LMFDB - Embedded newform 2671.2.a.a.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.829115 q^{2} -1.46533 q^{3} -1.31257 q^{4} -0.762476 q^{5} +1.21493 q^{6} +4.81734 q^{7} +2.74650 q^{8} -0.852803 q^{9} +O(q^{10})$	\(q-0.829115 q^{2} -1.46533 q^{3} -1.31257 q^{4} -0.762476 q^{5} +1.21493 q^{6} +4.81734 q^{7} +2.74650 q^{8} -0.852803 q^{9} +0.632180 q^{10} -2.30795 q^{11} +1.92335 q^{12} -0.0878566 q^{13} -3.99412 q^{14} +1.11728 q^{15} +0.347973 q^{16} -0.325850 q^{17} +0.707071 q^{18} +1.28444 q^{19} +1.00080 q^{20} -7.05900 q^{21} +1.91355 q^{22} -2.95098 q^{23} -4.02453 q^{24} -4.41863 q^{25} +0.0728432 q^{26} +5.64563 q^{27} -6.32308 q^{28} -8.42517 q^{29} -0.926354 q^{30} -1.17286 q^{31} -5.78151 q^{32} +3.38191 q^{33} +0.270167 q^{34} -3.67310 q^{35} +1.11936 q^{36} +5.44114 q^{37} -1.06495 q^{38} +0.128739 q^{39} -2.09414 q^{40} +9.32608 q^{41} +5.85272 q^{42} +4.59734 q^{43} +3.02934 q^{44} +0.650241 q^{45} +2.44670 q^{46} +0.942094 q^{47} -0.509897 q^{48} +16.2067 q^{49} +3.66355 q^{50} +0.477478 q^{51} +0.115318 q^{52} -0.518478 q^{53} -4.68088 q^{54} +1.75975 q^{55} +13.2308 q^{56} -1.88213 q^{57} +6.98544 q^{58} +2.01211 q^{59} -1.46651 q^{60} +11.6725 q^{61} +0.972434 q^{62} -4.10824 q^{63} +4.09759 q^{64} +0.0669885 q^{65} -2.80399 q^{66} -10.7027 q^{67} +0.427700 q^{68} +4.32416 q^{69} +3.04542 q^{70} -0.938154 q^{71} -2.34222 q^{72} +2.17898 q^{73} -4.51133 q^{74} +6.47476 q^{75} -1.68591 q^{76} -11.1181 q^{77} -0.106739 q^{78} -15.4830 q^{79} -0.265321 q^{80} -5.71432 q^{81} -7.73239 q^{82} -7.92425 q^{83} +9.26542 q^{84} +0.248452 q^{85} -3.81172 q^{86} +12.3457 q^{87} -6.33877 q^{88} -9.06262 q^{89} -0.539125 q^{90} -0.423235 q^{91} +3.87336 q^{92} +1.71863 q^{93} -0.781104 q^{94} -0.979352 q^{95} +8.47183 q^{96} +3.50254 q^{97} -13.4372 q^{98} +1.96822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	−0.829115	−0.586273	−0.293136	−	0.956071i	$-0.594699\pi$
$2$	−0.829115	−0.586273	−0.293136	+	0.956071i	$0.594699\pi$
$3$	−1.46533	−0.846010	−0.423005	−	0.906127i	$-0.639025\pi$
$3$	−1.46533	−0.846010	−0.423005	+	0.906127i	$0.639025\pi$
$4$	−1.31257	−0.656284
$5$	−0.762476	−0.340990	−0.170495	−	0.985359i	$-0.554537\pi$
$5$	−0.762476	−0.340990	−0.170495	+	0.985359i	$0.554537\pi$
$6$	1.21493	0.495992
$7$	4.81734	1.82078	0.910391	−	0.413749i	$-0.135781\pi$
$7$	4.81734	1.82078	0.910391	+	0.413749i	$0.135781\pi$
$8$	2.74650	0.971034
$9$	−0.852803	−0.284268
$10$	0.632180	0.199913
$11$	−2.30795	−0.695872	−0.347936	−	0.937518i	$-0.613117\pi$
$11$	−2.30795	−0.695872	−0.347936	+	0.937518i	$0.613117\pi$
$12$	1.92335	0.555223
$13$	−0.0878566	−0.0243670	−0.0121835	−	0.999926i	$-0.503878\pi$
$13$	−0.0878566	−0.0243670	−0.0121835	+	0.999926i	$0.503878\pi$
$14$	−3.99412	−1.06747
$15$	1.11728	0.288480
$16$	0.347973	0.0869934
$17$	−0.325850	−0.0790301	−0.0395151	−	0.999219i	$-0.512581\pi$
$17$	−0.325850	−0.0790301	−0.0395151	+	0.999219i	$0.512581\pi$
$18$	0.707071	0.166658
$19$	1.28444	0.294670	0.147335	−	0.989087i	$-0.452930\pi$
$19$	1.28444	0.294670	0.147335	+	0.989087i	$0.452930\pi$
$20$	1.00080	0.223786
$21$	−7.05900	−1.54040
$22$	1.91355	0.407971
$23$	−2.95098	−0.615322	−0.307661	−	0.951496i	$-0.599546\pi$
$23$	−2.95098	−0.615322	−0.307661	+	0.951496i	$0.599546\pi$
$24$	−4.02453	−0.821504
$25$	−4.41863	−0.883726
$26$	0.0728432	0.0142857
$27$	5.64563	1.08650
$28$	−6.32308	−1.19495
$29$	−8.42517	−1.56452	−0.782258	−	0.622955i	$-0.785932\pi$
$29$	−8.42517	−1.56452	−0.782258	+	0.622955i	$0.785932\pi$
$30$	−0.926354	−0.169128
$31$	−1.17286	−0.210651	−0.105326	−	0.994438i	$-0.533589\pi$
$31$	−1.17286	−0.210651	−0.105326	+	0.994438i	$0.533589\pi$
$32$	−5.78151	−1.02204
$33$	3.38191	0.588714
$34$	0.270167	0.0463332
$35$	−3.67310	−0.620868
$36$	1.11936	0.186560
$37$	5.44114	0.894519	0.447259	−	0.894404i	$-0.352400\pi$
$37$	5.44114	0.894519	0.447259	+	0.894404i	$0.352400\pi$
$38$	−1.06495	−0.172757
$39$	0.128739	0.0206147
$40$	−2.09414	−0.331113
$41$	9.32608	1.45649	0.728244	−	0.685318i	$-0.240337\pi$
$41$	9.32608	1.45649	0.728244	+	0.685318i	$0.240337\pi$
$42$	5.85272	0.903094
$43$	4.59734	0.701087	0.350544	−	0.936546i	$-0.385997\pi$
$43$	4.59734	0.701087	0.350544	+	0.936546i	$0.385997\pi$
$44$	3.02934	0.456690
$45$	0.650241	0.0969323
$46$	2.44670	0.360746
$47$	0.942094	0.137419	0.0687093	−	0.997637i	$-0.478112\pi$
$47$	0.942094	0.137419	0.0687093	+	0.997637i	$0.478112\pi$
$48$	−0.509897	−0.0735972
$49$	16.2067	2.31525
$50$	3.66355	0.518105
$51$	0.477478	0.0668603
$52$	0.115318	0.0159917
$53$	−0.518478	−0.0712185	−0.0356092	−	0.999366i	$-0.511337\pi$
$53$	−0.518478	−0.0712185	−0.0356092	+	0.999366i	$0.511337\pi$
$54$	−4.68088	−0.636987
$55$	1.75975	0.237285
$56$	13.2308	1.76804
$57$	−1.88213	−0.249294
$58$	6.98544	0.917233
$59$	2.01211	0.261955	0.130977	−	0.991385i	$-0.458188\pi$
$59$	2.01211	0.261955	0.130977	+	0.991385i	$0.458188\pi$
$60$	−1.46651	−0.189325
$61$	11.6725	1.49451	0.747256	−	0.664536i	$-0.231371\pi$
$61$	11.6725	1.49451	0.747256	+	0.664536i	$0.231371\pi$
$62$	0.972434	0.123499
$63$	−4.10824	−0.517589
$64$	4.09759	0.512199
$65$	0.0669885	0.00830890
$66$	−2.80399	−0.345147
$67$	−10.7027	−1.30754	−0.653769	−	0.756695i	$-0.726813\pi$
$67$	−10.7027	−1.30754	−0.653769	+	0.756695i	$0.726813\pi$
$68$	0.427700	0.0518662
$69$	4.32416	0.520568
$70$	3.04542	0.363998
$71$	−0.938154	−0.111338	−0.0556692	−	0.998449i	$-0.517729\pi$
$71$	−0.938154	−0.111338	−0.0556692	+	0.998449i	$0.517729\pi$
$72$	−2.34222	−0.276034
$73$	2.17898	0.255031	0.127515	−	0.991837i	$-0.459300\pi$
