LMFDB - Embedded newform 8021.2.a.c.1.13

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:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.46202 q^{2} +0.861982 q^{3} +4.06154 q^{4} +2.09605 q^{5} -2.12222 q^{6} +1.61995 q^{7} -5.07555 q^{8} -2.25699 q^{9} +O(q^{10})$	\(q-2.46202 q^{2} +0.861982 q^{3} +4.06154 q^{4} +2.09605 q^{5} -2.12222 q^{6} +1.61995 q^{7} -5.07555 q^{8} -2.25699 q^{9} -5.16051 q^{10} +1.07211 q^{11} +3.50098 q^{12} -1.00000 q^{13} -3.98834 q^{14} +1.80676 q^{15} +4.37303 q^{16} +6.24773 q^{17} +5.55674 q^{18} -1.80627 q^{19} +8.51318 q^{20} +1.39636 q^{21} -2.63956 q^{22} -5.74920 q^{23} -4.37504 q^{24} -0.606588 q^{25} +2.46202 q^{26} -4.53143 q^{27} +6.57947 q^{28} +9.80731 q^{29} -4.44827 q^{30} +7.54571 q^{31} -0.615376 q^{32} +0.924142 q^{33} -15.3820 q^{34} +3.39548 q^{35} -9.16684 q^{36} -9.42892 q^{37} +4.44708 q^{38} -0.861982 q^{39} -10.6386 q^{40} +10.5896 q^{41} -3.43788 q^{42} +4.69034 q^{43} +4.35443 q^{44} -4.73075 q^{45} +14.1546 q^{46} -0.665416 q^{47} +3.76947 q^{48} -4.37578 q^{49} +1.49343 q^{50} +5.38543 q^{51} -4.06154 q^{52} +9.02049 q^{53} +11.1565 q^{54} +2.24720 q^{55} -8.22212 q^{56} -1.55698 q^{57} -24.1458 q^{58} -11.8134 q^{59} +7.33821 q^{60} +10.7395 q^{61} -18.5777 q^{62} -3.65620 q^{63} -7.23099 q^{64} -2.09605 q^{65} -2.27526 q^{66} +11.3257 q^{67} +25.3754 q^{68} -4.95571 q^{69} -8.35974 q^{70} +11.9453 q^{71} +11.4555 q^{72} -10.9238 q^{73} +23.2142 q^{74} -0.522869 q^{75} -7.33626 q^{76} +1.73676 q^{77} +2.12222 q^{78} -6.27932 q^{79} +9.16607 q^{80} +2.86495 q^{81} -26.0718 q^{82} -8.99398 q^{83} +5.67139 q^{84} +13.0955 q^{85} -11.5477 q^{86} +8.45373 q^{87} -5.44156 q^{88} -15.3562 q^{89} +11.6472 q^{90} -1.61995 q^{91} -23.3506 q^{92} +6.50427 q^{93} +1.63827 q^{94} -3.78604 q^{95} -0.530444 q^{96} +10.6377 q^{97} +10.7732 q^{98} -2.41974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.46202	−1.74091	−0.870455	−	0.492247i	$-0.836176\pi$
$2$	−2.46202	−1.74091	−0.870455	+	0.492247i	$0.836176\pi$
$3$	0.861982	0.497666	0.248833	−	0.968546i	$-0.419953\pi$
$3$	0.861982	0.497666	0.248833	+	0.968546i	$0.419953\pi$
$4$	4.06154	2.03077
$5$	2.09605	0.937381	0.468690	−	0.883363i	$-0.344726\pi$
$5$	2.09605	0.937381	0.468690	+	0.883363i	$0.344726\pi$
$6$	−2.12222	−0.866392
$7$	1.61995	0.612282	0.306141	−	0.951986i	$-0.400962\pi$
$7$	1.61995	0.612282	0.306141	+	0.951986i	$0.400962\pi$
$8$	−5.07555	−1.79448
$9$	−2.25699	−0.752329
$10$	−5.16051	−1.63190
$11$	1.07211	0.323254	0.161627	−	0.986852i	$-0.448326\pi$
$11$	1.07211	0.323254	0.161627	+	0.986852i	$0.448326\pi$
$12$	3.50098	1.01064
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.98834	−1.06593
$15$	1.80676	0.466502
$16$	4.37303	1.09326
$17$	6.24773	1.51530	0.757648	−	0.652663i	$-0.226348\pi$
$17$	6.24773	1.51530	0.757648	+	0.652663i	$0.226348\pi$
$18$	5.55674	1.30974
$19$	−1.80627	−0.414388	−0.207194	−	0.978300i	$-0.566433\pi$
$19$	−1.80627	−0.414388	−0.207194	+	0.978300i	$0.566433\pi$
$20$	8.51318	1.90360
$21$	1.39636	0.304712
$22$	−2.63956	−0.562757
$23$	−5.74920	−1.19879	−0.599396	−	0.800453i	$-0.704592\pi$
$23$	−5.74920	−1.19879	−0.599396	+	0.800453i	$0.704592\pi$
$24$	−4.37504	−0.893051
$25$	−0.606588	−0.121318
$26$	2.46202	0.482842
$27$	−4.53143	−0.872074
$28$	6.57947	1.24340
$29$	9.80731	1.82117	0.910586	−	0.413320i	$-0.135631\pi$
$29$	9.80731	1.82117	0.910586	+	0.413320i	$0.135631\pi$
$30$	−4.44827	−0.812139
$31$	7.54571	1.35525	0.677625	−	0.735408i	$-0.263009\pi$
$31$	7.54571	1.35525	0.677625	+	0.735408i	$0.263009\pi$
$32$	−0.615376	−0.108784
$33$	0.924142	0.160873
$34$	−15.3820	−2.63800
$35$	3.39548	0.573941
$36$	−9.16684	−1.52781
$37$	−9.42892	−1.55010	−0.775052	−	0.631897i	$-0.782277\pi$
$37$	−9.42892	−1.55010	−0.775052	+	0.631897i	$0.782277\pi$
$38$	4.44708	0.721412
$39$	−0.861982	−0.138028
$40$	−10.6386	−1.68211
$41$	10.5896	1.65382	0.826909	−	0.562336i	$-0.190097\pi$
$41$	10.5896	1.65382	0.826909	+	0.562336i	$0.190097\pi$
$42$	−3.43788	−0.530476
$43$	4.69034	0.715271	0.357635	−	0.933861i	$-0.383583\pi$
$43$	4.69034	0.715271	0.357635	+	0.933861i	$0.383583\pi$
$44$	4.35443	0.656455
$45$	−4.73075	−0.705218
$46$	14.1546	2.08699
$47$	−0.665416	−0.0970609	−0.0485304	−	0.998822i	$-0.515454\pi$
$47$	−0.665416	−0.0970609	−0.0485304	+	0.998822i	$0.515454\pi$
$48$	3.76947	0.544077
$49$	−4.37578	−0.625111
$50$	1.49343	0.211203
$51$	5.38543	0.754111
$52$	−4.06154	−0.563234
$53$	9.02049	1.23906	0.619530	−	0.784973i	$-0.287323\pi$
$53$	9.02049	1.23906	0.619530	+	0.784973i	$0.287323\pi$
$54$	11.1565	1.51820
$55$	2.24720	0.303012
$56$	−8.22212	−1.09873
$57$	−1.55698	−0.206227
$58$	−24.1458	−3.17050
$59$	−11.8134	−1.53798	−0.768988	−	0.639264i	$-0.779239\pi$
$59$	−11.8134	−1.53798	−0.768988	+	0.639264i	$0.779239\pi$
$60$	7.33821	0.947359
$61$	10.7395	1.37505	0.687526	−	0.726160i	$-0.258697\pi$
$61$	10.7395	1.37505	0.687526	+	0.726160i	$0.258697\pi$
$62$	−18.5777	−2.35937
$63$	−3.65620	−0.460637
$64$	−7.23099	−0.903873
$65$	−2.09605	−0.259983
$66$	−2.27526	−0.280065
$67$	11.3257	1.38365	0.691825	−	0.722065i	$-0.256807\pi$
$67$	11.3257	1.38365	0.691825	+	0.722065i	$0.256807\pi$
$68$	25.3754	3.07722
$69$	−4.95571	−0.596597
$70$	−8.35974	−0.999180
$71$	11.9453	1.41765	0.708825	−	0.705384i	$-0.249225\pi$
$71$	11.9453	1.41765	0.708825	+	0.705384i	$0.249225\pi$
$72$	11.4555	1.35004
$73$	−10.9238	−1.27853	−0.639265	−	0.768987i	$-0.720761\pi$
$73$	−10.9238	−1.27853	−0.639265	+	0.768987i	$0.720761\pi$
$74$	23.2142	2.69859
