LMFDB - Embedded newform 6035.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71589 q^{2} -3.02116 q^{3} +0.944266 q^{4} +1.00000 q^{5} +5.18397 q^{6} -0.410823 q^{7} +1.81152 q^{8} +6.12740 q^{9} +O(q^{10})$	\(q-1.71589 q^{2} -3.02116 q^{3} +0.944266 q^{4} +1.00000 q^{5} +5.18397 q^{6} -0.410823 q^{7} +1.81152 q^{8} +6.12740 q^{9} -1.71589 q^{10} -6.26677 q^{11} -2.85278 q^{12} -4.80485 q^{13} +0.704926 q^{14} -3.02116 q^{15} -4.99689 q^{16} -1.00000 q^{17} -10.5139 q^{18} +0.789989 q^{19} +0.944266 q^{20} +1.24116 q^{21} +10.7531 q^{22} +5.84407 q^{23} -5.47289 q^{24} +1.00000 q^{25} +8.24458 q^{26} -9.44837 q^{27} -0.387926 q^{28} +3.69832 q^{29} +5.18397 q^{30} -1.26544 q^{31} +4.95106 q^{32} +18.9329 q^{33} +1.71589 q^{34} -0.410823 q^{35} +5.78590 q^{36} +2.15939 q^{37} -1.35553 q^{38} +14.5162 q^{39} +1.81152 q^{40} -8.72862 q^{41} -2.12969 q^{42} +5.70954 q^{43} -5.91750 q^{44} +6.12740 q^{45} -10.0278 q^{46} +7.78933 q^{47} +15.0964 q^{48} -6.83122 q^{49} -1.71589 q^{50} +3.02116 q^{51} -4.53706 q^{52} -4.68847 q^{53} +16.2123 q^{54} -6.26677 q^{55} -0.744214 q^{56} -2.38668 q^{57} -6.34590 q^{58} -8.60913 q^{59} -2.85278 q^{60} -11.3347 q^{61} +2.17135 q^{62} -2.51728 q^{63} +1.49832 q^{64} -4.80485 q^{65} -32.4867 q^{66} +15.5638 q^{67} -0.944266 q^{68} -17.6558 q^{69} +0.704926 q^{70} +1.00000 q^{71} +11.0999 q^{72} -1.61612 q^{73} -3.70526 q^{74} -3.02116 q^{75} +0.745960 q^{76} +2.57453 q^{77} -24.9082 q^{78} +16.4295 q^{79} -4.99689 q^{80} +10.1628 q^{81} +14.9773 q^{82} -3.28858 q^{83} +1.17199 q^{84} -1.00000 q^{85} -9.79692 q^{86} -11.1732 q^{87} -11.3524 q^{88} -0.415146 q^{89} -10.5139 q^{90} +1.97394 q^{91} +5.51835 q^{92} +3.82309 q^{93} -13.3656 q^{94} +0.789989 q^{95} -14.9579 q^{96} -5.51613 q^{97} +11.7216 q^{98} -38.3990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * 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 $

$2$	−1.71589	−1.21331	−0.606657	−	0.794963i	$-0.707490\pi$
$2$	−1.71589	−1.21331	−0.606657	+	0.794963i	$0.707490\pi$
$3$	−3.02116	−1.74427	−0.872133	−	0.489268i	$-0.837264\pi$
$3$	−3.02116	−1.74427	−0.872133	+	0.489268i	$0.837264\pi$
$4$	0.944266	0.472133
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.18397	2.11634
$7$	−0.410823	−0.155277	−0.0776383	−	0.996982i	$-0.524738\pi$
$7$	−0.410823	−0.155277	−0.0776383	+	0.996982i	$0.524738\pi$
$8$	1.81152	0.640469
$9$	6.12740	2.04247
$10$	−1.71589	−0.542611
$11$	−6.26677	−1.88950	−0.944751	−	0.327789i	$-0.893697\pi$
$11$	−6.26677	−1.88950	−0.944751	+	0.327789i	$0.893697\pi$
$12$	−2.85278	−0.823526
$13$	−4.80485	−1.33263	−0.666313	−	0.745672i	$-0.732128\pi$
$13$	−4.80485	−1.33263	−0.666313	+	0.745672i	$0.732128\pi$
$14$	0.704926	0.188399
$15$	−3.02116	−0.780060
$16$	−4.99689	−1.24922
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−10.5139	−2.47816
$19$	0.789989	0.181236	0.0906179	−	0.995886i	$-0.471116\pi$
$19$	0.789989	0.181236	0.0906179	+	0.995886i	$0.471116\pi$
$20$	0.944266	0.211144
$21$	1.24116	0.270844
$22$	10.7531	2.29256
$23$	5.84407	1.21857	0.609286	−	0.792951i	$-0.291456\pi$
$23$	5.84407	1.21857	0.609286	+	0.792951i	$0.291456\pi$
$24$	−5.47289	−1.11715
$25$	1.00000	0.200000
$26$	8.24458	1.61689
$27$	−9.44837	−1.81834
$28$	−0.387926	−0.0733112
$29$	3.69832	0.686761	0.343381	−	0.939196i	$-0.388428\pi$
$29$	3.69832	0.686761	0.343381	+	0.939196i	$0.388428\pi$
$30$	5.18397	0.946458
$31$	−1.26544	−0.227279	−0.113640	−	0.993522i	$-0.536251\pi$
$31$	−1.26544	−0.227279	−0.113640	+	0.993522i	$0.536251\pi$
$32$	4.95106	0.875233
$33$	18.9329	3.29580
$34$	1.71589	0.294272
$35$	−0.410823	−0.0694418
$36$	5.78590	0.964316
$37$	2.15939	0.355001	0.177501	−	0.984121i	$-0.443199\pi$
$37$	2.15939	0.355001	0.177501	+	0.984121i	$0.443199\pi$
$38$	−1.35553	−0.219896
$39$	14.5162	2.32445
$40$	1.81152	0.286426
$41$	−8.72862	−1.36318	−0.681591	−	0.731734i	$-0.738712\pi$
$41$	−8.72862	−1.36318	−0.681591	+	0.731734i	$0.738712\pi$
$42$	−2.12969	−0.328619
$43$	5.70954	0.870696	0.435348	−	0.900262i	$-0.356625\pi$
$43$	5.70954	0.870696	0.435348	+	0.900262i	$0.356625\pi$
$44$	−5.91750	−0.892097
$45$	6.12740	0.913419
$46$	−10.0278	−1.47851
$47$	7.78933	1.13619	0.568095	−	0.822963i	$-0.307680\pi$
$47$	7.78933	1.13619	0.568095	+	0.822963i	$0.307680\pi$
$48$	15.0964	2.17898
$49$	−6.83122	−0.975889
$50$	−1.71589	−0.242663
$51$	3.02116	0.423047
$52$	−4.53706	−0.629177
$53$	−4.68847	−0.644011	−0.322005	−	0.946738i	$-0.604357\pi$
$53$	−4.68847	−0.644011	−0.322005	+	0.946738i	$0.604357\pi$
$54$	16.2123	2.20622
$55$	−6.26677	−0.845011
$56$	−0.744214	−0.0994498
$57$	−2.38668	−0.316124
$58$	−6.34590	−0.833257
$59$	−8.60913	−1.12081	−0.560407	−	0.828218i	$-0.689355\pi$
$59$	−8.60913	−1.12081	−0.560407	+	0.828218i	$0.689355\pi$
$60$	−2.85278	−0.368292
$61$	−11.3347	−1.45126	−0.725632	−	0.688083i	$-0.758452\pi$
$61$	−11.3347	−1.45126	−0.725632	+	0.688083i	$0.758452\pi$
$62$	2.17135	0.275761
$63$	−2.51728	−0.317147
$64$	1.49832	0.187291
$65$	−4.80485	−0.595968
$66$	−32.4867	−3.99884
$67$	15.5638	1.90142	0.950709	−	0.310086i	$-0.100358\pi$
$67$	15.5638	1.90142	0.950709	+	0.310086i	$0.100358\pi$
$68$	−0.944266	−0.114509
$69$	−17.6558	−2.12551
$70$	0.704926	0.0842547
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	11.0999	1.30814
$73$	−1.61612	−0.189152	−0.0945761	−	0.995518i	$-0.530150\pi$
$73$	−1.61612	−0.189152	−0.0945761	+	0.995518i	$0.530150\pi$
$74$	−3.70526	−0.430728
$75$	−3.02116	−0.348853
$76$	0.745960	0.0855674
$77$	2.57453	0.293395