$73$	2.17898	0.255031	0.127515	+	0.991837i	$0.459300\pi$
$74$	−4.51133	−0.524432
$75$	6.47476	0.747641
$76$	−1.68591	−0.193387
$77$	−11.1181	−1.26703
$78$	−0.106739	−0.0120859
$79$	−15.4830	−1.74197	−0.870985	−	0.491309i	$-0.836519\pi$
$79$	−15.4830	−1.74197	−0.870985	+	0.491309i	$0.836519\pi$
$80$	−0.265321	−0.0296638
$81$	−5.71432	−0.634924
$82$	−7.73239	−0.853899
$83$	−7.92425	−0.869800	−0.434900	−	0.900479i	$-0.643216\pi$
$83$	−7.92425	−0.869800	−0.434900	+	0.900479i	$0.643216\pi$
$84$	9.26542	1.01094
$85$	0.248452	0.0269485
$86$	−3.81172	−0.411028
$87$	12.3457	1.32360
$88$	−6.33877	−0.675715
$89$	−9.06262	−0.960636	−0.480318	−	0.877094i	$-0.659479\pi$
$89$	−9.06262	−0.960636	−0.480318	+	0.877094i	$0.659479\pi$
$90$	−0.539125	−0.0568287
$91$	−0.423235	−0.0443670
$92$	3.87336	0.403826
$93$	1.71863	0.178213
$94$	−0.781104	−0.0805648
$95$	−0.979352	−0.100479
$96$	8.47183	0.864653
$97$	3.50254	0.355629	0.177814	−	0.984064i	$-0.443097\pi$
$97$	3.50254	0.355629	0.177814	+	0.984064i	$0.443097\pi$
$98$	−13.4372	−1.35737
$99$	1.96822	0.197814
$100$	5.79976	0.579976
$101$	3.69446	0.367612	0.183806	−	0.982963i	$-0.441158\pi$
$101$	3.69446	0.367612	0.183806	+	0.982963i	$0.441158\pi$
$102$	−0.395884	−0.0391983
$103$	8.57897	0.845311	0.422655	−	0.906291i	$-0.361098\pi$
$103$	8.57897	0.845311	0.422655	+	0.906291i	$0.361098\pi$
$104$	−0.241298	−0.0236612
$105$	5.38231	0.525260
$106$	0.429878	0.0417534
$107$	−8.80854	−0.851553	−0.425777	−	0.904828i	$-0.639999\pi$
$107$	−8.80854	−0.851553	−0.425777	+	0.904828i	$0.639999\pi$
$108$	−7.41028	−0.713055
$109$	8.82730	0.845502	0.422751	−	0.906246i	$-0.361065\pi$
$109$	8.82730	0.845502	0.422751	+	0.906246i	$0.361065\pi$
$110$	−1.45904	−0.139114
$111$	−7.97308	−0.756771
$112$	1.67631	0.158396
$113$	−8.12804	−0.764622	−0.382311	−	0.924034i	$-0.624872\pi$
$113$	−8.12804	−0.764622	−0.382311	+	0.924034i	$0.624872\pi$
$114$	1.56050	0.146154
$115$	2.25005	0.209818
$116$	11.0586	1.02677
$117$	0.0749243	0.00692676
$118$	−1.66827	−0.153577
$119$	−1.56973	−0.143897
$120$	3.06861	0.280124
$121$	−5.67339	−0.515763
$122$	−9.67785	−0.876192
$123$	−13.6658	−1.23220
$124$	1.53946	0.138247
$125$	7.18148	0.642331
$126$	3.40620	0.303448
$127$	−19.1041	−1.69522	−0.847609	−	0.530622i	$-0.821958\pi$
$127$	−19.1041	−1.69522	−0.847609	+	0.530622i	$0.821958\pi$
$128$	8.16565	0.721748
$129$	−6.73663	−0.593127
$130$	−0.0555412	−0.00487128
$131$	20.2336	1.76782	0.883908	−	0.467661i	$-0.154903\pi$
$131$	20.2336	1.76782	0.883908	+	0.467661i	$0.154903\pi$
$132$	−4.43898	−0.386364
$133$	6.18756	0.536530
$134$	8.87373	0.766573
$135$	−4.30466	−0.370486
$136$	−0.894946	−0.0767410
$137$	−18.6914	−1.59692	−0.798458	−	0.602050i	$-0.794351\pi$
$137$	−18.6914	−1.59692	−0.798458	+	0.602050i	$0.794351\pi$
$138$	−3.58523	−0.305195
$139$	−18.4501	−1.56492	−0.782459	−	0.622702i	$-0.786035\pi$
$139$	−18.4501	−1.56492	−0.782459	+	0.622702i	$0.786035\pi$
$140$	4.82120	0.407466
$141$	−1.38048	−0.116257
$142$	0.777837	0.0652747
$143$	0.202768	0.0169563
$144$	−0.296753	−0.0247294
$145$	6.42399	0.533483
$146$	−1.80663	−0.149518
$147$	−23.7482	−1.95872
$148$	−7.14188	−0.587059
$149$	−10.3161	−0.845127	−0.422564	−	0.906333i	$-0.638870\pi$
$149$	−10.3161	−0.845127	−0.422564	+	0.906333i	$0.638870\pi$
$150$	−5.36832	−0.438321
$151$	1.62952	0.132608	0.0663041	−	0.997799i	$-0.478879\pi$
$151$	1.62952	0.132608	0.0663041	+	0.997799i	$0.478879\pi$
$152$	3.52770	0.286135
$153$	0.277885	0.0224657
$154$	9.21822	0.742825
$155$	0.894276	0.0718300
$156$	−0.168979	−0.0135291
$157$	15.6180	1.24645	0.623224	−	0.782043i	$-0.285822\pi$
$157$	15.6180	1.24645	0.623224	+	0.782043i	$0.285822\pi$
$158$	12.8372	1.02127
$159$	0.759743	0.0602515
$160$	4.40826	0.348504
$161$	−14.2159	−1.12037
$162$	4.73783	0.372239
$163$	19.1389	1.49907	0.749537	−	0.661963i	$-0.230276\pi$
$163$	19.1389	1.49907	0.749537	+	0.661963i	$0.230276\pi$
$164$	−12.2411	−0.955871
$165$	−2.57862	−0.200745
$166$	6.57012	0.509940
$167$	−7.78860	−0.602700	−0.301350	−	0.953514i	$-0.597437\pi$
$167$	−7.78860	−0.602700	−0.301350	+	0.953514i	$0.597437\pi$
$168$	−19.3875	−1.49578
$169$	−12.9923	−0.999406
$170$	−0.205996	−0.0157991
$171$	−1.09537	−0.0837651
$172$	−6.03432	−0.460113
$173$	−16.1623	−1.22880	−0.614400	−	0.788995i	$-0.710602\pi$
$173$	−16.1623	−1.22880	−0.614400	+	0.788995i	$0.710602\pi$
$174$	−10.2360	−0.775988
$175$	−21.2860	−1.60907
$176$	−0.803104	−0.0605362
$177$	−2.94841	−0.221616
$178$	7.51395	0.563195
$179$	−12.9626	−0.968869	−0.484435	−	0.874827i	$-0.660975\pi$
$179$	−12.9626	−0.968869	−0.484435	+	0.874827i	$0.660975\pi$
$180$	−0.853486	−0.0636151
$181$	10.6941	0.794889	0.397444	−	0.917626i	$-0.369897\pi$
$181$	10.6941	0.794889	0.397444	+	0.917626i	$0.369897\pi$
$182$	0.350910	0.0260112
$183$	−17.1041	−1.26437
$184$	−8.10486	−0.597498
$185$	−4.14874	−0.305022
$186$	−1.42494	−0.104482
$187$	0.752043	0.0549948
$188$	−1.23656	−0.0901857
$189$	27.1969	1.97828
$190$	0.811995	0.0589083
$191$	21.3266	1.54314	0.771568	−	0.636147i	$-0.219473\pi$
$191$	21.3266	1.54314	0.771568	+	0.636147i	$0.219473\pi$
$192$	−6.00433	−0.433325
$193$	−13.6815	−0.984816	−0.492408	−	0.870364i	$-0.663883\pi$
$193$	−13.6815	−0.984816	−0.492408	+	0.870364i	$0.663883\pi$
$194$	−2.90401	−0.208496
$195$	−0.0981604	−0.00702941
$196$	−21.2724	−1.51946
$197$	−10.6182	−0.756512	−0.378256	−	0.925701i	$-0.623476\pi$
$197$	−10.6182	−0.756512	−0.378256	+	0.925701i	$0.623476\pi$
$198$	−1.63188	−0.115973
$199$	−27.6246	−1.95826	−0.979129	−	0.203238i	$-0.934853\pi$
$199$	−27.6246	−1.95826	−0.979129	+	0.203238i	$0.934853\pi$
$200$	−12.1358	−0.858128