$75$	−0.522869	−0.0603757
$76$	−7.33626	−0.841526
$77$	1.73676	0.197923
$78$	2.12222	0.240294
$79$	−6.27932	−0.706479	−0.353239	−	0.935533i	$-0.614920\pi$
$79$	−6.27932	−0.706479	−0.353239	+	0.935533i	$0.614920\pi$
$80$	9.16607	1.02480
$81$	2.86495	0.318327
$82$	−26.0718	−2.87915
$83$	−8.99398	−0.987217	−0.493609	−	0.869684i	$-0.664322\pi$
$83$	−8.99398	−0.987217	−0.493609	+	0.869684i	$0.664322\pi$
$84$	5.67139	0.618799
$85$	13.0955	1.42041
$86$	−11.5477	−1.24522
$87$	8.45373	0.906335
$88$	−5.44156	−0.580073
$89$	−15.3562	−1.62776	−0.813878	−	0.581036i	$-0.802648\pi$
$89$	−15.3562	−1.62776	−0.813878	+	0.581036i	$0.802648\pi$
$90$	11.6472	1.22772
$91$	−1.61995	−0.169816
$92$	−23.3506	−2.43447
$93$	6.50427	0.674461
$94$	1.63827	0.168974
$95$	−3.78604	−0.388439
$96$	−0.530444	−0.0541382
$97$	10.6377	1.08009	0.540046	−	0.841635i	$-0.318407\pi$
$97$	10.6377	1.08009	0.540046	+	0.841635i	$0.318407\pi$
$98$	10.7732	1.08826
$99$	−2.41974	−0.243193
$100$	−2.46368	−0.246368
$101$	12.6119	1.25493	0.627467	−	0.778643i	$-0.284092\pi$
$101$	12.6119	1.25493	0.627467	+	0.778643i	$0.284092\pi$
$102$	−13.2590	−1.31284
$103$	5.86005	0.577407	0.288704	−	0.957418i	$-0.406776\pi$
$103$	5.86005	0.577407	0.288704	+	0.957418i	$0.406776\pi$
$104$	5.07555	0.497699
$105$	2.92685	0.285631
$106$	−22.2086	−2.15709
$107$	−2.16873	−0.209659	−0.104830	−	0.994490i	$-0.533430\pi$
$107$	−2.16873	−0.209659	−0.104830	+	0.994490i	$0.533430\pi$
$108$	−18.4046	−1.77098
$109$	0.841927	0.0806420	0.0403210	−	0.999187i	$-0.487162\pi$
$109$	0.841927	0.0806420	0.0403210	+	0.999187i	$0.487162\pi$
$110$	−5.53265	−0.527517
$111$	−8.12756	−0.771434
$112$	7.08407	0.669381
$113$	−17.7325	−1.66813	−0.834066	−	0.551665i	$-0.813993\pi$
$113$	−17.7325	−1.66813	−0.834066	+	0.551665i	$0.813993\pi$
$114$	3.83331	0.359022
$115$	−12.0506	−1.12372
$116$	39.8328	3.69838
$117$	2.25699	0.208658
$118$	29.0849	2.67748
$119$	10.1210	0.927788
$120$	−9.17028	−0.837128
$121$	−9.85057	−0.895507
$122$	−26.4409	−2.39384
$123$	9.12805	0.823048
$124$	30.6472	2.75220
$125$	−11.7517	−1.05110
$126$	9.00162	0.801928
$127$	11.6863	1.03699	0.518495	−	0.855081i	$-0.326493\pi$
$127$	11.6863	1.03699	0.518495	+	0.855081i	$0.326493\pi$
$128$	19.0336	1.68235
$129$	4.04299	0.355966
$130$	5.16051	0.452606
$131$	−1.73191	−0.151317	−0.0756587	−	0.997134i	$-0.524106\pi$
$131$	−1.73191	−0.151317	−0.0756587	+	0.997134i	$0.524106\pi$
$132$	3.75344	0.326695
$133$	−2.92607	−0.253722
$134$	−27.8840	−2.40881
$135$	−9.49809	−0.817465
$136$	−31.7107	−2.71917
$137$	−16.6916	−1.42606	−0.713030	−	0.701134i	$-0.752678\pi$
$137$	−16.6916	−1.42606	−0.713030	+	0.701134i	$0.752678\pi$
$138$	12.2011	1.03862
$139$	7.90555	0.670540	0.335270	−	0.942122i	$-0.391172\pi$
$139$	7.90555	0.670540	0.335270	+	0.942122i	$0.391172\pi$
$140$	13.7909	1.16554
$141$	−0.573577	−0.0483039
$142$	−29.4097	−2.46800
$143$	−1.07211	−0.0896546
$144$	−9.86986	−0.822489
$145$	20.5566	1.70713
$146$	26.8945	2.22581
$147$	−3.77184	−0.311096
$148$	−38.2959	−3.14791
$149$	−1.40742	−0.115300	−0.0576501	−	0.998337i	$-0.518361\pi$
$149$	−1.40742	−0.115300	−0.0576501	+	0.998337i	$0.518361\pi$
$150$	1.28731	0.105109
$151$	21.6425	1.76124	0.880622	−	0.473820i	$-0.157125\pi$
$151$	21.6425	1.76124	0.880622	+	0.473820i	$0.157125\pi$
$152$	9.16784	0.743610
$153$	−14.1010	−1.14000
$154$	−4.27595	−0.344566
$155$	15.8162	1.27038
$156$	−3.50098	−0.280302
$157$	0.753749	0.0601557	0.0300778	−	0.999548i	$-0.490424\pi$
$157$	0.753749	0.0601557	0.0300778	+	0.999548i	$0.490424\pi$
$158$	15.4598	1.22992
$159$	7.77550	0.616638
$160$	−1.28986	−0.101972
$161$	−9.31339	−0.733998
$162$	−7.05355	−0.554180
$163$	15.5877	1.22092	0.610460	−	0.792047i	$-0.290985\pi$
$163$	15.5877	1.22092	0.610460	+	0.792047i	$0.290985\pi$
$164$	43.0101	3.35852
$165$	1.93705	0.150799
$166$	22.1434	1.71866
$167$	18.3639	1.42104	0.710519	−	0.703678i	$-0.248460\pi$
$167$	18.3639	1.42104	0.710519	+	0.703678i	$0.248460\pi$
$168$	−7.08732	−0.546799
$169$	1.00000	0.0769231
$170$	−32.2414	−2.47281
$171$	4.07674	0.311756
$172$	19.0500	1.45255
$173$	17.4467	1.32645	0.663225	−	0.748420i	$-0.269187\pi$
$173$	17.4467	1.32645	0.663225	+	0.748420i	$0.269187\pi$
$174$	−20.8132	−1.57785
$175$	−0.982640	−0.0742806
$176$	4.68838	0.353400
$177$	−10.1830	−0.765398
$178$	37.8073	2.83378
$179$	−20.7614	−1.55178	−0.775890	−	0.630868i	$-0.782699\pi$
$179$	−20.7614	−1.55178	−0.775890	+	0.630868i	$0.782699\pi$
$180$	−19.2141	−1.43214
$181$	4.87190	0.362125	0.181063	−	0.983472i	$-0.442046\pi$
$181$	4.87190	0.362125	0.181063	+	0.983472i	$0.442046\pi$
$182$	3.98834	0.295635
$183$	9.25726	0.684316
$184$	29.1804	2.15121
$185$	−19.7635	−1.45304
$186$	−16.0136	−1.17418
$187$	6.69827	0.489826
$188$	−2.70261	−0.197108
$189$	−7.34067	−0.533955
$190$	9.32129	0.676238
$191$	−11.7213	−0.848126	−0.424063	−	0.905633i	$-0.639397\pi$
$191$	−11.7213	−0.848126	−0.424063	+	0.905633i	$0.639397\pi$
$192$	−6.23298	−0.449827
$193$	13.1345	0.945446	0.472723	−	0.881211i	$-0.343271\pi$
$193$	13.1345	0.945446	0.472723	+	0.881211i	$0.343271\pi$
$194$	−26.1902	−1.88034
$195$	−1.80676	−0.129384
$196$	−17.7724	−1.26946
$197$	−0.426539	−0.0303897	−0.0151948	−	0.999885i	$-0.504837\pi$
$197$	−0.426539	−0.0303897	−0.0151948	+	0.999885i	$0.504837\pi$
$198$	5.95746	0.423378
$199$	13.8782	0.983801	0.491900	−	0.870652i	$-0.336302\pi$
$199$	13.8782	0.983801	0.491900	+	0.870652i	$0.336302\pi$
$200$	3.07877	0.217702
$201$	9.76253	0.688595
$202$	−31.0508	−2.18473
$203$	15.8873	1.11507
