LMFDB - Embedded newform 3311.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,2,Mod(1,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, 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("3311.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3311.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:	$26.4384681092$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	3311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66765 q^{2} +0.718543 q^{3} +5.11634 q^{4} +4.04126 q^{5} -1.91682 q^{6} +1.00000 q^{7} -8.31331 q^{8} -2.48370 q^{9} +O(q^{10})$	\(q-2.66765 q^{2} +0.718543 q^{3} +5.11634 q^{4} +4.04126 q^{5} -1.91682 q^{6} +1.00000 q^{7} -8.31331 q^{8} -2.48370 q^{9} -10.7807 q^{10} +1.00000 q^{11} +3.67631 q^{12} +5.51938 q^{13} -2.66765 q^{14} +2.90382 q^{15} +11.9443 q^{16} -4.96805 q^{17} +6.62563 q^{18} +4.54206 q^{19} +20.6765 q^{20} +0.718543 q^{21} -2.66765 q^{22} +5.54439 q^{23} -5.97347 q^{24} +11.3318 q^{25} -14.7238 q^{26} -3.94027 q^{27} +5.11634 q^{28} -4.35655 q^{29} -7.74637 q^{30} -4.05602 q^{31} -15.2365 q^{32} +0.718543 q^{33} +13.2530 q^{34} +4.04126 q^{35} -12.7074 q^{36} +6.45896 q^{37} -12.1166 q^{38} +3.96591 q^{39} -33.5962 q^{40} -5.14577 q^{41} -1.91682 q^{42} +1.00000 q^{43} +5.11634 q^{44} -10.0373 q^{45} -14.7905 q^{46} +6.28439 q^{47} +8.58248 q^{48} +1.00000 q^{49} -30.2292 q^{50} -3.56976 q^{51} +28.2390 q^{52} -8.65248 q^{53} +10.5113 q^{54} +4.04126 q^{55} -8.31331 q^{56} +3.26366 q^{57} +11.6217 q^{58} +5.41422 q^{59} +14.8569 q^{60} -9.21586 q^{61} +10.8200 q^{62} -2.48370 q^{63} +16.7571 q^{64} +22.3052 q^{65} -1.91682 q^{66} +4.74573 q^{67} -25.4183 q^{68} +3.98388 q^{69} -10.7807 q^{70} +16.4133 q^{71} +20.6477 q^{72} -1.37440 q^{73} -17.2302 q^{74} +8.14238 q^{75} +23.2387 q^{76} +1.00000 q^{77} -10.5796 q^{78} +7.80555 q^{79} +48.2700 q^{80} +4.61983 q^{81} +13.7271 q^{82} -4.75614 q^{83} +3.67631 q^{84} -20.0772 q^{85} -2.66765 q^{86} -3.13037 q^{87} -8.31331 q^{88} +8.49796 q^{89} +26.7759 q^{90} +5.51938 q^{91} +28.3670 q^{92} -2.91443 q^{93} -16.7645 q^{94} +18.3556 q^{95} -10.9481 q^{96} -2.08406 q^{97} -2.66765 q^{98} -2.48370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9}+O(q^{10}) $ 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9} + 2 q^{10} + 38 q^{11} + 2 q^{12} + 8 q^{13} + 6 q^{14} + 26 q^{15} + 70 q^{16} + 3 q^{17} + 27 q^{18} + 10 q^{19} + 9 q^{20} + 7 q^{21} + 6 q^{22} + 22 q^{23} - 16 q^{24} + 82 q^{25} + 5 q^{26} + 28 q^{27} + 50 q^{28} + 24 q^{29} + 4 q^{30} + 13 q^{31} + 42 q^{32} + 7 q^{33} + 10 q^{34} + 8 q^{35} + 74 q^{36} + 45 q^{37} - 14 q^{38} + 14 q^{39} - 27 q^{40} - 13 q^{41} + 38 q^{43} + 50 q^{44} - 2 q^{45} + 3 q^{46} - 4 q^{47} - 7 q^{48} + 38 q^{49} - 5 q^{50} + 16 q^{51} + 22 q^{52} + 14 q^{53} - 55 q^{54} + 8 q^{55} + 18 q^{56} + 18 q^{57} + 47 q^{58} + 35 q^{59} + 61 q^{60} + 30 q^{61} + 4 q^{62} + 61 q^{63} + 96 q^{64} + 17 q^{65} + 50 q^{67} - 67 q^{68} + 42 q^{69} + 2 q^{70} + 41 q^{71} + 26 q^{72} + 29 q^{73} - 23 q^{74} + 32 q^{75} + 35 q^{76} + 38 q^{77} - 8 q^{78} + 51 q^{79} + 9 q^{80} + 98 q^{81} - 2 q^{82} - 51 q^{83} + 2 q^{84} + 22 q^{85} + 6 q^{86} - 39 q^{87} + 18 q^{88} + 50 q^{89} - 95 q^{90} + 8 q^{91} + q^{92} + 56 q^{93} + 3 q^{94} + 17 q^{95} - 105 q^{96} + 8 q^{97} + 6 q^{98} + 61 q^{99}+O(q^{100}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9 + 2 * q^10 + 38 * q^11 + 2 * q^12 + 8 * q^13 + 6 * q^14 + 26 * q^15 + 70 * q^16 + 3 * q^17 + 27 * q^18 + 10 * q^19 + 9 * q^20 + 7 * q^21 + 6 * q^22 + 22 * q^23 - 16 * q^24 + 82 * q^25 + 5 * q^26 + 28 * q^27 + 50 * q^28 + 24 * q^29 + 4 * q^30 + 13 * q^31 + 42 * q^32 + 7 * q^33 + 10 * q^34 + 8 * q^35 + 74 * q^36 + 45 * q^37 - 14 * q^38 + 14 * q^39 - 27 * q^40 - 13 * q^41 + 38 * q^43 + 50 * q^44 - 2 * q^45 + 3 * q^46 - 4 * q^47 - 7 * q^48 + 38 * q^49 - 5 * q^50 + 16 * q^51 + 22 * q^52 + 14 * q^53 - 55 * q^54 + 8 * q^55 + 18 * q^56 + 18 * q^57 + 47 * q^58 + 35 * q^59 + 61 * q^60 + 30 * q^61 + 4 * q^62 + 61 * q^63 + 96 * q^64 + 17 * q^65 + 50 * q^67 - 67 * q^68 + 42 * q^69 + 2 * q^70 + 41 * q^71 + 26 * q^72 + 29 * q^73 - 23 * q^74 + 32 * q^75 + 35 * q^76 + 38 * q^77 - 8 * q^78 + 51 * q^79 + 9 * q^80 + 98 * q^81 - 2 * q^82 - 51 * q^83 + 2 * q^84 + 22 * q^85 + 6 * q^86 - 39 * q^87 + 18 * q^88 + 50 * q^89 - 95 * q^90 + 8 * q^91 + q^92 + 56 * q^93 + 3 * q^94 + 17 * q^95 - 105 * q^96 + 8 * q^97 + 6 * q^98 + 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.66765	−1.88631	−0.943156	−	0.332351i	$-0.892158\pi$
$2$	−2.66765	−1.88631	−0.943156	+	0.332351i	$0.892158\pi$
$3$	0.718543	0.414851	0.207425	−	0.978251i	$-0.433492\pi$
$3$	0.718543	0.414851	0.207425	+	0.978251i	$0.433492\pi$
$4$	5.11634	2.55817
$5$	4.04126	1.80731	0.903653	−	0.428265i	$-0.140875\pi$
$5$	4.04126	1.80731	0.903653	+	0.428265i	$0.140875\pi$
$6$	−1.91682	−0.782538
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.31331	−2.93920
$9$	−2.48370	−0.827899
$10$	−10.7807	−3.40914
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.67631	1.06126
$13$	5.51938	1.53080	0.765400	−	0.643555i	$-0.222541\pi$
$13$	5.51938	1.53080	0.765400	+	0.643555i	$0.222541\pi$
$14$	−2.66765	−0.712959
$15$	2.90382	0.749763
$16$	11.9443	2.98607
$17$	−4.96805	−1.20493	−0.602465	−	0.798145i	$-0.705815\pi$
$17$	−4.96805	−1.20493	−0.602465	+	0.798145i	$0.705815\pi$
$18$	6.62563	1.56167
$19$	4.54206	1.04202	0.521010	−	0.853551i	$-0.325555\pi$
$19$	4.54206	1.04202	0.521010	+	0.853551i	$0.325555\pi$
$20$	20.6765	4.62340
$21$	0.718543	0.156799
$22$	−2.66765	−0.568744
$23$	5.54439	1.15609	0.578043	−	0.816006i	$-0.303817\pi$
$23$	5.54439	1.15609	0.578043	+	0.816006i	$0.303817\pi$
$24$	−5.97347	−1.21933
$25$	11.3318	2.26636
$26$	−14.7238	−2.88757
$27$	−3.94027	−0.758306
$28$	5.11634	0.966898
$29$	−4.35655	−0.808991	−0.404496	−	0.914540i	$-0.632553\pi$
$29$	−4.35655	−0.808991	−0.404496	+	0.914540i	$0.632553\pi$
$30$	−7.74637	−1.41429
$31$	−4.05602	−0.728483	−0.364241	−	0.931305i	$-0.618672\pi$
$31$	−4.05602	−0.728483	−0.364241	+	0.931305i	$0.618672\pi$
$32$	−15.2365	−2.69346
$33$	0.718543	0.125082