$201$	15.6829	1.10619
$202$	−3.06313	−0.215521
$203$	−40.5869	−2.84864
$204$	−0.626722	−0.0438793
$205$	−7.11091	−0.496647
$206$	−7.11295	−0.495583
$207$	2.51660	0.174916
$208$	−0.0305718	−0.00211977
$209$	−2.96441	−0.205052
$210$	−4.46256	−0.307946
$211$	16.3254	1.12388	0.561942	−	0.827177i	$-0.310054\pi$
$211$	16.3254	1.12388	0.561942	+	0.827177i	$0.310054\pi$
$212$	0.680538	0.0467396
$213$	1.37471	0.0941934
$214$	7.30329	0.499243
$215$	−3.50536	−0.239064
$216$	15.5057	1.05503
$217$	−5.65005	−0.383550
$218$	−7.31884	−0.495695
$219$	−3.19293	−0.215759
$220$	−2.30980	−0.155726
$221$	0.0286280	0.00192573
$222$	6.61060	0.443674
$223$	−16.9376	−1.13423	−0.567113	−	0.823640i	$-0.691940\pi$
$223$	−16.9376	−1.13423	−0.567113	+	0.823640i	$0.691940\pi$
$224$	−27.8515	−1.86090
$225$	3.76822	0.251215
$226$	6.73908	0.448277
$227$	−10.4306	−0.692305	−0.346153	−	0.938178i	$-0.612512\pi$
$227$	−10.4306	−0.692305	−0.346153	+	0.938178i	$0.612512\pi$
$228$	2.47042	0.163607
$229$	22.8862	1.51236	0.756181	−	0.654363i	$-0.227063\pi$
$229$	22.8862	1.51236	0.756181	+	0.654363i	$0.227063\pi$
$230$	−1.86555	−0.123011
$231$	16.2918	1.07192
$232$	−23.1397	−1.51920
$233$	−18.3792	−1.20406	−0.602030	−	0.798474i	$-0.705641\pi$
$233$	−18.3792	−1.20406	−0.602030	+	0.798474i	$0.705641\pi$
$234$	−0.0621209	−0.00406097
$235$	−0.718324	−0.0468583
$236$	−2.64104	−0.171917
$237$	22.6877	1.47372
$238$	1.30148	0.0843627
$239$	−1.30359	−0.0843224	−0.0421612	−	0.999111i	$-0.513424\pi$
$239$	−1.30359	−0.0843224	−0.0421612	+	0.999111i	$0.513424\pi$
$240$	0.388784	0.0250959
$241$	−19.8504	−1.27868	−0.639339	−	0.768925i	$-0.720792\pi$
$241$	−19.8504	−1.27868	−0.639339	+	0.768925i	$0.720792\pi$
$242$	4.70389	0.302378
$243$	−8.56353	−0.549351
$244$	−15.3210	−0.980825
$245$	−12.3572	−0.789475
$246$	11.3305	0.722407
$247$	−0.112846	−0.00718023
$248$	−3.22125	−0.204550
$249$	11.6117	0.735859
$250$	−5.95427	−0.376581
$251$	25.6483	1.61891	0.809454	−	0.587183i	$-0.199763\pi$
$251$	25.6483	1.61891	0.809454	+	0.587183i	$0.199763\pi$
$252$	5.39234	0.339686
$253$	6.81070	0.428185
$254$	15.8395	0.993860
$255$	−0.364065	−0.0227987
$256$	−14.9654	−0.935340
$257$	15.7360	0.981587	0.490793	−	0.871276i	$-0.336707\pi$
$257$	15.7360	0.981587	0.490793	+	0.871276i	$0.336707\pi$
$258$	5.58544	0.347734
$259$	26.2118	1.62872
$260$	−0.0879270	−0.00545300
$261$	7.18501	0.444741
$262$	−16.7760	−1.03642
$263$	−8.39062	−0.517388	−0.258694	−	0.965959i	$-0.583292\pi$
$263$	−8.39062	−0.517388	−0.258694	+	0.965959i	$0.583292\pi$
$264$	9.28840	0.571662
$265$	0.395327	0.0242847
$266$	−5.13020	−0.314553
$267$	13.2797	0.812707
$268$	14.0480	0.858116
$269$	−6.01558	−0.366777	−0.183388	−	0.983041i	$-0.558707\pi$
$269$	−6.01558	−0.366777	−0.183388	+	0.983041i	$0.558707\pi$
$270$	3.56906	0.217206
$271$	−29.2536	−1.77703	−0.888514	−	0.458850i	$-0.848261\pi$
$271$	−29.2536	−1.77703	−0.888514	+	0.458850i	$0.848261\pi$
$272$	−0.113387	−0.00687510
$273$	0.620179	0.0375349
$274$	15.4973	0.936229
$275$	10.1980	0.614960
$276$	−5.67576	−0.341641
$277$	−18.6644	−1.12143	−0.560717	−	0.828007i	$-0.689474\pi$
$277$	−18.6644	−1.12143	−0.560717	+	0.828007i	$0.689474\pi$
$278$	15.2973	0.917469
$279$	1.00022	0.0598814
$280$	−10.0882	−0.602884
$281$	−14.6865	−0.876125	−0.438063	−	0.898944i	$-0.644335\pi$
$281$	−14.6865	−0.876125	−0.438063	+	0.898944i	$0.644335\pi$
$282$	1.14458	0.0681586
$283$	−4.56884	−0.271589	−0.135795	−	0.990737i	$-0.543359\pi$
$283$	−4.56884	−0.271589	−0.135795	+	0.990737i	$0.543359\pi$
$284$	1.23139	0.0730696
$285$	1.43508	0.0850065
$286$	−0.168118	−0.00994103
$287$	44.9268	2.65195
$288$	4.93049	0.290532
$289$	−16.8938	−0.993754
$290$	−5.32623	−0.312767
$291$	−5.13238	−0.300866
$292$	−2.86007	−0.167373
$293$	−9.19712	−0.537302	−0.268651	−	0.963238i	$-0.586578\pi$
$293$	−9.19712	−0.537302	−0.268651	+	0.963238i	$0.586578\pi$
$294$	19.6900	1.14834
$295$	−1.53419	−0.0893239
$296$	14.9441	0.868608
$297$	−13.0298	−0.756067
$298$	8.55322	0.495475
$299$	0.259263	0.0149936
$300$	−8.49857	−0.490665
$301$	22.1469	1.27653
$302$	−1.35106	−0.0777446
$303$	−5.41361	−0.311004
$304$	0.446950	0.0256343
$305$	−8.90001	−0.509613
$306$	−0.230399	−0.0131710
$307$	−1.55542	−0.0887728	−0.0443864	−	0.999014i	$-0.514133\pi$
$307$	−1.55542	−0.0887728	−0.0443864	+	0.999014i	$0.514133\pi$
$308$	14.5933	0.831532
$309$	−12.5710	−0.715141
$310$	−0.741457	−0.0421119
$311$	−15.3788	−0.872051	−0.436026	−	0.899934i	$-0.643614\pi$
$311$	−15.3788	−0.872051	−0.436026	+	0.899934i	$0.643614\pi$
$312$	0.353582	0.0200176
$313$	17.9167	1.01271	0.506356	−	0.862325i	$-0.330992\pi$
$313$	17.9167	1.01271	0.506356	+	0.862325i	$0.330992\pi$
$314$	−12.9491	−0.730759
$315$	3.13243	0.176492
$316$	20.3225	1.14323
$317$	−3.55649	−0.199752	−0.0998761	−	0.995000i	$-0.531845\pi$
$317$	−3.55649	−0.199752	−0.0998761	+	0.995000i	$0.531845\pi$
$318$	−0.629914	−0.0353238
$319$	19.4448	1.08870
$320$	−3.12431	−0.174654
$321$	12.9074	0.720422
$322$	11.7866	0.656840
$323$	−0.418533	−0.0232878
$324$	7.50044	0.416691
$325$	0.388206	0.0215338
$326$	−15.8683	−0.878866
$327$	−12.9349	−0.715303
$328$	25.6141	1.41430
$329$	4.53839	0.250209
$330$	2.13797	0.117692
$331$	4.83908	0.265980	0.132990	−	0.991117i	$-0.457542\pi$
$331$	4.83908	0.265980	0.132990	+	0.991117i	$0.457542\pi$
$332$	10.4011	0.570836
$333$	−4.64022	−0.254283
$334$	6.45764	0.353346
$335$	8.16051	0.445857
$336$	−2.45634	−0.134005
$337$	−22.5048	−1.22591	−0.612957	−	0.790116i	$-0.710020\pi$
$337$	−22.5048	−1.22591	−0.612957	+	0.790116i	$0.710020\pi$
$338$	10.7721	0.585925
$339$	11.9103	0.646878
