LMFDB - Embedded newform 6041.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81373 q^{2} -3.44120 q^{3} +5.91707 q^{4} +1.30649 q^{5} +9.68259 q^{6} -1.00000 q^{7} -11.0216 q^{8} +8.84183 q^{9} +O(q^{10})$	\(q-2.81373 q^{2} -3.44120 q^{3} +5.91707 q^{4} +1.30649 q^{5} +9.68259 q^{6} -1.00000 q^{7} -11.0216 q^{8} +8.84183 q^{9} -3.67611 q^{10} -2.17383 q^{11} -20.3618 q^{12} -1.19175 q^{13} +2.81373 q^{14} -4.49589 q^{15} +19.1776 q^{16} -3.23363 q^{17} -24.8785 q^{18} +5.00404 q^{19} +7.73060 q^{20} +3.44120 q^{21} +6.11657 q^{22} +6.02634 q^{23} +37.9274 q^{24} -3.29308 q^{25} +3.35326 q^{26} -20.1029 q^{27} -5.91707 q^{28} -4.29754 q^{29} +12.6502 q^{30} +3.46081 q^{31} -31.9174 q^{32} +7.48058 q^{33} +9.09857 q^{34} -1.30649 q^{35} +52.3177 q^{36} +3.89194 q^{37} -14.0800 q^{38} +4.10104 q^{39} -14.3996 q^{40} -8.02212 q^{41} -9.68259 q^{42} -6.78139 q^{43} -12.8627 q^{44} +11.5518 q^{45} -16.9565 q^{46} +6.70801 q^{47} -65.9939 q^{48} +1.00000 q^{49} +9.26584 q^{50} +11.1276 q^{51} -7.05167 q^{52} -10.2417 q^{53} +56.5640 q^{54} -2.84009 q^{55} +11.0216 q^{56} -17.2199 q^{57} +12.0921 q^{58} -8.59255 q^{59} -26.6025 q^{60} -7.58712 q^{61} -9.73778 q^{62} -8.84183 q^{63} +51.4518 q^{64} -1.55701 q^{65} -21.0483 q^{66} -1.49860 q^{67} -19.1336 q^{68} -20.7378 q^{69} +3.67611 q^{70} +11.8458 q^{71} -97.4510 q^{72} +10.1989 q^{73} -10.9509 q^{74} +11.3321 q^{75} +29.6093 q^{76} +2.17383 q^{77} -11.5392 q^{78} -1.75700 q^{79} +25.0554 q^{80} +42.6524 q^{81} +22.5721 q^{82} +15.3850 q^{83} +20.3618 q^{84} -4.22471 q^{85} +19.0810 q^{86} +14.7887 q^{87} +23.9591 q^{88} +1.83382 q^{89} -32.5035 q^{90} +1.19175 q^{91} +35.6583 q^{92} -11.9093 q^{93} -18.8745 q^{94} +6.53773 q^{95} +109.834 q^{96} +1.83824 q^{97} -2.81373 q^{98} -19.2206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.81373	−1.98961	−0.994804	−	0.101813i	$-0.967536\pi$
$2$	−2.81373	−1.98961	−0.994804	+	0.101813i	$0.967536\pi$
$3$	−3.44120	−1.98678	−0.993388	−	0.114809i	$-0.963375\pi$
$3$	−3.44120	−1.98678	−0.993388	+	0.114809i	$0.963375\pi$
$4$	5.91707	2.95854
$5$	1.30649	0.584280	0.292140	−	0.956375i	$-0.405633\pi$
$5$	1.30649	0.584280	0.292140	+	0.956375i	$0.405633\pi$
$6$	9.68259	3.95290
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−11.0216	−3.89672
$9$	8.84183	2.94728
$10$	−3.67611	−1.16249
$11$	−2.17383	−0.655435	−0.327717	−	0.944776i	$-0.606279\pi$
$11$	−2.17383	−0.655435	−0.327717	+	0.944776i	$0.606279\pi$
$12$	−20.3618	−5.87795
$13$	−1.19175	−0.330532	−0.165266	−	0.986249i	$-0.552848\pi$
$13$	−1.19175	−0.330532	−0.165266	+	0.986249i	$0.552848\pi$
$14$	2.81373	0.752001
$15$	−4.49589	−1.16083
$16$	19.1776	4.79440
$17$	−3.23363	−0.784271	−0.392136	−	0.919907i	$-0.628264\pi$
$17$	−3.23363	−0.784271	−0.392136	+	0.919907i	$0.628264\pi$
$18$	−24.8785	−5.86392
$19$	5.00404	1.14801	0.574003	−	0.818853i	$-0.305390\pi$
$19$	5.00404	1.14801	0.574003	+	0.818853i	$0.305390\pi$
$20$	7.73060	1.72862
$21$	3.44120	0.750930
$22$	6.11657	1.30406
$23$	6.02634	1.25658	0.628289	−	0.777980i	$-0.283755\pi$
$23$	6.02634	1.25658	0.628289	+	0.777980i	$0.283755\pi$
$24$	37.9274	7.74190
$25$	−3.29308	−0.658616
$26$	3.35326	0.657629
$27$	−20.1029	−3.86880
$28$	−5.91707	−1.11822
$29$	−4.29754	−0.798033	−0.399017	−	0.916944i	$-0.630648\pi$
$29$	−4.29754	−0.798033	−0.399017	+	0.916944i	$0.630648\pi$
$30$	12.6502	2.30960
$31$	3.46081	0.621579	0.310790	−	0.950479i	$-0.399407\pi$
$31$	3.46081	0.621579	0.310790	+	0.950479i	$0.399407\pi$
$32$	−31.9174	−5.64226
$33$	7.48058	1.30220
$34$	9.09857	1.56039
$35$	−1.30649	−0.220837
$36$	52.3177	8.71962
$37$	3.89194	0.639831	0.319915	−	0.947446i	$-0.396346\pi$
$37$	3.89194	0.639831	0.319915	+	0.947446i	$0.396346\pi$
$38$	−14.0800	−2.28408
$39$	4.10104	0.656693
$40$	−14.3996	−2.27678
$41$	−8.02212	−1.25284	−0.626422	−	0.779484i	$-0.715481\pi$
$41$	−8.02212	−1.25284	−0.626422	+	0.779484i	$0.715481\pi$
$42$	−9.68259	−1.49406
$43$	−6.78139	−1.03415	−0.517076	−	0.855940i	$-0.672979\pi$
$43$	−6.78139	−1.03415	−0.517076	+	0.855940i	$0.672979\pi$
$44$	−12.8627	−1.93913
$45$	11.5518	1.72204
$46$	−16.9565	−2.50010
$47$	6.70801	0.978464	0.489232	−	0.872154i	$-0.337277\pi$
$47$	6.70801	0.978464	0.489232	+	0.872154i	$0.337277\pi$
$48$	−65.9939	−9.52540
$49$	1.00000	0.142857
$50$	9.26584	1.31039
$51$	11.1276	1.55817
$52$	−7.05167	−0.977891
$53$	−10.2417	−1.40681	−0.703405	−	0.710789i	$-0.748338\pi$
$53$	−10.2417	−1.40681	−0.703405	+	0.710789i	$0.748338\pi$
$54$	56.5640	7.69739
$55$	−2.84009	−0.382958
$56$	11.0216	1.47282
$57$	−17.2199	−2.28083
$58$	12.0921	1.58777
$59$	−8.59255	−1.11865	−0.559327	−	0.828947i	$-0.688940\pi$
$59$	−8.59255	−1.11865	−0.559327	+	0.828947i	$0.688940\pi$
$60$	−26.6025	−3.43437
$61$	−7.58712	−0.971431	−0.485715	−	0.874117i	$-0.661441\pi$
$61$	−7.58712	−0.971431	−0.485715	+	0.874117i	$0.661441\pi$
$62$	−9.73778	−1.23670
$63$	−8.84183	−1.11397
$64$	51.4518	6.43148
$65$	−1.55701	−0.193123
$66$	−21.0483	−2.59087
$67$	−1.49860	−0.183083	−0.0915413	−	0.995801i	$-0.529179\pi$
$67$	−1.49860	−0.183083	−0.0915413	+	0.995801i	$0.529179\pi$
$68$	−19.1336	−2.32029
$69$	−20.7378	−2.49654
$70$	3.67611	0.439379
$71$	11.8458	1.40584	0.702921	−	0.711268i	$-0.251879\pi$
$71$	11.8458	1.40584	0.702921	+	0.711268i	$0.251879\pi$
$72$	−97.4510	−11.4847
$73$	10.1989	1.19370	0.596848	−	0.802355i	$-0.296420\pi$
$73$	10.1989	1.19370	0.596848	+	0.802355i	$0.296420\pi$
$74$	−10.9509	−1.27301
