LMFDB - Embedded newform 8017.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59088 q^{2} -0.557344 q^{3} +4.71265 q^{4} -1.39623 q^{5} +1.44401 q^{6} -3.59677 q^{7} -7.02815 q^{8} -2.68937 q^{9} +O(q^{10})$	\(q-2.59088 q^{2} -0.557344 q^{3} +4.71265 q^{4} -1.39623 q^{5} +1.44401 q^{6} -3.59677 q^{7} -7.02815 q^{8} -2.68937 q^{9} +3.61746 q^{10} -2.01269 q^{11} -2.62657 q^{12} +1.98887 q^{13} +9.31880 q^{14} +0.778179 q^{15} +8.78378 q^{16} +2.52615 q^{17} +6.96782 q^{18} +4.20084 q^{19} -6.57994 q^{20} +2.00464 q^{21} +5.21462 q^{22} -0.232540 q^{23} +3.91710 q^{24} -3.05055 q^{25} -5.15291 q^{26} +3.17094 q^{27} -16.9503 q^{28} +5.73353 q^{29} -2.01617 q^{30} +2.20911 q^{31} -8.70140 q^{32} +1.12176 q^{33} -6.54494 q^{34} +5.02191 q^{35} -12.6741 q^{36} -11.4730 q^{37} -10.8839 q^{38} -1.10848 q^{39} +9.81290 q^{40} -3.24371 q^{41} -5.19378 q^{42} +8.26170 q^{43} -9.48509 q^{44} +3.75497 q^{45} +0.602482 q^{46} +11.6906 q^{47} -4.89559 q^{48} +5.93677 q^{49} +7.90360 q^{50} -1.40793 q^{51} +9.37284 q^{52} +10.5201 q^{53} -8.21551 q^{54} +2.81017 q^{55} +25.2787 q^{56} -2.34131 q^{57} -14.8549 q^{58} -0.384949 q^{59} +3.66729 q^{60} +2.64790 q^{61} -5.72353 q^{62} +9.67304 q^{63} +4.97672 q^{64} -2.77691 q^{65} -2.90634 q^{66} -11.1544 q^{67} +11.9048 q^{68} +0.129605 q^{69} -13.0112 q^{70} -11.5360 q^{71} +18.9013 q^{72} -8.20319 q^{73} +29.7250 q^{74} +1.70020 q^{75} +19.7971 q^{76} +7.23917 q^{77} +2.87195 q^{78} -16.5756 q^{79} -12.2642 q^{80} +6.30080 q^{81} +8.40407 q^{82} -4.72510 q^{83} +9.44717 q^{84} -3.52708 q^{85} -21.4051 q^{86} -3.19555 q^{87} +14.1455 q^{88} -14.7026 q^{89} -9.72867 q^{90} -7.15350 q^{91} -1.09588 q^{92} -1.23123 q^{93} -30.2889 q^{94} -5.86533 q^{95} +4.84968 q^{96} -0.123525 q^{97} -15.3815 q^{98} +5.41285 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.59088	−1.83203	−0.916014	−	0.401147i	$-0.868612\pi$
$2$	−2.59088	−1.83203	−0.916014	+	0.401147i	$0.868612\pi$
$3$	−0.557344	−0.321783	−0.160891	−	0.986972i	$-0.551437\pi$
$3$	−0.557344	−0.321783	−0.160891	+	0.986972i	$0.551437\pi$
$4$	4.71265	2.35633
$5$	−1.39623	−0.624412	−0.312206	−	0.950014i	$-0.601068\pi$
$5$	−1.39623	−0.624412	−0.312206	+	0.950014i	$0.601068\pi$
$6$	1.44401	0.589515
$7$	−3.59677	−1.35945	−0.679726	−	0.733466i	$-0.737901\pi$
$7$	−3.59677	−1.35945	−0.679726	+	0.733466i	$0.737901\pi$
$8$	−7.02815	−2.48483
$9$	−2.68937	−0.896456
$10$	3.61746	1.14394
$11$	−2.01269	−0.606848	−0.303424	−	0.952856i	$-0.598130\pi$
$11$	−2.01269	−0.606848	−0.303424	+	0.952856i	$0.598130\pi$
$12$	−2.62657	−0.758225
$13$	1.98887	0.551612	0.275806	−	0.961213i	$-0.411055\pi$
$13$	1.98887	0.551612	0.275806	+	0.961213i	$0.411055\pi$
$14$	9.31880	2.49055
$15$	0.778179	0.200925
$16$	8.78378	2.19594
$17$	2.52615	0.612681	0.306340	−	0.951922i	$-0.400895\pi$
$17$	2.52615	0.612681	0.306340	+	0.951922i	$0.400895\pi$
$18$	6.96782	1.64233
$19$	4.20084	0.963739	0.481870	−	0.876243i	$-0.339958\pi$
$19$	4.20084	0.963739	0.481870	+	0.876243i	$0.339958\pi$
$20$	−6.57994	−1.47132
$21$	2.00464	0.437448
$22$	5.21462	1.11176
$23$	−0.232540	−0.0484879	−0.0242439	−	0.999706i	$-0.507718\pi$
$23$	−0.232540	−0.0484879	−0.0242439	+	0.999706i	$0.507718\pi$
$24$	3.91710	0.799574
$25$	−3.05055	−0.610110
$26$	−5.15291	−1.01057
$27$	3.17094	0.610247
$28$	−16.9503	−3.20331
$29$	5.73353	1.06469	0.532345	−	0.846527i	$-0.321311\pi$
$29$	5.73353	1.06469	0.532345	+	0.846527i	$0.321311\pi$
$30$	−2.01617	−0.368100
$31$	2.20911	0.396768	0.198384	−	0.980124i	$-0.436431\pi$
$31$	2.20911	0.396768	0.198384	+	0.980124i	$0.436431\pi$
$32$	−8.70140	−1.53821
$33$	1.12176	0.195273
$34$	−6.54494	−1.12245
$35$	5.02191	0.848858
$36$	−12.6741	−2.11234
$37$	−11.4730	−1.88614	−0.943071	−	0.332591i	$-0.892077\pi$
$37$	−11.4730	−1.88614	−0.943071	+	0.332591i	$0.892077\pi$
$38$	−10.8839	−1.76560
$39$	−1.10848	−0.177499
$40$	9.81290	1.55156
$41$	−3.24371	−0.506583	−0.253292	−	0.967390i	$-0.581513\pi$
$41$	−3.24371	−0.506583	−0.253292	+	0.967390i	$0.581513\pi$
$42$	−5.19378	−0.801417
$43$	8.26170	1.25990	0.629949	−	0.776637i	$-0.283076\pi$
$43$	8.26170	1.25990	0.629949	+	0.776637i	$0.283076\pi$
$44$	−9.48509	−1.42993
$45$	3.75497	0.559758
$46$	0.602482	0.0888311
$47$	11.6906	1.70525	0.852625	−	0.522523i	$-0.175009\pi$
$47$	11.6906	1.70525	0.852625	+	0.522523i	$0.175009\pi$
$48$	−4.89559	−0.706617
$49$	5.93677	0.848111
$50$	7.90360	1.11774
$51$	−1.40793	−0.197150
$52$	9.37284	1.29978
$53$	10.5201	1.44504	0.722522	−	0.691348i	$-0.242983\pi$
$53$	10.5201	1.44504	0.722522	+	0.691348i	$0.242983\pi$
$54$	−8.21551	−1.11799
$55$	2.81017	0.378923
$56$	25.2787	3.37800
$57$	−2.34131	−0.310115
$58$	−14.8549	−1.95054
$59$	−0.384949	−0.0501161	−0.0250580	−	0.999686i	$-0.507977\pi$
$59$	−0.384949	−0.0501161	−0.0250580	+	0.999686i	$0.507977\pi$
$60$	3.66729	0.473445
$61$	2.64790	0.339029	0.169514	−	0.985528i	$-0.445780\pi$
$61$	2.64790	0.339029	0.169514	+	0.985528i	$0.445780\pi$
$62$	−5.72353	−0.726889
$63$	9.67304	1.21869
$64$	4.97672	0.622090
$65$	−2.77691	−0.344434
$66$	−2.90634	−0.357746
$67$	−11.1544	−1.36273	−0.681363	−	0.731945i	$-0.738613\pi$
$67$	−11.1544	−1.36273	−0.681363	+	0.731945i	$0.738613\pi$
$68$	11.9048	1.44367
$69$	0.129605	0.0156026
$70$	−13.0112	−1.55513
$71$	−11.5360	−1.36907	−0.684535	−	0.728980i	$-0.739995\pi$
$71$	−11.5360	−1.36907	−0.684535	+	0.728980i	$0.739995\pi$
$72$	18.9013	2.22754
$73$	−8.20319	−0.960110	−0.480055	−	0.877238i	$-0.659383\pi$
$73$	−8.20319	−0.960110	−0.480055	+	0.877238i	$0.659383\pi$
