LMFDB - Embedded newform 481.2.a.c.1.7

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			1.7
Root			$0.494927$ 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)

$f(q)$	$=$	$q+2.20100 q^{2} -1.49493 q^{3} +2.84438 q^{4} -3.86285 q^{5} -3.29033 q^{6} -0.598265 q^{7} +1.85847 q^{8} -0.765193 q^{9} +O(q^{10})$	\(q+2.20100 q^{2} -1.49493 q^{3} +2.84438 q^{4} -3.86285 q^{5} -3.29033 q^{6} -0.598265 q^{7} +1.85847 q^{8} -0.765193 q^{9} -8.50211 q^{10} -5.08135 q^{11} -4.25214 q^{12} +1.00000 q^{13} -1.31678 q^{14} +5.77468 q^{15} -1.59826 q^{16} +0.367408 q^{17} -1.68419 q^{18} +7.77011 q^{19} -10.9874 q^{20} +0.894363 q^{21} -11.1840 q^{22} -5.21509 q^{23} -2.77828 q^{24} +9.92161 q^{25} +2.20100 q^{26} +5.62869 q^{27} -1.70169 q^{28} -0.409006 q^{29} +12.7100 q^{30} -2.15708 q^{31} -7.23472 q^{32} +7.59625 q^{33} +0.808662 q^{34} +2.31101 q^{35} -2.17650 q^{36} +1.00000 q^{37} +17.1020 q^{38} -1.49493 q^{39} -7.17901 q^{40} -4.05600 q^{41} +1.96849 q^{42} -8.79811 q^{43} -14.4533 q^{44} +2.95583 q^{45} -11.4784 q^{46} -6.09219 q^{47} +2.38929 q^{48} -6.64208 q^{49} +21.8374 q^{50} -0.549247 q^{51} +2.84438 q^{52} -2.11037 q^{53} +12.3887 q^{54} +19.6285 q^{55} -1.11186 q^{56} -11.6157 q^{57} -0.900221 q^{58} +10.4232 q^{59} +16.4254 q^{60} +0.0316518 q^{61} -4.74772 q^{62} +0.457788 q^{63} -12.7271 q^{64} -3.86285 q^{65} +16.7193 q^{66} +10.1726 q^{67} +1.04505 q^{68} +7.79618 q^{69} +5.08652 q^{70} -9.21649 q^{71} -1.42209 q^{72} +9.79556 q^{73} +2.20100 q^{74} -14.8321 q^{75} +22.1011 q^{76} +3.03999 q^{77} -3.29033 q^{78} -8.33729 q^{79} +6.17386 q^{80} -6.11890 q^{81} -8.92724 q^{82} +11.4020 q^{83} +2.54391 q^{84} -1.41924 q^{85} -19.3646 q^{86} +0.611435 q^{87} -9.44356 q^{88} -13.1013 q^{89} +6.50576 q^{90} -0.598265 q^{91} -14.8337 q^{92} +3.22467 q^{93} -13.4089 q^{94} -30.0148 q^{95} +10.8154 q^{96} -7.68599 q^{97} -14.6192 q^{98} +3.88821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.20100	1.55634	0.778169	−	0.628055i	$-0.216149\pi$
$2$	2.20100	1.55634	0.778169	+	0.628055i	$0.216149\pi$
$3$	−1.49493	−0.863097	−0.431548	−	0.902090i	$-0.642033\pi$
$3$	−1.49493	−0.863097	−0.431548	+	0.902090i	$0.642033\pi$
$4$	2.84438	1.42219
$5$	−3.86285	−1.72752	−0.863760	−	0.503904i	$-0.831896\pi$
$5$	−3.86285	−1.72752	−0.863760	+	0.503904i	$0.831896\pi$
$6$	−3.29033	−1.34327
$7$	−0.598265	−0.226123	−0.113061	−	0.993588i	$-0.536066\pi$
$7$	−0.598265	−0.226123	−0.113061	+	0.993588i	$0.536066\pi$
$8$	1.85847	0.657070
$9$	−0.765193	−0.255064
$10$	−8.50211	−2.68860
$11$	−5.08135	−1.53209	−0.766043	−	0.642790i	$-0.777777\pi$
$11$	−5.08135	−1.53209	−0.766043	+	0.642790i	$0.777777\pi$
$12$	−4.25214	−1.22749
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.31678	−0.351924
$15$	5.77468	1.49102
$16$	−1.59826	−0.399566
$17$	0.367408	0.0891094	0.0445547	−	0.999007i	$-0.485813\pi$
$17$	0.367408	0.0891094	0.0445547	+	0.999007i	$0.485813\pi$
$18$	−1.68419	−0.396966
$19$	7.77011	1.78259	0.891293	−	0.453428i	$-0.149799\pi$
$19$	7.77011	1.78259	0.891293	+	0.453428i	$0.149799\pi$
$20$	−10.9874	−2.45686
$21$	0.894363	0.195166
$22$	−11.1840	−2.38444
$23$	−5.21509	−1.08742	−0.543711	−	0.839273i	$-0.682981\pi$
$23$	−5.21509	−1.08742	−0.543711	+	0.839273i	$0.682981\pi$
$24$	−2.77828	−0.567115
$25$	9.92161	1.98432
$26$	2.20100	0.431651
$27$	5.62869	1.08324
$28$	−1.70169	−0.321590
$29$	−0.409006	−0.0759506	−0.0379753	−	0.999279i	$-0.512091\pi$
$29$	−0.409006	−0.0759506	−0.0379753	+	0.999279i	$0.512091\pi$
$30$	12.7100	2.32053
$31$	−2.15708	−0.387423	−0.193711	−	0.981059i	$-0.562052\pi$
$31$	−2.15708	−0.387423	−0.193711	+	0.981059i	$0.562052\pi$
$32$	−7.23472	−1.27893
$33$	7.59625	1.32234
$34$	0.808662	0.138684
$35$	2.31101	0.390632
$36$	−2.17650	−0.362750
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	17.1020	2.77431
$39$	−1.49493	−0.239380
$40$	−7.17901	−1.13510
$41$	−4.05600	−0.633441	−0.316720	−	0.948519i	$-0.602582\pi$
$41$	−4.05600	−0.633441	−0.316720	+	0.948519i	$0.602582\pi$
$42$	1.96849	0.303744
$43$	−8.79811	−1.34170	−0.670850	−	0.741593i	$-0.734071\pi$
$43$	−8.79811	−1.34170	−0.670850	+	0.741593i	$0.734071\pi$
$44$	−14.4533	−2.17892
$45$	2.95583	0.440628
$46$	−11.4784	−1.69240
$47$	−6.09219	−0.888637	−0.444318	−	0.895869i	$-0.646554\pi$
$47$	−6.09219	−0.888637	−0.444318	+	0.895869i	$0.646554\pi$
$48$	2.38929	0.344864
$49$	−6.64208	−0.948868
$50$	21.8374	3.08828
$51$	−0.549247	−0.0769100
$52$	2.84438	0.394444
$53$	−2.11037	−0.289881	−0.144941	−	0.989440i	$-0.546299\pi$
$53$	−2.11037	−0.289881	−0.144941	+	0.989440i	$0.546299\pi$
$54$	12.3887	1.68589
$55$	19.6285	2.64671
$56$	−1.11186	−0.148579
$57$	−11.6157	−1.53854
$58$	−0.900221	−0.118205
$59$	10.4232	1.35698	0.678490	−	0.734609i	$-0.262634\pi$
$59$	10.4232	1.35698	0.678490	+	0.734609i	$0.262634\pi$
$60$	16.4254	2.12051
$61$	0.0316518	0.00405260	0.00202630	−	0.999998i	$-0.499355\pi$
$61$	0.0316518	0.00405260	0.00202630	+	0.999998i	$0.499355\pi$
$62$	−4.74772	−0.602961
$63$	0.457788	0.0576759
$64$	−12.7271	−1.59088
$65$	−3.86285	−0.479128
$66$	16.7193	2.05800
$67$	10.1726	1.24278	0.621390	−	0.783502i	$-0.286568\pi$
$67$	10.1726	1.24278	0.621390	+	0.783502i	$0.286568\pi$
$68$	1.04505	0.126730
$69$	7.79618	0.938550
$70$	5.08652	0.607955
$71$	−9.21649	−1.09380	−0.546898	−	0.837199i	$-0.684192\pi$
$71$	−9.21649	−1.09380	−0.546898	+	0.837199i	$0.684192\pi$
$72$	−1.42209	−0.167595
$73$	9.79556	1.14648	0.573242	−	0.819386i	$-0.305686\pi$
$73$	9.79556	1.14648	0.573242	+	0.819386i	$0.305686\pi$
$74$	2.20100	0.255860