$204$	21.8731	1.53143
$205$	22.1963	1.55026
$206$	−14.4275	−1.00521
$207$	12.9759	0.901885
$208$	−4.37303	−0.303215
$209$	−1.93653	−0.133953
$210$	−7.20595	−0.497258
$211$	5.25818	0.361988	0.180994	−	0.983484i	$-0.442069\pi$
$211$	5.25818	0.361988	0.180994	+	0.983484i	$0.442069\pi$
$212$	36.6371	2.51625
$213$	10.2967	0.705516
$214$	5.33946	0.364998
$215$	9.83118	0.670481
$216$	22.9995	1.56492
$217$	12.2236	0.829795
$218$	−2.07284	−0.140390
$219$	−9.41609	−0.636280
$220$	9.12709	0.615348
$221$	−6.24773	−0.420268
$222$	20.0102	1.34300
$223$	8.56762	0.573730	0.286865	−	0.957971i	$-0.407387\pi$
$223$	8.56762	0.573730	0.286865	+	0.957971i	$0.407387\pi$
$224$	−0.996876	−0.0666066
$225$	1.36906	0.0912708
$226$	43.6577	2.90407
$227$	−11.4062	−0.757056	−0.378528	−	0.925590i	$-0.623570\pi$
$227$	−11.4062	−0.757056	−0.378528	+	0.925590i	$0.623570\pi$
$228$	−6.32372	−0.418799
$229$	20.1646	1.33252	0.666258	−	0.745721i	$-0.267895\pi$
$229$	20.1646	1.33252	0.666258	+	0.745721i	$0.267895\pi$
$230$	29.6688	1.95630
$231$	1.49706	0.0984993
$232$	−49.7775	−3.26805
$233$	−15.0511	−0.986033	−0.493017	−	0.870020i	$-0.664106\pi$
$233$	−15.0511	−0.986033	−0.493017	+	0.870020i	$0.664106\pi$
$234$	−5.55674	−0.363256
$235$	−1.39474	−0.0909830
$236$	−47.9806	−3.12327
$237$	−5.41266	−0.351590
$238$	−24.9180	−1.61520
$239$	7.02165	0.454193	0.227096	−	0.973872i	$-0.427077\pi$
$239$	7.02165	0.454193	0.227096	+	0.973872i	$0.427077\pi$
$240$	7.90099	0.510007
$241$	22.7870	1.46784	0.733918	−	0.679238i	$-0.237689\pi$
$241$	22.7870	1.46784	0.733918	+	0.679238i	$0.237689\pi$
$242$	24.2523	1.55900
$243$	16.0638	1.03049
$244$	43.6189	2.79241
$245$	−9.17183	−0.585967
$246$	−22.4734	−1.43285
$247$	1.80627	0.114930
$248$	−38.2986	−2.43197
$249$	−7.75265	−0.491304
$250$	28.9328	1.82987
$251$	−11.4825	−0.724770	−0.362385	−	0.932028i	$-0.618037\pi$
$251$	−11.4825	−0.724770	−0.362385	+	0.932028i	$0.618037\pi$
$252$	−14.8498	−0.935448
$253$	−6.16379	−0.387514
$254$	−28.7718	−1.80531
$255$	11.2881	0.706889
$256$	−32.3991	−2.02494
$257$	5.34673	0.333520	0.166760	−	0.985998i	$-0.446670\pi$
$257$	5.34673	0.333520	0.166760	+	0.985998i	$0.446670\pi$
$258$	−9.95393	−0.619704
$259$	−15.2743	−0.949101
$260$	−8.51318	−0.527965
$261$	−22.1350	−1.37012
$262$	4.26399	0.263430
$263$	4.46814	0.275518	0.137759	−	0.990466i	$-0.456010\pi$
$263$	4.46814	0.275518	0.137759	+	0.990466i	$0.456010\pi$
$264$	−4.69053	−0.288682
$265$	18.9074	1.16147
$266$	7.20403	0.441708
$267$	−13.2368	−0.810078
$268$	45.9996	2.80988
$269$	−13.1416	−0.801259	−0.400629	−	0.916240i	$-0.631208\pi$
$269$	−13.1416	−0.801259	−0.400629	+	0.916240i	$0.631208\pi$
$270$	23.3845	1.42313
$271$	17.7967	1.08107	0.540536	−	0.841321i	$-0.318222\pi$
$271$	17.7967	1.08107	0.540536	+	0.841321i	$0.318222\pi$
$272$	27.3215	1.65661
$273$	−1.39636	−0.0845118
$274$	41.0950	2.48264
$275$	−0.650331	−0.0392164
$276$	−20.1278	−1.21155
$277$	9.66624	0.580788	0.290394	−	0.956907i	$-0.406214\pi$
$277$	9.66624	0.580788	0.290394	+	0.956907i	$0.406214\pi$
$278$	−19.4636	−1.16735
$279$	−17.0306	−1.01959
$280$	−17.2339	−1.02993
$281$	11.0466	0.658986	0.329493	−	0.944158i	$-0.393122\pi$
$281$	11.0466	0.658986	0.329493	+	0.944158i	$0.393122\pi$
$282$	1.41216	0.0840927
$283$	6.46084	0.384057	0.192029	−	0.981389i	$-0.438493\pi$
$283$	6.46084	0.384057	0.192029	+	0.981389i	$0.438493\pi$
$284$	48.5165	2.87892
$285$	−3.26350	−0.193313
$286$	2.63956	0.156081
$287$	17.1546	1.01260
$288$	1.38890	0.0818415
$289$	22.0341	1.29612
$290$	−50.6107	−2.97196
$291$	9.16949	0.537525
$292$	−44.3673	−2.59640
$293$	30.0930	1.75805	0.879027	−	0.476772i	$-0.158193\pi$
$293$	30.0930	1.75805	0.879027	+	0.476772i	$0.158193\pi$
$294$	9.28635	0.541591
$295$	−24.7615	−1.44167
$296$	47.8570	2.78163
$297$	−4.85820	−0.281902
$298$	3.46509	0.200727
$299$	5.74920	0.332485
$300$	−2.12365	−0.122609
$301$	7.59810	0.437947
$302$	−53.2843	−3.06617
$303$	10.8713	0.624538
$304$	−7.89889	−0.453032
$305$	22.5105	1.28895
$306$	34.7170	1.98464
$307$	−34.5629	−1.97261	−0.986304	−	0.164939i	$-0.947257\pi$
$307$	−34.5629	−1.97261	−0.986304	+	0.164939i	$0.947257\pi$
$308$	7.05394	0.401935
$309$	5.05126	0.287356
$310$	−38.9397	−2.21163
$311$	25.6949	1.45703	0.728513	−	0.685032i	$-0.240212\pi$
$311$	25.6949	1.45703	0.728513	+	0.685032i	$0.240212\pi$
$312$	4.37504	0.247688
$313$	−1.76797	−0.0999316	−0.0499658	−	0.998751i	$-0.515911\pi$
$313$	−1.76797	−0.0999316	−0.0499658	+	0.998751i	$0.515911\pi$
$314$	−1.85574	−0.104726
$315$	−7.66356	−0.431792
$316$	−25.5037	−1.43470
$317$	−2.90409	−0.163110	−0.0815551	−	0.996669i	$-0.525989\pi$
$317$	−2.90409	−0.163110	−0.0815551	+	0.996669i	$0.525989\pi$
$318$	−19.1434	−1.07351
$319$	10.5145	0.588701
$320$	−15.1565	−0.847273
$321$	−1.86941	−0.104340
$322$	22.9298	1.27783
$323$	−11.2851	−0.627920
$324$	11.6361	0.646450
$325$	0.606588	0.0336475
$326$	−38.3771	−2.12551
$327$	0.725726	0.0401328
$328$	−53.7481	−2.96774
$329$	−1.07794	−0.0594286
$330$	−4.76904	−0.262527
$331$	29.1426	1.60182	0.800910	−	0.598784i	$-0.204349\pi$
$331$	29.1426	1.60182	0.800910	+	0.598784i	$0.204349\pi$
$332$	−36.5294	−2.00481
$333$	21.2809	1.16619
$334$	−45.2122	−2.47390
$335$	23.7391	1.29701
$336$	6.10634	0.333128
$337$	−24.4145	−1.32994	−0.664970	−	0.746870i	$-0.731556\pi$
$337$	−24.4145	−1.32994	−0.664970	+	0.746870i	$0.731556\pi$
$338$	−2.46202	−0.133916
$339$	−15.2851	−0.830172
$340$	53.1880	2.88452
$341$	8.08985	0.438090
$342$	−10.0370	−0.542739
$343$	−18.4281	−0.995026
