LMFDB - Embedded newform 8023.2.a.e.1.11

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:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.46646 q^{2} +2.78762 q^{3} +4.08340 q^{4} +2.84947 q^{5} -6.87554 q^{6} -3.94161 q^{7} -5.13862 q^{8} +4.77082 q^{9} +O(q^{10})$	\(q-2.46646 q^{2} +2.78762 q^{3} +4.08340 q^{4} +2.84947 q^{5} -6.87554 q^{6} -3.94161 q^{7} -5.13862 q^{8} +4.77082 q^{9} -7.02810 q^{10} +0.810317 q^{11} +11.3830 q^{12} +4.58475 q^{13} +9.72180 q^{14} +7.94325 q^{15} +4.50737 q^{16} +2.96680 q^{17} -11.7670 q^{18} +6.48949 q^{19} +11.6356 q^{20} -10.9877 q^{21} -1.99861 q^{22} -0.905142 q^{23} -14.3245 q^{24} +3.11950 q^{25} -11.3081 q^{26} +4.93639 q^{27} -16.0952 q^{28} +4.73633 q^{29} -19.5917 q^{30} -4.75767 q^{31} -0.839994 q^{32} +2.25886 q^{33} -7.31749 q^{34} -11.2315 q^{35} +19.4812 q^{36} +1.35732 q^{37} -16.0060 q^{38} +12.7805 q^{39} -14.6424 q^{40} -6.11549 q^{41} +27.1007 q^{42} -2.52163 q^{43} +3.30885 q^{44} +13.5943 q^{45} +2.23249 q^{46} -12.1177 q^{47} +12.5648 q^{48} +8.53627 q^{49} -7.69412 q^{50} +8.27032 q^{51} +18.7214 q^{52} +10.0878 q^{53} -12.1754 q^{54} +2.30898 q^{55} +20.2544 q^{56} +18.0902 q^{57} -11.6819 q^{58} +4.90435 q^{59} +32.4355 q^{60} -4.41224 q^{61} +11.7346 q^{62} -18.8047 q^{63} -6.94294 q^{64} +13.0641 q^{65} -5.57137 q^{66} +2.52742 q^{67} +12.1147 q^{68} -2.52319 q^{69} +27.7020 q^{70} -1.00000 q^{71} -24.5155 q^{72} +9.68642 q^{73} -3.34777 q^{74} +8.69599 q^{75} +26.4992 q^{76} -3.19395 q^{77} -31.5226 q^{78} +13.5042 q^{79} +12.8436 q^{80} -0.551705 q^{81} +15.0836 q^{82} +9.11709 q^{83} -44.8672 q^{84} +8.45383 q^{85} +6.21949 q^{86} +13.2031 q^{87} -4.16391 q^{88} +0.117973 q^{89} -33.5298 q^{90} -18.0713 q^{91} -3.69606 q^{92} -13.2626 q^{93} +29.8878 q^{94} +18.4916 q^{95} -2.34159 q^{96} +14.9514 q^{97} -21.0543 q^{98} +3.86588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.46646	−1.74405	−0.872024	−	0.489464i	$-0.837193\pi$
$2$	−2.46646	−1.74405	−0.872024	+	0.489464i	$0.837193\pi$
$3$	2.78762	1.60943	0.804717	−	0.593659i	$-0.202317\pi$
$3$	2.78762	1.60943	0.804717	+	0.593659i	$0.202317\pi$
$4$	4.08340	2.04170
$5$	2.84947	1.27432	0.637162	−	0.770730i	$-0.280108\pi$
$5$	2.84947	1.27432	0.637162	+	0.770730i	$0.280108\pi$
$6$	−6.87554	−2.80693
$7$	−3.94161	−1.48979	−0.744894	−	0.667183i	$-0.767500\pi$
$7$	−3.94161	−1.48979	−0.744894	+	0.667183i	$0.767500\pi$
$8$	−5.13862	−1.81678
$9$	4.77082	1.59027
$10$	−7.02810	−2.22248
$11$	0.810317	0.244320	0.122160	−	0.992510i	$-0.461018\pi$
$11$	0.810317	0.244320	0.122160	+	0.992510i	$0.461018\pi$
$12$	11.3830	3.28598
$13$	4.58475	1.27158	0.635790	−	0.771862i	$-0.280674\pi$
$13$	4.58475	1.27158	0.635790	+	0.771862i	$0.280674\pi$
$14$	9.72180	2.59826
$15$	7.94325	2.05094
$16$	4.50737	1.12684
$17$	2.96680	0.719556	0.359778	−	0.933038i	$-0.382853\pi$
$17$	2.96680	0.719556	0.359778	+	0.933038i	$0.382853\pi$
$18$	−11.7670	−2.77351
$19$	6.48949	1.48879	0.744396	−	0.667738i	$-0.232738\pi$
$19$	6.48949	1.48879	0.744396	+	0.667738i	$0.232738\pi$
$20$	11.6356	2.60179
$21$	−10.9877	−2.39771
$22$	−1.99861	−0.426105
$23$	−0.905142	−0.188735	−0.0943676	−	0.995537i	$-0.530083\pi$
$23$	−0.905142	−0.188735	−0.0943676	+	0.995537i	$0.530083\pi$
$24$	−14.3245	−2.92398
$25$	3.11950	0.623901
$26$	−11.3081	−2.21770
$27$	4.93639	0.950008
$28$	−16.0952	−3.04170
$29$	4.73633	0.879514	0.439757	−	0.898117i	$-0.355064\pi$
$29$	4.73633	0.879514	0.439757	+	0.898117i	$0.355064\pi$
$30$	−19.5917	−3.57693
$31$	−4.75767	−0.854503	−0.427251	−	0.904133i	$-0.640518\pi$
$31$	−4.75767	−0.854503	−0.427251	+	0.904133i	$0.640518\pi$
$32$	−0.839994	−0.148491
$33$	2.25886	0.393216
$34$	−7.31749	−1.25494
$35$	−11.2315	−1.89847
$36$	19.4812	3.24687
$37$	1.35732	0.223142	0.111571	−	0.993756i	$-0.464412\pi$
$37$	1.35732	0.223142	0.111571	+	0.993756i	$0.464412\pi$
$38$	−16.0060	−2.59652
$39$	12.7805	2.04652
$40$	−14.6424	−2.31516
$41$	−6.11549	−0.955079	−0.477540	−	0.878610i	$-0.658471\pi$
$41$	−6.11549	−0.955079	−0.477540	+	0.878610i	$0.658471\pi$
$42$	27.1007	4.18173
$43$	−2.52163	−0.384545	−0.192273	−	0.981342i	$-0.561586\pi$
$43$	−2.52163	−0.384545	−0.192273	+	0.981342i	$0.561586\pi$
$44$	3.30885	0.498828
$45$	13.5943	2.02653
$46$	2.23249	0.329163
$47$	−12.1177	−1.76755	−0.883774	−	0.467914i	$-0.845006\pi$
$47$	−12.1177	−1.76755	−0.883774	+	0.467914i	$0.845006\pi$
$48$	12.5648	1.81358
$49$	8.53627	1.21947
$50$	−7.69412	−1.08811
$51$	8.27032	1.15808
$52$	18.7214	2.59619
$53$	10.0878	1.38567	0.692836	−	0.721095i	$-0.256361\pi$
$53$	10.0878	1.38567	0.692836	+	0.721095i	$0.256361\pi$
$54$	−12.1754	−1.65686
$55$	2.30898	0.311342
$56$	20.2544	2.70661
$57$	18.0902	2.39611
$58$	−11.6819	−1.53391
$59$	4.90435	0.638493	0.319246	−	0.947672i	$-0.396570\pi$
$59$	4.90435	0.638493	0.319246	+	0.947672i	$0.396570\pi$
$60$	32.4355	4.18740
$61$	−4.41224	−0.564929	−0.282465	−	0.959278i	$-0.591152\pi$
$61$	−4.41224	−0.564929	−0.282465	+	0.959278i	$0.591152\pi$
$62$	11.7346	1.49029
$63$	−18.8047	−2.36917
$64$	−6.94294	−0.867867
$65$	13.0641	1.62041
$66$	−5.57137	−0.685788
$67$	2.52742	0.308773	0.154387	−	0.988011i	$-0.450660\pi$
$67$	2.52742	0.308773	0.154387	+	0.988011i	$0.450660\pi$
$68$	12.1147	1.46912
$69$	−2.52319	−0.303757
$70$	27.7020	3.31102
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−24.5155	−2.88917
$73$	9.68642	1.13371	0.566855	−	0.823818i	$-0.308160\pi$
$73$	9.68642	1.13371	0.566855	+	0.823818i	$0.308160\pi$
