LMFDB - Embedded newform 481.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [481,2,Mod(1,481)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(481, 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("481.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 481 = 13 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	481.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:	$3.84080433722$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.200018349.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 8x^{5} + 16x^{3} - x^{2} - 7x + 2 $ x^7 - 8x^5 + 16x^3 - x^2 - 7*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.29453$ of defining polynomial
Character	$\chi$	$=$	481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.920623 q^{2} -3.29453 q^{3} -1.15245 q^{4} +3.00569 q^{5} -3.03302 q^{6} +0.633057 q^{7} -2.90222 q^{8} +7.85390 q^{9} +O(q^{10})$	\(q+0.920623 q^{2} -3.29453 q^{3} -1.15245 q^{4} +3.00569 q^{5} -3.03302 q^{6} +0.633057 q^{7} -2.90222 q^{8} +7.85390 q^{9} +2.76711 q^{10} -4.87498 q^{11} +3.79679 q^{12} +1.00000 q^{13} +0.582806 q^{14} -9.90233 q^{15} -0.366943 q^{16} -6.64767 q^{17} +7.23048 q^{18} -0.429932 q^{19} -3.46392 q^{20} -2.08562 q^{21} -4.48801 q^{22} -3.17086 q^{23} +9.56144 q^{24} +4.03418 q^{25} +0.920623 q^{26} -15.9913 q^{27} -0.729568 q^{28} -9.89194 q^{29} -9.11631 q^{30} -8.34746 q^{31} +5.46663 q^{32} +16.0607 q^{33} -6.12000 q^{34} +1.90277 q^{35} -9.05125 q^{36} +1.00000 q^{37} -0.395805 q^{38} -3.29453 q^{39} -8.72318 q^{40} +3.87056 q^{41} -1.92007 q^{42} +11.1699 q^{43} +5.61818 q^{44} +23.6064 q^{45} -2.91916 q^{46} -3.70369 q^{47} +1.20890 q^{48} -6.59924 q^{49} +3.71396 q^{50} +21.9009 q^{51} -1.15245 q^{52} +3.24720 q^{53} -14.7219 q^{54} -14.6527 q^{55} -1.83727 q^{56} +1.41642 q^{57} -9.10675 q^{58} +2.68898 q^{59} +11.4120 q^{60} -3.27057 q^{61} -7.68486 q^{62} +4.97196 q^{63} +5.76659 q^{64} +3.00569 q^{65} +14.7859 q^{66} +4.02164 q^{67} +7.66113 q^{68} +10.4465 q^{69} +1.75174 q^{70} -9.96512 q^{71} -22.7937 q^{72} -3.00353 q^{73} +0.920623 q^{74} -13.2907 q^{75} +0.495476 q^{76} -3.08614 q^{77} -3.03302 q^{78} -7.43789 q^{79} -1.10292 q^{80} +29.1220 q^{81} +3.56332 q^{82} +13.0212 q^{83} +2.40358 q^{84} -19.9808 q^{85} +10.2832 q^{86} +32.5893 q^{87} +14.1483 q^{88} -2.33515 q^{89} +21.7326 q^{90} +0.633057 q^{91} +3.65426 q^{92} +27.5009 q^{93} -3.40970 q^{94} -1.29224 q^{95} -18.0099 q^{96} -0.462924 q^{97} -6.07541 q^{98} -38.2876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 7 q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 7 * q - q^2 - 7 * q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^9	\( 7 q - q^{2} - 7 q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9} - 11 q^{10} - 13 q^{11} + q^{12} + 7 q^{13} - 2 q^{14} - 11 q^{15} - 9 q^{16} - 10 q^{17} + 8 q^{18} - 2 q^{19} - 9 q^{20} + 4 q^{21} - 6 q^{22} - 24 q^{23} + 7 q^{25} - q^{26} - 13 q^{27} - 11 q^{28} - 17 q^{29} + 14 q^{30} - 11 q^{31} - q^{32} + 12 q^{33} + 4 q^{34} - 10 q^{35} - 23 q^{36} + 7 q^{37} + 5 q^{38} - 7 q^{39} - 10 q^{40} - 17 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{44} + 32 q^{45} - 12 q^{46} - 21 q^{47} + 11 q^{48} - 15 q^{49} + 27 q^{50} + 4 q^{51} + 3 q^{52} - 16 q^{53} - q^{54} + 11 q^{55} + 8 q^{56} + 11 q^{57} + 13 q^{58} - 18 q^{59} + 25 q^{60} - 20 q^{61} - 4 q^{62} + 18 q^{63} - 8 q^{64} - 2 q^{65} + 40 q^{66} + 7 q^{67} - 7 q^{68} + 33 q^{69} + 41 q^{70} - 35 q^{71} - 5 q^{72} + 8 q^{73} - q^{74} - 27 q^{75} + 50 q^{76} - 16 q^{77} - 4 q^{78} - 18 q^{79} - 8 q^{80} + 23 q^{81} + 41 q^{82} + 19 q^{83} + 13 q^{84} + 5 q^{85} + 38 q^{86} + 40 q^{87} - 6 q^{88} - q^{89} + 36 q^{90} - 2 q^{91} + 20 q^{92} + 14 q^{93} - q^{94} - 23 q^{95} - 5 q^{96} + 22 q^{97} - 16 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - q^2 - 7 * q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^9 - 11 * q^10 - 13 * q^11 + q^12 + 7 * q^13 - 2 * q^14 - 11 * q^15 - 9 * q^16 - 10 * q^17 + 8 * q^18 - 2 * q^19 - 9 * q^20 + 4 * q^21 - 6 * q^22 - 24 * q^23 + 7 * q^25 - q^26 - 13 * q^27 - 11 * q^28 - 17 * q^29 + 14 * q^30 - 11 * q^31 - q^32 + 12 * q^33 + 4 * q^34 - 10 * q^35 - 23 * q^36 + 7 * q^37 + 5 * q^38 - 7 * q^39 - 10 * q^40 - 17 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^44 + 32 * q^45 - 12 * q^46 - 21 * q^47 + 11 * q^48 - 15 * q^49 + 27 * q^50 + 4 * q^51 + 3 * q^52 - 16 * q^53 - q^54 + 11 * q^55 + 8 * q^56 + 11 * q^57 + 13 * q^58 - 18 * q^59 + 25 * q^60 - 20 * q^61 - 4 * q^62 + 18 * q^63 - 8 * q^64 - 2 * q^65 + 40 * q^66 + 7 * q^67 - 7 * q^68 + 33 * q^69 + 41 * q^70 - 35 * q^71 - 5 * q^72 + 8 * q^73 - q^74 - 27 * q^75 + 50 * q^76 - 16 * q^77 - 4 * q^78 - 18 * q^79 - 8 * q^80 + 23 * q^81 + 41 * q^82 + 19 * q^83 + 13 * q^84 + 5 * q^85 + 38 * q^86 + 40 * q^87 - 6 * q^88 - q^89 + 36 * q^90 - 2 * q^91 + 20 * q^92 + 14 * q^93 - q^94 - 23 * q^95 - 5 * q^96 + 22 * q^97 - 16 * q^98 - 23 * 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 $

$2$	0.920623	0.650979	0.325489	−	0.945546i	$-0.394471\pi$
$2$	0.920623	0.650979	0.325489	+	0.945546i	$0.394471\pi$
$3$	−3.29453	−1.90210	−0.951048	−	0.309045i	$-0.899991\pi$
$3$	−3.29453	−1.90210	−0.951048	+	0.309045i	$0.899991\pi$
$4$	−1.15245	−0.576227
$5$	3.00569	1.34419	0.672093	−	0.740467i	$-0.265395\pi$
$5$	3.00569	1.34419	0.672093	+	0.740467i	$0.265395\pi$
$6$	−3.03302	−1.23822
$7$	0.633057	0.239273	0.119636	−	0.992818i	$-0.461827\pi$
$7$	0.633057	0.239273	0.119636	+	0.992818i	$0.461827\pi$
$8$	−2.90222	−1.02609
$9$	7.85390	2.61797
$10$	2.76711	0.875036
$11$	−4.87498	−1.46986	−0.734930	−	0.678143i	$-0.762785\pi$
$11$	−4.87498	−1.46986	−0.734930	+	0.678143i	$0.762785\pi$
$12$	3.79679	1.09604
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.582806	0.155762
$15$	−9.90233	−2.55677
$16$	−0.366943	−0.0917358
$17$	−6.64767	−1.61230	−0.806148	−	0.591713i	$-0.798452\pi$
$17$	−6.64767	−1.61230	−0.806148	+	0.591713i	$0.798452\pi$
$18$	7.23048	1.70424
$19$	−0.429932	−0.0986331	−0.0493165	−	0.998783i	$-0.515704\pi$
$19$	−0.429932	−0.0986331	−0.0493165	+	0.998783i	$0.515704\pi$
$20$	−3.46392	−0.774556
$21$	−2.08562	−0.455120
$22$	−4.48801	−0.956848
$23$	−3.17086	−0.661169	−0.330585	−	0.943776i	$-0.607246\pi$