$34$	13.2530	2.27287
$35$	4.04126	0.683098
$36$	−12.7074	−2.11791
$37$	6.45896	1.06185	0.530924	−	0.847420i	$-0.321845\pi$
$37$	6.45896	1.06185	0.530924	+	0.847420i	$0.321845\pi$
$38$	−12.1166	−1.96557
$39$	3.96591	0.635054
$40$	−33.5962	−5.31203
$41$	−5.14577	−0.803634	−0.401817	−	0.915720i	$-0.631621\pi$
$41$	−5.14577	−0.803634	−0.401817	+	0.915720i	$0.631621\pi$
$42$	−1.91682	−0.295772
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.11634	0.771318
$45$	−10.0373	−1.49627
$46$	−14.7905	−2.18074
$47$	6.28439	0.916672	0.458336	−	0.888779i	$-0.348446\pi$
$47$	6.28439	0.916672	0.458336	+	0.888779i	$0.348446\pi$
$48$	8.58248	1.23877
$49$	1.00000	0.142857
$50$	−30.2292	−4.27506
$51$	−3.56976	−0.499866
$52$	28.2390	3.91605
$53$	−8.65248	−1.18851	−0.594255	−	0.804277i	$-0.702553\pi$
$53$	−8.65248	−1.18851	−0.594255	+	0.804277i	$0.702553\pi$
$54$	10.5113	1.43040
$55$	4.04126	0.544924
$56$	−8.31331	−1.11091
$57$	3.26366	0.432283
$58$	11.6217	1.52601
$59$	5.41422	0.704871	0.352436	−	0.935836i	$-0.385354\pi$
$59$	5.41422	0.704871	0.352436	+	0.935836i	$0.385354\pi$
$60$	14.8569	1.91802
$61$	−9.21586	−1.17997	−0.589985	−	0.807414i	$-0.700866\pi$
$61$	−9.21586	−1.17997	−0.589985	+	0.807414i	$0.700866\pi$
$62$	10.8200	1.37415
$63$	−2.48370	−0.312916
$64$	16.7571	2.09464
$65$	22.3052	2.76662
$66$	−1.91682	−0.235944
$67$	4.74573	0.579783	0.289891	−	0.957060i	$-0.406381\pi$
$67$	4.74573	0.579783	0.289891	+	0.957060i	$0.406381\pi$
$68$	−25.4183	−3.08242
$69$	3.98388	0.479603
$70$	−10.7807	−1.28854
$71$	16.4133	1.94789	0.973947	−	0.226774i	$-0.0728178\pi$
$71$	16.4133	1.94789	0.973947	+	0.226774i	$0.0728178\pi$
$72$	20.6477	2.43336
$73$	−1.37440	−0.160861	−0.0804304	−	0.996760i	$-0.525629\pi$
$73$	−1.37440	−0.160861	−0.0804304	+	0.996760i	$0.525629\pi$
$74$	−17.2302	−2.00297
$75$	8.14238	0.940201
$76$	23.2387	2.66567
$77$	1.00000	0.113961
$78$	−10.5796	−1.19791
$79$	7.80555	0.878193	0.439096	−	0.898440i	$-0.355299\pi$
$79$	7.80555	0.878193	0.439096	+	0.898440i	$0.355299\pi$
$80$	48.2700	5.39675
$81$	4.61983	0.513315
$82$	13.7271	1.51590
$83$	−4.75614	−0.522054	−0.261027	−	0.965331i	$-0.584061\pi$
$83$	−4.75614	−0.522054	−0.261027	+	0.965331i	$0.584061\pi$
$84$	3.67631	0.401119
$85$	−20.0772	−2.17768
$86$	−2.66765	−0.287660
$87$	−3.13037	−0.335611
$88$	−8.31331	−0.886201
$89$	8.49796	0.900782	0.450391	−	0.892832i	$-0.351285\pi$
$89$	8.49796	0.900782	0.450391	+	0.892832i	$0.351285\pi$
$90$	26.7759	2.82243
$91$	5.51938	0.578588
$92$	28.3670	2.95747
$93$	−2.91443	−0.302212
$94$	−16.7645	−1.72913
$95$	18.3556	1.88325
$96$	−10.9481	−1.11739
$97$	−2.08406	−0.211604	−0.105802	−	0.994387i	$-0.533741\pi$
$97$	−2.08406	−0.211604	−0.105802	+	0.994387i	$0.533741\pi$
$98$	−2.66765	−0.269473
$99$	−2.48370	−0.249621
$100$	57.9773	5.79773
$101$	1.94049	0.193086	0.0965429	−	0.995329i	$-0.469221\pi$
$101$	1.94049	0.193086	0.0965429	+	0.995329i	$0.469221\pi$
$102$	9.52286	0.942904
$103$	−6.58984	−0.649316	−0.324658	−	0.945831i	$-0.605249\pi$
$103$	−6.58984	−0.649316	−0.324658	+	0.945831i	$0.605249\pi$
$104$	−45.8843	−4.49932
$105$	2.90382	0.283384
$106$	23.0818	2.24190
$107$	−3.33886	−0.322780	−0.161390	−	0.986891i	$-0.551598\pi$
$107$	−3.33886	−0.322780	−0.161390	+	0.986891i	$0.551598\pi$
$108$	−20.1598	−1.93988
$109$	15.7840	1.51183	0.755915	−	0.654670i	$-0.227192\pi$
$109$	15.7840	1.51183	0.755915	+	0.654670i	$0.227192\pi$
$110$	−10.7807	−1.02790
$111$	4.64104	0.440508
$112$	11.9443	1.12863
$113$	−1.63450	−0.153761	−0.0768804	−	0.997040i	$-0.524496\pi$
$113$	−1.63450	−0.153761	−0.0768804	+	0.997040i	$0.524496\pi$
$114$	−8.70630	−0.815420
$115$	22.4063	2.08940
$116$	−22.2896	−2.06954
$117$	−13.7085	−1.26735
$118$	−14.4432	−1.32961
$119$	−4.96805	−0.455421
$120$	−24.1403	−2.20370
$121$	1.00000	0.0909091
$122$	24.5847	2.22579
$123$	−3.69746	−0.333388
$124$	−20.7520	−1.86358
$125$	25.5884	2.28870
$126$	6.62563	0.590258
$127$	4.27072	0.378965	0.189482	−	0.981884i	$-0.439319\pi$
$127$	4.27072	0.378965	0.189482	+	0.981884i	$0.439319\pi$
$128$	−14.2290	−1.25768
$129$	0.718543	0.0632642
$130$	−59.5025	−5.21872
$131$	−8.48525	−0.741359	−0.370680	−	0.928761i	$-0.620875\pi$
$131$	−8.48525	−0.741359	−0.370680	+	0.928761i	$0.620875\pi$
$132$	3.67631	0.319982
$133$	4.54206	0.393846
$134$	−12.6599	−1.09365
$135$	−15.9237	−1.37049
$136$	41.3010	3.54153
$137$	12.5750	1.07436	0.537179	−	0.843468i	$-0.319490\pi$
$137$	12.5750	1.07436	0.537179	+	0.843468i	$0.319490\pi$
$138$	−10.6276	−0.904681
$139$	−12.9013	−1.09427	−0.547137	−	0.837043i	$-0.684282\pi$
$139$	−12.9013	−1.09427	−0.547137	+	0.837043i	$0.684282\pi$
$140$	20.6765	1.74748
$141$	4.51560	0.380282
$142$	−43.7848	−3.67434
$143$	5.51938	0.461554
$144$	−29.6660	−2.47216
$145$	−17.6060	−1.46210
$146$	3.66640	0.303434
$147$	0.718543	0.0592644
$148$	33.0463	2.71639
$149$	−11.0637	−0.906375	−0.453187	−	0.891415i	$-0.649713\pi$
$149$	−11.0637	−0.906375	−0.453187	+	0.891415i	$0.649713\pi$
$150$	−21.7210	−1.77351
$151$	23.0736	1.87771	0.938853	−	0.344317i	$-0.111890\pi$
$151$	23.0736	1.87771	0.938853	+	0.344317i	$0.111890\pi$
$152$	−37.7595	−3.06270
$153$	12.3391	0.997560
$154$	−2.66765	−0.214965
$155$	−16.3914	−1.31659
$156$	20.2910	1.62458
$157$	3.59102	0.286594	0.143297	−	0.989680i	$-0.454230\pi$
$157$	3.59102	0.286594	0.143297	+	0.989680i	$0.454230\pi$
$158$	−20.8225	−1.65655
$159$	−6.21718	−0.493054
$160$	−61.5748	−4.86791
$161$	5.54439	0.436959
$162$	−12.3241	−0.968272
$163$	−23.6797	−1.85473	−0.927367	−	0.374153i	$-0.877933\pi$
$163$	−23.6797	−1.85473	−0.927367	+	0.374153i	$0.877933\pi$
$164$	−26.3275	−2.05583
$165$	2.90382	0.226062
$166$	12.6877	0.984757
$167$	−21.4040	−1.65629	−0.828144	−	0.560516i	$-0.810603\pi$
$167$	−21.4040	−1.65629	−0.828144	+	0.560516i	$0.810603\pi$
$168$	−5.97347	−0.460863
$169$	17.4635	1.34335
$170$	53.5589	4.10778
$171$	−11.2811	−0.862687
$172$	5.11634	0.390118
$173$	−2.77519	−0.210994	−0.105497	−	0.994420i	$-0.533643\pi$
$173$	−2.77519	−0.210994	−0.105497	+	0.994420i	$0.533643\pi$
$174$	8.35072	0.633067
$175$	11.3318	0.856603
$176$	11.9443	0.900334