$75$	11.3321	1.30852
$76$	29.6093	3.39642
$77$	2.17383	0.247731
$78$	−11.5392	−1.30656
$79$	−1.75700	−0.197678	−0.0988390	−	0.995103i	$-0.531513\pi$
$79$	−1.75700	−0.197678	−0.0988390	+	0.995103i	$0.531513\pi$
$80$	25.0554	2.80128
$81$	42.6524	4.73916
$82$	22.5721	2.49267
$83$	15.3850	1.68873	0.844363	−	0.535772i	$-0.179979\pi$
$83$	15.3850	1.68873	0.844363	+	0.535772i	$0.179979\pi$
$84$	20.3618	2.22166
$85$	−4.22471	−0.458234
$86$	19.0810	2.05756
$87$	14.7887	1.58551
$88$	23.9591	2.55404
$89$	1.83382	0.194384	0.0971920	−	0.995266i	$-0.469014\pi$
$89$	1.83382	0.194384	0.0971920	+	0.995266i	$0.469014\pi$
$90$	−32.5035	−3.42617
$91$	1.19175	0.124929
$92$	35.6583	3.71763
$93$	−11.9093	−1.23494
$94$	−18.8745	−1.94676
$95$	6.53773	0.670757
$96$	109.834	11.2099
$97$	1.83824	0.186645	0.0933224	−	0.995636i	$-0.470251\pi$
$97$	1.83824	0.186645	0.0933224	+	0.995636i	$0.470251\pi$
$98$	−2.81373	−0.284230
$99$	−19.2206	−1.93175
$100$	−19.4854	−1.94854
$101$	4.68490	0.466165	0.233083	−	0.972457i	$-0.425119\pi$
$101$	4.68490	0.466165	0.233083	+	0.972457i	$0.425119\pi$
$102$	−31.3100	−3.10015
$103$	15.3010	1.50766	0.753828	−	0.657072i	$-0.228205\pi$
$103$	15.3010	1.50766	0.753828	+	0.657072i	$0.228205\pi$
$104$	13.1350	1.28799
$105$	4.49589	0.438754
$106$	28.8175	2.79900
$107$	−6.14122	−0.593694	−0.296847	−	0.954925i	$-0.595935\pi$
$107$	−6.14122	−0.593694	−0.296847	+	0.954925i	$0.595935\pi$
$108$	−118.950	−11.4460
$109$	0.812230	0.0777975	0.0388988	−	0.999243i	$-0.487615\pi$
$109$	0.812230	0.0777975	0.0388988	+	0.999243i	$0.487615\pi$
$110$	7.99124	0.761935
$111$	−13.3929	−1.27120
$112$	−19.1776	−1.81211
$113$	−2.84639	−0.267766	−0.133883	−	0.990997i	$-0.542745\pi$
$113$	−2.84639	−0.267766	−0.133883	+	0.990997i	$0.542745\pi$
$114$	48.4521	4.53795
$115$	7.87336	0.734194
$116$	−25.4289	−2.36101
$117$	−10.5372	−0.974169
$118$	24.1771	2.22568
$119$	3.23363	0.296427
$120$	49.5518	4.52344
$121$	−6.27446	−0.570406
$122$	21.3481	1.93277
$123$	27.6057	2.48912
$124$	20.4779	1.83897
$125$	−10.8348	−0.969097
$126$	24.8785	2.21635
$127$	−8.39875	−0.745269	−0.372634	−	0.927978i	$-0.621545\pi$
$127$	−8.39875	−0.745269	−0.372634	+	0.927978i	$0.621545\pi$
$128$	−80.9366	−7.15386
$129$	23.3361	2.05463
$130$	4.38101	0.384240
$131$	−16.2881	−1.42309	−0.711547	−	0.702639i	$-0.752005\pi$
$131$	−16.2881	−1.42309	−0.711547	+	0.702639i	$0.752005\pi$
$132$	44.2631	3.85261
$133$	−5.00404	−0.433905
$134$	4.21664	0.364262
$135$	−26.2642	−2.26046
$136$	35.6398	3.05608
$137$	6.03494	0.515600	0.257800	−	0.966198i	$-0.417002\pi$
$137$	6.03494	0.515600	0.257800	+	0.966198i	$0.417002\pi$
$138$	58.3506	4.96713
$139$	21.6589	1.83708	0.918540	−	0.395328i	$-0.129369\pi$
$139$	21.6589	1.83708	0.918540	+	0.395328i	$0.129369\pi$
$140$	−7.73060	−0.653355
$141$	−23.0836	−1.94399
$142$	−33.3310	−2.79707
$143$	2.59066	0.216642
$144$	169.565	14.1304
$145$	−5.61470	−0.466275
$146$	−28.6971	−2.37498
$147$	−3.44120	−0.283825
$148$	23.0289	1.89296
$149$	−9.52329	−0.780178	−0.390089	−	0.920777i	$-0.627556\pi$
$149$	−9.52329	−0.780178	−0.390089	+	0.920777i	$0.627556\pi$
$150$	−31.8856	−2.60345
$151$	7.96382	0.648087	0.324043	−	0.946042i	$-0.394958\pi$
$151$	7.96382	0.648087	0.324043	+	0.946042i	$0.394958\pi$
$152$	−55.1525	−4.47346
$153$	−28.5912	−2.31146
$154$	−6.11657	−0.492887
$155$	4.52151	0.363177
$156$	24.2662	1.94285
$157$	9.15175	0.730389	0.365194	−	0.930931i	$-0.381002\pi$
$157$	9.15175	0.730389	0.365194	+	0.930931i	$0.381002\pi$
$158$	4.94373	0.393302
$159$	35.2438	2.79502
$160$	−41.6998	−3.29666
$161$	−6.02634	−0.474942
$162$	−120.012	−9.42907
$163$	−9.80806	−0.768227	−0.384113	−	0.923286i	$-0.625493\pi$
$163$	−9.80806	−0.768227	−0.384113	+	0.923286i	$0.625493\pi$
$164$	−47.4675	−3.70659
$165$	9.77330	0.760851
$166$	−43.2893	−3.35990
$167$	−6.18463	−0.478581	−0.239291	−	0.970948i	$-0.576915\pi$
$167$	−6.18463	−0.478581	−0.239291	+	0.970948i	$0.576915\pi$
$168$	−37.9274	−2.92616
$169$	−11.5797	−0.890749
$170$	11.8872	0.911706
$171$	44.2449	3.38349
$172$	−40.1260	−3.05958
$173$	−4.66551	−0.354712	−0.177356	−	0.984147i	$-0.556754\pi$
$173$	−4.66551	−0.354712	−0.177356	+	0.984147i	$0.556754\pi$
$174$	−41.6113	−3.15455
$175$	3.29308	0.248934
$176$	−41.6889	−3.14242
$177$	29.5686	2.22251
$178$	−5.15986	−0.386748
$179$	−11.4341	−0.854623	−0.427311	−	0.904105i	$-0.640539\pi$
$179$	−11.4341	−0.854623	−0.427311	+	0.904105i	$0.640539\pi$
$180$	68.3527	5.09471
$181$	11.7219	0.871284	0.435642	−	0.900120i	$-0.356521\pi$
$181$	11.7219	0.871284	0.435642	+	0.900120i	$0.356521\pi$
$182$	−3.35326	−0.248560
$183$	26.1088	1.93001
$184$	−66.4198	−4.89653
$185$	5.08478	0.373841
$186$	33.5096	2.45704
$187$	7.02937	0.514038
$188$	39.6918	2.89482
$189$	20.1029	1.46227
$190$	−18.3954	−1.33454
$191$	20.3014	1.46896	0.734478	−	0.678632i	$-0.237427\pi$
$191$	20.3014	1.46896	0.734478	+	0.678632i	$0.237427\pi$
$192$	−177.056	−12.7779
$193$	−26.6999	−1.92190	−0.960950	−	0.276721i	$-0.910752\pi$
$193$	−26.6999	−1.92190	−0.960950	+	0.276721i	$0.910752\pi$
$194$	−5.17230	−0.371350
$195$	5.35798	0.383693
$196$	5.91707	0.422648
$197$	2.77891	0.197989	0.0989947	−	0.995088i	$-0.468437\pi$
$197$	2.77891	0.197989	0.0989947	+	0.995088i	$0.468437\pi$
$198$	54.0817	3.84342
$199$	5.02151	0.355965	0.177983	−	0.984034i	$-0.443043\pi$
$199$	5.02151	0.355965	0.177983	+	0.984034i	$0.443043\pi$
$200$	36.2950	2.56644
$201$	5.15696	0.363744
$202$	−13.1820	−0.927486
$203$	4.29754	0.301628
