LMFDB - Embedded newform 3610.2.a.bi.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.17969$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.17969 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.17969 q^{6} -3.34610 q^{7} -1.00000 q^{8} +7.11045 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.17969 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.17969 q^{6} -3.34610 q^{7} -1.00000 q^{8} +7.11045 q^{9} -1.00000 q^{10} +6.18432 q^{11} +3.17969 q^{12} -0.738619 q^{13} +3.34610 q^{14} +3.17969 q^{15} +1.00000 q^{16} +0.868133 q^{17} -7.11045 q^{18} +1.00000 q^{20} -10.6396 q^{21} -6.18432 q^{22} -1.14347 q^{23} -3.17969 q^{24} +1.00000 q^{25} +0.738619 q^{26} +13.0700 q^{27} -3.34610 q^{28} -7.78988 q^{29} -3.17969 q^{30} +6.47773 q^{31} -1.00000 q^{32} +19.6643 q^{33} -0.868133 q^{34} -3.34610 q^{35} +7.11045 q^{36} +1.68113 q^{37} -2.34858 q^{39} -1.00000 q^{40} +9.69096 q^{41} +10.6396 q^{42} +1.85830 q^{43} +6.18432 q^{44} +7.11045 q^{45} +1.14347 q^{46} +0.331695 q^{47} +3.17969 q^{48} +4.19642 q^{49} -1.00000 q^{50} +2.76040 q^{51} -0.738619 q^{52} -7.10488 q^{53} -13.0700 q^{54} +6.18432 q^{55} +3.34610 q^{56} +7.78988 q^{58} +4.86030 q^{59} +3.17969 q^{60} +7.22757 q^{61} -6.47773 q^{62} -23.7923 q^{63} +1.00000 q^{64} -0.738619 q^{65} -19.6643 q^{66} +2.92493 q^{67} +0.868133 q^{68} -3.63589 q^{69} +3.34610 q^{70} -6.89058 q^{71} -7.11045 q^{72} +7.81666 q^{73} -1.68113 q^{74} +3.17969 q^{75} -20.6934 q^{77} +2.34858 q^{78} -2.29894 q^{79} +1.00000 q^{80} +20.2271 q^{81} -9.69096 q^{82} -11.4468 q^{83} -10.6396 q^{84} +0.868133 q^{85} -1.85830 q^{86} -24.7694 q^{87} -6.18432 q^{88} +2.32821 q^{89} -7.11045 q^{90} +2.47150 q^{91} -1.14347 q^{92} +20.5972 q^{93} -0.331695 q^{94} -3.17969 q^{96} -6.84406 q^{97} -4.19642 q^{98} +43.9733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.17969	1.83580	0.917898	−	0.396816i	$-0.129885\pi$
$3$	3.17969	1.83580	0.917898	+	0.396816i	$0.129885\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.17969	−1.29810
$7$	−3.34610	−1.26471	−0.632354	−	0.774679i	$-0.717911\pi$
$7$	−3.34610	−1.26471	−0.632354	+	0.774679i	$0.717911\pi$
$8$	−1.00000	−0.353553
$9$	7.11045	2.37015
$10$	−1.00000	−0.316228
$11$	6.18432	1.86464	0.932322	−	0.361629i	$-0.117779\pi$
$11$	6.18432	1.86464	0.932322	+	0.361629i	$0.117779\pi$
$12$	3.17969	0.917898
$13$	−0.738619	−0.204856	−0.102428	−	0.994740i	$-0.532661\pi$
$13$	−0.738619	−0.204856	−0.102428	+	0.994740i	$0.532661\pi$
$14$	3.34610	0.894284
$15$	3.17969	0.820993
$16$	1.00000	0.250000
$17$	0.868133	0.210553	0.105277	−	0.994443i	$-0.466427\pi$
$17$	0.868133	0.210553	0.105277	+	0.994443i	$0.466427\pi$
$18$	−7.11045	−1.67595
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	−10.6396	−2.32175
$22$	−6.18432	−1.31850
$23$	−1.14347	−0.238430	−0.119215	−	0.992868i	$-0.538038\pi$
$23$	−1.14347	−0.238430	−0.119215	+	0.992868i	$0.538038\pi$
$24$	−3.17969	−0.649052
$25$	1.00000	0.200000
$26$	0.738619	0.144855
$27$	13.0700	2.51532
$28$	−3.34610	−0.632354
$29$	−7.78988	−1.44655	−0.723273	−	0.690563i	$-0.757363\pi$
$29$	−7.78988	−1.44655	−0.723273	+	0.690563i	$0.757363\pi$
$30$	−3.17969	−0.580530
$31$	6.47773	1.16344	0.581718	−	0.813391i	$-0.302381\pi$
$31$	6.47773	1.16344	0.581718	+	0.813391i	$0.302381\pi$
$32$	−1.00000	−0.176777
$33$	19.6643	3.42311
$34$	−0.868133	−0.148884
$35$	−3.34610	−0.565595
$36$	7.11045	1.18507
$37$	1.68113	0.276377	0.138188	−	0.990406i	$-0.455872\pi$
$37$	1.68113	0.276377	0.138188	+	0.990406i	$0.455872\pi$
$38$	0	0
$39$	−2.34858	−0.376074
$40$	−1.00000	−0.158114
$41$	9.69096	1.51347	0.756737	−	0.653720i	$-0.226793\pi$
$41$	9.69096	1.51347	0.756737	+	0.653720i	$0.226793\pi$
$42$	10.6396	1.64172
$43$	1.85830	0.283388	0.141694	−	0.989911i	$-0.454745\pi$
$43$	1.85830	0.283388	0.141694	+	0.989911i	$0.454745\pi$
$44$	6.18432	0.932322
$45$	7.11045	1.05996
$46$	1.14347	0.168596
$47$	0.331695	0.0483827	0.0241913	−	0.999707i	$-0.492299\pi$
$47$	0.331695	0.0483827	0.0241913	+	0.999707i	$0.492299\pi$
$48$	3.17969	0.458949
$49$	4.19642	0.599488
$50$	−1.00000	−0.141421
$51$	2.76040	0.386533
$52$	−0.738619	−0.102428
$53$	−7.10488	−0.975930	−0.487965	−	0.872863i	$-0.662261\pi$
$53$	−7.10488	−0.975930	−0.487965	+	0.872863i	$0.662261\pi$
$54$	−13.0700	−1.77860
$55$	6.18432	0.833894
$56$	3.34610	0.447142
$57$	0	0
$58$	7.78988	1.02286
$59$	4.86030	0.632757	0.316378	−	0.948633i	$-0.397533\pi$
$59$	4.86030	0.632757	0.316378	+	0.948633i	$0.397533\pi$
$60$	3.17969	0.410497
$61$	7.22757	0.925396	0.462698	−	0.886516i	$-0.346881\pi$
$61$	7.22757	0.925396	0.462698	+	0.886516i	$0.346881\pi$
$62$	−6.47773	−0.822673
$63$	−23.7923	−2.99755
$64$	1.00000	0.125000
$65$	−0.738619	−0.0916144
$66$	−19.6643	−2.42050
$67$	2.92493	0.357337	0.178669	−	0.983909i	$-0.442821\pi$
$67$	2.92493	0.357337	0.178669	+	0.983909i	$0.442821\pi$
$68$	0.868133	0.105277
$69$	−3.63589	−0.437710
$70$	3.34610	0.399936
$71$	−6.89058	−0.817762	−0.408881	−	0.912588i	$-0.634081\pi$
$71$	−6.89058	−0.817762	−0.408881	+	0.912588i	$0.634081\pi$
$72$	−7.11045	−0.837974
$73$	7.81666	0.914871	0.457435	−	0.889243i	$-0.348768\pi$
$73$	7.81666	0.914871	0.457435	+	0.889243i	$0.348768\pi$
$74$	−1.68113	−0.195428
$75$	3.17969	0.367159
$76$	0	0
$77$	−20.6934	−2.35823
$78$	2.34858	0.265924
$79$	−2.29894	−0.258651	−0.129325	−	0.991602i	$-0.541281\pi$
$79$	−2.29894	−0.258651	−0.129325	+	0.991602i	$0.541281\pi$
$80$	1.00000	0.111803
$81$	20.2271	2.24746
$82$	−9.69096	−1.07019
