LMFDB - Embedded newform 8014.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.13974 q^{3} +1.00000 q^{4} +3.30555 q^{5} +3.13974 q^{6} +0.656006 q^{7} -1.00000 q^{8} +6.85799 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.13974 q^{3} +1.00000 q^{4} +3.30555 q^{5} +3.13974 q^{6} +0.656006 q^{7} -1.00000 q^{8} +6.85799 q^{9} -3.30555 q^{10} +5.95452 q^{11} -3.13974 q^{12} +4.94401 q^{13} -0.656006 q^{14} -10.3786 q^{15} +1.00000 q^{16} -0.532100 q^{17} -6.85799 q^{18} -6.02208 q^{19} +3.30555 q^{20} -2.05969 q^{21} -5.95452 q^{22} -8.12726 q^{23} +3.13974 q^{24} +5.92665 q^{25} -4.94401 q^{26} -12.1131 q^{27} +0.656006 q^{28} -7.59990 q^{29} +10.3786 q^{30} -6.76567 q^{31} -1.00000 q^{32} -18.6957 q^{33} +0.532100 q^{34} +2.16846 q^{35} +6.85799 q^{36} -3.86211 q^{37} +6.02208 q^{38} -15.5229 q^{39} -3.30555 q^{40} +10.8582 q^{41} +2.05969 q^{42} +10.7818 q^{43} +5.95452 q^{44} +22.6694 q^{45} +8.12726 q^{46} -1.25178 q^{47} -3.13974 q^{48} -6.56966 q^{49} -5.92665 q^{50} +1.67066 q^{51} +4.94401 q^{52} -0.381307 q^{53} +12.1131 q^{54} +19.6830 q^{55} -0.656006 q^{56} +18.9078 q^{57} +7.59990 q^{58} -1.34723 q^{59} -10.3786 q^{60} +9.35980 q^{61} +6.76567 q^{62} +4.49889 q^{63} +1.00000 q^{64} +16.3427 q^{65} +18.6957 q^{66} -12.9860 q^{67} -0.532100 q^{68} +25.5175 q^{69} -2.16846 q^{70} +11.5488 q^{71} -6.85799 q^{72} +7.66285 q^{73} +3.86211 q^{74} -18.6081 q^{75} -6.02208 q^{76} +3.90620 q^{77} +15.5229 q^{78} -6.09822 q^{79} +3.30555 q^{80} +17.4581 q^{81} -10.8582 q^{82} -7.09025 q^{83} -2.05969 q^{84} -1.75888 q^{85} -10.7818 q^{86} +23.8617 q^{87} -5.95452 q^{88} +3.67451 q^{89} -22.6694 q^{90} +3.24330 q^{91} -8.12726 q^{92} +21.2425 q^{93} +1.25178 q^{94} -19.9063 q^{95} +3.13974 q^{96} +13.1972 q^{97} +6.56966 q^{98} +40.8361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.13974	−1.81273	−0.906366	−	0.422493i	$-0.861155\pi$
$3$	−3.13974	−1.81273	−0.906366	+	0.422493i	$0.861155\pi$
$4$	1.00000	0.500000
$5$	3.30555	1.47829	0.739143	−	0.673549i	$-0.235231\pi$
$5$	3.30555	1.47829	0.739143	+	0.673549i	$0.235231\pi$
$6$	3.13974	1.28180
$7$	0.656006	0.247947	0.123974	−	0.992286i	$-0.460436\pi$
$7$	0.656006	0.247947	0.123974	+	0.992286i	$0.460436\pi$
$8$	−1.00000	−0.353553
$9$	6.85799	2.28600
$10$	−3.30555	−1.04531
$11$	5.95452	1.79536	0.897678	−	0.440652i	$-0.145253\pi$
$11$	5.95452	1.79536	0.897678	+	0.440652i	$0.145253\pi$
$12$	−3.13974	−0.906366
$13$	4.94401	1.37122	0.685611	−	0.727968i	$-0.259535\pi$
$13$	4.94401	1.37122	0.685611	+	0.727968i	$0.259535\pi$
$14$	−0.656006	−0.175325
$15$	−10.3786	−2.67974
$16$	1.00000	0.250000
$17$	−0.532100	−0.129053	−0.0645265	−	0.997916i	$-0.520554\pi$
$17$	−0.532100	−0.129053	−0.0645265	+	0.997916i	$0.520554\pi$
$18$	−6.85799	−1.61644
$19$	−6.02208	−1.38156	−0.690779	−	0.723066i	$-0.742732\pi$
$19$	−6.02208	−1.38156	−0.690779	+	0.723066i	$0.742732\pi$
$20$	3.30555	0.739143
$21$	−2.05969	−0.449462
$22$	−5.95452	−1.26951
$23$	−8.12726	−1.69465	−0.847325	−	0.531075i	$-0.821788\pi$
$23$	−8.12726	−1.69465	−0.847325	+	0.531075i	$0.821788\pi$
$24$	3.13974	0.640898
$25$	5.92665	1.18533
$26$	−4.94401	−0.969600
$27$	−12.1131	−2.33117
$28$	0.656006	0.123974
$29$	−7.59990	−1.41127	−0.705633	−	0.708578i	$-0.749337\pi$
$29$	−7.59990	−1.41127	−0.705633	+	0.708578i	$0.749337\pi$
$30$	10.3786	1.89486
$31$	−6.76567	−1.21515	−0.607575	−	0.794262i	$-0.707858\pi$
$31$	−6.76567	−1.21515	−0.607575	+	0.794262i	$0.707858\pi$
$32$	−1.00000	−0.176777
$33$	−18.6957	−3.25450
$34$	0.532100	0.0912543
$35$	2.16846	0.366537
$36$	6.85799	1.14300
$37$	−3.86211	−0.634928	−0.317464	−	0.948270i	$-0.602831\pi$
$37$	−3.86211	−0.634928	−0.317464	+	0.948270i	$0.602831\pi$
$38$	6.02208	0.976910
$39$	−15.5229	−2.48566
$40$	−3.30555	−0.522653
$41$	10.8582	1.69577	0.847883	−	0.530184i	$-0.177877\pi$
$41$	10.8582	1.69577	0.847883	+	0.530184i	$0.177877\pi$
$42$	2.05969	0.317817
$43$	10.7818	1.64420	0.822102	−	0.569341i	$-0.192801\pi$
$43$	10.7818	1.64420	0.822102	+	0.569341i	$0.192801\pi$
$44$	5.95452	0.897678
$45$	22.6694	3.37936
$46$	8.12726	1.19830
$47$	−1.25178	−0.182592	−0.0912958	−	0.995824i	$-0.529101\pi$
$47$	−1.25178	−0.182592	−0.0912958	+	0.995824i	$0.529101\pi$
$48$	−3.13974	−0.453183
$49$	−6.56966	−0.938522
$50$	−5.92665	−0.838154
$51$	1.67066	0.233939
$52$	4.94401	0.685611
$53$	−0.381307	−0.0523765	−0.0261883	−	0.999657i	$-0.508337\pi$
$53$	−0.381307	−0.0523765	−0.0261883	+	0.999657i	$0.508337\pi$
$54$	12.1131	1.64839
$55$	19.6830	2.65405
$56$	−0.656006	−0.0876625
$57$	18.9078	2.50440
$58$	7.59990	0.997915
$59$	−1.34723	−0.175395	−0.0876975	−	0.996147i	$-0.527951\pi$
$59$	−1.34723	−0.175395	−0.0876975	+	0.996147i	$0.527951\pi$
$60$	−10.3786	−1.33987
$61$	9.35980	1.19840	0.599200	−	0.800599i	$-0.295485\pi$
$61$	9.35980	1.19840	0.599200	+	0.800599i	$0.295485\pi$
$62$	6.76567	0.859241
$63$	4.49889	0.566806
$64$	1.00000	0.125000
$65$	16.3427	2.02706
$66$	18.6957	2.30128
$67$	−12.9860	−1.58649	−0.793245	−	0.608903i	$-0.791610\pi$
$67$	−12.9860	−1.58649	−0.793245	+	0.608903i	$0.791610\pi$
$68$	−0.532100	−0.0645265
$69$	25.5175	3.07195
$70$	−2.16846	−0.259181
$71$	11.5488	1.37059	0.685295	−	0.728265i	$-0.259673\pi$
$71$	11.5488	1.37059	0.685295	+	0.728265i	$0.259673\pi$
$72$	−6.85799	−0.808222
$73$	7.66285	0.896869	0.448435	−	0.893816i	$-0.351982\pi$
$73$	7.66285	0.896869	0.448435	+	0.893816i	$0.351982\pi$
$74$	3.86211	0.448962
$75$	−18.6081	−2.14868
$76$	−6.02208	−0.690779
$77$	3.90620	0.445153