$75$	−14.8321	−1.71266
$76$	22.1011	2.53517
$77$	3.03999	0.346440
$78$	−3.29033	−0.372556
$79$	−8.33729	−0.938018	−0.469009	−	0.883193i	$-0.655389\pi$
$79$	−8.33729	−0.938018	−0.469009	+	0.883193i	$0.655389\pi$
$80$	6.17386	0.690258
$81$	−6.11890	−0.679878
$82$	−8.92724	−0.985848
$83$	11.4020	1.25153	0.625767	−	0.780010i	$-0.284786\pi$
$83$	11.4020	1.25153	0.625767	+	0.780010i	$0.284786\pi$
$84$	2.54391	0.277563
$85$	−1.41924	−0.153938
$86$	−19.3646	−2.08814
$87$	0.611435	0.0655527
$88$	−9.44356	−1.00669
$89$	−13.1013	−1.38873	−0.694366	−	0.719622i	$-0.744315\pi$
$89$	−13.1013	−1.38873	−0.694366	+	0.719622i	$0.744315\pi$
$90$	6.50576	0.685767
$91$	−0.598265	−0.0627152
$92$	−14.8337	−1.54652
$93$	3.22467	0.334383
$94$	−13.4089	−1.38302
$95$	−30.0148	−3.07945
$96$	10.8154	1.10384
$97$	−7.68599	−0.780394	−0.390197	−	0.920731i	$-0.627593\pi$
$97$	−7.68599	−0.780394	−0.390197	+	0.920731i	$0.627593\pi$
$98$	−14.6192	−1.47676
$99$	3.88821	0.390780
$100$	28.2208	2.82208
$101$	7.94676	0.790732	0.395366	−	0.918524i	$-0.370618\pi$
$101$	7.94676	0.790732	0.395366	+	0.918524i	$0.370618\pi$
$102$	−1.20889	−0.119698
$103$	−9.20450	−0.906946	−0.453473	−	0.891270i	$-0.649815\pi$
$103$	−9.20450	−0.906946	−0.453473	+	0.891270i	$0.649815\pi$
$104$	1.85847	0.182238
$105$	−3.45479	−0.337153
$106$	−4.64491	−0.451153
$107$	−1.92029	−0.185642	−0.0928208	−	0.995683i	$-0.529588\pi$
$107$	−1.92029	−0.185642	−0.0928208	+	0.995683i	$0.529588\pi$
$108$	16.0101	1.54058
$109$	15.5110	1.48568	0.742840	−	0.669469i	$-0.233478\pi$
$109$	15.5110	1.48568	0.742840	+	0.669469i	$0.233478\pi$
$110$	43.2022	4.11917
$111$	−1.49493	−0.141892
$112$	0.956186	0.0903511
$113$	0.747009	0.0702727	0.0351364	−	0.999383i	$-0.488813\pi$
$113$	0.747009	0.0702727	0.0351364	+	0.999383i	$0.488813\pi$
$114$	−25.5662	−2.39449
$115$	20.1451	1.87854
$116$	−1.16337	−0.108016
$117$	−0.765193	−0.0707421
$118$	22.9413	2.11192
$119$	−0.219807	−0.0201497
$120$	10.7321	0.979702
$121$	14.8201	1.34729
$122$	0.0696655	0.00630722
$123$	6.06343	0.546721
$124$	−6.13555	−0.550988
$125$	−19.0114	−1.70044
$126$	1.00759	0.0897632
$127$	−17.1762	−1.52414	−0.762072	−	0.647493i	$-0.775818\pi$
$127$	−17.1762	−1.52414	−0.762072	+	0.647493i	$0.775818\pi$
$128$	−13.5427	−1.19702
$129$	13.1525	1.15802
$130$	−8.50211	−0.745685
$131$	−15.0090	−1.31134	−0.655671	−	0.755047i	$-0.727614\pi$
$131$	−15.0090	−1.31134	−0.655671	+	0.755047i	$0.727614\pi$
$132$	21.6066	1.88061
$133$	−4.64859	−0.403083
$134$	22.3898	1.93419
$135$	−21.7428	−1.87132
$136$	0.682818	0.0585511
$137$	7.22103	0.616934	0.308467	−	0.951235i	$-0.400184\pi$
$137$	7.22103	0.616934	0.308467	+	0.951235i	$0.400184\pi$
$138$	17.1594	1.46070
$139$	−18.7129	−1.58721	−0.793604	−	0.608434i	$-0.791798\pi$
$139$	−18.7129	−1.58721	−0.793604	+	0.608434i	$0.791798\pi$
$140$	6.57338	0.555552
$141$	9.10738	0.766980
$142$	−20.2855	−1.70232
$143$	−5.08135	−0.424924
$144$	1.22298	0.101915
$145$	1.57993	0.131206
$146$	21.5600	1.78432
$147$	9.92942	0.818965
$148$	2.84438	0.233807
$149$	8.86300	0.726086	0.363043	−	0.931772i	$-0.381738\pi$
$149$	8.86300	0.726086	0.363043	+	0.931772i	$0.381738\pi$
$150$	−32.6453	−2.66548
$151$	4.84709	0.394451	0.197225	−	0.980358i	$-0.436807\pi$
$151$	4.84709	0.394451	0.197225	+	0.980358i	$0.436807\pi$
$152$	14.4406	1.17128
$153$	−0.281138	−0.0227286
$154$	6.69101	0.539177
$155$	8.33247	0.669280
$156$	−4.25214	−0.340444
$157$	−21.2952	−1.69954	−0.849770	−	0.527153i	$-0.823259\pi$
$157$	−21.2952	−1.69954	−0.849770	+	0.527153i	$0.823259\pi$
$158$	−18.3503	−1.45987
$159$	3.15485	0.250196
$160$	27.9466	2.20938
$161$	3.12001	0.245891
$162$	−13.4677	−1.05812
$163$	−21.4253	−1.67816	−0.839079	−	0.544010i	$-0.816905\pi$
$163$	−21.4253	−1.67816	−0.839079	+	0.544010i	$0.816905\pi$
$164$	−11.5368	−0.900873
$165$	−29.3432	−2.28436
$166$	25.0958	1.94781
$167$	−7.42810	−0.574803	−0.287402	−	0.957810i	$-0.592791\pi$
$167$	−7.42810	−0.574803	−0.287402	+	0.957810i	$0.592791\pi$
$168$	1.66215	0.128238
$169$	1.00000	0.0769231
$170$	−3.12374	−0.239580
$171$	−5.94563	−0.454674
$172$	−25.0252	−1.90815
$173$	13.4166	1.02004	0.510022	−	0.860161i	$-0.329637\pi$
$173$	13.4166	1.02004	0.510022	+	0.860161i	$0.329637\pi$
$174$	1.34576	0.102022
$175$	−5.93575	−0.448701
$176$	8.12135	0.612170
$177$	−15.5819	−1.17121
$178$	−28.8358	−2.16134
$179$	−15.7421	−1.17662	−0.588309	−	0.808637i	$-0.700206\pi$
$179$	−15.7421	−1.17662	−0.588309	+	0.808637i	$0.700206\pi$
$180$	8.40749	0.626657
$181$	−1.96483	−0.146044	−0.0730221	−	0.997330i	$-0.523264\pi$
$181$	−1.96483	−0.146044	−0.0730221	+	0.997330i	$0.523264\pi$
$182$	−1.31678	−0.0976061
$183$	−0.0473172	−0.00349779
$184$	−9.69211	−0.714512
$185$	−3.86285	−0.284002
$186$	7.09749	0.520413
$187$	−1.86693	−0.136523
$188$	−17.3285	−1.26381
$189$	−3.36745	−0.244946
$190$	−66.0624	−4.79267
$191$	12.2798	0.888535	0.444268	−	0.895894i	$-0.353464\pi$
$191$	12.2798	0.888535	0.444268	+	0.895894i	$0.353464\pi$
$192$	19.0260	1.37309
$193$	9.71734	0.699469	0.349735	−	0.936849i	$-0.386272\pi$
$193$	9.71734	0.699469	0.349735	+	0.936849i	$0.386272\pi$
$194$	−16.9168	−1.21456
$195$	5.77468	0.413533
$196$	−18.8926	−1.34947
$197$	21.7579	1.55018	0.775092	−	0.631848i	$-0.217703\pi$
$197$	21.7579	1.55018	0.775092	+	0.631848i	$0.217703\pi$
$198$	8.55794	0.608186
$199$	22.0882	1.56579	0.782894	−	0.622155i	$-0.213743\pi$
$199$	22.0882	1.56579	0.782894	+	0.622155i	$0.213743\pi$
$200$	18.4391	1.30384
$201$	−15.2073	−1.07264
$202$	17.4908	1.23065
$203$	0.244694	0.0171742
