LMFDB - Embedded newform 8011.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61747 q^{2} -3.23549 q^{3} +4.85115 q^{4} -2.81151 q^{5} +8.46879 q^{6} -1.74803 q^{7} -7.46281 q^{8} +7.46837 q^{9} +O(q^{10})$	\(q-2.61747 q^{2} -3.23549 q^{3} +4.85115 q^{4} -2.81151 q^{5} +8.46879 q^{6} -1.74803 q^{7} -7.46281 q^{8} +7.46837 q^{9} +7.35905 q^{10} -3.63094 q^{11} -15.6958 q^{12} +3.83351 q^{13} +4.57543 q^{14} +9.09660 q^{15} +9.83138 q^{16} -1.69270 q^{17} -19.5483 q^{18} -6.76820 q^{19} -13.6391 q^{20} +5.65574 q^{21} +9.50389 q^{22} +6.13870 q^{23} +24.1458 q^{24} +2.90459 q^{25} -10.0341 q^{26} -14.4574 q^{27} -8.47998 q^{28} -9.17536 q^{29} -23.8101 q^{30} +8.73580 q^{31} -10.8077 q^{32} +11.7479 q^{33} +4.43060 q^{34} +4.91461 q^{35} +36.2302 q^{36} +2.00820 q^{37} +17.7156 q^{38} -12.4033 q^{39} +20.9818 q^{40} -3.29567 q^{41} -14.8037 q^{42} +5.95256 q^{43} -17.6143 q^{44} -20.9974 q^{45} -16.0679 q^{46} +2.61734 q^{47} -31.8093 q^{48} -3.94438 q^{49} -7.60268 q^{50} +5.47671 q^{51} +18.5969 q^{52} -8.44031 q^{53} +37.8417 q^{54} +10.2084 q^{55} +13.0452 q^{56} +21.8984 q^{57} +24.0162 q^{58} -8.56127 q^{59} +44.1290 q^{60} -9.44727 q^{61} -22.8657 q^{62} -13.0550 q^{63} +8.62615 q^{64} -10.7779 q^{65} -30.7497 q^{66} +7.17640 q^{67} -8.21155 q^{68} -19.8617 q^{69} -12.8639 q^{70} -0.547913 q^{71} -55.7350 q^{72} -0.141527 q^{73} -5.25641 q^{74} -9.39776 q^{75} -32.8336 q^{76} +6.34701 q^{77} +32.4652 q^{78} +4.88223 q^{79} -27.6410 q^{80} +24.3715 q^{81} +8.62631 q^{82} -9.32642 q^{83} +27.4368 q^{84} +4.75905 q^{85} -15.5806 q^{86} +29.6868 q^{87} +27.0970 q^{88} +6.13607 q^{89} +54.9601 q^{90} -6.70109 q^{91} +29.7798 q^{92} -28.2646 q^{93} -6.85080 q^{94} +19.0289 q^{95} +34.9683 q^{96} +17.4044 q^{97} +10.3243 q^{98} -27.1173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * 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 $

$2$	−2.61747	−1.85083	−0.925416	−	0.378954i	$-0.876284\pi$
$2$	−2.61747	−1.85083	−0.925416	+	0.378954i	$0.876284\pi$
$3$	−3.23549	−1.86801	−0.934005	−	0.357261i	$-0.883711\pi$
$3$	−3.23549	−1.86801	−0.934005	+	0.357261i	$0.883711\pi$
$4$	4.85115	2.42558
$5$	−2.81151	−1.25735	−0.628673	−	0.777670i	$-0.716402\pi$
$5$	−2.81151	−1.25735	−0.628673	+	0.777670i	$0.716402\pi$
$6$	8.46879	3.45737
$7$	−1.74803	−0.660694	−0.330347	−	0.943859i	$-0.607166\pi$
$7$	−1.74803	−0.660694	−0.330347	+	0.943859i	$0.607166\pi$
$8$	−7.46281	−2.63850
$9$	7.46837	2.48946
$10$	7.35905	2.32713
$11$	−3.63094	−1.09477	−0.547386	−	0.836881i	$-0.684377\pi$
$11$	−3.63094	−1.09477	−0.547386	+	0.836881i	$0.684377\pi$
$12$	−15.6958	−4.53100
$13$	3.83351	1.06322	0.531612	−	0.846988i	$-0.321587\pi$
$13$	3.83351	1.06322	0.531612	+	0.846988i	$0.321587\pi$
$14$	4.57543	1.22283
$15$	9.09660	2.34873
$16$	9.83138	2.45784
$17$	−1.69270	−0.410540	−0.205270	−	0.978705i	$-0.565807\pi$
$17$	−1.69270	−0.410540	−0.205270	+	0.978705i	$0.565807\pi$
$18$	−19.5483	−4.60757
$19$	−6.76820	−1.55273	−0.776366	−	0.630282i	$-0.782939\pi$
$19$	−6.76820	−1.55273	−0.776366	+	0.630282i	$0.782939\pi$
$20$	−13.6391	−3.04979
$21$	5.65574	1.23418
$22$	9.50389	2.02624
$23$	6.13870	1.28001	0.640004	−	0.768371i	$-0.278933\pi$
$23$	6.13870	1.28001	0.640004	+	0.768371i	$0.278933\pi$
$24$	24.1458	4.92874
$25$	2.90459	0.580918
$26$	−10.0341	−1.96785
$27$	−14.4574	−2.78232
$28$	−8.47998	−1.60256
$29$	−9.17536	−1.70382	−0.851911	−	0.523687i	$-0.824556\pi$
$29$	−9.17536	−1.70382	−0.851911	+	0.523687i	$0.824556\pi$
$30$	−23.8101	−4.34711
$31$	8.73580	1.56900	0.784498	−	0.620131i	$-0.212920\pi$
$31$	8.73580	1.56900	0.784498	+	0.620131i	$0.212920\pi$
$32$	−10.8077	−1.91055
$33$	11.7479	2.04504
$34$	4.43060	0.759841
$35$	4.91461	0.830721
$36$	36.2302	6.03837
$37$	2.00820	0.330146	0.165073	−	0.986281i	$-0.447214\pi$
$37$	2.00820	0.330146	0.165073	+	0.986281i	$0.447214\pi$
$38$	17.7156	2.87385
$39$	−12.4033	−1.98611
$40$	20.9818	3.31751
$41$	−3.29567	−0.514697	−0.257348	−	0.966319i	$-0.582849\pi$
$41$	−3.29567	−0.514697	−0.257348	+	0.966319i	$0.582849\pi$
$42$	−14.8037	−2.28426
$43$	5.95256	0.907757	0.453878	−	0.891064i	$-0.350040\pi$
$43$	5.95256	0.907757	0.453878	+	0.891064i	$0.350040\pi$
$44$	−17.6143	−2.65545
$45$	−20.9974	−3.13011
$46$	−16.0679	−2.36908
$47$	2.61734	0.381778	0.190889	−	0.981612i	$-0.438863\pi$
$47$	2.61734	0.381778	0.190889	+	0.981612i	$0.438863\pi$
$48$	−31.8093	−4.59128
$49$	−3.94438	−0.563483
$50$	−7.60268	−1.07518
$51$	5.47671	0.766893
$52$	18.5969	2.57893
$53$	−8.44031	−1.15937	−0.579683	−	0.814842i	$-0.696824\pi$
$53$	−8.44031	−1.15937	−0.579683	+	0.814842i	$0.696824\pi$
$54$	37.8417	5.14961
$55$	10.2084	1.37651
$56$	13.0452	1.74324
$57$	21.8984	2.90052
$58$	24.0162	3.15349
$59$	−8.56127	−1.11458	−0.557291	−	0.830317i	$-0.688159\pi$
$59$	−8.56127	−1.11458	−0.557291	+	0.830317i	$0.688159\pi$
$60$	44.1290	5.69703
$61$	−9.44727	−1.20960	−0.604799	−	0.796378i	$-0.706747\pi$
$61$	−9.44727	−1.20960	−0.604799	+	0.796378i	$0.706747\pi$
$62$	−22.8657	−2.90395
$63$	−13.0550	−1.64477
$64$	8.62615	1.07827
$65$	−10.7779	−1.33684
$66$	−30.7497	−3.78503
$67$	7.17640	0.876737	0.438368	−	0.898795i	$-0.355557\pi$
$67$	7.17640	0.876737	0.438368	+	0.898795i	$0.355557\pi$
$68$	−8.21155	−0.995797
$69$	−19.8617	−2.39107
$70$	−12.8639	−1.53752
$71$	−0.547913	−0.0650253	−0.0325127	−	0.999471i	$-0.510351\pi$
$71$	−0.547913	−0.0650253	−0.0325127	+	0.999471i	$0.510351\pi$
$72$	−55.7350	−6.56844
$73$	−0.141527	−0.0165645	−0.00828224	−	0.999966i	$-0.502636\pi$
