LMFDB - Embedded newform 6001.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69808 q^{2} +2.45523 q^{3} +5.27961 q^{4} -1.37053 q^{5} -6.62441 q^{6} +5.08280 q^{7} -8.84865 q^{8} +3.02818 q^{9} +O(q^{10})$	\(q-2.69808 q^{2} +2.45523 q^{3} +5.27961 q^{4} -1.37053 q^{5} -6.62441 q^{6} +5.08280 q^{7} -8.84865 q^{8} +3.02818 q^{9} +3.69780 q^{10} -4.31476 q^{11} +12.9627 q^{12} +0.343099 q^{13} -13.7138 q^{14} -3.36498 q^{15} +13.3151 q^{16} -1.00000 q^{17} -8.17025 q^{18} -0.907977 q^{19} -7.23588 q^{20} +12.4795 q^{21} +11.6415 q^{22} +7.15622 q^{23} -21.7255 q^{24} -3.12164 q^{25} -0.925708 q^{26} +0.0691789 q^{27} +26.8352 q^{28} -8.10141 q^{29} +9.07897 q^{30} -5.39938 q^{31} -18.2278 q^{32} -10.5937 q^{33} +2.69808 q^{34} -6.96614 q^{35} +15.9876 q^{36} +0.457896 q^{37} +2.44979 q^{38} +0.842389 q^{39} +12.1274 q^{40} -9.21935 q^{41} -33.6705 q^{42} -1.61661 q^{43} -22.7802 q^{44} -4.15021 q^{45} -19.3080 q^{46} -10.7325 q^{47} +32.6917 q^{48} +18.8349 q^{49} +8.42242 q^{50} -2.45523 q^{51} +1.81143 q^{52} +4.21444 q^{53} -0.186650 q^{54} +5.91351 q^{55} -44.9759 q^{56} -2.22930 q^{57} +21.8582 q^{58} -6.62963 q^{59} -17.7658 q^{60} +10.6612 q^{61} +14.5679 q^{62} +15.3916 q^{63} +22.5499 q^{64} -0.470229 q^{65} +28.5827 q^{66} -15.9201 q^{67} -5.27961 q^{68} +17.5702 q^{69} +18.7952 q^{70} +1.41127 q^{71} -26.7953 q^{72} -12.9475 q^{73} -1.23544 q^{74} -7.66436 q^{75} -4.79377 q^{76} -21.9310 q^{77} -2.27283 q^{78} -4.81875 q^{79} -18.2488 q^{80} -8.91468 q^{81} +24.8745 q^{82} +15.4797 q^{83} +65.8868 q^{84} +1.37053 q^{85} +4.36174 q^{86} -19.8909 q^{87} +38.1797 q^{88} +8.21465 q^{89} +11.1976 q^{90} +1.74390 q^{91} +37.7821 q^{92} -13.2567 q^{93} +28.9572 q^{94} +1.24441 q^{95} -44.7536 q^{96} -19.4192 q^{97} -50.8179 q^{98} -13.0658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.69808	−1.90783	−0.953914	−	0.300081i	$-0.902986\pi$
$2$	−2.69808	−1.90783	−0.953914	+	0.300081i	$0.902986\pi$
$3$	2.45523	1.41753	0.708765	−	0.705445i	$-0.249253\pi$
$3$	2.45523	1.41753	0.708765	+	0.705445i	$0.249253\pi$
$4$	5.27961	2.63981
$5$	−1.37053	−0.612921	−0.306460	−	0.951883i	$-0.599145\pi$
$5$	−1.37053	−0.612921	−0.306460	+	0.951883i	$0.599145\pi$
$6$	−6.62441	−2.70440
$7$	5.08280	1.92112	0.960559	−	0.278076i	$-0.0896968\pi$
$7$	5.08280	1.92112	0.960559	+	0.278076i	$0.0896968\pi$
$8$	−8.84865	−3.12847
$9$	3.02818	1.00939
$10$	3.69780	1.16935
$11$	−4.31476	−1.30095	−0.650474	−	0.759529i	$-0.725430\pi$
$11$	−4.31476	−1.30095	−0.650474	+	0.759529i	$0.725430\pi$
$12$	12.9627	3.74201
$13$	0.343099	0.0951586	0.0475793	−	0.998867i	$-0.484849\pi$
$13$	0.343099	0.0951586	0.0475793	+	0.998867i	$0.484849\pi$
$14$	−13.7138	−3.66516
$15$	−3.36498	−0.868834
$16$	13.3151	3.32877
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.17025	−1.92575
$19$	−0.907977	−0.208304	−0.104152	−	0.994561i	$-0.533213\pi$
$19$	−0.907977	−0.208304	−0.104152	+	0.994561i	$0.533213\pi$
$20$	−7.23588	−1.61799
$21$	12.4795	2.72324
$22$	11.6415	2.48198
$23$	7.15622	1.49217	0.746087	−	0.665848i	$-0.231930\pi$
$23$	7.15622	1.49217	0.746087	+	0.665848i	$0.231930\pi$
$24$	−21.7255	−4.43470
$25$	−3.12164	−0.624328
$26$	−0.925708	−0.181546
$27$	0.0691789	0.0133135
$28$	26.8352	5.07138
$29$	−8.10141	−1.50439	−0.752197	−	0.658938i	$-0.771006\pi$
$29$	−8.10141	−1.50439	−0.752197	+	0.658938i	$0.771006\pi$
$30$	9.07897	1.65759
$31$	−5.39938	−0.969757	−0.484878	−	0.874582i	$-0.661136\pi$
$31$	−5.39938	−0.969757	−0.484878	+	0.874582i	$0.661136\pi$
$32$	−18.2278	−3.22226
$33$	−10.5937	−1.84413
$34$	2.69808	0.462716
$35$	−6.96614	−1.17749
$36$	15.9876	2.66460
$37$	0.457896	0.0752777	0.0376389	−	0.999291i	$-0.488016\pi$
$37$	0.457896	0.0752777	0.0376389	+	0.999291i	$0.488016\pi$
$38$	2.44979	0.397408
$39$	0.842389	0.134890
$40$	12.1274	1.91750
$41$	−9.21935	−1.43982	−0.719910	−	0.694067i	$-0.755817\pi$
$41$	−9.21935	−1.43982	−0.719910	+	0.694067i	$0.755817\pi$
$42$	−33.6705	−5.19548
$43$	−1.61661	−0.246531	−0.123265	−	0.992374i	$-0.539337\pi$
$43$	−1.61661	−0.246531	−0.123265	+	0.992374i	$0.539337\pi$
$44$	−22.7802	−3.43425
$45$	−4.15021	−0.618677
$46$	−19.3080	−2.84681
$47$	−10.7325	−1.56550	−0.782751	−	0.622335i	$-0.786184\pi$
$47$	−10.7325	−1.56550	−0.782751	+	0.622335i	$0.786184\pi$
$48$	32.6917	4.71864
$49$	18.8349	2.69069
$50$	8.42242	1.19111
$51$	−2.45523	−0.343802
$52$	1.81143	0.251200
$53$	4.21444	0.578899	0.289449	−	0.957193i	$-0.406528\pi$
$53$	4.21444	0.578899	0.289449	+	0.957193i	$0.406528\pi$
$54$	−0.186650	−0.0253998
$55$	5.91351	0.797378
$56$	−44.9759	−6.01016
$57$	−2.22930	−0.295277
$58$	21.8582	2.87013
$59$	−6.62963	−0.863104	−0.431552	−	0.902088i	$-0.642034\pi$
$59$	−6.62963	−0.863104	−0.431552	+	0.902088i	$0.642034\pi$
$60$	−17.7658	−2.29355
$61$	10.6612	1.36502	0.682510	−	0.730876i	$-0.260888\pi$
$61$	10.6612	1.36502	0.682510	+	0.730876i	$0.260888\pi$
$62$	14.5679	1.85013
$63$	15.3916	1.93916
$64$	22.5499	2.81874
$65$	−0.470229	−0.0583247
$66$	28.5827	3.51829
$67$	−15.9201	−1.94495	−0.972477	−	0.232998i	$-0.925146\pi$
$67$	−15.9201	−1.94495	−0.972477	+	0.232998i	$0.925146\pi$
$68$	−5.27961	−0.640247
$69$	17.5702	2.11520
$70$	18.7952	2.24645
$71$	1.41127	0.167487	0.0837436	−	0.996487i	$-0.473312\pi$
$71$	1.41127	0.167487	0.0837436	+	0.996487i	$0.473312\pi$
$72$	−26.7953	−3.15785
$73$	−12.9475	−1.51539	−0.757696	−	0.652607i	$-0.773675\pi$
$73$	−12.9475	−1.51539	−0.757696	+	0.652607i	$0.773675\pi$
$74$	−1.23544	−0.143617
$75$	−7.66436	−0.885004
