LMFDB - Embedded newform 6007.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62005 q^{2} +0.737084 q^{3} +4.86469 q^{4} -2.98180 q^{5} -1.93120 q^{6} -0.252259 q^{7} -7.50563 q^{8} -2.45671 q^{9} +O(q^{10})$	\(q-2.62005 q^{2} +0.737084 q^{3} +4.86469 q^{4} -2.98180 q^{5} -1.93120 q^{6} -0.252259 q^{7} -7.50563 q^{8} -2.45671 q^{9} +7.81248 q^{10} -5.71102 q^{11} +3.58568 q^{12} -2.83680 q^{13} +0.660932 q^{14} -2.19784 q^{15} +9.93580 q^{16} +1.75221 q^{17} +6.43671 q^{18} +4.17719 q^{19} -14.5055 q^{20} -0.185936 q^{21} +14.9632 q^{22} +5.74178 q^{23} -5.53229 q^{24} +3.89114 q^{25} +7.43258 q^{26} -4.02205 q^{27} -1.22716 q^{28} -7.49346 q^{29} +5.75846 q^{30} +6.59365 q^{31} -11.0211 q^{32} -4.20950 q^{33} -4.59089 q^{34} +0.752185 q^{35} -11.9511 q^{36} +4.07297 q^{37} -10.9445 q^{38} -2.09096 q^{39} +22.3803 q^{40} -1.45872 q^{41} +0.487163 q^{42} +2.83107 q^{43} -27.7823 q^{44} +7.32541 q^{45} -15.0438 q^{46} -0.677541 q^{47} +7.32352 q^{48} -6.93637 q^{49} -10.1950 q^{50} +1.29153 q^{51} -13.8002 q^{52} +11.0444 q^{53} +10.5380 q^{54} +17.0291 q^{55} +1.89336 q^{56} +3.07894 q^{57} +19.6333 q^{58} +12.6332 q^{59} -10.6918 q^{60} +2.15924 q^{61} -17.2757 q^{62} +0.619726 q^{63} +9.00420 q^{64} +8.45878 q^{65} +11.0291 q^{66} +8.06822 q^{67} +8.52396 q^{68} +4.23218 q^{69} -1.97077 q^{70} +2.75376 q^{71} +18.4391 q^{72} +0.325010 q^{73} -10.6714 q^{74} +2.86810 q^{75} +20.3207 q^{76} +1.44065 q^{77} +5.47844 q^{78} +0.137581 q^{79} -29.6266 q^{80} +4.40553 q^{81} +3.82194 q^{82} -8.90324 q^{83} -0.904520 q^{84} -5.22475 q^{85} -7.41757 q^{86} -5.52331 q^{87} +42.8648 q^{88} -0.906790 q^{89} -19.1930 q^{90} +0.715608 q^{91} +27.9320 q^{92} +4.86008 q^{93} +1.77520 q^{94} -12.4556 q^{95} -8.12346 q^{96} +9.13331 q^{97} +18.1737 q^{98} +14.0303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.62005	−1.85266	−0.926329	−	0.376715i	$-0.877054\pi$
$2$	−2.62005	−1.85266	−0.926329	+	0.376715i	$0.877054\pi$
$3$	0.737084	0.425556	0.212778	−	0.977101i	$-0.431749\pi$
$3$	0.737084	0.425556	0.212778	+	0.977101i	$0.431749\pi$
$4$	4.86469	2.43234
$5$	−2.98180	−1.33350	−0.666751	−	0.745281i	$-0.732316\pi$
$5$	−2.98180	−1.33350	−0.666751	+	0.745281i	$0.732316\pi$
$6$	−1.93120	−0.788410
$7$	−0.252259	−0.0953449	−0.0476724	−	0.998863i	$-0.515180\pi$
$7$	−0.252259	−0.0953449	−0.0476724	+	0.998863i	$0.515180\pi$
$8$	−7.50563	−2.65364
$9$	−2.45671	−0.818902
$10$	7.81248	2.47052
$11$	−5.71102	−1.72194	−0.860968	−	0.508659i	$-0.830141\pi$
$11$	−5.71102	−1.72194	−0.860968	+	0.508659i	$0.830141\pi$
$12$	3.58568	1.03510
$13$	−2.83680	−0.786787	−0.393394	−	0.919370i	$-0.628699\pi$
$13$	−2.83680	−0.786787	−0.393394	+	0.919370i	$0.628699\pi$
$14$	0.660932	0.176641
$15$	−2.19784	−0.567480
$16$	9.93580	2.48395
$17$	1.75221	0.424974	0.212487	−	0.977164i	$-0.431844\pi$
$17$	1.75221	0.424974	0.212487	+	0.977164i	$0.431844\pi$
$18$	6.43671	1.51715
$19$	4.17719	0.958314	0.479157	−	0.877729i	$-0.340942\pi$
$19$	4.17719	0.958314	0.479157	+	0.877729i	$0.340942\pi$
$20$	−14.5055	−3.24353
$21$	−0.185936	−0.0405746
$22$	14.9632	3.19016
$23$	5.74178	1.19724	0.598622	−	0.801032i	$-0.295715\pi$
$23$	5.74178	1.19724	0.598622	+	0.801032i	$0.295715\pi$
$24$	−5.53229	−1.12927
$25$	3.89114	0.778227
$26$	7.43258	1.45765
$27$	−4.02205	−0.774045
$28$	−1.22716	−0.231911
$29$	−7.49346	−1.39150	−0.695750	−	0.718284i	$-0.744928\pi$
$29$	−7.49346	−1.39150	−0.695750	+	0.718284i	$0.744928\pi$
$30$	5.75846	1.05135
$31$	6.59365	1.18426	0.592128	−	0.805844i	$-0.298288\pi$
$31$	6.59365	1.18426	0.592128	+	0.805844i	$0.298288\pi$
$32$	−11.0211	−1.94827
$33$	−4.20950	−0.732780
$34$	−4.59089	−0.787331
$35$	0.752185	0.127143
$36$	−11.9511	−1.99185
$37$	4.07297	0.669591	0.334796	−	0.942291i	$-0.391333\pi$
$37$	4.07297	0.669591	0.334796	+	0.942291i	$0.391333\pi$
$38$	−10.9445	−1.77543
$39$	−2.09096	−0.334822
$40$	22.3803	3.53864
$41$	−1.45872	−0.227814	−0.113907	−	0.993491i	$-0.536337\pi$
$41$	−1.45872	−0.227814	−0.113907	+	0.993491i	$0.536337\pi$
$42$	0.487163	0.0751708
$43$	2.83107	0.431735	0.215867	−	0.976423i	$-0.430742\pi$
$43$	2.83107	0.431735	0.215867	+	0.976423i	$0.430742\pi$
$44$	−27.7823	−4.18834
$45$	7.32541	1.09201
$46$	−15.0438	−2.21808
$47$	−0.677541	−0.0988296	−0.0494148	−	0.998778i	$-0.515736\pi$
$47$	−0.677541	−0.0988296	−0.0494148	+	0.998778i	$0.515736\pi$
$48$	7.32352	1.05706
$49$	−6.93637	−0.990909
$50$	−10.1950	−1.44179
$51$	1.29153	0.180850
$52$	−13.8002	−1.91374
$53$	11.0444	1.51707	0.758534	−	0.651633i	$-0.225916\pi$
$53$	11.0444	1.51707	0.758534	+	0.651633i	$0.225916\pi$
$54$	10.5380	1.43404
$55$	17.0291	2.29621
$56$	1.89336	0.253011
$57$	3.07894	0.407816
$58$	19.6333	2.57798
$59$	12.6332	1.64471	0.822353	−	0.568977i	$-0.192661\pi$
$59$	12.6332	1.64471	0.822353	+	0.568977i	$0.192661\pi$
$60$	−10.6918	−1.38031
$61$	2.15924	0.276462	0.138231	−	0.990400i	$-0.455858\pi$
$61$	2.15924	0.276462	0.138231	+	0.990400i	$0.455858\pi$
$62$	−17.2757	−2.19402
$63$	0.619726	0.0780781
$64$	9.00420	1.12553
$65$	8.45878	1.04918
$66$	11.0291	1.35759
$67$	8.06822	0.985691	0.492845	−	0.870117i	$-0.335957\pi$
$67$	8.06822	0.985691	0.492845	+	0.870117i	$0.335957\pi$
$68$	8.52396	1.03368
$69$	4.23218	0.509494
$70$	−1.97077	−0.235552
$71$	2.75376	0.326811	0.163406	−	0.986559i	$-0.447752\pi$
$71$	2.75376	0.326811	0.163406	+	0.986559i	$0.447752\pi$
$72$	18.4391	2.17307
$73$	0.325010	0.0380395	0.0190198	−	0.999819i	$-0.493945\pi$
$73$	0.325010	0.0380395	0.0190198	+	0.999819i	$0.493945\pi$
$74$	−10.6714	−1.24052
