LMFDB - Embedded newform 378.2.v.b.67.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

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:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.58806 - 0.691418i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0337396 + 0.191347i) q^{5} +(0.772092 - 1.55044i) q^{6} +(-1.90403 - 1.83703i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.04388 - 2.19603i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.58806 - 0.691418i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0337396 + 0.191347i) q^{5} +(0.772092 - 1.55044i) q^{6} +(-1.90403 - 1.83703i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.04388 - 2.19603i) q^{9} +(0.0971494 + 0.168268i) q^{10} +(-0.802209 - 4.54955i) q^{11} +(-0.405149 - 1.68400i) q^{12} +(-0.896734 + 5.08563i) q^{13} +(-2.63939 - 0.183356i) q^{14} +(0.0787201 + 0.327199i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.45343 + 4.24947i) q^{17} +(0.154126 - 2.99604i) q^{18} +(2.61284 - 4.52557i) q^{19} +(0.182581 + 0.0664541i) q^{20} +(-4.29387 - 1.60083i) q^{21} +(-3.53892 - 2.96951i) q^{22} +(4.12504 + 3.46132i) q^{23} +(-1.39282 - 1.02959i) q^{24} +(4.66299 + 1.69719i) q^{25} +(2.58204 + 4.47223i) q^{26} +(1.72744 - 4.90061i) q^{27} +(-2.13975 + 1.55611i) q^{28} +(0.702296 + 3.98292i) q^{29} +(0.270623 + 0.200049i) q^{30} +(-1.28435 + 7.28392i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-4.41960 - 6.67031i) q^{33} +(4.61094 + 1.67825i) q^{34} +(0.415751 - 0.302350i) q^{35} +(-1.80775 - 2.39417i) q^{36} -8.94278 q^{37} +(-0.907430 - 5.14629i) q^{38} +(2.09223 + 8.69632i) q^{39} +(0.182581 - 0.0664541i) q^{40} +(0.766737 - 4.34838i) q^{41} +(-4.31829 + 1.53374i) q^{42} +(-9.22420 + 7.74002i) q^{43} -4.61973 q^{44} +(0.351244 + 0.465184i) q^{45} +5.38485 q^{46} +(-0.715807 - 4.05954i) q^{47} +(-1.72877 + 0.106571i) q^{48} +(0.250669 + 6.99551i) q^{49} +(4.66299 - 1.69719i) q^{50} +(6.83436 + 5.05207i) q^{51} +(4.85265 + 1.76622i) q^{52} +(3.60328 - 6.24106i) q^{53} +(-1.82675 - 4.86446i) q^{54} +0.897609 q^{55} +(-0.638896 + 2.56745i) q^{56} +(1.02029 - 8.99345i) q^{57} +(3.09816 + 2.59966i) q^{58} +(4.07621 - 1.48362i) q^{59} +(0.335898 - 0.0207066i) q^{60} +(1.33303 + 7.56001i) q^{61} +(3.69814 + 6.40537i) q^{62} +(-7.92578 + 0.426639i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.942865 - 0.343175i) q^{65} +(-7.67320 - 2.26889i) q^{66} +(-9.94542 - 8.34520i) q^{67} +(4.61094 - 1.67825i) q^{68} +(8.94403 + 2.64466i) q^{69} +(0.124137 - 0.498853i) q^{70} +(4.19642 - 7.26842i) q^{71} +(-2.92376 - 0.672041i) q^{72} +4.16401 q^{73} +(-6.85057 + 5.74831i) q^{74} +(8.57858 - 0.528831i) q^{75} +(-4.00310 - 3.35900i) q^{76} +(-6.83021 + 10.1362i) q^{77} +(7.19262 + 5.31691i) q^{78} +(-4.54942 + 3.81742i) q^{79} +(0.0971494 - 0.168268i) q^{80} +(-0.645082 - 8.97685i) q^{81} +(-2.20773 - 3.82390i) q^{82} +(1.24531 + 7.06248i) q^{83} +(-2.32213 + 3.95066i) q^{84} +(-0.895901 + 0.326081i) q^{85} +(-2.09096 + 11.8584i) q^{86} +(3.86915 + 5.83954i) q^{87} +(-3.53892 + 2.96951i) q^{88} +(-4.02206 + 6.96641i) q^{89} +(0.568083 + 0.130577i) q^{90} +(11.0499 - 8.03588i) q^{91} +(4.12504 - 3.46132i) q^{92} +(2.99660 + 12.4553i) q^{93} +(-3.15776 - 2.64968i) q^{94} +(0.777798 + 0.652650i) q^{95} +(-1.25581 + 1.19287i) q^{96} +(-6.79587 + 5.70241i) q^{97} +(4.68865 + 5.19774i) q^{98} +(-11.6306 - 7.53708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.58806	−	0.691418i	0.916868	−	0.399190i
$3$	1.58806	−	0.691418i	0.916868	−	0.399190i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.0337396	+	0.191347i	−0.0150888	+	0.0855730i	−0.991422	−	0.130698i	$-0.958278\pi$
$5$	−0.0337396	+	0.191347i	−0.0150888	+	0.0855730i	0.976333	+	0.216271i	$0.0693894\pi$
$6$	0.772092	−	1.55044i	0.315205	−	0.632966i
$7$	−1.90403	−	1.83703i	−0.719656	−	0.694331i
$7$	−1.90403	−	1.83703i	−0.719656	−	0.694331i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.04388	−	2.19603i	0.681294	−	0.732009i
$10$	0.0971494	+	0.168268i	0.0307214	+	0.0532109i
$11$	−0.802209	−	4.54955i	−0.241875	−	1.37174i	−0.827640	−	0.561260i	$-0.810317\pi$
$11$	−0.802209	−	4.54955i	−0.241875	−	1.37174i	0.585765	−	0.810481i	$-0.300794\pi$
$12$	−0.405149	−	1.68400i	−0.116957	−	0.486129i
$13$	−0.896734	+	5.08563i	−0.248709	+	1.41050i	0.563009	+	0.826451i	$0.309644\pi$
$13$	−0.896734	+	5.08563i	−0.248709	+	1.41050i	−0.811718	+	0.584050i	$0.801467\pi$
$14$	−2.63939	−	0.183356i	−0.705407	−	0.0490040i
$15$	0.0787201	+	0.327199i	0.0203254	+	0.0844825i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.45343	+	4.24947i	0.595044	+	1.03065i	0.993541	+	0.113477i	$0.0361988\pi$
$17$	2.45343	+	4.24947i	0.595044	+	1.03065i	−0.398496	+	0.917170i	$0.630468\pi$
$18$	0.154126	−	2.99604i	0.0363278	−	0.706173i
$19$	2.61284	−	4.52557i	0.599427	−	1.03824i	−0.393479	−	0.919334i	$-0.628729\pi$
$19$	2.61284	−	4.52557i	0.599427	−	1.03824i	0.992906	−	0.118904i	$-0.0379380\pi$
$20$	0.182581	+	0.0664541i	0.0408264	+	0.0148596i
$21$	−4.29387	−	1.60083i	−0.937000	−	0.349330i
$22$	−3.53892	−	2.96951i	−0.754501	−	0.633101i
$23$	4.12504	+	3.46132i	0.860130	+	0.721735i	0.961996	−	0.273063i	$-0.0880369\pi$
$23$	4.12504	+	3.46132i	0.860130	+	0.721735i	−0.101866	+	0.994798i	$0.532481\pi$
$24$	−1.39282	−	1.02959i	−0.284307	−	0.210165i
$25$	4.66299	+	1.69719i	0.932598	+	0.339438i
$26$	2.58204	+	4.47223i	0.506380	+	0.877077i
$27$	1.72744	−	4.90061i	0.332446	−	0.943122i
$28$	−2.13975	+	1.55611i	−0.404375	+	0.294077i
$29$	0.702296	+	3.98292i	0.130413	+	0.739609i	0.977945	+	0.208864i	$0.0669766\pi$
$29$	0.702296	+	3.98292i	0.130413	+	0.739609i	−0.847532	+	0.530745i	$0.821912\pi$
$30$	0.270623	+	0.200049i	0.0494087	+	0.0365238i
$31$	−1.28435	+	7.28392i	−0.230676	+	1.30823i	0.620854	+	0.783926i	$0.286786\pi$
$31$	−1.28435	+	7.28392i	−0.230676	+	1.30823i	−0.851531	+	0.524305i	$0.824325\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−4.41960	−	6.67031i	−0.769353	−	1.16115i
$34$	4.61094	+	1.67825i	0.790770	+	0.287817i
$35$	0.415751	−	0.302350i	0.0702747	−	0.0511065i
$36$	−1.80775	−	2.39417i	−0.301292	−	0.399028i
$37$	−8.94278			−1.47018			−0.735092	−	0.677967i	$-0.762861\pi$
$37$	−8.94278			−1.47018			−0.735092	+	0.677967i	$0.762861\pi$
$38$	−0.907430	−	5.14629i	−0.147205	−	0.834839i
$39$	2.09223	+	8.69632i	0.335024	+	1.39253i
$40$	0.182581	−	0.0664541i	0.0288686	−	0.0105073i
$41$	0.766737	−	4.34838i	0.119744	−	0.679103i	−0.864547	−	0.502552i	$-0.832395\pi$
$41$	0.766737	−	4.34838i	0.119744	−	0.679103i	0.984291	−	0.176552i	$-0.0564942\pi$
$42$	−4.31829	+	1.53374i	−0.666327	+	0.236661i
$43$	−9.22420	+	7.74002i	−1.40668	+	1.18034i	−0.448634	+	0.893715i	$0.648089\pi$
$43$	−9.22420	+	7.74002i	−1.40668	+	1.18034i	−0.958042	+	0.286627i	$0.907466\pi$
$44$	−4.61973			−0.696451
$45$	0.351244	+	0.465184i	0.0523603	+	0.0693456i
$46$	5.38485			0.793953
$47$	−0.715807	−	4.05954i	−0.104411	−	0.592145i	−0.991454	−	0.130458i	$-0.958355\pi$
$47$	−0.715807	−	4.05954i	−0.104411	−	0.592145i	0.887043	−	0.461687i	$-0.152756\pi$
$48$	−1.72877	+	0.106571i	−0.249526	+	0.0153822i
$49$	0.250669	+	6.99551i	0.0358098	+	0.999359i
$50$	4.66299	−	1.69719i	0.659446	−	0.240019i
$51$	6.83436	+	5.05207i	0.957001	+	0.707432i
$52$	4.85265	+	1.76622i	0.672942	+	0.244931i
$53$	3.60328	−	6.24106i	0.494949	−	0.857276i	−0.505034	−	0.863099i	$-0.668520\pi$
$53$	3.60328	−	6.24106i	0.494949	−	0.857276i	0.999983	+	0.00582304i	$0.00185354\pi$
$54$	−1.82675	−	4.86446i	−0.248590	−	0.661969i
$55$	0.897609			0.121034
$56$	−0.638896	+	2.56745i	−0.0853761	+	0.343090i
$57$	1.02029	−	8.99345i	0.135141	−	1.19121i
$58$	3.09816	+	2.59966i	0.406808	+	0.341353i
$59$	4.07621	−	1.48362i	0.530677	−	0.193151i	−0.0627638	−	0.998028i	$-0.519991\pi$
$59$	4.07621	−	1.48362i	0.530677	−	0.193151i	0.593440	+	0.804878i	$0.297769\pi$
$60$	0.335898	−	0.0207066i	0.0433642	−	0.00267321i
$61$	1.33303	+	7.56001i	0.170677	+	0.967960i	0.943016	+	0.332748i	$0.107976\pi$
$61$	1.33303	+	7.56001i	0.170677	+	0.967960i	−0.772338	+	0.635212i	$0.780913\pi$
$62$	3.69814	+	6.40537i	0.469665	+	0.813483i
$63$	−7.92578	+	0.426639i	−0.998554	+	0.0537515i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.942865	−	0.343175i	−0.116948	−	0.0425656i
$66$	−7.67320	−	2.26889i	−0.944506	−	0.279281i
$67$	−9.94542	−	8.34520i	−1.21503	−	1.01953i	−0.999070	−	0.0431252i	$-0.986269\pi$
$67$	−9.94542	−	8.34520i	−1.21503	−	1.01953i	−0.215957	−	0.976403i	$-0.569287\pi$
$68$	4.61094	−	1.67825i	0.559159	−	0.203517i