$23$	−3.17086	−0.661169	−0.330585	+	0.943776i	$0.607246\pi$
$24$	9.56144	1.95172
$25$	4.03418	0.806836
$26$	0.920623	0.180549
$27$	−15.9913	−3.07752
$28$	−0.729568	−0.137875
$29$	−9.89194	−1.83689	−0.918444	−	0.395551i	$-0.870554\pi$
$29$	−9.89194	−1.83689	−0.918444	+	0.395551i	$0.870554\pi$
$30$	−9.11631	−1.66440
$31$	−8.34746	−1.49925	−0.749624	−	0.661864i	$-0.769766\pi$
$31$	−8.34746	−1.49925	−0.749624	+	0.661864i	$0.769766\pi$
$32$	5.46663	0.966372
$33$	16.0607	2.79581
$34$	−6.12000	−1.04957
$35$	1.90277	0.321627
$36$	−9.05125	−1.50854
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−0.395805	−0.0642080
$39$	−3.29453	−0.527546
$40$	−8.72318	−1.37926
$41$	3.87056	0.604480	0.302240	−	0.953232i	$-0.402266\pi$
$41$	3.87056	0.604480	0.302240	+	0.953232i	$0.402266\pi$
$42$	−1.92007	−0.296273
$43$	11.1699	1.70339	0.851695	−	0.524037i	$-0.175575\pi$
$43$	11.1699	1.70339	0.851695	+	0.524037i	$0.175575\pi$
$44$	5.61818	0.846973
$45$	23.6064	3.51903
$46$	−2.91916	−0.430407
$47$	−3.70369	−0.540239	−0.270120	−	0.962827i	$-0.587063\pi$
$47$	−3.70369	−0.540239	−0.270120	+	0.962827i	$0.587063\pi$
$48$	1.20890	0.174490
$49$	−6.59924	−0.942748
$50$	3.71396	0.525233
$51$	21.9009	3.06674
$52$	−1.15245	−0.159817
$53$	3.24720	0.446037	0.223018	−	0.974814i	$-0.428409\pi$
$53$	3.24720	0.446037	0.223018	+	0.974814i	$0.428409\pi$
$54$	−14.7219	−2.00340
$55$	−14.6527	−1.97577
$56$	−1.83727	−0.245516
$57$	1.41642	0.187609
$58$	−9.10675	−1.19577
$59$	2.68898	0.350075	0.175037	−	0.984562i	$-0.443995\pi$
$59$	2.68898	0.350075	0.175037	+	0.984562i	$0.443995\pi$
$60$	11.4120	1.47328
$61$	−3.27057	−0.418754	−0.209377	−	0.977835i	$-0.567144\pi$
$61$	−3.27057	−0.418754	−0.209377	+	0.977835i	$0.567144\pi$
$62$	−7.68486	−0.975978
$63$	4.97196	0.626408
$64$	5.76659	0.720823
$65$	3.00569	0.372810
$66$	14.7859	1.82002
$67$	4.02164	0.491321	0.245661	−	0.969356i	$-0.420995\pi$
$67$	4.02164	0.491321	0.245661	+	0.969356i	$0.420995\pi$
$68$	7.66113	0.929049
$69$	10.4465	1.25761
$70$	1.75174	0.209373
$71$	−9.96512	−1.18264	−0.591321	−	0.806436i	$-0.701393\pi$
$71$	−9.96512	−1.18264	−0.591321	+	0.806436i	$0.701393\pi$
$72$	−22.7937	−2.68627
$73$	−3.00353	−0.351536	−0.175768	−	0.984432i	$-0.556241\pi$
$73$	−3.00353	−0.351536	−0.175768	+	0.984432i	$0.556241\pi$
$74$	0.920623	0.107020
$75$	−13.2907	−1.53468
$76$	0.495476	0.0568350
$77$	−3.08614	−0.351698
$78$	−3.03302	−0.343421
$79$	−7.43789	−0.836829	−0.418414	−	0.908256i	$-0.637414\pi$
$79$	−7.43789	−0.836829	−0.418414	+	0.908256i	$0.637414\pi$
$80$	−1.10292	−0.123310
$81$	29.1220	3.23578
$82$	3.56332	0.393503
$83$	13.0212	1.42927	0.714633	−	0.699500i	$-0.246594\pi$
$83$	13.0212	1.42927	0.714633	+	0.699500i	$0.246594\pi$
$84$	2.40358	0.262252
$85$	−19.9808	−2.16723
$86$	10.2832	1.10887
$87$	32.5893	3.49394
$88$	14.1483	1.50821
$89$	−2.33515	−0.247525	−0.123762	−	0.992312i	$-0.539496\pi$
$89$	−2.33515	−0.247525	−0.123762	+	0.992312i	$0.539496\pi$
$90$	21.7326	2.29082
$91$	0.633057	0.0663624
$92$	3.65426	0.380983
$93$	27.5009	2.85171
$94$	−3.40970	−0.351684
$95$	−1.29224	−0.132581
$96$	−18.0099	−1.83813
$97$	−0.462924	−0.0470029	−0.0235014	−	0.999724i	$-0.507481\pi$
$97$	−0.462924	−0.0470029	−0.0235014	+	0.999724i	$0.507481\pi$
$98$	−6.07541	−0.613709
$99$	−38.2876	−3.84804
$100$	−4.64921	−0.464921
$101$	3.09068	0.307534	0.153767	−	0.988107i	$-0.450860\pi$
$101$	3.09068	0.307534	0.153767	+	0.988107i	$0.450860\pi$
$102$	20.1625	1.99638
$103$	13.4285	1.32315	0.661574	−	0.749880i	$-0.269889\pi$
$103$	13.4285	1.32315	0.661574	+	0.749880i	$0.269889\pi$
$104$	−2.90222	−0.284586
$105$	−6.26873	−0.611766
$106$	2.98944	0.290360
$107$	−14.5604	−1.40761	−0.703806	−	0.710393i	$-0.748517\pi$
$107$	−14.5604	−1.40761	−0.703806	+	0.710393i	$0.748517\pi$
$108$	18.4292	1.77335
$109$	3.31616	0.317630	0.158815	−	0.987308i	$-0.449233\pi$
$109$	3.31616	0.317630	0.158815	+	0.987308i	$0.449233\pi$
$110$	−13.4896	−1.28618
$111$	−3.29453	−0.312702
$112$	−0.232296	−0.0219499
$113$	1.31859	0.124042	0.0620212	−	0.998075i	$-0.480245\pi$
$113$	1.31859	0.124042	0.0620212	+	0.998075i	$0.480245\pi$
$114$	1.30399	0.122130
$115$	−9.53061	−0.888734
$116$	11.4000	1.05846
$117$	7.85390	0.726093
$118$	2.47553	0.227891
$119$	−4.20835	−0.385779
$120$	28.7387	2.62348
$121$	12.7654	1.16049
$122$	−3.01097	−0.272600
$123$	−12.7517	−1.14978
$124$	9.62006	0.863907
$125$	−2.90295	−0.259648
$126$	4.57730	0.407778
$127$	−1.87806	−0.166651	−0.0833254	−	0.996522i	$-0.526554\pi$
$127$	−1.87806	−0.166651	−0.0833254	+	0.996522i	$0.526554\pi$
$128$	−5.62440	−0.497131
$129$	−36.7995	−3.24001
$130$	2.76711	0.242691
$131$	20.3755	1.78022	0.890109	−	0.455747i	$-0.150628\pi$
$131$	20.3755	1.78022	0.890109	+	0.455747i	$0.150628\pi$
$132$	−18.5092	−1.61102
$133$	−0.272171	−0.0236002
$134$	3.70241	0.319840
$135$	−48.0649	−4.13677
$136$	19.2930	1.65436
$137$	−3.39674	−0.290203	−0.145102	−	0.989417i	$-0.546351\pi$
$137$	−3.39674	−0.290203	−0.145102	+	0.989417i	$0.546351\pi$
$138$	9.61725	0.818675
$139$	−2.82146	−0.239313	−0.119657	−	0.992815i	$-0.538179\pi$
$139$	−2.82146	−0.239313	−0.119657	+	0.992815i	$0.538179\pi$
$140$	−2.19286	−0.185330
$141$	12.2019	1.02759
$142$	−9.17411	−0.769874
$143$	−4.87498	−0.407666
$144$	−2.88193	−0.240161
$145$	−29.7321	−2.46912
$146$	−2.76512	−0.228843
$147$	21.7414	1.79320
$148$	−1.15245	−0.0947311
$149$	−2.52611	−0.206947	−0.103474	−	0.994632i	$-0.532996\pi$
$149$	−2.52611	−0.206947	−0.103474	+	0.994632i	$0.532996\pi$
$150$	−12.2357	−0.999044
$151$	−17.0608	−1.38839	−0.694195	−	0.719787i	$-0.744240\pi$
$151$	−17.0608	−1.38839	−0.694195	+	0.719787i	$0.744240\pi$
$152$	1.24776	0.101206
$153$	−52.2101	−4.22094
$154$	−2.84117	−0.228948
$155$	−25.0899	−2.01527
$156$	3.79679	0.303986
$157$	3.41492	0.272540	0.136270	−	0.990672i	$-0.456489\pi$
$157$	3.41492	0.272540	0.136270	+	0.990672i	$0.456489\pi$
$158$	−6.84750	−0.544757
$159$	−10.6980	−0.848404
$160$	16.4310	1.29898
$161$	−2.00733	−0.158200
$162$	26.8104	2.10642
$163$	−3.53069	−0.276545	−0.138272	−	0.990394i	$-0.544155\pi$
$163$	−3.53069	−0.276545	−0.138272	+	0.990394i	$0.544155\pi$
$164$	−4.46064	−0.348317
$165$	48.2736	3.75809
$166$	11.9876	0.930421
$167$	−1.30605	−0.101065	−0.0505327	−	0.998722i	$-0.516092\pi$