$340$	−0.326111	−0.0176858
$341$	2.70689	0.146586
$342$	0.908188	0.0491092
$343$	44.3519	2.39478
$344$	12.6266	0.680780
$345$	−3.29707	−0.177508
$346$	13.4004	0.720412
$347$	−34.6498	−1.86010	−0.930050	−	0.367432i	$-0.880237\pi$
$347$	−34.6498	−1.86010	−0.930050	+	0.367432i	$0.880237\pi$
$348$	−16.2045	−0.868655
$349$	−3.46696	−0.185582	−0.0927911	−	0.995686i	$-0.529579\pi$
$349$	−3.46696	−0.185582	−0.0927911	+	0.995686i	$0.529579\pi$
$350$	17.6486	0.943355
$351$	−0.496006	−0.0264748
$352$	13.3434	0.711206
$353$	2.26747	0.120685	0.0603427	−	0.998178i	$-0.480781\pi$
$353$	2.26747	0.120685	0.0603427	+	0.998178i	$0.480781\pi$
$354$	2.44457	0.129928
$355$	0.715320	0.0379652
$356$	11.8953	0.630450
$357$	2.30017	0.121738
$358$	10.7475	0.568022
$359$	30.3787	1.60333	0.801663	−	0.597776i	$-0.203949\pi$
$359$	30.3787	1.60333	0.801663	+	0.597776i	$0.203949\pi$
$360$	1.78589	0.0941246
$361$	−17.3502	−0.913170
$362$	−8.86667	−0.466022
$363$	8.31340	0.436340
$364$	0.555524	0.0291174
$365$	−1.66142	−0.0869628
$366$	14.1813	0.741267
$367$	36.9144	1.92692	0.963459	−	0.267855i	$-0.0863148\pi$
$367$	36.9144	1.92692	0.963459	+	0.267855i	$0.0863148\pi$
$368$	−1.02686	−0.0535289
$369$	−7.95330	−0.414032
$370$	3.43978	0.178826
$371$	−2.49768	−0.129673
$372$	−2.25581	−0.116959
$373$	−4.79749	−0.248404	−0.124202	−	0.992257i	$-0.539637\pi$
$373$	−4.79749	−0.248404	−0.124202	+	0.992257i	$0.539637\pi$
$374$	−0.623530	−0.0322420
$375$	−10.5232	−0.543418
$376$	2.58746	0.133438
$377$	0.740207	0.0381226
$378$	−22.5494	−1.15981
$379$	20.3028	1.04288	0.521442	−	0.853287i	$-0.325394\pi$
$379$	20.3028	1.04288	0.521442	+	0.853287i	$0.325394\pi$
$380$	1.28547	0.0659430
$381$	27.9939	1.43417
$382$	−17.6822	−0.904698
$383$	−35.0045	−1.78864	−0.894322	−	0.447424i	$-0.852342\pi$
$383$	−35.0045	−1.78864	−0.894322	+	0.447424i	$0.852342\pi$
$384$	−11.9654	−0.610606
$385$	8.47732	0.432044
$386$	11.3435	0.577371
$387$	−3.92062	−0.199296
$388$	−4.59732	−0.233394
$389$	3.10157	0.157256	0.0786280	−	0.996904i	$-0.474946\pi$
$389$	3.10157	0.157256	0.0786280	+	0.996904i	$0.474946\pi$
$390$	0.0813862	0.00412115
$391$	0.961575	0.0486289
$392$	44.5118	2.24818
$393$	−29.6489	−1.49559
$394$	8.80367	0.443522
$395$	11.8054	0.593994
$396$	−2.58343	−0.129822
$397$	−4.84018	−0.242922	−0.121461	−	0.992596i	$-0.538758\pi$
$397$	−4.84018	−0.242922	−0.121461	+	0.992596i	$0.538758\pi$
$398$	22.9040	1.14807
$399$	−9.06683	−0.453909
$400$	−1.53757	−0.0768783
$401$	−10.0138	−0.500063	−0.250032	−	0.968238i	$-0.580441\pi$
$401$	−10.0138	−0.500063	−0.250032	+	0.968238i	$0.580441\pi$
$402$	−13.0030	−0.648529
$403$	0.103043	0.00513295
$404$	−4.84923	−0.241258
$405$	4.35703	0.216503
$406$	33.6512	1.67008
$407$	−12.5579	−0.622470
$408$	1.31139	0.0649236
$409$	−3.87807	−0.191758	−0.0958791	−	0.995393i	$-0.530566\pi$
$409$	−3.87807	−0.191758	−0.0958791	+	0.995393i	$0.530566\pi$
$410$	5.89576	0.291171
$411$	27.3891	1.35101
$412$	−11.2605	−0.554764
$413$	9.69303	0.476963
$414$	−2.08655	−0.102548
$415$	6.04205	0.296593
$416$	0.507944	0.0249040
$417$	27.0355	1.32394
$418$	2.45784	0.120217
$419$	−21.5940	−1.05494	−0.527468	−	0.849575i	$-0.676859\pi$
$419$	−21.5940	−1.05494	−0.527468	+	0.849575i	$0.676859\pi$
$420$	−7.06466	−0.344720
$421$	18.8599	0.919174	0.459587	−	0.888133i	$-0.347997\pi$
$421$	18.8599	0.919174	0.459587	+	0.888133i	$0.347997\pi$
$422$	−13.5356	−0.658902
$423$	−0.803421	−0.0390636
$424$	−1.42400	−0.0691556
$425$	1.43981	0.0698410
$426$	−1.13979	−0.0552230
$427$	56.2304	2.72118
$428$	11.5618	0.558861
$429$	−0.297123	−0.0143452
$430$	2.90635	0.140156
$431$	4.77040	0.229782	0.114891	−	0.993378i	$-0.463348\pi$
$431$	4.77040	0.229782	0.114891	+	0.993378i	$0.463348\pi$
$432$	1.96453	0.0945185
$433$	−4.97469	−0.239068	−0.119534	−	0.992830i	$-0.538140\pi$
$433$	−4.97469	−0.239068	−0.119534	+	0.992830i	$0.538140\pi$
$434$	4.68454	0.224865
$435$	−9.41328	−0.451332
$436$	−11.5864	−0.554889
$437$	−3.79034	−0.181317
$438$	2.64731	0.126493
$439$	−19.2796	−0.920165	−0.460082	−	0.887876i	$-0.652180\pi$
$439$	−19.2796	−0.920165	−0.460082	+	0.887876i	$0.652180\pi$
$440$	4.83316	0.230412
$441$	−13.8211	−0.658149
$442$	−0.0237359	−0.00112900
$443$	28.1588	1.33787	0.668933	−	0.743323i	$-0.266751\pi$
$443$	28.1588	1.33787	0.668933	+	0.743323i	$0.266751\pi$
$444$	10.4652	0.496657
$445$	6.91003	0.327567
$446$	14.0432	0.664966
$447$	15.1165	0.714986
$448$	19.7395	0.932602
$449$	15.7599	0.743757	0.371879	−	0.928281i	$-0.378714\pi$
$449$	15.7599	0.743757	0.371879	+	0.928281i	$0.378714\pi$
$450$	−3.12429	−0.147280
$451$	−21.5241	−1.01353
$452$	10.6686	0.501809
$453$	−2.38778	−0.112188
$454$	8.64819	0.405880
$455$	0.322706	0.0151287
$456$	−5.16926	−0.242073
$457$	−29.5344	−1.38156	−0.690781	−	0.723064i	$-0.742733\pi$
$457$	−29.5344	−1.38156	−0.690781	+	0.723064i	$0.742733\pi$
$458$	−18.9753	−0.886656
$459$	−1.83963	−0.0858665
$460$	−2.95334	−0.137700
$461$	−27.1578	−1.26487	−0.632433	−	0.774615i	$-0.717944\pi$
$461$	−27.1578	−1.26487	−0.632433	+	0.774615i	$0.717944\pi$
$462$	−13.5078	−0.628437
$463$	−31.7800	−1.47694	−0.738472	−	0.674284i	$-0.764452\pi$
$463$	−31.7800	−1.47694	−0.738472	+	0.674284i	$0.764452\pi$
$464$	−2.93174	−0.136102
$465$	−1.31041	−0.0607688
$466$	15.2384	0.705907
$467$	−3.13289	−0.144973	−0.0724864	−	0.997369i	$-0.523093\pi$
$467$	−3.13289	−0.144973	−0.0724864	+	0.997369i	$0.523093\pi$
$468$	−0.0983433	−0.00454592
$469$	−51.5583	−2.38074
$470$	0.595573	0.0274717
$471$	−22.8855	−1.05451
$472$	5.52627	0.254367
$473$	−10.6104	−0.487867
$474$	−18.8107	−0.864004
$475$	−5.67545	−0.260407
