LMFDB - Embedded newform 4003.2.a.c.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +O(q^{10})$	\(q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +2.79236 q^{10} -3.88772 q^{11} -4.40911 q^{12} -6.48475 q^{13} +2.21034 q^{14} +0.812040 q^{15} +15.4891 q^{16} +4.70499 q^{17} +6.48411 q^{18} +0.952589 q^{19} -5.62503 q^{20} +0.642784 q^{21} +10.6658 q^{22} +5.52793 q^{23} +7.71864 q^{24} -3.96402 q^{25} +17.7906 q^{26} +4.27907 q^{27} -4.45259 q^{28} +1.89102 q^{29} -2.22779 q^{30} -8.55568 q^{31} -23.1441 q^{32} +3.10168 q^{33} -12.9079 q^{34} +0.820048 q^{35} -13.0618 q^{36} -8.60810 q^{37} -2.61338 q^{38} +5.17363 q^{39} +9.84724 q^{40} -9.32339 q^{41} -1.76344 q^{42} -3.57557 q^{43} -21.4855 q^{44} +2.40564 q^{45} -15.1656 q^{46} +1.56027 q^{47} -12.3574 q^{48} -6.35088 q^{49} +10.8751 q^{50} -3.75371 q^{51} -35.8379 q^{52} +0.105651 q^{53} -11.7394 q^{54} +3.95705 q^{55} +7.79475 q^{56} -0.759989 q^{57} -5.18792 q^{58} -7.49240 q^{59} +4.48773 q^{60} -14.5640 q^{61} +23.4720 q^{62} +1.90422 q^{63} +32.5162 q^{64} +6.60038 q^{65} -8.50929 q^{66} +11.0343 q^{67} +26.0021 q^{68} -4.41026 q^{69} -2.24976 q^{70} +12.2178 q^{71} +22.8661 q^{72} -14.5805 q^{73} +23.6158 q^{74} +3.16255 q^{75} +5.26447 q^{76} +3.13227 q^{77} -14.1936 q^{78} -7.18098 q^{79} -15.7653 q^{80} +3.67657 q^{81} +25.5782 q^{82} -4.55351 q^{83} +3.55234 q^{84} -4.78888 q^{85} +9.80938 q^{86} -1.50869 q^{87} +37.6127 q^{88} -15.1320 q^{89} -6.59973 q^{90} +5.22465 q^{91} +30.5501 q^{92} +6.82584 q^{93} -4.28052 q^{94} -0.969575 q^{95} +18.4647 q^{96} -4.22485 q^{97} +17.4233 q^{98} +9.18861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.74344	−1.93991	−0.969954	−	0.243288i	$-0.921774\pi$
$2$	−2.74344	−1.93991	−0.969954	+	0.243288i	$0.921774\pi$
$3$	−0.797814	−0.460618	−0.230309	−	0.973118i	$-0.573974\pi$
$3$	−0.797814	−0.460618	−0.230309	+	0.973118i	$0.573974\pi$
$4$	5.52649	2.76324
$5$	−1.01783	−0.455188	−0.227594	−	0.973756i	$-0.573086\pi$
$5$	−1.01783	−0.455188	−0.227594	+	0.973756i	$0.573086\pi$
$6$	2.18876	0.893557
$7$	−0.805682	−0.304519	−0.152259	−	0.988341i	$-0.548655\pi$
$7$	−0.805682	−0.304519	−0.152259	+	0.988341i	$0.548655\pi$
$8$	−9.67473	−3.42053
$9$	−2.36349	−0.787831
$10$	2.79236	0.883023
$11$	−3.88772	−1.17219	−0.586096	−	0.810241i	$-0.699336\pi$
$11$	−3.88772	−1.17219	−0.586096	+	0.810241i	$0.699336\pi$
$12$	−4.40911	−1.27280
$13$	−6.48475	−1.79855	−0.899273	−	0.437387i	$-0.855904\pi$
$13$	−6.48475	−1.79855	−0.899273	+	0.437387i	$0.855904\pi$
$14$	2.21034	0.590739
$15$	0.812040	0.209668
$16$	15.4891	3.87228
$17$	4.70499	1.14113	0.570564	−	0.821253i	$-0.306725\pi$
$17$	4.70499	1.14113	0.570564	+	0.821253i	$0.306725\pi$
$18$	6.48411	1.52832
$19$	0.952589	0.218539	0.109269	−	0.994012i	$-0.465149\pi$
$19$	0.952589	0.218539	0.109269	+	0.994012i	$0.465149\pi$
$20$	−5.62503	−1.25780
$21$	0.642784	0.140267
$22$	10.6658	2.27395
$23$	5.52793	1.15265	0.576327	−	0.817219i	$-0.304486\pi$
$23$	5.52793	1.15265	0.576327	+	0.817219i	$0.304486\pi$
$24$	7.71864	1.57556
$25$	−3.96402	−0.792804
$26$	17.7906	3.48902
$27$	4.27907	0.823508
$28$	−4.45259	−0.841460
$29$	1.89102	0.351154	0.175577	−	0.984466i	$-0.443821\pi$
$29$	1.89102	0.351154	0.175577	+	0.984466i	$0.443821\pi$
$30$	−2.22779	−0.406737
$31$	−8.55568	−1.53665	−0.768323	−	0.640063i	$-0.778908\pi$
$31$	−8.55568	−1.53665	−0.768323	+	0.640063i	$0.778908\pi$
$32$	−23.1441	−4.09133
$33$	3.10168	0.539934
$34$	−12.9079	−2.21368
$35$	0.820048	0.138613
$36$	−13.0618	−2.17697
$37$	−8.60810	−1.41516	−0.707581	−	0.706632i	$-0.750214\pi$
$37$	−8.60810	−1.41516	−0.707581	+	0.706632i	$0.750214\pi$
$38$	−2.61338	−0.423946
$39$	5.17363	0.828444
$40$	9.84724	1.55699
$41$	−9.32339	−1.45607	−0.728034	−	0.685541i	$-0.759566\pi$
$41$	−9.32339	−1.45607	−0.728034	+	0.685541i	$0.759566\pi$
$42$	−1.76344	−0.272105
$43$	−3.57557	−0.545270	−0.272635	−	0.962118i	$-0.587895\pi$
$43$	−3.57557	−0.545270	−0.272635	+	0.962118i	$0.587895\pi$
$44$	−21.4855	−3.23906
$45$	2.40564	0.358611
$46$	−15.1656	−2.23604
$47$	1.56027	0.227589	0.113795	−	0.993504i	$-0.463699\pi$
$47$	1.56027	0.227589	0.113795	+	0.993504i	$0.463699\pi$
$48$	−12.3574	−1.78364
$49$	−6.35088	−0.907268
$50$	10.8751	1.53797
$51$	−3.75371	−0.525624
$52$	−35.8379	−4.96983
$53$	0.105651	0.0145122	0.00725611	−	0.999974i	$-0.497690\pi$
$53$	0.105651	0.0145122	0.00725611	+	0.999974i	$0.497690\pi$
$54$	−11.7394	−1.59753
$55$	3.95705	0.533568
$56$	7.79475	1.04162
$57$	−0.759989	−0.100663
$58$	−5.18792	−0.681207
$59$	−7.49240	−0.975428	−0.487714	−	0.873004i	$-0.662169\pi$
$59$	−7.49240	−0.975428	−0.487714	+	0.873004i	$0.662169\pi$
$60$	4.48773	0.579364
$61$	−14.5640	−1.86473	−0.932367	−	0.361514i	$-0.882260\pi$
$61$	−14.5640	−1.86473	−0.932367	+	0.361514i	$0.882260\pi$
$62$	23.4720	2.98095
$63$	1.90422	0.239909
$64$	32.5162	4.06453
$65$	6.60038	0.818677
$66$	−8.50929	−1.04742
$67$	11.0343	1.34806	0.674029	−	0.738705i	$-0.264562\pi$
$67$	11.0343	1.34806	0.674029	+	0.738705i	$0.264562\pi$
$68$	26.0021	3.15321
$69$	−4.41026	−0.530933
$70$	−2.24976	−0.268897
$71$	12.2178	1.44999	0.724996	−	0.688753i	$-0.241842\pi$
$71$	12.2178	1.44999	0.724996	+	0.688753i	$0.241842\pi$
$72$	22.8661	2.69480
$73$	−14.5805	−1.70651	−0.853257	−	0.521491i	$-0.825376\pi$
$73$	−14.5805	−1.70651	−0.853257	+	0.521491i	$0.825376\pi$
$74$	23.6158	2.74529
$75$	3.16255	0.365180
$76$	5.26447	0.603877
$77$	3.13227	0.356955
$78$	−14.1936	−1.60710