$204$	−1.56227	−0.109381
$205$	15.6677	1.09428
$206$	−20.2591	−1.41152
$207$	3.99055	0.277362
$208$	−1.59826	−0.110820
$209$	−39.4827	−2.73107
$210$	−7.60397	−0.524724
$211$	−0.643134	−0.0442752	−0.0221376	−	0.999755i	$-0.507047\pi$
$211$	−0.643134	−0.0442752	−0.0221376	+	0.999755i	$0.507047\pi$
$212$	−6.00269	−0.412266
$213$	13.7780	0.944052
$214$	−4.22655	−0.288921
$215$	33.9858	2.31781
$216$	10.4608	0.711766
$217$	1.29050	0.0876051
$218$	34.1395	2.31222
$219$	−14.6436	−0.989526
$220$	55.8309	3.76412
$221$	0.367408	0.0247145
$222$	−3.29033	−0.220832
$223$	0.833940	0.0558448	0.0279224	−	0.999610i	$-0.491111\pi$
$223$	0.833940	0.0558448	0.0279224	+	0.999610i	$0.491111\pi$
$224$	4.32828	0.289195
$225$	−7.59195	−0.506130
$226$	1.64416	0.109368
$227$	3.72334	0.247127	0.123563	−	0.992337i	$-0.460568\pi$
$227$	3.72334	0.247127	0.123563	+	0.992337i	$0.460568\pi$
$228$	−33.0396	−2.18810
$229$	−6.91609	−0.457028	−0.228514	−	0.973541i	$-0.573387\pi$
$229$	−6.91609	−0.457028	−0.228514	+	0.973541i	$0.573387\pi$
$230$	44.3393	2.92365
$231$	−4.54457	−0.299011
$232$	−0.760128	−0.0499048
$233$	14.5329	0.952079	0.476039	−	0.879424i	$-0.342072\pi$
$233$	14.5329	0.952079	0.476039	+	0.879424i	$0.342072\pi$
$234$	−1.68419	−0.110099
$235$	23.5332	1.53514
$236$	29.6474	1.92988
$237$	12.4636	0.809600
$238$	−0.483794	−0.0313597
$239$	−21.7580	−1.40741	−0.703703	−	0.710494i	$-0.748472\pi$
$239$	−21.7580	−1.40741	−0.703703	+	0.710494i	$0.748472\pi$
$240$	−9.22947	−0.595760
$241$	−6.31042	−0.406490	−0.203245	−	0.979128i	$-0.565149\pi$
$241$	−6.31042	−0.406490	−0.203245	+	0.979128i	$0.565149\pi$
$242$	32.6190	2.09683
$243$	−7.73876	−0.496441
$244$	0.0900298	0.00576357
$245$	25.6574	1.63919
$246$	13.3456	0.850882
$247$	7.77011	0.494400
$248$	−4.00887	−0.254564
$249$	−17.0452	−1.08019
$250$	−41.8441	−2.64645
$251$	24.7318	1.56106	0.780529	−	0.625120i	$-0.214950\pi$
$251$	24.7318	1.56106	0.780529	+	0.625120i	$0.214950\pi$
$252$	1.30212	0.0820260
$253$	26.4997	1.66602
$254$	−37.8048	−2.37208
$255$	2.12166	0.132864
$256$	−4.35341	−0.272088
$257$	16.0959	1.00404	0.502018	−	0.864857i	$-0.332591\pi$
$257$	16.0959	1.00404	0.502018	+	0.864857i	$0.332591\pi$
$258$	28.9487	1.80227
$259$	−0.598265	−0.0371744
$260$	−10.9874	−0.681410
$261$	0.312969	0.0193723
$262$	−33.0347	−2.04089
$263$	−10.5077	−0.647931	−0.323965	−	0.946069i	$-0.605016\pi$
$263$	−10.5077	−0.647931	−0.323965	+	0.946069i	$0.605016\pi$
$264$	14.1174	0.868868
$265$	8.15203	0.500775
$266$	−10.2315	−0.627334
$267$	19.5855	1.19861
$268$	28.9347	1.76747
$269$	−1.62628	−0.0991561	−0.0495780	−	0.998770i	$-0.515788\pi$
$269$	−1.62628	−0.0991561	−0.0495780	+	0.998770i	$0.515788\pi$
$270$	−47.8558	−2.91241
$271$	−12.5433	−0.761953	−0.380976	−	0.924585i	$-0.624412\pi$
$271$	−12.5433	−0.761953	−0.380976	+	0.924585i	$0.624412\pi$
$272$	−0.587215	−0.0356051
$273$	0.894363	0.0541293
$274$	15.8934	0.960158
$275$	−50.4152	−3.04015
$276$	22.1753	1.33480
$277$	−22.9486	−1.37885	−0.689424	−	0.724358i	$-0.742136\pi$
$277$	−22.9486	−1.37885	−0.689424	+	0.724358i	$0.742136\pi$
$278$	−41.1870	−2.47023
$279$	1.65058	0.0988177
$280$	4.29495	0.256672
$281$	14.3898	0.858423	0.429211	−	0.903204i	$-0.358792\pi$
$281$	14.3898	0.858423	0.429211	+	0.903204i	$0.358792\pi$
$282$	20.0453	1.19368
$283$	2.83817	0.168712	0.0843558	−	0.996436i	$-0.473117\pi$
$283$	2.83817	0.168712	0.0843558	+	0.996436i	$0.473117\pi$
$284$	−26.2152	−1.55559
$285$	44.8699	2.65786
$286$	−11.1840	−0.661326
$287$	2.42656	0.143235
$288$	5.53596	0.326209
$289$	−16.8650	−0.992060
$290$	3.47742	0.204201
$291$	11.4900	0.673555
$292$	27.8623	1.63052
$293$	24.9160	1.45561	0.727803	−	0.685786i	$-0.240542\pi$
$293$	24.9160	1.45561	0.727803	+	0.685786i	$0.240542\pi$
$294$	21.8546	1.27459
$295$	−40.2631	−2.34421
$296$	1.85847	0.108022
$297$	−28.6013	−1.65962
$298$	19.5074	1.13003
$299$	−5.21509	−0.301596
$300$	−42.1881	−2.43573
$301$	5.26360	0.303389
$302$	10.6684	0.613899
$303$	−11.8798	−0.682478
$304$	−12.4187	−0.712261
$305$	−0.122266	−0.00700095
$306$	−0.618782	−0.0353734
$307$	−16.7278	−0.954704	−0.477352	−	0.878712i	$-0.658403\pi$
$307$	−16.7278	−0.954704	−0.477352	+	0.878712i	$0.658403\pi$
$308$	8.64690	0.492703
$309$	13.7601	0.782782
$310$	18.3397	1.04163
$311$	5.48005	0.310745	0.155373	−	0.987856i	$-0.450342\pi$
$311$	5.48005	0.310745	0.155373	+	0.987856i	$0.450342\pi$
$312$	−2.77828	−0.157289
$313$	12.3172	0.696211	0.348106	−	0.937455i	$-0.386825\pi$
$313$	12.3172	0.696211	0.348106	+	0.937455i	$0.386825\pi$
$314$	−46.8706	−2.64506
$315$	−1.76837	−0.0996362
$316$	−23.7144	−1.33404
$317$	5.30060	0.297711	0.148856	−	0.988859i	$-0.452441\pi$
$317$	5.30060	0.297711	0.148856	+	0.988859i	$0.452441\pi$
$318$	6.94380	0.389389
$319$	2.07831	0.116363
$320$	49.1627	2.74828
$321$	2.87070	0.160227
$322$	6.86712	0.382690
$323$	2.85480	0.158845
$324$	−17.4045	−0.966915
$325$	9.92161	0.550352
$326$	−47.1569	−2.61178
$327$	−23.1877	−1.28229
$328$	−7.53797	−0.416215
$329$	3.64474	0.200941
$330$	−64.5842	−3.55524
$331$	−11.0231	−0.605883	−0.302941	−	0.953009i	$-0.597969\pi$
$331$	−11.0231	−0.605883	−0.302941	+	0.953009i	$0.597969\pi$
$332$	32.4317	1.77992
$333$	−0.765193	−0.0419323
$334$	−16.3492	−0.894589
$335$	−39.2952	−2.14693
$336$	−1.42943	−0.0779817
$337$	5.09217	0.277388	0.138694	−	0.990335i	$-0.455710\pi$
$337$	5.09217	0.277388	0.138694	+	0.990335i	$0.455710\pi$
$338$	2.20100	0.119718
$339$	−1.11672	−0.0606521
$340$	−4.03686	−0.218929
$341$	10.9609	0.593564
$342$	−13.0863	−0.707627
$343$	8.16158	0.440684
