685
$265$	18.6668	1.14669
$266$	28.1811	1.72790
$267$	26.8973	1.64609
$268$	−24.7472	−1.51168
$269$	19.3512	1.17987	0.589933	−	0.807452i	$-0.299154\pi$
$269$	19.3512	1.17987	0.589933	+	0.807452i	$0.299154\pi$
$270$	49.3151	3.00122
$271$	23.7678	1.44379	0.721895	−	0.692003i	$-0.243272\pi$
$271$	23.7678	1.44379	0.721895	+	0.692003i	$0.243272\pi$
$272$	23.5031	1.42508
$273$	−16.0439	−0.971020
$274$	6.33921	0.382966
$275$	3.87417	0.233621
$276$	−73.0599	−4.39769
$277$	−27.8278	−1.67201	−0.836006	−	0.548720i	$-0.815115\pi$
$277$	−27.8278	−1.67201	−0.836006	+	0.548720i	$0.815115\pi$
$278$	−31.9419	−1.91575
$279$	9.42795	0.564437
$280$	−65.0039	−3.88473
$281$	−9.33820	−0.557070	−0.278535	−	0.960426i	$-0.589849\pi$
$281$	−9.33820	−0.557070	−0.278535	+	0.960426i	$0.589849\pi$
$282$	−16.5914	−0.988001
$283$	−24.6263	−1.46388	−0.731940	−	0.681369i	$-0.761385\pi$
$283$	−24.6263	−1.46388	−0.731940	+	0.681369i	$0.761385\pi$
$284$	5.65827	0.335757
$285$	−20.4950	−1.21402
$286$	28.3163	1.67438
$287$	−5.21170	−0.307637
$288$	−152.480	−8.98499
$289$	−15.0192	−0.883482
$290$	53.6212	3.14874
$291$	−0.657697	−0.0385549
$292$	−85.5499	−5.00643
$293$	−12.2437	−0.715287	−0.357643	−	0.933858i	$-0.616420\pi$
$293$	−12.2437	−0.715287	−0.357643	+	0.933858i	$0.616420\pi$
$294$	−20.6324	−1.20331
$295$	12.8859	0.750246
$296$	−90.3537	−5.25170
$297$	−50.1025	−2.90724
$298$	37.0264	2.14488
$299$	−7.57420	−0.438027
$300$	−11.1499	−0.643738
$301$	−26.4541	−1.52479
$302$	−15.5583	−0.895282
$303$	−20.0013	−1.14905
$304$	55.1653	3.16395
$305$	2.79798	0.160212
$306$	−22.8715	−1.30748
$307$	−33.5798	−1.91650	−0.958251	−	0.285929i	$-0.907698\pi$
$307$	−33.5798	−1.91650	−0.958251	+	0.285929i	$0.907698\pi$
$308$	102.147	5.82038
$309$	36.2669	2.06315
$310$	9.25425	0.525606
$311$	−11.2094	−0.635624	−0.317812	−	0.948154i	$-0.602948\pi$
$311$	−11.2094	−0.635624	−0.317812	+	0.948154i	$0.602948\pi$
$312$	−52.6890	−2.98293
$313$	−27.6842	−1.56480	−0.782402	−	0.622774i	$-0.786006\pi$
$313$	−27.6842	−1.56480	−0.782402	+	0.622774i	$0.786006\pi$
$314$	−8.89903	−0.502201
$315$	37.7056	2.12447
$316$	−41.9823	−2.36169
$317$	17.1843	0.965165	0.482583	−	0.875850i	$-0.339699\pi$
$317$	17.1843	0.965165	0.482583	+	0.875850i	$0.339699\pi$
$318$	73.8733	4.14261
$319$	−54.4773	−3.05014
$320$	−80.1045	−4.47798
$321$	−8.68115	−0.484535
$322$	−36.9806	−2.06085
$323$	4.64925	0.258691
$324$	44.5137	2.47298
$325$	−1.15592	−0.0641189
$326$	−27.8403	−1.54193
$327$	−26.1653	−1.44694
$328$	−17.1155	−0.945047
$329$	−6.20483	−0.342083
$330$	−100.545	−5.53484
$331$	−12.6084	−0.693023	−0.346512	−	0.938046i	$-0.612634\pi$
$331$	−12.6084	−0.693023	−0.346512	+	0.938046i	$0.612634\pi$
$332$	16.2524	0.891968
$333$	52.4098	2.87204
$334$	−4.52877	−0.247803
$335$	9.10980	0.497722
$336$	−153.339	−8.36534
$337$	−17.8017	−0.969718	−0.484859	−	0.874592i	$-0.661129\pi$
$337$	−17.8017	−0.969718	−0.484859	+	0.874592i	$0.661129\pi$
$338$	27.5270	1.49727
$339$	2.97864	0.161778
$340$	−16.5872	−0.899565
$341$	−9.40200	−0.509147
$342$	−53.6829	−2.90284
$343$	13.8628	0.748521
$344$	−86.8767	−4.68408
$345$	26.8944	1.44795
$346$	37.1443	1.99689
$347$	11.2470	0.603773	0.301887	−	0.953344i	$-0.402384\pi$
$347$	11.2470	0.603773	0.301887	+	0.953344i	$0.402384\pi$
$348$	156.786	8.40459
$349$	−18.1266	−0.970293	−0.485146	−	0.874433i	$-0.661234\pi$
$349$	−18.1266	−0.970293	−0.485146	+	0.874433i	$0.661234\pi$
$350$	−5.64371	−0.301669
$351$	14.9489	0.797911
$352$	152.061	8.10486
$353$	−31.8732	−1.69644	−0.848220	−	0.529644i	$-0.822325\pi$
$353$	−31.8732	−1.69644	−0.848220	+	0.529644i	$0.822325\pi$
$354$	50.9955	2.71038
$355$	−2.08289	−0.110548
$356$	51.0945	2.70801
$357$	−12.9232	−0.683969
$358$	−56.8667	−3.00550
$359$	−0.164001	−0.00865565	−0.00432783	−	0.999991i	$-0.501378\pi$