$79$	−7.18098	−0.807924	−0.403962	−	0.914776i	$-0.632367\pi$
$79$	−7.18098	−0.807924	−0.403962	+	0.914776i	$0.632367\pi$
$80$	−15.7653	−1.76261
$81$	3.67657	0.408508
$82$	25.5782	2.82464
$83$	−4.55351	−0.499812	−0.249906	−	0.968270i	$-0.580400\pi$
$83$	−4.55351	−0.499812	−0.249906	+	0.968270i	$0.580400\pi$
$84$	3.55234	0.387592
$85$	−4.78888	−0.519427
$86$	9.80938	1.05777
$87$	−1.50869	−0.161748
$88$	37.6127	4.00953
$89$	−15.1320	−1.60399	−0.801993	−	0.597334i	$-0.796227\pi$
$89$	−15.1320	−1.60399	−0.801993	+	0.597334i	$0.796227\pi$
$90$	−6.59973	−0.695673
$91$	5.22465	0.547692
$92$	30.5501	3.18506
$93$	6.82584	0.707807
$94$	−4.28052	−0.441502
$95$	−0.969575	−0.0994763
$96$	18.4647	1.88454
$97$	−4.22485	−0.428968	−0.214484	−	0.976727i	$-0.568807\pi$
$97$	−4.22485	−0.428968	−0.214484	+	0.976727i	$0.568807\pi$
$98$	17.4233	1.76002
$99$	9.18861	0.923490
$100$	−21.9071	−2.19071
$101$	−18.3759	−1.82847	−0.914237	−	0.405179i	$-0.867209\pi$
$101$	−18.3759	−1.82847	−0.914237	+	0.405179i	$0.867209\pi$
$102$	10.2981	1.01966
$103$	−3.01970	−0.297540	−0.148770	−	0.988872i	$-0.547531\pi$
$103$	−3.01970	−0.297540	−0.148770	+	0.988872i	$0.547531\pi$
$104$	62.7382	6.15199
$105$	−0.654246	−0.0638479
$106$	−0.289846	−0.0281524
$107$	0.648338	0.0626772	0.0313386	−	0.999509i	$-0.490023\pi$
$107$	0.648338	0.0626772	0.0313386	+	0.999509i	$0.490023\pi$
$108$	23.6482	2.27555
$109$	10.4532	1.00124	0.500618	−	0.865668i	$-0.333106\pi$
$109$	10.4532	1.00124	0.500618	+	0.865668i	$0.333106\pi$
$110$	−10.8559	−1.03507
$111$	6.86767	0.651850
$112$	−12.4793	−1.17918
$113$	−2.58698	−0.243362	−0.121681	−	0.992569i	$-0.538829\pi$
$113$	−2.58698	−0.243362	−0.121681	+	0.992569i	$0.538829\pi$
$114$	2.08499	0.195277
$115$	−5.62650	−0.524674
$116$	10.4507	0.970325
$117$	15.3267	1.41695
$118$	20.5550	1.89224
$119$	−3.79072	−0.347495
$120$	−7.85627	−0.717176
$121$	4.11440	0.374036
$122$	39.9556	3.61741
$123$	7.43834	0.670692
$124$	−47.2829	−4.24613
$125$	9.12386	0.816063
$126$	−5.22413	−0.465402
$127$	−13.9480	−1.23768	−0.618841	−	0.785516i	$-0.712398\pi$
$127$	−13.9480	−1.23768	−0.618841	+	0.785516i	$0.712398\pi$
$128$	−42.9183	−3.79348
$129$	2.85264	0.251161
$130$	−18.1078	−1.58816
$131$	−1.46981	−0.128418	−0.0642089	−	0.997936i	$-0.520452\pi$
$131$	−1.46981	−0.128418	−0.0642089	+	0.997936i	$0.520452\pi$
$132$	17.1414	1.49197
$133$	−0.767484	−0.0665493
$134$	−30.2721	−2.61511
$135$	−4.35537	−0.374851
$136$	−45.5195	−3.90326
$137$	4.58002	0.391297	0.195649	−	0.980674i	$-0.437319\pi$
$137$	4.58002	0.391297	0.195649	+	0.980674i	$0.437319\pi$
$138$	12.0993	1.02996
$139$	1.51770	0.128730	0.0643648	−	0.997926i	$-0.479498\pi$
$139$	1.51770	0.128730	0.0643648	+	0.997926i	$0.479498\pi$
$140$	4.53199	0.383023
$141$	−1.24481	−0.104832
$142$	−33.5190	−2.81285
$143$	25.2109	2.10824
$144$	−36.6084	−3.05070
$145$	−1.92474	−0.159841
$146$	40.0007	3.31048
$147$	5.06682	0.417904
$148$	−47.5726	−3.91044
$149$	3.03447	0.248594	0.124297	−	0.992245i	$-0.460333\pi$
$149$	3.03447	0.248594	0.124297	+	0.992245i	$0.460333\pi$
$150$	−8.67629	−0.708416
$151$	−18.9250	−1.54010	−0.770049	−	0.637985i	$-0.779768\pi$
$151$	−18.9250	−1.54010	−0.770049	+	0.637985i	$0.779768\pi$
$152$	−9.21604	−0.747520
$153$	−11.1202	−0.899015
$154$	−8.59320	−0.692460
$155$	8.70824	0.699462
$156$	28.5920	2.28919
$157$	−0.0164040	−0.00130918	−0.000654590	−	1.00000i	$-0.500208\pi$
$157$	−0.0164040	−0.00130918	−0.000654590		1.00000i	$0.500208\pi$
$158$	19.7006	1.56730
$159$	−0.0842895	−0.00668459
$160$	23.5567	1.86232
$161$	−4.45375	−0.351005
$162$	−10.0865	−0.792468
$163$	−7.46977	−0.585078	−0.292539	−	0.956254i	$-0.594500\pi$
$163$	−7.46977	−0.585078	−0.292539	+	0.956254i	$0.594500\pi$
$164$	−51.5256	−4.02347
$165$	−3.15699	−0.245771
$166$	12.4923	0.969590
$167$	−24.1373	−1.86780	−0.933900	−	0.357534i	$-0.883617\pi$
$167$	−24.1373	−1.86780	−0.933900	+	0.357534i	$0.883617\pi$
$168$	−6.21876	−0.479788
$169$	29.0520	2.23477
$170$	13.1380	1.00764
$171$	−2.25144	−0.172172
$172$	−19.7604	−1.50671
$173$	10.7158	0.814707	0.407354	−	0.913271i	$-0.366452\pi$
$173$	10.7158	0.814707	0.407354	+	0.913271i	$0.366452\pi$
$174$	4.13900	0.313776
$175$	3.19374	0.241424
$176$	−60.2174	−4.53906
$177$	5.97755	0.449300
$178$	41.5137	3.11159
$179$	7.54167	0.563691	0.281845	−	0.959460i	$-0.409053\pi$
$179$	7.54167	0.563691	0.281845	+	0.959460i	$0.409053\pi$
$180$	13.2947	0.990930
$181$	18.6305	1.38480	0.692398	−	0.721516i	$-0.256554\pi$
$181$	18.6305	1.38480	0.692398	+	0.721516i	$0.256554\pi$
$182$	−14.3335	−1.06247
$183$	11.6194	0.858931
$184$	−53.4812	−3.94269
$185$	8.76159	0.644165
$186$	−18.7263	−1.37308
$187$	−18.2917	−1.33762
$188$	8.62283	0.628885
$189$	−3.44757	−0.250774
$190$	2.65998	0.192975
$191$	−6.17183	−0.446578	−0.223289	−	0.974752i	$-0.571679\pi$
$191$	−6.17183	−0.446578	−0.223289	+	0.974752i	$0.571679\pi$
$192$	−25.9419	−1.87220
$193$	20.8423	1.50026	0.750130	−	0.661290i	$-0.229991\pi$
$193$	20.8423	1.50026	0.750130	+	0.661290i	$0.229991\pi$
$194$	11.5906	0.832159
$195$	−5.26588	−0.377098
$196$	−35.0981	−2.50700
$197$	26.6764	1.90062	0.950308	−	0.311311i	$-0.100768\pi$
$197$	26.6764	1.90062	0.950308	+	0.311311i	$0.100768\pi$
$198$	−25.2084	−1.79149
$199$	20.3869	1.44519	0.722594	−	0.691272i	$-0.242949\pi$
$199$	20.3869	1.44519	0.722594	+	0.691272i	$0.242949\pi$
$200$	38.3508	2.71181
$201$	−8.80334	−0.620940
$202$	50.4134	3.54707
$203$	−1.52356	−0.106933
$204$	−20.7448	−1.45243
$205$	9.48964	0.662785