$78$	−24.9082	−2.82030
$79$	16.4295	1.84846	0.924231	−	0.381833i	$-0.124707\pi$
$79$	16.4295	1.84846	0.924231	+	0.381833i	$0.124707\pi$
$80$	−4.99689	−0.558670
$81$	10.1628	1.12920
$82$	14.9773	1.65397
$83$	−3.28858	−0.360969	−0.180484	−	0.983578i	$-0.557767\pi$
$83$	−3.28858	−0.360969	−0.180484	+	0.983578i	$0.557767\pi$
$84$	1.17199	0.127874
$85$	−1.00000	−0.108465
$86$	−9.79692	−1.05643
$87$	−11.1732	−1.19789
$88$	−11.3524	−1.21017
$89$	−0.415146	−0.0440054	−0.0220027	−	0.999758i	$-0.507004\pi$
$89$	−0.415146	−0.0440054	−0.0220027	+	0.999758i	$0.507004\pi$
$90$	−10.5139	−1.10826
$91$	1.97394	0.206925
$92$	5.51835	0.575328
$93$	3.82309	0.396436
$94$	−13.3656	−1.37856
$95$	0.789989	0.0810511
$96$	−14.9579	−1.52664
$97$	−5.51613	−0.560079	−0.280039	−	0.959989i	$-0.590347\pi$
$97$	−5.51613	−0.560079	−0.280039	+	0.959989i	$0.590347\pi$
$98$	11.7216	1.18406
$99$	−38.3990	−3.85925
$100$	0.944266	0.0944266
$101$	−12.8927	−1.28287	−0.641435	−	0.767177i	$-0.721661\pi$
$101$	−12.8927	−1.28287	−0.641435	+	0.767177i	$0.721661\pi$
$102$	−5.18397	−0.513289
$103$	5.20535	0.512898	0.256449	−	0.966558i	$-0.417447\pi$
$103$	5.20535	0.512898	0.256449	+	0.966558i	$0.417447\pi$
$104$	−8.70408	−0.853505
$105$	1.24116	0.121125
$106$	8.04488	0.781388
$107$	−11.3351	−1.09581	−0.547904	−	0.836541i	$-0.684574\pi$
$107$	−11.3351	−1.09581	−0.547904	+	0.836541i	$0.684574\pi$
$108$	−8.92178	−0.858498
$109$	12.6935	1.21581	0.607907	−	0.794009i	$-0.292010\pi$
$109$	12.6935	1.21581	0.607907	+	0.794009i	$0.292010\pi$
$110$	10.7531	1.02526
$111$	−6.52385	−0.619216
$112$	2.05284	0.193975
$113$	17.8274	1.67707	0.838533	−	0.544851i	$-0.183414\pi$
$113$	17.8274	1.67707	0.838533	+	0.544851i	$0.183414\pi$
$114$	4.09527	0.383558
$115$	5.84407	0.544962
$116$	3.49220	0.324243
$117$	−29.4412	−2.72184
$118$	14.7723	1.35990
$119$	0.410823	0.0376601
$120$	−5.47289	−0.499604
$121$	28.2724	2.57022
$122$	19.4491	1.76084
$123$	26.3705	2.37775
$124$	−1.19491	−0.107306
$125$	1.00000	0.0894427
$126$	4.31936	0.384799
$127$	−13.2394	−1.17480	−0.587401	−	0.809296i	$-0.699849\pi$
$127$	−13.2394	−1.17480	−0.587401	+	0.809296i	$0.699849\pi$
$128$	−12.4731	−1.10248
$129$	−17.2494	−1.51873
$130$	8.24458	0.723097
$131$	17.9274	1.56632	0.783160	−	0.621820i	$-0.213607\pi$
$131$	17.9274	1.56632	0.783160	+	0.621820i	$0.213607\pi$
$132$	17.8777	1.55605
$133$	−0.324546	−0.0281417
$134$	−26.7057	−2.30702
$135$	−9.44837	−0.813186
$136$	−1.81152	−0.155336
$137$	20.0022	1.70890	0.854452	−	0.519531i	$-0.173893\pi$
$137$	20.0022	1.70890	0.854452	+	0.519531i	$0.173893\pi$
$138$	30.2954	2.57892
$139$	17.5128	1.48541	0.742706	−	0.669617i	$-0.233542\pi$
$139$	17.5128	1.48541	0.742706	+	0.669617i	$0.233542\pi$
$140$	−0.387926	−0.0327858
$141$	−23.5328	−1.98182
$142$	−1.71589	−0.143994
$143$	30.1109	2.51800
$144$	−30.6180	−2.55150
$145$	3.69832	0.307129
$146$	2.77307	0.229501
$147$	20.6382	1.70221
$148$	2.03904	0.167608
$149$	−13.6865	−1.12124	−0.560621	−	0.828072i	$-0.689438\pi$
$149$	−13.6865	−1.12124	−0.560621	+	0.828072i	$0.689438\pi$
$150$	5.18397	0.423269
$151$	−8.31443	−0.676619	−0.338309	−	0.941035i	$-0.609855\pi$
$151$	−8.31443	−0.676619	−0.338309	+	0.941035i	$0.609855\pi$
$152$	1.43108	0.116076
$153$	−6.12740	−0.495371
$154$	−4.41761	−0.355981
$155$	−1.26544	−0.101642
$156$	13.7072	1.09745
$157$	−18.4417	−1.47181	−0.735903	−	0.677087i	$-0.763242\pi$
$157$	−18.4417	−1.47181	−0.735903	+	0.677087i	$0.763242\pi$
$158$	−28.1911	−2.24277
$159$	14.1646	1.12333
$160$	4.95106	0.391416
$161$	−2.40088	−0.189216
$162$	−17.4383	−1.37008
$163$	4.02055	0.314914	0.157457	−	0.987526i	$-0.449670\pi$
$163$	4.02055	0.314914	0.157457	+	0.987526i	$0.449670\pi$
$164$	−8.24214	−0.643603
$165$	18.9329	1.47392
$166$	5.64284	0.437969
$167$	22.1585	1.71467	0.857336	−	0.514756i	$-0.172118\pi$
$167$	22.1585	1.71467	0.857336	+	0.514756i	$0.172118\pi$
$168$	2.24839	0.173467
$169$	10.0866	0.775891
$170$	1.71589	0.131602
$171$	4.84058	0.370168
$172$	5.39132	0.411085
$173$	8.06858	0.613443	0.306721	−	0.951799i	$-0.400768\pi$
$173$	8.06858	0.613443	0.306721	+	0.951799i	$0.400768\pi$
$174$	19.1720	1.45342
$175$	−0.410823	−0.0310553
$176$	31.3144	2.36041
$177$	26.0095	1.95500
$178$	0.712343	0.0533924
$179$	21.5580	1.61132	0.805660	−	0.592378i	$-0.201811\pi$
$179$	21.5580	1.61132	0.805660	+	0.592378i	$0.201811\pi$
$180$	5.78590	0.431255
$181$	−13.5490	−1.00709	−0.503544	−	0.863970i	$-0.667971\pi$
$181$	−13.5490	−1.00709	−0.503544	+	0.863970i	$0.667971\pi$
$182$	−3.38706	−0.251066
$183$	34.2440	2.53139
$184$	10.5866	0.780457
$185$	2.15939	0.158761
$186$	−6.55999	−0.481001
$187$	6.26677	0.458272
$188$	7.35520	0.536433
$189$	3.88161	0.282345
$190$	−1.35553	−0.0983406
$191$	−10.2156	−0.739173	−0.369587	−	0.929196i	$-0.620501\pi$
$191$	−10.2156	−0.739173	−0.369587	+	0.929196i	$0.620501\pi$
$192$	−4.52668	−0.326685
$193$	8.93341	0.643041	0.321520	−	0.946903i	$-0.395806\pi$
$193$	8.93341	0.643041	0.321520	+	0.946903i	$0.395806\pi$
$194$	9.46506	0.679552
$195$	14.5162	1.03953
$196$	−6.45049	−0.460750
$197$	3.38832	0.241408	0.120704	−	0.992689i	$-0.461485\pi$
$197$	3.38832	0.241408	0.120704	+	0.992689i	$0.461485\pi$
$198$	65.8883	4.68248
$199$	−1.81496	−0.128659	−0.0643296	−	0.997929i	$-0.520491\pi$
$199$	−1.81496	−0.128659	−0.0643296	+	0.997929i	$0.520491\pi$
$200$	1.81152	0.128094
$201$	−47.0206	−3.31658
$202$	22.1224	1.55653
$203$	−1.51936	−0.106638
$204$	2.85278	0.199734
$205$	−8.72862	−0.609633
$206$	−8.93178	−0.622307
$207$	35.8089	2.48889