$344$	−23.8061	−1.28354
$345$	−10.3874	−0.559239
$346$	−42.9542	−2.30923
$347$	−1.02741	−0.0551541	−0.0275770	−	0.999620i	$-0.508779\pi$
$347$	−1.02741	−0.0551541	−0.0275770	+	0.999620i	$0.508779\pi$
$348$	34.3352	1.84056
$349$	−35.5121	−1.90092	−0.950460	−	0.310846i	$-0.899388\pi$
$349$	−35.5121	−1.90092	−0.950460	+	0.310846i	$0.899388\pi$
$350$	2.41928	0.129316
$351$	4.53143	0.241870
$352$	−0.659753	−0.0351649
$353$	19.9986	1.06442	0.532208	−	0.846614i	$-0.321363\pi$
$353$	19.9986	1.06442	0.532208	+	0.846614i	$0.321363\pi$
$354$	25.0706	1.33249
$355$	25.0380	1.32888
$356$	−62.3699	−3.30560
$357$	8.72410	0.461729
$358$	51.1150	2.70151
$359$	−4.33805	−0.228954	−0.114477	−	0.993426i	$-0.536519\pi$
$359$	−4.33805	−0.228954	−0.114477	+	0.993426i	$0.536519\pi$
$360$	24.0112	1.26550
$361$	−15.7374	−0.828283
$362$	−11.9947	−0.630428
$363$	−8.49102	−0.445663
$364$	−6.57947	−0.344858
$365$	−22.8967	−1.19847
$366$	−22.7915	−1.19133
$367$	28.2747	1.47593	0.737965	−	0.674839i	$-0.235787\pi$
$367$	28.2747	1.47593	0.737965	+	0.674839i	$0.235787\pi$
$368$	−25.1414	−1.31059
$369$	−23.9006	−1.24421
$370$	48.6580	2.52961
$371$	14.6127	0.758654
$372$	26.4174	1.36968
$373$	−36.1735	−1.87299	−0.936495	−	0.350680i	$-0.885951\pi$
$373$	−36.1735	−1.87299	−0.936495	+	0.350680i	$0.885951\pi$
$374$	−16.4913	−0.852743
$375$	−10.1297	−0.523097
$376$	3.37735	0.174174
$377$	−9.80731	−0.505102
$378$	18.0729	0.929568
$379$	−2.35542	−0.120990	−0.0604948	−	0.998169i	$-0.519268\pi$
$379$	−2.35542	−0.120990	−0.0604948	+	0.998169i	$0.519268\pi$
$380$	−15.3771	−0.788830
$381$	10.0734	0.516074
$382$	28.8582	1.47651
$383$	25.7036	1.31339	0.656697	−	0.754155i	$-0.271953\pi$
$383$	25.7036	1.31339	0.656697	+	0.754155i	$0.271953\pi$
$384$	16.4066	0.837247
$385$	3.64034	0.185529
$386$	−32.3375	−1.64594
$387$	−10.5860	−0.538119
$388$	43.2053	2.19342
$389$	1.38616	0.0702811	0.0351405	−	0.999382i	$-0.488812\pi$
$389$	1.38616	0.0702811	0.0351405	+	0.999382i	$0.488812\pi$
$390$	4.44827	0.225247
$391$	−35.9194	−1.81652
$392$	22.2095	1.12175
$393$	−1.49287	−0.0753055
$394$	1.05015	0.0529057
$395$	−13.1617	−0.662239
$396$	−9.82789	−0.493870
$397$	−29.4951	−1.48032	−0.740159	−	0.672432i	$-0.765250\pi$
$397$	−29.4951	−1.48032	−0.740159	+	0.672432i	$0.765250\pi$
$398$	−34.1684	−1.71271
$399$	−2.52222	−0.126269
$400$	−2.65263	−0.132631
$401$	−1.76600	−0.0881898	−0.0440949	−	0.999027i	$-0.514040\pi$
$401$	−1.76600	−0.0881898	−0.0440949	+	0.999027i	$0.514040\pi$
$402$	−24.0355	−1.19878
$403$	−7.54571	−0.375879
$404$	51.2239	2.54848
$405$	6.00506	0.298394
$406$	−39.1149	−1.94124
$407$	−10.1089	−0.501078
$408$	−27.3340	−1.35324
$409$	−1.60684	−0.0794530	−0.0397265	−	0.999211i	$-0.512649\pi$
$409$	−1.60684	−0.0794530	−0.0397265	+	0.999211i	$0.512649\pi$
$410$	−54.6477	−2.69886
$411$	−14.3879	−0.709701
$412$	23.8008	1.17258
$413$	−19.1371	−0.941674
$414$	−31.9468	−1.57010
$415$	−18.8518	−0.925398
$416$	0.615376	0.0301713
$417$	6.81445	0.333705
$418$	4.76778	0.233200
$419$	−5.08871	−0.248600	−0.124300	−	0.992245i	$-0.539668\pi$
$419$	−5.08871	−0.248600	−0.124300	+	0.992245i	$0.539668\pi$
$420$	11.8875	0.580051
$421$	−5.77609	−0.281509	−0.140755	−	0.990045i	$-0.544953\pi$
$421$	−5.77609	−0.281509	−0.140755	+	0.990045i	$0.544953\pi$
$422$	−12.9457	−0.630189
$423$	1.50183	0.0730217
$424$	−45.7840	−2.22347
$425$	−3.78980	−0.183832
$426$	−25.3506	−1.22824
$427$	17.3974	0.841919
$428$	−8.80840	−0.425770
$429$	−0.924142	−0.0446180
$430$	−24.2046	−1.16725
$431$	−11.2740	−0.543047	−0.271524	−	0.962432i	$-0.587528\pi$
$431$	−11.2740	−0.543047	−0.271524	+	0.962432i	$0.587528\pi$
$432$	−19.8161	−0.953401
$433$	18.7754	0.902288	0.451144	−	0.892451i	$-0.351016\pi$
$433$	18.7754	0.902288	0.451144	+	0.892451i	$0.351016\pi$
$434$	−30.0948	−1.44460
$435$	17.7194	0.849581
$436$	3.41952	0.163765
$437$	10.3846	0.496764
$438$	23.1826	1.10771
$439$	−14.2188	−0.678628	−0.339314	−	0.940673i	$-0.610195\pi$
$439$	−14.2188	−0.678628	−0.339314	+	0.940673i	$0.610195\pi$
$440$	−11.4058	−0.543749
$441$	9.87607	0.470289
$442$	15.3820	0.731648
$443$	−19.1794	−0.911242	−0.455621	−	0.890174i	$-0.650583\pi$
$443$	−19.1794	−0.911242	−0.455621	+	0.890174i	$0.650583\pi$
$444$	−33.0104	−1.56661
$445$	−32.1873	−1.52583
$446$	−21.0936	−0.998813
$447$	−1.21317	−0.0573809
$448$	−11.7138	−0.553425
$449$	25.7033	1.21301	0.606506	−	0.795079i	$-0.292571\pi$
$449$	25.7033	1.21301	0.606506	+	0.795079i	$0.292571\pi$
$450$	−3.37066	−0.158894
$451$	11.3532	0.534603
$452$	−72.0212	−3.38759
$453$	18.6555	0.876511
$454$	28.0823	1.31797
$455$	−3.39548	−0.159183
$456$	7.90252	0.370069
$457$	0.891689	0.0417115	0.0208557	−	0.999782i	$-0.493361\pi$
$457$	0.891689	0.0417115	0.0208557	+	0.999782i	$0.493361\pi$
$458$	−49.6457	−2.31979
$459$	−28.3111	−1.32145
$460$	−48.9440	−2.28202
$461$	−25.9204	−1.20723	−0.603616	−	0.797275i	$-0.706274\pi$
$461$	−25.9204	−1.20723	−0.603616	+	0.797275i	$0.706274\pi$
$462$	−3.68579	−0.171479
$463$	−9.50406	−0.441691	−0.220846	−	0.975309i	$-0.570882\pi$
$463$	−9.50406	−0.441691	−0.220846	+	0.975309i	$0.570882\pi$
$464$	42.8876	1.99101
$465$	13.6333	0.632227
$466$	37.0562	1.71660
$467$	−24.5471	−1.13590	−0.567952	−	0.823062i	$-0.692264\pi$
$467$	−24.5471	−1.13590	−0.567952	+	0.823062i	$0.692264\pi$
$468$	9.16684	0.423737
$469$	18.3470	0.847184
$470$	3.43388	0.158393
$471$	0.649718	0.0299374
$472$	59.9596	2.75986
$473$	5.02858	0.231214
$474$	13.3261	0.612087
$475$	1.09567	0.0502726
$476$	41.1068	1.88412
$477$	−20.3591	−0.932180