$74$	−3.34777	−0.389170
$75$	8.69599	1.00413
$76$	26.4992	3.03967
$77$	−3.19395	−0.363984
$78$	−31.5226	−3.56924
$79$	13.5042	1.51934	0.759672	−	0.650306i	$-0.225359\pi$
$79$	13.5042	1.51934	0.759672	+	0.650306i	$0.225359\pi$
$80$	12.8436	1.43596
$81$	−0.551705	−0.0613006
$82$	15.0836	1.66570
$83$	9.11709	1.00073	0.500365	−	0.865814i	$-0.333199\pi$
$83$	9.11709	1.00073	0.500365	+	0.865814i	$0.333199\pi$
$84$	−44.8672	−4.89541
$85$	8.45383	0.916947
$86$	6.21949	0.670665
$87$	13.2031	1.41552
$88$	−4.16391	−0.443874
$89$	0.117973	0.0125051	0.00625257	−	0.999980i	$-0.498010\pi$
$89$	0.117973	0.0125051	0.00625257	+	0.999980i	$0.498010\pi$
$90$	−33.5298	−3.53436
$91$	−18.0713	−1.89439
$92$	−3.69606	−0.385341
$93$	−13.2626	−1.37527
$94$	29.8878	3.08269
$95$	18.4916	1.89720
$96$	−2.34159	−0.238987
$97$	14.9514	1.51809	0.759043	−	0.651040i	$-0.225667\pi$
$97$	14.9514	1.51809	0.759043	+	0.651040i	$0.225667\pi$
$98$	−21.0543	−2.12681
$99$	3.86588	0.388535
$100$	12.7382	1.27382
$101$	17.5762	1.74890	0.874451	−	0.485114i	$-0.161222\pi$
$101$	17.5762	1.74890	0.874451	+	0.485114i	$0.161222\pi$
$102$	−20.3984	−2.01974
$103$	−3.06507	−0.302010	−0.151005	−	0.988533i	$-0.548251\pi$
$103$	−3.06507	−0.302010	−0.151005	+	0.988533i	$0.548251\pi$
$104$	−23.5593	−2.31018
$105$	−31.3092	−3.05546
$106$	−24.8812	−2.41668
$107$	−12.7659	−1.23413	−0.617063	−	0.786914i	$-0.711677\pi$
$107$	−12.7659	−1.23413	−0.617063	+	0.786914i	$0.711677\pi$
$108$	20.1573	1.93963
$109$	17.2302	1.65036	0.825178	−	0.564873i	$-0.191075\pi$
$109$	17.2302	1.65036	0.825178	+	0.564873i	$0.191075\pi$
$110$	−5.69499	−0.542996
$111$	3.78369	0.359132
$112$	−17.7663	−1.67876
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−44.6188	−4.17893
$115$	−2.57918	−0.240510
$116$	19.3403	1.79571
$117$	21.8730	2.02216
$118$	−12.0964	−1.11356
$119$	−11.6940	−1.07198
$120$	−40.8174	−3.72610
$121$	−10.3434	−0.940308
$122$	10.8826	0.985263
$123$	−17.0477	−1.53714
$124$	−19.4275	−1.74464
$125$	−5.35842	−0.479272
$126$	46.3810	4.13195
$127$	−6.22561	−0.552433	−0.276217	−	0.961095i	$-0.589081\pi$
$127$	−6.22561	−0.552433	−0.276217	+	0.961095i	$0.589081\pi$
$128$	18.8044	1.66209
$129$	−7.02935	−0.618900
$130$	−32.2221	−2.82606
$131$	−12.7150	−1.11092	−0.555459	−	0.831544i	$-0.687457\pi$
$131$	−12.7150	−1.11092	−0.555459	+	0.831544i	$0.687457\pi$
$132$	9.22382	0.802830
$133$	−25.5790	−2.21798
$134$	−6.23376	−0.538515
$135$	14.0661	1.21062
$136$	−15.2453	−1.30727
$137$	3.90297	0.333454	0.166727	−	0.986003i	$-0.446680\pi$
$137$	3.90297	0.333454	0.166727	+	0.986003i	$0.446680\pi$
$138$	6.22334	0.529766
$139$	−6.89274	−0.584634	−0.292317	−	0.956321i	$-0.594426\pi$
$139$	−6.89274	−0.584634	−0.292317	+	0.956321i	$0.594426\pi$
$140$	−45.8628	−3.87611
$141$	−33.7795	−2.84475
$142$	2.46646	0.206980
$143$	3.71510	0.310672
$144$	21.5039	1.79199
$145$	13.4961	1.12079
$146$	−23.8911	−1.97724
$147$	23.7959	1.96265
$148$	5.54249	0.455590
$149$	3.06122	0.250785	0.125393	−	0.992107i	$-0.459981\pi$
$149$	3.06122	0.250785	0.125393	+	0.992107i	$0.459981\pi$
$150$	−21.4483	−1.75124
$151$	−15.1707	−1.23458	−0.617288	−	0.786737i	$-0.711769\pi$
$151$	−15.1707	−1.23458	−0.617288	+	0.786737i	$0.711769\pi$
$152$	−33.3470	−2.70480
$153$	14.1541	1.14429
$154$	7.87774	0.634806
$155$	−13.5569	−1.08891
$156$	52.1881	4.17839
$157$	12.4739	0.995524	0.497762	−	0.867314i	$-0.334155\pi$
$157$	12.4739	0.995524	0.497762	+	0.867314i	$0.334155\pi$
$158$	−33.3076	−2.64981
$159$	28.1211	2.23015
$160$	−2.39354	−0.189226
$161$	3.56771	0.281175
$162$	1.36076	0.106911
$163$	−1.63385	−0.127973	−0.0639867	−	0.997951i	$-0.520382\pi$
$163$	−1.63385	−0.127973	−0.0639867	+	0.997951i	$0.520382\pi$
$164$	−24.9720	−1.94999
$165$	6.43655	0.501085
$166$	−22.4869	−1.74532
$167$	4.80133	0.371538	0.185769	−	0.982593i	$-0.440522\pi$
$167$	4.80133	0.371538	0.185769	+	0.982593i	$0.440522\pi$
$168$	56.4616	4.35611
$169$	8.01993	0.616918
$170$	−20.8510	−1.59920
$171$	30.9602	2.36759
$172$	−10.2968	−0.785126
$173$	−5.63813	−0.428659	−0.214329	−	0.976761i	$-0.568757\pi$
$173$	−5.63813	−0.428659	−0.214329	+	0.976761i	$0.568757\pi$
$174$	−32.5648	−2.46873
$175$	−12.2959	−0.929480
$176$	3.65240	0.275310
$177$	13.6715	1.02761
$178$	−0.290976	−0.0218096
$179$	−16.1221	−1.20502	−0.602511	−	0.798110i	$-0.705833\pi$
$179$	−16.1221	−1.20502	−0.602511	+	0.798110i	$0.705833\pi$
$180$	55.5112	4.13756
$181$	−23.3884	−1.73845	−0.869225	−	0.494418i	$-0.835381\pi$
$181$	−23.3884	−1.73845	−0.869225	+	0.494418i	$0.835381\pi$
$182$	44.5720	3.30390
$183$	−12.2996	−0.909216
$184$	4.65118	0.342890
$185$	3.86765	0.284355
$186$	32.7116	2.39853
$187$	2.40405	0.175802
$188$	−49.4814	−3.60881
$189$	−19.4573	−1.41531
$190$	−45.6088	−3.30881
$191$	4.54605	0.328941	0.164470	−	0.986382i	$-0.447409\pi$
$191$	4.54605	0.328941	0.164470	+	0.986382i	$0.447409\pi$
$192$	−19.3543	−1.39677
$193$	23.8591	1.71742	0.858709	−	0.512463i	$-0.171267\pi$
$193$	23.8591	1.71742	0.858709	+	0.512463i	$0.171267\pi$
$194$	−36.8770	−2.64762
$195$	36.4178	2.60793
$196$	34.8570	2.48979
$197$	14.6046	1.04053	0.520267	−	0.854004i	$-0.325832\pi$
$197$	14.6046	1.04053	0.520267	+	0.854004i	$0.325832\pi$
$198$	−9.53502	−0.677624
$199$	−8.69245	−0.616191	−0.308096	−	0.951355i	$-0.599692\pi$
$199$	−8.69245	−0.616191	−0.308096	+	0.951355i	$0.599692\pi$
$200$	−16.0300	−1.13349
$201$	7.04548	0.496950
$202$	−43.3510	−3.05017
$203$	−18.6688	−1.31029
$204$	33.7710	2.36445
$205$	−17.4259	−1.21708
