LMFDB - Embedded newform 4003.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} +O(q^{10})$	\(q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} -4.60888 q^{10} -4.43026 q^{11} -11.6727 q^{12} +3.63606 q^{13} +3.89470 q^{14} -4.24040 q^{15} +9.80823 q^{16} -3.52069 q^{17} -7.31915 q^{18} -7.25290 q^{19} +8.53856 q^{20} +3.58331 q^{21} +11.5935 q^{22} -0.195235 q^{23} +17.9451 q^{24} -1.89817 q^{25} -9.51518 q^{26} +0.489037 q^{27} -7.21545 q^{28} -5.52454 q^{29} +11.0967 q^{30} -10.6216 q^{31} -10.7605 q^{32} +10.6666 q^{33} +9.21329 q^{34} -2.62118 q^{35} +13.5597 q^{36} -10.2608 q^{37} +18.9801 q^{38} -8.75443 q^{39} -13.1268 q^{40} +3.71977 q^{41} -9.37716 q^{42} -10.5086 q^{43} -21.4786 q^{44} +4.92588 q^{45} +0.510910 q^{46} -0.699387 q^{47} -23.6150 q^{48} -4.78499 q^{49} +4.96731 q^{50} +8.47667 q^{51} +17.6281 q^{52} +10.9746 q^{53} -1.27976 q^{54} -7.80259 q^{55} +11.0927 q^{56} +17.4626 q^{57} +14.4572 q^{58} -0.122480 q^{59} -20.5581 q^{60} +6.99841 q^{61} +27.7956 q^{62} -4.16258 q^{63} +8.54267 q^{64} +6.40383 q^{65} -27.9134 q^{66} -3.16616 q^{67} -17.0688 q^{68} +0.470062 q^{69} +6.85935 q^{70} -6.44739 q^{71} -20.8460 q^{72} +6.88859 q^{73} +26.8515 q^{74} +4.57017 q^{75} -35.1631 q^{76} +6.59352 q^{77} +22.9094 q^{78} -1.12889 q^{79} +17.2743 q^{80} -9.56809 q^{81} -9.73425 q^{82} +11.3563 q^{83} +17.3724 q^{84} -6.20065 q^{85} +27.5000 q^{86} +13.3013 q^{87} +33.0201 q^{88} +14.1517 q^{89} -12.8905 q^{90} -5.41151 q^{91} -0.946529 q^{92} +25.5733 q^{93} +1.83022 q^{94} -12.7738 q^{95} +25.9078 q^{96} -9.84146 q^{97} +12.5218 q^{98} -12.3909 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.61690	−1.85043	−0.925213	−	0.379449i	$-0.876113\pi$
$2$	−2.61690	−1.85043	−0.925213	+	0.379449i	$0.876113\pi$
$3$	−2.40767	−1.39007	−0.695035	−	0.718976i	$-0.744611\pi$
$3$	−2.40767	−1.39007	−0.695035	+	0.718976i	$0.744611\pi$
$4$	4.84815	2.42407
$5$	1.76120	0.787633	0.393817	−	0.919189i	$-0.371154\pi$
$5$	1.76120	0.787633	0.393817	+	0.919189i	$0.371154\pi$
$6$	6.30063	2.57222
$7$	−1.48829	−0.562521	−0.281260	−	0.959631i	$-0.590752\pi$
$7$	−1.48829	−0.562521	−0.281260	+	0.959631i	$0.590752\pi$
$8$	−7.45330	−2.63514
$9$	2.79688	0.932295
$10$	−4.60888	−1.45746
$11$	−4.43026	−1.33577	−0.667887	−	0.744263i	$-0.732801\pi$
$11$	−4.43026	−1.33577	−0.667887	+	0.744263i	$0.732801\pi$
$12$	−11.6727	−3.36963
$13$	3.63606	1.00846	0.504230	−	0.863569i	$-0.331776\pi$
$13$	3.63606	1.00846	0.504230	+	0.863569i	$0.331776\pi$
$14$	3.89470	1.04090
$15$	−4.24040	−1.09487
$16$	9.80823	2.45206
$17$	−3.52069	−0.853894	−0.426947	−	0.904277i	$-0.640411\pi$
$17$	−3.52069	−0.853894	−0.426947	+	0.904277i	$0.640411\pi$
$18$	−7.31915	−1.72514
$19$	−7.25290	−1.66393	−0.831965	−	0.554829i	$-0.812784\pi$
$19$	−7.25290	−1.66393	−0.831965	+	0.554829i	$0.812784\pi$
$20$	8.53856	1.90928
$21$	3.58331	0.781943
$22$	11.5935	2.47175
$23$	−0.195235	−0.0407093	−0.0203547	−	0.999793i	$-0.506480\pi$
$23$	−0.195235	−0.0407093	−0.0203547	+	0.999793i	$0.506480\pi$
$24$	17.9451	3.66303
$25$	−1.89817	−0.379634
$26$	−9.51518	−1.86608
$27$	0.489037	0.0941152
$28$	−7.21545	−1.36359
$29$	−5.52454	−1.02588	−0.512941	−	0.858424i	$-0.671444\pi$
$29$	−5.52454	−1.02588	−0.512941	+	0.858424i	$0.671444\pi$
$30$	11.0967	2.02597
$31$	−10.6216	−1.90769	−0.953847	−	0.300293i	$-0.902916\pi$
$31$	−10.6216	−1.90769	−0.953847	+	0.300293i	$0.902916\pi$
$32$	−10.7605	−1.90221
$33$	10.6666	1.85682
$34$	9.21329	1.58007
$35$	−2.62118	−0.443060
$36$	13.5597	2.25995
$37$	−10.2608	−1.68687	−0.843434	−	0.537232i	$-0.819470\pi$
$37$	−10.2608	−1.68687	−0.843434	+	0.537232i	$0.819470\pi$
$38$	18.9801	3.07898
$39$	−8.75443	−1.40183
$40$	−13.1268	−2.07552
$41$	3.71977	0.580930	0.290465	−	0.956886i	$-0.406190\pi$
$41$	3.71977	0.580930	0.290465	+	0.956886i	$0.406190\pi$
$42$	−9.37716	−1.44693
$43$	−10.5086	−1.60255	−0.801275	−	0.598296i	$-0.795845\pi$
$43$	−10.5086	−1.60255	−0.801275	+	0.598296i	$0.795845\pi$
$44$	−21.4786	−3.23801
$45$	4.92588	0.734306
$46$	0.510910	0.0753296
$47$	−0.699387	−0.102016	−0.0510080	−	0.998698i	$-0.516243\pi$
$47$	−0.699387	−0.102016	−0.0510080	+	0.998698i	$0.516243\pi$
$48$	−23.6150	−3.40853
$49$	−4.78499	−0.683570
$50$	4.96731	0.702484
$51$	8.47667	1.18697
$52$	17.6281	2.44458
$53$	10.9746	1.50748	0.753739	−	0.657174i	$-0.228248\pi$
$53$	10.9746	1.50748	0.753739	+	0.657174i	$0.228248\pi$
$54$	−1.27976	−0.174153
$55$	−7.80259	−1.05210
$56$	11.0927	1.48232
$57$	17.4626	2.31298
$58$	14.4572	1.89832
$59$	−0.122480	−0.0159455	−0.00797275	−	0.999968i	$-0.502538\pi$
$59$	−0.122480	−0.0159455	−0.00797275	+	0.999968i	$0.502538\pi$
$60$	−20.5581	−2.65403
$61$	6.99841	0.896055	0.448028	−	0.894020i	$-0.352127\pi$
$61$	6.99841	0.896055	0.448028	+	0.894020i	$0.352127\pi$
$62$	27.7956	3.53005
$63$	−4.16258	−0.524435
$64$	8.54267	1.06783
$65$	6.40383	0.794297
$66$	−27.9134	−3.43591
$67$	−3.16616	−0.386808	−0.193404	−	0.981119i	$-0.561953\pi$
$67$	−3.16616	−0.386808	−0.193404	+	0.981119i	$0.561953\pi$
$68$	−17.0688	−2.06990
$69$	0.470062	0.0565888
$70$	6.85935	0.819850
$71$	−6.44739	−0.765164	−0.382582	−	0.923922i	$-0.624965\pi$
$71$	−6.44739	−0.765164	−0.382582	+	0.923922i	$0.624965\pi$
$72$	−20.8460	−2.45673
$73$	6.88859	0.806249	0.403124	−	0.915145i	$-0.367924\pi$
$73$	6.88859	0.806249	0.403124	+	0.915145i	$0.367924\pi$
$74$	26.8515	3.12142
$75$	4.57017	0.527718
$76$	−35.1631	−4.03349
$77$	6.59352	0.751401