$73$	−0.141527	−0.0165645	−0.00828224	+	0.999966i	$0.502636\pi$
$74$	−5.25641	−0.611045
$75$	−9.39776	−1.08516
$76$	−32.8336	−3.76627
$77$	6.34701	0.723309
$78$	32.4652	3.67596
$79$	4.88223	0.549294	0.274647	−	0.961545i	$-0.411439\pi$
$79$	4.88223	0.549294	0.274647	+	0.961545i	$0.411439\pi$
$80$	−27.6410	−3.09036
$81$	24.3715	2.70794
$82$	8.62631	0.952617
$83$	−9.32642	−1.02371	−0.511854	−	0.859072i	$-0.671041\pi$
$83$	−9.32642	−1.02371	−0.511854	+	0.859072i	$0.671041\pi$
$84$	27.4368	2.99361
$85$	4.75905	0.516191
$86$	−15.5806	−1.68010
$87$	29.6868	3.18275
$88$	27.0970	2.88855
$89$	6.13607	0.650422	0.325211	−	0.945642i	$-0.394565\pi$
$89$	6.13607	0.650422	0.325211	+	0.945642i	$0.394565\pi$
$90$	54.9601	5.79330
$91$	−6.70109	−0.702466
$92$	29.7798	3.10476
$93$	−28.2646	−2.93090
$94$	−6.85080	−0.706606
$95$	19.0289	1.95232
$96$	34.9683	3.56893
$97$	17.4044	1.76714	0.883572	−	0.468295i	$-0.155132\pi$
$97$	17.4044	1.76714	0.883572	+	0.468295i	$0.155132\pi$
$98$	10.3243	1.04291
$99$	−27.1173	−2.72539
$100$	14.0906	1.40906
$101$	−1.00301	−0.0998031	−0.0499016	−	0.998754i	$-0.515891\pi$
$101$	−1.00301	−0.0998031	−0.0499016	+	0.998754i	$0.515891\pi$
$102$	−14.3351	−1.41939
$103$	−7.28424	−0.717738	−0.358869	−	0.933388i	$-0.616837\pi$
$103$	−7.28424	−0.717738	−0.358869	+	0.933388i	$0.616837\pi$
$104$	−28.6087	−2.80532
$105$	−15.9012	−1.55179
$106$	22.0923	2.14579
$107$	−3.81384	−0.368697	−0.184349	−	0.982861i	$-0.559018\pi$
$107$	−3.81384	−0.368697	−0.184349	+	0.982861i	$0.559018\pi$
$108$	−70.1349	−6.74873
$109$	−16.3239	−1.56354	−0.781771	−	0.623566i	$-0.785683\pi$
$109$	−16.3239	−1.56354	−0.781771	+	0.623566i	$0.785683\pi$
$110$	−26.7203	−2.54768
$111$	−6.49751	−0.616716
$112$	−17.1856	−1.62388
$113$	−11.8085	−1.11085	−0.555423	−	0.831568i	$-0.687444\pi$
$113$	−11.8085	−1.11085	−0.555423	+	0.831568i	$0.687444\pi$
$114$	−57.3185	−5.36837
$115$	−17.2590	−1.60941
$116$	−44.5111	−4.13275
$117$	28.6301	2.64685
$118$	22.4089	2.06290
$119$	2.95890	0.271242
$120$	−67.8862	−6.19714
$121$	2.18376	0.198524
$122$	24.7279	2.23876
$123$	10.6631	0.961458
$124$	42.3787	3.80572
$125$	5.89127	0.526931
$126$	34.1710	3.04419
$127$	−7.33656	−0.651015	−0.325507	−	0.945540i	$-0.605535\pi$
$127$	−7.33656	−0.651015	−0.325507	+	0.945540i	$0.605535\pi$
$128$	−0.963243	−0.0851395
$129$	−19.2594	−1.69570
$130$	28.2109	2.47426
$131$	10.6694	0.932188	0.466094	−	0.884735i	$-0.345661\pi$
$131$	10.6694	0.932188	0.466094	+	0.884735i	$0.345661\pi$
$132$	56.9907	4.96041
$133$	11.8310	1.02588
$134$	−18.7840	−1.62269
$135$	40.6470	3.49834
$136$	12.6323	1.08321
$137$	2.97076	0.253809	0.126905	−	0.991915i	$-0.459496\pi$
$137$	2.97076	0.253809	0.126905	+	0.991915i	$0.459496\pi$
$138$	51.9874	4.42546
$139$	−21.7455	−1.84443	−0.922216	−	0.386676i	$-0.873623\pi$
$139$	−21.7455	−1.84443	−0.922216	+	0.386676i	$0.873623\pi$
$140$	23.8415	2.01498
$141$	−8.46836	−0.713165
$142$	1.43415	0.120351
$143$	−13.9192	−1.16399
$144$	73.4244	6.11870
$145$	25.7966	2.14229
$146$	0.370442	0.0306580
$147$	12.7620	1.05259
$148$	9.74209	0.800795
$149$	−8.79334	−0.720378	−0.360189	−	0.932879i	$-0.617288\pi$
$149$	−8.79334	−0.720378	−0.360189	+	0.932879i	$0.617288\pi$
$150$	24.5984	2.00845
$151$	−8.66087	−0.704811	−0.352406	−	0.935847i	$-0.614636\pi$
$151$	−8.66087	−0.704811	−0.352406	+	0.935847i	$0.614636\pi$
$152$	50.5098	4.09689
$153$	−12.6417	−1.02202
$154$	−16.6131	−1.33872
$155$	−24.5608	−1.97277
$156$	−60.1701	−4.81746
$157$	−1.44170	−0.115060	−0.0575301	−	0.998344i	$-0.518323\pi$
$157$	−1.44170	−0.115060	−0.0575301	+	0.998344i	$0.518323\pi$
$158$	−12.7791	−1.01665
$159$	27.3085	2.16571
$160$	30.3860	2.40223
$161$	−10.7307	−0.845694
$162$	−63.7917	−5.01195
$163$	14.8367	1.16210	0.581051	−	0.813867i	$-0.302642\pi$
$163$	14.8367	1.16210	0.581051	+	0.813867i	$0.302642\pi$
$164$	−15.9878	−1.24844
$165$	−33.0293	−2.57132
$166$	24.4116	1.89471
$167$	23.1355	1.79028	0.895140	−	0.445784i	$-0.147075\pi$
$167$	23.1355	1.79028	0.895140	+	0.445784i	$0.147075\pi$
$168$	−42.2077	−3.25639
$169$	1.69576	0.130443
$170$	−12.4567	−0.955383
$171$	−50.5475	−3.86546
$172$	28.8768	2.20183
$173$	25.0760	1.90649	0.953246	−	0.302195i	$-0.0977194\pi$
$173$	25.0760	1.90649	0.953246	+	0.302195i	$0.0977194\pi$
$174$	−77.7042	−5.89074
$175$	−5.07732	−0.383809
$176$	−35.6972	−2.69078
$177$	27.6999	2.08205
$178$	−16.0610	−1.20382
$179$	24.6177	1.84002	0.920008	−	0.391900i	$-0.128182\pi$
$179$	24.6177	1.84002	0.920008	+	0.391900i	$0.128182\pi$
$180$	−101.862	−7.59232
$181$	−4.35989	−0.324068	−0.162034	−	0.986785i	$-0.551805\pi$
$181$	−4.35989	−0.324068	−0.162034	+	0.986785i	$0.551805\pi$
$182$	17.5399	1.30015
$183$	30.5665	2.25954
$184$	−45.8120	−3.37730
$185$	−5.64608	−0.415108
$186$	73.9817	5.42460
$187$	6.14610	0.449448
$188$	12.6971	0.926031
$189$	25.2720	1.83826
$190$	−49.8075	−3.61342
$191$	−6.49084	−0.469661	−0.234830	−	0.972036i	$-0.575453\pi$
$191$	−6.49084	−0.469661	−0.234830	+	0.972036i	$0.575453\pi$
$192$	−27.9098	−2.01422
$193$	4.85604	0.349546	0.174773	−	0.984609i	$-0.444081\pi$
$193$	4.85604	0.349546	0.174773	+	0.984609i	$0.444081\pi$
$194$	−45.5554	−3.27069
$195$	34.8719	2.49723
$196$	−19.1348	−1.36677
$197$	2.10966	0.150307	0.0751535	−	0.997172i	$-0.476055\pi$
$197$	2.10966	0.150307	0.0751535	+	0.997172i	$0.476055\pi$
$198$	70.9786	5.04423
$199$	19.6729	1.39457	0.697287	−	0.716792i	$-0.254390\pi$
$199$	19.6729	1.39457	0.697287	+	0.716792i	$0.254390\pi$