$206$	8.28437	0.577199
$207$	−13.0652	−0.908096
$208$	−100.443	−6.96447
$209$	−3.70340	−0.256170
$210$	1.79489	0.123859
$211$	−2.19410	−0.151048	−0.0755239	−	0.997144i	$-0.524063\pi$
$211$	−2.19410	−0.151048	−0.0755239	+	0.997144i	$0.524063\pi$
$212$	0.583877	0.0401008
$213$	−9.74757	−0.667893
$214$	−1.77868	−0.121588
$215$	3.63933	0.248200
$216$	−41.3989	−2.81684
$217$	6.89315	0.467938
$218$	−28.6778	−1.94231
$219$	11.6325	0.786051
$220$	21.8686	1.47438
$221$	−30.5107	−2.05237
$222$	−18.8411	−1.26453
$223$	−5.24656	−0.351336	−0.175668	−	0.984449i	$-0.556209\pi$
$223$	−5.24656	−0.351336	−0.175668	+	0.984449i	$0.556209\pi$
$224$	18.6467	1.24589
$225$	9.36893	0.624595
$226$	7.09723	0.472100
$227$	9.70655	0.644246	0.322123	−	0.946698i	$-0.395603\pi$
$227$	9.70655	0.644246	0.322123	+	0.946698i	$0.395603\pi$
$228$	−4.20007	−0.278157
$229$	0.146497	0.00968082	0.00484041	−	0.999988i	$-0.498459\pi$
$229$	0.146497	0.00968082	0.00484041	+	0.999988i	$0.498459\pi$
$230$	15.4360	1.01782
$231$	−2.49897	−0.164420
$232$	−18.2951	−1.20113
$233$	12.0852	0.791727	0.395863	−	0.918309i	$-0.370445\pi$
$233$	12.0852	0.791727	0.395863	+	0.918309i	$0.370445\pi$
$234$	−42.0479	−2.74875
$235$	−1.58809	−0.103596
$236$	−41.4067	−2.69534
$237$	5.72909	0.372144
$238$	10.3996	0.674108
$239$	−19.9018	−1.28734	−0.643669	−	0.765304i	$-0.722589\pi$
$239$	−19.9018	−1.28734	−0.643669	+	0.765304i	$0.722589\pi$
$240$	12.5778	0.811892
$241$	−11.0969	−0.714817	−0.357408	−	0.933948i	$-0.616340\pi$
$241$	−11.0969	−0.714817	−0.357408	+	0.933948i	$0.616340\pi$
$242$	−11.2876	−0.725596
$243$	−15.7704	−1.01167
$244$	−80.4880	−5.15272
$245$	6.46412	0.412978
$246$	−20.4067	−1.30108
$247$	−6.17731	−0.393053
$248$	82.7739	5.25615
$249$	3.63285	0.230223
$250$	−25.0308	−1.58309
$251$	−9.84628	−0.621492	−0.310746	−	0.950493i	$-0.600579\pi$
$251$	−9.84628	−0.621492	−0.310746	+	0.950493i	$0.600579\pi$
$252$	10.5237	0.662928
$253$	−21.4911	−1.35113
$254$	38.2655	2.40099
$255$	3.82064	0.239258
$256$	52.7117	3.29448
$257$	9.73479	0.607239	0.303620	−	0.952793i	$-0.401805\pi$
$257$	9.73479	0.607239	0.303620	+	0.952793i	$0.401805\pi$
$258$	−7.82607	−0.487230
$259$	6.93539	0.430944
$260$	36.4770	2.26220
$261$	−4.46942	−0.276650
$262$	4.03234	0.249119
$263$	2.81849	0.173796	0.0868978	−	0.996217i	$-0.472305\pi$
$263$	2.81849	0.173796	0.0868978	+	0.996217i	$0.472305\pi$
$264$	−30.0079	−1.84686
$265$	−0.107534	−0.00660579
$266$	2.10555	0.129099
$267$	12.0725	0.738825
$268$	60.9811	3.72501
$269$	−18.2497	−1.11271	−0.556353	−	0.830946i	$-0.687800\pi$
$269$	−18.2497	−1.11271	−0.556353	+	0.830946i	$0.687800\pi$
$270$	11.9487	0.727176
$271$	−2.39730	−0.145626	−0.0728129	−	0.997346i	$-0.523198\pi$
$271$	−2.39730	−0.145626	−0.0728129	+	0.997346i	$0.523198\pi$
$272$	72.8761	4.41876
$273$	−4.16830	−0.252277
$274$	−12.5650	−0.759081
$275$	15.4110	0.929319
$276$	−24.3733	−1.46710
$277$	17.0259	1.02299	0.511493	−	0.859287i	$-0.329093\pi$
$277$	17.0259	1.02299	0.511493	+	0.859287i	$0.329093\pi$
$278$	−4.16373	−0.249724
$279$	20.2213	1.21062
$280$	−7.93374	−0.474132
$281$	12.5202	0.746894	0.373447	−	0.927652i	$-0.378176\pi$
$281$	12.5202	0.746894	0.373447	+	0.927652i	$0.378176\pi$
$282$	3.41506	0.203364
$283$	20.6286	1.22625	0.613123	−	0.789988i	$-0.289913\pi$
$283$	20.6286	1.22625	0.613123	+	0.789988i	$0.289913\pi$
$284$	67.5218	4.00668
$285$	0.773541	0.0458206
$286$	−69.1648	−4.08980
$287$	7.51168	0.443401
$288$	54.7008	3.22327
$289$	5.13690	0.302171
$290$	5.28043	0.310077
$291$	3.37064	0.197591
$292$	−80.5787	−4.71551
$293$	−30.6108	−1.78830	−0.894150	−	0.447768i	$-0.852219\pi$
$293$	−30.6108	−1.78830	−0.894150	+	0.447768i	$0.852219\pi$
$294$	−13.9005	−0.810696
$295$	7.62600	0.444003
$296$	83.2810	4.84061
$297$	−16.6358	−0.965310
$298$	−8.32490	−0.482249
$299$	−35.8473	−2.07310
$300$	17.4778	1.00908
$301$	2.88077	0.166045
$302$	51.9198	2.98765
$303$	14.6606	0.842229
$304$	14.7548	0.846243
$305$	14.8237	0.848804
$306$	30.5077	1.74401
$307$	19.6573	1.12190	0.560951	−	0.827849i	$-0.310436\pi$
$307$	19.6573	1.12190	0.560951	+	0.827849i	$0.310436\pi$
$308$	17.3104	0.986354
$309$	2.40916	0.137052
$310$	−23.8906	−1.35689
$311$	−14.8863	−0.844127	−0.422064	−	0.906566i	$-0.638694\pi$
$311$	−14.8863	−0.844127	−0.422064	+	0.906566i	$0.638694\pi$
$312$	−50.0535	−2.83372
$313$	−12.0163	−0.679202	−0.339601	−	0.940570i	$-0.610292\pi$
$313$	−12.0163	−0.679202	−0.339601	+	0.940570i	$0.610292\pi$
$314$	0.0450034	0.00253969
$315$	−1.93818	−0.109204
$316$	−39.6856	−2.23249
$317$	28.1671	1.58202	0.791011	−	0.611802i	$-0.209555\pi$
$317$	28.1671	1.58202	0.791011	+	0.611802i	$0.209555\pi$
$318$	0.231244	0.0129675
$319$	−7.35178	−0.411620
$320$	−33.0960	−1.85012
$321$	−0.517254	−0.0288703
$322$	12.2186	0.680917
$323$	4.48192	0.249381
$324$	20.3185	1.12881
$325$	25.7057	1.42589
$326$	20.4929	1.13500
$327$	−8.33973	−0.461188
$328$	90.2013	4.98053
$329$	−1.25708	−0.0693052
$330$	8.66103	0.476774
$331$	−28.4684	−1.56476	−0.782381	−	0.622799i	$-0.785995\pi$
$331$	−28.4684	−1.56476	−0.782381	+	0.622799i	$0.785995\pi$
$332$	−25.1649	−1.38110
$333$	20.3452	1.11491
$334$	66.2193	3.62336
$335$	−11.2311	−0.613619
$336$	9.95615	0.543153
$337$	26.5305	1.44521	0.722604	−	0.691263i	$-0.242945\pi$
$337$	26.5305	1.44521	0.722604	+	0.691263i	$0.242945\pi$
$338$	−79.7026	−4.33525
$339$	2.06393	0.112097
$340$	−26.4657	−1.43530
$341$	33.2621	1.80124
$342$	6.17669	0.333997
$343$	10.7566	0.580799