$83$	−11.4468	−1.25645	−0.628223	−	0.778034i	$-0.716217\pi$
$83$	−11.4468	−1.25645	−0.628223	+	0.778034i	$0.716217\pi$
$84$	−10.6396	−1.16087
$85$	0.868133	0.0941623
$86$	−1.85830	−0.200386
$87$	−24.7694	−2.65556
$88$	−6.18432	−0.659251
$89$	2.32821	0.246790	0.123395	−	0.992358i	$-0.460622\pi$
$89$	2.32821	0.246790	0.123395	+	0.992358i	$0.460622\pi$
$90$	−7.11045	−0.749507
$91$	2.47150	0.259083
$92$	−1.14347	−0.119215
$93$	20.5972	2.13583
$94$	−0.331695	−0.0342117
$95$	0	0
$96$	−3.17969	−0.324526
$97$	−6.84406	−0.694909	−0.347454	−	0.937697i	$-0.612954\pi$
$97$	−6.84406	−0.694909	−0.347454	+	0.937697i	$0.612954\pi$
$98$	−4.19642	−0.423902
$99$	43.9733	4.41948
$100$	1.00000	0.100000
$101$	10.1868	1.01363	0.506814	−	0.862056i	$-0.330823\pi$
$101$	10.1868	1.01363	0.506814	+	0.862056i	$0.330823\pi$
$102$	−2.76040	−0.273320
$103$	2.07050	0.204012	0.102006	−	0.994784i	$-0.467474\pi$
$103$	2.07050	0.204012	0.102006	+	0.994784i	$0.467474\pi$
$104$	0.738619	0.0724275
$105$	−10.6396	−1.03832
$106$	7.10488	0.690086
$107$	−14.6371	−1.41503	−0.707513	−	0.706700i	$-0.750183\pi$
$107$	−14.6371	−1.41503	−0.707513	+	0.706700i	$0.750183\pi$
$108$	13.0700	1.25766
$109$	−8.69520	−0.832849	−0.416425	−	0.909170i	$-0.636717\pi$
$109$	−8.69520	−0.832849	−0.416425	+	0.909170i	$0.636717\pi$
$110$	−6.18432	−0.589652
$111$	5.34549	0.507371
$112$	−3.34610	−0.316177
$113$	10.8308	1.01888	0.509439	−	0.860507i	$-0.329853\pi$
$113$	10.8308	1.01888	0.509439	+	0.860507i	$0.329853\pi$
$114$	0	0
$115$	−1.14347	−0.106629
$116$	−7.78988	−0.723273
$117$	−5.25191	−0.485539
$118$	−4.86030	−0.447427
$119$	−2.90486	−0.266288
$120$	−3.17969	−0.290265
$121$	27.2459	2.47690
$122$	−7.22757	−0.654354
$123$	30.8143	2.77843
$124$	6.47773	0.581718
$125$	1.00000	0.0894427
$126$	23.7923	2.11959
$127$	−11.2245	−0.996012	−0.498006	−	0.867174i	$-0.665934\pi$
$127$	−11.2245	−0.996012	−0.498006	+	0.867174i	$0.665934\pi$
$128$	−1.00000	−0.0883883
$129$	5.90882	0.520243
$130$	0.738619	0.0647811
$131$	15.1861	1.32682	0.663408	−	0.748258i	$-0.269109\pi$
$131$	15.1861	1.32682	0.663408	+	0.748258i	$0.269109\pi$
$132$	19.6643	1.71155
$133$	0	0
$134$	−2.92493	−0.252676
$135$	13.0700	1.12488
$136$	−0.868133	−0.0744418
$137$	−8.55026	−0.730498	−0.365249	−	0.930910i	$-0.619016\pi$
$137$	−8.55026	−0.730498	−0.365249	+	0.930910i	$0.619016\pi$
$138$	3.63589	0.309507
$139$	8.80419	0.746762	0.373381	−	0.927678i	$-0.378198\pi$
$139$	8.80419	0.746762	0.373381	+	0.927678i	$0.378198\pi$
$140$	−3.34610	−0.282797
$141$	1.05469	0.0888208
$142$	6.89058	0.578245
$143$	−4.56786	−0.381983
$144$	7.11045	0.592537
$145$	−7.78988	−0.646915
$146$	−7.81666	−0.646911
$147$	13.3433	1.10054
$148$	1.68113	0.138188
$149$	0.761538	0.0623877	0.0311938	−	0.999513i	$-0.490069\pi$
$149$	0.761538	0.0623877	0.0311938	+	0.999513i	$0.490069\pi$
$150$	−3.17969	−0.259621
$151$	−6.08784	−0.495421	−0.247711	−	0.968834i	$-0.579678\pi$
$151$	−6.08784	−0.495421	−0.247711	+	0.968834i	$0.579678\pi$
$152$	0	0
$153$	6.17282	0.499043
$154$	20.6934	1.66752
$155$	6.47773	0.520304
$156$	−2.34858	−0.188037
$157$	24.3756	1.94538	0.972692	−	0.232101i	$-0.0745601\pi$
$157$	24.3756	1.94538	0.972692	+	0.232101i	$0.0745601\pi$
$158$	2.29894	0.182894
$159$	−22.5913	−1.79161
$160$	−1.00000	−0.0790569
$161$	3.82618	0.301545
$162$	−20.2271	−1.58919
$163$	−4.30992	−0.337579	−0.168789	−	0.985652i	$-0.553986\pi$
$163$	−4.30992	−0.337579	−0.168789	+	0.985652i	$0.553986\pi$
$164$	9.69096	0.756737
$165$	19.6643	1.53086
$166$	11.4468	0.888441
$167$	5.21156	0.403283	0.201641	−	0.979459i	$-0.435372\pi$
$167$	5.21156	0.403283	0.201641	+	0.979459i	$0.435372\pi$
$168$	10.6396	0.820862
$169$	−12.4544	−0.958034
$170$	−0.868133	−0.0665828
$171$	0	0
$172$	1.85830	0.141694
$173$	7.03575	0.534918	0.267459	−	0.963569i	$-0.413816\pi$
$173$	7.03575	0.534918	0.267459	+	0.963569i	$0.413816\pi$
$174$	24.7694	1.87777
$175$	−3.34610	−0.252942
$176$	6.18432	0.466161
$177$	15.4543	1.16161
$178$	−2.32821	−0.174507
$179$	3.19944	0.239138	0.119569	−	0.992826i	$-0.461849\pi$
$179$	3.19944	0.239138	0.119569	+	0.992826i	$0.461849\pi$
$180$	7.11045	0.529982
$181$	−4.73520	−0.351964	−0.175982	−	0.984393i	$-0.556310\pi$
$181$	−4.73520	−0.351964	−0.175982	+	0.984393i	$0.556310\pi$
$182$	−2.47150	−0.183199
$183$	22.9815	1.69884
$184$	1.14347	0.0842978
$185$	1.68113	0.123599
$186$	−20.5972	−1.51026
$187$	5.36882	0.392607
$188$	0.331695	0.0241913
$189$	−43.7335	−3.18114
$190$	0	0
$191$	−18.4307	−1.33360	−0.666800	−	0.745237i	$-0.732336\pi$
$191$	−18.4307	−1.33360	−0.666800	+	0.745237i	$0.732336\pi$
$192$	3.17969	0.229475
$193$	−13.5495	−0.975318	−0.487659	−	0.873034i	$-0.662149\pi$
$193$	−13.5495	−0.975318	−0.487659	+	0.873034i	$0.662149\pi$
$194$	6.84406	0.491375
$195$	−2.34858	−0.168185
$196$	4.19642	0.299744
$197$	8.19100	0.583585	0.291792	−	0.956482i	$-0.405748\pi$
$197$	8.19100	0.583585	0.291792	+	0.956482i	$0.405748\pi$
$198$	−43.9733	−3.12505
$199$	5.94246	0.421249	0.210625	−	0.977567i	$-0.432450\pi$
$199$	5.94246	0.421249	0.210625	+	0.977567i	$0.432450\pi$
$200$	−1.00000	−0.0707107
$201$	9.30039	0.655999
$202$	−10.1868	−0.716743
$203$	26.0658	1.82946
$204$	2.76040	0.193266
$205$	9.69096	0.676846
$206$	−2.07050	−0.144258
$207$	−8.13060	−0.565115
$208$	−0.738619	−0.0512140
$209$	0	0
$210$	10.6396	0.734201
$211$	−1.74362	−0.120035	−0.0600177	−	0.998197i	$-0.519116\pi$
$211$	−1.74362	−0.120035	−0.0600177	+	0.998197i	$0.519116\pi$
$212$	−7.10488	−0.487965