$208$	24.0093	1.66475
$209$	−4.95068	−0.342446
$210$	−2.12969	−0.146963
$211$	−15.8718	−1.09266	−0.546329	−	0.837571i	$-0.683975\pi$
$211$	−15.8718	−1.09266	−0.546329	+	0.837571i	$0.683975\pi$
$212$	−4.42716	−0.304059
$213$	−3.02116	−0.207006
$214$	19.4498	1.32956
$215$	5.70954	0.389387
$216$	−17.1159	−1.16459
$217$	0.519871	0.0352911
$218$	−21.7805	−1.47516
$219$	4.88254	0.329932
$220$	−5.91750	−0.398958
$221$	4.80485	0.323209
$222$	11.1942	0.751305
$223$	−20.5497	−1.37611	−0.688055	−	0.725658i	$-0.741535\pi$
$223$	−20.5497	−1.37611	−0.688055	+	0.725658i	$0.741535\pi$
$224$	−2.03401	−0.135903
$225$	6.12740	0.408493
$226$	−30.5899	−2.03481
$227$	6.80720	0.451810	0.225905	−	0.974149i	$-0.427466\pi$
$227$	6.80720	0.451810	0.225905	+	0.974149i	$0.427466\pi$
$228$	−2.25366	−0.149252
$229$	3.60720	0.238370	0.119185	−	0.992872i	$-0.461972\pi$
$229$	3.60720	0.238370	0.119185	+	0.992872i	$0.461972\pi$
$230$	−10.0278	−0.661210
$231$	−7.77807	−0.511760
$232$	6.69958	0.439849
$233$	10.3028	0.674956	0.337478	−	0.941333i	$-0.390426\pi$
$233$	10.3028	0.674956	0.337478	+	0.941333i	$0.390426\pi$
$234$	50.5178	3.30245
$235$	7.78933	0.508120
$236$	−8.12931	−0.529173
$237$	−49.6361	−3.22421
$238$	−0.704926	−0.0456935
$239$	−8.81051	−0.569905	−0.284952	−	0.958542i	$-0.591978\pi$
$239$	−8.81051	−0.569905	−0.284952	+	0.958542i	$0.591978\pi$
$240$	15.0964	0.974469
$241$	26.4023	1.70072	0.850359	−	0.526202i	$-0.176385\pi$
$241$	26.4023	1.70072	0.850359	+	0.526202i	$0.176385\pi$
$242$	−48.5122	−3.11848
$243$	−2.35840	−0.151292
$244$	−10.7030	−0.685190
$245$	−6.83122	−0.436431
$246$	−45.2489	−2.88496
$247$	−3.79578	−0.241520
$248$	−2.29236	−0.145565
$249$	9.93533	0.629626
$250$	−1.71589	−0.108522
$251$	11.6920	0.737993	0.368997	−	0.929431i	$-0.379701\pi$
$251$	11.6920	0.737993	0.368997	+	0.929431i	$0.379701\pi$
$252$	−2.37698	−0.149736
$253$	−36.6234	−2.30249
$254$	22.7172	1.42541
$255$	3.02116	0.189192
$256$	18.4057	1.15036
$257$	8.38878	0.523278	0.261639	−	0.965166i	$-0.415737\pi$
$257$	8.38878	0.523278	0.261639	+	0.965166i	$0.415737\pi$
$258$	29.5980	1.84269
$259$	−0.887126	−0.0551233
$260$	−4.53706	−0.281376
$261$	22.6611	1.40269
$262$	−30.7613	−1.90044
$263$	2.21758	0.136742	0.0683710	−	0.997660i	$-0.478220\pi$
$263$	2.21758	0.136742	0.0683710	+	0.997660i	$0.478220\pi$
$264$	34.2973	2.11085
$265$	−4.68847	−0.288010
$266$	0.556883	0.0341447
$267$	1.25422	0.0767571
$268$	14.6963	0.897722
$269$	−28.7319	−1.75181	−0.875907	−	0.482480i	$-0.839736\pi$
$269$	−28.7319	−1.75181	−0.875907	+	0.482480i	$0.839736\pi$
$270$	16.2123	0.986651
$271$	28.2758	1.71763	0.858817	−	0.512282i	$-0.171200\pi$
$271$	28.2758	1.71763	0.858817	+	0.512282i	$0.171200\pi$
$272$	4.99689	0.302981
$273$	−5.96359	−0.360933
$274$	−34.3215	−2.07344
$275$	−6.26677	−0.377900
$276$	−16.6718	−1.00353
$277$	20.0470	1.20451	0.602254	−	0.798305i	$-0.294269\pi$
$277$	20.0470	1.20451	0.602254	+	0.798305i	$0.294269\pi$
$278$	−30.0499	−1.80227
$279$	−7.75384	−0.464210
$280$	−0.744214	−0.0444753
$281$	1.04224	0.0621751	0.0310876	−	0.999517i	$-0.490103\pi$
$281$	1.04224	0.0621751	0.0310876	+	0.999517i	$0.490103\pi$
$282$	40.3796	2.40457
$283$	−9.28341	−0.551841	−0.275921	−	0.961180i	$-0.588983\pi$
$283$	−9.28341	−0.551841	−0.275921	+	0.961180i	$0.588983\pi$
$284$	0.944266	0.0560319
$285$	−2.38668	−0.141375
$286$	−51.6669	−3.05513
$287$	3.58592	0.211670
$288$	30.3371	1.78763
$289$	1.00000	0.0588235
$290$	−6.34590	−0.372644
$291$	16.6651	0.976926
$292$	−1.52604	−0.0893050
$293$	23.8983	1.39615	0.698075	−	0.716024i	$-0.254040\pi$
$293$	23.8983	1.39615	0.698075	+	0.716024i	$0.254040\pi$
$294$	−35.4128	−2.06532
$295$	−8.60913	−0.501243
$296$	3.91177	0.227367
$297$	59.2108	3.43576
$298$	23.4845	1.36042
$299$	−28.0799	−1.62390
$300$	−2.85278	−0.164705
$301$	−2.34561	−0.135199
$302$	14.2666	0.820952
$303$	38.9508	2.23767
$304$	−3.94749	−0.226404
$305$	−11.3347	−0.649025
$306$	10.5139	0.601041
$307$	−21.5979	−1.23266	−0.616329	−	0.787489i	$-0.711381\pi$
$307$	−21.5979	−1.23266	−0.616329	+	0.787489i	$0.711381\pi$
$308$	2.43105	0.138522
$309$	−15.7262	−0.894631
$310$	2.17135	0.123324
$311$	19.2316	1.09053	0.545263	−	0.838265i	$-0.316430\pi$
$311$	19.2316	1.09053	0.545263	+	0.838265i	$0.316430\pi$
$312$	26.2964	1.48874
$313$	2.59721	0.146803	0.0734015	−	0.997302i	$-0.476615\pi$
$313$	2.59721	0.146803	0.0734015	+	0.997302i	$0.476615\pi$
$314$	31.6438	1.78576
$315$	−2.51728	−0.141832
$316$	15.5138	0.872720
$317$	−0.592028	−0.0332516	−0.0166258	−	0.999862i	$-0.505292\pi$
$317$	−0.592028	−0.0332516	−0.0166258	+	0.999862i	$0.505292\pi$
$318$	−24.3049	−1.36295
$319$	−23.1765	−1.29764
$320$	1.49832	0.0837589
$321$	34.2452	1.91138
$322$	4.11963	0.229578
$323$	−0.789989	−0.0439561
$324$	9.59642	0.533134
$325$	−4.80485	−0.266525
$326$	−6.89881	−0.382090
$327$	−38.3490	−2.12070
$328$	−15.8121	−0.873075
$329$	−3.20004	−0.176424
$330$	−32.4867	−1.78833
$331$	−4.40394	−0.242062	−0.121031	−	0.992649i	$-0.538620\pi$
$331$	−4.40394	−0.242062	−0.121031	+	0.992649i	$0.538620\pi$
$332$	−3.10530	−0.170425
$333$	13.2314	0.725078
$334$	−38.0214	−2.08044
$335$	15.5638	0.850340
$336$	−6.20195	−0.338344
$337$	−29.7344	−1.61974	−0.809868	−	0.586612i	$-0.800461\pi$
$337$	−29.7344	−1.61974	−0.809868	+	0.586612i	$0.800461\pi$
$338$	−17.3074	−0.941400
$339$	−53.8596	−2.92525
$340$	−0.944266	−0.0512100
$341$	7.93021	0.429445
$342$	−8.30588	−0.449131
$343$	5.68219	0.306809
$344$	10.3429	0.557654
$345$	−17.6558	−0.950559
$346$	−13.8448	−0.744299
