LMFDB - Embedded newform 1110.2.a.s.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1110.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.67673$ of defining polynomial
Character	$\chi$	$=$	1110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.22069 q^{11} +1.00000 q^{12} -6.60629 q^{13} +5.13277 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.63841 q^{17} +1.00000 q^{18} -7.51836 q^{19} +1.00000 q^{20} +5.13277 q^{21} +2.22069 q^{22} -6.10064 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.60629 q^{26} +1.00000 q^{27} +5.13277 q^{28} -7.29767 q^{29} +1.00000 q^{30} -0.967873 q^{31} +1.00000 q^{32} +2.22069 q^{33} +5.63841 q^{34} +5.13277 q^{35} +1.00000 q^{36} -1.00000 q^{37} -7.51836 q^{38} -6.60629 q^{39} +1.00000 q^{40} -1.03213 q^{41} +5.13277 q^{42} +5.29767 q^{43} +2.22069 q^{44} +1.00000 q^{45} -6.10064 q^{46} -5.85911 q^{47} +1.00000 q^{48} +19.3453 q^{49} +1.00000 q^{50} +5.63841 q^{51} -6.60629 q^{52} -9.63841 q^{53} +1.00000 q^{54} +2.22069 q^{55} +5.13277 q^{56} -7.51836 q^{57} -7.29767 q^{58} -10.2655 q^{59} +1.00000 q^{60} +6.32134 q^{61} -0.967873 q^{62} +5.13277 q^{63} +1.00000 q^{64} -6.60629 q^{65} +2.22069 q^{66} +1.49436 q^{67} +5.63841 q^{68} -6.10064 q^{69} +5.13277 q^{70} +0.329796 q^{71} +1.00000 q^{72} +12.8718 q^{73} -1.00000 q^{74} +1.00000 q^{75} -7.51836 q^{76} +11.3983 q^{77} -6.60629 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.03213 q^{82} +9.04767 q^{83} +5.13277 q^{84} +5.63841 q^{85} +5.29767 q^{86} -7.29767 q^{87} +2.22069 q^{88} -2.27649 q^{89} +1.00000 q^{90} -33.9086 q^{91} -6.10064 q^{92} -0.967873 q^{93} -5.85911 q^{94} -7.51836 q^{95} +1.00000 q^{96} +17.5982 q^{97} +19.3453 q^{98} +2.22069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} + 3 q^{19} + 4 q^{20} + 4 q^{21} + 2 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} + 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 3 q^{38} - 3 q^{39} + 4 q^{40} - 11 q^{41} + 4 q^{42} - 5 q^{43} + 2 q^{44} + 4 q^{45} - q^{46} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 6 q^{51} - 3 q^{52} - 22 q^{53} + 4 q^{54} + 2 q^{55} + 4 q^{56} + 3 q^{57} - 3 q^{58} - 8 q^{59} + 4 q^{60} - 5 q^{61} + 3 q^{62} + 4 q^{63} + 4 q^{64} - 3 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - q^{69} + 4 q^{70} - 18 q^{71} + 4 q^{72} - 5 q^{73} - 4 q^{74} + 4 q^{75} + 3 q^{76} - 4 q^{77} - 3 q^{78} + 16 q^{79} + 4 q^{80} + 4 q^{81} - 11 q^{82} - q^{83} + 4 q^{84} + 6 q^{85} - 5 q^{86} - 3 q^{87} + 2 q^{88} - 5 q^{89} + 4 q^{90} - 13 q^{91} - q^{92} + 3 q^{93} + 3 q^{95} + 4 q^{96} + 7 q^{97} + 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 + 3 * q^19 + 4 * q^20 + 4 * q^21 + 2 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 + 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 3 * q^38 - 3 * q^39 + 4 * q^40 - 11 * q^41 + 4 * q^42 - 5 * q^43 + 2 * q^44 + 4 * q^45 - q^46 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 6 * q^51 - 3 * q^52 - 22 * q^53 + 4 * q^54 + 2 * q^55 + 4 * q^56 + 3 * q^57 - 3 * q^58 - 8 * q^59 + 4 * q^60 - 5 * q^61 + 3 * q^62 + 4 * q^63 + 4 * q^64 - 3 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - q^69 + 4 * q^70 - 18 * q^71 + 4 * q^72 - 5 * q^73 - 4 * q^74 + 4 * q^75 + 3 * q^76 - 4 * q^77 - 3 * q^78 + 16 * q^79 + 4 * q^80 + 4 * q^81 - 11 * q^82 - q^83 + 4 * q^84 + 6 * q^85 - 5 * q^86 - 3 * q^87 + 2 * q^88 - 5 * q^89 + 4 * q^90 - 13 * q^91 - q^92 + 3 * q^93 + 3 * q^95 + 4 * q^96 + 7 * q^97 + 14 * q^98 + 2 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	5.13277	1.94001	0.970003	−	0.243094i	$-0.0781625\pi$
$7$	5.13277	1.94001	0.970003	+	0.243094i	$0.0781625\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	2.22069	0.669564	0.334782	−	0.942296i	$-0.391337\pi$
$11$	2.22069	0.669564	0.334782	+	0.942296i	$0.391337\pi$
$12$	1.00000	0.288675
$13$	−6.60629	−1.83225	−0.916127	−	0.400888i	$-0.868702\pi$
$13$	−6.60629	−1.83225	−0.916127	+	0.400888i	$0.868702\pi$
$14$	5.13277	1.37179
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	5.63841	1.36752	0.683758	−	0.729709i	$-0.260344\pi$
$17$	5.63841	1.36752	0.683758	+	0.729709i	$0.260344\pi$
$18$	1.00000	0.235702
$19$	−7.51836	−1.72483	−0.862415	−	0.506201i	$-0.831049\pi$
$19$	−7.51836	−1.72483	−0.862415	+	0.506201i	$0.831049\pi$
$20$	1.00000	0.223607
$21$	5.13277	1.12006
$22$	2.22069	0.473454
$23$	−6.10064	−1.27207	−0.636036	−	0.771659i	$-0.719427\pi$
$23$	−6.10064	−1.27207	−0.636036	+	0.771659i	$0.719427\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.60629	−1.29560
$27$	1.00000	0.192450
$28$	5.13277	0.970003
$29$	−7.29767	−1.35514	−0.677572	−	0.735457i	$-0.736968\pi$
$29$	−7.29767	−1.35514	−0.677572	+	0.735457i	$0.736968\pi$
$30$	1.00000	0.182574
$31$	−0.967873	−0.173835	−0.0869176	−	0.996216i	$-0.527702\pi$
$31$	−0.967873	−0.173835	−0.0869176	+	0.996216i	$0.527702\pi$
$32$	1.00000	0.176777
$33$	2.22069	0.386573
$34$	5.63841	0.966980
$35$	5.13277	0.867597
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−7.51836	−1.21964
$39$	−6.60629	−1.05785
$40$	1.00000	0.158114
$41$	−1.03213	−0.161191	−0.0805955	−	0.996747i	$-0.525682\pi$
$41$	−1.03213	−0.161191	−0.0805955	+	0.996747i	$0.525682\pi$
$42$	5.13277	0.792004
$43$	5.29767	0.807887	0.403944	−	0.914784i	$-0.367639\pi$
$43$	5.29767	0.807887	0.403944	+	0.914784i	$0.367639\pi$
$44$	2.22069	0.334782
$45$	1.00000	0.149071
$46$	−6.10064	−0.899491
$47$	−5.85911	−0.854638	−0.427319	−	0.904101i	$-0.640542\pi$
$47$	−5.85911	−0.854638	−0.427319	+	0.904101i	$0.640542\pi$
$48$	1.00000	0.144338
$49$	19.3453	2.76362
$50$	1.00000	0.141421
$51$	5.63841	0.789536
$52$	−6.60629	−0.916127
$53$	−9.63841	−1.32394	−0.661969	−	0.749531i	$-0.730279\pi$
$53$	−9.63841	−1.32394	−0.661969	+	0.749531i	$0.730279\pi$
$54$	1.00000	0.136083
$55$	2.22069	0.299438
$56$	5.13277	0.685895
$57$	−7.51836	−0.995832
$58$	−7.29767	−0.958231