$74$	29.7250	3.45546
$75$	1.70020	0.196323
$76$	19.7971	2.27088
$77$	7.23917	0.824980
$78$	2.87195	0.325184
$79$	−16.5756	−1.86490	−0.932448	−	0.361304i	$-0.882332\pi$
$79$	−16.5756	−1.86490	−0.932448	+	0.361304i	$0.882332\pi$
$80$	−12.2642	−1.37117
$81$	6.30080	0.700089
$82$	8.40407	0.928074
$83$	−4.72510	−0.518647	−0.259323	−	0.965791i	$-0.583500\pi$
$83$	−4.72510	−0.518647	−0.259323	+	0.965791i	$0.583500\pi$
$84$	9.44717	1.03077
$85$	−3.52708	−0.382565
$86$	−21.4051	−2.30817
$87$	−3.19555	−0.342599
$88$	14.1455	1.50791
$89$	−14.7026	−1.55847	−0.779236	−	0.626731i	$-0.784393\pi$
$89$	−14.7026	−1.55847	−0.779236	+	0.626731i	$0.784393\pi$
$90$	−9.72867	−1.02549
$91$	−7.15350	−0.749891
$92$	−1.09588	−0.114253
$93$	−1.23123	−0.127673
$94$	−30.2889	−3.12406
$95$	−5.86533	−0.601770
$96$	4.84968	0.494968
$97$	−0.123525	−0.0125421	−0.00627103	−	0.999980i	$-0.501996\pi$
$97$	−0.123525	−0.0125421	−0.00627103	+	0.999980i	$0.501996\pi$
$98$	−15.3815	−1.55376
$99$	5.41285	0.544012
$100$	−14.3762	−1.43762
$101$	−13.5110	−1.34439	−0.672196	−	0.740373i	$-0.734649\pi$
$101$	−13.5110	−1.34439	−0.672196	+	0.740373i	$0.734649\pi$
$102$	3.64778	0.361184
$103$	−7.66829	−0.755579	−0.377790	−	0.925891i	$-0.623316\pi$
$103$	−7.66829	−0.755579	−0.377790	+	0.925891i	$0.623316\pi$
$104$	−13.9781	−1.37066
$105$	−2.79893	−0.273148
$106$	−27.2562	−2.64736
$107$	−3.87882	−0.374979	−0.187490	−	0.982267i	$-0.560035\pi$
$107$	−3.87882	−0.374979	−0.187490	+	0.982267i	$0.560035\pi$
$108$	14.9435	1.43794
$109$	−15.3375	−1.46907	−0.734535	−	0.678571i	$-0.762599\pi$
$109$	−15.3375	−1.46907	−0.734535	+	0.678571i	$0.762599\pi$
$110$	−7.28080	−0.694198
$111$	6.39438	0.606928
$112$	−31.5933	−2.98528
$113$	11.6649	1.09734	0.548672	−	0.836038i	$-0.315134\pi$
$113$	11.6649	1.09734	0.548672	+	0.836038i	$0.315134\pi$
$114$	6.06606	0.568139
$115$	0.324678	0.0302764
$116$	27.0201	2.50876
$117$	−5.34879	−0.494496
$118$	0.997356	0.0918140
$119$	−9.08598	−0.832910
$120$	−5.46916	−0.499264
$121$	−6.94909	−0.631736
$122$	−6.86039	−0.621110
$123$	1.80787	0.163010
$124$	10.4108	0.934914
$125$	11.2404	1.00537
$126$	−25.0617	−2.23267
$127$	−5.58304	−0.495415	−0.247707	−	0.968835i	$-0.579677\pi$
$127$	−5.58304	−0.495415	−0.247707	+	0.968835i	$0.579677\pi$
$128$	4.50873	0.398519
$129$	−4.60461	−0.405413
$130$	7.19464	0.631012
$131$	−15.7969	−1.38018	−0.690089	−	0.723725i	$-0.742429\pi$
$131$	−15.7969	−1.38018	−0.690089	+	0.723725i	$0.742429\pi$
$132$	5.28646	0.460127
$133$	−15.1095	−1.31016
$134$	28.8997	2.49655
$135$	−4.42735	−0.381046
$136$	−17.7541	−1.52240
$137$	9.90345	0.846109	0.423055	−	0.906104i	$-0.360958\pi$
$137$	9.90345	0.846109	0.423055	+	0.906104i	$0.360958\pi$
$138$	−0.335790	−0.0285843
$139$	18.6780	1.58425	0.792123	−	0.610361i	$-0.208976\pi$
$139$	18.6780	1.58425	0.792123	+	0.610361i	$0.208976\pi$
$140$	23.6665	2.00019
$141$	−6.51569	−0.548720
$142$	29.8883	2.50817
$143$	−4.00297	−0.334745
$144$	−23.6228	−1.96857
$145$	−8.00532	−0.664806
$146$	21.2535	1.75895
$147$	−3.30883	−0.272907
$148$	−54.0680	−4.44437
$149$	−0.0974832	−0.00798614	−0.00399307	−	0.999992i	$-0.501271\pi$
$149$	−0.0974832	−0.00798614	−0.00399307	+	0.999992i	$0.501271\pi$
$150$	−4.40502	−0.359669
$151$	−21.6106	−1.75865	−0.879324	−	0.476225i	$-0.842005\pi$
$151$	−21.6106	−1.75865	−0.879324	+	0.476225i	$0.842005\pi$
$152$	−29.5241	−2.39472
$153$	−6.79374	−0.549241
$154$	−18.7558	−1.51139
$155$	−3.08442	−0.247747
$156$	−5.22390	−0.418246
$157$	−0.208763	−0.0166611	−0.00833056	−	0.999965i	$-0.502652\pi$
$157$	−0.208763	−0.0166611	−0.00833056	+	0.999965i	$0.502652\pi$
$158$	42.9453	3.41654
$159$	−5.86330	−0.464990
$160$	12.1491	0.960474
$161$	0.836392	0.0659169
$162$	−16.3246	−1.28258
$163$	16.4807	1.29087	0.645436	−	0.763815i	$-0.276676\pi$
$163$	16.4807	1.29087	0.645436	+	0.763815i	$0.276676\pi$
$164$	−15.2865	−1.19367
$165$	−1.56623	−0.121931
$166$	12.2422	0.950176
$167$	−19.5380	−1.51190	−0.755948	−	0.654632i	$-0.772824\pi$
$167$	−19.5380	−1.51190	−0.755948	+	0.654632i	$0.772824\pi$
$168$	−14.0889	−1.08698
$169$	−9.04441	−0.695724
$170$	9.13823	0.700870
$171$	−11.2976	−0.863949
$172$	38.9345	2.96873
$173$	9.45751	0.719041	0.359520	−	0.933137i	$-0.382940\pi$
$173$	9.45751	0.719041	0.359520	+	0.933137i	$0.382940\pi$
$174$	8.27929	0.627651
$175$	10.9721	0.829415
$176$	−17.6790	−1.33260
$177$	0.214549	0.0161265
$178$	38.0926	2.85516
$179$	1.77899	0.132968	0.0664841	−	0.997787i	$-0.478822\pi$
$179$	1.77899	0.132968	0.0664841	+	0.997787i	$0.478822\pi$
$180$	17.6959	1.31897
$181$	20.8942	1.55306	0.776529	−	0.630082i	$-0.216979\pi$
$181$	20.8942	1.55306	0.776529	+	0.630082i	$0.216979\pi$
$182$	18.5339	1.37382
$183$	−1.47579	−0.109094
$184$	1.63432	0.120484
$185$	16.0189	1.17773
$186$	3.18998	0.233900
$187$	−5.08434	−0.371804
$188$	55.0937	4.01812
$189$	−11.4051	−0.829601
$190$	15.1964	1.10246
$191$	24.6818	1.78592	0.892958	−	0.450141i	$-0.148626\pi$
$191$	24.6818	1.78592	0.892958	+	0.450141i	$0.148626\pi$
$192$	−2.77375	−0.200178
$193$	−0.400264	−0.0288117	−0.0144058	−	0.999896i	$-0.504586\pi$
$193$	−0.400264	−0.0288117	−0.0144058	+	0.999896i	$0.504586\pi$
$194$	0.320038	0.0229774
$195$	1.54770	0.110833
$196$	27.9779	1.99842
$197$	11.4800	0.817919	0.408960	−	0.912552i	$-0.365892\pi$
$197$	11.4800	0.817919	0.408960	+	0.912552i	$0.365892\pi$
$198$	−14.0240	−0.996645
$199$	0.963053	0.0682690	0.0341345	−	0.999417i	$-0.489133\pi$
$199$	0.963053	0.0682690	0.0341345	+	0.999417i	$0.489133\pi$
$200$	21.4397	1.51602
$201$	6.21684	0.438502