$344$	34.5927	1.86511
$345$	4.48890	0.241675
$346$	−29.3982	−1.58046
$347$	15.1453	0.813041	0.406520	−	0.913642i	$-0.366742\pi$
$347$	15.1453	0.813041	0.406520	+	0.913642i	$0.366742\pi$
$348$	−8.33774	−0.446950
$349$	−14.4188	−0.771821	−0.385911	−	0.922536i	$-0.626113\pi$
$349$	−14.4188	−0.771821	−0.385911	+	0.922536i	$0.626113\pi$
$350$	−8.76184	−0.468340
$351$	−27.7487	−1.48112
$352$	89.9777	4.79583
$353$	−16.2620	−0.865539	−0.432769	−	0.901505i	$-0.642464\pi$
$353$	−16.2620	−0.865539	−0.432769	+	0.901505i	$0.642464\pi$
$354$	−16.3991	−0.871600
$355$	−12.4357	−0.660019
$356$	−83.6267	−4.43220
$357$	3.02429	0.160062
$358$	−20.6902	−1.09351
$359$	11.1924	0.590714	0.295357	−	0.955387i	$-0.404561\pi$
$359$	11.1924	0.590714	0.295357	+	0.955387i	$0.404561\pi$
$360$	−23.2739	−1.22664
$361$	−18.0926	−0.952241
$362$	−51.1118	−2.68638
$363$	−3.28253	−0.172288
$364$	28.8739	1.51341
$365$	14.8404	0.776784
$366$	−31.8772	−1.66625
$367$	29.6788	1.54922	0.774609	−	0.632440i	$-0.217947\pi$
$367$	29.6788	1.54922	0.774609	+	0.632440i	$0.217947\pi$
$368$	85.6227	4.46339
$369$	22.0358	1.14714
$370$	−24.0369	−1.24962
$371$	−0.0851207	−0.00441925
$372$	37.7229	1.95584
$373$	−27.7563	−1.43717	−0.718583	−	0.695442i	$-0.755209\pi$
$373$	−27.7563	−1.43717	−0.718583	+	0.695442i	$0.755209\pi$
$374$	50.1822	2.59486
$375$	−7.27915	−0.375894
$376$	−15.0952	−0.778476
$377$	−12.2628	−0.631567
$378$	9.45821	0.486478
$379$	−13.0067	−0.668111	−0.334056	−	0.942553i	$-0.608417\pi$
$379$	−13.0067	−0.668111	−0.334056	+	0.942553i	$0.608417\pi$
$380$	−5.35835	−0.274877
$381$	11.1279	0.570099
$382$	16.9321	0.866321
$383$	−12.3805	−0.632614	−0.316307	−	0.948657i	$-0.602443\pi$
$383$	−12.3805	−0.632614	−0.316307	+	0.948657i	$0.602443\pi$
$384$	34.2409	1.74735
$385$	−3.18812	−0.162482
$386$	−57.1796	−2.91037
$387$	8.45084	0.429580
$388$	−23.3486	−1.18534
$389$	−5.71573	−0.289799	−0.144899	−	0.989446i	$-0.546286\pi$
$389$	−5.71573	−0.289799	−0.144899	+	0.989446i	$0.546286\pi$
$390$	14.4467	0.731535
$391$	26.0089	1.31532
$392$	61.4430	3.10334
$393$	1.17263	0.0591516
$394$	−73.1853	−3.68702
$395$	7.30903	0.367757
$396$	50.7807	2.55183
$397$	16.2062	0.813367	0.406683	−	0.913569i	$-0.366685\pi$
$397$	16.2062	0.813367	0.406683	+	0.913569i	$0.366685\pi$
$398$	−55.9303	−2.80353
$399$	0.612309	0.0306538
$400$	−61.3991	−3.06996
$401$	−34.6508	−1.73038	−0.865189	−	0.501446i	$-0.832802\pi$
$401$	−34.6508	−1.73038	−0.865189	+	0.501446i	$0.832802\pi$
$402$	24.1515	1.20457
$403$	55.4815	2.76373
$404$	−101.554	−5.05252
$405$	−3.74213	−0.185948
$406$	4.17981	0.207440
$407$	33.4659	1.65884
$408$	36.3161	1.79791
$409$	6.50847	0.321823	0.160912	−	0.986969i	$-0.448557\pi$
$409$	6.50847	0.321823	0.160912	+	0.986969i	$0.448557\pi$
$410$	−26.0343	−1.28574
$411$	−3.65400	−0.180239
$412$	−16.6883	−0.822174
$413$	6.03649	0.297036
$414$	35.8437	1.76162
$415$	4.63470	0.227509
$416$	150.083	7.35845
$417$	−1.21084	−0.0592952
$418$	10.1601	0.496946
$419$	−3.93852	−0.192409	−0.0962047	−	0.995362i	$-0.530670\pi$
$419$	−3.93852	−0.192409	−0.0962047	+	0.995362i	$0.530670\pi$
$420$	−3.61568	−0.176427
$421$	18.9035	0.921302	0.460651	−	0.887581i	$-0.347616\pi$
$421$	18.9035	0.921302	0.460651	+	0.887581i	$0.347616\pi$
$422$	6.01938	0.293019
$423$	−3.68769	−0.179302
$424$	−1.02214	−0.0496395
$425$	−18.6507	−0.904690
$426$	26.7419	1.29565
$427$	11.7340	0.567847
$428$	3.58304	0.173193
$429$	−20.1136	−0.971096
$430$	−9.98430	−0.481486
$431$	4.12628	0.198756	0.0993779	−	0.995050i	$-0.468315\pi$
$431$	4.12628	0.198756	0.0993779	+	0.995050i	$0.468315\pi$
$432$	66.2790	3.18885
$433$	−27.0909	−1.30190	−0.650952	−	0.759119i	$-0.725630\pi$
$433$	−27.0909	−1.30190	−0.650952	+	0.759119i	$0.725630\pi$
$434$	−18.9110	−0.907756
$435$	1.53559	0.0736258
$436$	57.7696	2.76666
$437$	5.26585	0.251900
$438$	−31.9131	−1.52487
$439$	27.4441	1.30983	0.654917	−	0.755701i	$-0.272704\pi$
$439$	27.4441	1.30983	0.654917	+	0.755701i	$0.272704\pi$
$440$	−38.2834	−1.82509
$441$	15.0102	0.714774
$442$	83.7044	3.98141
$443$	17.7325	0.842497	0.421249	−	0.906945i	$-0.361592\pi$
$443$	17.7325	0.842497	0.421249	+	0.906945i	$0.361592\pi$
$444$	37.9541	1.80122
$445$	15.4018	0.730115
$446$	14.3937	0.681559
$447$	−2.42094	−0.114507
$448$	−26.1977	−1.23773
$449$	−5.95846	−0.281197	−0.140599	−	0.990067i	$-0.544903\pi$
$449$	−5.95846	−0.281197	−0.140599	+	0.990067i	$0.544903\pi$
$450$	−25.7031	−1.21166
$451$	36.2468	1.70679
$452$	−14.2969	−0.672469
$453$	15.0987	0.709397
$454$	−26.6294	−1.24978
$455$	−5.31781	−0.249303
$456$	7.35269	0.344321
$457$	−9.70648	−0.454050	−0.227025	−	0.973889i	$-0.572900\pi$
$457$	−9.70648	−0.454050	−0.227025	+	0.973889i	$0.572900\pi$
$458$	−0.401908	−0.0187799
$459$	20.1330	0.939727
$460$	−31.0948	−1.44980
$461$	−4.88230	−0.227391	−0.113696	−	0.993516i	$-0.536269\pi$
$461$	−4.88230	−0.227391	−0.113696	+	0.993516i	$0.536269\pi$
$462$	6.85578	0.318960
$463$	12.1435	0.564356	0.282178	−	0.959362i	$-0.408943\pi$
$463$	12.1435	0.564356	0.282178	+	0.959362i	$0.408943\pi$
$464$	29.2903	1.35977
$465$	−6.94756	−0.322185
$466$	−33.1550	−1.53588
$467$	35.6792	1.65104	0.825519	−	0.564375i	$-0.190883\pi$
$467$	35.6792	1.65104	0.825519	+	0.564375i	$0.190883\pi$
$468$	84.7026	3.91538
$469$	−8.89015	−0.410509
$470$	4.35685	0.200966
$471$	0.0130873	0.000603032 0
$472$	72.4870	3.33648
$473$	13.9008	0.639161
$474$	−15.7174	−0.721926
$475$	−3.77608	−0.173259
$476$	−20.9494	−0.960213
$477$	−0.249704	−0.0114332
