LMFDB - Embedded newform 8023.2.a.d.1.1

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:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.77651 q^{2} +2.27500 q^{3} +5.70902 q^{4} +0.808124 q^{5} -6.31657 q^{6} +0.0647974 q^{7} -10.2981 q^{8} +2.17564 q^{9} +O(q^{10})$	\(q-2.77651 q^{2} +2.27500 q^{3} +5.70902 q^{4} +0.808124 q^{5} -6.31657 q^{6} +0.0647974 q^{7} -10.2981 q^{8} +2.17564 q^{9} -2.24377 q^{10} +1.89232 q^{11} +12.9880 q^{12} +2.74874 q^{13} -0.179911 q^{14} +1.83848 q^{15} +17.1749 q^{16} +1.85964 q^{17} -6.04069 q^{18} +1.76617 q^{19} +4.61360 q^{20} +0.147414 q^{21} -5.25406 q^{22} +3.95046 q^{23} -23.4283 q^{24} -4.34694 q^{25} -7.63191 q^{26} -1.87542 q^{27} +0.369930 q^{28} +3.44073 q^{29} -5.10458 q^{30} -3.56845 q^{31} -27.0900 q^{32} +4.30504 q^{33} -5.16330 q^{34} +0.0523644 q^{35} +12.4208 q^{36} -0.983525 q^{37} -4.90380 q^{38} +6.25340 q^{39} -8.32217 q^{40} -2.67835 q^{41} -0.409298 q^{42} -9.75254 q^{43} +10.8033 q^{44} +1.75819 q^{45} -10.9685 q^{46} +13.3557 q^{47} +39.0729 q^{48} -6.99580 q^{49} +12.0693 q^{50} +4.23068 q^{51} +15.6926 q^{52} -3.53476 q^{53} +5.20713 q^{54} +1.52923 q^{55} -0.667293 q^{56} +4.01805 q^{57} -9.55322 q^{58} +3.91496 q^{59} +10.4959 q^{60} +8.08701 q^{61} +9.90785 q^{62} +0.140976 q^{63} +40.8659 q^{64} +2.22132 q^{65} -11.9530 q^{66} +1.44680 q^{67} +10.6167 q^{68} +8.98731 q^{69} -0.145390 q^{70} +1.00000 q^{71} -22.4051 q^{72} +16.0308 q^{73} +2.73077 q^{74} -9.88929 q^{75} +10.0831 q^{76} +0.122618 q^{77} -17.3626 q^{78} +10.2094 q^{79} +13.8794 q^{80} -10.7935 q^{81} +7.43648 q^{82} +4.49182 q^{83} +0.841592 q^{84} +1.50282 q^{85} +27.0781 q^{86} +7.82766 q^{87} -19.4874 q^{88} +5.06015 q^{89} -4.88163 q^{90} +0.178111 q^{91} +22.5533 q^{92} -8.11824 q^{93} -37.0821 q^{94} +1.42729 q^{95} -61.6297 q^{96} -5.21879 q^{97} +19.4239 q^{98} +4.11701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−2.77651	−1.96329	−0.981645	−	0.190716i	$-0.938919\pi$
$2$	−2.77651	−1.96329	−0.981645	+	0.190716i	$0.938919\pi$
$3$	2.27500	1.31347	0.656737	−	0.754120i	$-0.271936\pi$
$3$	2.27500	1.31347	0.656737	+	0.754120i	$0.271936\pi$
$4$	5.70902	2.85451
$5$	0.808124	0.361404	0.180702	−	0.983538i	$-0.442163\pi$
$5$	0.808124	0.361404	0.180702	+	0.983538i	$0.442163\pi$
$6$	−6.31657	−2.57873
$7$	0.0647974	0.0244911	0.0122456	−	0.999925i	$-0.496102\pi$
$7$	0.0647974	0.0244911	0.0122456	+	0.999925i	$0.496102\pi$
$8$	−10.2981	−3.64094
$9$	2.17564	0.725214
$10$	−2.24377	−0.709541
$11$	1.89232	0.570557	0.285278	−	0.958445i	$-0.407914\pi$
$11$	1.89232	0.570557	0.285278	+	0.958445i	$0.407914\pi$
$12$	12.9880	3.74932
$13$	2.74874	0.762364	0.381182	−	0.924500i	$-0.375517\pi$
$13$	2.74874	0.762364	0.381182	+	0.924500i	$0.375517\pi$
$14$	−0.179911	−0.0480832
$15$	1.83848	0.474695
$16$	17.1749	4.29372
$17$	1.85964	0.451028	0.225514	−	0.974240i	$-0.427594\pi$
$17$	1.85964	0.451028	0.225514	+	0.974240i	$0.427594\pi$
$18$	−6.04069	−1.42380
$19$	1.76617	0.405188	0.202594	−	0.979263i	$-0.435063\pi$
$19$	1.76617	0.405188	0.202594	+	0.979263i	$0.435063\pi$
$20$	4.61360	1.03163
$21$	0.147414	0.0321685
$22$	−5.25406	−1.12017
$23$	3.95046	0.823728	0.411864	−	0.911245i	$-0.364878\pi$
$23$	3.95046	0.823728	0.411864	+	0.911245i	$0.364878\pi$
$24$	−23.4283	−4.78228
$25$	−4.34694	−0.869387
$26$	−7.63191	−1.49674
$27$	−1.87542	−0.360925
$28$	0.369930	0.0699102
$29$	3.44073	0.638927	0.319463	−	0.947599i	$-0.396497\pi$
$29$	3.44073	0.638927	0.319463	+	0.947599i	$0.396497\pi$
$30$	−5.10458	−0.931964
$31$	−3.56845	−0.640913	−0.320457	−	0.947263i	$-0.603836\pi$
$31$	−3.56845	−0.640913	−0.320457	+	0.947263i	$0.603836\pi$
$32$	−27.0900	−4.78887
$33$	4.30504	0.749411
$34$	−5.16330	−0.885499
$35$	0.0523644	0.00885119
$36$	12.4208	2.07013
$37$	−0.983525	−0.161691	−0.0808453	−	0.996727i	$-0.525762\pi$
$37$	−0.983525	−0.161691	−0.0808453	+	0.996727i	$0.525762\pi$
$38$	−4.90380	−0.795502
$39$	6.25340	1.00134
$40$	−8.32217	−1.31585
$41$	−2.67835	−0.418289	−0.209144	−	0.977885i	$-0.567068\pi$
$41$	−2.67835	−0.418289	−0.209144	+	0.977885i	$0.567068\pi$
$42$	−0.409298	−0.0631560
$43$	−9.75254	−1.48725	−0.743625	−	0.668597i	$-0.766895\pi$
$43$	−9.75254	−1.48725	−0.743625	+	0.668597i	$0.766895\pi$
$44$	10.8033	1.62866
$45$	1.75819	0.262095
$46$	−10.9685	−1.61722
$47$	13.3557	1.94812	0.974061	−	0.226285i	$-0.0726581\pi$
$47$	13.3557	1.94812	0.974061	+	0.226285i	$0.0726581\pi$
$48$	39.0729	5.63969
$49$	−6.99580	−0.999400
$50$	12.0693	1.70686
$51$	4.23068	0.592414
$52$	15.6926	2.17617
$53$	−3.53476	−0.485537	−0.242768	−	0.970084i	$-0.578055\pi$
$53$	−3.53476	−0.485537	−0.242768	+	0.970084i	$0.578055\pi$
$54$	5.20713	0.708600
$55$	1.52923	0.206201
$56$	−0.667293	−0.0891708
$57$	4.01805	0.532204
$58$	−9.55322	−1.25440
$59$	3.91496	0.509684	0.254842	−	0.966983i	$-0.417977\pi$
$59$	3.91496	0.509684	0.254842	+	0.966983i	$0.417977\pi$
$60$	10.4959	1.35502
$61$	8.08701	1.03544	0.517718	−	0.855551i	$-0.326782\pi$
$61$	8.08701	1.03544	0.517718	+	0.855551i	$0.326782\pi$
$62$	9.90785	1.25830
$63$	0.140976	0.0177613
$64$	40.8659	5.10823
$65$	2.22132	0.275521
$66$	−11.9530	−1.47131
$67$	1.44680	0.176754	0.0883771	−	0.996087i	$-0.471832\pi$
$67$	1.44680	0.176754	0.0883771	+	0.996087i	$0.471832\pi$
$68$	10.6167	1.28746
$69$	8.98731	1.08195
$70$	−0.145390	−0.0173775
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−22.4051	−2.64046
$73$	16.0308	1.87626	0.938130	−	0.346282i	$-0.112556\pi$
$73$	16.0308	1.87626	0.938130	+	0.346282i	$0.112556\pi$