$478$	−17.2874	−0.790709
$479$	−0.560322	−0.0256018	−0.0128009	−	0.999918i	$-0.504075\pi$
$479$	−0.560322	−0.0256018	−0.0128009	+	0.999918i	$0.504075\pi$
$480$	−1.11183	−0.0507481
$481$	9.42892	0.429922
$482$	−56.1019	−2.55537
$483$	−8.02798	−0.365286
$484$	−40.0085	−1.81857
$485$	22.2971	1.01246
$486$	−39.5494	−1.79400
$487$	−17.0160	−0.771066	−0.385533	−	0.922694i	$-0.625982\pi$
$487$	−17.0160	−0.771066	−0.385533	+	0.922694i	$0.625982\pi$
$488$	−54.5089	−2.46750
$489$	13.4363	0.607610
$490$	22.5812	1.02012
$491$	39.0243	1.76114	0.880572	−	0.473912i	$-0.157159\pi$
$491$	39.0243	1.76114	0.880572	+	0.473912i	$0.157159\pi$
$492$	37.0739	1.67142
$493$	61.2734	2.75961
$494$	−4.44708	−0.200084
$495$	−5.07190	−0.227965
$496$	32.9976	1.48164
$497$	19.3508	0.868002
$498$	19.0872	0.855317
$499$	38.9175	1.74219	0.871093	−	0.491119i	$-0.163412\pi$
$499$	38.9175	1.74219	0.871093	+	0.491119i	$0.163412\pi$
$500$	−47.7299	−2.13455
$501$	15.8293	0.707202
$502$	28.2702	1.26176
$503$	−3.80123	−0.169489	−0.0847443	−	0.996403i	$-0.527007\pi$
$503$	−3.80123	−0.169489	−0.0847443	+	0.996403i	$0.527007\pi$
$504$	18.5572	0.826604
$505$	26.4352	1.17635
$506$	15.1754	0.674628
$507$	0.861982	0.0382820
$508$	47.4643	2.10589
$509$	38.6940	1.71508	0.857540	−	0.514417i	$-0.171992\pi$
$509$	38.6940	1.71508	0.857540	+	0.514417i	$0.171992\pi$
$510$	−27.7916	−1.23063
$511$	−17.6959	−0.782820
$512$	41.7000	1.84290
$513$	8.18501	0.361377
$514$	−13.1637	−0.580628
$515$	12.2829	0.541251
$516$	16.4208	0.722884
$517$	−0.713401	−0.0313753
$518$	37.6057	1.65230
$519$	15.0388	0.660129
$520$	10.6386	0.466533
$521$	−17.6906	−0.775038	−0.387519	−	0.921862i	$-0.626668\pi$
$521$	−17.6906	−0.775038	−0.387519	+	0.921862i	$0.626668\pi$
$522$	54.4967	2.38526
$523$	−24.0101	−1.04989	−0.524943	−	0.851137i	$-0.675913\pi$
$523$	−24.0101	−1.04989	−0.524943	+	0.851137i	$0.675913\pi$
$524$	−7.03421	−0.307291
$525$	−0.847019	−0.0369669
$526$	−11.0007	−0.479652
$527$	47.1435	2.05360
$528$	4.04130	0.175875
$529$	10.0533	0.437100
$530$	−46.5503	−2.02202
$531$	26.6627	1.15706
$532$	−11.8843	−0.515251
$533$	−10.5896	−0.458686
$534$	32.5892	1.41027
$535$	−4.54577	−0.196531
$536$	−57.4840	−2.48293
$537$	−17.8960	−0.772268
$538$	32.3549	1.39492
$539$	−4.69133	−0.202070
$540$	−38.5769	−1.66008
$541$	15.2875	0.657259	0.328630	−	0.944459i	$-0.393413\pi$
$541$	15.2875	0.657259	0.328630	+	0.944459i	$0.393413\pi$
$542$	−43.8158	−1.88205
$543$	4.19949	0.180217
$544$	−3.84470	−0.164840
$545$	1.76472	0.0755922
$546$	3.43788	0.147128
$547$	37.2556	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$547$	37.2556	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$548$	−67.7936	−2.89600
$549$	−24.2389	−1.03449
$550$	1.60113	0.0682723
$551$	−17.7147	−0.754671
$552$	25.1530	1.07058
$553$	−10.1722	−0.432564
$554$	−23.7985	−1.01110
$555$	−17.0357	−0.723127
$556$	32.1087	1.36171
$557$	36.5212	1.54745	0.773726	−	0.633521i	$-0.218391\pi$
$557$	36.5212	1.54745	0.773726	+	0.633521i	$0.218391\pi$
$558$	41.9296	1.77502
$559$	−4.69034	−0.198380
$560$	14.8485	0.627465
$561$	5.77379	0.243770
$562$	−27.1970	−1.14724
$563$	−30.6850	−1.29322	−0.646610	−	0.762821i	$-0.723814\pi$
$563$	−30.6850	−1.29322	−0.646610	+	0.762821i	$0.723814\pi$
$564$	−2.32961	−0.0980941
$565$	−37.1681	−1.56367
$566$	−15.9067	−0.668609
$567$	4.64106	0.194906
$568$	−60.6292	−2.54394
$569$	1.20675	0.0505896	0.0252948	−	0.999680i	$-0.491948\pi$
$569$	1.20675	0.0505896	0.0252948	+	0.999680i	$0.491948\pi$
$570$	8.03479	0.336540
$571$	30.3315	1.26934	0.634668	−	0.772785i	$-0.281137\pi$
$571$	30.3315	1.26934	0.634668	+	0.772785i	$0.281137\pi$
$572$	−4.35443	−0.182068
$573$	−10.1036	−0.422083
$574$	−42.2349	−1.76285
$575$	3.48740	0.145435
$576$	16.3202	0.680010
$577$	−7.66150	−0.318952	−0.159476	−	0.987202i	$-0.550981\pi$
$577$	−7.66150	−0.318952	−0.159476	+	0.987202i	$0.550981\pi$
$578$	−54.2483	−2.25643
$579$	11.3218	0.470516
$580$	83.4914	3.46679
$581$	−14.5698	−0.604455
$582$	−22.5755	−0.935783
$583$	9.67098	0.400531
$584$	55.4441	2.29429
$585$	4.73075	0.195592
$586$	−74.0897	−3.06062
$587$	−19.6544	−0.811223	−0.405611	−	0.914046i	$-0.632941\pi$
$587$	−19.6544	−0.811223	−0.405611	+	0.914046i	$0.632941\pi$
$588$	−15.3195	−0.631765
$589$	−13.6296	−0.561599
$590$	60.9632	2.50982
$591$	−0.367669	−0.0151239
$592$	−41.2329	−1.69466
$593$	−17.0040	−0.698269	−0.349135	−	0.937073i	$-0.613524\pi$
$593$	−17.0040	−0.698269	−0.349135	+	0.937073i	$0.613524\pi$
$594$	11.9610	0.490765
$595$	21.2140	0.869691
$596$	−5.71628	−0.234148
$597$	11.9628	0.489604
$598$	−14.1546	−0.578826
$599$	−0.192914	−0.00788227	−0.00394113	−	0.999992i	$-0.501255\pi$
$599$	−0.192914	−0.00788227	−0.00394113	+	0.999992i	$0.501255\pi$
$600$	2.65385	0.108343
$601$	−20.0409	−0.817486	−0.408743	−	0.912650i	$-0.634033\pi$
$601$	−20.0409	−0.817486	−0.408743	+	0.912650i	$0.634033\pi$
$602$	−18.7067	−0.762427
$603$	−25.5619	−1.04096
$604$	87.9020	3.57668
$605$	−20.6473	−0.839431
$606$	−26.7653	−1.08726
$607$	−34.4452	−1.39809	−0.699043	−	0.715080i	$-0.746390\pi$
$607$	−34.4452	−1.39809	−0.699043	+	0.715080i	$0.746390\pi$
$608$	1.11154	0.0450788
$609$	13.6946	0.554932
$610$	−55.4213	−2.24394
$611$	0.665416	0.0269198
$612$	−57.2719	−2.31508
$613$	39.1710	1.58210	0.791050	−	0.611751i	$-0.209535\pi$
$613$	39.1710	1.58210	0.791050	+	0.611751i	$0.209535\pi$
$614$	85.0945	3.43413
$615$	19.1328	0.771509
$616$	−8.81504	−0.355168
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−12.4363	−0.500261