$204$	65.8426	4.60990
$205$	−10.4808	−0.732012
$206$	−43.0530	−2.99964
$207$	53.2839	3.70348
$208$	−22.8549	−1.58470
$209$	−10.8779	−0.752443
$210$	−12.6502	−0.872948
$211$	3.92767	0.270392	0.135196	−	0.990819i	$-0.456834\pi$
$211$	3.92767	0.270392	0.135196	+	0.990819i	$0.456834\pi$
$212$	−60.6011	−4.16210
$213$	−40.7638	−2.79309
$214$	17.2797	1.18122
$215$	−8.85982	−0.604235
$216$	221.566	15.0756
$217$	−3.46081	−0.234935
$218$	−2.28540	−0.154787
$219$	−35.0965	−2.37160
$220$	−16.8050	−1.13299
$221$	3.85368	0.259227
$222$	37.6841	2.52919
$223$	6.87879	0.460638	0.230319	−	0.973115i	$-0.426023\pi$
$223$	6.87879	0.460638	0.230319	+	0.973115i	$0.426023\pi$
$224$	31.9174	2.13257
$225$	−29.1169	−1.94112
$226$	8.00898	0.532749
$227$	17.4393	1.15749	0.578745	−	0.815509i	$-0.303543\pi$
$227$	17.4393	1.15749	0.578745	+	0.815509i	$0.303543\pi$
$228$	−101.891	−6.74792
$229$	16.7317	1.10566	0.552832	−	0.833293i	$-0.313547\pi$
$229$	16.7317	1.10566	0.552832	+	0.833293i	$0.313547\pi$
$230$	−22.1535	−1.46076
$231$	−7.48058	−0.492186
$232$	47.3657	3.10971
$233$	26.9728	1.76705	0.883523	−	0.468389i	$-0.155165\pi$
$233$	26.9728	1.76705	0.883523	+	0.468389i	$0.155165\pi$
$234$	29.6490	1.93821
$235$	8.76395	0.571697
$236$	−50.8427	−3.30958
$237$	6.04619	0.392742
$238$	−9.09857	−0.589773
$239$	−19.6994	−1.27425	−0.637124	−	0.770762i	$-0.719876\pi$
$239$	−19.6994	−1.27425	−0.637124	+	0.770762i	$0.719876\pi$
$240$	−86.2205	−5.56551
$241$	−9.67566	−0.623264	−0.311632	−	0.950203i	$-0.600876\pi$
$241$	−9.67566	−0.623264	−0.311632	+	0.950203i	$0.600876\pi$
$242$	17.6546	1.13488
$243$	−86.4668	−5.54685
$244$	−44.8935	−2.87401
$245$	1.30649	0.0834686
$246$	−77.6749	−4.95237
$247$	−5.96357	−0.379453
$248$	−38.1436	−2.42212
$249$	−52.9429	−3.35512
$250$	30.4863	1.92812
$251$	−28.0154	−1.76832	−0.884158	−	0.467188i	$-0.845267\pi$
$251$	−28.0154	−1.76832	−0.884158	+	0.467188i	$0.845267\pi$
$252$	−52.3177	−3.29571
$253$	−13.1002	−0.823605
$254$	23.6318	1.48279
$255$	14.5381	0.910409
$256$	124.830	7.80188
$257$	10.1468	0.632941	0.316470	−	0.948602i	$-0.397502\pi$
$257$	10.1468	0.632941	0.316470	+	0.948602i	$0.397502\pi$
$258$	−65.6614	−4.08790
$259$	−3.89194	−0.241833
$260$	−9.21295	−0.571363
$261$	−37.9981	−2.35202
$262$	45.8302	2.83140
$263$	7.46530	0.460330	0.230165	−	0.973152i	$-0.426073\pi$
$263$	7.46530	0.460330	0.230165	+	0.973152i	$0.426073\pi$
$264$	−82.4478	−5.07431
$265$	−13.3807	−0.821972
$266$	14.0800	0.863301
$267$	−6.31052	−0.386197
$268$	−8.86730	−0.541657
$269$	−17.7727	−1.08362	−0.541810	−	0.840501i	$-0.682261\pi$
$269$	−17.7727	−1.08362	−0.541810	+	0.840501i	$0.682261\pi$
$270$	73.9004	4.49744
$271$	−10.4867	−0.637023	−0.318512	−	0.947919i	$-0.603183\pi$
$271$	−10.4867	−0.637023	−0.318512	+	0.947919i	$0.603183\pi$
$272$	−62.0134	−3.76011
$273$	−4.10104	−0.248207
$274$	−16.9807	−1.02584
$275$	7.15860	0.431680
$276$	−122.707	−7.38610
$277$	5.39499	0.324153	0.162077	−	0.986778i	$-0.448181\pi$
$277$	5.39499	0.324153	0.162077	+	0.986778i	$0.448181\pi$
$278$	−60.9422	−3.65507
$279$	30.5999	1.83197
$280$	14.3996	0.860541
$281$	3.07457	0.183414	0.0917068	−	0.995786i	$-0.470768\pi$
$281$	3.07457	0.183414	0.0917068	+	0.995786i	$0.470768\pi$
$282$	64.9509	3.86777
$283$	−21.3714	−1.27040	−0.635199	−	0.772349i	$-0.719082\pi$
$283$	−21.3714	−1.27040	−0.635199	+	0.772349i	$0.719082\pi$
$284$	70.0927	4.15924
$285$	−22.4976	−1.33264
$286$	−7.28942	−0.431033
$287$	8.02212	0.473531
$288$	−282.209	−16.6293
$289$	−6.54362	−0.384919
$290$	15.7982	0.927705
$291$	−6.32573	−0.370821
$292$	60.3479	3.53159
$293$	−1.54332	−0.0901618	−0.0450809	−	0.998983i	$-0.514355\pi$
$293$	−1.54332	−0.0901618	−0.0450809	+	0.998983i	$0.514355\pi$
$294$	9.68259	0.564700
$295$	−11.2261	−0.653608
$296$	−42.8953	−2.49324
$297$	43.7002	2.53574
$298$	26.7960	1.55225
$299$	−7.18189	−0.415339
$300$	67.0531	3.87131
$301$	6.78139	0.390873
$302$	−22.4080	−1.28944
$303$	−16.1217	−0.926166
$304$	95.9656	5.50400
$305$	−9.91250	−0.567588
$306$	80.4480	4.59890
$307$	16.9981	0.970131	0.485065	−	0.874478i	$-0.338796\pi$
$307$	16.9981	0.970131	0.485065	+	0.874478i	$0.338796\pi$
$308$	12.8627	0.732921
$309$	−52.6538	−2.99537
$310$	−12.7223	−0.722579
$311$	−26.3570	−1.49457	−0.747284	−	0.664505i	$-0.768642\pi$
$311$	−26.3570	−1.49457	−0.747284	+	0.664505i	$0.768642\pi$
$312$	−45.2000	−2.55895
$313$	4.95127	0.279862	0.139931	−	0.990161i	$-0.455312\pi$
$313$	4.95127	0.279862	0.139931	+	0.990161i	$0.455312\pi$
$314$	−25.7505	−1.45319
$315$	−11.5518	−0.650868
$316$	−10.3963	−0.584838
$317$	−8.68444	−0.487766	−0.243883	−	0.969805i	$-0.578421\pi$
$317$	−8.68444	−0.487766	−0.243883	+	0.969805i	$0.578421\pi$
$318$	−99.1666	−5.56099
$319$	9.34212	0.523059
$320$	67.2213	3.75779
$321$	21.1331	1.17954
$322$	16.9565	0.944948
$323$	−16.1812	−0.900348
$324$	252.378	14.0210
$325$	3.92453	0.217694
$326$	27.5972	1.52847
$327$	−2.79504	−0.154566
$328$	88.4165	4.88198
$329$	−6.70801	−0.369825
$330$	−27.4994	−1.51379
$331$	−21.2639	−1.16877	−0.584386	−	0.811476i	$-0.698665\pi$
$331$	−21.2639	−1.16877	−0.584386	+	0.811476i	$0.698665\pi$
$332$	91.0343	4.99616
$333$	34.4119	1.88576
$334$	17.4019	0.952188
$335$	−1.95790	−0.106972
$336$	65.9939	3.60026
$337$	11.3939	0.620665	0.310332	−	0.950628i	$-0.399560\pi$
$337$	11.3939	0.620665	0.310332	+	0.950628i	$0.399560\pi$
$338$	32.5822	1.77224
$339$	9.79499	0.531991
$340$	−24.9979	−1.35570
$341$	−7.52321	−0.407405
$342$	−124.493	−6.73182