$59$	−10.2655	−1.33646	−0.668230	−	0.743955i	$-0.732948\pi$
$59$	−10.2655	−1.33646	−0.668230	+	0.743955i	$0.732948\pi$
$60$	1.00000	0.129099
$61$	6.32134	0.809365	0.404682	−	0.914457i	$-0.367382\pi$
$61$	6.32134	0.809365	0.404682	+	0.914457i	$0.367382\pi$
$62$	−0.967873	−0.122920
$63$	5.13277	0.646668
$64$	1.00000	0.125000
$65$	−6.60629	−0.819409
$66$	2.22069	0.273349
$67$	1.49436	0.182565	0.0912825	−	0.995825i	$-0.470903\pi$
$67$	1.49436	0.182565	0.0912825	+	0.995825i	$0.470903\pi$
$68$	5.63841	0.683758
$69$	−6.10064	−0.734431
$70$	5.13277	0.613484
$71$	0.329796	0.0391396	0.0195698	−	0.999808i	$-0.493770\pi$
$71$	0.329796	0.0391396	0.0195698	+	0.999808i	$0.493770\pi$
$72$	1.00000	0.117851
$73$	12.8718	1.50653	0.753267	−	0.657715i	$-0.228477\pi$
$73$	12.8718	1.50653	0.753267	+	0.657715i	$0.228477\pi$
$74$	−1.00000	−0.116248
$75$	1.00000	0.115470
$76$	−7.51836	−0.862415
$77$	11.3983	1.29896
$78$	−6.60629	−0.748015
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.03213	−0.113979
$83$	9.04767	0.993111	0.496556	−	0.868005i	$-0.334598\pi$
$83$	9.04767	0.993111	0.496556	+	0.868005i	$0.334598\pi$
$84$	5.13277	0.560031
$85$	5.63841	0.611572
$86$	5.29767	0.571262
$87$	−7.29767	−0.782392
$88$	2.22069	0.236727
$89$	−2.27649	−0.241307	−0.120654	−	0.992695i	$-0.538499\pi$
$89$	−2.27649	−0.241307	−0.120654	+	0.992695i	$0.538499\pi$
$90$	1.00000	0.105409
$91$	−33.9086	−3.55458
$92$	−6.10064	−0.636036
$93$	−0.967873	−0.100364
$94$	−5.85911	−0.604321
$95$	−7.51836	−0.771368
$96$	1.00000	0.102062
$97$	17.5982	1.78682	0.893411	−	0.449239i	$-0.148305\pi$
$97$	17.5982	1.78682	0.893411	+	0.449239i	$0.148305\pi$
$98$	19.3453	1.95417
$99$	2.22069	0.223188
$100$	1.00000	0.100000
$101$	7.61901	0.758120	0.379060	−	0.925372i	$-0.376247\pi$
$101$	7.61901	0.758120	0.379060	+	0.925372i	$0.376247\pi$
$102$	5.63841	0.558286
$103$	5.85911	0.577315	0.288657	−	0.957432i	$-0.406791\pi$
$103$	5.85911	0.577315	0.288657	+	0.957432i	$0.406791\pi$
$104$	−6.60629	−0.647800
$105$	5.13277	0.500907
$106$	−9.63841	−0.936165
$107$	5.65926	0.547101	0.273551	−	0.961858i	$-0.411802\pi$
$107$	5.65926	0.547101	0.273551	+	0.961858i	$0.411802\pi$
$108$	1.00000	0.0962250
$109$	−3.16772	−0.303413	−0.151706	−	0.988426i	$-0.548477\pi$
$109$	−3.16772	−0.303413	−0.151706	+	0.988426i	$0.548477\pi$
$110$	2.22069	0.211735
$111$	−1.00000	−0.0949158
$112$	5.13277	0.485001
$113$	−0.702331	−0.0660697	−0.0330348	−	0.999454i	$-0.510517\pi$
$113$	−0.702331	−0.0660697	−0.0330348	+	0.999454i	$0.510517\pi$
$114$	−7.51836	−0.704159
$115$	−6.10064	−0.568888
$116$	−7.29767	−0.677572
$117$	−6.60629	−0.610751
$118$	−10.2655	−0.945020
$119$	28.9407	2.65299
$120$	1.00000	0.0912871
$121$	−6.06852	−0.551683
$122$	6.32134	0.572307
$123$	−1.03213	−0.0930637
$124$	−0.967873	−0.0869176
$125$	1.00000	0.0894427
$126$	5.13277	0.457264
$127$	−19.3132	−1.71377	−0.856885	−	0.515507i	$-0.827604\pi$
$127$	−19.3132	−1.71377	−0.856885	+	0.515507i	$0.827604\pi$
$128$	1.00000	0.0883883
$129$	5.29767	0.466434
$130$	−6.60629	−0.579410
$131$	−18.5953	−1.62468	−0.812341	−	0.583183i	$-0.801807\pi$
$131$	−18.5953	−1.62468	−0.812341	+	0.583183i	$0.801807\pi$
$132$	2.22069	0.193287
$133$	−38.5900	−3.34618
$134$	1.49436	0.129093
$135$	1.00000	0.0860663
$136$	5.63841	0.483490
$137$	−19.5074	−1.66663	−0.833316	−	0.552798i	$-0.813560\pi$
$137$	−19.5074	−1.66663	−0.833316	+	0.552798i	$0.813560\pi$
$138$	−6.10064	−0.519321
$139$	10.9036	0.924833	0.462417	−	0.886663i	$-0.346982\pi$
$139$	10.9036	0.924833	0.462417	+	0.886663i	$0.346982\pi$
$140$	5.13277	0.433798
$141$	−5.85911	−0.493426
$142$	0.329796	0.0276759
$143$	−14.6705	−1.22681
$144$	1.00000	0.0833333
$145$	−7.29767	−0.606038
$146$	12.8718	1.06528
$147$	19.3453	1.59558
$148$	−1.00000	−0.0821995
$149$	−12.6720	−1.03813	−0.519065	−	0.854735i	$-0.673720\pi$
$149$	−12.6720	−1.03813	−0.519065	+	0.854735i	$0.673720\pi$
$150$	1.00000	0.0816497
$151$	10.5420	0.857898	0.428949	−	0.903329i	$-0.358884\pi$
$151$	10.5420	0.857898	0.428949	+	0.903329i	$0.358884\pi$
$152$	−7.51836	−0.609820
$153$	5.63841	0.455839
$154$	11.3983	0.918502
$155$	−0.967873	−0.0777415
$156$	−6.60629	−0.528926
$157$	−15.4990	−1.23695	−0.618476	−	0.785804i	$-0.712250\pi$
$157$	−15.4990	−1.23695	−0.618476	+	0.785804i	$0.712250\pi$
$158$	4.00000	0.318223
$159$	−9.63841	−0.764376
$160$	1.00000	0.0790569
$161$	−31.3132	−2.46783
$162$	1.00000	0.0785674
$163$	−4.12149	−0.322820	−0.161410	−	0.986887i	$-0.551604\pi$
$163$	−4.12149	−0.322820	−0.161410	+	0.986887i	$0.551604\pi$
$164$	−1.03213	−0.0805955
$165$	2.22069	0.172881
$166$	9.04767	0.702236
$167$	21.9474	1.69834	0.849169	−	0.528121i	$-0.177103\pi$
$167$	21.9474	1.69834	0.849169	+	0.528121i	$0.177103\pi$
$168$	5.13277	0.396002
$169$	30.6430	2.35715
$170$	5.63841	0.432446
$171$	−7.51836	−0.574944
$172$	5.29767	0.403944
$173$	−0.425841	−0.0323761	−0.0161880	−	0.999869i	$-0.505153\pi$
$173$	−0.425841	−0.0323761	−0.0161880	+	0.999869i	$0.505153\pi$
$174$	−7.29767	−0.553235
$175$	5.13277	0.388001
$176$	2.22069	0.167391
$177$	−10.2655	−0.771605
$178$	−2.27649	−0.170630
$179$	−17.5424	−1.31118	−0.655589	−	0.755118i	$-0.727580\pi$
$179$	−17.5424	−1.31118	−0.655589	+	0.755118i	$0.727580\pi$
$180$	1.00000	0.0745356
$181$	18.5311	1.37740	0.688702	−	0.725044i	$-0.258181\pi$
$181$	18.5311	1.37740	0.688702	+	0.725044i	$0.258181\pi$
$182$	−33.9086	−2.51347
$183$	6.32134	0.467287
$184$	−6.10064	−0.449746
$185$	−1.00000	−0.0735215
$186$	−0.967873	−0.0709679
$187$	12.5212	0.915640
$188$	−5.85911	−0.427319
$189$	5.13277	0.373354
$190$	−7.51836	−0.545439
$191$	16.1695	1.16998	0.584992	−	0.811039i	$-0.301098\pi$
$191$	16.1695	1.16998	0.584992	+	0.811039i	$0.301098\pi$
$192$	1.00000	0.0721688
$193$	−11.8591	−0.853637	−0.426819	−	0.904337i	$-0.640366\pi$
$193$	−11.8591	−0.853637	−0.426819	+	0.904337i	$0.640366\pi$
$194$	17.5982	1.26347
$195$	−6.60629	−0.473086
