LMFDB - Embedded newform 6007.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$0$
Dimension:	$261$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65529 q^{2} +2.71142 q^{3} +5.05057 q^{4} +3.32212 q^{5} -7.19960 q^{6} -2.23518 q^{7} -8.10014 q^{8} +4.35179 q^{9} +O(q^{10})$	\(q-2.65529 q^{2} +2.71142 q^{3} +5.05057 q^{4} +3.32212 q^{5} -7.19960 q^{6} -2.23518 q^{7} -8.10014 q^{8} +4.35179 q^{9} -8.82118 q^{10} +6.54387 q^{11} +13.6942 q^{12} +4.42483 q^{13} +5.93506 q^{14} +9.00765 q^{15} +11.4071 q^{16} +3.70955 q^{17} -11.5553 q^{18} +2.28371 q^{19} +16.7786 q^{20} -6.06052 q^{21} -17.3759 q^{22} -6.28017 q^{23} -21.9629 q^{24} +6.03645 q^{25} -11.7492 q^{26} +3.66527 q^{27} -11.2889 q^{28} +6.19123 q^{29} -23.9179 q^{30} -4.80501 q^{31} -14.0889 q^{32} +17.7432 q^{33} -9.84992 q^{34} -7.42554 q^{35} +21.9790 q^{36} +7.26306 q^{37} -6.06391 q^{38} +11.9976 q^{39} -26.9096 q^{40} -5.61532 q^{41} +16.0924 q^{42} +5.52453 q^{43} +33.0502 q^{44} +14.4572 q^{45} +16.6757 q^{46} -6.99832 q^{47} +30.9294 q^{48} -2.00395 q^{49} -16.0285 q^{50} +10.0581 q^{51} +22.3479 q^{52} +5.56547 q^{53} -9.73236 q^{54} +21.7395 q^{55} +18.1053 q^{56} +6.19209 q^{57} -16.4395 q^{58} -9.47029 q^{59} +45.4937 q^{60} +4.97368 q^{61} +12.7587 q^{62} -9.72706 q^{63} +14.5958 q^{64} +14.6998 q^{65} -47.1133 q^{66} -7.55563 q^{67} +18.7353 q^{68} -17.0282 q^{69} +19.7170 q^{70} -4.74028 q^{71} -35.2501 q^{72} +12.7900 q^{73} -19.2855 q^{74} +16.3674 q^{75} +11.5340 q^{76} -14.6268 q^{77} -31.8570 q^{78} +2.32537 q^{79} +37.8957 q^{80} -3.11729 q^{81} +14.9103 q^{82} +15.9447 q^{83} -30.6091 q^{84} +12.3235 q^{85} -14.6692 q^{86} +16.7870 q^{87} -53.0062 q^{88} -3.64195 q^{89} -38.3879 q^{90} -9.89031 q^{91} -31.7184 q^{92} -13.0284 q^{93} +18.5826 q^{94} +7.58674 q^{95} -38.2008 q^{96} -11.1903 q^{97} +5.32107 q^{98} +28.4775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) $ 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * 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 $

$2$	−2.65529	−1.87757	−0.938787	−	0.344498i	$-0.888049\pi$
$2$	−2.65529	−1.87757	−0.938787	+	0.344498i	$0.888049\pi$
$3$	2.71142	1.56544	0.782719	−	0.622375i	$-0.213832\pi$
$3$	2.71142	1.56544	0.782719	+	0.622375i	$0.213832\pi$
$4$	5.05057	2.52528
$5$	3.32212	1.48570	0.742848	−	0.669460i	$-0.233475\pi$
$5$	3.32212	1.48570	0.742848	+	0.669460i	$0.233475\pi$
$6$	−7.19960	−2.93923
$7$	−2.23518	−0.844820	−0.422410	−	0.906405i	$-0.638816\pi$
$7$	−2.23518	−0.844820	−0.422410	+	0.906405i	$0.638816\pi$
$8$	−8.10014	−2.86383
$9$	4.35179	1.45060
$10$	−8.82118	−2.78950
$11$	6.54387	1.97305	0.986525	−	0.163609i	$-0.0523136\pi$
$11$	6.54387	1.97305	0.986525	+	0.163609i	$0.0523136\pi$
$12$	13.6942	3.95318
$13$	4.42483	1.22723	0.613613	−	0.789607i	$-0.289715\pi$
$13$	4.42483	1.22723	0.613613	+	0.789607i	$0.289715\pi$
$14$	5.93506	1.58621
$15$	9.00765	2.32576
$16$	11.4071	2.85177
$17$	3.70955	0.899697	0.449849	−	0.893105i	$-0.351478\pi$
$17$	3.70955	0.899697	0.449849	+	0.893105i	$0.351478\pi$
$18$	−11.5553	−2.72360
$19$	2.28371	0.523918	0.261959	−	0.965079i	$-0.415631\pi$
$19$	2.28371	0.523918	0.261959	+	0.965079i	$0.415631\pi$
$20$	16.7786	3.75180
$21$	−6.06052	−1.32251
$22$	−17.3759	−3.70455
$23$	−6.28017	−1.30951	−0.654753	−	0.755843i	$-0.727227\pi$
$23$	−6.28017	−1.30951	−0.654753	+	0.755843i	$0.727227\pi$
$24$	−21.9629	−4.48315
$25$	6.03645	1.20729
$26$	−11.7492	−2.30421
$27$	3.66527	0.705382
$28$	−11.2889	−2.13341
$29$	6.19123	1.14968	0.574841	−	0.818265i	$-0.305064\pi$
$29$	6.19123	1.14968	0.574841	+	0.818265i	$0.305064\pi$
$30$	−23.9179	−4.36679
$31$	−4.80501	−0.863005	−0.431502	−	0.902112i	$-0.642016\pi$
$31$	−4.80501	−0.863005	−0.431502	+	0.902112i	$0.642016\pi$
$32$	−14.0889	−2.49058
$33$	17.7432	3.08869
$34$	−9.84992	−1.68925
$35$	−7.42554	−1.25515
$36$	21.9790	3.66317
$37$	7.26306	1.19404	0.597020	−	0.802226i	$-0.296351\pi$
$37$	7.26306	1.19404	0.597020	+	0.802226i	$0.296351\pi$
$38$	−6.06391	−0.983696
$39$	11.9976	1.92115
$40$	−26.9096	−4.25478
$41$	−5.61532	−0.876965	−0.438483	−	0.898740i	$-0.644484\pi$
$41$	−5.61532	−0.876965	−0.438483	+	0.898740i	$0.644484\pi$
$42$	16.0924	2.48312
$43$	5.52453	0.842483	0.421242	−	0.906948i	$-0.361594\pi$
$43$	5.52453	0.842483	0.421242	+	0.906948i	$0.361594\pi$
$44$	33.0502	4.98251
$45$	14.4572	2.15515
$46$	16.6757	2.45869
$47$	−6.99832	−1.02081	−0.510405	−	0.859934i	$-0.670505\pi$
$47$	−6.99832	−1.02081	−0.510405	+	0.859934i	$0.670505\pi$
$48$	30.9294	4.46427
$49$	−2.00395	−0.286279
$50$	−16.0285	−2.26678
$51$	10.0581	1.40842
$52$	22.3479	3.09910
$53$	5.56547	0.764477	0.382238	−	0.924064i	$-0.375153\pi$
$53$	5.56547	0.764477	0.382238	+	0.924064i	$0.375153\pi$
$54$	−9.73236	−1.32441
$55$	21.7395	2.93135
$56$	18.1053	2.41942
$57$	6.19209	0.820162
$58$	−16.4395	−2.15861
$59$	−9.47029	−1.23293	−0.616463	−	0.787384i	$-0.711435\pi$
$59$	−9.47029	−1.23293	−0.616463	+	0.787384i	$0.711435\pi$
$60$	45.4937	5.87321
$61$	4.97368	0.636815	0.318408	−	0.947954i	$-0.396852\pi$
$61$	4.97368	0.636815	0.318408	+	0.947954i	$0.396852\pi$
$62$	12.7587	1.62036
$63$	−9.72706	−1.22549
$64$	14.5958	1.82448
$65$	14.6998	1.82329
$66$	−47.1133	−5.79924
$67$	−7.55563	−0.923067	−0.461534	−	0.887123i	$-0.652701\pi$
$67$	−7.55563	−0.923067	−0.461534	+	0.887123i	$0.652701\pi$
$68$	18.7353	2.27199
$69$	−17.0282	−2.04995
$70$	19.7170	2.35663
$71$	−4.74028	−0.562568	−0.281284	−	0.959625i	$-0.590760\pi$
$71$	−4.74028	−0.562568	−0.281284	+	0.959625i	$0.590760\pi$