$69$	8.94403	+	2.64466i	1.07674	+	0.318380i
$70$	0.124137	−	0.498853i	0.0148372	−	0.0596244i
$71$	4.19642	−	7.26842i	0.498024	−	0.862602i	−0.501974	−	0.864883i	$-0.667393\pi$
$71$	4.19642	−	7.26842i	0.498024	−	0.862602i	0.999997	+	0.00228062i	$0.000725944\pi$
$72$	−2.92376	−	0.672041i	−0.344568	−	0.0792008i
$73$	4.16401			0.487361			0.243680	−	0.969856i	$-0.421645\pi$
$73$	4.16401			0.487361			0.243680	+	0.969856i	$0.421645\pi$
$74$	−6.85057	+	5.74831i	−0.796362	+	0.668227i
$75$	8.57858	−	0.528831i	0.990569	−	0.0610641i
$76$	−4.00310	−	3.35900i	−0.459187	−	0.385304i
$77$	−6.83021	+	10.1362i	−0.778375	+	1.15512i
$78$	7.19262	+	5.31691i	0.814404	+	0.602021i
$79$	−4.54942	+	3.81742i	−0.511850	+	0.429493i	−0.861780	−	0.507283i	$-0.830650\pi$
$79$	−4.54942	+	3.81742i	−0.511850	+	0.429493i	0.349930	+	0.936776i	$0.386206\pi$
$80$	0.0971494	−	0.168268i	0.0108616	−	0.0188129i
$81$	−0.645082	−	8.97685i	−0.0716757	−	0.997428i
$82$	−2.20773	−	3.82390i	−0.243803	−	0.422279i
$83$	1.24531	+	7.06248i	0.136690	+	0.775208i	0.973668	+	0.227971i	$0.0732092\pi$
$83$	1.24531	+	7.06248i	0.136690	+	0.775208i	−0.836978	+	0.547237i	$0.815680\pi$
$84$	−2.32213	+	3.95066i	−0.253366	+	0.431052i
$85$	−0.895901	+	0.326081i	−0.0971741	+	0.0353685i
$86$	−2.09096	+	11.8584i	−0.225474	+	1.27872i
$87$	3.86915	+	5.83954i	0.414816	+	0.626064i
$88$	−3.53892	+	2.96951i	−0.377250	+	0.316551i
$89$	−4.02206	+	6.96641i	−0.426337	+	0.738438i	−0.996544	−	0.0830631i	$-0.973530\pi$
$89$	−4.02206	+	6.96641i	−0.426337	+	0.738438i	0.570207	+	0.821501i	$0.306863\pi$
$90$	0.568083	+	0.130577i	0.0598812	+	0.0137640i
$91$	11.0499	−	8.03588i	1.15834	−	0.842389i
$92$	4.12504	−	3.46132i	0.430065	−	0.360867i
$93$	2.99660	+	12.4553i	0.310733	+	1.29156i
$94$	−3.15776	−	2.64968i	−0.325698	−	0.273293i
$95$	0.777798	+	0.652650i	0.0798004	+	0.0669605i
$96$	−1.25581	+	1.19287i	−0.128171	+	0.121747i
$97$	−6.79587	+	5.70241i	−0.690016	+	0.578992i	−0.918914	−	0.394458i	$-0.870932\pi$
$97$	−6.79587	+	5.70241i	−0.690016	+	0.578992i	0.228898	+	0.973450i	$0.426488\pi$
$98$	4.68865	+	5.19774i	0.473625	+	0.525052i
$99$	−11.6306	−	7.53708i	−1.16892	−	0.757505i
$100$	2.48112	−	4.29743i	0.248112	−	0.429743i
$101$	13.1678	−	11.0491i	1.31025	−	1.09943i	0.321970	−	0.946750i	$-0.395655\pi$
$101$	13.1678	−	11.0491i	1.31025	−	1.09943i	0.988276	−	0.152677i	$-0.0487895\pi$
$102$	8.48283	−	0.522928i	0.839925	−	0.0517776i
$103$	−0.132329	+	0.750475i	−0.0130388	+	0.0739465i	−0.990633	−	0.136552i	$-0.956398\pi$
$103$	−0.132329	+	0.750475i	−0.0130388	+	0.0739465i	0.977594	+	0.210499i	$0.0675089\pi$
$104$	4.85265	−	1.76622i	0.475842	−	0.173192i
$105$	0.451188	−	0.767608i	0.0440314	−	0.0749109i
$106$	−1.25141	−	7.09708i	−0.121547	−	0.689329i
$107$	6.61899	+	11.4644i	0.639882	+	1.10831i	0.985458	+	0.169918i	$0.0543501\pi$
$107$	6.61899	+	11.4644i	0.639882	+	1.10831i	−0.345576	+	0.938391i	$0.612317\pi$
$108$	−4.52619	−	2.55218i	−0.435533	−	0.245584i
$109$	2.77831	−	4.81218i	0.266114	−	0.460923i	−0.701741	−	0.712432i	$-0.747594\pi$
$109$	2.77831	−	4.81218i	0.266114	−	0.460923i	0.967855	+	0.251509i	$0.0809268\pi$
$110$	0.687609	−	0.576972i	0.0655609	−	0.0550121i
$111$	−14.2017	+	6.18320i	−1.34797	+	0.586883i
$112$	1.16090	+	2.37746i	0.109695	+	0.224649i
$113$	−13.3324	−	11.1872i	−1.25421	−	1.05241i	−0.996274	−	0.0862457i	$-0.972513\pi$
$113$	−13.3324	−	11.1872i	−1.25421	−	1.05241i	−0.257937	−	0.966162i	$-0.583043\pi$
$114$	−4.99929	−	7.54522i	−0.468226	−	0.706674i
$115$	−0.801490	+	0.672530i	−0.0747393	+	0.0627138i
$116$	4.04436			0.375509
$117$	9.33537	+	12.3637i	0.863056	+	1.14302i
$118$	2.16890	−	3.75665i	0.199664	−	0.345828i
$119$	3.13497	−	12.5981i	0.287383	−	1.15487i
$120$	0.244003	−	0.231773i	0.0222743	−	0.0211579i
$121$	−9.71825	+	3.53716i	−0.883478	+	0.321560i
$122$	5.88064	+	4.93445i	0.532408	+	0.446744i
$123$	−1.78892	−	7.43564i	−0.161302	−	0.670449i
$124$	6.95024	+	2.52968i	0.624150	+	0.227172i
$125$	−0.967827	+	1.67633i	−0.0865651	+	0.149935i
$126$	−5.79726	+	5.42142i	−0.516461	+	0.482978i
$127$	4.54867	+	7.87853i	0.403630	+	0.699107i	0.994161	−	0.107908i	$-0.0344151\pi$
$127$	4.54867	+	7.87853i	0.403630	+	0.699107i	−0.590531	+	0.807015i	$0.701082\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−9.29701	+	18.6694i	−0.818556	+	1.64375i
$130$	−0.942865	+	0.343175i	−0.0826948	+	0.0300984i
$131$	−2.55113	−	2.14065i	−0.222893	−	0.187029i	0.524502	−	0.851409i	$-0.324251\pi$
$131$	−2.55113	−	2.14065i	−0.222893	−	0.187029i	−0.747395	+	0.664380i	$0.768696\pi$
$132$	−7.33643	+	3.19417i	−0.638554	+	0.278016i
$133$	−13.2885	+	3.81697i	−1.15226	+	0.330974i
$134$	−12.9828			−1.12155
$135$	0.879433	+	0.495886i	0.0756896	+	0.0426790i
$136$	2.45343	−	4.24947i	0.210380	−	0.364389i
$137$	−8.69485	−	3.16467i	−0.742851	−	0.270376i	−0.0572567	−	0.998359i	$-0.518235\pi$
$137$	−8.69485	−	3.16467i	−0.742851	−	0.270376i	−0.685594	+	0.727984i	$0.740458\pi$
$138$	8.55148	−	3.72318i	0.727951	−	0.316938i
$139$	8.88551	−	3.23406i	0.753659	−	0.274309i	0.0635142	−	0.997981i	$-0.479769\pi$
$139$	8.88551	−	3.23406i	0.753659	−	0.274309i	0.690145	+	0.723672i	$0.257547\pi$
$140$	−0.225562	−	0.461937i	−0.0190635	−	0.0390408i
$141$	−3.94359	−	5.95189i	−0.332110	−	0.501239i
$142$	−1.45740	−	8.26534i	−0.122302	−	0.693612i
$143$	23.8567			1.99500
$144$	−2.67171	+	1.36454i	−0.222642	+	0.113712i
$145$	−0.785814			−0.0652583
$146$	3.18982	−	2.67658i	0.263991	−	0.221515i
$147$	5.23490	+	10.9360i	0.431767	+	0.901985i
$148$	−1.55290	+	8.80692i	−0.127647	+	0.723924i
$149$	−7.45350	+	2.71285i	−0.610615	+	0.222246i	−0.628772	−	0.777590i	$-0.716442\pi$
$149$	−7.45350	+	2.71285i	−0.610615	+	0.222246i	0.0181574	+	0.999835i	$0.494220\pi$
$150$	6.23165	−	5.91931i	0.508812	−	0.483310i
$151$	−1.06392	−	6.03379i	−0.0865806	−	0.491023i	−0.997004	−	0.0773459i	$-0.975355\pi$
$151$	−1.06392	−	6.03379i	−0.0865806	−	0.491023i	0.910424	−	0.413677i	$-0.135756\pi$
$152$	−5.22568			−0.423859
$153$	14.3465	+	3.29761i	1.15984	+	0.266596i
$154$	1.28315	+	12.1551i	0.103399	+	0.979488i
$155$	−1.35042	−	0.491514i	−0.108469	−	0.0394794i
$156$	8.92751	−	0.550341i	0.714773	−	0.0440625i
$157$	2.74504	−	0.999112i	0.219078	−	0.0797378i	−0.230150	−	0.973155i	$-0.573922\pi$
$157$	2.74504	−	0.999112i	0.219078	−	0.0797378i	0.449227	+	0.893417i	$0.351699\pi$
$158$	−1.03127	+	5.84863i	−0.0820435	+	0.465292i
$159$	1.40705	−	12.4026i	0.111586	−	0.983588i
$160$	−0.0337396	−	0.191347i	−0.00266735	−	0.0151273i
$161$	−1.49567	−	14.1683i	−0.117875	−	1.11662i
$162$	−6.26437	−	6.46202i	−0.492175	−	0.507704i
$163$	−5.96193	−	10.3264i	−0.466974	−	0.808823i	0.532314	−	0.846547i	$-0.321323\pi$
$163$	−5.96193	−	10.3264i	−0.466974	−	0.808823i	−0.999288	+	0.0377239i	$0.987989\pi$
$164$	−4.14918	−	1.51018i	−0.323996	−	0.117925i
$165$	1.42546	−	0.620623i	0.110972	−	0.0483154i
$166$	5.49364	+	4.60971i	0.426389	+	0.357783i
$167$	−3.21514	−	2.69782i	−0.248795	−	0.208763i	0.509858	−	0.860258i	$-0.329698\pi$
$167$	−3.21514	−	2.69782i	−0.248795	−	0.208763i	−0.758653	+	0.651495i	$0.774142\pi$
$168$	0.760575	+	4.51902i	0.0586797	+	0.348650i
$169$	−12.8435	−	4.67466i	−0.987963	−	0.359589i
$170$	−0.476699	+	0.825666i	−0.0365611	+	0.0633257i
$171$	−4.59794	−	14.9876i	−0.351614	−	1.14613i
$172$	6.02067	+	10.4281i	0.459072	+	0.795135i
$173$	−4.24383	−	1.54463i	−0.322652	−	0.117436i	0.175616	−	0.984459i	$-0.443808\pi$
$173$	−4.24383	−	1.54463i	−0.322652	−	0.117436i	−0.498268	+	0.867023i	$0.666031\pi$
$174$	6.71752	+	1.98631i	0.509254	+	0.150582i
$175$	−5.76069	−	11.7975i	−0.435467	−	0.891810i
$176$	−0.802209	+	4.54955i	−0.0604687	+	0.342935i
$177$	5.44747	−	5.17444i	0.409457	−	0.388934i
$178$	1.39685	+	7.92191i	0.104698	+	0.593772i
$179$	9.81363	+	16.9977i	0.733505	+	1.27047i	0.955376	+	0.295392i	$0.0954502\pi$
$179$	9.81363	+	16.9977i	0.733505	+	1.27047i	−0.221871	+	0.975076i	$0.571216\pi$
$180$	0.519110	−	0.265129i	0.0386922	−	0.0197616i
$181$	−4.03731	−	6.99282i	−0.300091	−	0.519772i	0.676066	−	0.736842i	$-0.263684\pi$
$181$	−4.03731	−	6.99282i	−0.300091	−	0.519772i	−0.976156	+	0.217069i	$0.930350\pi$
$182$	3.29931	−	13.2585i	0.244561	−	0.982789i
$183$	7.34406	+	11.0841i	0.542889	+	0.819359i
$184$	0.935070	−	5.30305i	0.0689343	−	0.390946i
$185$	0.301726	−	1.71117i	0.0221834	−	0.125808i
$186$	10.3017	+	7.61517i	0.755355	+	0.558371i
$187$	17.3650	−	14.5710i	1.26985	−	1.06553i
$188$	−4.12217			−0.300640
$189$	−12.2916	+	6.15755i	−0.894086	+	0.447896i
$190$	1.01534			0.0736608