$202$	35.0053	2.46296
$203$	−20.6222	−1.44740
$204$	−6.63510	−0.464550
$205$	4.52897	0.316317
$206$	19.8676	1.38424
$207$	0.625385	0.0434672
$208$	17.4698	1.21131
$209$	−8.45497	−0.584843
$210$	7.25170	0.500415
$211$	−0.720742	−0.0496179	−0.0248089	−	0.999692i	$-0.507898\pi$
$211$	−0.720742	−0.0496179	−0.0248089	+	0.999692i	$0.507898\pi$
$212$	49.5774	3.40499
$213$	6.42951	0.440543
$214$	10.0495	0.686972
$215$	−11.5352	−0.786695
$216$	−22.2858	−1.51636
$217$	−7.94566	−0.539387
$218$	39.7377	2.69138
$219$	4.57200	0.308947
$220$	13.2433	0.892866
$221$	5.02417	0.337962
$222$	−16.5671	−1.11191
$223$	−19.1978	−1.28558	−0.642791	−	0.766041i	$-0.722224\pi$
$223$	−19.1978	−1.28558	−0.642791	+	0.766041i	$0.722224\pi$
$224$	31.2970	2.09112
$225$	8.20404	0.546936
$226$	−30.2224	−2.01037
$227$	1.04013	0.0690359	0.0345179	−	0.999404i	$-0.489010\pi$
$227$	1.04013	0.0690359	0.0345179	+	0.999404i	$0.489010\pi$
$228$	−11.0338	−0.730731
$229$	−0.0274832	−0.00181614	−0.000908069	−	1.00000i	$-0.500289\pi$
$229$	−0.0274832	−0.00181614	−0.000908069		1.00000i	$0.500289\pi$
$230$	−0.841202	−0.0554672
$231$	−4.03471	−0.265465
$232$	−40.2961	−2.64557
$233$	16.1598	1.05867	0.529333	−	0.848414i	$-0.322442\pi$
$233$	16.1598	1.05867	0.529333	+	0.848414i	$0.322442\pi$
$234$	13.8581	0.905931
$235$	−16.3227	−1.06478
$236$	−1.81413	−0.118090
$237$	9.23829	0.600091
$238$	23.5407	1.52591
$239$	−16.8428	−1.08947	−0.544735	−	0.838608i	$-0.683370\pi$
$239$	−16.8428	−1.08947	−0.544735	+	0.838608i	$0.683370\pi$
$240$	6.83536	0.441220
$241$	−8.68185	−0.559247	−0.279624	−	0.960110i	$-0.590210\pi$
$241$	−8.68185	−0.559247	−0.279624	+	0.960110i	$0.590210\pi$
$242$	18.0043	1.15736
$243$	−13.0245	−0.835523
$244$	12.4786	0.798862
$245$	−8.28909	−0.529571
$246$	−4.68396	−0.298638
$247$	8.35491	0.531610
$248$	−15.5259	−0.985899
$249$	2.63351	0.166892
$250$	−29.1225	−1.84187
$251$	19.8850	1.25513	0.627564	−	0.778565i	$-0.284052\pi$
$251$	19.8850	1.25513	0.627564	+	0.778565i	$0.284052\pi$
$252$	45.5857	2.87163
$253$	0.468029	0.0294248
$254$	14.4650	0.907614
$255$	1.96580	0.123103
$256$	−21.6350	−1.35219
$257$	−16.0942	−1.00393	−0.501965	−	0.864888i	$-0.667389\pi$
$257$	−16.0942	−1.00393	−0.501965	+	0.864888i	$0.667389\pi$
$258$	11.9300	0.742728
$259$	41.2656	2.56412
$260$	−13.0866	−0.811597
$261$	−15.4196	−0.954448
$262$	40.9277	2.52852
$263$	5.88447	0.362852	0.181426	−	0.983405i	$-0.441929\pi$
$263$	5.88447	0.362852	0.181426	+	0.983405i	$0.441929\pi$
$264$	−7.88389	−0.485220
$265$	−14.6884	−0.902302
$266$	39.1468	2.40024
$267$	8.19440	0.501489
$268$	−52.5668	−3.21103
$269$	11.1225	0.678153	0.339076	−	0.940759i	$-0.389885\pi$
$269$	11.1225	0.678153	0.339076	+	0.940759i	$0.389885\pi$
$270$	11.4707	0.698086
$271$	5.96053	0.362077	0.181038	−	0.983476i	$-0.442054\pi$
$271$	5.96053	0.362077	0.181038	+	0.983476i	$0.442054\pi$
$272$	22.1891	1.34541
$273$	3.98696	0.241302
$274$	−25.6586	−1.55010
$275$	6.13979	0.370244
$276$	0.610781	0.0367647
$277$	23.0034	1.38214	0.691070	−	0.722788i	$-0.257140\pi$
$277$	23.0034	1.38214	0.691070	+	0.722788i	$0.257140\pi$
$278$	−48.3924	−2.90238
$279$	−5.94111	−0.355685
$280$	−35.2948	−2.10927
$281$	−14.0646	−0.839021	−0.419511	−	0.907750i	$-0.637798\pi$
$281$	−14.0646	−0.839021	−0.419511	+	0.907750i	$0.637798\pi$
$282$	16.8814	1.00527
$283$	−25.6821	−1.52664	−0.763321	−	0.646019i	$-0.776433\pi$
$283$	−25.6821	−1.52664	−0.763321	+	0.646019i	$0.776433\pi$
$284$	−54.3651	−3.22597
$285$	3.26901	0.193639
$286$	10.3712	0.613262
$287$	11.6669	0.688676
$288$	23.4013	1.37893
$289$	−10.6186	−0.624623
$290$	20.7408	1.21794
$291$	0.0688459	0.00403582
$292$	−38.6588	−2.26233
$293$	27.9000	1.62993	0.814967	−	0.579508i	$-0.196755\pi$
$293$	27.9000	1.62993	0.814967	+	0.579508i	$0.196755\pi$
$294$	8.57277	0.499974
$295$	0.537476	0.0312931
$296$	80.6336	4.68674
$297$	−6.38210	−0.370327
$298$	0.252567	0.0146308
$299$	−0.462490	−0.0267465
$300$	8.01247	0.462600
$301$	−29.7155	−1.71277
$302$	55.9905	3.22189
$303$	7.53026	0.432602
$304$	36.8993	2.11632
$305$	−3.69707	−0.211694
$306$	17.6017	1.00622
$307$	16.5047	0.941973	0.470987	−	0.882140i	$-0.343898\pi$
$307$	16.5047	0.941973	0.470987	+	0.882140i	$0.343898\pi$
$308$	34.1157	1.94392
$309$	4.27388	0.243132
$310$	7.99136	0.453879
$311$	−12.9077	−0.731931	−0.365965	−	0.930628i	$-0.619261\pi$
$311$	−12.9077	−0.731931	−0.365965	+	0.930628i	$0.619261\pi$
$312$	7.79059	0.441055
$313$	17.2785	0.976638	0.488319	−	0.872665i	$-0.337610\pi$
$313$	17.2785	0.976638	0.488319	+	0.872665i	$0.337610\pi$
$314$	0.540880	0.0305237
$315$	−13.5058	−0.760964
$316$	−78.1148	−4.39430
$317$	−3.08197	−0.173101	−0.0865504	−	0.996247i	$-0.527584\pi$
$317$	−3.08197	−0.173101	−0.0865504	+	0.996247i	$0.527584\pi$
$318$	15.1911	0.851875
$319$	−11.5398	−0.646105
$320$	−6.94864	−0.388441
$321$	2.16184	0.120662
$322$	−2.16699	−0.120762
$323$	10.6119	0.590464
$324$	29.6935	1.64964
$325$	−6.06713	−0.336544
$326$	−42.6996	−2.36491
$327$	8.54828	0.472721
$328$	22.7973	1.25877
$329$	−42.0484	−2.31821
$330$	4.05791	0.223381
$331$	−8.77686	−0.482420	−0.241210	−	0.970473i	$-0.577544\pi$
$331$	−8.77686	−0.482420	−0.241210	+	0.970473i	$0.577544\pi$
$332$	−22.2677	−1.22210
$333$	30.8550	1.69084
$334$	50.6206	2.76984
$335$	15.5741	0.850903
$336$	17.6083	0.960612
$337$	−14.5272	−0.791348	−0.395674	−	0.918391i	$-0.629489\pi$
$337$	−14.5272	−0.791348	−0.395674	+	0.918391i	$0.629489\pi$
$338$	23.4330	1.27459
$339$	−6.50138	−0.353107
$340$	−16.6219	−0.901448
$341$	−4.44624	−0.240778