$72$	−35.2501	−4.15427
$73$	12.7900	1.49696	0.748478	−	0.663159i	$-0.230785\pi$
$73$	12.7900	1.49696	0.748478	+	0.663159i	$0.230785\pi$
$74$	−19.2855	−2.24190
$75$	16.3674	1.88994
$76$	11.5340	1.32304
$77$	−14.6268	−1.66687
$78$	−31.8570	−3.60710
$79$	2.32537	0.261625	0.130812	−	0.991407i	$-0.458241\pi$
$79$	2.32537	0.261625	0.130812	+	0.991407i	$0.458241\pi$
$80$	37.8957	4.23687
$81$	−3.11729	−0.346365
$82$	14.9103	1.64657
$83$	15.9447	1.75016	0.875081	−	0.483976i	$-0.160808\pi$
$83$	15.9447	1.75016	0.875081	+	0.483976i	$0.160808\pi$
$84$	−30.6091	−3.33972
$85$	12.3235	1.33668
$86$	−14.6692	−1.58182
$87$	16.7870	1.79976
$88$	−53.0062	−5.65049
$89$	−3.64195	−0.386046	−0.193023	−	0.981194i	$-0.561829\pi$
$89$	−3.64195	−0.386046	−0.193023	+	0.981194i	$0.561829\pi$
$90$	−38.3879	−4.04644
$91$	−9.89031	−1.03679
$92$	−31.7184	−3.30687
$93$	−13.0284	−1.35098
$94$	18.5826	1.91665
$95$	7.58674	0.778383
$96$	−38.2008	−3.89885
$97$	−11.1903	−1.13620	−0.568099	−	0.822960i	$-0.692321\pi$
$97$	−11.1903	−1.13620	−0.568099	+	0.822960i	$0.692321\pi$
$98$	5.32107	0.537509
$99$	28.4775	2.86210
$100$	30.4875	3.04875
$101$	−12.5784	−1.25160	−0.625799	−	0.779984i	$-0.715227\pi$
$101$	−12.5784	−1.25160	−0.625799	+	0.779984i	$0.715227\pi$
$102$	−26.7073	−2.64441
$103$	−7.83233	−0.771743	−0.385871	−	0.922553i	$-0.626099\pi$
$103$	−7.83233	−0.771743	−0.385871	+	0.922553i	$0.626099\pi$
$104$	−35.8417	−3.51457
$105$	−20.1338	−1.96485
$106$	−14.7779	−1.43536
$107$	−5.75511	−0.556367	−0.278184	−	0.960528i	$-0.589732\pi$
$107$	−5.75511	−0.556367	−0.278184	+	0.960528i	$0.589732\pi$
$108$	18.5117	1.78129
$109$	−16.8297	−1.61199	−0.805996	−	0.591921i	$-0.798370\pi$
$109$	−16.8297	−1.61199	−0.805996	+	0.591921i	$0.798370\pi$
$110$	−57.7247	−5.50383
$111$	19.6932	1.86920
$112$	−25.4970	−2.40924
$113$	6.87713	0.646946	0.323473	−	0.946237i	$-0.395150\pi$
$113$	6.87713	0.646946	0.323473	+	0.946237i	$0.395150\pi$
$114$	−16.4418	−1.53991
$115$	−20.8635	−1.94553
$116$	31.2692	2.90327
$117$	19.2559	1.78021
$118$	25.1464	2.31491
$119$	−8.29152	−0.760082
$120$	−72.9632	−6.66060
$121$	31.8222	2.89293
$122$	−13.2066	−1.19567
$123$	−15.2255	−1.37283
$124$	−24.2680	−2.17933
$125$	3.44322	0.307971
$126$	25.8282	2.30096
$127$	3.44883	0.306034	0.153017	−	0.988224i	$-0.451101\pi$
$127$	3.44883	0.306034	0.153017	+	0.988224i	$0.451101\pi$
$128$	−10.5784	−0.935010
$129$	14.9793	1.31886
$130$	−39.0322	−3.42335
$131$	−4.98184	−0.435266	−0.217633	−	0.976031i	$-0.569834\pi$
$131$	−4.98184	−0.435266	−0.217633	+	0.976031i	$0.569834\pi$
$132$	89.6130	7.79981
$133$	−5.10451	−0.442617
$134$	20.0624	1.73313
$135$	12.1765	1.04798
$136$	−30.0478	−2.57658
$137$	−1.42878	−0.122069	−0.0610343	−	0.998136i	$-0.519440\pi$
$137$	−1.42878	−0.122069	−0.0610343	+	0.998136i	$0.519440\pi$
$138$	45.2147	3.84893
$139$	−22.0327	−1.86879	−0.934394	−	0.356240i	$-0.884058\pi$
$139$	−22.0327	−1.86879	−0.934394	+	0.356240i	$0.884058\pi$
$140$	−37.5032	−3.16960
$141$	−18.9754	−1.59802
$142$	12.5868	1.05626
$143$	28.9555	2.42138
$144$	49.6413	4.13677
$145$	20.5680	1.70808
$146$	−33.9612	−2.81065
$147$	−5.43355	−0.448152
$148$	36.6826	3.01529
$149$	7.69630	0.630505	0.315253	−	0.949008i	$-0.397911\pi$
$149$	7.69630	0.630505	0.315253	+	0.949008i	$0.397911\pi$
$150$	−43.4601	−3.54850
$151$	−3.71424	−0.302261	−0.151130	−	0.988514i	$-0.548291\pi$
$151$	−3.71424	−0.302261	−0.151130	+	0.988514i	$0.548291\pi$
$152$	−18.4984	−1.50041
$153$	16.1432	1.30510
$154$	38.8383	3.12968
$155$	−15.9628	−1.28216
$156$	60.5945	4.85144
$157$	1.24066	0.0990152	0.0495076	−	0.998774i	$-0.484235\pi$
$157$	1.24066	0.0990152	0.0495076	+	0.998774i	$0.484235\pi$
$158$	−6.17454	−0.491220
$159$	15.0903	1.19674
$160$	−46.8048	−3.70025
$161$	14.0373	1.10630
$162$	8.27730	0.650326
$163$	−5.38035	−0.421422	−0.210711	−	0.977548i	$-0.567578\pi$
$163$	−5.38035	−0.421422	−0.210711	+	0.977548i	$0.567578\pi$
$164$	−28.3605	−2.21459
$165$	58.9449	4.58885
$166$	−42.3379	−3.28606
$167$	−16.8427	−1.30333	−0.651663	−	0.758509i	$-0.725928\pi$
$167$	−16.8427	−1.30333	−0.651663	+	0.758509i	$0.725928\pi$
$168$	49.0911	3.78746
$169$	6.57912	0.506086
$170$	−32.7226	−2.50971
$171$	9.93822	0.759995
$172$	27.9020	2.12751
$173$	−8.34909	−0.634769	−0.317385	−	0.948297i	$-0.602805\pi$
$173$	−8.34909	−0.634769	−0.317385	+	0.948297i	$0.602805\pi$
$174$	−44.5744	−3.37917
$175$	−13.4926	−1.01994
$176$	74.6465	5.62669
$177$	−25.6779	−1.93007
$178$	9.67043	0.724829
$179$	−18.7037	−1.39798	−0.698989	−	0.715132i	$-0.746366\pi$
$179$	−18.7037	−1.39798	−0.698989	+	0.715132i	$0.746366\pi$
$180$	73.0168	5.44235
$181$	10.0735	0.748757	0.374378	−	0.927276i	$-0.377856\pi$
$181$	10.0735	0.748757	0.374378	+	0.927276i	$0.377856\pi$
$182$	26.2616	1.94664
$183$	13.4857	0.996895
$184$	50.8703	3.75021
$185$	24.1287	1.77398
$186$	34.5942	2.53657
$187$	24.2748	1.77515
$188$	−35.3455	−2.57783
$189$	−8.19256	−0.595921
$190$	−20.1450	−1.46147
$191$	26.2456	1.89906	0.949532	−	0.313671i	$-0.101559\pi$
$191$	26.2456	1.89906	0.949532	+	0.313671i	$0.101559\pi$
$192$	39.5754	2.85611
$193$	4.47596	0.322187	0.161093	−	0.986939i	$-0.448498\pi$
$193$	4.47596	0.322187	0.161093	+	0.986939i	$0.448498\pi$
$194$	29.7134	2.13330
$195$	39.8573	2.85424
$196$	−10.1211	−0.722935
$197$	21.6549	1.54284	0.771422	−	0.636323i	$-0.219546\pi$
$197$	21.6549	1.54284	0.771422	+	0.636323i	$0.219546\pi$
$198$	−75.6162	−5.37381
$199$	−12.5971	−0.892988	−0.446494	−	0.894787i	$-0.647328\pi$