$78$	22.9094	2.59398
$79$	−1.12889	−0.127011	−0.0635053	−	0.997982i	$-0.520228\pi$
$79$	−1.12889	−0.127011	−0.0635053	+	0.997982i	$0.520228\pi$
$80$	17.2743	1.93132
$81$	−9.56809	−1.06312
$82$	−9.73425	−1.07497
$83$	11.3563	1.24651	0.623256	−	0.782018i	$-0.285809\pi$
$83$	11.3563	1.24651	0.623256	+	0.782018i	$0.285809\pi$
$84$	17.3724	1.89549
$85$	−6.20065	−0.672555
$86$	27.5000	2.96540
$87$	13.3013	1.42605
$88$	33.0201	3.51995
$89$	14.1517	1.50007	0.750037	−	0.661396i	$-0.230036\pi$
$89$	14.1517	1.50007	0.750037	+	0.661396i	$0.230036\pi$
$90$	−12.8905	−1.35878
$91$	−5.41151	−0.567280
$92$	−0.946529	−0.0986824
$93$	25.5733	2.65183
$94$	1.83022	0.188773
$95$	−12.7738	−1.31057
$96$	25.9078	2.64420
$97$	−9.84146	−0.999249	−0.499624	−	0.866242i	$-0.666529\pi$
$97$	−9.84146	−0.999249	−0.499624	+	0.866242i	$0.666529\pi$
$98$	12.5218	1.26490
$99$	−12.3909	−1.24534
$100$	−9.20260	−0.920260
$101$	6.07715	0.604699	0.302349	−	0.953197i	$-0.402229\pi$
$101$	6.07715	0.604699	0.302349	+	0.953197i	$0.402229\pi$
$102$	−22.1826	−2.19640
$103$	9.32815	0.919130	0.459565	−	0.888144i	$-0.348005\pi$
$103$	9.32815	0.919130	0.459565	+	0.888144i	$0.348005\pi$
$104$	−27.1006	−2.65744
$105$	6.31094	0.615885
$106$	−28.7194	−2.78947
$107$	3.10481	0.300154	0.150077	−	0.988674i	$-0.452048\pi$
$107$	3.10481	0.300154	0.150077	+	0.988674i	$0.452048\pi$
$108$	2.37092	0.228142
$109$	−15.8448	−1.51766	−0.758830	−	0.651289i	$-0.774229\pi$
$109$	−15.8448	−1.51766	−0.758830	+	0.651289i	$0.774229\pi$
$110$	20.4186	1.94683
$111$	24.7047	2.34487
$112$	−14.5975	−1.37933
$113$	−4.31065	−0.405512	−0.202756	−	0.979229i	$-0.564990\pi$
$113$	−4.31065	−0.405512	−0.202756	+	0.979229i	$0.564990\pi$
$114$	−45.6978	−4.27999
$115$	−0.343848	−0.0320640
$116$	−26.7838	−2.48681
$117$	10.1696	0.940182
$118$	0.320517	0.0295060
$119$	5.23981	0.480333
$120$	31.6049	2.88512
$121$	8.62723	0.784293
$122$	−18.3141	−1.65808
$123$	−8.95598	−0.807534
$124$	−51.4950	−4.62439
$125$	−12.1491	−1.08665
$126$	10.8930	0.970428
$127$	8.51277	0.755387	0.377693	−	0.925931i	$-0.376717\pi$
$127$	8.51277	0.755387	0.377693	+	0.925931i	$0.376717\pi$
$128$	−0.834281	−0.0737407
$129$	25.3013	2.22766
$130$	−16.7582	−1.46979
$131$	−7.91504	−0.691540	−0.345770	−	0.938319i	$-0.612382\pi$
$131$	−7.91504	−0.691540	−0.345770	+	0.938319i	$0.612382\pi$
$132$	51.7133	4.50107
$133$	10.7944	0.935995
$134$	8.28551	0.715759
$135$	0.861293	0.0741283
$136$	26.2408	2.25013
$137$	−20.2312	−1.72847	−0.864236	−	0.503087i	$-0.832198\pi$
$137$	−20.2312	−1.72847	−0.864236	+	0.503087i	$0.832198\pi$
$138$	−1.23010	−0.104713
$139$	1.94813	0.165238	0.0826191	−	0.996581i	$-0.473672\pi$
$139$	1.94813	0.165238	0.0826191	+	0.996581i	$0.473672\pi$
$140$	−12.7079	−1.07401
$141$	1.68389	0.141809
$142$	16.8721	1.41588
$143$	−16.1087	−1.34708
$144$	27.4325	2.28604
$145$	−9.72984	−0.808019
$146$	−18.0267	−1.49190
$147$	11.5207	0.950211
$148$	−49.7460	−4.08909
$149$	−13.0589	−1.06983	−0.534913	−	0.844907i	$-0.679656\pi$
$149$	−13.0589	−1.06983	−0.534913	+	0.844907i	$0.679656\pi$
$150$	−11.9597	−0.976502
$151$	−14.8544	−1.20883	−0.604417	−	0.796668i	$-0.706594\pi$
$151$	−14.8544	−1.20883	−0.604417	+	0.796668i	$0.706594\pi$
$152$	54.0580	4.38469
$153$	−9.84697	−0.796080
$154$	−17.2545	−1.39041
$155$	−18.7068	−1.50256
$156$	−42.4428	−3.39814
$157$	22.9854	1.83443	0.917216	−	0.398390i	$-0.130431\pi$
$157$	22.9854	1.83443	0.917216	+	0.398390i	$0.130431\pi$
$158$	2.95420	0.235023
$159$	−26.4232	−2.09550
$160$	−18.9514	−1.49824
$161$	0.290567	0.0228999
$162$	25.0387	1.96723
$163$	−15.1865	−1.18950	−0.594750	−	0.803911i	$-0.702749\pi$
$163$	−15.1865	−1.18950	−0.594750	+	0.803911i	$0.702749\pi$
$164$	18.0340	1.40822
$165$	18.7861	1.46249
$166$	−29.7182	−2.30658
$167$	−13.4947	−1.04425	−0.522126	−	0.852868i	$-0.674861\pi$
$167$	−13.4947	−1.04425	−0.522126	+	0.852868i	$0.674861\pi$
$168$	−26.7075	−2.06053
$169$	0.220908	0.0169929
$170$	16.2265	1.24451
$171$	−20.2855	−1.55127
$172$	−50.9473	−3.88470
$173$	14.5178	1.10377	0.551886	−	0.833920i	$-0.313908\pi$
$173$	14.5178	1.10377	0.551886	+	0.833920i	$0.313908\pi$
$174$	−34.8081	−2.63879
$175$	2.82503	0.213552
$176$	−43.4530	−3.27539
$177$	0.294891	0.0221654
$178$	−37.0334	−2.77577
$179$	−7.92449	−0.592304	−0.296152	−	0.955141i	$-0.595704\pi$
$179$	−7.92449	−0.592304	−0.296152	+	0.955141i	$0.595704\pi$
$180$	23.8814	1.78001
$181$	4.17278	0.310160	0.155080	−	0.987902i	$-0.450436\pi$
$181$	4.17278	0.310160	0.155080	+	0.987902i	$0.450436\pi$
$182$	14.1614	1.04971
$183$	−16.8499	−1.24558
$184$	1.45515	0.107275
$185$	−18.0714	−1.32863
$186$	−66.9227	−4.90701
$187$	15.5976	1.14061
$188$	−3.39073	−0.247294
$189$	−0.727829	−0.0529418
$190$	33.4278	2.42510
$191$	23.1021	1.67161	0.835806	−	0.549025i	$-0.185001\pi$
$191$	23.1021	1.67161	0.835806	+	0.549025i	$0.185001\pi$
$192$	−20.5680	−1.48436
$193$	4.70682	0.338805	0.169402	−	0.985547i	$-0.445816\pi$
$193$	4.70682	0.338805	0.169402	+	0.985547i	$0.445816\pi$
$194$	25.7541	1.84903
$195$	−15.4183	−1.10413
$196$	−23.1983	−1.65702
$197$	2.45191	0.174691	0.0873455	−	0.996178i	$-0.472162\pi$
$197$	2.45191	0.174691	0.0873455	+	0.996178i	$0.472162\pi$
$198$	32.4258	2.30440
$199$	−0.434301	−0.0307868	−0.0153934	−	0.999882i	$-0.504900\pi$
$199$	−0.434301	−0.0307868	−0.0153934	+	0.999882i	$0.504900\pi$
$200$	14.1476	1.00039
$201$	7.62308	0.537690
$202$	−15.9033	−1.11895
$203$	8.22213	0.577080
$204$	41.0962	2.87731
$205$	6.55126	0.457560