$76$	−4.79377	−0.549883
$77$	−21.9310	−2.49927
$78$	−2.27283	−0.257347
$79$	−4.81875	−0.542151	−0.271076	−	0.962558i	$-0.587379\pi$
$79$	−4.81875	−0.542151	−0.271076	+	0.962558i	$0.587379\pi$
$80$	−18.2488	−2.04027
$81$	−8.91468	−0.990520
$82$	24.8745	2.74693
$83$	15.4797	1.69912	0.849560	−	0.527492i	$-0.176868\pi$
$83$	15.4797	1.69912	0.849560	+	0.527492i	$0.176868\pi$
$84$	65.8868	7.18883
$85$	1.37053	0.148655
$86$	4.36174	0.470338
$87$	−19.8909	−2.13252
$88$	38.1797	4.06997
$89$	8.21465	0.870751	0.435375	−	0.900249i	$-0.356616\pi$
$89$	8.21465	0.870751	0.435375	+	0.900249i	$0.356616\pi$
$90$	11.1976	1.18033
$91$	1.74390	0.182811
$92$	37.7821	3.93905
$93$	−13.2567	−1.37466
$94$	28.9572	2.98671
$95$	1.24441	0.127674
$96$	−44.7536	−4.56765
$97$	−19.4192	−1.97172	−0.985860	−	0.167572i	$-0.946407\pi$
$97$	−19.4192	−1.97172	−0.985860	+	0.167572i	$0.946407\pi$
$98$	−50.8179	−5.13338
$99$	−13.0658	−1.31317
$100$	−16.4811	−1.64811
$101$	4.81132	0.478744	0.239372	−	0.970928i	$-0.423058\pi$
$101$	4.81132	0.478744	0.239372	+	0.970928i	$0.423058\pi$
$102$	6.62441	0.655914
$103$	−0.993832	−0.0979252	−0.0489626	−	0.998801i	$-0.515592\pi$
$103$	−0.993832	−0.0979252	−0.0489626	+	0.998801i	$0.515592\pi$
$104$	−3.03596	−0.297701
$105$	−17.1035	−1.66913
$106$	−11.3709	−1.10444
$107$	−14.2568	−1.37826	−0.689128	−	0.724640i	$-0.742006\pi$
$107$	−14.2568	−1.37826	−0.689128	+	0.724640i	$0.742006\pi$
$108$	0.365238	0.0351450
$109$	6.43752	0.616603	0.308302	−	0.951289i	$-0.400239\pi$
$109$	6.43752	0.616603	0.308302	+	0.951289i	$0.400239\pi$
$110$	−15.9551	−1.52126
$111$	1.12424	0.106708
$112$	67.6780	6.39497
$113$	2.01402	0.189463	0.0947315	−	0.995503i	$-0.469801\pi$
$113$	2.01402	0.189463	0.0947315	+	0.995503i	$0.469801\pi$
$114$	6.01481	0.563338
$115$	−9.80783	−0.914585
$116$	−42.7723	−3.97131
$117$	1.03896	0.0960523
$118$	17.8872	1.64665
$119$	−5.08280	−0.465940
$120$	29.7755	2.71812
$121$	7.61712	0.692465
$122$	−28.7646	−2.60422
$123$	−22.6357	−2.04099
$124$	−28.5066	−2.55997
$125$	11.1310	0.995585
$126$	−41.5277	−3.69959
$127$	−17.2758	−1.53298	−0.766490	−	0.642256i	$-0.777999\pi$
$127$	−17.2758	−1.53298	−0.766490	+	0.642256i	$0.777999\pi$
$128$	−24.3857	−2.15541
$129$	−3.96916	−0.349465
$130$	1.26871	0.111273
$131$	15.9559	1.39408	0.697038	−	0.717034i	$-0.254501\pi$
$131$	15.9559	1.39408	0.697038	+	0.717034i	$0.254501\pi$
$132$	−55.9308	−4.86815
$133$	−4.61506	−0.400177
$134$	42.9537	3.71064
$135$	−0.0948120	−0.00816012
$136$	8.84865	0.758765
$137$	−2.15130	−0.183798	−0.0918988	−	0.995768i	$-0.529294\pi$
$137$	−2.15130	−0.183798	−0.0918988	+	0.995768i	$0.529294\pi$
$138$	−47.4057	−4.03544
$139$	5.71741	0.484944	0.242472	−	0.970158i	$-0.422042\pi$
$139$	5.71741	0.484944	0.242472	+	0.970158i	$0.422042\pi$
$140$	−36.7786	−3.10835
$141$	−26.3509	−2.21915
$142$	−3.80772	−0.319537
$143$	−1.48039	−0.123796
$144$	40.3204	3.36004
$145$	11.1033	0.922075
$146$	34.9334	2.89111
$147$	46.2440	3.81414
$148$	2.41752	0.198719
$149$	−10.7203	−0.878239	−0.439119	−	0.898429i	$-0.644709\pi$
$149$	−10.7203	−0.878239	−0.439119	+	0.898429i	$0.644709\pi$
$150$	20.6790	1.68843
$151$	13.8338	1.12578	0.562888	−	0.826533i	$-0.309690\pi$
$151$	13.8338	1.12578	0.562888	+	0.826533i	$0.309690\pi$
$152$	8.03436	0.651673
$153$	−3.02818	−0.244814
$154$	59.1716	4.76818
$155$	7.40002	0.594384
$156$	4.44749	0.356084
$157$	10.0129	0.799119	0.399559	−	0.916707i	$-0.369163\pi$
$157$	10.0129	0.799119	0.399559	+	0.916707i	$0.369163\pi$
$158$	13.0013	1.03433
$159$	10.3474	0.820606
$160$	24.9818	1.97499
$161$	36.3736	2.86664
$162$	24.0525	1.88974
$163$	−7.36824	−0.577125	−0.288562	−	0.957461i	$-0.593177\pi$
$163$	−7.36824	−0.577125	−0.288562	+	0.957461i	$0.593177\pi$
$164$	−48.6746	−3.80085
$165$	14.5191	1.13031
$166$	−41.7655	−3.24163
$167$	14.2585	1.10335	0.551677	−	0.834058i	$-0.313988\pi$
$167$	14.2585	1.10335	0.551677	+	0.834058i	$0.313988\pi$
$168$	−110.426	−8.51958
$169$	−12.8823	−0.990945
$170$	−3.69780	−0.283608
$171$	−2.74951	−0.210261
$172$	−8.53508	−0.650793
$173$	−8.39516	−0.638272	−0.319136	−	0.947709i	$-0.603393\pi$
$173$	−8.39516	−0.638272	−0.319136	+	0.947709i	$0.603393\pi$
$174$	53.6671	4.06849
$175$	−15.8667	−1.19941
$176$	−57.4514	−4.33056
$177$	−16.2773	−1.22348
$178$	−22.1637	−1.66124
$179$	−18.6459	−1.39366	−0.696830	−	0.717237i	$-0.745407\pi$
$179$	−18.6459	−1.39366	−0.696830	+	0.717237i	$0.745407\pi$
$180$	−21.9115	−1.63319
$181$	20.1923	1.50088	0.750441	−	0.660937i	$-0.229841\pi$
$181$	20.1923	1.50088	0.750441	+	0.660937i	$0.229841\pi$
$182$	−4.70519	−0.348772
$183$	26.1756	1.93496
$184$	−63.3228	−4.66822
$185$	−0.627562	−0.0461393
$186$	35.7677	2.62261
$187$	4.31476	0.315526
$188$	−56.6637	−4.13262
$189$	0.351623	0.0255768
$190$	−3.35752	−0.243580
$191$	1.68248	0.121740	0.0608698	−	0.998146i	$-0.480613\pi$
$191$	1.68248	0.121740	0.0608698	+	0.998146i	$0.480613\pi$
$192$	55.3653	3.99565
$193$	−19.6139	−1.41184	−0.705919	−	0.708293i	$-0.749466\pi$
$193$	−19.6139	−1.41184	−0.705919	+	0.708293i	$0.749466\pi$
$194$	52.3944	3.76170
$195$	−1.15452	−0.0826770
$196$	99.4408	7.10291
$197$	3.38894	0.241452	0.120726	−	0.992686i	$-0.461478\pi$
$197$	3.38894	0.241452	0.120726	+	0.992686i	$0.461478\pi$
$198$	35.2526	2.50530
$199$	−9.24037	−0.655032	−0.327516	−	0.944846i	$-0.606212\pi$
$199$	−9.24037	−0.655032	−0.327516	+	0.944846i	$0.606212\pi$
$200$	27.6223	1.95319
$201$	−39.0877	−2.75703
$202$	−12.9813	−0.913362
$203$	−41.1779	−2.89012