$200$	−21.6764	−1.53275
$201$	−23.2191	−1.63775
$202$	2.62535	0.184719
$203$	16.0388	1.12571
$204$	26.5684	1.86016
$205$	9.26580	0.647152
$206$	19.0663	1.32841
$207$	45.8461	3.18653
$208$	37.6886	2.61324
$209$	24.5750	1.69989
$210$	41.6208	2.87211
$211$	−6.26286	−0.431153	−0.215577	−	0.976487i	$-0.569163\pi$
$211$	−6.26286	−0.431153	−0.215577	+	0.976487i	$0.569163\pi$
$212$	−40.9452	−2.81213
$213$	1.77277	0.121468
$214$	9.98260	0.682397
$215$	−16.7357	−1.14136
$216$	107.893	7.34116
$217$	−15.2705	−1.03663
$218$	42.7272	2.89385
$219$	0.457908	0.0309426
$220$	49.5227	3.33882
$221$	−6.48898	−0.436496
$222$	17.0070	1.14144
$223$	−7.07342	−0.473671	−0.236836	−	0.971550i	$-0.576110\pi$
$223$	−7.07342	−0.473671	−0.236836	+	0.971550i	$0.576110\pi$
$224$	18.8923	1.26229
$225$	21.6926	1.44617
$226$	30.9083	2.05599
$227$	17.4040	1.15514	0.577571	−	0.816341i	$-0.304001\pi$
$227$	17.4040	1.15514	0.577571	+	0.816341i	$0.304001\pi$
$228$	106.233	7.03543
$229$	21.6726	1.43216	0.716081	−	0.698017i	$-0.245934\pi$
$229$	21.6726	1.43216	0.716081	+	0.698017i	$0.245934\pi$
$230$	45.1750	2.97875
$231$	−20.5357	−1.35115
$232$	68.4740	4.49554
$233$	−21.8627	−1.43228	−0.716138	−	0.697959i	$-0.754092\pi$
$233$	−21.8627	−1.43228	−0.716138	+	0.697959i	$0.754092\pi$
$234$	−74.9383	−4.89887
$235$	−7.35867	−0.480027
$236$	−41.5320	−2.70351
$237$	−15.7964	−1.02609
$238$	−7.74483	−0.502023
$239$	6.61652	0.427987	0.213994	−	0.976835i	$-0.431353\pi$
$239$	6.61652	0.427987	0.213994	+	0.976835i	$0.431353\pi$
$240$	89.4322	5.77282
$241$	−3.96437	−0.255368	−0.127684	−	0.991815i	$-0.540754\pi$
$241$	−3.96437	−0.255368	−0.127684	+	0.991815i	$0.540754\pi$
$242$	−5.71593	−0.367434
$243$	−35.4815	−2.27614
$244$	−45.8301	−2.93397
$245$	11.0897	0.708493
$246$	−27.9103	−1.77950
$247$	−25.9459	−1.65090
$248$	−65.1936	−4.13980
$249$	30.1755	1.91230
$250$	−15.4202	−0.975260
$251$	17.1217	1.08071	0.540357	−	0.841436i	$-0.318289\pi$
$251$	17.1217	1.08071	0.540357	+	0.841436i	$0.318289\pi$
$252$	−63.3316	−3.98952
$253$	−22.2893	−1.40132
$254$	19.2032	1.20492
$255$	−15.3978	−0.964250
$256$	−14.7310	−0.920690
$257$	−16.8648	−1.05200	−0.525998	−	0.850486i	$-0.676308\pi$
$257$	−16.8648	−1.05200	−0.525998	+	0.850486i	$0.676308\pi$
$258$	50.4110	3.13845
$259$	−3.51040	−0.218126
$260$	−52.2854	−3.24260
$261$	−68.5250	−4.24159
$262$	−27.9268	−1.72532
$263$	3.79727	0.234150	0.117075	−	0.993123i	$-0.462648\pi$
$263$	3.79727	0.234150	0.117075	+	0.993123i	$0.462648\pi$
$264$	−87.6721	−5.39585
$265$	23.7300	1.45772
$266$	−30.9674	−1.89873
$267$	−19.8532	−1.21499
$268$	34.8138	2.12659
$269$	15.9813	0.974396	0.487198	−	0.873292i	$-0.338019\pi$
$269$	15.9813	0.974396	0.487198	+	0.873292i	$0.338019\pi$
$270$	−106.392	−6.47484
$271$	24.9441	1.51525	0.757624	−	0.652692i	$-0.226360\pi$
$271$	24.9441	1.51525	0.757624	+	0.652692i	$0.226360\pi$
$272$	−16.6416	−1.00904
$273$	21.6813	1.31221
$274$	−7.77588	−0.469758
$275$	−10.5464	−0.635972
$276$	−96.3521	−5.79972
$277$	9.47609	0.569363	0.284682	−	0.958622i	$-0.408112\pi$
$277$	9.47609	0.569363	0.284682	+	0.958622i	$0.408112\pi$
$278$	56.9183	3.41373
$279$	65.2423	3.90595
$280$	−36.6768	−2.19186
$281$	−27.6294	−1.64823	−0.824115	−	0.566423i	$-0.808327\pi$
$281$	−27.6294	−1.64823	−0.824115	+	0.566423i	$0.808327\pi$
$282$	22.1657	1.31995
$283$	−5.88791	−0.350000	−0.175000	−	0.984568i	$-0.555993\pi$
$283$	−5.88791	−0.350000	−0.175000	+	0.984568i	$0.555993\pi$
$284$	−2.65801	−0.157724
$285$	−61.5677	−3.64695
$286$	36.4332	2.15434
$287$	5.76093	0.340057
$288$	−80.7161	−4.75624
$289$	−14.1348	−0.831457
$290$	−67.5219	−3.96502
$291$	−56.3116	−3.30104
$292$	−0.686569	−0.0401784
$293$	−10.7936	−0.630567	−0.315284	−	0.948997i	$-0.602100\pi$
$293$	−10.7936	−0.630567	−0.315284	+	0.948997i	$0.602100\pi$
$294$	−33.4041	−1.94817
$295$	24.0701	1.40142
$296$	−14.9868	−0.871091
$297$	52.4939	3.04600
$298$	23.0163	1.33330
$299$	23.5328	1.36093
$300$	−45.5900	−2.63214
$301$	−10.4053	−0.599750
$302$	22.6696	1.30449
$303$	3.24522	0.186433
$304$	−66.5408	−3.81637
$305$	26.5611	1.52088
$306$	33.0893	1.89159
$307$	1.41759	0.0809059	0.0404530	−	0.999181i	$-0.487120\pi$
$307$	1.41759	0.0809059	0.0404530	+	0.999181i	$0.487120\pi$
$308$	30.7903	1.75444
$309$	23.5681	1.34074
$310$	64.2872	3.65127
$311$	28.6400	1.62402	0.812012	−	0.583640i	$-0.198372\pi$
$311$	28.6400	1.62402	0.812012	+	0.583640i	$0.198372\pi$
$312$	92.5631	5.24036
$313$	13.5736	0.767223	0.383611	−	0.923495i	$-0.374680\pi$
$313$	13.5736	0.767223	0.383611	+	0.923495i	$0.374680\pi$
$314$	3.77361	0.212957
$315$	36.7042	2.06805
$316$	23.6844	1.33235
$317$	−6.32724	−0.355373	−0.177687	−	0.984087i	$-0.556861\pi$
$317$	−6.32724	−0.355373	−0.177687	+	0.984087i	$0.556861\pi$
$318$	−71.4792	−4.00836
$319$	33.3152	1.86529
$320$	−24.2525	−1.35576
$321$	12.3396	0.688730
$322$	28.0872	1.56524
$323$	11.4565	0.637459
$324$	118.230	6.56832
$325$	11.1348	0.617645
$326$	−38.8347	−2.15086
$327$	52.8156	2.92071
$328$	24.5949	1.35803
$329$	−4.57519	−0.252239
$330$	86.4531	4.75909
$331$	9.76040	0.536480	0.268240	−	0.963352i	$-0.413558\pi$
$331$	9.76040	0.536480	0.268240	+	0.963352i	$0.413558\pi$
$332$	−45.2439	−2.48308
$333$	14.9980	0.821885
$334$	−60.5566	−3.31351
$335$	−20.1765	−1.10236
$336$	55.6037	3.03343
$337$	16.2174	0.883417	0.441708	−	0.897159i	$-0.354373\pi$
$337$	16.2174	0.883417	0.441708	+	0.897159i	$0.354373\pi$
$338$	−4.43861	−0.241428
$339$	38.2061	2.07507
$340$	23.0869	1.25206
$341$	−31.7192	−1.71769