$478$	54.5994	2.49732
$479$	−6.26099	−0.286072	−0.143036	−	0.989717i	$-0.545686\pi$
$479$	−6.26099	−0.286072	−0.143036	+	0.989717i	$0.545686\pi$
$480$	−18.7939	−0.857821
$481$	55.8214	2.54524
$482$	30.4438	1.38668
$483$	3.55327	0.161679
$484$	22.7382	1.03355
$485$	4.30018	0.195261
$486$	43.2653	1.96255
$487$	−31.5411	−1.42926	−0.714631	−	0.699502i	$-0.753405\pi$
$487$	−31.5411	−1.42926	−0.714631	+	0.699502i	$0.753405\pi$
$488$	140.903	6.37838
$489$	5.95949	0.269497
$490$	−17.7340	−0.801139
$491$	−6.02337	−0.271831	−0.135916	−	0.990720i	$-0.543398\pi$
$491$	−6.02337	−0.271831	−0.135916	+	0.990720i	$0.543398\pi$
$492$	41.1079	1.85329
$493$	8.89724	0.400712
$494$	16.9471	0.762486
$495$	−9.35245	−0.420361
$496$	−132.520	−5.95032
$497$	−9.84369	−0.441550
$498$	−9.96653	−0.446611
$499$	15.1184	0.676794	0.338397	−	0.941003i	$-0.390115\pi$
$499$	15.1184	0.676794	0.338397	+	0.941003i	$0.390115\pi$
$500$	50.4229	2.25498
$501$	19.2571	0.860343
$502$	27.0127	1.20564
$503$	−43.1616	−1.92448	−0.962241	−	0.272199i	$-0.912249\pi$
$503$	−43.1616	−1.92448	−0.962241	+	0.272199i	$0.912249\pi$
$504$	−18.4228	−0.820618
$505$	18.7036	0.832300
$506$	58.9596	2.62107
$507$	−23.1781	−1.02938
$508$	−77.0833	−3.42002
$509$	−15.4551	−0.685036	−0.342518	−	0.939511i	$-0.611280\pi$
$509$	−15.4551	−0.685036	−0.342518	+	0.939511i	$0.611280\pi$
$510$	−10.4817	−0.464138
$511$	11.7472	0.519666
$512$	−58.7749	−2.59751
$513$	4.07620	0.179969
$514$	−26.7069	−1.17799
$515$	3.07354	0.135436
$516$	15.7651	0.694020
$517$	−6.06591	−0.266778
$518$	−19.0269	−0.835992
$519$	−8.54922	−0.375269
$520$	−63.8569	−2.80031
$521$	−2.81455	−0.123308	−0.0616538	−	0.998098i	$-0.519637\pi$
$521$	−2.81455	−0.123308	−0.0616538	+	0.998098i	$0.519637\pi$
$522$	12.2616	0.536676
$523$	−7.98193	−0.349025	−0.174513	−	0.984655i	$-0.555835\pi$
$523$	−7.98193	−0.349025	−0.174513	+	0.984655i	$0.555835\pi$
$524$	−8.12288	−0.354850
$525$	−2.54801	−0.111204
$526$	−7.73238	−0.337148
$527$	−40.2544	−1.75351
$528$	48.0423	2.09077
$529$	7.55803	0.328610
$530$	0.295015	0.0128146
$531$	17.7082	0.768472
$532$	−4.24149	−0.183892
$533$	60.4599	2.61881
$534$	−33.1202	−1.43325
$535$	−0.659899	−0.0285299
$536$	−106.754	−4.61107
$537$	−6.01685	−0.259646
$538$	50.0672	2.15855
$539$	24.6905	1.06349
$540$	−24.0699	−1.03580
$541$	23.0203	0.989718	0.494859	−	0.868973i	$-0.335220\pi$
$541$	23.0203	0.989718	0.494859	+	0.868973i	$0.335220\pi$
$542$	6.57687	0.282501
$543$	−14.8637	−0.637863
$544$	−108.892	−4.66873
$545$	−10.6396	−0.455751
$546$	11.4355	0.489394
$547$	−16.1124	−0.688915	−0.344458	−	0.938802i	$-0.611937\pi$
$547$	−16.1124	−0.688915	−0.344458	+	0.938802i	$0.611937\pi$
$548$	25.3114	1.08125
$549$	34.4220	1.46909
$550$	−42.2793	−1.80279
$551$	1.80137	0.0767409
$552$	42.6681	1.81608
$553$	5.78558	0.246028
$554$	−46.7096	−1.98450
$555$	−6.99013	−0.296714
$556$	8.38756	0.355712
$557$	26.4079	1.11894	0.559469	−	0.828851i	$-0.311005\pi$
$557$	26.4079	1.11894	0.559469	+	0.828851i	$0.311005\pi$
$558$	−55.4760	−2.34848
$559$	23.1867	0.980693
$560$	12.7018	0.536749
$561$	14.5934	0.616133
$562$	−34.3485	−1.44891
$563$	39.7996	1.67735	0.838677	−	0.544629i	$-0.183330\pi$
$563$	39.7996	1.67735	0.838677	+	0.544629i	$0.183330\pi$
$564$	−6.87942	−0.289676
$565$	2.63310	0.110776
$566$	−56.5936	−2.37880
$567$	−2.96215	−0.124398
$568$	−118.204	−4.95974
$569$	10.4109	0.436447	0.218223	−	0.975899i	$-0.429974\pi$
$569$	10.4109	0.436447	0.218223	+	0.975899i	$0.429974\pi$
$570$	−2.12217	−0.0888878
$571$	11.5107	0.481707	0.240854	−	0.970561i	$-0.422573\pi$
$571$	11.5107	0.481707	0.240854	+	0.970561i	$0.422573\pi$
$572$	139.328	5.82559
$573$	4.92398	0.205702
$574$	−20.6079	−0.860157
$575$	−21.9128	−0.913828
$576$	−76.8518	−3.20216
$577$	−35.3312	−1.47086	−0.735429	−	0.677602i	$-0.763019\pi$
$577$	−35.3312	−1.47086	−0.735429	+	0.677602i	$0.763019\pi$
$578$	−14.0928	−0.586184
$579$	−16.6283	−0.691047
$580$	−10.6371	−0.441680
$581$	3.66868	0.152202
$582$	−9.24718	−0.383308
$583$	−0.410740	−0.0170111
$584$	141.062	5.83719
$585$	−15.6000	−0.644979
$586$	83.9789	3.46914
$587$	0.728241	0.0300577	0.0150289	−	0.999887i	$-0.495216\pi$
$587$	0.728241	0.0300577	0.0150289	+	0.999887i	$0.495216\pi$
$588$	28.0017	1.15477
$589$	−8.15005	−0.335817
$590$	−20.9215	−0.861325
$591$	−21.2828	−0.875459
$592$	−133.332	−5.47990
$593$	−30.6506	−1.25867	−0.629334	−	0.777135i	$-0.716672\pi$
$593$	−30.6506	−1.25867	−0.629334	+	0.777135i	$0.716672\pi$
$594$	45.6395	1.87261
$595$	3.85831	0.158175
$596$	16.7700	0.686925
$597$	−16.2650	−0.665681
$598$	98.3450	4.02163
$599$	24.8892	1.01695	0.508473	−	0.861078i	$-0.330210\pi$
$599$	24.8892	1.01695	0.508473	+	0.861078i	$0.330210\pi$
$600$	−30.5968	−1.24911
$601$	43.2468	1.76407	0.882037	−	0.471179i	$-0.156171\pi$
$601$	43.2468	1.76407	0.882037	+	0.471179i	$0.156171\pi$
$602$	−7.90324	−0.322112
$603$	−26.0795	−1.06204
$604$	−104.589	−4.25567
$605$	−4.18776	−0.170257
$606$	−40.2205	−1.63385
$607$	−41.7585	−1.69492	−0.847462	−	0.530856i	$-0.821871\pi$
$607$	−41.7585	−1.69492	−0.847462	+	0.530856i	$0.821871\pi$
$608$	−22.0468	−0.894115
$609$	1.21552	0.0492554
$610$	−40.6681	−1.64660
$611$	−10.1180	−0.409330
$612$	−61.4557	−2.48420
$613$	38.7321	1.56437	0.782187	−	0.623044i	$-0.214104\pi$
$613$	38.7321	1.56437	0.782187	+	0.623044i	$0.214104\pi$
$614$	−53.9287	−2.17639
$615$	−7.57097	−0.305291
$616$	−30.3038	−1.22098
$617$	−23.8056	−0.958376	−0.479188	−	0.877712i	$-0.659069\pi$