$344$	−16.3511	−0.881591
$345$	−30.1155	−1.62136
$346$	29.5298	1.58753
$347$	19.5395	1.04893	0.524467	−	0.851431i	$-0.324264\pi$
$347$	19.5395	1.04893	0.524467	+	0.851431i	$0.324264\pi$
$348$	1.73915	0.0932283
$349$	−17.0674	−0.913595	−0.456797	−	0.889571i	$-0.651004\pi$
$349$	−17.0674	−0.913595	−0.456797	+	0.889571i	$0.651004\pi$
$350$	−13.0646	−0.698330
$351$	5.62869	0.300437
$352$	36.7622	1.95943
$353$	5.66028	0.301266	0.150633	−	0.988590i	$-0.451869\pi$
$353$	5.66028	0.301266	0.150633	+	0.988590i	$0.451869\pi$
$354$	−34.2956	−1.82279
$355$	35.6019	1.88955
$356$	−37.2650	−1.97504
$357$	0.328596	0.0173911
$358$	−34.6482	−1.83121
$359$	−35.0397	−1.84932	−0.924662	−	0.380790i	$-0.875652\pi$
$359$	−35.0397	−1.84932	−0.924662	+	0.380790i	$0.875652\pi$
$360$	5.49333	0.289524
$361$	41.3746	2.17761
$362$	−4.32457	−0.227294
$363$	−22.1550	−1.16284
$364$	−1.70169	−0.0891929
$365$	−37.8388	−1.98057
$366$	−0.104145	−0.00544374
$367$	−16.1349	−0.842234	−0.421117	−	0.907006i	$-0.638362\pi$
$367$	−16.1349	−0.842234	−0.421117	+	0.907006i	$0.638362\pi$
$368$	8.33510	0.434497
$369$	3.10362	0.161568
$370$	−8.50211	−0.442004
$371$	1.26256	0.0655488
$372$	9.17219	0.475556
$373$	15.4975	0.802429	0.401215	−	0.915984i	$-0.368588\pi$
$373$	15.4975	0.802429	0.401215	+	0.915984i	$0.368588\pi$
$374$	−4.10910	−0.212476
$375$	28.4207	1.46764
$376$	−11.3222	−0.583897
$377$	−0.409006	−0.0210649
$378$	−7.41174	−0.381219
$379$	23.8507	1.22513	0.612564	−	0.790421i	$-0.290138\pi$
$379$	23.8507	1.22513	0.612564	+	0.790421i	$0.290138\pi$
$380$	−85.3734	−4.37956
$381$	25.6772	1.31548
$382$	27.0278	1.38286
$383$	3.25894	0.166524	0.0832620	−	0.996528i	$-0.473466\pi$
$383$	3.25894	0.166524	0.0832620	+	0.996528i	$0.473466\pi$
$384$	20.2454	1.03314
$385$	−11.7430	−0.598481
$386$	21.3878	1.08861
$387$	6.73225	0.342220
$388$	−21.8619	−1.10987
$389$	−32.6138	−1.65359	−0.826794	−	0.562505i	$-0.809838\pi$
$389$	−32.6138	−1.65359	−0.826794	+	0.562505i	$0.809838\pi$
$390$	12.7100	0.643598
$391$	−1.91606	−0.0968995
$392$	−12.3441	−0.623473
$393$	22.4373	1.13181
$394$	47.8890	2.41261
$395$	32.2057	1.62044
$396$	11.0596	0.555764
$397$	24.9973	1.25458	0.627288	−	0.778787i	$-0.284165\pi$
$397$	24.9973	1.25458	0.627288	+	0.778787i	$0.284165\pi$
$398$	48.6159	2.43690
$399$	6.94930	0.347900
$400$	−15.8574	−0.792868
$401$	−28.2236	−1.40942	−0.704711	−	0.709495i	$-0.748923\pi$
$401$	−28.2236	−1.40942	−0.704711	+	0.709495i	$0.748923\pi$
$402$	−33.4711	−1.66939
$403$	−2.15708	−0.107452
$404$	22.6036	1.12457
$405$	23.6364	1.17450
$406$	0.538571	0.0267288
$407$	−5.08135	−0.251873
$408$	−1.02076	−0.0505353
$409$	−3.56531	−0.176293	−0.0881467	−	0.996108i	$-0.528094\pi$
$409$	−3.56531	−0.176293	−0.0881467	+	0.996108i	$0.528094\pi$
$410$	34.4846	1.70307
$411$	−10.7949	−0.532474
$412$	−26.1811	−1.28985
$413$	−6.23582	−0.306844
$414$	8.78318	0.431670
$415$	−44.0443	−2.16205
$416$	−7.23472	−0.354711
$417$	27.9744	1.36991
$418$	−86.9012	−4.25047
$419$	−35.6326	−1.74077	−0.870384	−	0.492374i	$-0.836129\pi$
$419$	−35.6326	−1.74077	−0.870384	+	0.492374i	$0.836129\pi$
$420$	−9.82673	−0.479495
$421$	−17.4162	−0.848814	−0.424407	−	0.905472i	$-0.639517\pi$
$421$	−17.4162	−0.848814	−0.424407	+	0.905472i	$0.639517\pi$
$422$	−1.41554	−0.0689072
$423$	4.66170	0.226660
$424$	−3.92206	−0.190472
$425$	3.64527	0.176822
$426$	30.3253	1.46926
$427$	−0.0189362	−0.000916386 0
$428$	−5.46204	−0.264018
$429$	7.59625	0.366750
$430$	74.8026	3.60730
$431$	10.5866	0.509938	0.254969	−	0.966949i	$-0.417935\pi$
$431$	10.5866	0.509938	0.254969	+	0.966949i	$0.417935\pi$
$432$	−8.99614	−0.432827
$433$	35.9734	1.72877	0.864386	−	0.502828i	$-0.167707\pi$
$433$	35.9734	1.72877	0.864386	+	0.502828i	$0.167707\pi$
$434$	2.84039	0.136343
$435$	−2.36188	−0.113243
$436$	44.1190	2.11292
$437$	−40.5218	−1.93842
$438$	−32.2306	−1.54004
$439$	32.3114	1.54214	0.771070	−	0.636750i	$-0.219722\pi$
$439$	32.3114	1.54214	0.771070	+	0.636750i	$0.219722\pi$
$440$	36.4791	1.73907
$441$	5.08247	0.242022
$442$	0.808662	0.0384641
$443$	−34.4938	−1.63885	−0.819425	−	0.573187i	$-0.805707\pi$
$443$	−34.4938	−1.63885	−0.819425	+	0.573187i	$0.805707\pi$
$444$	−4.25214	−0.201798
$445$	50.6083	2.39906
$446$	1.83550	0.0869134
$447$	−13.2495	−0.626682
$448$	7.61415	0.359735
$449$	5.19145	0.245000	0.122500	−	0.992469i	$-0.460909\pi$
$449$	5.19145	0.245000	0.122500	+	0.992469i	$0.460909\pi$
$450$	−16.7098	−0.787709
$451$	20.6100	0.970485
$452$	2.12478	0.0999411
$453$	−7.24605	−0.340449
$454$	8.19505	0.384613
$455$	2.31101	0.108342
$456$	−21.5876	−1.01093
$457$	2.64625	0.123786	0.0618931	−	0.998083i	$-0.480286\pi$
$457$	2.64625	0.123786	0.0618931	+	0.998083i	$0.480286\pi$
$458$	−15.2223	−0.711290
$459$	2.06802	0.0965270
$460$	57.3003	2.67164
$461$	−1.16843	−0.0544194	−0.0272097	−	0.999630i	$-0.508662\pi$
$461$	−1.16843	−0.0544194	−0.0272097	+	0.999630i	$0.508662\pi$
$462$	−10.0026	−0.465362
$463$	−1.57528	−0.0732095	−0.0366047	−	0.999330i	$-0.511654\pi$
$463$	−1.57528	−0.0732095	−0.0366047	+	0.999330i	$0.511654\pi$
$464$	0.653700	0.0303473
$465$	−12.4564	−0.577653
$466$	31.9867	1.48176
$467$	−4.78747	−0.221538	−0.110769	−	0.993846i	$-0.535331\pi$
$467$	−4.78747	−0.221538	−0.110769	+	0.993846i	$0.535331\pi$
$468$	−2.17650	−0.100609
$469$	−6.08590	−0.281021
$470$	51.7965	2.38919
$471$	31.8347	1.46687
$472$	19.3712	0.891632
$473$	44.7063	2.05560
$474$	27.4324	1.26001
$475$	77.0920	3.53722
$476$	−0.625215	−0.0286567
$477$	1.61484	0.0739384
$478$	−47.8892	−2.19040
