LMFDB - Embedded newform 8021.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58382 q^{2} -0.446323 q^{3} +4.67613 q^{4} +3.71919 q^{5} +1.15322 q^{6} -4.18348 q^{7} -6.91464 q^{8} -2.80080 q^{9} +O(q^{10})$	\(q-2.58382 q^{2} -0.446323 q^{3} +4.67613 q^{4} +3.71919 q^{5} +1.15322 q^{6} -4.18348 q^{7} -6.91464 q^{8} -2.80080 q^{9} -9.60973 q^{10} -1.28767 q^{11} -2.08706 q^{12} -1.00000 q^{13} +10.8094 q^{14} -1.65996 q^{15} +8.51394 q^{16} +3.38012 q^{17} +7.23676 q^{18} +5.31373 q^{19} +17.3914 q^{20} +1.86718 q^{21} +3.32711 q^{22} +1.48451 q^{23} +3.08616 q^{24} +8.83240 q^{25} +2.58382 q^{26} +2.58903 q^{27} -19.5625 q^{28} -0.268859 q^{29} +4.28904 q^{30} -6.68960 q^{31} -8.16920 q^{32} +0.574716 q^{33} -8.73362 q^{34} -15.5592 q^{35} -13.0969 q^{36} +2.94549 q^{37} -13.7297 q^{38} +0.446323 q^{39} -25.7169 q^{40} +1.72597 q^{41} -4.82447 q^{42} +2.89541 q^{43} -6.02131 q^{44} -10.4167 q^{45} -3.83571 q^{46} -12.5469 q^{47} -3.79996 q^{48} +10.5015 q^{49} -22.8213 q^{50} -1.50862 q^{51} -4.67613 q^{52} +8.91686 q^{53} -6.68958 q^{54} -4.78909 q^{55} +28.9273 q^{56} -2.37164 q^{57} +0.694684 q^{58} -14.8635 q^{59} -7.76219 q^{60} -4.99541 q^{61} +17.2847 q^{62} +11.7171 q^{63} +4.07988 q^{64} -3.71919 q^{65} -1.48496 q^{66} -6.03862 q^{67} +15.8059 q^{68} -0.662571 q^{69} +40.2022 q^{70} +0.687077 q^{71} +19.3665 q^{72} -2.19751 q^{73} -7.61061 q^{74} -3.94210 q^{75} +24.8477 q^{76} +5.38695 q^{77} -1.15322 q^{78} -0.126914 q^{79} +31.6650 q^{80} +7.24685 q^{81} -4.45959 q^{82} +11.7716 q^{83} +8.73120 q^{84} +12.5713 q^{85} -7.48123 q^{86} +0.119998 q^{87} +8.90378 q^{88} -11.7688 q^{89} +26.9149 q^{90} +4.18348 q^{91} +6.94177 q^{92} +2.98572 q^{93} +32.4190 q^{94} +19.7628 q^{95} +3.64610 q^{96} +15.1004 q^{97} -27.1341 q^{98} +3.60650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.58382	−1.82704	−0.913519	−	0.406797i	$-0.866646\pi$
$2$	−2.58382	−1.82704	−0.913519	+	0.406797i	$0.866646\pi$
$3$	−0.446323	−0.257685	−0.128842	−	0.991665i	$-0.541126\pi$
$3$	−0.446323	−0.257685	−0.128842	+	0.991665i	$0.541126\pi$
$4$	4.67613	2.33807
$5$	3.71919	1.66327	0.831637	−	0.555320i	$-0.187404\pi$
$5$	3.71919	1.66327	0.831637	+	0.555320i	$0.187404\pi$
$6$	1.15322	0.470799
$7$	−4.18348	−1.58121	−0.790604	−	0.612328i	$-0.790233\pi$
$7$	−4.18348	−1.58121	−0.790604	+	0.612328i	$0.790233\pi$
$8$	−6.91464	−2.44470
$9$	−2.80080	−0.933599
$10$	−9.60973	−3.03886
$11$	−1.28767	−0.388247	−0.194124	−	0.980977i	$-0.562186\pi$
$11$	−1.28767	−0.388247	−0.194124	+	0.980977i	$0.562186\pi$
$12$	−2.08706	−0.602483
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	10.8094	2.88893
$15$	−1.65996	−0.428600
$16$	8.51394	2.12848
$17$	3.38012	0.819799	0.409900	−	0.912131i	$-0.365564\pi$
$17$	3.38012	0.819799	0.409900	+	0.912131i	$0.365564\pi$
$18$	7.23676	1.70572
$19$	5.31373	1.21905	0.609527	−	0.792766i	$-0.291360\pi$
$19$	5.31373	1.21905	0.609527	+	0.792766i	$0.291360\pi$
$20$	17.3914	3.88884
$21$	1.86718	0.407453
$22$	3.32711	0.709342
$23$	1.48451	0.309542	0.154771	−	0.987950i	$-0.450536\pi$
$23$	1.48451	0.309542	0.154771	+	0.987950i	$0.450536\pi$
$24$	3.08616	0.629960
$25$	8.83240	1.76648
$26$	2.58382	0.506729
$27$	2.58903	0.498259
$28$	−19.5625	−3.69697
$29$	−0.268859	−0.0499259	−0.0249629	−	0.999688i	$-0.507947\pi$
$29$	−0.268859	−0.0499259	−0.0249629	+	0.999688i	$0.507947\pi$
$30$	4.28904	0.783068
$31$	−6.68960	−1.20149	−0.600744	−	0.799442i	$-0.705129\pi$
$31$	−6.68960	−1.20149	−0.600744	+	0.799442i	$0.705129\pi$
$32$	−8.16920	−1.44412
$33$	0.574716	0.100045
$34$	−8.73362	−1.49780
$35$	−15.5592	−2.62998
$36$	−13.0969	−2.18281
$37$	2.94549	0.484235	0.242117	−	0.970247i	$-0.422158\pi$
$37$	2.94549	0.484235	0.242117	+	0.970247i	$0.422158\pi$
$38$	−13.7297	−2.22726
$39$	0.446323	0.0714688
$40$	−25.7169	−4.06620
$41$	1.72597	0.269551	0.134776	−	0.990876i	$-0.456969\pi$
$41$	1.72597	0.269551	0.134776	+	0.990876i	$0.456969\pi$
$42$	−4.82447	−0.744432
$43$	2.89541	0.441546	0.220773	−	0.975325i	$-0.429142\pi$
$43$	2.89541	0.441546	0.220773	+	0.975325i	$0.429142\pi$
$44$	−6.02131	−0.907747
$45$	−10.4167	−1.55283
$46$	−3.83571	−0.565545
$47$	−12.5469	−1.83016	−0.915080	−	0.403273i	$-0.867872\pi$
$47$	−12.5469	−1.83016	−0.915080	+	0.403273i	$0.867872\pi$
$48$	−3.79996	−0.548477
$49$	10.5015	1.50022
$50$	−22.8213	−3.22743
$51$	−1.50862	−0.211250
$52$	−4.67613	−0.648463
$53$	8.91686	1.22483	0.612413	−	0.790538i	$-0.290199\pi$
$53$	8.91686	1.22483	0.612413	+	0.790538i	$0.290199\pi$
$54$	−6.68958	−0.910337
$55$	−4.78909	−0.645761
$56$	28.9273	3.86557
$57$	−2.37164	−0.314131
$58$	0.694684	0.0912164
$59$	−14.8635	−1.93507	−0.967534	−	0.252740i	$-0.918668\pi$
$59$	−14.8635	−1.93507	−0.967534	+	0.252740i	$0.918668\pi$
$60$	−7.76219	−1.00209
$61$	−4.99541	−0.639597	−0.319798	−	0.947486i	$-0.603615\pi$
$61$	−4.99541	−0.639597	−0.319798	+	0.947486i	$0.603615\pi$
$62$	17.2847	2.19516
$63$	11.7171	1.47621
$64$	4.07988	0.509985
$65$	−3.71919	−0.461309
$66$	−1.48496	−0.182786
$67$	−6.03862	−0.737735	−0.368867	−	0.929482i	$-0.620254\pi$
$67$	−6.03862	−0.737735	−0.368867	+	0.929482i	$0.620254\pi$
$68$	15.8059	1.91674
$69$	−0.662571	−0.0797642
$70$	40.2022	4.80508
$71$	0.687077	0.0815410	0.0407705	−	0.999169i	$-0.487019\pi$
$71$	0.687077	0.0815410	0.0407705	+	0.999169i	$0.487019\pi$
$72$	19.3665	2.28236
$73$	−2.19751	−0.257200	−0.128600	−	0.991697i	$-0.541048\pi$
$73$	−2.19751	−0.257200	−0.128600	+	0.991697i	$0.541048\pi$
$74$	−7.61061	−0.884715