$476$	2.06037	0.0944371
$477$	0.442160	0.0202451
$478$	1.08083	0.0494359
$479$	9.89503	0.452115	0.226058	−	0.974114i	$-0.427416\pi$
$479$	9.89503	0.452115	0.226058	+	0.974114i	$0.427416\pi$
$480$	−6.45957	−0.294837
$481$	−0.478040	−0.0217968
$482$	16.4583	0.749654
$483$	20.8309	0.947841
$484$	7.44671	0.338487
$485$	−2.67060	−0.121266
$486$	7.10015	0.322069
$487$	33.2521	1.50680	0.753399	−	0.657564i	$-0.228413\pi$
$487$	33.2521	1.50680	0.753399	+	0.657564i	$0.228413\pi$
$488$	32.0586	1.45122
$489$	−28.0448	−1.26823
$490$	10.2456	0.462848
$491$	1.42572	0.0643418	0.0321709	−	0.999482i	$-0.489758\pi$
$491$	1.42572	0.0643418	0.0321709	+	0.999482i	$0.489758\pi$
$492$	17.9373	0.808676
$493$	2.74534	0.123644
$494$	0.0935624	0.00420957
$495$	−1.50072	−0.0674524
$496$	−0.408123	−0.0183253
$497$	−4.51940	−0.202723
$498$	−9.62740	−0.431414
$499$	−1.71086	−0.0765886	−0.0382943	−	0.999267i	$-0.512192\pi$
$499$	−1.71086	−0.0765886	−0.0382943	+	0.999267i	$0.512192\pi$
$500$	−9.42618	−0.421552
$501$	11.4129	0.509890
$502$	−21.2654	−0.949121
$503$	−1.87657	−0.0836721	−0.0418361	−	0.999124i	$-0.513321\pi$
$503$	−1.87657	−0.0836721	−0.0418361	+	0.999124i	$0.513321\pi$
$504$	−11.2833	−0.502597
$505$	−2.81694	−0.125352
$506$	−5.64685	−0.251033
$507$	19.0380	0.845507
$508$	25.0755	1.11254
$509$	17.0831	0.757195	0.378598	−	0.925561i	$-0.376406\pi$
$509$	17.0831	0.757195	0.378598	+	0.925561i	$0.376406\pi$
$510$	0.301852	0.0133662
$511$	10.4969	0.464355
$512$	−3.92323	−0.173384
$513$	7.25146	0.320160
$514$	−13.0470	−0.575478
$515$	−6.54125	−0.288242
$516$	8.84228	0.389260
$517$	−2.17430	−0.0956257
$518$	−21.7326	−0.954876
$519$	23.6832	1.03958
$520$	0.183984	0.00806823
$521$	27.8140	1.21855	0.609277	−	0.792957i	$-0.291460\pi$
$521$	27.8140	1.21855	0.609277	+	0.792957i	$0.291460\pi$
$522$	−5.95720	−0.260739
$523$	33.2831	1.45537	0.727684	−	0.685912i	$-0.240597\pi$
$523$	33.2831	1.45537	0.727684	+	0.685912i	$0.240597\pi$
$524$	−26.5580	−1.16019
$525$	31.1911	1.36129
$526$	6.95678	0.303330
$527$	0.382175	0.0166478
$528$	1.17681	0.0512142
$529$	−14.2917	−0.621379
$530$	−0.327772	−0.0142375
$531$	−1.71594	−0.0744653
$532$	−8.12160	−0.352116
$533$	−0.819357	−0.0354903
$534$	−11.0104	−0.476468
$535$	6.71630	0.290371
$536$	−29.3948	−1.26966
$537$	18.9945	0.819673
$538$	4.98761	0.215031
$539$	−37.4042	−1.61111
$540$	5.65016	0.243144
$541$	−37.8543	−1.62748	−0.813742	−	0.581226i	$-0.802573\pi$
$541$	−37.8543	−1.62748	−0.813742	+	0.581226i	$0.802573\pi$
$542$	24.2546	1.04182
$543$	−15.6705	−0.672484
$544$	1.88390	0.0807717
$545$	−6.73060	−0.288307
$546$	−0.514200	−0.0220057
$547$	4.08258	0.174558	0.0872792	−	0.996184i	$-0.472183\pi$
$547$	4.08258	0.174558	0.0872792	+	0.996184i	$0.472183\pi$
$548$	24.5338	1.04803
$549$	−9.95435	−0.424841
$550$	−8.45528	−0.360534
$551$	−10.8216	−0.461016
$552$	11.8763	0.505489
$553$	−74.5867	−3.17175
$554$	15.4749	0.657466
$555$	6.07928	0.258051
$556$	24.2170	1.02703
$557$	−22.2265	−0.941765	−0.470883	−	0.882196i	$-0.656064\pi$
$557$	−22.2265	−0.941765	−0.470883	+	0.882196i	$0.656064\pi$
$558$	−0.829294	−0.0351068
$559$	−0.403906	−0.0170834
$560$	−1.27814	−0.0540114
$561$	−1.10199	−0.0465262
$562$	12.1768	0.513648
$563$	−28.0514	−1.18223	−0.591114	−	0.806588i	$-0.701312\pi$
$563$	−28.0514	−1.18223	−0.591114	+	0.806588i	$0.701312\pi$
$564$	1.81198	0.0762980
$565$	6.19744	0.260728
$566$	3.78809	0.159225
$567$	−27.5278	−1.15606
$568$	−2.57664	−0.108113
$569$	12.6477	0.530221	0.265110	−	0.964218i	$-0.414592\pi$
$569$	12.6477	0.530221	0.265110	+	0.964218i	$0.414592\pi$
$570$	−1.18984	−0.0498370
$571$	24.5898	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$571$	24.5898	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$572$	−0.266147	−0.0111282
$573$	−31.2505	−1.30551
$574$	−37.2495	−1.55476
$575$	13.0393	0.543776
$576$	−3.49443	−0.145601
$577$	39.5674	1.64721	0.823607	−	0.567161i	$-0.191958\pi$
$577$	39.5674	1.64721	0.823607	+	0.567161i	$0.191958\pi$
$578$	14.0069	0.582611
$579$	20.0479	0.833164
$580$	−8.43193	−0.350117
$581$	−38.1738	−1.58372
$582$	4.25533	0.176389
$583$	1.19662	0.0495589
$584$	5.98458	0.247644
$585$	−0.0571280	−0.00236195
$586$	7.62547	0.315005
$587$	22.9724	0.948173	0.474086	−	0.880478i	$-0.342778\pi$
$587$	22.9724	0.948173	0.474086	+	0.880478i	$0.342778\pi$
$588$	31.1712	1.28548
$589$	−1.50646	−0.0620727
$590$	1.27202	0.0523682
$591$	15.5591	0.640017
$592$	1.89337	0.0778172
$593$	32.1949	1.32209	0.661043	−	0.750348i	$-0.270114\pi$
$593$	32.1949	1.32209	0.661043	+	0.750348i	$0.270114\pi$
$594$	10.8032	0.443261
$595$	1.19688	0.0490672
$596$	13.5406	0.554644
$597$	40.4793	1.65671
$598$	−0.214959	−0.00879031
$599$	19.3285	0.789743	0.394872	−	0.918736i	$-0.370789\pi$
$599$	19.3285	0.789743	0.394872	+	0.918736i	$0.370789\pi$
$600$	17.7829	0.725985
$601$	−26.1425	−1.06637	−0.533187	−	0.845998i	$-0.679006\pi$
$601$	−26.1425	−1.06637	−0.533187	+	0.845998i	$0.679006\pi$
$602$	−18.3623	−0.748393
$603$	9.12725	0.371690
$604$	−2.13885	−0.0870287
$605$	4.32582	0.175870
$606$	4.48850	0.182333
$607$	12.2702	0.498031	0.249016	−	0.968499i	$-0.419893\pi$
$607$	12.2702	0.498031	0.249016	+	0.968499i	$0.419893\pi$
$608$	−7.42598	−0.301163
$609$	59.4733	2.40998
$610$	7.37913	0.298772
$611$	−0.0827692	−0.00334848
$612$	−0.364744	−0.0147439
$613$	−23.0880	−0.932514	−0.466257	−	0.884649i	$-0.654398\pi$
$613$	−23.0880	−0.932514	−0.466257	+	0.884649i	$0.654398\pi$
$614$	1.28963	0.0520451
$615$	10.4198	0.420169
$616$	−30.5360	−1.23033
$617$	16.8484	0.678293	0.339146	−	0.940734i	$-0.389862\pi$