$75$	2.86810	0.331179
$76$	20.3207	2.33095
$77$	1.44065	0.164178
$78$	5.47844	0.620311
$79$	0.137581	0.0154791	0.00773955	−	0.999970i	$-0.497536\pi$
$79$	0.137581	0.0154791	0.00773955	+	0.999970i	$0.497536\pi$
$80$	−29.6266	−3.31235
$81$	4.40553	0.489503
$82$	3.82194	0.422062
$83$	−8.90324	−0.977258	−0.488629	−	0.872492i	$-0.662503\pi$
$83$	−8.90324	−0.977258	−0.488629	+	0.872492i	$0.662503\pi$
$84$	−0.904520	−0.0986913
$85$	−5.22475	−0.566703
$86$	−7.41757	−0.799857
$87$	−5.52331	−0.592161
$88$	42.8648	4.56940
$89$	−0.906790	−0.0961196	−0.0480598	−	0.998844i	$-0.515304\pi$
$89$	−0.906790	−0.0961196	−0.0480598	+	0.998844i	$0.515304\pi$
$90$	−19.1930	−2.02312
$91$	0.715608	0.0750161
$92$	27.9320	2.91211
$93$	4.86008	0.503967
$94$	1.77520	0.183097
$95$	−12.4556	−1.27791
$96$	−8.12346	−0.829097
$97$	9.13331	0.927347	0.463674	−	0.886006i	$-0.346531\pi$
$97$	9.13331	0.927347	0.463674	+	0.886006i	$0.346531\pi$
$98$	18.1737	1.83582
$99$	14.0303	1.41010
$100$	18.9292	1.89292
$101$	−4.49736	−0.447504	−0.223752	−	0.974646i	$-0.571831\pi$
$101$	−4.49736	−0.447504	−0.223752	+	0.974646i	$0.571831\pi$
$102$	−3.38387	−0.335053
$103$	5.85921	0.577325	0.288663	−	0.957431i	$-0.406789\pi$
$103$	5.85921	0.577325	0.288663	+	0.957431i	$0.406789\pi$
$104$	21.2920	2.08785
$105$	0.554424	0.0541063
$106$	−28.9370	−2.81061
$107$	−10.4802	−1.01316	−0.506580	−	0.862193i	$-0.669090\pi$
$107$	−10.4802	−1.01316	−0.506580	+	0.862193i	$0.669090\pi$
$108$	−19.5660	−1.88274
$109$	16.5819	1.58825	0.794127	−	0.607752i	$-0.207929\pi$
$109$	16.5819	1.58825	0.794127	+	0.607752i	$0.207929\pi$
$110$	−44.6172	−4.25408
$111$	3.00212	0.284949
$112$	−2.50639	−0.236832
$113$	−14.3877	−1.35348	−0.676738	−	0.736224i	$-0.736607\pi$
$113$	−14.3877	−1.35348	−0.676738	+	0.736224i	$0.736607\pi$
$114$	−8.06700	−0.755544
$115$	−17.1208	−1.59653
$116$	−36.4533	−3.38461
$117$	6.96919	0.644302
$118$	−33.0998	−3.04708
$119$	−0.442011	−0.0405191
$120$	16.4962	1.50589
$121$	21.6157	1.96506
$122$	−5.65732	−0.512190
$123$	−1.07520	−0.0969478
$124$	32.0761	2.88051
$125$	3.30641	0.295734
$126$	−1.62372	−0.144652
$127$	−21.9149	−1.94463	−0.972315	−	0.233674i	$-0.924925\pi$
$127$	−21.9149	−1.94463	−0.972315	+	0.233674i	$0.924925\pi$
$128$	−1.54936	−0.136946
$129$	2.08674	0.183727
$130$	−22.1625	−1.94378
$131$	0.705954	0.0616795	0.0308397	−	0.999524i	$-0.490182\pi$
$131$	0.705954	0.0616795	0.0308397	+	0.999524i	$0.490182\pi$
$132$	−20.4779	−1.78237
$133$	−1.05373	−0.0913703
$134$	−21.1392	−1.82615
$135$	11.9930	1.03219
$136$	−13.1515	−1.12773
$137$	13.4225	1.14676	0.573380	−	0.819290i	$-0.305632\pi$
$137$	13.4225	1.14676	0.573380	+	0.819290i	$0.305632\pi$
$138$	−11.0885	−0.943919
$139$	−9.59348	−0.813708	−0.406854	−	0.913493i	$-0.633374\pi$
$139$	−9.59348	−0.813708	−0.406854	+	0.913493i	$0.633374\pi$
$140$	3.65915	0.309254
$141$	−0.499405	−0.0420575
$142$	−7.21500	−0.605469
$143$	16.2010	1.35480
$144$	−24.4093	−2.03411
$145$	22.3440	1.85557
$146$	−0.851543	−0.0704742
$147$	−5.11269	−0.421687
$148$	19.8137	1.62868
$149$	6.46143	0.529341	0.264670	−	0.964339i	$-0.414737\pi$
$149$	6.46143	0.529341	0.264670	+	0.964339i	$0.414737\pi$
$150$	−7.51457	−0.613562
$151$	−20.2956	−1.65164	−0.825818	−	0.563937i	$-0.809286\pi$
$151$	−20.2956	−1.65164	−0.825818	+	0.563937i	$0.809286\pi$
$152$	−31.3525	−2.54302
$153$	−4.30467	−0.348012
$154$	−3.77459	−0.304165
$155$	−19.6610	−1.57921
$156$	−10.1719	−0.814402
$157$	−2.98701	−0.238389	−0.119195	−	0.992871i	$-0.538031\pi$
$157$	−2.98701	−0.238389	−0.119195	+	0.992871i	$0.538031\pi$
$158$	−0.360471	−0.0286775
$159$	8.14068	0.645598
$160$	32.8626	2.59802
$161$	−1.44841	−0.114151
$162$	−11.5427	−0.906882
$163$	1.73806	0.136136	0.0680678	−	0.997681i	$-0.478317\pi$
$163$	1.73806	0.136136	0.0680678	+	0.997681i	$0.478317\pi$
$164$	−7.09623	−0.554123
$165$	12.5519	0.977164
$166$	23.3270	1.81052
$167$	−11.6457	−0.901169	−0.450584	−	0.892734i	$-0.648784\pi$
$167$	−11.6457	−0.901169	−0.450584	+	0.892734i	$0.648784\pi$
$168$	1.39557	0.107670
$169$	−4.95255	−0.380966
$170$	13.6891	1.04991
$171$	−10.2621	−0.784765
$172$	13.7723	1.05013
$173$	−7.62890	−0.580015	−0.290007	−	0.957024i	$-0.593658\pi$
$173$	−7.62890	−0.580015	−0.290007	+	0.957024i	$0.593658\pi$
$174$	14.4714	1.09707
$175$	−0.981573	−0.0742000
$176$	−56.7435	−4.27720
$177$	9.31176	0.699915
$178$	2.37584	0.178077
$179$	8.11083	0.606232	0.303116	−	0.952954i	$-0.401973\pi$
$179$	8.11083	0.606232	0.303116	+	0.952954i	$0.401973\pi$
$180$	35.6358	2.65614
$181$	−10.4960	−0.780162	−0.390081	−	0.920781i	$-0.627553\pi$
$181$	−10.4960	−0.780162	−0.390081	+	0.920781i	$0.627553\pi$
$182$	−1.87493	−0.138979
$183$	1.59154	0.117650
$184$	−43.0957	−3.17706
$185$	−12.1448	−0.892901
$186$	−12.7337	−0.933678
$187$	−10.0069	−0.731778
$188$	−3.29603	−0.240387
$189$	1.01460	0.0738012
$190$	32.6342	2.36754
$191$	−23.1341	−1.67393	−0.836964	−	0.547258i	$-0.815672\pi$
$191$	−23.1341	−1.67393	−0.836964	+	0.547258i	$0.815672\pi$
$192$	6.63686	0.478974
$193$	11.8340	0.851832	0.425916	−	0.904763i	$-0.359952\pi$
$193$	11.8340	0.851832	0.425916	+	0.904763i	$0.359952\pi$
$194$	−23.9298	−1.71806
$195$	6.23483	0.446486
$196$	−33.7432	−2.41023
$197$	10.8807	0.775215	0.387607	−	0.921825i	$-0.373302\pi$
$197$	10.8807	0.775215	0.387607	+	0.921825i	$0.373302\pi$
$198$	−36.7601	−2.61243
$199$	12.6531	0.896957	0.448478	−	0.893794i	$-0.351966\pi$
$199$	12.6531	0.896957	0.448478	+	0.893794i	$0.351966\pi$
$200$	−29.2054	−2.06514
$201$	5.94696	0.419466
$202$	11.7833	0.829071