$342$	29.2707	1.58278
$343$	3.82418	0.206486
$344$	−58.0644	−3.13063
$345$	−0.180958	−0.00974243
$346$	−24.5032	−1.31730
$347$	−6.96628	−0.373970	−0.186985	−	0.982363i	$-0.559872\pi$
$347$	−6.96628	−0.373970	−0.186985	+	0.982363i	$0.559872\pi$
$348$	−15.0595	−0.807275
$349$	−17.1641	−0.918772	−0.459386	−	0.888237i	$-0.651931\pi$
$349$	−17.1641	−0.918772	−0.459386	+	0.888237i	$0.651931\pi$
$350$	−28.4274	−1.51951
$351$	6.30657	0.336620
$352$	17.5132	0.933456
$353$	10.0110	0.532831	0.266416	−	0.963858i	$-0.414161\pi$
$353$	10.0110	0.532831	0.266416	+	0.963858i	$0.414161\pi$
$354$	−0.555870	−0.0295442
$355$	16.1069	0.854864
$356$	−69.2882	−3.67227
$357$	5.06401	0.268016
$358$	−4.60915	−0.243601
$359$	29.4470	1.55415	0.777076	−	0.629407i	$-0.216702\pi$
$359$	29.4470	1.55415	0.777076	+	0.629407i	$0.216702\pi$
$360$	−26.3905	−1.39090
$361$	−1.35294	−0.0712071
$362$	−54.1345	−2.84524
$363$	3.87304	0.203282
$364$	−33.7120	−1.76699
$365$	11.4535	0.599505
$366$	3.82360	0.199863
$367$	19.0986	0.996937	0.498468	−	0.866908i	$-0.333896\pi$
$367$	19.0986	0.996937	0.498468	+	0.866908i	$0.333896\pi$
$368$	−2.04258	−0.106477
$369$	8.72354	0.454129
$370$	−41.5029	−2.15763
$371$	−37.8383	−1.96447
$372$	−5.80238	−0.300839
$373$	−4.54317	−0.235236	−0.117618	−	0.993059i	$-0.537526\pi$
$373$	−4.54317	−0.235236	−0.117618	+	0.993059i	$0.537526\pi$
$374$	13.1729	0.681155
$375$	−6.26477	−0.323511
$376$	−82.1633	−4.23725
$377$	11.4032	0.587297
$378$	29.5493	1.51985
$379$	24.6039	1.26382	0.631909	−	0.775042i	$-0.282272\pi$
$379$	24.6039	1.26382	0.631909	+	0.775042i	$0.282272\pi$
$380$	−27.6413	−1.41797
$381$	3.11168	0.159416
$382$	−63.9476	−3.27185
$383$	−21.9184	−1.11998	−0.559988	−	0.828500i	$-0.689194\pi$
$383$	−21.9184	−1.11998	−0.559988	+	0.828500i	$0.689194\pi$
$384$	−2.51291	−0.128237
$385$	−10.1075	−0.515128
$386$	1.03704	0.0527838
$387$	−22.2187	−1.12944
$388$	−0.582130	−0.0295532
$389$	13.3505	0.676898	0.338449	−	0.940985i	$-0.390098\pi$
$389$	13.3505	0.676898	0.338449	+	0.940985i	$0.390098\pi$
$390$	−4.00989	−0.203049
$391$	−0.587429	−0.0297076
$392$	−41.7245	−2.10741
$393$	8.80428	0.444117
$394$	−29.7434	−1.49845
$395$	23.1433	1.16446
$396$	25.5089	1.28187
$397$	−10.7162	−0.537830	−0.268915	−	0.963164i	$-0.586665\pi$
$397$	−10.7162	−0.537830	−0.268915	+	0.963164i	$0.586665\pi$
$398$	−2.49515	−0.125071
$399$	8.42117	0.421586
$400$	−26.7953	−1.33977
$401$	−31.2919	−1.56264	−0.781321	−	0.624129i	$-0.785454\pi$
$401$	−31.2919	−1.56264	−0.781321	+	0.624129i	$0.785454\pi$
$402$	−16.1071	−0.803348
$403$	4.39362	0.218862
$404$	−63.6725	−3.16783
$405$	−8.79735	−0.437144
$406$	53.4297	2.65167
$407$	23.0915	1.14460
$408$	9.89516	0.489884
$409$	35.3462	1.74776	0.873878	−	0.486146i	$-0.161598\pi$
$409$	35.3462	1.74776	0.873878	+	0.486146i	$0.161598\pi$
$410$	−11.7340	−0.579501
$411$	−5.51963	−0.272263
$412$	−36.1380	−1.78039
$413$	1.38457	0.0681304
$414$	−1.62030	−0.0796332
$415$	6.59731	0.323849
$416$	−17.3059	−0.848493
$417$	−10.4101	−0.509783
$418$	21.9058	1.07145
$419$	27.4890	1.34292	0.671462	−	0.741039i	$-0.265667\pi$
$419$	27.4890	1.34292	0.671462	+	0.741039i	$0.265667\pi$
$420$	−13.1904	−0.643626
$421$	−5.55865	−0.270912	−0.135456	−	0.990783i	$-0.543250\pi$
$421$	−5.55865	−0.270912	−0.135456	+	0.990783i	$0.543250\pi$
$422$	1.86735	0.0909014
$423$	−31.4403	−1.52868
$424$	−73.9366	−3.59068
$425$	−7.70613	−0.373802
$426$	−16.6581	−0.807087
$427$	−9.52389	−0.460893
$428$	−18.2795	−0.883573
$429$	2.23103	0.107715
$430$	29.8863	1.44125
$431$	15.7371	0.758031	0.379016	−	0.925390i	$-0.376263\pi$
$431$	15.7371	0.758031	0.379016	+	0.925390i	$0.376263\pi$
$432$	27.8528	1.34007
$433$	−16.5629	−0.795960	−0.397980	−	0.917394i	$-0.630289\pi$
$433$	−16.5629	−0.795960	−0.397980	+	0.917394i	$0.630289\pi$
$434$	20.5862	0.988171
$435$	4.46172	0.213923
$436$	−72.2804	−3.46161
$437$	−0.976862	−0.0467297
$438$	−11.8455	−0.565999
$439$	33.4289	1.59548	0.797738	−	0.603004i	$-0.206030\pi$
$439$	33.4289	1.59548	0.797738	+	0.603004i	$0.206030\pi$
$440$	−19.7503	−0.941558
$441$	−15.9662	−0.760294
$442$	−13.0170	−0.619156
$443$	−14.2157	−0.675408	−0.337704	−	0.941252i	$-0.609650\pi$
$443$	−14.2157	−0.675408	−0.337704	+	0.941252i	$0.609650\pi$
$444$	30.1345	1.43012
$445$	20.5282	0.973128
$446$	49.7393	2.35522
$447$	0.0543317	0.00256980
$448$	−17.9001	−0.845702
$449$	33.2424	1.56881	0.784404	−	0.620250i	$-0.212969\pi$
$449$	33.2424	1.56881	0.784404	+	0.620250i	$0.212969\pi$
$450$	−21.2557	−1.00200
$451$	6.52858	0.307419
$452$	54.9727	2.58570
$453$	12.0446	0.565902
$454$	−2.69485	−0.126476
$455$	9.98792	0.468241
$456$	16.4551	0.770581
$457$	5.86661	0.274428	0.137214	−	0.990541i	$-0.456185\pi$
$457$	5.86661	0.274428	0.137214	+	0.990541i	$0.456185\pi$
$458$	0.0712055	0.00332722
$459$	8.01025	0.373886
$460$	1.53010	0.0713411
$461$	4.71386	0.219547	0.109773	−	0.993957i	$-0.464988\pi$
$461$	4.71386	0.219547	0.109773	+	0.993957i	$0.464988\pi$
$462$	10.4534	0.486338
$463$	34.9537	1.62444	0.812218	−	0.583354i	$-0.198260\pi$
$463$	34.9537	1.62444	0.812218	+	0.583354i	$0.198260\pi$
$464$	50.3621	2.33800
$465$	1.71908	0.0797206
$466$	−41.8682	−1.93951
$467$	−0.992927	−0.0459472	−0.0229736	−	0.999736i	$-0.507313\pi$
$467$	−0.992927	−0.0459472	−0.0229736	+	0.999736i	$0.507313\pi$
$468$	−25.2070	−1.16519
$469$	40.1198	1.85256
$470$	42.2903	1.95070
$471$	0.116353	0.00536126
$472$	2.70548	0.124530
$473$	−16.6282	−0.764566
$474$	−23.9353	−1.09938
$475$	−12.8149	−0.587986
$476$	−42.8190	−1.96261