$204$	−12.9627	−0.907570
$205$	12.6354	0.882496
$206$	2.68143	0.186824
$207$	21.6703	1.50619
$208$	4.56840	0.316761
$209$	3.91770	0.270993
$210$	46.1466	3.18442
$211$	−22.5137	−1.54991	−0.774953	−	0.632019i	$-0.782227\pi$
$211$	−22.5137	−1.54991	−0.774953	+	0.632019i	$0.782227\pi$
$212$	22.2506	1.52818
$213$	3.46500	0.237418
$214$	38.4659	2.62947
$215$	2.21562	0.151104
$216$	−0.612140	−0.0416508
$217$	−27.4440	−1.86302
$218$	−17.3689	−1.17637
$219$	−31.7892	−2.14812
$220$	31.2211	2.10492
$221$	−0.343099	−0.0230794
$222$	−3.03329	−0.203581
$223$	−4.84053	−0.324146	−0.162073	−	0.986779i	$-0.551818\pi$
$223$	−4.84053	−0.324146	−0.162073	+	0.986779i	$0.551818\pi$
$224$	−92.6484	−6.19033
$225$	−9.45288	−0.630192
$226$	−5.43398	−0.361463
$227$	−2.30711	−0.153128	−0.0765640	−	0.997065i	$-0.524395\pi$
$227$	−2.30711	−0.153128	−0.0765640	+	0.997065i	$0.524395\pi$
$228$	−11.7698	−0.779475
$229$	1.49537	0.0988169	0.0494085	−	0.998779i	$-0.484266\pi$
$229$	1.49537	0.0988169	0.0494085	+	0.998779i	$0.484266\pi$
$230$	26.4623	1.74487
$231$	−53.8459	−3.54280
$232$	71.6865	4.70645
$233$	−9.21668	−0.603805	−0.301902	−	0.953339i	$-0.597622\pi$
$233$	−9.21668	−0.603805	−0.301902	+	0.953339i	$0.597622\pi$
$234$	−2.80321	−0.183251
$235$	14.7093	0.959529
$236$	−35.0019	−2.27843
$237$	−11.8312	−0.768516
$238$	13.7138	0.888932
$239$	−7.59798	−0.491473	−0.245736	−	0.969337i	$-0.579030\pi$
$239$	−7.59798	−0.491473	−0.245736	+	0.969337i	$0.579030\pi$
$240$	−44.8050	−2.89215
$241$	−9.45104	−0.608795	−0.304398	−	0.952545i	$-0.598455\pi$
$241$	−9.45104	−0.608795	−0.304398	+	0.952545i	$0.598455\pi$
$242$	−20.5516	−1.32110
$243$	−22.0952	−1.41741
$244$	56.2868	3.60339
$245$	−25.8138	−1.64918
$246$	61.0727	3.89386
$247$	−0.311526	−0.0198219
$248$	47.7772	3.03385
$249$	38.0063	2.40855
$250$	−30.0322	−1.89940
$251$	−15.0148	−0.947723	−0.473861	−	0.880599i	$-0.657140\pi$
$251$	−15.0148	−0.947723	−0.473861	+	0.880599i	$0.657140\pi$
$252$	81.2618	5.11901
$253$	−30.8773	−1.94124
$254$	46.6114	2.92466
$255$	3.36498	0.210723
$256$	20.6946	1.29341
$257$	19.8439	1.23783	0.618914	−	0.785459i	$-0.287573\pi$
$257$	19.8439	1.23783	0.618914	+	0.785459i	$0.287573\pi$
$258$	10.7091	0.666719
$259$	2.32740	0.144617
$260$	−2.48263	−0.153966
$261$	−24.5325	−1.51852
$262$	−43.0503	−2.65966
$263$	−12.4170	−0.765667	−0.382834	−	0.923817i	$-0.625052\pi$
$263$	−12.4170	−0.765667	−0.382834	+	0.923817i	$0.625052\pi$
$264$	93.7402	5.76931
$265$	−5.77603	−0.354819
$266$	12.4518	0.763468
$267$	20.1689	1.23432
$268$	−84.0522	−5.13430
$269$	21.1767	1.29117	0.645583	−	0.763690i	$-0.276614\pi$
$269$	21.1767	1.29117	0.645583	+	0.763690i	$0.276614\pi$
$270$	0.255810	0.0155681
$271$	2.26570	0.137631	0.0688157	−	0.997629i	$-0.478078\pi$
$271$	2.26570	0.137631	0.0688157	+	0.997629i	$0.478078\pi$
$272$	−13.3151	−0.807346
$273$	4.28170	0.259140
$274$	5.80436	0.350654
$275$	13.4691	0.812218
$276$	92.7638	5.58373
$277$	18.7510	1.12664	0.563318	−	0.826240i	$-0.309525\pi$
$277$	18.7510	1.12664	0.563318	+	0.826240i	$0.309525\pi$
$278$	−15.4260	−0.925190
$279$	−16.3503	−0.978865
$280$	61.6409	3.68375
$281$	16.5714	0.988569	0.494285	−	0.869300i	$-0.335430\pi$
$281$	16.5714	0.988569	0.494285	+	0.869300i	$0.335430\pi$
$282$	71.0967	4.23375
$283$	−12.3438	−0.733761	−0.366881	−	0.930268i	$-0.619574\pi$
$283$	−12.3438	−0.733761	−0.366881	+	0.930268i	$0.619574\pi$
$284$	7.45097	0.442134
$285$	3.05532	0.180982
$286$	3.99420	0.236182
$287$	−46.8601	−2.76607
$288$	−55.1971	−3.25252
$289$	1.00000	0.0588235
$290$	−29.9574	−1.75916
$291$	−47.6787	−2.79497
$292$	−68.3579	−4.00034
$293$	20.7061	1.20966	0.604832	−	0.796353i	$-0.293240\pi$
$293$	20.7061	1.20966	0.604832	+	0.796353i	$0.293240\pi$
$294$	−124.770	−7.27672
$295$	9.08612	0.529014
$296$	−4.05176	−0.235504
$297$	−0.298490	−0.0173202
$298$	28.9241	1.67553
$299$	2.45529	0.141993
$300$	−40.4648	−2.33624
$301$	−8.21691	−0.473615
$302$	−37.3246	−2.14779
$303$	11.8129	0.678634
$304$	−12.0898	−0.693397
$305$	−14.6115	−0.836650
$306$	8.17025	0.467062
$307$	31.0240	1.77063	0.885315	−	0.464991i	$-0.153942\pi$
$307$	31.0240	1.77063	0.885315	+	0.464991i	$0.153942\pi$
$308$	−115.787	−6.59760
$309$	−2.44009	−0.138812
$310$	−19.9658	−1.13398
$311$	18.3834	1.04243	0.521214	−	0.853426i	$-0.325479\pi$
$311$	18.3834	1.04243	0.521214	+	0.853426i	$0.325479\pi$
$312$	−7.45400	−0.422000
$313$	29.1290	1.64647	0.823234	−	0.567702i	$-0.192167\pi$
$313$	29.1290	1.64647	0.823234	+	0.567702i	$0.192167\pi$
$314$	−27.0156	−1.52458
$315$	−21.0947	−1.18855
$316$	−25.4411	−1.43117
$317$	−27.6317	−1.55195	−0.775974	−	0.630764i	$-0.782741\pi$
$317$	−27.6317	−1.55195	−0.775974	+	0.630764i	$0.782741\pi$
$318$	−27.9182	−1.56558
$319$	34.9556	1.95714
$320$	−30.9054	−1.72766
$321$	−35.0037	−1.95372
$322$	−98.1388	−5.46906
$323$	0.907977	0.0505212
$324$	−47.0661	−2.61478
$325$	−1.07103	−0.0594102
$326$	19.8801	1.10105
$327$	15.8056	0.874053
$328$	81.5788	4.50443
$329$	−54.5514	−3.00751
$330$	−39.1735	−2.15643
$331$	16.4824	0.905952	0.452976	−	0.891523i	$-0.350362\pi$
$331$	16.4824	0.905952	0.452976	+	0.891523i	$0.350362\pi$
$332$	81.7269	4.48535
$333$	1.38659	0.0759847
$334$	−38.4705	−2.10501
$335$	21.8191	1.19210
$336$	166.165	9.06506
$337$	−6.72274	−0.366211	−0.183105	−	0.983093i	$-0.558615\pi$
$337$	−6.72274	−0.366211	−0.183105	+	0.983093i	$0.558615\pi$
$338$	34.7574	1.89055
$339$	4.94489	0.268570
$340$	7.23588	0.392421
$341$	23.2970	1.26160
$342$	7.41840	0.401141
$343$	60.1542	3.24802