$359$	−0.164001	−0.00865565	−0.00432783	+	0.999991i	$0.501378\pi$
$360$	123.827	6.52628
$361$	−8.08751	−0.425658
$362$	20.8974	1.09835
$363$	69.3855	3.64180
$364$	−30.4772	−1.59744
$365$	31.4921	1.64837
$366$	11.0729	0.578791
$367$	28.8522	1.50607	0.753036	−	0.657979i	$-0.228588\pi$
$367$	28.8522	1.50607	0.753036	+	0.657979i	$0.228588\pi$
$368$	−72.3904	−3.77361
$369$	9.92789	0.516825
$370$	51.4442	2.67446
$371$	27.6271	1.43433
$372$	27.0590	1.40294
$373$	−13.1621	−0.681509	−0.340755	−	0.940152i	$-0.610683\pi$
$373$	−13.1621	−0.681509	−0.340755	+	0.940152i	$0.610683\pi$
$374$	22.8086	1.17940
$375$	35.1254	1.81387
$376$	−20.3770	−1.05086
$377$	16.2541	0.837131
$378$	72.9868	3.75404
$379$	−15.8581	−0.814576	−0.407288	−	0.913300i	$-0.633526\pi$
$379$	−15.8581	−0.814576	−0.407288	+	0.913300i	$0.633526\pi$
$380$	−38.9326	−1.99720
$381$	−51.1189	−2.61890
$382$	−56.8714	−2.90979
$383$	20.8527	1.06552	0.532760	−	0.846266i	$-0.321155\pi$
$383$	20.8527	1.06552	0.532760	+	0.846266i	$0.321155\pi$
$384$	−162.324	−8.28354
$385$	−37.6019	−1.91637
$386$	−26.3967	−1.34356
$387$	50.3930	2.56162
$388$	−1.24937	−0.0634273
$389$	13.6841	0.693811	0.346906	−	0.937900i	$-0.387232\pi$
$389$	13.6841	0.693811	0.346906	+	0.937900i	$0.387232\pi$
$390$	29.9993	1.51907
$391$	−6.10096	−0.308539
$392$	−25.3401	−1.27987
$393$	−46.0805	−2.32445
$394$	−34.5680	−1.74151
$395$	15.4543	0.777589
$396$	−194.582	−9.77813
$397$	−22.5537	−1.13194	−0.565968	−	0.824427i	$-0.691497\pi$
$397$	−22.5537	−1.13194	−0.565968	+	0.824427i	$0.691497\pi$
$398$	−12.2467	−0.613869
$399$	−30.3327	−1.51853
$400$	−11.0477	−0.552385
$401$	14.2841	0.713312	0.356656	−	0.934236i	$-0.383917\pi$
$401$	14.2841	0.713312	0.356656	+	0.934236i	$0.383917\pi$
$402$	36.0517	1.79809
$403$	2.80523	0.139739
$404$	−37.9948	−1.89031
$405$	−16.3861	−0.814233
$406$	79.3598	3.93856
$407$	−52.2656	−2.59071
$408$	−42.4406	−2.10112
$409$	0.295720	0.0146224	0.00731121	−	0.999973i	$-0.497673\pi$
$409$	0.295720	0.0146224	0.00731121	+	0.999973i	$0.497673\pi$
$410$	9.74498	0.481270
$411$	−6.82319	−0.336563
$412$	68.8932	3.39413
$413$	19.0712	0.938435
$414$	70.4451	3.46219
$415$	−5.98276	−0.293682
$416$	−45.3697	−2.22443
$417$	34.3806	1.68362
$418$	53.5351	2.61849
$419$	−8.23478	−0.402295	−0.201148	−	0.979561i	$-0.564467\pi$
$419$	−8.23478	−0.402295	−0.201148	+	0.979561i	$0.564467\pi$
$420$	108.218	5.28050
$421$	−15.5547	−0.758089	−0.379045	−	0.925378i	$-0.623747\pi$
$421$	−15.5547	−0.758089	−0.379045	+	0.925378i	$0.623747\pi$
$422$	33.0316	1.60795
$423$	11.8197	0.574694
$424$	90.7289	4.40618
$425$	−0.931084	−0.0451642
$426$	−8.24297	−0.399373
$427$	4.14104	0.200399
$428$	−16.4909	−0.797116
$429$	−30.4782	−1.47150
$430$	49.4645	2.38539
$431$	8.43123	0.406118	0.203059	−	0.979166i	$-0.434912\pi$
$431$	8.43123	0.406118	0.203059	+	0.979166i	$0.434912\pi$
$432$	142.874	6.87401
$433$	−35.3999	−1.70121	−0.850606	−	0.525803i	$-0.823765\pi$
$433$	−35.3999	−1.70121	−0.850606	+	0.525803i	$0.823765\pi$
$434$	13.6964	0.657447
$435$	−57.7151	−2.76723
$436$	−49.7040	−2.38039
$437$	−14.3199	−0.685012
$438$	124.629	5.95500
$439$	2.04220	0.0974687	0.0487343	−	0.998812i	$-0.484481\pi$
$439$	2.04220	0.0974687	0.0487343	+	0.998812i	$0.484481\pi$
$440$	−123.487	−5.88699
$441$	14.6986	0.699931
$442$	−6.80529	−0.323695
$443$	25.3750	1.20560	0.602800	−	0.797892i	$-0.294052\pi$
$443$	25.3750	1.20560	0.602800	+	0.797892i	$0.294052\pi$
$444$	150.420	7.13863
$445$	−18.8086	−0.891615
$446$	−26.0786	−1.23486
$447$	−39.8533	−1.88500
$448$	−118.555	−5.60122
$449$	−16.8903	−0.797102	−0.398551	−	0.917146i	$-0.630487\pi$
$449$	−16.8903	−0.797102	−0.398551	+	0.917146i	$0.630487\pi$
$450$	10.7508	0.506798
$451$	−9.90057	−0.466199
$452$	5.65827	0.266143
$453$	16.7462	0.786804
$454$	76.3019	3.58102
$455$	11.2191	0.525960