$477$	−28.2923	−1.29542
$478$	43.6376	1.99594
$479$	−8.14006	−0.371929	−0.185964	−	0.982556i	$-0.559541\pi$
$479$	−8.14006	−0.371929	−0.185964	+	0.982556i	$0.559541\pi$
$480$	−6.77125	−0.309064
$481$	−22.8182	−1.04042
$482$	22.4936	1.02456
$483$	−0.466158	−0.0212109
$484$	−32.7487	−1.48858
$485$	0.172469	0.00783141
$486$	33.7449	1.53070
$487$	−3.79629	−0.172026	−0.0860132	−	0.996294i	$-0.527413\pi$
$487$	−3.79629	−0.172026	−0.0860132	+	0.996294i	$0.527413\pi$
$488$	−18.6098	−0.842428
$489$	−9.18544	−0.415380
$490$	21.4760	0.970188
$491$	−7.88537	−0.355862	−0.177931	−	0.984043i	$-0.556940\pi$
$491$	−7.88537	−0.355862	−0.177931	+	0.984043i	$0.556940\pi$
$492$	8.51984	0.384104
$493$	14.4837	0.652315
$494$	−21.6466	−0.973925
$495$	−7.55758	−0.339688
$496$	19.4043	0.871280
$497$	41.4923	1.86119
$498$	−6.82309	−0.305750
$499$	−19.2956	−0.863791	−0.431895	−	0.901924i	$-0.642155\pi$
$499$	−19.2956	−0.863791	−0.431895	+	0.901924i	$0.642155\pi$
$500$	52.9721	2.36898
$501$	10.8894	0.486502
$502$	−51.5195	−2.29943
$503$	6.82096	0.304132	0.152066	−	0.988370i	$-0.451407\pi$
$503$	6.82096	0.304132	0.152066	+	0.988370i	$0.451407\pi$
$504$	−67.9836	−3.02823
$505$	18.8644	0.839455
$506$	−1.21261	−0.0539070
$507$	5.04085	0.223872
$508$	−26.3109	−1.16736
$509$	7.91552	0.350849	0.175425	−	0.984493i	$-0.443870\pi$
$509$	7.91552	0.350849	0.175425	+	0.984493i	$0.443870\pi$
$510$	−5.09314	−0.225528
$511$	29.5050	1.30522
$512$	47.0362	2.07873
$513$	13.3206	0.588119
$514$	41.6981	1.83923
$515$	10.7067	0.471793
$516$	−21.6999	−0.955285
$517$	−23.5295	−1.03483
$518$	−106.914	−4.69754
$519$	−5.27108	−0.231375
$520$	19.5166	0.855857
$521$	−32.6487	−1.43037	−0.715183	−	0.698937i	$-0.753657\pi$
$521$	−32.6487	−1.43037	−0.715183	+	0.698937i	$0.753657\pi$
$522$	39.9503	1.74858
$523$	−15.2355	−0.666202	−0.333101	−	0.942891i	$-0.608095\pi$
$523$	−15.2355	−0.666202	−0.333101	+	0.942891i	$0.608095\pi$
$524$	−74.4451	−3.25215
$525$	−6.11525	−0.266891
$526$	−15.2460	−0.664755
$527$	5.58053	0.243092
$528$	9.85328	0.428809
$529$	−22.9459	−0.997649
$530$	38.0559	1.65304
$531$	1.03527	0.0449268
$532$	−71.2057	−3.08716
$533$	−6.45132	−0.279438
$534$	−21.2307	−0.918742
$535$	5.41571	0.234142
$536$	78.3948	3.38614
$537$	−0.991511	−0.0427869
$538$	−28.8171	−1.24239
$539$	−11.9489	−0.514674
$540$	−20.8645	−0.897867
$541$	−36.8415	−1.58394	−0.791971	−	0.610559i	$-0.790945\pi$
$541$	−36.8415	−1.58394	−0.791971	+	0.610559i	$0.790945\pi$
$542$	−15.4430	−0.663334
$543$	−11.6453	−0.499747
$544$	−21.9810	−0.942428
$545$	21.4147	0.917305
$546$	−10.3297	−0.442072
$547$	13.4025	0.573048	0.286524	−	0.958073i	$-0.407500\pi$
$547$	13.4025	0.573048	0.286524	+	0.958073i	$0.407500\pi$
$548$	46.6715	1.99371
$549$	−7.12117	−0.303924
$550$	−15.9075	−0.678296
$551$	24.0857	1.02608
$552$	−0.910881	−0.0387696
$553$	59.6185	2.53524
$554$	−59.5990	−2.53212
$555$	−8.92802	−0.378973
$556$	88.0228	3.73300
$557$	−27.5197	−1.16605	−0.583024	−	0.812455i	$-0.698130\pi$
$557$	−27.5197	−1.16605	−0.583024	+	0.812455i	$0.698130\pi$
$558$	15.3927	0.651624
$559$	16.4314	0.694975
$560$	44.1114	1.86405
$561$	2.83373	0.119640
$562$	36.4396	1.53711
$563$	−17.7122	−0.746481	−0.373241	−	0.927735i	$-0.621753\pi$
$563$	−17.7122	−0.746481	−0.373241	+	0.927735i	$0.621753\pi$
$564$	−30.7062	−1.29296
$565$	−16.2869	−0.685195
$566$	66.5392	2.79685
$567$	−22.6625	−0.951738
$568$	81.0766	3.40190
$569$	33.1601	1.39014	0.695071	−	0.718941i	$-0.255373\pi$
$569$	33.1601	1.39014	0.695071	+	0.718941i	$0.255373\pi$
$570$	−8.46960	−0.354753
$571$	19.3455	0.809584	0.404792	−	0.914409i	$-0.367344\pi$
$571$	19.3455	0.809584	0.404792	+	0.914409i	$0.367344\pi$
$572$	−18.8646	−0.788768
$573$	−13.7563	−0.574677
$574$	−30.2275	−1.26167
$575$	0.709373	0.0295829
$576$	−13.3842	−0.557676
$577$	7.47519	0.311196	0.155598	−	0.987820i	$-0.450270\pi$
$577$	7.47519	0.311196	0.155598	+	0.987820i	$0.450270\pi$
$578$	27.5115	1.14433
$579$	0.223085	0.00927110
$580$	−37.7263	−1.56650
$581$	16.9951	0.705076
$582$	−0.178371	−0.00739373
$583$	−21.1736	−0.876921
$584$	57.6532	2.38571
$585$	7.46814	0.308769
$586$	−72.2854	−2.98608
$587$	8.55737	0.353200	0.176600	−	0.984283i	$-0.443490\pi$
$587$	8.55737	0.353200	0.176600	+	0.984283i	$0.443490\pi$
$588$	−15.5933	−0.643059
$589$	9.28011	0.382380
$590$	−1.39254	−0.0573298
$591$	−6.39834	−0.263192
$592$	−100.776	−4.14186
$593$	13.5436	0.556170	0.278085	−	0.960556i	$-0.410300\pi$
$593$	13.5436	0.556170	0.278085	+	0.960556i	$0.410300\pi$
$594$	16.5352	0.678449
$595$	12.6861	0.520079
$596$	−0.459404	−0.0188179
$597$	−0.536752	−0.0219678
$598$	1.19826	0.0490004
$599$	−40.0966	−1.63830	−0.819152	−	0.573576i	$-0.805556\pi$
$599$	−40.0966	−1.63830	−0.819152	+	0.573576i	$0.805556\pi$
$600$	−11.9493	−0.487828
$601$	−36.6112	−1.49340	−0.746702	−	0.665159i	$-0.768364\pi$
$601$	−36.6112	−1.49340	−0.746702	+	0.665159i	$0.768364\pi$
$602$	76.9891	3.13784
$603$	29.9983	1.22162
$604$	−101.843	−4.14395
$605$	9.70252	0.394464
$606$	−19.5100	−0.792539
$607$	−28.8455	−1.17080	−0.585400	−	0.810744i	$-0.699063\pi$
$607$	−28.8455	−1.17080	−0.585400	+	0.810744i	$0.699063\pi$
$608$	−36.5532	−1.48243
$609$	11.4937	0.465747
$610$	9.57866	0.387829
$611$	23.2511	0.940637
$612$	−32.0165	−1.29419
$613$	33.4232	1.34995	0.674975	−	0.737841i	$-0.264155\pi$
$613$	33.4232	1.34995	0.674975	+	0.737841i	$0.264155\pi$
$614$	−42.7617	−1.72572
$615$	−2.52419	−0.101785
$616$	−50.8780	−2.04993
$617$	17.4419	0.702183	0.351091	−	0.936341i	$-0.385811\pi$
$617$	17.4419	0.702183	0.351091	+	0.936341i	$0.385811\pi$