$617$	16.8484	0.678293	0.339146	+	0.940734i	$0.389862\pi$
$618$	10.4228	0.419268
$619$	−30.5901	−1.22952	−0.614759	−	0.788715i	$-0.710747\pi$
$619$	−30.5901	−1.22952	−0.614759	+	0.788715i	$0.710747\pi$
$620$	−1.17380	−0.0471409
$621$	−16.6601	−0.668549
$622$	12.7508	0.511260
$623$	−43.6577	−1.74911
$624$	0.0447978	0.00179335
$625$	16.6174	0.664698
$626$	−14.8550	−0.593725
$627$	4.34384	0.173476
$628$	−20.4996	−0.818025
$629$	−1.77299	−0.0706939
$630$	−2.59715	−0.103473
$631$	13.8635	0.551899	0.275949	−	0.961172i	$-0.411008\pi$
$631$	13.8635	0.551899	0.275949	+	0.961172i	$0.411008\pi$
$632$	−42.5240	−1.69151
$633$	−23.9221	−0.950817
$634$	2.94873	0.117109
$635$	14.5664	0.578051
$636$	−0.997214	−0.0395421
$637$	−1.42387	−0.0564157
$638$	−16.1220	−0.638276
$639$	0.800060	0.0316499
$640$	−6.22611	−0.246109
$641$	−40.1096	−1.58423	−0.792117	−	0.610370i	$-0.791021\pi$
$641$	−40.1096	−1.58423	−0.792117	+	0.610370i	$0.791021\pi$
$642$	−10.7017	−0.422364
$643$	35.0634	1.38277	0.691383	−	0.722489i	$-0.257002\pi$
$643$	35.0634	1.38277	0.691383	+	0.722489i	$0.257002\pi$
$644$	18.6593	0.735279
$645$	5.13651	0.202250
$646$	0.347012	0.0136530
$647$	27.8429	1.09462	0.547310	−	0.836930i	$-0.315652\pi$
$647$	27.8429	1.09462	0.547310	+	0.836930i	$0.315652\pi$
$648$	−15.6944	−0.616533
$649$	−4.64385	−0.182287
$650$	−0.321867	−0.0126247
$651$	8.27920	0.324487
$652$	−25.1211	−0.983818
$653$	−23.9191	−0.936026	−0.468013	−	0.883722i	$-0.655030\pi$
$653$	−23.9191	−0.936026	−0.468013	+	0.883722i	$0.655030\pi$
$654$	10.7245	0.419362
$655$	−15.4276	−0.602807
$656$	3.24523	0.126705
$657$	−1.85824	−0.0724970
$658$	−3.76284	−0.146691
$659$	3.46437	0.134953	0.0674764	−	0.997721i	$-0.478505\pi$
$659$	3.46437	0.134953	0.0674764	+	0.997721i	$0.478505\pi$
$660$	3.38462	0.131746
$661$	−30.9571	−1.20409	−0.602045	−	0.798462i	$-0.705647\pi$
$661$	−30.9571	−1.20409	−0.602045	+	0.798462i	$0.705647\pi$
$662$	−4.01215	−0.155937
$663$	−0.0419496	−0.00162919
$664$	−21.7640	−0.844605
$665$	−4.71787	−0.182951
$666$	3.84728	0.149079
$667$	24.8625	0.962680
$668$	10.2231	0.395542
$669$	24.8192	0.959567
$670$	−6.76600	−0.261394
$671$	−26.9395	−1.03999
$672$	40.8116	1.57434
$673$	34.2486	1.32019	0.660094	−	0.751183i	$-0.270516\pi$
$673$	34.2486	1.32019	0.660094	+	0.751183i	$0.270516\pi$
$674$	18.6591	0.718720
$675$	−24.9460	−0.960171
$676$	17.0533	0.655895
$677$	11.7153	0.450255	0.225127	−	0.974329i	$-0.427720\pi$
$677$	11.7153	0.450255	0.225127	+	0.974329i	$0.427720\pi$
$678$	−9.87499	−0.379247
$679$	16.8729	0.647523
$680$	0.682375	0.0261679
$681$	15.2843	0.585697
$682$	−2.24432	−0.0859396
$683$	−39.4535	−1.50965	−0.754824	−	0.655928i	$-0.772278\pi$
$683$	−39.4535	−1.50965	−0.754824	+	0.655928i	$0.772278\pi$
$684$	1.43775	0.0549737
$685$	14.2518	0.544532
$686$	−36.7728	−1.40399
$687$	−33.5358	−1.27947
$688$	1.59975	0.0609900
$689$	0.0455517	0.00173538
$690$	2.73365	0.104068
$691$	−15.7130	−0.597752	−0.298876	−	0.954292i	$-0.596612\pi$
$691$	−15.7130	−0.597752	−0.298876	+	0.954292i	$0.596612\pi$
$692$	21.2142	0.806442
$693$	9.48158	0.360176
$694$	28.7287	1.09053
$695$	14.0678	0.533621
$696$	33.9074	1.28526
$697$	−3.03890	−0.115106
$698$	2.87451	0.108802
$699$	26.9316	1.01865
$700$	27.9394	1.05601
$701$	−37.2162	−1.40564	−0.702818	−	0.711370i	$-0.748075\pi$
$701$	−37.2162	−1.40564	−0.702818	+	0.711370i	$0.748075\pi$
$702$	0.411246	0.0155215
$703$	6.98880	0.263588
$704$	−9.45701	−0.356424
$705$	1.05258	0.0396426
$706$	−1.88000	−0.0707546
$707$	17.7974	0.669342
$708$	3.87000	0.145443
$709$	−12.1898	−0.457798	−0.228899	−	0.973450i	$-0.573513\pi$
$709$	−12.1898	−0.457798	−0.228899	+	0.973450i	$0.573513\pi$
$710$	−0.593082	−0.0222580
$711$	13.2039	0.495186
$712$	−24.8905	−0.932810
$713$	3.46108	0.129618
$714$	−1.90711	−0.0713716
$715$	−0.154606	−0.00578193
$716$	17.0143	0.635854
$717$	1.91020	0.0713376
$718$	−25.1874	−0.939986
$719$	−15.0239	−0.560296	−0.280148	−	0.959957i	$-0.590384\pi$
$719$	−15.0239	−0.560296	−0.280148	+	0.959957i	$0.590384\pi$
$720$	0.226267	0.00843246
$721$	41.3278	1.53913
$722$	14.3853	0.535366
$723$	29.0875	1.08177
$724$	−14.0368	−0.521673
$725$	37.2277	1.38260
$726$	−6.89276	−0.255814
$727$	−31.7008	−1.17572	−0.587859	−	0.808963i	$-0.700029\pi$
$727$	−31.7008	−1.17572	−0.587859	+	0.808963i	$0.700029\pi$
$728$	−1.16241	−0.0430819
$729$	29.6914	1.09968
$730$	1.37751	0.0509839
$731$	−1.49804	−0.0554070
$732$	22.4503	0.829787
$733$	38.8820	1.43614	0.718070	−	0.695971i	$-0.245026\pi$
$733$	38.8820	1.43614	0.718070	+	0.695971i	$0.245026\pi$
$734$	−30.6063	−1.12970
$735$	18.1075	0.667903
$736$	17.0611	0.628881
$737$	24.7011	0.909878
$738$	6.59420	0.242736
$739$	−33.0471	−1.21566	−0.607829	−	0.794068i	$-0.707959\pi$
$739$	−33.0471	−1.21566	−0.607829	+	0.794068i	$0.707959\pi$
$740$	5.44551	0.200181
$741$	0.165357	0.00607454
$742$	2.07087	0.0760239
$743$	−30.3743	−1.11432	−0.557162	−	0.830404i	$-0.688110\pi$
$743$	−30.3743	−1.11432	−0.557162	+	0.830404i	$0.688110\pi$
$744$	4.72021	0.173051
$745$	7.86577	0.288180
$746$	3.97767	0.145633
$747$	6.75782	0.247256
$748$	−0.987108	−0.0360922
$749$	−42.4337	−1.55049
$750$	8.72498	0.318591
$751$	−23.2521	−0.848480	−0.424240	−	0.905550i	$-0.639459\pi$
$751$	−23.2521	−0.848480	−0.424240	+	0.905550i	$0.639459\pi$
$752$	0.327824	0.0119545
$753$	−37.5833	−1.36961
$754$	−0.613716	−0.0223502
$755$	−1.24247	−0.0452180
$756$	−35.6978	−1.29832
$757$	7.44889	0.270734	0.135367	−	0.990796i	$-0.456779\pi$
$757$	7.44889	0.270734	0.135367	+	0.990796i	$0.456779\pi$
$758$	−16.8333	−0.611414
$759$	−9.97993	−0.362249
$760$	−2.68979	−0.0975689