$479$	−17.0825	−0.780518	−0.390259	−	0.920705i	$-0.627615\pi$
$479$	−17.0825	−0.780518	−0.390259	+	0.920705i	$0.627615\pi$
$480$	−41.7782	−1.90691
$481$	1.00000	0.0455961
$482$	−13.8892	−0.632636
$483$	−4.66418	−0.212228
$484$	42.1541	1.91610
$485$	29.6898	1.34815
$486$	−17.0330	−0.772631
$487$	24.7074	1.11960	0.559800	−	0.828627i	$-0.310878\pi$
$487$	24.7074	1.11960	0.559800	+	0.828627i	$0.310878\pi$
$488$	0.0588241	0.00266284
$489$	32.0292	1.44841
$490$	56.4717	2.55113
$491$	−25.8976	−1.16874	−0.584370	−	0.811487i	$-0.698658\pi$
$491$	−25.8976	−1.16874	−0.584370	+	0.811487i	$0.698658\pi$
$492$	17.2467	0.777540
$493$	−0.150272	−0.00676791
$494$	17.1020	0.769454
$495$	−15.0196	−0.675080
$496$	3.44758	0.154801
$497$	5.51391	0.247332
$498$	−37.5164	−1.68115
$499$	5.95278	0.266483	0.133241	−	0.991084i	$-0.457461\pi$
$499$	5.95278	0.266483	0.133241	+	0.991084i	$0.457461\pi$
$500$	−54.0758	−2.41834
$501$	11.1045	0.496111
$502$	54.4346	2.42953
$503$	−19.1097	−0.852059	−0.426030	−	0.904709i	$-0.640088\pi$
$503$	−19.1097	−0.852059	−0.426030	+	0.904709i	$0.640088\pi$
$504$	0.850788	0.0378971
$505$	−30.6971	−1.36600
$506$	58.3257	2.59290
$507$	−1.49493	−0.0663920
$508$	−48.8557	−2.16762
$509$	−12.1443	−0.538286	−0.269143	−	0.963100i	$-0.586740\pi$
$509$	−12.1443	−0.538286	−0.269143	+	0.963100i	$0.586740\pi$
$510$	4.66976	0.206781
$511$	−5.86034	−0.259246
$512$	17.5037	0.773560
$513$	43.7355	1.93097
$514$	35.4270	1.56262
$515$	35.5556	1.56677
$516$	37.4108	1.64692
$517$	30.9566	1.36147
$518$	−1.31678	−0.0578559
$519$	−20.0568	−0.880396
$520$	−7.17901	−0.314820
$521$	23.5459	1.03156	0.515782	−	0.856720i	$-0.327501\pi$
$521$	23.5459	1.03156	0.515782	+	0.856720i	$0.327501\pi$
$522$	0.688843	0.0301498
$523$	12.7057	0.555582	0.277791	−	0.960642i	$-0.410398\pi$
$523$	12.7057	0.555582	0.277791	+	0.960642i	$0.410398\pi$
$524$	−42.6913	−1.86498
$525$	8.87352	0.387272
$526$	−23.1273	−1.00840
$527$	−0.792526	−0.0345230
$528$	−12.1408	−0.528361
$529$	4.19717	0.182486
$530$	17.9426	0.779376
$531$	−7.97573	−0.346117
$532$	−13.2223	−0.573261
$533$	−4.05600	−0.175685
$534$	43.1075	1.86544
$535$	7.41780	0.320699
$536$	18.9055	0.816593
$537$	23.5332	1.01553
$538$	−3.57944	−0.154320
$539$	33.7507	1.45375
$540$	−61.8447	−2.66137
$541$	−22.8248	−0.981313	−0.490656	−	0.871353i	$-0.663243\pi$
$541$	−22.8248	−0.981313	−0.490656	+	0.871353i	$0.663243\pi$
$542$	−27.6078	−1.18586
$543$	2.93727	0.126050
$544$	−2.65809	−0.113965
$545$	−59.9165	−2.56654
$546$	1.96849	0.0842435
$547$	8.20566	0.350849	0.175424	−	0.984493i	$-0.443870\pi$
$547$	8.20566	0.350849	0.175424	+	0.984493i	$0.443870\pi$
$548$	20.5393	0.877397
$549$	−0.0242198	−0.00103367
$550$	−110.964	−4.73150
$551$	−3.17802	−0.135388
$552$	14.4890	0.616693
$553$	4.98791	0.212107
$554$	−50.5098	−2.14596
$555$	5.77468	0.245121
$556$	−53.2266	−2.25731
$557$	34.7806	1.47370	0.736851	−	0.676055i	$-0.236312\pi$
$557$	34.7806	1.47370	0.736851	+	0.676055i	$0.236312\pi$
$558$	3.63292	0.153794
$559$	−8.79811	−0.372121
$560$	−3.69360	−0.156083
$561$	2.79092	0.117833
$562$	31.6719	1.33600
$563$	2.73885	0.115429	0.0577144	−	0.998333i	$-0.481619\pi$
$563$	2.73885	0.115429	0.0577144	+	0.998333i	$0.481619\pi$
$564$	25.9048	1.09079
$565$	−2.88558	−0.121397
$566$	6.24680	0.262572
$567$	3.66072	0.153736
$568$	−17.1286	−0.718701
$569$	43.1840	1.81037	0.905184	−	0.425019i	$-0.139733\pi$
$569$	43.1840	1.81037	0.905184	+	0.425019i	$0.139733\pi$
$570$	98.7584	4.13654
$571$	−30.8831	−1.29242	−0.646208	−	0.763161i	$-0.723646\pi$
$571$	−30.8831	−1.29242	−0.646208	+	0.763161i	$0.723646\pi$
$572$	−14.4533	−0.604323
$573$	−18.3574	−0.766892
$574$	5.34085	0.222923
$575$	−51.7421	−2.15779
$576$	9.73866	0.405777
$577$	−3.62257	−0.150810	−0.0754049	−	0.997153i	$-0.524025\pi$
$577$	−3.62257	−0.150810	−0.0754049	+	0.997153i	$0.524025\pi$
$578$	−37.1198	−1.54398
$579$	−14.5267	−0.603710
$580$	4.49392	0.186600
$581$	−6.82143	−0.283000
$582$	25.2894	1.04828
$583$	10.7235	0.444123
$584$	18.2048	0.753320
$585$	2.95583	0.122208
$586$	54.8399	2.26542
$587$	12.5863	0.519493	0.259746	−	0.965677i	$-0.416361\pi$
$587$	12.5863	0.519493	0.259746	+	0.965677i	$0.416361\pi$
$588$	28.2430	1.16472
$589$	−16.7607	−0.690614
$590$	−88.6190	−3.64839
$591$	−32.5264	−1.33796
$592$	−1.59826	−0.0656883
$593$	29.3938	1.20706	0.603530	−	0.797340i	$-0.293760\pi$
$593$	29.3938	1.20706	0.603530	+	0.797340i	$0.293760\pi$
$594$	−62.9514	−2.58293
$595$	0.849082	0.0348090
$596$	25.2097	1.03263
$597$	−33.0202	−1.35143
$598$	−11.4784	−0.469386
$599$	−25.8822	−1.05752	−0.528759	−	0.848772i	$-0.677342\pi$
$599$	−25.8822	−1.05752	−0.528759	+	0.848772i	$0.677342\pi$
$600$	−27.5651	−1.12534
$601$	−13.2908	−0.542144	−0.271072	−	0.962559i	$-0.587378\pi$
$601$	−13.2908	−0.542144	−0.271072	+	0.962559i	$0.587378\pi$
$602$	11.5852	0.472176
$603$	−7.78399	−0.316989
$604$	13.7870	0.560984
$605$	−57.2480	−2.32746
$606$	−26.1474	−1.06217
$607$	−19.7544	−0.801807	−0.400903	−	0.916120i	$-0.631304\pi$
$607$	−19.7544	−0.801807	−0.400903	+	0.916120i	$0.631304\pi$
$608$	−56.2146	−2.27980
$609$	−0.365800	−0.0148230
$610$	−0.269107	−0.0108958
$611$	−6.09219	−0.246464
$612$	−0.799662	−0.0323244
$613$	−17.0472	−0.688532	−0.344266	−	0.938872i	$-0.611872\pi$
$613$	−17.0472	−0.688532	−0.344266	+	0.938872i	$0.611872\pi$
$614$	−36.8177	−1.48584
$615$	−23.4221	−0.944470
$616$	5.64975	0.227635
$617$	−26.2215	−1.05564	−0.527819	−	0.849357i	$-0.676990\pi$
$617$	−26.2215	−1.05564	−0.527819	+	0.849357i	$0.676990\pi$
$618$	30.2858	1.21827
$619$	32.1983	1.29416	0.647079	−	0.762423i	$-0.275990\pi$