$199$	−12.5971	−0.892988	−0.446494	+	0.894787i	$0.647328\pi$
$200$	−48.8961	−3.45748
$201$	−20.4865	−1.44500
$202$	33.3993	2.34997
$203$	−13.8385	−0.971275
$204$	50.7993	3.55666
$205$	−18.6547	−1.30290
$206$	20.7971	1.44900
$207$	−27.3300	−1.89957
$208$	50.4744	3.49977
$209$	14.9443	1.03372
$210$	53.4610	3.68916
$211$	−19.2571	−1.32571	−0.662857	−	0.748746i	$-0.730656\pi$
$211$	−19.2571	−1.32571	−0.662857	+	0.748746i	$0.730656\pi$
$212$	28.1088	1.93052
$213$	−12.8529	−0.880666
$214$	15.2815	1.04462
$215$	18.3531	1.25167
$216$	−29.6892	−2.02010
$217$	10.7401	0.729084
$218$	44.6877	3.02663
$219$	34.6791	2.34339
$220$	109.797	7.40249
$221$	16.4141	1.10413
$222$	−52.2912	−3.50955
$223$	−4.80634	−0.321856	−0.160928	−	0.986966i	$-0.551449\pi$
$223$	−4.80634	−0.321856	−0.160928	+	0.986966i	$0.551449\pi$
$224$	31.4912	2.10409
$225$	26.2694	1.75129
$226$	−18.2608	−1.21469
$227$	18.7461	1.24422	0.622110	−	0.782930i	$-0.286276\pi$
$227$	18.7461	1.24422	0.622110	+	0.782930i	$0.286276\pi$
$228$	31.2736	2.07114
$229$	−12.2438	−0.809092	−0.404546	−	0.914518i	$-0.632571\pi$
$229$	−12.2438	−0.809092	−0.404546	+	0.914518i	$0.632571\pi$
$230$	55.3985	3.65287
$231$	−39.6593	−2.60939
$232$	−50.1498	−3.29250
$233$	28.3570	1.85773	0.928865	−	0.370419i	$-0.120786\pi$
$233$	28.3570	1.85773	0.928865	+	0.370419i	$0.120786\pi$
$234$	−51.1301	−3.34248
$235$	−23.2492	−1.51661
$236$	−47.8303	−3.11349
$237$	6.30506	0.409558
$238$	22.0164	1.42711
$239$	−24.0061	−1.55282	−0.776411	−	0.630227i	$-0.782962\pi$
$239$	−24.0061	−1.55282	−0.776411	+	0.630227i	$0.782962\pi$
$240$	102.751	6.63255
$241$	−24.6768	−1.58957	−0.794785	−	0.606890i	$-0.792417\pi$
$241$	−24.6768	−1.58957	−0.794785	+	0.606890i	$0.792417\pi$
$242$	−84.4972	−5.43169
$243$	−19.4481	−1.24760
$244$	25.1199	1.60814
$245$	−6.65736	−0.425323
$246$	40.4281	2.57760
$247$	10.1050	0.642967
$248$	38.9212	2.47150
$249$	43.2329	2.73977
$250$	−9.14276	−0.578239
$251$	4.62007	0.291617	0.145808	−	0.989313i	$-0.453422\pi$
$251$	4.62007	0.291617	0.145808	+	0.989313i	$0.453422\pi$
$252$	−49.1271	−3.09472
$253$	−41.0966	−2.58372
$254$	−9.15764	−0.574602
$255$	33.4143	2.09248
$256$	−1.10283	−0.0689268
$257$	16.9029	1.05437	0.527187	−	0.849749i	$-0.323247\pi$
$257$	16.9029	1.05437	0.527187	+	0.849749i	$0.323247\pi$
$258$	−39.7744	−2.47625
$259$	−16.2343	−1.00875
$260$	74.2423	4.60431
$261$	26.9429	1.66773
$262$	13.2282	0.817244
$263$	7.10615	0.438184	0.219092	−	0.975704i	$-0.429691\pi$
$263$	7.10615	0.438184	0.219092	+	0.975704i	$0.429691\pi$
$264$	−143.722	−8.84549
$265$	18.4891	1.13578
$266$	13.5540	0.831046
$267$	−9.87484	−0.604331
$268$	−38.1602	−2.33101
$269$	−21.8288	−1.33092	−0.665461	−	0.746432i	$-0.731765\pi$
$269$	−21.8288	−1.33092	−0.665461	+	0.746432i	$0.731765\pi$
$270$	−32.3320	−1.96767
$271$	−20.0743	−1.21943	−0.609713	−	0.792622i	$-0.708715\pi$
$271$	−20.0743	−1.21943	−0.609713	+	0.792622i	$0.708715\pi$
$272$	42.3151	2.56573
$273$	−26.8168	−1.62302
$274$	3.79381	0.229193
$275$	39.5018	2.38205
$276$	−86.0019	−5.17671
$277$	−4.48126	−0.269253	−0.134626	−	0.990896i	$-0.542983\pi$
$277$	−4.48126	−0.269253	−0.134626	+	0.990896i	$0.542983\pi$
$278$	58.5032	3.50879
$279$	−20.9104	−1.25187
$280$	60.1479	3.59453
$281$	−18.3098	−1.09227	−0.546135	−	0.837697i	$-0.683901\pi$
$281$	−18.3098	−1.09227	−0.546135	+	0.837697i	$0.683901\pi$
$282$	50.3851	3.00039
$283$	−3.75083	−0.222964	−0.111482	−	0.993766i	$-0.535560\pi$
$283$	−3.75083	−0.222964	−0.111482	+	0.993766i	$0.535560\pi$
$284$	−23.9411	−1.42064
$285$	20.5708	1.21851
$286$	−76.8853	−4.54632
$287$	12.5513	0.740878
$288$	−61.3118	−3.61283
$289$	−3.23927	−0.190545
$290$	−54.6139	−3.20704
$291$	−30.3415	−1.77865
$292$	64.5968	3.78024
$293$	22.3921	1.30816	0.654081	−	0.756425i	$-0.273056\pi$
$293$	22.3921	1.30816	0.654081	+	0.756425i	$0.273056\pi$
$294$	14.4276	0.841438
$295$	−31.4614	−1.83175
$296$	−58.8318	−3.41953
$297$	23.9851	1.39175
$298$	−20.4359	−1.18382
$299$	−27.7887	−1.60706
$300$	82.6644	4.77263
$301$	−12.3483	−0.711747
$302$	9.86238	0.567516
$303$	−34.1053	−1.95930
$304$	26.0505	1.49410
$305$	16.5232	0.946113
$306$	−42.8648	−2.45042
$307$	−6.20476	−0.354125	−0.177062	−	0.984200i	$-0.556659\pi$
$307$	−6.20476	−0.354125	−0.177062	+	0.984200i	$0.556659\pi$
$308$	−73.8734	−4.20933
$309$	−21.2367	−1.20812
$310$	42.3859	2.40735
$311$	16.0993	0.912910	0.456455	−	0.889747i	$-0.349119\pi$
$311$	16.0993	0.912910	0.456455	+	0.889747i	$0.349119\pi$
$312$	−97.1820	−5.50185
$313$	−3.94898	−0.223210	−0.111605	−	0.993753i	$-0.535599\pi$
$313$	−3.94898	−0.223210	−0.111605	+	0.993753i	$0.535599\pi$
$314$	−3.29431	−0.185908
$315$	−32.3144	−1.82071
$316$	11.7445	0.660677
$317$	−9.95331	−0.559034	−0.279517	−	0.960141i	$-0.590174\pi$
$317$	−9.95331	−0.559034	−0.279517	+	0.960141i	$0.590174\pi$
$318$	−40.0692	−2.24697
$319$	40.5146	2.26838
$320$	48.4890	2.71062
$321$	−15.6045	−0.870959
$322$	−37.2732	−2.07715
$323$	8.47152	0.471368
$324$	−15.7441	−0.874670
$325$	26.7103	1.48162
$326$	14.2864	0.791250
$327$	−45.6323	−2.52347
$328$	45.4849	2.51148
$329$	15.6425	0.862401
$330$	−156.516	−8.61591
$331$	31.8172	1.74883	0.874416	−	0.485177i	$-0.161245\pi$
$331$	31.8172	1.74883	0.874416	+	0.485177i	$0.161245\pi$
$332$	80.5299	4.41966
$333$	31.6073	1.73207
$334$	44.7222	2.44709
$335$	−25.1007	−1.37140
$336$	−69.1329	−3.77151
$337$	−8.50870	−0.463498	−0.231749	−	0.972776i	$-0.574445\pi$
$337$	−8.50870	−0.463498	−0.231749	+	0.972776i	$0.574445\pi$