$167$	−1.30605	−0.101065	−0.0505327	+	0.998722i	$0.516092\pi$
$168$	6.05293	0.466994
$169$	1.00000	0.0769231
$170$	−18.3948	−1.41082
$171$	−3.37664	−0.258218
$172$	−12.8728	−0.981539
$173$	−8.88350	−0.675400	−0.337700	−	0.941254i	$-0.609649\pi$
$173$	−8.88350	−0.675400	−0.337700	+	0.941254i	$0.609649\pi$
$174$	30.0024	2.27448
$175$	2.55387	0.193054
$176$	1.78884	0.134839
$177$	−8.85890	−0.665876
$178$	−2.14979	−0.161133
$179$	12.2467	0.915365	0.457682	−	0.889116i	$-0.348680\pi$
$179$	12.2467	0.915365	0.457682	+	0.889116i	$0.348680\pi$
$180$	−27.2053	−2.02776
$181$	−1.55989	−0.115946	−0.0579730	−	0.998318i	$-0.518464\pi$
$181$	−1.55989	−0.115946	−0.0579730	+	0.998318i	$0.518464\pi$
$182$	0.582806	0.0432005
$183$	10.7750	0.796510
$184$	9.20252	0.678419
$185$	3.00569	0.220983
$186$	25.3180	1.85640
$187$	32.4072	2.36985
$188$	4.26833	0.311300
$189$	−10.1234	−0.736368
$190$	−1.18967	−0.0863075
$191$	−22.5986	−1.63517	−0.817587	−	0.575805i	$-0.804689\pi$
$191$	−22.5986	−1.63517	−0.817587	+	0.575805i	$0.804689\pi$
$192$	−18.9982	−1.37107
$193$	−2.14433	−0.154352	−0.0771760	−	0.997017i	$-0.524590\pi$
$193$	−2.14433	−0.154352	−0.0771760	+	0.997017i	$0.524590\pi$
$194$	−0.426179	−0.0305979
$195$	−9.90233	−0.709120
$196$	7.60532	0.543237
$197$	−10.0770	−0.717953	−0.358977	−	0.933347i	$-0.616874\pi$
$197$	−10.0770	−0.717953	−0.358977	+	0.933347i	$0.616874\pi$
$198$	−35.2484	−2.50499
$199$	21.0610	1.49297	0.746486	−	0.665401i	$-0.231740\pi$
$199$	21.0610	1.49297	0.746486	+	0.665401i	$0.231740\pi$
$200$	−11.7081	−0.827887
$201$	−13.2494	−0.934540
$202$	2.84535	0.200198
$203$	−6.26216	−0.439518
$204$	−25.2398	−1.76714
$205$	11.6337	0.812533
$206$	12.3626	0.861341
$207$	−24.9036	−1.73092
$208$	−0.366943	−0.0254429
$209$	2.09591	0.144977
$210$	−5.77114	−0.398246
$211$	16.3116	1.12294	0.561468	−	0.827499i	$-0.310237\pi$
$211$	16.3116	1.12294	0.561468	+	0.827499i	$0.310237\pi$
$212$	−3.74224	−0.257018
$213$	32.8303	2.24950
$214$	−13.4047	−0.916325
$215$	33.5732	2.28967
$216$	46.4102	3.15782
$217$	−5.28441	−0.358729
$218$	3.05293	0.206770
$219$	9.89520	0.668656
$220$	16.8865	1.13849
$221$	−6.64767	−0.447171
$222$	−3.03302	−0.203563
$223$	25.6068	1.71476	0.857378	−	0.514687i	$-0.172092\pi$
$223$	25.6068	1.71476	0.857378	+	0.514687i	$0.172092\pi$
$224$	3.46068	0.231227
$225$	31.6840	2.11227
$226$	1.21392	0.0807489
$227$	21.7244	1.44190	0.720950	−	0.692987i	$-0.243706\pi$
$227$	21.7244	1.44190	0.720950	+	0.692987i	$0.243706\pi$
$228$	−1.63236	−0.108106
$229$	7.39894	0.488936	0.244468	−	0.969657i	$-0.421387\pi$
$229$	7.39894	0.488936	0.244468	+	0.969657i	$0.421387\pi$
$230$	−8.77410	−0.578547
$231$	10.1674	0.668963
$232$	28.7086	1.88481
$233$	14.0091	0.917767	0.458883	−	0.888497i	$-0.348250\pi$
$233$	14.0091	0.917767	0.458883	+	0.888497i	$0.348250\pi$
$234$	7.23048	0.472671
$235$	−11.1322	−0.726182
$236$	−3.09892	−0.201723
$237$	24.5043	1.59173
$238$	−3.87430	−0.251134
$239$	−15.8521	−1.02539	−0.512693	−	0.858572i	$-0.671352\pi$
$239$	−15.8521	−1.02539	−0.512693	+	0.858572i	$0.671352\pi$
$240$	3.63359	0.234547
$241$	−0.563838	−0.0363200	−0.0181600	−	0.999835i	$-0.505781\pi$
$241$	−0.563838	−0.0363200	−0.0181600	+	0.999835i	$0.505781\pi$
$242$	11.7521	0.755454
$243$	−47.9693	−3.07723
$244$	3.76918	0.241297
$245$	−19.8353	−1.26723
$246$	−11.7395	−0.748481
$247$	−0.429932	−0.0273559
$248$	24.2262	1.53836
$249$	−42.8988	−2.71860
$250$	−2.67252	−0.169025
$251$	3.07036	0.193799	0.0968996	−	0.995294i	$-0.469107\pi$
$251$	3.07036	0.193799	0.0968996	+	0.995294i	$0.469107\pi$
$252$	−5.72996	−0.360953
$253$	15.4578	0.971826
$254$	−1.72898	−0.108486
$255$	65.8274	4.12227
$256$	−16.7111	−1.04445
$257$	−0.298397	−0.0186135	−0.00930674	−	0.999957i	$-0.502962\pi$
$257$	−0.298397	−0.0186135	−0.00930674	+	0.999957i	$0.502962\pi$
$258$	−33.8784	−2.10918
$259$	0.633057	0.0393362
$260$	−3.46392	−0.214823
$261$	−77.6903	−4.80891
$262$	18.7582	1.15888
$263$	−9.08859	−0.560426	−0.280213	−	0.959938i	$-0.590405\pi$
$263$	−9.08859	−0.560426	−0.280213	+	0.959938i	$0.590405\pi$
$264$	−46.6118	−2.86876
$265$	9.76007	0.599556
$266$	−0.250567	−0.0153632
$267$	7.69320	0.470816
$268$	−4.63475	−0.283112
$269$	−6.23995	−0.380456	−0.190228	−	0.981740i	$-0.560923\pi$
$269$	−6.23995	−0.380456	−0.190228	+	0.981740i	$0.560923\pi$
$270$	−44.2496	−2.69295
$271$	−2.08208	−0.126477	−0.0632386	−	0.997998i	$-0.520143\pi$
$271$	−2.08208	−0.126477	−0.0632386	+	0.997998i	$0.520143\pi$
$272$	2.43932	0.147905
$273$	−2.08562	−0.126228
$274$	−3.12712	−0.188916
$275$	−19.6665	−1.18594
$276$	−12.0391	−0.724667
$277$	13.2270	0.794732	0.397366	−	0.917660i	$-0.369924\pi$
$277$	13.2270	0.794732	0.397366	+	0.917660i	$0.369924\pi$
$278$	−2.59750	−0.155788
$279$	−65.5601	−3.92498
$280$	−5.52227	−0.330019
$281$	−23.7964	−1.41957	−0.709787	−	0.704417i	$-0.751209\pi$
$281$	−23.7964	−1.41957	−0.709787	+	0.704417i	$0.751209\pi$
$282$	11.2334	0.668937
$283$	−8.38655	−0.498529	−0.249264	−	0.968435i	$-0.580189\pi$
$283$	−8.38655	−0.498529	−0.249264	+	0.968435i	$0.580189\pi$
$284$	11.4843	0.681470
$285$	4.25732	0.252182
$286$	−4.48801	−0.265382
$287$	2.45028	0.144636
$288$	42.9343	2.52993
$289$	27.1915	1.59950
$290$	−27.3721	−1.60734
$291$	1.52512	0.0894039
$292$	3.46143	0.202565
$293$	−13.3811	−0.781730	−0.390865	−	0.920448i	$-0.627824\pi$
$293$	−13.3811	−0.781730	−0.390865	+	0.920448i	$0.627824\pi$
$294$	20.0156	1.16733
$295$	8.08223	0.470566
$296$	−2.90222	−0.168688
$297$	77.9571	4.52353
$298$	−2.32560	−0.134718
$299$	−3.17086	−0.183375
$300$	15.3169	0.884323
$301$	7.07117	0.407575
$302$	−15.7066	−0.903812
$303$	−10.1823	−0.584958
$304$	0.157761	0.00904819
$305$	−9.83034	−0.562883
$306$	−48.0658	−2.74774
$307$	5.33139	0.304278	0.152139	−	0.988359i	$-0.451384\pi$
$307$	5.33139	0.304278	0.152139	+	0.988359i	$0.451384\pi$
$308$	3.55663	0.202658
$309$	−44.2405	−2.51675
$310$	−23.0983	−1.31190
$311$	7.40767	0.420051	0.210025	−	0.977696i	$-0.432645\pi$
$311$	7.40767	0.420051	0.210025	+	0.977696i	$0.432645\pi$
$312$	9.56144	0.541310
$313$	−16.7739	−0.948114	−0.474057	−	0.880494i	$-0.657211\pi$
$313$	−16.7739	−0.948114	−0.474057	+	0.880494i	$0.657211\pi$
$314$	3.14385	0.177418
$315$	14.9442	0.842009
$316$	8.57183	0.482203
$317$	−0.764110	−0.0429167	−0.0214583	−	0.999770i	$-0.506831\pi$