$619$	−19.1204	−0.768514	−0.384257	−	0.923226i	$-0.625542\pi$
$619$	−19.1204	−0.768514	−0.384257	+	0.923226i	$0.625542\pi$
$620$	64.2380	2.57986
$621$	26.0521	1.04543
$622$	−63.2614	−2.53655
$623$	−24.8762	−0.996645
$624$	−3.76947	−0.150900
$625$	−21.5991	−0.863964
$626$	4.35278	0.173972
$627$	−1.66925	−0.0666636
$628$	3.06138	0.122162
$629$	−58.9093	−2.34887
$630$	18.8678	0.751712
$631$	10.1908	0.405691	0.202846	−	0.979211i	$-0.434981\pi$
$631$	10.1908	0.405691	0.202846	+	0.979211i	$0.434981\pi$
$632$	31.8710	1.26776
$633$	4.53246	0.180149
$634$	7.14994	0.283960
$635$	24.4950	0.972054
$636$	31.5805	1.25225
$637$	4.37578	0.173375
$638$	−25.8870	−1.02488
$639$	−26.9605	−1.06654
$640$	39.8953	1.57700
$641$	−31.4730	−1.24311	−0.621555	−	0.783371i	$-0.713499\pi$
$641$	−31.4730	−1.24311	−0.621555	+	0.783371i	$0.713499\pi$
$642$	4.60252	0.181647
$643$	38.9123	1.53455	0.767275	−	0.641318i	$-0.221612\pi$
$643$	38.9123	1.53455	0.767275	+	0.641318i	$0.221612\pi$
$644$	−37.8267	−1.49058
$645$	8.47430	0.333675
$646$	27.7842	1.09315
$647$	18.5325	0.728586	0.364293	−	0.931284i	$-0.381311\pi$
$647$	18.5325	0.728586	0.364293	+	0.931284i	$0.381311\pi$
$648$	−14.5412	−0.571232
$649$	−12.6653	−0.497157
$650$	−1.49343	−0.0585772
$651$	10.5366	0.412960
$652$	63.3099	2.47941
$653$	33.4600	1.30939	0.654696	−	0.755893i	$-0.272797\pi$
$653$	33.4600	1.30939	0.654696	+	0.755893i	$0.272797\pi$
$654$	−1.78675	−0.0698675
$655$	−3.63016	−0.141842
$656$	46.3086	1.80805
$657$	24.6548	0.961874
$658$	2.65390	0.103460
$659$	−45.8469	−1.78594	−0.892970	−	0.450116i	$-0.851383\pi$
$659$	−45.8469	−1.78594	−0.892970	+	0.450116i	$0.851383\pi$
$660$	7.86739	0.306238
$661$	−6.31898	−0.245780	−0.122890	−	0.992420i	$-0.539216\pi$
$661$	−6.31898	−0.245780	−0.122890	+	0.992420i	$0.539216\pi$
$662$	−71.7496	−2.78863
$663$	−5.38543	−0.209153
$664$	45.6494	1.77154
$665$	−6.13317	−0.237834
$666$	−52.3941	−2.03023
$667$	−56.3842	−2.18320
$668$	74.5855	2.88580
$669$	7.38514	0.285526
$670$	−58.4462	−2.25797
$671$	11.5140	0.444491
$672$	−0.859290	−0.0331478
$673$	21.2221	0.818052	0.409026	−	0.912523i	$-0.365869\pi$
$673$	21.2221	0.818052	0.409026	+	0.912523i	$0.365869\pi$
$674$	60.1089	2.31531
$675$	2.74871	0.105798
$676$	4.06154	0.156213
$677$	9.83953	0.378164	0.189082	−	0.981961i	$-0.439449\pi$
$677$	9.83953	0.378164	0.189082	+	0.981961i	$0.439449\pi$
$678$	37.6322	1.44525
$679$	17.2325	0.661321
$680$	−66.4670	−2.54889
$681$	−9.83194	−0.376761
$682$	−19.9174	−0.762676
$683$	7.92854	0.303377	0.151688	−	0.988428i	$-0.451529\pi$
$683$	7.92854	0.303377	0.151688	+	0.988428i	$0.451529\pi$
$684$	16.5578	0.633104
$685$	−34.9864	−1.33676
$686$	45.3704	1.73225
$687$	17.3815	0.663147
$688$	20.5110	0.781975
$689$	−9.02049	−0.343653
$690$	25.5740	0.973585
$691$	−6.72619	−0.255876	−0.127938	−	0.991782i	$-0.540836\pi$
$691$	−6.72619	−0.255876	−0.127938	+	0.991782i	$0.540836\pi$
$692$	70.8606	2.69372
$693$	−3.91985	−0.148903
$694$	2.52949	0.0960183
$695$	16.5704	0.628552
$696$	−42.9073	−1.62640
$697$	66.1609	2.50602
$698$	87.4315	3.30933
$699$	−12.9738	−0.490715
$700$	−3.99103	−0.150847
$701$	−34.3687	−1.29809	−0.649045	−	0.760750i	$-0.724831\pi$
$701$	−34.3687	−1.29809	−0.649045	+	0.760750i	$0.724831\pi$
$702$	−11.1565	−0.421074
$703$	17.0312	0.642344
$704$	−7.75243	−0.292181
$705$	−1.20224	−0.0452791
$706$	−49.2368	−1.85305
$707$	20.4306	0.768374
$708$	−41.3585	−1.55435
$709$	12.8276	0.481751	0.240876	−	0.970556i	$-0.422565\pi$
$709$	12.8276	0.481751	0.240876	+	0.970556i	$0.422565\pi$
$710$	−61.6440	−2.31346
$711$	14.1723	0.531504
$712$	77.9413	2.92097
$713$	−43.3818	−1.62466
$714$	−21.4789	−0.803828
$715$	−2.24720	−0.0840405
$716$	−84.3232	−3.15131
$717$	6.05254	0.226036
$718$	10.6804	0.398588
$719$	10.9049	0.406683	0.203342	−	0.979108i	$-0.434820\pi$
$719$	10.9049	0.406683	0.203342	+	0.979108i	$0.434820\pi$
$720$	−20.6877	−0.770985
$721$	9.49296	0.353536
$722$	38.7457	1.44197
$723$	19.6420	0.730492
$724$	19.7874	0.735393
$725$	−5.94900	−0.220940
$726$	20.9051	0.775860
$727$	2.49591	0.0925682	0.0462841	−	0.998928i	$-0.485262\pi$
$727$	2.49591	0.0925682	0.0462841	+	0.998928i	$0.485262\pi$
$728$	8.22212	0.304732
$729$	5.25189	0.194515
$730$	56.3721	2.08643
$731$	29.3040	1.08385
$732$	37.5987	1.38969
$733$	−11.4348	−0.422353	−0.211176	−	0.977448i	$-0.567729\pi$
$733$	−11.4348	−0.422353	−0.211176	+	0.977448i	$0.567729\pi$
$734$	−69.6129	−2.56946
$735$	−7.90596	−0.291616
$736$	3.53792	0.130410
$737$	12.1424	0.447271
$738$	58.8437	2.16607
$739$	16.6609	0.612880	0.306440	−	0.951890i	$-0.400862\pi$
$739$	16.6609	0.612880	0.306440	+	0.951890i	$0.400862\pi$
$740$	−80.2701	−2.95079
$741$	1.55698	0.0571970
$742$	−35.9768	−1.32075
$743$	33.5440	1.23061	0.615305	−	0.788289i	$-0.289033\pi$
$743$	33.5440	1.23061	0.615305	+	0.788289i	$0.289033\pi$
$744$	−33.0128	−1.21031
$745$	−2.95001	−0.108080
$746$	89.0598	3.26071
$747$	20.2993	0.742712
$748$	27.2053	0.994724
$749$	−3.51323	−0.128371
$750$	24.9396	0.910665
$751$	−1.89249	−0.0690578	−0.0345289	−	0.999404i	$-0.510993\pi$
$751$	−1.89249	−0.0690578	−0.0345289	+	0.999404i	$0.510993\pi$
$752$	−2.90988	−0.106112
$753$	−9.89773	−0.360693
$754$	24.1458	0.879338
$755$	45.3637	1.65096
$756$	−29.8144	−1.08434
$757$	14.6684	0.533133	0.266567	−	0.963817i	$-0.414111\pi$
$757$	14.6684	0.533133	0.266567	+	0.963817i	$0.414111\pi$
$758$	5.79908	0.210632
$759$	−5.31308	−0.192853
$760$	19.2162	0.697046
$761$	−22.3364	−0.809695	−0.404847	−	0.914384i	$-0.632675\pi$