$74$	2.73077	0.317445
$75$	−9.88929	−1.14192
$76$	10.0831	1.15661
$77$	0.122618	0.0139736
$78$	−17.3626	−1.96593
$79$	10.2094	1.14865	0.574324	−	0.818628i	$-0.305265\pi$
$79$	10.2094	1.14865	0.574324	+	0.818628i	$0.305265\pi$
$80$	13.8794	1.55177
$81$	−10.7935	−1.19928
$82$	7.43648	0.821222
$83$	4.49182	0.493041	0.246521	−	0.969138i	$-0.420713\pi$
$83$	4.49182	0.493041	0.246521	+	0.969138i	$0.420713\pi$
$84$	0.841592	0.0918252
$85$	1.50282	0.163003
$86$	27.0781	2.91990
$87$	7.82766	0.839213
$88$	−19.4874	−2.07736
$89$	5.06015	0.536375	0.268188	−	0.963367i	$-0.413575\pi$
$89$	5.06015	0.536375	0.268188	+	0.963367i	$0.413575\pi$
$90$	−4.88163	−0.514569
$91$	0.178111	0.0186711
$92$	22.5533	2.35134
$93$	−8.11824	−0.841823
$94$	−37.0821	−3.82473
$95$	1.42729	0.146437
$96$	−61.6297	−6.29006
$97$	−5.21879	−0.529888	−0.264944	−	0.964264i	$-0.585353\pi$
$97$	−5.21879	−0.529888	−0.264944	+	0.964264i	$0.585353\pi$
$98$	19.4239	1.96211
$99$	4.11701	0.413775
$100$	−24.8167	−2.48167
$101$	−2.80269	−0.278878	−0.139439	−	0.990231i	$-0.544530\pi$
$101$	−2.80269	−0.278878	−0.139439	+	0.990231i	$0.544530\pi$
$102$	−11.7465	−1.16308
$103$	12.1522	1.19739	0.598697	−	0.800975i	$-0.295685\pi$
$103$	12.1522	1.19739	0.598697	+	0.800975i	$0.295685\pi$
$104$	−28.3069	−2.77572
$105$	0.119129	0.0116258
$106$	9.81430	0.953249
$107$	18.9648	1.83340	0.916701	−	0.399575i	$-0.130842\pi$
$107$	18.9648	1.83340	0.916701	+	0.399575i	$0.130842\pi$
$108$	−10.7068	−1.03026
$109$	−4.61177	−0.441728	−0.220864	−	0.975305i	$-0.570888\pi$
$109$	−4.61177	−0.441728	−0.220864	+	0.975305i	$0.570888\pi$
$110$	−4.24593	−0.404833
$111$	−2.23752	−0.212376
$112$	1.11289	0.105158
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−11.1562	−1.04487
$115$	3.19246	0.297699
$116$	19.6432	1.82382
$117$	5.98027	0.552877
$118$	−10.8699	−1.00066
$119$	0.120500	0.0110462
$120$	−18.9330	−1.72834
$121$	−7.41912	−0.674465
$122$	−22.4537	−2.03286
$123$	−6.09327	−0.549411
$124$	−20.3724	−1.82949
$125$	−7.55348	−0.675604
$126$	−0.391421	−0.0348706
$127$	−5.04363	−0.447550	−0.223775	−	0.974641i	$-0.571838\pi$
$127$	−5.04363	−0.447550	−0.223775	+	0.974641i	$0.571838\pi$
$128$	−59.2846	−5.24007
$129$	−22.1871	−1.95346
$130$	−6.16753	−0.540928
$131$	15.9897	1.39703	0.698515	−	0.715595i	$-0.253845\pi$
$131$	15.9897	1.39703	0.698515	+	0.715595i	$0.253845\pi$
$132$	24.5776	2.13920
$133$	0.114444	0.00992352
$134$	−4.01705	−0.347020
$135$	−1.51557	−0.130440
$136$	−19.1508	−1.64217
$137$	−0.128724	−0.0109977	−0.00549883	−	0.999985i	$-0.501750\pi$
$137$	−0.128724	−0.0109977	−0.00549883	+	0.999985i	$0.501750\pi$
$138$	−24.9534	−2.12417
$139$	−6.23517	−0.528860	−0.264430	−	0.964405i	$-0.585184\pi$
$139$	−6.23517	−0.528860	−0.264430	+	0.964405i	$0.585184\pi$
$140$	0.298949	0.0252658
$141$	30.3842	2.55881
$142$	−2.77651	−0.233000
$143$	5.20150	0.434972
$144$	37.3663	3.11386
$145$	2.78053	0.230911
$146$	−44.5097	−3.68365
$147$	−15.9155	−1.31269
$148$	−5.61496	−0.461547
$149$	23.2745	1.90672	0.953361	−	0.301834i	$-0.0975987\pi$
$149$	23.2745	1.90672	0.953361	+	0.301834i	$0.0975987\pi$
$150$	27.4577	2.24192
$151$	4.83145	0.393178	0.196589	−	0.980486i	$-0.437014\pi$
$151$	4.83145	0.393178	0.196589	+	0.980486i	$0.437014\pi$
$152$	−18.1883	−1.47527
$153$	4.04590	0.327092
$154$	−0.340449	−0.0274342
$155$	−2.88375	−0.231629
$156$	35.7008	2.85835
$157$	−2.20505	−0.175982	−0.0879912	−	0.996121i	$-0.528045\pi$
$157$	−2.20505	−0.175982	−0.0879912	+	0.996121i	$0.528045\pi$
$158$	−28.3465	−2.25513
$159$	−8.04159	−0.637740
$160$	−21.8920	−1.73072
$161$	0.255980	0.0201740
$162$	29.9683	2.35453
$163$	4.63077	0.362710	0.181355	−	0.983418i	$-0.441952\pi$
$163$	4.63077	0.362710	0.181355	+	0.983418i	$0.441952\pi$
$164$	−15.2908	−1.19401
$165$	3.47901	0.270840
$166$	−12.4716	−0.967984
$167$	−9.91744	−0.767434	−0.383717	−	0.923451i	$-0.625356\pi$
$167$	−9.91744	−0.767434	−0.383717	+	0.923451i	$0.625356\pi$
$168$	−1.51809	−0.117123
$169$	−5.44442	−0.418801
$170$	−4.17259	−0.320023
$171$	3.84256	0.293848
$172$	−55.6775	−4.24537
$173$	17.5880	1.33719	0.668596	−	0.743626i	$-0.266896\pi$
$173$	17.5880	1.33719	0.668596	+	0.743626i	$0.266896\pi$
$174$	−21.7336	−1.64762
$175$	−0.281670	−0.0212923
$176$	32.5004	2.44981
$177$	8.90654	0.669457
$178$	−14.0496	−1.05306
$179$	15.0184	1.12253	0.561265	−	0.827636i	$-0.310315\pi$
$179$	15.0184	1.12253	0.561265	+	0.827636i	$0.310315\pi$
$180$	10.0375	0.748153
$181$	4.93867	0.367088	0.183544	−	0.983011i	$-0.441243\pi$
$181$	4.93867	0.367088	0.183544	+	0.983011i	$0.441243\pi$
$182$	−0.494529	−0.0366569
$183$	18.3980	1.36002
$184$	−40.6824	−2.99915
$185$	−0.794810	−0.0584356
$186$	22.5404	1.65274
$187$	3.51903	0.257337
$188$	76.2477	5.56093
$189$	−0.121522	−0.00883946
$190$	−3.96288	−0.287498
$191$	−13.0301	−0.942826	−0.471413	−	0.881912i	$-0.656256\pi$
$191$	−13.0301	−0.942826	−0.471413	+	0.881912i	$0.656256\pi$
$192$	92.9700	6.70953
$193$	−10.4070	−0.749113	−0.374557	−	0.927204i	$-0.622205\pi$
$193$	−10.4070	−0.749113	−0.374557	+	0.927204i	$0.622205\pi$
$194$	14.4900	1.04032
$195$	5.05352	0.361890
$196$	−39.9392	−2.85280
$197$	−11.3991	−0.812154	−0.406077	−	0.913839i	$-0.633104\pi$
$197$	−11.3991	−0.812154	−0.406077	+	0.913839i	$0.633104\pi$
$198$	−11.4309	−0.812361
$199$	−21.0523	−1.49236	−0.746180	−	0.665744i	$-0.768114\pi$
$199$	−21.0523	−1.49236	−0.746180	+	0.665744i	$0.768114\pi$
$200$	44.7653	3.16539
$201$	3.29147	0.232162
$202$	7.78171	0.547519
$203$	0.222950	0.0156480
$204$	24.1530	1.69105
$205$	−2.16444	−0.151171