$342$	132.307	7.15432
$343$	19.1311	1.03298
$344$	−44.4228	−2.39512
$345$	55.8414	3.00640
$346$	−65.6357	−3.52860
$347$	−22.2032	−1.19193	−0.595965	−	0.803011i	$-0.703230\pi$
$347$	−22.2032	−1.19193	−0.595965	+	0.803011i	$0.703230\pi$
$348$	144.015	7.72001
$349$	36.0320	1.92875	0.964375	−	0.264537i	$-0.0852192\pi$
$349$	36.0320	1.92875	0.964375	+	0.264537i	$0.0852192\pi$
$350$	13.2897	0.710366
$351$	−55.4224	−2.95823
$352$	39.2423	2.09162
$353$	−1.86622	−0.0993286	−0.0496643	−	0.998766i	$-0.515815\pi$
$353$	−1.86622	−0.0993286	−0.0496643	+	0.998766i	$0.515815\pi$
$354$	−72.5036	−3.85352
$355$	1.54046	0.0817593
$356$	29.7670	1.57765
$357$	−9.57347	−0.506682
$358$	−64.4362	−3.40556
$359$	14.0075	0.739290	0.369645	−	0.929173i	$-0.379479\pi$
$359$	14.0075	0.739290	0.369645	+	0.929173i	$0.379479\pi$
$360$	156.700	8.25880
$361$	26.8086	1.41098
$362$	11.4119	0.599795
$363$	−7.06552	−0.370844
$364$	−32.5080	−1.70388
$365$	0.397904	0.0208273
$366$	−80.0069	−4.18203
$367$	34.2928	1.79007	0.895036	−	0.445994i	$-0.147150\pi$
$367$	34.2928	1.79007	0.895036	+	0.445994i	$0.147150\pi$
$368$	60.3519	3.14606
$369$	−24.6133	−1.28132
$370$	14.7784	0.768295
$371$	14.7539	0.765987
$372$	−137.116	−7.10912
$373$	18.5233	0.959099	0.479549	−	0.877515i	$-0.340800\pi$
$373$	18.5233	0.959099	0.479549	+	0.877515i	$0.340800\pi$
$374$	−16.0872	−0.831852
$375$	−19.0611	−0.984312
$376$	−19.5327	−1.00732
$377$	−35.1738	−1.81154
$378$	−66.1486	−3.40232
$379$	8.82872	0.453501	0.226750	−	0.973953i	$-0.427190\pi$
$379$	8.82872	0.453501	0.226750	+	0.973953i	$0.427190\pi$
$380$	92.3120	4.73550
$381$	23.7373	1.21610
$382$	16.9896	0.869262
$383$	−8.50928	−0.434804	−0.217402	−	0.976082i	$-0.569758\pi$
$383$	−8.50928	−0.434804	−0.217402	+	0.976082i	$0.569758\pi$
$384$	3.11656	0.159041
$385$	−17.8447	−0.909450
$386$	−12.7105	−0.646950
$387$	44.4559	2.25982
$388$	84.4312	4.28634
$389$	21.1180	1.07073	0.535363	−	0.844622i	$-0.320175\pi$
$389$	21.1180	1.07073	0.535363	+	0.844622i	$0.320175\pi$
$390$	−91.2761	−4.62195
$391$	−10.3910	−0.525495
$392$	29.4362	1.48675
$393$	−34.5206	−1.74134
$394$	−5.52197	−0.278193
$395$	−13.7264	−0.690652
$396$	−131.550	−6.61063
$397$	2.71510	0.136267	0.0681334	−	0.997676i	$-0.478296\pi$
$397$	2.71510	0.136267	0.0681334	+	0.997676i	$0.478296\pi$
$398$	−51.4932	−2.58112
$399$	−38.2792	−1.91636
$400$	28.5561	1.42781
$401$	5.47983	0.273650	0.136825	−	0.990595i	$-0.456310\pi$
$401$	5.47983	0.273650	0.136825	+	0.990595i	$0.456310\pi$
$402$	60.7754	3.03120
$403$	33.4888	1.66819
$404$	−4.86575	−0.242080
$405$	−68.5207	−3.40482
$406$	−41.9812	−2.08349
$407$	−7.29167	−0.361435
$408$	−40.8717	−2.02345
$409$	−24.3064	−1.20188	−0.600938	−	0.799296i	$-0.705206\pi$
$409$	−24.3064	−1.20188	−0.600938	+	0.799296i	$0.705206\pi$
$410$	−24.2530	−1.19777
$411$	−9.61185	−0.474118
$412$	−35.3370	−1.74093
$413$	14.9654	0.736399
$414$	−120.001	−5.89772
$415$	26.2213	1.28715
$416$	−41.4315	−2.03135
$417$	70.3574	3.44541
$418$	−64.3243	−3.14620
$419$	−3.92260	−0.191632	−0.0958159	−	0.995399i	$-0.530546\pi$
$419$	−3.92260	−0.191632	−0.0958159	+	0.995399i	$0.530546\pi$
$420$	−77.1390	−3.76400
$421$	14.0682	0.685641	0.342820	−	0.939401i	$-0.388618\pi$
$421$	14.0682	0.685641	0.342820	+	0.939401i	$0.388618\pi$
$422$	16.3929	0.797992
$423$	19.5473	0.950420
$424$	62.9884	3.05899
$425$	−4.91660	−0.238490
$426$	−4.64016	−0.224817
$427$	16.5141	0.799175
$428$	−18.5015	−0.894304
$429$	45.0355	2.17434
$430$	43.8051	2.11247
$431$	27.4360	1.32155	0.660773	−	0.750586i	$-0.270229\pi$
$431$	27.4360	1.32155	0.660773	+	0.750586i	$0.270229\pi$
$432$	−142.136	−6.83851
$433$	−38.5113	−1.85073	−0.925367	−	0.379071i	$-0.876244\pi$
$433$	−38.5113	−1.85073	−0.925367	+	0.379071i	$0.876244\pi$
$434$	39.9700	1.91862
$435$	−83.4646	−4.00182
$436$	−79.1895	−3.79249
$437$	−41.5480	−1.98751
$438$	−1.19856	−0.0572695
$439$	12.5924	0.601004	0.300502	−	0.953781i	$-0.402846\pi$
$439$	12.5924	0.601004	0.300502	+	0.953781i	$0.402846\pi$
$440$	−76.1836	−3.63191
$441$	−29.4581	−1.40277
$442$	16.9847	0.807880
$443$	−19.1225	−0.908536	−0.454268	−	0.890865i	$-0.650099\pi$
$443$	−19.1225	−0.908536	−0.454268	+	0.890865i	$0.650099\pi$
$444$	−31.5204	−1.49589
$445$	−17.2516	−0.817805
$446$	18.5145	0.876686
$447$	28.4507	1.34567
$448$	−15.0788	−0.712406
$449$	14.5929	0.688681	0.344341	−	0.938845i	$-0.388103\pi$
$449$	14.5929	0.688681	0.344341	+	0.938845i	$0.388103\pi$
$450$	−56.7796	−2.67662
$451$	11.9664	0.563475
$452$	−57.2847	−2.69444
$453$	28.0221	1.31659
$454$	−45.5544	−2.13797
$455$	18.8402	0.883242
$456$	−163.424	−7.65302
$457$	28.2802	1.32289	0.661447	−	0.749992i	$-0.269943\pi$
$457$	28.2802	1.32289	0.661447	+	0.749992i	$0.269943\pi$
$458$	−56.7273	−2.65069
$459$	24.4720	1.14226
$460$	−83.7262	−3.90375
$461$	10.1280	0.471706	0.235853	−	0.971789i	$-0.424212\pi$
$461$	10.1280	0.471706	0.235853	+	0.971789i	$0.424212\pi$
$462$	53.7515	2.50075
$463$	−28.3083	−1.31560	−0.657798	−	0.753194i	$-0.728512\pi$
$463$	−28.3083	−1.31560	−0.657798	+	0.753194i	$0.728512\pi$
$464$	−90.2064	−4.18773
$465$	79.4662	3.68515
$466$	57.2251	2.65090
$467$	−4.65573	−0.215441	−0.107721	−	0.994181i	$-0.534355\pi$
$467$	−4.65573	−0.215441	−0.107721	+	0.994181i	$0.534355\pi$
$468$	138.889	6.42014
$469$	−12.5446	−0.579255
$470$	19.2611	0.888448
$471$	4.66460	0.214934
$472$	63.8911	2.94083
$473$	−21.6134	−0.993786
$474$	41.3466	1.89911
$475$	−19.6588	−0.902010
$476$	14.3541	0.657917
$477$	−63.0354	−2.88619
$478$	−17.3186	−0.792132