$347$	15.5566	0.835123	0.417561	−	0.908649i	$-0.362885\pi$
$347$	15.5566	0.835123	0.417561	+	0.908649i	$0.362885\pi$
$348$	−10.5505	−0.565566
$349$	−20.2240	−1.08257	−0.541284	−	0.840840i	$-0.682062\pi$
$349$	−20.2240	−1.08257	−0.541284	+	0.840840i	$0.682062\pi$
$350$	0.704926	0.0376799
$351$	45.3980	2.42317
$352$	−31.0272	−1.65375
$353$	−35.1520	−1.87095	−0.935476	−	0.353390i	$-0.885029\pi$
$353$	−35.1520	−1.87095	−0.935476	+	0.353390i	$0.885029\pi$
$354$	−44.6294	−2.37203
$355$	1.00000	0.0530745
$356$	−0.392008	−0.0207764
$357$	−1.24116	−0.0656892
$358$	−36.9911	−1.95504
$359$	13.9707	0.737344	0.368672	−	0.929560i	$-0.379813\pi$
$359$	13.9707	0.737344	0.368672	+	0.929560i	$0.379813\pi$
$360$	11.0999	0.585016
$361$	−18.3759	−0.967154
$362$	23.2485	1.22191
$363$	−85.4154	−4.48315
$364$	1.86393	0.0976964
$365$	−1.61612	−0.0845914
$366$	−58.7589	−3.07137
$367$	−9.75100	−0.508998	−0.254499	−	0.967073i	$-0.581911\pi$
$367$	−9.75100	−0.508998	−0.254499	+	0.967073i	$0.581911\pi$
$368$	−29.2022	−1.52227
$369$	−53.4837	−2.78425
$370$	−3.70526	−0.192627
$371$	1.92613	0.0999998
$372$	3.61001	0.187170
$373$	11.9797	0.620284	0.310142	−	0.950690i	$-0.399623\pi$
$373$	11.9797	0.620284	0.310142	+	0.950690i	$0.399623\pi$
$374$	−10.7531	−0.556028
$375$	−3.02116	−0.156012
$376$	14.1105	0.727695
$377$	−17.7699	−0.915195
$378$	−6.66040	−0.342574
$379$	28.8499	1.48192	0.740959	−	0.671550i	$-0.234371\pi$
$379$	28.8499	1.48192	0.740959	+	0.671550i	$0.234371\pi$
$380$	0.745960	0.0382669
$381$	39.9982	2.04917
$382$	17.5288	0.896850
$383$	12.5455	0.641044	0.320522	−	0.947241i	$-0.396142\pi$
$383$	12.5455	0.641044	0.320522	+	0.947241i	$0.396142\pi$
$384$	37.6832	1.92301
$385$	2.57453	0.131210
$386$	−15.3287	−0.780211
$387$	34.9846	1.77837
$388$	−5.20870	−0.264432
$389$	18.1365	0.919559	0.459780	−	0.888033i	$-0.347928\pi$
$389$	18.1365	0.919559	0.459780	+	0.888033i	$0.347928\pi$
$390$	−24.9082	−1.26127
$391$	−5.84407	−0.295547
$392$	−12.3749	−0.625027
$393$	−54.1614	−2.73208
$394$	−5.81397	−0.292904
$395$	16.4295	0.826658
$396$	−36.2589	−1.82208
$397$	−29.1882	−1.46492	−0.732458	−	0.680813i	$-0.761627\pi$
$397$	−29.1882	−1.46492	−0.732458	+	0.680813i	$0.761627\pi$
$398$	3.11427	0.156104
$399$	0.980504	0.0490866
$400$	−4.99689	−0.249845
$401$	5.77688	0.288484	0.144242	−	0.989542i	$-0.453926\pi$
$401$	5.77688	0.288484	0.144242	+	0.989542i	$0.453926\pi$
$402$	80.6820	4.02405
$403$	6.08024	0.302878
$404$	−12.1741	−0.605685
$405$	10.1628	0.504995
$406$	2.60704	0.129385
$407$	−13.5324	−0.670775
$408$	5.47289	0.270948
$409$	−35.1366	−1.73739	−0.868697	−	0.495345i	$-0.835042\pi$
$409$	−35.1366	−1.73739	−0.868697	+	0.495345i	$0.835042\pi$
$410$	14.9773	0.739677
$411$	−60.4298	−2.98078
$412$	4.91523	0.242156
$413$	3.53683	0.174036
$414$	−61.4440	−3.01981
$415$	−3.28858	−0.161430
$416$	−23.7891	−1.16636
$417$	−52.9088	−2.59096
$418$	8.49480	0.415494
$419$	−16.7758	−0.819550	−0.409775	−	0.912187i	$-0.634393\pi$
$419$	−16.7758	−0.819550	−0.409775	+	0.912187i	$0.634393\pi$
$420$	1.17199	0.0571871
$421$	−5.27123	−0.256904	−0.128452	−	0.991716i	$-0.541001\pi$
$421$	−5.27123	−0.256904	−0.128452	+	0.991716i	$0.541001\pi$
$422$	27.2342	1.32574
$423$	47.7283	2.32063
$424$	−8.49325	−0.412469
$425$	−1.00000	−0.0485071
$426$	5.18397	0.251164
$427$	4.65657	0.225347
$428$	−10.7034	−0.517368
$429$	−90.9698	−4.39206
$430$	−9.79692	−0.472449
$431$	8.08509	0.389445	0.194723	−	0.980858i	$-0.437619\pi$
$431$	8.08509	0.389445	0.194723	+	0.980858i	$0.437619\pi$
$432$	47.2125	2.27151
$433$	−14.1861	−0.681741	−0.340871	−	0.940110i	$-0.610722\pi$
$433$	−14.1861	−0.681741	−0.340871	+	0.940110i	$0.610722\pi$
$434$	−0.892040	−0.0428193
$435$	−11.1732	−0.535715
$436$	11.9860	0.574026
$437$	4.61675	0.220849
$438$	−8.37789	−0.400311
$439$	−37.2290	−1.77684	−0.888422	−	0.459028i	$-0.848198\pi$
$439$	−37.2290	−1.77684	−0.888422	+	0.459028i	$0.848198\pi$
$440$	−11.3524	−0.541203
$441$	−41.8576	−1.99322
$442$	−8.24458	−0.392154
$443$	−6.08704	−0.289204	−0.144602	−	0.989490i	$-0.546190\pi$
$443$	−6.08704	−0.289204	−0.144602	+	0.989490i	$0.546190\pi$
$444$	−6.16025	−0.292353
$445$	−0.415146	−0.0196798
$446$	35.2610	1.66966
$447$	41.3491	1.95575
$448$	−0.615546	−0.0290818
$449$	−31.9110	−1.50598	−0.752988	−	0.658035i	$-0.771388\pi$
$449$	−31.9110	−1.50598	−0.752988	+	0.658035i	$0.771388\pi$
$450$	−10.5139	−0.495631
$451$	54.7003	2.57573
$452$	16.8339	0.791798
$453$	25.1192	1.18020
$454$	−11.6804	−0.548187
$455$	1.97394	0.0925399
$456$	−4.32352	−0.202467
$457$	14.6002	0.682967	0.341484	−	0.939888i	$-0.389071\pi$
$457$	14.6002	0.682967	0.341484	+	0.939888i	$0.389071\pi$
$458$	−6.18954	−0.289218
$459$	9.44837	0.441012
$460$	5.51835	0.257295
$461$	−3.95809	−0.184347	−0.0921734	−	0.995743i	$-0.529381\pi$
$461$	−3.95809	−0.184347	−0.0921734	+	0.995743i	$0.529381\pi$
$462$	13.3463	0.620926
$463$	17.4073	0.808987	0.404494	−	0.914541i	$-0.367448\pi$
$463$	17.4073	0.808987	0.404494	+	0.914541i	$0.367448\pi$
$464$	−18.4801	−0.857918
$465$	3.82309	0.177291
$466$	−17.6784	−0.818934
$467$	−24.0130	−1.11119	−0.555594	−	0.831454i	$-0.687509\pi$
$467$	−24.0130	−1.11119	−0.555594	+	0.831454i	$0.687509\pi$
$468$	−27.8004	−1.28507
$469$	−6.39396	−0.295245
$470$	−13.3656	−0.616510
$471$	55.7152	2.56722
$472$	−15.5956	−0.717846
$473$	−35.7804	−1.64518
$474$	85.1699	3.91198
$475$	0.789989	0.0362472
$476$	0.387926	0.0177806
$477$	−28.7281	−1.31537
$478$	15.1178	0.691474
$479$	−21.6914	−0.991107	−0.495553	−	0.868578i	$-0.665035\pi$