$206$	−33.7408	−2.35083
$207$	8.59478	0.597379
$208$	47.2093	3.27337
$209$	3.34217	0.231183
$210$	−0.330763	−0.0228248
$211$	−4.69284	−0.323068	−0.161534	−	0.986867i	$-0.551644\pi$
$211$	−4.69284	−0.323068	−0.161534	+	0.986867i	$0.551644\pi$
$212$	−20.1800	−1.38597
$213$	2.27500	0.155881
$214$	−52.6561	−3.59950
$215$	−7.88127	−0.537498
$216$	19.3133	1.31411
$217$	−0.231227	−0.0156967
$218$	12.8046	0.867240
$219$	36.4701	2.46442
$220$	8.73041	0.588604
$221$	5.11166	0.343848
$222$	6.21251	0.416956
$223$	11.4325	0.765578	0.382789	−	0.923836i	$-0.374964\pi$
$223$	11.4325	0.765578	0.382789	+	0.923836i	$0.374964\pi$
$224$	−1.75536	−0.117285
$225$	−9.45737	−0.630491
$226$	2.77651	0.184691
$227$	3.41894	0.226923	0.113462	−	0.993542i	$-0.463806\pi$
$227$	3.41894	0.226923	0.113462	+	0.993542i	$0.463806\pi$
$228$	22.9391	1.51918
$229$	10.4081	0.687784	0.343892	−	0.939009i	$-0.388255\pi$
$229$	10.4081	0.687784	0.343892	+	0.939009i	$0.388255\pi$
$230$	−8.86391	−0.584469
$231$	0.278956	0.0183539
$232$	−35.4331	−2.32629
$233$	4.95425	0.324563	0.162282	−	0.986744i	$-0.448115\pi$
$233$	4.95425	0.324563	0.162282	+	0.986744i	$0.448115\pi$
$234$	−16.6043	−1.08546
$235$	10.7930	0.704059
$236$	22.3506	1.45490
$237$	23.2264	1.50872
$238$	−0.334569	−0.0216869
$239$	−0.540985	−0.0349934	−0.0174967	−	0.999847i	$-0.505570\pi$
$239$	−0.540985	−0.0349934	−0.0174967	+	0.999847i	$0.505570\pi$
$240$	31.5757	2.03821
$241$	−10.4044	−0.670208	−0.335104	−	0.942181i	$-0.608771\pi$
$241$	−10.4044	−0.670208	−0.335104	+	0.942181i	$0.608771\pi$
$242$	20.5993	1.32417
$243$	−18.9290	−1.21430
$244$	46.1689	2.95566
$245$	−5.65348	−0.361187
$246$	16.9180	1.07865
$247$	4.85476	0.308901
$248$	36.7484	2.33353
$249$	10.2189	0.647597
$250$	20.9723	1.32641
$251$	−5.12432	−0.323444	−0.161722	−	0.986836i	$-0.551705\pi$
$251$	−5.12432	−0.323444	−0.161722	+	0.986836i	$0.551705\pi$
$252$	0.804834	0.0506998
$253$	7.47554	0.469983
$254$	14.0037	0.878671
$255$	3.41891	0.214101
$256$	82.8728	5.17955
$257$	16.8150	1.04889	0.524446	−	0.851444i	$-0.324272\pi$
$257$	16.8150	1.04889	0.524446	+	0.851444i	$0.324272\pi$
$258$	61.6027	3.83522
$259$	−0.0637299	−0.00395998
$260$	12.6816	0.786478
$261$	7.48578	0.463358
$262$	−44.3957	−2.74278
$263$	−10.7247	−0.661312	−0.330656	−	0.943751i	$-0.607270\pi$
$263$	−10.7247	−0.661312	−0.330656	+	0.943751i	$0.607270\pi$
$264$	−44.3339	−2.72856
$265$	−2.85652	−0.175475
$266$	−0.317754	−0.0194827
$267$	11.5119	0.704515
$268$	8.25979	0.504547
$269$	−9.09405	−0.554474	−0.277237	−	0.960802i	$-0.589419\pi$
$269$	−9.09405	−0.554474	−0.277237	+	0.960802i	$0.589419\pi$
$270$	4.20800	0.256091
$271$	−9.46710	−0.575085	−0.287543	−	0.957768i	$-0.592838\pi$
$271$	−9.46710	−0.575085	−0.287543	+	0.957768i	$0.592838\pi$
$272$	31.9390	1.93659
$273$	0.405204	0.0245241
$274$	0.357404	0.0215916
$275$	−8.22580	−0.496035
$276$	51.3087	3.08842
$277$	16.8303	1.01123	0.505617	−	0.862758i	$-0.331265\pi$
$277$	16.8303	1.01123	0.505617	+	0.862758i	$0.331265\pi$
$278$	17.3120	1.03831
$279$	−7.76367	−0.464799
$280$	−0.539256	−0.0322267
$281$	−6.66991	−0.397894	−0.198947	−	0.980010i	$-0.563752\pi$
$281$	−6.66991	−0.397894	−0.198947	+	0.980010i	$0.563752\pi$
$282$	−84.3620	−5.02368
$283$	12.7318	0.756830	0.378415	−	0.925636i	$-0.376469\pi$
$283$	12.7318	0.756830	0.378415	+	0.925636i	$0.376469\pi$
$284$	5.70902	0.338768
$285$	3.24709	0.192341
$286$	−14.4420	−0.853976
$287$	−0.173551	−0.0102444
$288$	−58.9380	−3.47296
$289$	−13.5418	−0.796574
$290$	−7.72018	−0.453345
$291$	−11.8728	−0.695994
$292$	91.5200	5.35581
$293$	18.7635	1.09617	0.548087	−	0.836422i	$-0.315356\pi$
$293$	18.7635	1.09617	0.548087	+	0.836422i	$0.315356\pi$
$294$	44.1895	2.57718
$295$	3.16377	0.184202
$296$	10.1285	0.588706
$297$	−3.54890	−0.205928
$298$	−64.6219	−3.74345
$299$	10.8588	0.627980
$300$	−56.4582	−3.25961
$301$	−0.631940	−0.0364244
$302$	−13.4146	−0.771922
$303$	−6.37614	−0.366299
$304$	30.3338	1.73976
$305$	6.53531	0.374211
$306$	−11.2335	−0.642176
$307$	17.8824	1.02060	0.510300	−	0.859996i	$-0.329534\pi$
$307$	17.8824	1.02060	0.510300	+	0.859996i	$0.329534\pi$
$308$	0.700026	0.0398877
$309$	27.6464	1.57275
$310$	8.00677	0.454754
$311$	32.8704	1.86391	0.931955	−	0.362574i	$-0.118102\pi$
$311$	32.8704	1.86391	0.931955	+	0.362574i	$0.118102\pi$
$312$	−64.3983	−3.64584
$313$	−8.36790	−0.472982	−0.236491	−	0.971634i	$-0.575997\pi$
$313$	−8.36790	−0.472982	−0.236491	+	0.971634i	$0.575997\pi$
$314$	6.12236	0.345505
$315$	0.113926	0.00641901
$316$	58.2857	3.27883
$317$	9.82410	0.551776	0.275888	−	0.961190i	$-0.411028\pi$
$317$	9.82410	0.551776	0.275888	+	0.961190i	$0.411028\pi$
$318$	22.3276	1.25207
$319$	6.51096	0.364544
$320$	33.0247	1.84614
$321$	43.1451	2.40812
$322$	−0.710731	−0.0396075
$323$	3.28444	0.182751
$324$	−61.6204	−3.42335
$325$	−11.9486	−0.662789
$326$	−12.8574	−0.712104
$327$	−10.4918	−0.580198
$328$	27.5821	1.52296
$329$	0.865412	0.0477117
$330$	−9.65950	−0.531738
$331$	−9.22124	−0.506845	−0.253422	−	0.967356i	$-0.581556\pi$
$331$	−9.22124	−0.506845	−0.253422	+	0.967356i	$0.581556\pi$
$332$	25.6439	1.40739
$333$	−2.13980	−0.117260
$334$	27.5359	1.50670
$335$	1.16919	0.0638797
$336$	2.53182	0.138122
$337$	15.5889	0.849180	0.424590	−	0.905386i	$-0.360418\pi$
$337$	15.5889	0.849180	0.424590	+	0.905386i	$0.360418\pi$
$338$	15.1165	0.822229
$339$	−2.27500	−0.123561
$340$	8.57961	0.465295
$341$	−6.75266	−0.365677
$342$	−10.6689	−0.576909
$343$	−0.906892	−0.0489676
$344$	100.433	5.41499
$345$	7.26286	0.391019