$75$	−3.94210	−0.455195
$76$	24.8477	2.85023
$77$	5.38695	0.613900
$78$	−1.15322	−0.130576
$79$	−0.126914	−0.0142790	−0.00713948	−	0.999975i	$-0.502273\pi$
$79$	−0.126914	−0.0142790	−0.00713948	+	0.999975i	$0.502273\pi$
$80$	31.6650	3.54025
$81$	7.24685	0.805205
$82$	−4.45959	−0.492480
$83$	11.7716	1.29210	0.646052	−	0.763294i	$-0.276419\pi$
$83$	11.7716	1.29210	0.646052	+	0.763294i	$0.276419\pi$
$84$	8.73120	0.952652
$85$	12.5713	1.36355
$86$	−7.48123	−0.806721
$87$	0.119998	0.0128651
$88$	8.90378	0.949146
$89$	−11.7688	−1.24749	−0.623746	−	0.781627i	$-0.714390\pi$
$89$	−11.7688	−1.24749	−0.623746	+	0.781627i	$0.714390\pi$
$90$	26.9149	2.83708
$91$	4.18348	0.438548
$92$	6.94177	0.723729
$93$	2.98572	0.309605
$94$	32.4190	3.34377
$95$	19.7628	2.02762
$96$	3.64610	0.372129
$97$	15.1004	1.53321	0.766607	−	0.642117i	$-0.221944\pi$
$97$	15.1004	1.53321	0.766607	+	0.642117i	$0.221944\pi$
$98$	−27.1341	−2.74096
$99$	3.60650	0.362467
$100$	41.3015	4.13015
$101$	−17.7123	−1.76244	−0.881221	−	0.472705i	$-0.843278\pi$
$101$	−17.7123	−1.76244	−0.881221	+	0.472705i	$0.843278\pi$
$102$	3.89801	0.385961
$103$	6.75264	0.665358	0.332679	−	0.943040i	$-0.392048\pi$
$103$	6.75264	0.665358	0.332679	+	0.943040i	$0.392048\pi$
$104$	6.91464	0.678036
$105$	6.94442	0.677706
$106$	−23.0396	−2.23780
$107$	−15.9900	−1.54582	−0.772908	−	0.634518i	$-0.781198\pi$
$107$	−15.9900	−1.54582	−0.772908	+	0.634518i	$0.781198\pi$
$108$	12.1066	1.16496
$109$	4.16814	0.399236	0.199618	−	0.979874i	$-0.436030\pi$
$109$	4.16814	0.399236	0.199618	+	0.979874i	$0.436030\pi$
$110$	12.3742	1.17983
$111$	−1.31464	−0.124780
$112$	−35.6179	−3.36558
$113$	2.55137	0.240013	0.120006	−	0.992773i	$-0.461708\pi$
$113$	2.55137	0.240013	0.120006	+	0.992773i	$0.461708\pi$
$114$	6.12789	0.573930
$115$	5.52119	0.514853
$116$	−1.25722	−0.116730
$117$	2.80080	0.258934
$118$	38.4047	3.53544
$119$	−14.1407	−1.29627
$120$	11.4780	1.04780
$121$	−9.34191	−0.849264
$122$	12.9072	1.16857
$123$	−0.770339	−0.0694592
$124$	−31.2814	−2.80916
$125$	14.2535	1.27487
$126$	−30.2749	−2.69710
$127$	19.7616	1.75356	0.876781	−	0.480890i	$-0.159687\pi$
$127$	19.7616	1.75356	0.876781	+	0.480890i	$0.159687\pi$
$128$	5.79672	0.512363
$129$	−1.29229	−0.113780
$130$	9.60973	0.842829
$131$	22.2796	1.94658	0.973289	−	0.229585i	$-0.0737368\pi$
$131$	22.2796	1.94658	0.973289	+	0.229585i	$0.0737368\pi$
$132$	2.68745	0.233912
$133$	−22.2299	−1.92758
$134$	15.6027	1.34787
$135$	9.62910	0.828741
$136$	−23.3723	−2.00416
$137$	15.7699	1.34732	0.673659	−	0.739043i	$-0.264722\pi$
$137$	15.7699	1.34732	0.673659	+	0.739043i	$0.264722\pi$
$138$	1.71197	0.145732
$139$	−14.5414	−1.23338	−0.616691	−	0.787205i	$-0.711527\pi$
$139$	−14.5414	−1.23338	−0.616691	+	0.787205i	$0.711527\pi$
$140$	−72.7568	−6.14907
$141$	5.59998	0.471604
$142$	−1.77528	−0.148978
$143$	1.28767	0.107680
$144$	−23.8458	−1.98715
$145$	−0.999939	−0.0830404
$146$	5.67798	0.469913
$147$	−4.68708	−0.386584
$148$	13.7735	1.13217
$149$	17.9376	1.46950	0.734752	−	0.678336i	$-0.237298\pi$
$149$	17.9376	1.46950	0.734752	+	0.678336i	$0.237298\pi$
$150$	10.1857	0.831658
$151$	15.4756	1.25939	0.629694	−	0.776843i	$-0.283180\pi$
$151$	15.4756	1.25939	0.629694	+	0.776843i	$0.283180\pi$
$152$	−36.7425	−2.98021
$153$	−9.46702	−0.765364
$154$	−13.9189	−1.12162
$155$	−24.8799	−1.99840
$156$	2.08706	0.167099
$157$	2.43032	0.193961	0.0969803	−	0.995286i	$-0.469082\pi$
$157$	2.43032	0.193961	0.0969803	+	0.995286i	$0.469082\pi$
$158$	0.327923	0.0260882
$159$	−3.97980	−0.315619
$160$	−30.3828	−2.40197
$161$	−6.21043	−0.489450
$162$	−18.7246	−1.47114
$163$	−4.14422	−0.324601	−0.162300	−	0.986741i	$-0.551891\pi$
$163$	−4.14422	−0.324601	−0.162300	+	0.986741i	$0.551891\pi$
$164$	8.07086	0.630228
$165$	2.13748	0.166403
$166$	−30.4158	−2.36072
$167$	−24.9211	−1.92845	−0.964225	−	0.265086i	$-0.914600\pi$
$167$	−24.9211	−1.92845	−0.964225	+	0.265086i	$0.914600\pi$
$168$	−12.9109	−0.996098
$169$	1.00000	0.0769231
$170$	−32.4820	−2.49126
$171$	−14.8827	−1.13811
$172$	13.5393	1.03236
$173$	−13.9956	−1.06407	−0.532033	−	0.846724i	$-0.678572\pi$
$173$	−13.9956	−1.06407	−0.532033	+	0.846724i	$0.678572\pi$
$174$	−0.310053	−0.0235051
$175$	−36.9502	−2.79317
$176$	−10.9631	−0.826378
$177$	6.63394	0.498637
$178$	30.4085	2.27921
$179$	10.8702	0.812478	0.406239	−	0.913767i	$-0.366840\pi$
$179$	10.8702	0.812478	0.406239	+	0.913767i	$0.366840\pi$
$180$	−48.7099	−3.63062
$181$	11.2796	0.838408	0.419204	−	0.907892i	$-0.362309\pi$
$181$	11.2796	0.838408	0.419204	+	0.907892i	$0.362309\pi$
$182$	−10.8094	−0.801244
$183$	2.22957	0.164814
$184$	−10.2649	−0.756736
$185$	10.9548	0.805415
$186$	−7.71457	−0.565660
$187$	−4.35248	−0.318285
$188$	−58.6711	−4.27903
$189$	−10.8312	−0.787851
$190$	−51.0635	−3.70454
$191$	−11.7427	−0.849675	−0.424837	−	0.905270i	$-0.639669\pi$
$191$	−11.7427	−0.849675	−0.424837	+	0.905270i	$0.639669\pi$
$192$	−1.82094	−0.131415
$193$	−9.84366	−0.708562	−0.354281	−	0.935139i	$-0.615274\pi$
$193$	−9.84366	−0.708562	−0.354281	+	0.935139i	$0.615274\pi$
$194$	−39.0167	−2.80124
$195$	1.65996	0.118872
$196$	49.1066	3.50761
$197$	−15.4980	−1.10418	−0.552092	−	0.833783i	$-0.686170\pi$
$197$	−15.4980	−1.10418	−0.552092	+	0.833783i	$0.686170\pi$
$198$	−9.31855	−0.662241
$199$	−3.67327	−0.260392	−0.130196	−	0.991488i	$-0.541561\pi$
$199$	−3.67327	−0.260392	−0.130196	+	0.991488i	$0.541561\pi$
$200$	−61.0729	−4.31851
$201$	2.69517	0.190103
$202$	45.7654	3.22005
$203$	1.12477	0.0789432
$204$	−7.05452	−0.493915