$479$	39.0733	1.78531	0.892653	−	0.450744i	$-0.148841\pi$
$479$	39.0733	1.78531	0.892653	+	0.450744i	$0.148841\pi$
$480$	−98.3136	−4.48738
$481$	7.69845	0.351019
$482$	10.3766	0.472643
$483$	34.7189	1.57976
$484$	10.5938	0.481534
$485$	−48.9325	−2.22191
$486$	92.8719	4.21275
$487$	34.1657	1.54819	0.774097	−	0.633067i	$-0.218204\pi$
$487$	34.1657	1.54819	0.774097	+	0.633067i	$0.218204\pi$
$488$	70.5031	3.19153
$489$	−48.0041	−2.17082
$490$	−29.0269	−1.31130
$491$	−12.6040	−0.568812	−0.284406	−	0.958704i	$-0.591796\pi$
$491$	−12.6040	−0.568812	−0.284406	+	0.958704i	$0.591796\pi$
$492$	51.7283	2.33209
$493$	15.5311	0.699487
$494$	67.9127	3.05554
$495$	76.2404	3.42675
$496$	85.8850	3.85635
$497$	0.957770	0.0429619
$498$	−78.9835	−3.53934
$499$	40.0119	1.79118	0.895589	−	0.444882i	$-0.146754\pi$
$499$	40.0119	1.79118	0.895589	+	0.444882i	$0.146754\pi$
$500$	28.5794	1.27811
$501$	−74.8547	−3.34426
$502$	−44.8157	−2.00022
$503$	−21.7216	−0.968518	−0.484259	−	0.874925i	$-0.660911\pi$
$503$	−21.7216	−0.968518	−0.484259	+	0.874925i	$0.660911\pi$
$504$	97.4267	4.33973
$505$	2.81997	0.125487
$506$	58.3416	2.59360
$507$	−5.48662	−0.243669
$508$	−35.5908	−1.57909
$509$	−37.2644	−1.65171	−0.825857	−	0.563880i	$-0.809308\pi$
$509$	−37.2644	−1.65171	−0.825857	+	0.563880i	$0.809308\pi$
$510$	40.3034	1.78466
$511$	0.247394	0.0109441
$512$	40.4846	1.78918
$513$	97.8504	4.32020
$514$	44.1431	1.94707
$515$	20.4797	0.902444
$516$	−93.4304	−4.11304
$517$	−9.50341	−0.417959
$518$	9.18838	0.403714
$519$	−81.1330	−3.56134
$520$	80.4337	3.52725
$521$	39.6572	1.73741	0.868706	−	0.495328i	$-0.164952\pi$
$521$	39.6572	1.73741	0.868706	+	0.495328i	$0.164952\pi$
$522$	179.362	7.85047
$523$	28.4087	1.24223	0.621113	−	0.783721i	$-0.286681\pi$
$523$	28.4087	1.24223	0.621113	+	0.783721i	$0.286681\pi$
$524$	51.7588	2.26109
$525$	16.4276	0.716959
$526$	−9.93924	−0.433371
$527$	−14.7871	−0.644136
$528$	115.498	5.02640
$529$	14.6837	0.638422
$530$	−62.1126	−2.69800
$531$	−63.9388	−2.77471
$532$	57.3942	2.48835
$533$	−12.6340	−0.547237
$534$	51.9651	2.24875
$535$	10.7226	0.463580
$536$	−53.5561	−2.31327
$537$	−79.6503	−3.43717
$538$	−41.8305	−1.80344
$539$	14.3218	0.616885
$540$	197.185	8.48549
$541$	8.69135	0.373670	0.186835	−	0.982391i	$-0.440177\pi$
$541$	8.69135	0.373670	0.186835	+	0.982391i	$0.440177\pi$
$542$	−65.2905	−2.80447
$543$	14.1064	0.605362
$544$	18.2943	0.784360
$545$	45.8947	1.96591
$546$	−56.7502	−2.42868
$547$	0.917385	0.0392246	0.0196123	−	0.999808i	$-0.493757\pi$
$547$	0.917385	0.0392246	0.0196123	+	0.999808i	$0.493757\pi$
$548$	14.4116	0.615633
$549$	−70.5557	−3.01124
$550$	27.6049	1.17708
$551$	62.1007	2.64558
$552$	148.224	6.30883
$553$	−8.53430	−0.362915
$554$	−24.8034	−1.05380
$555$	18.2678	0.775426
$556$	−105.491	−4.47381
$557$	−2.30405	−0.0976259	−0.0488130	−	0.998808i	$-0.515544\pi$
$557$	−2.30405	−0.0976259	−0.0488130	+	0.998808i	$0.515544\pi$
$558$	−170.770	−7.22926
$559$	22.8192	0.965148
$560$	48.3174	2.04178
$561$	−19.8856	−0.839572
$562$	72.3190	3.05059
$563$	25.6871	1.08258	0.541290	−	0.840836i	$-0.317936\pi$
$563$	25.6871	1.08258	0.541290	+	0.840836i	$0.317936\pi$
$564$	−41.0813	−1.72984
$565$	33.1996	1.39672
$566$	15.4114	0.647791
$567$	−42.6022	−1.78912
$568$	4.08897	0.171569
$569$	10.8389	0.454388	0.227194	−	0.973849i	$-0.427045\pi$
$569$	10.8389	0.454388	0.227194	+	0.973849i	$0.427045\pi$
$570$	161.152	6.74990
$571$	−36.4356	−1.52478	−0.762391	−	0.647117i	$-0.775974\pi$
$571$	−36.4356	−1.52478	−0.762391	+	0.647117i	$0.775974\pi$
$572$	−67.5244	−2.82334
$573$	21.0010	0.877330
$574$	−15.0791	−0.629389
$575$	17.8304	0.743580
$576$	64.4233	2.68430
$577$	5.51347	0.229529	0.114764	−	0.993393i	$-0.463389\pi$
$577$	5.51347	0.229529	0.114764	+	0.993393i	$0.463389\pi$
$578$	36.9973	1.53889
$579$	−15.7117	−0.652954
$580$	125.143	5.19629
$581$	16.3029	0.676358
$582$	147.394	6.10967
$583$	30.6463	1.26924
$584$	1.05619	0.0437054
$585$	−80.4937	−3.32800
$586$	28.2519	1.16707
$587$	−3.34362	−0.138006	−0.0690029	−	0.997616i	$-0.521982\pi$
$587$	−3.34362	−0.138006	−0.0690029	+	0.997616i	$0.521982\pi$
$588$	61.9104	2.55314
$589$	−59.1257	−2.43623
$590$	−63.0028	−2.59378
$591$	−6.82578	−0.280775
$592$	19.7434	0.811448
$593$	0.268963	0.0110450	0.00552250	−	0.999985i	$-0.498242\pi$
$593$	0.268963	0.0110450	0.00552250	+	0.999985i	$0.498242\pi$
$594$	−137.401	−5.63764
$595$	−8.31897	−0.341045
$596$	−42.6578	−1.74733
$597$	−63.6513	−2.60508
$598$	−61.5963	−2.51886
$599$	3.69748	0.151075	0.0755374	−	0.997143i	$-0.475933\pi$
$599$	3.69748	0.151075	0.0755374	+	0.997143i	$0.475933\pi$
$600$	70.1337	2.86320
$601$	−6.20771	−0.253218	−0.126609	−	0.991953i	$-0.540409\pi$
$601$	−6.20771	−0.253218	−0.126609	+	0.991953i	$0.540409\pi$
$602$	27.2355	1.11004
$603$	53.5960	2.18260
$604$	−42.0152	−1.70957
$605$	−6.13966	−0.249613
$606$	−8.49427	−0.345056
$607$	−22.2007	−0.901099	−0.450549	−	0.892752i	$-0.648772\pi$
$607$	−22.2007	−0.901099	−0.450549	+	0.892752i	$0.648772\pi$
$608$	73.1489	2.96658
$609$	−51.8934	−2.10283
$610$	−69.5229	−2.81490
$611$	10.0336	0.405915
$612$	−61.3269	−2.47899
$613$	−6.23938	−0.252006	−0.126003	−	0.992030i	$-0.540215\pi$
$613$	−6.23938	−0.252006	−0.126003	+	0.992030i	$0.540215\pi$
$614$	−3.71049	−0.149743
$615$	−29.9794	−1.20889
$616$	−47.3665	−1.90845
$617$	−34.8115	−1.40146	−0.700728	−	0.713428i	$-0.747141\pi$
$617$	−34.8115	−1.40146	−0.700728	+	0.713428i	$0.747141\pi$
$618$	−61.6887	−2.48148