$206$	7.55985	0.526720
$207$	−4.31827	−0.300141
$208$	20.6652	1.43287
$209$	5.25855	0.363741
$210$	77.2227	5.32887
$211$	8.24053	0.567302	0.283651	−	0.958928i	$-0.408454\pi$
$211$	8.24053	0.567302	0.283651	+	0.958928i	$0.408454\pi$
$212$	41.1927	2.82913
$213$	−2.78762	−0.191005
$214$	31.4865	2.15237
$215$	−7.18532	−0.490035
$216$	−25.3662	−1.72595
$217$	18.7529	1.27303
$218$	−42.4976	−2.87830
$219$	27.0021	1.82463
$220$	9.42848	0.635668
$221$	13.6021	0.914973
$222$	−9.33231	−0.626344
$223$	22.3753	1.49836	0.749180	−	0.662366i	$-0.230448\pi$
$223$	22.3753	1.49836	0.749180	+	0.662366i	$0.230448\pi$
$224$	3.31093	0.221221
$225$	14.8826	0.992174
$226$	−2.46646	−0.164066
$227$	11.5241	0.764881	0.382441	−	0.923980i	$-0.375084\pi$
$227$	11.5241	0.764881	0.382441	+	0.923980i	$0.375084\pi$
$228$	73.8697	4.89214
$229$	11.2335	0.742328	0.371164	−	0.928567i	$-0.378959\pi$
$229$	11.2335	0.742328	0.371164	+	0.928567i	$0.378959\pi$
$230$	6.36143	0.419460
$231$	−8.90352	−0.585809
$232$	−24.3382	−1.59788
$233$	−0.269893	−0.0176813	−0.00884063	−	0.999961i	$-0.502814\pi$
$233$	−0.269893	−0.0176813	−0.00884063	+	0.999961i	$0.502814\pi$
$234$	−53.9489	−3.52675
$235$	−34.5291	−2.25243
$236$	20.0265	1.30361
$237$	37.6446	2.44528
$238$	28.8427	1.86959
$239$	22.0550	1.42662	0.713311	−	0.700848i	$-0.247195\pi$
$239$	22.0550	1.42662	0.713311	+	0.700848i	$0.247195\pi$
$240$	35.8032	2.31109
$241$	3.28496	0.211603	0.105802	−	0.994387i	$-0.466259\pi$
$241$	3.28496	0.211603	0.105802	+	0.994387i	$0.466259\pi$
$242$	25.5115	1.63994
$243$	−16.3471	−1.04867
$244$	−18.0169	−1.15342
$245$	24.3239	1.55400
$246$	42.0473	2.68084
$247$	29.7527	1.89312
$248$	24.4479	1.55244
$249$	25.4150	1.61061
$250$	13.2163	0.835873
$251$	−8.88061	−0.560539	−0.280269	−	0.959921i	$-0.590424\pi$
$251$	−8.88061	−0.560539	−0.280269	+	0.959921i	$0.590424\pi$
$252$	−76.7872	−4.83714
$253$	−0.733452	−0.0461117
$254$	15.3552	0.963470
$255$	23.5661	1.47576
$256$	−32.4944	−2.03090
$257$	−17.8561	−1.11383	−0.556916	−	0.830569i	$-0.688016\pi$
$257$	−17.8561	−1.11383	−0.556916	+	0.830569i	$0.688016\pi$
$258$	17.3376	1.07939
$259$	−5.35002	−0.332434
$260$	53.3461	3.30838
$261$	22.5962	1.39867
$262$	31.3611	1.93749
$263$	−26.7976	−1.65241	−0.826204	−	0.563371i	$-0.809504\pi$
$263$	−26.7976	−1.65241	−0.826204	+	0.563371i	$0.809504\pi$
$264$	−11.6074	−0.714386
$265$	28.7451	1.76580
$266$	63.0896	3.86827
$267$	0.328865	0.0201262
$268$	10.3205	0.630423
$269$	−15.8145	−0.964226	−0.482113	−	0.876109i	$-0.660131\pi$
$269$	−15.8145	−0.964226	−0.482113	+	0.876109i	$0.660131\pi$
$270$	−34.6934	−2.11137
$271$	−10.3023	−0.625819	−0.312909	−	0.949783i	$-0.601304\pi$
$271$	−10.3023	−0.625819	−0.312909	+	0.949783i	$0.601304\pi$
$272$	13.3725	0.810826
$273$	−50.3759	−3.04889
$274$	−9.62651	−0.581559
$275$	2.52779	0.152431
$276$	−10.3032	−0.620180
$277$	−11.8791	−0.713744	−0.356872	−	0.934153i	$-0.616157\pi$
$277$	−11.8791	−0.713744	−0.356872	+	0.934153i	$0.616157\pi$
$278$	17.0006	1.01963
$279$	−22.6980	−1.35889
$280$	57.7145	3.44910
$281$	29.0562	1.73335	0.866673	−	0.498877i	$-0.166254\pi$
$281$	29.0562	1.73335	0.866673	+	0.498877i	$0.166254\pi$
$282$	83.3157	4.96138
$283$	−7.99188	−0.475068	−0.237534	−	0.971379i	$-0.576339\pi$
$283$	−7.99188	−0.475068	−0.237534	+	0.971379i	$0.576339\pi$
$284$	−4.08340	−0.242305
$285$	51.5477	3.05342
$286$	−9.16313	−0.541827
$287$	24.1049	1.42287
$288$	−4.00747	−0.236142
$289$	−8.19808	−0.482240
$290$	−33.2874	−1.95470
$291$	41.6789	2.44326
$292$	39.5535	2.31470
$293$	−12.8292	−0.749491	−0.374746	−	0.927128i	$-0.622270\pi$
$293$	−12.8292	−0.749491	−0.374746	+	0.927128i	$0.622270\pi$
$294$	−58.6915	−3.42296
$295$	13.9748	0.813646
$296$	−6.97476	−0.405399
$297$	4.00004	0.232106
$298$	−7.55037	−0.437381
$299$	−4.14985	−0.239992
$300$	35.5092	2.05013
$301$	9.93928	0.572890
$302$	37.4179	2.15316
$303$	48.9959	2.81474
$304$	29.2506	1.67764
$305$	−12.5726	−0.719903
$306$	−34.9105	−1.99570
$307$	−19.0883	−1.08942	−0.544712	−	0.838623i	$-0.683361\pi$
$307$	−19.0883	−1.08942	−0.544712	+	0.838623i	$0.683361\pi$
$308$	−13.0422	−0.743148
$309$	−8.54424	−0.486065
$310$	33.4374	1.89912
$311$	7.32886	0.415582	0.207791	−	0.978173i	$-0.433373\pi$
$311$	7.32886	0.415582	0.207791	+	0.978173i	$0.433373\pi$
$312$	−65.6743	−3.71808
$313$	7.78800	0.440204	0.220102	−	0.975477i	$-0.429361\pi$
$313$	7.78800	0.440204	0.220102	+	0.975477i	$0.429361\pi$
$314$	−30.7663	−1.73624
$315$	−53.5836	−3.01909
$316$	55.1432	3.10205
$317$	−5.78187	−0.324742	−0.162371	−	0.986730i	$-0.551914\pi$
$317$	−5.78187	−0.324742	−0.162371	+	0.986730i	$0.551914\pi$
$318$	−69.3594	−3.88948
$319$	3.83793	0.214883
$320$	−19.7837	−1.10594
$321$	−35.5864	−1.98624
$322$	−8.79961	−0.490383
$323$	19.2531	1.07127
$324$	−2.25284	−0.125158
$325$	14.3021	0.793340
$326$	4.02983	0.223192
$327$	48.0313	2.65614
$328$	31.4252	1.73517
$329$	47.7632	2.63327
$330$	−15.8755	−0.873916
$331$	−21.6310	−1.18895	−0.594474	−	0.804115i	$-0.702640\pi$
$331$	−21.6310	−1.18895	−0.594474	+	0.804115i	$0.702640\pi$
$332$	37.2288	2.04319
$333$	6.47554	0.354857
$334$	−11.8423	−0.647980
$335$	7.20181	0.393477
$336$	−49.5257	−2.70185
$337$	−34.8159	−1.89654	−0.948270	−	0.317465i	$-0.897169\pi$
$337$	−34.8159	−1.89654	−0.948270	+	0.317465i	$0.897169\pi$
$338$	−19.7808	−1.07593
$339$	2.78762	0.151403
$340$	34.5204	1.87213
$341$	−3.85522	−0.208772
$342$	−76.3621	−4.12919
$343$	−6.05536	−0.326959
$344$	12.9577	0.698632
$345$	−7.18977	−0.387084