$206$	−24.4108	−1.70078
$207$	−0.546050	−0.0379531
$208$	35.6633	2.47280
$209$	32.1322	2.22263
$210$	−16.5151	−1.13965
$211$	−23.1304	−1.59236	−0.796180	−	0.605060i	$-0.793149\pi$
$211$	−23.1304	−1.59236	−0.796180	+	0.605060i	$0.793149\pi$
$212$	53.2065	3.65424
$213$	15.5232	1.06363
$214$	−8.12497	−0.555412
$215$	−18.5078	−1.26222
$216$	−3.64494	−0.248007
$217$	15.8080	1.07312
$218$	41.4643	2.80831
$219$	−16.5855	−1.12074
$220$	−37.8281	−2.55037
$221$	−12.8014	−0.861118
$222$	−64.6496	−4.33900
$223$	28.6313	1.91730	0.958648	−	0.284595i	$-0.0918590\pi$
$223$	28.6313	1.91730	0.958648	+	0.284595i	$0.0918590\pi$
$224$	16.0148	1.07003
$225$	−5.30896	−0.353931
$226$	11.2805	0.750369
$227$	11.3003	0.750030	0.375015	−	0.927019i	$-0.377638\pi$
$227$	11.3003	0.750030	0.375015	+	0.927019i	$0.377638\pi$
$228$	84.6612	5.60683
$229$	−24.1168	−1.59368	−0.796840	−	0.604190i	$-0.793497\pi$
$229$	−24.1168	−1.59368	−0.796840	+	0.604190i	$0.793497\pi$
$230$	0.899816	0.0593321
$231$	−15.8750	−1.04450
$232$	41.1761	2.70334
$233$	22.9575	1.50400	0.751999	−	0.659165i	$-0.229090\pi$
$233$	22.9575	1.50400	0.751999	+	0.659165i	$0.229090\pi$
$234$	−26.6129	−1.73974
$235$	−1.23176	−0.0803513
$236$	−0.593799	−0.0386531
$237$	2.71801	0.176554
$238$	−13.7120	−0.888820
$239$	−5.38387	−0.348254	−0.174127	−	0.984723i	$-0.555710\pi$
$239$	−5.38387	−0.348254	−0.174127	+	0.984723i	$0.555710\pi$
$240$	−41.5908	−2.68467
$241$	11.0695	0.713051	0.356525	−	0.934286i	$-0.383961\pi$
$241$	11.0695	0.713051	0.356525	+	0.934286i	$0.383961\pi$
$242$	−22.5766	−1.45128
$243$	21.5697	1.38370
$244$	33.9293	2.17210
$245$	−8.42734	−0.538403
$246$	23.4369	1.49428
$247$	−26.3720	−1.67801
$248$	79.1659	5.02704
$249$	−27.3422	−1.73274
$250$	31.7928	2.01076
$251$	−3.36425	−0.212350	−0.106175	−	0.994347i	$-0.533860\pi$
$251$	−3.36425	−0.212350	−0.106175	+	0.994347i	$0.533860\pi$
$252$	−20.1808	−1.27127
$253$	0.864943	0.0543785
$254$	−22.2770	−1.39779
$255$	14.9291	0.934899
$256$	−14.9021	−0.931383
$257$	−10.8281	−0.675440	−0.337720	−	0.941247i	$-0.609656\pi$
$257$	−10.8281	−0.675440	−0.337720	+	0.941247i	$0.609656\pi$
$258$	−66.2109	−4.12211
$259$	15.2711	0.948899
$260$	31.0467	1.92543
$261$	−15.4515	−0.956424
$262$	20.7128	1.27964
$263$	−20.8743	−1.28717	−0.643584	−	0.765376i	$-0.722553\pi$
$263$	−20.8743	−1.28717	−0.643584	+	0.765376i	$0.722553\pi$
$264$	−79.5015	−4.89298
$265$	19.3285	1.18734
$266$	−28.2479	−1.73199
$267$	−34.0726	−2.08521
$268$	−15.3500	−0.937651
$269$	−24.4283	−1.48942	−0.744710	−	0.667389i	$-0.767412\pi$
$269$	−24.4283	−1.48942	−0.744710	+	0.667389i	$0.767412\pi$
$270$	−2.25391	−0.137169
$271$	25.2413	1.53330	0.766651	−	0.642064i	$-0.221922\pi$
$271$	25.2413	1.53330	0.766651	+	0.642064i	$0.221922\pi$
$272$	−34.5318	−2.09380
$273$	13.0291	0.788559
$274$	52.9431	3.19841
$275$	8.40939	0.507105
$276$	2.27893	0.137175
$277$	−21.1908	−1.27323	−0.636617	−	0.771180i	$-0.719667\pi$
$277$	−21.1908	−1.27323	−0.636617	+	0.771180i	$0.719667\pi$
$278$	−5.09805	−0.305761
$279$	−29.7074	−1.77853
$280$	19.5364	1.16753
$281$	−24.5594	−1.46509	−0.732546	−	0.680717i	$-0.761668\pi$
$281$	−24.5594	−1.46509	−0.732546	+	0.680717i	$0.761668\pi$
$282$	−4.40658	−0.262408
$283$	−3.27857	−0.194891	−0.0974454	−	0.995241i	$-0.531067\pi$
$283$	−3.27857	−0.194891	−0.0974454	+	0.995241i	$0.531067\pi$
$284$	−31.2579	−1.85481
$285$	30.7552	1.82178
$286$	42.1548	2.49266
$287$	−5.53610	−0.326785
$288$	−30.0959	−1.77342
$289$	−4.60472	−0.270866
$290$	25.4620	1.49518
$291$	23.6950	1.38903
$292$	33.3969	1.95441
$293$	−25.3559	−1.48131	−0.740653	−	0.671888i	$-0.765484\pi$
$293$	−25.3559	−1.48131	−0.740653	+	0.671888i	$0.765484\pi$
$294$	−30.1485	−1.75829
$295$	−0.215711	−0.0125592
$296$	76.4770	4.44514
$297$	−2.16656	−0.125717
$298$	34.1737	1.97963
$299$	−0.709886	−0.0410538
$300$	22.1568	1.27923
$301$	15.6399	0.901468
$302$	38.8724	2.23686
$303$	−14.6318	−0.840574
$304$	−71.1381	−4.08005
$305$	12.3256	0.705763
$306$	25.7685	1.47309
$307$	−12.5025	−0.713557	−0.356779	−	0.934189i	$-0.616125\pi$
$307$	−12.5025	−0.713557	−0.356779	+	0.934189i	$0.616125\pi$
$308$	31.9663	1.82145
$309$	−22.4591	−1.27765
$310$	48.9537	2.78038
$311$	21.0691	1.19472	0.597359	−	0.801974i	$-0.296217\pi$
$311$	21.0691	1.19472	0.597359	+	0.801974i	$0.296217\pi$
$312$	65.2494	3.69402
$313$	−18.4189	−1.04110	−0.520550	−	0.853831i	$-0.674273\pi$
$313$	−18.4189	−1.04110	−0.520550	+	0.853831i	$0.674273\pi$
$314$	−60.1503	−3.39448
$315$	−7.33113	−0.413063
$316$	−5.47304	−0.307883
$317$	28.9100	1.62375	0.811874	−	0.583833i	$-0.198448\pi$
$317$	28.9100	1.62375	0.811874	+	0.583833i	$0.198448\pi$
$318$	69.1469	3.87756
$319$	24.4752	1.37035
$320$	15.0454	0.841062
$321$	−7.47537	−0.417235
$322$	−0.760383	−0.0423745
$323$	25.5352	1.42082
$324$	−46.3875	−2.57708
$325$	−6.90185	−0.382846
$326$	39.7415	2.20108
$327$	38.1491	2.10965
$328$	−27.7246	−1.53083
$329$	1.04089	0.0573862
$330$	−49.1612	−2.70623
$331$	16.5980	0.912311	0.456156	−	0.889900i	$-0.349226\pi$
$331$	16.5980	0.912311	0.456156	+	0.889900i	$0.349226\pi$
$332$	55.0568	3.02164
$333$	−28.6983	−1.57266
$334$	35.3143	1.93231
$335$	−5.57625	−0.304663
$336$	35.1460	1.91737
$337$	−18.4316	−1.00403	−0.502015	−	0.864859i	$-0.667408\pi$
$337$	−18.4316	−1.00403	−0.502015	+	0.864859i	$0.667408\pi$
$338$	−0.578092	−0.0314441
$339$	10.3786	0.563689
$340$	−30.0617	−1.63032
$341$	47.0564	2.54825
$342$	53.0851	2.87051
$343$	17.5395	0.947043