$213$	−21.9099	−1.50124
$214$	14.6371	1.00057
$215$	1.85830	0.126735
$216$	−13.0700	−0.889299
$217$	−21.6752	−1.47141
$218$	8.69520	0.588913
$219$	24.8546	1.67952
$220$	6.18432	0.416947
$221$	−0.641219	−0.0431331
$222$	−5.34549	−0.358766
$223$	26.4409	1.77061	0.885307	−	0.465007i	$-0.153948\pi$
$223$	26.4409	1.77061	0.885307	+	0.465007i	$0.153948\pi$
$224$	3.34610	0.223571
$225$	7.11045	0.474030
$226$	−10.8308	−0.720456
$227$	−27.4472	−1.82174	−0.910869	−	0.412697i	$-0.864587\pi$
$227$	−27.4472	−1.82174	−0.910869	+	0.412697i	$0.864587\pi$
$228$	0	0
$229$	−11.5722	−0.764711	−0.382355	−	0.924015i	$-0.624887\pi$
$229$	−11.5722	−0.764711	−0.382355	+	0.924015i	$0.624887\pi$
$230$	1.14347	0.0753983
$231$	−65.7987	−4.32923
$232$	7.78988	0.511431
$233$	12.8579	0.842347	0.421173	−	0.906980i	$-0.361618\pi$
$233$	12.8579	0.842347	0.421173	+	0.906980i	$0.361618\pi$
$234$	5.25191	0.343328
$235$	0.331695	0.0216374
$236$	4.86030	0.316378
$237$	−7.30992	−0.474831
$238$	2.90486	0.188294
$239$	−11.3142	−0.731853	−0.365926	−	0.930644i	$-0.619248\pi$
$239$	−11.3142	−0.731853	−0.365926	+	0.930644i	$0.619248\pi$
$240$	3.17969	0.205248
$241$	−23.7950	−1.53277	−0.766385	−	0.642382i	$-0.777946\pi$
$241$	−23.7950	−1.53277	−0.766385	+	0.642382i	$0.777946\pi$
$242$	−27.2459	−1.75143
$243$	25.1062	1.61056
$244$	7.22757	0.462698
$245$	4.19642	0.268099
$246$	−30.8143	−1.96465
$247$	0	0
$248$	−6.47773	−0.411337
$249$	−36.3972	−2.30658
$250$	−1.00000	−0.0632456
$251$	26.0737	1.64576	0.822879	−	0.568216i	$-0.192366\pi$
$251$	26.0737	1.64576	0.822879	+	0.568216i	$0.192366\pi$
$252$	−23.7923	−1.49877
$253$	−7.07160	−0.444588
$254$	11.2245	0.704287
$255$	2.76040	0.172863
$256$	1.00000	0.0625000
$257$	−10.1528	−0.633316	−0.316658	−	0.948540i	$-0.602561\pi$
$257$	−10.1528	−0.633316	−0.316658	+	0.948540i	$0.602561\pi$
$258$	−5.90882	−0.367867
$259$	−5.62525	−0.349536
$260$	−0.738619	−0.0458072
$261$	−55.3896	−3.42853
$262$	−15.1861	−0.938201
$263$	17.1265	1.05607	0.528033	−	0.849224i	$-0.322930\pi$
$263$	17.1265	1.05607	0.528033	+	0.849224i	$0.322930\pi$
$264$	−19.6643	−1.21025
$265$	−7.10488	−0.436449
$266$	0	0
$267$	7.40300	0.453056
$268$	2.92493	0.178669
$269$	22.8094	1.39071	0.695356	−	0.718666i	$-0.255247\pi$
$269$	22.8094	1.39071	0.695356	+	0.718666i	$0.255247\pi$
$270$	−13.0700	−0.795413
$271$	17.7903	1.08068	0.540342	−	0.841446i	$-0.318295\pi$
$271$	17.7903	1.08068	0.540342	+	0.841446i	$0.318295\pi$
$272$	0.868133	0.0526383
$273$	7.85860	0.475624
$274$	8.55026	0.516540
$275$	6.18432	0.372929
$276$	−3.63589	−0.218855
$277$	−20.8729	−1.25413	−0.627066	−	0.778966i	$-0.715744\pi$
$277$	−20.8729	−1.25413	−0.627066	+	0.778966i	$0.715744\pi$
$278$	−8.80419	−0.528041
$279$	46.0596	2.75752
$280$	3.34610	0.199968
$281$	−27.1987	−1.62254	−0.811271	−	0.584671i	$-0.801224\pi$
$281$	−27.1987	−1.62254	−0.811271	+	0.584671i	$0.801224\pi$
$282$	−1.05469	−0.0628058
$283$	−19.6937	−1.17067	−0.585334	−	0.810792i	$-0.699036\pi$
$283$	−19.6937	−1.17067	−0.585334	+	0.810792i	$0.699036\pi$
$284$	−6.89058	−0.408881
$285$	0	0
$286$	4.56786	0.270103
$287$	−32.4270	−1.91410
$288$	−7.11045	−0.418987
$289$	−16.2463	−0.955667
$290$	7.78988	0.457438
$291$	−21.7620	−1.27571
$292$	7.81666	0.457435
$293$	−14.7771	−0.863286	−0.431643	−	0.902045i	$-0.642066\pi$
$293$	−14.7771	−0.863286	−0.431643	+	0.902045i	$0.642066\pi$
$294$	−13.3433	−0.778198
$295$	4.86030	0.282978
$296$	−1.68113	−0.0977139
$297$	80.8289	4.69017
$298$	−0.761538	−0.0441147
$299$	0.844589	0.0488439
$300$	3.17969	0.183580
$301$	−6.21806	−0.358403
$302$	6.08784	0.350316
$303$	32.3910	1.86081
$304$	0	0
$305$	7.22757	0.413850
$306$	−6.17282	−0.352876
$307$	−4.23895	−0.241930	−0.120965	−	0.992657i	$-0.538599\pi$
$307$	−4.23895	−0.241930	−0.120965	+	0.992657i	$0.538599\pi$
$308$	−20.6934	−1.17912
$309$	6.58354	0.374524
$310$	−6.47773	−0.367911
$311$	−6.98685	−0.396188	−0.198094	−	0.980183i	$-0.563475\pi$
$311$	−6.98685	−0.396188	−0.198094	+	0.980183i	$0.563475\pi$
$312$	2.34858	0.132962
$313$	−7.61968	−0.430690	−0.215345	−	0.976538i	$-0.569088\pi$
$313$	−7.61968	−0.430690	−0.215345	+	0.976538i	$0.569088\pi$
$314$	−24.3756	−1.37559
$315$	−23.7923	−1.34054
$316$	−2.29894	−0.129325
$317$	13.7384	0.771628	0.385814	−	0.922577i	$-0.373921\pi$
$317$	13.7384	0.771628	0.385814	+	0.922577i	$0.373921\pi$
$318$	22.5913	1.26686
$319$	−48.1752	−2.69729
$320$	1.00000	0.0559017
$321$	−46.5416	−2.59770
$322$	−3.82618	−0.213224
$323$	0	0
$324$	20.2271	1.12373
$325$	−0.738619	−0.0409712
$326$	4.30992	0.238704
$327$	−27.6481	−1.52894
$328$	−9.69096	−0.535094
$329$	−1.10989	−0.0611900
$330$	−19.6643	−1.08248
$331$	−6.64425	−0.365201	−0.182600	−	0.983187i	$-0.558451\pi$
$331$	−6.64425	−0.365201	−0.182600	+	0.983187i	$0.558451\pi$
$332$	−11.4468	−0.628223
$333$	11.9536	0.655054
$334$	−5.21156	−0.285164
$335$	2.92493	0.159806
$336$	−10.6396	−0.580437
$337$	−18.4078	−1.00273	−0.501367	−	0.865235i	$-0.667169\pi$
$337$	−18.4078	−1.00273	−0.501367	+	0.865235i	$0.667169\pi$
$338$	12.4544	0.677432
$339$	34.4387	1.87045
$340$	0.868133	0.0470811
$341$	40.0604	2.16939
$342$	0	0
$343$	9.38108	0.506531
$344$	−1.85830	−0.100193
$345$	−3.63589	−0.195750
$346$	−7.03575	−0.378244
$347$	7.41748	0.398191	0.199096	−	0.979980i	$-0.436200\pi$
$347$	7.41748	0.398191	0.199096	+	0.979980i	$0.436200\pi$
$348$	−24.7694	−1.32778
$349$	19.1516	1.02516	0.512581	−	0.858639i	$-0.328689\pi$
$349$	19.1516	1.02516	0.512581	+	0.858639i	$0.328689\pi$
$350$	3.34610	0.178857