$205$	6.41921	0.448337
$206$	−17.4476	−1.21563
$207$	−4.15781	−0.288988
$208$	−8.51394	−0.590335
$209$	−6.84233	−0.473294
$210$	−17.9431	−1.23819
$211$	−23.6377	−1.62729	−0.813643	−	0.581365i	$-0.802519\pi$
$211$	−23.6377	−1.62729	−0.813643	+	0.581365i	$0.802519\pi$
$212$	41.6964	2.86372
$213$	−0.306658	−0.0210119
$214$	41.3154	2.82426
$215$	10.7686	0.734412
$216$	−17.9022	−1.21809
$217$	27.9858	1.89980
$218$	−10.7697	−0.729418
$219$	0.980801	0.0662764
$220$	−22.3944	−1.50983
$221$	−3.38012	−0.227371
$222$	3.39679	0.227977
$223$	−13.6750	−0.915747	−0.457874	−	0.889017i	$-0.651389\pi$
$223$	−13.6750	−0.915747	−0.457874	+	0.889017i	$0.651389\pi$
$224$	34.1757	2.28346
$225$	−24.7378	−1.64918
$226$	−6.59229	−0.438513
$227$	16.6318	1.10389	0.551944	−	0.833881i	$-0.313886\pi$
$227$	16.6318	1.10389	0.551944	+	0.833881i	$0.313886\pi$
$228$	−11.0901	−0.734459
$229$	−8.40384	−0.555341	−0.277671	−	0.960676i	$-0.589562\pi$
$229$	−8.40384	−0.555341	−0.277671	+	0.960676i	$0.589562\pi$
$230$	−14.2658	−0.940656
$231$	−2.40432	−0.158192
$232$	1.85906	0.122054
$233$	21.5400	1.41113	0.705565	−	0.708645i	$-0.250693\pi$
$233$	21.5400	1.41113	0.705565	+	0.708645i	$0.250693\pi$
$234$	−7.23676	−0.473081
$235$	−46.6645	−3.04406
$236$	−69.5039	−4.52432
$237$	0.0566447	0.00367947
$238$	36.5370	2.36834
$239$	−3.97130	−0.256882	−0.128441	−	0.991717i	$-0.540997\pi$
$239$	−3.97130	−0.256882	−0.128441	+	0.991717i	$0.540997\pi$
$240$	−14.1328	−0.912268
$241$	15.6787	1.00996	0.504978	−	0.863132i	$-0.331500\pi$
$241$	15.6787	1.00996	0.504978	+	0.863132i	$0.331500\pi$
$242$	24.1378	1.55164
$243$	−11.0015	−0.705748
$244$	−23.3592	−1.49542
$245$	39.0573	2.49528
$246$	1.99042	0.126904
$247$	−5.31373	−0.338105
$248$	46.2562	2.93727
$249$	−5.25394	−0.332955
$250$	−36.8284	−2.32923
$251$	−5.63780	−0.355855	−0.177927	−	0.984044i	$-0.556939\pi$
$251$	−5.63780	−0.355855	−0.177927	+	0.984044i	$0.556939\pi$
$252$	54.7906	3.45148
$253$	−1.91156	−0.120179
$254$	−51.0605	−3.20382
$255$	−5.61087	−0.351366
$256$	−23.1374	−1.44609
$257$	13.0924	0.816680	0.408340	−	0.912830i	$-0.366108\pi$
$257$	13.0924	0.816680	0.408340	+	0.912830i	$0.366108\pi$
$258$	3.33904	0.207880
$259$	−12.3224	−0.765676
$260$	−17.3914	−1.07857
$261$	0.753019	0.0466107
$262$	−57.5665	−3.55647
$263$	18.1177	1.11718	0.558591	−	0.829443i	$-0.311342\pi$
$263$	18.1177	1.11718	0.558591	+	0.829443i	$0.311342\pi$
$264$	−3.97396	−0.244580
$265$	33.1635	2.03722
$266$	57.4381	3.52176
$267$	5.25269	0.321459
$268$	−28.2374	−1.72487
$269$	−6.94746	−0.423594	−0.211797	−	0.977314i	$-0.567932\pi$
$269$	−6.94746	−0.423594	−0.211797	+	0.977314i	$0.567932\pi$
$270$	−24.8799	−1.51414
$271$	12.0291	0.730716	0.365358	−	0.930867i	$-0.380947\pi$
$271$	12.0291	0.730716	0.365358	+	0.930867i	$0.380947\pi$
$272$	28.7781	1.74493
$273$	−1.86718	−0.113007
$274$	−40.7467	−2.46160
$275$	−11.3732	−0.685831
$276$	−3.09827	−0.186494
$277$	−16.4426	−0.987941	−0.493970	−	0.869479i	$-0.664455\pi$
$277$	−16.4426	−0.987941	−0.493970	+	0.869479i	$0.664455\pi$
$278$	37.5723	2.25344
$279$	18.7362	1.12171
$280$	107.586	6.42951
$281$	9.51005	0.567322	0.283661	−	0.958925i	$-0.408451\pi$
$281$	9.51005	0.567322	0.283661	+	0.958925i	$0.408451\pi$
$282$	−14.4694	−0.861638
$283$	9.29976	0.552813	0.276407	−	0.961041i	$-0.410856\pi$
$283$	9.29976	0.552813	0.276407	+	0.961041i	$0.410856\pi$
$284$	3.21286	0.190648
$285$	−8.82059	−0.522486
$286$	−3.32711	−0.196736
$287$	−7.22056	−0.426216
$288$	22.8803	1.34823
$289$	−5.57479	−0.327929
$290$	2.58366	0.151718
$291$	−6.73965	−0.395086
$292$	−10.2759	−0.601349
$293$	25.8487	1.51010	0.755049	−	0.655668i	$-0.227613\pi$
$293$	25.8487	1.51010	0.755049	+	0.655668i	$0.227613\pi$
$294$	12.1106	0.706303
$295$	−55.2804	−3.21855
$296$	−20.3670	−1.18381
$297$	−3.33381	−0.193447
$298$	−46.3475	−2.68484
$299$	−1.48451	−0.0858515
$300$	−18.4338	−1.06428
$301$	−12.1129	−0.698177
$302$	−39.9863	−2.30095
$303$	7.90541	0.454154
$304$	45.2408	2.59474
$305$	−18.5789	−1.06382
$306$	24.4611	1.39835
$307$	8.98247	0.512657	0.256328	−	0.966590i	$-0.417487\pi$
$307$	8.98247	0.512657	0.256328	+	0.966590i	$0.417487\pi$
$308$	25.1901	1.43534
$309$	−3.01386	−0.171452
$310$	64.2853	3.65116
$311$	26.7126	1.51473	0.757367	−	0.652989i	$-0.226485\pi$
$311$	26.7126	1.51473	0.757367	+	0.652989i	$0.226485\pi$
$312$	−3.08616	−0.174720
$313$	−7.70333	−0.435418	−0.217709	−	0.976014i	$-0.569858\pi$
$313$	−7.70333	−0.435418	−0.217709	+	0.976014i	$0.569858\pi$
$314$	−6.27951	−0.354373
$315$	43.5781	2.45535
$316$	−0.593467	−0.0333851
$317$	−6.04563	−0.339556	−0.169778	−	0.985482i	$-0.554305\pi$
$317$	−6.04563	−0.339556	−0.169778	+	0.985482i	$0.554305\pi$
$318$	10.2831	0.576647
$319$	0.346202	0.0193836
$320$	15.1739	0.848245
$321$	7.13672	0.398333
$322$	16.0466	0.894244
$323$	17.9610	0.999379
$324$	33.8872	1.88262
$325$	−8.83240	−0.489934
$326$	10.7079	0.593057
$327$	−1.86034	−0.102877
$328$	−11.9345	−0.658970
$329$	52.4899	2.89386
$330$	−5.52287	−0.304024
$331$	−28.9724	−1.59247	−0.796233	−	0.604990i	$-0.793177\pi$
$331$	−28.9724	−1.59247	−0.796233	+	0.604990i	$0.793177\pi$
$332$	55.0456	3.02102
$333$	−8.24970	−0.452081
$334$	64.3916	3.52335
$335$	−22.4588	−1.22706
$336$	15.8971	0.867257
$337$	10.5685	0.575702	0.287851	−	0.957675i	$-0.407059\pi$
$337$	10.5685	0.575702	0.287851	+	0.957675i	$0.407059\pi$
$338$	−2.58382	−0.140541
$339$	−1.13874	−0.0618476
$340$	58.7851	3.18807
$341$	8.61400	0.466474
$342$	38.4542	2.07936
$343$	−14.6486	−0.790952