$344$	78.3239	4.22294
$345$	0.827874	0.0445713
$346$	−37.9917	−2.04245
$347$	0.788247	0.0423153	0.0211577	−	0.999776i	$-0.493265\pi$
$347$	0.788247	0.0423153	0.0211577	+	0.999776i	$0.493265\pi$
$348$	64.4866	3.45684
$349$	19.5283	1.04532	0.522662	−	0.852540i	$-0.324939\pi$
$349$	19.5283	1.04532	0.522662	+	0.852540i	$0.324939\pi$
$350$	−7.39280	−0.395162
$351$	1.77817	0.0949115
$352$	47.6719	2.54092
$353$	−3.56229	−0.189602	−0.0948008	−	0.995496i	$-0.530221\pi$
$353$	−3.56229	−0.189602	−0.0948008	+	0.995496i	$0.530221\pi$
$354$	−0.771699	−0.0410153
$355$	−11.3551	−0.602669
$356$	68.6093	3.63629
$357$	−12.6158	−0.667696
$358$	20.7376	1.09602
$359$	13.6592	0.720904	0.360452	−	0.932778i	$-0.382623\pi$
$359$	13.6592	0.720904	0.360452	+	0.932778i	$0.382623\pi$
$360$	−36.7140	−1.93500
$361$	33.6045	1.76866
$362$	−10.9197	−0.573928
$363$	−20.7715	−1.09022
$364$	−26.2358	−1.37513
$365$	12.1322	0.635028
$366$	44.0944	2.30485
$367$	−1.58747	−0.0828653	−0.0414326	−	0.999141i	$-0.513192\pi$
$367$	−1.58747	−0.0828653	−0.0414326	+	0.999141i	$0.513192\pi$
$368$	−1.91491	−0.0998216
$369$	10.4038	0.541598
$370$	47.2909	2.45854
$371$	−16.3334	−0.847987
$372$	123.983	6.42823
$373$	22.6914	1.17491	0.587457	−	0.809255i	$-0.300129\pi$
$373$	22.6914	1.17491	0.587457	+	0.809255i	$0.300129\pi$
$374$	−40.8173	−2.11061
$375$	29.2510	1.51051
$376$	5.21274	0.268827
$377$	−20.0876	−1.03456
$378$	1.90465	0.0979648
$379$	18.2407	0.936963	0.468481	−	0.883473i	$-0.344801\pi$
$379$	18.2407	0.936963	0.468481	+	0.883473i	$0.344801\pi$
$380$	−61.9293	−3.17691
$381$	−20.4960	−1.05004
$382$	−60.4559	−3.09319
$383$	2.45006	0.125192	0.0625961	−	0.998039i	$-0.480062\pi$
$383$	2.45006	0.125192	0.0625961	+	0.998039i	$0.480062\pi$
$384$	2.00867	0.102505
$385$	11.6125	0.591828
$386$	−12.3173	−0.626933
$387$	−29.3914	−1.49405
$388$	−47.7128	−2.42225
$389$	34.3681	1.74253	0.871265	−	0.490813i	$-0.163300\pi$
$389$	34.3681	1.74253	0.871265	+	0.490813i	$0.163300\pi$
$390$	40.3481	2.04311
$391$	0.687363	0.0347614
$392$	35.6640	1.80130
$393$	19.0568	0.961289
$394$	−6.41638	−0.323253
$395$	−1.98821	−0.100038
$396$	−60.0730	−3.01878
$397$	30.2228	1.51684	0.758421	−	0.651765i	$-0.225971\pi$
$397$	30.2228	1.51684	0.758421	+	0.651765i	$0.225971\pi$
$398$	1.13652	0.0569687
$399$	−25.9894	−1.30110
$400$	−18.6177	−0.930883
$401$	17.5844	0.878124	0.439062	−	0.898457i	$-0.355311\pi$
$401$	17.5844	0.878124	0.439062	+	0.898457i	$0.355311\pi$
$402$	−19.9488	−0.994956
$403$	−38.6207	−1.92383
$404$	29.4629	1.46583
$405$	−16.8513	−0.837350
$406$	−21.5164	−1.06784
$407$	45.4581	2.25328
$408$	−63.1792	−3.12784
$409$	−38.3349	−1.89554	−0.947770	−	0.318954i	$-0.896668\pi$
$409$	−38.3349	−1.89554	−0.947770	+	0.318954i	$0.896668\pi$
$410$	−17.1440	−0.846681
$411$	48.7102	2.40270
$412$	45.2242	2.22804
$413$	0.182285	0.00896968
$414$	1.42896	0.0702294
$415$	20.0007	0.981795
$416$	−39.1258	−1.91830
$417$	−4.69046	−0.229693
$418$	−84.0868	−4.11282
$419$	−24.3393	−1.18905	−0.594527	−	0.804076i	$-0.702661\pi$
$419$	−24.3393	−1.18905	−0.594527	+	0.804076i	$0.702661\pi$
$420$	30.5964	1.49295
$421$	6.91001	0.336773	0.168387	−	0.985721i	$-0.446144\pi$
$421$	6.91001	0.336773	0.168387	+	0.985721i	$0.446144\pi$
$422$	60.5298	2.94654
$423$	−1.95610	−0.0951090
$424$	−81.7970	−3.97241
$425$	6.68287	0.324167
$426$	−40.6226	−1.96817
$427$	−10.4157	−0.504050
$428$	15.0526	0.727594
$429$	38.7844	1.87253
$430$	48.4330	2.33565
$431$	−36.3378	−1.75033	−0.875166	−	0.483823i	$-0.839248\pi$
$431$	−36.3378	−1.75033	−0.875166	+	0.483823i	$0.839248\pi$
$432$	4.79659	0.230776
$433$	10.2929	0.494646	0.247323	−	0.968933i	$-0.420449\pi$
$433$	10.2929	0.494646	0.247323	+	0.968933i	$0.420449\pi$
$434$	−41.3679	−1.98572
$435$	23.4263	1.12320
$436$	−76.8180	−3.67892
$437$	1.41602	0.0677375
$438$	43.4024	2.07385
$439$	−11.1746	−0.533335	−0.266668	−	0.963789i	$-0.585923\pi$
$439$	−11.1746	−0.533335	−0.266668	+	0.963789i	$0.585923\pi$
$440$	58.1550	2.77243
$441$	−13.3831	−0.637289
$442$	33.5000	1.59343
$443$	23.6305	1.12272	0.561360	−	0.827572i	$-0.310278\pi$
$443$	23.6305	1.12272	0.561360	+	0.827572i	$0.310278\pi$
$444$	119.772	5.68412
$445$	24.9239	1.18151
$446$	−74.9252	−3.54781
$447$	31.4415	1.48713
$448$	−12.7140	−0.600679
$449$	26.0017	1.22710	0.613548	−	0.789658i	$-0.289742\pi$
$449$	26.0017	1.22710	0.613548	+	0.789658i	$0.289742\pi$
$450$	13.8930	0.654922
$451$	−16.4796	−0.775992
$452$	−20.8986	−0.982989
$453$	35.7645	1.68036
$454$	−29.5718	−1.38787
$455$	−9.53076	−0.446809
$456$	−130.154	−6.09502
$457$	−9.27877	−0.434043	−0.217021	−	0.976167i	$-0.569634\pi$
$457$	−9.27877	−0.434043	−0.217021	+	0.976167i	$0.569634\pi$
$458$	63.1111	2.94899
$459$	−1.72175	−0.0803644
$460$	−1.66703	−0.0777256
$461$	−2.80330	−0.130563	−0.0652813	−	0.997867i	$-0.520794\pi$
$461$	−2.80330	−0.130563	−0.0652813	+	0.997867i	$0.520794\pi$
$462$	41.5433	1.93277
$463$	4.14501	0.192635	0.0963175	−	0.995351i	$-0.469294\pi$
$463$	4.14501	0.192635	0.0963175	+	0.995351i	$0.469294\pi$
$464$	−54.1860	−2.51552
$465$	45.0397	2.08867
$466$	−60.0774	−2.78303
$467$	16.2885	0.753743	0.376871	−	0.926266i	$-0.377000\pi$
$467$	16.2885	0.753743	0.376871	+	0.926266i	$0.377000\pi$
$468$	49.3038	2.27907
$469$	4.71217	0.217588
$470$	3.22339	0.148684
$471$	−55.3412	−2.54999
$472$	0.912878	0.0420186
$473$	46.5559	2.14064
$474$	−7.11274	−0.326699
$475$	13.7672	0.631684
$476$	25.4034	1.16436
$477$	30.6947	1.40541