$317$	−0.764110	−0.0429167	−0.0214583	+	0.999770i	$0.506831\pi$
$318$	−9.84880	−0.552293
$319$	48.2230	2.69997
$320$	17.3326	0.968921
$321$	47.9697	2.67741
$322$	−1.84800	−0.102985
$323$	2.85804	0.159026
$324$	−33.5618	−1.86454
$325$	4.03418	0.223776
$326$	−3.25043	−0.180025
$327$	−10.9252	−0.604163
$328$	−11.2332	−0.620251
$329$	−2.34465	−0.129265
$330$	44.4418	2.44644
$331$	−21.6503	−1.19001	−0.595003	−	0.803723i	$-0.702849\pi$
$331$	−21.6503	−1.19001	−0.595003	+	0.803723i	$0.702849\pi$
$332$	−15.0064	−0.823581
$333$	7.85390	0.430391
$334$	−1.20238	−0.0657914
$335$	12.0878	0.660427
$336$	0.765305	0.0417508
$337$	24.0408	1.30958	0.654792	−	0.755809i	$-0.272756\pi$
$337$	24.0408	1.30958	0.654792	+	0.755809i	$0.272756\pi$
$338$	0.920623	0.0500753
$339$	−4.34412	−0.235940
$340$	23.0270	1.24881
$341$	40.6937	2.20369
$342$	−3.10861	−0.168094
$343$	−8.60909	−0.464847
$344$	−32.4175	−1.74783
$345$	31.3988	1.69046
$346$	−8.17835	−0.439671
$347$	−24.9465	−1.33920	−0.669600	−	0.742722i	$-0.733534\pi$
$347$	−24.9465	−1.33920	−0.669600	+	0.742722i	$0.733534\pi$
$348$	−37.5576	−2.01330
$349$	−0.613561	−0.0328432	−0.0164216	−	0.999865i	$-0.505227\pi$
$349$	−0.613561	−0.0328432	−0.0164216	+	0.999865i	$0.505227\pi$
$350$	2.35115	0.125674
$351$	−15.9913	−0.853552
$352$	−26.6497	−1.42043
$353$	24.8586	1.32309	0.661546	−	0.749904i	$-0.269901\pi$
$353$	24.8586	1.32309	0.661546	+	0.749904i	$0.269901\pi$
$354$	−8.15571	−0.433471
$355$	−29.9521	−1.58969
$356$	2.69115	0.142631
$357$	13.8645	0.733788
$358$	11.2746	0.595883
$359$	10.1506	0.535729	0.267865	−	0.963457i	$-0.413682\pi$
$359$	10.1506	0.535729	0.267865	+	0.963457i	$0.413682\pi$
$360$	−68.5110	−3.61084
$361$	−18.8152	−0.990272
$362$	−1.43607	−0.0754783
$363$	−42.0559	−2.20736
$364$	−0.729568	−0.0382398
$365$	−9.02768	−0.472530
$366$	9.91970	0.518511
$367$	−10.4850	−0.547313	−0.273657	−	0.961827i	$-0.588233\pi$
$367$	−10.4850	−0.547313	−0.273657	+	0.961827i	$0.588233\pi$
$368$	1.16352	0.0606529
$369$	30.3990	1.58251
$370$	2.76711	0.143855
$371$	2.05566	0.106725
$372$	−31.6935	−1.64323
$373$	0.786344	0.0407153	0.0203577	−	0.999793i	$-0.493520\pi$
$373$	0.786344	0.0407153	0.0203577	+	0.999793i	$0.493520\pi$
$374$	29.8348	1.54272
$375$	9.56385	0.493875
$376$	10.7489	0.554334
$377$	−9.89194	−0.509461
$378$	−9.31982	−0.479360
$379$	−31.3953	−1.61267	−0.806333	−	0.591462i	$-0.798551\pi$
$379$	−31.3953	−1.61267	−0.806333	+	0.591462i	$0.798551\pi$
$380$	1.48925	0.0763968
$381$	6.18731	0.316986
$382$	−20.8047	−1.06446
$383$	10.2431	0.523400	0.261700	−	0.965149i	$-0.415717\pi$
$383$	10.2431	0.523400	0.261700	+	0.965149i	$0.415717\pi$
$384$	18.5297	0.945591
$385$	−9.27597	−0.472747
$386$	−1.97412	−0.100480
$387$	87.7271	4.45942
$388$	0.533499	0.0270843
$389$	2.96707	0.150436	0.0752181	−	0.997167i	$-0.476035\pi$
$389$	2.96707	0.150436	0.0752181	+	0.997167i	$0.476035\pi$
$390$	−9.11631	−0.461622
$391$	21.0788	1.06600
$392$	19.1524	0.967345
$393$	−67.1277	−3.38615
$394$	−9.27707	−0.467372
$395$	−22.3560	−1.12485
$396$	44.1246	2.21735
$397$	15.7503	0.790483	0.395241	−	0.918577i	$-0.370661\pi$
$397$	15.7503	0.790483	0.395241	+	0.918577i	$0.370661\pi$
$398$	19.3892	0.971892
$399$	0.896674	0.0448899
$400$	−1.48032	−0.0740158
$401$	21.3351	1.06542	0.532712	−	0.846296i	$-0.321173\pi$
$401$	21.3351	1.06542	0.532712	+	0.846296i	$0.321173\pi$
$402$	−12.1977	−0.608365
$403$	−8.34746	−0.415817
$404$	−3.56186	−0.177209
$405$	87.5317	4.34949
$406$	−5.76509	−0.286117
$407$	−4.87498	−0.241644
$408$	−63.5613	−3.14675
$409$	−38.1429	−1.88604	−0.943022	−	0.332732i	$-0.892030\pi$
$409$	−38.1429	−1.88604	−0.943022	+	0.332732i	$0.892030\pi$
$410$	10.7103	0.528942
$411$	11.1907	0.551994
$412$	−15.4757	−0.762434
$413$	1.70227	0.0837634
$414$	−22.9268	−1.12679
$415$	39.1378	1.92120
$416$	5.46663	0.268023
$417$	9.29538	0.455196
$418$	1.92954	0.0943768
$419$	−12.3287	−0.602297	−0.301148	−	0.953577i	$-0.597370\pi$
$419$	−12.3287	−0.602297	−0.301148	+	0.953577i	$0.597370\pi$
$420$	7.22443	0.352516
$421$	−4.75922	−0.231950	−0.115975	−	0.993252i	$-0.536999\pi$
$421$	−4.75922	−0.231950	−0.115975	+	0.993252i	$0.536999\pi$
$422$	15.0168	0.731007
$423$	−29.0884	−1.41433
$424$	−9.42408	−0.457674
$425$	−26.8179	−1.30086
$426$	30.2243	1.46437
$427$	−2.07046	−0.100197
$428$	16.7802	0.811103
$429$	16.0607	0.775419
$430$	30.9083	1.49053
$431$	−33.3343	−1.60566	−0.802829	−	0.596209i	$-0.796673\pi$
$431$	−33.3343	−1.60566	−0.802829	+	0.596209i	$0.796673\pi$
$432$	5.86789	0.282319
$433$	−17.7771	−0.854315	−0.427158	−	0.904177i	$-0.640485\pi$
$433$	−17.7771	−0.854315	−0.427158	+	0.904177i	$0.640485\pi$
$434$	−4.86495	−0.233525
$435$	97.9533	4.69650
$436$	−3.82172	−0.183027
$437$	1.36325	0.0652131
$438$	9.10975	0.435281
$439$	−15.4602	−0.737875	−0.368938	−	0.929454i	$-0.620278\pi$
$439$	−15.4602	−0.737875	−0.368938	+	0.929454i	$0.620278\pi$
$440$	42.5253	2.02731
$441$	−51.8297	−2.46808
$442$	−6.12000	−0.291099
$443$	27.2260	1.29355	0.646773	−	0.762683i	$-0.276118\pi$
$443$	27.2260	1.29355	0.646773	+	0.762683i	$0.276118\pi$
$444$	3.79679	0.180188
$445$	−7.01873	−0.332720
$446$	23.5742	1.11627
$447$	8.32235	0.393634
$448$	3.65058	0.172474
$449$	−41.9875	−1.98151	−0.990756	−	0.135652i	$-0.956687\pi$
$449$	−41.9875	−1.98151	−0.990756	+	0.135652i	$0.956687\pi$
$450$	29.1691	1.37504
$451$	−18.8689	−0.888501
$452$	−1.51961	−0.0714765
$453$	56.2073	2.64085
$454$	20.0000	0.938646
$455$	1.90277	0.0892034
$456$	−4.11076	−0.192504
$457$	17.5419	0.820577	0.410288	−	0.911956i	$-0.365428\pi$
$457$	17.5419	0.820577	0.410288	+	0.911956i	$0.365428\pi$
$458$	6.81163	0.318287
$459$	106.305	4.96188
$460$	10.9836	0.512113
$461$	−0.112873	−0.00525702	−0.00262851	−	0.999997i	$-0.500837\pi$
$461$	−0.112873	−0.00525702	−0.00262851	+	0.999997i	$0.500837\pi$
$462$	9.36030	0.435480
$463$	−0.705578	−0.0327910	−0.0163955	−	0.999866i	$-0.505219\pi$
$463$	−0.705578	−0.0327910	−0.0163955	+	0.999866i	$0.505219\pi$
$464$	3.62978	0.168508
$465$	82.6593	3.83323
$466$	12.8971	0.597446
$467$	−34.8122	−1.61092	−0.805458	−	0.592652i	$-0.798081\pi$
$467$	−34.8122	−1.61092	−0.805458	+	0.592652i	$0.798081\pi$
$468$	−9.05125	−0.418394
$469$	2.54592	0.117560
$470$	−10.2485	−0.472729
$471$	−11.2505	−0.518397