$346$	13.9062	0.747602
$347$	35.2368	1.89161	0.945805	−	0.324735i	$-0.105275\pi$
$347$	35.2368	1.89161	0.945805	+	0.324735i	$0.105275\pi$
$348$	53.9135	2.89007
$349$	0.890710	0.0476786	0.0238393	−	0.999716i	$-0.492411\pi$
$349$	0.890710	0.0476786	0.0238393	+	0.999716i	$0.492411\pi$
$350$	30.3272	1.62106
$351$	22.6321	1.20801
$352$	−0.680662	−0.0362794
$353$	−8.75548	−0.466007	−0.233004	−	0.972476i	$-0.574855\pi$
$353$	−8.75548	−0.466007	−0.233004	+	0.972476i	$0.574855\pi$
$354$	−33.7201	−1.79220
$355$	−2.84947	−0.151234
$356$	0.481732	0.0255318
$357$	−32.5984	−1.72529
$358$	39.7644	2.10162
$359$	−11.2107	−0.591680	−0.295840	−	0.955237i	$-0.595600\pi$
$359$	−11.2107	−0.591680	−0.295840	+	0.955237i	$0.595600\pi$
$360$	−69.8562	−3.68174
$361$	23.1135	1.21650
$362$	57.6865	3.03194
$363$	−28.8334	−1.51336
$364$	−73.7923	−3.86777
$365$	27.6012	1.44471
$366$	30.3365	1.58572
$367$	5.41736	0.282784	0.141392	−	0.989954i	$-0.454842\pi$
$367$	5.41736	0.282784	0.141392	+	0.989954i	$0.454842\pi$
$368$	−4.07981	−0.212675
$369$	−29.1759	−1.51884
$370$	−9.53939	−0.495929
$371$	−39.7623	−2.06436
$372$	−54.1564	−2.80788
$373$	26.4889	1.37154	0.685772	−	0.727817i	$-0.259465\pi$
$373$	26.4889	1.37154	0.685772	+	0.727817i	$0.259465\pi$
$374$	−5.92948	−0.306606
$375$	−14.9372	−0.771356
$376$	62.2683	3.21124
$377$	21.7149	1.11837
$378$	47.9906	2.46837
$379$	24.1507	1.24054	0.620269	−	0.784389i	$-0.287023\pi$
$379$	24.1507	1.24054	0.620269	+	0.784389i	$0.287023\pi$
$380$	75.5088	3.87352
$381$	−17.3546	−0.889104
$382$	−11.2126	−0.573688
$383$	−19.7044	−1.00685	−0.503423	−	0.864040i	$-0.667926\pi$
$383$	−19.7044	−1.00685	−0.503423	+	0.864040i	$0.667926\pi$
$384$	52.4196	2.67503
$385$	−9.10108	−0.463834
$386$	−58.8475	−2.99526
$387$	−12.0303	−0.611532
$388$	61.0527	3.09948
$389$	−7.42910	−0.376670	−0.188335	−	0.982105i	$-0.560309\pi$
$389$	−7.42910	−0.376670	−0.188335	+	0.982105i	$0.560309\pi$
$390$	−89.8229	−4.54836
$391$	−2.68538	−0.135805
$392$	−43.8646	−2.21550
$393$	−35.4447	−1.78795
$394$	−36.0216	−1.81474
$395$	38.4799	1.93614
$396$	15.7859	0.793273
$397$	−23.7459	−1.19177	−0.595887	−	0.803068i	$-0.703199\pi$
$397$	−23.7459	−1.19177	−0.595887	+	0.803068i	$0.703199\pi$
$398$	21.4395	1.07467
$399$	−71.3046	−3.56970
$400$	14.0608	0.703039
$401$	14.7540	0.736778	0.368389	−	0.929672i	$-0.379909\pi$
$401$	14.7540	0.736778	0.368389	+	0.929672i	$0.379909\pi$
$402$	−17.3774	−0.866704
$403$	−21.8127	−1.08657
$404$	71.7709	3.57074
$405$	−1.57207	−0.0781168
$406$	46.0457	2.28521
$407$	1.09986	0.0545180
$408$	−42.4980	−2.10397
$409$	−7.43778	−0.367774	−0.183887	−	0.982947i	$-0.558868\pi$
$409$	−7.43778	−0.367774	−0.183887	+	0.982947i	$0.558868\pi$
$410$	42.9803	2.12265
$411$	10.8800	0.536671
$412$	−12.5159	−0.616614
$413$	−19.3310	−0.951218
$414$	10.6508	0.523460
$415$	25.9789	1.27525
$416$	−3.85116	−0.188819
$417$	−19.2143	−0.940930
$418$	−12.9700	−0.634382
$419$	19.4960	0.952444	0.476222	−	0.879325i	$-0.342006\pi$
$419$	19.4960	0.952444	0.476222	+	0.879325i	$0.342006\pi$
$420$	−127.848	−6.23834
$421$	−21.8406	−1.06445	−0.532223	−	0.846604i	$-0.678643\pi$
$421$	−21.8406	−1.06445	−0.532223	+	0.846604i	$0.678643\pi$
$422$	−20.3249	−0.989401
$423$	−57.8114	−2.81089
$424$	−51.8376	−2.51746
$425$	9.25496	0.448931
$426$	6.87554	0.333121
$427$	17.3913	0.841625
$428$	−52.1283	−2.51971
$429$	10.3563	0.500006
$430$	17.7223	0.854644
$431$	−26.0369	−1.25415	−0.627077	−	0.778957i	$-0.715749\pi$
$431$	−26.0369	−1.25415	−0.627077	+	0.778957i	$0.715749\pi$
$432$	22.2501	1.07051
$433$	3.70727	0.178160	0.0890801	−	0.996024i	$-0.471607\pi$
$433$	3.70727	0.178160	0.0890801	+	0.996024i	$0.471607\pi$
$434$	−46.2531	−2.22022
$435$	37.6219	1.80383
$436$	70.3579	3.36953
$437$	−5.87391	−0.280987
$438$	−66.5994	−3.18224
$439$	−27.5322	−1.31404	−0.657019	−	0.753874i	$-0.728183\pi$
$439$	−27.5322	−1.31404	−0.657019	+	0.753874i	$0.728183\pi$
$440$	−11.8650	−0.565640
$441$	40.7250	1.93929
$442$	−33.5489	−1.59576
$443$	24.8346	1.17993	0.589963	−	0.807430i	$-0.299142\pi$
$443$	24.8346	1.17993	0.589963	+	0.807430i	$0.299142\pi$
$444$	15.4503	0.733241
$445$	0.336162	0.0159356
$446$	−55.1877	−2.61321
$447$	8.53352	0.403622
$448$	27.3663	1.29294
$449$	−22.0969	−1.04282	−0.521408	−	0.853307i	$-0.674593\pi$
$449$	−22.0969	−1.04282	−0.521408	+	0.853307i	$0.674593\pi$
$450$	−36.7073	−1.73040
$451$	−4.95549	−0.233345
$452$	4.08340	0.192067
$453$	−42.2902	−1.98697
$454$	−28.4237	−1.33399
$455$	−51.4937	−2.41406
$456$	−92.9589	−4.35320
$457$	6.78816	0.317537	0.158768	−	0.987316i	$-0.449248\pi$
$457$	6.78816	0.317537	0.158768	+	0.987316i	$0.449248\pi$
$458$	−27.7068	−1.29465
$459$	14.6453	0.683584
$460$	−10.5318	−0.491049
$461$	−18.3463	−0.854474	−0.427237	−	0.904140i	$-0.640513\pi$
$461$	−18.3463	−0.854474	−0.427237	+	0.904140i	$0.640513\pi$
$462$	21.9601	1.02168
$463$	16.1831	0.752091	0.376046	−	0.926601i	$-0.377284\pi$
$463$	16.1831	0.752091	0.376046	+	0.926601i	$0.377284\pi$
$464$	21.3484	0.991075
$465$	−37.7914	−1.75253
$466$	0.665679	0.0308370
$467$	27.1745	1.25749	0.628743	−	0.777613i	$-0.283570\pi$
$467$	27.1745	1.25749	0.628743	+	0.777613i	$0.283570\pi$
$468$	89.3164	4.12865
$469$	−9.96209	−0.460006
$470$	85.1644	3.92834
$471$	34.7725	1.60223
$472$	−25.2016	−1.16000
$473$	−2.04332	−0.0939519
$474$	−92.8489	−4.26469
$475$	20.2440	0.928859
$476$	−47.7512	−2.18867
$477$	48.1273	2.20360
$478$	−54.3978	−2.48810
$479$	−7.64566	−0.349339	−0.174670	−	0.984627i	$-0.555886\pi$