$478$	14.0890	0.644418
$479$	−8.24999	−0.376952	−0.188476	−	0.982078i	$-0.560355\pi$
$479$	−8.24999	−0.376952	−0.188476	+	0.982078i	$0.560355\pi$
$480$	45.6288	2.08266
$481$	−37.3089	−1.70114
$482$	−28.9678	−1.31945
$483$	−0.699589	−0.0318324
$484$	41.8260	1.90118
$485$	−17.3328	−0.787042
$486$	−56.4457	−2.56043
$487$	−16.5879	−0.751671	−0.375836	−	0.926686i	$-0.622644\pi$
$487$	−16.5879	−0.751671	−0.375836	+	0.926686i	$0.622644\pi$
$488$	−52.1613	−2.36123
$489$	36.5641	1.65349
$490$	22.0535	0.996274
$491$	4.73711	0.213783	0.106891	−	0.994271i	$-0.465910\pi$
$491$	4.73711	0.213783	0.106891	+	0.994271i	$0.465910\pi$
$492$	−43.4199	−1.95752
$493$	19.4502	0.875994
$494$	69.0127	3.10503
$495$	−21.8229	−0.980868
$496$	−104.179	−4.67777
$497$	9.59558	0.430421
$498$	71.5516	3.20630
$499$	7.17103	0.321019	0.160510	−	0.987034i	$-0.448686\pi$
$499$	7.17103	0.321019	0.160510	+	0.987034i	$0.448686\pi$
$500$	−58.9004	−2.63411
$501$	32.4909	1.45158
$502$	8.80390	0.392937
$503$	10.6565	0.475151	0.237575	−	0.971369i	$-0.423647\pi$
$503$	10.6565	0.475151	0.237575	+	0.971369i	$0.423647\pi$
$504$	31.0249	1.38196
$505$	10.7031	0.476281
$506$	−2.26347	−0.100623
$507$	−0.531873	−0.0236213
$508$	41.2712	1.83111
$509$	23.2019	1.02841	0.514203	−	0.857669i	$-0.328088\pi$
$509$	23.2019	1.02841	0.514203	+	0.857669i	$0.328088\pi$
$510$	−39.0680	−1.72996
$511$	−10.2522	−0.453532
$512$	40.6659	1.79719
$513$	−3.54694	−0.156601
$514$	28.3361	1.24985
$515$	16.4288	0.723937
$516$	122.664	5.40000
$517$	3.09847	0.136270
$518$	−39.9628	−1.75587
$519$	−34.9542	−1.53432
$520$	−47.7297	−2.09308
$521$	22.1982	0.972522	0.486261	−	0.873814i	$-0.338360\pi$
$521$	22.1982	0.972522	0.486261	+	0.873814i	$0.338360\pi$
$522$	40.4350	1.76979
$523$	−40.3270	−1.76338	−0.881688	−	0.471832i	$-0.843593\pi$
$523$	−40.3270	−1.76338	−0.881688	+	0.471832i	$0.843593\pi$
$524$	−38.3733	−1.67634
$525$	−6.80174	−0.296852
$526$	54.6260	2.38181
$527$	37.3954	1.62897
$528$	104.621	4.55303
$529$	−22.9619	−0.998343
$530$	−50.5806	−2.19708
$531$	−0.342562	−0.0148659
$532$	52.3329	2.26892
$533$	13.5253	0.585845
$534$	89.1644	3.85852
$535$	5.46820	0.236411
$536$	23.5984	1.01929
$537$	19.0796	0.823345
$538$	63.9263	2.75606
$539$	21.1988	0.913096
$540$	4.17567	0.179692
$541$	−30.7491	−1.32201	−0.661003	−	0.750383i	$-0.729869\pi$
$541$	−30.7491	−1.32201	−0.661003	+	0.750383i	$0.729869\pi$
$542$	−66.0539	−2.83726
$543$	−10.0467	−0.431144
$544$	37.8844	1.62428
$545$	−27.9059	−1.19536
$546$	−34.0959	−1.45917
$547$	5.79418	0.247741	0.123871	−	0.992298i	$-0.460469\pi$
$547$	5.79418	0.247741	0.123871	+	0.992298i	$0.460469\pi$
$548$	−98.0840	−4.18994
$549$	19.5738	0.835387
$550$	−22.0065	−0.938360
$551$	40.0690	1.70700
$552$	−3.50352	−0.149120
$553$	1.68012	0.0714461
$554$	55.4542	2.35602
$555$	43.5099	1.84689
$556$	9.44481	0.400549
$557$	12.2178	0.517687	0.258843	−	0.965919i	$-0.416659\pi$
$557$	12.2178	0.517687	0.258843	+	0.965919i	$0.416659\pi$
$558$	77.7411	3.29104
$559$	−38.2099	−1.61611
$560$	−25.7091	−1.08641
$561$	−37.5539	−1.58553
$562$	64.2695	2.71104
$563$	−13.0681	−0.550755	−0.275377	−	0.961336i	$-0.588803\pi$
$563$	−13.0681	−0.550755	−0.275377	+	0.961336i	$0.588803\pi$
$564$	8.16376	0.343757
$565$	−7.59192	−0.319394
$566$	8.57968	0.360631
$567$	14.2401	0.598028
$568$	48.0543	2.01631
$569$	−13.2688	−0.556256	−0.278128	−	0.960544i	$-0.589714\pi$
$569$	−13.2688	−0.556256	−0.278128	+	0.960544i	$0.589714\pi$
$570$	−80.4831	−3.37106
$571$	−5.33049	−0.223074	−0.111537	−	0.993760i	$-0.535577\pi$
$571$	−5.33049	−0.223074	−0.111537	+	0.993760i	$0.535577\pi$
$572$	−78.0973	−3.26541
$573$	−55.6224	−2.32366
$574$	14.4874	0.604692
$575$	0.370589	0.0154546
$576$	23.8929	0.995536
$577$	22.6552	0.943149	0.471575	−	0.881826i	$-0.343686\pi$
$577$	22.6552	0.943149	0.471575	+	0.881826i	$0.343686\pi$
$578$	12.0501	0.501217
$579$	−11.3325	−0.470962
$580$	−47.1717	−1.95870
$581$	−16.9014	−0.701189
$582$	−62.0074	−2.57029
$583$	−48.6204	−2.01365
$584$	−51.3427	−2.12458
$585$	17.9108	0.740519
$586$	66.3537	2.74104
$587$	−8.55594	−0.353141	−0.176571	−	0.984288i	$-0.556500\pi$
$587$	−8.55594	−0.353141	−0.176571	+	0.984288i	$0.556500\pi$
$588$	55.8540	2.30338
$589$	77.0373	3.17427
$590$	0.564494	0.0232399
$591$	−5.90338	−0.242833
$592$	−100.640	−4.13630
$593$	−6.46079	−0.265313	−0.132656	−	0.991162i	$-0.542351\pi$
$593$	−6.46079	−0.265313	−0.132656	+	0.991162i	$0.542351\pi$
$594$	5.66967	0.232629
$595$	9.22837	0.378326
$596$	−63.3114	−2.59333
$597$	1.04565	0.0427958
$598$	1.85770	0.0759669
$599$	−38.3984	−1.56892	−0.784458	−	0.620182i	$-0.787059\pi$
$599$	−38.3984	−1.56892	−0.784458	+	0.620182i	$0.787059\pi$
$600$	−34.0628	−1.39061
$601$	33.8140	1.37930	0.689652	−	0.724141i	$-0.257764\pi$
$601$	33.8140	1.37930	0.689652	+	0.724141i	$0.257764\pi$
$602$	−40.9279	−1.66810
$603$	−8.85538	−0.360619
$604$	−72.0163	−2.93030
$605$	15.1943	0.617735
$606$	38.2898	1.55542
$607$	7.56070	0.306880	0.153440	−	0.988158i	$-0.450965\pi$
$607$	7.56070	0.306880	0.153440	+	0.988158i	$0.450965\pi$
$608$	78.0449	3.16514
$609$	−19.7962	−0.802182
$610$	−32.2549	−1.30596
$611$	−2.54301	−0.102879
$612$	−47.7395	−1.92976
$613$	7.21496	0.291409	0.145705	−	0.989328i	$-0.453455\pi$
$613$	7.21496	0.291409	0.145705	+	0.989328i	$0.453455\pi$
$614$	32.7178	1.32038
$615$	−15.7733	−0.636040
$616$	−49.1435	−1.98005
$617$	−35.2460	−1.41895	−0.709475	−	0.704731i	$-0.751068\pi$
$617$	−35.2460	−1.41895	−0.709475	+	0.704731i	$0.751068\pi$