$619$	32.1983	1.29416	0.647079	+	0.762423i	$0.275990\pi$
$620$	23.7007	0.951843
$621$	−29.3541	−1.17794
$622$	12.0616	0.483625
$623$	7.83803	0.314024
$624$	2.38929	0.0956481
$625$	23.8303	0.953212
$626$	27.1102	1.08354
$627$	59.0237	2.35718
$628$	−60.5716	−2.41707
$629$	0.367408	0.0146495
$630$	−3.89217	−0.155068
$631$	17.9167	0.713252	0.356626	−	0.934247i	$-0.383927\pi$
$631$	17.9167	0.713252	0.356626	+	0.934247i	$0.383927\pi$
$632$	−15.4946	−0.616344
$633$	0.961439	0.0382138
$634$	11.6666	0.463340
$635$	66.3492	2.63299
$636$	8.97358	0.355825
$637$	−6.64208	−0.263169
$638$	4.57434	0.181100
$639$	7.05240	0.278988
$640$	52.3136	2.06788
$641$	−40.6067	−1.60387	−0.801934	−	0.597412i	$-0.796196\pi$
$641$	−40.6067	−1.60387	−0.801934	+	0.597412i	$0.796196\pi$
$642$	6.31839	0.249367
$643$	30.8957	1.21841	0.609203	−	0.793014i	$-0.291489\pi$
$643$	30.8957	1.21841	0.609203	+	0.793014i	$0.291489\pi$
$644$	8.87448	0.349704
$645$	−50.8063	−2.00050
$646$	6.28339	0.247217
$647$	−23.0487	−0.906137	−0.453068	−	0.891476i	$-0.649671\pi$
$647$	−23.0487	−0.906137	−0.453068	+	0.891476i	$0.649671\pi$
$648$	−11.3718	−0.446727
$649$	−52.9638	−2.07901
$650$	21.8374	0.856534
$651$	−1.92921	−0.0756117
$652$	−60.9416	−2.38666
$653$	−27.5982	−1.08000	−0.540000	−	0.841665i	$-0.681576\pi$
$653$	−27.5982	−1.08000	−0.540000	+	0.841665i	$0.681576\pi$
$654$	−51.0361	−1.99567
$655$	57.9775	2.26537
$656$	6.48256	0.253102
$657$	−7.49549	−0.292427
$658$	8.02206	0.312732
$659$	15.4982	0.603724	0.301862	−	0.953352i	$-0.402392\pi$
$659$	15.4982	0.603724	0.301862	+	0.953352i	$0.402392\pi$
$660$	−83.4631	−3.24880
$661$	0.876740	0.0341012	0.0170506	−	0.999855i	$-0.494572\pi$
$661$	0.876740	0.0341012	0.0170506	+	0.999855i	$0.494572\pi$
$662$	−24.2617	−0.942959
$663$	−0.549247	−0.0213310
$664$	21.1904	0.822345
$665$	17.9568	0.696334
$666$	−1.68419	−0.0652609
$667$	2.13301	0.0825903
$668$	−21.1283	−0.817479
$669$	−1.24668	−0.0481994
$670$	−86.4885	−3.34134
$671$	−0.160834	−0.00620893
$672$	−6.47047	−0.249604
$673$	10.2083	0.393501	0.196751	−	0.980454i	$-0.436961\pi$
$673$	10.2083	0.393501	0.196751	+	0.980454i	$0.436961\pi$
$674$	11.2078	0.431710
$675$	55.8457	2.14950
$676$	2.84438	0.109399
$677$	−6.45622	−0.248133	−0.124066	−	0.992274i	$-0.539594\pi$
$677$	−6.45622	−0.248133	−0.124066	+	0.992274i	$0.539594\pi$
$678$	−2.45790	−0.0943953
$679$	4.59826	0.176465
$680$	−2.63762	−0.101148
$681$	−5.56612	−0.213294
$682$	24.1248	0.923787
$683$	50.6827	1.93932	0.969661	−	0.244455i	$-0.0786091\pi$
$683$	50.6827	1.93932	0.969661	+	0.244455i	$0.0786091\pi$
$684$	−16.9116	−0.646633
$685$	−27.8937	−1.06577
$686$	17.9636	0.685853
$687$	10.3390	0.394459
$688$	14.0617	0.536098
$689$	−2.11037	−0.0803986
$690$	−66.2840	−2.52339
$691$	−6.57611	−0.250167	−0.125083	−	0.992146i	$-0.539920\pi$
$691$	−6.57611	−0.250167	−0.125083	+	0.992146i	$0.539920\pi$
$692$	38.1618	1.45070
$693$	−2.32618	−0.0883644
$694$	43.0063	1.63250
$695$	72.2852	2.74193
$696$	1.13634	0.0430727
$697$	−1.49021	−0.0564455
$698$	−37.5652	−1.42186
$699$	−21.7256	−0.821736
$700$	−16.8835	−0.638137
$701$	−10.5075	−0.396862	−0.198431	−	0.980115i	$-0.563585\pi$
$701$	−10.5075	−0.396862	−0.198431	+	0.980115i	$0.563585\pi$
$702$	12.3887	0.467582
$703$	7.77011	0.293055
$704$	64.6707	2.43737
$705$	−35.1804	−1.32497
$706$	12.4582	0.468872
$707$	−4.75427	−0.178803
$708$	−44.3208	−1.66568
$709$	−39.2030	−1.47230	−0.736150	−	0.676818i	$-0.763358\pi$
$709$	−39.2030	−1.47230	−0.736150	+	0.676818i	$0.763358\pi$
$710$	78.3597	2.94079
$711$	6.37963	0.239255
$712$	−24.3484	−0.912494
$713$	11.2494	0.421292
$714$	0.723237	0.0270665
$715$	19.6285	0.734064
$716$	−44.7764	−1.67337
$717$	32.5266	1.21473
$718$	−77.1222	−2.87817
$719$	−18.6925	−0.697111	−0.348556	−	0.937288i	$-0.613328\pi$
$719$	−18.6925	−0.697111	−0.348556	+	0.937288i	$0.613328\pi$
$720$	−4.72419	−0.176060
$721$	5.50673	0.205081
$722$	91.0653	3.38910
$723$	9.43361	0.350840
$724$	−5.58871	−0.207703
$725$	−4.05800	−0.150710
$726$	−48.7631	−1.80977
$727$	−2.22232	−0.0824211	−0.0412106	−	0.999150i	$-0.513121\pi$
$727$	−2.22232	−0.0824211	−0.0412106	+	0.999150i	$0.513121\pi$
$728$	−1.11186	−0.0412083
$729$	29.9256	1.10835
$730$	−83.2829	−3.08244
$731$	−3.23249	−0.119558
$732$	−0.134588	−0.00497452
$733$	14.1676	0.523294	0.261647	−	0.965164i	$-0.415734\pi$
$733$	14.1676	0.523294	0.261647	+	0.965164i	$0.415734\pi$
$734$	−35.5128	−1.31080
$735$	−38.3559	−1.41478
$736$	37.7297	1.39074
$737$	−51.6905	−1.90404
$738$	6.83106	0.251455
$739$	−3.46738	−0.127550	−0.0637748	−	0.997964i	$-0.520314\pi$
$739$	−3.46738	−0.127550	−0.0637748	+	0.997964i	$0.520314\pi$
$740$	−10.9874	−0.403905
$741$	−11.6157	−0.426715
$742$	2.77889	0.102016
$743$	−7.45490	−0.273494	−0.136747	−	0.990606i	$-0.543665\pi$
$743$	−7.45490	−0.273494	−0.136747	+	0.990606i	$0.543665\pi$
$744$	5.99297	0.219713
$745$	−34.2365	−1.25433
$746$	34.1099	1.24885
$747$	−8.72474	−0.319222
$748$	−5.31025	−0.194162
$749$	1.14884	0.0419778
$750$	62.5539	2.28414
$751$	−2.81714	−0.102799	−0.0513994	−	0.998678i	$-0.516368\pi$
$751$	−2.81714	−0.102799	−0.0513994	+	0.998678i	$0.516368\pi$
$752$	9.73693	0.355069
$753$	−36.9723	−1.34734
$754$	−0.900221	−0.0327841
$755$	−18.7236	−0.681421
$756$	−9.57830	−0.348359
$757$	−3.88894	−0.141346	−0.0706729	−	0.997500i	$-0.522515\pi$
$757$	−3.88894	−0.141346	−0.0706729	+	0.997500i	$0.522515\pi$
$758$	52.4953	1.90671
$759$	−39.6151	−1.43794
$760$	−55.7817	−2.02341
$761$	−23.5586	−0.854000	−0.427000	−	0.904252i	$-0.640430\pi$