$338$	−17.4695	−0.950214
$339$	18.6468	1.01275
$340$	62.2409	3.37549
$341$	−31.4433	−1.70275
$342$	−26.3889	−1.42695
$343$	20.1255	1.08667
$344$	−44.7495	−2.41273
$345$	−56.5696	−3.04560
$346$	22.1693	1.19183
$347$	−24.4436	−1.31220	−0.656100	−	0.754674i	$-0.727795\pi$
$347$	−24.4436	−1.31220	−0.656100	+	0.754674i	$0.727795\pi$
$348$	84.7839	4.54489
$349$	0.646587	0.0346110	0.0173055	−	0.999850i	$-0.494491\pi$
$349$	0.646587	0.0346110	0.0173055	+	0.999850i	$0.494491\pi$
$350$	35.8267	1.91502
$351$	16.2182	0.865664
$352$	−92.1956	−4.91404
$353$	13.9730	0.743709	0.371855	−	0.928291i	$-0.378722\pi$
$353$	13.9730	0.743709	0.371855	+	0.928291i	$0.378722\pi$
$354$	68.1823	3.62385
$355$	−15.7478	−0.835805
$356$	−18.3939	−0.974875
$357$	−22.4818	−1.18986
$358$	49.6637	2.62481
$359$	4.33452	0.228767	0.114384	−	0.993437i	$-0.463511\pi$
$359$	4.33452	0.228767	0.114384	+	0.993437i	$0.463511\pi$
$360$	−117.105	−6.17197
$361$	−13.7847	−0.725509
$362$	−26.7480	−1.40585
$363$	86.2833	4.52870
$364$	−49.9517	−2.61818
$365$	42.4899	2.22402
$366$	−35.8086	−1.87174
$367$	−12.8321	−0.669831	−0.334916	−	0.942248i	$-0.608708\pi$
$367$	−12.8321	−0.669831	−0.334916	+	0.942248i	$0.608708\pi$
$368$	−71.6385	−3.73441
$369$	−24.4367	−1.27212
$370$	−64.0688	−3.33078
$371$	−12.4399	−0.645845
$372$	−65.8008	−3.41161
$373$	0.550567	0.0285073	0.0142536	−	0.999898i	$-0.495463\pi$
$373$	0.550567	0.0285073	0.0142536	+	0.999898i	$0.495463\pi$
$374$	−64.4566	−3.33297
$375$	9.33602	0.482110
$376$	56.6874	2.92343
$377$	27.3951	1.41092
$378$	21.7536	1.11889
$379$	20.6217	1.05927	0.529633	−	0.848227i	$-0.322330\pi$
$379$	20.6217	1.05927	0.529633	+	0.848227i	$0.322330\pi$
$380$	38.3173	1.96564
$381$	9.35122	0.479078
$382$	−69.6896	−3.56563
$383$	−6.78855	−0.346879	−0.173439	−	0.984845i	$-0.555488\pi$
$383$	−6.78855	−0.346879	−0.173439	+	0.984845i	$0.555488\pi$
$384$	−28.6826	−1.46370
$385$	−48.5918	−2.47647
$386$	−11.8850	−0.604929
$387$	24.0416	1.22210
$388$	−56.5171	−2.86922
$389$	−1.91611	−0.0971505	−0.0485752	−	0.998820i	$-0.515468\pi$
$389$	−1.91611	−0.0971505	−0.0485752	+	0.998820i	$0.515468\pi$
$390$	−105.833	−5.35905
$391$	−23.2966	−1.17816
$392$	16.2323	0.819854
$393$	−13.5079	−0.681382
$394$	−57.4999	−2.89681
$395$	7.72516	0.388695
$396$	143.828	7.22762
$397$	−19.7358	−0.990514	−0.495257	−	0.868747i	$-0.664926\pi$
$397$	−19.7358	−0.990514	−0.495257	+	0.868747i	$0.664926\pi$
$398$	33.4491	1.67665
$399$	−13.8405	−0.692890
$400$	68.8584	3.44292
$401$	9.70926	0.484857	0.242429	−	0.970169i	$-0.422056\pi$
$401$	9.70926	0.484857	0.242429	+	0.970169i	$0.422056\pi$
$402$	54.3975	2.71310
$403$	−21.2613	−1.05910
$404$	−63.5281	−3.16064
$405$	−10.3560	−0.514593
$406$	36.7453	1.82364
$407$	47.5285	2.35590
$408$	−81.4723	−4.03348
$409$	−6.51614	−0.322203	−0.161101	−	0.986938i	$-0.551505\pi$
$409$	−6.51614	−0.322203	−0.161101	+	0.986938i	$0.551505\pi$
$410$	49.5337	2.44630
$411$	−3.87401	−0.191091
$412$	−39.5577	−1.94887
$413$	21.1678	1.04160
$414$	72.5691	3.56657
$415$	52.9703	2.60021
$416$	−62.3408	−3.05651
$417$	−59.7399	−2.92547
$418$	−39.6814	−1.94088
$419$	−3.39430	−0.165822	−0.0829112	−	0.996557i	$-0.526422\pi$
$419$	−3.39430	−0.165822	−0.0829112	+	0.996557i	$0.526422\pi$
$420$	−101.687	−4.96181
$421$	4.37973	0.213455	0.106727	−	0.994288i	$-0.465963\pi$
$421$	4.37973	0.213455	0.106727	+	0.994288i	$0.465963\pi$
$422$	51.1332	2.48913
$423$	−30.4552	−1.48078
$424$	−45.0811	−2.18933
$425$	22.3925	1.08620
$426$	34.1282	1.65351
$427$	−11.1171	−0.537994
$428$	−29.0666	−1.40499
$429$	78.5105	3.79052
$430$	−48.7329	−2.35011
$431$	−26.5309	−1.27795	−0.638975	−	0.769227i	$-0.720641\pi$
$431$	−26.5309	−1.27795	−0.638975	+	0.769227i	$0.720641\pi$
$432$	41.8101	2.01159
$433$	30.8836	1.48417	0.742084	−	0.670306i	$-0.233837\pi$
$433$	30.8836	1.48417	0.742084	+	0.670306i	$0.233837\pi$
$434$	−28.5180	−1.36891
$435$	55.7684	2.67389
$436$	−84.9995	−4.07074
$437$	−14.3421	−0.686074
$438$	−92.0830	−4.39989
$439$	13.8440	0.660740	0.330370	−	0.943852i	$-0.392826\pi$
$439$	13.8440	0.660740	0.330370	+	0.943852i	$0.392826\pi$
$440$	−176.093	−8.39490
$441$	−8.72077	−0.415275
$442$	−43.5842	−2.07309
$443$	32.3233	1.53573	0.767863	−	0.640614i	$-0.221320\pi$
$443$	32.3233	1.53573	0.767863	+	0.640614i	$0.221320\pi$
$444$	99.4618	4.72025
$445$	−12.0990	−0.573546
$446$	12.7622	0.604309
$447$	20.8679	0.987017
$448$	−32.6244	−1.54136
$449$	22.4351	1.05878	0.529390	−	0.848379i	$-0.322421\pi$
$449$	22.4351	1.05878	0.529390	+	0.848379i	$0.322421\pi$
$450$	−69.7529	−3.28818
$451$	−36.7459	−1.73030
$452$	34.7334	1.63372
$453$	−10.0709	−0.473170
$454$	−49.7763	−2.33612
$455$	−32.8568	−1.54035
$456$	−50.1568	−2.34881
$457$	28.8363	1.34891	0.674453	−	0.738318i	$-0.264379\pi$
$457$	28.8363	1.34891	0.674453	+	0.738318i	$0.264379\pi$
$458$	32.5108	1.51913
$459$	13.5965	0.634630
$460$	−105.372	−4.91301
$461$	25.9393	1.20811	0.604057	−	0.796941i	$-0.293550\pi$
$461$	25.9393	1.20811	0.604057	+	0.796941i	$0.293550\pi$
$462$	105.307	4.89932
$463$	5.80106	0.269598	0.134799	−	0.990873i	$-0.456961\pi$
$463$	5.80106	0.269598	0.134799	+	0.990873i	$0.456961\pi$
$464$	70.6239	3.27863
$465$	−43.2818	−2.00715
$466$	−75.2961	−3.48802
$467$	−34.6947	−1.60548	−0.802740	−	0.596329i	$-0.796625\pi$
$467$	−34.6947	−1.60548	−0.802740	+	0.596329i	$0.796625\pi$
$468$	97.2534	4.49554
$469$	16.8882	0.779826
$470$	61.7335	2.84755
$471$	3.36394	0.155002
$472$	76.7107	3.53090
$473$	36.1518	1.66226
$474$	−16.7418	−0.768975