$761$	−36.0508	−1.30684	−0.653421	−	0.756995i	$-0.726667\pi$
$761$	−36.0508	−1.30684	−0.653421	+	0.756995i	$0.726667\pi$
$762$	−23.2101	−0.840815
$763$	42.5241	1.53947
$764$	−27.9926	−1.01274
$765$	−0.211881	−0.00766057
$766$	29.0227	1.04863
$767$	−0.176777	−0.00638306
$768$	21.9293	0.791307
$769$	20.3768	0.734807	0.367404	−	0.930062i	$-0.380247\pi$
$769$	20.3768	0.734807	0.367404	+	0.930062i	$0.380247\pi$
$770$	−7.02867	−0.253296
$771$	−23.0585	−0.830432
$772$	17.9579	0.646320
$773$	40.7475	1.46559	0.732793	−	0.680452i	$-0.238217\pi$
$773$	40.7475	1.46559	0.732793	+	0.680452i	$0.238217\pi$
$774$	3.25065	0.116842
$775$	5.18243	0.186158
$776$	9.61972	0.345328
$777$	−38.4090	−1.37792
$778$	−2.57156	−0.0921950
$779$	11.9788	0.429183
$780$	0.128842	0.00461329
$781$	2.16521	0.0774772
$782$	−0.797256	−0.0285098
$783$	−47.5654	−1.69985
$784$	5.63951	0.201411
$785$	−11.9083	−0.425026
$786$	24.5824	0.876823
$787$	50.2436	1.79099	0.895495	−	0.445072i	$-0.146822\pi$
$787$	50.2436	1.79099	0.895495	+	0.445072i	$0.146822\pi$
$788$	13.9371	0.496487
$789$	12.2950	0.437715
$790$	−9.78803	−0.348242
$791$	−39.1555	−1.39221
$792$	5.40572	0.192084
$793$	−1.02551	−0.0364168
$794$	4.01307	0.142418
$795$	−0.579285	−0.0205451
$796$	36.2592	1.28517
$797$	−50.1412	−1.77609	−0.888045	−	0.459756i	$-0.847937\pi$
$797$	−50.1412	−1.77609	−0.888045	+	0.459756i	$0.847937\pi$
$798$	7.51744	0.266115
$799$	−0.306981	−0.0108602
$800$	25.5464	0.903200
$801$	7.72863	0.273078
$802$	8.30256	0.293174
$803$	−5.02898	−0.177469
$804$	−20.5849	−0.725975
$805$	10.8392	0.382033
$806$	−0.0854347	−0.00300931
$807$	8.81483	0.310297
$808$	10.1468	0.356964
$809$	−29.9513	−1.05303	−0.526515	−	0.850166i	$-0.676502\pi$
$809$	−29.9513	−1.05303	−0.526515	+	0.850166i	$0.676502\pi$
$810$	−3.61248	−0.126930
$811$	3.23082	0.113449	0.0567247	−	0.998390i	$-0.481934\pi$
$811$	3.23082	0.113449	0.0567247	+	0.998390i	$0.481934\pi$
$812$	53.2731	1.86952
$813$	42.8662	1.50338
$814$	10.4119	0.364937
$815$	−14.5929	−0.511168
$816$	0.166150	0.00581640
$817$	5.90499	0.206589
$818$	3.21536	0.112423
$819$	0.360936	0.0126121
$820$	9.33355	0.325942
$821$	−26.5433	−0.926367	−0.463183	−	0.886263i	$-0.653293\pi$
$821$	−26.5433	−0.926367	−0.463183	+	0.886263i	$0.653293\pi$
$822$	−22.7087	−0.792058
$823$	−7.79978	−0.271883	−0.135942	−	0.990717i	$-0.543406\pi$
$823$	−7.79978	−0.271883	−0.135942	+	0.990717i	$0.543406\pi$
$824$	23.5621	0.820826
$825$	−14.9434	−0.520262
$826$	−8.03663	−0.279630
$827$	40.7771	1.41796	0.708980	−	0.705228i	$-0.249156\pi$
$827$	40.7771	1.41796	0.708980	+	0.705228i	$0.249156\pi$
$828$	−3.30321	−0.114795
$829$	11.7356	0.407593	0.203796	−	0.979013i	$-0.434672\pi$
$829$	11.7356	0.407593	0.203796	+	0.979013i	$0.434672\pi$
$830$	−5.00955	−0.173884
$831$	27.3495	0.948744
$832$	−0.360000	−0.0124808
$833$	−5.28095	−0.182974
$834$	−22.4156	−0.776187
$835$	5.93862	0.205514
$836$	3.89099	0.134573
$837$	−6.62153	−0.228873
$838$	17.9039	0.618480
$839$	−31.9796	−1.10406	−0.552029	−	0.833825i	$-0.686146\pi$
$839$	−31.9796	−1.10406	−0.552029	+	0.833825i	$0.686146\pi$
$840$	14.7825	0.510045
$841$	41.9835	1.44771
$842$	−15.6370	−0.538887
$843$	21.5206	0.741210
$844$	−21.4281	−0.737587
$845$	9.90630	0.340787
$846$	0.666128	0.0229020
$847$	−27.3306	−0.939091
$848$	−0.180417	−0.00619553
$849$	6.69487	0.229767
$850$	−1.19377	−0.0409459
$851$	−16.0567	−0.550417
$852$	−1.80440	−0.0618176
$853$	14.4223	0.493811	0.246906	−	0.969040i	$-0.420586\pi$
$853$	14.4223	0.493811	0.246906	+	0.969040i	$0.420586\pi$
$854$	−46.6215	−1.59535
$855$	0.835194	0.0285630
$856$	−24.1926	−0.826888
$857$	30.4608	1.04052	0.520261	−	0.854007i	$-0.325835\pi$
$857$	30.4608	1.04052	0.520261	+	0.854007i	$0.325835\pi$
$858$	0.246349	0.00841021
$859$	−39.3679	−1.34321	−0.671607	−	0.740908i	$-0.734396\pi$
$859$	−39.3679	−1.34321	−0.671607	+	0.740908i	$0.734396\pi$
$860$	4.60102	0.156894
$861$	−65.8327	−2.24357
$862$	−3.95521	−0.134715
$863$	30.4460	1.03639	0.518196	−	0.855262i	$-0.326604\pi$
$863$	30.4460	1.03639	0.518196	+	0.855262i	$0.326604\pi$
$864$	−32.6403	−1.11045
$865$	12.3234	0.419008
$866$	4.12459	0.140159
$867$	24.7551	0.840726
$868$	7.41608	0.251718
$869$	35.7339	1.21219
$870$	7.80469	0.264604
$871$	0.940298	0.0318608
$872$	24.2442	0.821011
$873$	−2.98697	−0.101094
$874$	3.14263	0.106301
$875$	34.5956	1.16954
$876$	4.19095	0.141599
$877$	38.0005	1.28319	0.641593	−	0.767045i	$-0.278274\pi$
$877$	38.0005	1.28319	0.641593	+	0.767045i	$0.278274\pi$
$878$	15.9850	0.539467
$879$	13.4768	0.454562
$880$	0.612347	0.0206422
$881$	35.6078	1.19966	0.599829	−	0.800128i	$-0.295235\pi$
$881$	35.6078	1.19966	0.599829	+	0.800128i	$0.295235\pi$
$882$	11.4593	0.385855
$883$	19.0658	0.641616	0.320808	−	0.947144i	$-0.396046\pi$
$883$	19.0658	0.641616	0.320808	+	0.947144i	$0.396046\pi$
$884$	−0.0375763	−0.00126383
$885$	2.24809	0.0755689
$886$	−23.3469	−0.784355
$887$	−42.7388	−1.43503	−0.717514	−	0.696544i	$-0.754720\pi$
$887$	−42.7388	−1.43503	−0.717514	+	0.696544i	$0.754720\pi$
$888$	−21.8981	−0.734851
$889$	−92.0310	−3.08662
$890$	−5.72921	−0.192043
$891$	13.1883	0.441826
$892$	22.2318	0.744375
$893$	1.21006	0.0404931
$894$	−12.5333	−0.419177
$895$	9.88366	0.330374
$896$	39.3367	1.31415
$897$	−0.379906	−0.0126847
$898$	−13.0668	−0.436045
$899$	9.88153	0.329567
$900$	−4.94605	−0.164868
$901$	0.168946	0.00562840
$902$	17.8459	0.594204
$903$	−32.4526	−1.07995
$904$	−22.3237	−0.742474
$905$	−8.15402	−0.271049
$906$	1.97975	0.0657727
$907$	−13.4677	−0.447186	−0.223593	−	0.974683i	$-0.571779\pi$