$196$	19.3453	1.38181
$197$	0.100645	0.00717066	0.00358533	−	0.999994i	$-0.498859\pi$
$197$	0.100645	0.00717066	0.00358533	+	0.999994i	$0.498859\pi$
$198$	2.22069	0.157818
$199$	−2.70693	−0.191889	−0.0959446	−	0.995387i	$-0.530587\pi$
$199$	−2.70693	−0.191889	−0.0959446	+	0.995387i	$0.530587\pi$
$200$	1.00000	0.0707107
$201$	1.49436	0.105404
$202$	7.61901	0.536072
$203$	−37.4573	−2.62898
$204$	5.63841	0.394768
$205$	−1.03213	−0.0720868
$206$	5.85911	0.408223
$207$	−6.10064	−0.424024
$208$	−6.60629	−0.458064
$209$	−16.6960	−1.15489
$210$	5.13277	0.354195
$211$	11.8033	0.812573	0.406287	−	0.913746i	$-0.366823\pi$
$211$	11.8033	0.812573	0.406287	+	0.913746i	$0.366823\pi$
$212$	−9.63841	−0.661969
$213$	0.329796	0.0225972
$214$	5.65926	0.386859
$215$	5.29767	0.361298
$216$	1.00000	0.0680414
$217$	−4.96787	−0.337241
$218$	−3.16772	−0.214545
$219$	12.8718	0.869798
$220$	2.22069	0.149719
$221$	−37.2490	−2.50564
$222$	−1.00000	−0.0671156
$223$	13.1692	0.881872	0.440936	−	0.897538i	$-0.354646\pi$
$223$	13.1692	0.881872	0.440936	+	0.897538i	$0.354646\pi$
$224$	5.13277	0.342948
$225$	1.00000	0.0666667
$226$	−0.702331	−0.0467183
$227$	5.57946	0.370322	0.185161	−	0.982708i	$-0.440719\pi$
$227$	5.57946	0.370322	0.185161	+	0.982708i	$0.440719\pi$
$228$	−7.51836	−0.497916
$229$	−1.75990	−0.116298	−0.0581488	−	0.998308i	$-0.518520\pi$
$229$	−1.75990	−0.116298	−0.0581488	+	0.998308i	$0.518520\pi$
$230$	−6.10064	−0.402265
$231$	11.3983	0.749954
$232$	−7.29767	−0.479115
$233$	−6.07664	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$233$	−6.07664	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$234$	−6.60629	−0.431866
$235$	−5.85911	−0.382206
$236$	−10.2655	−0.668230
$237$	4.00000	0.259828
$238$	28.9407	1.87595
$239$	13.9403	0.901726	0.450863	−	0.892593i	$-0.351116\pi$
$239$	13.9403	0.901726	0.450863	+	0.892593i	$0.351116\pi$
$240$	1.00000	0.0645497
$241$	−3.89406	−0.250838	−0.125419	−	0.992104i	$-0.540028\pi$
$241$	−3.89406	−0.250838	−0.125419	+	0.992104i	$0.540028\pi$
$242$	−6.06852	−0.390099
$243$	1.00000	0.0641500
$244$	6.32134	0.404682
$245$	19.3453	1.23593
$246$	−1.03213	−0.0658060
$247$	49.6685	3.16033
$248$	−0.967873	−0.0614600
$249$	9.04767	0.573373
$250$	1.00000	0.0632456
$251$	20.9308	1.32114	0.660570	−	0.750765i	$-0.270315\pi$
$251$	20.9308	1.32114	0.660570	+	0.750765i	$0.270315\pi$
$252$	5.13277	0.323334
$253$	−13.5477	−0.851734
$254$	−19.3132	−1.21182
$255$	5.63841	0.353091
$256$	1.00000	0.0625000
$257$	−4.43044	−0.276363	−0.138182	−	0.990407i	$-0.544126\pi$
$257$	−4.43044	−0.276363	−0.138182	+	0.990407i	$0.544126\pi$
$258$	5.29767	0.329818
$259$	−5.13277	−0.318935
$260$	−6.60629	−0.409704
$261$	−7.29767	−0.451714
$262$	−18.5953	−1.14882
$263$	4.20975	0.259584	0.129792	−	0.991541i	$-0.458569\pi$
$263$	4.20975	0.259584	0.129792	+	0.991541i	$0.458569\pi$
$264$	2.22069	0.136674
$265$	−9.63841	−0.592083
$266$	−38.5900	−2.36611
$267$	−2.27649	−0.139319
$268$	1.49436	0.0912825
$269$	12.5071	0.762570	0.381285	−	0.924457i	$-0.375482\pi$
$269$	12.5071	0.762570	0.381285	+	0.924457i	$0.375482\pi$
$270$	1.00000	0.0608581
$271$	−6.70693	−0.407417	−0.203709	−	0.979032i	$-0.565299\pi$
$271$	−6.70693	−0.407417	−0.203709	+	0.979032i	$0.565299\pi$
$272$	5.63841	0.341879
$273$	−33.9086	−2.05224
$274$	−19.5074	−1.17849
$275$	2.22069	0.133913
$276$	−6.10064	−0.367216
$277$	−27.0477	−1.62514	−0.812569	−	0.582866i	$-0.801931\pi$
$277$	−27.0477	−1.62514	−0.812569	+	0.582866i	$0.801931\pi$
$278$	10.9036	0.653956
$279$	−0.967873	−0.0579451
$280$	5.13277	0.306742
$281$	−1.39371	−0.0831420	−0.0415710	−	0.999136i	$-0.513236\pi$
$281$	−1.39371	−0.0831420	−0.0415710	+	0.999136i	$0.513236\pi$
$282$	−5.85911	−0.348905
$283$	−15.3132	−0.910276	−0.455138	−	0.890421i	$-0.650410\pi$
$283$	−15.3132	−0.910276	−0.455138	+	0.890421i	$0.650410\pi$
$284$	0.329796	0.0195698
$285$	−7.51836	−0.445349
$286$	−14.6705	−0.867487
$287$	−5.29767	−0.312712
$288$	1.00000	0.0589256
$289$	14.7917	0.870100
$290$	−7.29767	−0.428534
$291$	17.5982	1.03162
$292$	12.8718	0.753267
$293$	−12.8672	−0.751712	−0.375856	−	0.926678i	$-0.622651\pi$
$293$	−12.8672	−0.751712	−0.375856	+	0.926678i	$0.622651\pi$
$294$	19.3453	1.12824
$295$	−10.2655	−0.597683
$296$	−1.00000	−0.0581238
$297$	2.22069	0.128858
$298$	−12.6720	−0.734068
$299$	40.3026	2.33076
$300$	1.00000	0.0577350
$301$	27.1917	1.56731
$302$	10.5420	0.606626
$303$	7.61901	0.437701
$304$	−7.51836	−0.431208
$305$	6.32134	0.361959
$306$	5.63841	0.322327
$307$	−4.08970	−0.233411	−0.116706	−	0.993167i	$-0.537233\pi$
$307$	−4.08970	−0.233411	−0.116706	+	0.993167i	$0.537233\pi$
$308$	11.3983	0.649479
$309$	5.85911	0.333313
$310$	−0.967873	−0.0549715
$311$	−10.3090	−0.584567	−0.292283	−	0.956332i	$-0.594415\pi$
$311$	−10.3090	−0.584567	−0.292283	+	0.956332i	$0.594415\pi$
$312$	−6.60629	−0.374007
$313$	−2.64653	−0.149591	−0.0747955	−	0.997199i	$-0.523830\pi$
$313$	−2.64653	−0.149591	−0.0747955	+	0.997199i	$0.523830\pi$
$314$	−15.4990	−0.874657
$315$	5.13277	0.289199
$316$	4.00000	0.225018
$317$	−8.06885	−0.453192	−0.226596	−	0.973989i	$-0.572760\pi$
$317$	−8.06885	−0.453192	−0.226596	+	0.973989i	$0.572760\pi$
$318$	−9.63841	−0.540495
$319$	−16.2059	−0.907356
$320$	1.00000	0.0559017
$321$	5.65926	0.315869
$322$	−31.3132	−1.74502
$323$	−42.3916	−2.35873
$324$	1.00000	0.0555556
$325$	−6.60629	−0.366451
$326$	−4.12149	−0.228268
$327$	−3.16772	−0.175175
$328$	−1.03213	−0.0569897
$329$	−30.0735	−1.65800
$330$	2.22069	0.122245
$331$	19.6833	1.08189	0.540945	−	0.841058i	$-0.318067\pi$
$331$	19.6833	1.08189	0.540945	+	0.841058i	$0.318067\pi$
$332$	9.04767	0.496556
$333$	−1.00000	−0.0547997
$334$	21.9474	1.20091
$335$	1.49436	0.0816456
$336$	5.13277	0.280016
$337$	−23.4891	−1.27953	−0.639765	−	0.768570i	$-0.720968\pi$
$337$	−23.4891	−1.27953	−0.639765	+	0.768570i	$0.720968\pi$
$338$	30.6430	1.66676