$203$	1.89029	0.132672
$204$	6.28288	0.439889
$205$	4.34962	0.303791
$206$	−15.3515	−1.06959
$207$	−14.1059	−0.980425
$208$	−28.1859	−1.95434
$209$	−23.8560	−1.65016
$210$	−1.45262	−0.100240
$211$	13.6560	0.940118	0.470059	−	0.882635i	$-0.344233\pi$
$211$	13.6560	0.940118	0.470059	+	0.882635i	$0.344233\pi$
$212$	53.7277	3.69003
$213$	2.02975	0.139076
$214$	27.4587	1.87704
$215$	−8.44170	−0.575719
$216$	30.1881	2.05404
$217$	−1.66331	−0.112913
$218$	−43.4454	−2.94249
$219$	0.239560	0.0161879
$220$	82.8413	5.58516
$221$	−4.97068	−0.334364
$222$	−7.86572	−0.527912
$223$	−6.56259	−0.439464	−0.219732	−	0.975560i	$-0.570518\pi$
$223$	−6.56259	−0.439464	−0.219732	+	0.975560i	$0.570518\pi$
$224$	2.78016	0.185757
$225$	−9.55938	−0.637292
$226$	37.6964	2.50753
$227$	−14.9270	−0.990737	−0.495369	−	0.868683i	$-0.664967\pi$
$227$	−14.9270	−0.990737	−0.495369	+	0.868683i	$0.664967\pi$
$228$	14.9781	0.991949
$229$	−9.07405	−0.599630	−0.299815	−	0.953997i	$-0.596925\pi$
$229$	−9.07405	−0.599630	−0.299815	+	0.953997i	$0.596925\pi$
$230$	44.8575	2.95782
$231$	1.06188	0.0698668
$232$	56.2432	3.69254
$233$	2.82670	0.185183	0.0925916	−	0.995704i	$-0.470485\pi$
$233$	2.82670	0.185183	0.0925916	+	0.995704i	$0.470485\pi$
$234$	−18.2597	−1.19367
$235$	2.02029	0.131789
$236$	61.4567	4.00049
$237$	0.101409	0.00658723
$238$	1.15809	0.0750680
$239$	−10.9029	−0.705248	−0.352624	−	0.935765i	$-0.614711\pi$
$239$	−10.9029	−0.705248	−0.352624	+	0.935765i	$0.614711\pi$
$240$	−21.8373	−1.40959
$241$	0.141077	0.00908757	0.00454379	−	0.999990i	$-0.498554\pi$
$241$	0.141077	0.00908757	0.00454379	+	0.999990i	$0.498554\pi$
$242$	−56.6343	−3.64059
$243$	15.3134	0.982355
$244$	10.5040	0.672450
$245$	20.6829	1.32138
$246$	2.81709	0.179611
$247$	−11.8499	−0.753989
$248$	−49.4896	−3.14259
$249$	−6.56244	−0.415878
$250$	−8.66298	−0.547895
$251$	17.6773	1.11578	0.557891	−	0.829914i	$-0.311611\pi$
$251$	17.6773	1.11578	0.557891	+	0.829914i	$0.311611\pi$
$252$	3.01477	0.189913
$253$	−32.7914	−2.06158
$254$	57.4181	3.60273
$255$	−3.85108	−0.241164
$256$	−13.9490	−0.871812
$257$	9.88064	0.616337	0.308169	−	0.951332i	$-0.400284\pi$
$257$	9.88064	0.616337	0.308169	+	0.951332i	$0.400284\pi$
$258$	−5.46737	−0.340384
$259$	−1.02744	−0.0638421
$260$	41.1493	2.55197
$261$	18.4092	1.13950
$262$	−1.84964	−0.114271
$263$	−15.7281	−0.969836	−0.484918	−	0.874560i	$-0.661151\pi$
$263$	−15.7281	−0.969836	−0.484918	+	0.874560i	$0.661151\pi$
$264$	31.5950	1.94454
$265$	−32.9323	−2.02301
$266$	2.76084	0.169278
$267$	−0.668381	−0.0409043
$268$	39.2494	2.39754
$269$	−15.4900	−0.944442	−0.472221	−	0.881480i	$-0.656548\pi$
$269$	−15.4900	−0.944442	−0.472221	+	0.881480i	$0.656548\pi$
$270$	−31.4222	−1.91230
$271$	−16.9543	−1.02990	−0.514951	−	0.857219i	$-0.672190\pi$
$271$	−16.9543	−1.02990	−0.514951	+	0.857219i	$0.672190\pi$
$272$	17.4096	1.05561
$273$	0.527464	0.0319236
$274$	−35.1676	−2.12455
$275$	−22.2223	−1.34006
$276$	20.5882	1.23926
$277$	1.52444	0.0915945	0.0457973	−	0.998951i	$-0.485417\pi$
$277$	1.52444	0.0915945	0.0457973	+	0.998951i	$0.485417\pi$
$278$	25.1354	1.50752
$279$	−16.1987	−0.969789
$280$	−5.64563	−0.337391
$281$	−9.50989	−0.567313	−0.283656	−	0.958926i	$-0.591547\pi$
$281$	−9.50989	−0.567313	−0.283656	+	0.958926i	$0.591547\pi$
$282$	1.30847	0.0779182
$283$	−0.155435	−0.00923963	−0.00461981	−	0.999989i	$-0.501471\pi$
$283$	−0.155435	−0.00923963	−0.00461981	+	0.999989i	$0.501471\pi$
$284$	13.3962	0.794917
$285$	−9.18080	−0.543824
$286$	−42.4476	−2.50998
$287$	0.367976	0.0217209
$288$	27.0755	1.59544
$289$	−13.9298	−0.819397
$290$	−58.5425	−3.43773
$291$	6.73202	0.394638
$292$	1.58107	0.0925251
$293$	−26.1373	−1.52696	−0.763479	−	0.645833i	$-0.776510\pi$
$293$	−26.1373	−1.52696	−0.763479	+	0.645833i	$0.776510\pi$
$294$	13.3955	0.781243
$295$	−37.6698	−2.19322
$296$	−30.5702	−1.77686
$297$	22.9700	1.33286
$298$	−16.9293	−0.980687
$299$	−16.2883	−0.941976
$300$	13.9524	0.805541
$301$	−0.714163	−0.0411637
$302$	53.1757	3.05992
$303$	−3.31493	−0.190438
$304$	41.5038	2.38040
$305$	−6.43841	−0.368663
$306$	11.2785	0.644747
$307$	32.4071	1.84957	0.924786	−	0.380488i	$-0.124244\pi$
$307$	32.4071	1.84957	0.924786	+	0.380488i	$0.124244\pi$
$308$	7.00833	0.399337
$309$	4.31874	0.245684
$310$	51.5128	2.92573
$311$	24.6246	1.39634	0.698168	−	0.715934i	$-0.253999\pi$
$311$	24.6246	1.39634	0.698168	+	0.715934i	$0.253999\pi$
$312$	15.6940	0.888498
$313$	−18.3379	−1.03652	−0.518260	−	0.855223i	$-0.673420\pi$
$313$	−18.3379	−1.03652	−0.518260	+	0.855223i	$0.673420\pi$
$314$	7.82613	0.441654
$315$	−1.84790	−0.104117
$316$	0.669290	0.0376505
$317$	−9.84857	−0.553151	−0.276575	−	0.960992i	$-0.589200\pi$
$317$	−9.84857	−0.553151	−0.276575	+	0.960992i	$0.589200\pi$
$318$	−21.3290	−1.19607
$319$	42.7953	2.39608
$320$	−26.8487	−1.50089
$321$	−7.72480	−0.431156
$322$	3.79492	0.211483
$323$	7.31933	0.407258
$324$	21.4315	1.19064
$325$	−11.0384	−0.612299
$326$	−4.55382	−0.252213
$327$	12.2222	0.675891
$328$	10.9486	0.604538
$329$	0.170916	0.00942289
$330$	−32.8866	−1.81035
$331$	7.56390	0.415750	0.207875	−	0.978155i	$-0.433345\pi$
$331$	7.56390	0.415750	0.207875	+	0.978155i	$0.433345\pi$
$332$	−43.3115	−2.37703
$333$	−10.0061	−0.548330
$334$	30.5123	1.66956
$335$	−24.0578	−1.31442
$336$	−1.84742	−0.100785
$337$	4.19760	0.228658	0.114329	−	0.993443i	$-0.463528\pi$
$337$	4.19760	0.228658	0.114329	+	0.993443i	$0.463528\pi$
$338$	12.9760	0.705799
$339$	−10.6049	−0.575980
$340$	−25.4167	−1.37842
$341$	−37.6565	−2.03921
$342$	26.8874	1.45390