$479$	−21.6914	−0.991107	−0.495553	+	0.868578i	$0.665035\pi$
$480$	−14.9579	−0.682734
$481$	−10.3755	−0.473083
$482$	−45.3033	−2.06351
$483$	7.25343	0.330042
$484$	26.6967	1.21349
$485$	−5.51613	−0.250475
$486$	4.04675	0.183565
$487$	19.5223	0.884638	0.442319	−	0.896858i	$-0.354156\pi$
$487$	19.5223	0.884638	0.442319	+	0.896858i	$0.354156\pi$
$488$	−20.5331	−0.929489
$489$	−12.1467	−0.549294
$490$	11.7216	0.529528
$491$	4.34269	0.195983	0.0979913	−	0.995187i	$-0.468758\pi$
$491$	4.34269	0.195983	0.0979913	+	0.995187i	$0.468758\pi$
$492$	24.9008	1.12262
$493$	−3.69832	−0.166564
$494$	6.51312	0.293039
$495$	−38.3990	−1.72591
$496$	6.32326	0.283923
$497$	−0.410823	−0.0184279
$498$	−17.0479	−0.763935
$499$	19.0281	0.851814	0.425907	−	0.904767i	$-0.359955\pi$
$499$	19.0281	0.851814	0.425907	+	0.904767i	$0.359955\pi$
$500$	0.944266	0.0422289
$501$	−66.9442	−2.99085
$502$	−20.0622	−0.895418
$503$	15.2778	0.681204	0.340602	−	0.940208i	$-0.389369\pi$
$503$	15.2778	0.681204	0.340602	+	0.940208i	$0.389369\pi$
$504$	−4.56010	−0.203123
$505$	−12.8927	−0.573717
$506$	62.8416	2.79365
$507$	−30.4732	−1.35336
$508$	−12.5015	−0.554663
$509$	−39.5752	−1.75414	−0.877070	−	0.480363i	$-0.840505\pi$
$509$	−39.5752	−1.75414	−0.877070	+	0.480363i	$0.840505\pi$
$510$	−5.18397	−0.229550
$511$	0.663938	0.0293709
$512$	−6.63600	−0.293273
$513$	−7.46411	−0.329548
$514$	−14.3942	−0.634901
$515$	5.20535	0.229375
$516$	−16.2880	−0.717041
$517$	−48.8139	−2.14684
$518$	1.52221	0.0668819
$519$	−24.3765	−1.07001
$520$	−8.70408	−0.381699
$521$	33.0991	1.45010	0.725048	−	0.688698i	$-0.241817\pi$
$521$	33.0991	1.45010	0.725048	+	0.688698i	$0.241817\pi$
$522$	−38.8839	−1.70190
$523$	39.5583	1.72977	0.864883	−	0.501974i	$-0.167393\pi$
$523$	39.5583	1.72977	0.864883	+	0.501974i	$0.167393\pi$
$524$	16.9282	0.739512
$525$	1.24116	0.0541687
$526$	−3.80512	−0.165911
$527$	1.26544	0.0551233
$528$	−94.6057	−4.11719
$529$	11.1531	0.484917
$530$	8.04488	0.349447
$531$	−52.7516	−2.28922
$532$	−0.306457	−0.0132866
$533$	41.9397	1.81661
$534$	−2.15210	−0.0931305
$535$	−11.3351	−0.490061
$536$	28.1941	1.21780
$537$	−65.1301	−2.81057
$538$	49.3006	2.12550
$539$	42.8097	1.84394
$540$	−8.92178	−0.383932
$541$	10.6838	0.459334	0.229667	−	0.973269i	$-0.426236\pi$
$541$	10.6838	0.459334	0.229667	+	0.973269i	$0.426236\pi$
$542$	−48.5181	−2.08403
$543$	40.9336	1.75663
$544$	−4.95106	−0.212275
$545$	12.6935	0.543728
$546$	10.2329	0.437926
$547$	38.2948	1.63737	0.818683	−	0.574245i	$-0.194704\pi$
$547$	38.2948	1.63737	0.818683	+	0.574245i	$0.194704\pi$
$548$	18.8874	0.806830
$549$	−69.4524	−2.96416
$550$	10.7531	0.458512
$551$	2.92163	0.124466
$552$	−31.9839	−1.36133
$553$	−6.74961	−0.287023
$554$	−34.3984	−1.46145
$555$	−6.52385	−0.276922
$556$	16.5367	0.701313
$557$	41.2554	1.74805	0.874025	−	0.485882i	$-0.161501\pi$
$557$	41.2554	1.74805	0.874025	+	0.485882i	$0.161501\pi$
$558$	13.3047	0.563234
$559$	−27.4335	−1.16031
$560$	2.05284	0.0867483
$561$	−18.9329	−0.799348
$562$	−1.78837	−0.0754380
$563$	−27.0412	−1.13965	−0.569825	−	0.821766i	$-0.692989\pi$
$563$	−27.0412	−1.13965	−0.569825	+	0.821766i	$0.692989\pi$
$564$	−22.2212	−0.935683
$565$	17.8274	0.750006
$566$	15.9293	0.669557
$567$	−4.17512	−0.175339
$568$	1.81152	0.0760097
$569$	1.70324	0.0714036	0.0357018	−	0.999362i	$-0.488633\pi$
$569$	1.70324	0.0714036	0.0357018	+	0.999362i	$0.488633\pi$
$570$	4.09527	0.171532
$571$	−11.8935	−0.497729	−0.248865	−	0.968538i	$-0.580057\pi$
$571$	−11.8935	−0.497729	−0.248865	+	0.968538i	$0.580057\pi$
$572$	28.4327	1.18883
$573$	30.8629	1.28932
$574$	−6.15303	−0.256822
$575$	5.84407	0.243714
$576$	9.18083	0.382535
$577$	3.35368	0.139615	0.0698077	−	0.997560i	$-0.477761\pi$
$577$	3.35368	0.139615	0.0698077	+	0.997560i	$0.477761\pi$
$578$	−1.71589	−0.0713715
$579$	−26.9892	−1.12163
$580$	3.49220	0.145006
$581$	1.35103	0.0560500
$582$	−28.5954	−1.18532
$583$	29.3816	1.21686
$584$	−2.92763	−0.121146
$585$	−29.4412	−1.21725
$586$	−41.0067	−1.69397
$587$	6.28439	0.259385	0.129692	−	0.991554i	$-0.458601\pi$
$587$	6.28439	0.259385	0.129692	+	0.991554i	$0.458601\pi$
$588$	19.4880	0.803670
$589$	−0.999682	−0.0411912
$590$	14.7723	0.608165
$591$	−10.2366	−0.421079
$592$	−10.7902	−0.443476
$593$	−18.2775	−0.750568	−0.375284	−	0.926910i	$-0.622455\pi$
$593$	−18.2775	−0.750568	−0.375284	+	0.926910i	$0.622455\pi$
$594$	−101.599	−4.16866
$595$	0.410823	0.0168421
$596$	−12.9237	−0.529376
$597$	5.48329	0.224416
$598$	48.1818	1.97030
$599$	17.7480	0.725163	0.362582	−	0.931952i	$-0.381895\pi$
$599$	17.7480	0.725163	0.362582	+	0.931952i	$0.381895\pi$
$600$	−5.47289	−0.223430
$601$	21.7762	0.888270	0.444135	−	0.895960i	$-0.353511\pi$
$601$	21.7762	0.888270	0.444135	+	0.895960i	$0.353511\pi$
$602$	4.02480	0.164039
$603$	95.3654	3.88358
$604$	−7.85104	−0.319454
$605$	28.2724	1.14944
$606$	−66.8352	−2.71500
$607$	−13.4264	−0.544962	−0.272481	−	0.962161i	$-0.587844\pi$
$607$	−13.4264	−0.544962	−0.272481	+	0.962161i	$0.587844\pi$
$608$	3.91128	0.158624
$609$	4.59021	0.186005
$610$	19.4491	0.787472
$611$	−37.4266	−1.51412
$612$	−5.78590	−0.233881
$613$	−27.1989	−1.09855	−0.549277	−	0.835640i	$-0.685097\pi$
$613$	−27.1989	−1.09855	−0.549277	+	0.835640i	$0.685097\pi$
$614$	37.0596	1.49560
$615$	26.3705	1.06336
$616$	4.66382	0.187911
$617$	35.0049	1.40924	0.704622	−	0.709583i	$-0.251116\pi$
$617$	35.0049	1.40924	0.704622	+	0.709583i	$0.251116\pi$
$618$	26.9843	1.08547
$619$	−16.7831	−0.674571	−0.337286	−	0.941402i	$-0.609509\pi$