$191$	2.60459	−	2.18551i	0.188461	−	0.158138i	−0.543675	−	0.839296i	$-0.682968\pi$
$191$	2.60459	−	2.18551i	0.188461	−	0.158138i	0.732137	+	0.681158i	$0.238523\pi$
$192$	−0.195246	+	1.72101i	−0.0140907	+	0.124203i
$193$	0.458322	−	2.59927i	0.0329907	−	0.187100i	−0.963859	−	0.266413i	$-0.914162\pi$
$193$	0.458322	−	2.59927i	0.0329907	−	0.187100i	0.996850	+	0.0793131i	$0.0252727\pi$
$194$	−1.54050	+	8.73660i	−0.110601	+	0.627251i
$195$	−1.73461	+	0.106931i	−0.124218	+	0.00765746i
$196$	6.93276	+	0.967897i	0.495197	+	0.0691355i
$197$	−1.63189	−	2.82651i	−0.116267	−	0.201381i	0.802018	−	0.597299i	$-0.203760\pi$
$197$	−1.63189	−	2.82651i	−0.116267	−	0.201381i	−0.918286	+	0.395919i	$0.870426\pi$
$198$	−13.7543	+	1.70225i	−0.977473	+	0.120973i
$199$	−5.35016	−	9.26675i	−0.379263	−	0.656902i	0.611692	−	0.791096i	$-0.290489\pi$
$199$	−5.35016	−	9.26675i	−0.379263	−	0.656902i	−0.990955	+	0.134193i	$0.957156\pi$
$200$	−0.861685	−	4.88686i	−0.0609304	−	0.345553i
$201$	−21.5640	−	6.37626i	−1.52100	−	0.449746i
$202$	2.98490	−	16.9282i	0.210017	−	1.19106i
$203$	5.97953	−	8.87373i	0.419681	−	0.622814i
$204$	6.16209	−	5.85324i	0.431433	−	0.409809i
$205$	0.806181	+	0.293426i	0.0563061	+	0.0204937i
$206$	0.381026	+	0.659957i	0.0265474	+	0.0459814i
$207$	16.0322	−	1.98417i	1.11432	−	0.137909i
$208$	2.58204	−	4.47223i	0.179032	−	0.310093i
$209$	−22.6854	−	8.25680i	−1.56918	−	0.571135i
$210$	−0.147779	−	0.878040i	−0.0101977	−	0.0605905i
$211$	−15.8841	−	13.3284i	−1.09351	−	0.917563i	−0.0965376	−	0.995329i	$-0.530777\pi$
$211$	−15.8841	−	13.3284i	−1.09351	−	0.917563i	−0.996972	+	0.0777662i	$0.975221\pi$
$212$	−5.52055	−	4.63229i	−0.379153	−	0.318147i
$213$	1.63867	−	14.4442i	0.112280	−	0.989699i
$214$	12.4396	+	4.52766i	0.850356	+	0.309504i
$215$	−1.16981	−	2.02617i	−0.0797803	−	0.138184i
$216$	−5.10777	+	0.954295i	−0.347540	+	0.0649316i
$217$	15.8262	−	11.5094i	1.07435	−	0.781311i
$218$	−0.964898	−	5.47221i	−0.0653512	−	0.370625i
$219$	6.61271	−	2.87907i	0.446846	−	0.194550i
$220$	0.155868	−	0.883973i	0.0105086	−	0.0595974i
$221$	−23.8113	+	8.66660i	−1.60172	+	0.582979i
$222$	−6.90465	+	13.8653i	−0.463410	+	0.930577i
$223$	6.07337	+	2.21053i	0.406703	+	0.148028i	0.537267	−	0.843412i	$-0.319457\pi$
$223$	6.07337	+	2.21053i	0.406703	+	0.148028i	−0.130564	+	0.991440i	$0.541679\pi$
$224$	2.41750	+	1.07502i	0.161526	+	0.0718280i
$225$	13.2577	−	6.77120i	0.883845	−	0.451413i
$226$	−17.4043			−1.15771
$227$	1.07201	+	6.07969i	0.0711520	+	0.403523i	0.999494	+	0.0317967i	$0.0101229\pi$
$227$	1.07201	+	6.07969i	0.0711520	+	0.403523i	−0.928342	+	0.371726i	$0.878766\pi$
$228$	−8.67965	−	2.56649i	−0.574824	−	0.169970i
$229$	−15.3853	+	5.59979i	−1.01669	+	0.370045i	−0.795998	−	0.605299i	$-0.793054\pi$
$229$	−15.3853	+	5.59979i	−1.01669	+	0.370045i	−0.220691	+	0.975344i	$0.570831\pi$
$230$	−0.181683	+	1.03038i	−0.0119798	+	0.0679410i
$231$	−3.83848	+	20.8194i	−0.252554	+	1.36982i
$232$	3.09816	−	2.59966i	0.203404	−	0.170676i
$233$	−4.61671			−0.302451			−0.151225	−	0.988499i	$-0.548322\pi$
$233$	−4.61671			−0.302451			−0.151225	+	0.988499i	$0.548322\pi$
$234$	15.0985	+	3.47048i	0.987022	+	0.226872i
$235$	0.800933			0.0522471
$236$	−0.753252	−	4.27191i	−0.0490325	−	0.278077i
$237$	−4.58534	+	9.20785i	−0.297850	+	0.598114i
$238$	−5.69639	−	11.6659i	−0.369242	−	0.756185i
$239$	−3.79727	+	1.38209i	−0.245625	+	0.0894002i	−0.461899	−	0.886932i	$-0.652832\pi$
$239$	−3.79727	+	1.38209i	−0.245625	+	0.0894002i	0.216274	+	0.976333i	$0.430610\pi$
$240$	0.0379361	−	0.334391i	0.00244876	−	0.0215848i
$241$	22.2754	+	8.10759i	1.43489	+	0.522256i	0.938328	−	0.345747i	$-0.112375\pi$
$241$	22.2754	+	8.10759i	1.43489	+	0.522256i	0.496559	+	0.868003i	$0.334597\pi$
$242$	−5.17098	+	8.95639i	−0.332403	+	0.575739i
$243$	−7.23118	−	13.8098i	−0.463881	−	0.885898i
$244$	7.67664			0.491446
$245$	−1.34703	−	0.188061i	−0.0860584	−	0.0120148i
$246$	−6.14993	−	4.54613i	−0.392105	−	0.289851i
$247$	20.6724	+	17.3462i	1.31535	+	1.10371i
$248$	6.95024	−	2.52968i	0.441341	−	0.160635i
$249$	6.86075	+	10.3546i	0.434782	+	0.656198i
$250$	0.336123	+	1.90625i	0.0212583	+	0.120562i
$251$	−12.0184	−	20.8164i	−0.758592	−	1.31392i	−0.943569	−	0.331177i	$-0.892554\pi$
$251$	−12.0184	−	20.8164i	−0.758592	−	1.31392i	0.184976	−	0.982743i	$-0.440779\pi$
$252$	−0.956140	+	7.87945i	−0.0602311	+	0.496359i
$253$	12.4383	−	21.5438i	0.781989	−	1.35445i
$254$	8.54871	+	3.11148i	0.536394	+	0.195231i
$255$	−1.19729	+	1.13728i	−0.0749771	+	0.0712192i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−4.91964	+	1.79060i	−0.306879	+	0.111695i	−0.490869	−	0.871233i	$-0.663321\pi$
$257$	−4.91964	+	1.79060i	−0.306879	+	0.111695i	0.183990	+	0.982928i	$0.441098\pi$
$258$	4.87854	+	20.2776i	0.303725	+	1.26243i
$259$	17.0273	+	16.4281i	1.05803	+	1.02079i
$260$	−0.501688	+	0.868949i	−0.0311134	+	0.0538899i
$261$	10.1820	+	6.59835i	0.630250	+	0.408428i
$262$	−3.33026			−0.205744
$263$	4.31245	−	3.61858i	0.265917	−	0.223131i	−0.500073	−	0.865983i	$-0.666693\pi$
$263$	4.31245	−	3.61858i	0.265917	−	0.223131i	0.765990	+	0.642852i	$0.222249\pi$
$264$	−3.56686	+	7.16264i	−0.219525	+	0.440830i
$265$	1.07264	+	0.900048i	0.0658915	+	0.0552895i
$266$	−7.72610	+	11.4657i	−0.473717	+	0.703005i
$267$	−1.57058	+	13.8440i	−0.0961180	+	0.847240i
$268$	−9.94542	+	8.34520i	−0.607513	+	0.509764i
$269$	0.645983	−	1.11888i	0.0393863	−	0.0682190i	−0.845660	−	0.533722i	$-0.820793\pi$
$269$	0.645983	−	1.11888i	0.0393863	−	0.0682190i	0.885047	+	0.465503i	$0.154126\pi$
$270$	0.992434	−	0.185419i	0.0603976	−	0.0112842i
$271$	3.54979	+	6.14842i	0.215634	+	0.373490i	0.953469	−	0.301492i	$-0.0974847\pi$
$271$	3.54979	+	6.14842i	0.215634	+	0.373490i	−0.737834	+	0.674982i	$0.764151\pi$
$272$	−0.852067	−	4.83231i	−0.0516642	−	0.293002i
$273$	11.9917	−	20.4015i	0.725771	−	1.23476i
$274$	−8.69485	+	3.16467i	−0.525275	+	0.191184i
$275$	3.98076	−	22.5760i	0.240049	−	1.36138i
$276$	4.15760	−	8.34891i	0.250258	−	0.502545i
$277$	−7.94393	+	6.66575i	−0.477305	+	0.400506i	−0.849451	−	0.527668i	$-0.823067\pi$
$277$	−7.94393	+	6.66575i	−0.477305	+	0.400506i	0.372146	+	0.928174i	$0.378622\pi$
$278$	4.72788	−	8.18893i	0.283559	−	0.491139i
$279$	13.3706	+	17.7080i	0.800479	+	1.06015i
$280$	−0.469718	−	0.208876i	−0.0280710	−	0.0124827i
$281$	0.712587	−	0.597931i	0.0425094	−	0.0356696i	−0.621285	−	0.783584i	$-0.713389\pi$
$281$	0.712587	−	0.597931i	0.0425094	−	0.0356696i	0.663795	+	0.747915i	$0.268945\pi$
$282$	−6.84676	−	2.02452i	−0.407719	−	0.120558i
$283$	−5.37136	−	4.50710i	−0.319294	−	0.267920i	0.469027	−	0.883184i	$-0.344605\pi$
$283$	−5.37136	−	4.50710i	−0.319294	−	0.267920i	−0.788321	+	0.615264i	$0.789049\pi$
$284$	−6.42929	−	5.39482i	−0.381508	−	0.320123i
$285$	1.68645	+	0.498666i	0.0998965	+	0.0295384i
$286$	18.2753	−	15.3348i	1.08064	−	0.906766i
$287$	−9.44798	+	6.87094i	−0.557697	+	0.405579i
$288$	−1.16954	+	2.76264i	−0.0689156	+	0.162790i
$289$	−3.53864	+	6.12911i	−0.208155	+	0.360536i
$290$	−0.601969	+	0.505112i	−0.0353488	+	0.0296612i
$291$	−6.84952	+	13.7546i	−0.401526	+	0.806307i
$292$	0.723073	−	4.10075i	0.0423147	−	0.239978i
$293$	−21.1293	+	7.69042i	−1.23438	+	0.449279i	−0.875097	−	0.483948i	$-0.839202\pi$
$293$	−21.1293	+	7.69042i	−1.23438	+	0.449279i	−0.359287	+	0.933227i	$0.616980\pi$
$294$	11.0397	+	5.01253i	0.643847	+	0.292336i
$295$	0.146356	+	0.830027i	0.00852118	+	0.0483260i
$296$	4.47139	+	7.74468i	0.259894	+	0.450150i
$297$	−23.6813	−	3.92777i	−1.37413	−	0.227912i
$298$	−3.96593	+	6.86919i	−0.229740	+	0.397921i
$299$	−21.3021	+	17.8745i	−1.23193	+	1.03371i
$300$	0.968859	−	8.54008i	0.0559371	−	0.493062i
$301$	31.7818	+	2.20785i	1.83187	+	0.127259i
$302$	−4.69346	−	3.93828i	−0.270078	−	0.226622i
$303$	13.2718	−	26.6511i	0.762443	−	1.53107i
$304$	−4.00310	+	3.35900i	−0.229594	+	0.192652i
$305$	−1.49156			−0.0854066
$306$	13.1097	−	6.69562i	0.749432	−	0.382763i
$307$	−2.99691	+	5.19080i	−0.171043	+	0.296255i	−0.938785	−	0.344504i	$-0.888047\pi$
$307$	−2.99691	+	5.19080i	−0.171043	+	0.296255i	0.767742	+	0.640759i	$0.221380\pi$
$308$	8.79612	+	8.48657i	0.501205	+	0.483567i
$309$	0.308745	+	1.28330i	0.0175639	+	0.0730042i
$310$	−1.35042	+	0.491514i	−0.0766989	+	0.0279161i
$311$	−16.9118	−	14.1906i	−0.958978	−	0.804678i	0.0218088	−	0.999762i	$-0.493057\pi$
$311$	−16.9118	−	14.1906i	−0.958978	−	0.804678i	−0.980786	+	0.195084i	$0.937502\pi$
$312$	6.48512	−	6.16008i	0.367148	−	0.348746i
$313$	2.09458	+	0.762365i	0.118393	+	0.0430914i	0.400537	−	0.916281i	$-0.368824\pi$