$177$	3.89035	0.292416
$178$	−22.6696	−1.69915
$179$	−3.19007	−0.238437	−0.119219	−	0.992868i	$-0.538039\pi$
$179$	−3.19007	−0.238437	−0.119219	+	0.992868i	$0.538039\pi$
$180$	−51.3541	−3.82771
$181$	10.9975	0.817436	0.408718	−	0.912661i	$-0.365976\pi$
$181$	10.9975	0.817436	0.408718	+	0.912661i	$0.365976\pi$
$182$	−14.7238	−1.09140
$183$	−6.62199	−0.489512
$184$	−46.0922	−3.39796
$185$	26.1024	1.91908
$186$	7.77466	0.570066
$187$	−4.96805	−0.363300
$188$	32.1531	2.34501
$189$	−3.94027	−0.286613
$190$	−48.9664	−3.55239
$191$	−20.1120	−1.45526	−0.727628	−	0.685972i	$-0.759377\pi$
$191$	−20.1120	−1.45526	−0.727628	+	0.685972i	$0.759377\pi$
$192$	12.0407	0.868963
$193$	18.0089	1.29631	0.648155	−	0.761508i	$-0.275541\pi$
$193$	18.0089	1.29631	0.648155	+	0.761508i	$0.275541\pi$
$194$	5.55954	0.399152
$195$	16.0273	1.14774
$196$	5.11634	0.365453
$197$	3.97398	0.283134	0.141567	−	0.989929i	$-0.454786\pi$
$197$	3.97398	0.283134	0.141567	+	0.989929i	$0.454786\pi$
$198$	6.62563	0.470863
$199$	11.0924	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$199$	11.0924	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$200$	−94.2046	−6.66127
$201$	3.41001	0.240523
$202$	−5.17654	−0.364220
$203$	−4.35655	−0.305770
$204$	−18.2641	−1.27874
$205$	−20.7954	−1.45241
$206$	17.5794	1.22481
$207$	−13.7706	−0.957122
$208$	65.9250	4.57108
$209$	4.54206	0.314181
$210$	−7.74637	−0.534550
$211$	−26.1500	−1.80024	−0.900119	−	0.435645i	$-0.856520\pi$
$211$	−26.1500	−1.80024	−0.900119	+	0.435645i	$0.856520\pi$
$212$	−44.2691	−3.04041
$213$	11.7936	0.808086
$214$	8.90691	0.608864
$215$	4.04126	0.275612
$216$	32.7567	2.22881
$217$	−4.05602	−0.275341
$218$	−42.1060	−2.85178
$219$	−0.987562	−0.0667333
$220$	20.6765	1.39401
$221$	−27.4206	−1.84451
$222$	−12.3807	−0.830936
$223$	−26.5212	−1.77599	−0.887996	−	0.459852i	$-0.847902\pi$
$223$	−26.5212	−1.77599	−0.887996	+	0.459852i	$0.847902\pi$
$224$	−15.2365	−1.01803
$225$	−28.1447	−1.87631
$226$	4.36027	0.290041
$227$	−9.71559	−0.644847	−0.322423	−	0.946596i	$-0.604497\pi$
$227$	−9.71559	−0.644847	−0.322423	+	0.946596i	$0.604497\pi$
$228$	16.6980	1.10585
$229$	−10.0568	−0.664574	−0.332287	−	0.943178i	$-0.607820\pi$
$229$	−10.0568	−0.664574	−0.332287	+	0.943178i	$0.607820\pi$
$230$	−59.7722	−3.94126
$231$	0.718543	0.0472767
$232$	36.2173	2.37779
$233$	−1.75180	−0.114764	−0.0573820	−	0.998352i	$-0.518275\pi$
$233$	−1.75180	−0.114764	−0.0573820	+	0.998352i	$0.518275\pi$
$234$	36.5693	2.39061
$235$	25.3969	1.65671
$236$	27.7010	1.80318
$237$	5.60862	0.364319
$238$	13.2530	0.859066
$239$	13.0129	0.841735	0.420867	−	0.907122i	$-0.361726\pi$
$239$	13.0129	0.841735	0.420867	+	0.907122i	$0.361726\pi$
$240$	34.6840	2.23885
$241$	19.3503	1.24646	0.623230	−	0.782039i	$-0.285820\pi$
$241$	19.3503	1.24646	0.623230	+	0.782039i	$0.285820\pi$
$242$	−2.66765	−0.171483
$243$	15.1404	0.971255
$244$	−47.1515	−3.01857
$245$	4.04126	0.258187
$246$	9.86351	0.628874
$247$	25.0693	1.59512
$248$	33.7189	2.14116
$249$	−3.41749	−0.216575
$250$	−68.2609	−4.31720
$251$	12.7283	0.803402	0.401701	−	0.915771i	$-0.368419\pi$
$251$	12.7283	0.803402	0.401701	+	0.915771i	$0.368419\pi$
$252$	−12.7074	−0.800494
$253$	5.54439	0.348573
$254$	−11.3928	−0.714846
$255$	−14.4263	−0.903412
$256$	4.44380	0.277737
$257$	8.99621	0.561168	0.280584	−	0.959829i	$-0.409472\pi$
$257$	8.99621	0.561168	0.280584	+	0.959829i	$0.409472\pi$
$258$	−1.91682	−0.119336
$259$	6.45896	0.401341
$260$	114.121	7.07750
$261$	10.8203	0.669763
$262$	22.6356	1.39843
$263$	0.691192	0.0426207	0.0213104	−	0.999773i	$-0.493216\pi$
$263$	0.691192	0.0426207	0.0213104	+	0.999773i	$0.493216\pi$
$264$	−5.97347	−0.367641
$265$	−34.9669	−2.14800
$266$	−12.1166	−0.742917
$267$	6.10615	0.373690
$268$	24.2808	1.48318
$269$	−12.4212	−0.757335	−0.378668	−	0.925533i	$-0.623618\pi$
$269$	−12.4212	−0.757335	−0.378668	+	0.925533i	$0.623618\pi$
$270$	42.4787	2.58517
$271$	5.61315	0.340975	0.170487	−	0.985360i	$-0.445466\pi$
$271$	5.61315	0.340975	0.170487	+	0.985360i	$0.445466\pi$
$272$	−59.3399	−3.59801
$273$	3.96591	0.240028
$274$	−33.5458	−2.02657
$275$	11.3318	0.683333
$276$	20.3829	1.22691
$277$	28.9996	1.74242	0.871210	−	0.490911i	$-0.163336\pi$
$277$	28.9996	1.74242	0.871210	+	0.490911i	$0.163336\pi$
$278$	34.4161	2.06414
$279$	10.0739	0.603110
$280$	−33.5962	−2.00776
$281$	2.30609	0.137570	0.0687848	−	0.997632i	$-0.478088\pi$
$281$	2.30609	0.137570	0.0687848	+	0.997632i	$0.478088\pi$
$282$	−12.0460	−0.717331
$283$	−4.99388	−0.296856	−0.148428	−	0.988923i	$-0.547421\pi$
$283$	−4.99388	−0.296856	−0.148428	+	0.988923i	$0.547421\pi$
$284$	83.9758	4.98305
$285$	13.1893	0.781268
$286$	−14.7238	−0.870634
$287$	−5.14577	−0.303745
$288$	37.8429	2.22991
$289$	7.68156	0.451857
$290$	46.9665	2.75797
$291$	−1.49749	−0.0877842
$292$	−7.03188	−0.411510
$293$	25.4346	1.48591	0.742953	−	0.669343i	$-0.233424\pi$
$293$	25.4346	1.48591	0.742953	+	0.669343i	$0.233424\pi$
$294$	−1.91682	−0.111791
$295$	21.8803	1.27392
$296$	−53.6953	−3.12098
$297$	−3.94027	−0.228638
$298$	29.5141	1.70971
$299$	30.6016	1.76974
$300$	41.6592	2.40519
$301$	1.00000	0.0576390
$302$	−61.5524	−3.54194
$303$	1.39432	0.0801018
$304$	54.2516	3.11154
$305$	−37.2437	−2.13257
$306$	−32.9165	−1.88171
$307$	−0.258332	−0.0147438	−0.00737188	−	0.999973i	$-0.502347\pi$
$307$	−0.258332	−0.0147438	−0.00737188	+	0.999973i	$0.502347\pi$
$308$	5.11634	0.291531
$309$	−4.73508	−0.269369
$310$	43.7266	2.48350
$311$	23.8530	1.35258	0.676289	−	0.736636i	$-0.263587\pi$
$311$	23.8530	1.35258	0.676289	+	0.736636i	$0.263587\pi$
$312$	−32.9698	−1.86655
$313$	−29.0283	−1.64078	−0.820388	−	0.571807i	$-0.806243\pi$
$313$	−29.0283	−1.64078	−0.820388	+	0.571807i	$0.806243\pi$
$314$	−9.57957	−0.540607
$315$	−10.0373	−0.565536
$316$	39.9359	2.24657
$317$	−20.6165	−1.15794	−0.578968	−	0.815350i	$-0.696544\pi$
$317$	−20.6165	−1.15794	−0.578968	+	0.815350i	$0.696544\pi$
$318$	16.5852	0.930054
$319$	−4.35655	−0.243920
$320$	67.7199	3.78566
$321$	−2.39912	−0.133906
$322$	−14.7905	−0.824241
$323$	−22.5652	−1.25556
$324$	23.6367	1.31315
$325$	62.5444	3.46934