$456$	−99.6143	−4.66487
$457$	6.73725	0.315155	0.157578	−	0.987507i	$-0.449632\pi$
$457$	6.73725	0.315155	0.157578	+	0.987507i	$0.449632\pi$
$458$	−69.8645	−3.26455
$459$	12.0412	0.562034
$460$	51.0890	2.38204
$461$	10.8932	0.507346	0.253673	−	0.967290i	$-0.418361\pi$
$461$	10.8932	0.507346	0.253673	+	0.967290i	$0.418361\pi$
$462$	−148.808	−6.92317
$463$	−1.98721	−0.0923534	−0.0461767	−	0.998933i	$-0.514704\pi$
$463$	−1.98721	−0.0923534	−0.0461767	+	0.998933i	$0.514704\pi$
$464$	155.349	7.21189
$465$	−9.96080	−0.461921
$466$	−11.2463	−0.520976
$467$	5.62698	0.260385	0.130193	−	0.991489i	$-0.458440\pi$
$467$	5.62698	0.260385	0.130193	+	0.991489i	$0.458440\pi$
$468$	58.0567	2.68367
$469$	13.4826	0.622568
$470$	11.6019	0.535158
$471$	9.57845	0.441352
$472$	62.6310	2.88283
$473$	−50.2543	−2.31069
$474$	61.1597	2.80916
$475$	−2.18539	−0.100273
$476$	−24.5491	−1.12521
$477$	−52.6274	−2.40964
$478$	79.3609	3.62988
$479$	1.15457	0.0527536	0.0263768	−	0.999652i	$-0.491603\pi$
$479$	1.15457	0.0527536	0.0263768	+	0.999652i	$0.491603\pi$
$480$	161.098	7.35309
$481$	15.5942	0.711037
$482$	13.9256	0.634295
$483$	39.8039	1.81114
$484$	131.806	5.99118
$485$	0.459912	0.0208835
$486$	6.18135	0.280392
$487$	−34.2532	−1.55216	−0.776080	−	0.630634i	$-0.782795\pi$
$487$	−34.2532	−1.55216	−0.776080	+	0.630634i	$0.782795\pi$
$488$	13.5994	0.615616
$489$	29.9658	1.35510
$490$	14.4278	0.651780
$491$	−30.5895	−1.38049	−0.690243	−	0.723578i	$-0.742496\pi$
$491$	−30.5895	−1.38049	−0.690243	+	0.723578i	$0.742496\pi$
$492$	28.4938	1.28460
$493$	13.0926	0.589660
$494$	−15.9730	−0.718661
$495$	71.6286	3.21947
$496$	26.8110	1.20385
$497$	−3.08270	−0.138278
$498$	−23.6765	−1.06097
$499$	−35.7706	−1.60131	−0.800656	−	0.599124i	$-0.795515\pi$
$499$	−35.7706	−1.60131	−0.800656	+	0.599124i	$0.795515\pi$
$500$	66.7247	2.98402
$501$	4.87453	0.217778
$502$	−38.6289	−1.72409
$503$	32.0197	1.42769	0.713845	−	0.700304i	$-0.246952\pi$
$503$	32.0197	1.42769	0.713845	+	0.700304i	$0.246952\pi$
$504$	183.266	8.16330
$505$	13.9864	0.622389
$506$	−70.2512	−3.12305
$507$	−29.6287	−1.31586
$508$	−97.1064	−4.30840
$509$	−37.1828	−1.64810	−0.824049	−	0.566519i	$-0.808290\pi$
$509$	−37.1828	−1.64810	−0.824049	+	0.566519i	$0.808290\pi$
$510$	24.1642	1.07001
$511$	46.6086	2.06185
$512$	−95.4966	−4.22039
$513$	28.2625	1.24782
$514$	74.9734	3.30693
$515$	−25.3606	−1.11752
$516$	144.632	6.36706
$517$	−11.7872	−0.518400
$518$	76.1379	3.34531
$519$	−39.9801	−1.75493
$520$	36.8442	1.61572
$521$	25.8334	1.13178	0.565890	−	0.824481i	$-0.308533\pi$
$521$	25.8334	1.13178	0.565890	+	0.824481i	$0.308533\pi$
$522$	−151.174	−6.61672
$523$	8.81798	0.385583	0.192792	−	0.981240i	$-0.438246\pi$
$523$	8.81798	0.385583	0.192792	+	0.981240i	$0.438246\pi$
$524$	−87.5352	−3.82400
$525$	6.07459	0.265117
$526$	72.4912	3.16076
$527$	2.25959	0.0984294
$528$	−291.295	−12.6770
$529$	−4.20884	−0.182993
$530$	−51.6578	−2.24387
$531$	−36.3292	−1.57655
$532$	−57.6205	−2.49817
$533$	2.95399	0.127951
$534$	−74.4345	−3.22109
$535$	6.07052	0.262452
$536$	44.2776	1.91250
$537$	61.2083	2.64134
$538$	−53.5518	−2.30878
$539$	−14.6581	−0.631369
$540$	−100.832	−4.33912
$541$	−0.515542	−0.0221649	−0.0110824	−	0.999939i	$-0.503528\pi$
$541$	−0.515542	−0.0221649	−0.0110824	+	0.999939i	$0.503528\pi$
$542$	−65.7739	−2.82523
$543$	−22.4929	−0.965264
$544$	−36.5449	−1.56685
$545$	18.2968	0.783748
$546$	44.3992	1.90011
$547$	8.81805	0.377033	0.188516	−	0.982070i	$-0.439632\pi$
$547$	8.81805	0.377033	0.188516	+	0.982070i	$0.439632\pi$
$548$	−12.9614	−0.553686
$549$	−7.88836	−0.336667
$550$	−10.7212	−0.457155
$551$	30.7303	1.30915
$552$	130.718	5.56374
$553$	22.8725	0.972636
$554$	77.0096	3.27182
$555$	−55.3719	−2.35041
$556$	65.3099	2.76976
$557$	−30.6025	−1.29667	−0.648335	−	0.761356i	$-0.724534\pi$