$343$	3.51557	0.189823
$344$	−21.2490	−1.14567
$345$	−12.6195	−0.679411
$346$	19.9881	1.07457
$347$	20.0968	1.07885	0.539426	−	0.842033i	$-0.318641\pi$
$347$	20.0968	1.07885	0.539426	+	0.842033i	$0.318641\pi$
$348$	−26.8692	−1.44034
$349$	3.80854	0.203866	0.101933	−	0.994791i	$-0.467497\pi$
$349$	3.80854	0.203866	0.101933	+	0.994791i	$0.467497\pi$
$350$	2.57178	0.137467
$351$	11.4098	0.609008
$352$	62.9415	3.35479
$353$	14.7965	0.787536	0.393768	−	0.919210i	$-0.371171\pi$
$353$	14.7965	0.787536	0.393768	+	0.919210i	$0.371171\pi$
$354$	−24.3973	−1.29670
$355$	−8.21116	−0.435803
$356$	−4.41125	−0.233796
$357$	−0.325799	−0.0172431
$358$	−21.2508	−1.12314
$359$	32.6820	1.72489	0.862445	−	0.506151i	$-0.168932\pi$
$359$	32.6820	1.72489	0.862445	+	0.506151i	$0.168932\pi$
$360$	−54.9818	−2.89780
$361$	−1.55106	−0.0816346
$362$	27.5001	1.44537
$363$	15.9326	0.836245
$364$	3.48121	0.182465
$365$	−0.969114	−0.0507258
$366$	−4.16992	−0.217965
$367$	−24.9812	−1.30401	−0.652005	−	0.758215i	$-0.726072\pi$
$367$	−24.9812	−1.30401	−0.652005	+	0.758215i	$0.726072\pi$
$368$	57.0492	2.97389
$369$	3.58366	0.186558
$370$	31.8200	1.65424
$371$	−2.78605	−0.144645
$372$	23.6428	1.22582
$373$	−6.43821	−0.333358	−0.166679	−	0.986011i	$-0.553304\pi$
$373$	−6.43821	−0.333358	−0.166679	+	0.986011i	$0.553304\pi$
$374$	26.2186	1.35573
$375$	2.43710	0.125852
$376$	5.08538	0.262258
$377$	21.2575	1.09481
$378$	−2.65830	−0.136728
$379$	4.88262	0.250803	0.125402	−	0.992106i	$-0.459978\pi$
$379$	4.88262	0.250803	0.125402	+	0.992106i	$0.459978\pi$
$380$	−60.5924	−3.10832
$381$	−16.1531	−0.827549
$382$	60.6127	3.10122
$383$	−31.5597	−1.61263	−0.806313	−	0.591489i	$-0.798541\pi$
$383$	−31.5597	−1.61263	−0.806313	+	0.591489i	$0.798541\pi$
$384$	−1.14201	−0.0582780
$385$	−4.29574	−0.218931
$386$	−31.0058	−1.57815
$387$	−6.95512	−0.353548
$388$	44.4307	2.25563
$389$	33.2938	1.68806	0.844031	−	0.536294i	$-0.180176\pi$
$389$	33.2938	1.68806	0.844031	+	0.536294i	$0.180176\pi$
$390$	−16.3356	−0.827186
$391$	10.0608	0.508797
$392$	52.0618	2.62952
$393$	0.520348	0.0262481
$394$	−28.5079	−1.43621
$395$	−0.410240	−0.0206414
$396$	68.2530	3.42984
$397$	8.54305	0.428763	0.214382	−	0.976750i	$-0.431226\pi$
$397$	8.54305	0.428763	0.214382	+	0.976750i	$0.431226\pi$
$398$	−33.1519	−1.66175
$399$	−0.776691	−0.0388832
$400$	38.6615	1.93308
$401$	16.6174	0.829831	0.414916	−	0.909860i	$-0.363811\pi$
$401$	16.6174	0.829831	0.414916	+	0.909860i	$0.363811\pi$
$402$	−15.5814	−0.777128
$403$	−18.7049	−0.931757
$404$	−21.8782	−1.08848
$405$	−13.1364	−0.652753
$406$	−4.95267	−0.245797
$407$	−23.2608	−1.15299
$408$	−9.69374	−0.479911
$409$	−16.3638	−0.809136	−0.404568	−	0.914508i	$-0.632578\pi$
$409$	−16.3638	−0.809136	−0.404568	+	0.914508i	$0.632578\pi$
$410$	−11.3963	−0.562821
$411$	9.89350	0.488011
$412$	28.5032	1.40425
$413$	−3.18684	−0.156814
$414$	36.9581	1.81639
$415$	26.5477	1.30317
$416$	31.2646	1.53287
$417$	−7.07121	−0.346278
$418$	62.5041	3.05717
$419$	14.3960	0.703293	0.351646	−	0.936133i	$-0.385622\pi$
$419$	14.3960	0.703293	0.351646	+	0.936133i	$0.385622\pi$
$420$	2.69710	0.131605
$421$	10.9345	0.532915	0.266458	−	0.963847i	$-0.414147\pi$
$421$	10.9345	0.532915	0.266458	+	0.963847i	$0.414147\pi$
$422$	−35.7795	−1.74172
$423$	1.66452	0.0809317
$424$	−82.8954	−4.02576
$425$	6.81809	0.330726
$426$	−5.31806	−0.257661
$427$	−0.544686	−0.0263592
$428$	−50.9829	−2.46435
$429$	11.9415	0.576542
$430$	22.1177	1.06661
$431$	33.4263	1.61009	0.805045	−	0.593214i	$-0.202141\pi$
$431$	33.4263	1.61009	0.805045	+	0.593214i	$0.202141\pi$
$432$	−39.9623	−1.92269
$433$	13.8145	0.663881	0.331941	−	0.943300i	$-0.392297\pi$
$433$	13.8145	0.663881	0.331941	+	0.943300i	$0.392297\pi$
$434$	4.35796	0.209189
$435$	16.4694	0.789648
$436$	80.6655	3.86318
$437$	23.9845	1.14734
$438$	−0.627659	−0.0299907
$439$	5.12643	0.244671	0.122336	−	0.992489i	$-0.460962\pi$
$439$	5.12643	0.244671	0.122336	+	0.992489i	$0.460962\pi$
$440$	−127.814	−6.09331
$441$	17.0406	0.811458
$442$	13.0234	0.619462
$443$	−23.3128	−1.10762	−0.553812	−	0.832642i	$-0.686827\pi$
$443$	−23.3128	−1.10762	−0.553812	+	0.832642i	$0.686827\pi$
$444$	14.6044	0.693093
$445$	2.70387	0.128176
$446$	17.1944	0.814176
$447$	4.76262	0.225264
$448$	−2.27139	−0.107313
$449$	−29.1650	−1.37638	−0.688190	−	0.725531i	$-0.741594\pi$
$449$	−29.1650	−1.37638	−0.688190	+	0.725531i	$0.741594\pi$
$450$	25.0461	1.18068
$451$	8.33079	0.392282
$452$	−69.9914	−3.29212
$453$	−14.9596	−0.702863
$454$	39.1094	1.83550
$455$	−2.13380	−0.100034
$456$	−23.1094	−1.08220
$457$	11.9683	0.559855	0.279928	−	0.960021i	$-0.409690\pi$
$457$	11.9683	0.559855	0.279928	+	0.960021i	$0.409690\pi$
$458$	23.7745	1.11091
$459$	−7.04749	−0.328949
$460$	−83.2875	−3.88330
$461$	33.2169	1.54707	0.773533	−	0.633756i	$-0.218488\pi$
$461$	33.2169	1.54707	0.773533	+	0.633756i	$0.218488\pi$
$462$	−2.78219	−0.129439
$463$	−1.92537	−0.0894794	−0.0447397	−	0.998999i	$-0.514246\pi$
$463$	−1.92537	−0.0894794	−0.0447397	+	0.998999i	$0.514246\pi$
$464$	−74.4535	−3.45642
$465$	−14.4918	−0.672041
$466$	−7.40611	−0.343081
$467$	−24.7140	−1.14363	−0.571815	−	0.820383i	$-0.693760\pi$
$467$	−24.7140	−1.14363	−0.571815	+	0.820383i	$0.693760\pi$
$468$	33.9029	1.56716
$469$	−2.03528	−0.0939805
$470$	−5.29328	−0.244161
$471$	−2.20168	−0.101448
$472$	−94.8204	−4.36446
$473$	−16.1683	−0.743419
$474$	−0.265697	−0.0122039
$475$	16.2540	0.745786
$476$	−2.15024	−0.0985562
$477$	−27.1329	−1.24233
$478$	28.5661	1.30658