$313$	2.09458	+	0.762365i	0.118393	+	0.0430914i	−0.282144	+	0.959372i	$0.591046\pi$
$314$	1.46060	−	2.52984i	0.0824267	−	0.142767i
$315$	0.185777	−	1.53097i	0.0104673	−	0.0862603i
$316$	2.96943	+	5.14320i	0.167043	+	0.289327i
$317$	1.71943	+	9.75137i	0.0965727	+	0.547691i	0.994254	+	0.107046i	$0.0341392\pi$
$317$	1.71943	+	9.75137i	0.0965727	+	0.547691i	−0.897681	+	0.440645i	$0.854750\pi$
$318$	−6.89435	−	10.4054i	−0.386616	−	0.583503i
$319$	17.5571	−	6.39026i	0.983008	−	0.357786i
$320$	−0.148842	−	0.124893i	−0.00832050	−	0.00698173i
$321$	18.4381	+	13.6297i	1.02911	+	0.760738i
$322$	−10.2529	−	9.89212i	−0.571373	−	0.551266i
$323$	25.6417			1.42674
$324$	−8.95249	−	0.923532i	−0.497361	−	0.0513074i
$325$	−12.8127	+	22.1923i	−0.710723	+	1.23101i
$326$	−11.2048	−	4.07820i	−0.620574	−	0.225871i
$327$	1.08491	−	9.56302i	0.0599956	−	0.528836i
$328$	−4.14918	+	1.51018i	−0.229100	+	0.0833856i
$329$	−6.09457	+	9.04445i	−0.336004	+	0.498637i
$330$	0.693037	−	1.39169i	0.0381504	−	0.0766101i
$331$	−4.77377	−	27.0734i	−0.262390	−	1.48809i	−0.776365	−	0.630283i	$-0.782939\pi$
$331$	−4.77377	−	27.0734i	−0.262390	−	1.48809i	0.513975	−	0.857805i	$-0.328172\pi$
$332$	7.17143			0.393583
$333$	−18.2780	+	19.6386i	−1.00163	+	1.07619i
$334$	−4.19706			−0.229653
$335$	1.93238	−	1.62146i	0.105577	−	0.0885900i
$336$	3.48740	+	2.97288i	0.190253	+	0.162184i
$337$	−4.06682	+	23.0641i	−0.221534	+	1.25638i	0.647667	+	0.761923i	$0.275745\pi$
$337$	−4.06682	+	23.0641i	−0.221534	+	1.25638i	−0.869201	+	0.494458i	$0.835366\pi$
$338$	−12.8435	+	4.67466i	−0.698596	+	0.254268i
$339$	−28.9078	−	8.54776i	−1.57006	−	0.464251i
$340$	0.165556	+	0.938913i	0.00897852	+	0.0509197i
$341$	34.1689			1.85035
$342$	−13.1561	−	8.52568i	−0.711399	−	0.461016i
$343$	12.3737	−	13.7802i	0.668115	−	0.744058i
$344$	11.3152	+	4.11838i	0.610072	+	0.222048i
$345$	−0.807817	+	1.62218i	−0.0434914	+	0.0873355i
$346$	−4.24383	+	1.54463i	−0.228150	+	0.0830397i
$347$	−1.23690	+	7.01482i	−0.0664004	+	0.376576i	0.933440	+	0.358733i	$0.116791\pi$
$347$	−1.23690	+	7.01482i	−0.0664004	+	0.376576i	−0.999841	+	0.0178429i	$0.994320\pi$
$348$	6.42269	−	2.79634i	0.344293	−	0.149900i
$349$	3.49456	+	19.8186i	0.187059	+	1.06087i	0.923281	+	0.384126i	$0.125497\pi$
$349$	3.49456	+	19.8186i	0.187059	+	1.06087i	−0.736221	+	0.676741i	$0.763392\pi$
$350$	−11.9963	−	5.33453i	−0.641227	−	0.285143i
$351$	23.3736	+	13.1797i	1.24759	+	0.703479i
$352$	2.30987	+	4.00081i	0.123116	+	0.213244i
$353$	32.6050	+	11.8673i	1.73539	+	0.631631i	0.998991	−	0.0449150i	$-0.0143017\pi$
$353$	32.6050	+	11.8673i	1.73539	+	0.631631i	0.736401	+	0.676546i	$0.236524\pi$
$354$	0.846939	−	7.46541i	0.0450143	−	0.396782i
$355$	1.24920	+	1.04821i	0.0663009	+	0.0556330i
$356$	6.16215	+	5.17066i	0.326593	+	0.274044i
$357$	−3.73204	−	22.1742i	−0.197520	−	1.17358i
$358$	18.4436	+	6.71292i	0.974774	+	0.354789i
$359$	−7.54823	+	13.0739i	−0.398380	+	0.690015i	−0.993526	−	0.113603i	$-0.963761\pi$
$359$	−7.54823	+	13.0739i	−0.398380	+	0.690015i	0.595146	+	0.803618i	$0.297094\pi$
$360$	0.227240	−	0.536778i	0.0119766	−	0.0282907i
$361$	−4.15387	−	7.19471i	−0.218625	−	0.378669i
$362$	−7.58766	−	2.76168i	−0.398798	−	0.145151i
$363$	−12.9875	+	12.3366i	−0.681669	+	0.647503i
$364$	−5.99501	−	12.2774i	−0.314224	−	0.643510i
$365$	−0.140492	+	0.796772i	−0.00735371	+	0.0417049i
$366$	12.7506	+	3.77023i	0.666484	+	0.197073i
$367$	3.27205	+	18.5567i	0.170800	+	0.968653i	0.942881	+	0.333130i	$0.108105\pi$
$367$	3.27205	+	18.5567i	0.170800	+	0.968653i	−0.772081	+	0.635524i	$0.780784\pi$
$368$	−2.69243	−	4.66342i	−0.140352	−	0.243098i
$369$	−7.98205	−	10.5714i	−0.415529	−	0.550323i
$370$	−0.868786	−	1.50478i	−0.0451660	−	0.0782299i
$371$	−18.3258	+	5.26386i	−0.951426	+	0.273286i
$372$	12.7865	−	0.788228i	0.662948	−	0.0408677i
$373$	2.65396	−	15.0513i	0.137417	−	0.779329i	−0.835730	−	0.549141i	$-0.814955\pi$
$373$	2.65396	−	15.0513i	0.137417	−	0.779329i	0.973146	−	0.230188i	$-0.0739340\pi$
$374$	3.93633	−	22.3240i	0.203543	−	1.15435i
$375$	−0.377928	+	3.33128i	−0.0195161	+	0.172027i
$376$	−3.15776	+	2.64968i	−0.162849	+	0.136647i
$377$	−20.8854			−1.07565
$378$	−5.45795	+	12.6179i	−0.280727	+	0.648994i
$379$	−3.19239			−0.163982			−0.0819910	−	0.996633i	$-0.526128\pi$
$379$	−3.19239			−0.163982			−0.0819910	+	0.996633i	$0.526128\pi$
$380$	0.777798	−	0.652650i	0.0399002	−	0.0334803i
$381$	12.6709	+	9.36657i	0.649152	+	0.479864i
$382$	0.590412	−	3.34840i	0.0302081	−	0.171319i
$383$	−5.99079	+	33.9754i	−0.306115	+	1.73606i	0.312095	+	0.950051i	$0.398969\pi$
$383$	−5.99079	+	33.9754i	−0.306115	+	1.73606i	−0.618210	+	0.786013i	$0.712142\pi$
$384$	0.956678	+	1.44387i	0.0488202	+	0.0736823i
$385$	−1.70908	−	1.64893i	−0.0871026	−	0.0840374i
$386$	−1.31968	−	2.28576i	−0.0671702	−	0.116342i
$387$	−1.85588	+	36.0763i	−0.0943396	+	1.83386i
$388$	4.43569	+	7.68284i	0.225188	+	0.390037i
$389$	−4.13420	−	23.4462i	−0.209612	−	1.18877i	−0.890015	−	0.455932i	$-0.849306\pi$
$389$	−4.13420	−	23.4462i	−0.209612	−	1.18877i	0.680403	−	0.732838i	$-0.261805\pi$
$390$	−1.26005	+	1.19690i	−0.0638052	+	0.0606072i
$391$	−4.58826	+	26.0213i	−0.232038	+	1.31595i
$392$	5.93296	−	3.71484i	0.299659	−	0.187628i
$393$	−5.53143	−	1.63559i	−0.279024	−	0.0825046i
$394$	−3.06695	−	1.11628i	−0.154511	−	0.0562373i
$395$	−0.576956	−	0.999317i	−0.0290298	−	0.0502811i
$396$	−9.44220	+	10.1451i	−0.474488	+	0.509809i
$397$	−5.27600	+	9.13830i	−0.264795	+	0.458638i	−0.967510	−	0.252833i	$-0.918638\pi$
$397$	−5.27600	+	9.13830i	−0.264795	+	0.458638i	0.702715	+	0.711472i	$0.251971\pi$
$398$	−10.0550	−	3.65972i	−0.504012	−	0.183445i
$399$	−18.4639	+	15.2495i	−0.924350	+	0.763430i
$400$	−3.80130	−	3.18967i	−0.190065	−	0.159484i
$401$	14.3582	+	12.0479i	0.717012	+	0.601645i	0.926557	−	0.376154i	$-0.122754\pi$
$401$	14.3582	+	12.0479i	0.717012	+	0.601645i	−0.209545	+	0.977799i	$0.567198\pi$
$402$	−20.6175	+	8.97655i	−1.02831	+	0.447710i
$403$	−35.8916	−	13.0635i	−1.78789	−	0.650739i
$404$	−8.59468	−	14.8864i	−0.427601	−	0.740627i
$405$	1.73946	+	0.179441i	0.0864344	+	0.00891651i
$406$	−1.12334	−	10.6412i	−0.0557504	−	0.528116i
$407$	7.17398	+	40.6856i	0.355601	+	2.01671i
$408$	0.958044	−	8.44476i	0.0474303	−	0.418078i
$409$	−1.13755	+	6.45139i	−0.0562484	+	0.319001i	−0.999930	−	0.0118552i	$-0.996226\pi$
$409$	−1.13755	+	6.45139i	−0.0562484	+	0.319001i	0.943681	+	0.330856i	$0.107337\pi$
$410$	0.806181	−	0.293426i	0.0398144	−	0.0144913i
$411$	−15.9961	+	0.986085i	−0.789028	+	0.0486400i
$412$	0.716095	+	0.260637i	0.0352795	+	0.0128407i
$413$	−10.4867	−	4.66324i	−0.516015	−	0.229463i
$414$	11.0060	−	11.8253i	0.540916	−	0.581181i
$415$	−1.39340			−0.0683994
$416$	−0.896734	−	5.08563i	−0.0439660	−	0.249344i
$417$	11.8747	−	11.2795i	0.581504	−	0.552359i
$418$	−22.6854	+	8.25680i	−1.10958	+	0.403853i
$419$	1.56895	−	8.89798i	0.0766484	−	0.434695i	−0.922200	−	0.386714i	$-0.873610\pi$
$419$	1.56895	−	8.89798i	0.0766484	−	0.434695i	0.998848	−	0.0479810i	$-0.0152787\pi$
$420$	−0.677599	−	0.577627i	−0.0330634	−	0.0281853i
$421$	5.74301	−	4.81896i	0.279897	−	0.234862i	−0.492021	−	0.870583i	$-0.663742\pi$
$421$	5.74301	−	4.81896i	0.279897	−	0.234862i	0.771919	+	0.635721i	$0.219297\pi$
$422$	−20.7353			−1.00938
$423$	−10.3779	−	6.72530i	−0.504591	−	0.326995i
$424$	−7.20656			−0.349982
$425$	4.22817	+	23.9791i	0.205096	+	1.16316i
$426$	−8.02924	−	12.1182i	−0.389018	−	0.587129i
$427$	11.3498	−	16.8433i	0.549255	−	0.815105i
$428$	12.4396	−	4.52766i	0.601292	−	0.218853i
$429$	37.8859	−	16.4950i	1.82915	−	0.796384i
$430$	−2.19852	−	0.800196i	−0.106022	−	0.0385889i
$431$	9.43335	−	16.3390i	0.454388	−	0.787024i	−0.544264	−	0.838914i	$-0.683191\pi$
$431$	9.43335	−	16.3390i	0.454388	−	0.787024i	0.998653	+	0.0518899i	$0.0165245\pi$
$432$	−3.29937	+	4.01424i	−0.158741	+	0.193135i
$433$	30.3589			1.45896			0.729478	−	0.684004i	$-0.239763\pi$
$433$	30.3589			1.45896			0.729478	+	0.684004i	$0.239763\pi$
$434$	4.72546	−	18.9896i	0.226829	−	0.911531i
$435$	−1.24792	+	0.543326i	−0.0598333	+	0.0260505i
$436$	−4.25662	−	3.57173i	−0.203855	−	0.171055i
$437$	26.4425	−	9.62428i	1.26492	−	0.460392i
$438$	3.21500	−	6.45607i	0.153619	−	0.308483i
$439$	−1.30017	−	7.37361i	−0.0620536	−	0.351923i	−0.999987	−	0.00510790i	$-0.998374\pi$
$439$	−1.30017	−	7.37361i	−0.0620536	−	0.351923i	0.937933	−	0.346816i	$-0.112737\pi$
$440$	−0.448805	−	0.777352i	−0.0213959	−	0.0370588i
$441$	15.8747	+	13.7475i	0.755937	+	0.654644i
$442$	−12.6697	+	21.9446i	−0.602637	+	1.04380i