$344$	14.3048	0.771264
$345$	−24.0805	−1.29645
$346$	22.6508	1.21771
$347$	15.1340	0.812433	0.406217	−	0.913777i	$-0.366848\pi$
$347$	15.1340	0.812433	0.406217	+	0.913777i	$0.366848\pi$
$348$	−105.016	−5.62945
$349$	32.0493	1.71556	0.857780	−	0.514017i	$-0.171843\pi$
$349$	32.0493	1.71556	0.857780	+	0.514017i	$0.171843\pi$
$350$	42.8095	2.28826
$351$	0.0237352	0.00126689
$352$	78.6486	4.19199
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	43.9174	2.33418
$355$	−1.93419	−0.102656
$356$	43.3702	2.29861
$357$	−12.4795	−0.660483
$358$	50.3080	2.65886
$359$	−21.4704	−1.13317	−0.566583	−	0.824005i	$-0.691735\pi$
$359$	−21.4704	−1.13317	−0.566583	+	0.824005i	$0.691735\pi$
$360$	36.7238	1.93551
$361$	−18.1756	−0.956609
$362$	−54.4804	−2.86342
$363$	18.7018	0.981590
$364$	9.20714	0.482585
$365$	17.7450	0.928816
$366$	−70.6238	−3.69157
$367$	17.7094	0.924422	0.462211	−	0.886770i	$-0.347056\pi$
$367$	17.7094	0.924422	0.462211	+	0.886770i	$0.347056\pi$
$368$	95.2857	4.96711
$369$	−27.9178	−1.45334
$370$	1.69321	0.0880258
$371$	21.4212	1.11213
$372$	−69.9905	−3.62884
$373$	−4.74151	−0.245506	−0.122753	−	0.992437i	$-0.539172\pi$
$373$	−4.74151	−0.245506	−0.122753	+	0.992437i	$0.539172\pi$
$374$	−11.6415	−0.601970
$375$	27.3291	1.41127
$376$	94.9684	4.89762
$377$	−2.77959	−0.143156
$378$	−0.948705	−0.0487961
$379$	−13.4199	−0.689335	−0.344668	−	0.938725i	$-0.612008\pi$
$379$	−13.4199	−0.689335	−0.344668	+	0.938725i	$0.612008\pi$
$380$	6.57001	0.337035
$381$	−42.4162	−2.17305
$382$	−4.53945	−0.232258
$383$	7.57053	0.386836	0.193418	−	0.981116i	$-0.438043\pi$
$383$	7.57053	0.386836	0.193418	+	0.981116i	$0.438043\pi$
$384$	−59.8725	−3.05536
$385$	30.0572	1.53186
$386$	52.9197	2.69354
$387$	−4.89538	−0.248846
$388$	−102.526	−5.20496
$389$	−9.08610	−0.460684	−0.230342	−	0.973110i	$-0.573984\pi$
$389$	−9.08610	−0.460684	−0.230342	+	0.973110i	$0.573984\pi$
$390$	3.11499	0.157734
$391$	−7.15622	−0.361905
$392$	−166.663	−8.41775
$393$	39.1755	1.97614
$394$	−9.14361	−0.460649
$395$	6.60425	0.332296
$396$	−68.9826	−3.46651
$397$	14.7335	0.739453	0.369726	−	0.929141i	$-0.379451\pi$
$397$	14.7335	0.739453	0.369726	+	0.929141i	$0.379451\pi$
$398$	24.9312	1.24969
$399$	−11.3311	−0.567263
$400$	−41.5649	−2.07825
$401$	19.2357	0.960587	0.480293	−	0.877108i	$-0.340530\pi$
$401$	19.2357	0.960587	0.480293	+	0.877108i	$0.340530\pi$
$402$	105.462	5.25994
$403$	−1.85252	−0.0922807
$404$	25.4019	1.26379
$405$	12.2179	0.607110
$406$	111.101	5.51385
$407$	−1.97571	−0.0979324
$408$	21.7255	1.07557
$409$	−8.87367	−0.438775	−0.219387	−	0.975638i	$-0.570406\pi$
$409$	−8.87367	−0.438775	−0.219387	+	0.975638i	$0.570406\pi$
$410$	−34.0913	−1.68365
$411$	−5.28193	−0.260539
$412$	−5.24705	−0.258504
$413$	−33.6971	−1.65812
$414$	−58.4681	−2.87355
$415$	−21.2155	−1.04143
$416$	−6.25396	−0.306625
$417$	14.0376	0.687423
$418$	−10.5702	−0.517008
$419$	−22.9326	−1.12033	−0.560166	−	0.828380i	$-0.689263\pi$
$419$	−22.9326	−1.12033	−0.560166	+	0.828380i	$0.689263\pi$
$420$	−90.3000	−4.40619
$421$	11.8605	0.578045	0.289023	−	0.957322i	$-0.406670\pi$
$421$	11.8605	0.578045	0.289023	+	0.957322i	$0.406670\pi$
$422$	60.7436	2.95695
$423$	−32.5000	−1.58020
$424$	−37.2921	−1.81107
$425$	3.12164	0.151422
$426$	−9.34884	−0.452953
$427$	54.1885	2.62237
$428$	−75.2703	−3.63833
$429$	−3.63470	−0.175485
$430$	−5.97790	−0.288280
$431$	14.3315	0.690326	0.345163	−	0.938543i	$-0.387824\pi$
$431$	14.3315	0.690326	0.345163	+	0.938543i	$0.387824\pi$
$432$	0.921124	0.0443176
$433$	−16.3271	−0.784633	−0.392316	−	0.919830i	$-0.628326\pi$
$433$	−16.3271	−0.784633	−0.392316	+	0.919830i	$0.628326\pi$
$434$	74.0459	3.55432
$435$	27.2611	1.30707
$436$	33.9876	1.62771
$437$	−6.49768	−0.310826
$438$	85.7697	4.09823
$439$	3.06063	0.146076	0.0730380	−	0.997329i	$-0.476731\pi$
$439$	3.06063	0.146076	0.0730380	+	0.997329i	$0.476731\pi$
$440$	−52.3266	−2.49457
$441$	57.0353	2.71597
$442$	0.925708	0.0440314
$443$	33.1438	1.57471	0.787354	−	0.616501i	$-0.211450\pi$
$443$	33.1438	1.57471	0.787354	+	0.616501i	$0.211450\pi$
$444$	5.93557	0.281690
$445$	−11.2584	−0.533701
$446$	13.0601	0.618414
$447$	−26.3208	−1.24493
$448$	114.617	5.41513
$449$	1.59508	0.0752762	0.0376381	−	0.999291i	$-0.488017\pi$
$449$	1.59508	0.0752762	0.0376381	+	0.999291i	$0.488017\pi$
$450$	25.5046	1.20230
$451$	39.7792	1.87313
$452$	10.6332	0.500146
$453$	33.9652	1.59582
$454$	6.22475	0.292142
$455$	−2.39008	−0.112049
$456$	19.7262	0.923766
$457$	−4.67070	−0.218486	−0.109243	−	0.994015i	$-0.534843\pi$
$457$	−4.67070	−0.218486	−0.109243	+	0.994015i	$0.534843\pi$
$458$	−4.03463	−0.188526
$459$	−0.0691789	−0.00322900
$460$	−51.7815	−2.41433
$461$	31.3262	1.45901	0.729503	−	0.683978i	$-0.239752\pi$
$461$	31.3262	1.45901	0.729503	+	0.683978i	$0.239752\pi$
$462$	145.280	6.75905
$463$	−5.38202	−0.250124	−0.125062	−	0.992149i	$-0.539913\pi$
$463$	−5.38202	−0.250124	−0.125062	+	0.992149i	$0.539913\pi$
$464$	−107.871	−5.00779
$465$	18.1688	0.842558
$466$	24.8673	1.15196
$467$	−40.0264	−1.85220	−0.926101	−	0.377277i	$-0.876861\pi$
$467$	−40.0264	−1.85220	−0.926101	+	0.377277i	$0.876861\pi$
$468$	5.48533	0.253560
$469$	−80.9189	−3.73649
$470$	−39.6868	−1.83062
$471$	24.5841	1.13277
$472$	58.6632	2.70019
$473$	6.97528	0.320724
$474$	31.9213	1.46620
$475$	2.83438	0.130050
$476$	−26.8352	−1.22999
$477$	12.7621	0.584336
$478$	20.4999	0.937645
$479$	28.5638	1.30511	0.652556	−	0.757740i	$-0.273697\pi$
$479$	28.5638	1.30511	0.652556	+	0.757740i	$0.273697\pi$