$344$	−20.0207	−1.07945
$345$	−2.46423	−0.132670
$346$	36.1621	1.94409
$347$	−11.4343	−0.613827	−0.306913	−	0.951737i	$-0.599296\pi$
$347$	−11.4343	−0.613827	−0.306913	+	0.951737i	$0.599296\pi$
$348$	0.561126	0.0300795
$349$	−23.9852	−1.28390	−0.641948	−	0.766748i	$-0.721874\pi$
$349$	−23.9852	−1.28390	−0.641948	+	0.766748i	$0.721874\pi$
$350$	95.4728	5.10323
$351$	−2.58903	−0.138192
$352$	10.5192	0.560677
$353$	−19.8756	−1.05787	−0.528934	−	0.848663i	$-0.677408\pi$
$353$	−19.8756	−1.05787	−0.528934	+	0.848663i	$0.677408\pi$
$354$	−17.1409	−0.911029
$355$	2.55537	0.135625
$356$	−55.0325	−2.91672
$357$	6.31131	0.334030
$358$	−28.0867	−1.48443
$359$	−18.9350	−0.999350	−0.499675	−	0.866213i	$-0.666547\pi$
$359$	−18.9350	−0.999350	−0.499675	+	0.866213i	$0.666547\pi$
$360$	72.0278	3.79620
$361$	9.23573	0.486091
$362$	−29.1445	−1.53180
$363$	4.16951	0.218842
$364$	19.5625	1.02535
$365$	−8.17298	−0.427793
$366$	−5.76080	−0.301122
$367$	−18.6112	−0.971494	−0.485747	−	0.874099i	$-0.661452\pi$
$367$	−18.6112	−0.971494	−0.485747	+	0.874099i	$0.661452\pi$
$368$	12.6390	0.658855
$369$	−4.83409	−0.251653
$370$	−28.3053	−1.47152
$371$	−37.3036	−1.93670
$372$	13.9616	0.723876
$373$	27.4813	1.42293	0.711463	−	0.702724i	$-0.248033\pi$
$373$	27.4813	1.42293	0.711463	+	0.702724i	$0.248033\pi$
$374$	11.2460	0.581518
$375$	−6.36164	−0.328514
$376$	86.7576	4.47418
$377$	0.268859	0.0138469
$378$	27.9858	1.43943
$379$	−21.4630	−1.10248	−0.551240	−	0.834347i	$-0.685845\pi$
$379$	−21.4630	−1.10248	−0.551240	+	0.834347i	$0.685845\pi$
$380$	92.4134	4.74071
$381$	−8.82007	−0.451866
$382$	30.3411	1.55239
$383$	10.4959	0.536316	0.268158	−	0.963375i	$-0.413585\pi$
$383$	10.4959	0.536316	0.268158	+	0.963375i	$0.413585\pi$
$384$	−2.58721	−0.132028
$385$	20.0351	1.02108
$386$	25.4343	1.29457
$387$	−8.10946	−0.412227
$388$	70.6115	3.58475
$389$	−8.02348	−0.406807	−0.203403	−	0.979095i	$-0.565200\pi$
$389$	−8.02348	−0.406807	−0.203403	+	0.979095i	$0.565200\pi$
$390$	−4.28904	−0.217184
$391$	5.01783	0.253762
$392$	−72.6144	−3.66758
$393$	−9.94389	−0.501603
$394$	40.0439	2.01738
$395$	−0.472018	−0.0237498
$396$	16.8645	0.847471
$397$	−8.44935	−0.424061	−0.212030	−	0.977263i	$-0.568008\pi$
$397$	−8.44935	−0.424061	−0.212030	+	0.977263i	$0.568008\pi$
$398$	9.49108	0.475745
$399$	9.92171	0.496707
$400$	75.1985	3.75993
$401$	−19.2905	−0.963321	−0.481661	−	0.876358i	$-0.659966\pi$
$401$	−19.2905	−0.963321	−0.481661	+	0.876358i	$0.659966\pi$
$402$	−6.96385	−0.347325
$403$	6.68960	0.333233
$404$	−82.8251	−4.12070
$405$	26.9524	1.33928
$406$	−2.90620	−0.144232
$407$	−3.79281	−0.188003
$408$	10.4316	0.516441
$409$	−23.2994	−1.15208	−0.576041	−	0.817421i	$-0.695403\pi$
$409$	−23.2994	−1.15208	−0.576041	+	0.817421i	$0.695403\pi$
$410$	−16.5861	−0.819129
$411$	−7.03849	−0.347183
$412$	31.5762	1.55565
$413$	62.1814	3.05975
$414$	10.7430	0.527992
$415$	43.7809	2.14912
$416$	8.16920	0.400528
$417$	6.49015	0.317824
$418$	17.6794	0.864726
$419$	−1.63988	−0.0801135	−0.0400567	−	0.999197i	$-0.512754\pi$
$419$	−1.63988	−0.0801135	−0.0400567	+	0.999197i	$0.512754\pi$
$420$	32.4730	1.58452
$421$	−16.1832	−0.788721	−0.394360	−	0.918956i	$-0.629034\pi$
$421$	−16.1832	−0.788721	−0.394360	+	0.918956i	$0.629034\pi$
$422$	61.0755	2.97311
$423$	35.1414	1.70863
$424$	−61.6569	−2.99433
$425$	29.8546	1.44816
$426$	0.792349	0.0383894
$427$	20.8982	1.01134
$428$	−74.7715	−3.61422
$429$	−0.574716	−0.0277476
$430$	−27.8241	−1.34180
$431$	−15.5310	−0.748104	−0.374052	−	0.927408i	$-0.622032\pi$
$431$	−15.5310	−0.748104	−0.374052	+	0.927408i	$0.622032\pi$
$432$	22.0428	1.06054
$433$	1.05054	0.0504858	0.0252429	−	0.999681i	$-0.491964\pi$
$433$	1.05054	0.0504858	0.0252429	+	0.999681i	$0.491964\pi$
$434$	−72.3104	−3.47101
$435$	0.446296	0.0213982
$436$	19.4908	0.933439
$437$	7.88829	0.377348
$438$	−2.53421	−0.121089
$439$	−26.3321	−1.25676	−0.628382	−	0.777905i	$-0.716283\pi$
$439$	−26.3321	−1.25676	−0.628382	+	0.777905i	$0.716283\pi$
$440$	33.1149	1.57869
$441$	−29.4127	−1.40060
$442$	8.73362	0.415416
$443$	−10.0017	−0.475193	−0.237597	−	0.971364i	$-0.576360\pi$
$443$	−10.0017	−0.475193	−0.237597	+	0.971364i	$0.576360\pi$
$444$	−6.14742	−0.291743
$445$	−43.7705	−2.07492
$446$	35.3338	1.67310
$447$	−8.00595	−0.378669
$448$	−17.0681	−0.806393
$449$	−7.16089	−0.337943	−0.168972	−	0.985621i	$-0.554045\pi$
$449$	−7.16089	−0.337943	−0.168972	+	0.985621i	$0.554045\pi$
$450$	63.9179	3.01312
$451$	−2.22248	−0.104652
$452$	11.9306	0.561166
$453$	−6.90713	−0.324525
$454$	−42.9735	−2.01685
$455$	15.5592	0.729426
$456$	16.3990	0.767955
$457$	−10.2821	−0.480975	−0.240488	−	0.970652i	$-0.577307\pi$
$457$	−10.2821	−0.480975	−0.240488	+	0.970652i	$0.577307\pi$
$458$	21.7140	1.01463
$459$	8.75122	0.408472
$460$	25.8178	1.20376
$461$	23.0775	1.07483	0.537413	−	0.843319i	$-0.319402\pi$
$461$	23.0775	1.07483	0.537413	+	0.843319i	$0.319402\pi$
$462$	6.21232	0.289024
$463$	31.9434	1.48454	0.742268	−	0.670103i	$-0.233750\pi$
$463$	31.9434	1.48454	0.742268	+	0.670103i	$0.233750\pi$
$464$	−2.28905	−0.106266
$465$	11.1045	0.514958
$466$	−55.6554	−2.57819
$467$	−11.5041	−0.532345	−0.266172	−	0.963925i	$-0.585759\pi$
$467$	−11.5041	−0.532345	−0.266172	+	0.963925i	$0.585759\pi$
$468$	13.0969	0.605404
$469$	25.2625	1.16651
$470$	120.573	5.56160
$471$	−1.08471	−0.0499806
$472$	102.776	4.73065
$473$	−3.72833	−0.171429
$474$	−0.146360	−0.00672252
$475$	46.9330	2.15343
$476$	−66.1236	−3.03077
$477$	−24.9743	−1.14350
$478$	10.2611	0.469334