$479$	5.74052	0.262291	0.131146	−	0.991363i	$-0.458134\pi$
$479$	5.74052	0.262291	0.131146	+	0.991363i	$0.458134\pi$
$480$	24.2225	1.10560
$481$	−11.5542	−0.526826
$482$	−0.369630	−0.0168362
$483$	−1.06760	−0.0485776
$484$	105.154	4.77971
$485$	−27.2337	−1.23662
$486$	−40.1220	−1.81997
$487$	−39.8857	−1.80739	−0.903697	−	0.428173i	$-0.859157\pi$
$487$	−39.8857	−1.80739	−0.903697	+	0.428173i	$0.859157\pi$
$488$	−16.2064	−0.733631
$489$	1.28110	0.0579333
$490$	−54.1902	−2.44806
$491$	3.46237	0.156255	0.0781273	−	0.996943i	$-0.475106\pi$
$491$	3.46237	0.156255	0.0781273	+	0.996943i	$0.475106\pi$
$492$	−5.23052	−0.235810
$493$	−13.1301	−0.591351
$494$	31.0473	1.39688
$495$	−41.8355	−1.88037
$496$	65.5132	2.94163
$497$	−0.694660	−0.0311597
$498$	17.1940	0.770479
$499$	14.0359	0.628335	0.314167	−	0.949368i	$-0.398275\pi$
$499$	14.0359	0.628335	0.314167	+	0.949368i	$0.398275\pi$
$500$	16.0847	0.719328
$501$	−8.58384	−0.383498
$502$	−46.3155	−2.06716
$503$	37.2487	1.66084	0.830419	−	0.557140i	$-0.188101\pi$
$503$	37.2487	1.66084	0.830419	+	0.557140i	$0.188101\pi$
$504$	−4.65143	−0.207191
$505$	13.4102	0.596747
$506$	85.9152	3.81940
$507$	−3.65045	−0.162122
$508$	−106.609	−4.73001
$509$	19.8285	0.878884	0.439442	−	0.898271i	$-0.355176\pi$
$509$	19.8285	0.878884	0.439442	+	0.898271i	$0.355176\pi$
$510$	10.0900	0.446794
$511$	−0.0819866	−0.00362687
$512$	39.6458	1.75211
$513$	−16.8009	−0.741778
$514$	−25.8878	−1.14186
$515$	−17.4710	−0.769865
$516$	10.1513	0.446888
$517$	3.86945	0.170178
$518$	2.69195	0.118278
$519$	−5.62314	−0.246829
$520$	−63.4885	−2.78415
$521$	−26.5381	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$521$	−26.5381	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$522$	−48.2332	−2.11111
$523$	36.0596	1.57678	0.788388	−	0.615178i	$-0.210916\pi$
$523$	36.0596	1.57678	0.788388	+	0.615178i	$0.210916\pi$
$524$	3.43424	0.150026
$525$	−0.723502	−0.0315762
$526$	41.2085	1.79677
$527$	11.5535	0.503277
$528$	−41.8248	−1.82019
$529$	9.96802	0.433392
$530$	86.2844	3.74795
$531$	−31.0361	−1.34685
$532$	−5.12608	−0.222244
$533$	4.13811	0.179241
$534$	1.75119	0.0757816
$535$	31.2499	1.35105
$536$	−60.5571	−2.61567
$537$	5.97837	0.257986
$538$	40.5847	1.74973
$539$	39.6137	1.70628
$540$	58.3420	2.51064
$541$	−20.4544	−0.879404	−0.439702	−	0.898144i	$-0.644916\pi$
$541$	−20.4544	−0.879404	−0.439702	+	0.898144i	$0.644916\pi$
$542$	44.4213	1.90806
$543$	−7.73644	−0.332002
$544$	−19.3112	−0.827963
$545$	−49.4438	−2.11794
$546$	−1.38198	−0.0591434
$547$	−31.8336	−1.36111	−0.680554	−	0.732698i	$-0.738261\pi$
$547$	−31.8336	−1.36111	−0.680554	+	0.732698i	$0.738261\pi$
$548$	65.2962	2.78931
$549$	−5.30461	−0.226395
$550$	58.2237	2.48267
$551$	−31.3016	−1.33349
$552$	−31.7652	−1.35202
$553$	−0.0347061	−0.00147585
$554$	−3.99411	−0.169693
$555$	−8.95172	−0.379980
$556$	−46.6693	−1.97922
$557$	−9.18967	−0.389379	−0.194689	−	0.980865i	$-0.562370\pi$
$557$	−9.18967	−0.389379	−0.194689	+	0.980865i	$0.562370\pi$
$558$	42.4414	1.79669
$559$	−8.03119	−0.339683
$560$	7.47356	0.315816
$561$	−7.37594	−0.311412
$562$	24.9164	1.05104
$563$	−5.13622	−0.216466	−0.108233	−	0.994126i	$-0.534519\pi$
$563$	−5.13622	−0.216466	−0.108233	+	0.994126i	$0.534519\pi$
$564$	−2.42945	−0.102298
$565$	42.9011	1.80486
$566$	0.407247	0.0171179
$567$	−1.11133	−0.0466716
$568$	−20.6687	−0.867240
$569$	32.8326	1.37642	0.688208	−	0.725513i	$-0.258398\pi$
$569$	32.8326	1.37642	0.688208	+	0.725513i	$0.258398\pi$
$570$	24.0542	1.00752
$571$	−25.0903	−1.04999	−0.524997	−	0.851104i	$-0.675934\pi$
$571$	−25.0903	−1.04999	−0.524997	+	0.851104i	$0.675934\pi$
$572$	78.8129	3.29533
$573$	−17.0518	−0.712350
$574$	−0.964117	−0.0402415
$575$	22.3420	0.931728
$576$	−22.1207	−0.921695
$577$	21.0746	0.877349	0.438674	−	0.898646i	$-0.355448\pi$
$577$	21.0746	0.877349	0.438674	+	0.898646i	$0.355448\pi$
$578$	36.4967	1.51806
$579$	8.72268	0.362502
$580$	108.697	4.51338
$581$	2.24592	0.0931765
$582$	−17.6383	−0.731130
$583$	−63.0749	−2.61230
$584$	−2.43940	−0.100943
$585$	−20.7807	−0.859178
$586$	68.4812	2.82893
$587$	−14.8634	−0.613478	−0.306739	−	0.951794i	$-0.599238\pi$
$587$	−14.8634	−0.613478	−0.306739	+	0.951794i	$0.599238\pi$
$588$	−24.8716	−1.02569
$589$	27.5430	1.13489
$590$	98.6969	4.06329
$591$	8.01997	0.329897
$592$	40.4682	1.66323
$593$	0.541557	0.0222391	0.0111195	−	0.999938i	$-0.496460\pi$
$593$	0.541557	0.0222391	0.0111195	+	0.999938i	$0.496460\pi$
$594$	−60.1827	−2.46933
$595$	1.31799	0.0540322
$596$	31.4328	1.28754
$597$	9.32643	0.381705
$598$	42.6762	1.74516
$599$	−28.9273	−1.18194	−0.590969	−	0.806694i	$-0.701255\pi$
$599$	−28.9273	−1.18194	−0.590969	+	0.806694i	$0.701255\pi$
$600$	−21.5269	−0.878831
$601$	−9.47262	−0.386396	−0.193198	−	0.981160i	$-0.561886\pi$
$601$	−9.47262	−0.386396	−0.193198	+	0.981160i	$0.561886\pi$
$602$	1.87115	0.0762622
$603$	−19.8213	−0.807184
$604$	−98.7319	−4.01734
$605$	−64.4537	−2.62042
$606$	8.68530	0.352816
$607$	−19.2151	−0.779917	−0.389959	−	0.920832i	$-0.627511\pi$
$607$	−19.2151	−0.779917	−0.389959	+	0.920832i	$0.627511\pi$
$608$	−46.0371	−1.86705
$609$	1.39330	0.0564595
$610$	16.8690	0.683006
$611$	1.92205	0.0777578
$612$	−20.9409	−0.846484
$613$	−8.49268	−0.343016	−0.171508	−	0.985183i	$-0.554864\pi$
$613$	−8.49268	−0.343016	−0.171508	+	0.985183i	$0.554864\pi$
$614$	−84.9084	−3.42662
$615$	3.20604	0.129280
$616$	−10.8130	−0.435669
$617$	−15.1621	−0.610404	−0.305202	−	0.952288i	$-0.598724\pi$
$617$	−15.1621	−0.610404	−0.305202	+	0.952288i	$0.598724\pi$
$618$	−11.3153	−0.455169