$479$	−7.64566	−0.349339	−0.174670	+	0.984627i	$0.555886\pi$
$480$	−6.67229	−0.304547
$481$	6.22298	0.283743
$482$	−8.10222	−0.369046
$483$	9.94543	0.452533
$484$	−42.2362	−1.91983
$485$	42.6037	1.93453
$486$	40.3194	1.82893
$487$	−1.05895	−0.0479856	−0.0239928	−	0.999712i	$-0.507638\pi$
$487$	−1.05895	−0.0479856	−0.0239928	+	0.999712i	$0.507638\pi$
$488$	22.6728	1.02635
$489$	−4.55456	−0.205964
$490$	−59.9938	−2.71024
$491$	35.5665	1.60510	0.802548	−	0.596588i	$-0.203477\pi$
$491$	35.5665	1.60510	0.802548	+	0.596588i	$0.203477\pi$
$492$	−69.6125	−3.13837
$493$	14.0518	0.632860
$494$	−73.3837	−3.30169
$495$	11.0157	0.495120
$496$	−21.4446	−0.962891
$497$	3.94161	0.176805
$498$	−62.6849	−2.80898
$499$	30.7783	1.37783	0.688913	−	0.724844i	$-0.258088\pi$
$499$	30.7783	1.37783	0.688913	+	0.724844i	$0.258088\pi$
$500$	−21.8806	−0.978530
$501$	13.3843	0.597965
$502$	21.9036	0.977606
$503$	17.0944	0.762199	0.381100	−	0.924534i	$-0.375545\pi$
$503$	17.0944	0.762199	0.381100	+	0.924534i	$0.375545\pi$
$504$	96.6303	4.30426
$505$	50.0831	2.22867
$506$	1.80903	0.0804210
$507$	22.3565	0.992888
$508$	−25.4217	−1.12790
$509$	−16.7375	−0.741875	−0.370937	−	0.928658i	$-0.620964\pi$
$509$	−16.7375	−0.741875	−0.370937	+	0.928658i	$0.620964\pi$
$510$	−58.1247	−2.57380
$511$	−38.1801	−1.68899
$512$	42.5372	1.87990
$513$	32.0347	1.41436
$514$	44.0413	1.94258
$515$	−8.73383	−0.384858
$516$	−28.7037	−1.26361
$517$	−9.81918	−0.431847
$518$	13.1956	0.579781
$519$	−15.7170	−0.689898
$520$	−67.1316	−2.94392
$521$	27.5788	1.20825	0.604124	−	0.796890i	$-0.293523\pi$
$521$	27.5788	1.20825	0.604124	+	0.796890i	$0.293523\pi$
$522$	−55.7325	−2.43935
$523$	−22.4681	−0.982463	−0.491232	−	0.871029i	$-0.663453\pi$
$523$	−22.4681	−0.982463	−0.491232	+	0.871029i	$0.663453\pi$
$524$	−51.9206	−2.26816
$525$	−34.2762	−1.49594
$526$	66.0950	2.88188
$527$	−14.1151	−0.614862
$528$	10.1815	0.443093
$529$	−22.1807	−0.964379
$530$	−70.8984	−3.07963
$531$	23.3978	1.01538
$532$	−104.450	−4.52846
$533$	−28.0380	−1.21446
$534$	−0.811130	−0.0351010
$535$	−36.3761	−1.57267
$536$	−12.9874	−0.560972
$537$	−44.9423	−1.93940
$538$	39.0057	1.68166
$539$	6.91708	0.297940
$540$	57.4376	2.47172
$541$	−27.3128	−1.17427	−0.587134	−	0.809489i	$-0.699744\pi$
$541$	−27.3128	−1.17427	−0.587134	+	0.809489i	$0.699744\pi$
$542$	25.4101	1.09146
$543$	−65.1981	−2.79792
$544$	−2.49210	−0.106848
$545$	49.0971	2.10309
$546$	124.250	5.31740
$547$	20.1892	0.863230	0.431615	−	0.902058i	$-0.357944\pi$
$547$	20.1892	0.863230	0.431615	+	0.902058i	$0.357944\pi$
$548$	15.9374	0.680813
$549$	−21.0500	−0.898393
$550$	−6.23467	−0.265847
$551$	30.7364	1.30941
$552$	12.9657	0.551858
$553$	−53.2284	−2.26350
$554$	29.2992	1.24480
$555$	10.7815	0.457651
$556$	−28.1458	−1.19365
$557$	34.4477	1.45960	0.729799	−	0.683662i	$-0.239614\pi$
$557$	34.4477	1.45960	0.729799	+	0.683662i	$0.239614\pi$
$558$	55.9836	2.36998
$559$	−11.5610	−0.488980
$560$	−50.6246	−2.13928
$561$	6.70158	0.282941
$562$	−71.6657	−3.02304
$563$	26.1452	1.10189	0.550945	−	0.834542i	$-0.314268\pi$
$563$	26.1452	1.10189	0.550945	+	0.834542i	$0.314268\pi$
$564$	−137.935	−5.80813
$565$	2.84947	0.119878
$566$	19.7116	0.828541
$567$	2.17461	0.0913249
$568$	5.13862	0.215612
$569$	29.6829	1.24437	0.622186	−	0.782870i	$-0.286245\pi$
$569$	29.6829	1.24437	0.622186	+	0.782870i	$0.286245\pi$
$570$	−127.140	−5.32531
$571$	−9.73579	−0.407430	−0.203715	−	0.979030i	$-0.565302\pi$
$571$	−9.73579	−0.407430	−0.203715	+	0.979030i	$0.565302\pi$
$572$	15.1702	0.634300
$573$	12.6727	0.529408
$574$	−59.4536	−2.48154
$575$	−2.82359	−0.117752
$576$	−33.1235	−1.38015
$577$	−17.6138	−0.733274	−0.366637	−	0.930364i	$-0.619491\pi$
$577$	−17.6138	−0.733274	−0.366637	+	0.930364i	$0.619491\pi$
$578$	20.2202	0.841049
$579$	66.5102	2.76407
$580$	55.1098	2.28831
$581$	−35.9360	−1.49088
$582$	−102.799	−4.26116
$583$	8.17435	0.338547
$584$	−49.7748	−2.05970
$585$	62.3267	2.57689
$586$	31.6427	1.30715
$587$	11.1600	0.460621	0.230310	−	0.973117i	$-0.426026\pi$
$587$	11.1600	0.460621	0.230310	+	0.973117i	$0.426026\pi$
$588$	97.1681	4.00715
$589$	−30.8749	−1.27218
$590$	−34.4683	−1.41904
$591$	40.7121	1.67467
$592$	6.11795	0.251446
$593$	25.9056	1.06382	0.531908	−	0.846802i	$-0.321475\pi$
$593$	25.9056	1.06382	0.531908	+	0.846802i	$0.321475\pi$
$594$	−9.86591	−0.404803
$595$	−33.3217	−1.36606
$596$	12.5002	0.512028
$597$	−24.2312	−0.991719
$598$	10.2354	0.418557
$599$	23.4698	0.958950	0.479475	−	0.877556i	$-0.340827\pi$
$599$	23.4698	0.958950	0.479475	+	0.877556i	$0.340827\pi$
$600$	−44.6854	−1.82427
$601$	−3.47529	−0.141760	−0.0708800	−	0.997485i	$-0.522581\pi$
$601$	−3.47529	−0.141760	−0.0708800	+	0.997485i	$0.522581\pi$
$602$	−24.5148	−0.999148
$603$	12.0579	0.491034
$604$	−61.9482	−2.52064
$605$	−29.4732	−1.19826
$606$	−120.846	−4.90904
$607$	−31.2430	−1.26811	−0.634057	−	0.773287i	$-0.718611\pi$
$607$	−31.2430	−1.26811	−0.634057	+	0.773287i	$0.718611\pi$
$608$	−5.45114	−0.221073
$609$	−52.0414	−2.10882
$610$	31.0097	1.25554
$611$	−55.5566	−2.24758
$612$	57.7969	2.33630
$613$	−19.5259	−0.788643	−0.394321	−	0.918973i	$-0.629020\pi$
$613$	−19.5259	−0.788643	−0.394321	+	0.918973i	$0.629020\pi$
$614$	47.0803	1.90001
$615$	−48.5769	−1.95881
$616$	16.4125	0.661278
$617$	46.6982	1.88000	0.940000	−	0.341175i	$-0.110825\pi$
$617$	46.6982	1.88000	0.940000	+	0.341175i	$0.110825\pi$
$618$	21.0740	0.847720
$619$	−6.75037	−0.271320	−0.135660	−	0.990755i	$-0.543316\pi$