$619$	−16.7831	−0.674571	−0.337286	+	0.941402i	$0.609509\pi$
$620$	−1.19491	−0.0479888
$621$	−55.2169	−2.21578
$622$	−32.9993	−1.32315
$623$	0.170551	0.00683300
$624$	−72.5360	−2.90376
$625$	1.00000	0.0400000
$626$	−4.45652	−0.178118
$627$	14.9568	0.597316
$628$	−17.4139	−0.694888
$629$	−2.15939	−0.0861004
$630$	4.31936	0.172087
$631$	−23.0113	−0.916064	−0.458032	−	0.888936i	$-0.651445\pi$
$631$	−23.0113	−0.916064	−0.458032	+	0.888936i	$0.651445\pi$
$632$	29.7623	1.18388
$633$	47.9512	1.90589
$634$	1.01585	0.0403447
$635$	−13.2394	−0.525388
$636$	13.3752	0.530360
$637$	32.8230	1.30049
$638$	39.7683	1.57444
$639$	6.12740	0.242396
$640$	−12.4731	−0.493042
$641$	20.2025	0.797949	0.398975	−	0.916962i	$-0.369366\pi$
$641$	20.2025	0.797949	0.398975	+	0.916962i	$0.369366\pi$
$642$	−58.7609	−2.31911
$643$	−13.5848	−0.535731	−0.267866	−	0.963456i	$-0.586318\pi$
$643$	−13.5848	−0.535731	−0.267866	+	0.963456i	$0.586318\pi$
$644$	−2.26707	−0.0893349
$645$	−17.2494	−0.679195
$646$	1.35553	0.0533327
$647$	−13.5429	−0.532426	−0.266213	−	0.963914i	$-0.585772\pi$
$647$	−13.5429	−0.532426	−0.266213	+	0.963914i	$0.585772\pi$
$648$	18.4102	0.723219
$649$	53.9514	2.11778
$650$	8.24458	0.323379
$651$	−1.57061	−0.0615572
$652$	3.79647	0.148681
$653$	−29.7370	−1.16370	−0.581849	−	0.813297i	$-0.697670\pi$
$653$	−29.7370	−1.16370	−0.581849	+	0.813297i	$0.697670\pi$
$654$	65.8025	2.57308
$655$	17.9274	0.700480
$656$	43.6160	1.70292
$657$	−9.90259	−0.386337
$658$	5.49090	0.214058
$659$	−25.8485	−1.00692	−0.503458	−	0.864020i	$-0.667939\pi$
$659$	−25.8485	−1.00692	−0.503458	+	0.864020i	$0.667939\pi$
$660$	17.8777	0.695889
$661$	34.2118	1.33068	0.665342	−	0.746539i	$-0.268286\pi$
$661$	34.2118	1.33068	0.665342	+	0.746539i	$0.268286\pi$
$662$	7.55666	0.293698
$663$	−14.5162	−0.563763
$664$	−5.95733	−0.231189
$665$	−0.324546	−0.0125853
$666$	−22.7036	−0.879748
$667$	21.6132	0.836868
$668$	20.9235	0.809554
$669$	62.0839	2.40030
$670$	−26.7057	−1.03173
$671$	71.0322	2.74217
$672$	6.14507	0.237051
$673$	20.5082	0.790533	0.395266	−	0.918567i	$-0.370652\pi$
$673$	20.5082	0.790533	0.395266	+	0.918567i	$0.370652\pi$
$674$	51.0209	1.96525
$675$	−9.44837	−0.363668
$676$	9.52442	0.366324
$677$	−5.57616	−0.214309	−0.107155	−	0.994242i	$-0.534174\pi$
$677$	−5.57616	−0.214309	−0.107155	+	0.994242i	$0.534174\pi$
$678$	92.4169	3.54925
$679$	2.26616	0.0869670
$680$	−1.81152	−0.0694686
$681$	−20.5656	−0.788077
$682$	−13.6073	−0.521052
$683$	−41.3103	−1.58070	−0.790348	−	0.612658i	$-0.790100\pi$
$683$	−41.3103	−1.58070	−0.790348	+	0.612658i	$0.790100\pi$
$684$	4.57079	0.174769
$685$	20.0022	0.764245
$686$	−9.74999	−0.372256
$687$	−10.8979	−0.415781
$688$	−28.5300	−1.08769
$689$	22.5274	0.858225
$690$	30.2954	1.15333
$691$	−48.1237	−1.83071	−0.915355	−	0.402647i	$-0.868090\pi$
$691$	−48.1237	−1.83071	−0.915355	+	0.402647i	$0.868090\pi$
$692$	7.61889	0.289627
$693$	15.7752	0.599250
$694$	−26.6934	−1.01327
$695$	17.5128	0.664297
$696$	−20.2405	−0.767214
$697$	8.72862	0.330620
$698$	34.7022	1.31350
$699$	−31.1262	−1.17730
$700$	−0.387926	−0.0146622
$701$	−27.0990	−1.02351	−0.511757	−	0.859130i	$-0.671005\pi$
$701$	−27.0990	−1.02351	−0.511757	+	0.859130i	$0.671005\pi$
$702$	−77.8978	−2.94006
$703$	1.70589	0.0643389
$704$	−9.38965	−0.353886
$705$	−23.5328	−0.886297
$706$	60.3168	2.27005
$707$	5.29661	0.199200
$708$	24.5599	0.923019
$709$	−4.76383	−0.178910	−0.0894548	−	0.995991i	$-0.528512\pi$
$709$	−4.76383	−0.178910	−0.0894548	+	0.995991i	$0.528512\pi$
$710$	−1.71589	−0.0643961
$711$	100.670	3.77542
$712$	−0.752045	−0.0281841
$713$	−7.39530	−0.276956
$714$	2.12969	0.0797017
$715$	30.1109	1.12608
$716$	20.3565	0.760758
$717$	26.6180	0.994066
$718$	−23.9721	−0.894631
$719$	−18.4917	−0.689624	−0.344812	−	0.938672i	$-0.612057\pi$
$719$	−18.4917	−0.689624	−0.344812	+	0.938672i	$0.612057\pi$
$720$	−30.6180	−1.14106
$721$	−2.13848	−0.0796410
$722$	31.5310	1.17346
$723$	−79.7654	−2.96651
$724$	−12.7938	−0.475480
$725$	3.69832	0.137352
$726$	146.563	5.43947
$727$	−32.5451	−1.20703	−0.603516	−	0.797351i	$-0.706234\pi$
$727$	−32.5451	−1.20703	−0.603516	+	0.797351i	$0.706234\pi$
$728$	3.57584	0.132529
$729$	−23.3634	−0.865310
$730$	2.77307	0.102636
$731$	−5.70954	−0.211175
$732$	32.3355	1.19515
$733$	7.10417	0.262399	0.131199	−	0.991356i	$-0.458117\pi$
$733$	7.10417	0.262399	0.131199	+	0.991356i	$0.458117\pi$
$734$	16.7316	0.617575
$735$	20.6382	0.761252
$736$	28.9343	1.06653
$737$	−97.5346	−3.59273
$738$	91.7720	3.37818
$739$	−47.8987	−1.76198	−0.880991	−	0.473133i	$-0.843123\pi$
$739$	−47.8987	−1.76198	−0.880991	+	0.473133i	$0.843123\pi$
$740$	2.03904	0.0749565
$741$	11.4676	0.421274
$742$	−3.30502	−0.121331
$743$	−26.0928	−0.957253	−0.478627	−	0.878019i	$-0.658865\pi$
$743$	−26.0928	−0.957253	−0.478627	+	0.878019i	$0.658865\pi$
$744$	6.92560	0.253905
$745$	−13.6865	−0.501435
$746$	−20.5558	−0.752600
$747$	−20.1505	−0.737267
$748$	5.91750	0.216365
$749$	4.65673	0.170153
$750$	5.18397	0.189292
$751$	−10.7834	−0.393491	−0.196745	−	0.980455i	$-0.563037\pi$
$751$	−10.7834	−0.393491	−0.196745	+	0.980455i	$0.563037\pi$
$752$	−38.9225	−1.41936
$753$	−35.3234	−1.28726
$754$	30.4911	1.11042
$755$	−8.31443	−0.302593
$756$	3.66527	0.133305
$757$	−17.4418	−0.633934	−0.316967	−	0.948437i	$-0.602665\pi$
$757$	−17.4418	−0.633934	−0.316967	+	0.948437i	$0.602665\pi$
$758$	−49.5031	−1.79803
$759$	110.645	4.01616
$760$	1.43108	0.0519107
$761$	28.9111	1.04803	0.524014	−	0.851710i	$-0.324434\pi$