$443$	36.3535	+	13.2316i	1.72721	+	0.628651i	0.998425	−	0.0560964i	$-0.0178654\pi$
$443$	36.3535	+	13.2316i	1.72721	+	0.628651i	0.728780	+	0.684748i	$0.240088\pi$
$444$	3.62316	+	15.0596i	0.171948	+	0.714699i
$445$	−1.19730	−	1.00465i	−0.0567574	−	0.0476251i
$446$	6.07337	−	2.21053i	0.287582	−	0.104671i
$447$	−9.96091	+	9.46166i	−0.471135	+	0.447521i
$448$	2.54293	−	0.730426i	0.120142	−	0.0345094i
$449$	1.03306	−	1.78931i	0.0487529	−	0.0844426i	−0.840619	−	0.541627i	$-0.817809\pi$
$449$	1.03306	−	1.78931i	0.0487529	−	0.0844426i	0.889372	+	0.457184i	$0.151142\pi$
$450$	5.80353	−	13.7089i	0.273581	−	0.646244i
$451$	−20.3983			−0.960517
$452$	−13.3324	+	11.1872i	−0.627105	+	0.526204i
$453$	−5.86144	−	8.84642i	−0.275394	−	0.415641i
$454$	4.72916	+	3.96823i	0.221950	+	0.186238i
$455$	1.16482	+	2.38548i	0.0546078	+	0.111833i
$456$	−8.29871	+	3.61313i	−0.388622	+	0.169200i
$457$	8.66541	−	7.27115i	0.405351	−	0.340130i	−0.417207	−	0.908812i	$-0.636991\pi$
$457$	8.66541	−	7.27115i	0.405351	−	0.340130i	0.822558	+	0.568682i	$0.192546\pi$
$458$	−8.18635	+	14.1792i	−0.382523	+	0.662549i
$459$	25.0631	−	4.68259i	1.16985	−	0.218565i
$460$	0.523136	+	0.906097i	0.0243913	+	0.0422470i
$461$	−0.284378	−	1.61279i	−0.0132448	−	0.0751151i	0.977469	−	0.211079i	$-0.0676979\pi$
$461$	−0.284378	−	1.61279i	−0.0132448	−	0.0751151i	−0.990714	+	0.135964i	$0.956587\pi$
$462$	10.4420	+	18.4159i	0.485806	+	0.856786i
$463$	−14.4848	+	5.27205i	−0.673168	+	0.245013i	−0.655911	−	0.754838i	$-0.727715\pi$
$463$	−14.4848	+	5.27205i	−0.673168	+	0.245013i	−0.0172565	+	0.999851i	$0.505493\pi$
$464$	0.702296	−	3.98292i	0.0326033	−	0.184902i
$465$	−2.48440	+	0.153152i	−0.115211	+	0.00710225i
$466$	−3.53660	+	2.96756i	−0.163830	+	0.137470i
$467$	3.42982	−	5.94062i	0.158713	−	0.274899i	−0.775692	−	0.631112i	$-0.782599\pi$
$467$	3.42982	−	5.94062i	0.158713	−	0.274899i	0.934405	+	0.356213i	$0.115932\pi$
$468$	13.7969	−	7.04662i	0.637763	−	0.325730i
$469$	3.60604	+	34.1595i	0.166511	+	1.57734i
$470$	0.613550	−	0.514830i	0.0283009	−	0.0237473i
$471$	3.66849	−	3.48462i	0.169035	−	0.160563i
$472$	−3.32295	−	2.78829i	−0.152951	−	0.128341i
$473$	42.6133	+	35.7568i	1.95936	+	1.64410i
$474$	2.40612	+	10.0010i	0.110517	+	0.459362i
$475$	19.8644	−	16.6682i	0.911441	−	0.764790i
$476$	−11.8624	−	5.27499i	−0.543710	−	0.241779i
$477$	−6.34087	−	20.6689i	−0.290329	−	0.946365i
$478$	−2.02049	+	3.49958i	−0.0924149	+	0.160067i
$479$	−19.4943	+	16.3577i	−0.890718	+	0.747401i	−0.968354	−	0.249581i	$-0.919707\pi$
$479$	−19.4943	+	16.3577i	−0.890718	+	0.747401i	0.0776359	+	0.996982i	$0.475263\pi$
$480$	−0.185881	−	0.280543i	−0.00848429	−	0.0128050i
$481$	8.01930	−	45.4797i	0.365649	−	2.07370i
$482$	22.2754	−	8.10759i	1.01462	−	0.369291i
$483$	−12.1714	−	21.4659i	−0.553818	−	0.976734i
$484$	1.79586	+	10.1848i	0.0816300	+	0.462947i
$485$	−0.861849	−	1.49277i	−0.0391346	−	0.0677830i
$486$	−14.4162	−	5.93079i	−0.653930	−	0.269026i
$487$	−3.74032	+	6.47842i	−0.169490	+	0.293565i	−0.938241	−	0.345983i	$-0.887545\pi$
$487$	−3.74032	+	6.47842i	−0.169490	+	0.293565i	0.768751	+	0.639549i	$0.220879\pi$
$488$	5.88064	−	4.93445i	0.266204	−	0.223372i
$489$	−16.6077	−	12.2767i	−0.751028	−	0.555173i
$490$	−1.15277	+	0.721789i	−0.0520767	+	0.0326071i
$491$	2.79606	+	2.34618i	0.126185	+	0.105881i	0.703696	−	0.710501i	$-0.251532\pi$
$491$	2.79606	+	2.34618i	0.126185	+	0.105881i	−0.577511	+	0.816383i	$0.695976\pi$
$492$	−7.63332	+	0.470559i	−0.344136	+	0.0212144i
$493$	−15.2022	+	12.7562i	−0.684674	+	0.574510i
$494$	26.9859			1.21415
$495$	1.83461	−	1.97118i	0.0824595	−	0.0885978i
$496$	3.69814	−	6.40537i	0.166052	−	0.287610i
$497$	−21.3424	+	6.13035i	−0.957337	+	0.274984i
$498$	11.9115	+	3.52211i	0.533766	+	0.157829i
$499$	−12.4158	+	4.51900i	−0.555809	+	0.202298i	−0.604626	−	0.796510i	$-0.706677\pi$
$499$	−12.4158	+	4.51900i	−0.555809	+	0.202298i	0.0488164	+	0.998808i	$0.484455\pi$
$500$	1.48280	+	1.24421i	0.0663127	+	0.0556429i
$501$	−6.97115	−	2.06130i	−0.311448	−	0.0920922i
$502$	−22.5871	−	8.22104i	−1.00811	−	0.366923i
$503$	−0.209877	+	0.363518i	−0.00935797	+	0.0162085i	−0.870666	−	0.491874i	$-0.836312\pi$
$503$	−0.209877	+	0.363518i	−0.00935797	+	0.0162085i	0.861308	+	0.508082i	$0.169645\pi$
$504$	4.33237	+	6.65061i	0.192979	+	0.296242i
$505$	1.66994	+	2.89241i	0.0743112	+	0.128711i
$506$	−4.31978	−	24.4987i	−0.192037	−	1.08910i
$507$	−23.6285	+	1.45659i	−1.04938	+	0.0646893i
$508$	8.54871	−	3.11148i	0.379288	−	0.138049i
$509$	−28.6008	−	23.9989i	−1.26771	−	1.06373i	−0.994816	−	0.101690i	$-0.967575\pi$
$509$	−28.6008	−	23.9989i	−1.26771	−	1.06373i	−0.272893	−	0.962044i	$-0.587980\pi$
$510$	−0.186147	+	1.64081i	−0.00824273	+	0.0726562i
$511$	−7.92841	−	7.64940i	−0.350732	−	0.338390i
$512$	1.00000			0.0441942
$513$	−17.6645	−	20.6222i	−0.779908	−	0.910491i
$514$	−2.61769	+	4.53397i	−0.115461	+	0.199985i
$515$	−0.139136	−	0.0506415i	−0.00613109	−	0.00223153i
$516$	16.7714	+	12.3977i	0.738318	+	0.545777i
$517$	−17.8949	+	6.51320i	−0.787015	+	0.286450i
$518$	23.6035	+	1.63971i	1.03708	+	0.0720449i
$519$	−7.80745	+	0.481294i	−0.342709	+	0.0211264i
$520$	0.174234	+	0.988133i	0.00764069	+	0.0433325i
$521$	−42.7727			−1.87391			−0.936953	−	0.349455i	$-0.886367\pi$
$521$	−42.7727			−1.87391			−0.936953	+	0.349455i	$0.886367\pi$
$522$	12.0412	−	1.49024i	0.527029	−	0.0652258i
$523$	27.2302			1.19069			0.595347	−	0.803468i	$-0.297014\pi$
$523$	27.2302			1.19069			0.595347	+	0.803468i	$0.297014\pi$
$524$	−2.55113	+	2.14065i	−0.111446	+	0.0935147i
$525$	−17.3054	−	14.7522i	−0.755268	−	0.643837i
$526$	0.977554	−	5.54398i	0.0426234	−	0.241729i
$527$	−34.1039	+	12.4128i	−1.48559	+	0.540710i
$528$	1.87168	+	7.77963i	0.0814545	+	0.338565i
$529$	1.04131	+	5.90555i	0.0452743	+	0.256763i
$530$	1.40023			0.0608220
$531$	5.07322	−	11.9838i	0.220159	−	0.520053i
$532$	1.45146	+	13.7495i	0.0629287	+	0.596114i
$533$	21.4267	+	7.79869i	0.928094	+	0.337799i
$534$	7.69563	+	11.6147i	0.333022	+	0.502616i
$535$	−2.41701	+	0.879719i	−0.104496	+	0.0380336i
$536$	−2.25444	+	12.7856i	−0.0973771	+	0.552253i
$537$	27.3372	+	20.2081i	1.17969	+	0.872044i
$538$	−0.224348	−	1.27234i	−0.00967231	−	0.0548544i
$539$	31.6253	−	6.75229i	1.36220	−	0.290842i
$540$	0.641064	−	0.779963i	0.0275870	−	0.0335643i
$541$	−8.82208	−	15.2803i	−0.379291	−	0.656951i	0.611668	−	0.791114i	$-0.290499\pi$
$541$	−8.82208	−	15.2803i	−0.379291	−	0.656951i	−0.990959	+	0.134163i	$0.957165\pi$
$542$	6.67142	+	2.42820i	0.286562	+	0.104300i
$543$	−11.2465	−	8.31357i	−0.482632	−	0.356769i
$544$	−3.75887	−	3.15407i	−0.161160	−	0.135230i
$545$	0.827057	+	0.693983i	0.0354272	+	0.0297270i
$546$	−3.92768	−	23.3366i	−0.168089	−	0.998714i
$547$	12.2415	+	4.45553i	0.523408	+	0.190505i	0.590192	−	0.807263i	$-0.299052\pi$
$547$	12.2415	+	4.45553i	0.523408	+	0.190505i	−0.0667847	+	0.997767i	$0.521274\pi$
$548$	−4.62643	+	8.01321i	−0.197631	+	0.342308i
$549$	19.3266	+	12.5244i	0.824838	+	0.534528i
$550$	−11.4621	−	19.8530i	−0.488747	−	0.846535i
$551$	19.8600	+	7.22843i	0.846063	+	0.307942i
$552$	−2.18167	−	9.06809i	−0.0928580	−	0.385964i
$553$	15.6749	+	1.08892i	0.666566	+	0.0463058i
$554$	−1.80074	+	10.2125i	−0.0765063	+	0.433889i
$555$	−0.703976	−	2.92607i	−0.0298821	−	0.124205i
$556$	−1.64198	−	9.31210i	−0.0696353	−	0.394921i
$557$	−15.5586	−	26.9482i	−0.659237	−	1.14183i	−0.980813	−	0.194949i	$-0.937546\pi$
$557$	−15.5586	−	26.9482i	−0.659237	−	1.14183i	0.321576	−	0.946884i	$-0.395787\pi$
$558$	21.6250	+	4.97061i	0.915458	+	0.210423i
$559$	−31.0912	−	53.8516i	−1.31502	−	2.27768i
$560$	−0.494088	+	0.141921i	−0.0208790	+	0.00599726i
$561$	17.5021	−	35.1461i	0.738938	−	1.48387i
$562$	0.161530	−	0.916084i	0.00681375	−	0.0386427i
$563$	7.57153	−	42.9403i	0.319102	−	1.80972i	−0.229137	−	0.973394i	$-0.573590\pi$
$563$	7.57153	−	42.9403i	0.319102	−	1.80972i	0.548238	−	0.836322i	$-0.315299\pi$
$564$	−6.54626	+	2.85014i	−0.275647	+	0.120013i
$565$	2.59048	−	2.17367i	0.108982	−	0.0914470i
$566$	−7.01181			−0.294728
$567$	−15.2625	+	18.2772i	−0.640963	+	0.767572i
$568$	−8.39284			−0.352156
$569$	25.4043	−	21.3168i	1.06500	−	0.893645i	0.0704140	−	0.997518i	$-0.477568\pi$
$569$	25.4043	−	21.3168i	1.06500	−	0.893645i	0.994591	+	0.103873i	$0.0331235\pi$
$570$	1.61243	−	0.702027i	0.0675372	−	0.0294047i
$571$	2.26116	−	12.8237i	0.0946267	−	0.536655i	−0.900234	−	0.435406i	$-0.856605\pi$
$571$	2.26116	−	12.8237i	0.0946267	−	0.536655i	0.994861	−	0.101249i	$-0.0322839\pi$