$761$	−23.5586	−0.854000	−0.427000	+	0.904252i	$0.640430\pi$
$762$	56.5154	2.04734
$763$	−9.27966	−0.335946
$764$	34.9284	1.26367
$765$	1.08599	0.0392641
$766$	7.17291	0.259168
$767$	10.4232	0.376359
$768$	6.50802	0.234838
$769$	−18.7907	−0.677612	−0.338806	−	0.940856i	$-0.610023\pi$
$769$	−18.7907	−0.677612	−0.338806	+	0.940856i	$0.610023\pi$
$770$	−25.8464	−0.931439
$771$	−24.0622	−0.866580
$772$	27.6398	0.994778
$773$	−4.07609	−0.146607	−0.0733033	−	0.997310i	$-0.523354\pi$
$773$	−4.07609	−0.146607	−0.0733033	+	0.997310i	$0.523354\pi$
$774$	14.8177	0.532610
$775$	−21.4017	−0.768771
$776$	−14.2842	−0.512773
$777$	0.894363	0.0320851
$778$	−71.7829	−2.57354
$779$	−31.5156	−1.12916
$780$	16.4254	0.588123
$781$	46.8322	1.67579
$782$	−4.21725	−0.150808
$783$	−2.30217	−0.0822728
$784$	10.6158	0.379136
$785$	82.2601	2.93599
$786$	49.3845	1.76149
$787$	13.0602	0.465547	0.232773	−	0.972531i	$-0.425220\pi$
$787$	13.0602	0.465547	0.232773	+	0.972531i	$0.425220\pi$
$788$	61.8876	2.20466
$789$	15.7082	0.559227
$790$	70.8846	2.52196
$791$	−0.446909	−0.0158903
$792$	7.22615	0.256770
$793$	0.0316518	0.00112399
$794$	55.0188	1.95255
$795$	−12.1867	−0.432218
$796$	62.8271	2.22685
$797$	41.9538	1.48608	0.743039	−	0.669248i	$-0.233384\pi$
$797$	41.9538	1.48608	0.743039	+	0.669248i	$0.233384\pi$
$798$	15.2954	0.541450
$799$	−2.23832	−0.0791859
$800$	−71.7801	−2.53781
$801$	10.0250	0.354216
$802$	−62.1201	−2.19354
$803$	−49.7747	−1.75651
$804$	−43.2553	−1.52550
$805$	−12.0521	−0.424781
$806$	−4.74772	−0.167231
$807$	2.43117	0.0855813
$808$	14.7688	0.519566
$809$	47.9051	1.68425	0.842126	−	0.539280i	$-0.181304\pi$
$809$	47.9051	1.68425	0.842126	+	0.539280i	$0.181304\pi$
$810$	52.0236	1.82792
$811$	−41.5385	−1.45861	−0.729306	−	0.684187i	$-0.760157\pi$
$811$	−41.5385	−1.45861	−0.729306	+	0.684187i	$0.760157\pi$
$812$	0.696003	0.0244249
$813$	18.7514	0.657639
$814$	−11.1840	−0.392000
$815$	82.7626	2.89905
$816$	0.877843	0.0307307
$817$	−68.3623	−2.39169
$818$	−7.84723	−0.274372
$819$	0.457788	0.0159964
$820$	44.5649	1.55628
$821$	−42.9369	−1.49851	−0.749255	−	0.662282i	$-0.769588\pi$
$821$	−42.9369	−1.49851	−0.749255	+	0.662282i	$0.769588\pi$
$822$	−23.7595	−0.828709
$823$	−43.7112	−1.52368	−0.761838	−	0.647768i	$-0.775703\pi$
$823$	−43.7112	−1.52368	−0.761838	+	0.647768i	$0.775703\pi$
$824$	−17.1063	−0.595927
$825$	75.3670	2.62394
$826$	−13.7250	−0.477554
$827$	−22.1635	−0.770701	−0.385351	−	0.922770i	$-0.625920\pi$
$827$	−22.1635	−0.770701	−0.385351	+	0.922770i	$0.625920\pi$
$828$	11.3506	0.394462
$829$	18.7838	0.652387	0.326194	−	0.945303i	$-0.394234\pi$
$829$	18.7838	0.652387	0.326194	+	0.945303i	$0.394234\pi$
$830$	−96.9412	−3.36488
$831$	34.3065	1.19008
$832$	−12.7271	−0.441231
$833$	−2.44035	−0.0845531
$834$	61.5716	2.13205
$835$	28.6936	0.992984
$836$	−112.304	−3.88410
$837$	−12.1415	−0.419672
$838$	−78.4272	−2.70922
$839$	−21.9012	−0.756114	−0.378057	−	0.925782i	$-0.623408\pi$
$839$	−21.9012	−0.756114	−0.378057	+	0.925782i	$0.623408\pi$
$840$	−6.42064	−0.221533
$841$	−28.8327	−0.994232
$842$	−38.3330	−1.32104
$843$	−21.5117	−0.740902
$844$	−1.82932	−0.0629677
$845$	−3.86285	−0.132886
$846$	10.2604	0.352759
$847$	−8.86637	−0.304652
$848$	3.37293	0.115827
$849$	−4.24286	−0.145614
$850$	8.02323	0.275195
$851$	−5.21509	−0.178771
$852$	39.1898	1.34262
$853$	−51.3609	−1.75857	−0.879283	−	0.476300i	$-0.841978\pi$
$853$	−51.3609	−1.75857	−0.879283	+	0.476300i	$0.841978\pi$
$854$	−0.0416784	−0.00142621
$855$	22.9671	0.785458
$856$	−3.56881	−0.121980
$857$	−22.3052	−0.761932	−0.380966	−	0.924589i	$-0.624408\pi$
$857$	−22.3052	−0.761932	−0.380966	+	0.924589i	$0.624408\pi$
$858$	16.7193	0.570788
$859$	−16.4330	−0.560688	−0.280344	−	0.959900i	$-0.590448\pi$
$859$	−16.4330	−0.560688	−0.280344	+	0.959900i	$0.590448\pi$
$860$	96.6685	3.29637
$861$	−3.62754	−0.123626
$862$	23.3010	0.793636
$863$	−35.1825	−1.19763	−0.598813	−	0.800889i	$-0.704361\pi$
$863$	−35.1825	−1.19763	−0.598813	+	0.800889i	$0.704361\pi$
$864$	−40.7220	−1.38539
$865$	−51.8262	−1.76214
$866$	79.1773	2.69056
$867$	25.2120	0.856243
$868$	3.67068	0.124591
$869$	42.3647	1.43712
$870$	−5.19849	−0.176245
$871$	10.1726	0.344685
$872$	28.8267	0.976196
$873$	5.88126	0.199051
$874$	−89.1883	−3.01684
$875$	11.3739	0.384507
$876$	−41.6521	−1.40729
$877$	−43.1921	−1.45849	−0.729247	−	0.684251i	$-0.760129\pi$
$877$	−43.1921	−1.45849	−0.729247	+	0.684251i	$0.760129\pi$
$878$	71.1173	2.40009
$879$	−37.2475	−1.25633
$880$	−31.3715	−1.05753
$881$	40.0846	1.35049	0.675243	−	0.737596i	$-0.264039\pi$
$881$	40.0846	1.35049	0.675243	+	0.737596i	$0.264039\pi$
$882$	11.1865	0.376669
$883$	40.5496	1.36460	0.682301	−	0.731071i	$-0.260979\pi$
$883$	40.5496	1.36460	0.682301	+	0.731071i	$0.260979\pi$
$884$	1.04505	0.0351487
$885$	60.1905	2.02328
$886$	−75.9207	−2.55060
$887$	−27.7027	−0.930166	−0.465083	−	0.885267i	$-0.653976\pi$
$887$	−27.7027	−0.930166	−0.465083	+	0.885267i	$0.653976\pi$
$888$	−2.77828	−0.0932331
$889$	10.2759	0.344644
$890$	111.389	3.73375
$891$	31.0923	1.04163
$892$	2.37204	0.0794218
$893$	−47.3370	−1.58407
$894$	−29.1622	−0.975329
$895$	60.8092	2.03263
$896$	8.10215	0.270674
$897$	7.79618	0.260307
$898$	11.4264	0.381303
$899$	0.882258	0.0294250
$900$	−21.5944	−0.719812
$901$	−0.775365	−0.0258311
$902$	45.3624	1.51040
$903$	−7.86870	−0.261854
$904$	1.38830	0.0461741
$905$	7.58982	0.252294
$906$	−15.9485	−0.529854
$907$	12.4041	0.411872	0.205936	−	0.978565i	$-0.433976\pi$
$907$	12.4041	0.411872	0.205936	+	0.978565i	$0.433976\pi$