$480$	61.3363	2.79961
$481$	0.157104	0.00716332
$482$	25.4996	1.16148
$483$	89.3058	4.06355
$484$	40.2154	1.82797
$485$	26.6146	1.20851
$486$	59.6144	2.70416
$487$	−22.7672	−1.03168	−0.515840	−	0.856685i	$-0.672520\pi$
$487$	−22.7672	−1.03168	−0.515840	+	0.856685i	$0.672520\pi$
$488$	−94.3368	−4.27042
$489$	−18.0907	−0.818092
$490$	69.6476	3.14636
$491$	−12.3647	−0.558009	−0.279004	−	0.960290i	$-0.590004\pi$
$491$	−12.3647	−0.558009	−0.279004	+	0.960290i	$0.590004\pi$
$492$	−119.508	−5.38782
$493$	8.10141	0.364869
$494$	0.840521	0.0378168
$495$	17.9072	0.804867
$496$	−71.8932	−3.22810
$497$	7.17321	0.321763
$498$	−102.544	−4.59511
$499$	−20.7358	−0.928261	−0.464131	−	0.885767i	$-0.653633\pi$
$499$	−20.7358	−0.928261	−0.464131	+	0.885767i	$0.653633\pi$
$500$	58.7672	2.62815
$501$	35.0079	1.56404
$502$	40.5109	1.80809
$503$	31.2280	1.39239	0.696193	−	0.717855i	$-0.254876\pi$
$503$	31.2280	1.39239	0.696193	+	0.717855i	$0.254876\pi$
$504$	−136.195	−6.06661
$505$	−6.59407	−0.293432
$506$	83.3094	3.70355
$507$	−31.6290	−1.40469
$508$	−91.2096	−4.04677
$509$	−14.6390	−0.648861	−0.324430	−	0.945910i	$-0.605173\pi$
$509$	−14.6390	−0.648861	−0.324430	+	0.945910i	$0.605173\pi$
$510$	−9.07897	−0.402024
$511$	−65.8097	−2.91125
$512$	−7.06422	−0.312197
$513$	−0.0628129	−0.00277326
$514$	−53.5404	−2.36156
$515$	1.36208	0.0600204
$516$	−20.9556	−0.922519
$517$	46.3083	2.03664
$518$	−6.27949	−0.275905
$519$	−20.6121	−0.904770
$520$	4.16089	0.182467
$521$	0.176484	0.00773190	0.00386595	−	0.999993i	$-0.498769\pi$
$521$	0.176484	0.00773190	0.00386595	+	0.999993i	$0.498769\pi$
$522$	66.1906	2.89708
$523$	−5.63669	−0.246475	−0.123238	−	0.992377i	$-0.539328\pi$
$523$	−5.63669	−0.246475	−0.123238	+	0.992377i	$0.539328\pi$
$524$	84.2411	3.68009
$525$	−38.9564	−1.70020
$526$	33.5021	1.46076
$527$	5.39938	0.235201
$528$	−141.057	−6.13870
$529$	28.2114	1.22658
$530$	15.5842	0.676933
$531$	−20.0757	−0.871210
$532$	−24.3658	−1.05639
$533$	−3.16315	−0.137011
$534$	−54.4172	−2.35486
$535$	19.5394	0.844761
$536$	140.872	6.08473
$537$	−45.7800	−1.97555
$538$	−57.1364	−2.46332
$539$	−81.2678	−3.50045
$540$	−0.500571	−0.0215411
$541$	−34.5577	−1.48575	−0.742875	−	0.669430i	$-0.766539\pi$
$541$	−34.5577	−1.48575	−0.742875	+	0.669430i	$0.766539\pi$
$542$	−6.11303	−0.262577
$543$	49.5768	2.12755
$544$	18.2278	0.781512
$545$	−8.82284	−0.377929
$546$	−11.5523	−0.494394
$547$	−4.03717	−0.172617	−0.0863085	−	0.996268i	$-0.527507\pi$
$547$	−4.03717	−0.172617	−0.0863085	+	0.996268i	$0.527507\pi$
$548$	−11.3580	−0.485190
$549$	32.2838	1.37784
$550$	−36.3407	−1.54957
$551$	7.35589	0.313372
$552$	−155.472	−6.61734
$553$	−24.4927	−1.04154
$554$	−50.5915	−2.14943
$555$	−1.54081	−0.0654038
$556$	30.1857	1.28016
$557$	−4.26779	−0.180832	−0.0904161	−	0.995904i	$-0.528820\pi$
$557$	−4.26779	−0.180832	−0.0904161	+	0.995904i	$0.528820\pi$
$558$	44.1143	1.86751
$559$	−0.554658	−0.0234595
$560$	−92.7548	−3.91961
$561$	10.5937	0.447268
$562$	−44.7110	−1.88602
$563$	8.09890	0.341328	0.170664	−	0.985329i	$-0.445409\pi$
$563$	8.09890	0.341328	0.170664	+	0.985329i	$0.445409\pi$
$564$	−139.123	−5.85812
$565$	−2.76028	−0.116126
$566$	33.3044	1.39989
$567$	−45.3115	−1.90291
$568$	−12.4878	−0.523978
$569$	−32.7168	−1.37156	−0.685780	−	0.727809i	$-0.740539\pi$
$569$	−32.7168	−1.37156	−0.685780	+	0.727809i	$0.740539\pi$
$570$	−8.24349	−0.345282
$571$	12.1979	0.510466	0.255233	−	0.966880i	$-0.417848\pi$
$571$	12.1979	0.510466	0.255233	+	0.966880i	$0.417848\pi$
$572$	−7.81588	−0.326799
$573$	4.13087	0.172570
$574$	126.432	5.27718
$575$	−22.3391	−0.931606
$576$	68.2851	2.84521
$577$	−6.14165	−0.255680	−0.127840	−	0.991795i	$-0.540804\pi$
$577$	−6.14165	−0.255680	−0.127840	+	0.991795i	$0.540804\pi$
$578$	−2.69808	−0.112225
$579$	−48.1567	−2.00132
$580$	58.6209	2.43410
$581$	78.6803	3.26421
$582$	128.641	5.33233
$583$	−18.1843	−0.753117
$584$	114.568	4.74086
$585$	−1.42394	−0.0588725
$586$	−55.8667	−2.30783
$587$	−34.6002	−1.42810	−0.714051	−	0.700094i	$-0.753141\pi$
$587$	−34.6002	−1.42810	−0.714051	+	0.700094i	$0.753141\pi$
$588$	244.150	10.0686
$589$	4.90251	0.202004
$590$	−24.5150	−1.00927
$591$	8.32064	0.342265
$592$	6.09693	0.250582
$593$	28.9083	1.18712	0.593561	−	0.804789i	$-0.297721\pi$
$593$	28.9083	1.18712	0.593561	+	0.804789i	$0.297721\pi$
$594$	0.805349	0.0330439
$595$	6.96614	0.285584
$596$	−56.5989	−2.31838
$597$	−22.6873	−0.928528
$598$	−6.62457	−0.270899
$599$	−16.9652	−0.693179	−0.346590	−	0.938017i	$-0.612660\pi$
$599$	−16.9652	−0.693179	−0.346590	+	0.938017i	$0.612660\pi$
$600$	67.8192	2.76871
$601$	24.4845	0.998745	0.499372	−	0.866388i	$-0.333564\pi$
$601$	24.4845	0.998745	0.499372	+	0.866388i	$0.333564\pi$
$602$	22.1698	0.903575
$603$	−48.2090	−1.96322
$604$	73.0370	2.97183
$605$	−10.4395	−0.424426
$606$	−31.8722	−1.29472
$607$	43.3901	1.76115	0.880574	−	0.473908i	$-0.157157\pi$
$607$	43.3901	1.76115	0.880574	+	0.473908i	$0.157157\pi$
$608$	16.5504	0.671209
$609$	−101.101	−4.09683
$610$	39.4228	1.59618
$611$	−3.68233	−0.148971
$612$	−15.9876	−0.646260
$613$	−4.18551	−0.169051	−0.0845256	−	0.996421i	$-0.526937\pi$
$613$	−4.18551	−0.169051	−0.0845256	+	0.996421i	$0.526937\pi$
$614$	−83.7050	−3.37806
$615$	31.0229	1.25096
$616$	194.060	7.81890
$617$	−6.82787	−0.274880	−0.137440	−	0.990510i	$-0.543887\pi$
$617$	−6.82787	−0.274880	−0.137440	+	0.990510i	$0.543887\pi$
$618$	6.58355	0.264829
$619$	1.77321	0.0712713	0.0356357	−	0.999365i	$-0.488654\pi$