$618$	58.7732	2.36420
$619$	−3.86634	−0.155401	−0.0777007	−	0.996977i	$-0.524758\pi$
$619$	−3.86634	−0.155401	−0.0777007	+	0.996977i	$0.524758\pi$
$620$	−90.6931	−3.64232
$621$	−0.0954772	−0.00383137
$622$	−55.1356	−2.21074
$623$	−21.0618	−0.843823
$624$	−85.8654	−3.43737
$625$	−11.9061	−0.476244
$626$	48.2005	1.92648
$627$	−77.3639	−3.08962
$628$	111.436	4.44680
$629$	36.1252	1.44041
$630$	19.1848	0.764341
$631$	38.0254	1.51377	0.756883	−	0.653550i	$-0.226721\pi$
$631$	38.0254	1.51377	0.756883	+	0.653550i	$0.226721\pi$
$632$	8.41399	0.334691
$633$	55.6903	2.21349
$634$	−75.6545	−3.00462
$635$	14.9927	0.594968
$636$	−128.104	−5.07964
$637$	−17.3985	−0.689354
$638$	−64.0490	−2.53572
$639$	−18.0326	−0.713358
$640$	−1.46934	−0.0580806
$641$	3.60359	0.142333	0.0711666	−	0.997464i	$-0.477328\pi$
$641$	3.60359	0.142333	0.0711666	+	0.997464i	$0.477328\pi$
$642$	19.5623	0.772061
$643$	10.1135	0.398836	0.199418	−	0.979915i	$-0.436095\pi$
$643$	10.1135	0.398836	0.199418	+	0.979915i	$0.436095\pi$
$644$	1.40871	0.0555109
$645$	44.5607	1.75458
$646$	−66.8231	−2.62912
$647$	8.75023	0.344007	0.172003	−	0.985096i	$-0.444976\pi$
$647$	8.75023	0.344007	0.172003	+	0.985096i	$0.444976\pi$
$648$	71.3139	2.80147
$649$	0.542617	0.0212996
$650$	18.0614	0.708427
$651$	−38.0605	−1.49171
$652$	−73.6264	−2.88343
$653$	14.7981	0.579093	0.289546	−	0.957164i	$-0.406496\pi$
$653$	14.7981	0.579093	0.289546	+	0.957164i	$0.406496\pi$
$654$	−99.8324	−3.90375
$655$	−13.9400	−0.544680
$656$	36.4843	1.42447
$657$	19.2666	0.751661
$658$	−2.72390	−0.106189
$659$	7.43544	0.289644	0.144822	−	0.989458i	$-0.453739\pi$
$659$	7.43544	0.289644	0.144822	+	0.989458i	$0.453739\pi$
$660$	91.0776	3.54519
$661$	−30.2159	−1.17526	−0.587632	−	0.809129i	$-0.699940\pi$
$661$	−30.2159	−1.17526	−0.587632	+	0.809129i	$0.699940\pi$
$662$	−43.4354	−1.68816
$663$	30.8217	1.19701
$664$	−84.6417	−3.28473
$665$	19.0111	0.737221
$666$	75.1005	2.91009
$667$	1.07859	0.0417630
$668$	−65.4244	−2.53134
$669$	−68.9349	−2.66518
$670$	14.5925	0.563756
$671$	−31.0048	−1.19693
$672$	−38.5583	−1.48742
$673$	15.5550	0.599601	0.299801	−	0.954002i	$-0.403080\pi$
$673$	15.5550	0.599601	0.299801	+	0.954002i	$0.403080\pi$
$674$	48.2335	1.85788
$675$	−0.928275	−0.0357293
$676$	1.07099	0.0411920
$677$	−13.4736	−0.517831	−0.258915	−	0.965900i	$-0.583365\pi$
$677$	−13.4736	−0.517831	−0.258915	+	0.965900i	$0.583365\pi$
$678$	−27.1598	−1.04306
$679$	14.6469	0.562098
$680$	46.2153	1.77228
$681$	−27.2075	−1.04259
$682$	−123.142	−4.71534
$683$	40.6659	1.55604	0.778019	−	0.628240i	$-0.216225\pi$
$683$	40.6659	1.55604	0.778019	+	0.628240i	$0.216225\pi$
$684$	−98.3471	−3.76040
$685$	−35.6313	−1.36140
$686$	−45.8990	−1.75243
$687$	58.0653	2.21533
$688$	−103.071	−3.92954
$689$	39.9043	1.52023
$690$	−2.16646	−0.0824758
$691$	25.3391	0.963945	0.481972	−	0.876186i	$-0.339921\pi$
$691$	25.3391	0.963945	0.481972	+	0.876186i	$0.339921\pi$
$692$	70.3846	2.67562
$693$	18.4413	0.700527
$694$	−2.06276	−0.0783014
$695$	3.43105	0.130147
$696$	−99.1385	−3.75784
$697$	−13.0962	−0.496053
$698$	−51.1034	−1.93429
$699$	−55.2742	−2.09066
$700$	13.6961	0.517665
$701$	37.2790	1.40801	0.704004	−	0.710196i	$-0.251394\pi$
$701$	37.2790	1.40801	0.704004	+	0.710196i	$0.251394\pi$
$702$	−4.65328	−0.175627
$703$	74.4207	2.80683
$704$	−37.8463	−1.42639
$705$	2.96568	0.111694
$706$	9.32214	0.350843
$707$	−9.04456	−0.340156
$708$	1.42967	0.0537305
$709$	−43.4171	−1.63056	−0.815282	−	0.579065i	$-0.803418\pi$
$709$	−43.4171	−1.63056	−0.815282	+	0.579065i	$0.803418\pi$
$710$	29.7152	1.11519
$711$	−3.15739	−0.118411
$712$	−105.477	−3.95290
$713$	2.07371	0.0776610
$714$	33.0141	1.23552
$715$	−28.3706	−1.06100
$716$	−38.4191	−1.43579
$717$	12.9626	0.484097
$718$	−35.7446	−1.33398
$719$	−15.2021	−0.566944	−0.283472	−	0.958981i	$-0.591486\pi$
$719$	−15.2021	−0.566944	−0.283472	+	0.958981i	$0.591486\pi$
$720$	48.3141	1.80056
$721$	−13.8830	−0.517030
$722$	−87.9396	−3.27277
$723$	−26.6518	−0.991190
$724$	20.2302	0.751850
$725$	10.4865	0.389460
$726$	54.3569	2.01737
$727$	−7.01976	−0.260349	−0.130174	−	0.991491i	$-0.541554\pi$
$727$	−7.01976	−0.260349	−0.130174	+	0.991491i	$0.541554\pi$
$728$	40.3336	1.49486
$729$	−23.2285	−0.860316
$730$	−31.7487	−1.17507
$731$	36.9976	1.36841
$732$	−81.6907	−3.01938
$733$	−14.8121	−0.547098	−0.273549	−	0.961858i	$-0.588198\pi$
$733$	−14.8121	−0.547098	−0.273549	+	0.961858i	$0.588198\pi$
$734$	4.15425	0.153336
$735$	20.2903	0.748417
$736$	2.10083	0.0774376
$737$	14.0269	0.516688
$738$	−27.2256	−1.00219
$739$	23.2873	0.856635	0.428318	−	0.903628i	$-0.359106\pi$
$739$	23.2873	0.856635	0.428318	+	0.903628i	$0.359106\pi$
$740$	−87.6127	−3.22071
$741$	63.4950	2.33255
$742$	42.7428	1.56914
$743$	−54.0546	−1.98307	−0.991536	−	0.129829i	$-0.958557\pi$
$743$	−54.0546	−1.98307	−0.991536	+	0.129829i	$0.958557\pi$
$744$	−190.606	−6.98794
$745$	−22.9993	−0.842630
$746$	−59.3809	−2.17409
$747$	31.7622	1.16212
$748$	75.6194	2.76492
$749$	−4.62086	−0.168843
$750$	−76.5467	−2.79509
$751$	−2.26744	−0.0827399	−0.0413700	−	0.999144i	$-0.513172\pi$
$751$	−2.26744	−0.0827399	−0.0413700	+	0.999144i	$0.513172\pi$
$752$	−6.85975	−0.250149
$753$	8.10002	0.295181
$754$	52.5670	1.91438
$755$	−26.1616	−0.952118
$756$	−3.52862	−0.128335
$757$	4.18030	0.151936	0.0759678	−	0.997110i	$-0.475795\pi$
$757$	4.18030	0.151936	0.0759678	+	0.997110i	$0.475795\pi$
$758$	−47.7341	−1.73378