$78$	15.5229	1.75763
$79$	−6.09822	−0.686103	−0.343051	−	0.939317i	$-0.611461\pi$
$79$	−6.09822	−0.686103	−0.343051	+	0.939317i	$0.611461\pi$
$80$	3.30555	0.369571
$81$	17.4581	1.93979
$82$	−10.8582	−1.19909
$83$	−7.09025	−0.778256	−0.389128	−	0.921184i	$-0.627224\pi$
$83$	−7.09025	−0.778256	−0.389128	+	0.921184i	$0.627224\pi$
$84$	−2.05969	−0.224731
$85$	−1.75888	−0.190777
$86$	−10.7818	−1.16263
$87$	23.8617	2.55825
$88$	−5.95452	−0.634754
$89$	3.67451	0.389497	0.194749	−	0.980853i	$-0.437611\pi$
$89$	3.67451	0.389497	0.194749	+	0.980853i	$0.437611\pi$
$90$	−22.6694	−2.38957
$91$	3.24330	0.339990
$92$	−8.12726	−0.847325
$93$	21.2425	2.20274
$94$	1.25178	0.129112
$95$	−19.9063	−2.04234
$96$	3.13974	0.320449
$97$	13.1972	1.33997	0.669984	−	0.742376i	$-0.266301\pi$
$97$	13.1972	1.33997	0.669984	+	0.742376i	$0.266301\pi$
$98$	6.56966	0.663635
$99$	40.8361	4.10418
$100$	5.92665	0.592665
$101$	−0.402995	−0.0400995	−0.0200498	−	0.999799i	$-0.506382\pi$
$101$	−0.402995	−0.0400995	−0.0200498	+	0.999799i	$0.506382\pi$
$102$	−1.67066	−0.165420
$103$	−8.13503	−0.801569	−0.400784	−	0.916172i	$-0.631262\pi$
$103$	−8.13503	−0.801569	−0.400784	+	0.916172i	$0.631262\pi$
$104$	−4.94401	−0.484800
$105$	−6.80841	−0.664433
$106$	0.381307	0.0370358
$107$	17.4554	1.68748	0.843739	−	0.536753i	$-0.180349\pi$
$107$	17.4554	1.68748	0.843739	+	0.536753i	$0.180349\pi$
$108$	−12.1131	−1.16558
$109$	14.9128	1.42839	0.714194	−	0.699948i	$-0.246793\pi$
$109$	14.9128	1.42839	0.714194	+	0.699948i	$0.246793\pi$
$110$	−19.6830	−1.87670
$111$	12.1261	1.15095
$112$	0.656006	0.0619868
$113$	−17.6526	−1.66061	−0.830306	−	0.557307i	$-0.811835\pi$
$113$	−17.6526	−1.66061	−0.830306	+	0.557307i	$0.811835\pi$
$114$	−18.9078	−1.77088
$115$	−26.8650	−2.50518
$116$	−7.59990	−0.705633
$117$	33.9060	3.13461
$118$	1.34723	0.124023
$119$	−0.349061	−0.0319983
$120$	10.3786	0.947430
$121$	24.4563	2.22330
$122$	−9.35980	−0.847397
$123$	−34.0920	−3.07397
$124$	−6.76567	−0.607575
$125$	3.06307	0.273969
$126$	−4.49889	−0.400793
$127$	−2.73024	−0.242270	−0.121135	−	0.992636i	$-0.538653\pi$
$127$	−2.73024	−0.242270	−0.121135	+	0.992636i	$0.538653\pi$
$128$	−1.00000	−0.0883883
$129$	−33.8520	−2.98050
$130$	−16.3427	−1.43335
$131$	5.65994	0.494511	0.247255	−	0.968950i	$-0.420471\pi$
$131$	5.65994	0.494511	0.247255	+	0.968950i	$0.420471\pi$
$132$	−18.6957	−1.62725
$133$	−3.95052	−0.342553
$134$	12.9860	1.12182
$135$	−40.0405	−3.44613
$136$	0.532100	0.0456272
$137$	−10.1009	−0.862975	−0.431487	−	0.902119i	$-0.642011\pi$
$137$	−10.1009	−0.862975	−0.431487	+	0.902119i	$0.642011\pi$
$138$	−25.5175	−2.17219
$139$	4.17896	0.354454	0.177227	−	0.984170i	$-0.443287\pi$
$139$	4.17896	0.354454	0.177227	+	0.984170i	$0.443287\pi$
$140$	2.16846	0.183268
$141$	3.93028	0.330990
$142$	−11.5488	−0.969154
$143$	29.4392	2.46183
$144$	6.85799	0.571499
$145$	−25.1218	−2.08625
$146$	−7.66285	−0.634182
$147$	20.6270	1.70129
$148$	−3.86211	−0.317464
$149$	15.2148	1.24645	0.623223	−	0.782044i	$-0.285823\pi$
$149$	15.2148	1.24645	0.623223	+	0.782044i	$0.285823\pi$
$150$	18.6081	1.51935
$151$	8.82531	0.718193	0.359097	−	0.933300i	$-0.383085\pi$
$151$	8.82531	0.718193	0.359097	+	0.933300i	$0.383085\pi$
$152$	6.02208	0.488455
$153$	−3.64913	−0.295015
$154$	−3.90620	−0.314771
$155$	−22.3643	−1.79634
$156$	−15.5229	−1.24283
$157$	15.0905	1.20436	0.602178	−	0.798362i	$-0.294300\pi$
$157$	15.0905	1.20436	0.602178	+	0.798362i	$0.294300\pi$
$158$	6.09822	0.485148
$159$	1.19721	0.0949446
$160$	−3.30555	−0.261326
$161$	−5.33153	−0.420183
$162$	−17.4581	−1.37164
$163$	11.7379	0.919379	0.459690	−	0.888080i	$-0.347961\pi$
$163$	11.7379	0.919379	0.459690	+	0.888080i	$0.347961\pi$
$164$	10.8582	0.847883
$165$	−61.7994	−4.81108
$166$	7.09025	0.550310
$167$	8.68534	0.672092	0.336046	−	0.941846i	$-0.390910\pi$
$167$	8.68534	0.672092	0.336046	+	0.941846i	$0.390910\pi$
$168$	2.05969	0.158909
$169$	11.4432	0.880249
$170$	1.75888	0.134900
$171$	−41.2993	−3.15824
$172$	10.7818	0.822102
$173$	0.616250	0.0468526	0.0234263	−	0.999726i	$-0.492542\pi$
$173$	0.616250	0.0468526	0.0234263	+	0.999726i	$0.492542\pi$
$174$	−23.8617	−1.80895
$175$	3.88792	0.293899
$176$	5.95452	0.448839
$177$	4.22997	0.317944
$178$	−3.67451	−0.275416
$179$	13.6002	1.01653	0.508263	−	0.861202i	$-0.330288\pi$
$179$	13.6002	1.01653	0.508263	+	0.861202i	$0.330288\pi$
$180$	22.6694	1.68968
$181$	−18.4195	−1.36911	−0.684554	−	0.728962i	$-0.740003\pi$
$181$	−18.4195	−1.36911	−0.684554	+	0.728962i	$0.740003\pi$
$182$	−3.24330	−0.240410
$183$	−29.3874	−2.17238
$184$	8.12726	0.599149
$185$	−12.7664	−0.938605
$186$	−21.2425	−1.55757
$187$	−3.16840	−0.231696
$188$	−1.25178	−0.0912958
$189$	−7.94628	−0.578007
$190$	19.9063	1.44415
$191$	20.2382	1.46439	0.732194	−	0.681096i	$-0.238497\pi$
$191$	20.2382	1.46439	0.732194	+	0.681096i	$0.238497\pi$
$192$	−3.13974	−0.226592
$193$	4.89983	0.352697	0.176349	−	0.984328i	$-0.443571\pi$
$193$	4.89983	0.352697	0.176349	+	0.984328i	$0.443571\pi$
$194$	−13.1972	−0.947500
$195$	−51.3118	−3.67451
$196$	−6.56966	−0.469261
$197$	−0.117625	−0.00838046	−0.00419023	−	0.999991i	$-0.501334\pi$
$197$	−0.117625	−0.00838046	−0.00419023	+	0.999991i	$0.501334\pi$
$198$	−40.8361	−2.90209
$199$	10.2168	0.724251	0.362126	−	0.932129i	$-0.382051\pi$
$199$	10.2168	0.724251	0.362126	+	0.932129i	$0.382051\pi$
$200$	−5.92665	−0.419077
$201$	40.7727	2.87588
$202$	0.402995	0.0283546
$203$	−4.98558	−0.349919
$204$	1.67066	0.116969
$205$	35.8923	2.50683