$557$	−30.6025	−1.29667	−0.648335	+	0.761356i	$0.724534\pi$
$558$	−26.0905	−1.10450
$559$	14.9941	0.634185
$560$	107.226	4.53114
$561$	−24.5500	−1.03650
$562$	25.8422	1.09009
$563$	−2.77858	−0.117103	−0.0585515	−	0.998284i	$-0.518648\pi$
$563$	−2.77858	−0.117103	−0.0585515	+	0.998284i	$0.518648\pi$
$564$	33.9235	1.42844
$565$	−2.08289	−0.0876280
$566$	68.1497	2.86455
$567$	−24.2516	−1.01847
$568$	−10.1238	−0.424783
$569$	8.18712	0.343222	0.171611	−	0.985165i	$-0.445103\pi$
$569$	8.18712	0.343222	0.171611	+	0.985165i	$0.445103\pi$
$570$	56.7169	2.37561
$571$	42.8772	1.79436	0.897178	−	0.441669i	$-0.145613\pi$
$571$	42.8772	1.79436	0.897178	+	0.441669i	$0.145613\pi$
$572$	−57.8969	−2.42079
$573$	61.2134	2.55723
$574$	14.4227	0.601990
$575$	2.86777	0.119594
$576$	225.839	9.40995
$577$	−25.0721	−1.04376	−0.521882	−	0.853018i	$-0.674770\pi$
$577$	−25.0721	−1.04376	−0.521882	+	0.853018i	$0.674770\pi$
$578$	41.5635	1.72881
$579$	28.4121	1.18077
$580$	−109.636	−4.55241
$581$	−8.85453	−0.367348
$582$	1.82008	0.0754449
$583$	52.4826	2.17361
$584$	153.065	6.33389
$585$	−21.3715	−0.883603
$586$	33.8828	1.39969
$587$	−31.2107	−1.28820	−0.644101	−	0.764941i	$-0.722768\pi$
$587$	−31.2107	−1.28820	−0.644101	+	0.764941i	$0.722768\pi$
$588$	42.1860	1.73972
$589$	5.30360	0.218531
$590$	−35.6599	−1.46810
$591$	37.2072	1.53050
$592$	149.042	6.12558
$593$	−41.1475	−1.68972	−0.844862	−	0.534985i	$-0.820317\pi$
$593$	−41.1475	−1.68972	−0.844862	+	0.534985i	$0.820317\pi$
$594$	138.652	5.68894
$595$	9.03690	0.370477
$596$	−75.7059	−3.10104
$597$	13.1817	0.539490
$598$	20.9605	0.857140
$599$	−16.2113	−0.662376	−0.331188	−	0.943565i	$-0.607449\pi$
$599$	−16.2113	−0.662376	−0.331188	+	0.943565i	$0.607449\pi$
$600$	19.9493	0.814427
$601$	−23.5406	−0.960242	−0.480121	−	0.877202i	$-0.659407\pi$
$601$	−23.5406	−0.960242	−0.480121	+	0.877202i	$0.659407\pi$
$602$	73.2079	2.98373
$603$	−25.6833	−1.04590
$604$	31.8113	1.29438
$605$	−48.5197	−1.97260
$606$	55.3508	2.24847
$607$	25.7909	1.04682	0.523410	−	0.852081i	$-0.324660\pi$
$607$	25.7909	1.04682	0.523410	+	0.852081i	$0.324660\pi$
$608$	−85.7764	−3.47869
$609$	−85.4188	−3.46134
$610$	−7.74303	−0.313506
$611$	3.51689	0.142278
$612$	46.7642	1.89033
$613$	7.31445	0.295428	0.147714	−	0.989030i	$-0.452808\pi$
$613$	7.31445	0.295428	0.147714	+	0.989030i	$0.452808\pi$
$614$	92.9274	3.75025
$615$	−10.4890	−0.422957
$616$	−182.761	−7.36366
$617$	−16.4649	−0.662852	−0.331426	−	0.943481i	$-0.607530\pi$
$617$	−16.4649	−0.662852	−0.331426	+	0.943481i	$0.607530\pi$
$618$	−100.364	−4.03722
$619$	−1.37508	−0.0552693	−0.0276346	−	0.999618i	$-0.508797\pi$
$619$	−1.37508	−0.0552693	−0.0276346	+	0.999618i	$0.508797\pi$
$620$	−18.9217	−0.759913
$621$	−37.0873	−1.48826
$622$	31.0203	1.24380
$623$	−27.8369	−1.11526
$624$	86.9125	3.47928
$625$	−21.2546	−0.850182
$626$	76.6121	3.06204
$627$	−57.6224	−2.30122
$628$	18.1954	0.726074
$629$	12.5610	0.500841
$630$	−104.345	−4.15720
$631$	36.9572	1.47124	0.735622	−	0.677392i	$-0.236890\pi$
$631$	36.9572	1.47124	0.735622	+	0.677392i	$0.236890\pi$
$632$	75.1144	2.98789
$633$	−35.5535	−1.41313
$634$	−47.5551	−1.88865
$635$	35.7463	1.41855
$636$	−151.045	−5.98932
$637$	4.37348	0.173283
$638$	150.758	5.96857
$639$	5.87230	0.232305
$640$	113.509	4.48684
$641$	−37.3190	−1.47401	−0.737006	−	0.675887i	$-0.763761\pi$
$641$	−37.3190	−1.47401	−0.737006	+	0.675887i	$0.763761\pi$
$642$	24.0239	0.948146
$643$	25.5881	1.00910	0.504548	−	0.863384i	$-0.331659\pi$
$643$	25.5881	1.00910	0.504548	+	0.863384i	$0.331659\pi$
$644$	75.6122	2.97954
$645$	−53.2411	−2.09636
$646$	−12.8662	−0.506212
$647$	−13.4034	−0.526941	−0.263471	−	0.964667i	$-0.584867\pi$
$647$	−13.4034	−0.526941	−0.263471	+	0.964667i	$0.584867\pi$
$648$	−79.6436	−3.12870
$649$	36.2292	1.42212