$351$	−9.65372	−0.515277
$352$	−6.18432	−0.329626
$353$	−1.60338	−0.0853394	−0.0426697	−	0.999089i	$-0.513586\pi$
$353$	−1.60338	−0.0853394	−0.0426697	+	0.999089i	$0.513586\pi$
$354$	−15.4543	−0.821385
$355$	−6.89058	−0.365714
$356$	2.32821	0.123395
$357$	−9.23658	−0.488851
$358$	−3.19944	−0.169096
$359$	−21.5987	−1.13993	−0.569967	−	0.821668i	$-0.693044\pi$
$359$	−21.5987	−1.13993	−0.569967	+	0.821668i	$0.693044\pi$
$360$	−7.11045	−0.374754
$361$	0	0
$362$	4.73520	0.248876
$363$	86.6335	4.54708
$364$	2.47150	0.129542
$365$	7.81666	0.409143
$366$	−22.9815	−1.20126
$367$	19.7419	1.03052	0.515260	−	0.857034i	$-0.327695\pi$
$367$	19.7419	1.03052	0.515260	+	0.857034i	$0.327695\pi$
$368$	−1.14347	−0.0596076
$369$	68.9071	3.58716
$370$	−1.68113	−0.0873980
$371$	23.7737	1.23427
$372$	20.5972	1.06792
$373$	−23.1601	−1.19918	−0.599592	−	0.800306i	$-0.704670\pi$
$373$	−23.1601	−1.19918	−0.599592	+	0.800306i	$0.704670\pi$
$374$	−5.36882	−0.277615
$375$	3.17969	0.164199
$376$	−0.331695	−0.0171059
$377$	5.75375	0.296333
$378$	43.7335	2.24941
$379$	−3.52957	−0.181302	−0.0906508	−	0.995883i	$-0.528895\pi$
$379$	−3.52957	−0.181302	−0.0906508	+	0.995883i	$0.528895\pi$
$380$	0	0
$381$	−35.6904	−1.82847
$382$	18.4307	0.942997
$383$	36.6818	1.87435	0.937177	−	0.348854i	$-0.113429\pi$
$383$	36.6818	1.87435	0.937177	+	0.348854i	$0.113429\pi$
$384$	−3.17969	−0.162263
$385$	−20.6934	−1.05463
$386$	13.5495	0.689654
$387$	13.2133	0.671672
$388$	−6.84406	−0.347454
$389$	−24.5847	−1.24650	−0.623248	−	0.782024i	$-0.714187\pi$
$389$	−24.5847	−1.24650	−0.623248	+	0.782024i	$0.714187\pi$
$390$	2.34858	0.118925
$391$	−0.992686	−0.0502023
$392$	−4.19642	−0.211951
$393$	48.2872	2.43577
$394$	−8.19100	−0.412657
$395$	−2.29894	−0.115672
$396$	43.9733	2.20974
$397$	20.3558	1.02163	0.510813	−	0.859692i	$-0.329344\pi$
$397$	20.3558	1.02163	0.510813	+	0.859692i	$0.329344\pi$
$398$	−5.94246	−0.297868
$399$	0	0
$400$	1.00000	0.0500000
$401$	20.1463	1.00606	0.503029	−	0.864269i	$-0.332219\pi$
$401$	20.1463	1.00606	0.503029	+	0.864269i	$0.332219\pi$
$402$	−9.30039	−0.463861
$403$	−4.78458	−0.238337
$404$	10.1868	0.506814
$405$	20.2271	1.00509
$406$	−26.0658	−1.29362
$407$	10.3967	0.515344
$408$	−2.76040	−0.136660
$409$	12.8843	0.637089	0.318544	−	0.947908i	$-0.396806\pi$
$409$	12.8843	0.637089	0.318544	+	0.947908i	$0.396806\pi$
$410$	−9.69096	−0.478602
$411$	−27.1872	−1.34105
$412$	2.07050	0.102006
$413$	−16.2631	−0.800253
$414$	8.13060	0.399597
$415$	−11.4468	−0.561899
$416$	0.738619	0.0362138
$417$	27.9946	1.37090
$418$	0	0
$419$	20.0166	0.977876	0.488938	−	0.872319i	$-0.337384\pi$
$419$	20.0166	0.977876	0.488938	+	0.872319i	$0.337384\pi$
$420$	−10.6396	−0.519159
$421$	6.69810	0.326446	0.163223	−	0.986589i	$-0.447811\pi$
$421$	6.69810	0.326446	0.163223	+	0.986589i	$0.447811\pi$
$422$	1.74362	0.0848779
$423$	2.35850	0.114674
$424$	7.10488	0.345043
$425$	0.868133	0.0421106
$426$	21.9099	1.06154
$427$	−24.1842	−1.17036
$428$	−14.6371	−0.707513
$429$	−14.5244	−0.701244
$430$	−1.85830	−0.0896152
$431$	−28.0180	−1.34958	−0.674790	−	0.738010i	$-0.735766\pi$
$431$	−28.0180	−1.34958	−0.674790	+	0.738010i	$0.735766\pi$
$432$	13.0700	0.628829
$433$	−22.6178	−1.08694	−0.543471	−	0.839428i	$-0.682890\pi$
$433$	−22.6178	−1.08694	−0.543471	+	0.839428i	$0.682890\pi$
$434$	21.6752	1.04044
$435$	−24.7694	−1.18760
$436$	−8.69520	−0.416425
$437$	0	0
$438$	−24.8546	−1.18760
$439$	−4.13500	−0.197353	−0.0986763	−	0.995120i	$-0.531461\pi$
$439$	−4.13500	−0.197353	−0.0986763	+	0.995120i	$0.531461\pi$
$440$	−6.18432	−0.294826
$441$	29.8384	1.42088
$442$	0.641219	0.0304997
$443$	−28.9398	−1.37497	−0.687485	−	0.726199i	$-0.741285\pi$
$443$	−28.9398	−1.37497	−0.687485	+	0.726199i	$0.741285\pi$
$444$	5.34549	0.253686
$445$	2.32821	0.110368
$446$	−26.4409	−1.25201
$447$	2.42146	0.114531
$448$	−3.34610	−0.158089
$449$	−5.56140	−0.262459	−0.131229	−	0.991352i	$-0.541892\pi$
$449$	−5.56140	−0.262459	−0.131229	+	0.991352i	$0.541892\pi$
$450$	−7.11045	−0.335190
$451$	59.9320	2.82209
$452$	10.8308	0.509439
$453$	−19.3575	−0.909493
$454$	27.4472	1.28816
$455$	2.47150	0.115865
$456$	0	0
$457$	−3.44090	−0.160959	−0.0804793	−	0.996756i	$-0.525645\pi$
$457$	−3.44090	−0.160959	−0.0804793	+	0.996756i	$0.525645\pi$
$458$	11.5722	0.540732
$459$	11.3465	0.529608
$460$	−1.14347	−0.0533146
$461$	−5.07784	−0.236499	−0.118249	−	0.992984i	$-0.537728\pi$
$461$	−5.07784	−0.236499	−0.118249	+	0.992984i	$0.537728\pi$
$462$	65.7987	3.06123
$463$	−5.12810	−0.238323	−0.119162	−	0.992875i	$-0.538021\pi$
$463$	−5.12810	−0.238323	−0.119162	+	0.992875i	$0.538021\pi$
$464$	−7.78988	−0.361636
$465$	20.5972	0.955173
$466$	−12.8579	−0.595629
$467$	29.6221	1.37075	0.685373	−	0.728193i	$-0.259639\pi$
$467$	29.6221	1.37075	0.685373	+	0.728193i	$0.259639\pi$
$468$	−5.25191	−0.242770
$469$	−9.78713	−0.451928
$470$	−0.331695	−0.0152999
$471$	77.5069	3.57133
$472$	−4.86030	−0.223713
$473$	11.4923	0.528418
$474$	7.30992	0.335756
$475$	0	0
$476$	−2.90486	−0.133144
$477$	−50.5189	−2.31310
$478$	11.3142	0.517498
$479$	−37.6842	−1.72183	−0.860917	−	0.508746i	$-0.830109\pi$
$479$	−37.6842	−1.72183	−0.860917	+	0.508746i	$0.830109\pi$
$480$	−3.17969	−0.145132
$481$	−1.24172	−0.0566174
$482$	23.7950	1.08383
$483$	12.1661	0.553575
$484$	27.2459	1.23845
$485$	−6.84406	−0.310773
$486$	−25.1062	−1.13884
$487$	−17.7543	−0.804523	−0.402262	−	0.915525i	$-0.631776\pi$
$487$	−17.7543	−0.804523	−0.402262	+	0.915525i	$0.631776\pi$