$206$	8.13503	0.566795
$207$	−55.7367	−3.87397
$208$	4.94401	0.342805
$209$	−35.8586	−2.48039
$210$	6.80841	0.469825
$211$	16.6218	1.14429	0.572145	−	0.820152i	$-0.306111\pi$
$211$	16.6218	1.14429	0.572145	+	0.820152i	$0.306111\pi$
$212$	−0.381307	−0.0261883
$213$	−36.2603	−2.48451
$214$	−17.4554	−1.19323
$215$	35.6396	2.43060
$216$	12.1131	0.824193
$217$	−4.43832	−0.301293
$218$	−14.9128	−1.01002
$219$	−24.0594	−1.62578
$220$	19.6830	1.32702
$221$	−2.63071	−0.176960
$222$	−12.1261	−0.813847
$223$	21.5177	1.44093	0.720465	−	0.693491i	$-0.243928\pi$
$223$	21.5177	1.44093	0.720465	+	0.693491i	$0.243928\pi$
$224$	−0.656006	−0.0438313
$225$	40.6449	2.70966
$226$	17.6526	1.17423
$227$	8.38809	0.556737	0.278368	−	0.960474i	$-0.410206\pi$
$227$	8.38809	0.556737	0.278368	+	0.960474i	$0.410206\pi$
$228$	18.9078	1.25220
$229$	28.0125	1.85112	0.925559	−	0.378603i	$-0.123595\pi$
$229$	28.0125	1.85112	0.925559	+	0.378603i	$0.123595\pi$
$230$	26.8650	1.77143
$231$	−12.2645	−0.806944
$232$	7.59990	0.498958
$233$	−1.60537	−0.105171	−0.0525855	−	0.998616i	$-0.516746\pi$
$233$	−1.60537	−0.105171	−0.0525855	+	0.998616i	$0.516746\pi$
$234$	−33.9060	−2.21650
$235$	−4.13783	−0.269923
$236$	−1.34723	−0.0876975
$237$	19.1468	1.24372
$238$	0.349061	0.0226262
$239$	20.7073	1.33944	0.669721	−	0.742613i	$-0.266414\pi$
$239$	20.7073	1.33944	0.669721	+	0.742613i	$0.266414\pi$
$240$	−10.3786	−0.669934
$241$	1.47798	0.0952049	0.0476025	−	0.998866i	$-0.484842\pi$
$241$	1.47798	0.0952049	0.0476025	+	0.998866i	$0.484842\pi$
$242$	−24.4563	−1.57211
$243$	−18.4746	−1.18515
$244$	9.35980	0.599200
$245$	−21.7163	−1.38740
$246$	34.0920	2.17362
$247$	−29.7732	−1.89442
$248$	6.76567	0.429621
$249$	22.2616	1.41077
$250$	−3.06307	−0.193726
$251$	17.2330	1.08774	0.543870	−	0.839170i	$-0.316959\pi$
$251$	17.2330	1.08774	0.543870	+	0.839170i	$0.316959\pi$
$252$	4.49889	0.283403
$253$	−48.3939	−3.04250
$254$	2.73024	0.171311
$255$	5.52243	0.345828
$256$	1.00000	0.0625000
$257$	−2.93624	−0.183158	−0.0915788	−	0.995798i	$-0.529191\pi$
$257$	−2.93624	−0.183158	−0.0915788	+	0.995798i	$0.529191\pi$
$258$	33.8520	2.10753
$259$	−2.53357	−0.157428
$260$	16.3427	1.01353
$261$	−52.1200	−3.22615
$262$	−5.65994	−0.349672
$263$	−14.2711	−0.879994	−0.439997	−	0.897999i	$-0.645020\pi$
$263$	−14.2711	−0.879994	−0.439997	+	0.897999i	$0.645020\pi$
$264$	18.6957	1.15064
$265$	−1.26043	−0.0774275
$266$	3.95052	0.242222
$267$	−11.5370	−0.706054
$268$	−12.9860	−0.793245
$269$	14.2481	0.868719	0.434360	−	0.900740i	$-0.356975\pi$
$269$	14.2481	0.868719	0.434360	+	0.900740i	$0.356975\pi$
$270$	40.0405	2.43678
$271$	−18.8711	−1.14634	−0.573169	−	0.819437i	$-0.694286\pi$
$271$	−18.8711	−1.14634	−0.573169	+	0.819437i	$0.694286\pi$
$272$	−0.532100	−0.0322633
$273$	−10.1831	−0.616312
$274$	10.1009	0.610215
$275$	35.2903	2.12809
$276$	25.5175	1.53597
$277$	−3.30833	−0.198778	−0.0993890	−	0.995049i	$-0.531689\pi$
$277$	−3.30833	−0.198778	−0.0993890	+	0.995049i	$0.531689\pi$
$278$	−4.17896	−0.250637
$279$	−46.3989	−2.77783
$280$	−2.16846	−0.129590
$281$	−4.91708	−0.293328	−0.146664	−	0.989186i	$-0.546854\pi$
$281$	−4.91708	−0.293328	−0.146664	+	0.989186i	$0.546854\pi$
$282$	−3.93028	−0.234045
$283$	3.31116	0.196828	0.0984141	−	0.995146i	$-0.468623\pi$
$283$	3.31116	0.196828	0.0984141	+	0.995146i	$0.468623\pi$
$284$	11.5488	0.685295
$285$	62.5005	3.70221
$286$	−29.4392	−1.74078
$287$	7.12305	0.420460
$288$	−6.85799	−0.404111
$289$	−16.7169	−0.983345
$290$	25.1218	1.47520
$291$	−41.4357	−2.42900
$292$	7.66285	0.448435
$293$	7.55274	0.441236	0.220618	−	0.975360i	$-0.429193\pi$
$293$	7.55274	0.441236	0.220618	+	0.975360i	$0.429193\pi$
$294$	−20.6270	−1.20299
$295$	−4.45335	−0.259284
$296$	3.86211	0.224481
$297$	−72.1278	−4.18528
$298$	−15.2148	−0.881370
$299$	−40.1812	−2.32374
$300$	−18.6081	−1.07434
$301$	7.07290	0.407675
$302$	−8.82531	−0.507839
$303$	1.26530	0.0726897
$304$	−6.02208	−0.345390
$305$	30.9393	1.77158
$306$	3.64913	0.208607
$307$	14.1404	0.807033	0.403516	−	0.914972i	$-0.367788\pi$
$307$	14.1404	0.807033	0.403516	+	0.914972i	$0.367788\pi$
$308$	3.90620	0.222577
$309$	25.5419	1.45303
$310$	22.3643	1.27020
$311$	−5.34238	−0.302939	−0.151469	−	0.988462i	$-0.548400\pi$
$311$	−5.34238	−0.302939	−0.151469	+	0.988462i	$0.548400\pi$
$312$	15.5229	0.878813
$313$	−4.19517	−0.237125	−0.118563	−	0.992947i	$-0.537829\pi$
$313$	−4.19517	−0.237125	−0.118563	+	0.992947i	$0.537829\pi$
$314$	−15.0905	−0.851608
$315$	14.8713	0.837902
$316$	−6.09822	−0.343051
$317$	−29.2448	−1.64255	−0.821276	−	0.570531i	$-0.806737\pi$
$317$	−29.2448	−1.64255	−0.821276	+	0.570531i	$0.806737\pi$
$318$	−1.19721	−0.0671360
$319$	−45.2538	−2.53372
$320$	3.30555	0.184786
$321$	−54.8055	−3.05895
$322$	5.33153	0.297115
$323$	3.20434	0.178294
$324$	17.4581	0.969894
$325$	29.3014	1.62535
$326$	−11.7379	−0.650099
$327$	−46.8224	−2.58929
$328$	−10.8582	−0.599544
$329$	−0.821179	−0.0452730
$330$	61.7994	3.40195
$331$	0.658685	0.0362046	0.0181023	−	0.999836i	$-0.494238\pi$
$331$	0.658685	0.0362046	0.0181023	+	0.999836i	$0.494238\pi$
$332$	−7.09025	−0.389128
$333$	−26.4864	−1.45144
$334$	−8.68534	−0.475241
$335$	−42.9258	−2.34529
$336$	−2.05969	−0.112365
$337$	22.7381	1.23862	0.619311	−	0.785146i	$-0.287412\pi$
$337$	22.7381	1.23862	0.619311	+	0.785146i	$0.287412\pi$
$338$	−11.4432	−0.622430
$339$	55.4245	3.01025
$340$	−1.75888	−0.0953887
$341$	−40.2863	−2.18163
$342$	41.2993	2.23321
$343$	−8.90178	−0.480651
$344$	−10.7818	−0.581314