$617$	−23.8056	−0.958376	−0.479188	+	0.877712i	$0.659069\pi$
$618$	−6.60939	−0.265869
$619$	23.1020	0.928548	0.464274	−	0.885692i	$-0.346315\pi$
$619$	23.1020	0.928548	0.464274	+	0.885692i	$0.346315\pi$
$620$	48.1260	1.93279
$621$	23.6544	0.949219
$622$	40.8399	1.63753
$623$	12.1915	0.488444
$624$	80.1349	3.20796
$625$	10.5335	0.421342
$626$	32.9661	1.31759
$627$	2.95463	0.117997
$628$	−0.0906564	−0.00361758
$629$	−40.5010	−1.61488
$630$	5.31728	0.211846
$631$	7.46573	0.297206	0.148603	−	0.988897i	$-0.452522\pi$
$631$	7.46573	0.297206	0.148603	+	0.988897i	$0.452522\pi$
$632$	69.4741	2.76353
$633$	1.75048	0.0695754
$634$	−77.2749	−3.06898
$635$	14.1967	0.563378
$636$	−0.465825	−0.0184712
$637$	41.1839	1.63176
$638$	20.1692	0.798506
$639$	−28.8768	−1.14235
$640$	43.6836	1.72675
$641$	14.0511	0.554985	0.277493	−	0.960728i	$-0.410497\pi$
$641$	14.0511	0.554985	0.277493	+	0.960728i	$0.410497\pi$
$642$	1.41906	0.0560057
$643$	−17.2338	−0.679636	−0.339818	−	0.940491i	$-0.610365\pi$
$643$	−17.2338	−0.679636	−0.339818	+	0.940491i	$0.610365\pi$
$644$	−24.6136	−0.969912
$645$	−2.90351	−0.114326
$646$	−12.2959	−0.483776
$647$	43.2827	1.70162	0.850809	−	0.525475i	$-0.176112\pi$
$647$	43.2827	1.70162	0.850809	+	0.525475i	$0.176112\pi$
$648$	−35.5698	−1.39732
$649$	29.1284	1.14339
$650$	−70.5221	−2.76611
$651$	−5.49946	−0.215541
$652$	−41.2816	−1.61671
$653$	6.07160	0.237600	0.118800	−	0.992918i	$-0.462095\pi$
$653$	6.07160	0.237600	0.118800	+	0.992918i	$0.462095\pi$
$654$	22.8796	0.894662
$655$	1.49602	0.0584542
$656$	−144.411	−5.63830
$657$	34.4608	1.34444
$658$	3.44874	0.134446
$659$	1.38048	0.0537759	0.0268879	−	0.999638i	$-0.491440\pi$
$659$	1.38048	0.0537759	0.0268879	+	0.999638i	$0.491440\pi$
$660$	−17.4471	−0.679126
$661$	5.64104	0.219411	0.109706	−	0.993964i	$-0.465009\pi$
$661$	5.64104	0.219411	0.109706	+	0.993964i	$0.465009\pi$
$662$	78.1014	3.03550
$663$	24.3419	0.945359
$664$	44.0539	1.70962
$665$	0.781169	0.0302924
$666$	−55.8159	−2.16282
$667$	10.4534	0.404759
$668$	−133.395	−5.16119
$669$	4.18578	0.161832
$670$	30.8119	1.19037
$671$	56.6210	2.18583
$672$	−14.8766	−0.573879
$673$	−40.0651	−1.54440	−0.772198	−	0.635382i	$-0.780843\pi$
$673$	−40.0651	−1.54440	−0.772198	+	0.635382i	$0.780843\pi$
$674$	−72.7849	−2.80357
$675$	−16.9623	−0.652880
$676$	160.556	6.17522
$677$	13.5849	0.522112	0.261056	−	0.965324i	$-0.415929\pi$
$677$	13.5849	0.522112	0.261056	+	0.965324i	$0.415929\pi$
$678$	−5.66227	−0.217458
$679$	3.40388	0.130629
$680$	46.3311	1.77672
$681$	−7.74403	−0.296752
$682$	−91.2528	−3.49425
$683$	−30.6600	−1.17317	−0.586585	−	0.809888i	$-0.699528\pi$
$683$	−30.6600	−1.17317	−0.586585	+	0.809888i	$0.699528\pi$
$684$	−12.4425	−0.475753
$685$	−4.66168	−0.178114
$686$	−29.5100	−1.12670
$687$	−0.116878	−0.00445916
$688$	−55.3824	−2.11143
$689$	−0.685118	−0.0261009
$690$	−12.3151	−0.468826
$691$	−3.12360	−0.118828	−0.0594138	−	0.998233i	$-0.518923\pi$
$691$	−3.12360	−0.118828	−0.0594138	+	0.998233i	$0.518923\pi$
$692$	59.2208	2.25124
$693$	−7.40309	−0.281220
$694$	−41.5502	−1.57722
$695$	−1.54476	−0.0585962
$696$	14.5961	0.553265
$697$	−43.8664	−1.66156
$698$	39.5572	1.49726
$699$	−9.64173	−0.364684
$700$	17.6502	0.667113
$701$	−9.69683	−0.366244	−0.183122	−	0.983090i	$-0.558620\pi$
$701$	−9.69683	−0.366244	−0.183122	+	0.983090i	$0.558620\pi$
$702$	76.1271	2.87323
$703$	−8.19998	−0.309268
$704$	−126.414	−4.76441
$705$	1.26700	0.0477182
$706$	44.6139	1.67907
$707$	14.8052	0.556805
$708$	33.0348	1.24153
$709$	26.1289	0.981291	0.490646	−	0.871359i	$-0.336761\pi$
$709$	26.1289	0.981291	0.490646	+	0.871359i	$0.336761\pi$
$710$	34.1167	1.28038
$711$	16.9722	0.636507
$712$	146.398	5.48649
$713$	−47.2952	−1.77122
$714$	−8.29698	−0.310507
$715$	−25.6605	−0.959647
$716$	41.6790	1.55762
$717$	15.8779	0.592972
$718$	−30.7058	−1.14593
$719$	29.9678	1.11761	0.558806	−	0.829298i	$-0.311260\pi$
$719$	29.9678	1.11761	0.558806	+	0.829298i	$0.311260\pi$
$720$	37.2612	1.38864
$721$	2.43291	0.0906064
$722$	49.6360	1.84726
$723$	8.85330	0.329258
$724$	102.961	3.82653
$725$	−7.49605	−0.278396
$726$	9.00543	0.334223
$727$	−47.9143	−1.77704	−0.888522	−	0.458833i	$-0.848268\pi$
$727$	−47.9143	−1.77704	−0.888522	+	0.458833i	$0.848268\pi$
$728$	−50.5470	−1.87340
$729$	1.55216	0.0574876
$730$	−40.7139	−1.50689
$731$	−16.8230	−0.622222
$732$	64.2145	2.37344
$733$	−14.4450	−0.533537	−0.266769	−	0.963761i	$-0.585956\pi$
$733$	−14.4450	−0.533537	−0.266769	+	0.963761i	$0.585956\pi$
$734$	−81.4220	−3.00534
$735$	−5.15717	−0.190225
$736$	−127.939	−4.71588
$737$	−42.8984	−1.58018
$738$	−60.4539	−2.22534
$739$	−38.5129	−1.41672	−0.708360	−	0.705851i	$-0.750565\pi$
$739$	−38.5129	−1.41672	−0.708360	+	0.705851i	$0.750565\pi$
$740$	48.4209	1.77999
$741$	4.92834	0.181047
$742$	0.233524	0.00857293
$743$	31.8480	1.16839	0.584196	−	0.811613i	$-0.301410\pi$
$743$	31.8480	1.16839	0.584196	+	0.811613i	$0.301410\pi$
$744$	−66.0382	−2.42108
$745$	−3.08858	−0.113157
$746$	76.1478	2.78797
$747$	10.7622	0.393768
$748$	−101.089	−3.69617
$749$	−0.522354	−0.0190864
$750$	19.9699	0.729199
$751$	−21.3377	−0.778622	−0.389311	−	0.921106i	$-0.627287\pi$
$751$	−21.3377	−0.778622	−0.389311	+	0.921106i	$0.627287\pi$
$752$	24.1672	0.881288
$753$	7.85550	0.286270
$754$	33.6424	1.22518
$755$	19.2625	0.701034
$756$	−19.0530	−0.692949
$757$	30.0001	1.09037	0.545187	−	0.838315i	$-0.316459\pi$
$757$	30.0001	1.09037	0.545187	+	0.838315i	$0.316459\pi$