$339$	−0.702331	−0.0381454
$340$	5.63841	0.305786
$341$	−2.14935	−0.116394
$342$	−7.51836	−0.406547
$343$	63.3658	3.42143
$344$	5.29767	0.285631
$345$	−6.10064	−0.328448
$346$	−0.425841	−0.0228933
$347$	18.7069	1.00424	0.502120	−	0.864798i	$-0.332553\pi$
$347$	18.7069	1.00424	0.502120	+	0.864798i	$0.332553\pi$
$348$	−7.29767	−0.391196
$349$	16.1123	0.862470	0.431235	−	0.902240i	$-0.358078\pi$
$349$	16.1123	0.862470	0.431235	+	0.902240i	$0.358078\pi$
$350$	5.13277	0.274358
$351$	−6.60629	−0.352617
$352$	2.22069	0.118363
$353$	2.37320	0.126313	0.0631565	−	0.998004i	$-0.479883\pi$
$353$	2.37320	0.126313	0.0631565	+	0.998004i	$0.479883\pi$
$354$	−10.2655	−0.545607
$355$	0.329796	0.0175038
$356$	−2.27649	−0.120654
$357$	28.9407	1.53170
$358$	−17.5424	−0.927143
$359$	−18.5953	−0.981424	−0.490712	−	0.871322i	$-0.663263\pi$
$359$	−18.5953	−0.981424	−0.490712	+	0.871322i	$0.663263\pi$
$360$	1.00000	0.0527046
$361$	37.5258	1.97504
$362$	18.5311	0.973972
$363$	−6.06852	−0.318515
$364$	−33.9086	−1.77729
$365$	12.8718	0.673742
$366$	6.32134	0.330422
$367$	−29.9520	−1.56348	−0.781740	−	0.623605i	$-0.785668\pi$
$367$	−29.9520	−1.56348	−0.781740	+	0.623605i	$0.785668\pi$
$368$	−6.10064	−0.318018
$369$	−1.03213	−0.0537304
$370$	−1.00000	−0.0519875
$371$	−49.4718	−2.56845
$372$	−0.967873	−0.0501819
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	12.5212	0.647455
$375$	1.00000	0.0516398
$376$	−5.85911	−0.302160
$377$	48.2105	2.48297
$378$	5.13277	0.264001
$379$	23.3185	1.19779	0.598896	−	0.800827i	$-0.295606\pi$
$379$	23.3185	1.19779	0.598896	+	0.800827i	$0.295606\pi$
$380$	−7.51836	−0.385684
$381$	−19.3132	−0.989446
$382$	16.1695	0.827304
$383$	−16.6063	−0.848542	−0.424271	−	0.905535i	$-0.639470\pi$
$383$	−16.6063	−0.848542	−0.424271	+	0.905535i	$0.639470\pi$
$384$	1.00000	0.0510310
$385$	11.3983	0.580912
$386$	−11.8591	−0.603613
$387$	5.29767	0.269296
$388$	17.5982	0.893411
$389$	15.5795	0.789910	0.394955	−	0.918701i	$-0.370760\pi$
$389$	15.5795	0.789910	0.394955	+	0.918701i	$0.370760\pi$
$390$	−6.60629	−0.334522
$391$	−34.3980	−1.73958
$392$	19.3453	0.977087
$393$	−18.5953	−0.938011
$394$	0.100645	0.00507042
$395$	4.00000	0.201262
$396$	2.22069	0.111594
$397$	−23.2126	−1.16501	−0.582503	−	0.812829i	$-0.697926\pi$
$397$	−23.2126	−1.16501	−0.582503	+	0.812829i	$0.697926\pi$
$398$	−2.70693	−0.135686
$399$	−38.5900	−1.93192
$400$	1.00000	0.0500000
$401$	5.72351	0.285818	0.142909	−	0.989736i	$-0.454354\pi$
$401$	5.72351	0.285818	0.142909	+	0.989736i	$0.454354\pi$
$402$	1.49436	0.0745319
$403$	6.39405	0.318510
$404$	7.61901	0.379060
$405$	1.00000	0.0496904
$406$	−37.4573	−1.85897
$407$	−2.22069	−0.110076
$408$	5.63841	0.279143
$409$	28.0254	1.38577	0.692885	−	0.721049i	$-0.256340\pi$
$409$	28.0254	1.38577	0.692885	+	0.721049i	$0.256340\pi$
$410$	−1.03213	−0.0509731
$411$	−19.5074	−0.962230
$412$	5.85911	0.288657
$413$	−52.6907	−2.59274
$414$	−6.10064	−0.299830
$415$	9.04767	0.444133
$416$	−6.60629	−0.323900
$417$	10.9036	0.533953
$418$	−16.6960	−0.816627
$419$	16.2415	0.793451	0.396726	−	0.917937i	$-0.370146\pi$
$419$	16.2415	0.793451	0.396726	+	0.917937i	$0.370146\pi$
$420$	5.13277	0.250454
$421$	6.03495	0.294126	0.147063	−	0.989127i	$-0.453018\pi$
$421$	6.03495	0.294126	0.147063	+	0.989127i	$0.453018\pi$
$422$	11.8033	0.574576
$423$	−5.85911	−0.284879
$424$	−9.63841	−0.468083
$425$	5.63841	0.273503
$426$	0.329796	0.0159787
$427$	32.4460	1.57017
$428$	5.65926	0.273551
$429$	−14.6705	−0.708300
$430$	5.29767	0.255476
$431$	−33.2924	−1.60364	−0.801819	−	0.597568i	$-0.796134\pi$
$431$	−33.2924	−1.60364	−0.801819	+	0.597568i	$0.796134\pi$
$432$	1.00000	0.0481125
$433$	8.67054	0.416680	0.208340	−	0.978057i	$-0.433194\pi$
$433$	8.67054	0.416680	0.208340	+	0.978057i	$0.433194\pi$
$434$	−4.96787	−0.238466
$435$	−7.29767	−0.349896
$436$	−3.16772	−0.151706
$437$	45.8669	2.19411
$438$	12.8718	0.615040
$439$	32.8874	1.56963	0.784814	−	0.619731i	$-0.212758\pi$
$439$	32.8874	1.56963	0.784814	+	0.619731i	$0.212758\pi$
$440$	2.22069	0.105867
$441$	19.3453	0.921207
$442$	−37.2490	−1.77175
$443$	14.8185	0.704049	0.352025	−	0.935991i	$-0.385493\pi$
$443$	14.8185	0.704049	0.352025	+	0.935991i	$0.385493\pi$
$444$	−1.00000	−0.0474579
$445$	−2.27649	−0.107916
$446$	13.1692	0.623578
$447$	−12.6720	−0.599364
$448$	5.13277	0.242501
$449$	9.22882	0.435535	0.217767	−	0.976001i	$-0.430123\pi$
$449$	9.22882	0.435535	0.217767	+	0.976001i	$0.430123\pi$
$450$	1.00000	0.0471405
$451$	−2.29204	−0.107928
$452$	−0.702331	−0.0330348
$453$	10.5420	0.495308
$454$	5.57946	0.261857
$455$	−33.9086	−1.58966
$456$	−7.51836	−0.352080
$457$	−36.4753	−1.70624	−0.853121	−	0.521713i	$-0.825293\pi$
$457$	−36.4753	−1.70624	−0.853121	+	0.521713i	$0.825293\pi$
$458$	−1.75990	−0.0822348
$459$	5.63841	0.263179
$460$	−6.10064	−0.284444
$461$	26.6642	1.24188	0.620938	−	0.783860i	$-0.286752\pi$
$461$	26.6642	1.24188	0.620938	+	0.783860i	$0.286752\pi$
$462$	11.3983	0.530298
$463$	6.25249	0.290578	0.145289	−	0.989389i	$-0.453589\pi$
$463$	6.25249	0.290578	0.145289	+	0.989389i	$0.453589\pi$
$464$	−7.29767	−0.338786
$465$	−0.967873	−0.0448841
$466$	−6.07664	−0.281495
$467$	16.1748	0.748480	0.374240	−	0.927332i	$-0.377904\pi$
$467$	16.1748	0.748480	0.374240	+	0.927332i	$0.377904\pi$
$468$	−6.60629	−0.305376
$469$	7.67020	0.354177
$470$	−5.85911	−0.270260
$471$	−15.4990	−0.714154
$472$	−10.2655	−0.472510
$473$	11.7645	0.540932
$474$	4.00000	0.183726
$475$	−7.51836	−0.344966
$476$	28.9407	1.32649
$477$	−9.63841	−0.441313
$478$	13.9403	0.637617
$479$	7.72351	0.352896	0.176448	−	0.984310i	$-0.443539\pi$
$479$	7.72351	0.352896	0.176448	+	0.984310i	$0.443539\pi$
$480$	1.00000	0.0456435
$481$	6.60629	0.301221
$482$	−3.89406	−0.177369
$483$	−31.3132	−1.42480
$484$	−6.06852	−0.275842
$485$	17.5982	0.799091
$486$	1.00000	0.0453609
$487$	35.8429	1.62420	0.812098	−	0.583522i	$-0.198326\pi$