$345$	84.3493	4.54121
$346$	−0.616250	−0.0331298
$347$	22.4768	1.20662	0.603308	−	0.797508i	$-0.293849\pi$
$347$	22.4768	1.20662	0.603308	+	0.797508i	$0.293849\pi$
$348$	23.8617	1.27912
$349$	−11.2286	−0.601053	−0.300527	−	0.953773i	$-0.597162\pi$
$349$	−11.2286	−0.601053	−0.300527	+	0.953773i	$0.597162\pi$
$350$	−3.88792	−0.207818
$351$	−59.8873	−3.19655
$352$	−5.95452	−0.317377
$353$	2.49248	0.132661	0.0663306	−	0.997798i	$-0.478871\pi$
$353$	2.49248	0.132661	0.0663306	+	0.997798i	$0.478871\pi$
$354$	−4.22997	−0.224821
$355$	38.1751	2.02613
$356$	3.67451	0.194749
$357$	1.09596	0.0580044
$358$	−13.6002	−0.718793
$359$	23.7774	1.25492	0.627461	−	0.778648i	$-0.284094\pi$
$359$	23.7774	1.25492	0.627461	+	0.778648i	$0.284094\pi$
$360$	−22.6694	−1.19478
$361$	17.2654	0.908705
$362$	18.4195	0.968105
$363$	−76.7866	−4.03025
$364$	3.24330	0.169995
$365$	25.3299	1.32583
$366$	29.3874	1.53610
$367$	25.0074	1.30538	0.652688	−	0.757627i	$-0.273641\pi$
$367$	25.0074	1.30538	0.652688	+	0.757627i	$0.273641\pi$
$368$	−8.12726	−0.423662
$369$	74.4654	3.87652
$370$	12.7664	0.663694
$371$	−0.250140	−0.0129866
$372$	21.2425	1.10137
$373$	7.69085	0.398217	0.199109	−	0.979977i	$-0.436195\pi$
$373$	7.69085	0.398217	0.199109	+	0.979977i	$0.436195\pi$
$374$	3.16840	0.163834
$375$	−9.61726	−0.496633
$376$	1.25178	0.0645559
$377$	−37.5740	−1.93516
$378$	7.94628	0.408712
$379$	−15.7202	−0.807492	−0.403746	−	0.914871i	$-0.632292\pi$
$379$	−15.7202	−0.807492	−0.403746	+	0.914871i	$0.632292\pi$
$380$	−19.9063	−1.02117
$381$	8.57226	0.439170
$382$	−20.2382	−1.03548
$383$	−29.4802	−1.50637	−0.753185	−	0.657809i	$-0.771484\pi$
$383$	−29.4802	−1.50637	−0.753185	+	0.657809i	$0.771484\pi$
$384$	3.13974	0.160224
$385$	12.9121	0.658064
$386$	−4.89983	−0.249395
$387$	73.9412	3.75864
$388$	13.1972	0.669984
$389$	12.8752	0.652797	0.326399	−	0.945232i	$-0.394165\pi$
$389$	12.8752	0.652797	0.326399	+	0.945232i	$0.394165\pi$
$390$	51.3118	2.59827
$391$	4.32451	0.218700
$392$	6.56966	0.331818
$393$	−17.7708	−0.896416
$394$	0.117625	0.00592588
$395$	−20.1579	−1.01426
$396$	40.8361	2.05209
$397$	20.3213	1.01990	0.509949	−	0.860204i	$-0.329664\pi$
$397$	20.3213	1.01990	0.509949	+	0.860204i	$0.329664\pi$
$398$	−10.2168	−0.512123
$399$	12.4036	0.620958
$400$	5.92665	0.296332
$401$	24.6179	1.22936	0.614679	−	0.788777i	$-0.289285\pi$
$401$	24.6179	1.22936	0.614679	+	0.788777i	$0.289285\pi$
$402$	−40.7727	−2.03356
$403$	−33.4496	−1.66624
$404$	−0.402995	−0.0200498
$405$	57.7085	2.86756
$406$	4.98558	0.247430
$407$	−22.9970	−1.13992
$408$	−1.67066	−0.0827098
$409$	5.00710	0.247585	0.123793	−	0.992308i	$-0.460494\pi$
$409$	5.00710	0.247585	0.123793	+	0.992308i	$0.460494\pi$
$410$	−35.8923	−1.77259
$411$	31.7141	1.56434
$412$	−8.13503	−0.400784
$413$	−0.883795	−0.0434887
$414$	55.7367	2.73931
$415$	−23.4371	−1.15048
$416$	−4.94401	−0.242400
$417$	−13.1209	−0.642531
$418$	35.8586	1.75390
$419$	21.2045	1.03591	0.517953	−	0.855409i	$-0.326694\pi$
$419$	21.2045	1.03591	0.517953	+	0.855409i	$0.326694\pi$
$420$	−6.80841	−0.332216
$421$	32.0665	1.56282	0.781412	−	0.624016i	$-0.214500\pi$
$421$	32.0665	1.56282	0.781412	+	0.624016i	$0.214500\pi$
$422$	−16.6218	−0.809136
$423$	−8.58473	−0.417404
$424$	0.381307	0.0185179
$425$	−3.15357	−0.152970
$426$	36.2603	1.75682
$427$	6.14009	0.297140
$428$	17.4554	0.843739
$429$	−92.4316	−4.46264
$430$	−35.6396	−1.71870
$431$	−16.1383	−0.777353	−0.388676	−	0.921374i	$-0.627068\pi$
$431$	−16.1383	−0.777353	−0.388676	+	0.921374i	$0.627068\pi$
$432$	−12.1131	−0.582792
$433$	−17.7867	−0.854773	−0.427386	−	0.904069i	$-0.640566\pi$
$433$	−17.7867	−0.854773	−0.427386	+	0.904069i	$0.640566\pi$
$434$	4.43832	0.213046
$435$	78.8761	3.78182
$436$	14.9128	0.714194
$437$	48.9429	2.34126
$438$	24.0594	1.14960
$439$	10.1631	0.485060	0.242530	−	0.970144i	$-0.422023\pi$
$439$	10.1631	0.485060	0.242530	+	0.970144i	$0.422023\pi$
$440$	−19.6830	−0.938348
$441$	−45.0546	−2.14546
$442$	2.63071	0.125130
$443$	−31.3504	−1.48950	−0.744750	−	0.667343i	$-0.767431\pi$
$443$	−31.3504	−1.48950	−0.744750	+	0.667343i	$0.767431\pi$
$444$	12.1261	0.575477
$445$	12.1463	0.575789
$446$	−21.5177	−1.01889
$447$	−47.7706	−2.25947
$448$	0.656006	0.0309934
$449$	−3.99517	−0.188544	−0.0942719	−	0.995546i	$-0.530052\pi$
$449$	−3.99517	−0.188544	−0.0942719	+	0.995546i	$0.530052\pi$
$450$	−40.6449	−1.91602
$451$	64.6554	3.04450
$452$	−17.6526	−0.830306
$453$	−27.7092	−1.30189
$454$	−8.38809	−0.393672
$455$	10.7209	0.502603
$456$	−18.9078	−0.885438
$457$	19.6887	0.921000	0.460500	−	0.887660i	$-0.347670\pi$
$457$	19.6887	0.921000	0.460500	+	0.887660i	$0.347670\pi$
$458$	−28.0125	−1.30894
$459$	6.44538	0.300845
$460$	−26.8650	−1.25259
$461$	38.7974	1.80697	0.903486	−	0.428617i	$-0.140999\pi$
$461$	38.7974	1.80697	0.903486	+	0.428617i	$0.140999\pi$
$462$	12.2645	0.570595
$463$	−39.1112	−1.81765	−0.908826	−	0.417176i	$-0.863020\pi$
$463$	−39.1112	−1.81765	−0.908826	+	0.417176i	$0.863020\pi$
$464$	−7.59990	−0.352816
$465$	70.2180	3.25628
$466$	1.60537	0.0743672
$467$	24.2457	1.12196	0.560978	−	0.827831i	$-0.310425\pi$
$467$	24.2457	1.12196	0.560978	+	0.827831i	$0.310425\pi$
$468$	33.9060	1.56730
$469$	−8.51889	−0.393366
$470$	4.13783	0.190864
$471$	−47.3804	−2.18317
$472$	1.34723	0.0620115
$473$	64.2002	2.95193
$474$	−19.1468	−0.879443
$475$	−35.6907	−1.63760
$476$	−0.349061	−0.0159992
$477$	−2.61500	−0.119733
$478$	−20.7073	−0.947128
$479$	−42.2295	−1.92952	−0.964758	−	0.263138i	$-0.915242\pi$