$618$	−11.0731	−0.445425
$619$	−41.9092	−1.68447	−0.842237	−	0.539108i	$-0.818762\pi$
$619$	−41.9092	−1.68447	−0.842237	+	0.539108i	$0.818762\pi$
$620$	−14.5358	−0.583771
$621$	−0.737368	−0.0295896
$622$	33.4424	1.34092
$623$	52.8819	2.11867
$624$	−9.73667	−0.389779
$625$	−0.441421	−0.0176569
$626$	−44.7665	−1.78923
$627$	4.71233	0.188192
$628$	−0.983829	−0.0392590
$629$	−28.9824	−1.15560
$630$	34.9918	1.39411
$631$	22.6982	0.903600	0.451800	−	0.892119i	$-0.350782\pi$
$631$	22.6982	0.903600	0.451800	+	0.892119i	$0.350782\pi$
$632$	116.495	4.63394
$633$	0.401701	0.0159662
$634$	7.98501	0.317125
$635$	7.79520	0.309343
$636$	−27.6317	−1.09567
$637$	11.8075	0.467828
$638$	29.8982	1.18368
$639$	31.0245	1.22731
$640$	−6.29521	−0.248840
$641$	−9.71250	−0.383621	−0.191810	−	0.981432i	$-0.561436\pi$
$641$	−9.71250	−0.383621	−0.191810	+	0.981432i	$0.561436\pi$
$642$	−5.60105	−0.221056
$643$	29.8908	1.17878	0.589390	−	0.807849i	$-0.299368\pi$
$643$	29.8908	1.17878	0.589390	+	0.807849i	$0.299368\pi$
$644$	3.94163	0.155322
$645$	6.42908	0.253145
$646$	−27.4942	−1.08175
$647$	−49.1992	−1.93422	−0.967110	−	0.254360i	$-0.918135\pi$
$647$	−49.1992	−1.93422	−0.967110	+	0.254360i	$0.918135\pi$
$648$	−44.2830	−1.73960
$649$	0.774781	0.0304128
$650$	15.7192	0.616558
$651$	4.42847	0.173565
$652$	77.6680	3.04171
$653$	−9.39762	−0.367757	−0.183879	−	0.982949i	$-0.558865\pi$
$653$	−9.39762	−0.367757	−0.183879	+	0.982949i	$0.558865\pi$
$654$	−22.1476	−0.866038
$655$	22.0560	0.861800
$656$	−28.4921	−1.11243
$657$	22.0614	0.860697
$658$	108.942	4.24702
$659$	−28.3179	−1.10311	−0.551554	−	0.834139i	$-0.685965\pi$
$659$	−28.3179	−1.10311	−0.551554	+	0.834139i	$0.685965\pi$
$660$	−7.38110	−0.287309
$661$	−30.5729	−1.18915	−0.594573	−	0.804041i	$-0.702679\pi$
$661$	−30.5729	−1.18915	−0.594573	+	0.804041i	$0.702679\pi$
$662$	22.7398	0.883807
$663$	−2.80019	−0.108750
$664$	33.2087	1.28875
$665$	21.0963	0.818078
$666$	−79.9415	−3.09767
$667$	−1.33327	−0.0516246
$668$	−92.0758	−3.56252
$669$	10.6998	0.413678
$670$	−40.3506	−1.55888
$671$	−5.32939	−0.205739
$672$	−17.4432	−0.672885
$673$	−27.7283	−1.06885	−0.534424	−	0.845217i	$-0.679471\pi$
$673$	−27.7283	−1.06885	−0.534424	+	0.845217i	$0.679471\pi$
$674$	37.6383	1.44977
$675$	−9.67309	−0.372317
$676$	−42.6231	−1.63935
$677$	3.77175	0.144960	0.0724801	−	0.997370i	$-0.476909\pi$
$677$	3.77175	0.144960	0.0724801	+	0.997370i	$0.476909\pi$
$678$	16.8443	0.646901
$679$	0.444291	0.0170503
$680$	24.7888	0.950608
$681$	−0.579710	−0.0222146
$682$	11.5197	0.441111
$683$	46.3806	1.77470	0.887351	−	0.461094i	$-0.152543\pi$
$683$	46.3806	1.77470	0.887351	+	0.461094i	$0.152543\pi$
$684$	−53.2417	−2.03575
$685$	−13.8275	−0.528321
$686$	−9.90799	−0.378289
$687$	0.0153176	0.000584402 0
$688$	72.5689	2.76666
$689$	20.9230	0.797104
$690$	0.468839	0.0178484
$691$	33.7297	1.28314	0.641569	−	0.767066i	$-0.278284\pi$
$691$	33.7297	1.28314	0.641569	+	0.767066i	$0.278284\pi$
$692$	44.5699	1.69429
$693$	−19.4688	−0.739559
$694$	18.0488	0.685123
$695$	−26.0787	−0.989222
$696$	22.4588	0.851299
$697$	−8.19410	−0.310374
$698$	44.4700	1.68322
$699$	−9.00659	−0.340661
$700$	51.7078	1.95437
$701$	−0.351247	−0.0132664	−0.00663320	−	0.999978i	$-0.502111\pi$
$701$	−0.351247	−0.0132664	−0.00663320	+	0.999978i	$0.502111\pi$
$702$	−16.3396	−0.616697
$703$	−48.1961	−1.81775
$704$	−10.0166	−0.377514
$705$	9.09739	0.342627
$706$	−25.9372	−0.976161
$707$	48.5959	1.82764
$708$	1.01109	0.0379993
$709$	−28.4368	−1.06797	−0.533983	−	0.845496i	$-0.679305\pi$
$709$	−28.4368	−1.06797	−0.533983	+	0.845496i	$0.679305\pi$
$710$	−41.7309	−1.56613
$711$	44.5778	1.67180
$712$	103.332	3.87253
$713$	−0.513705	−0.0192384
$714$	−13.1202	−0.491013
$715$	5.58905	0.209019
$716$	8.38377	0.313316
$717$	9.38723	0.350573
$718$	−76.2935	−2.84725
$719$	22.4580	0.837543	0.418771	−	0.908092i	$-0.362461\pi$
$719$	22.4580	0.837543	0.418771	+	0.908092i	$0.362461\pi$
$720$	32.9828	1.22920
$721$	27.5811	1.02717
$722$	3.50529	0.130453
$723$	4.83878	0.179956
$724$	98.4673	3.65951
$725$	−17.4904	−0.649578
$726$	−10.0346	−0.372418
$727$	−7.90985	−0.293360	−0.146680	−	0.989184i	$-0.546859\pi$
$727$	−7.90985	−0.293360	−0.146680	+	0.989184i	$0.546859\pi$
$728$	50.2759	1.86335
$729$	−11.6433	−0.431232
$730$	−29.6747	−1.09831
$731$	20.8703	0.771914
$732$	−6.95489	−0.257060
$733$	−48.1819	−1.77964	−0.889820	−	0.456312i	$-0.849170\pi$
$733$	−48.1819	−1.77964	−0.889820	+	0.456312i	$0.849170\pi$
$734$	−49.4821	−1.82642
$735$	4.61988	0.170407
$736$	2.02342	0.0745843
$737$	22.4503	0.826968
$738$	−22.6016	−0.831978
$739$	4.43799	0.163254	0.0816271	−	0.996663i	$-0.473988\pi$
$739$	4.43799	0.163254	0.0816271	+	0.996663i	$0.473988\pi$
$740$	75.4913	2.77512
$741$	−4.65656	−0.171063
$742$	98.0345	3.59896
$743$	14.1111	0.517685	0.258842	−	0.965920i	$-0.416659\pi$
$743$	14.1111	0.517685	0.258842	+	0.965920i	$0.416659\pi$
$744$	8.65329	0.317245
$745$	0.136109	0.00498664
$746$	11.7708	0.430959
$747$	12.7075	0.464944
$748$	−23.9607	−0.876091
$749$	13.9512	0.509766
$750$	16.2313	0.592682
$751$	−36.8847	−1.34594	−0.672970	−	0.739670i	$-0.734982\pi$
$751$	−36.8847	−1.34594	−0.672970	+	0.739670i	$0.734982\pi$
$752$	102.688	3.74463
$753$	−11.0828	−0.403878
$754$	−29.5444	−1.07594
$755$	30.1733	1.09812
$756$	−53.7484	−1.95481
$757$	−42.2065	−1.53402	−0.767011	−	0.641634i	$-0.778257\pi$
$757$	−42.2065	−1.53402	−0.767011	+	0.641634i	$0.778257\pi$
$758$	−63.7458	−2.31535
$759$	−0.260853	−0.00946838