$761$	−22.3364	−0.809695	−0.404847	+	0.914384i	$0.632675\pi$
$762$	−24.8008	−0.898439
$763$	1.36388	0.0493756
$764$	−47.6067	−1.72235
$765$	−29.5564	−1.06861
$766$	−63.2828	−2.28650
$767$	11.8134	0.426558
$768$	−27.9274	−1.00774
$769$	0.408255	0.0147221	0.00736103	−	0.999973i	$-0.497657\pi$
$769$	0.408255	0.0147221	0.00736103	+	0.999973i	$0.497657\pi$
$770$	−8.96259	−0.322989
$771$	4.60879	0.165981
$772$	53.3465	1.91998
$773$	47.2755	1.70038	0.850191	−	0.526474i	$-0.176486\pi$
$773$	47.2755	1.70038	0.850191	+	0.526474i	$0.176486\pi$
$774$	26.0630	0.936816
$775$	−4.57714	−0.164416
$776$	−53.9921	−1.93820
$777$	−13.1662	−0.472335
$778$	−3.41275	−0.122353
$779$	−19.1277	−0.685322
$780$	−7.33821	−0.262750
$781$	12.8067	0.458261
$782$	88.4343	3.16241
$783$	−44.4411	−1.58820
$784$	−19.1354	−0.683407
$785$	1.57989	0.0563888
$786$	3.67548	0.131100
$787$	7.90451	0.281765	0.140883	−	0.990026i	$-0.455006\pi$
$787$	7.90451	0.281765	0.140883	+	0.990026i	$0.455006\pi$
$788$	−1.73241	−0.0617144
$789$	3.85146	0.137116
$790$	32.4045	1.15290
$791$	−28.7256	−1.02137
$792$	12.2815	0.436405
$793$	−10.7395	−0.381371
$794$	72.6175	2.57710
$795$	16.2978	0.578024
$796$	56.3669	1.99787
$797$	4.91985	0.174270	0.0871349	−	0.996197i	$-0.472229\pi$
$797$	4.91985	0.174270	0.0871349	+	0.996197i	$0.472229\pi$
$798$	6.20975	0.219823
$799$	−4.15734	−0.147076
$800$	0.373280	0.0131974
$801$	34.6588	1.22461
$802$	4.34793	0.153531
$803$	−11.7115	−0.413290
$804$	39.6509	1.39838
$805$	−19.5213	−0.688036
$806$	18.5777	0.654371
$807$	−11.3278	−0.398759
$808$	−64.0125	−2.25195
$809$	5.74676	0.202045	0.101023	−	0.994884i	$-0.467789\pi$
$809$	5.74676	0.202045	0.101023	+	0.994884i	$0.467789\pi$
$810$	−14.7846	−0.519477
$811$	49.6950	1.74503	0.872514	−	0.488589i	$-0.162488\pi$
$811$	49.6950	1.74503	0.872514	+	0.488589i	$0.162488\pi$
$812$	64.5269	2.26445
$813$	15.3404	0.538012
$814$	24.8882	0.872332
$815$	32.6725	1.14447
$816$	23.5506	0.824437
$817$	−8.47205	−0.296399
$818$	3.95607	0.138321
$819$	3.65620	0.127758
$820$	90.1511	3.14821
$821$	44.4519	1.55138	0.775692	−	0.631112i	$-0.217401\pi$
$821$	44.4519	1.55138	0.775692	+	0.631112i	$0.217401\pi$
$822$	35.4232	1.23553
$823$	20.7645	0.723805	0.361902	−	0.932216i	$-0.382127\pi$
$823$	20.7645	0.723805	0.361902	+	0.932216i	$0.382127\pi$
$824$	−29.7430	−1.03615
$825$	−0.560574	−0.0195167
$826$	47.1159	1.63937
$827$	4.87217	0.169422	0.0847109	−	0.996406i	$-0.473003\pi$
$827$	4.87217	0.169422	0.0847109	+	0.996406i	$0.473003\pi$
$828$	52.7020	1.83152
$829$	−3.76033	−0.130602	−0.0653009	−	0.997866i	$-0.520801\pi$
$829$	−3.76033	−0.130602	−0.0653009	+	0.997866i	$0.520801\pi$
$830$	46.4135	1.61104
$831$	8.33213	0.289038
$832$	7.23099	0.250689
$833$	−27.3386	−0.947228
$834$	−16.7773	−0.580951
$835$	38.4915	1.33205
$836$	−7.86530	−0.272027
$837$	−34.1929	−1.18188
$838$	12.5285	0.432790
$839$	42.5976	1.47063	0.735317	−	0.677723i	$-0.237033\pi$
$839$	42.5976	1.47063	0.735317	+	0.677723i	$0.237033\pi$
$840$	−14.8554	−0.512558
$841$	67.1833	2.31667
$842$	14.2208	0.490083
$843$	9.52198	0.327955
$844$	21.3563	0.735115
$845$	2.09605	0.0721062
$846$	−3.69755	−0.127124
$847$	−15.9574	−0.548303
$848$	39.4469	1.35461
$849$	5.56913	0.191132
$850$	9.33056	0.320035
$851$	54.2087	1.85825
$852$	41.8203	1.43274
$853$	−19.4839	−0.667115	−0.333557	−	0.942730i	$-0.608249\pi$
$853$	−19.4839	−0.667115	−0.333557	+	0.942730i	$0.608249\pi$
$854$	−42.8327	−1.46571
$855$	8.54503	0.292234
$856$	11.0075	0.376229
$857$	−3.07651	−0.105091	−0.0525457	−	0.998619i	$-0.516734\pi$
$857$	−3.07651	−0.105091	−0.0525457	+	0.998619i	$0.516734\pi$
$858$	2.27526	0.0776760
$859$	12.5303	0.427527	0.213764	−	0.976885i	$-0.431428\pi$
$859$	12.5303	0.427527	0.213764	+	0.976885i	$0.431428\pi$
$860$	39.9297	1.36159
$861$	14.7869	0.503938
$862$	27.7567	0.945397
$863$	−3.84060	−0.130736	−0.0653678	−	0.997861i	$-0.520822\pi$
$863$	−3.84060	−0.130736	−0.0653678	+	0.997861i	$0.520822\pi$
$864$	2.78853	0.0948679
$865$	36.5692	1.24339
$866$	−46.2254	−1.57080
$867$	18.9930	0.645036
$868$	49.6468	1.68512
$869$	−6.73214	−0.228372
$870$	−43.6255	−1.47904
$871$	−11.3257	−0.383756
$872$	−4.27324	−0.144710
$873$	−24.0091	−0.812584
$874$	−25.5672	−0.864823
$875$	−19.0371	−0.643570
$876$	−38.2438	−1.29214
$877$	−39.8981	−1.34726	−0.673631	−	0.739068i	$-0.735266\pi$
$877$	−39.8981	−1.34726	−0.673631	+	0.739068i	$0.735266\pi$
$878$	35.0071	1.18143
$879$	25.9397	0.874923
$880$	9.82706	0.331270
$881$	2.59734	0.0875065	0.0437533	−	0.999042i	$-0.486068\pi$
$881$	2.59734	0.0875065	0.0437533	+	0.999042i	$0.486068\pi$
$882$	−24.3151	−0.818731
$883$	0.0735091	0.00247378	0.00123689	−	0.999999i	$-0.499606\pi$
$883$	0.0735091	0.00247378	0.00123689	+	0.999999i	$0.499606\pi$
$884$	−25.3754	−0.853467
$885$	−21.3439	−0.717469
$886$	47.2201	1.58639
$887$	−49.8423	−1.67354	−0.836770	−	0.547554i	$-0.815559\pi$
$887$	−49.8423	−1.67354	−0.836770	+	0.547554i	$0.815559\pi$
$888$	41.2519	1.38432
$889$	18.9311	0.634930
$890$	79.2459	2.65633
$891$	3.07155	0.102901
$892$	34.7977	1.16511
$893$	1.20192	0.0402208
$894$	2.98685	0.0998950
$895$	−43.5169	−1.45461
$896$	30.8334	1.03007
$897$	4.95571	0.165466
$898$	−63.2820	−2.11175
$899$	74.0031	2.46814
$900$	5.56050	0.185350
$901$	56.3575	1.87754
$902$	−27.9519	−0.930697
$903$	6.54943	0.217951
$904$	90.0021	2.99343
$905$	10.2117	0.339449
$906$	−45.9301	−1.52593
$907$	−14.7939	−0.491222	−0.245611	−	0.969368i	$-0.578989\pi$
$907$	−14.7939	−0.491222	−0.245611	+	0.969368i	$0.578989\pi$
$908$	−46.3267	−1.53741