$907$	−13.4677	−0.447186	−0.223593	+	0.974683i	$0.571779\pi$
$908$	13.6909	0.454349
$909$	−3.15064	−0.104500
$910$	−0.267560	−0.00886954
$911$	14.2047	0.470624	0.235312	−	0.971920i	$-0.424389\pi$
$911$	14.2047	0.470624	0.235312	+	0.971920i	$0.424389\pi$
$912$	−0.654930	−0.0216869
$913$	18.2887	0.605269
$914$	24.4874	0.809973
$915$	13.0415	0.431138
$916$	−30.0397	−0.992539
$917$	97.4720	3.21881
$918$	1.52526	0.0503412
$919$	44.5803	1.47057	0.735284	−	0.677759i	$-0.237049\pi$
$919$	44.5803	1.47057	0.735284	+	0.677759i	$0.237049\pi$
$920$	6.17976	0.203741
$921$	2.27921	0.0751026
$922$	22.5170	0.741556
$923$	0.0824230	0.00271299
$924$	−21.3841	−0.703484
$925$	−24.0424	−0.790509
$926$	26.3493	0.865892
$927$	−7.31616	−0.240294
$928$	48.7102	1.59899
$929$	7.40180	0.242845	0.121423	−	0.992601i	$-0.461254\pi$
$929$	7.40180	0.242845	0.121423	+	0.992601i	$0.461254\pi$
$930$	1.08648	0.0356271
$931$	20.8165	0.682233
$932$	24.1239	0.790205
$933$	22.5350	0.737764
$934$	2.59753	0.0849936
$935$	−0.573415	−0.0187527
$936$	0.205780	0.00672612
$937$	26.0165	0.849921	0.424961	−	0.905212i	$-0.360288\pi$
$937$	26.0165	0.849921	0.424961	+	0.905212i	$0.360288\pi$
$938$	42.7477	1.39576
$939$	−26.2539	−0.856764
$940$	0.942850	0.0307524
$941$	−19.0129	−0.619804	−0.309902	−	0.950769i	$-0.600296\pi$
$941$	−19.0129	−0.619804	−0.309902	+	0.950769i	$0.600296\pi$
$942$	18.9747	0.618229
$943$	−27.5211	−0.896209
$944$	0.700162	0.0227883
$945$	−20.7370	−0.674574
$946$	8.79724	0.286023
$947$	−4.96694	−0.161404	−0.0807019	−	0.996738i	$-0.525716\pi$
$947$	−4.96694	−0.161404	−0.0807019	+	0.996738i	$0.525716\pi$
$948$	−29.7792	−0.967182
$949$	−0.191438	−0.00621434
$950$	4.70560	0.152670
$951$	5.21143	0.168992
$952$	−4.31125	−0.139729
$953$	1.01936	0.0330204	0.0165102	−	0.999864i	$-0.494744\pi$
$953$	1.01936	0.0330204	0.0165102	+	0.999864i	$0.494744\pi$
$954$	−0.366601	−0.0118691
$955$	−16.2610	−0.526193
$956$	1.71106	0.0553395
$957$	−28.4931	−0.921052
$958$	−8.20411	−0.265063
$959$	−90.0429	−2.90764
$960$	4.57815	0.147759
$961$	−29.6244	−0.955626
$962$	0.396350	0.0127788
$963$	7.51194	0.242069
$964$	26.0550	0.839176
$965$	10.4318	0.335812
$966$	−17.2712	−0.555693
$967$	−23.3540	−0.751012	−0.375506	−	0.926820i	$-0.622531\pi$
$967$	−23.3540	−0.751012	−0.375506	+	0.926820i	$0.622531\pi$
$968$	−15.5820	−0.500823
$969$	0.613290	0.0197017
$970$	2.21423	0.0710948
$971$	22.9875	0.737704	0.368852	−	0.929488i	$-0.379751\pi$
$971$	22.9875	0.737704	0.368852	+	0.929488i	$0.379751\pi$
$972$	11.2402	0.360530
$973$	−88.8804	−2.84937
$974$	−27.5698	−0.883394
$975$	−0.568850	−0.0182178
$976$	4.06173	0.130013
$977$	−1.74825	−0.0559314	−0.0279657	−	0.999609i	$-0.508903\pi$
$977$	−1.74825	−0.0559314	−0.0279657	+	0.999609i	$0.508903\pi$
$978$	23.2524	0.743529
$979$	20.9160	0.668479
$980$	16.2197	0.518120
$981$	−7.52794	−0.240349
$982$	−1.18209	−0.0377219
$983$	−16.8941	−0.538839	−0.269419	−	0.963023i	$-0.586832\pi$
$983$	−16.8941	−0.538839	−0.269419	+	0.963023i	$0.586832\pi$
$984$	−37.5331	−1.19651
$985$	8.09609	0.257963
$986$	−2.27620	−0.0724890
$987$	−6.65024	−0.211679
$988$	0.148118	0.00471227
$989$	−13.5666	−0.431394
$990$	1.24427	0.0395455
$991$	55.1623	1.75229	0.876144	−	0.482050i	$-0.160108\pi$
$991$	55.1623	1.75229	0.876144	+	0.482050i	$0.160108\pi$
$992$	6.78089	0.215293
$993$	−7.09085	−0.225021
$994$	3.74710	0.118851
$995$	21.0631	0.667746
$996$	−15.2411	−0.482933
$997$	−38.7083	−1.22591	−0.612953	−	0.790120i	$-0.710018\pi$
$997$	−38.7083	−1.22591	−0.612953	+	0.790120i	$0.710018\pi$
$998$	1.41850	0.0449018
$999$	30.7187	0.971897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.40	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.40	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.829115 q^{2} -1.46533 q^{3} -1.31257 q^{4} -0.762476 q^{5} +1.21493 q^{6} +4.81734 q^{7} +2.74650 q^{8} -0.852803 q^{9} +O(q^{10})\)	\(q-0.829115 q^{2} -1.46533 q^{3} -1.31257 q^{4} -0.762476 q^{5} +1.21493 q^{6} +4.81734 q^{7} +2.74650 q^{8} -0.852803 q^{9} +0.632180 q^{10} -2.30795 q^{11} +1.92335 q^{12} -0.0878566 q^{13} -3.99412 q^{14} +1.11728 q^{15} +0.347973 q^{16} -0.325850 q^{17} +0.707071 q^{18} +1.28444 q^{19} +1.00080 q^{20} -7.05900 q^{21} +1.91355 q^{22} -2.95098 q^{23} -4.02453 q^{24} -4.41863 q^{25} +0.0728432 q^{26} +5.64563 q^{27} -6.32308 q^{28} -8.42517 q^{29} -0.926354 q^{30} -1.17286 q^{31} -5.78151 q^{32} +3.38191 q^{33} +0.270167 q^{34} -3.67310 q^{35} +1.11936 q^{36} +5.44114 q^{37} -1.06495 q^{38} +0.128739 q^{39} -2.09414 q^{40} +9.32608 q^{41} +5.85272 q^{42} +4.59734 q^{43} +3.02934 q^{44} +0.650241 q^{45} +2.44670 q^{46} +0.942094 q^{47} -0.509897 q^{48} +16.2067 q^{49} +3.66355 q^{50} +0.477478 q^{51} +0.115318 q^{52} -0.518478 q^{53} -4.68088 q^{54} +1.75975 q^{55} +13.2308 q^{56} -1.88213 q^{57} +6.98544 q^{58} +2.01211 q^{59} -1.46651 q^{60} +11.6725 q^{61} +0.972434 q^{62} -4.10824 q^{63} +4.09759 q^{64} +0.0669885 q^{65} -2.80399 q^{66} -10.7027 q^{67} +0.427700 q^{68} +4.32416 q^{69} +3.04542 q^{70} -0.938154 q^{71} -2.34222 q^{72} +2.17898 q^{73} -4.51133 q^{74} +6.47476 q^{75} -1.68591 q^{76} -11.1181 q^{77} -0.106739 q^{78} -15.4830 q^{79} -0.265321 q^{80} -5.71432 q^{81} -7.73239 q^{82} -7.92425 q^{83} +9.26542 q^{84} +0.248452 q^{85} -3.81172 q^{86} +12.3457 q^{87} -6.33877 q^{88} -9.06262 q^{89} -0.539125 q^{90} -0.423235 q^{91} +3.87336 q^{92} +1.71863 q^{93} -0.781104 q^{94} -0.979352 q^{95} +8.47183 q^{96} +3.50254 q^{97} -13.4372 q^{98} +1.96822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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