$572$	4.14267	−	23.4943i	0.173214	−	0.982345i
$573$	2.62515	−	5.27158i	0.109667	−	0.220224i
$574$	−2.82102	+	11.3365i	−0.117747	+	0.473176i
$575$	13.3605	+	23.1410i	0.557171	+	0.965048i
$576$	0.879875	+	2.86807i	0.0366614	+	0.119503i
$577$	−3.14064	−	5.43974i	−0.130746	−	0.226459i	0.793218	−	0.608938i	$-0.208404\pi$
$577$	−3.14064	−	5.43974i	−0.130746	−	0.226459i	−0.923965	+	0.382478i	$0.875071\pi$
$578$	1.22896	+	6.96976i	0.0511179	+	0.289904i
$579$	−1.06934	−	4.44470i	−0.0444402	−	0.184715i
$580$	−0.136455	+	0.773876i	−0.00566600	+	0.0321335i
$581$	10.6029	−	15.7348i	0.439881	−	0.652791i
$582$	3.59423	+	14.9394i	0.148986	+	0.619258i
$583$	−31.2846	−	11.3867i	−1.29568	−	0.471588i
$584$	−2.08201	−	3.60614i	−0.0861540	−	0.149223i
$585$	−2.68073	+	1.36915i	−0.110834	+	0.0566074i
$586$	−11.2426	+	19.4728i	−0.464429	+	0.804415i
$587$	27.0214	+	9.83500i	1.11529	+	0.405934i	0.832933	−	0.553374i	$-0.186660\pi$
$587$	27.0214	+	9.83500i	1.11529	+	0.405934i	0.282361	+	0.959308i	$0.408882\pi$
$588$	11.6789	−	3.25635i	0.481629	−	0.134290i
$589$	29.6081	+	24.8442i	1.21998	+	1.02369i
$590$	0.645646	+	0.541761i	0.0265808	+	0.0223040i
$591$	−4.54584	−	3.36036i	−0.186991	−	0.138227i
$592$	8.40347	+	3.05861i	0.345380	+	0.125708i
$593$	4.87366	+	8.44142i	0.200137	+	0.346648i	0.948572	−	0.316560i	$-0.102528\pi$
$593$	4.87366	+	8.44142i	0.200137	+	0.346648i	−0.748435	+	0.663208i	$0.769195\pi$
$594$	−20.6657	+	12.2132i	−0.847923	+	0.501114i
$595$	2.30484	+	1.02492i	0.0944893	+	0.0420178i
$596$	1.37735	+	7.81135i	0.0564185	+	0.319965i
$597$	−14.9036	−	11.0170i	−0.609963	−	0.450895i
$598$	−4.82878	+	27.3854i	−0.197464	+	1.11987i
$599$	27.8629	−	10.1413i	1.13845	−	0.414361i	0.297096	−	0.954848i	$-0.403982\pi$
$599$	27.8629	−	10.1413i	1.13845	−	0.414361i	0.841353	+	0.540486i	$0.181760\pi$
$600$	−4.74727	−	7.16485i	−0.193807	−	0.292504i
$601$	11.8191	+	4.30182i	0.482113	+	0.175475i	0.571632	−	0.820510i	$-0.306311\pi$
$601$	11.8191	+	4.30182i	0.482113	+	0.175475i	−0.0895186	+	0.995985i	$0.528533\pi$
$602$	25.7654	−	18.7376i	1.05012	−	0.763688i
$603$	−38.6536	+	4.78381i	−1.57409	+	0.194812i
$604$	−6.12687			−0.249299
$605$	−0.348934	−	1.97890i	−0.0141862	−	0.0804538i
$606$	−6.96426	−	28.9469i	−0.282904	−	1.17589i
$607$	−19.0006	+	6.91565i	−0.771210	+	0.280697i	−0.697502	−	0.716582i	$-0.745705\pi$
$607$	−19.0006	+	6.91565i	−0.771210	+	0.280697i	−0.0737076	+	0.997280i	$0.523483\pi$
$608$	−0.907430	+	5.14629i	−0.0368011	+	0.208710i
$609$	3.36041	−	18.2264i	0.136171	−	0.738571i
$610$	−1.14260	+	0.958757i	−0.0462626	+	0.0388190i
$611$	21.2872			0.861189
$612$	5.73875	−	13.5559i	0.231975	−	0.547965i
$613$	24.3288			0.982629			0.491315	−	0.870982i	$-0.336517\pi$
$613$	24.3288			0.982629			0.491315	+	0.870982i	$0.336517\pi$
$614$	1.04082	+	5.90276i	0.0420039	+	0.238216i
$615$	1.48314	−	0.0914291i	0.0598062	−	0.00368678i
$616$	12.1933	+	0.847057i	0.491281	+	0.0341289i
$617$	31.1297	−	11.3303i	1.25324	−	0.456141i	0.371742	−	0.928336i	$-0.378761\pi$
$617$	31.1297	−	11.3303i	1.25324	−	0.456141i	0.881494	+	0.472195i	$0.156538\pi$
$618$	1.06140	+	0.784604i	0.0426957	+	0.0315614i
$619$	14.4316	+	5.25266i	0.580054	+	0.211122i	0.615349	−	0.788255i	$-0.289015\pi$
$619$	14.4316	+	5.25266i	0.580054	+	0.211122i	−0.0352956	+	0.999377i	$0.511237\pi$
$620$	−0.718545	+	1.24456i	−0.0288575	+	0.0499826i
$621$	24.0883	−	14.2360i	0.966631	−	0.571270i
$622$	−22.0767			−0.885196
$623$	20.4556	−	5.87563i	0.819537	−	0.235402i
$624$	1.00827	−	8.88745i	0.0403630	−	0.355783i
$625$	18.7184	+	15.7066i	0.748736	+	0.628264i
$626$	2.09458	−	0.762365i	0.0837163	−	0.0304702i
$627$	−41.7347	+	2.57275i	−1.66672	+	0.102746i
$628$	−0.507263	−	2.87683i	−0.0202420	−	0.114798i
$629$	−21.9405	−	38.0021i	−0.874825	−	1.51524i
$630$	−0.841775	−	1.29221i	−0.0335371	−	0.0514827i
$631$	−7.34071	+	12.7145i	−0.292229	+	0.506155i	−0.974336	−	0.225096i	$-0.927730\pi$
$631$	−7.34071	+	12.7145i	−0.292229	+	0.506155i	0.682108	+	0.731252i	$0.261064\pi$
$632$	5.58069	+	2.03121i	0.221988	+	0.0807971i
$633$	−34.4405	−	10.1837i	−1.36889	−	0.404766i
$634$	7.58522	+	6.36475i	0.301247	+	0.252777i
$635$	−1.66100	+	0.604556i	−0.0659150	+	0.0239911i
$636$	−11.9698	−	3.53936i	−0.474634	−	0.140345i
$637$	−35.8014	−	4.99830i	−1.41850	−	0.198040i
$638$	9.34193	−	16.1807i	0.369851	−	0.640600i
$639$	−7.38465	−	24.0713i	−0.292132	−	0.952244i
$640$	−0.194299			−0.00768034
$641$	2.57030	−	2.15674i	0.101521	−	0.0851862i	−0.590614	−	0.806954i	$-0.701115\pi$
$641$	2.57030	−	2.15674i	0.101521	−	0.0851862i	0.692135	+	0.721768i	$0.256670\pi$
$642$	22.8854	−	1.41078i	0.903215	−	0.0556791i
$643$	−15.5818	−	13.0746i	−0.614484	−	0.515614i	0.281580	−	0.959538i	$-0.409142\pi$
$643$	−15.5818	−	13.0746i	−0.614484	−	0.515614i	−0.896064	+	0.443924i	$0.853586\pi$
$644$	−14.2127	−	0.987346i	−0.560060	−	0.0389069i
$645$	−3.25866	−	2.40885i	−0.128310	−	0.0948486i
$646$	19.6427	−	16.4822i	0.772831	−	0.648482i
$647$	8.36839	−	14.4945i	0.328995	−	0.569836i	−0.653318	−	0.757084i	$-0.726623\pi$
$647$	8.36839	−	14.4945i	0.328995	−	0.569836i	0.982313	+	0.187248i	$0.0599567\pi$
$648$	−7.45164	+	5.04708i	−0.292728	+	0.198268i
$649$	−10.0198	−	17.3547i	−0.393310	−	0.681233i
$650$	4.44982	+	25.2362i	0.174536	+	0.989844i
$651$	17.1752	−	29.2202i	0.673148	−	1.14523i
$652$	−11.2048	+	4.07820i	−0.438812	+	0.159715i
$653$	1.00621	−	5.70650i	0.0393760	−	0.223312i	−0.958770	−	0.284185i	$-0.908277\pi$
$653$	1.00621	−	5.70650i	0.0393760	−	0.223312i	0.998146	+	0.0608722i	$0.0193882\pi$
$654$	−5.31590	−	8.02306i	−0.207868	−	0.313727i
$655$	0.495681	−	0.415926i	0.0193679	−	0.0162516i
$656$	−2.20773	+	3.82390i	−0.0861974	+	0.149298i
$657$	8.51076	−	9.14429i	0.332036	−	0.356753i
$658$	1.14495	+	10.8460i	0.0446349	+	0.422820i
$659$	−17.9962	+	15.1006i	−0.701032	+	0.588236i	−0.922067	−	0.387030i	$-0.873501\pi$
$659$	−17.9962	+	15.1006i	−0.701032	+	0.588236i	0.221035	+	0.975266i	$0.429057\pi$
$660$	−0.363666	−	1.51157i	−0.0141557	−	0.0588379i
$661$	16.4717	+	13.8214i	0.640674	+	0.537589i	0.904225	−	0.427056i	$-0.140449\pi$
$661$	16.4717	+	13.8214i	0.640674	+	0.537589i	−0.263551	+	0.964645i	$0.584894\pi$
$662$	−21.0594	−	17.6709i	−0.818495	−	0.686799i
$663$	−31.8216	+	30.2267i	−1.23585	+	1.17391i
$664$	5.49364	−	4.60971i	0.213194	−	0.178891i
$665$	−0.282017	−	2.67150i	−0.0109361	−	0.103596i
$666$	−1.37831	+	26.7929i	−0.0534085	+	1.03820i
$667$	−10.8891	+	18.8605i	−0.421629	+	0.730283i
$668$	−3.21514	+	2.69782i	−0.124397	+	0.104382i
$669$	11.1733	−	0.688782i	0.431984	−	0.0266299i
$670$	0.438036	−	2.48422i	0.0169228	−	0.0959740i
$671$	33.3253	−	12.1294i	1.28651	−	0.468251i
$672$	4.58244	+	0.0356987i	0.176771	+	0.00137711i
$673$	−1.38186	−	7.83694i	−0.0532669	−	0.302092i	0.946522	−	0.322639i	$-0.104570\pi$
$673$	−1.38186	−	7.83694i	−0.0532669	−	0.302092i	−0.999789	+	0.0205476i	$0.993459\pi$
$674$	11.7100	+	20.2822i	0.451050	+	0.781242i
$675$	16.3723	−	19.9197i	0.630170	−	0.766709i
$676$	−6.83390	+	11.8367i	−0.262842	+	0.455256i
$677$	−16.1037	+	13.5126i	−0.618917	+	0.519333i	−0.897463	−	0.441090i	$-0.854592\pi$
$677$	−16.1037	+	13.5126i	−0.618917	+	0.519333i	0.278546	+	0.960423i	$0.410147\pi$
$678$	−27.6391	+	12.0336i	−1.06147	+	0.462148i
$679$	23.4150	+	1.62662i	0.898586	+	0.0624240i
$680$	0.730345	+	0.612832i	0.0280074	+	0.0235010i
$681$	5.90603	+	8.91371i	0.226319	+	0.341574i
$682$	26.1749	−	21.9633i	1.00229	−	0.841020i
$683$	−6.61908			−0.253272			−0.126636	−	0.991949i	$-0.540418\pi$
$683$	−6.61908			−0.253272			−0.126636	+	0.991949i	$0.540418\pi$
$684$	−15.5583	+	1.92552i	−0.594888	+	0.0736241i
$685$	0.898910	−	1.55696i	0.0343456	−	0.0594883i
$686$	0.621057	−	18.5098i	0.0237121	−	0.706709i
$687$	−20.5610	+	19.5305i	−0.784452	+	0.745135i
$688$	11.3152	−	4.11838i	0.431386	−	0.157012i
$689$	28.5086	+	23.9215i	1.08609	+	0.911338i
$690$	0.423896	+	1.76192i	0.0161374	+	0.0670751i
$691$	−23.0643	−	8.39470i	−0.877406	−	0.319350i	−0.136243	−	0.990675i	$-0.543503\pi$
$691$	−23.0643	−	8.39470i	−0.877406	−	0.319350i	−0.741162	+	0.671326i	$0.765725\pi$
$692$	−2.25809	+	3.91113i	−0.0858399	+	0.148679i
$693$	8.29914	+	35.7165i	0.315258	+	1.35676i
$694$	3.56152	+	6.16873i	0.135193	+	0.234162i
$695$	0.319034	+	1.80933i	0.0121016	+	0.0686318i
$696$	3.12262	−	6.27055i	0.118362	−	0.237685i
$697$	20.3594	−	7.41023i	0.771169	−	0.280682i
$698$	15.4162	+	12.9357i	0.583510	+	0.489623i
$699$	−7.33162	+	3.19207i	−0.277307	+	0.120735i
$700$	−12.6186	+	3.62456i	−0.476940	+	0.136995i