$346$	−48.8333	−2.62530
$347$	−27.3320	−1.46726	−0.733630	−	0.679549i	$-0.762175\pi$
$347$	−27.3320	−1.46726	−0.733630	+	0.679549i	$0.762175\pi$
$348$	44.6883	2.39554
$349$	11.7105	0.626850	0.313425	−	0.949613i	$-0.398524\pi$
$349$	11.7105	0.626850	0.313425	+	0.949613i	$0.398524\pi$
$350$	0.782061	0.0418029
$351$	−5.15505	−0.275156
$352$	−51.2629	−2.73232
$353$	−32.3476	−1.72169	−0.860845	−	0.508868i	$-0.830064\pi$
$353$	−32.3476	−1.72169	−0.860845	+	0.508868i	$0.830064\pi$
$354$	−24.7291	−1.31434
$355$	0.808124	0.0428908
$356$	28.8885	1.53109
$357$	0.274137	0.0145089
$358$	−41.6988	−2.20385
$359$	29.8905	1.57756	0.788781	−	0.614675i	$-0.210713\pi$
$359$	29.8905	1.57756	0.788781	+	0.614675i	$0.210713\pi$
$360$	−18.1061	−0.954273
$361$	−15.8806	−0.835823
$362$	−13.7123	−0.720701
$363$	−16.8785	−0.885892
$364$	1.01684	0.0532970
$365$	12.9549	0.678088
$366$	−51.0822	−2.67011
$367$	21.6455	1.12988	0.564942	−	0.825130i	$-0.308898\pi$
$367$	21.6455	1.12988	0.564942	+	0.825130i	$0.308898\pi$
$368$	67.8486	3.53685
$369$	−5.82714	−0.303349
$370$	2.20680	0.114726
$371$	−0.229043	−0.0118913
$372$	−46.3472	−2.40299
$373$	−15.2523	−0.789736	−0.394868	−	0.918738i	$-0.629210\pi$
$373$	−15.2523	−0.789736	−0.394868	+	0.918738i	$0.629210\pi$
$374$	−9.77063	−0.505228
$375$	−17.1842	−0.887388
$376$	−137.538	−7.09300
$377$	9.45766	0.487094
$378$	0.337408	0.0173544
$379$	−13.6637	−0.701856	−0.350928	−	0.936402i	$-0.614134\pi$
$379$	−13.6637	−0.701856	−0.350928	+	0.936402i	$0.614134\pi$
$380$	8.14842	0.418005
$381$	−11.4743	−0.587845
$382$	36.1783	1.85104
$383$	−21.7653	−1.11216	−0.556079	−	0.831130i	$-0.687695\pi$
$383$	−21.7653	−1.11216	−0.556079	+	0.831130i	$0.687695\pi$
$384$	−134.873	−6.88269
$385$	0.0990902	0.00505011
$386$	28.8952	1.47073
$387$	−21.2180	−1.07857
$388$	−29.7942	−1.51257
$389$	−17.3816	−0.881283	−0.440641	−	0.897683i	$-0.645249\pi$
$389$	−17.3816	−0.881283	−0.440641	+	0.897683i	$0.645249\pi$
$390$	−14.0312	−0.710495
$391$	7.34642	0.371525
$392$	72.0437	3.63876
$393$	36.3767	1.83496
$394$	31.6498	1.59450
$395$	8.25046	0.415126
$396$	23.5041	1.18113
$397$	−27.0035	−1.35527	−0.677634	−	0.735399i	$-0.736995\pi$
$397$	−27.0035	−1.35527	−0.677634	+	0.735399i	$0.736995\pi$
$398$	58.4521	2.92994
$399$	0.260360	0.0130343
$400$	−74.6580	−3.73290
$401$	31.6792	1.58198	0.790992	−	0.611826i	$-0.209565\pi$
$401$	31.6792	1.58198	0.790992	+	0.611826i	$0.209565\pi$
$402$	−9.13880	−0.455802
$403$	−9.80876	−0.488609
$404$	−16.0006	−0.796061
$405$	−8.72249	−0.433424
$406$	−0.619024	−0.0307216
$407$	−1.86115	−0.0922536
$408$	−43.5681	−2.15694
$409$	−1.28090	−0.0633366	−0.0316683	−	0.999498i	$-0.510082\pi$
$409$	−1.28090	−0.0633366	−0.0316683	+	0.999498i	$0.510082\pi$
$410$	6.00960	0.296793
$411$	−0.292848	−0.0144451
$412$	69.3773	3.41798
$413$	0.253679	0.0124827
$414$	−23.8635	−1.17283
$415$	3.62995	0.178187
$416$	−74.4633	−3.65086
$417$	−14.1850	−0.694644
$418$	−9.27958	−0.453879
$419$	−6.94097	−0.339089	−0.169544	−	0.985523i	$-0.554230\pi$
$419$	−6.94097	−0.339089	−0.169544	+	0.985523i	$0.554230\pi$
$420$	0.680110	0.0331860
$421$	−32.0209	−1.56060	−0.780302	−	0.625403i	$-0.784934\pi$
$421$	−32.0209	−1.56060	−0.780302	+	0.625403i	$0.784934\pi$
$422$	13.0297	0.634277
$423$	29.0571	1.41280
$424$	36.4014	1.76781
$425$	−8.08372	−0.392118
$426$	−6.31657	−0.306039
$427$	0.524018	0.0253590
$428$	108.271	5.23346
$429$	11.8334	0.571324
$430$	21.8824	1.05526
$431$	13.1659	0.634178	0.317089	−	0.948396i	$-0.397295\pi$
$431$	13.1659	0.634178	0.317089	+	0.948396i	$0.397295\pi$
$432$	−32.2101	−1.54971
$433$	26.4103	1.26920	0.634599	−	0.772842i	$-0.281165\pi$
$433$	26.4103	1.26920	0.634599	+	0.772842i	$0.281165\pi$
$434$	0.642004	0.0308172
$435$	6.32572	0.303295
$436$	−26.3287	−1.26092
$437$	6.97720	0.333765
$438$	−101.260	−4.83837
$439$	−37.6327	−1.79611	−0.898056	−	0.439881i	$-0.855021\pi$
$439$	−37.6327	−1.79611	−0.898056	+	0.439881i	$0.855021\pi$
$440$	−15.7482	−0.750768
$441$	−15.2204	−0.724779
$442$	−14.1926	−0.675073
$443$	−24.2804	−1.15360	−0.576798	−	0.816887i	$-0.695698\pi$
$443$	−24.2804	−1.15360	−0.576798	+	0.816887i	$0.695698\pi$
$444$	−12.7741	−0.606230
$445$	4.08923	0.193848
$446$	−31.7425	−1.50305
$447$	52.9496	2.50443
$448$	2.64800	0.125106
$449$	−3.16357	−0.149298	−0.0746491	−	0.997210i	$-0.523784\pi$
$449$	−3.16357	−0.149298	−0.0746491	+	0.997210i	$0.523784\pi$
$450$	26.2585	1.23784
$451$	−5.06831	−0.238657
$452$	−5.70902	−0.268530
$453$	10.9916	0.516429
$454$	−9.49274	−0.445516
$455$	0.143936	0.00674783
$456$	−41.3785	−1.93772
$457$	10.4410	0.488412	0.244206	−	0.969723i	$-0.421473\pi$
$457$	10.4410	0.488412	0.244206	+	0.969723i	$0.421473\pi$
$458$	−28.8981	−1.35032
$459$	−3.48760	−0.162787
$460$	18.2258	0.849784
$461$	−30.9367	−1.44086	−0.720432	−	0.693526i	$-0.756056\pi$
$461$	−30.9367	−1.44086	−0.720432	+	0.693526i	$0.756056\pi$
$462$	−0.774523	−0.0360341
$463$	6.57286	0.305467	0.152733	−	0.988267i	$-0.451192\pi$
$463$	6.57286	0.305467	0.152733	+	0.988267i	$0.451192\pi$
$464$	59.0940	2.74337
$465$	−6.56055	−0.304238
$466$	−13.7555	−0.637212
$467$	−4.44571	−0.205723	−0.102861	−	0.994696i	$-0.532800\pi$
$467$	−4.44571	−0.205723	−0.102861	+	0.994696i	$0.532800\pi$
$468$	34.1415	1.57819
$469$	0.0937487	0.00432891
$470$	−29.9670	−1.38227
$471$	−5.01650	−0.231148
$472$	−40.3168	−1.85573
$473$	−18.4550	−0.848560
$474$	−64.4885	−2.96205
$475$	−7.67745	−0.352265
$476$	0.687935	0.0315315
$477$	−7.69037	−0.352118
$478$	1.50205	0.0687023
$479$	39.5203	1.80573	0.902864	−	0.429927i	$-0.141461\pi$