$479$	−27.5409	−1.25838	−0.629189	−	0.777253i	$-0.716613\pi$
$479$	−27.5409	−1.25838	−0.629189	+	0.777253i	$0.716613\pi$
$480$	13.5606	0.618952
$481$	−2.94549	−0.134303
$482$	−40.5111	−1.84523
$483$	2.77186	0.126124
$484$	−43.6840	−1.98564
$485$	56.1613	2.55015
$486$	28.4259	1.28943
$487$	−38.9715	−1.76597	−0.882984	−	0.469402i	$-0.844469\pi$
$487$	−38.9715	−1.76597	−0.882984	+	0.469402i	$0.844469\pi$
$488$	34.5415	1.56362
$489$	1.84966	0.0836446
$490$	−100.917	−4.55896
$491$	−19.3718	−0.874236	−0.437118	−	0.899404i	$-0.644001\pi$
$491$	−19.3718	−0.874236	−0.437118	+	0.899404i	$0.644001\pi$
$492$	−3.60221	−0.162400
$493$	−0.908776	−0.0409292
$494$	13.7297	0.617730
$495$	13.4133	0.602882
$496$	−56.9548	−2.55735
$497$	−2.87437	−0.128933
$498$	13.5752	0.608321
$499$	−37.1869	−1.66472	−0.832358	−	0.554239i	$-0.813009\pi$
$499$	−37.1869	−1.66472	−0.832358	+	0.554239i	$0.813009\pi$
$500$	66.6510	2.98072
$501$	11.1228	0.496932
$502$	14.5671	0.650160
$503$	−10.2509	−0.457063	−0.228531	−	0.973537i	$-0.573392\pi$
$503$	−10.2509	−0.457063	−0.228531	+	0.973537i	$0.573392\pi$
$504$	−81.0195	−3.60889
$505$	−65.8755	−2.93142
$506$	4.93913	0.219571
$507$	−0.446323	−0.0198219
$508$	92.4080	4.09994
$509$	9.00656	0.399209	0.199604	−	0.979877i	$-0.436034\pi$
$509$	9.00656	0.399209	0.199604	+	0.979877i	$0.436034\pi$
$510$	14.4975	0.641959
$511$	9.19326	0.406686
$512$	48.1896	2.12970
$513$	13.7574	0.607404
$514$	−33.8284	−1.49211
$515$	25.1144	1.10667
$516$	−6.04291	−0.266024
$517$	16.1563	0.710554
$518$	31.8389	1.39892
$519$	6.24656	0.274193
$520$	25.7169	1.12776
$521$	−35.1545	−1.54014	−0.770072	−	0.637956i	$-0.779780\pi$
$521$	−35.1545	−1.54014	−0.770072	+	0.637956i	$0.779780\pi$
$522$	−1.94567	−0.0851595
$523$	6.91469	0.302358	0.151179	−	0.988506i	$-0.451693\pi$
$523$	6.91469	0.302358	0.151179	+	0.988506i	$0.451693\pi$
$524$	104.182	4.55122
$525$	16.4917	0.719758
$526$	−46.8128	−2.04113
$527$	−22.6116	−0.984979
$528$	4.89310	0.212945
$529$	−20.7962	−0.904184
$530$	−85.6887	−3.72208
$531$	41.6298	1.80658
$532$	−103.950	−4.50680
$533$	−1.72597	−0.0747600
$534$	−13.5720	−0.587318
$535$	−59.4701	−2.57111
$536$	41.7549	1.80354
$537$	−4.85162	−0.209363
$538$	17.9510	0.773922
$539$	−13.5225	−0.582456
$540$	45.0269	1.93765
$541$	−43.0202	−1.84958	−0.924792	−	0.380472i	$-0.875762\pi$
$541$	−43.0202	−1.84958	−0.924792	+	0.380472i	$0.875762\pi$
$542$	−31.0810	−1.33504
$543$	−5.03435	−0.216045
$544$	−27.6129	−1.18389
$545$	15.5021	0.664038
$546$	4.82447	0.206468
$547$	−25.7040	−1.09903	−0.549513	−	0.835485i	$-0.685187\pi$
$547$	−25.7040	−1.09903	−0.549513	+	0.835485i	$0.685187\pi$
$548$	73.7423	3.15012
$549$	13.9911	0.597127
$550$	29.3864	1.25304
$551$	−1.42864	−0.0608623
$552$	4.58144	0.194999
$553$	0.530943	0.0225780
$554$	42.4848	1.80500
$555$	−4.88939	−0.207543
$556$	−67.9973	−2.88373
$557$	−8.48886	−0.359685	−0.179842	−	0.983695i	$-0.557559\pi$
$557$	−8.48886	−0.359685	−0.179842	+	0.983695i	$0.557559\pi$
$558$	−48.4110	−2.04940
$559$	−2.89541	−0.122463
$560$	−132.470	−5.59788
$561$	1.94261	0.0820171
$562$	−24.5723	−1.03652
$563$	18.4090	0.775846	0.387923	−	0.921692i	$-0.373193\pi$
$563$	18.4090	0.775846	0.387923	+	0.921692i	$0.373193\pi$
$564$	26.1863	1.10264
$565$	9.48905	0.399207
$566$	−24.0289	−1.01001
$567$	−30.3171	−1.27320
$568$	−4.75089	−0.199343
$569$	31.3569	1.31455	0.657275	−	0.753651i	$-0.271709\pi$
$569$	31.3569	1.31455	0.657275	+	0.753651i	$0.271709\pi$
$570$	22.7908	0.954602
$571$	42.5110	1.77903	0.889515	−	0.456906i	$-0.151042\pi$
$571$	42.5110	1.77903	0.889515	+	0.456906i	$0.151042\pi$
$572$	6.02131	0.251764
$573$	5.24105	0.218948
$574$	18.6566	0.778713
$575$	13.1118	0.546800
$576$	−11.4269	−0.476121
$577$	−22.2803	−0.927540	−0.463770	−	0.885956i	$-0.653504\pi$
$577$	−22.2803	−0.927540	−0.463770	+	0.885956i	$0.653504\pi$
$578$	14.4043	0.599139
$579$	4.39345	0.182586
$580$	−4.67585	−0.194154
$581$	−49.2464	−2.04308
$582$	17.4141	0.721836
$583$	−11.4820	−0.475535
$584$	15.1950	0.628774
$585$	10.4167	0.430678
$586$	−66.7884	−2.75901
$587$	−6.72286	−0.277482	−0.138741	−	0.990329i	$-0.544306\pi$
$587$	−6.72286	−0.277482	−0.138741	+	0.990329i	$0.544306\pi$
$588$	−21.9174	−0.903858
$589$	−35.5467	−1.46468
$590$	142.835	5.88041
$591$	6.91709	0.284531
$592$	25.0777	1.03069
$593$	−43.6261	−1.79151	−0.895755	−	0.444548i	$-0.853364\pi$
$593$	−43.6261	−1.79151	−0.895755	+	0.444548i	$0.853364\pi$
$594$	8.61397	0.353436
$595$	−52.5919	−2.15606
$596$	83.8785	3.43580
$597$	1.63947	0.0670989
$598$	3.83571	0.156854
$599$	4.05364	0.165627	0.0828137	−	0.996565i	$-0.473609\pi$
$599$	4.05364	0.165627	0.0828137	+	0.996565i	$0.473609\pi$
$600$	27.2582	1.11281
$601$	−4.73007	−0.192943	−0.0964717	−	0.995336i	$-0.530756\pi$
$601$	−4.73007	−0.192943	−0.0964717	+	0.995336i	$0.530756\pi$
$602$	31.2976	1.27559
$603$	16.9129	0.688748
$604$	72.3661	2.94453
$605$	−34.7444	−1.41256
$606$	−20.4262	−0.829756
$607$	−6.77264	−0.274893	−0.137447	−	0.990509i	$-0.543890\pi$
$607$	−6.77264	−0.274893	−0.137447	+	0.990509i	$0.543890\pi$
$608$	−43.4089	−1.76046
$609$	−0.502009	−0.0203425
$610$	48.0046	1.94365
$611$	12.5469	0.507595
$612$	−44.2690	−1.78947
$613$	−9.70197	−0.391859	−0.195929	−	0.980618i	$-0.562772\pi$
$613$	−9.70197	−0.391859	−0.195929	+	0.980618i	$0.562772\pi$
$614$	−23.2091	−0.936643
$615$	−2.86504	−0.115530
$616$	−37.2488	−1.50080
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	7.78727	0.313250
$619$	−6.23769	−0.250714	−0.125357	−	0.992112i	$-0.540008\pi$