$326$	63.1690	3.49861
$327$	11.3415	0.627184
$328$	42.7784	2.36204
$329$	6.28439	0.346470
$330$	−7.74637	−0.426423
$331$	30.8442	1.69535	0.847676	−	0.530515i	$-0.178001\pi$
$331$	30.8442	1.69535	0.847676	+	0.530515i	$0.178001\pi$
$332$	−24.3341	−1.33550
$333$	−16.0421	−0.879102
$334$	57.0982	3.12427
$335$	19.1787	1.04785
$336$	8.58248	0.468213
$337$	−8.60361	−0.468668	−0.234334	−	0.972156i	$-0.575291\pi$
$337$	−8.60361	−0.468668	−0.234334	+	0.972156i	$0.575291\pi$
$338$	−46.5865	−2.53397
$339$	−1.17446	−0.0637878
$340$	−102.722	−5.57088
$341$	−4.05602	−0.219646
$342$	30.0940	1.62730
$343$	1.00000	0.0539949
$344$	−8.31331	−0.448223
$345$	16.0999	0.866790
$346$	7.40322	0.398000
$347$	−35.2002	−1.88965	−0.944823	−	0.327582i	$-0.893766\pi$
$347$	−35.2002	−1.88965	−0.944823	+	0.327582i	$0.893766\pi$
$348$	−16.0160	−0.858550
$349$	32.3400	1.73112	0.865560	−	0.500805i	$-0.166963\pi$
$349$	32.3400	1.73112	0.865560	+	0.500805i	$0.166963\pi$
$350$	−30.2292	−1.61582
$351$	−21.7478	−1.16081
$352$	−15.2365	−0.812110
$353$	−30.5999	−1.62867	−0.814335	−	0.580395i	$-0.802898\pi$
$353$	−30.5999	−1.62867	−0.814335	+	0.580395i	$0.802898\pi$
$354$	−10.3781	−0.551589
$355$	66.3302	3.52044
$356$	43.4785	2.30435
$357$	−3.56976	−0.188932
$358$	8.50999	0.449767
$359$	−26.3034	−1.38824	−0.694119	−	0.719860i	$-0.744206\pi$
$359$	−26.3034	−1.38824	−0.694119	+	0.719860i	$0.744206\pi$
$360$	83.4428	4.39782
$361$	1.63029	0.0858048
$362$	−29.3374	−1.54194
$363$	0.718543	0.0377137
$364$	28.2390	1.48013
$365$	−5.55429	−0.290725
$366$	17.6651	0.923372
$367$	−21.6637	−1.13083	−0.565417	−	0.824805i	$-0.691285\pi$
$367$	−21.6637	−1.13083	−0.565417	+	0.824805i	$0.691285\pi$
$368$	66.2238	3.45215
$369$	12.7805	0.665328
$370$	−69.6319	−3.61999
$371$	−8.65248	−0.449215
$372$	−14.9112	−0.773110
$373$	6.51494	0.337331	0.168665	−	0.985673i	$-0.446054\pi$
$373$	6.51494	0.337331	0.168665	+	0.985673i	$0.446054\pi$
$374$	13.2530	0.685297
$375$	18.3864	0.949468
$376$	−52.2440	−2.69428
$377$	−24.0454	−1.23840
$378$	10.5113	0.540641
$379$	−0.504547	−0.0259168	−0.0129584	−	0.999916i	$-0.504125\pi$
$379$	−0.504547	−0.0259168	−0.0129584	+	0.999916i	$0.504125\pi$
$380$	93.9138	4.81767
$381$	3.06869	0.157214
$382$	53.6519	2.74507
$383$	−17.2899	−0.883471	−0.441735	−	0.897145i	$-0.645637\pi$
$383$	−17.2899	−0.883471	−0.441735	+	0.897145i	$0.645637\pi$
$384$	−10.2242	−0.521750
$385$	4.04126	0.205962
$386$	−48.0415	−2.44525
$387$	−2.48370	−0.126253
$388$	−10.6628	−0.541320
$389$	−23.4726	−1.19011	−0.595054	−	0.803686i	$-0.702869\pi$
$389$	−23.4726	−1.19011	−0.595054	+	0.803686i	$0.702869\pi$
$390$	−42.7551	−2.16499
$391$	−27.5448	−1.39300
$392$	−8.31331	−0.419885
$393$	−6.09701	−0.307554
$394$	−10.6012	−0.534079
$395$	31.5443	1.58716
$396$	−12.7074	−0.638573
$397$	10.7754	0.540802	0.270401	−	0.962748i	$-0.412844\pi$
$397$	10.7754	0.540802	0.270401	+	0.962748i	$0.412844\pi$
$398$	−29.5906	−1.48324
$399$	3.26366	0.163388
$400$	135.350	6.76751
$401$	37.8190	1.88859	0.944294	−	0.329102i	$-0.106746\pi$
$401$	37.8190	1.88859	0.944294	+	0.329102i	$0.106746\pi$
$402$	−9.09670	−0.453702
$403$	−22.3867	−1.11516
$404$	9.92821	0.493947
$405$	18.6700	0.927718
$406$	11.6217	0.576777
$407$	6.45896	0.320159
$408$	29.6765	1.46921
$409$	22.3467	1.10497	0.552487	−	0.833522i	$-0.313679\pi$
$409$	22.3467	1.10497	0.552487	+	0.833522i	$0.313679\pi$
$410$	55.4748	2.73970
$411$	9.03570	0.445698
$412$	−33.7159	−1.66106
$413$	5.41422	0.266416
$414$	36.7351	1.80543
$415$	−19.2208	−0.943512
$416$	−84.0961	−4.12315
$417$	−9.27014	−0.453961
$418$	−12.1166	−0.592643
$419$	−19.3391	−0.944775	−0.472388	−	0.881391i	$-0.656608\pi$
$419$	−19.3391	−0.944775	−0.472388	+	0.881391i	$0.656608\pi$
$420$	14.8569	0.724944
$421$	−22.7545	−1.10899	−0.554494	−	0.832188i	$-0.687088\pi$
$421$	−22.7545	−1.10899	−0.554494	+	0.832188i	$0.687088\pi$
$422$	69.7589	3.39581
$423$	−15.6085	−0.758912
$424$	71.9307	3.49327
$425$	−56.2969	−2.73080
$426$	−31.4612	−1.52430
$427$	−9.21586	−0.445987
$428$	−17.0828	−0.825727
$429$	3.96591	0.191476
$430$	−10.7807	−0.519890
$431$	13.3893	0.644941	0.322470	−	0.946580i	$-0.395487\pi$
$431$	13.3893	0.644941	0.322470	+	0.946580i	$0.395487\pi$
$432$	−47.0637	−2.26435
$433$	8.99946	0.432486	0.216243	−	0.976340i	$-0.430620\pi$
$433$	8.99946	0.432486	0.216243	+	0.976340i	$0.430620\pi$
$434$	10.8200	0.519378
$435$	−12.6506	−0.606552
$436$	80.7562	3.86752
$437$	25.1830	1.20466
$438$	2.63447	0.125880
$439$	−14.6762	−0.700458	−0.350229	−	0.936664i	$-0.613896\pi$
$439$	−14.6762	−0.700458	−0.350229	+	0.936664i	$0.613896\pi$
$440$	−33.5962	−1.60164
$441$	−2.48370	−0.118271
$442$	73.1484	3.47932
$443$	−38.5012	−1.82925	−0.914623	−	0.404309i	$-0.867512\pi$
$443$	−38.5012	−1.82925	−0.914623	+	0.404309i	$0.867512\pi$
$444$	23.7452	1.12690
$445$	34.3425	1.62799
$446$	70.7492	3.35007
$447$	−7.94976	−0.376011
$448$	16.7571	0.791699
$449$	−15.3942	−0.726496	−0.363248	−	0.931692i	$-0.618332\pi$
$449$	−15.3942	−0.726496	−0.363248	+	0.931692i	$0.618332\pi$
$450$	75.0802	3.53931
$451$	−5.14577	−0.242305
$452$	−8.36266	−0.393347
$453$	16.5794	0.778968
$454$	25.9178	1.21638
$455$	22.3052	1.04569
$456$	−27.1318	−1.27056
$457$	19.6770	0.920451	0.460225	−	0.887802i	$-0.347769\pi$
$457$	19.6770	0.920451	0.460225	+	0.887802i	$0.347769\pi$
$458$	26.8281	1.25359
$459$	19.5755	0.913705
$460$	114.639	5.34505
$461$	−39.2452	−1.82783	−0.913915	−	0.405905i	$-0.866956\pi$
$461$	−39.2452	−1.82783	−0.913915	+	0.405905i	$0.866956\pi$
$462$	−1.91682	−0.0891785
$463$	3.25597	0.151318	0.0756589	−	0.997134i	$-0.475894\pi$
$463$	3.25597	0.151318	0.0756589	+	0.997134i	$0.475894\pi$
$464$	−52.0359	−2.41571
$465$	−11.7780	−0.546190
$466$	4.67318	0.216481
$467$	−12.6213	−0.584043	−0.292022	−	0.956412i	$-0.594328\pi$
$467$	−12.6213	−0.584043	−0.292022	+	0.956412i	$0.594328\pi$
$468$	−70.1372	−3.24209
$469$	4.74573	0.219137
$470$	−67.7499	−3.12507
$471$	2.58030	0.118894
$472$	−45.0100	−2.07176
$473$	1.00000	0.0459800
$474$	−14.9618	−0.687220
$475$	51.4696	2.36159
$476$	−25.4183	−1.16504
$477$	21.4901	0.983966
$478$	−34.7138	−1.58777