$701$	13.8025			0.521315			0.260657	−	0.965431i	$-0.416061\pi$
$701$	13.8025			0.521315			0.260657	+	0.965431i	$0.416061\pi$
$702$	26.3770	−	4.92806i	0.995535	−	0.185998i
$703$	−23.3661	+	40.4712i	−0.881268	+	1.52640i
$704$	4.34113	+	1.58004i	0.163613	+	0.0595501i
$705$	1.27193	−	0.553779i	0.0479037	−	0.0208565i
$706$	32.6050	−	11.8673i	1.22711	−	0.446630i
$707$	−45.3694	−	3.15177i	−1.70629	−	0.118535i
$708$	−4.14988	−	6.26324i	−0.155962	−	0.235387i
$709$	−4.42032	−	25.0689i	−0.166009	−	0.941482i	−0.948018	−	0.318216i	$-0.896916\pi$
$709$	−4.42032	−	25.0689i	−0.166009	−	0.941482i	0.782010	−	0.623266i	$-0.214195\pi$
$710$	1.63072			0.0611998
$711$	−0.915329	+	17.7930i	−0.0343275	+	0.667291i
$712$	8.04412			0.301466
$713$	−30.5100	+	25.6009i	−1.14261	+	0.958761i
$714$	−17.1122	−	14.5875i	−0.640408	−	0.545924i
$715$	−0.804917	+	4.56491i	−0.0301022	+	0.170718i
$716$	18.4436	−	6.71292i	0.689269	−	0.250873i
$717$	−5.07470	+	4.82035i	−0.189518	+	0.180019i
$718$	2.62147	+	14.8671i	0.0978325	+	0.554836i
$719$	−18.9461			−0.706571			−0.353285	−	0.935516i	$-0.614936\pi$
$719$	−18.9461			−0.706571			−0.353285	+	0.935516i	$0.614936\pi$
$720$	−0.170959	−	0.557263i	−0.00637125	−	0.0207680i
$721$	1.63060	−	1.18584i	0.0607268	−	0.0441629i
$722$	−7.80671	−	2.84141i	−0.290536	−	0.105746i
$723$	40.9805	−	2.52626i	1.52408	−	0.0939527i
$724$	−7.58766	+	2.76168i	−0.281993	+	0.102637i
$725$	−3.48496	+	19.7642i	−0.129428	+	0.734025i
$726$	−2.01922	+	17.7986i	−0.0749404	+	0.660568i
$727$	2.22934	+	12.6432i	0.0826816	+	0.468911i	0.997833	+	0.0658000i	$0.0209599\pi$
$727$	2.22934	+	12.6432i	0.0826816	+	0.468911i	−0.915151	+	0.403111i	$0.867929\pi$
$728$	−12.4842	−	5.55151i	−0.462695	−	0.205753i
$729$	−21.0319	−	16.9310i	−0.778959	−	0.627075i
$730$	0.404532	+	0.700669i	0.0149724	+	0.0259329i
$731$	−55.5219	−	20.2083i	−2.05355	−	0.747431i
$732$	12.1910	−	5.30776i	0.450591	−	0.196180i
$733$	17.5366	+	14.7150i	0.647729	+	0.543509i	0.906381	−	0.422461i	$-0.138834\pi$
$733$	17.5366	+	14.7150i	0.647729	+	0.543509i	−0.258652	+	0.965971i	$0.583278\pi$
$734$	14.4346	+	12.1120i	0.532790	+	0.447064i
$735$	−2.26919	+	0.632706i	−0.0837004	+	0.0233377i
$736$	−5.06011	−	1.84173i	−0.186518	−	0.0678870i
$737$	−29.9886	+	51.9418i	−1.10464	+	1.91330i
$738$	−12.9097	−	2.96737i	−0.475214	−	0.109230i
$739$	11.0298	+	19.1042i	0.405739	+	0.702761i	0.994407	−	0.105614i	$-0.0336808\pi$
$739$	11.0298	+	19.1042i	0.405739	+	0.702761i	−0.588668	+	0.808375i	$0.700347\pi$
$740$	−1.63278	−	0.594285i	−0.0600223	−	0.0218463i
$741$	44.8225	+	13.2536i	1.64659	+	0.486882i
$742$	−10.6548	+	15.8119i	−0.391150	+	0.580474i
$743$	−4.08079	+	23.1433i	−0.149709	+	0.849045i	0.813755	+	0.581208i	$0.197420\pi$
$743$	−4.08079	+	23.1433i	−0.149709	+	0.849045i	−0.963464	+	0.267836i	$0.913691\pi$
$744$	9.28835	−	8.82281i	0.340527	−	0.323460i
$745$	−0.267618	−	1.51774i	−0.00980476	−	0.0556056i
$746$	−7.64176	−	13.2359i	−0.279785	−	0.484602i
$747$	18.0547	+	11.7002i	0.660586	+	0.428087i
$748$	−11.3342	−	19.6314i	−0.414419	−	0.717795i
$749$	8.45769	−	33.9879i	0.309037	−	1.24189i
$750$	1.85180	+	2.79484i	0.0676180	+	0.102053i
$751$	1.62507	−	9.21624i	0.0592997	−	0.336305i	−0.940696	−	0.339251i	$-0.889826\pi$
$751$	1.62507	−	9.21624i	0.0592997	−	0.336305i	0.999996	+	0.00294541i	$0.000937554\pi$
$752$	−0.715807	+	4.05954i	−0.0261028	+	0.148036i
$753$	−33.4787	−	24.7480i	−1.22003	−	0.901869i
$754$	−15.9992	+	13.4249i	−0.582655	+	0.488906i
$755$	1.19044			0.0433247
$756$	3.92958	+	13.1742i	0.142918	+	0.479139i
$757$	−1.31192			−0.0476824			−0.0238412	−	0.999716i	$-0.507590\pi$
$757$	−1.31192			−0.0476824			−0.0238412	+	0.999716i	$0.507590\pi$
$758$	−2.44551	+	2.05203i	−0.0888250	+	0.0745330i
$759$	4.85705	−	42.8129i	0.176300	−	1.55401i
$760$	0.176313	−	0.999918i	0.00639553	−	0.0362709i
$761$	0.571869	−	3.24323i	0.0207302	−	0.117567i	−0.972687	−	0.232122i	$-0.925433\pi$
$761$	0.571869	−	3.24323i	0.0207302	−	0.117567i	0.993417	+	0.114555i	$0.0365442\pi$
$762$	15.7272	−	0.969511i	0.569737	−	0.0351217i
$763$	−14.1301	+	4.05871i	−0.511544	+	0.146935i
$764$	−1.70002	−	2.94453i	−0.0615047	−	0.106529i
$765$	−1.11503	+	2.63390i	−0.0403141	+	0.0952287i
$766$	17.2498	+	29.8775i	0.623260	+	1.07952i
$767$	3.88986	+	22.0605i	0.140455	+	0.796558i
$768$	1.66096	+	0.491130i	0.0599348	+	0.0177221i
$769$	−6.14587	+	34.8549i	−0.221626	+	1.25690i	0.647406	+	0.762145i	$0.275854\pi$
$769$	−6.14587	+	34.8549i	−0.221626	+	1.25690i	−0.869032	+	0.494756i	$0.835257\pi$
$770$	−2.36914	−	0.164582i	−0.0853779	−	0.00593113i
$771$	−6.57464	+	6.24512i	−0.236780	+	0.224912i
$772$	−2.48020	−	0.902717i	−0.0892642	−	0.0324895i
$773$	16.8218	+	29.1361i	0.605037	+	1.04795i	0.992046	+	0.125878i	$0.0401749\pi$
$773$	16.8218	+	29.1361i	0.605037	+	1.04795i	−0.387009	+	0.922076i	$0.626492\pi$
$774$	21.7677	+	28.8290i	0.782424	+	1.03624i
$775$	−18.3511	+	31.7851i	−0.659191	+	1.14175i
$776$	8.33637	+	3.03419i	0.299258	+	0.108921i
$777$	38.3992	+	14.3159i	1.37756	+	0.513580i
$778$	−18.2379	−	15.3034i	−0.653861	−	0.548654i
$779$	−17.6756	−	14.8316i	−0.633292	−	0.531395i
$780$	−0.195905	+	1.72682i	−0.00701453	+	0.0618301i
$781$	−36.4344	−	13.2610i	−1.30373	−	0.474518i
$782$	13.2114	+	22.8828i	0.472437	+	0.818286i
$783$	20.7319	+	3.43858i	0.740897	+	0.122885i
$784$	2.15705	−	6.65936i	0.0770376	−	0.237834i
$785$	0.0985605	+	0.558965i	0.00351778	+	0.0199503i
$786$	−5.28866	+	2.30260i	−0.188640	+	0.0821310i
$787$	−0.668590	+	3.79176i	−0.0238327	+	0.135162i	−0.994403	−	0.105658i	$-0.966305\pi$
$787$	−0.668590	+	3.79176i	−0.0238327	+	0.135162i	0.970570	+	0.240820i	$0.0774162\pi$
$788$	−3.06695	+	1.11628i	−0.109255	+	0.0397657i
$789$	4.34650	−	8.72824i	0.154739	−	0.310733i
$790$	−1.08432	−	0.394661i	−0.0385785	−	0.0140414i
$791$	4.83412	+	45.7929i	0.171881	+	1.62821i
$792$	−0.712019	+	13.8409i	−0.0253005	+	0.491815i
$793$	−39.6428			−1.40776
$794$	1.83234	+	10.3917i	0.0650272	+	0.368787i
$795$	2.32572	+	0.687693i	0.0824849	+	0.0243900i
$796$	−10.0550	+	3.65972i	−0.356390	+	0.129715i
$797$	7.34652	−	41.6642i	0.260227	−	1.47582i	−0.522063	−	0.852907i	$-0.674837\pi$
$797$	7.34652	−	41.6642i	0.260227	−	1.47582i	0.782290	−	0.622914i	$-0.214051\pi$
$798$	−4.34196	+	23.5502i	−0.153704	+	0.833666i
$799$	15.4947	−	13.0016i	0.548163	−	0.459964i
$800$	−4.96225			−0.175442
$801$	7.07782	+	23.0711i	0.250082	+	0.815177i
$802$	18.7432			0.661847
$803$	−3.34041	−	18.9444i	−0.117880	−	0.668533i
$804$	−10.0239	+	20.1291i	−0.353517	+	0.709900i
$805$	2.76152	+	0.191840i	0.0973307	+	0.00676148i
$806$	−35.8916	+	13.0635i	−1.26423	+	0.460142i
$807$	0.252251	−	2.22349i	0.00887966	−	0.0782705i
$808$	−16.1527	−	5.87911i	−0.568250	−	0.206826i
$809$	−13.7724	+	23.8546i	−0.484213	+	0.838682i	−0.999836	−	0.0181338i	$-0.994228\pi$
$809$	−13.7724	+	23.8546i	−0.484213	+	0.838682i	0.515622	+	0.856816i	$0.327561\pi$
$810$	1.44785	−	0.980643i	0.0508721	−	0.0344563i
$811$	−8.45474			−0.296886			−0.148443	−	0.988921i	$-0.547426\pi$
$811$	−8.45474			−0.296886			−0.148443	+	0.988921i	$0.547426\pi$
$812$	−7.70059	−	7.42959i	−0.270238	−	0.260728i
$813$	9.88841	+	7.30968i	0.346802	+	0.256362i
$814$	31.6478	+	26.5557i	1.10926	+	0.930776i
$815$	2.17707	−	0.792389i	0.0762595	−	0.0277562i
$816$	−4.69428	−	7.08488i	−0.164333	−	0.248020i
$817$	10.9267	+	61.9682i	0.382276	+	2.16799i
$818$	3.27546	+	5.67326i	0.114524	+	0.198361i
$819$	4.93759	−	40.6902i	0.172533	−	1.42183i
$820$	0.428960	−	0.742980i	0.0149799	−	0.0259460i
$821$	5.59256	+	2.03553i	0.195182	+	0.0710404i	0.437762	−	0.899091i	$-0.355771\pi$
$821$	5.59256	+	2.03553i	0.195182	+	0.0710404i	−0.242580	+	0.970131i	$0.577994\pi$
$822$	−11.6199	+	11.0375i	−0.405289	+	0.384975i
$823$	−38.3378	−	32.1692i	−1.33637	−	1.12135i	−0.982542	−	0.186039i	$-0.940435\pi$
$823$	−38.3378	−	32.1692i	−1.33637	−	1.12135i	−0.353829	−	0.935310i	$-0.615121\pi$
$824$	0.716095	−	0.260637i	0.0249464	−	0.00907973i
$825$	−9.28775	−	38.6045i	−0.323358	−	1.34403i
$826$	−11.0307	+	3.16845i	−0.383808	+	0.110244i
$827$	−4.86382	+	8.42438i	−0.169132	+	0.292945i	−0.938115	−	0.346324i	$-0.887430\pi$
$827$	−4.86382	+	8.42438i	−0.169132	+	0.292945i	0.768983	+	0.639269i	$0.220763\pi$
$828$	0.829944	−	16.1332i	0.0288425	−	0.560668i
$829$	−30.0143			−1.04244			−0.521220	−	0.853423i	$-0.674523\pi$
$829$	−30.0143			−1.04244			−0.521220	+	0.853423i	$0.674523\pi$
$830$	−1.06741	+	0.895661i	−0.0370502	+	0.0310888i
$831$	−8.00664	+	16.0782i	−0.277747	+	0.557747i
$832$	−3.95592	−	3.31941i	−0.137147	−	0.115080i