$472$	−7.80400	−0.359208
$473$	−54.4529	−2.50375
$474$	22.5592	1.03618
$475$	−1.73442	−0.0795807
$476$	4.84993	0.222296
$477$	25.5031	1.16771
$478$	−14.5938	−0.667504
$479$	5.37958	0.245799	0.122900	−	0.992419i	$-0.460781\pi$
$479$	5.37958	0.245799	0.122900	+	0.992419i	$0.460781\pi$
$480$	−54.1323	−2.47079
$481$	1.00000	0.0455961
$482$	−0.519082	−0.0236435
$483$	6.61320	0.300911
$484$	−14.7115	−0.668705
$485$	−1.39141	−0.0631806
$486$	−44.1616	−2.00321
$487$	−21.4608	−0.972482	−0.486241	−	0.873825i	$-0.661632\pi$
$487$	−21.4608	−0.972482	−0.486241	+	0.873825i	$0.661632\pi$
$488$	9.49193	0.429679
$489$	11.6319	0.526015
$490$	−18.2608	−0.824939
$491$	−14.5382	−0.656100	−0.328050	−	0.944660i	$-0.606391\pi$
$491$	−14.5382	−0.656100	−0.328050	+	0.944660i	$0.606391\pi$
$492$	14.6957	0.662533
$493$	65.7584	2.96161
$494$	−0.395805	−0.0178081
$495$	−115.081	−5.17249
$496$	3.06304	0.137535
$497$	−6.30848	−0.282974
$498$	−39.4936	−1.76975
$499$	11.3767	0.509292	0.254646	−	0.967034i	$-0.418041\pi$
$499$	11.3767	0.509292	0.254646	+	0.967034i	$0.418041\pi$
$500$	3.34552	0.149616
$501$	4.30282	0.192236
$502$	2.82664	0.126159
$503$	33.7478	1.50474	0.752370	−	0.658741i	$-0.228910\pi$
$503$	33.7478	1.50474	0.752370	+	0.658741i	$0.228910\pi$
$504$	−14.4297	−0.642751
$505$	9.28962	0.413383
$506$	14.2308	0.632638
$507$	−3.29453	−0.146315
$508$	2.16438	0.0960286
$509$	−35.6118	−1.57846	−0.789232	−	0.614096i	$-0.789521\pi$
$509$	−35.6118	−1.57846	−0.789232	+	0.614096i	$0.789521\pi$
$510$	60.6022	2.68351
$511$	−1.90140	−0.0841132
$512$	−4.13584	−0.182780
$513$	6.87516	0.303546
$514$	−0.274711	−0.0121170
$515$	40.3619	1.77856
$516$	42.4097	1.86698
$517$	18.0554	0.794076
$518$	0.582806	0.0256070
$519$	29.2669	1.28468
$520$	−8.72318	−0.382537
$521$	3.10952	0.136231	0.0681153	−	0.997677i	$-0.478301\pi$
$521$	3.10952	0.136231	0.0681153	+	0.997677i	$0.478301\pi$
$522$	−71.5235	−3.13050
$523$	5.70311	0.249380	0.124690	−	0.992196i	$-0.460206\pi$
$523$	5.70311	0.249380	0.124690	+	0.992196i	$0.460206\pi$
$524$	−23.4819	−1.02581
$525$	−8.41378	−0.367207
$526$	−8.36716	−0.364826
$527$	55.4911	2.41723
$528$	−5.89338	−0.256476
$529$	−12.9457	−0.562855
$530$	8.98534	0.390298
$531$	21.1189	0.916484
$532$	0.313664	0.0135991
$533$	3.87056	0.167653
$534$	7.08253	0.306491
$535$	−43.7642	−1.89209
$536$	−11.6717	−0.504140
$537$	−40.3472	−1.74111
$538$	−5.74464	−0.247669
$539$	32.1711	1.38571
$540$	55.3925	2.38371
$541$	20.5286	0.882591	0.441296	−	0.897362i	$-0.354519\pi$
$541$	20.5286	0.882591	0.441296	+	0.897362i	$0.354519\pi$
$542$	−1.91681	−0.0823339
$543$	5.13911	0.220540
$544$	−36.3403	−1.55808
$545$	9.96735	0.426954
$546$	−1.92007	−0.0821714
$547$	−9.48164	−0.405406	−0.202703	−	0.979240i	$-0.564973\pi$
$547$	−9.48164	−0.405406	−0.202703	+	0.979240i	$0.564973\pi$
$548$	3.91459	0.167223
$549$	−25.6867	−1.09628
$550$	−18.1055	−0.772020
$551$	4.25286	0.181178
$552$	−30.3179	−1.29042
$553$	−4.70861	−0.200230
$554$	12.1770	0.517353
$555$	−9.90233	−0.420330
$556$	3.25160	0.137899
$557$	−46.9303	−1.98850	−0.994251	−	0.107072i	$-0.965853\pi$
$557$	−46.9303	−1.98850	−0.994251	+	0.107072i	$0.965853\pi$
$558$	−60.3561	−2.55508
$559$	11.1699	0.472436
$560$	−0.698210	−0.0295048
$561$	−106.766	−4.50768
$562$	−21.9075	−0.924112
$563$	6.49297	0.273646	0.136823	−	0.990596i	$-0.456311\pi$
$563$	6.49297	0.273646	0.136823	+	0.990596i	$0.456311\pi$
$564$	−14.0621	−0.592123
$565$	3.96327	0.166736
$566$	−7.72085	−0.324532
$567$	18.4359	0.774234
$568$	28.9210	1.21350
$569$	20.7747	0.870920	0.435460	−	0.900208i	$-0.356586\pi$
$569$	20.7747	0.870920	0.435460	+	0.900208i	$0.356586\pi$
$570$	3.91939	0.164165
$571$	−6.68371	−0.279705	−0.139852	−	0.990172i	$-0.544663\pi$
$571$	−6.68371	−0.279705	−0.139852	+	0.990172i	$0.544663\pi$
$572$	5.61818	0.234908
$573$	74.4515	3.11026
$574$	2.25579	0.0941547
$575$	−12.7918	−0.533455
$576$	45.2902	1.88709
$577$	−12.0286	−0.500759	−0.250380	−	0.968148i	$-0.580555\pi$
$577$	−12.0286	−0.500759	−0.250380	+	0.968148i	$0.580555\pi$
$578$	25.0331	1.04124
$579$	7.06454	0.293592
$580$	34.2649	1.42277
$581$	8.24318	0.341985
$582$	1.40406	0.0582000
$583$	−15.8300	−0.655612
$584$	8.71690	0.360708
$585$	23.6064	0.976004
$586$	−12.3189	−0.508889
$587$	−3.26124	−0.134606	−0.0673028	−	0.997733i	$-0.521439\pi$
$587$	−3.26124	−0.134606	−0.0673028	+	0.997733i	$0.521439\pi$
$588$	−25.0559	−1.03329
$589$	3.58884	0.147875
$590$	7.44069	0.306328
$591$	33.1988	1.36562
$592$	−0.366943	−0.0150813
$593$	−20.2981	−0.833542	−0.416771	−	0.909012i	$-0.636838\pi$
$593$	−20.2981	−0.833542	−0.416771	+	0.909012i	$0.636838\pi$
$594$	71.7691	2.94472
$595$	−12.6490	−0.518559
$596$	2.91123	0.119249
$597$	−69.3858	−2.83977
$598$	−2.91916	−0.119373
$599$	−36.2385	−1.48066	−0.740332	−	0.672241i	$-0.765332\pi$
$599$	−36.2385	−1.48066	−0.740332	+	0.672241i	$0.765332\pi$
$600$	38.5726	1.57472
$601$	31.8090	1.29752	0.648758	−	0.760995i	$-0.275289\pi$
$601$	31.8090	1.29752	0.648758	+	0.760995i	$0.275289\pi$
$602$	6.50988	0.265323
$603$	31.5855	1.28626
$604$	19.6618	0.800028
$605$	38.3688	1.55991
$606$	−9.37407	−0.380795
$607$	25.1962	1.02268	0.511341	−	0.859378i	$-0.329149\pi$
$607$	25.1962	1.02268	0.511341	+	0.859378i	$0.329149\pi$
$608$	−2.35027	−0.0953162
$609$	20.6308	0.836004
$610$	−9.05003	−0.366425
$611$	−3.70369	−0.149835
$612$	60.1697	2.43222
$613$	17.6112	0.711309	0.355655	−	0.934617i	$-0.384258\pi$
$613$	17.6112	0.711309	0.355655	+	0.934617i	$0.384258\pi$
$614$	4.90820	0.198079
$615$	−38.3275	−1.54552
$616$	8.95665	0.360874
$617$	−37.6461	−1.51557	−0.757787	−	0.652503i	$-0.773719\pi$
$617$	−37.6461	−1.51557	−0.757787	+	0.652503i	$0.773719\pi$
$618$	−40.7288	−1.63835
$619$	22.1909	0.891926	0.445963	−	0.895051i	$-0.352861\pi$
$619$	22.1909	0.891926	0.445963	+	0.895051i	$0.352861\pi$
$620$	28.9149	1.16125
$621$	50.7061	2.03476
$622$	6.81967	0.273444
$623$	−1.47828	−0.0592260
$624$	1.20890	0.0483949
$625$	−28.8963	−1.15585
$626$	−15.4424	−0.617202
$627$	−6.90501	−0.275760
$628$	−3.93553	−0.157045
$629$	−6.64767	−0.265060
$630$	13.7580	0.548130
$631$	−10.8741	−0.432890	−0.216445	−	0.976295i	$-0.569446\pi$
$631$	−10.8741	−0.432890	−0.216445	+	0.976295i	$0.569446\pi$
$632$	21.5864	0.858661
$633$	−53.7389	−2.13593