$343$	−1.00000	−0.0539949
$344$	74.7416	4.02980
$345$	−27.0938	−1.45868
$346$	13.1275	0.705739
$347$	15.6482	0.840039	0.420020	−	0.907515i	$-0.362023\pi$
$347$	15.6482	0.840039	0.420020	+	0.907515i	$0.362023\pi$
$348$	87.5057	4.69080
$349$	−11.1403	−0.596326	−0.298163	−	0.954515i	$-0.596374\pi$
$349$	−11.1403	−0.596326	−0.298163	+	0.954515i	$0.596374\pi$
$350$	−9.26584	−0.495280
$351$	23.9576	1.27876
$352$	69.3831	3.69813
$353$	−29.6823	−1.57983	−0.789916	−	0.613215i	$-0.789876\pi$
$353$	−29.6823	−1.57983	−0.789916	+	0.613215i	$0.789876\pi$
$354$	−83.1981	−4.42193
$355$	15.4765	0.821406
$356$	10.8508	0.575092
$357$	−11.1276	−0.588933
$358$	32.1724	1.70036
$359$	−26.2233	−1.38401	−0.692006	−	0.721891i	$-0.743273\pi$
$359$	−26.2233	−1.38401	−0.692006	+	0.721891i	$0.743273\pi$
$360$	−127.319	−6.71029
$361$	6.04043	0.317917
$362$	−32.9823	−1.73351
$363$	21.5916	1.13327
$364$	7.05167	0.369608
$365$	13.3248	0.697453
$366$	−73.4630	−3.83997
$367$	−2.86919	−0.149771	−0.0748854	−	0.997192i	$-0.523859\pi$
$367$	−2.86919	−0.149771	−0.0748854	+	0.997192i	$0.523859\pi$
$368$	115.571	6.02454
$369$	−70.9302	−3.69248
$370$	−14.3072	−0.743796
$371$	10.2417	0.531725
$372$	−70.4683	−3.65361
$373$	−33.0289	−1.71017	−0.855085	−	0.518488i	$-0.826495\pi$
$373$	−33.0289	−1.71017	−0.855085	+	0.518488i	$0.826495\pi$
$374$	−19.7787	−1.02273
$375$	37.2848	1.92538
$376$	−73.9329	−3.81280
$377$	5.12159	0.263776
$378$	−56.5640	−2.90934
$379$	23.9515	1.23031	0.615153	−	0.788408i	$-0.289094\pi$
$379$	23.9515	1.23031	0.615153	+	0.788408i	$0.289094\pi$
$380$	38.6843	1.98446
$381$	28.9017	1.48068
$382$	−57.1226	−2.92265
$383$	33.3211	1.70263	0.851314	−	0.524657i	$-0.175806\pi$
$383$	33.3211	1.70263	0.851314	+	0.524657i	$0.175806\pi$
$384$	278.519	14.2131
$385$	2.84009	0.144744
$386$	75.1263	3.82383
$387$	−59.9598	−3.04793
$388$	10.8770	0.552195
$389$	−31.5711	−1.60072	−0.800358	−	0.599522i	$-0.795357\pi$
$389$	−31.5711	−1.60072	−0.800358	+	0.599522i	$0.795357\pi$
$390$	−15.0759	−0.763398
$391$	−19.4870	−0.985498
$392$	−11.0216	−0.556674
$393$	56.0504	2.82737
$394$	−7.81911	−0.393921
$395$	−2.29551	−0.115499
$396$	−113.730	−5.71514
$397$	−7.73776	−0.388347	−0.194173	−	0.980967i	$-0.562202\pi$
$397$	−7.73776	−0.388347	−0.194173	+	0.980967i	$0.562202\pi$
$398$	−14.1292	−0.708231
$399$	17.2199	0.862073
$400$	−63.1534	−3.15767
$401$	−20.3536	−1.01641	−0.508205	−	0.861236i	$-0.669691\pi$
$401$	−20.3536	−1.01641	−0.508205	+	0.861236i	$0.669691\pi$
$402$	−14.5103	−0.723708
$403$	−4.12442	−0.205452
$404$	27.7209	1.37917
$405$	55.7250	2.76900
$406$	−12.0921	−0.600122
$407$	−8.46042	−0.419367
$408$	−122.643	−6.07175
$409$	1.92415	0.0951432	0.0475716	−	0.998868i	$-0.484852\pi$
$409$	1.92415	0.0951432	0.0475716	+	0.998868i	$0.484852\pi$
$410$	29.4902	1.45642
$411$	−20.7674	−1.02438
$412$	90.5373	4.46045
$413$	8.59255	0.422812
$414$	−149.926	−7.36848
$415$	20.1004	0.986689
$416$	38.0376	1.86495
$417$	−74.5324	−3.64987
$418$	30.6076	1.49707
$419$	24.4449	1.19421	0.597106	−	0.802162i	$-0.296317\pi$
$419$	24.4449	1.19421	0.597106	+	0.802162i	$0.296317\pi$
$420$	26.6025	1.29807
$421$	31.4476	1.53266	0.766331	−	0.642446i	$-0.222080\pi$
$421$	31.4476	1.53266	0.766331	+	0.642446i	$0.222080\pi$
$422$	−11.0514	−0.537973
$423$	59.3111	2.88380
$424$	112.880	5.48195
$425$	10.6486	0.516534
$426$	114.698	5.55716
$427$	7.58712	0.367166
$428$	−36.3381	−1.75647
$429$	−8.91498	−0.430419
$430$	24.9291	1.20219
$431$	−5.57298	−0.268441	−0.134221	−	0.990951i	$-0.542853\pi$
$431$	−5.57298	−0.268441	−0.134221	+	0.990951i	$0.542853\pi$
$432$	−385.525	−18.5486
$433$	−8.01428	−0.385142	−0.192571	−	0.981283i	$-0.561683\pi$
$433$	−8.01428	−0.385142	−0.192571	+	0.981283i	$0.561683\pi$
$434$	9.73778	0.467428
$435$	19.3213	0.926384
$436$	4.80603	0.230167
$437$	30.1560	1.44256
$438$	98.7522	4.71856
$439$	16.8037	0.801997	0.400998	−	0.916079i	$-0.368663\pi$
$439$	16.8037	0.801997	0.400998	+	0.916079i	$0.368663\pi$
$440$	31.3023	1.49228
$441$	8.84183	0.421039
$442$	−10.8432	−0.515759
$443$	32.3150	1.53533	0.767667	−	0.640849i	$-0.221418\pi$
$443$	32.3150	1.53533	0.767667	+	0.640849i	$0.221418\pi$
$444$	−79.2469	−3.76089
$445$	2.39586	0.113575
$446$	−19.3551	−0.916489
$447$	32.7715	1.55004
$448$	−51.4518	−2.43087
$449$	8.98909	0.424221	0.212111	−	0.977246i	$-0.431966\pi$
$449$	8.98909	0.424221	0.212111	+	0.977246i	$0.431966\pi$
$450$	81.9270	3.86207
$451$	17.4387	0.821157
$452$	−16.8423	−0.792196
$453$	−27.4051	−1.28760
$454$	−49.0696	−2.30295
$455$	1.55701	0.0729938
$456$	189.790	8.88775
$457$	−17.2264	−0.805819	−0.402910	−	0.915240i	$-0.632001\pi$
$457$	−17.2264	−0.805819	−0.402910	+	0.915240i	$0.632001\pi$
$458$	−47.0785	−2.19984
$459$	65.0053	3.03419
$460$	46.5872	2.17214
$461$	8.86724	0.412988	0.206494	−	0.978448i	$-0.433795\pi$
$461$	8.86724	0.412988	0.206494	+	0.978448i	$0.433795\pi$
$462$	21.0483	0.979256
$463$	−22.7238	−1.05606	−0.528032	−	0.849225i	$-0.677070\pi$
$463$	−22.7238	−1.05606	−0.528032	+	0.849225i	$0.677070\pi$
$464$	−82.4166	−3.82609
$465$	−15.5594	−0.721550
$466$	−75.8941	−3.51573
$467$	18.6704	0.863962	0.431981	−	0.901883i	$-0.357815\pi$
$467$	18.6704	0.863962	0.431981	+	0.901883i	$0.357815\pi$
$468$	−62.3497	−2.88211
$469$	1.49860	0.0691987
$470$	−24.6594	−1.13745
$471$	−31.4930	−1.45112
$472$	94.7035	4.35908
$473$	14.7416	0.677819
$474$	−17.0123	−0.781402
$475$	−16.4787	−0.756095
$476$	19.1336	0.876989
$477$	−90.5557	−4.14626