$619$	8.36737	0.336313	0.168157	−	0.985760i	$-0.446219\pi$
$619$	8.36737	0.336313	0.168157	+	0.985760i	$0.446219\pi$
$620$	−119.148	−4.78511
$621$	−88.7495	−3.56139
$622$	−74.9643	−3.00580
$623$	−10.7260	−0.429730
$624$	−121.941	−4.88155
$625$	−31.0863	−1.24345
$626$	−35.5284	−1.42000
$627$	−79.5120	−3.17540
$628$	−6.99391	−0.279087
$629$	−3.39929	−0.135538
$630$	−96.0721	−3.82760
$631$	−40.8372	−1.62570	−0.812852	−	0.582470i	$-0.802086\pi$
$631$	−40.8372	−1.62570	−0.812852	+	0.582470i	$0.802086\pi$
$632$	−36.4351	−1.44931
$633$	20.2634	0.805398
$634$	16.5614	0.657736
$635$	20.6268	0.818550
$636$	132.478	5.25309
$637$	−15.1208	−0.599108
$638$	−87.2016	−3.45234
$639$	−4.09202	−0.161878
$640$	2.70817	0.107050
$641$	26.9021	1.06257	0.531285	−	0.847193i	$-0.321709\pi$
$641$	26.9021	1.06257	0.531285	+	0.847193i	$0.321709\pi$
$642$	−32.2986	−1.27472
$643$	24.6570	0.972379	0.486189	−	0.873853i	$-0.338386\pi$
$643$	24.6570	0.972379	0.486189	+	0.873853i	$0.338386\pi$
$644$	−52.0561	−2.05130
$645$	54.1481	2.13208
$646$	−29.9872	−1.17983
$647$	−17.2299	−0.677376	−0.338688	−	0.940899i	$-0.609983\pi$
$647$	−17.2299	−0.677376	−0.338688	+	0.940899i	$0.609983\pi$
$648$	−181.880	−7.14491
$649$	31.0855	1.22021
$650$	−29.1449	−1.14316
$651$	49.4074	1.93643
$652$	71.9753	2.81877
$653$	−39.6863	−1.55304	−0.776522	−	0.630090i	$-0.783018\pi$
$653$	−39.6863	−1.55304	−0.776522	+	0.630090i	$0.783018\pi$
$654$	−138.243	−5.40574
$655$	−29.9971	−1.17208
$656$	−32.4009	−1.26504
$657$	−1.05698	−0.0412366
$658$	11.9754	0.466851
$659$	−6.18919	−0.241097	−0.120548	−	0.992707i	$-0.538465\pi$
$659$	−6.18919	−0.241097	−0.120548	+	0.992707i	$0.538465\pi$
$660$	−160.230	−6.23694
$661$	−19.2305	−0.747981	−0.373991	−	0.927433i	$-0.622011\pi$
$661$	−19.2305	−0.747981	−0.373991	+	0.927433i	$0.622011\pi$
$662$	−25.5476	−0.992934
$663$	20.9950	0.815378
$664$	69.6013	2.70105
$665$	−33.2631	−1.28989
$666$	−39.2568	−1.52117
$667$	−56.3248	−2.18091
$668$	112.234	4.34246
$669$	22.8860	0.884823
$670$	52.8114	2.04028
$671$	34.3025	1.32423
$672$	−61.1257	−2.35797
$673$	−32.7228	−1.26137	−0.630685	−	0.776039i	$-0.717226\pi$
$673$	−32.7228	−1.26137	−0.630685	+	0.776039i	$0.717226\pi$
$674$	−42.4485	−1.63505
$675$	−41.9927	−1.61630
$676$	8.22640	0.316400
$677$	28.4456	1.09325	0.546626	−	0.837377i	$-0.315912\pi$
$677$	28.4456	1.09325	0.546626	+	0.837377i	$0.315912\pi$
$678$	−100.003	−3.84061
$679$	−30.4234	−1.16754
$680$	−35.5159	−1.36197
$681$	−56.3103	−2.15782
$682$	83.0241	3.17916
$683$	−0.910694	−0.0348468	−0.0174234	−	0.999848i	$-0.505546\pi$
$683$	−0.910694	−0.0348468	−0.0174234	+	0.999848i	$0.505546\pi$
$684$	−245.214	−9.37597
$685$	−8.35232	−0.319126
$686$	−50.0752	−1.91188
$687$	−70.1213	−2.67529
$688$	58.5219	2.23112
$689$	−32.3560	−1.23266
$690$	−146.163	−5.56434
$691$	−48.0085	−1.82633	−0.913165	−	0.407590i	$-0.866369\pi$
$691$	−48.0085	−1.82633	−0.913165	+	0.407590i	$0.866369\pi$
$692$	121.647	4.62434
$693$	47.4019	1.80065
$694$	58.1162	2.20606
$695$	61.1378	2.31909
$696$	−221.547	−8.39770
$697$	5.57858	0.211304
$698$	−94.3128	−3.56979
$699$	70.7366	2.67550
$700$	−24.6308	−0.930959
$701$	−36.2545	−1.36932	−0.684658	−	0.728865i	$-0.740048\pi$
$701$	−36.2545	−1.36932	−0.684658	+	0.728865i	$0.740048\pi$
$702$	145.066	5.47518
$703$	−13.5919	−0.512629
$704$	−31.3211	−1.18046
$705$	23.8089	0.896694
$706$	4.88476	0.183841
$707$	1.75329	0.0659394
$708$	134.376	5.05017
$709$	37.9917	1.42681	0.713404	−	0.700753i	$-0.247153\pi$
$709$	37.9917	1.42681	0.713404	+	0.700753i	$0.247153\pi$
$710$	−4.03212	−0.151323
$711$	36.4623	1.36744
$712$	−45.7923	−1.71614
$713$	53.6265	2.00833
$714$	25.0583	0.937783
$715$	39.1341	1.46353
$716$	119.424	4.46310
$717$	−21.4077	−0.799484
$718$	−36.6643	−1.36830
$719$	−49.3444	−1.84023	−0.920117	−	0.391643i	$-0.871907\pi$
$719$	−49.3444	−1.84023	−0.920117	+	0.391643i	$0.871907\pi$
$720$	−206.433	−7.69332
$721$	12.7331	0.474205
$722$	−70.1706	−2.61148
$723$	12.8267	0.477029
$724$	−21.1505	−0.786052
$725$	−26.6506	−0.989780
$726$	18.4938	0.686369
$727$	37.6764	1.39734	0.698670	−	0.715444i	$-0.253776\pi$
$727$	37.6764	1.39734	0.698670	+	0.715444i	$0.253776\pi$
$728$	50.0090	1.85346
$729$	41.6856	1.54391
$730$	−1.04150	−0.0385477
$731$	−10.0759	−0.372671
$732$	148.283	5.48069
$733$	−1.40895	−0.0520408	−0.0260204	−	0.999661i	$-0.508283\pi$
$733$	−1.40895	−0.0520408	−0.0260204	+	0.999661i	$0.508283\pi$
$734$	−89.7605	−3.31312
$735$	−35.8805	−1.32347
$736$	−66.3454	−2.44553
$737$	−26.0571	−0.959826
$738$	64.4245	2.37150
$739$	−32.2880	−1.18773	−0.593866	−	0.804564i	$-0.702399\pi$
$739$	−32.2880	−1.18773	−0.593866	+	0.804564i	$0.702399\pi$
$740$	−27.3900	−1.00688
$741$	83.9477	3.08390
$742$	−38.6180	−1.41771
$743$	−46.0870	−1.69077	−0.845384	−	0.534160i	$-0.820628\pi$
$743$	−46.0870	−1.69077	−0.845384	+	0.534160i	$0.820628\pi$
$744$	210.933	7.73318
$745$	24.7226	0.905765
$746$	−48.4841	−1.77513
$747$	−69.6532	−2.54848
$748$	29.8157	1.09017
$749$	6.66671	0.243596
$750$	49.8919	1.82180
$751$	−21.3960	−0.780750	−0.390375	−	0.920656i	$-0.627655\pi$
$751$	−21.3960	−0.780750	−0.390375	+	0.920656i	$0.627655\pi$
$752$	25.7320	0.938351
$753$	−55.3972	−2.01879
$754$	92.0664	3.35286
$755$	24.3501	0.886191
$756$	122.598	4.45885
$757$	−10.7555	−0.390914	−0.195457	−	0.980712i	$-0.562619\pi$
$757$	−10.7555	−0.390914	−0.195457	+	0.980712i	$0.562619\pi$
$758$	−23.1089	−0.839353
$759$	72.1167	2.61767
$760$	−142.009	−5.15120
$761$	−5.91303	−0.214347	−0.107174	−	0.994240i	$-0.534180\pi$