$479$	39.5203	1.80573	0.902864	+	0.429927i	$0.141461\pi$
$480$	−49.8045	−2.27325
$481$	−2.70346	−0.123267
$482$	28.8880	1.31581
$483$	0.582355	0.0264981
$484$	−42.3559	−1.92527
$485$	−4.21743	−0.191504
$486$	52.5566	2.38402
$487$	16.1177	0.730365	0.365182	−	0.930936i	$-0.381007\pi$
$487$	16.1177	0.730365	0.365182	+	0.930936i	$0.381007\pi$
$488$	−83.2812	−3.76996
$489$	10.5350	0.476410
$490$	15.6969	0.709116
$491$	−32.8699	−1.48340	−0.741700	−	0.670732i	$-0.765980\pi$
$491$	−32.8699	−1.48340	−0.741700	+	0.670732i	$0.765980\pi$
$492$	−34.7866	−1.56830
$493$	6.39850	0.288174
$494$	−13.4793	−0.606462
$495$	3.32706	0.149540
$496$	−61.2877	−2.75190
$497$	0.0647974	0.00290656
$498$	−28.3729	−1.27142
$499$	9.70745	0.434565	0.217283	−	0.976109i	$-0.430281\pi$
$499$	9.70745	0.434565	0.217283	+	0.976109i	$0.430281\pi$
$500$	−43.1230	−1.92852
$501$	−22.5622	−1.00801
$502$	14.2277	0.635015
$503$	13.2607	0.591265	0.295633	−	0.955302i	$-0.404470\pi$
$503$	13.2607	0.591265	0.295633	+	0.955302i	$0.404470\pi$
$504$	−1.45179	−0.0646679
$505$	−2.26492	−0.100788
$506$	−20.7559	−0.922714
$507$	−12.3861	−0.550085
$508$	−28.7942	−1.27754
$509$	2.09989	0.0930762	0.0465381	−	0.998917i	$-0.485181\pi$
$509$	2.09989	0.0930762	0.0465381	+	0.998917i	$0.485181\pi$
$510$	−9.49266	−0.420342
$511$	1.03875	0.0459518
$512$	−111.528	−4.92889
$513$	−3.31232	−0.146242
$514$	−46.6871	−2.05928
$515$	9.82051	0.432743
$516$	−126.666	−5.57618
$517$	25.2732	1.11151
$518$	0.176947	0.00777460
$519$	40.0128	1.75637
$520$	−22.8755	−1.00316
$521$	14.1245	0.618803	0.309402	−	0.950931i	$-0.399871\pi$
$521$	14.1245	0.618803	0.309402	+	0.950931i	$0.399871\pi$
$522$	−20.7844	−0.909707
$523$	−22.7865	−0.996383	−0.498191	−	0.867067i	$-0.666002\pi$
$523$	−22.7865	−0.996383	−0.498191	+	0.867067i	$0.666002\pi$
$524$	91.2857	3.98784
$525$	−0.640801	−0.0279668
$526$	29.7772	1.29835
$527$	−6.63603	−0.289070
$528$	73.9385	3.21776
$529$	−7.39386	−0.321472
$530$	7.93117	0.344508
$531$	8.51754	0.369630
$532$	0.653361	0.0283268
$533$	−7.36210	−0.318888
$534$	−31.9628	−1.38317
$535$	15.3260	0.662599
$536$	−14.8993	−0.643552
$537$	34.1670	1.47441
$538$	25.2497	1.08859
$539$	−13.2383	−0.570214
$540$	−8.65243	−0.372341
$541$	30.0074	1.29012	0.645060	−	0.764132i	$-0.276832\pi$
$541$	30.0074	1.29012	0.645060	+	0.764132i	$0.276832\pi$
$542$	26.2855	1.12906
$543$	11.2355	0.482161
$544$	−50.3775	−2.15992
$545$	−3.72689	−0.159642
$546$	−1.12505	−0.0481479
$547$	37.7676	1.61482	0.807412	−	0.589988i	$-0.200868\pi$
$547$	37.7676	1.61482	0.807412	+	0.589988i	$0.200868\pi$
$548$	−0.734889	−0.0313929
$549$	17.5944	0.750912
$550$	22.8390	0.973860
$551$	6.07692	0.258886
$552$	−92.5526	−3.93930
$553$	0.661543	0.0281317
$554$	−46.7295	−1.98535
$555$	−1.80820	−0.0767536
$556$	−35.5967	−1.50964
$557$	35.6879	1.51214	0.756072	−	0.654488i	$-0.227116\pi$
$557$	35.6879	1.51214	0.756072	+	0.654488i	$0.227116\pi$
$558$	21.5559	0.912535
$559$	−26.8072	−1.13382
$560$	0.899351	0.0380045
$561$	8.00581	0.338006
$562$	18.5191	0.781181
$563$	−23.8555	−1.00539	−0.502696	−	0.864464i	$-0.667658\pi$
$563$	−23.8555	−1.00539	−0.502696	+	0.864464i	$0.667658\pi$
$564$	173.464	7.30414
$565$	−0.808124	−0.0339980
$566$	−35.3501	−1.48588
$567$	−0.699392	−0.0293717
$568$	−10.2981	−0.432100
$569$	24.5315	1.02842	0.514208	−	0.857666i	$-0.328086\pi$
$569$	24.5315	1.02842	0.514208	+	0.857666i	$0.328086\pi$
$570$	−9.01557	−0.377621
$571$	−3.59181	−0.150313	−0.0751563	−	0.997172i	$-0.523946\pi$
$571$	−3.59181	−0.150313	−0.0751563	+	0.997172i	$0.523946\pi$
$572$	29.6955	1.24163
$573$	−29.6436	−1.23838
$574$	0.481865	0.0201127
$575$	−17.1724	−0.716138
$576$	88.9094	3.70456
$577$	8.73783	0.363760	0.181880	−	0.983321i	$-0.441782\pi$
$577$	8.73783	0.363760	0.181880	+	0.983321i	$0.441782\pi$
$578$	37.5988	1.56391
$579$	−23.6760	−0.983941
$580$	15.8741	0.659137
$581$	0.291059	0.0120751
$582$	32.9649	1.36644
$583$	−6.68890	−0.277026
$584$	−165.087	−6.83136
$585$	4.83280	0.199812
$586$	−52.0970	−2.15211
$587$	2.30683	0.0952131	0.0476065	−	0.998866i	$-0.484841\pi$
$587$	2.30683	0.0952131	0.0476065	+	0.998866i	$0.484841\pi$
$588$	−90.8617	−3.74708
$589$	−6.30251	−0.259690
$590$	−8.78425	−0.361642
$591$	−25.9331	−1.06674
$592$	−16.8919	−0.694253
$593$	−12.6469	−0.519346	−0.259673	−	0.965697i	$-0.583615\pi$
$593$	−12.6469	−0.519346	−0.259673	+	0.965697i	$0.583615\pi$
$594$	9.85356	0.404297
$595$	0.0973787	0.00399214
$596$	132.875	5.44275
$597$	−47.8941	−1.96018
$598$	−30.1496	−1.23291
$599$	−38.6916	−1.58090	−0.790448	−	0.612530i	$-0.790152\pi$
$599$	−38.6916	−1.58090	−0.790448	+	0.612530i	$0.790152\pi$
$600$	101.841	4.15765
$601$	−38.9299	−1.58798	−0.793991	−	0.607930i	$-0.792000\pi$
$601$	−38.9299	−1.58798	−0.793991	+	0.607930i	$0.792000\pi$
$602$	1.75459	0.0715117
$603$	3.14771	0.128185
$604$	27.5828	1.12233
$605$	−5.99557	−0.243754
$606$	17.7034	0.719152
$607$	44.4595	1.80455	0.902277	−	0.431157i	$-0.141894\pi$
$607$	44.4595	1.80455	0.902277	+	0.431157i	$0.141894\pi$
$608$	−47.8456	−1.94039
$609$	0.507212	0.0205533
$610$	−18.1454	−0.734684
$611$	36.7112	1.48518
$612$	23.0981	0.933687
$613$	−31.9102	−1.28884	−0.644420	−	0.764672i	$-0.722901\pi$
$613$	−31.9102	−1.28884	−0.644420	+	0.764672i	$0.722901\pi$
$614$	−49.6506	−2.00374
$615$	−4.92411	−0.198559
$616$	−1.26273	−0.0508770
$617$	−6.80414	−0.273924	−0.136962	−	0.990576i	$-0.543734\pi$
$617$	−6.80414	−0.273924	−0.136962	+	0.990576i	$0.543734\pi$
$618$	−76.7605	−3.08776