$650$	3.19885	0.125469
$651$	−14.7421	−0.577787
$652$	56.9236	2.22930
$653$	30.1571	1.18014	0.590068	−	0.807353i	$-0.299101\pi$
$653$	30.1571	1.18014	0.590068	+	0.807353i	$0.299101\pi$
$654$	72.4088	2.83141
$655$	32.2230	1.25906
$656$	28.2327	1.10230
$657$	−88.7858	−3.46386
$658$	17.1710	0.669394
$659$	−18.2537	−0.711063	−0.355531	−	0.934664i	$-0.615700\pi$
$659$	−18.2537	−0.711063	−0.355531	+	0.934664i	$0.615700\pi$
$660$	205.580	8.00218
$661$	0.459770	0.0178830	0.00894150	−	0.999960i	$-0.497154\pi$
$661$	0.459770	0.0178830	0.00894150	+	0.999960i	$0.497154\pi$
$662$	34.8921	1.35612
$663$	7.32486	0.284474
$664$	−29.0788	−1.12848
$665$	21.2109	0.822525
$666$	−145.037	−5.62006
$667$	−40.3256	−1.56141
$668$	9.25974	0.358270
$669$	28.0697	1.08524
$670$	−25.2101	−0.973950
$671$	7.86665	0.303689
$672$	238.427	9.19751
$673$	−46.5499	−1.79437	−0.897184	−	0.441657i	$-0.854391\pi$
$673$	−46.5499	−1.79437	−0.897184	+	0.441657i	$0.854391\pi$
$674$	49.2636	1.89756
$675$	−5.65999	−0.217853
$676$	−56.2831	−2.16474
$677$	−2.88322	−0.110811	−0.0554056	−	0.998464i	$-0.517645\pi$
$677$	−2.88322	−0.110811	−0.0554056	+	0.998464i	$0.517645\pi$
$678$	−8.24297	−0.316569
$679$	0.680674	0.0261219
$680$	29.6777	1.13809
$681$	−82.1273	−3.14713
$682$	26.0187	0.996308
$683$	18.5354	0.709239	0.354619	−	0.935011i	$-0.384610\pi$
$683$	18.5354	0.709239	0.354619	+	0.935011i	$0.384610\pi$
$684$	109.763	4.19688
$685$	4.77130	0.182302
$686$	−38.3633	−1.46472
$687$	75.1985	2.86900
$688$	143.306	5.46351
$689$	−15.6590	−0.596560
$690$	−74.4264	−2.83337
$691$	1.60973	0.0612370	0.0306185	−	0.999531i	$-0.490252\pi$
$691$	1.60973	0.0612370	0.0306185	+	0.999531i	$0.490252\pi$
$692$	−75.9469	−2.88707
$693$	106.011	4.02702
$694$	−31.1246	−1.18147
$695$	−24.0415	−0.911947
$696$	−280.520	−10.6331
$697$	2.37941	0.0901267
$698$	50.1627	1.89869
$699$	12.1050	0.457852
$700$	11.5394	0.436148
$701$	−33.0971	−1.25006	−0.625030	−	0.780601i	$-0.714913\pi$
$701$	−33.0971	−1.25006	−0.625030	+	0.780601i	$0.714913\pi$
$702$	−41.3689	−1.56137
$703$	29.4826	1.11196
$704$	−225.217	−8.48819
$705$	−12.4877	−0.470315
$706$	88.2046	3.31962
$707$	20.7001	0.778506
$708$	−104.268	−3.91862
$709$	31.1825	1.17108	0.585542	−	0.810642i	$-0.300882\pi$
$709$	31.1825	1.17108	0.585542	+	0.810642i	$0.300882\pi$
$710$	5.76411	0.216323
$711$	−43.5702	−1.63401
$712$	−91.4181	−3.42604
$713$	−6.95963	−0.260640
$714$	35.7632	1.33840
$715$	21.3127	0.797050
$716$	116.272	4.34530
$717$	−85.4200	−3.19007
$718$	0.453850	0.0169375
$719$	−3.55171	−0.132457	−0.0662283	−	0.997804i	$-0.521097\pi$
$719$	−3.55171	−0.132457	−0.0662283	+	0.997804i	$0.521097\pi$
$720$	−204.258	−7.61225
$721$	−37.5339	−1.39784
$722$	22.3810	0.832936
$723$	−14.9888	−0.557440
$724$	−42.7279	−1.58797
$725$	−6.15420	−0.228561
$726$	−192.015	−7.12633
$727$	31.8443	1.18104	0.590521	−	0.807023i	$-0.298922\pi$
$727$	31.8443	1.18104	0.590521	+	0.807023i	$0.298922\pi$
$728$	54.5297	2.02100
$729$	−30.2543	−1.12053
$730$	−87.1501	−3.22557
$731$	12.0777	0.446709
$732$	−22.6402	−0.836806
$733$	−8.51031	−0.314335	−0.157168	−	0.987572i	$-0.550236\pi$
$733$	−8.51031	−0.314335	−0.157168	+	0.987572i	$0.550236\pi$
$734$	−79.8444	−2.94711
$735$	−15.5293	−0.572806
$736$	112.560	4.14900
$737$	25.6126	0.943451
$738$	−27.4740	−1.01133
$739$	27.1849	1.00001	0.500007	−	0.866021i	$-0.333331\pi$
$739$	27.1849	1.00001	0.500007	+	0.866021i	$0.333331\pi$
$740$	−105.185	−3.86669
$741$	17.1925	0.631584
$742$	−76.4540	−2.80672
$743$	1.21250	0.0444824	0.0222412	−	0.999753i	$-0.492920\pi$
$743$	1.21250	0.0444824	0.0222412	+	0.999753i	$0.492920\pi$
$744$	−48.4138	−1.77493
$745$	27.8684	1.02102
$746$	36.4243	1.33359
$747$	16.8672	0.617138
$748$	−46.6355	−1.70516
$749$	8.98443	0.328284
$750$	−97.2045	−3.54941