$488$	−7.22757	−0.327177
$489$	−13.7042	−0.619726
$490$	−4.19642	−0.189575
$491$	−22.2980	−1.00629	−0.503147	−	0.864201i	$-0.667825\pi$
$491$	−22.2980	−1.00629	−0.503147	+	0.864201i	$0.667825\pi$
$492$	30.8143	1.38921
$493$	−6.76266	−0.304575
$494$	0	0
$495$	43.9733	1.97645
$496$	6.47773	0.290859
$497$	23.0566	1.03423
$498$	36.3972	1.63100
$499$	−18.8766	−0.845034	−0.422517	−	0.906355i	$-0.638853\pi$
$499$	−18.8766	−0.845034	−0.422517	+	0.906355i	$0.638853\pi$
$500$	1.00000	0.0447214
$501$	16.5712	0.740345
$502$	−26.0737	−1.16373
$503$	40.8605	1.82188	0.910939	−	0.412541i	$-0.135359\pi$
$503$	40.8605	1.82188	0.910939	+	0.412541i	$0.135359\pi$
$504$	23.7923	1.05979
$505$	10.1868	0.453308
$506$	7.07160	0.314371
$507$	−39.6013	−1.75876
$508$	−11.2245	−0.498006
$509$	−13.3122	−0.590053	−0.295027	−	0.955489i	$-0.595328\pi$
$509$	−13.3122	−0.590053	−0.295027	+	0.955489i	$0.595328\pi$
$510$	−2.76040	−0.122232
$511$	−26.1554	−1.15704
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	10.1528	0.447822
$515$	2.07050	0.0912369
$516$	5.90882	0.260121
$517$	2.05131	0.0902165
$518$	5.62525	0.247159
$519$	22.3715	0.982001
$520$	0.738619	0.0323906
$521$	−27.6686	−1.21218	−0.606091	−	0.795395i	$-0.707263\pi$
$521$	−27.6686	−1.21218	−0.606091	+	0.795395i	$0.707263\pi$
$522$	55.3896	2.42434
$523$	−1.07454	−0.0469863	−0.0234932	−	0.999724i	$-0.507479\pi$
$523$	−1.07454	−0.0469863	−0.0234932	+	0.999724i	$0.507479\pi$
$524$	15.1861	0.663408
$525$	−10.6396	−0.464350
$526$	−17.1265	−0.746752
$527$	5.62354	0.244965
$528$	19.6643	0.855777
$529$	−21.6925	−0.943151
$530$	7.10488	0.308616
$531$	34.5589	1.49973
$532$	0	0
$533$	−7.15792	−0.310044
$534$	−7.40300	−0.320359
$535$	−14.6371	−0.632819
$536$	−2.92493	−0.126338
$537$	10.1732	0.439008
$538$	−22.8094	−0.983382
$539$	25.9520	1.11783
$540$	13.0700	0.562442
$541$	15.4497	0.664235	0.332117	−	0.943238i	$-0.392237\pi$
$541$	15.4497	0.664235	0.332117	+	0.943238i	$0.392237\pi$
$542$	−17.7903	−0.764159
$543$	−15.0565	−0.646135
$544$	−0.868133	−0.0372209
$545$	−8.69520	−0.372461
$546$	−7.85860	−0.336317
$547$	−33.6021	−1.43672	−0.718362	−	0.695670i	$-0.755108\pi$
$547$	−33.6021	−1.43672	−0.718362	+	0.695670i	$0.755108\pi$
$548$	−8.55026	−0.365249
$549$	51.3913	2.19333
$550$	−6.18432	−0.263700
$551$	0	0
$552$	3.63589	0.154754
$553$	7.69249	0.327118
$554$	20.8729	0.886805
$555$	5.34549	0.226903
$556$	8.80419	0.373381
$557$	−14.2489	−0.603744	−0.301872	−	0.953349i	$-0.597611\pi$
$557$	−14.2489	−0.603744	−0.301872	+	0.953349i	$0.597611\pi$
$558$	−46.0596	−1.94986
$559$	−1.37257	−0.0580537
$560$	−3.34610	−0.141399
$561$	17.0712	0.720746
$562$	27.1987	1.14731
$563$	14.7721	0.622571	0.311286	−	0.950316i	$-0.399240\pi$
$563$	14.7721	0.622571	0.311286	+	0.950316i	$0.399240\pi$
$564$	1.05469	0.0444104
$565$	10.8308	0.455656
$566$	19.6937	0.827787
$567$	−67.6821	−2.84238
$568$	6.89058	0.289122
$569$	19.4550	0.815598	0.407799	−	0.913072i	$-0.366296\pi$
$569$	19.4550	0.815598	0.407799	+	0.913072i	$0.366296\pi$
$570$	0	0
$571$	−39.3956	−1.64866	−0.824328	−	0.566112i	$-0.808447\pi$
$571$	−39.3956	−1.64866	−0.824328	+	0.566112i	$0.808447\pi$
$572$	−4.56786	−0.190992
$573$	−58.6040	−2.44822
$574$	32.4270	1.35348
$575$	−1.14347	−0.0476861
$576$	7.11045	0.296269
$577$	−15.8953	−0.661728	−0.330864	−	0.943678i	$-0.607340\pi$
$577$	−15.8953	−0.661728	−0.330864	+	0.943678i	$0.607340\pi$
$578$	16.2463	0.675759
$579$	−43.0834	−1.79049
$580$	−7.78988	−0.323457
$581$	38.3021	1.58904
$582$	21.7620	0.902064
$583$	−43.9389	−1.81976
$584$	−7.81666	−0.323456
$585$	−5.25191	−0.217140
$586$	14.7771	0.610435
$587$	−12.8650	−0.530996	−0.265498	−	0.964111i	$-0.585536\pi$
$587$	−12.8650	−0.530996	−0.265498	+	0.964111i	$0.585536\pi$
$588$	13.3433	0.550269
$589$	0	0
$590$	−4.86030	−0.200095
$591$	26.0449	1.07134
$592$	1.68113	0.0690942
$593$	2.17780	0.0894316	0.0447158	−	0.999000i	$-0.485762\pi$
$593$	2.17780	0.0894316	0.0447158	+	0.999000i	$0.485762\pi$
$594$	−80.8289	−3.31645
$595$	−2.90486	−0.119088
$596$	0.761538	0.0311938
$597$	18.8952	0.773328
$598$	−0.844589	−0.0345378
$599$	3.53422	0.144404	0.0722021	−	0.997390i	$-0.476997\pi$
$599$	3.53422	0.144404	0.0722021	+	0.997390i	$0.476997\pi$
$600$	−3.17969	−0.129810
$601$	22.4038	0.913869	0.456935	−	0.889500i	$-0.348947\pi$
$601$	22.4038	0.913869	0.456935	+	0.889500i	$0.348947\pi$
$602$	6.21806	0.253429
$603$	20.7976	0.846943
$604$	−6.08784	−0.247711
$605$	27.2459	1.10770
$606$	−32.3910	−1.31579
$607$	−12.5717	−0.510269	−0.255134	−	0.966906i	$-0.582120\pi$
$607$	−12.5717	−0.510269	−0.255134	+	0.966906i	$0.582120\pi$
$608$	0	0
$609$	82.8812	3.35851
$610$	−7.22757	−0.292636
$611$	−0.244996	−0.00991148
$612$	6.17282	0.249521
$613$	−46.8901	−1.89387	−0.946937	−	0.321420i	$-0.895840\pi$
$613$	−46.8901	−1.89387	−0.946937	+	0.321420i	$0.895840\pi$
$614$	4.23895	0.171070
$615$	30.8143	1.24255
$616$	20.6934	0.833761
$617$	0.528391	0.0212722	0.0106361	−	0.999943i	$-0.496614\pi$
$617$	0.528391	0.0212722	0.0106361	+	0.999943i	$0.496614\pi$
$618$	−6.58354	−0.264829
$619$	21.8634	0.878766	0.439383	−	0.898300i	$-0.355197\pi$
$619$	21.8634	0.878766	0.439383	+	0.898300i	$0.355197\pi$
$620$	6.47773	0.260152
$621$	−14.9451	−0.599728
$622$	6.98685	0.280147
$623$	−7.79044	−0.312117
$624$	−2.34858	−0.0940185
$625$	1.00000	0.0400000
$626$	7.61968	0.304544
$627$	0	0
$628$	24.3756	0.972692
$629$	1.45945	0.0581920
$630$	23.7923	0.947908
$631$	30.1257	1.19928	0.599642	−	0.800268i	$-0.295310\pi$