$478$	55.4287	2.53525
$479$	22.4297	1.02484	0.512420	−	0.858735i	$-0.328749\pi$
$479$	22.4297	1.02484	0.512420	+	0.858735i	$0.328749\pi$
$480$	143.497	6.54973
$481$	−4.63822	−0.211485
$482$	27.2247	1.24005
$483$	20.7378	0.943603
$484$	−37.1264	−1.68757
$485$	2.40164	0.109053
$486$	243.294	11.0360
$487$	3.82975	0.173543	0.0867713	−	0.996228i	$-0.472345\pi$
$487$	3.82975	0.173543	0.0867713	+	0.996228i	$0.472345\pi$
$488$	83.6221	3.78539
$489$	33.7515	1.52629
$490$	−3.67611	−0.166070
$491$	10.2932	0.464524	0.232262	−	0.972653i	$-0.425387\pi$
$491$	10.2932	0.464524	0.232262	+	0.972653i	$0.425387\pi$
$492$	163.345	7.36415
$493$	13.8967	0.625874
$494$	16.7799	0.754962
$495$	−25.1116	−1.12868
$496$	66.3700	2.98010
$497$	−11.8458	−0.531358
$498$	148.967	6.67537
$499$	9.37052	0.419482	0.209741	−	0.977757i	$-0.432738\pi$
$499$	9.37052	0.419482	0.209741	+	0.977757i	$0.432738\pi$
$500$	−64.1105	−2.86711
$501$	21.2825	0.950833
$502$	78.8277	3.51825
$503$	7.47321	0.333214	0.166607	−	0.986023i	$-0.446719\pi$
$503$	7.47321	0.333214	0.166607	+	0.986023i	$0.446719\pi$
$504$	97.4510	4.34081
$505$	6.12078	0.272371
$506$	36.8605	1.63865
$507$	39.8481	1.76972
$508$	−49.6960	−2.20490
$509$	4.54548	0.201475	0.100737	−	0.994913i	$-0.467880\pi$
$509$	4.54548	0.201475	0.100737	+	0.994913i	$0.467880\pi$
$510$	−40.9062	−1.81136
$511$	−10.1989	−0.451174
$512$	−189.365	−8.36883
$513$	−100.596	−4.44140
$514$	−28.5504	−1.25930
$515$	19.9907	0.880894
$516$	138.081	6.07869
$517$	−14.5821	−0.641319
$518$	10.9509	0.481153
$519$	16.0549	0.704734
$520$	17.1607	0.752548
$521$	15.5692	0.682098	0.341049	−	0.940046i	$-0.389218\pi$
$521$	15.5692	0.682098	0.341049	+	0.940046i	$0.389218\pi$
$522$	106.916	4.67960
$523$	5.98628	0.261762	0.130881	−	0.991398i	$-0.458219\pi$
$523$	5.98628	0.261762	0.130881	+	0.991398i	$0.458219\pi$
$524$	−96.3776	−4.21028
$525$	−11.3321	−0.494575
$526$	−21.0053	−0.915876
$527$	−11.1910	−0.487487
$528$	143.460	6.24328
$529$	13.3168	0.578990
$530$	37.6498	1.63540
$531$	−75.9738	−3.29698
$532$	−29.6093	−1.28373
$533$	9.56036	0.414105
$534$	17.7561	0.768381
$535$	−8.02345	−0.346884
$536$	16.5169	0.713421
$537$	39.3469	1.69794
$538$	50.0076	2.15598
$539$	−2.17383	−0.0936335
$540$	−155.407	−6.68767
$541$	−3.87837	−0.166744	−0.0833721	−	0.996518i	$-0.526569\pi$
$541$	−3.87837	−0.166744	−0.0833721	+	0.996518i	$0.526569\pi$
$542$	29.5068	1.26743
$543$	−40.3374	−1.73105
$544$	103.209	4.42506
$545$	1.06117	0.0454556
$546$	11.5392	0.493833
$547$	31.9457	1.36590	0.682951	−	0.730465i	$-0.260696\pi$
$547$	31.9457	1.36590	0.682951	+	0.730465i	$0.260696\pi$
$548$	35.7092	1.52542
$549$	−67.0840	−2.86307
$550$	−20.1424	−0.858873
$551$	−21.5051	−0.916147
$552$	228.564	9.72831
$553$	1.75700	0.0747153
$554$	−15.1800	−0.644938
$555$	−17.4977	−0.742737
$556$	128.157	5.43507
$557$	−31.1800	−1.32114	−0.660569	−	0.750765i	$-0.729685\pi$
$557$	−31.1800	−1.32114	−0.660569	+	0.750765i	$0.729685\pi$
$558$	−86.0997	−3.64489
$559$	8.08172	0.341820
$560$	−25.0554	−1.05878
$561$	−24.1894	−1.02128
$562$	−8.65102	−0.364921
$563$	0.889648	0.0374942	0.0187471	−	0.999824i	$-0.494032\pi$
$563$	0.889648	0.0374942	0.0187471	+	0.999824i	$0.494032\pi$
$564$	−136.587	−5.75136
$565$	−3.71879	−0.156450
$566$	60.1333	2.52759
$567$	−42.6524	−1.79123
$568$	−130.560	−5.47817
$569$	16.3752	0.686485	0.343242	−	0.939247i	$-0.388475\pi$
$569$	16.3752	0.686485	0.343242	+	0.939247i	$0.388475\pi$
$570$	63.3022	2.65144
$571$	−18.5992	−0.778353	−0.389177	−	0.921163i	$-0.627240\pi$
$571$	−18.5992	−0.778353	−0.389177	+	0.921163i	$0.627240\pi$
$572$	15.3291	0.640944
$573$	−69.8610	−2.91849
$574$	−22.5721	−0.942140
$575$	−19.8452	−0.827603
$576$	454.928	18.9553
$577$	25.8963	1.07808	0.539038	−	0.842281i	$-0.318788\pi$
$577$	25.8963	1.07808	0.539038	+	0.842281i	$0.318788\pi$
$578$	18.4120	0.765837
$579$	91.8796	3.81838
$580$	−33.2226	−1.37949
$581$	−15.3850	−0.638278
$582$	17.7989	0.737788
$583$	22.2638	0.922073
$584$	−112.408	−4.65150
$585$	−13.7668	−0.569188
$586$	4.34249	0.179387
$587$	−40.0560	−1.65329	−0.826643	−	0.562726i	$-0.809752\pi$
$587$	−40.0560	−1.65329	−0.826643	+	0.562726i	$0.809752\pi$
$588$	−20.3618	−0.839707
$589$	17.3180	0.713577
$590$	31.5872	1.30042
$591$	−9.56279	−0.393361
$592$	74.6381	3.06761
$593$	0.154309	0.00633673	0.00316837	−	0.999995i	$-0.498991\pi$
$593$	0.154309	0.00633673	0.00316837	+	0.999995i	$0.498991\pi$
$594$	−122.961	−5.04514
$595$	4.22471	0.173196
$596$	−56.3500	−2.30819
$597$	−17.2800	−0.707223
$598$	20.2079	0.826362
$599$	−1.79216	−0.0732258	−0.0366129	−	0.999330i	$-0.511657\pi$
$599$	−1.79216	−0.0732258	−0.0366129	+	0.999330i	$0.511657\pi$
$600$	−124.898	−5.09895
$601$	16.5587	0.675442	0.337721	−	0.941246i	$-0.390344\pi$
$601$	16.5587	0.675442	0.337721	+	0.941246i	$0.390344\pi$
$602$	−19.0810	−0.777683
$603$	−13.2503	−0.539595
$604$	47.1225	1.91739
$605$	−8.19753	−0.333277
$606$	45.3620	1.84271
$607$	−37.1857	−1.50932	−0.754660	−	0.656116i	$-0.772198\pi$
$607$	−37.1857	−1.50932	−0.754660	+	0.656116i	$0.772198\pi$
$608$	−159.716	−6.47735
$609$	−14.7887	−0.599267
$610$	27.8911	1.12928
$611$	−7.99427	−0.323414
$612$	−169.176	−6.83855
$613$	−13.2928	−0.536890	−0.268445	−	0.963295i	$-0.586510\pi$
$613$	−13.2928	−0.536890	−0.268445	+	0.963295i	$0.586510\pi$
$614$	−47.8280	−1.93018
$615$	36.0666	1.45434
$616$	−23.9591	−0.965338
$617$	5.35110	0.215427	0.107714	−	0.994182i	$-0.465647\pi$
$617$	5.35110	0.215427	0.107714	+	0.994182i	$0.465647\pi$