$479$	40.0532	1.83008	0.915038	−	0.403368i	$-0.132161\pi$
$479$	40.0532	1.83008	0.915038	+	0.403368i	$0.132161\pi$
$480$	−44.2441	−2.01946
$481$	35.6495	1.62548
$482$	−51.6196	−2.35121
$483$	3.98388	0.181273
$484$	5.11634	0.232561
$485$	−8.42223	−0.382434
$486$	−40.3892	−1.83209
$487$	−13.9768	−0.633348	−0.316674	−	0.948534i	$-0.602566\pi$
$487$	−13.9768	−0.633348	−0.316674	+	0.948534i	$0.602566\pi$
$488$	76.6143	3.46817
$489$	−17.0149	−0.769438
$490$	−10.7807	−0.487021
$491$	−16.9512	−0.764999	−0.382499	−	0.923956i	$-0.624937\pi$
$491$	−16.9512	−0.764999	−0.382499	+	0.923956i	$0.624937\pi$
$492$	−18.9175	−0.852865
$493$	21.6436	0.974778
$494$	−66.8761	−3.00890
$495$	−10.0373	−0.451141
$496$	−48.4463	−2.17530
$497$	16.4133	0.736235
$498$	9.11666	0.408528
$499$	38.3649	1.71745	0.858725	−	0.512437i	$-0.171257\pi$
$499$	38.3649	1.71745	0.858725	+	0.512437i	$0.171257\pi$
$500$	130.919	5.85488
$501$	−15.3797	−0.687112
$502$	−33.9546	−1.51547
$503$	2.55024	0.113710	0.0568548	−	0.998382i	$-0.481893\pi$
$503$	2.55024	0.113710	0.0568548	+	0.998382i	$0.481893\pi$
$504$	20.6477	0.919723
$505$	7.84202	0.348965
$506$	−14.7905	−0.657517
$507$	12.5483	0.557289
$508$	21.8505	0.969457
$509$	42.3211	1.87585	0.937924	−	0.346841i	$-0.112746\pi$
$509$	42.3211	1.87585	0.937924	+	0.346841i	$0.112746\pi$
$510$	38.4844	1.70412
$511$	−1.37440	−0.0607997
$512$	16.6036	0.733781
$513$	−17.8969	−0.790169
$514$	−23.9987	−1.05854
$515$	−26.6312	−1.17351
$516$	3.67631	0.161841
$517$	6.28439	0.276387
$518$	−17.2302	−0.757053
$519$	−1.99409	−0.0875309
$520$	−185.430	−8.13166
$521$	25.2903	1.10799	0.553994	−	0.832521i	$-0.313103\pi$
$521$	25.2903	1.10799	0.553994	+	0.832521i	$0.313103\pi$
$522$	−28.8649	−1.26338
$523$	−20.0521	−0.876818	−0.438409	−	0.898776i	$-0.644458\pi$
$523$	−20.0521	−0.876818	−0.438409	+	0.898776i	$0.644458\pi$
$524$	−43.4134	−1.89652
$525$	8.14238	0.355362
$526$	−1.84386	−0.0803960
$527$	20.1505	0.877771
$528$	8.58248	0.373505
$529$	7.74029	0.336534
$530$	93.2795	4.05180
$531$	−13.4473	−0.583562
$532$	23.2387	1.00753
$533$	−28.4014	−1.23020
$534$	−16.2890	−0.704896
$535$	−13.4932	−0.583362
$536$	−39.4527	−1.70410
$537$	−2.29220	−0.0989159
$538$	33.1354	1.42857
$539$	1.00000	0.0430730
$540$	−81.4709	−3.50595
$541$	20.8151	0.894910	0.447455	−	0.894306i	$-0.352330\pi$
$541$	20.8151	0.894910	0.447455	+	0.894306i	$0.352330\pi$
$542$	−14.9739	−0.643185
$543$	7.90216	0.339114
$544$	75.6959	3.24543
$545$	63.7871	2.73234
$546$	−10.5796	−0.452767
$547$	−14.9240	−0.638106	−0.319053	−	0.947737i	$-0.603365\pi$
$547$	−14.9240	−0.638106	−0.319053	+	0.947737i	$0.603365\pi$
$548$	64.3382	2.74839
$549$	22.8894	0.976896
$550$	−30.2292	−1.28898
$551$	−19.7877	−0.842985
$552$	−33.1192	−1.40965
$553$	7.80555	0.331926
$554$	−77.3608	−3.28675
$555$	18.7557	0.796134
$556$	−66.0075	−2.79934
$557$	29.0292	1.23000	0.615002	−	0.788525i	$-0.289155\pi$
$557$	29.0292	1.23000	0.615002	+	0.788525i	$0.289155\pi$
$558$	−26.8737	−1.13765
$559$	5.51938	0.233445
$560$	48.2700	2.03978
$561$	−3.56976	−0.150715
$562$	−6.15183	−0.259499
$563$	−8.06217	−0.339780	−0.169890	−	0.985463i	$-0.554341\pi$
$563$	−8.06217	−0.339780	−0.169890	+	0.985463i	$0.554341\pi$
$564$	23.1034	0.972828
$565$	−6.60544	−0.277893
$566$	13.3219	0.559962
$567$	4.61983	0.194015
$568$	−136.448	−5.72525
$569$	−38.3710	−1.60860	−0.804298	−	0.594226i	$-0.797458\pi$
$569$	−38.3710	−1.60860	−0.804298	+	0.594226i	$0.797458\pi$
$570$	−35.1844	−1.47371
$571$	−6.07796	−0.254355	−0.127177	−	0.991880i	$-0.540592\pi$
$571$	−6.07796	−0.254355	−0.127177	+	0.991880i	$0.540592\pi$
$572$	28.2390	1.18073
$573$	−14.4514	−0.603715
$574$	13.7271	0.572958
$575$	62.8279	2.62010
$576$	−41.6196	−1.73415
$577$	−22.4641	−0.935191	−0.467595	−	0.883943i	$-0.654880\pi$
$577$	−22.4641	−0.935191	−0.467595	+	0.883943i	$0.654880\pi$
$578$	−20.4917	−0.852343
$579$	12.9402	0.537776
$580$	−90.0781	−3.74029
$581$	−4.75614	−0.197318
$582$	3.99477	0.165588
$583$	−8.65248	−0.358349
$584$	11.4258	0.472802
$585$	−55.3994	−2.29049
$586$	−67.8506	−2.80288
$587$	16.2393	0.670266	0.335133	−	0.942171i	$-0.391219\pi$
$587$	16.2393	0.670266	0.335133	+	0.942171i	$0.391219\pi$
$588$	3.67631	0.151609
$589$	−18.4227	−0.759093
$590$	−58.3688	−2.40301
$591$	2.85547	0.117459
$592$	77.1477	3.17075
$593$	−32.2290	−1.32348	−0.661742	−	0.749731i	$-0.730183\pi$
$593$	−32.2290	−1.32348	−0.661742	+	0.749731i	$0.730183\pi$
$594$	10.5113	0.431282
$595$	−20.0772	−0.823085
$596$	−56.6058	−2.31866
$597$	7.97035	0.326205
$598$	−81.6343	−3.33827
$599$	12.6481	0.516786	0.258393	−	0.966040i	$-0.416807\pi$
$599$	12.6481	0.516786	0.258393	+	0.966040i	$0.416807\pi$
$600$	−67.6901	−2.76344
$601$	28.7633	1.17328	0.586639	−	0.809848i	$-0.300451\pi$
$601$	28.7633	1.17328	0.586639	+	0.809848i	$0.300451\pi$
$602$	−2.66765	−0.108725
$603$	−11.7869	−0.480001
$604$	118.053	4.80350
$605$	4.04126	0.164301
$606$	−3.71957	−0.151097
$607$	14.2489	0.578346	0.289173	−	0.957277i	$-0.406620\pi$
$607$	14.2489	0.578346	0.289173	+	0.957277i	$0.406620\pi$
$608$	−69.2052	−2.80664
$609$	−3.13037	−0.126849
$610$	99.3531	4.02269
$611$	34.6859	1.40324
$612$	63.1313	2.55193
$613$	28.5551	1.15333	0.576664	−	0.816981i	$-0.304354\pi$
$613$	28.5551	1.15333	0.576664	+	0.816981i	$0.304354\pi$
$614$	0.689137	0.0278113
$615$	−14.9424	−0.602535
$616$	−8.31331	−0.334953
$617$	18.1765	0.731759	0.365880	−	0.930662i	$-0.380768\pi$
$617$	18.1765	0.731759	0.365880	+	0.930662i	$0.380768\pi$
$618$	12.6315	0.508115
$619$	−46.0766	−1.85197	−0.925987	−	0.377556i	$-0.876764\pi$
$619$	−46.0766	−1.85197	−0.925987	+	0.377556i	$0.876764\pi$
$620$	−83.8642	−3.36807
$621$	−21.8464	−0.876666
$622$	−63.6314	−2.55139
$623$	8.49796	0.340463
$624$	47.3699	1.89632
$625$	46.7505	1.87002
$626$	77.4373	3.09502
$627$	3.26366	0.130338
$628$	18.3729	0.733158
$629$	−32.0885	−1.27945
$630$	26.7759	1.06678
$631$	−16.0331	−0.638269	−0.319135	−	0.947709i	$-0.603392\pi$
$631$	−16.0331	−0.638269	−0.319135	+	0.947709i	$0.603392\pi$
$632$	−64.8899	−2.58118
$633$	−18.7899	−0.746830
$634$	54.9975	2.18423
$635$	17.2591	0.684906