$475$	13.7855	0.632522
$476$	−41.8769	−1.91942
$477$	24.2198	1.10895
$478$	63.7430	2.91554
$479$	−0.706445	−0.0322783	−0.0161391	−	0.999870i	$-0.505137\pi$
$479$	−0.706445	−0.0322783	−0.0161391	+	0.999870i	$0.505137\pi$
$480$	−126.907	−5.79251
$481$	32.1378	1.46536
$482$	65.5240	2.98454
$483$	38.0611	1.73184
$484$	160.720	7.30546
$485$	−37.1753	−1.68804
$486$	51.6403	2.34245
$487$	−31.4128	−1.42345	−0.711724	−	0.702459i	$-0.752085\pi$
$487$	−31.4128	−1.42345	−0.711724	+	0.702459i	$0.752085\pi$
$488$	−40.2875	−1.82373
$489$	−14.5884	−0.659710
$490$	17.6772	0.798575
$491$	−11.4070	−0.514789	−0.257394	−	0.966306i	$-0.582864\pi$
$491$	−11.4070	−0.514789	−0.257394	+	0.966306i	$0.582864\pi$
$492$	−76.8973	−3.46680
$493$	22.9666	1.03437
$494$	−26.8318	−1.20722
$495$	94.6057	4.25221
$496$	−54.8112	−2.46109
$497$	10.5954	0.475269
$498$	−114.796	−5.14412
$499$	41.1933	1.84406	0.922032	−	0.387113i	$-0.126528\pi$
$499$	41.1933	1.84406	0.922032	+	0.387113i	$0.126528\pi$
$500$	17.3902	0.777715
$501$	−45.6676	−2.04028
$502$	−12.2676	−0.547532
$503$	31.7494	1.41564	0.707818	−	0.706395i	$-0.249680\pi$
$503$	31.7494	1.41564	0.707818	+	0.706395i	$0.249680\pi$
$504$	78.7905	3.50961
$505$	−41.7869	−1.85949
$506$	109.123	4.85113
$507$	17.8387	0.792246
$508$	17.4185	0.772823
$509$	−1.86283	−0.0825686	−0.0412843	−	0.999147i	$-0.513145\pi$
$509$	−1.86283	−0.0825686	−0.0412843	+	0.999147i	$0.513145\pi$
$510$	−88.7246	−3.92879
$511$	−28.5880	−1.26466
$512$	24.0852	1.06443
$513$	8.37041	0.369563
$514$	−44.8821	−1.97966
$515$	−26.0199	−1.14657
$516$	75.6540	3.33048
$517$	−45.7961	−2.01411
$518$	43.1067	1.89400
$519$	−22.6379	−0.993692
$520$	−119.070	−5.22158
$521$	−2.26410	−0.0991922	−0.0495961	−	0.998769i	$-0.515793\pi$
$521$	−2.26410	−0.0991922	−0.0495961	+	0.998769i	$0.515793\pi$
$522$	−71.5413	−3.13128
$523$	−3.62903	−0.158686	−0.0793432	−	0.996847i	$-0.525282\pi$
$523$	−3.62903	−0.158686	−0.0793432	+	0.996847i	$0.525282\pi$
$524$	−25.1611	−1.09917
$525$	−36.5841	−1.59666
$526$	−18.8689	−0.822723
$527$	−17.8244	−0.776443
$528$	202.398	8.80824
$529$	16.4405	0.714806
$530$	−49.0941	−2.13251
$531$	−41.2127	−1.78848
$532$	−25.7807	−1.11773
$533$	−24.8468	−1.07624
$534$	26.2206	1.13468
$535$	−19.1191	−0.826592
$536$	61.2017	2.64351
$537$	−50.7135	−2.18845
$538$	57.9617	2.49891
$539$	−13.1136	−0.564842
$540$	61.4980	2.64645
$541$	−29.3364	−1.26127	−0.630635	−	0.776080i	$-0.717205\pi$
$541$	−29.3364	−1.26127	−0.630635	+	0.776080i	$0.717205\pi$
$542$	53.3031	2.28956
$543$	27.3135	1.17213
$544$	−52.2633	−2.24077
$545$	−55.9102	−2.39493
$546$	71.2063	3.04735
$547$	1.48297	0.0634071	0.0317035	−	0.999497i	$-0.489907\pi$
$547$	1.48297	0.0634071	0.0317035	+	0.999497i	$0.489907\pi$
$548$	−7.21613	−0.308258
$549$	21.6444	0.923762
$550$	−104.889	−4.47247
$551$	14.1389	0.602340
$552$	137.931	5.87071
$553$	−5.19764	−0.221026
$554$	11.8990	0.505542
$555$	65.4231	2.77706
$556$	−111.278	−4.71922
$557$	−16.1559	−0.684549	−0.342275	−	0.939600i	$-0.611197\pi$
$557$	−16.1559	−0.684549	−0.342275	+	0.939600i	$0.611197\pi$
$558$	55.5232	2.35048
$559$	24.4451	1.03392
$560$	−84.7038	−3.57939
$561$	65.8191	2.77888
$562$	48.6178	2.05082
$563$	26.3506	1.11055	0.555274	−	0.831668i	$-0.312614\pi$
$563$	26.3506	1.11055	0.555274	+	0.831668i	$0.312614\pi$
$564$	−95.8364	−4.03544
$565$	22.8466	0.961165
$566$	9.95954	0.418631
$567$	6.96771	0.292616
$568$	38.3970	1.61110
$569$	2.27792	0.0954955	0.0477477	−	0.998859i	$-0.484796\pi$
$569$	2.27792	0.0954955	0.0477477	+	0.998859i	$0.484796\pi$
$570$	−54.6215	−2.28784
$571$	33.6216	1.40702	0.703510	−	0.710685i	$-0.251615\pi$
$571$	33.6216	1.40702	0.703510	+	0.710685i	$0.251615\pi$
$572$	146.242	6.11467
$573$	71.1628	2.97287
$574$	−33.3273	−1.39105
$575$	−37.9100	−1.58095
$576$	63.5180	2.64658
$577$	41.4268	1.72462	0.862310	−	0.506381i	$-0.169017\pi$
$577$	41.4268	1.72462	0.862310	+	0.506381i	$0.169017\pi$
$578$	8.60119	0.357762
$579$	12.1362	0.504363
$580$	103.880	4.31338
$581$	−35.6394	−1.47857
$582$	80.5654	3.33954
$583$	36.4197	1.50835
$584$	−103.601	−4.28703
$585$	63.9705	2.64485
$586$	−59.4576	−2.45617
$587$	41.5414	1.71460	0.857298	−	0.514820i	$-0.172141\pi$
$587$	41.5414	1.71460	0.857298	+	0.514820i	$0.172141\pi$
$588$	−27.4425	−1.13171
$589$	−10.9732	−0.452144
$590$	83.5392	3.43925
$591$	58.7154	2.41523
$592$	82.8504	3.40513
$593$	−29.3876	−1.20680	−0.603402	−	0.797437i	$-0.706189\pi$
$593$	−29.3876	−1.20680	−0.603402	+	0.797437i	$0.706189\pi$
$594$	−63.6873	−2.61312
$595$	−27.5454	−1.12925
$596$	38.8707	1.59220
$597$	−34.1561	−1.39792
$598$	73.7870	3.01738
$599$	1.18250	0.0483156	0.0241578	−	0.999708i	$-0.492310\pi$
$599$	1.18250	0.0483156	0.0241578	+	0.999708i	$0.492310\pi$
$600$	−132.578	−5.41247
$601$	−8.00903	−0.326695	−0.163348	−	0.986569i	$-0.552229\pi$
$601$	−8.00903	−0.326695	−0.163348	+	0.986569i	$0.552229\pi$
$602$	32.7884	1.33636
$603$	−32.8805	−1.33900
$604$	−18.7590	−0.763293
$605$	105.717	4.29801
$606$	90.5595	3.67873
$607$	−6.49039	−0.263437	−0.131718	−	0.991287i	$-0.542049\pi$
$607$	−6.49039	−0.263437	−0.131718	+	0.991287i	$0.542049\pi$
$608$	−32.1748	−1.30486
$609$	−37.5221	−1.52047
$610$	−43.8738	−1.77640
$611$	−30.9664	−1.25277
$612$	81.5322	3.29574
$613$	−28.6991	−1.15915	−0.579573	−	0.814921i	$-0.696780\pi$
$613$	−28.6991	−1.15915	−0.579573	+	0.814921i	$0.696780\pi$
$614$	16.4754	0.664895
$615$	−50.5808	−2.03961
$616$	118.479	4.77364
$617$	−12.5264	−0.504294	−0.252147	−	0.967689i	$-0.581137\pi$