$619$	1.77321	0.0712713	0.0356357	+	0.999365i	$0.488654\pi$
$620$	39.0693	1.56906
$621$	0.495059	0.0198660
$622$	−49.5998	−1.98877
$623$	41.7534	1.67282
$624$	11.2165	0.449019
$625$	0.352836	0.0141135
$626$	−78.5923	−3.14118
$627$	9.61887	0.384141
$628$	52.8644	2.10952
$629$	−0.457896	−0.0182575
$630$	56.9151	2.26755
$631$	−5.80687	−0.231168	−0.115584	−	0.993298i	$-0.536874\pi$
$631$	−5.80687	−0.231168	−0.115584	+	0.993298i	$0.536874\pi$
$632$	42.6394	1.69610
$633$	−55.2764	−2.19704
$634$	74.5523	2.96085
$635$	23.6771	0.939595
$636$	54.6305	2.16624
$637$	6.46223	0.256043
$638$	−94.3129	−3.73388
$639$	4.27358	0.169060
$640$	33.4214	1.32109
$641$	−45.8600	−1.81136	−0.905680	−	0.423962i	$-0.860639\pi$
$641$	−45.8600	−1.81136	−0.905680	+	0.423962i	$0.860639\pi$
$642$	94.4428	3.72736
$643$	38.0011	1.49862	0.749308	−	0.662222i	$-0.230386\pi$
$643$	38.0011	1.49862	0.749308	+	0.662222i	$0.230386\pi$
$644$	192.039	7.56738
$645$	5.43986	0.214194
$646$	−2.44979	−0.0963857
$647$	21.6055	0.849398	0.424699	−	0.905335i	$-0.360380\pi$
$647$	21.6055	0.849398	0.424699	+	0.905335i	$0.360380\pi$
$648$	78.8828	3.09881
$649$	28.6052	1.12285
$650$	2.88973	0.113344
$651$	−67.3814	−2.64088
$652$	−38.9014	−1.52350
$653$	33.6916	1.31845	0.659227	−	0.751944i	$-0.270884\pi$
$653$	33.6916	1.31845	0.659227	+	0.751944i	$0.270884\pi$
$654$	−42.6448	−1.66754
$655$	−21.8681	−0.854458
$656$	−122.756	−4.79284
$657$	−39.2074	−1.52963
$658$	147.184	5.73782
$659$	−26.7235	−1.04100	−0.520500	−	0.853862i	$-0.674255\pi$
$659$	−26.7235	−1.04100	−0.520500	+	0.853862i	$0.674255\pi$
$660$	76.6550	2.98379
$661$	−13.8411	−0.538358	−0.269179	−	0.963090i	$-0.586752\pi$
$661$	−13.8411	−0.538358	−0.269179	+	0.963090i	$0.586752\pi$
$662$	−44.4706	−1.72840
$663$	−0.842389	−0.0327157
$664$	−136.975	−5.31564
$665$	6.32510	0.245277
$666$	−3.74113	−0.144966
$667$	−57.9755	−2.24482
$668$	75.2793	2.91264
$669$	−11.8846	−0.459486
$670$	−58.8695	−2.27433
$671$	−46.0003	−1.77582
$672$	−227.474	−8.77499
$673$	−15.6914	−0.604858	−0.302429	−	0.953172i	$-0.597797\pi$
$673$	−15.6914	−0.604858	−0.302429	+	0.953172i	$0.597797\pi$
$674$	18.1385	0.698667
$675$	−0.215952	−0.00831198
$676$	−68.0135	−2.61590
$677$	25.6030	0.984003	0.492002	−	0.870594i	$-0.336265\pi$
$677$	25.6030	0.984003	0.492002	+	0.870594i	$0.336265\pi$
$678$	−13.3417	−0.512384
$679$	−98.7039	−3.78791
$680$	−12.1274	−0.465063
$681$	−5.66449	−0.217064
$682$	−62.8571	−2.40692
$683$	−25.1967	−0.964125	−0.482062	−	0.876137i	$-0.660112\pi$
$683$	−25.1967	−0.964125	−0.482062	+	0.876137i	$0.660112\pi$
$684$	−14.5164	−0.555047
$685$	2.94842	0.112653
$686$	−162.301	−6.19667
$687$	3.67149	0.140076
$688$	−21.5253	−0.820645
$689$	1.44597	0.0550872
$690$	64.9711	2.47341
$691$	18.7959	0.715030	0.357515	−	0.933907i	$-0.383624\pi$
$691$	18.7959	0.715030	0.357515	+	0.933907i	$0.383624\pi$
$692$	−44.3232	−1.68492
$693$	−66.4111	−2.52275
$694$	−40.8325	−1.54998
$695$	−7.83590	−0.297232
$696$	176.007	6.67154
$697$	9.21935	0.349208
$698$	−86.4715	−3.27299
$699$	−22.6291	−0.855911
$700$	−83.7699	−3.16620
$701$	−0.0617794	−0.00233338	−0.00116669	−	0.999999i	$-0.500371\pi$
$701$	−0.0617794	−0.00233338	−0.00116669	+	0.999999i	$0.500371\pi$
$702$	−0.0640395	−0.00241701
$703$	−0.415759	−0.0156807
$704$	−97.2973	−3.66703
$705$	36.1148	1.36016
$706$	2.69808	0.101543
$707$	24.4550	0.919724
$708$	−85.9378	−3.22974
$709$	−9.20209	−0.345592	−0.172796	−	0.984958i	$-0.555280\pi$
$709$	−9.20209	−0.345592	−0.172796	+	0.984958i	$0.555280\pi$
$710$	5.21860	0.195851
$711$	−14.5920	−0.547243
$712$	−72.6885	−2.72412
$713$	−38.6391	−1.44705
$714$	33.6705	1.26009
$715$	2.02892	0.0758774
$716$	−98.4431	−3.67899
$717$	−18.6548	−0.696677
$718$	57.9289	2.16189
$719$	−37.8621	−1.41202	−0.706009	−	0.708203i	$-0.749506\pi$
$719$	−37.8621	−1.41202	−0.706009	+	0.708203i	$0.749506\pi$
$720$	−55.2605	−2.05944
$721$	−5.05145	−0.188126
$722$	49.0391	1.82505
$723$	−23.2045	−0.862985
$724$	106.608	3.96204
$725$	25.2897	0.939236
$726$	−50.4589	−1.87271
$727$	−12.8986	−0.478382	−0.239191	−	0.970973i	$-0.576882\pi$
$727$	−12.8986	−0.478382	−0.239191	+	0.970973i	$0.576882\pi$
$728$	−15.4312	−0.571918
$729$	−27.5048	−1.01870
$730$	−47.8774	−1.77202
$731$	1.61661	0.0597925
$732$	138.197	5.10792
$733$	−19.3605	−0.715096	−0.357548	−	0.933895i	$-0.616387\pi$
$733$	−19.3605	−0.715096	−0.357548	+	0.933895i	$0.616387\pi$
$734$	−47.7813	−1.76364
$735$	−63.3789	−2.33777
$736$	−130.442	−4.80817
$737$	68.6915	2.53028
$738$	75.3244	2.77273
$739$	30.6691	1.12818	0.564090	−	0.825713i	$-0.309227\pi$
$739$	30.6691	1.12818	0.564090	+	0.825713i	$0.309227\pi$
$740$	−3.31329	−0.121799
$741$	−0.764870	−0.0280982
$742$	−57.7960	−2.12176
$743$	−1.39940	−0.0513391	−0.0256695	−	0.999670i	$-0.508172\pi$
$743$	−1.39940	−0.0513391	−0.0256695	+	0.999670i	$0.508172\pi$
$744$	117.304	4.30058
$745$	14.6925	0.538291
$746$	12.7930	0.468384
$747$	46.8753	1.71508
$748$	22.7802	0.832928
$749$	−72.4644	−2.64779
$750$	−73.7361	−2.69246
$751$	1.27261	0.0464383	0.0232191	−	0.999730i	$-0.492608\pi$
$751$	1.27261	0.0464383	0.0232191	+	0.999730i	$0.492608\pi$
$752$	−142.905	−5.21120
$753$	−36.8647	−1.34343
$754$	7.49954	0.273117
$755$	−18.9596	−0.690012
$756$	1.85643	0.0675178
$757$	2.89066	0.105063	0.0525315	−	0.998619i	$-0.483271\pi$
$757$	2.89066	0.105063	0.0525315	+	0.998619i	$0.483271\pi$
$758$	36.2080	1.31513
$759$	−75.8111	−2.75177
$760$	−11.0114	−0.399424
$761$	40.0461	1.45167	0.725835	−	0.687869i	$-0.241454\pi$