$636$	−31.8092	−1.26132
$637$	5.51938	0.218686
$638$	11.6217	0.460109
$639$	−40.7655	−1.61266
$640$	−57.5032	−2.27301
$641$	4.25668	0.168129	0.0840644	−	0.996460i	$-0.473210\pi$
$641$	4.25668	0.168129	0.0840644	+	0.996460i	$0.473210\pi$
$642$	6.39999	0.252588
$643$	−2.47779	−0.0977145	−0.0488572	−	0.998806i	$-0.515558\pi$
$643$	−2.47779	−0.0977145	−0.0488572	+	0.998806i	$0.515558\pi$
$644$	28.3670	1.11782
$645$	2.90382	0.114338
$646$	60.1960	2.36838
$647$	39.8310	1.56592	0.782959	−	0.622073i	$-0.213709\pi$
$647$	39.8310	1.56592	0.782959	+	0.622073i	$0.213709\pi$
$648$	−38.4061	−1.50873
$649$	5.41422	0.212527
$650$	−166.846	−6.54426
$651$	−2.91443	−0.114225
$652$	−121.153	−4.74473
$653$	−28.3938	−1.11113	−0.555567	−	0.831472i	$-0.687499\pi$
$653$	−28.3938	−1.11113	−0.555567	+	0.831472i	$0.687499\pi$
$654$	−30.2550	−1.18306
$655$	−34.2911	−1.33986
$656$	−61.4625	−2.39971
$657$	3.41358	0.133176
$658$	−16.7645	−0.653550
$659$	−37.1416	−1.44683	−0.723415	−	0.690414i	$-0.757428\pi$
$659$	−37.1416	−1.44683	−0.723415	+	0.690414i	$0.757428\pi$
$660$	14.8569	0.578306
$661$	5.24905	0.204165	0.102082	−	0.994776i	$-0.467450\pi$
$661$	5.24905	0.204165	0.102082	+	0.994776i	$0.467450\pi$
$662$	−82.2815	−3.19796
$663$	−19.7029	−0.765195
$664$	39.5393	1.53442
$665$	18.3556	0.711801
$666$	42.7947	1.65826
$667$	−24.1544	−0.935263
$668$	−109.510	−4.23707
$669$	−19.0566	−0.736772
$670$	−51.1621	−1.97656
$671$	−9.21586	−0.355774
$672$	−10.9481	−0.422332
$673$	−33.2139	−1.28030	−0.640150	−	0.768250i	$-0.721128\pi$
$673$	−33.2139	−1.28030	−0.640150	+	0.768250i	$0.721128\pi$
$674$	22.9514	0.884055
$675$	−44.6503	−1.71859
$676$	89.3494	3.43652
$677$	21.1752	0.813830	0.406915	−	0.913466i	$-0.366605\pi$
$677$	21.1752	0.813830	0.406915	+	0.913466i	$0.366605\pi$
$678$	3.13304	0.120324
$679$	−2.08406	−0.0799789
$680$	166.908	6.40063
$681$	−6.98107	−0.267515
$682$	10.8200	0.414321
$683$	13.5577	0.518769	0.259385	−	0.965774i	$-0.416480\pi$
$683$	13.5577	0.518769	0.259385	+	0.965774i	$0.416480\pi$
$684$	−57.7179	−2.20690
$685$	50.8190	1.94169
$686$	−2.66765	−0.101851
$687$	−7.22627	−0.275699
$688$	11.9443	0.455372
$689$	−47.7563	−1.81937
$690$	−42.9489	−1.63504
$691$	−16.7121	−0.635759	−0.317879	−	0.948131i	$-0.602971\pi$
$691$	−16.7121	−0.635759	−0.317879	+	0.948131i	$0.602971\pi$
$692$	−14.1988	−0.539758
$693$	−2.48370	−0.0943478
$694$	93.9017	3.56446
$695$	−52.1375	−1.97769
$696$	26.0237	0.986426
$697$	25.5645	0.968323
$698$	−86.2717	−3.26543
$699$	−1.25874	−0.0476100
$700$	57.9773	2.19134
$701$	46.2335	1.74621	0.873107	−	0.487529i	$-0.162102\pi$
$701$	46.2335	1.74621	0.873107	+	0.487529i	$0.162102\pi$
$702$	58.0156	2.18966
$703$	29.3370	1.10647
$704$	16.7571	0.631558
$705$	18.2487	0.687287
$706$	81.6298	3.07218
$707$	1.94049	0.0729796
$708$	19.9044	0.748051
$709$	−19.9411	−0.748904	−0.374452	−	0.927246i	$-0.622169\pi$
$709$	−19.9411	−0.748904	−0.374452	+	0.927246i	$0.622169\pi$
$710$	−176.946	−6.64065
$711$	−19.3866	−0.727055
$712$	−70.6461	−2.64757
$713$	−22.4882	−0.842189
$714$	9.52286	0.356384
$715$	22.3052	0.834169
$716$	−16.3215	−0.609963
$717$	9.35033	0.349194
$718$	70.1681	2.61865
$719$	10.7564	0.401145	0.200573	−	0.979679i	$-0.435720\pi$
$719$	10.7564	0.401145	0.200573	+	0.979679i	$0.435720\pi$
$720$	−119.888	−4.46796
$721$	−6.58984	−0.245418
$722$	−4.34904	−0.161855
$723$	13.9040	0.517095
$724$	56.2669	2.09114
$725$	−49.3675	−1.83346
$726$	−1.91682	−0.0711398
$727$	31.8213	1.18019	0.590093	−	0.807335i	$-0.299091\pi$
$727$	31.8213	1.18019	0.590093	+	0.807335i	$0.299091\pi$
$728$	−45.8843	−1.70058
$729$	−2.98050	−0.110389
$730$	14.8169	0.548398
$731$	−4.96805	−0.183750
$732$	−33.8804	−1.25226
$733$	8.57434	0.316700	0.158350	−	0.987383i	$-0.449382\pi$
$733$	8.57434	0.316700	0.158350	+	0.987383i	$0.449382\pi$
$734$	57.7910	2.13311
$735$	2.90382	0.107109
$736$	−84.4773	−3.11387
$737$	4.74573	0.174811
$738$	−34.0939	−1.25502
$739$	25.4431	0.935939	0.467970	−	0.883745i	$-0.344986\pi$
$739$	25.4431	0.935939	0.467970	+	0.883745i	$0.344986\pi$
$740$	133.549	4.90935
$741$	18.0134	0.661738
$742$	23.0818	0.847359
$743$	10.4730	0.384219	0.192109	−	0.981374i	$-0.438467\pi$
$743$	10.4730	0.384219	0.192109	+	0.981374i	$0.438467\pi$
$744$	24.2285	0.888260
$745$	−44.7114	−1.63810
$746$	−17.3796	−0.636311
$747$	11.8128	0.432208
$748$	−25.4183	−0.929384
$749$	−3.33886	−0.121999
$750$	−49.0484	−1.79099
$751$	44.1902	1.61252	0.806261	−	0.591560i	$-0.201488\pi$
$751$	44.1902	1.61252	0.806261	+	0.591560i	$0.201488\pi$
$752$	75.0625	2.73725
$753$	9.14582	0.333292
$754$	64.1448	2.33602
$755$	93.2466	3.39359
$756$	−20.1598	−0.733204
$757$	17.8450	0.648589	0.324294	−	0.945956i	$-0.394873\pi$
$757$	17.8450	0.648589	0.324294	+	0.945956i	$0.394873\pi$
$758$	1.34595	0.0488872
$759$	3.98388	0.144606
$760$	−152.596	−5.53524
$761$	−25.8790	−0.938112	−0.469056	−	0.883168i	$-0.655406\pi$
$761$	−25.8790	−0.938112	−0.469056	+	0.883168i	$0.655406\pi$
$762$	−8.18619	−0.296554
$763$	15.7840	0.571418
$764$	−102.900	−3.72280
$765$	49.8657	1.80290
$766$	46.1233	1.66650
$767$	29.8831	1.07902
$768$	3.19306	0.115220
$769$	24.2088	0.872993	0.436497	−	0.899706i	$-0.356219\pi$
$769$	24.2088	0.872993	0.436497	+	0.899706i	$0.356219\pi$
$770$	−10.7807	−0.388508
$771$	6.46416	0.232801
$772$	92.1399	3.31619
$773$	50.6535	1.82188	0.910940	−	0.412539i	$-0.135358\pi$
$773$	50.6535	1.82188	0.910940	+	0.412539i	$0.135358\pi$
$774$	6.62563	0.238153
$775$	−45.9620	−1.65100
$776$	17.3254	0.621947
$777$	4.64104	0.166496
$778$	62.6166	2.24491
$779$	−23.3724	−0.837402
$780$	82.0010	2.93611
$781$	16.4133	0.587312
$782$	73.4799	2.62764
$783$	17.1660	0.613463
$784$	11.9443	0.426582
$785$	14.5122	0.517964
$786$	16.2647	0.580142
$787$	−26.6822	−0.951118	−0.475559	−	0.879684i	$-0.657754\pi$
$787$	−26.6822	−0.951118	−0.475559	+	0.879684i	$0.657754\pi$
$788$	20.3322	0.724306
$789$	0.496651	0.0176812
$790$	−84.1490	−2.99389
$791$	−1.63450	−0.0581161
$792$	20.6477	0.733685
$793$	−50.8658	−1.80630
$794$	−28.7450	−1.02012
$795$	−25.1252	−0.891101
$796$	56.7524	2.01154