$618$	148.154	5.95961
$619$	37.0566	1.48943	0.744716	−	0.667382i	$-0.232585\pi$
$619$	37.0566	1.48943	0.744716	+	0.667382i	$0.232585\pi$
$620$	26.7541	1.07447
$621$	−121.147	−4.86145
$622$	74.1614	2.97360
$623$	−1.83382	−0.0734703
$624$	78.6483	3.14845
$625$	2.30980	0.0923918
$626$	−13.9315	−0.556816
$627$	37.4331	1.49493
$628$	54.1516	2.16088
$629$	−12.5851	−0.501801
$630$	32.5035	1.29497
$631$	44.3327	1.76486	0.882428	−	0.470447i	$-0.155907\pi$
$631$	44.3327	1.76486	0.882428	+	0.470447i	$0.155907\pi$
$632$	19.3649	0.770296
$633$	−13.5159	−0.537208
$634$	24.4357	0.970464
$635$	−10.9729	−0.435446
$636$	208.540	8.26916
$637$	−1.19175	−0.0472189
$638$	−26.2862	−1.04068
$639$	104.739	4.14340
$640$	−105.743	−4.17986
$641$	7.45926	0.294623	0.147312	−	0.989090i	$-0.452938\pi$
$641$	7.45926	0.294623	0.147312	+	0.989090i	$0.452938\pi$
$642$	−59.4630	−2.34682
$643$	−9.47799	−0.373776	−0.186888	−	0.982381i	$-0.559840\pi$
$643$	−9.47799	−0.373776	−0.186888	+	0.982381i	$0.559840\pi$
$644$	−35.6583	−1.40513
$645$	30.4884	1.20048
$646$	45.5296	1.79134
$647$	−35.6048	−1.39977	−0.699884	−	0.714256i	$-0.746765\pi$
$647$	−35.6048	−1.39977	−0.699884	+	0.714256i	$0.746765\pi$
$648$	−470.097	−18.4672
$649$	18.6787	0.733205
$650$	−11.0426	−0.433125
$651$	11.9093	0.466763
$652$	−58.0350	−2.27283
$653$	−26.8725	−1.05160	−0.525801	−	0.850607i	$-0.676234\pi$
$653$	−26.8725	−1.05160	−0.525801	+	0.850607i	$0.676234\pi$
$654$	7.86449	0.307526
$655$	−21.2802	−0.831486
$656$	−153.845	−6.00664
$657$	90.1773	3.51815
$658$	18.8745	0.735806
$659$	−38.2434	−1.48975	−0.744875	−	0.667204i	$-0.767491\pi$
$659$	−38.2434	−1.48975	−0.744875	+	0.667204i	$0.767491\pi$
$660$	57.8294	2.25100
$661$	0.537694	0.0209139	0.0104569	−	0.999945i	$-0.496671\pi$
$661$	0.537694	0.0209139	0.0104569	+	0.999945i	$0.496671\pi$
$662$	59.8310	2.32540
$663$	−13.2613	−0.515025
$664$	−169.567	−6.58049
$665$	−6.53773	−0.253522
$666$	−96.8256	−3.75192
$667$	−25.8984	−1.00279
$668$	−36.5949	−1.41590
$669$	−23.6713	−0.915184
$670$	5.50900	0.212831
$671$	16.4931	0.636709
$672$	−109.834	−4.23695
$673$	18.5128	0.713617	0.356809	−	0.934177i	$-0.383865\pi$
$673$	18.5128	0.713617	0.356809	+	0.934177i	$0.383865\pi$
$674$	−32.0593	−1.23488
$675$	66.2004	2.54805
$676$	−68.5181	−2.63531
$677$	46.9992	1.80633	0.903163	−	0.429299i	$-0.141239\pi$
$677$	46.9992	1.80633	0.903163	+	0.429299i	$0.141239\pi$
$678$	−27.5605	−1.05845
$679$	−1.83824	−0.0705451
$680$	46.5630	1.78561
$681$	−60.0122	−2.29967
$682$	21.1683	0.810575
$683$	26.1959	1.00236	0.501179	−	0.865343i	$-0.332900\pi$
$683$	26.1959	1.00236	0.501179	+	0.865343i	$0.332900\pi$
$684$	261.800	10.0102
$685$	7.88460	0.301255
$686$	2.81373	0.107429
$687$	−57.5771	−2.19670
$688$	−130.051	−4.95814
$689$	12.2056	0.464996
$690$	76.2345	2.90220
$691$	28.4206	1.08117	0.540586	−	0.841289i	$-0.318203\pi$
$691$	28.4206	1.08117	0.540586	+	0.841289i	$0.318203\pi$
$692$	−27.6062	−1.04943
$693$	19.2206	0.730132
$694$	−44.0298	−1.67135
$695$	28.2971	1.07337
$696$	−162.995	−6.17830
$697$	25.9406	0.982570
$698$	31.3457	1.18645
$699$	−92.8186	−3.51072
$700$	19.4854	0.736479
$701$	−18.2822	−0.690510	−0.345255	−	0.938509i	$-0.612208\pi$
$701$	−18.2822	−0.690510	−0.345255	+	0.938509i	$0.612208\pi$
$702$	−67.4102	−2.54423
$703$	19.4754	0.734529
$704$	−111.848	−4.21541
$705$	−30.1585	−1.13583
$706$	83.5181	3.14324
$707$	−4.68490	−0.176194
$708$	174.960	6.57539
$709$	46.2581	1.73726	0.868629	−	0.495462i	$-0.165001\pi$
$709$	46.2581	1.73726	0.868629	+	0.495462i	$0.165001\pi$
$710$	−43.5466	−1.63428
$711$	−15.5351	−0.582612
$712$	−20.2116	−0.757460
$713$	20.8560	0.781063
$714$	31.3100	1.17175
$715$	3.38468	0.126580
$716$	−67.6562	−2.52843
$717$	67.7894	2.53164
$718$	73.7853	2.75364
$719$	6.22936	0.232316	0.116158	−	0.993231i	$-0.462942\pi$
$719$	6.22936	0.232316	0.116158	+	0.993231i	$0.462942\pi$
$720$	221.535	8.25613
$721$	−15.3010	−0.569840
$722$	−16.9961	−0.632530
$723$	33.2958	1.23829
$724$	69.3595	2.57773
$725$	14.1522	0.525598
$726$	−60.7531	−2.25476
$727$	32.0946	1.19032	0.595161	−	0.803607i	$-0.297088\pi$
$727$	32.0946	1.19032	0.595161	+	0.803607i	$0.297088\pi$
$728$	−13.1350	−0.486815
$729$	169.592	6.28118
$730$	−37.4924	−1.38766
$731$	21.9285	0.811055
$732$	154.487	5.71002
$733$	0.0717696	0.00265087	0.00132543	−	0.999999i	$-0.499578\pi$
$733$	0.0717696	0.00265087	0.00132543	+	0.999999i	$0.499578\pi$
$734$	8.07314	0.297985
$735$	−4.49589	−0.165833
$736$	−192.345	−7.08994
$737$	3.25769	0.119999
$738$	199.578	7.34658
$739$	48.0143	1.76623	0.883116	−	0.469154i	$-0.155441\pi$
$739$	48.0143	1.76623	0.883116	+	0.469154i	$0.155441\pi$
$740$	30.0870	1.10602
$741$	20.5218	0.753887
$742$	−28.8175	−1.05792
$743$	−11.1671	−0.409681	−0.204840	−	0.978795i	$-0.565667\pi$
$743$	−11.1671	−0.409681	−0.204840	+	0.978795i	$0.565667\pi$
$744$	131.260	4.81221
$745$	−12.4421	−0.455843
$746$	92.9343	3.40257
$747$	136.032	4.97714
$748$	41.5933	1.52080
$749$	6.14122	0.224395
$750$	−104.909	−3.83075
$751$	2.82519	0.103093	0.0515463	−	0.998671i	$-0.483585\pi$
$751$	2.82519	0.103093	0.0515463	+	0.998671i	$0.483585\pi$
$752$	128.644	4.69115
$753$	96.4064	3.51325
$754$	−14.4108	−0.524810
$755$	10.4047	0.378664
$756$	118.950	4.32618
$757$	−3.88702	−0.141276	−0.0706382	−	0.997502i	$-0.522504\pi$
$757$	−3.88702	−0.141276	−0.0706382	+	0.997502i	$0.522504\pi$
$758$	−67.3930	−2.44782
$759$	45.0805	1.63632
$760$	−72.0562	−2.61375