$619$	−40.0076	−1.60804	−0.804021	−	0.594601i	$-0.797310\pi$
$619$	−40.0076	−1.60804	−0.804021	+	0.594601i	$0.797310\pi$
$620$	−95.6444	−3.84117
$621$	−23.0937	−0.926720
$622$	−64.5179	−2.58693
$623$	0.228746	0.00916451
$624$	−20.7754	−0.831681
$625$	−29.3147	−1.17259
$626$	48.0463	1.92032
$627$	−17.5839	−0.702233
$628$	−14.5309	−0.579845
$629$	7.13670	0.284559
$630$	4.84160	0.192894
$631$	−1.96465	−0.0782114	−0.0391057	−	0.999235i	$-0.512451\pi$
$631$	−1.96465	−0.0782114	−0.0391057	+	0.999235i	$0.512451\pi$
$632$	−1.03263	−0.0410760
$633$	10.0656	0.400073
$634$	25.8038	1.02480
$635$	65.3458	2.59317
$636$	39.6018	1.57031
$637$	19.6771	0.779635
$638$	−112.126	−4.43911
$639$	−6.76518	−0.267626
$640$	4.61989	0.182617
$641$	6.25326	0.246989	0.123494	−	0.992345i	$-0.460590\pi$
$641$	6.25326	0.246989	0.123494	+	0.992345i	$0.460590\pi$
$642$	20.2394	0.798785
$643$	45.4951	1.79415	0.897075	−	0.441877i	$-0.145687\pi$
$643$	45.4951	1.79415	0.897075	+	0.441877i	$0.145687\pi$
$644$	−7.04608	−0.277654
$645$	−6.22224	−0.245001
$646$	−19.1770	−0.754510
$647$	−48.8992	−1.92243	−0.961214	−	0.275805i	$-0.911056\pi$
$647$	−48.8992	−1.92243	−0.961214	+	0.275805i	$0.911056\pi$
$648$	−33.0663	−1.29897
$649$	−72.1486	−2.83208
$650$	28.9212	1.13438
$651$	−1.22600	−0.0480506
$652$	8.45513	0.331128
$653$	−32.0570	−1.25449	−0.627244	−	0.778823i	$-0.715817\pi$
$653$	−32.0570	−1.25449	−0.627244	+	0.778823i	$0.715817\pi$
$654$	−32.0229	−1.25219
$655$	−2.10501	−0.0822497
$656$	−14.4936	−0.565879
$657$	−0.798454	−0.0311506
$658$	−0.447809	−0.0174574
$659$	−16.3647	−0.637479	−0.318739	−	0.947842i	$-0.603259\pi$
$659$	−16.3647	−0.637479	−0.318739	+	0.947842i	$0.603259\pi$
$660$	61.0610	2.37680
$661$	22.4963	0.875006	0.437503	−	0.899217i	$-0.355863\pi$
$661$	22.4963	0.875006	0.437503	+	0.899217i	$0.355863\pi$
$662$	−19.8178	−0.770242
$663$	−3.66381	−0.142291
$664$	66.8245	2.59329
$665$	3.14202	0.121842
$666$	26.2165	1.01587
$667$	−43.0258	−1.66597
$668$	−56.6525	−2.19195
$669$	−4.83719	−0.187016
$670$	63.0329	2.43517
$671$	−12.3314	−0.476050
$672$	2.04921	0.0790501
$673$	−24.8262	−0.956982	−0.478491	−	0.878093i	$-0.658816\pi$
$673$	−24.8262	−0.956982	−0.478491	+	0.878093i	$0.658816\pi$
$674$	−10.9979	−0.423625
$675$	−15.6504	−0.602383
$676$	−24.0926	−0.926639
$677$	48.0748	1.84767	0.923833	−	0.382797i	$-0.125039\pi$
$677$	48.0748	1.84767	0.923833	+	0.382797i	$0.125039\pi$
$678$	27.7855	1.06709
$679$	−2.30396	−0.0884178
$680$	39.2150	1.50383
$681$	−11.0024	−0.421614
$682$	98.6620	3.77796
$683$	−41.6520	−1.59377	−0.796886	−	0.604130i	$-0.793521\pi$
$683$	−41.6520	−1.59377	−0.796886	+	0.604130i	$0.793521\pi$
$684$	−49.9221	−1.90882
$685$	−40.0232	−1.52921
$686$	−9.21099	−0.351677
$687$	−6.68834	−0.255176
$688$	28.1290	1.07241
$689$	−31.3309	−1.19361
$690$	33.0638	1.25872
$691$	7.93010	0.301675	0.150838	−	0.988559i	$-0.451803\pi$
$691$	7.93010	0.301675	0.150838	+	0.988559i	$0.451803\pi$
$692$	−37.1122	−1.41079
$693$	−3.53926	−0.134446
$694$	−52.6547	−1.99875
$695$	28.6058	1.08508
$696$	41.4560	1.57138
$697$	−2.55599	−0.0968151
$698$	−9.97858	−0.377695
$699$	2.08352	0.0788058
$700$	−4.77505	−0.180480
$701$	45.4329	1.71598	0.857988	−	0.513670i	$-0.171714\pi$
$701$	45.4329	1.71598	0.857988	+	0.513670i	$0.171714\pi$
$702$	−29.8942	−1.12828
$703$	17.0136	0.641679
$704$	−51.4231	−1.93808
$705$	1.48913	0.0560838
$706$	−38.7676	−1.45904
$707$	1.13450	0.0426672
$708$	45.2988	1.70243
$709$	39.7202	1.49172	0.745861	−	0.666101i	$-0.232038\pi$
$709$	39.7202	1.49172	0.745861	+	0.666101i	$0.232038\pi$
$710$	21.5137	0.807394
$711$	−0.337997	−0.0126759
$712$	6.80604	0.255067
$713$	37.8593	1.41784
$714$	0.853612	0.0319456
$715$	−48.3082	−1.80663
$716$	39.4567	1.47456
$717$	−8.03634	−0.300122
$718$	−85.6286	−3.19563
$719$	−17.6891	−0.659693	−0.329847	−	0.944035i	$-0.606997\pi$
$719$	−17.6891	−0.659693	−0.329847	+	0.944035i	$0.606997\pi$
$720$	72.7838	2.71249
$721$	−1.47804	−0.0550450
$722$	4.06385	0.151241
$723$	0.103986	0.00386727
$724$	−51.0598	−1.89762
$725$	−29.1581	−1.08290
$726$	−41.7443	−1.54928
$727$	−3.61606	−0.134112	−0.0670561	−	0.997749i	$-0.521361\pi$
$727$	−3.61606	−0.134112	−0.0670561	+	0.997749i	$0.521361\pi$
$728$	−5.37109	−0.199066
$729$	−1.92930	−0.0714557
$730$	2.53913	0.0939775
$731$	4.96064	0.183476
$732$	7.74234	0.286165
$733$	−29.1343	−1.07610	−0.538050	−	0.842913i	$-0.680839\pi$
$733$	−29.1343	−1.07610	−0.538050	+	0.842913i	$0.680839\pi$
$734$	65.4522	2.41589
$735$	15.2450	0.562321
$736$	−63.2805	−2.33255
$737$	−46.0778	−1.69730
$738$	−9.38937	−0.345628
$739$	−24.9631	−0.918284	−0.459142	−	0.888363i	$-0.651843\pi$
$739$	−24.9631	−0.918284	−0.459142	+	0.888363i	$0.651843\pi$
$740$	−59.0805	−2.17184
$741$	−8.73436	−0.320865
$742$	7.29961	0.267977
$743$	−29.0731	−1.06659	−0.533294	−	0.845930i	$-0.679046\pi$
$743$	−29.0731	−1.06659	−0.533294	+	0.845930i	$0.679046\pi$
$744$	−36.4780	−1.33735
$745$	−19.2667	−0.705877
$746$	16.8685	0.617599
$747$	21.8726	0.800278
$748$	−48.6805	−1.77993
$749$	2.64372	0.0965996
$750$	−6.38535	−0.233160
$751$	19.9005	0.726179	0.363089	−	0.931754i	$-0.381722\pi$
$751$	19.9005	0.726179	0.363089	+	0.931754i	$0.381722\pi$
$752$	−6.73191	−0.245488
$753$	13.0297	0.474828
$754$	−55.6957	−2.02832
$755$	60.5175	2.20246
$756$	4.93570	0.179510
$757$	11.3696	0.413234	0.206617	−	0.978422i	$-0.433755\pi$
$757$	11.3696	0.413234	0.206617	+	0.978422i	$0.433755\pi$
$758$	−12.7927	−0.464653
$759$	−24.1700	−0.877316
$760$	93.4869	3.39112