$617$	−12.5264	−0.504294	−0.252147	+	0.967689i	$0.581137\pi$
$618$	56.3897	2.26833
$619$	−32.6496	−1.31230	−0.656150	−	0.754631i	$-0.727816\pi$
$619$	−32.6496	−1.31230	−0.656150	+	0.754631i	$0.727816\pi$
$620$	−80.6212	−3.23782
$621$	−23.0185	−0.923702
$622$	−42.7484	−1.71406
$623$	8.14042	0.326139
$624$	136.857	5.47868
$625$	−18.7435	−0.749740
$626$	10.4857	0.419093
$627$	40.5202	1.61822
$628$	6.26602	0.250041
$629$	26.9427	1.07427
$630$	85.8041	3.41852
$631$	−45.2477	−1.80128	−0.900642	−	0.434562i	$-0.856903\pi$
$631$	−45.2477	−1.80128	−0.900642	+	0.434562i	$0.856903\pi$
$632$	−18.8358	−0.749250
$633$	−52.2141	−2.07532
$634$	26.4289	1.04963
$635$	11.4574	0.454674
$636$	76.2147	3.02211
$637$	−8.86714	−0.351329
$638$	−107.578	−4.25905
$639$	−20.6287	−0.816060
$640$	−35.1428	−1.38914
$641$	6.82470	0.269559	0.134780	−	0.990876i	$-0.456967\pi$
$641$	6.82470	0.269559	0.134780	+	0.990876i	$0.456967\pi$
$642$	41.4345	1.63529
$643$	−40.1316	−1.58264	−0.791318	−	0.611405i	$-0.790605\pi$
$643$	−40.1316	−1.58264	−0.791318	+	0.611405i	$0.790605\pi$
$644$	70.8965	2.79371
$645$	49.7630	1.95942
$646$	−22.4943	−0.885028
$647$	24.4223	0.960141	0.480070	−	0.877230i	$-0.340611\pi$
$647$	24.4223	0.960141	0.480070	+	0.877230i	$0.340611\pi$
$648$	25.2505	0.991931
$649$	−61.9723	−2.43263
$650$	−70.9236	−2.78185
$651$	29.1209	1.14134
$652$	−27.1738	−1.06421
$653$	8.89790	0.348202	0.174101	−	0.984728i	$-0.444298\pi$
$653$	8.89790	0.348202	0.174101	+	0.984728i	$0.444298\pi$
$654$	121.167	4.73801
$655$	−16.5503	−0.646672
$656$	−64.0544	−2.50091
$657$	55.6594	2.17148
$658$	−41.5355	−1.61922
$659$	4.90760	0.191173	0.0955864	−	0.995421i	$-0.469527\pi$
$659$	4.90760	0.191173	0.0955864	+	0.995421i	$0.469527\pi$
$660$	297.705	11.5881
$661$	16.1551	0.628361	0.314180	−	0.949363i	$-0.398270\pi$
$661$	16.1551	0.628361	0.314180	+	0.949363i	$0.398270\pi$
$662$	−84.4839	−3.28356
$663$	44.5055	1.72845
$664$	−129.155	−5.01217
$665$	−16.9578	−0.657594
$666$	−83.9266	−3.25209
$667$	−38.8819	−1.50552
$668$	−85.0651	−3.29127
$669$	−13.0320	−0.503846
$670$	66.6496	2.57490
$671$	32.5471	1.25647
$672$	85.3858	3.29383
$673$	−15.3092	−0.590127	−0.295064	−	0.955478i	$-0.595341\pi$
$673$	−15.3092	−0.590127	−0.295064	+	0.955478i	$0.595341\pi$
$674$	22.5931	0.870252
$675$	22.1253	0.851601
$676$	33.2283	1.27801
$677$	−6.05465	−0.232699	−0.116350	−	0.993208i	$-0.537119\pi$
$677$	−6.05465	−0.232699	−0.116350	+	0.993208i	$0.537119\pi$
$678$	−49.5126	−1.90152
$679$	25.0123	0.959883
$680$	−99.8224	−3.82802
$681$	50.8285	1.94775
$682$	83.4912	3.19704
$683$	51.5076	1.97088	0.985442	−	0.170012i	$-0.0543808\pi$
$683$	51.5076	1.97088	0.985442	+	0.170012i	$0.0543808\pi$
$684$	50.1936	1.91920
$685$	−4.74656	−0.181357
$686$	−53.4390	−2.04031
$687$	−33.1980	−1.26658
$688$	63.0188	2.40257
$689$	24.6263	0.938186
$690$	150.209	5.71834
$691$	30.8527	1.17369	0.586846	−	0.809699i	$-0.300369\pi$
$691$	30.8527	1.17369	0.586846	+	0.809699i	$0.300369\pi$
$692$	−42.1676	−1.60297
$693$	−63.6526	−2.41796
$694$	64.9048	2.46375
$695$	−73.1952	−2.77645
$696$	−135.977	−5.15420
$697$	−20.8303	−0.789003
$698$	−1.71688	−0.0649847
$699$	76.8877	2.90816
$700$	−68.1452	−2.57565
$701$	18.7189	0.707005	0.353502	−	0.935434i	$-0.384991\pi$
$701$	18.7189	0.707005	0.353502	+	0.935434i	$0.384991\pi$
$702$	−43.0640	−1.62535
$703$	16.5867	0.625580
$704$	95.5131	3.59979
$705$	−63.0384	−2.37416
$706$	−37.1024	−1.39637
$707$	28.1151	1.05738
$708$	−129.688	−4.87398
$709$	−23.2344	−0.872586	−0.436293	−	0.899805i	$-0.643709\pi$
$709$	−23.2344	−0.872586	−0.436293	+	0.899805i	$0.643709\pi$
$710$	41.8149	1.56929
$711$	10.1195	0.379512
$712$	29.5003	1.10557
$713$	30.1763	1.13011
$714$	59.6957	2.23405
$715$	96.1935	3.59743
$716$	−94.4641	−3.53029
$717$	−65.0905	−2.43085
$718$	−11.5094	−0.429527
$719$	27.5640	1.02796	0.513982	−	0.857801i	$-0.328170\pi$
$719$	27.5640	1.02796	0.513982	+	0.857801i	$0.328170\pi$
$720$	164.914	6.14599
$721$	17.5067	0.651984
$722$	36.6023	1.36220
$723$	−66.9091	−2.48838
$724$	50.8768	1.89082
$725$	37.3731	1.38800
$726$	−229.107	−8.50297
$727$	−14.1911	−0.526318	−0.263159	−	0.964752i	$-0.584764\pi$
$727$	−14.1911	−0.526318	−0.263159	+	0.964752i	$0.584764\pi$
$728$	80.1129	2.96918
$729$	−43.3800	−1.60667
$730$	−112.823	−4.17577
$731$	20.4935	0.757980
$732$	68.1106	2.51744
$733$	−21.0021	−0.775731	−0.387866	−	0.921716i	$-0.626788\pi$
$733$	−21.0021	−0.775731	−0.387866	+	0.921716i	$0.626788\pi$
$734$	34.0730	1.25766
$735$	−18.0509	−0.665817
$736$	88.4804	3.26143
$737$	−49.4430	−1.82126
$738$	64.8865	2.38851
$739$	16.3401	0.601082	0.300541	−	0.953769i	$-0.402833\pi$
$739$	16.3401	0.601082	0.300541	+	0.953769i	$0.402833\pi$
$740$	121.864	4.47980
$741$	27.3989	1.00652
$742$	33.0314	1.21262
$743$	40.0013	1.46750	0.733752	−	0.679417i	$-0.237767\pi$
$743$	40.0013	1.46750	0.733752	+	0.679417i	$0.237767\pi$
$744$	105.532	3.86898
$745$	25.5680	0.936739
$746$	−1.46191	−0.0535245
$747$	69.3882	2.53878
$748$	122.601	4.48275
$749$	12.8637	0.470030
$750$	−24.7898	−0.905197
$751$	5.00997	0.182816	0.0914082	−	0.995814i	$-0.470863\pi$
$751$	5.00997	0.182816	0.0914082	+	0.995814i	$0.470863\pi$
$752$	−79.8305	−2.91112
$753$	12.5270	0.456508
$754$	−72.7420	−2.64911
$755$	−12.3391	−0.449067
$756$	−41.3771	−1.50487
$757$	−4.97910	−0.180969	−0.0904843	−	0.995898i	$-0.528841\pi$
$757$	−4.97910	−0.180969	−0.0904843	+	0.995898i	$0.528841\pi$
$758$	−54.7567	−1.98885
$759$	−111.430	−4.04466
$760$	−61.4537	−2.22916