$761$	−5.91303	−0.214347	−0.107174	+	0.994240i	$0.534180\pi$
$762$	−62.1318	−2.25080
$763$	28.5346	1.03302
$764$	−31.4880	−1.13920
$765$	35.5423	1.28504
$766$	22.2728	0.804748
$767$	−32.8197	−1.18505
$768$	47.6621	1.71986
$769$	16.6090	0.598936	0.299468	−	0.954106i	$-0.403191\pi$
$769$	16.6090	0.598936	0.299468	+	0.954106i	$0.403191\pi$
$770$	46.7079	1.68324
$771$	54.5658	1.96514
$772$	23.5574	0.847850
$773$	−38.4852	−1.38421	−0.692107	−	0.721794i	$-0.743318\pi$
$773$	−38.4852	−1.38421	−0.692107	+	0.721794i	$0.743318\pi$
$774$	−116.362	−4.18255
$775$	25.3739	0.911458
$776$	−129.885	−4.66261
$777$	11.3579	0.407461
$778$	−55.2758	−1.98173
$779$	22.3057	0.799186
$780$	169.169	6.05722
$781$	1.98944	0.0711878
$782$	27.1981	0.972603
$783$	132.652	4.74058
$784$	−38.7787	−1.38495
$785$	4.05336	0.144670
$786$	90.3568	3.22292
$787$	−12.6118	−0.449561	−0.224781	−	0.974409i	$-0.572167\pi$
$787$	−12.6118	−0.449561	−0.224781	+	0.974409i	$0.572167\pi$
$788$	10.2343	0.364581
$789$	−12.2860	−0.437393
$790$	35.9285	1.27828
$791$	20.6416	0.733930
$792$	202.371	7.19094
$793$	−36.2161	−1.28607
$794$	−7.10668	−0.252207
$795$	−76.7782	−2.72304
$796$	95.4361	3.38264
$797$	−4.48768	−0.158962	−0.0794809	−	0.996836i	$-0.525326\pi$
$797$	−4.48768	−0.158962	−0.0794809	+	0.996836i	$0.525326\pi$
$798$	100.195	3.54685
$799$	−4.43037	−0.156735
$800$	−31.3920	−1.10988
$801$	45.8264	1.61920
$802$	−14.3433	−0.506479
$803$	0.513876	0.0181343
$804$	−112.640	−3.97249
$805$	30.1694	1.06333
$806$	−87.6558	−3.08754
$807$	−51.7072	−1.82018
$808$	7.48526	0.263331
$809$	1.04022	0.0365722	0.0182861	−	0.999833i	$-0.494179\pi$
$809$	1.04022	0.0365722	0.0182861	+	0.999833i	$0.494179\pi$
$810$	179.351	6.30175
$811$	11.4571	0.402314	0.201157	−	0.979559i	$-0.435530\pi$
$811$	11.4571	0.402314	0.201157	+	0.979559i	$0.435530\pi$
$812$	77.8068	2.73048
$813$	−80.7064	−2.83050
$814$	19.0857	0.668954
$815$	−41.7136	−1.46116
$816$	53.8436	1.88490
$817$	−40.2881	−1.40950
$818$	63.6214	2.22447
$819$	−50.0463	−1.74876
$820$	44.9498	1.56972
$821$	−50.3380	−1.75681	−0.878405	−	0.477917i	$-0.841392\pi$
$821$	−50.3380	−1.75681	−0.878405	+	0.477917i	$0.841392\pi$
$822$	25.1587	0.877512
$823$	−24.5938	−0.857286	−0.428643	−	0.903474i	$-0.641008\pi$
$823$	−24.5938	−0.857286	−0.428643	+	0.903474i	$0.641008\pi$
$824$	54.3609	1.89375
$825$	34.1227	1.18800
$826$	−39.1715	−1.36295
$827$	−28.9579	−1.00696	−0.503482	−	0.864006i	$-0.667948\pi$
$827$	−28.9579	−1.00696	−0.503482	+	0.864006i	$0.667948\pi$
$828$	222.407	7.72917
$829$	−16.9200	−0.587655	−0.293828	−	0.955858i	$-0.594929\pi$
$829$	−16.9200	−0.587655	−0.293828	+	0.955858i	$0.594929\pi$
$830$	−68.6336	−2.38231
$831$	−30.6598	−1.06358
$832$	33.0684	1.14644
$833$	6.67666	0.231332
$834$	−184.158	−6.37688
$835$	−65.0458	−2.25100
$836$	119.217	4.12320
$837$	−126.297	−4.36545
$838$	10.2673	0.354678
$839$	10.4936	0.362278	0.181139	−	0.983457i	$-0.442022\pi$
$839$	10.4936	0.362278	0.181139	+	0.983457i	$0.442022\pi$
$840$	118.667	4.09441
$841$	55.1872	1.90301
$842$	−36.8230	−1.26901
$843$	89.3944	3.07891
$844$	−30.3821	−1.04579
$845$	−4.76765	−0.164012
$846$	−51.1644	−1.75907
$847$	−3.81728	−0.131163
$848$	−82.9799	−2.84954
$849$	19.0503	0.653803
$850$	12.8691	0.441405
$851$	12.3278	0.422590
$852$	8.59996	0.294630
$853$	−27.4466	−0.939754	−0.469877	−	0.882732i	$-0.655702\pi$
$853$	−27.4466	−0.939754	−0.469877	+	0.882732i	$0.655702\pi$
$854$	−43.2253	−1.47914
$855$	142.115	4.86022
$856$	28.4619	0.972809
$857$	−43.7288	−1.49375	−0.746874	−	0.664966i	$-0.768446\pi$
$857$	−43.7288	−1.49375	−0.746874	+	0.664966i	$0.768446\pi$
$858$	−117.879	−4.02433
$859$	2.48487	0.0847827	0.0423913	−	0.999101i	$-0.486502\pi$
$859$	2.48487	0.0847827	0.0423913	+	0.999101i	$0.486502\pi$
$860$	−81.1873	−2.76847
$861$	−18.6394	−0.635230
$862$	−71.8130	−2.44596
$863$	20.6889	0.704259	0.352130	−	0.935951i	$-0.385458\pi$
$863$	20.6889	0.704259	0.352130	+	0.935951i	$0.385458\pi$
$864$	156.251	5.31578
$865$	−70.5014	−2.39712
$866$	100.802	3.42540
$867$	45.7328	1.55317
$868$	−74.0794	−2.51442
$869$	−17.7271	−0.601351
$870$	218.466	7.40670
$871$	27.5108	0.932167
$872$	121.822	4.12541
$873$	129.982	4.39923
$874$	108.751	3.67855
$875$	−10.2981	−0.348140
$876$	2.22138	0.0750536
$877$	−14.6000	−0.493008	−0.246504	−	0.969142i	$-0.579282\pi$
$877$	−14.6000	−0.493008	−0.246504	+	0.969142i	$0.579282\pi$
$878$	−32.9603	−1.11236
$879$	34.9225	1.17791
$880$	100.363	3.38324
$881$	−36.7959	−1.23968	−0.619842	−	0.784726i	$-0.712803\pi$
$881$	−36.7959	−1.23968	−0.619842	+	0.784726i	$0.712803\pi$
$882$	77.1057	2.59628
$883$	18.4706	0.621584	0.310792	−	0.950478i	$-0.399406\pi$
$883$	18.4706	0.621584	0.310792	+	0.950478i	$0.399406\pi$
$884$	−31.4790	−1.05875
$885$	−77.8785	−2.61786
$886$	50.0525	1.68155
$887$	30.1170	1.01123	0.505615	−	0.862759i	$-0.331265\pi$
$887$	30.1170	1.01123	0.505615	+	0.862759i	$0.331265\pi$
$888$	48.4897	1.62721
$889$	12.8246	0.430122
$890$	45.1556	1.51362
$891$	−88.4915	−2.96458
$892$	−34.3143	−1.14893
$893$	−17.7147	−0.592799
$894$	−74.4690	−2.49061
$895$	−69.2130	−2.31354
$896$	1.68378	0.0562512
$897$	−76.1399	−2.54224
$898$	−38.1965	−1.27463
$899$	−80.1541	−2.67329
$900$	105.234	3.50780
$901$	14.2869	0.475966
$902$	−31.3217	−1.04290
$903$	33.6661	1.12034
$904$	88.1243	2.93097
$905$	12.2579	0.407465
$906$	−73.3471	−2.43679
$907$	−0.896574	−0.0297702	−0.0148851	−	0.999889i	$-0.504738\pi$
$907$	−0.896574	−0.0297702	−0.0148851	+	0.999889i	$0.504738\pi$