$761$	28.9111	1.04803	0.524014	+	0.851710i	$0.324434\pi$
$762$	−68.6323	−2.48629
$763$	−5.21477	−0.188787
$764$	−9.64622	−0.348988
$765$	−6.12740	−0.221537
$766$	−21.5266	−0.777788
$767$	41.3656	1.49362
$768$	−55.6067	−2.00653
$769$	−1.01574	−0.0366284	−0.0183142	−	0.999832i	$-0.505830\pi$
$769$	−1.01574	−0.0366284	−0.0183142	+	0.999832i	$0.505830\pi$
$770$	−4.41761	−0.159200
$771$	−25.3438	−0.912736
$772$	8.43551	0.303601
$773$	−8.53116	−0.306844	−0.153422	−	0.988161i	$-0.549029\pi$
$773$	−8.53116	−0.306844	−0.153422	+	0.988161i	$0.549029\pi$
$774$	−60.0296	−2.15772
$775$	−1.26544	−0.0454559
$776$	−9.99258	−0.358713
$777$	2.68015	0.0961498
$778$	−31.1203	−1.11572
$779$	−6.89551	−0.247057
$780$	13.7072	0.490795
$781$	−6.26677	−0.224243
$782$	10.0278	0.358592
$783$	−34.9431	−1.24876
$784$	34.1349	1.21910
$785$	−18.4417	−0.658212
$786$	92.9348	3.31487
$787$	−10.9714	−0.391090	−0.195545	−	0.980695i	$-0.562648\pi$
$787$	−10.9714	−0.391090	−0.195545	+	0.980695i	$0.562648\pi$
$788$	3.19947	0.113977
$789$	−6.69967	−0.238515
$790$	−28.1911	−1.00300
$791$	−7.32393	−0.260409
$792$	−69.5605	−2.47173
$793$	54.4617	1.93399
$794$	50.0837	1.77740
$795$	14.1646	0.502367
$796$	−1.71381	−0.0607443
$797$	34.5104	1.22242	0.611211	−	0.791467i	$-0.290683\pi$
$797$	34.5104	1.22242	0.611211	+	0.791467i	$0.290683\pi$
$798$	−1.68243	−0.0595575
$799$	−7.78933	−0.275567
$800$	4.95106	0.175047
$801$	−2.54376	−0.0898795
$802$	−9.91247	−0.350022
$803$	10.1278	0.357403
$804$	−44.4000	−1.56587
$805$	−2.40088	−0.0846198
$806$	−10.4330	−0.367487
$807$	86.8036	3.05563
$808$	−23.3553	−0.821638
$809$	−17.4712	−0.614253	−0.307127	−	0.951669i	$-0.599367\pi$
$809$	−17.4712	−0.614253	−0.307127	+	0.951669i	$0.599367\pi$
$810$	−17.4383	−0.612718
$811$	−56.4119	−1.98089	−0.990445	−	0.137906i	$-0.955963\pi$
$811$	−56.4119	−1.98089	−0.990445	+	0.137906i	$0.955963\pi$
$812$	−1.43468	−0.0503473
$813$	−85.4258	−2.99601
$814$	23.2200	0.813862
$815$	4.02055	0.140834
$816$	−15.0964	−0.528480
$817$	4.51047	0.157801
$818$	60.2904	2.10801
$819$	12.0951	0.422638
$820$	−8.24214	−0.287828
$821$	−5.53983	−0.193341	−0.0966707	−	0.995316i	$-0.530819\pi$
$821$	−5.53983	−0.193341	−0.0966707	+	0.995316i	$0.530819\pi$
$822$	103.691	3.61663
$823$	−36.4078	−1.26910	−0.634548	−	0.772884i	$-0.718814\pi$
$823$	−36.4078	−1.26910	−0.634548	+	0.772884i	$0.718814\pi$
$824$	9.42959	0.328495
$825$	18.9329	0.659159
$826$	−6.06880	−0.211160
$827$	13.1476	0.457186	0.228593	−	0.973522i	$-0.426587\pi$
$827$	13.1476	0.457186	0.228593	+	0.973522i	$0.426587\pi$
$828$	33.8132	1.17509
$829$	−16.4639	−0.571814	−0.285907	−	0.958257i	$-0.592295\pi$
$829$	−16.4639	−0.571814	−0.285907	+	0.958257i	$0.592295\pi$
$830$	5.64284	0.195866
$831$	−60.5652	−2.10098
$832$	−7.19922	−0.249588
$833$	6.83122	0.236688
$834$	90.7855	3.14365
$835$	22.1585	0.766825
$836$	−4.67476	−0.161680
$837$	11.9563	0.413271
$838$	28.7853	0.994372
$839$	−42.2768	−1.45956	−0.729778	−	0.683684i	$-0.760377\pi$
$839$	−42.2768	−1.45956	−0.729778	+	0.683684i	$0.760377\pi$
$840$	2.24839	0.0775768
$841$	−15.3224	−0.528359
$842$	9.04483	0.311706
$843$	−3.14879	−0.108450
$844$	−14.9872	−0.515880
$845$	10.0866	0.346989
$846$	−81.8964	−2.81566
$847$	−11.6150	−0.399095
$848$	23.4278	0.804514
$849$	28.0467	0.962559
$850$	1.71589	0.0588544
$851$	12.6196	0.432594
$852$	−2.85278	−0.0977346
$853$	−13.1361	−0.449770	−0.224885	−	0.974385i	$-0.572201\pi$
$853$	−13.1361	−0.449770	−0.224885	+	0.974385i	$0.572201\pi$
$854$	−7.99014	−0.273417
$855$	4.84058	0.165544
$856$	−20.5338	−0.701831
$857$	−13.7033	−0.468096	−0.234048	−	0.972225i	$-0.575197\pi$
$857$	−13.7033	−0.468096	−0.234048	+	0.972225i	$0.575197\pi$
$858$	156.094	5.32895
$859$	35.6300	1.21568	0.607840	−	0.794059i	$-0.292036\pi$
$859$	35.6300	1.21568	0.607840	+	0.794059i	$0.292036\pi$
$860$	5.39132	0.183843
$861$	−10.8336	−0.369209
$862$	−13.8731	−0.472520
$863$	13.8908	0.472847	0.236424	−	0.971650i	$-0.424025\pi$
$863$	13.8908	0.472847	0.236424	+	0.971650i	$0.424025\pi$
$864$	−46.7795	−1.59147
$865$	8.06858	0.274340
$866$	24.3418	0.827167
$867$	−3.02116	−0.102604
$868$	0.490897	0.0166621
$869$	−102.960	−3.49267
$870$	19.1720	0.649991
$871$	−74.7816	−2.53388
$872$	22.9945	0.778690
$873$	−33.7996	−1.14394
$874$	−7.92181	−0.267959
$875$	−0.410823	−0.0138884
$876$	4.61042	0.155772
$877$	10.5624	0.356668	0.178334	−	0.983970i	$-0.442929\pi$
$877$	10.5624	0.356668	0.178334	+	0.983970i	$0.442929\pi$
$878$	63.8807	2.15587
$879$	−72.2004	−2.43526
$880$	31.3144	1.05561
$881$	9.93169	0.334607	0.167304	−	0.985905i	$-0.446494\pi$
$881$	9.93169	0.334607	0.167304	+	0.985905i	$0.446494\pi$
$882$	71.8230	2.41840
$883$	−35.5953	−1.19788	−0.598938	−	0.800796i	$-0.704410\pi$
$883$	−35.5953	−1.19788	−0.598938	+	0.800796i	$0.704410\pi$
$884$	4.53706	0.152598
$885$	26.0095	0.874301
$886$	10.4447	0.350896
$887$	41.1432	1.38145	0.690727	−	0.723115i	$-0.257291\pi$
$887$	41.1432	1.38145	0.690727	+	0.723115i	$0.257291\pi$
$888$	−11.8181	−0.396589
$889$	5.43903	0.182419
$890$	0.712343	0.0238778
$891$	−63.6881	−2.13363
$892$	−19.4044	−0.649707
$893$	6.15348	0.205919
$894$	−70.9504	−2.37294
$895$	21.5580	0.720604
$896$	5.12423	0.171188
$897$	84.8337	2.83251
$898$	54.7557	1.82722
$899$	−4.68000	−0.156087
$900$	5.78590	0.192863
$901$	4.68847	0.156196
$902$	−93.8594	−3.12518
$903$	7.08646	0.235823
$904$	32.2948	1.07411
$905$	−13.5490	−0.450383
$906$	−43.1017	−1.43196
$907$	−25.1420	−0.834825	−0.417412	−	0.908717i	$-0.637063\pi$