$619$	−31.7154	−1.27475	−0.637375	−	0.770554i	$-0.719980\pi$
$619$	−31.7154	−1.27475	−0.637375	+	0.770554i	$0.719980\pi$
$620$	−16.4634	−0.661186
$621$	−7.40877	−0.297304
$622$	−91.2651	−3.65940
$623$	0.327885	0.0131364
$624$	107.401	4.29949
$625$	15.6305	0.625221
$626$	23.2336	0.928601
$627$	7.60345	0.303653
$628$	−12.5887	−0.502344
$629$	−1.82900	−0.0729270
$630$	−0.316317	−0.0126024
$631$	27.8062	1.10695	0.553474	−	0.832867i	$-0.313302\pi$
$631$	27.8062	1.10695	0.553474	+	0.832867i	$0.313302\pi$
$632$	−105.138	−4.18216
$633$	−10.6762	−0.424342
$634$	−27.2767	−1.08330
$635$	−4.07588	−0.161746
$636$	−45.9096	−1.82043
$637$	−19.2297	−0.761906
$638$	−18.0778	−0.715705
$639$	2.17564	0.0860670
$640$	−47.9093	−1.89378
$641$	34.5490	1.36460	0.682301	−	0.731071i	$-0.260979\pi$
$641$	34.5490	1.36460	0.682301	+	0.731071i	$0.260979\pi$
$642$	−119.793	−4.72785
$643$	26.6622	1.05145	0.525726	−	0.850654i	$-0.323794\pi$
$643$	26.6622	1.05145	0.525726	+	0.850654i	$0.323794\pi$
$644$	1.46139	0.0575870
$645$	−17.9299	−0.705989
$646$	−9.11930	−0.358794
$647$	−7.29392	−0.286754	−0.143377	−	0.989668i	$-0.545796\pi$
$647$	−7.29392	−0.286754	−0.143377	+	0.989668i	$0.545796\pi$
$648$	111.153	4.36650
$649$	7.40836	0.290804
$650$	33.1754	1.30125
$651$	−0.526041	−0.0206172
$652$	26.4371	1.03536
$653$	10.8166	0.423286	0.211643	−	0.977347i	$-0.432119\pi$
$653$	10.8166	0.423286	0.211643	+	0.977347i	$0.432119\pi$
$654$	29.1306	1.13910
$655$	12.9217	0.504892
$656$	−46.0004	−1.79601
$657$	34.8772	1.36069
$658$	−2.40283	−0.0936720
$659$	−14.5089	−0.565186	−0.282593	−	0.959240i	$-0.591195\pi$
$659$	−14.5089	−0.565186	−0.282593	+	0.959240i	$0.591195\pi$
$660$	19.8617	0.773116
$661$	−3.39163	−0.131919	−0.0659595	−	0.997822i	$-0.521011\pi$
$661$	−3.39163	−0.131919	−0.0659595	+	0.997822i	$0.521011\pi$
$662$	25.6029	0.995084
$663$	11.6290	0.451635
$664$	−46.2574	−1.79514
$665$	0.0924846	0.00358640
$666$	5.94117	0.230216
$667$	13.5924	0.526302
$668$	−56.6189	−2.19065
$669$	26.0090	1.00557
$670$	−3.24627	−0.125414
$671$	15.3032	0.590775
$672$	−3.99345	−0.154051
$673$	36.9113	1.42283	0.711413	−	0.702774i	$-0.248056\pi$
$673$	36.9113	1.42283	0.711413	+	0.702774i	$0.248056\pi$
$674$	−43.2827	−1.66719
$675$	8.15233	0.313783
$676$	−31.0823	−1.19547
$677$	15.3112	0.588456	0.294228	−	0.955735i	$-0.404938\pi$
$677$	15.3112	0.588456	0.294228	+	0.955735i	$0.404938\pi$
$678$	6.31657	0.242587
$679$	−0.338164	−0.0129776
$680$	−15.4762	−0.593486
$681$	7.77811	0.298058
$682$	18.7488	0.717931
$683$	0.906536	0.0346876	0.0173438	−	0.999850i	$-0.494479\pi$
$683$	0.906536	0.0346876	0.0173438	+	0.999850i	$0.494479\pi$
$684$	21.9373	0.838792
$685$	−0.104025	−0.00397460
$686$	2.51800	0.0961376
$687$	23.6784	0.903386
$688$	−167.499	−6.38583
$689$	−9.71614	−0.370156
$690$	−20.1654	−0.767685
$691$	−31.7285	−1.20701	−0.603505	−	0.797360i	$-0.706229\pi$
$691$	−31.7285	−1.20701	−0.603505	+	0.797360i	$0.706229\pi$
$692$	100.410	3.81703
$693$	0.266772	0.0101338
$694$	75.8877	2.88066
$695$	−5.03879	−0.191132
$696$	−80.6103	−3.05553
$697$	−4.98077	−0.188660
$698$	−32.5144	−1.23069
$699$	11.2709	0.426306
$700$	−1.60806	−0.0607790
$701$	17.4331	0.658441	0.329220	−	0.944253i	$-0.393214\pi$
$701$	17.4331	0.658441	0.329220	+	0.944253i	$0.393214\pi$
$702$	14.3130	0.540211
$703$	−1.73708	−0.0655151
$704$	77.3314	2.91453
$705$	24.5542	0.924763
$706$	89.8135	3.38018
$707$	−0.181607	−0.00683005
$708$	50.8476	1.91097
$709$	41.4337	1.55608	0.778038	−	0.628217i	$-0.216215\pi$
$709$	41.4337	1.55608	0.778038	+	0.628217i	$0.216215\pi$
$710$	−2.24377	−0.0842070
$711$	22.2120	0.833015
$712$	−52.1101	−1.95291
$713$	−14.0970	−0.527938
$714$	−0.761145	−0.0284852
$715$	4.20346	0.157201
$716$	85.7405	3.20427
$717$	−1.23074	−0.0459630
$718$	−82.9914	−3.09721
$719$	24.8367	0.926251	0.463126	−	0.886293i	$-0.346728\pi$
$719$	24.8367	0.926251	0.463126	+	0.886293i	$0.346728\pi$
$720$	30.1966	1.12536
$721$	0.787433	0.0293256
$722$	44.0928	1.64096
$723$	−23.6701	−0.880301
$724$	28.1950	1.04786
$725$	−14.9566	−0.555475
$726$	46.8634	1.73926
$727$	−7.49298	−0.277899	−0.138950	−	0.990299i	$-0.544373\pi$
$727$	−7.49298	−0.277899	−0.138950	+	0.990299i	$0.544373\pi$
$728$	−1.83422	−0.0679806
$729$	−10.6830	−0.395668
$730$	−35.9693	−1.33128
$731$	−18.1362	−0.670791
$732$	105.034	3.88218
$733$	7.42383	0.274205	0.137103	−	0.990557i	$-0.456221\pi$
$733$	7.42383	0.274205	0.137103	+	0.990557i	$0.456221\pi$
$734$	−60.0989	−2.21829
$735$	−12.8617	−0.474410
$736$	−107.018	−3.94473
$737$	2.73780	0.100848
$738$	16.1791	0.595562
$739$	12.9874	0.477750	0.238875	−	0.971050i	$-0.423221\pi$
$739$	12.9874	0.477750	0.238875	+	0.971050i	$0.423221\pi$
$740$	−4.53759	−0.166805
$741$	11.0446	0.405733
$742$	0.635942	0.0233462
$743$	3.84587	0.141091	0.0705457	−	0.997509i	$-0.477526\pi$
$743$	3.84587	0.141091	0.0705457	+	0.997509i	$0.477526\pi$
$744$	83.6028	3.06503
$745$	18.8087	0.689097
$746$	42.3483	1.55048
$747$	9.77259	0.357560
$748$	20.0902	0.734571
$749$	1.22887	0.0449021
$750$	47.7121	1.74220
$751$	19.8763	0.725295	0.362647	−	0.931926i	$-0.381873\pi$
$751$	19.8763	0.725295	0.362647	+	0.931926i	$0.381873\pi$
$752$	229.382	8.36469
$753$	−11.6578	−0.424835
$754$	−26.2593	−0.956308
$755$	3.90441	0.142096
$756$	−0.693774	−0.0252323
$757$	−28.2273	−1.02594	−0.512970	−	0.858407i	$-0.671455\pi$
$757$	−28.2273	−1.02594	−0.512970	+	0.858407i	$0.671455\pi$
$758$	37.9374	1.37795
$759$	17.0069	0.617311
$760$	−14.6984	−0.533167
$761$	27.5991	1.00047	0.500233	−	0.865891i	$-0.333248\pi$