$479$	−42.2295	−1.92952	−0.964758	+	0.263138i	$0.915242\pi$
$480$	10.3786	0.473715
$481$	−19.0943	−0.870627
$482$	−1.47798	−0.0673201
$483$	16.7396	0.761680
$484$	24.4563	1.11165
$485$	43.6238	1.98086
$486$	18.4746	0.838024
$487$	−18.6387	−0.844598	−0.422299	−	0.906457i	$-0.638777\pi$
$487$	−18.6387	−0.844598	−0.422299	+	0.906457i	$0.638777\pi$
$488$	−9.35980	−0.423698
$489$	−36.8538	−1.66659
$490$	21.7163	0.981043
$491$	37.1250	1.67543	0.837715	−	0.546108i	$-0.183891\pi$
$491$	37.1250	1.67543	0.837715	+	0.546108i	$0.183891\pi$
$492$	−34.0920	−1.53698
$493$	4.04390	0.182128
$494$	29.7732	1.33956
$495$	134.986	6.06715
$496$	−6.76567	−0.303788
$497$	7.57609	0.339834
$498$	−22.2616	−0.997564
$499$	−3.00415	−0.134484	−0.0672422	−	0.997737i	$-0.521420\pi$
$499$	−3.00415	−0.134484	−0.0672422	+	0.997737i	$0.521420\pi$
$500$	3.06307	0.136985
$501$	−27.2697	−1.21832
$502$	−17.2330	−0.769148
$503$	−16.4288	−0.732524	−0.366262	−	0.930512i	$-0.619363\pi$
$503$	−16.4288	−0.732524	−0.366262	+	0.930512i	$0.619363\pi$
$504$	−4.49889	−0.200396
$505$	−1.33212	−0.0592785
$506$	48.3939	2.15137
$507$	−35.9288	−1.59566
$508$	−2.73024	−0.121135
$509$	−7.82596	−0.346880	−0.173440	−	0.984844i	$-0.555488\pi$
$509$	−7.82596	−0.346880	−0.173440	+	0.984844i	$0.555488\pi$
$510$	−5.52243	−0.244537
$511$	5.02688	0.222376
$512$	−1.00000	−0.0441942
$513$	72.9461	3.22065
$514$	2.93624	0.129512
$515$	−26.8907	−1.18495
$516$	−33.8520	−1.49025
$517$	−7.45378	−0.327817
$518$	2.53357	0.111319
$519$	−1.93487	−0.0849312
$520$	−16.3427	−0.716673
$521$	3.23852	0.141882	0.0709411	−	0.997481i	$-0.477400\pi$
$521$	3.23852	0.141882	0.0709411	+	0.997481i	$0.477400\pi$
$522$	52.1200	2.28123
$523$	−5.61350	−0.245461	−0.122731	−	0.992440i	$-0.539165\pi$
$523$	−5.61350	−0.245461	−0.122731	+	0.992440i	$0.539165\pi$
$524$	5.65994	0.247255
$525$	−12.2071	−0.532760
$526$	14.2711	0.622249
$527$	3.60001	0.156819
$528$	−18.6957	−0.813625
$529$	43.0523	1.87184
$530$	1.26043	0.0547495
$531$	−9.23933	−0.400953
$532$	−3.95052	−0.171277
$533$	53.6830	2.32527
$534$	11.5370	0.499256
$535$	57.6997	2.49458
$536$	12.9860	0.560909
$537$	−42.7011	−1.84269
$538$	−14.2481	−0.614277
$539$	−39.1192	−1.68498
$540$	−40.0405	−1.72307
$541$	11.6223	0.499681	0.249841	−	0.968287i	$-0.419622\pi$
$541$	11.6223	0.499681	0.249841	+	0.968287i	$0.419622\pi$
$542$	18.8711	0.810583
$543$	57.8324	2.48182
$544$	0.532100	0.0228136
$545$	49.2950	2.11157
$546$	10.1831	0.435798
$547$	1.97558	0.0844696	0.0422348	−	0.999108i	$-0.486552\pi$
$547$	1.97558	0.0844696	0.0422348	+	0.999108i	$0.486552\pi$
$548$	−10.1009	−0.431487
$549$	64.1895	2.73954
$550$	−35.2903	−1.50479
$551$	45.7672	1.94975
$552$	−25.5175	−1.08610
$553$	−4.00047	−0.170117
$554$	3.30833	0.140557
$555$	40.0832	1.70144
$556$	4.17896	0.177227
$557$	−18.5406	−0.785590	−0.392795	−	0.919626i	$-0.628492\pi$
$557$	−18.5406	−0.785590	−0.392795	+	0.919626i	$0.628492\pi$
$558$	46.3989	1.96422
$559$	53.3051	2.25457
$560$	2.16846	0.0916342
$561$	9.94796	0.420003
$562$	4.91708	0.207414
$563$	−22.8677	−0.963759	−0.481879	−	0.876238i	$-0.660046\pi$
$563$	−22.8677	−0.963759	−0.481879	+	0.876238i	$0.660046\pi$
$564$	3.93028	0.165495
$565$	−58.3514	−2.45486
$566$	−3.31116	−0.139179
$567$	11.4526	0.480965
$568$	−11.5488	−0.484577
$569$	38.7864	1.62601	0.813004	−	0.582258i	$-0.197831\pi$
$569$	38.7864	1.62601	0.813004	+	0.582258i	$0.197831\pi$
$570$	−62.5005	−2.61786
$571$	0.355368	0.0148717	0.00743585	−	0.999972i	$-0.497633\pi$
$571$	0.355368	0.0148717	0.00743585	+	0.999972i	$0.497633\pi$
$572$	29.4392	1.23092
$573$	−63.5429	−2.65454
$574$	−7.12305	−0.297310
$575$	−48.1674	−2.00872
$576$	6.85799	0.285750
$577$	12.3311	0.513349	0.256675	−	0.966498i	$-0.417373\pi$
$577$	12.3311	0.513349	0.256675	+	0.966498i	$0.417373\pi$
$578$	16.7169	0.695330
$579$	−15.3842	−0.639346
$580$	−25.1218	−1.04313
$581$	−4.65125	−0.192966
$582$	41.4357	1.71756
$583$	−2.27050	−0.0940345
$584$	−7.66285	−0.317091
$585$	112.078	4.63385
$586$	−7.55274	−0.312001
$587$	−18.2333	−0.752568	−0.376284	−	0.926504i	$-0.622798\pi$
$587$	−18.2333	−0.752568	−0.376284	+	0.926504i	$0.622798\pi$
$588$	20.6270	0.850645
$589$	40.7434	1.67880
$590$	4.45335	0.183341
$591$	0.369314	0.0151915
$592$	−3.86211	−0.158732
$593$	16.6757	0.684791	0.342395	−	0.939556i	$-0.388762\pi$
$593$	16.6757	0.684791	0.342395	+	0.939556i	$0.388762\pi$
$594$	72.1278	2.95944
$595$	−1.15384	−0.0473027
$596$	15.2148	0.623223
$597$	−32.0782	−1.31287
$598$	40.1812	1.64313
$599$	−9.26680	−0.378631	−0.189316	−	0.981916i	$-0.560627\pi$
$599$	−9.26680	−0.378631	−0.189316	+	0.981916i	$0.560627\pi$
$600$	18.6081	0.759675
$601$	−48.0151	−1.95857	−0.979287	−	0.202475i	$-0.935101\pi$
$601$	−48.0151	−1.95857	−0.979287	+	0.202475i	$0.935101\pi$
$602$	−7.07290	−0.288270
$603$	−89.0578	−3.62671
$604$	8.82531	0.359097
$605$	80.8416	3.28668
$606$	−1.26530	−0.0513993
$607$	31.8537	1.29290	0.646450	−	0.762956i	$-0.276253\pi$
$607$	31.8537	1.29290	0.646450	+	0.762956i	$0.276253\pi$
$608$	6.02208	0.244227
$609$	15.6534	0.634310
$610$	−30.9393	−1.25269
$611$	−6.18884	−0.250374
$612$	−3.64913	−0.147508
$613$	11.2171	0.453056	0.226528	−	0.974005i	$-0.427263\pi$
$613$	11.2171	0.453056	0.226528	+	0.974005i	$0.427263\pi$
$614$	−14.1404	−0.570658
$615$	−112.693	−4.54420
$616$	−3.90620	−0.157385
$617$	9.30953	0.374788	0.187394	−	0.982285i	$-0.439996\pi$
$617$	9.30953	0.374788	0.187394	+	0.982285i	$0.439996\pi$
$618$	−25.5419	−1.02745
$619$	−30.7086	−1.23428	−0.617141	−	0.786853i	$-0.711709\pi$