$761$	40.0461	1.45167	0.725835	+	0.687869i	$0.241454\pi$
$762$	114.442	4.14580
$763$	32.7207	1.18457
$764$	8.88282	0.321369
$765$	4.15021	0.150051
$766$	−20.4259	−0.738017
$767$	−2.27462	−0.0821317
$768$	50.8100	1.83345
$769$	−45.8627	−1.65385	−0.826925	−	0.562312i	$-0.809912\pi$
$769$	−45.8627	−1.65385	−0.826925	+	0.562312i	$0.809912\pi$
$770$	−81.0966	−2.92252
$771$	48.7214	1.75466
$772$	−103.554	−3.72698
$773$	4.18968	0.150692	0.0753462	−	0.997157i	$-0.475994\pi$
$773$	4.18968	0.150692	0.0753462	+	0.997157i	$0.475994\pi$
$774$	13.2081	0.474756
$775$	16.8549	0.605446
$776$	171.834	6.16846
$777$	5.71430	0.205000
$778$	24.5150	0.878905
$779$	8.37095	0.299921
$780$	−6.09543	−0.218251
$781$	−6.08929	−0.217892
$782$	19.3080	0.690453
$783$	−0.560447	−0.0200287
$784$	250.788	8.95671
$785$	−13.7230	−0.489796
$786$	−105.699	−3.77014
$787$	−36.2902	−1.29361	−0.646804	−	0.762657i	$-0.723895\pi$
$787$	−36.2902	−1.29361	−0.646804	+	0.762657i	$0.723895\pi$
$788$	17.8923	0.637386
$789$	−30.4867	−1.08536
$790$	−17.8188	−0.633963
$791$	10.2369	0.363981
$792$	115.615	4.10820
$793$	3.65783	0.129893
$794$	−39.7521	−1.41075
$795$	−14.1815	−0.502967
$796$	−48.7856	−1.72916
$797$	−49.3104	−1.74666	−0.873332	−	0.487125i	$-0.838046\pi$
$797$	−49.3104	−1.74666	−0.873332	+	0.487125i	$0.838046\pi$
$798$	30.5721	1.08224
$799$	10.7325	0.379690
$800$	56.9007	2.01174
$801$	24.8754	0.878929
$802$	−51.8995	−1.83263
$803$	55.8654	1.97145
$804$	−206.368	−7.27803
$805$	−49.8512	−1.75703
$806$	4.99825	0.176056
$807$	51.9938	1.83027
$808$	−42.5737	−1.49774
$809$	54.5286	1.91712	0.958562	−	0.284885i	$-0.0919554\pi$
$809$	54.5286	1.91712	0.958562	+	0.284885i	$0.0919554\pi$
$810$	−32.9647	−1.15826
$811$	−36.4899	−1.28133	−0.640667	−	0.767819i	$-0.721342\pi$
$811$	−36.4899	−1.28133	−0.640667	+	0.767819i	$0.721342\pi$
$812$	−217.403	−7.62936
$813$	5.56282	0.195097
$814$	5.33062	0.186838
$815$	10.0984	0.353732
$816$	−32.6917	−1.14444
$817$	1.46784	0.0513534
$818$	23.9418	0.837106
$819$	5.28085	0.184528
$820$	66.7101	2.32962
$821$	8.07418	0.281791	0.140895	−	0.990024i	$-0.455002\pi$
$821$	8.07418	0.281791	0.140895	+	0.990024i	$0.455002\pi$
$822$	14.2511	0.497063
$823$	35.6042	1.24108	0.620542	−	0.784173i	$-0.286913\pi$
$823$	35.6042	1.24108	0.620542	+	0.784173i	$0.286913\pi$
$824$	8.79407	0.306356
$825$	33.0698	1.15134
$826$	90.9172	3.16342
$827$	−30.8712	−1.07350	−0.536748	−	0.843743i	$-0.680347\pi$
$827$	−30.8712	−1.07350	−0.536748	+	0.843743i	$0.680347\pi$
$828$	114.411	3.97605
$829$	−14.4822	−0.502986	−0.251493	−	0.967859i	$-0.580922\pi$
$829$	−14.4822	−0.502986	−0.251493	+	0.967859i	$0.580922\pi$
$830$	57.2409	1.98686
$831$	46.0380	1.59704
$832$	7.73685	0.268227
$833$	−18.8349	−0.652589
$834$	−37.8745	−1.31149
$835$	−19.5417	−0.676269
$836$	20.6839	0.715369
$837$	−0.373523	−0.0129109
$838$	61.8740	2.13740
$839$	−19.8686	−0.685940	−0.342970	−	0.939346i	$-0.611433\pi$
$839$	−19.8686	−0.685940	−0.342970	+	0.939346i	$0.611433\pi$
$840$	151.343	5.22183
$841$	36.6329	1.26320
$842$	−32.0005	−1.10281
$843$	40.6868	1.40133
$844$	−118.864	−4.09145
$845$	17.6556	0.607371
$846$	87.6875	3.01476
$847$	38.7163	1.33031
$848$	56.1157	1.92702
$849$	−30.3069	−1.04013
$850$	−8.42242	−0.288887
$851$	3.27681	0.112327
$852$	18.2939	0.626738
$853$	−40.3617	−1.38196	−0.690980	−	0.722874i	$-0.742821\pi$
$853$	−40.3617	−1.38196	−0.690980	+	0.722874i	$0.742821\pi$
$854$	−146.205	−5.00302
$855$	3.76830	0.128873
$856$	126.153	4.31183
$857$	−48.8190	−1.66762	−0.833812	−	0.552048i	$-0.813846\pi$
$857$	−48.8190	−1.66762	−0.833812	+	0.552048i	$0.813846\pi$
$858$	9.80670	0.334795
$859$	14.9245	0.509216	0.254608	−	0.967044i	$-0.418054\pi$
$859$	14.9245	0.509216	0.254608	+	0.967044i	$0.418054\pi$
$860$	11.6976	0.398885
$861$	−115.053	−3.92098
$862$	−38.6676	−1.31702
$863$	14.7979	0.503727	0.251864	−	0.967763i	$-0.418957\pi$
$863$	14.7979	0.503727	0.251864	+	0.967763i	$0.418957\pi$
$864$	−1.26098	−0.0428995
$865$	11.5058	0.391210
$866$	44.0519	1.49694
$867$	2.45523	0.0833841
$868$	−144.894	−4.91801
$869$	20.7917	0.705310
$870$	−73.5525	−2.49366
$871$	−5.46219	−0.185079
$872$	−56.9634	−1.92902
$873$	−58.8047	−1.99024
$874$	17.5312	0.593003
$875$	56.5765	1.91264
$876$	−167.835	−5.67061
$877$	−44.0231	−1.48655	−0.743276	−	0.668984i	$-0.766729\pi$
$877$	−44.0231	−1.48655	−0.743276	+	0.668984i	$0.766729\pi$
$878$	−8.25782	−0.278688
$879$	50.8384	1.71474
$880$	78.7390	2.65429
$881$	−28.4423	−0.958245	−0.479123	−	0.877748i	$-0.659045\pi$
$881$	−28.4423	−0.958245	−0.479123	+	0.877748i	$0.659045\pi$
$882$	−153.886	−5.18159
$883$	22.9392	0.771965	0.385982	−	0.922506i	$-0.373863\pi$
$883$	22.9392	0.771965	0.385982	+	0.922506i	$0.373863\pi$
$884$	−1.81143	−0.0609250
$885$	22.3086	0.749894
$886$	−89.4244	−3.00427
$887$	26.8513	0.901580	0.450790	−	0.892630i	$-0.351142\pi$
$887$	26.8513	0.901580	0.450790	+	0.892630i	$0.351142\pi$
$888$	−9.94803	−0.333834
$889$	−87.8095	−2.94504
$890$	30.3761	1.01821
$891$	38.4647	1.28861
$892$	−25.5561	−0.855682
$893$	9.74489	0.326100
$894$	71.0154	2.37511
$895$	25.5548	0.854203
$896$	−123.947	−4.14079
$897$	6.02832	0.201280
$898$	−4.30363	−0.143614
$899$	43.7426	1.45890
$900$	−49.9075	−1.66358
$901$	−4.21444	−0.140404
$902$	−107.327	−3.57361
$903$	−20.1744	−0.671363
$904$	−17.8213	−0.592729
$905$	−27.6742	−0.919922
$906$	−91.6406	−3.04455
$907$	44.1205	1.46500	0.732498	−	0.680769i	$-0.238354\pi$
$907$	44.1205	1.46500	0.732498	+	0.680769i	$0.238354\pi$
$908$	−12.1806	−0.404228