$619$	−6.75037	−0.271320	−0.135660	+	0.990755i	$0.543316\pi$
$620$	−55.3581	−2.22324
$621$	−4.46813	−0.179300
$622$	−18.0763	−0.724794
$623$	−0.465004	−0.0186300
$624$	57.6067	2.30611
$625$	−30.8662	−1.23465
$626$	−19.2088	−0.767736
$627$	14.6588	0.585417
$628$	50.9359	2.03256
$629$	4.02690	0.160563
$630$	132.161	5.26544
$631$	0.331178	0.0131840	0.00659199	−	0.999978i	$-0.497902\pi$
$631$	0.331178	0.0131840	0.00659199	+	0.999978i	$0.497902\pi$
$632$	−69.3931	−2.76031
$633$	22.9715	0.913034
$634$	14.2607	0.566366
$635$	−17.7397	−0.703979
$636$	114.830	4.55329
$637$	39.1367	1.55065
$638$	−9.46608	−0.374766
$639$	−4.77082	−0.188731
$640$	53.5828	2.11804
$641$	10.4767	0.413803	0.206901	−	0.978362i	$-0.433662\pi$
$641$	10.4767	0.413803	0.206901	+	0.978362i	$0.433662\pi$
$642$	87.7724	3.46410
$643$	31.3669	1.23699	0.618494	−	0.785790i	$-0.287743\pi$
$643$	31.3669	1.23699	0.618494	+	0.785790i	$0.287743\pi$
$644$	14.5684	0.574076
$645$	−20.0299	−0.788678
$646$	−47.4868	−1.86834
$647$	19.2595	0.757169	0.378585	−	0.925567i	$-0.376411\pi$
$647$	19.2595	0.757169	0.378585	+	0.925567i	$0.376411\pi$
$648$	2.83500	0.111369
$649$	3.97408	0.155996
$650$	−35.2756	−1.38362
$651$	52.2759	2.04885
$652$	−6.67168	−0.261283
$653$	−44.2747	−1.73260	−0.866302	−	0.499521i	$-0.833509\pi$
$653$	−44.2747	−1.73260	−0.866302	+	0.499521i	$0.833509\pi$
$654$	−118.467	−4.63243
$655$	−36.2312	−1.41567
$656$	−27.5648	−1.07622
$657$	46.2122	1.80291
$658$	−117.806	−4.59255
$659$	46.7643	1.82168	0.910839	−	0.412761i	$-0.135436\pi$
$659$	46.7643	1.82168	0.910839	+	0.412761i	$0.135436\pi$
$660$	26.2830	1.02307
$661$	2.74145	0.106630	0.0533150	−	0.998578i	$-0.483021\pi$
$661$	2.74145	0.106630	0.0533150	+	0.998578i	$0.483021\pi$
$662$	53.3519	2.07358
$663$	37.9173	1.47259
$664$	−46.8493	−1.81810
$665$	−72.8868	−2.82643
$666$	−15.9716	−0.618888
$667$	−4.28705	−0.165995
$668$	19.6058	0.758569
$669$	62.3738	2.41151
$670$	−17.7630	−0.686243
$671$	−3.57531	−0.138023
$672$	9.22961	0.356040
$673$	12.9499	0.499183	0.249591	−	0.968351i	$-0.419704\pi$
$673$	12.9499	0.499183	0.249591	+	0.968351i	$0.419704\pi$
$674$	85.8717	3.30766
$675$	15.3991	0.592711
$676$	32.7486	1.25956
$677$	−0.929449	−0.0357216	−0.0178608	−	0.999840i	$-0.505686\pi$
$677$	−0.929449	−0.0357216	−0.0178608	+	0.999840i	$0.505686\pi$
$678$	−6.87554	−0.264054
$679$	−58.9326	−2.26163
$680$	−43.4410	−1.66589
$681$	32.1248	1.23103
$682$	9.50873	0.364108
$683$	−9.95783	−0.381026	−0.190513	−	0.981685i	$-0.561015\pi$
$683$	−9.95783	−0.381026	−0.190513	+	0.981685i	$0.561015\pi$
$684$	126.423	4.83391
$685$	11.1214	0.424928
$686$	14.9353	0.570232
$687$	31.3146	1.19473
$688$	−11.3659	−0.433322
$689$	46.2503	1.76199
$690$	17.7333	0.675093
$691$	0.277068	0.0105402	0.00527008	−	0.999986i	$-0.498322\pi$
$691$	0.277068	0.0105402	0.00527008	+	0.999986i	$0.498322\pi$
$692$	−23.0227	−0.875194
$693$	−15.2378	−0.578835
$694$	−86.9100	−3.29906
$695$	−19.6407	−0.745013
$696$	−67.8457	−2.57168
$697$	−18.1435	−0.687233
$698$	−2.19690	−0.0831538
$699$	−0.752359	−0.0284568
$700$	−50.2090	−1.89772
$701$	−16.4008	−0.619449	−0.309724	−	0.950826i	$-0.600237\pi$
$701$	−16.4008	−0.619449	−0.309724	+	0.950826i	$0.600237\pi$
$702$	−55.8211	−2.10683
$703$	8.80832	0.332212
$704$	−5.62598	−0.212037
$705$	−96.2539	−3.62513
$706$	21.5950	0.812739
$707$	−69.2787	−2.60549
$708$	55.8261	2.09808
$709$	16.2141	0.608934	0.304467	−	0.952523i	$-0.401522\pi$
$709$	16.2141	0.608934	0.304467	+	0.952523i	$0.401522\pi$
$710$	7.02810	0.263760
$711$	64.4263	2.41617
$712$	−0.606220	−0.0227190
$713$	4.30637	0.161275
$714$	80.4024	3.00898
$715$	10.5861	0.395897
$716$	−65.8330	−2.46030
$717$	61.4811	2.29605
$718$	27.6508	1.03192
$719$	−25.7949	−0.961989	−0.480994	−	0.876724i	$-0.659724\pi$
$719$	−25.7949	−0.961989	−0.480994	+	0.876724i	$0.659724\pi$
$720$	61.2748	2.28358
$721$	12.0813	0.449931
$722$	−57.0085	−2.12164
$723$	9.15723	0.340561
$724$	−95.5044	−3.54939
$725$	14.7750	0.548730
$726$	71.1164	2.63938
$727$	−3.10026	−0.114982	−0.0574911	−	0.998346i	$-0.518310\pi$
$727$	−3.10026	−0.114982	−0.0574911	+	0.998346i	$0.518310\pi$
$728$	92.8615	3.44167
$729$	−43.9144	−1.62646
$730$	−68.0771	−2.51965
$731$	−7.48118	−0.276702
$732$	−50.2244	−1.85635
$733$	29.1305	1.07596	0.537980	−	0.842957i	$-0.319187\pi$
$733$	29.1305	1.07596	0.537980	+	0.842957i	$0.319187\pi$
$734$	−13.3617	−0.493189
$735$	67.8057	2.50105
$736$	0.760314	0.0280256
$737$	2.04801	0.0754394
$738$	71.9612	2.64893
$739$	−22.7217	−0.835830	−0.417915	−	0.908486i	$-0.637239\pi$
$739$	−22.7217	−0.835830	−0.417915	+	0.908486i	$0.637239\pi$
$740$	15.7932	0.580569
$741$	82.9392	3.04685
$742$	98.0720	3.60034
$743$	37.6419	1.38095	0.690473	−	0.723358i	$-0.257402\pi$
$743$	37.6419	1.38095	0.690473	+	0.723358i	$0.257402\pi$
$744$	68.1514	2.49855
$745$	8.72287	0.319581
$746$	−65.3337	−2.39204
$747$	43.4960	1.59144
$748$	9.81671	0.358934
$749$	50.3181	1.83858
$750$	36.8421	1.34528
$751$	−0.0204791	−0.000747293 0	−0.000373646	−	1.00000i	$-0.500119\pi$
$751$	−0.0204791	−0.000747293 0	−0.000373646		1.00000i	$0.500119\pi$
$752$	−54.6190	−1.99175
$753$	−24.7558	−0.902150
$754$	−53.5588	−1.95050
$755$	−43.2286	−1.57325
$756$	−79.4520	−2.88964
$757$	−7.89705	−0.287023	−0.143512	−	0.989649i	$-0.545839\pi$
$757$	−7.89705	−0.287023	−0.143512	+	0.989649i	$0.545839\pi$
$758$	−59.5667	−2.16356
$759$	−2.04458	−0.0742137
$760$	−95.0216	−3.44679
$761$	24.1830	0.876633	0.438317	−	0.898821i	$-0.355575\pi$