$908$	10.5906	0.351461
$909$	−6.08080	−0.201687
$910$	5.08652	0.168616
$911$	5.63749	0.186778	0.0933892	−	0.995630i	$-0.470230\pi$
$911$	5.63749	0.186778	0.0933892	+	0.995630i	$0.470230\pi$
$912$	18.5650	0.614750
$913$	−57.9377	−1.91746
$914$	5.82438	0.192653
$915$	0.182779	0.00604249
$916$	−19.6720	−0.649981
$917$	8.97935	0.296524
$918$	4.55171	0.150229
$919$	−4.83524	−0.159500	−0.0797499	−	0.996815i	$-0.525412\pi$
$919$	−4.83524	−0.159500	−0.0797499	+	0.996815i	$0.525412\pi$
$920$	37.4392	1.23433
$921$	25.0068	0.824002
$922$	−2.57172	−0.0846950
$923$	−9.21649	−0.303365
$924$	−12.9265	−0.425250
$925$	9.92161	0.326221
$926$	−3.46718	−0.113939
$927$	7.04322	0.231330
$928$	2.95905	0.0971355
$929$	−1.88377	−0.0618045	−0.0309023	−	0.999522i	$-0.509838\pi$
$929$	−1.88377	−0.0618045	−0.0309023	+	0.999522i	$0.509838\pi$
$930$	−27.4165	−0.899024
$931$	−51.6097	−1.69144
$932$	41.3369	1.35404
$933$	−8.19228	−0.268203
$934$	−10.5372	−0.344787
$935$	7.21166	0.235846
$936$	−1.42209	−0.0464825
$937$	−31.5146	−1.02954	−0.514769	−	0.857329i	$-0.672122\pi$
$937$	−31.5146	−1.02954	−0.514769	+	0.857329i	$0.672122\pi$
$938$	−13.3950	−0.437364
$939$	−18.4134	−0.600897
$940$	66.9374	2.18326
$941$	−46.1846	−1.50557	−0.752787	−	0.658264i	$-0.771291\pi$
$941$	−46.1846	−1.50557	−0.752787	+	0.658264i	$0.771291\pi$
$942$	70.0681	2.28294
$943$	21.1524	0.688817
$944$	−16.6590	−0.542204
$945$	13.0079	0.423148
$946$	98.3984	3.19921
$947$	−6.68459	−0.217220	−0.108610	−	0.994084i	$-0.534640\pi$
$947$	−6.68459	−0.217220	−0.108610	+	0.994084i	$0.534640\pi$
$948$	35.4513	1.15141
$949$	9.79556	0.317977
$950$	169.679	5.50512
$951$	−7.92401	−0.256954
$952$	−0.408506	−0.0132397
$953$	4.62634	0.149862	0.0749309	−	0.997189i	$-0.476126\pi$
$953$	4.62634	0.149862	0.0749309	+	0.997189i	$0.476126\pi$
$954$	3.55425	0.115073
$955$	−47.4350	−1.53496
$956$	−61.8880	−2.00160
$957$	−3.10691	−0.100432
$958$	−37.5984	−1.21475
$959$	−4.32009	−0.139503
$960$	−73.4947	−2.37203
$961$	−26.3470	−0.849904
$962$	2.20100	0.0709629
$963$	1.46939	0.0473506
$964$	−17.9492	−0.578105
$965$	−37.5366	−1.20835
$966$	−10.2658	−0.330298
$967$	19.1026	0.614299	0.307149	−	0.951661i	$-0.400625\pi$
$967$	19.1026	0.614299	0.307149	+	0.951661i	$0.400625\pi$
$968$	27.5429	0.885261
$969$	−4.26771	−0.137099
$970$	65.3471	2.09817
$971$	−35.8510	−1.15051	−0.575256	−	0.817973i	$-0.695098\pi$
$971$	−35.8510	−1.15051	−0.575256	+	0.817973i	$0.695098\pi$
$972$	−22.0120	−0.706034
$973$	11.1953	0.358904
$974$	54.3810	1.74248
$975$	−14.8321	−0.475007
$976$	−0.0505880	−0.00161928
$977$	−31.7092	−1.01447	−0.507233	−	0.861809i	$-0.669332\pi$
$977$	−31.7092	−1.01447	−0.507233	+	0.861809i	$0.669332\pi$
$978$	70.4962	2.25422
$979$	66.5722	2.12766
$980$	72.9793	2.33124
$981$	−11.8689	−0.378944
$982$	−57.0004	−1.81896
$983$	9.27191	0.295728	0.147864	−	0.989008i	$-0.452760\pi$
$983$	9.27191	0.295728	0.147864	+	0.989008i	$0.452760\pi$
$984$	11.2687	0.359234
$985$	−84.0474	−2.67797
$986$	−0.330748	−0.0105332
$987$	−5.44862	−0.173432
$988$	22.1011	0.703131
$989$	45.8830	1.45899
$990$	−33.0580	−1.05065
$991$	−18.3895	−0.584161	−0.292081	−	0.956394i	$-0.594348\pi$
$991$	−18.3895	−0.584161	−0.292081	+	0.956394i	$0.594348\pi$
$992$	15.6059	0.495486
$993$	16.4787	0.522936
$994$	12.1361	0.384933
$995$	−85.3233	−2.70493
$996$	−48.4830	−1.53624
$997$	−27.1288	−0.859177	−0.429589	−	0.903025i	$-0.641341\pi$
$997$	−27.1288	−0.859177	−0.429589	+	0.903025i	$0.641341\pi$
$998$	13.1020	0.414738
$999$	5.62869	0.178084

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.20100 q^{2} -1.49493 q^{3} +2.84438 q^{4} -3.86285 q^{5} -3.29033 q^{6} -0.598265 q^{7} +1.85847 q^{8} -0.765193 q^{9} +O(q^{10})\)	\(q+2.20100 q^{2} -1.49493 q^{3} +2.84438 q^{4} -3.86285 q^{5} -3.29033 q^{6} -0.598265 q^{7} +1.85847 q^{8} -0.765193 q^{9} -8.50211 q^{10} -5.08135 q^{11} -4.25214 q^{12} +1.00000 q^{13} -1.31678 q^{14} +5.77468 q^{15} -1.59826 q^{16} +0.367408 q^{17} -1.68419 q^{18} +7.77011 q^{19} -10.9874 q^{20} +0.894363 q^{21} -11.1840 q^{22} -5.21509 q^{23} -2.77828 q^{24} +9.92161 q^{25} +2.20100 q^{26} +5.62869 q^{27} -1.70169 q^{28} -0.409006 q^{29} +12.7100 q^{30} -2.15708 q^{31} -7.23472 q^{32} +7.59625 q^{33} +0.808662 q^{34} +2.31101 q^{35} -2.17650 q^{36} +1.00000 q^{37} +17.1020 q^{38} -1.49493 q^{39} -7.17901 q^{40} -4.05600 q^{41} +1.96849 q^{42} -8.79811 q^{43} -14.4533 q^{44} +2.95583 q^{45} -11.4784 q^{46} -6.09219 q^{47} +2.38929 q^{48} -6.64208 q^{49} +21.8374 q^{50} -0.549247 q^{51} +2.84438 q^{52} -2.11037 q^{53} +12.3887 q^{54} +19.6285 q^{55} -1.11186 q^{56} -11.6157 q^{57} -0.900221 q^{58} +10.4232 q^{59} +16.4254 q^{60} +0.0316518 q^{61} -4.74772 q^{62} +0.457788 q^{63} -12.7271 q^{64} -3.86285 q^{65} +16.7193 q^{66} +10.1726 q^{67} +1.04505 q^{68} +7.79618 q^{69} +5.08652 q^{70} -9.21649 q^{71} -1.42209 q^{72} +9.79556 q^{73} +2.20100 q^{74} -14.8321 q^{75} +22.1011 q^{76} +3.03999 q^{77} -3.29033 q^{78} -8.33729 q^{79} +6.17386 q^{80} -6.11890 q^{81} -8.92724 q^{82} +11.4020 q^{83} +2.54391 q^{84} -1.41924 q^{85} -19.3646 q^{86} +0.611435 q^{87} -9.44356 q^{88} -13.1013 q^{89} +6.50576 q^{90} -0.598265 q^{91} -14.8337 q^{92} +3.22467 q^{93} -13.4089 q^{94} -30.0148 q^{95} +10.8154 q^{96} -7.68599 q^{97} -14.6192 q^{98} +3.88821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 7 q^{3} + 3 q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 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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