$909$	14.5695	0.483241
$910$	6.44861	0.213769
$911$	−23.8746	−0.791001	−0.395500	−	0.918466i	$-0.629429\pi$
$911$	−23.8746	−0.791001	−0.395500	+	0.918466i	$0.629429\pi$
$912$	−29.6833	−0.982911
$913$	−66.7912	−2.21047
$914$	12.6019	0.416834
$915$	−35.8746	−1.18598
$916$	7.89498	0.260858
$917$	81.1008	2.67818
$918$	0.186650	0.00616037
$919$	27.9168	0.920891	0.460445	−	0.887688i	$-0.347690\pi$
$919$	27.9168	0.920891	0.460445	+	0.887688i	$0.347690\pi$
$920$	86.7860	2.86125
$921$	76.1711	2.50992
$922$	−84.5204	−2.78353
$923$	0.484206	0.0159378
$924$	−284.285	−9.35230
$925$	−1.42939	−0.0469980
$926$	14.5211	0.477193
$927$	−3.00950	−0.0988449
$928$	147.671	4.84754
$929$	−29.0798	−0.954079	−0.477039	−	0.878882i	$-0.658290\pi$
$929$	−29.0798	−0.954079	−0.477039	+	0.878882i	$0.658290\pi$
$930$	−49.0208	−1.60746
$931$	−17.1016	−0.560483
$932$	−48.6605	−1.59393
$933$	45.1356	1.47767
$934$	107.994	3.53368
$935$	−5.91351	−0.193393
$936$	−9.19343	−0.300497
$937$	−57.0917	−1.86510	−0.932552	−	0.361036i	$-0.882423\pi$
$937$	−57.0917	−1.86510	−0.932552	+	0.361036i	$0.882423\pi$
$938$	218.325	7.12857
$939$	71.5185	2.33392
$940$	77.6594	2.53297
$941$	27.5914	0.899453	0.449726	−	0.893166i	$-0.351521\pi$
$941$	27.5914	0.899453	0.449726	+	0.893166i	$0.351521\pi$
$942$	−66.3297	−2.16114
$943$	−65.9757	−2.14846
$944$	−88.2741	−2.87308
$945$	−0.481910	−0.0156765
$946$	−18.8198	−0.611885
$947$	−28.6014	−0.929420	−0.464710	−	0.885463i	$-0.653841\pi$
$947$	−28.6014	−0.929420	−0.464710	+	0.885463i	$0.653841\pi$
$948$	−62.4639	−2.02873
$949$	−4.44228	−0.144203
$950$	−7.64736	−0.248113
$951$	−67.8422	−2.19993
$952$	44.9759	1.45768
$953$	−11.7963	−0.382121	−0.191060	−	0.981578i	$-0.561193\pi$
$953$	−11.7963	−0.382121	−0.191060	+	0.981578i	$0.561193\pi$
$954$	−34.4331	−1.11481
$955$	−2.30589	−0.0746168
$956$	−40.1144	−1.29739
$957$	85.8242	2.77430
$958$	−77.0673	−2.48993
$959$	−10.9346	−0.353097
$960$	−75.8799	−2.44901
$961$	−1.84671	−0.0595714
$962$	−0.423878	−0.0136664
$963$	−43.1720	−1.39120
$964$	−49.8978	−1.60710
$965$	26.8815	0.865345
$966$	−240.954	−7.75256
$967$	−20.5091	−0.659527	−0.329764	−	0.944064i	$-0.606969\pi$
$967$	−20.5091	−0.659527	−0.329764	+	0.944064i	$0.606969\pi$
$968$	−67.4012	−2.16636
$969$	2.22930	0.0716153
$970$	−71.8083	−2.30563
$971$	−35.9164	−1.15261	−0.576307	−	0.817233i	$-0.695507\pi$
$971$	−35.9164	−1.15261	−0.576307	+	0.817233i	$0.695507\pi$
$972$	−116.654	−3.74168
$973$	29.0604	0.931635
$974$	61.4277	1.96827
$975$	−2.62964	−0.0842157
$976$	141.954	4.54384
$977$	1.17235	0.0375068	0.0187534	−	0.999824i	$-0.494030\pi$
$977$	1.17235	0.0375068	0.0187534	+	0.999824i	$0.494030\pi$
$978$	48.8102	1.56078
$979$	−35.4442	−1.13280
$980$	−136.287	−4.35352
$981$	19.4940	0.622394
$982$	33.3608	1.06459
$983$	−32.6115	−1.04015	−0.520073	−	0.854122i	$-0.674095\pi$
$983$	−32.6115	−1.04015	−0.520073	+	0.854122i	$0.674095\pi$
$984$	200.295	6.38517
$985$	−4.64465	−0.147991
$986$	−21.8582	−0.696108
$987$	−133.936	−4.26324
$988$	−1.64474	−0.0523261
$989$	−11.5688	−0.367867
$990$	−48.3149	−1.53555
$991$	−19.7856	−0.628511	−0.314255	−	0.949339i	$-0.601755\pi$
$991$	−19.7856	−0.628511	−0.314255	+	0.949339i	$0.601755\pi$
$992$	98.4190	3.12481
$993$	40.4680	1.28421
$994$	−19.3539	−0.613867
$995$	12.6642	0.401483
$996$	200.659	6.35812
$997$	3.50070	0.110868	0.0554341	−	0.998462i	$-0.482346\pi$
$997$	3.50070	0.110868	0.0554341	+	0.998462i	$0.482346\pi$
$998$	55.9467	1.77096
$999$	0.0316768	0.00100221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.4	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.4	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69808 q^{2} +2.45523 q^{3} +5.27961 q^{4} -1.37053 q^{5} -6.62441 q^{6} +5.08280 q^{7} -8.84865 q^{8} +3.02818 q^{9} +O(q^{10})\)	\(q-2.69808 q^{2} +2.45523 q^{3} +5.27961 q^{4} -1.37053 q^{5} -6.62441 q^{6} +5.08280 q^{7} -8.84865 q^{8} +3.02818 q^{9} +3.69780 q^{10} -4.31476 q^{11} +12.9627 q^{12} +0.343099 q^{13} -13.7138 q^{14} -3.36498 q^{15} +13.3151 q^{16} -1.00000 q^{17} -8.17025 q^{18} -0.907977 q^{19} -7.23588 q^{20} +12.4795 q^{21} +11.6415 q^{22} +7.15622 q^{23} -21.7255 q^{24} -3.12164 q^{25} -0.925708 q^{26} +0.0691789 q^{27} +26.8352 q^{28} -8.10141 q^{29} +9.07897 q^{30} -5.39938 q^{31} -18.2278 q^{32} -10.5937 q^{33} +2.69808 q^{34} -6.96614 q^{35} +15.9876 q^{36} +0.457896 q^{37} +2.44979 q^{38} +0.842389 q^{39} +12.1274 q^{40} -9.21935 q^{41} -33.6705 q^{42} -1.61661 q^{43} -22.7802 q^{44} -4.15021 q^{45} -19.3080 q^{46} -10.7325 q^{47} +32.6917 q^{48} +18.8349 q^{49} +8.42242 q^{50} -2.45523 q^{51} +1.81143 q^{52} +4.21444 q^{53} -0.186650 q^{54} +5.91351 q^{55} -44.9759 q^{56} -2.22930 q^{57} +21.8582 q^{58} -6.62963 q^{59} -17.7658 q^{60} +10.6612 q^{61} +14.5679 q^{62} +15.3916 q^{63} +22.5499 q^{64} -0.470229 q^{65} +28.5827 q^{66} -15.9201 q^{67} -5.27961 q^{68} +17.5702 q^{69} +18.7952 q^{70} +1.41127 q^{71} -26.7953 q^{72} -12.9475 q^{73} -1.23544 q^{74} -7.66436 q^{75} -4.79377 q^{76} -21.9310 q^{77} -2.27283 q^{78} -4.81875 q^{79} -18.2488 q^{80} -8.91468 q^{81} +24.8745 q^{82} +15.4797 q^{83} +65.8868 q^{84} +1.37053 q^{85} +4.36174 q^{86} -19.8909 q^{87} +38.1797 q^{88} +8.21465 q^{89} +11.1976 q^{90} +1.74390 q^{91} +37.7821 q^{92} -13.2567 q^{93} +28.9572 q^{94} +1.24441 q^{95} -44.7536 q^{96} -19.4192 q^{97} -50.8179 q^{98} -13.0658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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