$487$	35.8429	1.62420	0.812098	+	0.583522i	$0.198326\pi$
$488$	6.32134	0.286154
$489$	−4.12149	−0.186380
$490$	19.3453	0.873934
$491$	2.74718	0.123978	0.0619892	−	0.998077i	$-0.480256\pi$
$491$	2.74718	0.123978	0.0619892	+	0.998077i	$0.480256\pi$
$492$	−1.03213	−0.0465319
$493$	−41.1473	−1.85318
$494$	49.6685	2.23469
$495$	2.22069	0.0998128
$496$	−0.967873	−0.0434588
$497$	1.69277	0.0759310
$498$	9.04767	0.405436
$499$	−3.07698	−0.137744	−0.0688722	−	0.997625i	$-0.521940\pi$
$499$	−3.07698	−0.137744	−0.0688722	+	0.997625i	$0.521940\pi$
$500$	1.00000	0.0447214
$501$	21.9474	0.980536
$502$	20.9308	0.934187
$503$	8.88278	0.396063	0.198032	−	0.980196i	$-0.436545\pi$
$503$	8.88278	0.396063	0.198032	+	0.980196i	$0.436545\pi$
$504$	5.13277	0.228632
$505$	7.61901	0.339041
$506$	−13.5477	−0.602267
$507$	30.6430	1.36090
$508$	−19.3132	−0.856885
$509$	2.32836	0.103203	0.0516013	−	0.998668i	$-0.483568\pi$
$509$	2.32836	0.103203	0.0516013	+	0.998668i	$0.483568\pi$
$510$	5.63841	0.249673
$511$	66.0682	2.92268
$512$	1.00000	0.0441942
$513$	−7.51836	−0.331944
$514$	−4.43044	−0.195418
$515$	5.85911	0.258183
$516$	5.29767	0.233217
$517$	−13.0113	−0.572236
$518$	−5.13277	−0.225521
$519$	−0.425841	−0.0186923
$520$	−6.60629	−0.289705
$521$	−26.3344	−1.15373	−0.576865	−	0.816839i	$-0.695724\pi$
$521$	−26.3344	−1.15373	−0.576865	+	0.816839i	$0.695724\pi$
$522$	−7.29767	−0.319410
$523$	10.9887	0.480503	0.240252	−	0.970711i	$-0.422770\pi$
$523$	10.9887	0.480503	0.240252	+	0.970711i	$0.422770\pi$
$524$	−18.5953	−0.812341
$525$	5.13277	0.224013
$526$	4.20975	0.183554
$527$	−5.45727	−0.237722
$528$	2.22069	0.0966433
$529$	14.2179	0.618168
$530$	−9.63841	−0.418666
$531$	−10.2655	−0.445487
$532$	−38.5900	−1.67309
$533$	6.81852	0.295343
$534$	−2.27649	−0.0985134
$535$	5.65926	0.244671
$536$	1.49436	0.0645465
$537$	−17.5424	−0.757009
$538$	12.5071	0.539219
$539$	42.9601	1.85042
$540$	1.00000	0.0430331
$541$	−6.61934	−0.284588	−0.142294	−	0.989824i	$-0.545448\pi$
$541$	−6.61934	−0.284588	−0.142294	+	0.989824i	$0.545448\pi$
$542$	−6.70693	−0.288087
$543$	18.5311	0.795245
$544$	5.63841	0.241745
$545$	−3.16772	−0.135690
$546$	−33.9086	−1.45115
$547$	−23.1801	−0.991110	−0.495555	−	0.868577i	$-0.665035\pi$
$547$	−23.1801	−0.991110	−0.495555	+	0.868577i	$0.665035\pi$
$548$	−19.5074	−0.833316
$549$	6.32134	0.269788
$550$	2.22069	0.0946907
$551$	54.8665	2.33739
$552$	−6.10064	−0.259661
$553$	20.5311	0.873071
$554$	−27.0477	−1.14915
$555$	−1.00000	−0.0424476
$556$	10.9036	0.462417
$557$	11.3411	0.480537	0.240268	−	0.970706i	$-0.422765\pi$
$557$	11.3411	0.480537	0.240268	+	0.970706i	$0.422765\pi$
$558$	−0.967873	−0.0409734
$559$	−34.9979	−1.48025
$560$	5.13277	0.216899
$561$	12.5212	0.528645
$562$	−1.39371	−0.0587903
$563$	33.3705	1.40640	0.703198	−	0.710994i	$-0.251755\pi$
$563$	33.3705	1.40640	0.703198	+	0.710994i	$0.251755\pi$
$564$	−5.85911	−0.246713
$565$	−0.702331	−0.0295473
$566$	−15.3132	−0.643663
$567$	5.13277	0.215556
$568$	0.329796	0.0138379
$569$	−0.500343	−0.0209755	−0.0104877	−	0.999945i	$-0.503338\pi$
$569$	−0.500343	−0.0209755	−0.0104877	+	0.999945i	$0.503338\pi$
$570$	−7.51836	−0.314910
$571$	27.5463	1.15278	0.576388	−	0.817176i	$-0.304462\pi$
$571$	27.5463	1.15278	0.576388	+	0.817176i	$0.304462\pi$
$572$	−14.6705	−0.613406
$573$	16.1695	0.675490
$574$	−5.29767	−0.221120
$575$	−6.10064	−0.254414
$576$	1.00000	0.0416667
$577$	12.3902	0.515810	0.257905	−	0.966170i	$-0.416968\pi$
$577$	12.3902	0.515810	0.257905	+	0.966170i	$0.416968\pi$
$578$	14.7917	0.615253
$579$	−11.8591	−0.492848
$580$	−7.29767	−0.303019
$581$	46.4396	1.92664
$582$	17.5982	0.729467
$583$	−21.4040	−0.886462
$584$	12.8718	0.532640
$585$	−6.60629	−0.273136
$586$	−12.8672	−0.531540
$587$	0.808273	0.0333610	0.0166805	−	0.999861i	$-0.494690\pi$
$587$	0.808273	0.0333610	0.0166805	+	0.999861i	$0.494690\pi$
$588$	19.3453	0.797789
$589$	7.27682	0.299836
$590$	−10.2655	−0.422626
$591$	0.100645	0.00413998
$592$	−1.00000	−0.0410997
$593$	−24.4121	−1.00248	−0.501242	−	0.865307i	$-0.667123\pi$
$593$	−24.4121	−1.00248	−0.501242	+	0.865307i	$0.667123\pi$
$594$	2.22069	0.0911162
$595$	28.9407	1.18645
$596$	−12.6720	−0.519065
$597$	−2.70693	−0.110787
$598$	40.3026	1.64810
$599$	−29.3440	−1.19896	−0.599481	−	0.800389i	$-0.704626\pi$
$599$	−29.3440	−1.19896	−0.599481	+	0.800389i	$0.704626\pi$
$600$	1.00000	0.0408248
$601$	−9.55791	−0.389875	−0.194938	−	0.980816i	$-0.562450\pi$
$601$	−9.55791	−0.389875	−0.194938	+	0.980816i	$0.562450\pi$
$602$	27.1917	1.10825
$603$	1.49436	0.0608550
$604$	10.5420	0.428949
$605$	−6.06852	−0.246720
$606$	7.61901	0.309501
$607$	−31.4912	−1.27819	−0.639094	−	0.769129i	$-0.720690\pi$
$607$	−31.4912	−1.27819	−0.639094	+	0.769129i	$0.720690\pi$
$608$	−7.51836	−0.304910
$609$	−37.4573	−1.51785
$610$	6.32134	0.255944
$611$	38.7069	1.56591
$612$	5.63841	0.227919
$613$	6.41489	0.259095	0.129548	−	0.991573i	$-0.458648\pi$
$613$	6.41489	0.259095	0.129548	+	0.991573i	$0.458648\pi$
$614$	−4.08970	−0.165047
$615$	−1.03213	−0.0416194
$616$	11.3983	0.459251
$617$	−38.8153	−1.56265	−0.781323	−	0.624127i	$-0.785455\pi$
$617$	−38.8153	−1.56265	−0.781323	+	0.624127i	$0.785455\pi$
$618$	5.85911	0.235688
$619$	−0.00460032	−0.000184902 0	−9.24512e−5	−	1.00000i	$-0.500029\pi$
$619$	−0.00460032	−0.000184902 0	−9.24512e−5		1.00000i	$0.500029\pi$
$620$	−0.967873	−0.0388707
$621$	−6.10064	−0.244810
$622$	−10.3090	−0.413351
$623$	−11.6847	−0.468138
$624$	−6.60629	−0.264463
$625$	1.00000	0.0400000
$626$	−2.64653	−0.105777
$627$	−16.6960	−0.666773
$628$	−15.4990	−0.618476
$629$	−5.63841	−0.224818
$630$	5.13277	0.204495
$631$	34.5999	1.37740	0.688701	−	0.725046i	$-0.258181\pi$
$631$	34.5999	1.37740	0.688701	+	0.725046i	$0.258181\pi$
$632$	4.00000	0.159111
$633$	11.8033	0.469139
$634$	−8.06885	−0.320455
$635$	−19.3132	−0.766422
$636$	−9.63841	−0.382188