$761$	8.73199	0.316534	0.158267	−	0.987396i	$-0.449409\pi$
$761$	8.73199	0.316534	0.158267	+	0.987396i	$0.449409\pi$
$762$	42.3220	1.53317
$763$	−4.18292	−0.151432
$764$	−112.540	−4.07157
$765$	12.8357	0.464075
$766$	82.6882	2.98765
$767$	−35.8380	−1.29403
$768$	−10.2816	−0.371005
$769$	37.1623	1.34011	0.670053	−	0.742313i	$-0.266271\pi$
$769$	37.1623	1.34011	0.670053	+	0.742313i	$0.266271\pi$
$770$	11.2551	0.405605
$771$	7.28286	0.262286
$772$	57.5688	2.07195
$773$	15.4127	0.554356	0.277178	−	0.960819i	$-0.410601\pi$
$773$	15.4127	0.554356	0.277178	+	0.960819i	$0.410601\pi$
$774$	18.2228	0.655004
$775$	25.6568	0.921620
$776$	−68.5513	−2.46085
$777$	−0.757311	−0.0271684
$778$	−87.2316	−3.12740
$779$	−6.09337	−0.218318
$780$	30.3305	1.08601
$781$	−15.7268	−0.562748
$782$	−26.3599	−0.942627
$783$	30.1391	1.07708
$784$	−68.9183	−2.46137
$785$	8.90667	0.317893
$786$	−1.36334	−0.0486287
$787$	−25.9113	−0.923638	−0.461819	−	0.886974i	$-0.652803\pi$
$787$	−25.9113	−0.923638	−0.461819	+	0.886974i	$0.652803\pi$
$788$	52.9310	1.88559
$789$	−11.5929	−0.412719
$790$	1.07485	0.0382415
$791$	3.62941	0.129047
$792$	−105.306	−3.74189
$793$	−6.12533	−0.217517
$794$	−22.3832	−0.794352
$795$	−24.2739	−0.860906
$796$	61.5535	2.18171
$797$	−16.4350	−0.582159	−0.291079	−	0.956699i	$-0.594014\pi$
$797$	−16.4350	−0.582159	−0.291079	+	0.956699i	$0.594014\pi$
$798$	2.03497	0.0720372
$799$	−1.18720	−0.0420000
$800$	−42.8845	−1.51620
$801$	2.22772	0.0787125
$802$	−43.5384	−1.53739
$803$	−1.85614	−0.0655016
$804$	28.9301	1.02029
$805$	4.31888	0.152221
$806$	49.0078	1.72623
$807$	−11.4174	−0.401913
$808$	33.7555	1.18751
$809$	−24.3477	−0.856019	−0.428009	−	0.903774i	$-0.640785\pi$
$809$	−24.3477	−0.856019	−0.428009	+	0.903774i	$0.640785\pi$
$810$	34.4181	1.20933
$811$	43.2356	1.51821	0.759103	−	0.650970i	$-0.225638\pi$
$811$	43.2356	1.51821	0.759103	+	0.650970i	$0.225638\pi$
$812$	9.19567	0.322705
$813$	−12.4968	−0.438281
$814$	60.9445	2.13610
$815$	−5.18256	−0.181537
$816$	12.8324	0.449223
$817$	11.8259	0.413737
$818$	42.8739	1.49905
$819$	−1.75804	−0.0614309
$820$	21.1596	0.738924
$821$	37.2122	1.29872	0.649358	−	0.760483i	$-0.275038\pi$
$821$	37.2122	1.29872	0.649358	+	0.760483i	$0.275038\pi$
$822$	−25.9215	−0.904117
$823$	−16.5539	−0.577032	−0.288516	−	0.957475i	$-0.593162\pi$
$823$	−16.5539	−0.577032	−0.288516	+	0.957475i	$0.593162\pi$
$824$	−43.9771	−1.53202
$825$	−16.3797	−0.570269
$826$	8.34971	0.290523
$827$	−50.3346	−1.75030	−0.875152	−	0.483848i	$-0.839239\pi$
$827$	−50.3346	−1.75030	−0.875152	+	0.483848i	$0.839239\pi$
$828$	−68.6206	−2.38473
$829$	3.35659	0.116579	0.0582896	−	0.998300i	$-0.481435\pi$
$829$	3.35659	0.116579	0.0582896	+	0.998300i	$0.481435\pi$
$830$	−69.5564	−2.41434
$831$	1.12364	0.0389786
$832$	−25.5431	−0.885549
$833$	−12.1540	−0.421110
$834$	18.5269	0.641536
$835$	34.7251	1.20171
$836$	−116.052	−4.01374
$837$	−26.5200	−0.916666
$838$	−37.7184	−1.30296
$839$	26.9838	0.931585	0.465793	−	0.884894i	$-0.345769\pi$
$839$	26.9838	0.931585	0.465793	+	0.884894i	$0.345769\pi$
$840$	−4.16131	−0.143579
$841$	27.1519	0.936274
$842$	−28.6490	−0.987310
$843$	−7.00959	−0.241423
$844$	66.4322	2.28669
$845$	14.7675	0.508018
$846$	−4.36113	−0.149939
$847$	−5.45275	−0.187359
$848$	109.735	3.76832
$849$	−0.114568	−0.00393198
$850$	−17.8638	−0.612723
$851$	23.3861	0.801664
$852$	9.87411	0.338281
$853$	−27.2091	−0.931622	−0.465811	−	0.884884i	$-0.654237\pi$
$853$	−27.2091	−0.931622	−0.465811	+	0.884884i	$0.654237\pi$
$854$	1.42711	0.0488346
$855$	30.5997	1.04649
$856$	78.6606	2.68856
$857$	−28.3398	−0.968068	−0.484034	−	0.875049i	$-0.660829\pi$
$857$	−28.3398	−0.968068	−0.484034	+	0.875049i	$0.660829\pi$
$858$	−31.2874	−1.06814
$859$	−56.2912	−1.92063	−0.960315	−	0.278919i	$-0.910024\pi$
$859$	−56.2912	−1.92063	−0.960315	+	0.278919i	$0.910024\pi$
$860$	−41.0662	−1.40035
$861$	0.271229	0.00924347
$862$	−87.5788	−2.98295
$863$	−40.9166	−1.39282	−0.696408	−	0.717646i	$-0.745220\pi$
$863$	−40.9166	−1.39282	−0.696408	+	0.717646i	$0.745220\pi$
$864$	44.3273	1.50805
$865$	22.7479	0.773450
$866$	−36.1947	−1.22994
$867$	−10.2674	−0.348699
$868$	−8.09147	−0.274642
$869$	−0.785729	−0.0266540
$870$	−43.1508	−1.46295
$871$	−22.8880	−0.775529
$872$	−124.457	−4.21466
$873$	−22.4379	−0.759407
$874$	−62.8408	−2.12562
$875$	−0.834071	−0.0281968
$876$	1.16538	0.0393746
$877$	−12.2520	−0.413720	−0.206860	−	0.978371i	$-0.566324\pi$
$877$	−12.2520	−0.413720	−0.206860	+	0.978371i	$0.566324\pi$
$878$	−13.4315	−0.453292
$879$	−19.2654	−0.649806
$880$	169.198	5.70366
$881$	−27.9572	−0.941903	−0.470952	−	0.882159i	$-0.656089\pi$
$881$	−27.9572	−0.941903	−0.470952	+	0.882159i	$0.656089\pi$
$882$	−44.6473	−1.50335
$883$	−16.6430	−0.560083	−0.280041	−	0.959988i	$-0.590348\pi$
$883$	−16.6430	−0.560083	−0.280041	+	0.959988i	$0.590348\pi$
$884$	−24.1808	−0.813288
$885$	−27.7658	−0.933338
$886$	61.0808	2.05205
$887$	17.6150	0.591454	0.295727	−	0.955273i	$-0.404438\pi$
$887$	17.6150	0.591454	0.295727	+	0.955273i	$0.404438\pi$
$888$	−22.5328	−0.756152
$889$	5.52822	0.185410
$890$	−7.08428	−0.237466
$891$	−25.1600	−0.842893
$892$	−31.9250	−1.06893
$893$	−2.83022	−0.0947097
$894$	−12.4783	−0.417337
$895$	−24.1849	−0.808412
$896$	0.390840	0.0130571
$897$	−12.0058	−0.400864
$898$	76.4138	2.54996
$899$	−49.4093	−1.64789
$900$	−46.5034	−1.55011
$901$	19.3522	0.644714
$902$	−21.8271	−0.726764
$903$	−0.526398	−0.0175174
$904$	107.988	3.59164
$905$	31.2970	1.04035
$906$	39.1950	1.30217
$907$	12.1412	0.403142	0.201571	−	0.979474i	$-0.435395\pi$