$908$	84.4293	2.80188
$909$	−7.49085	−0.248456
$910$	−49.3137	−1.63473
$911$	57.8209	1.91569	0.957846	−	0.287281i	$-0.0927515\pi$
$911$	57.8209	1.91569	0.957846	+	0.287281i	$0.0927515\pi$
$912$	215.292	7.12902
$913$	33.8637	1.12073
$914$	−74.0227	−2.44845
$915$	−85.9380	−2.84102
$916$	105.137	3.47382
$917$	−18.6504	−0.615891
$918$	−64.0547	−2.11412
$919$	13.3501	0.440379	0.220189	−	0.975457i	$-0.429332\pi$
$919$	13.3501	0.440379	0.220189	+	0.975457i	$0.429332\pi$
$920$	128.801	4.24644
$921$	−4.58658	−0.151133
$922$	−26.5096	−0.873048
$923$	−2.10043	−0.0691364
$924$	−99.6217	−3.27731
$925$	5.83300	0.191788
$926$	74.0961	2.43495
$927$	−54.4014	−1.78678
$928$	99.1648	3.25524
$929$	12.8102	0.420290	0.210145	−	0.977670i	$-0.432606\pi$
$929$	12.8102	0.420290	0.210145	+	0.977670i	$0.432606\pi$
$930$	−208.000	−6.82060
$931$	26.6964	0.874938
$932$	−106.060	−3.47410
$933$	−92.6643	−3.03369
$934$	12.1862	0.398746
$935$	−17.2798	−0.565111
$936$	−213.661	−6.98372
$937$	13.1030	0.428057	0.214028	−	0.976827i	$-0.431341\pi$
$937$	13.1030	0.428057	0.214028	+	0.976827i	$0.431341\pi$
$938$	32.8351	1.07210
$939$	−43.9171	−1.43318
$940$	−35.6980	−1.16434
$941$	29.6016	0.964985	0.482493	−	0.875900i	$-0.339731\pi$
$941$	29.6016	0.964985	0.482493	+	0.875900i	$0.339731\pi$
$942$	−12.2095	−0.397806
$943$	−20.2311	−0.658816
$944$	−84.1691	−2.73947
$945$	−71.0524	−2.31133
$946$	56.5725	1.83933
$947$	34.9306	1.13509	0.567546	−	0.823342i	$-0.307893\pi$
$947$	34.9306	1.13509	0.567546	+	0.823342i	$0.307893\pi$
$948$	−76.6307	−2.48885
$949$	−0.542544	−0.0176117
$950$	51.4565	1.66947
$951$	20.4717	0.663840
$952$	−22.0817	−0.715672
$953$	−2.63907	−0.0854878	−0.0427439	−	0.999086i	$-0.513610\pi$
$953$	−2.63907	−0.0854878	−0.0427439	+	0.999086i	$0.513610\pi$
$954$	164.993	5.34186
$955$	18.2491	0.590526
$956$	32.0978	1.03812
$957$	−107.791	−3.48439
$958$	−102.273	−3.30430
$959$	−5.19299	−0.167690
$960$	78.4687	2.53257
$961$	45.3143	1.46175
$962$	−20.1505	−0.649677
$963$	−28.4831	−0.917857
$964$	−19.2318	−0.619414
$965$	−13.6528	−0.439500
$966$	−90.8757	−2.92388
$967$	−25.2419	−0.811726	−0.405863	−	0.913934i	$-0.633029\pi$
$967$	−25.2419	−0.811726	−0.405863	+	0.913934i	$0.633029\pi$
$968$	−16.2970	−0.523805
$969$	−37.0675	−1.19078
$970$	128.079	4.11238
$971$	−11.3521	−0.364307	−0.182154	−	0.983270i	$-0.558307\pi$
$971$	−11.3521	−0.364307	−0.182154	+	0.983270i	$0.558307\pi$
$972$	−172.126	−5.52096
$973$	38.0119	1.21861
$974$	−89.4276	−2.86545
$975$	−36.0264	−1.15377
$976$	−92.8796	−2.97301
$977$	51.8096	1.65754	0.828768	−	0.559592i	$-0.189042\pi$
$977$	51.8096	1.65754	0.828768	+	0.559592i	$0.189042\pi$
$978$	125.649	4.01782
$979$	−22.2797	−0.712063
$980$	53.7977	1.71850
$981$	−121.913	−3.89237
$982$	32.9907	1.05277
$983$	14.7078	0.469107	0.234553	−	0.972103i	$-0.424637\pi$
$983$	14.7078	0.469107	0.234553	+	0.972103i	$0.424637\pi$
$984$	−79.5766	−2.53681
$985$	−5.93133	−0.188988
$986$	−40.6523	−1.29463
$987$	14.8030	0.471184
$988$	−125.868	−4.00439
$989$	36.5410	1.16194
$990$	−199.557	−6.34234
$991$	0.0627450	0.00199316	0.000996581	−	1.00000i	$-0.499683\pi$
$991$	0.0627450	0.00199316	0.000996581		1.00000i	$0.499683\pi$
$992$	−94.4142	−2.99765
$993$	−31.5796	−1.00215
$994$	−2.50694	−0.0795152
$995$	−55.3105	−1.75346
$996$	146.386	4.63842
$997$	24.7086	0.782528	0.391264	−	0.920278i	$-0.372038\pi$
$997$	24.7086	0.782528	0.391264	+	0.920278i	$0.372038\pi$
$998$	−104.730	−3.31517
$999$	−29.0333	−0.918573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.15	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.15	✓	309	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61747 q^{2} -3.23549 q^{3} +4.85115 q^{4} -2.81151 q^{5} +8.46879 q^{6} -1.74803 q^{7} -7.46281 q^{8} +7.46837 q^{9} +O(q^{10})\)	\(q-2.61747 q^{2} -3.23549 q^{3} +4.85115 q^{4} -2.81151 q^{5} +8.46879 q^{6} -1.74803 q^{7} -7.46281 q^{8} +7.46837 q^{9} +7.35905 q^{10} -3.63094 q^{11} -15.6958 q^{12} +3.83351 q^{13} +4.57543 q^{14} +9.09660 q^{15} +9.83138 q^{16} -1.69270 q^{17} -19.5483 q^{18} -6.76820 q^{19} -13.6391 q^{20} +5.65574 q^{21} +9.50389 q^{22} +6.13870 q^{23} +24.1458 q^{24} +2.90459 q^{25} -10.0341 q^{26} -14.4574 q^{27} -8.47998 q^{28} -9.17536 q^{29} -23.8101 q^{30} +8.73580 q^{31} -10.8077 q^{32} +11.7479 q^{33} +4.43060 q^{34} +4.91461 q^{35} +36.2302 q^{36} +2.00820 q^{37} +17.7156 q^{38} -12.4033 q^{39} +20.9818 q^{40} -3.29567 q^{41} -14.8037 q^{42} +5.95256 q^{43} -17.6143 q^{44} -20.9974 q^{45} -16.0679 q^{46} +2.61734 q^{47} -31.8093 q^{48} -3.94438 q^{49} -7.60268 q^{50} +5.47671 q^{51} +18.5969 q^{52} -8.44031 q^{53} +37.8417 q^{54} +10.2084 q^{55} +13.0452 q^{56} +21.8984 q^{57} +24.0162 q^{58} -8.56127 q^{59} +44.1290 q^{60} -9.44727 q^{61} -22.8657 q^{62} -13.0550 q^{63} +8.62615 q^{64} -10.7779 q^{65} -30.7497 q^{66} +7.17640 q^{67} -8.21155 q^{68} -19.8617 q^{69} -12.8639 q^{70} -0.547913 q^{71} -55.7350 q^{72} -0.141527 q^{73} -5.25641 q^{74} -9.39776 q^{75} -32.8336 q^{76} +6.34701 q^{77} +32.4652 q^{78} +4.88223 q^{79} -27.6410 q^{80} +24.3715 q^{81} +8.62631 q^{82} -9.32642 q^{83} +27.4368 q^{84} +4.75905 q^{85} -15.5806 q^{86} +29.6868 q^{87} +27.0970 q^{88} +6.13607 q^{89} +54.9601 q^{90} -6.70109 q^{91} +29.7798 q^{92} -28.2646 q^{93} -6.85080 q^{94} +19.0289 q^{95} +34.9683 q^{96} +17.4044 q^{97} +10.3243 q^{98} -27.1173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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