$619$	−30.7086	−1.23428	−0.617141	+	0.786853i	$0.711709\pi$
$620$	−22.3643	−0.898170
$621$	98.4463	3.95051
$622$	5.34238	0.214210
$623$	2.41050	0.0965748
$624$	−15.5229	−0.621414
$625$	−19.5081	−0.780324
$626$	4.19517	0.167673
$627$	112.587	4.49628
$628$	15.0905	0.602178
$629$	2.05503	0.0819394
$630$	−14.8713	−0.592486
$631$	42.4125	1.68842	0.844208	−	0.536015i	$-0.180071\pi$
$631$	42.4125	1.68842	0.844208	+	0.536015i	$0.180071\pi$
$632$	6.09822	0.242574
$633$	−52.1881	−2.07429
$634$	29.2448	1.16146
$635$	−9.02495	−0.358144
$636$	1.19721	0.0474723
$637$	−32.4804	−1.28692
$638$	45.2538	1.79161
$639$	79.2016	3.13317
$640$	−3.30555	−0.130663
$641$	−12.7369	−0.503078	−0.251539	−	0.967847i	$-0.580937\pi$
$641$	−12.7369	−0.503078	−0.251539	+	0.967847i	$0.580937\pi$
$642$	54.8055	2.16300
$643$	5.17186	0.203958	0.101979	−	0.994787i	$-0.467482\pi$
$643$	5.17186	0.203958	0.101979	+	0.994787i	$0.467482\pi$
$644$	−5.33153	−0.210092
$645$	−111.899	−4.40603
$646$	−3.20434	−0.126073
$647$	3.84326	0.151094	0.0755471	−	0.997142i	$-0.475930\pi$
$647$	3.84326	0.151094	0.0755471	+	0.997142i	$0.475930\pi$
$648$	−17.4581	−0.685818
$649$	−8.02214	−0.314897
$650$	−29.3014	−1.14930
$651$	13.9352	0.546164
$652$	11.7379	0.459690
$653$	−25.3646	−0.992592	−0.496296	−	0.868154i	$-0.665307\pi$
$653$	−25.3646	−0.992592	−0.496296	+	0.868154i	$0.665307\pi$
$654$	46.8224	1.83090
$655$	18.7092	0.731029
$656$	10.8582	0.423941
$657$	52.5518	2.05024
$658$	0.821179	0.0320129
$659$	13.2111	0.514632	0.257316	−	0.966327i	$-0.417162\pi$
$659$	13.2111	0.514632	0.257316	+	0.966327i	$0.417162\pi$
$660$	−61.7994	−2.40554
$661$	−27.7415	−1.07902	−0.539510	−	0.841979i	$-0.681390\pi$
$661$	−27.7415	−1.07902	−0.539510	+	0.841979i	$0.681390\pi$
$662$	−0.658685	−0.0256005
$663$	8.25974	0.320782
$664$	7.09025	0.275155
$665$	−13.0586	−0.506392
$666$	26.4864	1.02633
$667$	61.7663	2.39160
$668$	8.68534	0.336046
$669$	−67.5600	−2.61202
$670$	42.9258	1.65837
$671$	55.7332	2.15155
$672$	2.05969	0.0794543
$673$	16.3543	0.630412	0.315206	−	0.949023i	$-0.397926\pi$
$673$	16.3543	0.630412	0.315206	+	0.949023i	$0.397926\pi$
$674$	−22.7381	−0.875838
$675$	−71.7901	−2.76320
$676$	11.4432	0.440125
$677$	−25.8334	−0.992858	−0.496429	−	0.868077i	$-0.665356\pi$
$677$	−25.8334	−0.992858	−0.496429	+	0.868077i	$0.665356\pi$
$678$	−55.4245	−2.12857
$679$	8.65741	0.332241
$680$	1.75888	0.0674500
$681$	−26.3364	−1.00921
$682$	40.2863	1.54264
$683$	−11.1058	−0.424953	−0.212477	−	0.977166i	$-0.568153\pi$
$683$	−11.1058	−0.424953	−0.212477	+	0.977166i	$0.568153\pi$
$684$	−41.2993	−1.57912
$685$	−33.3889	−1.27572
$686$	8.90178	0.339872
$687$	−87.9521	−3.35558
$688$	10.7818	0.411051
$689$	−1.88519	−0.0718199
$690$	−84.3493	−3.21112
$691$	−2.02795	−0.0771469	−0.0385734	−	0.999256i	$-0.512281\pi$
$691$	−2.02795	−0.0771469	−0.0385734	+	0.999256i	$0.512281\pi$
$692$	0.616250	0.0234263
$693$	26.7887	1.01762
$694$	−22.4768	−0.853206
$695$	13.8137	0.523985
$696$	−23.8617	−0.904477
$697$	−5.77764	−0.218844
$698$	11.2286	0.425009
$699$	5.04044	0.190647
$700$	3.88792	0.146949
$701$	−9.49612	−0.358664	−0.179332	−	0.983789i	$-0.557394\pi$
$701$	−9.49612	−0.358664	−0.179332	+	0.983789i	$0.557394\pi$
$702$	59.8873	2.26030
$703$	23.2579	0.877190
$704$	5.95452	0.224419
$705$	12.9917	0.489297
$706$	−2.49248	−0.0938056
$707$	−0.264367	−0.00994255
$708$	4.22997	0.158972
$709$	3.23312	0.121422	0.0607112	−	0.998155i	$-0.480663\pi$
$709$	3.23312	0.121422	0.0607112	+	0.998155i	$0.480663\pi$
$710$	−38.1751	−1.43269
$711$	−41.8215	−1.56843
$712$	−3.67451	−0.137708
$713$	54.9863	2.05925
$714$	−1.09596	−0.0410153
$715$	97.3127	3.63929
$716$	13.6002	0.508263
$717$	−65.0155	−2.42805
$718$	−23.7774	−0.887364
$719$	−25.1880	−0.939353	−0.469677	−	0.882838i	$-0.655630\pi$
$719$	−25.1880	−0.939353	−0.469677	+	0.882838i	$0.655630\pi$
$720$	22.6694	0.844839
$721$	−5.33663	−0.198747
$722$	−17.2654	−0.642551
$723$	−4.64047	−0.172581
$724$	−18.4195	−0.684554
$725$	−45.0419	−1.67281
$726$	76.7866	2.84982
$727$	2.12418	0.0787816	0.0393908	−	0.999224i	$-0.487458\pi$
$727$	2.12418	0.0787816	0.0393908	+	0.999224i	$0.487458\pi$
$728$	−3.24330	−0.120205
$729$	5.63122	0.208564
$730$	−25.3299	−0.937503
$731$	−5.73697	−0.212190
$732$	−29.3874	−1.08619
$733$	−12.4433	−0.459604	−0.229802	−	0.973237i	$-0.573808\pi$
$733$	−12.4433	−0.459604	−0.229802	+	0.973237i	$0.573808\pi$
$734$	−25.0074	−0.923040
$735$	68.1837	2.51499
$736$	8.12726	0.299575
$737$	−77.3253	−2.84831
$738$	−74.4654	−2.74111
$739$	−46.6152	−1.71477	−0.857384	−	0.514677i	$-0.827912\pi$
$739$	−46.6152	−1.71477	−0.857384	+	0.514677i	$0.827912\pi$
$740$	−12.7664	−0.469302
$741$	93.4802	3.43408
$742$	0.250140	0.00918292
$743$	16.2124	0.594775	0.297388	−	0.954757i	$-0.403885\pi$
$743$	16.2124	0.594775	0.297388	+	0.954757i	$0.403885\pi$
$744$	−21.2425	−0.778787
$745$	50.2933	1.84260
$746$	−7.69085	−0.281582
$747$	−48.6249	−1.77909
$748$	−3.16840	−0.115848
$749$	11.4509	0.418405
$750$	9.61726	0.351173
$751$	−30.9670	−1.13000	−0.565001	−	0.825090i	$-0.691124\pi$
$751$	−30.9670	−1.13000	−0.565001	+	0.825090i	$0.691124\pi$
$752$	−1.25178	−0.0456479
$753$	−54.1073	−1.97178
$754$	37.5740	1.36836
$755$	29.1725	1.06169
$756$	−7.94628	−0.289003
$757$	35.3212	1.28377	0.641885	−	0.766801i	$-0.278153\pi$
$757$	35.3212	1.28377	0.641885	+	0.766801i	$0.278153\pi$
$758$	15.7202	0.570983
$759$	151.945	5.51524
$760$	19.9063	0.722076
$761$	7.17350	0.260039	0.130020	−	0.991511i	$-0.458496\pi$