$751$	51.0029	1.86112	0.930562	−	0.366135i	$-0.119319\pi$
$751$	51.0029	1.86112	0.930562	+	0.366135i	$0.119319\pi$
$752$	33.6126	1.22573
$753$	41.5782	1.51519
$754$	−44.9811	−1.63811
$755$	−11.7102	−0.426178
$756$	−149.232	−5.42753
$757$	−1.96910	−0.0715680	−0.0357840	−	0.999360i	$-0.511393\pi$
$757$	−1.96910	−0.0715680	−0.0357840	+	0.999360i	$0.511393\pi$
$758$	43.8851	1.59398
$759$	75.6147	2.74464
$760$	69.6579	2.52676
$761$	21.7561	0.788659	0.394330	−	0.918969i	$-0.370977\pi$
$761$	21.7561	0.788659	0.394330	+	0.918969i	$0.370977\pi$
$762$	141.464	5.12472
$763$	27.0794	0.980340
$764$	116.282	4.20693
$765$	−17.2146	−0.622394
$766$	−57.7068	−2.08503
$767$	−10.8096	−0.390311
$768$	220.101	7.94220
$769$	−38.0359	−1.37161	−0.685805	−	0.727785i	$-0.740550\pi$
$769$	−38.0359	−1.37161	−0.685805	+	0.727785i	$0.740550\pi$
$770$	104.058	3.74998
$771$	−80.6974	−2.90625
$772$	53.9720	1.94250
$773$	21.6976	0.780409	0.390205	−	0.920728i	$-0.372404\pi$
$773$	21.6976	0.780409	0.390205	+	0.920728i	$0.372404\pi$
$774$	−139.455	−5.01262
$775$	−1.06213	−0.0381528
$776$	2.23537	0.0802451
$777$	−81.9509	−2.93997
$778$	−37.8688	−1.35766
$779$	5.58484	0.200098
$780$	−61.3379	−2.19625
$781$	−5.85614	−0.209549
$782$	16.8835	0.603754
$783$	79.5888	2.84427
$784$	41.7994	1.49284
$785$	−6.69798	−0.239061
$786$	127.521	4.54853
$787$	22.4219	0.799255	0.399627	−	0.916678i	$-0.369140\pi$
$787$	22.4219	0.799255	0.399627	+	0.916678i	$0.369140\pi$
$788$	70.6794	2.51785
$789$	−78.0257	−2.77779
$790$	−42.7675	−1.52160
$791$	−3.08270	−0.109608
$792$	348.146	12.3708
$793$	−2.34714	−0.0833493
$794$	62.4141	2.21499
$795$	55.6018	1.97199
$796$	25.0401	0.887523
$797$	−49.6188	−1.75759	−0.878794	−	0.477202i	$-0.841651\pi$
$797$	−49.6188	−1.75759	−0.878794	+	0.477202i	$0.841651\pi$
$798$	83.9415	2.97150
$799$	2.83283	0.100218
$800$	17.1780	0.607335
$801$	53.0272	1.87362
$802$	−39.5291	−1.39582
$803$	88.5415	3.12456
$804$	−73.7130	−2.59966
$805$	−27.8340	−0.981018
$806$	−7.76309	−0.273443
$807$	57.6404	2.02904
$808$	67.9801	2.39153
$809$	−16.3383	−0.574424	−0.287212	−	0.957867i	$-0.592728\pi$
$809$	−16.3383	−0.574424	−0.287212	+	0.957867i	$0.592728\pi$
$810$	45.3463	1.59331
$811$	49.5330	1.73934	0.869670	−	0.493633i	$-0.164332\pi$
$811$	49.5330	1.73934	0.869670	+	0.493633i	$0.164332\pi$
$812$	−162.263	−5.69431
$813$	70.7956	2.48291
$814$	144.638	5.06954
$815$	−20.9544	−0.734000
$816$	70.0073	2.45075
$817$	28.3481	0.991774
$818$	−0.818363	−0.0286134
$819$	−31.6300	−1.10524
$820$	−19.9251	−0.695813
$821$	−40.9057	−1.42762	−0.713809	−	0.700341i	$-0.753031\pi$
$821$	−40.9057	−1.42762	−0.713809	+	0.700341i	$0.753031\pi$
$822$	18.8822	0.658593
$823$	−24.8679	−0.866840	−0.433420	−	0.901192i	$-0.642693\pi$
$823$	−24.8679	−0.866840	−0.433420	+	0.901192i	$0.642693\pi$
$824$	−123.263	−4.29409
$825$	11.5398	0.401763
$826$	−52.7770	−1.83635
$827$	42.1498	1.46569	0.732846	−	0.680394i	$-0.238191\pi$
$827$	42.1498	1.46569	0.732846	+	0.680394i	$0.238191\pi$
$828$	−144.035	−5.00557
$829$	−22.6099	−0.785276	−0.392638	−	0.919693i	$-0.628437\pi$
$829$	−22.6099	−0.785276	−0.392638	+	0.919693i	$0.628437\pi$
$830$	16.5564	0.574682
$831$	−82.8891	−2.87539
$832$	67.1971	2.32964
$833$	3.52280	0.122058
$834$	−95.1434	−3.29455
$835$	−3.40865	−0.117961
$836$	−109.460	−3.78577
$837$	13.7359	0.474782
$838$	22.7886	0.787219
$839$	20.8151	0.718618	0.359309	−	0.933219i	$-0.383012\pi$
$839$	20.8151	0.718618	0.359309	+	0.933219i	$0.383012\pi$
$840$	−193.623	−6.68064
$841$	57.5383	1.98408
$842$	43.0454	1.48344
$843$	−27.8151	−0.958004
$844$	−67.5380	−2.32476
$845$	20.7186	0.712743
$846$	−32.7094	−1.12457
$847$	−71.8095	−2.46740
$848$	−149.661	−5.13937
$849$	−73.3528	−2.51746
$850$	2.57664	0.0883782
$851$	−38.6884	−1.32622
$852$	16.8540	0.577407
$853$	−36.1142	−1.23653	−0.618264	−	0.785971i	$-0.712164\pi$