$797$	−42.0793	−1.49052	−0.745262	−	0.666772i	$-0.767676\pi$
$797$	−42.0793	−1.49052	−0.745262	+	0.666772i	$0.767676\pi$
$798$	−8.70630	−0.308200
$799$	−31.2212	−1.10453
$800$	−172.657	−6.10435
$801$	−21.1063	−0.745756
$802$	−100.888	−3.56247
$803$	−1.37440	−0.0485014
$804$	17.4468	0.615300
$805$	22.4063	0.789720
$806$	59.7199	2.10354
$807$	−8.92518	−0.314181
$808$	−16.1319	−0.567517
$809$	4.33163	0.152292	0.0761461	−	0.997097i	$-0.475738\pi$
$809$	4.33163	0.152292	0.0761461	+	0.997097i	$0.475738\pi$
$810$	−49.8049	−1.74996
$811$	−12.5576	−0.440955	−0.220478	−	0.975392i	$-0.570762\pi$
$811$	−12.5576	−0.440955	−0.220478	+	0.975392i	$0.570762\pi$
$812$	−22.2896	−0.782212
$813$	4.03329	0.141454
$814$	−17.2302	−0.603920
$815$	−95.6957	−3.35207
$816$	−42.6382	−1.49264
$817$	4.54206	0.158906
$818$	−59.6131	−2.08432
$819$	−13.7085	−0.479012
$820$	−106.396	−3.71552
$821$	51.2305	1.78796	0.893978	−	0.448111i	$-0.147903\pi$
$821$	51.2305	1.78796	0.893978	+	0.448111i	$0.147903\pi$
$822$	−24.1041	−0.840726
$823$	−1.43072	−0.0498717	−0.0249359	−	0.999689i	$-0.507938\pi$
$823$	−1.43072	−0.0498717	−0.0249359	+	0.999689i	$0.507938\pi$
$824$	54.7833	1.90847
$825$	8.14238	0.283481
$826$	−14.4432	−0.502544
$827$	26.0424	0.905582	0.452791	−	0.891617i	$-0.350428\pi$
$827$	26.0424	0.905582	0.452791	+	0.891617i	$0.350428\pi$
$828$	−70.4550	−2.44848
$829$	−8.16785	−0.283681	−0.141841	−	0.989890i	$-0.545302\pi$
$829$	−8.16785	−0.283681	−0.141841	+	0.989890i	$0.545302\pi$
$830$	51.2743	1.77976
$831$	20.8375	0.722845
$832$	92.4888	3.20647
$833$	−4.96805	−0.172133
$834$	24.7295	0.856311
$835$	−86.4989	−2.99342
$836$	23.2387	0.803728
$837$	15.9818	0.552413
$838$	51.5898	1.78214
$839$	7.06951	0.244067	0.122033	−	0.992526i	$-0.461059\pi$
$839$	7.06951	0.244067	0.122033	+	0.992526i	$0.461059\pi$
$840$	−24.1403	−0.832921
$841$	−10.0205	−0.345533
$842$	60.7011	2.09190
$843$	1.65702	0.0570709
$844$	−133.792	−4.60532
$845$	70.5747	2.42784
$846$	41.6380	1.43154
$847$	1.00000	0.0343604
$848$	−103.348	−3.54898
$849$	−3.58832	−0.123151
$850$	150.180	5.15115
$851$	35.8110	1.22759
$852$	60.3402	2.06722
$853$	4.83085	0.165405	0.0827025	−	0.996574i	$-0.473645\pi$
$853$	4.83085	0.165405	0.0827025	+	0.996574i	$0.473645\pi$
$854$	24.5847	0.841270
$855$	−45.5898	−1.55914
$856$	27.7570	0.948714
$857$	−37.4447	−1.27909	−0.639543	−	0.768756i	$-0.720876\pi$
$857$	−37.4447	−1.27909	−0.639543	+	0.768756i	$0.720876\pi$
$858$	−10.5796	−0.361183
$859$	−40.8105	−1.39244	−0.696218	−	0.717831i	$-0.745135\pi$
$859$	−40.8105	−1.39244	−0.696218	+	0.717831i	$0.745135\pi$
$860$	20.6765	0.705062
$861$	−3.69746	−0.126009
$862$	−35.7180	−1.21656
$863$	−31.0252	−1.05611	−0.528055	−	0.849210i	$-0.677078\pi$
$863$	−31.0252	−1.05611	−0.528055	+	0.849210i	$0.677078\pi$
$864$	60.0360	2.04247
$865$	−11.2153	−0.381330
$866$	−24.0074	−0.815804
$867$	5.51953	0.187453
$868$	−20.7520	−0.704369
$869$	7.80555	0.264785
$870$	33.7474	1.14415
$871$	26.1935	0.887531
$872$	−131.217	−4.44357
$873$	5.17617	0.175187
$874$	−67.1792	−2.27237
$875$	25.5884	0.865046
$876$	−5.05271	−0.170715
$877$	22.0408	0.744266	0.372133	−	0.928179i	$-0.378626\pi$
$877$	22.0408	0.744266	0.372133	+	0.928179i	$0.378626\pi$
$878$	39.1510	1.32128
$879$	18.2759	0.616430
$880$	48.2700	1.62718
$881$	−25.4669	−0.858002	−0.429001	−	0.903304i	$-0.641134\pi$
$881$	−25.4669	−0.858002	−0.429001	+	0.903304i	$0.641134\pi$
$882$	6.62563	0.223096
$883$	−40.3906	−1.35925	−0.679625	−	0.733560i	$-0.737858\pi$
$883$	−40.3906	−1.35925	−0.679625	+	0.733560i	$0.737858\pi$
$884$	−140.293	−4.71857
$885$	15.7219	0.528486
$886$	102.708	3.45053
$887$	39.6915	1.33271	0.666355	−	0.745635i	$-0.267854\pi$
$887$	39.6915	1.33271	0.666355	+	0.745635i	$0.267854\pi$
$888$	−38.5824	−1.29474
$889$	4.27072	0.143235
$890$	−91.6136	−3.07089
$891$	4.61983	0.154770
$892$	−135.692	−4.54329
$893$	28.5441	0.955191
$894$	21.2071	0.709273
$895$	−12.8919	−0.430929
$896$	−14.2290	−0.475358
$897$	21.9886	0.734177
$898$	41.0662	1.37040
$899$	17.6703	0.589336
$900$	−143.998	−4.79994
$901$	42.9860	1.43207
$902$	13.7271	0.457062
$903$	0.718543	0.0239116
$904$	13.5881	0.451933
$905$	44.4437	1.47736
$906$	−44.2280	−1.46938
$907$	11.5260	0.382715	0.191357	−	0.981520i	$-0.438711\pi$
$907$	11.5260	0.382715	0.191357	+	0.981520i	$0.438711\pi$
$908$	−49.7083	−1.64963
$909$	−4.81958	−0.159855
$910$	−59.5025	−1.97249
$911$	39.9163	1.32249	0.661243	−	0.750172i	$-0.270029\pi$
$911$	39.9163	1.32249	0.661243	+	0.750172i	$0.270029\pi$
$912$	38.9821	1.29083
$913$	−4.75614	−0.157405
$914$	−52.4913	−1.73626
$915$	−26.7612	−0.884698
$916$	−51.4542	−1.70010
$917$	−8.48525	−0.280208
$918$	−52.2205	−1.72353
$919$	26.1430	0.862377	0.431188	−	0.902262i	$-0.358094\pi$
$919$	26.1430	0.862377	0.431188	+	0.902262i	$0.358094\pi$
$920$	−186.271	−6.14116
$921$	−0.185622	−0.00611646
$922$	104.692	3.44786
$923$	90.5909	2.98184
$924$	3.67631	0.120942
$925$	73.1916	2.40653
$926$	−8.68578	−0.285432
$927$	16.3672	0.537568
$928$	66.3787	2.17899
$929$	3.08427	0.101192	0.0505958	−	0.998719i	$-0.483888\pi$
$929$	3.08427	0.101192	0.0505958	+	0.998719i	$0.483888\pi$
$930$	31.4194	1.03028
$931$	4.54206	0.148860
$932$	−8.96280	−0.293586
$933$	17.1394	0.561119
$934$	33.6691	1.10169
$935$	−20.0772	−0.656595
$936$	113.963	3.72498
$937$	−9.73490	−0.318025	−0.159013	−	0.987277i	$-0.550831\pi$
$937$	−9.73490	−0.318025	−0.159013	+	0.987277i	$0.550831\pi$
$938$	−12.6599	−0.413361
$939$	−20.8581	−0.680678
$940$	129.939	4.23814
$941$	−30.4428	−0.992407	−0.496204	−	0.868206i	$-0.665273\pi$
$941$	−30.4428	−0.992407	−0.496204	+	0.868206i	$0.665273\pi$
$942$	−6.88333	−0.224271
$943$	−28.5302	−0.929070
$944$	64.6689	2.10479
$945$	−15.9237	−0.517997
$946$	−2.66765	−0.0867327
$947$	17.0361	0.553600	0.276800	−	0.960928i	$-0.410726\pi$
$947$	17.0361	0.553600	0.276800	+	0.960928i	$0.410726\pi$
$948$	28.6956	0.931991
$949$	−7.58581	−0.246246
$950$	−137.303	−4.45469
$951$	−14.8138	−0.480371
$952$	41.3010	1.33857
$953$	2.74726	0.0889925	0.0444962	−	0.999010i	$-0.485832\pi$
$953$	2.74726	0.0889925	0.0444962	+	0.999010i	$0.485832\pi$
$954$	−57.3281	−1.85607