$619$	−6.23769	−0.250714	−0.125357	+	0.992112i	$0.540008\pi$
$620$	−116.342	−4.67240
$621$	3.84344	0.154232
$622$	−69.0206	−2.76748
$623$	49.2346	1.97254
$624$	3.79996	0.152120
$625$	8.84934	0.353973
$626$	19.9040	0.795524
$627$	3.05389	0.121961
$628$	11.3645	0.453492
$629$	9.95609	0.396975
$630$	−112.598	−4.48601
$631$	43.2825	1.72305	0.861526	−	0.507714i	$-0.169509\pi$
$631$	43.2825	1.72305	0.861526	+	0.507714i	$0.169509\pi$
$632$	0.877566	0.0349077
$633$	10.5500	0.419326
$634$	15.6208	0.620382
$635$	73.4973	2.91665
$636$	−18.6101	−0.737937
$637$	−10.5015	−0.416086
$638$	−0.894523	−0.0354145
$639$	−1.92436	−0.0761266
$640$	21.5591	0.852199
$641$	−39.3475	−1.55413	−0.777067	−	0.629418i	$-0.783293\pi$
$641$	−39.3475	−1.55413	−0.777067	+	0.629418i	$0.783293\pi$
$642$	−18.4400	−0.727769
$643$	−45.3627	−1.78893	−0.894465	−	0.447139i	$-0.852443\pi$
$643$	−45.3627	−1.78893	−0.894465	+	0.447139i	$0.852443\pi$
$644$	−29.0408	−1.14437
$645$	−4.80627	−0.189247
$646$	−46.4081	−1.82590
$647$	−9.14636	−0.359581	−0.179790	−	0.983705i	$-0.557542\pi$
$647$	−9.14636	−0.359581	−0.179790	+	0.983705i	$0.557542\pi$
$648$	−50.1093	−1.96848
$649$	19.1393	0.751285
$650$	22.8213	0.895127
$651$	−12.4907	−0.489550
$652$	−19.3789	−0.758937
$653$	11.4336	0.447432	0.223716	−	0.974654i	$-0.428181\pi$
$653$	11.4336	0.447432	0.223716	+	0.974654i	$0.428181\pi$
$654$	4.80678	0.187960
$655$	82.8621	3.23769
$656$	14.6948	0.573735
$657$	6.15479	0.240121
$658$	−135.625	−5.28720
$659$	1.29895	0.0505999	0.0252999	−	0.999680i	$-0.491946\pi$
$659$	1.29895	0.0505999	0.0252999	+	0.999680i	$0.491946\pi$
$660$	9.99514	0.389060
$661$	0.785298	0.0305445	0.0152723	−	0.999883i	$-0.495138\pi$
$661$	0.785298	0.0305445	0.0152723	+	0.999883i	$0.495138\pi$
$662$	74.8594	2.90949
$663$	1.50862	0.0585901
$664$	−81.3965	−3.15880
$665$	−82.6773	−3.20609
$666$	21.3158	0.825969
$667$	−0.399124	−0.0154542
$668$	−116.534	−4.50884
$669$	6.10347	0.235974
$670$	58.0295	2.24188
$671$	6.43244	0.248322
$672$	−15.2534	−0.588413
$673$	−18.8436	−0.726367	−0.363184	−	0.931718i	$-0.618310\pi$
$673$	−18.8436	−0.726367	−0.363184	+	0.931718i	$0.618310\pi$
$674$	−27.3071	−1.05183
$675$	22.8673	0.880164
$676$	4.67613	0.179851
$677$	−17.0523	−0.655372	−0.327686	−	0.944787i	$-0.606269\pi$
$677$	−17.0523	−0.655372	−0.327686	+	0.944787i	$0.606269\pi$
$678$	2.94229	0.112998
$679$	−63.1723	−2.42433
$680$	−86.9262	−3.33347
$681$	−7.42313	−0.284455
$682$	−22.2570	−0.852266
$683$	−46.3422	−1.77323	−0.886617	−	0.462504i	$-0.846951\pi$
$683$	−46.3422	−1.77323	−0.886617	+	0.462504i	$0.846951\pi$
$684$	−69.5933	−2.66097
$685$	58.6515	2.24096
$686$	37.8495	1.44510
$687$	3.75082	0.143103
$688$	24.6514	0.939824
$689$	−8.91686	−0.339705
$690$	6.36713	0.242393
$691$	−33.5478	−1.27622	−0.638109	−	0.769946i	$-0.720283\pi$
$691$	−33.5478	−1.27622	−0.638109	+	0.769946i	$0.720283\pi$
$692$	−65.4453	−2.48786
$693$	−15.0877	−0.573136
$694$	29.5442	1.12148
$695$	−54.0822	−2.05145
$696$	−0.829743	−0.0314513
$697$	5.83398	0.220978
$698$	61.9733	2.34573
$699$	−9.61378	−0.363627
$700$	−172.784	−6.53062
$701$	−12.9685	−0.489814	−0.244907	−	0.969547i	$-0.578757\pi$
$701$	−12.9685	−0.489814	−0.244907	+	0.969547i	$0.578757\pi$
$702$	6.68958	0.252482
$703$	15.6515	0.590308
$704$	−5.25354	−0.198000
$705$	20.8274	0.784406
$706$	51.3549	1.93277
$707$	74.0992	2.78679
$708$	31.0212	1.16585
$709$	−20.1071	−0.755137	−0.377568	−	0.925982i	$-0.623240\pi$
$709$	−20.1071	−0.755137	−0.377568	+	0.925982i	$0.623240\pi$
$710$	−6.60262	−0.247792
$711$	0.355460	0.0133308
$712$	81.3771	3.04974
$713$	−9.93079	−0.371911
$714$	−16.3073	−0.610285
$715$	4.78909	0.179102
$716$	50.8305	1.89963
$717$	1.77248	0.0661946
$718$	48.9246	1.82585
$719$	−3.20923	−0.119684	−0.0598420	−	0.998208i	$-0.519060\pi$
$719$	−3.20923	−0.119684	−0.0598420	+	0.998208i	$0.519060\pi$
$720$	−88.6871	−3.30517
$721$	−28.2496	−1.05207
$722$	−23.8635	−0.888107
$723$	−6.99778	−0.260250
$724$	52.7450	1.96025
$725$	−2.37467	−0.0881931
$726$	−10.7733	−0.399833
$727$	36.8483	1.36663	0.683315	−	0.730124i	$-0.260538\pi$
$727$	36.8483	1.36663	0.683315	+	0.730124i	$0.260538\pi$
$728$	−28.9273	−1.07212
$729$	−16.8303	−0.623345
$730$	21.1175	0.781594
$731$	9.78684	0.361979
$732$	10.4257	0.385347
$733$	37.6660	1.39123	0.695613	−	0.718417i	$-0.255133\pi$
$733$	37.6660	1.39123	0.695613	+	0.718417i	$0.255133\pi$
$734$	48.0879	1.77496
$735$	−17.4321	−0.642994
$736$	−12.1273	−0.447017
$737$	7.77575	0.286423
$738$	12.4904	0.459779
$739$	−9.40556	−0.345989	−0.172995	−	0.984923i	$-0.555344\pi$
$739$	−9.40556	−0.345989	−0.172995	+	0.984923i	$0.555344\pi$
$740$	51.2262	1.88311
$741$	2.37164	0.0871243
$742$	96.3857	3.53843
$743$	−21.6328	−0.793629	−0.396815	−	0.917899i	$-0.629884\pi$
$743$	−21.6328	−0.793629	−0.396815	+	0.917899i	$0.629884\pi$
$744$	−20.6452	−0.756889
$745$	66.7134	2.44419
$746$	−71.0067	−2.59974
$747$	−32.9699	−1.20631
$748$	−20.3528	−0.744170
$749$	66.8941	2.44426
$750$	16.4373	0.600207
$751$	21.0445	0.767926	0.383963	−	0.923349i	$-0.374559\pi$
$751$	21.0445	0.767926	0.383963	+	0.923349i	$0.374559\pi$
$752$	−106.824	−3.89546
$753$	2.51628	0.0916983
$754$	−0.694684	−0.0252989
$755$	57.5569	2.09471
$756$	−50.6479	−1.84205
$757$	2.03770	0.0740616	0.0370308	−	0.999314i	$-0.488210\pi$
$757$	2.03770	0.0740616	0.0370308	+	0.999314i	$0.488210\pi$
$758$	55.4565	2.01427
$759$	0.853173	0.0309682
$760$	−136.653	−4.95691
$761$	11.7064	0.424357	0.212179	−	0.977231i	$-0.431944\pi$