$637$	−127.801	−5.06365
$638$	−16.2059	−0.641597
$639$	0.329796	0.0130465
$640$	1.00000	0.0395285
$641$	−40.8711	−1.61431	−0.807156	−	0.590338i	$-0.798995\pi$
$641$	−40.8711	−1.61431	−0.807156	+	0.590338i	$0.798995\pi$
$642$	5.65926	0.223353
$643$	11.4788	0.452680	0.226340	−	0.974048i	$-0.427324\pi$
$643$	11.4788	0.452680	0.226340	+	0.974048i	$0.427324\pi$
$644$	−31.3132	−1.23391
$645$	5.29767	0.208596
$646$	−42.3916	−1.66788
$647$	−17.7490	−0.697783	−0.348892	−	0.937163i	$-0.613442\pi$
$647$	−17.7490	−0.697783	−0.348892	+	0.937163i	$0.613442\pi$
$648$	1.00000	0.0392837
$649$	−22.7966	−0.894846
$650$	−6.60629	−0.259120
$651$	−4.96787	−0.194706
$652$	−4.12149	−0.161410
$653$	21.2768	0.832626	0.416313	−	0.909221i	$-0.363322\pi$
$653$	21.2768	0.832626	0.416313	+	0.909221i	$0.363322\pi$
$654$	−3.16772	−0.123868
$655$	−18.5953	−0.726580
$656$	−1.03213	−0.0402978
$657$	12.8718	0.502178
$658$	−30.0735	−1.17239
$659$	23.5548	0.917563	0.458781	−	0.888549i	$-0.348286\pi$
$659$	23.5548	0.917563	0.458781	+	0.888549i	$0.348286\pi$
$660$	2.22069	0.0864404
$661$	1.34357	0.0522587	0.0261294	−	0.999659i	$-0.491682\pi$
$661$	1.34357	0.0522587	0.0261294	+	0.999659i	$0.491682\pi$
$662$	19.6833	0.765012
$663$	−37.2490	−1.44663
$664$	9.04767	0.351118
$665$	−38.5900	−1.49646
$666$	−1.00000	−0.0387492
$667$	44.5205	1.72384
$668$	21.9474	0.849169
$669$	13.1692	0.509149
$670$	1.49436	0.0577321
$671$	14.0378	0.541922
$672$	5.13277	0.198001
$673$	17.5562	0.676742	0.338371	−	0.941013i	$-0.390124\pi$
$673$	17.5562	0.676742	0.338371	+	0.941013i	$0.390124\pi$
$674$	−23.4891	−0.904765
$675$	1.00000	0.0384900
$676$	30.6430	1.17858
$677$	−19.2073	−0.738196	−0.369098	−	0.929391i	$-0.620333\pi$
$677$	−19.2073	−0.738196	−0.369098	+	0.929391i	$0.620333\pi$
$678$	−0.702331	−0.0269728
$679$	90.3274	3.46645
$680$	5.63841	0.216223
$681$	5.57946	0.213805
$682$	−2.14935	−0.0823029
$683$	−34.7532	−1.32980	−0.664898	−	0.746935i	$-0.731525\pi$
$683$	−34.7532	−1.32980	−0.664898	+	0.746935i	$0.731525\pi$
$684$	−7.51836	−0.287472
$685$	−19.5074	−0.745340
$686$	63.3658	2.41932
$687$	−1.75990	−0.0671445
$688$	5.29767	0.201972
$689$	63.6741	2.42579
$690$	−6.10064	−0.232248
$691$	24.3344	0.925724	0.462862	−	0.886430i	$-0.346823\pi$
$691$	24.3344	0.925724	0.462862	+	0.886430i	$0.346823\pi$
$692$	−0.425841	−0.0161880
$693$	11.3983	0.432986
$694$	18.7069	0.710105
$695$	10.9036	0.413598
$696$	−7.29767	−0.276617
$697$	−5.81955	−0.220431
$698$	16.1123	0.609858
$699$	−6.07664	−0.229840
$700$	5.13277	0.194001
$701$	−8.81354	−0.332883	−0.166441	−	0.986051i	$-0.553228\pi$
$701$	−8.81354	−0.332883	−0.166441	+	0.986051i	$0.553228\pi$
$702$	−6.60629	−0.249338
$703$	7.51836	0.283560
$704$	2.22069	0.0836956
$705$	−5.85911	−0.220667
$706$	2.37320	0.0893167
$707$	39.1066	1.47076
$708$	−10.2655	−0.385803
$709$	−9.07238	−0.340720	−0.170360	−	0.985382i	$-0.554493\pi$
$709$	−9.07238	−0.340720	−0.170360	+	0.985382i	$0.554493\pi$
$710$	0.329796	0.0123770
$711$	4.00000	0.150012
$712$	−2.27649	−0.0853151
$713$	5.90465	0.221131
$714$	28.9407	1.08308
$715$	−14.6705	−0.548647
$716$	−17.5424	−0.655589
$717$	13.9403	0.520612
$718$	−18.5953	−0.693972
$719$	22.8665	0.852778	0.426389	−	0.904540i	$-0.359786\pi$
$719$	22.8665	0.852778	0.426389	+	0.904540i	$0.359786\pi$
$720$	1.00000	0.0372678
$721$	30.0735	1.11999
$722$	37.5258	1.39657
$723$	−3.89406	−0.144822
$724$	18.5311	0.688702
$725$	−7.29767	−0.271029
$726$	−6.06852	−0.225224
$727$	−2.86407	−0.106222	−0.0531112	−	0.998589i	$-0.516914\pi$
$727$	−2.86407	−0.106222	−0.0531112	+	0.998589i	$0.516914\pi$
$728$	−33.9086	−1.25673
$729$	1.00000	0.0370370
$730$	12.8718	0.476408
$731$	29.8704	1.10480
$732$	6.32134	0.233643
$733$	−21.6360	−0.799144	−0.399572	−	0.916702i	$-0.630841\pi$
$733$	−21.6360	−0.799144	−0.399572	+	0.916702i	$0.630841\pi$
$734$	−29.9520	−1.10555
$735$	19.3453	0.713564
$736$	−6.10064	−0.224873
$737$	3.31851	0.122239
$738$	−1.03213	−0.0379931
$739$	16.7278	0.615341	0.307671	−	0.951493i	$-0.400451\pi$
$739$	16.7278	0.615341	0.307671	+	0.951493i	$0.400451\pi$
$740$	−1.00000	−0.0367607
$741$	49.6685	1.82462
$742$	−49.4718	−1.81617
$743$	−21.6624	−0.794717	−0.397358	−	0.917663i	$-0.630073\pi$
$743$	−21.6624	−0.794717	−0.397358	+	0.917663i	$0.630073\pi$
$744$	−0.967873	−0.0354840
$745$	−12.6720	−0.464265
$746$	−6.00000	−0.219676
$747$	9.04767	0.331037
$748$	12.5212	0.457820
$749$	29.0477	1.06138
$750$	1.00000	0.0365148
$751$	24.8129	0.905435	0.452717	−	0.891654i	$-0.350455\pi$
$751$	24.8129	0.905435	0.452717	+	0.891654i	$0.350455\pi$
$752$	−5.85911	−0.213660
$753$	20.9308	0.762760
$754$	48.2105	1.75572
$755$	10.5420	0.383664
$756$	5.13277	0.186677
$757$	1.97281	0.0717030	0.0358515	−	0.999357i	$-0.488586\pi$
$757$	1.97281	0.0717030	0.0358515	+	0.999357i	$0.488586\pi$
$758$	23.3185	0.846967
$759$	−13.5477	−0.491749
$760$	−7.51836	−0.272720
$761$	25.4735	0.923414	0.461707	−	0.887032i	$-0.347237\pi$
$761$	25.4735	0.923414	0.461707	+	0.887032i	$0.347237\pi$
$762$	−19.3132	−0.699644
$763$	−16.2592	−0.588622
$764$	16.1695	0.584992
$765$	5.63841	0.203857
$766$	−16.6063	−0.600009
$767$	67.8171	2.44873
$768$	1.00000	0.0360844
$769$	−41.9675	−1.51339	−0.756694	−	0.653770i	$-0.773187\pi$
$769$	−41.9675	−1.51339	−0.756694	+	0.653770i	$0.773187\pi$
$770$	11.3983	0.410767
$771$	−4.43044	−0.159558
$772$	−11.8591	−0.426819
$773$	46.0410	1.65598	0.827990	−	0.560743i	$-0.189485\pi$
$773$	46.0410	1.65598	0.827990	+	0.560743i	$0.189485\pi$
$774$	5.29767	0.190421
$775$	−0.967873	−0.0347670
$776$	17.5982	0.631737
$777$	−5.13277	−0.184137
$778$	15.5795	0.558551
$779$	7.75990	0.278027
$780$	−6.60629	−0.236543
$781$	0.732376	0.0262065
$782$	−34.3980	−1.23007
$783$	−7.29767	−0.260797
$784$	19.3453	0.690905
$785$	−15.4990	−0.553182
$786$	−18.5953	−0.663274
$787$	−8.04801	−0.286881	−0.143440	−	0.989659i	$-0.545816\pi$