$955$	−81.2780	−2.63010
$956$	66.5785	2.15330
$957$	−3.13037	−0.101190
$958$	−106.848	−3.45209
$959$	12.5750	0.406069
$960$	48.6596	1.57048
$961$	−14.5487	−0.469313
$962$	−95.1002	−3.06615
$963$	8.29272	0.267229
$964$	99.0025	3.18866
$965$	72.7788	2.34283
$966$	−10.6276	−0.341937
$967$	−6.64655	−0.213739	−0.106869	−	0.994273i	$-0.534083\pi$
$967$	−6.64655	−0.213739	−0.106869	+	0.994273i	$0.534083\pi$
$968$	−8.31331	−0.267200
$969$	−16.2141	−0.520871
$970$	22.4675	0.721390
$971$	11.2351	0.360551	0.180276	−	0.983616i	$-0.442301\pi$
$971$	11.2351	0.360551	0.180276	+	0.983616i	$0.442301\pi$
$972$	77.4633	2.48464
$973$	−12.9013	−0.413597
$974$	37.2851	1.19469
$975$	44.9409	1.43926
$976$	−110.077	−3.52348
$977$	−28.9480	−0.926129	−0.463065	−	0.886325i	$-0.653250\pi$
$977$	−28.9480	−0.926129	−0.463065	+	0.886325i	$0.653250\pi$
$978$	45.3896	1.45140
$979$	8.49796	0.271596
$980$	20.6765	0.660486
$981$	−39.2026	−1.25164
$982$	45.2199	1.44303
$983$	29.0305	0.925930	0.462965	−	0.886377i	$-0.346786\pi$
$983$	29.0305	0.925930	0.462965	+	0.886377i	$0.346786\pi$
$984$	30.7381	0.979894
$985$	16.0599	0.511710
$986$	−57.7375	−1.83874
$987$	4.51560	0.143733
$988$	128.263	4.08060
$989$	5.54439	0.176301
$990$	26.7759	0.850993
$991$	−30.0705	−0.955220	−0.477610	−	0.878572i	$-0.658497\pi$
$991$	−30.0705	−0.955220	−0.477610	+	0.878572i	$0.658497\pi$
$992$	61.7997	1.96214
$993$	22.1629	0.703318
$994$	−43.7848	−1.38877
$995$	44.8272	1.42112
$996$	−17.4851	−0.554035
$997$	8.05959	0.255250	0.127625	−	0.991823i	$-0.459265\pi$
$997$	8.05959	0.255250	0.127625	+	0.991823i	$0.459265\pi$
$998$	−102.344	−3.23965
$999$	−25.4501	−0.805205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.2.a.k.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.2.a.k.1.2	✓	38	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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3311.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66765 q^{2} +0.718543 q^{3} +5.11634 q^{4} +4.04126 q^{5} -1.91682 q^{6} +1.00000 q^{7} -8.31331 q^{8} -2.48370 q^{9} +O(q^{10})\)	\(q-2.66765 q^{2} +0.718543 q^{3} +5.11634 q^{4} +4.04126 q^{5} -1.91682 q^{6} +1.00000 q^{7} -8.31331 q^{8} -2.48370 q^{9} -10.7807 q^{10} +1.00000 q^{11} +3.67631 q^{12} +5.51938 q^{13} -2.66765 q^{14} +2.90382 q^{15} +11.9443 q^{16} -4.96805 q^{17} +6.62563 q^{18} +4.54206 q^{19} +20.6765 q^{20} +0.718543 q^{21} -2.66765 q^{22} +5.54439 q^{23} -5.97347 q^{24} +11.3318 q^{25} -14.7238 q^{26} -3.94027 q^{27} +5.11634 q^{28} -4.35655 q^{29} -7.74637 q^{30} -4.05602 q^{31} -15.2365 q^{32} +0.718543 q^{33} +13.2530 q^{34} +4.04126 q^{35} -12.7074 q^{36} +6.45896 q^{37} -12.1166 q^{38} +3.96591 q^{39} -33.5962 q^{40} -5.14577 q^{41} -1.91682 q^{42} +1.00000 q^{43} +5.11634 q^{44} -10.0373 q^{45} -14.7905 q^{46} +6.28439 q^{47} +8.58248 q^{48} +1.00000 q^{49} -30.2292 q^{50} -3.56976 q^{51} +28.2390 q^{52} -8.65248 q^{53} +10.5113 q^{54} +4.04126 q^{55} -8.31331 q^{56} +3.26366 q^{57} +11.6217 q^{58} +5.41422 q^{59} +14.8569 q^{60} -9.21586 q^{61} +10.8200 q^{62} -2.48370 q^{63} +16.7571 q^{64} +22.3052 q^{65} -1.91682 q^{66} +4.74573 q^{67} -25.4183 q^{68} +3.98388 q^{69} -10.7807 q^{70} +16.4133 q^{71} +20.6477 q^{72} -1.37440 q^{73} -17.2302 q^{74} +8.14238 q^{75} +23.2387 q^{76} +1.00000 q^{77} -10.5796 q^{78} +7.80555 q^{79} +48.2700 q^{80} +4.61983 q^{81} +13.7271 q^{82} -4.75614 q^{83} +3.67631 q^{84} -20.0772 q^{85} -2.66765 q^{86} -3.13037 q^{87} -8.31331 q^{88} +8.49796 q^{89} +26.7759 q^{90} +5.51938 q^{91} +28.3670 q^{92} -2.91443 q^{93} -16.7645 q^{94} +18.3556 q^{95} -10.9481 q^{96} -2.08406 q^{97} -2.66765 q^{98} -2.48370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9}+O(q^{10}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9	\( 38 q + 6 q^{2} + 7 q^{3} + 50 q^{4} + 8 q^{5} + 38 q^{7} + 18 q^{8} + 61 q^{9} + 2 q^{10} + 38 q^{11} + 2 q^{12} + 8 q^{13} + 6 q^{14} + 26 q^{15} + 70 q^{16} + 3 q^{17} + 27 q^{18} + 10 q^{19} + 9 q^{20} + 7 q^{21} + 6 q^{22} + 22 q^{23} - 16 q^{24} + 82 q^{25} + 5 q^{26} + 28 q^{27} + 50 q^{28} + 24 q^{29} + 4 q^{30} + 13 q^{31} + 42 q^{32} + 7 q^{33} + 10 q^{34} + 8 q^{35} + 74 q^{36} + 45 q^{37} - 14 q^{38} + 14 q^{39} - 27 q^{40} - 13 q^{41} + 38 q^{43} + 50 q^{44} - 2 q^{45} + 3 q^{46} - 4 q^{47} - 7 q^{48} + 38 q^{49} - 5 q^{50} + 16 q^{51} + 22 q^{52} + 14 q^{53} - 55 q^{54} + 8 q^{55} + 18 q^{56} + 18 q^{57} + 47 q^{58} + 35 q^{59} + 61 q^{60} + 30 q^{61} + 4 q^{62} + 61 q^{63} + 96 q^{64} + 17 q^{65} + 50 q^{67} - 67 q^{68} + 42 q^{69} + 2 q^{70} + 41 q^{71} + 26 q^{72} + 29 q^{73} - 23 q^{74} + 32 q^{75} + 35 q^{76} + 38 q^{77} - 8 q^{78} + 51 q^{79} + 9 q^{80} + 98 q^{81} - 2 q^{82} - 51 q^{83} + 2 q^{84} + 22 q^{85} + 6 q^{86} - 39 q^{87} + 18 q^{88} + 50 q^{89} - 95 q^{90} + 8 q^{91} + q^{92} + 56 q^{93} + 3 q^{94} + 17 q^{95} - 105 q^{96} + 8 q^{97} + 6 q^{98} + 61 q^{99}+O(q^{100}) \) 38 * q + 6 * q^2 + 7 * q^3 + 50 * q^4 + 8 * q^5 + 38 * q^7 + 18 * q^8 + 61 * q^9 + 2 * q^10 + 38 * q^11 + 2 * q^12 + 8 * q^13 + 6 * q^14 + 26 * q^15 + 70 * q^16 + 3 * q^17 + 27 * q^18 + 10 * q^19 + 9 * q^20 + 7 * q^21 + 6 * q^22 + 22 * q^23 - 16 * q^24 + 82 * q^25 + 5 * q^26 + 28 * q^27 + 50 * q^28 + 24 * q^29 + 4 * q^30 + 13 * q^31 + 42 * q^32 + 7 * q^33 + 10 * q^34 + 8 * q^35 + 74 * q^36 + 45 * q^37 - 14 * q^38 + 14 * q^39 - 27 * q^40 - 13 * q^41 + 38 * q^43 + 50 * q^44 - 2 * q^45 + 3 * q^46 - 4 * q^47 - 7 * q^48 + 38 * q^49 - 5 * q^50 + 16 * q^51 + 22 * q^52 + 14 * q^53 - 55 * q^54 + 8 * q^55 + 18 * q^56 + 18 * q^57 + 47 * q^58 + 35 * q^59 + 61 * q^60 + 30 * q^61 + 4 * q^62 + 61 * q^63 + 96 * q^64 + 17 * q^65 + 50 * q^67 - 67 * q^68 + 42 * q^69 + 2 * q^70 + 41 * q^71 + 26 * q^72 + 29 * q^73 - 23 * q^74 + 32 * q^75 + 35 * q^76 + 38 * q^77 - 8 * q^78 + 51 * q^79 + 9 * q^80 + 98 * q^81 - 2 * q^82 - 51 * q^83 + 2 * q^84 + 22 * q^85 + 6 * q^86 - 39 * q^87 + 18 * q^88 + 50 * q^89 - 95 * q^90 + 8 * q^91 + q^92 + 56 * q^93 + 3 * q^94 + 17 * q^95 - 105 * q^96 + 8 * q^97 + 6 * q^98 + 61 * q^99

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