$761$	24.1830	0.876633	0.438317	+	0.898821i	$0.355575\pi$
$762$	42.8044	1.55064
$763$	−67.9147	−2.45868
$764$	18.5634	0.671599
$765$	40.3317	1.45820
$766$	48.5999	1.75599
$767$	22.4852	0.811895
$768$	−90.5821	−3.26860
$769$	32.6761	1.17833	0.589165	−	0.808013i	$-0.299457\pi$
$769$	32.6761	1.17833	0.589165	+	0.808013i	$0.299457\pi$
$770$	22.4474	0.808948
$771$	−49.7760	−1.79264
$772$	97.4265	3.50646
$773$	−0.0327969	−0.00117962	−0.000589812	−	1.00000i	$-0.500188\pi$
$773$	−0.0327969	−0.00117962	−0.000589812		1.00000i	$0.500188\pi$
$774$	29.6721	1.06654
$775$	−14.8416	−0.533125
$776$	−76.8297	−2.75802
$777$	−14.9138	−0.535031
$778$	18.3236	0.656931
$779$	−39.6864	−1.42191
$780$	148.709	5.32462
$781$	−0.810317	−0.0289954
$782$	6.62337	0.236851
$783$	23.3804	0.835546
$784$	38.4761	1.37415
$785$	35.5440	1.26862
$786$	87.4227	3.11826
$787$	22.1077	0.788055	0.394028	−	0.919099i	$-0.371081\pi$
$787$	22.1077	0.788055	0.394028	+	0.919099i	$0.371081\pi$
$788$	59.6364	2.12446
$789$	−74.7014	−2.65944
$790$	−94.9091	−3.37671
$791$	−3.94161	−0.140147
$792$	−19.8653	−0.705882
$793$	−20.2290	−0.718353
$794$	58.5683	2.07851
$795$	80.1303	2.84193
$796$	−35.4948	−1.25808
$797$	15.9084	0.563503	0.281751	−	0.959487i	$-0.409085\pi$
$797$	15.9084	0.563503	0.281751	+	0.959487i	$0.409085\pi$
$798$	175.870	6.22572
$799$	−35.9508	−1.27185
$800$	−2.62037	−0.0926439
$801$	0.562830	0.0198866
$802$	−36.3900	−1.28498
$803$	7.84907	0.276988
$804$	28.7695	1.01462
$805$	10.1661	0.358308
$806$	53.8001	1.89503
$807$	−44.0848	−1.55186
$808$	−90.3177	−3.17736
$809$	−0.824322	−0.0289816	−0.0144908	−	0.999895i	$-0.504613\pi$
$809$	−0.824322	−0.0289816	−0.0144908	+	0.999895i	$0.504613\pi$
$810$	3.87744	0.136239
$811$	−7.91092	−0.277790	−0.138895	−	0.990307i	$-0.544355\pi$
$811$	−7.91092	−0.277790	−0.138895	+	0.990307i	$0.544355\pi$
$812$	−76.2320	−2.67522
$813$	−28.7188	−1.00721
$814$	−2.71275	−0.0950820
$815$	−4.65563	−0.163079
$816$	37.2774	1.30497
$817$	−16.3641	−0.572508
$818$	18.3449	0.641416
$819$	−86.2149	−3.01259
$820$	−71.1571	−2.48491
$821$	39.3741	1.37417	0.687084	−	0.726578i	$-0.258891\pi$
$821$	39.3741	1.37417	0.687084	+	0.726578i	$0.258891\pi$
$822$	−26.8351	−0.935980
$823$	27.4922	0.958317	0.479158	−	0.877728i	$-0.340942\pi$
$823$	27.4922	0.958317	0.479158	+	0.877728i	$0.340942\pi$
$824$	15.7502	0.548684
$825$	7.04651	0.245328
$826$	47.6791	1.65897
$827$	1.28136	0.0445572	0.0222786	−	0.999752i	$-0.492908\pi$
$827$	1.28136	0.0445572	0.0222786	+	0.999752i	$0.492908\pi$
$828$	−17.6333	−0.612798
$829$	−27.6860	−0.961575	−0.480787	−	0.876837i	$-0.659649\pi$
$829$	−27.6860	−0.961575	−0.480787	+	0.876837i	$0.659649\pi$
$830$	−64.0758	−2.22411
$831$	−33.1143	−1.14872
$832$	−31.8316	−1.10356
$833$	25.3254	0.877474
$834$	47.3913	1.64103
$835$	13.6813	0.473459
$836$	21.4728	0.742651
$837$	−23.4857	−0.811785
$838$	−48.0861	−1.66111
$839$	14.1844	0.489699	0.244850	−	0.969561i	$-0.421261\pi$
$839$	14.1844	0.489699	0.244850	+	0.969561i	$0.421261\pi$
$840$	160.886	5.55109
$841$	−6.56717	−0.226454
$842$	53.8689	1.85644
$843$	80.9975	2.78970
$844$	33.6494	1.15826
$845$	22.8526	0.786153
$846$	142.589	4.90232
$847$	40.7696	1.40086
$848$	45.4697	1.56144
$849$	−22.2783	−0.764590
$850$	−22.8269	−0.782958
$851$	−1.22857	−0.0421148
$852$	−11.3830	−0.389974
$853$	13.3632	0.457547	0.228773	−	0.973480i	$-0.426529\pi$
$853$	13.3632	0.457547	0.228773	+	0.973480i	$0.426529\pi$
$854$	−42.8949	−1.46783
$855$	88.2204	3.01707
$856$	65.5991	2.24213
$857$	−31.5295	−1.07703	−0.538513	−	0.842617i	$-0.681014\pi$
$857$	−31.5295	−1.07703	−0.538513	+	0.842617i	$0.681014\pi$
$858$	−25.5433	−0.872034
$859$	−38.9288	−1.32823	−0.664117	−	0.747629i	$-0.731192\pi$
$859$	−38.9288	−1.32823	−0.664117	+	0.747629i	$0.731192\pi$
$860$	−29.3406	−1.00050
$861$	67.1952	2.29001
$862$	64.2189	2.18730
$863$	−34.3065	−1.16781	−0.583904	−	0.811823i	$-0.698475\pi$
$863$	−34.3065	−1.16781	−0.583904	+	0.811823i	$0.698475\pi$
$864$	−4.14654	−0.141068
$865$	−16.0657	−0.546250
$866$	−9.14383	−0.310720
$867$	−22.8531	−0.776133
$868$	76.5755	2.59914
$869$	10.9427	0.371206
$870$	−92.7927	−3.14597
$871$	11.5876	0.392630
$872$	−88.5395	−2.99833
$873$	71.3306	2.41418
$874$	14.4877	0.490055
$875$	21.1208	0.714013
$876$	110.260	3.72535
$877$	−41.2235	−1.39202	−0.696010	−	0.718032i	$-0.745043\pi$
$877$	−41.2235	−1.39202	−0.696010	+	0.718032i	$0.745043\pi$
$878$	67.9069	2.29175
$879$	−35.7630	−1.20626
$880$	10.4074	0.350834
$881$	42.8999	1.44533	0.722667	−	0.691196i	$-0.242916\pi$
$881$	42.8999	1.44533	0.722667	+	0.691196i	$0.242916\pi$
$882$	−100.446	−3.38221
$883$	−35.1005	−1.18123	−0.590614	−	0.806954i	$-0.701114\pi$
$883$	−35.1005	−1.18123	−0.590614	+	0.806954i	$0.701114\pi$
$884$	55.5427	1.86810
$885$	38.9565	1.30951
$886$	−61.2533	−2.05785
$887$	−27.5750	−0.925876	−0.462938	−	0.886391i	$-0.653205\pi$
$887$	−27.5750	−0.925876	−0.462938	+	0.886391i	$0.653205\pi$
$888$	−19.4430	−0.652463
$889$	24.5389	0.823008
$890$	−0.829128	−0.0277924
$891$	−0.447056	−0.0149769
$892$	91.3674	3.05921
$893$	−78.6377	−2.63151
$894$	−21.0476	−0.703936
$895$	−45.9395	−1.53559
$896$	−74.1197	−2.47617
$897$	−11.5682	−0.386251
$898$	54.5010	1.81872
$899$	−22.5339	−0.751548
$900$	60.7717	2.02572
$901$	29.9287	0.997068
$902$	12.2225	0.406964
$903$	27.7069	0.922029
$904$	−5.13862	−0.170908
$905$	−66.6448	−2.21535
$906$	104.307	3.46536
$907$	−28.3788	−0.942304	−0.471152	−	0.882052i	$-0.656162\pi$