$631$	30.1257	1.19928	0.599642	+	0.800268i	$0.295310\pi$
$632$	2.29894	0.0914469
$633$	−5.54416	−0.220361
$634$	−13.7384	−0.545623
$635$	−11.2245	−0.445430
$636$	−22.5913	−0.895804
$637$	−3.09955	−0.122809
$638$	48.1752	1.90727
$639$	−48.9951	−1.93822
$640$	−1.00000	−0.0395285
$641$	32.1983	1.27176	0.635879	−	0.771789i	$-0.280638\pi$
$641$	32.1983	1.27176	0.635879	+	0.771789i	$0.280638\pi$
$642$	46.5416	1.83685
$643$	−25.5914	−1.00923	−0.504614	−	0.863345i	$-0.668365\pi$
$643$	−25.5914	−1.00923	−0.504614	+	0.863345i	$0.668365\pi$
$644$	3.82618	0.150772
$645$	5.90882	0.232660
$646$	0	0
$647$	−18.8860	−0.742483	−0.371242	−	0.928536i	$-0.621068\pi$
$647$	−18.8860	−0.742483	−0.371242	+	0.928536i	$0.621068\pi$
$648$	−20.2271	−0.794597
$649$	30.0577	1.17987
$650$	0.738619	0.0289710
$651$	−68.9204	−2.70120
$652$	−4.30992	−0.168789
$653$	24.8305	0.971692	0.485846	−	0.874044i	$-0.338512\pi$
$653$	24.8305	0.971692	0.485846	+	0.874044i	$0.338512\pi$
$654$	27.6481	1.08112
$655$	15.1861	0.593370
$656$	9.69096	0.378368
$657$	55.5799	2.16838
$658$	1.10989	0.0432679
$659$	31.3822	1.22248	0.611239	−	0.791446i	$-0.290672\pi$
$659$	31.3822	1.22248	0.611239	+	0.791446i	$0.290672\pi$
$660$	19.6643	0.765430
$661$	−18.6331	−0.724744	−0.362372	−	0.932033i	$-0.618033\pi$
$661$	−18.6331	−0.724744	−0.362372	+	0.932033i	$0.618033\pi$
$662$	6.64425	0.258236
$663$	−2.03888	−0.0791836
$664$	11.4468	0.444220
$665$	0	0
$666$	−11.9536	−0.463193
$667$	8.90751	0.344900
$668$	5.21156	0.201641
$669$	84.0740	3.25049
$670$	−2.92493	−0.113000
$671$	44.6977	1.72553
$672$	10.6396	0.410431
$673$	−14.5762	−0.561871	−0.280935	−	0.959727i	$-0.590645\pi$
$673$	−14.5762	−0.561871	−0.280935	+	0.959727i	$0.590645\pi$
$674$	18.4078	0.709040
$675$	13.0700	0.503063
$676$	−12.4544	−0.479017
$677$	2.43643	0.0936394	0.0468197	−	0.998903i	$-0.485091\pi$
$677$	2.43643	0.0936394	0.0468197	+	0.998903i	$0.485091\pi$
$678$	−34.4387	−1.32261
$679$	22.9009	0.878857
$680$	−0.868133	−0.0332914
$681$	−87.2738	−3.34434
$682$	−40.0604	−1.53399
$683$	15.0962	0.577639	0.288820	−	0.957384i	$-0.406737\pi$
$683$	15.0962	0.577639	0.288820	+	0.957384i	$0.406737\pi$
$684$	0	0
$685$	−8.55026	−0.326689
$686$	−9.38108	−0.358171
$687$	−36.7960	−1.40385
$688$	1.85830	0.0708470
$689$	5.24779	0.199925
$690$	3.63589	0.138416
$691$	−12.2404	−0.465646	−0.232823	−	0.972519i	$-0.574796\pi$
$691$	−12.2404	−0.465646	−0.232823	+	0.972519i	$0.574796\pi$
$692$	7.03575	0.267459
$693$	−147.139	−5.58936
$694$	−7.41748	−0.281564
$695$	8.80419	0.333962
$696$	24.7694	0.938883
$697$	8.41304	0.318667
$698$	−19.1516	−0.724900
$699$	40.8841	1.54638
$700$	−3.34610	−0.126471
$701$	44.6920	1.68799	0.843997	−	0.536348i	$-0.180197\pi$
$701$	44.6920	1.68799	0.843997	+	0.536348i	$0.180197\pi$
$702$	9.65372	0.364356
$703$	0	0
$704$	6.18432	0.233080
$705$	1.05469	0.0397219
$706$	1.60338	0.0603441
$707$	−34.0862	−1.28194
$708$	15.4543	0.580807
$709$	−16.0501	−0.602774	−0.301387	−	0.953502i	$-0.597450\pi$
$709$	−16.0501	−0.602774	−0.301387	+	0.953502i	$0.597450\pi$
$710$	6.89058	0.258599
$711$	−16.3465	−0.613042
$712$	−2.32821	−0.0872534
$713$	−7.40711	−0.277398
$714$	9.23658	0.345670
$715$	−4.56786	−0.170828
$716$	3.19944	0.119569
$717$	−35.9756	−1.34353
$718$	21.5987	0.806054
$719$	−1.52730	−0.0569588	−0.0284794	−	0.999594i	$-0.509066\pi$
$719$	−1.52730	−0.0569588	−0.0284794	+	0.999594i	$0.509066\pi$
$720$	7.11045	0.264991
$721$	−6.92809	−0.258016
$722$	0	0
$723$	−75.6608	−2.81385
$724$	−4.73520	−0.175982
$725$	−7.78988	−0.289309
$726$	−86.6335	−3.21527
$727$	−37.9678	−1.40815	−0.704073	−	0.710128i	$-0.748637\pi$
$727$	−37.9678	−1.40815	−0.704073	+	0.710128i	$0.748637\pi$
$728$	−2.47150	−0.0915997
$729$	19.1486	0.709206
$730$	−7.81666	−0.289307
$731$	1.61325	0.0596682
$732$	22.9815	0.849419
$733$	−32.0221	−1.18276	−0.591381	−	0.806392i	$-0.701417\pi$
$733$	−32.0221	−1.18276	−0.591381	+	0.806392i	$0.701417\pi$
$734$	−19.7419	−0.728688
$735$	13.3433	0.492176
$736$	1.14347	0.0421489
$737$	18.0887	0.666307
$738$	−68.9071	−2.53650
$739$	−38.7246	−1.42451	−0.712253	−	0.701922i	$-0.752325\pi$
$739$	−38.7246	−1.42451	−0.712253	+	0.701922i	$0.752325\pi$
$740$	1.68113	0.0617997
$741$	0	0
$742$	−23.7737	−0.872758
$743$	−31.2269	−1.14560	−0.572801	−	0.819694i	$-0.694143\pi$
$743$	−31.2269	−1.14560	−0.572801	+	0.819694i	$0.694143\pi$
$744$	−20.5972	−0.755130
$745$	0.761538	0.0279006
$746$	23.1601	0.847951
$747$	−81.3916	−2.97796
$748$	5.36882	0.196303
$749$	48.9774	1.78960
$750$	−3.17969	−0.116106
$751$	−34.4631	−1.25758	−0.628788	−	0.777577i	$-0.716449\pi$
$751$	−34.4631	−1.25758	−0.628788	+	0.777577i	$0.716449\pi$
$752$	0.331695	0.0120957
$753$	82.9064	3.02128
$754$	−5.75375	−0.209539
$755$	−6.08784	−0.221559
$756$	−43.7335	−1.59057
$757$	−2.70297	−0.0982412	−0.0491206	−	0.998793i	$-0.515642\pi$
$757$	−2.70297	−0.0982412	−0.0491206	+	0.998793i	$0.515642\pi$
$758$	3.52957	0.128200
$759$	−22.4855	−0.816173
$760$	0	0
$761$	9.19327	0.333256	0.166628	−	0.986020i	$-0.446712\pi$
$761$	9.19327	0.333256	0.166628	+	0.986020i	$0.446712\pi$
$762$	35.6904	1.29293
$763$	29.0950	1.05331
$764$	−18.4307	−0.666800
$765$	6.17282	0.223179
$766$	−36.6818	−1.32537
$767$	−3.58991	−0.129624
$768$	3.17969	0.114737
$769$	0.0607369	0.00219023	0.00109511	−	0.999999i	$-0.499651\pi$
$769$	0.0607369	0.00219023	0.00109511	+	0.999999i	$0.499651\pi$
$770$	20.6934	0.745738
$771$	−32.2829	−1.16264
$772$	−13.5495	−0.487659
$773$	9.90058	0.356099	0.178049	−	0.984022i	$-0.443021\pi$