$761$	27.5991	1.00047	0.500233	+	0.865891i	$0.333248\pi$
$762$	31.8585	1.15411
$763$	−0.298831	−0.0108184
$764$	−74.3892	−2.69131
$765$	3.26959	0.118212
$766$	60.4317	2.18349
$767$	10.7612	0.388565
$768$	188.536	6.80320
$769$	4.04012	0.145691	0.0728453	−	0.997343i	$-0.476792\pi$
$769$	4.04012	0.145691	0.0728453	+	0.997343i	$0.476792\pi$
$770$	−0.275125	−0.00991483
$771$	38.2542	1.37769
$772$	−59.4138	−2.13835
$773$	−14.6544	−0.527081	−0.263540	−	0.964648i	$-0.584890\pi$
$773$	−14.6544	−0.527081	−0.263540	+	0.964648i	$0.584890\pi$
$774$	58.9121	2.11755
$775$	15.5118	0.557202
$776$	53.7438	1.92929
$777$	−0.144986	−0.00520134
$778$	48.2603	1.73021
$779$	−4.73044	−0.169486
$780$	28.8506	1.03302
$781$	1.89232	0.0677126
$782$	−20.3974	−0.729411
$783$	−6.45281	−0.230604
$784$	−120.152	−4.29114
$785$	−1.78196	−0.0636008
$786$	−101.000	−3.60256
$787$	23.7278	0.845805	0.422903	−	0.906175i	$-0.361011\pi$
$787$	23.7278	0.845805	0.422903	+	0.906175i	$0.361011\pi$
$788$	−65.0779	−2.31830
$789$	−24.3987	−0.868616
$790$	−22.9075	−0.815013
$791$	−0.0647974	−0.00230393
$792$	−42.3976	−1.50653
$793$	22.2291	0.789379
$794$	74.9756	2.66078
$795$	−6.49860	−0.230482
$796$	−120.188	−4.25996
$797$	29.2730	1.03690	0.518452	−	0.855107i	$-0.326509\pi$
$797$	29.2730	1.03690	0.518452	+	0.855107i	$0.326509\pi$
$798$	−0.722891	−0.0255901
$799$	24.8367	0.878658
$800$	117.758	4.16338
$801$	11.0091	0.388986
$802$	−87.9577	−3.10590
$803$	30.3354	1.07051
$804$	18.7910	0.662709
$805$	0.206863	0.00729098
$806$	27.2341	0.959281
$807$	−20.6890	−0.728287
$808$	28.8625	1.01538
$809$	−36.9164	−1.29791	−0.648956	−	0.760826i	$-0.724794\pi$
$809$	−36.9164	−1.29791	−0.648956	+	0.760826i	$0.724794\pi$
$810$	24.2181	0.850938
$811$	56.4508	1.98225	0.991127	−	0.132916i	$-0.0424342\pi$
$811$	56.4508	1.98225	0.991127	+	0.132916i	$0.0424342\pi$
$812$	1.27283	0.0446675
$813$	−21.5377	−0.755360
$814$	5.16750	0.181121
$815$	3.74223	0.131085
$816$	72.6614	2.54366
$817$	−17.2247	−0.602616
$818$	3.55644	0.124348
$819$	0.387506	0.0135406
$820$	−12.3568	−0.431520
$821$	34.4745	1.20317	0.601584	−	0.798809i	$-0.294536\pi$
$821$	34.4745	1.20317	0.601584	+	0.798809i	$0.294536\pi$
$822$	0.813096	0.0283600
$823$	−40.2154	−1.40182	−0.700911	−	0.713249i	$-0.747223\pi$
$823$	−40.2154	−1.40182	−0.700911	+	0.713249i	$0.747223\pi$
$824$	−125.145	−4.35965
$825$	−18.7137	−0.651528
$826$	−0.704343	−0.0245072
$827$	23.9465	0.832702	0.416351	−	0.909204i	$-0.363309\pi$
$827$	23.9465	0.832702	0.416351	+	0.909204i	$0.363309\pi$
$828$	49.0678	1.70522
$829$	−22.4402	−0.779381	−0.389690	−	0.920946i	$-0.627418\pi$
$829$	−22.4402	−0.779381	−0.389690	+	0.920946i	$0.627418\pi$
$830$	−10.0786	−0.349833
$831$	38.2890	1.32823
$832$	112.330	3.89433
$833$	−13.0097	−0.450758
$834$	39.3849	1.36379
$835$	−8.01452	−0.277354
$836$	19.0805	0.659914
$837$	6.69235	0.231321
$838$	19.2717	0.665730
$839$	−29.5184	−1.01909	−0.509545	−	0.860444i	$-0.670186\pi$
$839$	−29.5184	−1.01909	−0.509545	+	0.860444i	$0.670186\pi$
$840$	−1.22681	−0.0423289
$841$	−17.1614	−0.591773
$842$	88.9064	3.06392
$843$	−15.1741	−0.522623
$844$	−26.7915	−0.922202
$845$	−4.39977	−0.151357
$846$	−80.6774	−2.77375
$847$	−0.480740	−0.0165184
$848$	−60.7090	−2.08476
$849$	28.9650	0.994076
$850$	22.4446	0.769842
$851$	−3.88538	−0.133189
$852$	12.9880	0.444963
$853$	−48.0092	−1.64380	−0.821902	−	0.569628i	$-0.807087\pi$
$853$	−48.0092	−1.64380	−0.821902	+	0.569628i	$0.807087\pi$
$854$	−1.45494	−0.0497871
$855$	3.10527	0.106198
$856$	−195.303	−6.67531
$857$	−47.3629	−1.61788	−0.808942	−	0.587888i	$-0.799960\pi$
$857$	−47.3629	−1.61788	−0.808942	+	0.587888i	$0.799960\pi$
$858$	−32.8557	−1.12167
$859$	−22.1310	−0.755102	−0.377551	−	0.925989i	$-0.623234\pi$
$859$	−22.1310	−0.755102	−0.377551	+	0.925989i	$0.623234\pi$
$860$	−44.9943	−1.53429
$861$	−0.394828	−0.0134557
$862$	−36.5552	−1.24508
$863$	23.3819	0.795930	0.397965	−	0.917401i	$-0.369717\pi$
$863$	23.3819	0.795930	0.397965	+	0.917401i	$0.369717\pi$
$864$	50.8050	1.72842
$865$	14.2133	0.483267
$866$	−73.3285	−2.49180
$867$	−30.8075	−1.04628
$868$	−1.32008	−0.0448063
$869$	19.3195	0.655368
$870$	−17.5634	−0.595456
$871$	3.97687	0.134751
$872$	47.4927	1.60831
$873$	−11.3542	−0.384282
$874$	−19.3723	−0.655277
$875$	−0.489446	−0.0165463
$876$	208.208	7.03471
$877$	45.4272	1.53397	0.766984	−	0.641666i	$-0.221757\pi$
$877$	45.4272	1.53397	0.766984	+	0.641666i	$0.221757\pi$
$878$	104.488	3.52629
$879$	42.6869	1.43980
$880$	26.2643	0.885371
$881$	−38.3585	−1.29233	−0.646166	−	0.763197i	$-0.723628\pi$
$881$	−38.3585	−1.29233	−0.646166	+	0.763197i	$0.723628\pi$
$882$	42.2595	1.42295
$883$	14.2894	0.480877	0.240439	−	0.970664i	$-0.422709\pi$
$883$	14.2894	0.480877	0.240439	+	0.970664i	$0.422709\pi$
$884$	29.1826	0.981516
$885$	7.19759	0.241944
$886$	67.4147	2.26484
$887$	−39.4206	−1.32361	−0.661807	−	0.749674i	$-0.730210\pi$
$887$	−39.4206	−1.32361	−0.661807	+	0.749674i	$0.730210\pi$
$888$	23.0423	0.773250
$889$	−0.326815	−0.0109610
$890$	−11.3538	−0.380580
$891$	−20.4248	−0.684256
$892$	65.2685	2.18535
$893$	23.5884	0.789356
$894$	−147.015	−4.91692
$895$	12.1367	0.405687
$896$	−3.84149	−0.128335
$897$	24.7038	0.824836
$898$	8.78370	0.293116
$899$	−12.2781	−0.409496
$900$	−53.9923	−1.79974
$901$	−6.57337	−0.218991
$902$	14.0722	0.468554
$903$	−1.43767	−0.0478425
$904$	10.2981	0.342511
$905$	3.99106	0.132667
$906$	−30.5182	−1.01390
$907$	42.2037	1.40135	0.700675	−	0.713481i	$-0.252882\pi$
$907$	42.2037	1.40135	0.700675	+	0.713481i	$0.252882\pi$
$908$	19.5188	0.647755