$853$	−36.1142	−1.23653	−0.618264	+	0.785971i	$0.712164\pi$
$854$	−11.4597	−0.392144
$855$	−40.4052	−1.38183
$856$	29.5054	1.00847
$857$	35.8008	1.22293	0.611467	−	0.791270i	$-0.290580\pi$
$857$	35.8008	1.22293	0.611467	+	0.791270i	$0.290580\pi$
$858$	84.3442	2.87946
$859$	18.6231	0.635411	0.317705	−	0.948190i	$-0.397088\pi$
$859$	18.6231	0.635411	0.317705	+	0.948190i	$0.397088\pi$
$860$	−101.138	−3.44876
$861$	−15.5238	−0.529050
$862$	−23.3322	−0.794699
$863$	44.1627	1.50332	0.751658	−	0.659553i	$-0.229254\pi$
$863$	44.1627	1.50332	0.751658	+	0.659553i	$0.229254\pi$
$864$	−222.154	−7.55782
$865$	27.9572	0.950572
$866$	97.9643	3.32896
$867$	−44.7368	−1.51934
$868$	−28.0043	−0.950527
$869$	43.4503	1.47395
$870$	159.718	5.41496
$871$	−7.64191	−0.258936
$872$	88.9302	3.01156
$873$	−1.29663	−0.0438843
$874$	39.6282	1.34044
$875$	−36.3525	−1.22894
$876$	−254.822	−8.60965
$877$	−50.5740	−1.70776	−0.853881	−	0.520468i	$-0.825758\pi$
$877$	−50.5740	−1.70776	−0.853881	+	0.520468i	$0.825758\pi$
$878$	−5.65149	−0.190728
$879$	−36.4697	−1.23009
$880$	203.696	6.86659
$881$	−4.61852	−0.155602	−0.0778010	−	0.996969i	$-0.524790\pi$
$881$	−4.61852	−0.155602	−0.0778010	+	0.996969i	$0.524790\pi$
$882$	−40.6762	−1.36964
$883$	−47.0217	−1.58240	−0.791202	−	0.611555i	$-0.790545\pi$
$883$	−47.0217	−1.58240	−0.791202	+	0.611555i	$0.790545\pi$
$884$	13.9144	0.467993
$885$	38.3825	1.29021
$886$	−70.2216	−2.35914
$887$	−17.2561	−0.579403	−0.289701	−	0.957117i	$-0.593556\pi$
$887$	−17.2561	−0.579403	−0.289701	+	0.957117i	$0.593556\pi$
$888$	−269.131	−9.03145
$889$	52.9048	1.77437
$890$	52.0503	1.74473
$891$	−46.0703	−1.54341
$892$	53.3216	1.78534
$893$	6.64906	0.222502
$894$	110.288	3.68859
$895$	−42.8015	−1.43070
$896$	167.994	5.61230
$897$	−22.5608	−0.753284
$898$	46.7415	1.55978
$899$	14.9353	0.498119
$900$	−21.9816	−0.732721
$901$	−12.6132	−0.420206
$902$	27.3984	0.912268
$903$	−78.7972	−2.62221
$904$	−10.1238	−0.336711
$905$	15.7288	0.522842
$906$	−46.3427	−1.53963
$907$	−30.6788	−1.01867	−0.509336	−	0.860568i	$-0.670109\pi$
$907$	−30.6788	−1.01867	−0.509336	+	0.860568i	$0.670109\pi$
$908$	−156.010	−5.17739
$909$	−39.4320	−1.30788
$910$	−31.0473	−1.02921
$911$	51.7057	1.71309	0.856543	−	0.516075i	$-0.172607\pi$
$911$	51.7057	1.71309	0.856543	+	0.516075i	$0.172607\pi$
$912$	164.318	5.44110
$913$	−16.8208	−0.556686
$914$	−18.6444	−0.616701
$915$	8.33419	0.275520
$916$	142.848	4.71984
$917$	47.6903	1.57487
$918$	−33.3223	−1.09980
$919$	−3.20209	−0.105627	−0.0528136	−	0.998604i	$-0.516819\pi$
$919$	−3.20209	−0.105627	−0.0528136	+	0.998604i	$0.516819\pi$
$920$	−91.4083	−3.01364
$921$	−100.022	−3.29584
$922$	−30.1453	−0.992784
$923$	1.74727	0.0575121
$924$	304.260	10.0094
$925$	−5.90435	−0.194134
$926$	5.49932	0.180719
$927$	71.4991	2.34834
$928$	−241.552	−7.92932
$929$	−10.3211	−0.338626	−0.169313	−	0.985562i	$-0.554155\pi$
$929$	−10.3211	−0.338626	−0.169313	+	0.985562i	$0.554155\pi$
$930$	27.5651	0.903895
$931$	8.26853	0.270990
$932$	22.9948	0.753219
$933$	−33.3886	−1.09309
$934$	−15.5719	−0.509527
$935$	17.1672	0.561428
$936$	−103.875	−3.39525
$937$	46.5105	1.51943	0.759715	−	0.650256i	$-0.225338\pi$
$937$	46.5105	1.51943	0.759715	+	0.650256i	$0.225338\pi$
$938$	−37.3111	−1.21825
$939$	−82.4613	−2.69102
$940$	−23.7219	−0.773723
$941$	−9.02196	−0.294108	−0.147054	−	0.989128i	$-0.546979\pi$
$941$	−9.02196	−0.294108	−0.147054	+	0.989128i	$0.546979\pi$
$942$	−26.5070	−0.863645
$943$	−7.32868	−0.238655
$944$	−103.312	−3.36253
$945$	54.9346	1.78702
$946$	139.072	4.52161
$947$	−24.9398	−0.810434	−0.405217	−	0.914220i	$-0.632804\pi$
$947$	−24.9398	−0.810434	−0.405217	+	0.914220i	$0.632804\pi$
$948$	−125.050	−4.06144
$949$	−26.4177	−0.857556
$950$	6.04777	0.196216
$951$	51.1858	1.65981
$952$	43.9232	1.42356