$773$	9.90058	0.356099	0.178049	+	0.984022i	$0.443021\pi$
$774$	−13.2133	−0.474944
$775$	6.47773	0.232687
$776$	6.84406	0.245687
$777$	−17.8866	−0.641677
$778$	24.5847	0.881405
$779$	0	0
$780$	−2.34858	−0.0840927
$781$	−42.6136	−1.52483
$782$	0.992686	0.0354984
$783$	−101.814	−3.63852
$784$	4.19642	0.149872
$785$	24.3756	0.870002
$786$	−48.2872	−1.72235
$787$	11.1823	0.398606	0.199303	−	0.979938i	$-0.436132\pi$
$787$	11.1823	0.398606	0.199303	+	0.979938i	$0.436132\pi$
$788$	8.19100	0.291792
$789$	54.4571	1.93872
$790$	2.29894	0.0817926
$791$	−36.2411	−1.28859
$792$	−43.9733	−1.56252
$793$	−5.33842	−0.189573
$794$	−20.3558	−0.722399
$795$	−22.5913	−0.801232
$796$	5.94246	0.210625
$797$	16.8348	0.596320	0.298160	−	0.954516i	$-0.403627\pi$
$797$	16.8348	0.596320	0.298160	+	0.954516i	$0.403627\pi$
$798$	0	0
$799$	0.287955	0.0101871
$800$	−1.00000	−0.0353553
$801$	16.5546	0.584929
$802$	−20.1463	−0.711391
$803$	48.3407	1.70591
$804$	9.30039	0.327999
$805$	3.82618	0.134855
$806$	4.78458	0.168529
$807$	72.5268	2.55306
$808$	−10.1868	−0.358371
$809$	26.2435	0.922671	0.461335	−	0.887226i	$-0.347371\pi$
$809$	26.2435	0.922671	0.461335	+	0.887226i	$0.347371\pi$
$810$	−20.2271	−0.710709
$811$	44.0988	1.54852	0.774259	−	0.632869i	$-0.218123\pi$
$811$	44.0988	1.54852	0.774259	+	0.632869i	$0.218123\pi$
$812$	26.0658	0.914729
$813$	56.5677	1.98392
$814$	−10.3967	−0.364403
$815$	−4.30992	−0.150970
$816$	2.76040	0.0966332
$817$	0	0
$818$	−12.8843	−0.450490
$819$	17.5734	0.614066
$820$	9.69096	0.338423
$821$	−46.4039	−1.61951	−0.809753	−	0.586770i	$-0.800399\pi$
$821$	−46.4039	−1.61951	−0.809753	+	0.586770i	$0.800399\pi$
$822$	27.1872	0.948263
$823$	31.2787	1.09031	0.545154	−	0.838336i	$-0.316471\pi$
$823$	31.2787	1.09031	0.545154	+	0.838336i	$0.316471\pi$
$824$	−2.07050	−0.0721291
$825$	19.6643	0.684621
$826$	16.2631	0.565865
$827$	−19.7143	−0.685532	−0.342766	−	0.939421i	$-0.611364\pi$
$827$	−19.7143	−0.685532	−0.342766	+	0.939421i	$0.611364\pi$
$828$	−8.13060	−0.282558
$829$	−54.6267	−1.89726	−0.948632	−	0.316383i	$-0.897532\pi$
$829$	−54.6267	−1.89726	−0.948632	+	0.316383i	$0.897532\pi$
$830$	11.4468	0.397323
$831$	−66.3695	−2.30233
$832$	−0.738619	−0.0256070
$833$	3.64305	0.126224
$834$	−27.9946	−0.969375
$835$	5.21156	0.180354
$836$	0	0
$837$	84.6638	2.92641
$838$	−20.0166	−0.691462
$839$	38.1825	1.31821	0.659103	−	0.752053i	$-0.270936\pi$
$839$	38.1825	1.31821	0.659103	+	0.752053i	$0.270936\pi$
$840$	10.6396	0.367101
$841$	31.6823	1.09249
$842$	−6.69810	−0.230832
$843$	−86.4837	−2.97866
$844$	−1.74362	−0.0600177
$845$	−12.4544	−0.428446
$846$	−2.35850	−0.0810869
$847$	−91.1675	−3.13255
$848$	−7.10488	−0.243982
$849$	−62.6198	−2.14911
$850$	−0.868133	−0.0297767
$851$	−1.92233	−0.0658966
$852$	−21.9099	−0.750622
$853$	−33.2969	−1.14006	−0.570032	−	0.821623i	$-0.693069\pi$
$853$	−33.2969	−1.14006	−0.570032	+	0.821623i	$0.693069\pi$
$854$	24.1842	0.827567
$855$	0	0
$856$	14.6371	0.500287
$857$	−40.3813	−1.37940	−0.689699	−	0.724096i	$-0.742257\pi$
$857$	−40.3813	−1.37940	−0.689699	+	0.724096i	$0.742257\pi$
$858$	14.5244	0.495854
$859$	−7.75988	−0.264764	−0.132382	−	0.991199i	$-0.542262\pi$
$859$	−7.75988	−0.264764	−0.132382	+	0.991199i	$0.542262\pi$
$860$	1.85830	0.0633675
$861$	−103.108	−3.51390
$862$	28.0180	0.954298
$863$	−46.4111	−1.57985	−0.789926	−	0.613202i	$-0.789881\pi$
$863$	−46.4111	−1.57985	−0.789926	+	0.613202i	$0.789881\pi$
$864$	−13.0700	−0.444649
$865$	7.03575	0.239223
$866$	22.6178	0.768584
$867$	−51.6584	−1.75441
$868$	−21.6752	−0.735703
$869$	−14.2174	−0.482292
$870$	24.7694	0.839763
$871$	−2.16041	−0.0732027
$872$	8.69520	0.294457
$873$	−48.6643	−1.64704
$874$	0	0
$875$	−3.34610	−0.113119
$876$	24.8546	0.839758
$877$	−27.0500	−0.913413	−0.456706	−	0.889617i	$-0.650971\pi$
$877$	−27.0500	−0.913413	−0.456706	+	0.889617i	$0.650971\pi$
$878$	4.13500	0.139549
$879$	−46.9866	−1.58482
$880$	6.18432	0.208474
$881$	20.2036	0.680676	0.340338	−	0.940303i	$-0.389459\pi$
$881$	20.2036	0.680676	0.340338	+	0.940303i	$0.389459\pi$
$882$	−29.8384	−1.00471
$883$	−15.0372	−0.506043	−0.253022	−	0.967461i	$-0.581424\pi$
$883$	−15.0372	−0.506043	−0.253022	+	0.967461i	$0.581424\pi$
$884$	−0.641219	−0.0215665
$885$	15.4543	0.519489
$886$	28.9398	0.972250
$887$	29.1877	0.980026	0.490013	−	0.871715i	$-0.336992\pi$
$887$	29.1877	0.980026	0.490013	+	0.871715i	$0.336992\pi$
$888$	−5.34549	−0.179383
$889$	37.5583	1.25966
$890$	−2.32821	−0.0780419
$891$	125.091	4.19071
$892$	26.4409	0.885307
$893$	0	0
$894$	−2.42146	−0.0809857
$895$	3.19944	0.106946
$896$	3.34610	0.111786
$897$	2.68554	0.0896674
$898$	5.56140	0.185586
$899$	−50.4608	−1.68296
$900$	7.11045	0.237015
$901$	−6.16798	−0.205485
$902$	−59.9320	−1.99552
$903$	−19.7715	−0.657956
$904$	−10.8308	−0.360228
$905$	−4.73520	−0.157403
$906$	19.3575	0.643109
$907$	52.5475	1.74481	0.872406	−	0.488782i	$-0.162559\pi$
$907$	52.5475	1.74481	0.872406	+	0.488782i	$0.162559\pi$
$908$	−27.4472	−0.910869
$909$	72.4329	2.40245
$910$	−2.47150	−0.0819293
$911$	−28.5338	−0.945366	−0.472683	−	0.881233i	$-0.656714\pi$
$911$	−28.5338	−0.945366	−0.472683	+	0.881233i	$0.656714\pi$
$912$	0	0
$913$	−70.7905	−2.34282
$914$	3.44090	0.113815
$915$	22.9815	0.759744
$916$	−11.5722	−0.382355
$917$	−50.8143	−1.67804
$918$	−11.3465	−0.374489
$919$	27.0033	0.890756	0.445378	−	0.895343i	$-0.353069\pi$
$919$	27.0033	0.890756	0.445378	+	0.895343i	$0.353069\pi$
$920$	1.14347	0.0376991