$760$	41.2224	1.49529
$761$	−51.5448	−1.86850	−0.934248	−	0.356623i	$-0.883928\pi$
$761$	−51.5448	−1.86850	−0.934248	+	0.356623i	$0.883928\pi$
$762$	−8.06197	−0.292054
$763$	55.1656	1.99713
$764$	116.317	4.20820
$765$	9.48560	0.342953
$766$	56.7879	2.05183
$767$	−0.765612	−0.0276447
$768$	12.0581	0.435111
$769$	43.6026	1.57235	0.786175	−	0.618004i	$-0.212058\pi$
$769$	43.6026	1.57235	0.786175	+	0.618004i	$0.212058\pi$
$770$	26.1874	0.943728
$771$	8.97001	0.323047
$772$	−1.88631	−0.0678897
$773$	−22.9252	−0.824564	−0.412282	−	0.911056i	$-0.635268\pi$
$773$	−22.9252	−0.824564	−0.412282	+	0.911056i	$0.635268\pi$
$774$	57.5661	2.06917
$775$	−6.73899	−0.242072
$776$	0.868152	0.0311648
$777$	−22.9991	−0.825090
$778$	−34.5896	−1.24010
$779$	−13.6263	−0.488214
$780$	7.29375	0.261158
$781$	23.2183	0.830817
$782$	1.52196	0.0544251
$783$	18.1807	0.649724
$784$	52.1473	1.86240
$785$	0.291481	0.0104034
$786$	−22.8108	−0.813635
$787$	21.8156	0.777642	0.388821	−	0.921313i	$-0.372883\pi$
$787$	21.8156	0.777642	0.388821	+	0.921313i	$0.372883\pi$
$788$	54.1015	1.92728
$789$	−3.27968	−0.116760
$790$	−59.9614	−2.13333
$791$	−41.9561	−1.49179
$792$	−38.0423	−1.35178
$793$	5.26632	0.187013
$794$	27.7643	0.985319
$795$	8.18650	0.290345
$796$	4.53853	0.160864
$797$	−13.5730	−0.480781	−0.240390	−	0.970676i	$-0.577275\pi$
$797$	−13.5730	−0.480781	−0.240390	+	0.970676i	$0.577275\pi$
$798$	−21.8182	−0.772357
$799$	29.5322	1.04477
$800$	26.5440	0.938474
$801$	39.5407	1.39710
$802$	81.0735	2.86280
$803$	16.5104	0.582641
$804$	29.2978	1.03325
$805$	−1.16779	−0.0411593
$806$	−11.3833	−0.400961
$807$	−6.19908	−0.218218
$808$	94.9572	3.34058
$809$	−9.59421	−0.337314	−0.168657	−	0.985675i	$-0.553943\pi$
$809$	−9.59421	−0.337314	−0.168657	+	0.985675i	$0.553943\pi$
$810$	22.7929	0.800860
$811$	35.6427	1.25158	0.625792	−	0.779990i	$-0.284776\pi$
$811$	35.6427	1.25158	0.625792	+	0.779990i	$0.284776\pi$
$812$	−97.1853	−3.41054
$813$	−3.32207	−0.116510
$814$	−59.8272	−2.09694
$815$	−23.0109	−0.806036
$816$	−12.3670	−0.432931
$817$	34.7061	1.21421
$818$	−91.5776	−3.20194
$819$	19.2384	0.672244
$820$	21.3434	0.745345
$821$	−15.8072	−0.551675	−0.275837	−	0.961204i	$-0.588955\pi$
$821$	−15.8072	−0.551675	−0.275837	+	0.961204i	$0.588955\pi$
$822$	14.3007	0.498794
$823$	25.7858	0.898835	0.449418	−	0.893322i	$-0.351632\pi$
$823$	25.7858	0.898835	0.449418	+	0.893322i	$0.351632\pi$
$824$	53.8939	1.87748
$825$	−3.42198	−0.119138
$826$	−3.58726	−0.124817
$827$	6.06814	0.211010	0.105505	−	0.994419i	$-0.466354\pi$
$827$	6.06814	0.211010	0.105505	+	0.994419i	$0.466354\pi$
$828$	2.94722	0.102423
$829$	40.3629	1.40186	0.700931	−	0.713229i	$-0.252768\pi$
$829$	40.3629	1.40186	0.700931	+	0.713229i	$0.252768\pi$
$830$	−17.0928	−0.593301
$831$	−12.8208	−0.444749
$832$	9.89804	0.343153
$833$	14.9972	0.519621
$834$	26.9712	0.933937
$835$	27.2795	0.944046
$836$	−39.8453	−1.37808
$837$	7.00494	0.242126
$838$	−71.2205	−2.46027
$839$	16.6357	0.574327	0.287163	−	0.957882i	$-0.407288\pi$
$839$	16.6357	0.574327	0.287163	+	0.957882i	$0.407288\pi$
$840$	19.6713	0.678725
$841$	3.87342	0.133566
$842$	14.4018	0.496318
$843$	7.83880	0.269983
$844$	−3.39660	−0.116916
$845$	12.6281	0.434418
$846$	81.4581	2.80059
$847$	24.9943	0.858815
$848$	92.4060	3.17323
$849$	14.3138	0.491247
$850$	19.9656	0.684816
$851$	2.66792	0.0914550
$852$	30.3001	1.03806
$853$	43.2753	1.48172	0.740859	−	0.671661i	$-0.234419\pi$
$853$	43.2753	1.48172	0.740859	+	0.671661i	$0.234419\pi$
$854$	24.6752	0.844370
$855$	15.7740	0.539461
$856$	27.2609	0.931758
$857$	−28.4052	−0.970303	−0.485152	−	0.874430i	$-0.661236\pi$
$857$	−28.4052	−0.970303	−0.485152	+	0.874430i	$0.661236\pi$
$858$	−5.78032	−0.197337
$859$	35.7011	1.21811	0.609053	−	0.793129i	$-0.291550\pi$
$859$	35.7011	1.21811	0.609053	+	0.793129i	$0.291550\pi$
$860$	−54.3614	−1.85371
$861$	−6.50248	−0.221604
$862$	−40.7730	−1.38873
$863$	15.7983	0.537782	0.268891	−	0.963171i	$-0.413343\pi$
$863$	15.7983	0.537782	0.268891	+	0.963171i	$0.413343\pi$
$864$	−27.5916	−0.938685
$865$	−13.2048	−0.448978
$866$	42.9124	1.45822
$867$	5.91820	0.200993
$868$	−37.4451	−1.27097
$869$	33.3614	1.13171
$870$	−11.5598	−0.391913
$871$	−22.1846	−0.751697
$872$	107.794	3.65038
$873$	0.332204	0.0112434
$874$	2.53093	0.0856100
$875$	−40.4292	−1.36676
$876$	21.5462	0.727980
$877$	48.7407	1.64586	0.822929	−	0.568144i	$-0.192338\pi$
$877$	48.7407	1.64586	0.822929	+	0.568144i	$0.192338\pi$
$878$	−86.6103	−2.92296
$879$	−15.5499	−0.524484
$880$	24.6839	0.832094
$881$	−6.69185	−0.225454	−0.112727	−	0.993626i	$-0.535959\pi$
$881$	−6.69185	−0.225454	−0.112727	+	0.993626i	$0.535959\pi$
$882$	41.3664	1.39288
$883$	25.6549	0.863356	0.431678	−	0.902028i	$-0.357922\pi$
$883$	25.6549	0.863356	0.431678	+	0.902028i	$0.357922\pi$
$884$	23.6772	0.796349
$885$	−0.299559	−0.0100696
$886$	36.8311	1.23737
$887$	41.7268	1.40105	0.700525	−	0.713628i	$-0.252949\pi$
$887$	41.7268	1.40105	0.700525	+	0.713628i	$0.252949\pi$
$888$	−44.9407	−1.50811
$889$	20.0809	0.673493
$890$	−53.1860	−1.78280
$891$	−12.6815	−0.424847
$892$	−90.4727	−3.02925
$893$	49.1104	1.64342
$894$	−0.140767	−0.00470795
$895$	−2.48388	−0.0830269
$896$	−16.2169	−0.541767
$897$	0.257766	0.00860657
$898$	−86.1271	−2.87410
$899$	12.6660	0.422435
$900$	38.6628	1.28876
$901$	26.5752	0.885350
$902$	−16.9148	−0.563200
$903$	16.5617	0.551140
$904$	−81.9829	−2.72671
$905$	−29.1731	−0.969748
$906$	−31.2060	−1.03675
$907$	1.48177	0.0492014	0.0246007	−	0.999697i	$-0.492169\pi$