$761$	29.5233	1.07022	0.535110	−	0.844783i	$-0.320270\pi$
$761$	29.5233	1.07022	0.535110	+	0.844783i	$0.320270\pi$
$762$	−81.3217	−2.94597
$763$	−0.812230	−0.0294047
$764$	120.125	4.34596
$765$	−37.3542	−1.35054
$766$	−93.7565	−3.38756
$767$	10.2402	0.369751
$768$	−429.565	−15.5006
$769$	36.2104	1.30578	0.652890	−	0.757452i	$-0.273556\pi$
$769$	36.2104	1.30578	0.652890	+	0.757452i	$0.273556\pi$
$770$	−7.99124	−0.287984
$771$	−34.9172	−1.25751
$772$	−157.985	−5.68601
$773$	37.7284	1.35699	0.678497	−	0.734603i	$-0.262631\pi$
$773$	37.7284	1.35699	0.678497	+	0.734603i	$0.262631\pi$
$774$	168.711	6.06418
$775$	−11.3967	−0.409382
$776$	−20.2603	−0.727302
$777$	13.3929	0.480468
$778$	88.8325	3.18480
$779$	−40.1430	−1.43827
$780$	31.7035	1.13517
$781$	−25.7508	−0.921437
$782$	54.8311	1.96075
$783$	86.3929	3.08743
$784$	19.1776	0.684915
$785$	11.9567	0.426752
$786$	−157.711	−5.62535
$787$	−21.5785	−0.769189	−0.384595	−	0.923086i	$-0.625659\pi$
$787$	−21.5785	−0.769189	−0.384595	+	0.923086i	$0.625659\pi$
$788$	16.4430	0.585759
$789$	−25.6895	−0.914572
$790$	6.45893	0.229799
$791$	2.84639	0.101206
$792$	211.842	7.52747
$793$	9.04195	0.321089
$794$	21.7720	0.772658
$795$	46.0457	1.63307
$796$	29.7126	1.05314
$797$	−22.5131	−0.797456	−0.398728	−	0.917069i	$-0.630548\pi$
$797$	−22.5131	−0.797456	−0.398728	+	0.917069i	$0.630548\pi$
$798$	−48.4521	−1.71519
$799$	−21.6912	−0.767381
$800$	105.107	3.71608
$801$	16.2143	0.572903
$802$	57.2695	2.02225
$803$	−22.1708	−0.782389
$804$	30.5141	1.07615
$805$	−7.87336	−0.277499
$806$	11.6050	0.408768
$807$	61.1593	2.15291
$808$	−51.6351	−1.81652
$809$	25.2593	0.888071	0.444035	−	0.896009i	$-0.353546\pi$
$809$	25.2593	0.888071	0.444035	+	0.896009i	$0.353546\pi$
$810$	−156.795	−5.50922
$811$	0.576375	0.0202393	0.0101196	−	0.999949i	$-0.496779\pi$
$811$	0.576375	0.0202393	0.0101196	+	0.999949i	$0.496779\pi$
$812$	25.4289	0.892378
$813$	36.0869	1.26562
$814$	23.8053	0.834376
$815$	−12.8141	−0.448860
$816$	213.400	7.47050
$817$	−33.9343	−1.18721
$818$	−5.41404	−0.189298
$819$	10.5372	0.368201
$820$	−62.0158	−2.16569
$821$	40.3894	1.40960	0.704800	−	0.709406i	$-0.251037\pi$
$821$	40.3894	1.40960	0.704800	+	0.709406i	$0.251037\pi$
$822$	58.4339	2.03812
$823$	−26.2832	−0.916175	−0.458088	−	0.888907i	$-0.651465\pi$
$823$	−26.2832	−0.916175	−0.458088	+	0.888907i	$0.651465\pi$
$824$	−168.642	−5.87491
$825$	−24.6341	−0.857651
$826$	−24.1771	−0.841229
$827$	−0.958031	−0.0333140	−0.0166570	−	0.999861i	$-0.505302\pi$
$827$	−0.958031	−0.0333140	−0.0166570	+	0.999861i	$0.505302\pi$
$828$	315.284	10.9569
$829$	−47.2303	−1.64038	−0.820189	−	0.572093i	$-0.806132\pi$
$829$	−47.2303	−1.64038	−0.820189	+	0.572093i	$0.806132\pi$
$830$	−56.5571	−1.96312
$831$	−18.5652	−0.644020
$832$	−61.3177	−2.12581
$833$	−3.23363	−0.112039
$834$	209.714	7.26180
$835$	−8.08016	−0.279626
$836$	−64.3656	−2.22613
$837$	−69.5722	−2.40477
$838$	−68.7814	−2.37601
$839$	0.0191395	0.000660768 0	0.000330384	−	1.00000i	$-0.499895\pi$
$839$	0.0191395	0.000660768 0	0.000330384		1.00000i	$0.499895\pi$
$840$	−49.5518	−1.70970
$841$	−10.5311	−0.363143
$842$	−88.4850	−3.04939
$843$	−10.5802	−0.364402
$844$	23.2403	0.799964
$845$	−15.1288	−0.520447
$846$	−166.885	−5.73764
$847$	6.27446	0.215593
$848$	−196.412	−6.74482
$849$	73.5432	2.52399
$850$	−29.9623	−1.02770
$851$	23.4541	0.803998
$852$	−241.203	−8.26347
$853$	−51.0614	−1.74831	−0.874154	−	0.485648i	$-0.838584\pi$
$853$	−51.0614	−1.74831	−0.874154	+	0.485648i	$0.838584\pi$
$854$	−21.3481	−0.730517
$855$	57.8055	1.97691
$856$	67.6860	2.31346
$857$	24.0577	0.821796	0.410898	−	0.911681i	$-0.365215\pi$
$857$	24.0577	0.821796	0.410898	+	0.911681i	$0.365215\pi$
$858$	25.0843	0.856365
$859$	45.0229	1.53616	0.768082	−	0.640352i	$-0.221211\pi$
$859$	45.0229	1.53616	0.768082	+	0.640352i	$0.221211\pi$
$860$	−52.4242	−1.78765
$861$	−27.6057	−0.940799
$862$	15.6809	0.534093
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	641.632	21.8288
$865$	−6.09545	−0.207252
$866$	22.5500	0.766281
$867$	22.5179	0.764747
$868$	−20.4779	−0.695064
$869$	3.81942	0.129565
$870$	−54.3648	−1.84314
$871$	1.78595	0.0605146
$872$	−8.95206	−0.303155
$873$	16.2534	0.550093
$874$	−84.8510	−2.87013
$875$	10.8348	0.366284
$876$	−207.669	−7.01648
$877$	41.0095	1.38479	0.692397	−	0.721517i	$-0.256555\pi$
$877$	41.0095	1.38479	0.692397	+	0.721517i	$0.256555\pi$
$878$	−47.2811	−1.59566
$879$	5.31087	0.179131
$880$	−54.4661	−1.83605
$881$	−47.1171	−1.58742	−0.793708	−	0.608299i	$-0.791852\pi$
$881$	−47.1171	−1.58742	−0.793708	+	0.608299i	$0.791852\pi$
$882$	−24.8785	−0.837703
$883$	52.6564	1.77203	0.886014	−	0.463659i	$-0.153464\pi$
$883$	52.6564	1.77203	0.886014	+	0.463659i	$0.153464\pi$
$884$	22.8025	0.766932
$885$	38.6311	1.29857
$886$	−90.9258	−3.05471
$887$	−5.91097	−0.198471	−0.0992355	−	0.995064i	$-0.531640\pi$
$887$	−5.91097	−0.198471	−0.0992355	+	0.995064i	$0.531640\pi$
$888$	147.611	4.95351
$889$	8.39875	0.281685
$890$	−6.74131	−0.225969
$891$	−92.7192	−3.10621
$892$	40.7023	1.36281
$893$	33.5672	1.12328
$894$	−92.2101	−3.08397
$895$	−14.9385	−0.499339
$896$	80.9366	2.70390
$897$	24.7143	0.825186
$898$	−25.2929	−0.844034
$899$	−14.8730	−0.496041
$900$	−172.287	−5.74289
$901$	33.1180	1.10332
$902$	−49.0678	−1.63378
$903$	−23.3361	−0.776576
$904$	31.3718	1.04341
$905$	15.3146	0.509074
$906$	77.1104	2.56182
$907$	38.9376	1.29290	0.646450	−	0.762956i	$-0.276253\pi$
$907$	38.9376	1.29290	0.646450	+	0.762956i	$0.276253\pi$