$909$	−28.4650	−0.944123
$910$	8.35974	0.277123
$911$	−23.1757	−0.767845	−0.383923	−	0.923365i	$-0.625427\pi$
$911$	−23.1757	−0.767845	−0.383923	+	0.923365i	$0.625427\pi$
$912$	−6.80870	−0.225459
$913$	−9.64256	−0.319122
$914$	−2.19536	−0.0726159
$915$	19.4036	0.641465
$916$	81.8994	2.70603
$917$	−2.80559	−0.0926489
$918$	69.7026	2.30053
$919$	−26.9805	−0.890003	−0.445002	−	0.895530i	$-0.646797\pi$
$919$	−26.9805	−0.890003	−0.445002	+	0.895530i	$0.646797\pi$
$920$	61.1634	2.01650
$921$	−29.7926	−0.981699
$922$	63.8165	2.10168
$923$	−11.9453	−0.393186
$924$	6.08037	0.200030
$925$	5.71947	0.188055
$926$	23.3992	0.768945
$927$	−13.2260	−0.434400
$928$	−6.03518	−0.198115
$929$	−39.8449	−1.30727	−0.653635	−	0.756810i	$-0.726757\pi$
$929$	−39.8449	−1.30727	−0.653635	+	0.756810i	$0.726757\pi$
$930$	−33.5653	−1.10065
$931$	7.90385	0.259038
$932$	−61.1308	−2.00241
$933$	22.1486	0.725112
$934$	60.4354	1.97751
$935$	14.0399	0.459153
$936$	−11.4555	−0.374433
$937$	33.7360	1.10211	0.551053	−	0.834470i	$-0.314226\pi$
$937$	33.7360	1.10211	0.551053	+	0.834470i	$0.314226\pi$
$938$	−45.1706	−1.47487
$939$	−1.52396	−0.0497325
$940$	−5.66480	−0.184766
$941$	−41.7588	−1.36130	−0.680649	−	0.732610i	$-0.738302\pi$
$941$	−41.7588	−1.36130	−0.680649	+	0.732610i	$0.738302\pi$
$942$	−1.59962	−0.0521184
$943$	−60.8817	−1.98258
$944$	−51.6604	−1.68140
$945$	−15.3864	−0.500519
$946$	−12.3805	−0.402523
$947$	9.92705	0.322586	0.161293	−	0.986907i	$-0.448434\pi$
$947$	9.92705	0.322586	0.161293	+	0.986907i	$0.448434\pi$
$948$	−21.9837	−0.713999
$949$	10.9238	0.354600
$950$	−2.69755	−0.0875201
$951$	−2.50328	−0.0811744
$952$	−51.3695	−1.66490
$953$	5.11948	0.165836	0.0829180	−	0.996556i	$-0.473576\pi$
$953$	5.11948	0.165836	0.0829180	+	0.996556i	$0.473576\pi$
$954$	50.1246	1.62284
$955$	−24.5685	−0.795017
$956$	28.5187	0.922361
$957$	9.06335	0.292976
$958$	1.37952	0.0445704
$959$	−27.0395	−0.873150
$960$	−13.0646	−0.421659
$961$	25.9377	0.836702
$962$	−23.2142	−0.748455
$963$	4.89480	0.157733
$964$	92.5501	2.98084
$965$	27.5306	0.886242
$966$	19.7650	0.635930
$967$	−34.4432	−1.10762	−0.553810	−	0.832643i	$-0.686827\pi$
$967$	−34.4432	−1.10762	−0.553810	+	0.832643i	$0.686827\pi$
$968$	49.9971	1.60697
$969$	−9.72756	−0.312494
$970$	−54.8958	−1.76260
$971$	3.50594	0.112511	0.0562555	−	0.998416i	$-0.482084\pi$
$971$	3.50594	0.112511	0.0562555	+	0.998416i	$0.482084\pi$
$972$	65.2439	2.09270
$973$	12.8066	0.410560
$974$	41.8936	1.34236
$975$	0.522869	0.0167452
$976$	46.9641	1.50328
$977$	−45.5511	−1.45731	−0.728655	−	0.684881i	$-0.759854\pi$
$977$	−45.5511	−1.45731	−0.728655	+	0.684881i	$0.759854\pi$
$978$	−33.0804	−1.05779
$979$	−16.4636	−0.526179
$980$	−37.2518	−1.18996
$981$	−1.90022	−0.0606693
$982$	−96.0787	−3.06599
$983$	−3.30066	−0.105275	−0.0526373	−	0.998614i	$-0.516763\pi$
$983$	−3.30066	−0.105275	−0.0526373	+	0.998614i	$0.516763\pi$
$984$	−46.3299	−1.47694
$985$	−0.894047	−0.0284867
$986$	−150.856	−4.80424
$987$	−0.929163	−0.0295756
$988$	7.33626	0.233397
$989$	−26.9657	−0.857460
$990$	12.4871	0.396866
$991$	20.3731	0.647174	0.323587	−	0.946198i	$-0.395111\pi$
$991$	20.3731	0.647174	0.323587	+	0.946198i	$0.395111\pi$
$992$	−4.64345	−0.147430
$993$	25.1204	0.797171
$994$	−47.6420	−1.51111
$995$	29.0894	0.922196
$996$	−31.4877	−0.997726
$997$	42.5126	1.34639	0.673193	−	0.739467i	$-0.264922\pi$
$997$	42.5126	1.34639	0.673193	+	0.739467i	$0.264922\pi$
$998$	−95.8156	−3.03299
$999$	42.7265	1.35181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.13	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.13	✓	169	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)

\(f(q)\)	\(=\)	\(q-2.46202 q^{2} +0.861982 q^{3} +4.06154 q^{4} +2.09605 q^{5} -2.12222 q^{6} +1.61995 q^{7} -5.07555 q^{8} -2.25699 q^{9} +O(q^{10})\)	\(q-2.46202 q^{2} +0.861982 q^{3} +4.06154 q^{4} +2.09605 q^{5} -2.12222 q^{6} +1.61995 q^{7} -5.07555 q^{8} -2.25699 q^{9} -5.16051 q^{10} +1.07211 q^{11} +3.50098 q^{12} -1.00000 q^{13} -3.98834 q^{14} +1.80676 q^{15} +4.37303 q^{16} +6.24773 q^{17} +5.55674 q^{18} -1.80627 q^{19} +8.51318 q^{20} +1.39636 q^{21} -2.63956 q^{22} -5.74920 q^{23} -4.37504 q^{24} -0.606588 q^{25} +2.46202 q^{26} -4.53143 q^{27} +6.57947 q^{28} +9.80731 q^{29} -4.44827 q^{30} +7.54571 q^{31} -0.615376 q^{32} +0.924142 q^{33} -15.3820 q^{34} +3.39548 q^{35} -9.16684 q^{36} -9.42892 q^{37} +4.44708 q^{38} -0.861982 q^{39} -10.6386 q^{40} +10.5896 q^{41} -3.43788 q^{42} +4.69034 q^{43} +4.35443 q^{44} -4.73075 q^{45} +14.1546 q^{46} -0.665416 q^{47} +3.76947 q^{48} -4.37578 q^{49} +1.49343 q^{50} +5.38543 q^{51} -4.06154 q^{52} +9.02049 q^{53} +11.1565 q^{54} +2.24720 q^{55} -8.22212 q^{56} -1.55698 q^{57} -24.1458 q^{58} -11.8134 q^{59} +7.33821 q^{60} +10.7395 q^{61} -18.5777 q^{62} -3.65620 q^{63} -7.23099 q^{64} -2.09605 q^{65} -2.27526 q^{66} +11.3257 q^{67} +25.3754 q^{68} -4.95571 q^{69} -8.35974 q^{70} +11.9453 q^{71} +11.4555 q^{72} -10.9238 q^{73} +23.2142 q^{74} -0.522869 q^{75} -7.33626 q^{76} +1.73676 q^{77} +2.12222 q^{78} -6.27932 q^{79} +9.16607 q^{80} +2.86495 q^{81} -26.0718 q^{82} -8.99398 q^{83} +5.67139 q^{84} +13.0955 q^{85} -11.5477 q^{86} +8.45373 q^{87} -5.44156 q^{88} -15.3562 q^{89} +11.6472 q^{90} -1.61995 q^{91} -23.3506 q^{92} +6.50427 q^{93} +1.63827 q^{94} -3.78604 q^{95} -0.530444 q^{96} +10.6377 q^{97} +10.7732 q^{98} -2.41974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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