$761$	7.17350	0.260039	0.130020	+	0.991511i	$0.458496\pi$
$762$	−8.57226	−0.310540
$763$	9.78290	0.354165
$764$	20.2382	0.732194
$765$	−12.0624	−0.436117
$766$	29.4802	1.06516
$767$	−6.66074	−0.240506
$768$	−3.13974	−0.113296
$769$	19.7169	0.711010	0.355505	−	0.934674i	$-0.384309\pi$
$769$	19.7169	0.711010	0.355505	+	0.934674i	$0.384309\pi$
$770$	−12.9121	−0.465321
$771$	9.21904	0.332016
$772$	4.89983	0.176349
$773$	18.8571	0.678244	0.339122	−	0.940742i	$-0.389870\pi$
$773$	18.8571	0.678244	0.339122	+	0.940742i	$0.389870\pi$
$774$	−73.9412	−2.65776
$775$	−40.0977	−1.44035
$776$	−13.1972	−0.473750
$777$	7.95477	0.285376
$778$	−12.8752	−0.461597
$779$	−65.3889	−2.34280
$780$	−51.3118	−1.83726
$781$	68.7676	2.46070
$782$	−4.32451	−0.154644
$783$	92.0584	3.28990
$784$	−6.56966	−0.234631
$785$	49.8825	1.78038
$786$	17.7708	0.633862
$787$	−37.1689	−1.32493	−0.662464	−	0.749093i	$-0.730489\pi$
$787$	−37.1689	−1.32493	−0.662464	+	0.749093i	$0.730489\pi$
$788$	−0.117625	−0.00419023
$789$	44.8076	1.59519
$790$	20.1579	0.717187
$791$	−11.5802	−0.411744
$792$	−40.8361	−1.45105
$793$	46.2750	1.64327
$794$	−20.3213	−0.721177
$795$	3.95742	0.140355
$796$	10.2168	0.362126
$797$	−51.3927	−1.82042	−0.910211	−	0.414145i	$-0.864081\pi$
$797$	−51.3927	−1.82042	−0.910211	+	0.414145i	$0.864081\pi$
$798$	−12.4036	−0.439083
$799$	0.666074	0.0235640
$800$	−5.92665	−0.209539
$801$	25.1998	0.890390
$802$	−24.6179	−0.869288
$803$	45.6286	1.61020
$804$	40.7727	1.43794
$805$	−17.6236	−0.621151
$806$	33.4496	1.17821
$807$	−44.7353	−1.57476
$808$	0.402995	0.0141773
$809$	38.4966	1.35347	0.676734	−	0.736228i	$-0.263395\pi$
$809$	38.4966	1.35347	0.676734	+	0.736228i	$0.263395\pi$
$810$	−57.7085	−2.02767
$811$	−48.4911	−1.70275	−0.851376	−	0.524555i	$-0.824232\pi$
$811$	−48.4911	−1.70275	−0.851376	+	0.524555i	$0.824232\pi$
$812$	−4.98558	−0.174960
$813$	59.2504	2.07800
$814$	22.9970	0.806046
$815$	38.8000	1.35911
$816$	1.67066	0.0584847
$817$	−64.9286	−2.27156
$818$	−5.00710	−0.175069
$819$	22.2425	0.777217
$820$	35.8923	1.25341
$821$	−4.37527	−0.152698	−0.0763490	−	0.997081i	$-0.524326\pi$
$821$	−4.37527	−0.152698	−0.0763490	+	0.997081i	$0.524326\pi$
$822$	−31.7141	−1.10616
$823$	−17.3897	−0.606168	−0.303084	−	0.952964i	$-0.598016\pi$
$823$	−17.3897	−0.606168	−0.303084	+	0.952964i	$0.598016\pi$
$824$	8.13503	0.283397
$825$	−110.803	−3.85765
$826$	0.883795	0.0307512
$827$	50.4763	1.75523	0.877617	−	0.479363i	$-0.159132\pi$
$827$	50.4763	1.75523	0.877617	+	0.479363i	$0.159132\pi$
$828$	−55.7367	−1.93698
$829$	−11.0430	−0.383541	−0.191770	−	0.981440i	$-0.561423\pi$
$829$	−11.0430	−0.383541	−0.191770	+	0.981440i	$0.561423\pi$
$830$	23.4371	0.813515
$831$	10.3873	0.360331
$832$	4.94401	0.171403
$833$	3.49571	0.121119
$834$	13.1209	0.454338
$835$	28.7098	0.993544
$836$	−35.8586	−1.24019
$837$	81.9533	2.83272
$838$	−21.2045	−0.732496
$839$	−35.1151	−1.21231	−0.606153	−	0.795348i	$-0.707288\pi$
$839$	−35.1151	−1.21231	−0.606153	+	0.795348i	$0.707288\pi$
$840$	6.80841	0.234912
$841$	28.7584	0.991670
$842$	−32.0665	−1.10508
$843$	15.4384	0.531725
$844$	16.6218	0.572145
$845$	37.8262	1.30126
$846$	8.58473	0.295149
$847$	16.0435	0.551261
$848$	−0.381307	−0.0130941
$849$	−10.3962	−0.356797
$850$	3.15357	0.108166
$851$	31.3884	1.07598
$852$	−36.2603	−1.24226
$853$	34.6597	1.18672	0.593362	−	0.804936i	$-0.297800\pi$
$853$	34.6597	1.18672	0.593362	+	0.804936i	$0.297800\pi$
$854$	−6.14009	−0.210110
$855$	−136.517	−4.66878
$856$	−17.4554	−0.596614
$857$	−39.0669	−1.33450	−0.667249	−	0.744834i	$-0.732528\pi$
$857$	−39.0669	−1.33450	−0.667249	+	0.744834i	$0.732528\pi$
$858$	92.4316	3.15556
$859$	15.8970	0.542399	0.271200	−	0.962523i	$-0.412580\pi$
$859$	15.8970	0.542399	0.271200	+	0.962523i	$0.412580\pi$
$860$	35.6396	1.21530
$861$	−22.3645	−0.762181
$862$	16.1383	0.549671
$863$	−5.72240	−0.194793	−0.0973964	−	0.995246i	$-0.531051\pi$
$863$	−5.72240	−0.194793	−0.0973964	+	0.995246i	$0.531051\pi$
$864$	12.1131	0.412096
$865$	2.03704	0.0692615
$866$	17.7867	0.604416
$867$	52.4867	1.78254
$868$	−4.43832	−0.150647
$869$	−36.3120	−1.23180
$870$	−78.8761	−2.67415
$871$	−64.2028	−2.17543
$872$	−14.9128	−0.505012
$873$	90.5060	3.06316
$874$	−48.9429	−1.65552
$875$	2.00939	0.0679299
$876$	−24.0594	−0.812892
$877$	−42.2614	−1.42707	−0.713533	−	0.700622i	$-0.752906\pi$
$877$	−42.2614	−1.42707	−0.713533	+	0.700622i	$0.752906\pi$
$878$	−10.1631	−0.342989
$879$	−23.7137	−0.799842
$880$	19.6830	0.663512
$881$	12.0409	0.405667	0.202834	−	0.979213i	$-0.434985\pi$
$881$	12.0409	0.405667	0.202834	+	0.979213i	$0.434985\pi$
$882$	45.0546	1.51707
$883$	−40.1020	−1.34954	−0.674769	−	0.738029i	$-0.735757\pi$
$883$	−40.1020	−1.34954	−0.674769	+	0.738029i	$0.735757\pi$
$884$	−2.63071	−0.0884802
$885$	13.9824	0.470012
$886$	31.3504	1.05324
$887$	−6.85521	−0.230175	−0.115088	−	0.993355i	$-0.536715\pi$
$887$	−6.85521	−0.230175	−0.115088	+	0.993355i	$0.536715\pi$
$888$	−12.1261	−0.406924
$889$	−1.79106	−0.0600701
$890$	−12.1463	−0.407144
$891$	103.955	3.48261
$892$	21.5177	0.720465
$893$	7.53834	0.252261
$894$	47.7706	1.59769
$895$	44.9561	1.50272
$896$	−0.656006	−0.0219156
$897$	126.159	4.21232
$898$	3.99517	0.133321
$899$	51.4184	1.71490
$900$	40.6449	1.35483
$901$	0.202893	0.00675935
$902$	−64.6554	−2.15279
$903$	−22.2071	−0.739006
$904$	17.6526	0.587115
$905$	−60.8864	−2.02393
$906$	27.7092	0.920577
$907$	−45.7695	−1.51975	−0.759876	−	0.650068i	$-0.774740\pi$