$908$	103.190	3.42447
$909$	41.4231	1.37392
$910$	−4.38101	−0.145229
$911$	−40.3894	−1.33816	−0.669080	−	0.743191i	$-0.733312\pi$
$911$	−40.3894	−1.33816	−0.669080	+	0.743191i	$0.733312\pi$
$912$	−330.236	−10.9352
$913$	−33.4444	−1.10685
$914$	48.4706	1.60326
$915$	34.1108	1.12767
$916$	99.0028	3.27115
$917$	16.2881	0.537879
$918$	−182.907	−6.03684
$919$	−9.03653	−0.298088	−0.149044	−	0.988831i	$-0.547620\pi$
$919$	−9.03653	−0.298088	−0.149044	+	0.988831i	$0.547620\pi$
$920$	−86.7769	−2.86095
$921$	−58.4937	−1.92743
$922$	−24.9500	−0.821685
$923$	−14.1173	−0.464676
$924$	−44.2631	−1.45615
$925$	−12.8165	−0.421403
$926$	63.9385	2.10115
$927$	135.289	4.44348
$928$	137.167	4.50271
$929$	2.51395	0.0824800	0.0412400	−	0.999149i	$-0.486869\pi$
$929$	2.51395	0.0824800	0.0412400	+	0.999149i	$0.486869\pi$
$930$	43.7800	1.43560
$931$	5.00404	0.164001
$932$	159.600	5.22787
$933$	90.6995	2.96937
$934$	−52.5334	−1.71894
$935$	9.18381	0.300343
$936$	116.137	3.79606
$937$	−25.2221	−0.823972	−0.411986	−	0.911190i	$-0.635165\pi$
$937$	−25.2221	−0.823972	−0.411986	+	0.911190i	$0.635165\pi$
$938$	−4.21664	−0.137678
$939$	−17.0383	−0.556023
$940$	51.8570	1.69139
$941$	−21.4312	−0.698637	−0.349319	−	0.937004i	$-0.613587\pi$
$941$	−21.4312	−0.698637	−0.349319	+	0.937004i	$0.613587\pi$
$942$	88.6127	2.88716
$943$	−48.3440	−1.57430
$944$	−164.785	−5.36328
$945$	26.2642	0.854375
$946$	−41.4788	−1.34859
$947$	−28.0612	−0.911866	−0.455933	−	0.890014i	$-0.650694\pi$
$947$	−28.0612	−0.911866	−0.455933	+	0.890014i	$0.650694\pi$
$948$	35.7757	1.16194
$949$	−12.1546	−0.394554
$950$	46.3666	1.50433
$951$	29.8848	0.969082
$952$	−35.6398	−1.15509
$953$	31.1822	1.01009	0.505045	−	0.863093i	$-0.331476\pi$
$953$	31.1822	1.01009	0.505045	+	0.863093i	$0.331476\pi$
$954$	254.799	8.24943
$955$	26.5236	0.858283
$956$	−116.563	−3.76991
$957$	−32.1481	−1.03920
$958$	−63.1112	−2.03903
$959$	−6.03494	−0.194879
$960$	−231.322	−7.46588
$961$	−19.0228	−0.613639
$962$	13.0507	0.420771
$963$	−54.2996	−1.74978
$964$	−57.2516	−1.84395
$965$	−34.8832	−1.12293
$966$	−58.3506	−1.87740
$967$	24.6160	0.791597	0.395798	−	0.918337i	$-0.370468\pi$
$967$	24.6160	0.791597	0.395798	+	0.918337i	$0.370468\pi$
$968$	69.1545	2.22271
$969$	55.6828	1.78879
$970$	−6.75757	−0.216972
$971$	24.0038	0.770320	0.385160	−	0.922850i	$-0.374146\pi$
$971$	24.0038	0.770320	0.385160	+	0.922850i	$0.374146\pi$
$972$	−511.630	−16.4105
$973$	−21.6589	−0.694351
$974$	−10.7759	−0.345282
$975$	−13.5051	−0.432509
$976$	−145.503	−4.65743
$977$	6.62617	0.211990	0.105995	−	0.994367i	$-0.466197\pi$
$977$	6.62617	0.211990	0.105995	+	0.994367i	$0.466197\pi$
$978$	−94.9675	−3.03672
$979$	−3.98640	−0.127406
$980$	7.73060	0.246945
$981$	7.18160	0.229291
$982$	−28.9622	−0.924220
$983$	53.3912	1.70291	0.851457	−	0.524425i	$-0.175720\pi$
$983$	53.3912	1.70291	0.851457	+	0.524425i	$0.175720\pi$
$984$	−304.258	−9.69940
$985$	3.63063	0.115681
$986$	−39.1015	−1.24524
$987$	23.0836	0.734758
$988$	−35.2869	−1.12262
$989$	−40.8669	−1.29949
$990$	70.6572	2.24563
$991$	44.8745	1.42548	0.712742	−	0.701426i	$-0.247453\pi$
$991$	44.8745	1.42548	0.712742	+	0.701426i	$0.247453\pi$
$992$	−110.460	−3.50711
$993$	73.1734	2.32209
$994$	33.3310	1.05719
$995$	6.56055	0.207984
$996$	−313.267	−9.92624
$997$	18.2195	0.577017	0.288508	−	0.957477i	$-0.406841\pi$
$997$	18.2195	0.577017	0.288508	+	0.957477i	$0.406841\pi$
$998$	−26.3661	−0.834605
$999$	−78.2392	−2.47538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.1	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.1	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81373 q^{2} -3.44120 q^{3} +5.91707 q^{4} +1.30649 q^{5} +9.68259 q^{6} -1.00000 q^{7} -11.0216 q^{8} +8.84183 q^{9} +O(q^{10})\)	\(q-2.81373 q^{2} -3.44120 q^{3} +5.91707 q^{4} +1.30649 q^{5} +9.68259 q^{6} -1.00000 q^{7} -11.0216 q^{8} +8.84183 q^{9} -3.67611 q^{10} -2.17383 q^{11} -20.3618 q^{12} -1.19175 q^{13} +2.81373 q^{14} -4.49589 q^{15} +19.1776 q^{16} -3.23363 q^{17} -24.8785 q^{18} +5.00404 q^{19} +7.73060 q^{20} +3.44120 q^{21} +6.11657 q^{22} +6.02634 q^{23} +37.9274 q^{24} -3.29308 q^{25} +3.35326 q^{26} -20.1029 q^{27} -5.91707 q^{28} -4.29754 q^{29} +12.6502 q^{30} +3.46081 q^{31} -31.9174 q^{32} +7.48058 q^{33} +9.09857 q^{34} -1.30649 q^{35} +52.3177 q^{36} +3.89194 q^{37} -14.0800 q^{38} +4.10104 q^{39} -14.3996 q^{40} -8.02212 q^{41} -9.68259 q^{42} -6.78139 q^{43} -12.8627 q^{44} +11.5518 q^{45} -16.9565 q^{46} +6.70801 q^{47} -65.9939 q^{48} +1.00000 q^{49} +9.26584 q^{50} +11.1276 q^{51} -7.05167 q^{52} -10.2417 q^{53} +56.5640 q^{54} -2.84009 q^{55} +11.0216 q^{56} -17.2199 q^{57} +12.0921 q^{58} -8.59255 q^{59} -26.6025 q^{60} -7.58712 q^{61} -9.73778 q^{62} -8.84183 q^{63} +51.4518 q^{64} -1.55701 q^{65} -21.0483 q^{66} -1.49860 q^{67} -19.1336 q^{68} -20.7378 q^{69} +3.67611 q^{70} +11.8458 q^{71} -97.4510 q^{72} +10.1989 q^{73} -10.9509 q^{74} +11.3321 q^{75} +29.6093 q^{76} +2.17383 q^{77} -11.5392 q^{78} -1.75700 q^{79} +25.0554 q^{80} +42.6524 q^{81} +22.5721 q^{82} +15.3850 q^{83} +20.3618 q^{84} -4.22471 q^{85} +19.0810 q^{86} +14.7887 q^{87} +23.9591 q^{88} +1.83382 q^{89} -32.5035 q^{90} +1.19175 q^{91} +35.6583 q^{92} -11.9093 q^{93} -18.8745 q^{94} +6.53773 q^{95} +109.834 q^{96} +1.83824 q^{97} -2.81373 q^{98} -19.2206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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