$761$	11.7064	0.424357	0.212179	+	0.977231i	$0.431944\pi$
$762$	22.7895	0.825576
$763$	−17.4374	−0.631275
$764$	−54.9106	−1.98660
$765$	−35.2097	−1.27301
$766$	−27.1196	−0.979870
$767$	14.8635	0.536691
$768$	10.3268	0.372635
$769$	−13.0813	−0.471724	−0.235862	−	0.971787i	$-0.575791\pi$
$769$	−13.0813	−0.471724	−0.235862	+	0.971787i	$0.575791\pi$
$770$	−51.7671	−1.86556
$771$	−5.84343	−0.210446
$772$	−46.0302	−1.65666
$773$	−26.4326	−0.950713	−0.475357	−	0.879793i	$-0.657681\pi$
$773$	−26.4326	−0.950713	−0.475357	+	0.879793i	$0.657681\pi$
$774$	20.9534	0.753154
$775$	−59.0853	−2.12240
$776$	−104.414	−3.74824
$777$	5.49976	0.197303
$778$	20.7312	0.743251
$779$	9.17133	0.328597
$780$	7.76219	0.277931
$781$	−0.884728	−0.0316581
$782$	−12.9652	−0.463633
$783$	−0.696084	−0.0248760
$784$	89.4094	3.19319
$785$	9.03883	0.322610
$786$	25.6932	0.916447
$787$	−26.9039	−0.959020	−0.479510	−	0.877536i	$-0.659186\pi$
$787$	−26.9039	−0.959020	−0.479510	+	0.877536i	$0.659186\pi$
$788$	−72.4705	−2.58165
$789$	−8.08632	−0.287881
$790$	1.21961	0.0433918
$791$	−10.6736	−0.379511
$792$	−24.9377	−0.886121
$793$	4.99541	0.177392
$794$	21.8316	0.774774
$795$	−14.8016	−0.524960
$796$	−17.1767	−0.608812
$797$	−40.9178	−1.44938	−0.724692	−	0.689073i	$-0.758018\pi$
$797$	−40.9178	−1.44938	−0.724692	+	0.689073i	$0.758018\pi$
$798$	−25.6359	−0.907502
$799$	−42.4101	−1.50036
$800$	−72.1537	−2.55102
$801$	32.9620	1.16466
$802$	49.8432	1.76002
$803$	2.82967	0.0998570
$804$	12.6030	0.444473
$805$	−23.0978	−0.814090
$806$	−17.2847	−0.608829
$807$	3.10081	0.109154
$808$	122.474	4.30863
$809$	25.6916	0.903267	0.451634	−	0.892204i	$-0.350841\pi$
$809$	25.6916	0.903267	0.451634	+	0.892204i	$0.350841\pi$
$810$	−69.6402	−2.44691
$811$	4.54876	0.159728	0.0798642	−	0.996806i	$-0.474551\pi$
$811$	4.54876	0.159728	0.0798642	+	0.996806i	$0.474551\pi$
$812$	5.25956	0.184574
$813$	−5.36886	−0.188294
$814$	9.79995	0.343488
$815$	−15.4132	−0.539900
$816$	−12.8443	−0.449641
$817$	15.3854	0.538268
$818$	60.2015	2.10490
$819$	−11.7171	−0.409428
$820$	30.0171	1.04824
$821$	36.5152	1.27439	0.637194	−	0.770703i	$-0.280095\pi$
$821$	36.5152	1.27439	0.637194	+	0.770703i	$0.280095\pi$
$822$	18.1862	0.634316
$823$	2.87349	0.100164	0.0500818	−	0.998745i	$-0.484052\pi$
$823$	2.87349	0.100164	0.0500818	+	0.998745i	$0.484052\pi$
$824$	−46.6921	−1.62660
$825$	5.07613	0.176728
$826$	−160.666	−5.59027
$827$	10.3568	0.360141	0.180070	−	0.983654i	$-0.442367\pi$
$827$	10.3568	0.360141	0.180070	+	0.983654i	$0.442367\pi$
$828$	−19.4425	−0.675673
$829$	10.1635	0.352994	0.176497	−	0.984301i	$-0.443523\pi$
$829$	10.1635	0.352994	0.176497	+	0.984301i	$0.443523\pi$
$830$	−113.122	−3.92653
$831$	7.33871	0.254577
$832$	−4.07988	−0.141444
$833$	35.4965	1.22988
$834$	−16.7694	−0.580676
$835$	−92.6863	−3.20754
$836$	−31.9956	−1.10659
$837$	−17.3196	−0.598652
$838$	4.23716	0.146370
$839$	1.15746	0.0399600	0.0199800	−	0.999800i	$-0.493640\pi$
$839$	1.15746	0.0399600	0.0199800	+	0.999800i	$0.493640\pi$
$840$	−48.0182	−1.65678
$841$	−28.9277	−0.997507
$842$	41.8145	1.44102
$843$	−4.24455	−0.146190
$844$	−110.533	−3.80470
$845$	3.71919	0.127944
$846$	−90.7991	−3.12174
$847$	39.0817	1.34286
$848$	75.9176	2.60702
$849$	−4.15070	−0.142452
$850$	−77.1389	−2.64584
$851$	4.37261	0.149891
$852$	−1.43397	−0.0491271
$853$	−18.6349	−0.638047	−0.319023	−	0.947747i	$-0.603355\pi$
$853$	−18.6349	−0.638047	−0.319023	+	0.947747i	$0.603355\pi$
$854$	−53.9973	−1.84775
$855$	−55.3516	−1.89298
$856$	110.565	3.77905
$857$	39.8485	1.36120	0.680600	−	0.732655i	$-0.261719\pi$
$857$	39.8485	1.36120	0.680600	+	0.732655i	$0.261719\pi$
$858$	1.48496	0.0506958
$859$	−19.9299	−0.680000	−0.340000	−	0.940425i	$-0.610427\pi$
$859$	−19.9299	−0.680000	−0.340000	+	0.940425i	$0.610427\pi$
$860$	50.3554	1.71710
$861$	3.22270	0.109829
$862$	40.1294	1.36681
$863$	25.0021	0.851082	0.425541	−	0.904939i	$-0.360084\pi$
$863$	25.0021	0.851082	0.425541	+	0.904939i	$0.360084\pi$
$864$	−21.1503	−0.719547
$865$	−52.0524	−1.76983
$866$	−2.71441	−0.0922394
$867$	2.48816	0.0845023
$868$	130.865	4.44186
$869$	0.163423	0.00554376
$870$	−1.15315	−0.0390954
$871$	6.03862	0.204611
$872$	−28.8212	−0.976010
$873$	−42.2932	−1.43141
$874$	−20.3819	−0.689429
$875$	−59.6291	−2.01583
$876$	4.58635	0.154958
$877$	−1.16265	−0.0392600	−0.0196300	−	0.999807i	$-0.506249\pi$
$877$	−1.16265	−0.0392600	−0.0196300	+	0.999807i	$0.506249\pi$
$878$	68.0375	2.29616
$879$	−11.5369	−0.389129
$880$	−40.7740	−1.37449
$881$	−9.28353	−0.312770	−0.156385	−	0.987696i	$-0.549984\pi$
$881$	−9.28353	−0.312770	−0.156385	+	0.987696i	$0.549984\pi$
$882$	75.9971	2.55895
$883$	−28.4301	−0.956749	−0.478375	−	0.878156i	$-0.658774\pi$
$883$	−28.4301	−0.956749	−0.478375	+	0.878156i	$0.658774\pi$
$884$	−15.8059	−0.531609
$885$	24.6729	0.829371
$886$	25.8425	0.868196
$887$	31.5555	1.05953	0.529765	−	0.848144i	$-0.322280\pi$
$887$	31.5555	1.05953	0.529765	+	0.848144i	$0.322280\pi$
$888$	9.09025	0.305049
$889$	−82.6725	−2.77275
$890$	113.095	3.79096
$891$	−9.33155	−0.312619
$892$	−63.9462	−2.14108
$893$	−66.6710	−2.23106
$894$	20.6860	0.691842
$895$	40.4284	1.35137
$896$	−24.2505	−0.810152
$897$	0.662571	0.0221226
$898$	18.5025	0.617435
$899$	1.79856	0.0599853
$900$	−115.677	−3.85590
$901$	30.1401	1.00411
$902$	5.74249	0.191204
$903$	5.40627	0.179909
$904$	−17.6418	−0.586759
$905$	41.9511	1.39450
$906$	17.8468	0.592919
$907$	−48.2986	−1.60373	−0.801864	−	0.597506i	$-0.796158\pi$