$761$	20.9783	0.760464	0.380232	−	0.924891i	$-0.375844\pi$
$761$	20.9783	0.760464	0.380232	+	0.924891i	$0.375844\pi$
$762$	−24.8302	−0.899503
$763$	37.6175	1.36184
$764$	132.555	4.79567
$765$	53.6295	1.93898
$766$	18.0256	0.651291
$767$	−41.9044	−1.51308
$768$	−2.99023	−0.107901
$769$	28.2528	1.01882	0.509412	−	0.860523i	$-0.329863\pi$
$769$	28.2528	1.01882	0.509412	+	0.860523i	$0.329863\pi$
$770$	129.025	4.64975
$771$	45.8308	1.65056
$772$	22.6061	0.813612
$773$	−27.0220	−0.971915	−0.485957	−	0.873983i	$-0.661529\pi$
$773$	−27.0220	−0.971915	−0.485957	+	0.873983i	$0.661529\pi$
$774$	−63.8375	−2.29459
$775$	−29.0052	−1.04190
$776$	90.6426	3.25388
$777$	−44.0179	−1.57913
$778$	5.08782	0.182407
$779$	−12.8237	−0.459458
$780$	201.302	7.20777
$781$	−31.0198	−1.10998
$782$	61.8592	2.21208
$783$	22.6925	0.810965
$784$	−22.8592	−0.816402
$785$	4.12161	0.147106
$786$	35.8673	1.27934
$787$	24.5273	0.874303	0.437151	−	0.899388i	$-0.355987\pi$
$787$	24.5273	0.874303	0.437151	+	0.899388i	$0.355987\pi$
$788$	109.369	3.89612
$789$	19.2677	0.685950
$790$	−20.5125	−0.729803
$791$	−15.3717	−0.546553
$792$	−230.672	−8.19658
$793$	22.0077	0.781517
$794$	52.4044	1.85976
$795$	50.1318	1.77799
$796$	−63.6227	−2.25505
$797$	−27.8128	−0.985179	−0.492590	−	0.870262i	$-0.663950\pi$
$797$	−27.8128	−0.985179	−0.492590	+	0.870262i	$0.663950\pi$
$798$	36.7504	1.30095
$799$	−25.9606	−0.918420
$800$	−85.0467	−3.00686
$801$	−15.8490	−0.559997
$802$	−25.7809	−0.910355
$803$	83.6961	2.95357
$804$	−103.468	−3.64905
$805$	46.6337	1.64362
$806$	56.4550	1.98854
$807$	−59.1869	−2.08348
$808$	101.887	3.58437
$809$	42.5546	1.49614	0.748070	−	0.663620i	$-0.230981\pi$
$809$	42.5546	1.49614	0.748070	+	0.663620i	$0.230981\pi$
$810$	27.4981	0.966186
$811$	−35.2361	−1.23731	−0.618653	−	0.785665i	$-0.712321\pi$
$811$	−35.2361	−1.23731	−0.618653	+	0.785665i	$0.712321\pi$
$812$	−69.8924	−2.45274
$813$	−54.4298	−1.90894
$814$	−126.202	−4.42338
$815$	−17.8742	−0.626104
$816$	114.734	4.01649
$817$	12.6164	0.441392
$818$	17.3023	0.604959
$819$	−43.0406	−1.50396
$820$	−94.2170	−3.29020
$821$	−38.5606	−1.34577	−0.672886	−	0.739746i	$-0.734946\pi$
$821$	−38.5606	−1.34577	−0.672886	+	0.739746i	$0.734946\pi$
$822$	10.2866	0.358787
$823$	12.3487	0.430450	0.215225	−	0.976565i	$-0.430952\pi$
$823$	12.3487	0.430450	0.215225	+	0.976565i	$0.430952\pi$
$824$	63.4430	2.21014
$825$	107.106	3.72895
$826$	−56.2068	−1.95568
$827$	−36.3226	−1.26306	−0.631530	−	0.775352i	$-0.717573\pi$
$827$	−36.3226	−1.26306	−0.631530	+	0.775352i	$0.717573\pi$
$828$	−138.032	−4.79694
$829$	42.7151	1.48356	0.741779	−	0.670644i	$-0.233982\pi$
$829$	42.7151	1.48356	0.741779	+	0.670644i	$0.233982\pi$
$830$	−140.651	−4.88208
$831$	−12.1506	−0.421499
$832$	64.5840	2.23905
$833$	−7.43375	−0.257564
$834$	158.627	5.49279
$835$	−55.9533	−1.93635
$836$	75.4771	2.61043
$837$	−17.6117	−0.608748
$838$	9.01285	0.311344
$839$	−27.2788	−0.941769	−0.470885	−	0.882195i	$-0.656065\pi$
$839$	−27.2788	−0.941769	−0.470885	+	0.882195i	$0.656065\pi$
$840$	163.086	5.62701
$841$	9.33128	0.321768
$842$	−11.6294	−0.400777
$843$	−49.6455	−1.70988
$844$	−97.2593	−3.34780
$845$	21.8566	0.751890
$846$	80.8675	2.78028
$847$	−71.1285	−2.44400
$848$	63.4859	2.18011
$849$	−10.1701	−0.349036
$850$	−59.4586	−2.03941
$851$	−45.6133	−1.56360
$852$	−64.9144	−2.22393
$853$	−5.77039	−0.197575	−0.0987873	−	0.995109i	$-0.531496\pi$
$853$	−5.77039	−0.197575	−0.0987873	+	0.995109i	$0.531496\pi$
$854$	29.5191	1.01012
$855$	33.0159	1.12912
$856$	46.6172	1.59334
$857$	−9.15989	−0.312896	−0.156448	−	0.987686i	$-0.550004\pi$
$857$	−9.15989	−0.312896	−0.156448	+	0.987686i	$0.550004\pi$
$858$	−208.468	−7.11699
$859$	37.5704	1.28188	0.640942	−	0.767589i	$-0.278544\pi$
$859$	37.5704	1.28188	0.640942	+	0.767589i	$0.278544\pi$
$860$	92.6937	3.16083
$861$	34.0317	1.15980
$862$	70.4474	2.39945
$863$	−14.3971	−0.490084	−0.245042	−	0.969512i	$-0.578802\pi$
$863$	−14.3971	−0.490084	−0.245042	+	0.969512i	$0.578802\pi$
$864$	−51.6395	−1.75681
$865$	−27.7366	−0.943074
$866$	−82.0048	−2.78664
$867$	−8.78301	−0.298287
$868$	54.2435	1.84114
$869$	15.2169	0.516199
$870$	−148.081	−5.02042
$871$	−33.4324	−1.13281
$872$	136.323	4.61647
$873$	−48.6977	−1.64817
$874$	38.0824	1.28816
$875$	−7.69624	−0.260180
$876$	175.149	5.91773
$877$	−31.8663	−1.07605	−0.538024	−	0.842930i	$-0.680829\pi$
$877$	−31.8663	−1.07605	−0.538024	+	0.842930i	$0.680829\pi$
$878$	−36.7599	−1.24059
$879$	60.7144	2.04785
$880$	247.984	8.35955
$881$	31.0393	1.04574	0.522871	−	0.852412i	$-0.324861\pi$
$881$	31.0393	1.04574	0.522871	+	0.852412i	$0.324861\pi$
$882$	23.1562	0.779709
$883$	15.5612	0.523675	0.261837	−	0.965112i	$-0.415672\pi$
$883$	15.5612	0.523675	0.261837	+	0.965112i	$0.415672\pi$
$884$	82.9006	2.78825
$885$	−85.3050	−2.86750
$886$	−85.8277	−2.88344
$887$	20.1215	0.675615	0.337807	−	0.941215i	$-0.390315\pi$
$887$	20.1215	0.675615	0.337807	+	0.941215i	$0.390315\pi$
$888$	−159.518	−5.35306
$889$	−7.70877	−0.258544
$890$	32.1263	1.07688
$891$	−20.3991	−0.683396
$892$	−24.2747	−0.812778
$893$	−15.9821	−0.534821
$894$	−55.4103	−1.85320
$895$	−62.1358	−2.07697
$896$	23.6448	0.789916
$897$	−75.3468	−2.51575
$898$	−59.5718	−1.98794
$899$	−29.7489	−0.992181
$900$	132.675	4.42251
$901$	20.6454	0.687797
$902$	97.5710	3.24876
$903$	−33.4815	−1.11420
$904$	−55.7057	−1.85274
$905$	33.4653	1.11242
$906$	26.7411	0.888412
$907$	14.9921	0.497806	0.248903	−	0.968528i	$-0.419930\pi$
$907$	14.9921	0.497806	0.248903	+	0.968528i	$0.419930\pi$