$907$	−45.7695	−1.51975	−0.759876	+	0.650068i	$0.774740\pi$
$908$	8.38809	0.278368
$909$	−2.76374	−0.0916674
$910$	−10.7209	−0.355394
$911$	55.7452	1.84692	0.923460	−	0.383695i	$-0.125349\pi$
$911$	55.7452	1.84692	0.923460	+	0.383695i	$0.125349\pi$
$912$	18.9078	0.626099
$913$	−42.2190	−1.39725
$914$	−19.6887	−0.651245
$915$	−97.1414	−3.21140
$916$	28.0125	0.925559
$917$	3.71295	0.122613
$918$	−6.44538	−0.212729
$919$	3.99221	0.131691	0.0658455	−	0.997830i	$-0.479026\pi$
$919$	3.99221	0.131691	0.0658455	+	0.997830i	$0.479026\pi$
$920$	26.8650	0.885714
$921$	−44.3971	−1.46293
$922$	−38.7974	−1.27772
$923$	57.0974	1.87938
$924$	−12.2645	−0.403472
$925$	−22.8894	−0.752598
$926$	39.1112	1.28527
$927$	−55.7900	−1.83238
$928$	7.59990	0.249479
$929$	34.4860	1.13145	0.565724	−	0.824594i	$-0.308597\pi$
$929$	34.4860	1.13145	0.565724	+	0.824594i	$0.308597\pi$
$930$	−70.2180	−2.30254
$931$	39.5630	1.29662
$932$	−1.60537	−0.0525855
$933$	16.7737	0.549147
$934$	−24.2457	−0.793342
$935$	−10.4733	−0.342513
$936$	−33.9060	−1.10825
$937$	17.7411	0.579576	0.289788	−	0.957091i	$-0.406415\pi$
$937$	17.7411	0.579576	0.289788	+	0.957091i	$0.406415\pi$
$938$	8.51889	0.278151
$939$	13.1718	0.429845
$940$	−4.13783	−0.134961
$941$	43.8052	1.42801	0.714005	−	0.700141i	$-0.246879\pi$
$941$	43.8052	1.42801	0.714005	+	0.700141i	$0.246879\pi$
$942$	47.3804	1.54374
$943$	−88.2473	−2.87373
$944$	−1.34723	−0.0438488
$945$	−26.2668	−0.854459
$946$	−64.2002	−2.08733
$947$	52.5229	1.70676	0.853382	−	0.521285i	$-0.174547\pi$
$947$	52.5229	1.70676	0.853382	+	0.521285i	$0.174547\pi$
$948$	19.1468	0.621860
$949$	37.8852	1.22981
$950$	35.6907	1.15796
$951$	91.8212	2.97751
$952$	0.349061	0.0113131
$953$	6.01489	0.194842	0.0974208	−	0.995243i	$-0.468941\pi$
$953$	6.01489	0.194842	0.0974208	+	0.995243i	$0.468941\pi$
$954$	2.61500	0.0846638
$955$	66.8985	2.16478
$956$	20.7073	0.669721
$957$	142.085	4.59296
$958$	42.2295	1.36437
$959$	−6.62623	−0.213972
$960$	−10.3786	−0.334967
$961$	14.7743	0.476591
$962$	19.0943	0.615626
$963$	119.709	3.85757
$964$	1.47798	0.0476025
$965$	16.1966	0.521388
$966$	−16.7396	−0.538589
$967$	−9.30735	−0.299304	−0.149652	−	0.988739i	$-0.547815\pi$
$967$	−9.30735	−0.299304	−0.149652	+	0.988739i	$0.547815\pi$
$968$	−24.4563	−0.786056
$969$	−10.0608	−0.323200
$970$	−43.6238	−1.40068
$971$	7.46575	0.239587	0.119794	−	0.992799i	$-0.461777\pi$
$971$	7.46575	0.239587	0.119794	+	0.992799i	$0.461777\pi$
$972$	−18.4746	−0.592573
$973$	2.74142	0.0878859
$974$	18.6387	0.597221
$975$	−91.9989	−2.94632
$976$	9.35980	0.299600
$977$	−14.2980	−0.457435	−0.228717	−	0.973493i	$-0.573453\pi$
$977$	−14.2980	−0.457435	−0.228717	+	0.973493i	$0.573453\pi$
$978$	36.8538	1.17846
$979$	21.8800	0.699287
$980$	−21.7163	−0.693702
$981$	102.272	3.26529
$982$	−37.1250	−1.18471
$983$	32.3787	1.03272	0.516360	−	0.856371i	$-0.327287\pi$
$983$	32.3787	1.03272	0.516360	+	0.856371i	$0.327287\pi$
$984$	34.0920	1.08681
$985$	−0.388816	−0.0123887
$986$	−4.04390	−0.128784
$987$	2.57829	0.0820679
$988$	−29.7732	−0.947212
$989$	−87.6261	−2.78635
$990$	−134.986	−4.29012
$991$	−38.4039	−1.21994	−0.609970	−	0.792424i	$-0.708819\pi$
$991$	−38.4039	−1.21994	−0.609970	+	0.792424i	$0.708819\pi$
$992$	6.76567	0.214810
$993$	−2.06810	−0.0656292
$994$	−7.57609	−0.240299
$995$	33.7722	1.07065
$996$	22.2616	0.705385
$997$	−35.9523	−1.13862	−0.569311	−	0.822122i	$-0.692790\pi$
$997$	−35.9523	−1.13862	−0.569311	+	0.822122i	$0.692790\pi$
$998$	3.00415	0.0950948
$999$	46.7822	1.48012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.6	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.6	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.13974 q^{3} +1.00000 q^{4} +3.30555 q^{5} +3.13974 q^{6} +0.656006 q^{7} -1.00000 q^{8} +6.85799 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.13974 q^{3} +1.00000 q^{4} +3.30555 q^{5} +3.13974 q^{6} +0.656006 q^{7} -1.00000 q^{8} +6.85799 q^{9} -3.30555 q^{10} +5.95452 q^{11} -3.13974 q^{12} +4.94401 q^{13} -0.656006 q^{14} -10.3786 q^{15} +1.00000 q^{16} -0.532100 q^{17} -6.85799 q^{18} -6.02208 q^{19} +3.30555 q^{20} -2.05969 q^{21} -5.95452 q^{22} -8.12726 q^{23} +3.13974 q^{24} +5.92665 q^{25} -4.94401 q^{26} -12.1131 q^{27} +0.656006 q^{28} -7.59990 q^{29} +10.3786 q^{30} -6.76567 q^{31} -1.00000 q^{32} -18.6957 q^{33} +0.532100 q^{34} +2.16846 q^{35} +6.85799 q^{36} -3.86211 q^{37} +6.02208 q^{38} -15.5229 q^{39} -3.30555 q^{40} +10.8582 q^{41} +2.05969 q^{42} +10.7818 q^{43} +5.95452 q^{44} +22.6694 q^{45} +8.12726 q^{46} -1.25178 q^{47} -3.13974 q^{48} -6.56966 q^{49} -5.92665 q^{50} +1.67066 q^{51} +4.94401 q^{52} -0.381307 q^{53} +12.1131 q^{54} +19.6830 q^{55} -0.656006 q^{56} +18.9078 q^{57} +7.59990 q^{58} -1.34723 q^{59} -10.3786 q^{60} +9.35980 q^{61} +6.76567 q^{62} +4.49889 q^{63} +1.00000 q^{64} +16.3427 q^{65} +18.6957 q^{66} -12.9860 q^{67} -0.532100 q^{68} +25.5175 q^{69} -2.16846 q^{70} +11.5488 q^{71} -6.85799 q^{72} +7.66285 q^{73} +3.86211 q^{74} -18.6081 q^{75} -6.02208 q^{76} +3.90620 q^{77} +15.5229 q^{78} -6.09822 q^{79} +3.30555 q^{80} +17.4581 q^{81} -10.8582 q^{82} -7.09025 q^{83} -2.05969 q^{84} -1.75888 q^{85} -10.7818 q^{86} +23.8617 q^{87} -5.95452 q^{88} +3.67451 q^{89} -22.6694 q^{90} +3.24330 q^{91} -8.12726 q^{92} +21.2425 q^{93} +1.25178 q^{94} -19.9063 q^{95} +3.13974 q^{96} +13.1972 q^{97} +6.56966 q^{98} +40.8361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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