$634$	−0.703457	−0.0279378
$635$	−5.64487	−0.224010
$636$	12.3289	0.488873
$637$	−6.59924	−0.261471
$638$	44.3952	1.75762
$639$	−78.2650	−3.09611
$640$	−16.9052	−0.668237
$641$	−21.7166	−0.857753	−0.428876	−	0.903363i	$-0.641090\pi$
$641$	−21.7166	−0.857753	−0.428876	+	0.903363i	$0.641090\pi$
$642$	44.1620	1.74294
$643$	−20.9448	−0.825981	−0.412991	−	0.910735i	$-0.635516\pi$
$643$	−20.9448	−0.825981	−0.412991	+	0.910735i	$0.635516\pi$
$644$	2.31336	0.0911590
$645$	−110.608	−4.35518
$646$	2.63118	0.103522
$647$	25.1668	0.989409	0.494705	−	0.869061i	$-0.335276\pi$
$647$	25.1668	0.989409	0.494705	+	0.869061i	$0.335276\pi$
$648$	−84.5185	−3.32020
$649$	−13.1087	−0.514561
$650$	3.71396	0.145673
$651$	17.4096	0.682337
$652$	4.06896	0.159353
$653$	21.6178	0.845971	0.422986	−	0.906136i	$-0.360982\pi$
$653$	21.6178	0.845971	0.422986	+	0.906136i	$0.360982\pi$
$654$	−10.0580	−0.393297
$655$	61.2426	2.39295
$656$	−1.42028	−0.0554525
$657$	−23.5894	−0.920310
$658$	−2.15854	−0.0841485
$659$	5.01233	0.195253	0.0976264	−	0.995223i	$-0.468875\pi$
$659$	5.01233	0.195253	0.0976264	+	0.995223i	$0.468875\pi$
$660$	−55.6331	−2.16552
$661$	−24.4367	−0.950478	−0.475239	−	0.879857i	$-0.657638\pi$
$661$	−24.4367	−0.950478	−0.475239	+	0.879857i	$0.657638\pi$
$662$	−19.9317	−0.774669
$663$	21.9009	0.850561
$664$	−37.7905	−1.46656
$665$	−0.818062	−0.0317231
$666$	7.23048	0.280175
$667$	31.3659	1.21449
$668$	1.50517	0.0582366
$669$	−84.3621	−3.26163
$670$	11.1283	0.429924
$671$	15.9440	0.615510
$672$	−11.4013	−0.439815
$673$	22.7484	0.876887	0.438444	−	0.898759i	$-0.355530\pi$
$673$	22.7484	0.876887	0.438444	+	0.898759i	$0.355530\pi$
$674$	22.1325	0.852511
$675$	−64.5117	−2.48306
$676$	−1.15245	−0.0443251
$677$	−43.7145	−1.68008	−0.840042	−	0.542522i	$-0.817470\pi$
$677$	−43.7145	−1.68008	−0.840042	+	0.542522i	$0.817470\pi$
$678$	−3.99930	−0.153592
$679$	−0.293057	−0.0112465
$680$	57.9888	2.22377
$681$	−71.5717	−2.74263
$682$	37.4635	1.43455
$683$	27.7170	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$683$	27.7170	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$684$	3.89142	0.148792
$685$	−10.2096	−0.390087
$686$	−7.92572	−0.302606
$687$	−24.3760	−0.930002
$688$	−4.09871	−0.156262
$689$	3.24720	0.123708
$690$	28.9065	1.10045
$691$	46.0035	1.75006	0.875028	−	0.484072i	$-0.160843\pi$
$691$	46.0035	1.75006	0.875028	+	0.484072i	$0.160843\pi$
$692$	10.2378	0.389184
$693$	−24.2382	−0.920733
$694$	−22.9663	−0.871791
$695$	−8.48044	−0.321682
$696$	−94.5812	−3.58509
$697$	−25.7302	−0.974601
$698$	−0.564859	−0.0213802
$699$	−46.1533	−1.74568
$700$	−2.94321	−0.111243
$701$	5.57642	0.210618	0.105309	−	0.994440i	$-0.466417\pi$
$701$	5.57642	0.210618	0.105309	+	0.994440i	$0.466417\pi$
$702$	−14.7219	−0.555644
$703$	−0.429932	−0.0162152
$704$	−28.1120	−1.05951
$705$	36.6752	1.38127
$706$	22.8854	0.861305
$707$	1.95657	0.0735845
$708$	10.2095	0.383695
$709$	11.8592	0.445383	0.222691	−	0.974889i	$-0.428516\pi$
$709$	11.8592	0.445383	0.222691	+	0.974889i	$0.428516\pi$
$710$	−27.5746	−1.03485
$711$	−58.4165	−2.19079
$712$	6.77711	0.253983
$713$	26.4686	0.991256
$714$	12.7640	0.477680
$715$	−14.6527	−0.547979
$716$	−14.1138	−0.527458
$717$	52.2251	1.95038
$718$	9.34489	0.348748
$719$	−38.2106	−1.42502	−0.712508	−	0.701664i	$-0.752441\pi$
$719$	−38.2106	−1.42502	−0.712508	+	0.701664i	$0.752441\pi$
$720$	−8.66221	−0.322821
$721$	8.50100	0.316594
$722$	−17.3217	−0.644646
$723$	1.85758	0.0690841
$724$	1.79770	0.0668112
$725$	−39.9059	−1.48207
$726$	−38.7176	−1.43695
$727$	−22.7439	−0.843523	−0.421762	−	0.906707i	$-0.638588\pi$
$727$	−22.7439	−0.843523	−0.421762	+	0.906707i	$0.638588\pi$
$728$	−1.83727	−0.0680938
$729$	70.6701	2.61741
$730$	−8.31109	−0.307607
$731$	−74.2537	−2.74637
$732$	−12.4177	−0.458970
$733$	3.73434	0.137931	0.0689655	−	0.997619i	$-0.478030\pi$
$733$	3.73434	0.137931	0.0689655	+	0.997619i	$0.478030\pi$
$734$	−9.65274	−0.356289
$735$	65.3478	2.41039
$736$	−17.3339	−0.638935
$737$	−19.6054	−0.722174
$738$	27.9860	1.03018
$739$	−29.1236	−1.07133	−0.535665	−	0.844431i	$-0.679939\pi$
$739$	−29.1236	−1.07133	−0.535665	+	0.844431i	$0.679939\pi$
$740$	−3.46392	−0.127336
$741$	1.41642	0.0520335
$742$	1.89249	0.0694754
$743$	−21.9341	−0.804682	−0.402341	−	0.915490i	$-0.631803\pi$
$743$	−21.9341	−0.804682	−0.402341	+	0.915490i	$0.631803\pi$
$744$	−79.8137	−2.92611
$745$	−7.59272	−0.278176
$746$	0.723926	0.0265048
$747$	102.267	3.74177
$748$	−37.3478	−1.36557
$749$	−9.21759	−0.336803
$750$	8.80469	0.321502
$751$	−12.5467	−0.457835	−0.228917	−	0.973446i	$-0.573519\pi$
$751$	−12.5467	−0.457835	−0.228917	+	0.973446i	$0.573519\pi$
$752$	1.35905	0.0495593
$753$	−10.1154	−0.368625
$754$	−9.10675	−0.331648
$755$	−51.2796	−1.86625
$756$	11.6667	0.424315
$757$	20.3532	0.739750	0.369875	−	0.929081i	$-0.379400\pi$
$757$	20.3532	0.739750	0.369875	+	0.929081i	$0.379400\pi$
$758$	−28.9032	−1.04981
$759$	−50.9263	−1.84851
$760$	3.75037	0.136040
$761$	8.35376	0.302824	0.151412	−	0.988471i	$-0.451618\pi$
$761$	8.35376	0.302824	0.151412	+	0.988471i	$0.451618\pi$
$762$	5.69618	0.206351
$763$	2.09932	0.0760003
$764$	26.0438	0.942231
$765$	−156.927	−5.67373
$766$	9.43006	0.340722
$767$	2.68898	0.0970933
$768$	55.0552	1.98663
$769$	14.6995	0.530079	0.265039	−	0.964238i	$-0.414615\pi$
$769$	14.6995	0.530079	0.265039	+	0.964238i	$0.414615\pi$
$770$	−8.53967	−0.307748
$771$	0.983076	0.0354046
$772$	2.47124	0.0889417
$773$	19.7707	0.711102	0.355551	−	0.934657i	$-0.384293\pi$
$773$	19.7707	0.711102	0.355551	+	0.934657i	$0.384293\pi$
$774$	80.7636	2.90299
$775$	−33.6752	−1.20965
$776$	1.34351	0.0482292
$777$	−2.08562	−0.0748212
$778$	2.73155	0.0979308
$779$	−1.66408	−0.0596217
$780$	11.4120	0.408614
$781$	48.5797	1.73832
$782$	19.4056	0.693944
$783$	158.185	5.65307
$784$	2.42155	0.0864838
$785$	10.2642	0.366344
$786$	−61.7993	−2.20431
$787$	−30.3145	−1.08060	−0.540298	−	0.841474i	$-0.681688\pi$
$787$	−30.3145	−1.08060	−0.540298	+	0.841474i	$0.681688\pi$
$788$	11.6132	0.413704
$789$	29.9426	1.06598
$790$	−20.5815	−0.732255
$791$	0.834741	0.0296800
$792$	111.119	3.94844
$793$	−3.27057	−0.116141
$794$	14.5000	0.514587
$795$	−32.1548	−1.14041
$796$	−24.2718	−0.860290
$797$	−41.7662	−1.47943	−0.739717	−	0.672918i	$-0.765040\pi$