$758$	35.6833	1.29607
$759$	17.1459	0.622356
$760$	9.38038	0.340262
$761$	27.0162	0.979338	0.489669	−	0.871908i	$-0.337118\pi$
$761$	27.0162	0.979338	0.489669	+	0.871908i	$0.337118\pi$
$762$	−30.5288	−1.10594
$763$	−8.42196	−0.304896
$764$	−34.1086	−1.23400
$765$	11.3185	0.409221
$766$	33.9652	1.22721
$767$	48.5864	1.75435
$768$	−42.0541	−1.51750
$769$	−19.1013	−0.688809	−0.344404	−	0.938821i	$-0.611919\pi$
$769$	−19.1013	−0.688809	−0.344404	+	0.938821i	$0.611919\pi$
$770$	8.74643	0.315199
$771$	−7.76655	−0.279706
$772$	115.185	4.14559
$773$	−42.3484	−1.52317	−0.761583	−	0.648067i	$-0.775578\pi$
$773$	−42.3484	−1.52317	−0.761583	+	0.648067i	$0.775578\pi$
$774$	−23.1844	−0.833346
$775$	33.9149	1.21826
$776$	40.8743	1.46730
$777$	−5.53315	−0.198501
$778$	15.6808	0.562183
$779$	−8.88136	−0.318208
$780$	−29.1018	−1.04201
$781$	−47.4996	−1.69967
$782$	−71.3538	−2.55161
$783$	8.09182	0.289178
$784$	−98.3694	−3.51319
$785$	0.0166965	0.000595923 0
$786$	−3.21706	−0.114749
$787$	−13.2466	−0.472190	−0.236095	−	0.971730i	$-0.575868\pi$
$787$	−13.2466	−0.472190	−0.236095	+	0.971730i	$0.575868\pi$
$788$	147.427	5.25187
$789$	−2.24863	−0.0800535
$790$	−20.0519	−0.713415
$791$	2.08428	0.0741084
$792$	−88.8973	−3.15883
$793$	94.4442	3.35381
$794$	−44.4609	−1.57786
$795$	0.0857925	0.00304275
$796$	112.668	3.99341
$797$	40.6437	1.43967	0.719836	−	0.694144i	$-0.244217\pi$
$797$	40.6437	1.43967	0.719836	+	0.694144i	$0.244217\pi$
$798$	−1.67984	−0.0594656
$799$	7.34106	0.259708
$800$	91.7435	3.24362
$801$	35.7643	1.26367
$802$	95.0625	3.35678
$803$	56.6848	2.00036
$804$	−48.6516	−1.71581
$805$	4.53317	0.159773
$806$	−152.210	−5.36138
$807$	14.5599	0.512533
$808$	177.782	6.25436
$809$	−7.82407	−0.275080	−0.137540	−	0.990496i	$-0.543920\pi$
$809$	−7.82407	−0.275080	−0.137540	+	0.990496i	$0.543920\pi$
$810$	10.2663	0.360722
$811$	17.7878	0.624612	0.312306	−	0.949981i	$-0.398899\pi$
$811$	17.7878	0.624612	0.312306	+	0.949981i	$0.398899\pi$
$812$	−8.41995	−0.295482
$813$	1.91260	0.0670779
$814$	−91.8119	−3.21801
$815$	7.60297	0.266320
$816$	−58.1416	−2.03536
$817$	−3.40605	−0.119163
$818$	−17.8556	−0.624308
$819$	−12.3484	−0.431488
$820$	52.4444	1.83144
$821$	2.07091	0.0722754	0.0361377	−	0.999347i	$-0.488495\pi$
$821$	2.07091	0.0722754	0.0361377	+	0.999347i	$0.488495\pi$
$822$	10.0246	0.349646
$823$	−12.2346	−0.426470	−0.213235	−	0.977001i	$-0.568400\pi$
$823$	−12.2346	−0.426470	−0.213235	+	0.977001i	$0.568400\pi$
$824$	29.2147	1.01774
$825$	−12.2951	−0.428061
$826$	−16.5608	−0.576223
$827$	−31.4470	−1.09352	−0.546759	−	0.837290i	$-0.684139\pi$
$827$	−31.4470	−1.09352	−0.546759	+	0.837290i	$0.684139\pi$
$828$	−72.2048	−2.50929
$829$	24.4672	0.849782	0.424891	−	0.905245i	$-0.360312\pi$
$829$	24.4672	0.849782	0.424891	+	0.905245i	$0.360312\pi$
$830$	−12.7150	−0.441346
$831$	−13.5835	−0.471206
$832$	−210.860	−7.31024
$833$	−29.8808	−1.03531
$834$	3.32188	0.115027
$835$	24.5677	0.850200
$836$	−20.4668	−0.707860
$837$	−36.6104	−1.26544
$838$	10.8051	0.373257
$839$	−3.29409	−0.113724	−0.0568622	−	0.998382i	$-0.518110\pi$
$839$	−3.29409	−0.113724	−0.0568622	+	0.998382i	$0.518110\pi$
$840$	6.32965	0.218394
$841$	−25.4240	−0.876691
$842$	−51.8608	−1.78724
$843$	−9.98881	−0.344033
$844$	−12.1257	−0.417382
$845$	−29.5701	−1.01724
$846$	10.1170	0.347829
$847$	−3.31490	−0.113901
$848$	1.63643	0.0561953
$849$	−16.4578	−0.564831
$850$	51.1671	1.75502
$851$	−47.5850	−1.63119
$852$	−53.8699	−1.84555
$853$	26.1441	0.895156	0.447578	−	0.894245i	$-0.352287\pi$
$853$	26.1441	0.895156	0.447578	+	0.894245i	$0.352287\pi$
$854$	−32.1915	−1.10157
$855$	2.29158	0.0783705
$856$	−6.27250	−0.214390
$857$	−46.8536	−1.60049	−0.800245	−	0.599673i	$-0.795297\pi$
$857$	−46.8536	−1.60049	−0.800245	+	0.599673i	$0.795297\pi$
$858$	55.1807	1.88384
$859$	−31.6175	−1.07877	−0.539387	−	0.842058i	$-0.681344\pi$
$859$	−31.6175	−1.07877	−0.539387	+	0.842058i	$0.681344\pi$
$860$	20.1127	0.685838
$861$	−5.99293	−0.204238
$862$	−11.3202	−0.385568
$863$	18.3228	0.623714	0.311857	−	0.950129i	$-0.399049\pi$
$863$	18.3228	0.623714	0.311857	+	0.950129i	$0.399049\pi$
$864$	−99.0350	−3.36924
$865$	−10.9069	−0.370845
$866$	74.3223	2.52557
$867$	−4.09830	−0.139185
$868$	38.0949	1.29303
$869$	27.9177	0.947042
$870$	−4.21280	−0.142827
$871$	−71.5549	−2.42454
$872$	−101.132	−3.42476
$873$	9.98539	0.337954
$874$	−14.4466	−0.488662
$875$	−7.35092	−0.248507
$876$	64.2869	2.17205
$877$	−27.3909	−0.924926	−0.462463	−	0.886639i	$-0.653034\pi$
$877$	−27.3909	−0.924926	−0.462463	+	0.886639i	$0.653034\pi$
$878$	−75.2913	−2.54096
$879$	24.4217	0.823724
$880$	61.2911	2.06612
$881$	34.2769	1.15482	0.577409	−	0.816455i	$-0.304064\pi$
$881$	34.2769	1.15482	0.577409	+	0.816455i	$0.304064\pi$
$882$	−41.1798	−1.38660
$883$	26.5819	0.894553	0.447276	−	0.894396i	$-0.352394\pi$
$883$	26.5819	0.894553	0.447276	+	0.894396i	$0.352394\pi$
$884$	−168.617	−5.67120
$885$	−6.08413	−0.204516
$886$	−48.6482	−1.63437
$887$	−33.2913	−1.11781	−0.558907	−	0.829231i	$-0.688779\pi$
$887$	−33.2913	−1.11781	−0.558907	+	0.829231i	$0.688779\pi$
$888$	−66.4428	−2.22967
$889$	11.2376	0.376898
$890$	−42.2540	−1.41636
$891$	−14.2935	−0.478850
$892$	−28.9951	−0.970827
$893$	1.48630	0.0497371
$894$	6.64173	0.222133
$895$	−7.67615	−0.256585
$896$	34.5785	1.15519
$897$	28.5995	0.954909
$898$	16.3467	0.545497
$899$	−16.1790	−0.539599
$900$	51.7773	1.72591
$901$	0.497084	0.0165603
$902$	−99.4410	−3.31102