$953$	23.8200	0.771604	0.385802	−	0.922582i	$-0.373925\pi$
$953$	23.8200	0.771604	0.385802	+	0.922582i	$0.373925\pi$
$954$	145.639	4.71523
$955$	−42.8051	−1.38514
$956$	−162.265	−5.24803
$957$	−162.268	−5.24539
$958$	−3.19511	−0.103229
$959$	7.06156	0.228030
$960$	−238.603	−7.70087
$961$	−28.4224	−0.916851
$962$	−43.1549	−1.39137
$963$	−17.1146	−0.551511
$964$	−28.4730	−0.917053
$965$	−19.8679	−0.639570
$966$	−110.152	−3.54408
$967$	4.77680	0.153612	0.0768058	−	0.997046i	$-0.475528\pi$
$967$	4.77680	0.153612	0.0768058	+	0.997046i	$0.475528\pi$
$968$	−235.826	−7.57975
$969$	13.8485	0.444877
$970$	−1.27274	−0.0408653
$971$	−36.1947	−1.16154	−0.580772	−	0.814067i	$-0.697249\pi$
$971$	−36.1947	−1.16154	−0.580772	+	0.814067i	$0.697249\pi$
$972$	−12.6387	−0.405386
$973$	−35.5817	−1.14070
$974$	94.7909	3.03730
$975$	−3.44307	−0.110267
$976$	−22.4327	−0.718055
$977$	34.1228	1.09169	0.545843	−	0.837887i	$-0.316209\pi$
$977$	34.1228	1.09169	0.545843	+	0.837887i	$0.316209\pi$
$978$	−82.9262	−2.65169
$979$	−52.8813	−1.69009
$980$	−29.4997	−0.942333
$981$	−51.5841	−1.64695
$982$	84.6522	2.70136
$983$	−53.8072	−1.71618	−0.858092	−	0.513496i	$-0.828350\pi$
$983$	−53.8072	−1.71618	−0.858092	+	0.513496i	$0.828350\pi$
$984$	−50.9810	−1.62522
$985$	−26.0181	−0.829006
$986$	−36.2319	−1.15386
$987$	−18.4819	−0.588287
$988$	32.6592	1.03903
$989$	−37.1996	−1.18288
$990$	−198.222	−6.29991
$991$	21.9278	0.696560	0.348280	−	0.937391i	$-0.386766\pi$
$991$	21.9278	0.696560	0.348280	+	0.937391i	$0.386766\pi$
$992$	−41.6884	−1.32361
$993$	−37.5560	−1.19180
$994$	8.53093	0.270585
$995$	−9.21762	−0.292218
$996$	48.4102	1.53393
$997$	18.2694	0.578599	0.289299	−	0.957239i	$-0.406578\pi$
$997$	18.2694	0.578599	0.289299	+	0.957239i	$0.406578\pi$
$998$	98.9901	3.13348
$999$	76.3576	2.41585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.4	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.4	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76736 q^{2} +2.97864 q^{3} +5.65827 q^{4} -2.08289 q^{5} -8.24297 q^{6} -3.08270 q^{7} -10.1238 q^{8} +5.87230 q^{9} +O(q^{10})\)	\(q-2.76736 q^{2} +2.97864 q^{3} +5.65827 q^{4} -2.08289 q^{5} -8.24297 q^{6} -3.08270 q^{7} -10.1238 q^{8} +5.87230 q^{9} +5.76411 q^{10} -5.85614 q^{11} +16.8540 q^{12} +1.74727 q^{13} +8.53093 q^{14} -6.20419 q^{15} +16.6995 q^{16} +1.40741 q^{17} -16.2508 q^{18} +3.30341 q^{19} -11.7856 q^{20} -9.18225 q^{21} +16.2060 q^{22} -4.33488 q^{23} -30.1550 q^{24} -0.661558 q^{25} -4.83532 q^{26} +8.55555 q^{27} -17.4428 q^{28} +9.30259 q^{29} +17.1692 q^{30} +1.60550 q^{31} -25.9660 q^{32} -17.4433 q^{33} -3.89481 q^{34} +6.42093 q^{35} +33.2271 q^{36} +8.92492 q^{37} -9.14171 q^{38} +5.20449 q^{39} +21.0867 q^{40} +1.69063 q^{41} +25.4106 q^{42} +8.58147 q^{43} -33.1356 q^{44} -12.2314 q^{45} +11.9962 q^{46} +2.01279 q^{47} +49.7419 q^{48} +2.50303 q^{49} +1.83077 q^{50} +4.19217 q^{51} +9.88653 q^{52} -8.96198 q^{53} -23.6763 q^{54} +12.1977 q^{55} +31.2085 q^{56} +9.83966 q^{57} -25.7436 q^{58} -6.18654 q^{59} -35.1050 q^{60} -1.34332 q^{61} -4.44298 q^{62} -18.1025 q^{63} +38.4583 q^{64} -3.63938 q^{65} +48.2720 q^{66} -4.37363 q^{67} +7.96352 q^{68} -12.9120 q^{69} -17.7690 q^{70} +1.00000 q^{71} -59.4497 q^{72} -15.1194 q^{73} -24.6985 q^{74} -1.97054 q^{75} +18.6916 q^{76} +18.0527 q^{77} -14.4027 q^{78} -7.41962 q^{79} -34.7833 q^{80} +7.86701 q^{81} -4.67858 q^{82} +2.87233 q^{83} -51.9557 q^{84} -2.93149 q^{85} -23.7480 q^{86} +27.7091 q^{87} +59.2861 q^{88} +9.03006 q^{89} +33.8486 q^{90} -5.38631 q^{91} -24.5279 q^{92} +4.78219 q^{93} -5.57011 q^{94} -6.88064 q^{95} -77.3435 q^{96} -0.220805 q^{97} -6.92679 q^{98} -34.3890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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