$759$	−2.08250	−0.0755899
$760$	95.2071	3.45353
$761$	5.73786	0.207997	0.103999	−	0.994577i	$-0.466836\pi$
$761$	5.73786	0.207997	0.103999	+	0.994577i	$0.466836\pi$
$762$	53.6358	1.94302
$763$	23.5817	0.853715
$764$	112.003	4.05211
$765$	−17.3425	−0.627019
$766$	−6.41155	−0.231659
$767$	−0.445343	−0.0160804
$768$	35.8794	1.29469
$769$	−5.59268	−0.201677	−0.100839	−	0.994903i	$-0.532153\pi$
$769$	−5.59268	−0.201677	−0.100839	+	0.994903i	$0.532153\pi$
$770$	−30.3887	−1.09513
$771$	26.0706	0.938909
$772$	22.8194	0.821287
$773$	−3.01849	−0.108567	−0.0542837	−	0.998526i	$-0.517288\pi$
$773$	−3.01849	−0.108567	−0.0542837	+	0.998526i	$0.517288\pi$
$774$	76.9142	2.76462
$775$	20.1616	0.724225
$776$	73.3514	2.63316
$777$	−36.7678	−1.31904
$778$	−89.9376	−3.22442
$779$	−26.9791	−0.966627
$780$	−74.7503	−2.67649
$781$	28.5636	1.02209
$782$	−1.79876	−0.0643235
$783$	−2.70171	−0.0965511
$784$	−46.9323	−1.67615
$785$	40.4819	1.44486
$786$	−49.8697	−1.77879
$787$	−17.3078	−0.616957	−0.308478	−	0.951231i	$-0.599820\pi$
$787$	−17.3078	−0.616957	−0.308478	+	0.951231i	$0.599820\pi$
$788$	11.8872	0.423464
$789$	50.2586	1.78925
$790$	5.20294	0.185112
$791$	6.41549	0.228109
$792$	92.3533	3.28163
$793$	25.4466	0.903636
$794$	−79.0901	−2.80680
$795$	−46.5367	−1.65048
$796$	−2.10556	−0.0746294
$797$	7.31305	0.259041	0.129521	−	0.991577i	$-0.458656\pi$
$797$	7.31305	0.259041	0.129521	+	0.991577i	$0.458656\pi$
$798$	68.0116	2.40759
$799$	2.46233	0.0871109
$800$	20.4253	0.722142
$801$	39.5806	1.39851
$802$	−46.0166	−1.62490
$803$	−30.5183	−1.07697
$804$	36.9578	1.30340
$805$	0.511746	0.0180367
$806$	101.066	3.55991
$807$	58.8153	2.07040
$808$	−45.2948	−1.59347
$809$	−7.05694	−0.248109	−0.124054	−	0.992275i	$-0.539590\pi$
$809$	−7.05694	−0.248109	−0.124054	+	0.992275i	$0.539590\pi$
$810$	44.0982	1.54945
$811$	56.2616	1.97561	0.987806	−	0.155690i	$-0.0497602\pi$
$811$	56.2616	1.97561	0.987806	+	0.155690i	$0.0497602\pi$
$812$	39.8621	1.39888
$813$	−60.7728	−2.13140
$814$	−118.959	−4.16952
$815$	−26.7465	−0.936890
$816$	83.1411	2.91052
$817$	76.2180	2.66653
$818$	100.319	3.50756
$819$	−15.1354	−0.528872
$820$	31.7615	1.10916
$821$	−15.7078	−0.548205	−0.274102	−	0.961701i	$-0.588381\pi$
$821$	−15.7078	−0.548205	−0.274102	+	0.961701i	$0.588381\pi$
$822$	−127.470	−4.44601
$823$	−16.1712	−0.563692	−0.281846	−	0.959460i	$-0.590947\pi$
$823$	−16.1712	−0.563692	−0.281846	+	0.959460i	$0.590947\pi$
$824$	−69.5255	−2.42204
$825$	−20.2470	−0.704912
$826$	−0.477022	−0.0165977
$827$	−18.0781	−0.628635	−0.314318	−	0.949318i	$-0.601776\pi$
$827$	−18.0781	−0.628635	−0.314318	+	0.949318i	$0.601776\pi$
$828$	−2.64733	−0.0920011
$829$	−3.67232	−0.127545	−0.0637724	−	0.997964i	$-0.520313\pi$
$829$	−3.67232	−0.127545	−0.0637724	+	0.997964i	$0.520313\pi$
$830$	−52.3397	−1.81674
$831$	51.0206	1.76988
$832$	31.0616	1.07687
$833$	16.8465	0.583696
$834$	12.2744	0.425029
$835$	−23.7669	−0.822488
$836$	155.782	5.38783
$837$	−5.19435	−0.179543
$838$	63.6935	2.20025
$839$	1.42606	0.0492330	0.0246165	−	0.999697i	$-0.492164\pi$
$839$	1.42606	0.0492330	0.0246165	+	0.999697i	$0.492164\pi$
$840$	−47.0373	−1.62294
$841$	1.52059	0.0524341
$842$	−18.0828	−0.623174
$843$	59.1310	2.03658
$844$	−112.139	−3.86000
$845$	0.389063	0.0133842
$846$	5.11892	0.175992
$847$	−12.8398	−0.441181
$848$	107.641	3.69642
$849$	7.89373	0.270912
$850$	−17.4884	−0.599846
$851$	2.00327	0.0686713
$852$	75.2587	2.57832
$853$	−8.38552	−0.287115	−0.143557	−	0.989642i	$-0.545854\pi$
$853$	−8.38552	−0.287115	−0.143557	+	0.989642i	$0.545854\pi$
$854$	27.2567	0.932706
$855$	−35.7269	−1.22183
$856$	−23.1411	−0.790947
$857$	−28.6399	−0.978319	−0.489159	−	0.872194i	$-0.662696\pi$
$857$	−28.6399	−0.978319	−0.489159	+	0.872194i	$0.662696\pi$
$858$	−101.495	−3.46498
$859$	19.5413	0.666740	0.333370	−	0.942796i	$-0.391814\pi$
$859$	19.5413	0.666740	0.333370	+	0.942796i	$0.391814\pi$
$860$	−89.7285	−3.05972
$861$	13.3291	0.454255
$862$	95.0923	3.23886
$863$	−45.7404	−1.55702	−0.778511	−	0.627631i	$-0.784025\pi$
$863$	−45.7404	−1.55702	−0.778511	+	0.627631i	$0.784025\pi$
$864$	−5.26229	−0.179027
$865$	25.5689	0.869367
$866$	−26.9355	−0.915306
$867$	11.0867	0.376522
$868$	76.6395	2.60132
$869$	5.00130	0.169657
$870$	−61.3041	−2.07840
$871$	−11.5123	−0.390081
$872$	118.096	3.99925
$873$	−27.5254	−0.931594
$874$	−3.70558	−0.125343
$875$	18.0813	0.611261
$876$	−80.4088	−2.71676
$877$	−48.3925	−1.63410	−0.817050	−	0.576567i	$-0.804392\pi$
$877$	−48.3925	−1.63410	−0.817050	+	0.576567i	$0.804392\pi$
$878$	29.2428	0.986896
$879$	61.0486	2.05912
$880$	−76.5295	−2.57981
$881$	40.2197	1.35504	0.677519	−	0.735505i	$-0.263055\pi$
$881$	40.2197	1.35504	0.677519	+	0.735505i	$0.263055\pi$
$882$	35.0221	1.17926
$883$	39.4907	1.32897	0.664484	−	0.747302i	$-0.268651\pi$
$883$	39.4907	1.32897	0.664484	+	0.747302i	$0.268651\pi$
$884$	−62.0632	−2.08741
$885$	0.519362	0.0174582
$886$	−61.8386	−2.07751
$887$	22.4731	0.754573	0.377286	−	0.926097i	$-0.376857\pi$
$887$	22.4731	0.754573	0.377286	+	0.926097i	$0.376857\pi$
$888$	−184.132	−6.17905
$889$	−12.6695	−0.424921
$890$	−65.2234	−2.18629
$891$	42.3892	1.42009
$892$	138.809	4.64767
$893$	5.07258	0.169748
$894$	−82.2792	−2.75183
$895$	−13.9566	−0.466519
$896$	1.24165	0.0414807
$897$	1.70917	0.0570676
$898$	−68.0437	−2.27065
$899$	58.6795	1.95707
$900$	−25.7386	−0.857953
$901$	−38.6382	−1.28723
$902$	43.1253	1.43591
$903$	−37.6557	−1.25310
$904$	32.1286	1.06858