$907$	12.1412	0.403142	0.201571	+	0.979474i	$0.435395\pi$
$908$	−72.6150	−2.40981
$909$	11.0487	0.366462
$910$	5.59068	0.185329
$911$	38.4630	1.27434	0.637168	−	0.770725i	$-0.280106\pi$
$911$	38.4630	1.27434	0.637168	+	0.770725i	$0.280106\pi$
$912$	30.5918	1.01299
$913$	50.8466	1.68278
$914$	−31.3577	−1.03722
$915$	−4.74566	−0.156887
$916$	−44.1424	−1.45851
$917$	−0.178083	−0.00588082
$918$	18.4648	0.609429
$919$	−27.6625	−0.912503	−0.456251	−	0.889851i	$-0.650808\pi$
$919$	−27.6625	−0.912503	−0.456251	+	0.889851i	$0.650808\pi$
$920$	128.503	4.23661
$921$	23.8868	0.787096
$922$	−87.0301	−2.86618
$923$	−7.81187	−0.257131
$924$	5.16573	0.169940
$925$	15.8485	0.521094
$926$	5.04457	0.165775
$927$	−14.3944	−0.472773
$928$	82.5859	2.71102
$929$	36.7694	1.20637	0.603183	−	0.797603i	$-0.293899\pi$
$929$	36.7694	1.20637	0.603183	+	0.797603i	$0.293899\pi$
$930$	37.9693	1.24506
$931$	−28.9745	−0.949602
$932$	13.7510	0.450429
$933$	18.1504	0.594219
$934$	64.7522	2.11876
$935$	29.8386	0.975827
$936$	−52.3082	−1.70975
$937$	28.8955	0.943976	0.471988	−	0.881605i	$-0.343537\pi$
$937$	28.8955	0.943976	0.471988	+	0.881605i	$0.343537\pi$
$938$	5.33255	0.174114
$939$	−13.5166	−0.441097
$940$	9.82809	0.320557
$941$	−19.2135	−0.626344	−0.313172	−	0.949696i	$-0.601392\pi$
$941$	−19.2135	−0.626344	−0.313172	+	0.949696i	$0.601392\pi$
$942$	5.76852	0.187949
$943$	−8.37567	−0.272749
$944$	125.521	4.08537
$945$	−3.02533	−0.0984140
$946$	42.3618	1.37730
$947$	−18.5595	−0.603102	−0.301551	−	0.953450i	$-0.597504\pi$
$947$	−18.5595	−0.603102	−0.301551	+	0.953450i	$0.597504\pi$
$948$	0.493323	0.0160224
$949$	−0.921988	−0.0299290
$950$	−42.5864	−1.38169
$951$	−7.25923	−0.235397
$952$	3.31757	0.107523
$953$	12.2392	0.396467	0.198234	−	0.980155i	$-0.436480\pi$
$953$	12.2392	0.396467	0.198234	+	0.980155i	$0.436480\pi$
$954$	71.0897	2.30161
$955$	68.9814	2.23219
$956$	−53.0390	−1.71540
$957$	31.5437	1.01966
$958$	−15.0405	−0.485936
$959$	−3.38594	−0.109338
$960$	−19.7898	−0.638713
$961$	12.4763	0.402460
$962$	30.2726	0.976029
$963$	25.7468	0.829679
$964$	0.686296	0.0221041
$965$	−35.2867	−1.13592
$966$	2.79718	0.0899978
$967$	44.6996	1.43744	0.718720	−	0.695299i	$-0.244728\pi$
$967$	44.6996	1.43744	0.718720	+	0.695299i	$0.244728\pi$
$968$	−162.240	−5.21458
$969$	5.39496	0.173311
$970$	71.3538	2.29103
$971$	12.0342	0.386194	0.193097	−	0.981180i	$-0.438147\pi$
$971$	12.0342	0.386194	0.193097	+	0.981180i	$0.438147\pi$
$972$	74.4949	2.38943
$973$	2.42004	0.0775829
$974$	104.503	3.34848
$975$	−8.13622	−0.260568
$976$	21.4537	0.686718
$977$	14.2647	0.456369	0.228185	−	0.973618i	$-0.426721\pi$
$977$	14.2647	0.456369	0.228185	+	0.973618i	$0.426721\pi$
$978$	−3.35655	−0.107331
$979$	5.17869	0.165512
$980$	100.616	3.21405
$981$	−40.7367	−1.30062
$982$	−9.07160	−0.289486
$983$	−3.24943	−0.103641	−0.0518204	−	0.998656i	$-0.516502\pi$
$983$	−3.24943	−0.103641	−0.0518204	+	0.998656i	$0.516502\pi$
$984$	8.07008	0.257265
$985$	−32.4440	−1.03375
$986$	34.4016	1.09557
$987$	0.125979	0.00400997
$988$	−57.6459	−1.83396
$989$	16.2554	0.516892
$990$	109.611	3.48368
$991$	18.7553	0.595783	0.297892	−	0.954600i	$-0.403717\pi$
$991$	18.7553	0.595783	0.297892	+	0.954600i	$0.403717\pi$
$992$	−72.6691	−2.30725
$993$	5.57524	0.176925
$994$	1.82005	0.0577284
$995$	−37.7291	−1.19609
$996$	−31.9242	−1.01156
$997$	−34.8864	−1.10486	−0.552432	−	0.833558i	$-0.686300\pi$
$997$	−34.8864	−1.10486	−0.552432	+	0.833558i	$0.686300\pi$
$998$	−36.7749	−1.16409
$999$	−16.3817	−0.518294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.15	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.15	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62005 q^{2} +0.737084 q^{3} +4.86469 q^{4} -2.98180 q^{5} -1.93120 q^{6} -0.252259 q^{7} -7.50563 q^{8} -2.45671 q^{9} +O(q^{10})\)	\(q-2.62005 q^{2} +0.737084 q^{3} +4.86469 q^{4} -2.98180 q^{5} -1.93120 q^{6} -0.252259 q^{7} -7.50563 q^{8} -2.45671 q^{9} +7.81248 q^{10} -5.71102 q^{11} +3.58568 q^{12} -2.83680 q^{13} +0.660932 q^{14} -2.19784 q^{15} +9.93580 q^{16} +1.75221 q^{17} +6.43671 q^{18} +4.17719 q^{19} -14.5055 q^{20} -0.185936 q^{21} +14.9632 q^{22} +5.74178 q^{23} -5.53229 q^{24} +3.89114 q^{25} +7.43258 q^{26} -4.02205 q^{27} -1.22716 q^{28} -7.49346 q^{29} +5.75846 q^{30} +6.59365 q^{31} -11.0211 q^{32} -4.20950 q^{33} -4.59089 q^{34} +0.752185 q^{35} -11.9511 q^{36} +4.07297 q^{37} -10.9445 q^{38} -2.09096 q^{39} +22.3803 q^{40} -1.45872 q^{41} +0.487163 q^{42} +2.83107 q^{43} -27.7823 q^{44} +7.32541 q^{45} -15.0438 q^{46} -0.677541 q^{47} +7.32352 q^{48} -6.93637 q^{49} -10.1950 q^{50} +1.29153 q^{51} -13.8002 q^{52} +11.0444 q^{53} +10.5380 q^{54} +17.0291 q^{55} +1.89336 q^{56} +3.07894 q^{57} +19.6333 q^{58} +12.6332 q^{59} -10.6918 q^{60} +2.15924 q^{61} -17.2757 q^{62} +0.619726 q^{63} +9.00420 q^{64} +8.45878 q^{65} +11.0291 q^{66} +8.06822 q^{67} +8.52396 q^{68} +4.23218 q^{69} -1.97077 q^{70} +2.75376 q^{71} +18.4391 q^{72} +0.325010 q^{73} -10.6714 q^{74} +2.86810 q^{75} +20.3207 q^{76} +1.44065 q^{77} +5.47844 q^{78} +0.137581 q^{79} -29.6266 q^{80} +4.40553 q^{81} +3.82194 q^{82} -8.90324 q^{83} -0.904520 q^{84} -5.22475 q^{85} -7.41757 q^{86} -5.52331 q^{87} +42.8648 q^{88} -0.906790 q^{89} -19.1930 q^{90} +0.715608 q^{91} +27.9320 q^{92} +4.86008 q^{93} +1.77520 q^{94} -12.4556 q^{95} -8.12346 q^{96} +9.13331 q^{97} +18.1737 q^{98} +14.0303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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