$907$	−25.1420	−0.834825	−0.417412	+	0.908717i	$0.637063\pi$
$908$	6.42781	0.213314
$909$	−78.9986	−2.62022
$910$	−3.38706	−0.112280
$911$	27.5883	0.914042	0.457021	−	0.889456i	$-0.348916\pi$
$911$	27.5883	0.914042	0.457021	+	0.889456i	$0.348916\pi$
$912$	11.9260	0.394909
$913$	20.6088	0.682052
$914$	−25.0522	−0.828654
$915$	34.2440	1.13207
$916$	3.40615	0.112542
$917$	−7.36497	−0.243213
$918$	−16.2123	−0.535087
$919$	−29.7952	−0.982853	−0.491426	−	0.870919i	$-0.663524\pi$
$919$	−29.7952	−0.982853	−0.491426	+	0.870919i	$0.663524\pi$
$920$	10.5866	0.349031
$921$	65.2507	2.15008
$922$	6.79164	0.223671
$923$	−4.80485	−0.158154
$924$	−7.34457	−0.241619
$925$	2.15939	0.0710002
$926$	−29.8690	−0.981556
$927$	31.8952	1.04758
$928$	18.3106	0.601076
$929$	2.02252	0.0663567	0.0331784	−	0.999449i	$-0.489437\pi$
$929$	2.02252	0.0663567	0.0331784	+	0.999449i	$0.489437\pi$
$930$	−6.55999	−0.215110
$931$	−5.39659	−0.176866
$932$	9.72854	0.318669
$933$	−58.1018	−1.90217
$934$	41.2035	1.34822
$935$	6.26677	0.204945
$936$	−53.3334	−1.74326
$937$	−1.62964	−0.0532380	−0.0266190	−	0.999646i	$-0.508474\pi$
$937$	−1.62964	−0.0532380	−0.0266190	+	0.999646i	$0.508474\pi$
$938$	10.9713	0.358226
$939$	−7.84659	−0.256064
$940$	7.35520	0.239900
$941$	4.50730	0.146934	0.0734669	−	0.997298i	$-0.476594\pi$
$941$	4.50730	0.146934	0.0734669	+	0.997298i	$0.476594\pi$
$942$	−95.6010	−3.11485
$943$	−51.0106	−1.66113
$944$	43.0189	1.40015
$945$	3.88161	0.126269
$946$	61.3950	1.99612
$947$	−48.8463	−1.58729	−0.793646	−	0.608380i	$-0.791819\pi$
$947$	−48.8463	−1.58729	−0.793646	+	0.608380i	$0.791819\pi$
$948$	−46.8697	−1.52226
$949$	7.76520	0.252069
$950$	−1.35553	−0.0439792
$951$	1.78861	0.0579997
$952$	0.744214	0.0241201
$953$	20.1866	0.653908	0.326954	−	0.945040i	$-0.393978\pi$
$953$	20.1866	0.653908	0.326954	+	0.945040i	$0.393978\pi$
$954$	49.2942	1.59596
$955$	−10.2156	−0.330568
$956$	−8.31947	−0.269071
$957$	70.0200	2.26342
$958$	37.2200	1.20252
$959$	−8.21736	−0.265353
$960$	−4.52668	−0.146098
$961$	−29.3987	−0.948344
$962$	17.8032	0.573999
$963$	−69.4549	−2.23815
$964$	24.9308	0.802966
$965$	8.93341	0.287577
$966$	−12.4461	−0.400445
$967$	−48.4715	−1.55874	−0.779369	−	0.626565i	$-0.784460\pi$
$967$	−48.4715	−1.55874	−0.779369	+	0.626565i	$0.784460\pi$
$968$	51.2160	1.64614
$969$	2.38668	0.0766713
$970$	9.46506	0.303905
$971$	38.7117	1.24232	0.621158	−	0.783685i	$-0.286662\pi$
$971$	38.7117	1.24232	0.621158	+	0.783685i	$0.286662\pi$
$972$	−2.22696	−0.0714298
$973$	−7.19465	−0.230650
$974$	−33.4980	−1.07334
$975$	14.5162	0.464891
$976$	56.6384	1.81295
$977$	−21.2178	−0.678817	−0.339408	−	0.940639i	$-0.610227\pi$
$977$	−21.2178	−0.678817	−0.339408	+	0.940639i	$0.610227\pi$
$978$	20.8424	0.666466
$979$	2.60162	0.0831482
$980$	−6.45049	−0.206053
$981$	77.7779	2.48326
$982$	−7.45156	−0.237789
$983$	42.7671	1.36406	0.682029	−	0.731325i	$-0.261098\pi$
$983$	42.7671	1.36406	0.682029	+	0.731325i	$0.261098\pi$
$984$	47.7707	1.52288
$985$	3.38832	0.107961
$986$	6.34590	0.202095
$987$	9.66782	0.307730
$988$	−3.58422	−0.114029
$989$	33.3669	1.06101
$990$	65.8883	2.09407
$991$	−1.10745	−0.0351795	−0.0175897	−	0.999845i	$-0.505599\pi$
$991$	−1.10745	−0.0351795	−0.0175897	+	0.999845i	$0.505599\pi$
$992$	−6.26526	−0.198922
$993$	13.3050	0.422221
$994$	0.704926	0.0223589
$995$	−1.81496	−0.0575382
$996$	9.38160	0.297267
$997$	−21.5071	−0.681135	−0.340568	−	0.940220i	$-0.610619\pi$
$997$	−21.5071	−0.681135	−0.340568	+	0.940220i	$0.610619\pi$
$998$	−32.6500	−1.03352
$999$	−20.4027	−0.645512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.7	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71589 q^{2} -3.02116 q^{3} +0.944266 q^{4} +1.00000 q^{5} +5.18397 q^{6} -0.410823 q^{7} +1.81152 q^{8} +6.12740 q^{9} +O(q^{10})\)	\(q-1.71589 q^{2} -3.02116 q^{3} +0.944266 q^{4} +1.00000 q^{5} +5.18397 q^{6} -0.410823 q^{7} +1.81152 q^{8} +6.12740 q^{9} -1.71589 q^{10} -6.26677 q^{11} -2.85278 q^{12} -4.80485 q^{13} +0.704926 q^{14} -3.02116 q^{15} -4.99689 q^{16} -1.00000 q^{17} -10.5139 q^{18} +0.789989 q^{19} +0.944266 q^{20} +1.24116 q^{21} +10.7531 q^{22} +5.84407 q^{23} -5.47289 q^{24} +1.00000 q^{25} +8.24458 q^{26} -9.44837 q^{27} -0.387926 q^{28} +3.69832 q^{29} +5.18397 q^{30} -1.26544 q^{31} +4.95106 q^{32} +18.9329 q^{33} +1.71589 q^{34} -0.410823 q^{35} +5.78590 q^{36} +2.15939 q^{37} -1.35553 q^{38} +14.5162 q^{39} +1.81152 q^{40} -8.72862 q^{41} -2.12969 q^{42} +5.70954 q^{43} -5.91750 q^{44} +6.12740 q^{45} -10.0278 q^{46} +7.78933 q^{47} +15.0964 q^{48} -6.83122 q^{49} -1.71589 q^{50} +3.02116 q^{51} -4.53706 q^{52} -4.68847 q^{53} +16.2123 q^{54} -6.26677 q^{55} -0.744214 q^{56} -2.38668 q^{57} -6.34590 q^{58} -8.60913 q^{59} -2.85278 q^{60} -11.3347 q^{61} +2.17135 q^{62} -2.51728 q^{63} +1.49832 q^{64} -4.80485 q^{65} -32.4867 q^{66} +15.5638 q^{67} -0.944266 q^{68} -17.6558 q^{69} +0.704926 q^{70} +1.00000 q^{71} +11.0999 q^{72} -1.61612 q^{73} -3.70526 q^{74} -3.02116 q^{75} +0.745960 q^{76} +2.57453 q^{77} -24.9082 q^{78} +16.4295 q^{79} -4.99689 q^{80} +10.1628 q^{81} +14.9773 q^{82} -3.28858 q^{83} +1.17199 q^{84} -1.00000 q^{85} -9.79692 q^{86} -11.1732 q^{87} -11.3524 q^{88} -0.415146 q^{89} -10.5139 q^{90} +1.97394 q^{91} +5.51835 q^{92} +3.82309 q^{93} -13.3656 q^{94} +0.789989 q^{95} -14.9579 q^{96} -5.51613 q^{97} +11.7216 q^{98} -38.3990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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