$787$	−8.04801	−0.286881	−0.143440	+	0.989659i	$0.545816\pi$
$788$	0.100645	0.00358533
$789$	4.20975	0.149871
$790$	4.00000	0.142314
$791$	−3.60490	−0.128176
$792$	2.22069	0.0789089
$793$	−41.7606	−1.48296
$794$	−23.2126	−0.823783
$795$	−9.63841	−0.341839
$796$	−2.70693	−0.0959446
$797$	−26.2662	−0.930397	−0.465198	−	0.885206i	$-0.654017\pi$
$797$	−26.2662	−0.930397	−0.465198	+	0.885206i	$0.654017\pi$
$798$	−38.5900	−1.36607
$799$	−33.0361	−1.16873
$800$	1.00000	0.0353553
$801$	−2.27649	−0.0804358
$802$	5.72351	0.202104
$803$	28.5844	1.00872
$804$	1.49436	0.0527020
$805$	−31.3132	−1.10365
$806$	6.39405	0.225221
$807$	12.5071	0.440270
$808$	7.61901	0.268036
$809$	13.3301	0.468662	0.234331	−	0.972157i	$-0.424710\pi$
$809$	13.3301	0.468662	0.234331	+	0.972157i	$0.424710\pi$
$810$	1.00000	0.0351364
$811$	−30.4251	−1.06837	−0.534186	−	0.845367i	$-0.679382\pi$
$811$	−30.4251	−1.06837	−0.534186	+	0.845367i	$0.679382\pi$
$812$	−37.4573	−1.31449
$813$	−6.70693	−0.235222
$814$	−2.22069	−0.0778353
$815$	−4.12149	−0.144369
$816$	5.63841	0.197384
$817$	−39.8298	−1.39347
$818$	28.0254	0.979887
$819$	−33.9086	−1.18486
$820$	−1.03213	−0.0360434
$821$	−26.2895	−0.917512	−0.458756	−	0.888562i	$-0.651705\pi$
$821$	−26.2895	−0.917512	−0.458756	+	0.888562i	$0.651705\pi$
$822$	−19.5074	−0.680399
$823$	24.4050	0.850705	0.425352	−	0.905028i	$-0.360150\pi$
$823$	24.4050	0.850705	0.425352	+	0.905028i	$0.360150\pi$
$824$	5.85911	0.204112
$825$	2.22069	0.0773146
$826$	−52.6907	−1.83334
$827$	−37.5887	−1.30709	−0.653543	−	0.756890i	$-0.726718\pi$
$827$	−37.5887	−1.30709	−0.653543	+	0.756890i	$0.726718\pi$
$828$	−6.10064	−0.212012
$829$	36.4481	1.26589	0.632947	−	0.774195i	$-0.281845\pi$
$829$	36.4481	1.26589	0.632947	+	0.774195i	$0.281845\pi$
$830$	9.04767	0.314049
$831$	−27.0477	−0.938273
$832$	−6.60629	−0.229032
$833$	109.077	3.77929
$834$	10.9036	0.377561
$835$	21.9474	0.759520
$836$	−16.6960	−0.577443
$837$	−0.967873	−0.0334546
$838$	16.2415	0.561055
$839$	−43.3277	−1.49584	−0.747919	−	0.663790i	$-0.768947\pi$
$839$	−43.3277	−1.49584	−0.747919	+	0.663790i	$0.768947\pi$
$840$	5.13277	0.177097
$841$	24.2560	0.836413
$842$	6.03495	0.207978
$843$	−1.39371	−0.0480021
$844$	11.8033	0.406287
$845$	30.6430	1.05415
$846$	−5.85911	−0.201440
$847$	−31.1483	−1.07027
$848$	−9.63841	−0.330984
$849$	−15.3132	−0.525548
$850$	5.63841	0.193396
$851$	6.10064	0.209127
$852$	0.329796	0.0112986
$853$	17.6430	0.604085	0.302043	−	0.953294i	$-0.402332\pi$
$853$	17.6430	0.604085	0.302043	+	0.953294i	$0.402332\pi$
$854$	32.4460	1.11028
$855$	−7.51836	−0.257123
$856$	5.65926	0.193429
$857$	35.6222	1.21683	0.608415	−	0.793619i	$-0.291806\pi$
$857$	35.6222	1.21683	0.608415	+	0.793619i	$0.291806\pi$
$858$	−14.6705	−0.500844
$859$	−5.49292	−0.187416	−0.0937080	−	0.995600i	$-0.529872\pi$
$859$	−5.49292	−0.187416	−0.0937080	+	0.995600i	$0.529872\pi$
$860$	5.29767	0.180649
$861$	−5.29767	−0.180544
$862$	−33.2924	−1.13394
$863$	−1.12501	−0.0382958	−0.0191479	−	0.999817i	$-0.506095\pi$
$863$	−1.12501	−0.0382958	−0.0191479	+	0.999817i	$0.506095\pi$
$864$	1.00000	0.0340207
$865$	−0.425841	−0.0144790
$866$	8.67054	0.294637
$867$	14.7917	0.502352
$868$	−4.96787	−0.168621
$869$	8.88278	0.301328
$870$	−7.29767	−0.247414
$871$	−9.87216	−0.334506
$872$	−3.16772	−0.107273
$873$	17.5982	0.595608
$874$	45.8669	1.55147
$875$	5.13277	0.173519
$876$	12.8718	0.434899
$877$	31.6367	1.06829	0.534147	−	0.845392i	$-0.320633\pi$
$877$	31.6367	1.06829	0.534147	+	0.845392i	$0.320633\pi$
$878$	32.8874	1.10990
$879$	−12.8672	−0.434001
$880$	2.22069	0.0748596
$881$	−24.8012	−0.835575	−0.417787	−	0.908545i	$-0.637194\pi$
$881$	−24.8012	−0.835575	−0.417787	+	0.908545i	$0.637194\pi$
$882$	19.3453	0.651392
$883$	−27.7980	−0.935478	−0.467739	−	0.883867i	$-0.654931\pi$
$883$	−27.7980	−0.935478	−0.467739	+	0.883867i	$0.654931\pi$
$884$	−37.2490	−1.25282
$885$	−10.2655	−0.345072
$886$	14.8185	0.497838
$887$	−28.5226	−0.957696	−0.478848	−	0.877898i	$-0.658946\pi$
$887$	−28.5226	−0.957696	−0.478848	+	0.877898i	$0.658946\pi$
$888$	−1.00000	−0.0335578
$889$	−99.1303	−3.32472
$890$	−2.27649	−0.0763081
$891$	2.22069	0.0743960
$892$	13.1692	0.440936
$893$	44.0509	1.47411
$894$	−12.6720	−0.423814
$895$	−17.5424	−0.586377
$896$	5.13277	0.171474
$897$	40.3026	1.34566
$898$	9.22882	0.307970
$899$	7.06322	0.235572
$900$	1.00000	0.0333333
$901$	−54.3453	−1.81051
$902$	−2.29204	−0.0763165
$903$	27.1917	0.904884
$904$	−0.702331	−0.0233592
$905$	18.5311	0.615994
$906$	10.5420	0.350236
$907$	41.1854	1.36754	0.683769	−	0.729698i	$-0.260340\pi$
$907$	41.1854	1.36754	0.683769	+	0.729698i	$0.260340\pi$
$908$	5.57946	0.185161
$909$	7.61901	0.252707
$910$	−33.9086	−1.12406
$911$	21.3440	0.707157	0.353578	−	0.935405i	$-0.384965\pi$
$911$	21.3440	0.707157	0.353578	+	0.935405i	$0.384965\pi$
$912$	−7.51836	−0.248958
$913$	20.0921	0.664952
$914$	−36.4753	−1.20650
$915$	6.32134	0.208977
$916$	−1.75990	−0.0581488
$917$	−95.4456	−3.15189
$918$	5.63841	0.186095
$919$	36.9089	1.21751	0.608756	−	0.793358i	$-0.291669\pi$
$919$	36.9089	1.21751	0.608756	+	0.793358i	$0.291669\pi$
$920$	−6.10064	−0.201132
$921$	−4.08970	−0.134760
$922$	26.6642	0.878138
$923$	−2.17873	−0.0717137
$924$	11.3983	0.374977
$925$	−1.00000	−0.0328798
$926$	6.25249	0.205469
$927$	5.85911	0.192438
$928$	−7.29767	−0.239558
$929$	21.0350	0.690136	0.345068	−	0.938578i	$-0.387856\pi$
$929$	21.0350	0.690136	0.345068	+	0.938578i	$0.387856\pi$
$930$	−0.967873	−0.0317378
$931$	−145.445	−4.76678
$932$	−6.07664	−0.199047
$933$	−10.3090	−0.337500
$934$	16.1748	0.529255
$935$	12.5212	0.409487
$936$	−6.60629	−0.215933
$937$	9.67652	0.316118	0.158059	−	0.987430i	$-0.449476\pi$
$937$	9.67652	0.316118	0.158059	+	0.987430i	$0.449476\pi$
$938$	7.67020	0.250441
$939$	−2.64653	−0.0863664
$940$	−5.85911	−0.191103
$941$	−48.1332	−1.56910	−0.784548	−	0.620068i	$-0.787105\pi$