$903$	−2.29832	−0.0764833
$904$	25.0283	0.832429
$905$	−18.9627	−0.630343
$906$	−41.4224	−1.37617
$907$	−21.7900	−0.723524	−0.361762	−	0.932271i	$-0.617825\pi$
$907$	−21.7900	−0.723524	−0.361762	+	0.932271i	$0.617825\pi$
$908$	53.6432	1.78021
$909$	43.4314	1.44053
$910$	14.5891	0.483624
$911$	−27.7332	−0.918842	−0.459421	−	0.888219i	$-0.651943\pi$
$911$	−27.7332	−0.918842	−0.459421	+	0.888219i	$0.651943\pi$
$912$	−11.7716	−0.389795
$913$	17.7028	0.585876
$914$	26.6292	0.880815
$915$	−11.8266	−0.390975
$916$	0.809616	0.0267505
$917$	1.18420	0.0391056
$918$	−55.2337	−1.82298
$919$	−28.3629	−0.935605	−0.467803	−	0.883833i	$-0.654954\pi$
$919$	−28.3629	−0.935605	−0.467803	+	0.883833i	$0.654954\pi$
$920$	54.4349	1.79467
$921$	−15.6829	−0.516768
$922$	13.3943	0.441119
$923$	−79.2297	−2.60788
$924$	−13.8105	−0.454333
$925$	34.1227	1.12195
$926$	−33.3150	−1.09480
$927$	7.13703	0.234411
$928$	−43.7659	−1.43669
$929$	50.4294	1.65454	0.827268	−	0.561807i	$-0.189894\pi$
$929$	50.4294	1.65454	0.827268	+	0.561807i	$0.189894\pi$
$930$	19.0602	0.625010
$931$	−6.04978	−0.198273
$932$	66.7886	2.18773
$933$	11.8765	0.388820
$934$	−97.8840	−3.20286
$935$	18.6179	0.608869
$936$	−148.281	−4.84673
$937$	−6.22652	−0.203411	−0.101706	−	0.994815i	$-0.532430\pi$
$937$	−6.22652	−0.203411	−0.101706	+	0.994815i	$0.532430\pi$
$938$	24.3896	0.796350
$939$	9.58679	0.312853
$940$	−8.77659	−0.286261
$941$	−38.6183	−1.25892	−0.629460	−	0.777033i	$-0.716724\pi$
$941$	−38.6183	−1.25892	−0.629460	+	0.777033i	$0.716724\pi$
$942$	−0.0359043	−0.00116983
$943$	−51.5391	−1.67834
$944$	−116.051	−3.77713
$945$	3.50904	0.114149
$946$	−38.1362	−1.23991
$947$	36.7639	1.19467	0.597334	−	0.801993i	$-0.296227\pi$
$947$	36.7639	1.19467	0.597334	+	0.801993i	$0.296227\pi$
$948$	31.6618	1.02833
$949$	94.5507	3.06924
$950$	10.3595	0.336106
$951$	−22.4721	−0.728708
$952$	36.6742	1.18862
$953$	−2.18751	−0.0708605	−0.0354302	−	0.999372i	$-0.511280\pi$
$953$	−2.18751	−0.0708605	−0.0354302	+	0.999372i	$0.511280\pi$
$954$	0.685050	0.0221793
$955$	6.28189	0.203277
$956$	−109.987	−3.55723
$957$	5.86535	0.189600
$958$	17.1767	0.554953
$959$	−3.69003	−0.119157
$960$	26.4045	0.852201
$961$	42.1996	1.36128
$962$	−153.143	−4.93753
$963$	−1.53234	−0.0493791
$964$	−61.3271	−1.97521
$965$	−21.2139	−0.682900
$966$	−9.74819	−0.313643
$967$	−43.3573	−1.39428	−0.697138	−	0.716937i	$-0.745543\pi$
$967$	−43.3573	−1.39428	−0.697138	+	0.716937i	$0.745543\pi$
$968$	−39.8057	−1.27940
$969$	−3.57574	−0.114869
$970$	−11.7973	−0.378789
$971$	8.17945	0.262491	0.131246	−	0.991350i	$-0.458102\pi$
$971$	8.17945	0.262491	0.131246	+	0.991350i	$0.458102\pi$
$972$	−87.1551	−2.79550
$973$	−1.22278	−0.0392006
$974$	86.5312	2.77264
$975$	−20.5084	−0.656793
$976$	−225.584	−7.22076
$977$	9.87257	0.315851	0.157926	−	0.987451i	$-0.449519\pi$
$977$	9.87257	0.315851	0.157926	+	0.987451i	$0.449519\pi$
$978$	−16.3495	−0.522800
$979$	58.8289	1.88018
$980$	35.7239	1.14116
$981$	−24.7061	−0.788805
$982$	16.5248	0.527327
$983$	−24.0265	−0.766325	−0.383162	−	0.923681i	$-0.625165\pi$
$983$	−24.0265	−0.766325	−0.383162	+	0.923681i	$0.625165\pi$
$984$	−71.9639	−2.29412
$985$	−27.1521	−0.865138
$986$	−24.4091	−0.777344
$987$	1.00292	0.0319233
$988$	−34.1388	−1.08610
$989$	−19.7655	−0.628507
$990$	25.6579	0.815463
$991$	1.09816	0.0348841	0.0174421	−	0.999848i	$-0.494448\pi$
$991$	1.09816	0.0348841	0.0174421	+	0.999848i	$0.494448\pi$
$992$	198.013	6.28692
$993$	22.7125	0.720759
$994$	27.0056	0.856567
$995$	−20.7504	−0.657833
$996$	20.0769	0.636162
$997$	−6.39804	−0.202628	−0.101314	−	0.994855i	$-0.532305\pi$
$997$	−6.39804	−0.202628	−0.101314	+	0.994855i	$0.532305\pi$
$998$	−41.4766	−1.31292
$999$	−36.8347	−1.16540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.2	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +O(q^{10})\)	\(q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +2.79236 q^{10} -3.88772 q^{11} -4.40911 q^{12} -6.48475 q^{13} +2.21034 q^{14} +0.812040 q^{15} +15.4891 q^{16} +4.70499 q^{17} +6.48411 q^{18} +0.952589 q^{19} -5.62503 q^{20} +0.642784 q^{21} +10.6658 q^{22} +5.52793 q^{23} +7.71864 q^{24} -3.96402 q^{25} +17.7906 q^{26} +4.27907 q^{27} -4.45259 q^{28} +1.89102 q^{29} -2.22779 q^{30} -8.55568 q^{31} -23.1441 q^{32} +3.10168 q^{33} -12.9079 q^{34} +0.820048 q^{35} -13.0618 q^{36} -8.60810 q^{37} -2.61338 q^{38} +5.17363 q^{39} +9.84724 q^{40} -9.32339 q^{41} -1.76344 q^{42} -3.57557 q^{43} -21.4855 q^{44} +2.40564 q^{45} -15.1656 q^{46} +1.56027 q^{47} -12.3574 q^{48} -6.35088 q^{49} +10.8751 q^{50} -3.75371 q^{51} -35.8379 q^{52} +0.105651 q^{53} -11.7394 q^{54} +3.95705 q^{55} +7.79475 q^{56} -0.759989 q^{57} -5.18792 q^{58} -7.49240 q^{59} +4.48773 q^{60} -14.5640 q^{61} +23.4720 q^{62} +1.90422 q^{63} +32.5162 q^{64} +6.60038 q^{65} -8.50929 q^{66} +11.0343 q^{67} +26.0021 q^{68} -4.41026 q^{69} -2.24976 q^{70} +12.2178 q^{71} +22.8661 q^{72} -14.5805 q^{73} +23.6158 q^{74} +3.16255 q^{75} +5.26447 q^{76} +3.13227 q^{77} -14.1936 q^{78} -7.18098 q^{79} -15.7653 q^{80} +3.67657 q^{81} +25.5782 q^{82} -4.55351 q^{83} +3.55234 q^{84} -4.78888 q^{85} +9.80938 q^{86} -1.50869 q^{87} +37.6127 q^{88} -15.1320 q^{89} -6.59973 q^{90} +5.22465 q^{91} +30.5501 q^{92} +6.82584 q^{93} -4.28052 q^{94} -0.969575 q^{95} +18.4647 q^{96} -4.22485 q^{97} +17.4233 q^{98} +9.18861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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