$921$	−13.4786	−0.444134
$922$	5.07784	0.167230
$923$	5.08951	0.167523
$924$	−65.7987	−2.16462
$925$	1.68113	0.0552753
$926$	5.12810	0.168520
$927$	14.7221	0.483539
$928$	7.78988	0.255715
$929$	−11.1634	−0.366258	−0.183129	−	0.983089i	$-0.558623\pi$
$929$	−11.1634	−0.366258	−0.183129	+	0.983089i	$0.558623\pi$
$930$	−20.5972	−0.675409
$931$	0	0
$932$	12.8579	0.421173
$933$	−22.2160	−0.727321
$934$	−29.6221	−0.969263
$935$	5.36882	0.175579
$936$	5.25191	0.171664
$937$	13.6769	0.446805	0.223403	−	0.974726i	$-0.428284\pi$
$937$	13.6769	0.446805	0.223403	+	0.974726i	$0.428284\pi$
$938$	9.78713	0.319561
$939$	−24.2283	−0.790659
$940$	0.331695	0.0108187
$941$	−3.43708	−0.112045	−0.0560227	−	0.998429i	$-0.517842\pi$
$941$	−3.43708	−0.112045	−0.0560227	+	0.998429i	$0.517842\pi$
$942$	−77.5069	−2.52531
$943$	−11.0813	−0.360858
$944$	4.86030	0.158189
$945$	−43.7335	−1.42265
$946$	−11.4923	−0.373648
$947$	40.8790	1.32839	0.664195	−	0.747559i	$-0.268774\pi$
$947$	40.8790	1.32839	0.664195	+	0.747559i	$0.268774\pi$
$948$	−7.30992	−0.237415
$949$	−5.77353	−0.187417
$950$	0	0
$951$	43.6840	1.41655
$952$	2.90486	0.0941472
$953$	−43.6004	−1.41236	−0.706178	−	0.708035i	$-0.749582\pi$
$953$	−43.6004	−1.41236	−0.706178	+	0.708035i	$0.749582\pi$
$954$	50.5189	1.63561
$955$	−18.4307	−0.596404
$956$	−11.3142	−0.365926
$957$	−153.182	−4.95168
$958$	37.6842	1.21752
$959$	28.6101	0.923868
$960$	3.17969	0.102624
$961$	10.9610	0.353582
$962$	1.24172	0.0400346
$963$	−104.077	−3.35382
$964$	−23.7950	−0.766385
$965$	−13.5495	−0.436175
$966$	−12.1661	−0.391437
$967$	23.0656	0.741740	0.370870	−	0.928685i	$-0.379060\pi$
$967$	23.0656	0.741740	0.370870	+	0.928685i	$0.379060\pi$
$968$	−27.2459	−0.875715
$969$	0	0
$970$	6.84406	0.219749
$971$	−32.8776	−1.05509	−0.527546	−	0.849526i	$-0.676888\pi$
$971$	−32.8776	−1.05509	−0.527546	+	0.849526i	$0.676888\pi$
$972$	25.1062	0.805281
$973$	−29.4598	−0.944437
$974$	17.7543	0.568884
$975$	−2.34858	−0.0752148
$976$	7.22757	0.231349
$977$	56.3104	1.80153	0.900765	−	0.434307i	$-0.143007\pi$
$977$	56.3104	1.80153	0.900765	+	0.434307i	$0.143007\pi$
$978$	13.7042	0.438212
$979$	14.3984	0.460175
$980$	4.19642	0.134050
$981$	−61.8268	−1.97398
$982$	22.2980	0.711557
$983$	−34.5066	−1.10059	−0.550294	−	0.834971i	$-0.685484\pi$
$983$	−34.5066	−1.10059	−0.550294	+	0.834971i	$0.685484\pi$
$984$	−30.8143	−0.982323
$985$	8.19100	0.260987
$986$	6.76266	0.215367
$987$	−3.52910	−0.112332
$988$	0	0
$989$	−2.12491	−0.0675683
$990$	−43.9733	−1.39756
$991$	41.8969	1.33090	0.665449	−	0.746443i	$-0.268240\pi$
$991$	41.8969	1.33090	0.665449	+	0.746443i	$0.268240\pi$
$992$	−6.47773	−0.205668
$993$	−21.1267	−0.670435
$994$	−23.0566	−0.731311
$995$	5.94246	0.188388
$996$	−36.3972	−1.15329
$997$	−32.8243	−1.03955	−0.519777	−	0.854302i	$-0.673985\pi$
$997$	−32.8243	−1.03955	−0.519777	+	0.854302i	$0.673985\pi$
$998$	18.8766	0.597529
$999$	21.9724	0.695175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bi.1.8		9
19.9	even	9		190.2.k.d.81.3	yes	18
19.17	even	9		190.2.k.d.61.3	✓	18
19.18	odd	2		3610.2.a.bj.1.2		9
95.9	even	18		950.2.l.i.651.1		18
95.17	odd	36		950.2.u.g.99.3		36
95.28	odd	36		950.2.u.g.499.3		36
95.47	odd	36		950.2.u.g.499.4		36
95.74	even	18		950.2.l.i.251.1		18
95.93	odd	36		950.2.u.g.99.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.3	✓	18	19.17	even	9
190.2.k.d.81.3	yes	18	19.9	even	9
950.2.l.i.251.1		18	95.74	even	18
950.2.l.i.651.1		18	95.9	even	18
950.2.u.g.99.3		36	95.17	odd	36
950.2.u.g.99.4		36	95.93	odd	36
950.2.u.g.499.3		36	95.28	odd	36
950.2.u.g.499.4		36	95.47	odd	36
3610.2.a.bi.1.8		9	1.1	even	1	trivial
3610.2.a.bj.1.2		9	19.18	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.17969 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.17969 q^{6} -3.34610 q^{7} -1.00000 q^{8} +7.11045 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.17969 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.17969 q^{6} -3.34610 q^{7} -1.00000 q^{8} +7.11045 q^{9} -1.00000 q^{10} +6.18432 q^{11} +3.17969 q^{12} -0.738619 q^{13} +3.34610 q^{14} +3.17969 q^{15} +1.00000 q^{16} +0.868133 q^{17} -7.11045 q^{18} +1.00000 q^{20} -10.6396 q^{21} -6.18432 q^{22} -1.14347 q^{23} -3.17969 q^{24} +1.00000 q^{25} +0.738619 q^{26} +13.0700 q^{27} -3.34610 q^{28} -7.78988 q^{29} -3.17969 q^{30} +6.47773 q^{31} -1.00000 q^{32} +19.6643 q^{33} -0.868133 q^{34} -3.34610 q^{35} +7.11045 q^{36} +1.68113 q^{37} -2.34858 q^{39} -1.00000 q^{40} +9.69096 q^{41} +10.6396 q^{42} +1.85830 q^{43} +6.18432 q^{44} +7.11045 q^{45} +1.14347 q^{46} +0.331695 q^{47} +3.17969 q^{48} +4.19642 q^{49} -1.00000 q^{50} +2.76040 q^{51} -0.738619 q^{52} -7.10488 q^{53} -13.0700 q^{54} +6.18432 q^{55} +3.34610 q^{56} +7.78988 q^{58} +4.86030 q^{59} +3.17969 q^{60} +7.22757 q^{61} -6.47773 q^{62} -23.7923 q^{63} +1.00000 q^{64} -0.738619 q^{65} -19.6643 q^{66} +2.92493 q^{67} +0.868133 q^{68} -3.63589 q^{69} +3.34610 q^{70} -6.89058 q^{71} -7.11045 q^{72} +7.81666 q^{73} -1.68113 q^{74} +3.17969 q^{75} -20.6934 q^{77} +2.34858 q^{78} -2.29894 q^{79} +1.00000 q^{80} +20.2271 q^{81} -9.69096 q^{82} -11.4468 q^{83} -10.6396 q^{84} +0.868133 q^{85} -1.85830 q^{86} -24.7694 q^{87} -6.18432 q^{88} +2.32821 q^{89} -7.11045 q^{90} +2.47150 q^{91} -1.14347 q^{92} +20.5972 q^{93} -0.331695 q^{94} -3.17969 q^{96} -6.84406 q^{97} -4.19642 q^{98} +43.9733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

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