$908$	94.6783	3.14201
$909$	−54.7386	−1.81556
$910$	87.2442	2.89212
$911$	−17.3583	−0.575105	−0.287553	−	0.957765i	$-0.592842\pi$
$911$	−17.3583	−0.575105	−0.287553	+	0.957765i	$0.592842\pi$
$912$	70.6337	2.33892
$913$	104.340	3.45316
$914$	−76.5688	−2.53267
$915$	44.8012	1.48108
$916$	−61.8381	−2.04319
$917$	11.1353	0.367721
$918$	−36.1026	−1.19156
$919$	−42.2903	−1.39503	−0.697513	−	0.716572i	$-0.745710\pi$
$919$	−42.2903	−1.39503	−0.697513	+	0.716572i	$0.745710\pi$
$920$	168.997	5.57166
$921$	−16.8237	−0.554360
$922$	−68.8764	−2.26832
$923$	−20.9749	−0.690399
$924$	−200.302	−6.58944
$925$	43.8431	1.44155
$926$	−15.4035	−0.506190
$927$	−34.0847	−1.11949
$928$	−87.2273	−2.86338
$929$	10.7518	0.352754	0.176377	−	0.984323i	$-0.443562\pi$
$929$	10.7518	0.352754	0.176377	+	0.984323i	$0.443562\pi$
$930$	114.926	3.76857
$931$	−4.57644	−0.149987
$932$	143.219	4.69129
$933$	43.6520	1.42910
$934$	92.1246	3.01441
$935$	80.6436	2.63733
$936$	−155.976	−5.09823
$937$	16.7112	0.545930	0.272965	−	0.962024i	$-0.411996\pi$
$937$	16.7112	0.545930	0.272965	+	0.962024i	$0.411996\pi$
$938$	−44.8431	−1.46418
$939$	−10.7073	−0.349421
$940$	−117.422	−3.82988
$941$	37.2319	1.21373	0.606863	−	0.794807i	$-0.292428\pi$
$941$	37.2319	1.21373	0.606863	+	0.794807i	$0.292428\pi$
$942$	−8.93224	−0.291028
$943$	35.2651	1.14839
$944$	−108.028	−3.51603
$945$	−27.2166	−0.885357
$946$	−95.9935	−3.12102
$947$	5.21832	0.169572	0.0847862	−	0.996399i	$-0.472979\pi$
$947$	5.21832	0.169572	0.0847862	+	0.996399i	$0.472979\pi$
$948$	31.8441	1.03425
$949$	56.5936	1.83711
$950$	−36.6045	−1.18761
$951$	−26.9876	−0.875133
$952$	67.1625	2.17675
$953$	−24.1844	−0.783409	−0.391705	−	0.920091i	$-0.628115\pi$
$953$	−24.1844	−0.783409	−0.391705	+	0.920091i	$0.628115\pi$
$954$	−64.3105	−2.08213
$955$	87.1909	2.82143
$956$	−121.244	−3.92132
$957$	109.852	3.55101
$958$	1.87582	0.0606049
$959$	3.19358	0.103126
$960$	131.474	4.24331
$961$	−7.91189	−0.255222
$962$	−85.3352	−2.75132
$963$	−25.0450	−0.807065
$964$	−124.632	−4.01412
$965$	14.8697	0.478671
$966$	−101.063	−3.25166
$967$	−14.6810	−0.472110	−0.236055	−	0.971740i	$-0.575855\pi$
$967$	−14.6810	−0.472110	−0.236055	+	0.971740i	$0.575855\pi$
$968$	−257.764	−8.28486
$969$	22.9698	0.737897
$970$	98.7113	3.16943
$971$	−44.8556	−1.43949	−0.719743	−	0.694241i	$-0.755740\pi$
$971$	−44.8556	−1.43949	−0.719743	+	0.694241i	$0.755740\pi$
$972$	−98.2238	−3.15053
$973$	49.2471	1.57879
$974$	83.4100	2.67263
$975$	72.4228	2.31938
$976$	56.7353	1.81605
$977$	−15.3395	−0.490755	−0.245378	−	0.969428i	$-0.578912\pi$
$977$	−15.3395	−0.490755	−0.245378	+	0.969428i	$0.578912\pi$
$978$	38.7364	1.23865
$979$	−23.8324	−0.761688
$980$	−33.6234	−1.07406
$981$	−73.2393	−2.33835
$982$	30.2888	0.966554
$983$	2.35374	0.0750726	0.0375363	−	0.999295i	$-0.488049\pi$
$983$	2.35374	0.0750726	0.0375363	+	0.999295i	$0.488049\pi$
$984$	123.328	3.93157
$985$	71.9400	2.29220
$986$	−60.9831	−1.94210
$987$	42.4135	1.35004
$988$	51.0361	1.62367
$989$	−34.6950	−1.10324
$990$	−251.206	−7.98384
$991$	43.5991	1.38497	0.692485	−	0.721432i	$-0.256516\pi$
$991$	43.5991	1.38497	0.692485	+	0.721432i	$0.256516\pi$
$992$	67.6971	2.14938
$993$	86.2697	2.73769
$994$	−28.1339	−0.892353
$995$	−41.8492	−1.32671
$996$	218.350	6.91870
$997$	30.0994	0.953258	0.476629	−	0.879105i	$-0.341859\pi$
$997$	30.0994	0.953258	0.476629	+	0.879105i	$0.341859\pi$
$998$	−109.380	−3.46237
$999$	26.6211	0.842254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.c.1.6	✓	261

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.c.1.6	✓	261	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65529 q^{2} +2.71142 q^{3} +5.05057 q^{4} +3.32212 q^{5} -7.19960 q^{6} -2.23518 q^{7} -8.10014 q^{8} +4.35179 q^{9} +O(q^{10})\)	\(q-2.65529 q^{2} +2.71142 q^{3} +5.05057 q^{4} +3.32212 q^{5} -7.19960 q^{6} -2.23518 q^{7} -8.10014 q^{8} +4.35179 q^{9} -8.82118 q^{10} +6.54387 q^{11} +13.6942 q^{12} +4.42483 q^{13} +5.93506 q^{14} +9.00765 q^{15} +11.4071 q^{16} +3.70955 q^{17} -11.5553 q^{18} +2.28371 q^{19} +16.7786 q^{20} -6.06052 q^{21} -17.3759 q^{22} -6.28017 q^{23} -21.9629 q^{24} +6.03645 q^{25} -11.7492 q^{26} +3.66527 q^{27} -11.2889 q^{28} +6.19123 q^{29} -23.9179 q^{30} -4.80501 q^{31} -14.0889 q^{32} +17.7432 q^{33} -9.84992 q^{34} -7.42554 q^{35} +21.9790 q^{36} +7.26306 q^{37} -6.06391 q^{38} +11.9976 q^{39} -26.9096 q^{40} -5.61532 q^{41} +16.0924 q^{42} +5.52453 q^{43} +33.0502 q^{44} +14.4572 q^{45} +16.6757 q^{46} -6.99832 q^{47} +30.9294 q^{48} -2.00395 q^{49} -16.0285 q^{50} +10.0581 q^{51} +22.3479 q^{52} +5.56547 q^{53} -9.73236 q^{54} +21.7395 q^{55} +18.1053 q^{56} +6.19209 q^{57} -16.4395 q^{58} -9.47029 q^{59} +45.4937 q^{60} +4.97368 q^{61} +12.7587 q^{62} -9.72706 q^{63} +14.5958 q^{64} +14.6998 q^{65} -47.1133 q^{66} -7.55563 q^{67} +18.7353 q^{68} -17.0282 q^{69} +19.7170 q^{70} -4.74028 q^{71} -35.2501 q^{72} +12.7900 q^{73} -19.2855 q^{74} +16.3674 q^{75} +11.5340 q^{76} -14.6268 q^{77} -31.8570 q^{78} +2.32537 q^{79} +37.8957 q^{80} -3.11729 q^{81} +14.9103 q^{82} +15.9447 q^{83} -30.6091 q^{84} +12.3235 q^{85} -14.6692 q^{86} +16.7870 q^{87} -53.0062 q^{88} -3.64195 q^{89} -38.3879 q^{90} -9.89031 q^{91} -31.7184 q^{92} -13.0284 q^{93} +18.5826 q^{94} +7.58674 q^{95} -38.2008 q^{96} -11.1903 q^{97} +5.32107 q^{98} +28.4775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * q^99

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