$907$	−48.2986	−1.60373	−0.801864	+	0.597506i	$0.796158\pi$
$908$	77.7723	2.58096
$909$	49.6086	1.64541
$910$	−40.2022	−1.33269
$911$	−20.9753	−0.694943	−0.347472	−	0.937691i	$-0.612960\pi$
$911$	−20.9753	−0.694943	−0.347472	+	0.937691i	$0.612960\pi$
$912$	−20.1920	−0.668623
$913$	−15.1580	−0.501655
$914$	26.5670	0.878760
$915$	8.29219	0.274131
$916$	−39.2974	−1.29842
$917$	−93.2063	−3.07794
$918$	−22.6116	−0.746294
$919$	30.2807	0.998868	0.499434	−	0.866352i	$-0.333541\pi$
$919$	30.2807	0.998868	0.499434	+	0.866352i	$0.333541\pi$
$920$	−38.1770	−1.25866
$921$	−4.00908	−0.132104
$922$	−59.6281	−1.96375
$923$	−0.687077	−0.0226154
$924$	−11.2429	−0.369864
$925$	26.0157	0.855391
$926$	−82.5361	−2.71230
$927$	−18.9128	−0.621177
$928$	2.19636	0.0720992
$929$	4.94370	0.162198	0.0810988	−	0.996706i	$-0.474157\pi$
$929$	4.94370	0.162198	0.0810988	+	0.996706i	$0.474157\pi$
$930$	−28.6920	−0.940847
$931$	55.8024	1.82885
$932$	100.724	3.29932
$933$	−11.9225	−0.390324
$934$	29.7244	0.972614
$935$	−16.1877	−0.529395
$936$	−19.3665	−0.633014
$937$	11.9298	0.389730	0.194865	−	0.980830i	$-0.437573\pi$
$937$	11.9298	0.389730	0.194865	+	0.980830i	$0.437573\pi$
$938$	−65.2737	−2.13126
$939$	3.43817	0.112200
$940$	−218.209	−7.11720
$941$	36.8517	1.20133	0.600665	−	0.799501i	$-0.294903\pi$
$941$	36.8517	1.20133	0.600665	+	0.799501i	$0.294903\pi$
$942$	2.80269	0.0913165
$943$	2.56222	0.0834374
$944$	−126.547	−4.11876
$945$	−40.2832	−1.31041
$946$	9.63335	0.313207
$947$	−19.7418	−0.641521	−0.320761	−	0.947160i	$-0.603939\pi$
$947$	−19.7418	−0.641521	−0.320761	+	0.947160i	$0.603939\pi$
$948$	0.264878	0.00860283
$949$	2.19751	0.0713343
$950$	−121.266	−3.93440
$951$	2.69830	0.0874984
$952$	97.7777	3.16899
$953$	28.8662	0.935069	0.467534	−	0.883975i	$-0.345142\pi$
$953$	28.8662	0.935069	0.467534	+	0.883975i	$0.345142\pi$
$954$	64.5292	2.08921
$955$	−43.6735	−1.41324
$956$	−18.5703	−0.600608
$957$	−0.154518	−0.00499485
$958$	71.1608	2.29910
$959$	−65.9733	−2.13039
$960$	−6.77244	−0.218580
$961$	13.7508	0.443573
$962$	7.61061	0.245376
$963$	44.7848	1.44317
$964$	73.3159	2.36135
$965$	−36.6105	−1.17853
$966$	−7.16198	−0.230433
$967$	−40.0515	−1.28797	−0.643985	−	0.765038i	$-0.722720\pi$
$967$	−40.0515	−1.28797	−0.643985	+	0.765038i	$0.722720\pi$
$968$	64.5959	2.07619
$969$	−8.01642	−0.257525
$970$	−145.111	−4.65923
$971$	21.2521	0.682012	0.341006	−	0.940061i	$-0.389232\pi$
$971$	21.2521	0.682012	0.341006	+	0.940061i	$0.389232\pi$
$972$	−51.4445	−1.65008
$973$	60.8336	1.95024
$974$	100.695	3.22649
$975$	3.94210	0.126248
$976$	−42.5306	−1.36137
$977$	37.6563	1.20473	0.602365	−	0.798221i	$-0.294225\pi$
$977$	37.6563	1.20473	0.602365	+	0.798221i	$0.294225\pi$
$978$	−4.77919	−0.152822
$979$	15.1543	0.484335
$980$	182.637	5.83412
$981$	−11.6741	−0.372726
$982$	50.0532	1.59726
$983$	25.9032	0.826184	0.413092	−	0.910689i	$-0.364449\pi$
$983$	25.9032	0.826184	0.413092	+	0.910689i	$0.364449\pi$
$984$	5.32662	0.169806
$985$	−57.6399	−1.83656
$986$	2.34811	0.0747792
$987$	−23.4274	−0.745704
$988$	−24.8477	−0.790511
$989$	4.29827	0.136677
$990$	−34.6575	−1.10149
$991$	53.0485	1.68514	0.842571	−	0.538586i	$-0.181041\pi$
$991$	53.0485	1.68514	0.842571	+	0.538586i	$0.181041\pi$
$992$	54.6487	1.73510
$993$	12.9310	0.410354
$994$	7.42687	0.235566
$995$	−13.6616	−0.433102
$996$	−24.5681	−0.778471
$997$	25.0190	0.792358	0.396179	−	0.918173i	$-0.370336\pi$
$997$	25.0190	0.792358	0.396179	+	0.918173i	$0.370336\pi$
$998$	96.0843	3.04150
$999$	7.62594	0.241274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.6	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.6	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58382 q^{2} -0.446323 q^{3} +4.67613 q^{4} +3.71919 q^{5} +1.15322 q^{6} -4.18348 q^{7} -6.91464 q^{8} -2.80080 q^{9} +O(q^{10})\)	\(q-2.58382 q^{2} -0.446323 q^{3} +4.67613 q^{4} +3.71919 q^{5} +1.15322 q^{6} -4.18348 q^{7} -6.91464 q^{8} -2.80080 q^{9} -9.60973 q^{10} -1.28767 q^{11} -2.08706 q^{12} -1.00000 q^{13} +10.8094 q^{14} -1.65996 q^{15} +8.51394 q^{16} +3.38012 q^{17} +7.23676 q^{18} +5.31373 q^{19} +17.3914 q^{20} +1.86718 q^{21} +3.32711 q^{22} +1.48451 q^{23} +3.08616 q^{24} +8.83240 q^{25} +2.58382 q^{26} +2.58903 q^{27} -19.5625 q^{28} -0.268859 q^{29} +4.28904 q^{30} -6.68960 q^{31} -8.16920 q^{32} +0.574716 q^{33} -8.73362 q^{34} -15.5592 q^{35} -13.0969 q^{36} +2.94549 q^{37} -13.7297 q^{38} +0.446323 q^{39} -25.7169 q^{40} +1.72597 q^{41} -4.82447 q^{42} +2.89541 q^{43} -6.02131 q^{44} -10.4167 q^{45} -3.83571 q^{46} -12.5469 q^{47} -3.79996 q^{48} +10.5015 q^{49} -22.8213 q^{50} -1.50862 q^{51} -4.67613 q^{52} +8.91686 q^{53} -6.68958 q^{54} -4.78909 q^{55} +28.9273 q^{56} -2.37164 q^{57} +0.694684 q^{58} -14.8635 q^{59} -7.76219 q^{60} -4.99541 q^{61} +17.2847 q^{62} +11.7171 q^{63} +4.07988 q^{64} -3.71919 q^{65} -1.48496 q^{66} -6.03862 q^{67} +15.8059 q^{68} -0.662571 q^{69} +40.2022 q^{70} +0.687077 q^{71} +19.3665 q^{72} -2.19751 q^{73} -7.61061 q^{74} -3.94210 q^{75} +24.8477 q^{76} +5.38695 q^{77} -1.15322 q^{78} -0.126914 q^{79} +31.6650 q^{80} +7.24685 q^{81} -4.45959 q^{82} +11.7716 q^{83} +8.73120 q^{84} +12.5713 q^{85} -7.48123 q^{86} +0.119998 q^{87} +8.90378 q^{88} -11.7688 q^{89} +26.9149 q^{90} +4.18348 q^{91} +6.94177 q^{92} +2.98572 q^{93} +32.4190 q^{94} +19.7628 q^{95} +3.64610 q^{96} +15.1004 q^{97} -27.1341 q^{98} +3.60650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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