$909$	−6.09765	−0.202246
$910$	−0.399640	−0.0132479
$911$	13.0160	0.431238	0.215619	−	0.976478i	$-0.430823\pi$
$911$	13.0160	0.431238	0.215619	+	0.976478i	$0.430823\pi$
$912$	69.0095	2.28513
$913$	8.49997	0.281308
$914$	−28.9897	−0.958894
$915$	14.8679	0.491516
$916$	59.4198	1.96329
$917$	1.03609	0.0342148
$918$	9.68337	0.319599
$919$	−55.6196	−1.83472	−0.917360	−	0.398058i	$-0.869684\pi$
$919$	−55.6196	−1.83472	−0.917360	+	0.398058i	$0.869684\pi$
$920$	−32.8764	−1.08390
$921$	40.6825	1.34053
$922$	85.8960	2.82883
$923$	2.74874	0.0904759
$924$	1.59256	0.0523915
$925$	4.27532	0.140572
$926$	−18.2496	−0.599720
$927$	26.4389	0.868367
$928$	−93.2091	−3.05974
$929$	31.1155	1.02087	0.510434	−	0.859917i	$-0.329485\pi$
$929$	31.1155	1.02087	0.510434	+	0.859917i	$0.329485\pi$
$930$	18.2154	0.597308
$931$	−12.3558	−0.404945
$932$	28.2839	0.926470
$933$	74.7803	2.44820
$934$	12.3436	0.403894
$935$	2.84381	0.0930027
$936$	−61.5857	−2.01299
$937$	−26.5504	−0.867362	−0.433681	−	0.901066i	$-0.642786\pi$
$937$	−26.5504	−0.867362	−0.433681	+	0.901066i	$0.642786\pi$
$938$	−0.260294	−0.00849891
$939$	−19.0370	−0.621249
$940$	61.6176	2.00974
$941$	−26.6620	−0.869155	−0.434578	−	0.900634i	$-0.643102\pi$
$941$	−26.6620	−0.869155	−0.434578	+	0.900634i	$0.643102\pi$
$942$	13.9284	0.453811
$943$	−10.5807	−0.344556
$944$	67.2389	2.18844
$945$	−0.0982052	−0.00319462
$946$	51.2404	1.66597
$947$	−31.2165	−1.01440	−0.507200	−	0.861828i	$-0.669319\pi$
$947$	−31.2165	−1.01440	−0.507200	+	0.861828i	$0.669319\pi$
$948$	132.600	4.30665
$949$	44.0645	1.43039
$950$	21.3165	0.691599
$951$	22.3499	0.724744
$952$	−1.24092	−0.0402185
$953$	−23.0242	−0.745828	−0.372914	−	0.927866i	$-0.621641\pi$
$953$	−23.0242	−0.745828	−0.372914	+	0.927866i	$0.621641\pi$
$954$	21.3524	0.691309
$955$	−10.5300	−0.340741
$956$	−3.08850	−0.0998891
$957$	14.8125	0.478819
$958$	−109.729	−3.54517
$959$	−0.00834100	−0.000269345 0
$960$	75.1313	2.42485
$961$	−18.2661	−0.589230
$962$	7.50618	0.242009
$963$	41.2607	1.32961
$964$	−59.3991	−1.91312
$965$	−8.41016	−0.270733
$966$	−1.61692	−0.0520234
$967$	41.5839	1.33725	0.668624	−	0.743601i	$-0.266884\pi$
$967$	41.5839	1.33725	0.668624	+	0.743601i	$0.266884\pi$
$968$	76.4031	2.45569
$969$	7.47212	0.240039
$970$	11.7097	0.375977
$971$	−44.9406	−1.44221	−0.721106	−	0.692825i	$-0.756366\pi$
$971$	−44.9406	−1.44221	−0.721106	+	0.692825i	$0.756366\pi$
$972$	−108.066	−3.46622
$973$	−0.404023	−0.0129524
$974$	−44.7511	−1.43392
$975$	−27.1831	−0.870556
$976$	138.893	4.44587
$977$	−7.70786	−0.246596	−0.123298	−	0.992370i	$-0.539347\pi$
$977$	−7.70786	−0.246596	−0.123298	+	0.992370i	$0.539347\pi$
$978$	−29.2506	−0.935331
$979$	9.57544	0.306032
$980$	−32.2758	−1.03101
$981$	−10.0336	−0.320347
$982$	91.2638	2.91234
$983$	−12.5318	−0.399701	−0.199850	−	0.979826i	$-0.564046\pi$
$983$	−12.5318	−0.399701	−0.199850	+	0.979826i	$0.564046\pi$
$984$	62.7493	2.00037
$985$	−9.21191	−0.293516
$986$	−17.7655	−0.565769
$987$	1.96882	0.0626681
$988$	27.7159	0.881760
$989$	−38.5270	−1.22509
$990$	−9.23761	−0.293591
$991$	4.51233	0.143339	0.0716695	−	0.997428i	$-0.477167\pi$
$991$	4.51233	0.143339	0.0716695	+	0.997428i	$0.477167\pi$
$992$	96.6692	3.06925
$993$	−20.9783	−0.665728
$994$	−0.179911	−0.00570643
$995$	−17.0129	−0.539345
$996$	58.3400	1.84857
$997$	15.5883	0.493687	0.246843	−	0.969055i	$-0.420607\pi$
$997$	15.5883	0.493687	0.246843	+	0.969055i	$0.420607\pi$
$998$	−26.9529	−0.853178
$999$	1.84452	0.0583581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.1	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.1	✓	165	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)

\(f(q)\)	\(=\)	\(q-2.77651 q^{2} +2.27500 q^{3} +5.70902 q^{4} +0.808124 q^{5} -6.31657 q^{6} +0.0647974 q^{7} -10.2981 q^{8} +2.17564 q^{9} +O(q^{10})\)	\(q-2.77651 q^{2} +2.27500 q^{3} +5.70902 q^{4} +0.808124 q^{5} -6.31657 q^{6} +0.0647974 q^{7} -10.2981 q^{8} +2.17564 q^{9} -2.24377 q^{10} +1.89232 q^{11} +12.9880 q^{12} +2.74874 q^{13} -0.179911 q^{14} +1.83848 q^{15} +17.1749 q^{16} +1.85964 q^{17} -6.04069 q^{18} +1.76617 q^{19} +4.61360 q^{20} +0.147414 q^{21} -5.25406 q^{22} +3.95046 q^{23} -23.4283 q^{24} -4.34694 q^{25} -7.63191 q^{26} -1.87542 q^{27} +0.369930 q^{28} +3.44073 q^{29} -5.10458 q^{30} -3.56845 q^{31} -27.0900 q^{32} +4.30504 q^{33} -5.16330 q^{34} +0.0523644 q^{35} +12.4208 q^{36} -0.983525 q^{37} -4.90380 q^{38} +6.25340 q^{39} -8.32217 q^{40} -2.67835 q^{41} -0.409298 q^{42} -9.75254 q^{43} +10.8033 q^{44} +1.75819 q^{45} -10.9685 q^{46} +13.3557 q^{47} +39.0729 q^{48} -6.99580 q^{49} +12.0693 q^{50} +4.23068 q^{51} +15.6926 q^{52} -3.53476 q^{53} +5.20713 q^{54} +1.52923 q^{55} -0.667293 q^{56} +4.01805 q^{57} -9.55322 q^{58} +3.91496 q^{59} +10.4959 q^{60} +8.08701 q^{61} +9.90785 q^{62} +0.140976 q^{63} +40.8659 q^{64} +2.22132 q^{65} -11.9530 q^{66} +1.44680 q^{67} +10.6167 q^{68} +8.98731 q^{69} -0.145390 q^{70} +1.00000 q^{71} -22.4051 q^{72} +16.0308 q^{73} +2.73077 q^{74} -9.88929 q^{75} +10.0831 q^{76} +0.122618 q^{77} -17.3626 q^{78} +10.2094 q^{79} +13.8794 q^{80} -10.7935 q^{81} +7.43648 q^{82} +4.49182 q^{83} +0.841592 q^{84} +1.50282 q^{85} +27.0781 q^{86} +7.82766 q^{87} -19.4874 q^{88} +5.06015 q^{89} -4.88163 q^{90} +0.178111 q^{91} +22.5533 q^{92} -8.11824 q^{93} -37.0821 q^{94} +1.42729 q^{95} -61.6297 q^{96} -5.21879 q^{97} +19.4239 q^{98} +4.11701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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