$907$	1.48177	0.0492014	0.0246007	+	0.999697i	$0.492169\pi$
$908$	4.90177	0.162671
$909$	36.3360	1.20519
$910$	−25.8775	−0.857830
$911$	35.3708	1.17189	0.585944	−	0.810351i	$-0.300724\pi$
$911$	35.3708	1.17189	0.585944	+	0.810351i	$0.300724\pi$
$912$	−20.5656	−0.680994
$913$	9.51014	0.314740
$914$	−15.1997	−0.502760
$915$	2.06054	0.0681194
$916$	−0.129519	−0.00427941
$917$	56.8177	1.87629
$918$	−20.7536	−0.684970
$919$	5.49952	0.181412	0.0907062	−	0.995878i	$-0.471088\pi$
$919$	5.49952	0.181412	0.0907062	+	0.995878i	$0.471088\pi$
$920$	−2.28189	−0.0752316
$921$	−9.19880	−0.303111
$922$	−12.2130	−0.402215
$923$	−22.9435	−0.755196
$924$	−19.0142	−0.625521
$925$	34.9988	1.15075
$926$	−90.5608	−2.97601
$927$	20.6229	0.677343
$928$	−49.8898	−1.63771
$929$	−29.4266	−0.965454	−0.482727	−	0.875771i	$-0.660354\pi$
$929$	−29.4266	−0.965454	−0.482727	+	0.875771i	$0.660354\pi$
$930$	−4.45394	−0.146050
$931$	24.9394	0.817357
$932$	76.1557	2.49456
$933$	7.19405	0.235523
$934$	2.57255	0.0841765
$935$	7.09890	0.232159
$936$	37.5921	1.22874
$937$	−49.9919	−1.63317	−0.816583	−	0.577228i	$-0.804134\pi$
$937$	−49.9919	−1.63317	−0.816583	+	0.577228i	$0.804134\pi$
$938$	−103.946	−3.39395
$939$	−9.63007	−0.314265
$940$	−76.9234	−2.50897
$941$	−48.1830	−1.57072	−0.785360	−	0.619040i	$-0.787522\pi$
$941$	−48.1830	−1.57072	−0.785360	+	0.619040i	$0.787522\pi$
$942$	−0.301457	−0.00982198
$943$	0.754292	0.0245631
$944$	−3.38131	−0.110052
$945$	15.9242	0.518013
$946$	43.0817	1.40071
$947$	55.7783	1.81255	0.906276	−	0.422687i	$-0.138913\pi$
$947$	55.7783	1.81255	0.906276	+	0.422687i	$0.138913\pi$
$948$	43.5368	1.41401
$949$	−16.3150	−0.529609
$950$	33.2018	1.07721
$951$	1.71772	0.0557008
$952$	63.8576	2.06964
$953$	−2.59449	−0.0840438	−0.0420219	−	0.999117i	$-0.513380\pi$
$953$	−2.59449	−0.0840438	−0.0420219	+	0.999117i	$0.513380\pi$
$954$	73.3020	2.37324
$955$	−34.4615	−1.11515
$956$	−79.3742	−2.56715
$957$	6.43164	0.207905
$958$	21.0899	0.681384
$959$	−35.6205	−1.15024
$960$	3.87278	0.124994
$961$	−26.1198	−0.842575
$962$	59.1191	1.90608
$963$	10.4316	0.336152
$964$	−40.9145	−1.31777
$965$	0.558860	0.0179904
$966$	1.20776	0.0388590
$967$	13.6082	0.437611	0.218805	−	0.975769i	$-0.429784\pi$
$967$	13.6082	0.437611	0.218805	+	0.975769i	$0.429784\pi$
$968$	48.8393	1.56975
$969$	−5.91450	−0.190001
$970$	−0.446846	−0.0143474
$971$	43.3066	1.38978	0.694888	−	0.719118i	$-0.255454\pi$
$971$	43.3066	1.38978	0.694888	+	0.719118i	$0.255454\pi$
$972$	−61.3800	−1.96877
$973$	−67.1805	−2.15371
$974$	9.83574	0.315157
$975$	3.38148	0.108294
$976$	23.2586	0.744488
$977$	19.1952	0.614109	0.307054	−	0.951692i	$-0.400657\pi$
$977$	19.1952	0.614109	0.307054	+	0.951692i	$0.400657\pi$
$978$	23.7984	0.760988
$979$	29.5917	0.945755
$980$	−39.0636	−1.24784
$981$	41.2483	1.31696
$982$	20.4300	0.651948
$983$	16.7708	0.534907	0.267453	−	0.963571i	$-0.413818\pi$
$983$	16.7708	0.534907	0.267453	+	0.963571i	$0.413818\pi$
$984$	−12.7059	−0.405051
$985$	−16.0288	−0.510719
$986$	−37.5256	−1.19506
$987$	23.4355	0.745959
$988$	39.3738	1.25265
$989$	−1.92117	−0.0610897
$990$	19.5808	0.622317
$991$	44.2152	1.40454	0.702272	−	0.711909i	$-0.252169\pi$
$991$	44.2152	1.40454	0.702272	+	0.711909i	$0.252169\pi$
$992$	−19.2223	−0.610310
$993$	4.89173	0.155234
$994$	−107.502	−3.40974
$995$	−1.34464	−0.0426280
$996$	12.4108	0.393251
$997$	−14.6058	−0.462572	−0.231286	−	0.972886i	$-0.574293\pi$
$997$	−14.6058	−0.462572	−0.231286	+	0.972886i	$0.574293\pi$
$998$	49.9926	1.58249
$999$	−36.3800	−1.15101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.17	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.17	✓	340	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59088 q^{2} -0.557344 q^{3} +4.71265 q^{4} -1.39623 q^{5} +1.44401 q^{6} -3.59677 q^{7} -7.02815 q^{8} -2.68937 q^{9} +O(q^{10})\)	\(q-2.59088 q^{2} -0.557344 q^{3} +4.71265 q^{4} -1.39623 q^{5} +1.44401 q^{6} -3.59677 q^{7} -7.02815 q^{8} -2.68937 q^{9} +3.61746 q^{10} -2.01269 q^{11} -2.62657 q^{12} +1.98887 q^{13} +9.31880 q^{14} +0.778179 q^{15} +8.78378 q^{16} +2.52615 q^{17} +6.96782 q^{18} +4.20084 q^{19} -6.57994 q^{20} +2.00464 q^{21} +5.21462 q^{22} -0.232540 q^{23} +3.91710 q^{24} -3.05055 q^{25} -5.15291 q^{26} +3.17094 q^{27} -16.9503 q^{28} +5.73353 q^{29} -2.01617 q^{30} +2.20911 q^{31} -8.70140 q^{32} +1.12176 q^{33} -6.54494 q^{34} +5.02191 q^{35} -12.6741 q^{36} -11.4730 q^{37} -10.8839 q^{38} -1.10848 q^{39} +9.81290 q^{40} -3.24371 q^{41} -5.19378 q^{42} +8.26170 q^{43} -9.48509 q^{44} +3.75497 q^{45} +0.602482 q^{46} +11.6906 q^{47} -4.89559 q^{48} +5.93677 q^{49} +7.90360 q^{50} -1.40793 q^{51} +9.37284 q^{52} +10.5201 q^{53} -8.21551 q^{54} +2.81017 q^{55} +25.2787 q^{56} -2.34131 q^{57} -14.8549 q^{58} -0.384949 q^{59} +3.66729 q^{60} +2.64790 q^{61} -5.72353 q^{62} +9.67304 q^{63} +4.97672 q^{64} -2.77691 q^{65} -2.90634 q^{66} -11.1544 q^{67} +11.9048 q^{68} +0.129605 q^{69} -13.0112 q^{70} -11.5360 q^{71} +18.9013 q^{72} -8.20319 q^{73} +29.7250 q^{74} +1.70020 q^{75} +19.7971 q^{76} +7.23917 q^{77} +2.87195 q^{78} -16.5756 q^{79} -12.2642 q^{80} +6.30080 q^{81} +8.40407 q^{82} -4.72510 q^{83} +9.44717 q^{84} -3.52708 q^{85} -21.4051 q^{86} -3.19555 q^{87} +14.1455 q^{88} -14.7026 q^{89} -9.72867 q^{90} -7.15350 q^{91} -1.09588 q^{92} -1.23123 q^{93} -30.2889 q^{94} -5.86533 q^{95} +4.84968 q^{96} -0.123525 q^{97} -15.3815 q^{98} +5.41285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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