$797$	−41.7662	−1.47943	−0.739717	+	0.672918i	$0.765040\pi$
$798$	0.825499	0.0292223
$799$	24.6209	0.871026
$800$	22.0534	0.779704
$801$	−18.3400	−0.648012
$802$	19.6416	0.693569
$803$	14.6421	0.516710
$804$	15.2693	0.538507
$805$	−6.03342	−0.212650
$806$	−7.68486	−0.270688
$807$	20.5577	0.723664
$808$	−8.96982	−0.315557
$809$	29.5099	1.03751	0.518757	−	0.854922i	$-0.326395\pi$
$809$	29.5099	1.03751	0.518757	+	0.854922i	$0.326395\pi$
$810$	80.5837	2.83142
$811$	1.87850	0.0659629	0.0329815	−	0.999456i	$-0.489500\pi$
$811$	1.87850	0.0659629	0.0329815	+	0.999456i	$0.489500\pi$
$812$	7.21685	0.253262
$813$	6.85945	0.240572
$814$	−4.48801	−0.157305
$815$	−10.6122	−0.371728
$816$	−8.03639	−0.281330
$817$	−4.80228	−0.168011
$818$	−35.1152	−1.22777
$819$	4.97196	0.173734
$820$	−13.4073	−0.468203
$821$	41.1862	1.43741	0.718704	−	0.695316i	$-0.244736\pi$
$821$	41.1862	1.43741	0.718704	+	0.695316i	$0.244736\pi$
$822$	10.3024	0.359336
$823$	−13.2262	−0.461038	−0.230519	−	0.973068i	$-0.574042\pi$
$823$	−13.2262	−0.461038	−0.230519	+	0.973068i	$0.574042\pi$
$824$	−38.9724	−1.35767
$825$	64.7919	2.25576
$826$	1.56715	0.0545282
$827$	5.60789	0.195005	0.0975027	−	0.995235i	$-0.468915\pi$
$827$	5.60789	0.195005	0.0975027	+	0.995235i	$0.468915\pi$
$828$	28.7002	0.997401
$829$	12.9093	0.448360	0.224180	−	0.974548i	$-0.428030\pi$
$829$	12.9093	0.448360	0.224180	+	0.974548i	$0.428030\pi$
$830$	36.0311	1.25066
$831$	−43.5766	−1.51165
$832$	5.76659	0.199920
$833$	43.8696	1.51999
$834$	8.55753	0.296323
$835$	−3.92559	−0.135851
$836$	−2.41543	−0.0835395
$837$	133.487	4.61397
$838$	−11.3501	−0.392082
$839$	44.6490	1.54146	0.770728	−	0.637165i	$-0.219893\pi$
$839$	44.6490	1.54146	0.770728	+	0.637165i	$0.219893\pi$
$840$	18.1932	0.627727
$841$	68.8506	2.37416
$842$	−4.38144	−0.150995
$843$	78.3978	2.70016
$844$	−18.7983	−0.647066
$845$	3.00569	0.103399
$846$	−26.7795	−0.920697
$847$	8.08121	0.277674
$848$	−1.19154	−0.0409176
$849$	27.6297	0.948249
$850$	−24.6892	−0.846832
$851$	−3.17086	−0.108696
$852$	−37.8354	−1.29622
$853$	20.7455	0.710313	0.355156	−	0.934807i	$-0.384428\pi$
$853$	20.7455	0.710313	0.355156	+	0.934807i	$0.384428\pi$
$854$	−1.90611	−0.0652258
$855$	−10.1491	−0.347093
$856$	42.2576	1.44434
$857$	−4.25963	−0.145506	−0.0727531	−	0.997350i	$-0.523179\pi$
$857$	−4.25963	−0.145506	−0.0727531	+	0.997350i	$0.523179\pi$
$858$	14.7859	0.504781
$859$	8.29008	0.282854	0.141427	−	0.989949i	$-0.454831\pi$
$859$	8.29008	0.282854	0.141427	+	0.989949i	$0.454831\pi$
$860$	−38.6916	−1.31937
$861$	−8.07252	−0.275111
$862$	−30.6883	−1.04525
$863$	35.2028	1.19832	0.599159	−	0.800630i	$-0.295502\pi$
$863$	35.2028	1.19832	0.599159	+	0.800630i	$0.295502\pi$
$864$	−87.4184	−2.97403
$865$	−26.7011	−0.907863
$866$	−16.3660	−0.556141
$867$	−89.5831	−3.04240
$868$	6.09004	0.206710
$869$	36.2596	1.23002
$870$	90.1780	3.05732
$871$	4.02164	0.136268
$872$	−9.62422	−0.325917
$873$	−3.63576	−0.123052
$874$	1.25504	0.0424524
$875$	−1.83773	−0.0621267
$876$	−11.4038	−0.385297
$877$	10.1386	0.342357	0.171178	−	0.985240i	$-0.445243\pi$
$877$	10.1386	0.342357	0.171178	+	0.985240i	$0.445243\pi$
$878$	−14.2330	−0.480341
$879$	44.0842	1.48692
$880$	5.37670	0.181249
$881$	−34.6580	−1.16766	−0.583829	−	0.811876i	$-0.698446\pi$
$881$	−34.6580	−1.16766	−0.583829	+	0.811876i	$0.698446\pi$
$882$	−47.7156	−1.60667
$883$	14.4040	0.484734	0.242367	−	0.970185i	$-0.422076\pi$
$883$	14.4040	0.484734	0.242367	+	0.970185i	$0.422076\pi$
$884$	7.66113	0.257672
$885$	−26.6271	−0.895061
$886$	25.0649	0.842070
$887$	−53.3094	−1.78996	−0.894978	−	0.446111i	$-0.852809\pi$
$887$	−53.3094	−1.78996	−0.894978	+	0.446111i	$0.852809\pi$
$888$	9.56144	0.320861
$889$	−1.18892	−0.0398750
$890$	−6.46160	−0.216593
$891$	−141.969	−4.75614
$892$	−29.5106	−0.988088
$893$	1.59233	0.0532854
$894$	7.66174	0.256247
$895$	36.8099	1.23042
$896$	−3.56056	−0.118950
$897$	10.4465	0.348797
$898$	−38.6547	−1.28992
$899$	82.5726	2.75395
$900$	−36.5144	−1.21715
$901$	−21.5863	−0.719144
$902$	−17.3711	−0.578395
$903$	−23.2961	−0.775247
$904$	−3.82683	−0.127279
$905$	−4.68856	−0.155853
$906$	51.7457	1.71914
$907$	−18.7587	−0.622873	−0.311436	−	0.950267i	$-0.600810\pi$
$907$	−18.7587	−0.622873	−0.311436	+	0.950267i	$0.600810\pi$
$908$	−25.0364	−0.830862
$909$	24.2738	0.805113
$910$	1.75174	0.0580695
$911$	−36.2341	−1.20049	−0.600244	−	0.799817i	$-0.704930\pi$
$911$	−36.2341	−1.20049	−0.600244	+	0.799817i	$0.704930\pi$
$912$	−0.519746	−0.0172105
$913$	−63.4782	−2.10082
$914$	16.1495	0.534178
$915$	32.3863	1.07066
$916$	−8.52693	−0.281738
$917$	12.8989	0.425958
$918$	97.8666	3.23008
$919$	14.8572	0.490094	0.245047	−	0.969511i	$-0.421197\pi$
$919$	14.8572	0.490094	0.245047	+	0.969511i	$0.421197\pi$
$920$	27.6599	0.911921
$921$	−17.5644	−0.578767
$922$	−0.103913	−0.00342221
$923$	−9.96512	−0.328006
$924$	−11.7174	−0.385474
$925$	4.03418	0.132643
$926$	−0.649571	−0.0213462
$927$	105.466	3.46396
$928$	−54.0756	−1.77512
$929$	41.5156	1.36208	0.681041	−	0.732246i	$-0.261528\pi$
$929$	41.5156	1.36208	0.681041	+	0.732246i	$0.261528\pi$
$930$	76.0980	2.49535
$931$	2.83722	0.0929862
$932$	−16.1448	−0.528842
$933$	−24.4048	−0.798976
$934$	−32.0489	−1.04867
$935$	97.4061	3.18552
$936$	−22.7937	−0.745037
$937$	22.3033	0.728618	0.364309	−	0.931278i	$-0.381305\pi$
$937$	22.3033	0.728618	0.364309	+	0.931278i	$0.381305\pi$
$938$	2.34384	0.0765290
$939$	55.2619	1.80340
$940$	12.8293	0.418445
$941$	56.8067	1.85185	0.925923	−	0.377713i	$-0.123289\pi$
$941$	56.8067	1.85185	0.925923	+	0.377713i	$0.123289\pi$
$942$	−10.3575	−0.337465
$943$	−12.2730	−0.399663
$944$	−0.986702	−0.0321144
$945$	−30.4278	−0.989816
$946$	−50.1306	−1.62989
$947$	12.3430	0.401093	0.200547	−	0.979684i	$-0.435728\pi$
$947$	12.3430	0.401093	0.200547	+	0.979684i	$0.435728\pi$
$948$	−28.2401	−0.917196
$949$	−3.00353	−0.0974987
$950$	−1.59675	−0.0518054
$951$	2.51738	0.0816316
$952$	12.2136	0.395844
$953$	−45.2181	−1.46476	−0.732378	−	0.680898i	$-0.761590\pi$
$953$	−45.2181	−1.46476	−0.732378	+	0.680898i	$0.761590\pi$
$954$	23.4788	0.760153
$955$	−67.9243	−2.19798
$956$	18.2688	0.590855
$957$	−158.872	−5.13560
$958$	4.95257	0.160010
$959$	−2.15033	−0.0694378
$960$	−57.1026	−1.84298