$905$	7.34910	0.244292
$906$	−93.5920	−3.10939
$907$	−12.6097	−0.418700	−0.209350	−	0.977841i	$-0.567135\pi$
$907$	−12.6097	−0.418700	−0.209350	+	0.977841i	$0.567135\pi$
$908$	54.7857	1.81813
$909$	16.9971	0.563757
$910$	24.9410	0.826786
$911$	−17.6461	−0.584642	−0.292321	−	0.956320i	$-0.594428\pi$
$911$	−17.6461	−0.584642	−0.292321	+	0.956320i	$0.594428\pi$
$912$	171.277	5.67155
$913$	−50.3112	−1.66506
$914$	24.2816	0.803163
$915$	−29.6760	−0.981060
$916$	−116.922	−3.86320
$917$	11.7799	0.389006
$918$	4.50564	0.148708
$919$	−47.2687	−1.55925	−0.779625	−	0.626246i	$-0.784590\pi$
$919$	−47.2687	−1.55925	−0.779625	+	0.626246i	$0.784590\pi$
$920$	2.56281	0.0844932
$921$	30.1020	0.991894
$922$	7.33594	0.241596
$923$	−23.4431	−0.771638
$924$	−76.9644	−2.53194
$925$	19.4768	0.640392
$926$	−10.8471	−0.356457
$927$	26.0898	0.856900
$928$	59.4469	1.95144
$929$	6.97371	0.228800	0.114400	−	0.993435i	$-0.463505\pi$
$929$	6.97371	0.228800	0.114400	+	0.993435i	$0.463505\pi$
$930$	−117.864	−3.86492
$931$	34.7051	1.13741
$932$	111.301	3.64580
$933$	−50.7275	−1.66074
$934$	−42.6254	−1.39474
$935$	27.4705	0.898382
$936$	−75.7973	−2.47751
$937$	37.8474	1.23642	0.618210	−	0.786013i	$-0.287858\pi$
$937$	37.8474	1.23642	0.618210	+	0.786013i	$0.287858\pi$
$938$	−12.3313	−0.402630
$939$	44.3468	1.44720
$940$	−5.97176	−0.194777
$941$	−54.7566	−1.78501	−0.892507	−	0.451034i	$-0.851055\pi$
$941$	−54.7566	−1.78501	−0.892507	+	0.451034i	$0.851055\pi$
$942$	144.822	4.71856
$943$	−0.726230	−0.0236493
$944$	−1.20131	−0.0390993
$945$	−1.28185	−0.0416987
$946$	−121.832	−3.96110
$947$	30.9147	1.00459	0.502297	−	0.864695i	$-0.332489\pi$
$947$	30.9147	1.00459	0.502297	+	0.864695i	$0.332489\pi$
$948$	13.1773	0.427979
$949$	25.0473	0.813070
$950$	−36.0274	−1.16888
$951$	−69.6058	−2.25712
$952$	−39.0539	−1.26574
$953$	12.5376	0.406134	0.203067	−	0.979165i	$-0.434909\pi$
$953$	12.5376	0.406134	0.203067	+	0.979165i	$0.434909\pi$
$954$	−80.3248	−2.60061
$955$	40.6875	1.31662
$956$	−26.1018	−0.844193
$957$	−58.9282	−1.90488
$958$	21.5894	0.697521
$959$	30.1100	0.972301
$960$	−36.2243	−1.16913
$961$	81.8182	2.63930
$962$	97.6336	3.14783
$963$	8.68380	0.279832
$964$	53.6667	1.72849
$965$	8.28967	0.266854
$966$	1.83075	0.0589035
$967$	−35.4798	−1.14095	−0.570477	−	0.821313i	$-0.693242\pi$
$967$	−35.4798	−1.14095	−0.570477	+	0.821313i	$0.693242\pi$
$968$	−64.3013	−2.06672
$969$	−61.4805	−1.97504
$970$	45.3581	1.45636
$971$	26.7694	0.859072	0.429536	−	0.903050i	$-0.358677\pi$
$971$	26.7694	0.859072	0.429536	+	0.903050i	$0.358677\pi$
$972$	104.573	3.35418
$973$	−2.89938	−0.0929499
$974$	43.4089	1.39091
$975$	16.6174	0.532182
$976$	68.6420	2.19718
$977$	14.1184	0.451687	0.225843	−	0.974164i	$-0.427486\pi$
$977$	14.1184	0.451687	0.225843	+	0.974164i	$0.427486\pi$
$978$	−95.6846	−3.05966
$979$	−62.6956	−2.00376
$980$	−40.8570	−1.30513
$981$	−44.3161	−1.41491
$982$	−12.3965	−0.395589
$983$	24.0925	0.768431	0.384216	−	0.923243i	$-0.374472\pi$
$983$	24.0925	0.768431	0.384216	+	0.923243i	$0.374472\pi$
$984$	66.7516	2.12796
$985$	4.31830	0.137592
$986$	−50.8992	−1.62096
$987$	−2.50612	−0.0797708
$988$	−127.855	−4.06761
$989$	2.05165	0.0652387
$990$	57.1083	1.81502
$991$	9.61494	0.305429	0.152714	−	0.988270i	$-0.451199\pi$
$991$	9.61494	0.305429	0.152714	+	0.988270i	$0.451199\pi$
$992$	114.294	3.62883
$993$	−39.9627	−1.26818
$994$	−25.1106	−0.796461
$995$	−0.764892	−0.0242487
$996$	−132.559	−4.20029
$997$	34.8116	1.10249	0.551247	−	0.834342i	$-0.314152\pi$
$997$	34.8116	1.10249	0.551247	+	0.834342i	$0.314152\pi$
$998$	−18.7658	−0.594022
$999$	−5.01792	−0.158760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.7	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.7	✓	179	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} +O(q^{10})\)	\(q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} -4.60888 q^{10} -4.43026 q^{11} -11.6727 q^{12} +3.63606 q^{13} +3.89470 q^{14} -4.24040 q^{15} +9.80823 q^{16} -3.52069 q^{17} -7.31915 q^{18} -7.25290 q^{19} +8.53856 q^{20} +3.58331 q^{21} +11.5935 q^{22} -0.195235 q^{23} +17.9451 q^{24} -1.89817 q^{25} -9.51518 q^{26} +0.489037 q^{27} -7.21545 q^{28} -5.52454 q^{29} +11.0967 q^{30} -10.6216 q^{31} -10.7605 q^{32} +10.6666 q^{33} +9.21329 q^{34} -2.62118 q^{35} +13.5597 q^{36} -10.2608 q^{37} +18.9801 q^{38} -8.75443 q^{39} -13.1268 q^{40} +3.71977 q^{41} -9.37716 q^{42} -10.5086 q^{43} -21.4786 q^{44} +4.92588 q^{45} +0.510910 q^{46} -0.699387 q^{47} -23.6150 q^{48} -4.78499 q^{49} +4.96731 q^{50} +8.47667 q^{51} +17.6281 q^{52} +10.9746 q^{53} -1.27976 q^{54} -7.80259 q^{55} +11.0927 q^{56} +17.4626 q^{57} +14.4572 q^{58} -0.122480 q^{59} -20.5581 q^{60} +6.99841 q^{61} +27.7956 q^{62} -4.16258 q^{63} +8.54267 q^{64} +6.40383 q^{65} -27.9134 q^{66} -3.16616 q^{67} -17.0688 q^{68} +0.470062 q^{69} +6.85935 q^{70} -6.44739 q^{71} -20.8460 q^{72} +6.88859 q^{73} +26.8515 q^{74} +4.57017 q^{75} -35.1631 q^{76} +6.59352 q^{77} +22.9094 q^{78} -1.12889 q^{79} +17.2743 q^{80} -9.56809 q^{81} -9.73425 q^{82} +11.3563 q^{83} +17.3724 q^{84} -6.20065 q^{85} +27.5000 q^{86} +13.3013 q^{87} +33.0201 q^{88} +14.1517 q^{89} -12.8905 q^{90} -5.41151 q^{91} -0.946529 q^{92} +25.5733 q^{93} +1.83022 q^{94} -12.7738 q^{95} +25.9078 q^{96} -9.84146 q^{97} +12.5218 q^{98} -12.3909 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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