$907$	−28.3788	−0.942304	−0.471152	+	0.882052i	$0.656162\pi$
$908$	47.0575	1.56166
$909$	83.8532	2.78123
$910$	127.007	4.21024
$911$	9.98519	0.330824	0.165412	−	0.986225i	$-0.447105\pi$
$911$	9.98519	0.330824	0.165412	+	0.986225i	$0.447105\pi$
$912$	81.5395	2.70004
$913$	7.38773	0.244498
$914$	−16.7427	−0.553799
$915$	−35.0475	−1.15864
$916$	45.8707	1.51561
$917$	50.1177	1.65503
$918$	−36.1220	−1.19220
$919$	−6.35574	−0.209656	−0.104828	−	0.994490i	$-0.533429\pi$
$919$	−6.35574	−0.209656	−0.104828	+	0.994490i	$0.533429\pi$
$920$	13.2534	0.436952
$921$	−53.2108	−1.75336
$922$	45.2504	1.49024
$923$	−4.58475	−0.150909
$924$	−36.3567	−1.19605
$925$	4.23417	0.139219
$926$	−39.9148	−1.31168
$927$	−14.6229	−0.480279
$928$	−3.97849	−0.130600
$929$	31.7310	1.04106	0.520530	−	0.853843i	$-0.325734\pi$
$929$	31.7310	1.04106	0.520530	+	0.853843i	$0.325734\pi$
$930$	93.2108	3.05650
$931$	55.3961	1.81553
$932$	−1.10208	−0.0360999
$933$	20.4301	0.668851
$934$	−67.0247	−2.19312
$935$	6.85028	0.224028
$936$	−112.397	−3.67382
$937$	8.45825	0.276319	0.138160	−	0.990410i	$-0.455881\pi$
$937$	8.45825	0.276319	0.138160	+	0.990410i	$0.455881\pi$
$938$	24.5710	0.802273
$939$	21.7100	0.708479
$940$	−140.996	−4.59879
$941$	−41.1167	−1.34037	−0.670183	−	0.742196i	$-0.733785\pi$
$941$	−41.1167	−1.34037	−0.670183	+	0.742196i	$0.733785\pi$
$942$	−85.7647	−2.79437
$943$	5.53539	0.180257
$944$	22.1058	0.719481
$945$	−55.4431	−1.80356
$946$	5.03976	0.163857
$947$	23.4957	0.763508	0.381754	−	0.924264i	$-0.375320\pi$
$947$	23.4957	0.763508	0.381754	+	0.924264i	$0.375320\pi$
$948$	153.718	4.99254
$949$	44.4098	1.44160
$950$	−49.9309	−1.61997
$951$	−16.1177	−0.522651
$952$	60.0909	1.94756
$953$	30.1212	0.975721	0.487861	−	0.872922i	$-0.337777\pi$
$953$	30.1212	0.975721	0.487861	+	0.872922i	$0.337777\pi$
$954$	−118.704	−3.84318
$955$	12.9539	0.419177
$956$	90.0596	2.91274
$957$	10.6987	0.345839
$958$	18.8577	0.609264
$959$	−15.3840	−0.496775
$960$	−55.1495	−1.77994
$961$	−8.36457	−0.269825
$962$	−15.3487	−0.494862
$963$	−60.9038	−1.96260
$964$	13.4138	0.432030
$965$	67.9860	2.18855
$966$	−24.5300	−0.789239
$967$	37.4814	1.20532	0.602660	−	0.797998i	$-0.294108\pi$
$967$	37.4814	1.20532	0.602660	+	0.797998i	$0.294108\pi$
$968$	53.1507	1.70833
$969$	53.6702	1.72414
$970$	−105.080	−3.37392
$971$	14.6928	0.471514	0.235757	−	0.971812i	$-0.424243\pi$
$971$	14.6928	0.471514	0.235757	+	0.971812i	$0.424243\pi$
$972$	−66.7518	−2.14107
$973$	27.1685	0.870981
$974$	2.61185	0.0836892
$975$	39.8690	1.27683
$976$	−19.8876	−0.636587
$977$	−6.44438	−0.206174	−0.103087	−	0.994672i	$-0.532872\pi$
$977$	−6.44438	−0.206174	−0.103087	+	0.994672i	$0.532872\pi$
$978$	11.2336	0.359212
$979$	0.0955957	0.00305525
$980$	99.3242	3.17279
$981$	82.2023	2.62452
$982$	−87.7233	−2.79936
$983$	43.5104	1.38777	0.693883	−	0.720088i	$-0.255898\pi$
$983$	43.5104	1.38777	0.693883	+	0.720088i	$0.255898\pi$
$984$	87.6015	2.79263
$985$	41.6154	1.32598
$986$	−34.6580	−1.10374
$987$	133.146	4.23807
$988$	121.492	3.86518
$989$	2.28243	0.0725772
$990$	−27.1698	−0.863513
$991$	−13.0058	−0.413142	−0.206571	−	0.978432i	$-0.566230\pi$
$991$	−13.0058	−0.413142	−0.206571	+	0.978432i	$0.566230\pi$
$992$	3.99642	0.126886
$993$	−60.2990	−1.91353
$994$	−9.72180	−0.308357
$995$	−24.7689	−0.785227
$996$	103.780	3.28838
$997$	33.2696	1.05366	0.526830	−	0.849971i	$-0.323380\pi$
$997$	33.2696	1.05366	0.526830	+	0.849971i	$0.323380\pi$
$998$	−75.9133	−2.40299
$999$	6.70026	0.211987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.11	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.11	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.46646 q^{2} +2.78762 q^{3} +4.08340 q^{4} +2.84947 q^{5} -6.87554 q^{6} -3.94161 q^{7} -5.13862 q^{8} +4.77082 q^{9} +O(q^{10})\)	\(q-2.46646 q^{2} +2.78762 q^{3} +4.08340 q^{4} +2.84947 q^{5} -6.87554 q^{6} -3.94161 q^{7} -5.13862 q^{8} +4.77082 q^{9} -7.02810 q^{10} +0.810317 q^{11} +11.3830 q^{12} +4.58475 q^{13} +9.72180 q^{14} +7.94325 q^{15} +4.50737 q^{16} +2.96680 q^{17} -11.7670 q^{18} +6.48949 q^{19} +11.6356 q^{20} -10.9877 q^{21} -1.99861 q^{22} -0.905142 q^{23} -14.3245 q^{24} +3.11950 q^{25} -11.3081 q^{26} +4.93639 q^{27} -16.0952 q^{28} +4.73633 q^{29} -19.5917 q^{30} -4.75767 q^{31} -0.839994 q^{32} +2.25886 q^{33} -7.31749 q^{34} -11.2315 q^{35} +19.4812 q^{36} +1.35732 q^{37} -16.0060 q^{38} +12.7805 q^{39} -14.6424 q^{40} -6.11549 q^{41} +27.1007 q^{42} -2.52163 q^{43} +3.30885 q^{44} +13.5943 q^{45} +2.23249 q^{46} -12.1177 q^{47} +12.5648 q^{48} +8.53627 q^{49} -7.69412 q^{50} +8.27032 q^{51} +18.7214 q^{52} +10.0878 q^{53} -12.1754 q^{54} +2.30898 q^{55} +20.2544 q^{56} +18.0902 q^{57} -11.6819 q^{58} +4.90435 q^{59} +32.4355 q^{60} -4.41224 q^{61} +11.7346 q^{62} -18.8047 q^{63} -6.94294 q^{64} +13.0641 q^{65} -5.57137 q^{66} +2.52742 q^{67} +12.1147 q^{68} -2.52319 q^{69} +27.7020 q^{70} -1.00000 q^{71} -24.5155 q^{72} +9.68642 q^{73} -3.34777 q^{74} +8.69599 q^{75} +26.4992 q^{76} -3.19395 q^{77} -31.5226 q^{78} +13.5042 q^{79} +12.8436 q^{80} -0.551705 q^{81} +15.0836 q^{82} +9.11709 q^{83} -44.8672 q^{84} +8.45383 q^{85} +6.21949 q^{86} +13.2031 q^{87} -4.16391 q^{88} +0.117973 q^{89} -33.5298 q^{90} -18.0713 q^{91} -3.69606 q^{92} -13.2626 q^{93} +29.8878 q^{94} +18.4916 q^{95} -2.34159 q^{96} +14.9514 q^{97} -21.0543 q^{98} +3.86588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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