$941$	−48.1332	−1.56910	−0.784548	+	0.620068i	$0.787105\pi$
$942$	−15.4990	−0.504983
$943$	6.29664	0.205047
$944$	−10.2655	−0.334115
$945$	5.13277	0.166969
$946$	11.7645	0.382497
$947$	−17.7871	−0.578002	−0.289001	−	0.957329i	$-0.593323\pi$
$947$	−17.7871	−0.578002	−0.289001	+	0.957329i	$0.593323\pi$
$948$	4.00000	0.129914
$949$	−85.0350	−2.76035
$950$	−7.51836	−0.243928
$951$	−8.06885	−0.261650
$952$	28.9407	0.937973
$953$	30.0442	0.973226	0.486613	−	0.873618i	$-0.338232\pi$
$953$	30.0442	0.973226	0.486613	+	0.873618i	$0.338232\pi$
$954$	−9.63841	−0.312055
$955$	16.1695	0.523233
$956$	13.9403	0.450863
$957$	−16.2059	−0.523862
$958$	7.72351	0.249535
$959$	−100.127	−3.23327
$960$	1.00000	0.0322749
$961$	−30.0632	−0.969781
$962$	6.60629	0.212995
$963$	5.65926	0.182367
$964$	−3.89406	−0.125419
$965$	−11.8591	−0.381758
$966$	−31.3132	−1.00749
$967$	15.7052	0.505044	0.252522	−	0.967591i	$-0.418740\pi$
$967$	15.7052	0.505044	0.252522	+	0.967591i	$0.418740\pi$
$968$	−6.06852	−0.195050
$969$	−42.3916	−1.36182
$970$	17.5982	0.565043
$971$	36.8693	1.18319	0.591597	−	0.806234i	$-0.298498\pi$
$971$	36.8693	1.18319	0.591597	+	0.806234i	$0.298498\pi$
$972$	1.00000	0.0320750
$973$	55.9658	1.79418
$974$	35.8429	1.14848
$975$	−6.60629	−0.211570
$976$	6.32134	0.202341
$977$	31.8404	1.01866	0.509332	−	0.860570i	$-0.329893\pi$
$977$	31.8404	1.01866	0.509332	+	0.860570i	$0.329893\pi$
$978$	−4.12149	−0.131791
$979$	−5.05539	−0.161571
$980$	19.3453	0.617964
$981$	−3.16772	−0.101138
$982$	2.74718	0.0876660
$983$	11.8708	0.378618	0.189309	−	0.981918i	$-0.439375\pi$
$983$	11.8708	0.378618	0.189309	+	0.981918i	$0.439375\pi$
$984$	−1.03213	−0.0329030
$985$	0.100645	0.00320682
$986$	−41.1473	−1.31040
$987$	−30.0735	−0.957249
$988$	49.6685	1.58016
$989$	−32.3192	−1.02769
$990$	2.22069	0.0705783
$991$	−13.9990	−0.444691	−0.222346	−	0.974968i	$-0.571371\pi$
$991$	−13.9990	−0.444691	−0.222346	+	0.974968i	$0.571371\pi$
$992$	−0.967873	−0.0307300
$993$	19.6833	0.624629
$994$	1.69277	0.0536913
$995$	−2.70693	−0.0858155
$996$	9.04767	0.286687
$997$	−26.4050	−0.836255	−0.418127	−	0.908388i	$-0.637313\pi$
$997$	−26.4050	−0.836255	−0.418127	+	0.908388i	$0.637313\pi$
$998$	−3.07698	−0.0974000
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.a.s.1.4	✓	4
3.2	odd	2		3330.2.a.bj.1.4		4
4.3	odd	2		8880.2.a.cg.1.1		4
5.4	even	2		5550.2.a.cj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.s.1.4	✓	4	1.1	even	1	trivial
3330.2.a.bj.1.4		4	3.2	odd	2
5550.2.a.cj.1.1		4	5.4	even	2
8880.2.a.cg.1.1		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.22069 q^{11} +1.00000 q^{12} -6.60629 q^{13} +5.13277 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.63841 q^{17} +1.00000 q^{18} -7.51836 q^{19} +1.00000 q^{20} +5.13277 q^{21} +2.22069 q^{22} -6.10064 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.60629 q^{26} +1.00000 q^{27} +5.13277 q^{28} -7.29767 q^{29} +1.00000 q^{30} -0.967873 q^{31} +1.00000 q^{32} +2.22069 q^{33} +5.63841 q^{34} +5.13277 q^{35} +1.00000 q^{36} -1.00000 q^{37} -7.51836 q^{38} -6.60629 q^{39} +1.00000 q^{40} -1.03213 q^{41} +5.13277 q^{42} +5.29767 q^{43} +2.22069 q^{44} +1.00000 q^{45} -6.10064 q^{46} -5.85911 q^{47} +1.00000 q^{48} +19.3453 q^{49} +1.00000 q^{50} +5.63841 q^{51} -6.60629 q^{52} -9.63841 q^{53} +1.00000 q^{54} +2.22069 q^{55} +5.13277 q^{56} -7.51836 q^{57} -7.29767 q^{58} -10.2655 q^{59} +1.00000 q^{60} +6.32134 q^{61} -0.967873 q^{62} +5.13277 q^{63} +1.00000 q^{64} -6.60629 q^{65} +2.22069 q^{66} +1.49436 q^{67} +5.63841 q^{68} -6.10064 q^{69} +5.13277 q^{70} +0.329796 q^{71} +1.00000 q^{72} +12.8718 q^{73} -1.00000 q^{74} +1.00000 q^{75} -7.51836 q^{76} +11.3983 q^{77} -6.60629 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.03213 q^{82} +9.04767 q^{83} +5.13277 q^{84} +5.63841 q^{85} +5.29767 q^{86} -7.29767 q^{87} +2.22069 q^{88} -2.27649 q^{89} +1.00000 q^{90} -33.9086 q^{91} -6.10064 q^{92} -0.967873 q^{93} -5.85911 q^{94} -7.51836 q^{95} +1.00000 q^{96} +17.5982 q^{97} +19.3453 q^{98} +2.22069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} + 3 q^{19} + 4 q^{20} + 4 q^{21} + 2 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} + 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 3 q^{38} - 3 q^{39} + 4 q^{40} - 11 q^{41} + 4 q^{42} - 5 q^{43} + 2 q^{44} + 4 q^{45} - q^{46} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 6 q^{51} - 3 q^{52} - 22 q^{53} + 4 q^{54} + 2 q^{55} + 4 q^{56} + 3 q^{57} - 3 q^{58} - 8 q^{59} + 4 q^{60} - 5 q^{61} + 3 q^{62} + 4 q^{63} + 4 q^{64} - 3 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - q^{69} + 4 q^{70} - 18 q^{71} + 4 q^{72} - 5 q^{73} - 4 q^{74} + 4 q^{75} + 3 q^{76} - 4 q^{77} - 3 q^{78} + 16 q^{79} + 4 q^{80} + 4 q^{81} - 11 q^{82} - q^{83} + 4 q^{84} + 6 q^{85} - 5 q^{86} - 3 q^{87} + 2 q^{88} - 5 q^{89} + 4 q^{90} - 13 q^{91} - q^{92} + 3 q^{93} + 3 q^{95} + 4 q^{96} + 7 q^{97} + 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 + 3 * q^19 + 4 * q^20 + 4 * q^21 + 2 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 + 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 3 * q^38 - 3 * q^39 + 4 * q^40 - 11 * q^41 + 4 * q^42 - 5 * q^43 + 2 * q^44 + 4 * q^45 - q^46 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 6 * q^51 - 3 * q^52 - 22 * q^53 + 4 * q^54 + 2 * q^55 + 4 * q^56 + 3 * q^57 - 3 * q^58 - 8 * q^59 + 4 * q^60 - 5 * q^61 + 3 * q^62 + 4 * q^63 + 4 * q^64 - 3 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - q^69 + 4 * q^70 - 18 * q^71 + 4 * q^72 - 5 * q^73 - 4 * q^74 + 4 * q^75 + 3 * q^76 - 4 * q^77 - 3 * q^78 + 16 * q^79 + 4 * q^80 + 4 * q^81 - 11 * q^82 - q^83 + 4 * q^84 + 6 * q^85 - 5 * q^86 - 3 * q^87 + 2 * q^88 - 5 * q^89 + 4 * q^90 - 13 * q^91 - q^92 + 3 * q^93 + 3 * q^95 + 4 * q^96 + 7 * q^97 + 14 * q^98 + 2 * q^99

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