$961$	38.6801	1.24774
$962$	0.920623	0.0296821
$963$	−114.356	−3.68508
$964$	0.649797	0.0209285
$965$	−6.44518	−0.207478
$966$	6.08827	0.195887
$967$	48.8784	1.57182	0.785912	−	0.618338i	$-0.212194\pi$
$967$	48.8784	1.57182	0.785912	+	0.618338i	$0.212194\pi$
$968$	−37.0480	−1.19077
$969$	−9.41589	−0.302482
$970$	−1.28096	−0.0411292
$971$	−51.7192	−1.65975	−0.829875	−	0.557950i	$-0.811588\pi$
$971$	−51.7192	−1.65975	−0.829875	+	0.557950i	$0.811588\pi$
$972$	55.2824	1.77318
$973$	−1.78614	−0.0572612
$974$	−19.7573	−0.633065
$975$	−13.2907	−0.425643
$976$	1.20012	0.0384148
$977$	−3.95789	−0.126624	−0.0633121	−	0.997994i	$-0.520166\pi$
$977$	−3.95789	−0.126624	−0.0633121	+	0.997994i	$0.520166\pi$
$978$	10.7086	0.342424
$979$	11.3838	0.363827
$980$	22.8592	0.730212
$981$	26.0448	0.831545
$982$	−13.3842	−0.427107
$983$	−7.83244	−0.249816	−0.124908	−	0.992168i	$-0.539864\pi$
$983$	−7.83244	−0.249816	−0.124908	+	0.992168i	$0.539864\pi$
$984$	37.0081	1.17978
$985$	−30.2882	−0.965063
$986$	60.5387	1.92794
$987$	7.72450	0.245874
$988$	0.495476	0.0157632
$989$	−35.4181	−1.12623
$990$	−105.946	−3.36718
$991$	13.9705	0.443787	0.221894	−	0.975071i	$-0.428776\pi$
$991$	13.9705	0.443787	0.221894	+	0.975071i	$0.428776\pi$
$992$	−45.6324	−1.44883
$993$	71.3274	2.26351
$994$	−5.80773	−0.184210
$995$	63.3027	2.00683
$996$	49.4388	1.56653
$997$	−8.42875	−0.266941	−0.133471	−	0.991053i	$-0.542612\pi$
$997$	−8.42875	−0.266941	−0.133471	+	0.991053i	$0.542612\pi$
$998$	10.4737	0.331538
$999$	−15.9913	−0.505942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	481.2.a.c.1.5	✓	7
3.2	odd	2		4329.2.a.n.1.3		7
4.3	odd	2		7696.2.a.s.1.7		7
13.12	even	2		6253.2.a.f.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
481.2.a.c.1.5	✓	7	1.1	even	1	trivial
4329.2.a.n.1.3		7	3.2	odd	2
6253.2.a.f.1.3		7	13.12	even	2
7696.2.a.s.1.7		7	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 481 = 13 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	481.a (trivial)

\(f(q)\)	\(=\)	\(q+0.920623 q^{2} -3.29453 q^{3} -1.15245 q^{4} +3.00569 q^{5} -3.03302 q^{6} +0.633057 q^{7} -2.90222 q^{8} +7.85390 q^{9} +O(q^{10})\)	\(q+0.920623 q^{2} -3.29453 q^{3} -1.15245 q^{4} +3.00569 q^{5} -3.03302 q^{6} +0.633057 q^{7} -2.90222 q^{8} +7.85390 q^{9} +2.76711 q^{10} -4.87498 q^{11} +3.79679 q^{12} +1.00000 q^{13} +0.582806 q^{14} -9.90233 q^{15} -0.366943 q^{16} -6.64767 q^{17} +7.23048 q^{18} -0.429932 q^{19} -3.46392 q^{20} -2.08562 q^{21} -4.48801 q^{22} -3.17086 q^{23} +9.56144 q^{24} +4.03418 q^{25} +0.920623 q^{26} -15.9913 q^{27} -0.729568 q^{28} -9.89194 q^{29} -9.11631 q^{30} -8.34746 q^{31} +5.46663 q^{32} +16.0607 q^{33} -6.12000 q^{34} +1.90277 q^{35} -9.05125 q^{36} +1.00000 q^{37} -0.395805 q^{38} -3.29453 q^{39} -8.72318 q^{40} +3.87056 q^{41} -1.92007 q^{42} +11.1699 q^{43} +5.61818 q^{44} +23.6064 q^{45} -2.91916 q^{46} -3.70369 q^{47} +1.20890 q^{48} -6.59924 q^{49} +3.71396 q^{50} +21.9009 q^{51} -1.15245 q^{52} +3.24720 q^{53} -14.7219 q^{54} -14.6527 q^{55} -1.83727 q^{56} +1.41642 q^{57} -9.10675 q^{58} +2.68898 q^{59} +11.4120 q^{60} -3.27057 q^{61} -7.68486 q^{62} +4.97196 q^{63} +5.76659 q^{64} +3.00569 q^{65} +14.7859 q^{66} +4.02164 q^{67} +7.66113 q^{68} +10.4465 q^{69} +1.75174 q^{70} -9.96512 q^{71} -22.7937 q^{72} -3.00353 q^{73} +0.920623 q^{74} -13.2907 q^{75} +0.495476 q^{76} -3.08614 q^{77} -3.03302 q^{78} -7.43789 q^{79} -1.10292 q^{80} +29.1220 q^{81} +3.56332 q^{82} +13.0212 q^{83} +2.40358 q^{84} -19.9808 q^{85} +10.2832 q^{86} +32.5893 q^{87} +14.1483 q^{88} -2.33515 q^{89} +21.7326 q^{90} +0.633057 q^{91} +3.65426 q^{92} +27.5009 q^{93} -3.40970 q^{94} -1.29224 q^{95} -18.0099 q^{96} -0.462924 q^{97} -6.07541 q^{98} -38.2876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 7 q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 7 * q - q^2 - 7 * q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^9	\( 7 q - q^{2} - 7 q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9} - 11 q^{10} - 13 q^{11} + q^{12} + 7 q^{13} - 2 q^{14} - 11 q^{15} - 9 q^{16} - 10 q^{17} + 8 q^{18} - 2 q^{19} - 9 q^{20} + 4 q^{21} - 6 q^{22} - 24 q^{23} + 7 q^{25} - q^{26} - 13 q^{27} - 11 q^{28} - 17 q^{29} + 14 q^{30} - 11 q^{31} - q^{32} + 12 q^{33} + 4 q^{34} - 10 q^{35} - 23 q^{36} + 7 q^{37} + 5 q^{38} - 7 q^{39} - 10 q^{40} - 17 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{44} + 32 q^{45} - 12 q^{46} - 21 q^{47} + 11 q^{48} - 15 q^{49} + 27 q^{50} + 4 q^{51} + 3 q^{52} - 16 q^{53} - q^{54} + 11 q^{55} + 8 q^{56} + 11 q^{57} + 13 q^{58} - 18 q^{59} + 25 q^{60} - 20 q^{61} - 4 q^{62} + 18 q^{63} - 8 q^{64} - 2 q^{65} + 40 q^{66} + 7 q^{67} - 7 q^{68} + 33 q^{69} + 41 q^{70} - 35 q^{71} - 5 q^{72} + 8 q^{73} - q^{74} - 27 q^{75} + 50 q^{76} - 16 q^{77} - 4 q^{78} - 18 q^{79} - 8 q^{80} + 23 q^{81} + 41 q^{82} + 19 q^{83} + 13 q^{84} + 5 q^{85} + 38 q^{86} + 40 q^{87} - 6 q^{88} - q^{89} + 36 q^{90} - 2 q^{91} + 20 q^{92} + 14 q^{93} - q^{94} - 23 q^{95} - 5 q^{96} + 22 q^{97} - 16 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - q^2 - 7 * q^3 + 3 * q^4 - 2 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^9 - 11 * q^10 - 13 * q^11 + q^12 + 7 * q^13 - 2 * q^14 - 11 * q^15 - 9 * q^16 - 10 * q^17 + 8 * q^18 - 2 * q^19 - 9 * q^20 + 4 * q^21 - 6 * q^22 - 24 * q^23 + 7 * q^25 - q^26 - 13 * q^27 - 11 * q^28 - 17 * q^29 + 14 * q^30 - 11 * q^31 - q^32 + 12 * q^33 + 4 * q^34 - 10 * q^35 - 23 * q^36 + 7 * q^37 + 5 * q^38 - 7 * q^39 - 10 * q^40 - 17 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^44 + 32 * q^45 - 12 * q^46 - 21 * q^47 + 11 * q^48 - 15 * q^49 + 27 * q^50 + 4 * q^51 + 3 * q^52 - 16 * q^53 - q^54 + 11 * q^55 + 8 * q^56 + 11 * q^57 + 13 * q^58 - 18 * q^59 + 25 * q^60 - 20 * q^61 - 4 * q^62 + 18 * q^63 - 8 * q^64 - 2 * q^65 + 40 * q^66 + 7 * q^67 - 7 * q^68 + 33 * q^69 + 41 * q^70 - 35 * q^71 - 5 * q^72 + 8 * q^73 - q^74 - 27 * q^75 + 50 * q^76 - 16 * q^77 - 4 * q^78 - 18 * q^79 - 8 * q^80 + 23 * q^81 + 41 * q^82 + 19 * q^83 + 13 * q^84 + 5 * q^85 + 38 * q^86 + 40 * q^87 - 6 * q^88 - q^89 + 36 * q^90 - 2 * q^91 + 20 * q^92 + 14 * q^93 - q^94 - 23 * q^95 - 5 * q^96 + 22 * q^97 - 16 * q^98 - 23 * q^99

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