$833$	−29.1122	+	18.2282i	−1.00868	+	0.631570i
$834$	1.84620	−	16.2735i	0.0639286	−	0.563504i
$835$	0.624697	−	0.524183i	0.0216185	−	0.0181401i
$836$	−12.0706	+	20.9069i	−0.417471	+	0.723082i
$837$	33.4770	+	18.8767i	1.15713	+	0.652473i
$838$	−4.51762	−	7.82475i	−0.156059	−	0.270301i
$839$	−3.72963	−	21.1518i	−0.128761	−	0.730241i	−0.979003	−	0.203848i	$-0.934655\pi$
$839$	−3.72963	−	21.1518i	−0.128761	−	0.730241i	0.850241	−	0.526393i	$-0.176456\pi$
$840$	−0.890362	−	0.00693621i	−0.0307204	−	0.000239322i
$841$	11.8807	−	4.32422i	0.409679	−	0.149111i
$842$	1.30184	−	7.38308i	0.0448642	−	0.254438i
$843$	0.718212	−	1.44225i	0.0247365	−	0.0496736i
$844$	−15.8841	+	13.3284i	−0.546755	+	0.458782i
$845$	1.32782	−	2.29985i	0.0456783	−	0.0791172i
$846$	−12.2729	+	1.51891i	−0.421950	+	0.0522210i
$847$	25.0017	+	11.1178i	0.859069	+	0.382013i
$848$	−5.52055	+	4.63229i	−0.189576	+	0.159073i
$849$	−11.6463	−	3.44371i	−0.399701	−	0.118188i
$850$	18.6525	+	15.6513i	0.639774	+	0.536834i
$851$	−36.8893	−	30.9538i	−1.26455	−	1.06108i
$852$	−13.9402	−	4.12198i	−0.477583	−	0.141217i
$853$	−0.865501	+	0.726242i	−0.0296342	+	0.0248661i	−0.657484	−	0.753468i	$-0.728379\pi$
$853$	−0.865501	+	0.726242i	−0.0296342	+	0.0248661i	0.627850	+	0.778334i	$0.283935\pi$
$854$	−2.13222	−	20.1982i	−0.0729631	−	0.691169i
$855$	3.02297	−	0.374126i	0.103383	−	0.0127948i
$856$	6.61899	−	11.4644i	0.226232	−	0.391846i
$857$	−11.4987	+	9.64857i	−0.392789	+	0.329589i	−0.817698	−	0.575647i	$-0.804750\pi$
$857$	−11.4987	+	9.64857i	−0.392789	+	0.329589i	0.424910	+	0.905236i	$0.360306\pi$
$858$	18.4196	−	36.9885i	0.628834	−	1.26277i
$859$	−3.67332	+	20.8324i	−0.125332	+	0.710794i	0.855778	+	0.517343i	$0.173079\pi$
$859$	−3.67332	+	20.8324i	−0.125332	+	0.710794i	−0.981110	+	0.193450i	$0.938032\pi$
$860$	−2.19852	+	0.800196i	−0.0749690	+	0.0272865i
$861$	−10.2533	+	17.4440i	−0.349431	+	0.594489i
$862$	−3.27617	−	18.5801i	−0.111587	−	0.632840i
$863$	−8.50565	−	14.7322i	−0.289536	−	0.501490i	0.684163	−	0.729329i	$-0.260168\pi$
$863$	−8.50565	−	14.7322i	−0.289536	−	0.501490i	−0.973699	+	0.227838i	$0.926834\pi$
$864$	0.0528425	+	5.19588i	0.00179774	+	0.176768i
$865$	0.438745	−	0.759929i	0.0149178	−	0.0258384i
$866$	23.2563	−	19.5143i	0.790280	−	0.663124i
$867$	−1.38181	+	12.1801i	−0.0469287	+	0.413657i
$868$	−8.58638	−	17.5844i	−0.291441	−	0.596852i
$869$	21.0171	+	17.6355i	0.712957	+	0.598242i
$870$	−0.606721	+	1.21836i	−0.0205698	+	0.0413063i
$871$	51.3590	−	43.0953i	1.74023	−	1.46023i
$872$	−5.55663			−0.188171
$873$	−1.36731	+	26.5790i	−0.0462763	+	0.899562i
$874$	14.0698	−	24.3695i	0.475917	−	0.824312i
$875$	4.92223	−	1.41385i	0.166402	−	0.0477969i
$876$	−1.68705	−	7.01220i	−0.0570000	−	0.236920i
$877$	40.3939	−	14.7022i	1.36401	−	0.496458i	0.446715	−	0.894676i	$-0.352594\pi$
$877$	40.3939	−	14.7022i	1.36401	−	0.496458i	0.917291	+	0.398219i	$0.130371\pi$
$878$	−5.73565	−	4.81279i	−0.193569	−	0.162424i
$879$	−28.2373	+	26.8220i	−0.952420	+	0.904684i
$880$	−0.843477	−	0.307000i	−0.0284336	−	0.0103490i
$881$	7.51336	−	13.0135i	0.253131	−	0.438437i	−0.711255	−	0.702934i	$-0.751873\pi$
$881$	7.51336	−	13.0135i	0.253131	−	0.438437i	0.964386	+	0.264498i	$0.0852061\pi$
$882$	20.9975	+	0.327174i	0.707021	+	0.0110165i
$883$	−5.57211	−	9.65118i	−0.187516	−	0.324788i	0.756905	−	0.653525i	$-0.226710\pi$
$883$	−5.57211	−	9.65118i	−0.187516	−	0.324788i	−0.944422	+	0.328737i	$0.893377\pi$
$884$	4.40015	+	24.9545i	0.147993	+	0.839310i
$885$	0.806318	+	1.21694i	0.0271041	+	0.0409070i
$886$	36.3535	−	13.2316i	1.22132	−	0.444524i
$887$	42.2834	+	35.4800i	1.41974	+	1.19130i	0.951481	+	0.307708i	$0.0995620\pi$
$887$	42.2834	+	35.4800i	1.41974	+	1.19130i	0.468256	+	0.883593i	$0.344882\pi$
$888$	12.4557	+	9.20743i	0.417984	+	0.308981i
$889$	5.81226	−	23.3570i	0.194937	−	0.783369i
$890$	−1.56296			−0.0523906
$891$	−40.3232	+	10.1361i	−1.35088	+	0.339573i
$892$	3.23157	−	5.59725i	0.108201	−	0.187410i
$893$	−20.2420	−	7.36750i	−0.677374	−	0.246544i
$894$	−1.54866	+	13.6508i	−0.0517950	+	0.456551i
$895$	−3.58357	+	1.30431i	−0.119785	+	0.0435983i
$896$	1.47849	−	2.19410i	0.0493928	−	0.0732998i
$897$	−21.4702	+	43.1145i	−0.716869	+	1.43955i
$898$	−0.358777	−	2.03472i	−0.0119725	−	0.0678996i
$899$	−29.9132			−0.997663
$900$	−4.36616	−	14.2321i	−0.145539	−	0.474402i
$901$	35.3616			1.17807
$902$	−15.6260	+	13.1118i	−0.520288	+	0.436574i
$903$	51.9980	−	18.4683i	1.73038	−	0.614586i
$904$	−3.02222	+	17.1399i	−0.100518	+	0.570063i
$905$	1.47427	−	0.536592i	0.0490065	−	0.0178369i
$906$	−10.1765	−	3.00909i	−0.338091	−	0.0999703i
$907$	−8.39142	−	47.5901i	−0.278633	−	1.58020i	−0.727182	−	0.686445i	$-0.759170\pi$
$907$	−8.39142	−	47.5901i	−0.278633	−	1.58020i	0.448549	−	0.893758i	$-0.351941\pi$
$908$	6.17348			0.204874
$909$	2.64932	−	51.5000i	0.0878724	−	1.70815i
$910$	2.42567	+	1.07865i	0.0804100	+	0.0357570i
$911$	−5.58480	−	2.03270i	−0.185033	−	0.0673464i	0.247842	−	0.968800i	$-0.420279\pi$
$911$	−5.58480	−	2.03270i	−0.185033	−	0.0673464i	−0.432875	+	0.901454i	$0.642501\pi$
$912$	−4.03470	+	8.10212i	−0.133602	+	0.268288i
$913$	31.1321	−	11.3312i	1.03032	−	0.375007i
$914$	1.96429	−	11.1400i	0.0649729	−	0.368480i
$915$	−2.36869	+	1.03129i	−0.0783066	+	0.0340935i
$916$	2.84309	+	16.1240i	0.0939383	+	0.532751i
$917$	0.924995	+	8.76235i	0.0305460	+	0.289358i
$918$	16.1895	−	19.6973i	0.534335	−	0.650109i
$919$	18.3954	+	31.8617i	0.606807	+	1.05102i	0.991763	+	0.128085i	$0.0408831\pi$
$919$	18.3954	+	31.8617i	0.606807	+	1.05102i	−0.384956	+	0.922935i	$0.625784\pi$
$920$	0.983173	+	0.357846i	0.0324143	+	0.0117978i
$921$	−1.17027	+	10.3154i	−0.0385617	+	0.339905i
$922$	−1.25453	−	1.05267i	−0.0413157	−	0.0346680i
$923$	33.2014	+	27.8593i	1.09284	+	0.917000i
$924$	19.8366	+	7.39542i	0.652575	+	0.243291i
$925$	−41.7001	−	15.1776i	−1.37109	−	0.499036i
$926$	−7.70722	+	13.3493i	−0.253275	+	0.438685i
$927$	1.37760	+	1.82448i	0.0452463	+	0.0599239i
$928$	−2.02218	−	3.50252i	−0.0663813	−	0.114976i
$929$	15.9905	+	5.82008i	0.524633	+	0.190951i	0.590740	−	0.806862i	$-0.298836\pi$
$929$	15.9905	+	5.82008i	0.524633	+	0.190951i	−0.0661075	+	0.997813i	$0.521058\pi$
$930$	−1.80472	+	1.71426i	−0.0591789	+	0.0562128i
$931$	32.3136	+	17.1437i	1.05904	+	0.561863i
$932$	−0.801683	+	4.54657i	−0.0262600	+	0.148928i
$933$	−36.6686	−	10.8425i	−1.20048	−	0.354969i
$934$	−1.19116	−	6.75542i	−0.0389760	−	0.221044i
$935$	2.20222	+	3.81436i	0.0720204	+	0.124743i
$936$	6.03959	−	14.2665i	0.197410	−	0.466316i
$937$	9.43039	+	16.3339i	0.308077	+	0.533606i	0.977942	−	0.208878i	$-0.0669811\pi$
$937$	9.43039	+	16.3339i	0.308077	+	0.533606i	−0.669864	+	0.742484i	$0.733648\pi$
$938$	24.7197	+	23.8498i	0.807127	+	0.778723i
$939$	3.85344	−	0.237547i	0.125752	−	0.00775205i
$940$	0.139080	−	0.788765i	0.00453631	−	0.0257267i
$941$	5.79531	−	32.8668i	0.188922	−	1.07143i	−0.731891	−	0.681422i	$-0.761362\pi$
$941$	5.79531	−	32.8668i	0.188922	−	1.07143i	0.920812	−	0.390006i	$-0.127527\pi$
$942$	0.570354	−	5.02743i	0.0185831	−	0.163803i
$943$	18.2140	−	15.2833i	0.593128	−	0.497693i
$944$	−4.33781			−0.141184
$945$	−0.763514	−	2.55972i	−0.0248371	−	0.0832678i
$946$	55.6278			1.80861
$947$	25.8585	−	21.6979i	0.840289	−	0.705086i	−0.117340	−	0.993092i	$-0.537437\pi$
$947$	25.8585	−	21.6979i	0.840289	−	0.705086i	0.957629	+	0.288005i	$0.0929921\pi$
$948$	8.27173	+	6.11460i	0.268653	+	0.198593i
$949$	−3.73401	+	21.1766i	−0.121211	+	0.687423i
$950$	4.50289	−	25.5372i	0.146093	−	0.828535i
$951$	9.47283	+	14.2969i	0.307177	+	0.463610i
$952$	−12.4778	+	3.58410i	−0.404407	+	0.116161i
$953$	−28.8315	−	49.9375i	−0.933942	−	1.61764i	−0.776509	−	0.630106i	$-0.783011\pi$
$953$	−28.8315	−	49.9375i	−0.933942	−	1.61764i	−0.157433	−	0.987530i	$-0.550322\pi$
$954$	−18.1431	−	11.7575i	−0.587405	−	0.380662i
$955$	0.330313	+	0.572119i	0.0106887	+	0.0185133i
$956$	0.701707	+	3.97958i	0.0226948	+	0.128709i
$957$	23.4634	−	22.2874i	0.758465	−	0.720450i
$958$	−4.41900	+	25.0614i	−0.142772	+	0.809697i
$959$	10.7417	+	21.9983i	0.346867	+	0.710362i
$960$	−0.322723	−	0.0954260i	−0.0104158	−	0.00307986i
$961$	−22.2755	−	8.10762i	−0.718565	−	0.261536i
$962$	−23.0907	−	39.9942i	−0.744472	−	1.28946i
$963$	38.7047	+	8.89646i	1.24724	+	0.286685i
$964$	11.8525	−	20.5291i	0.381744	−	0.661199i
$965$	0.481899	+	0.175397i	0.0155129	+	0.00564623i
$966$	−23.1219	−	8.62024i	−0.743934	−	0.277352i
$967$	−6.27261	−	5.26334i	−0.201713	−	0.169258i	0.536335	−	0.844005i	$-0.319808\pi$
$967$	−6.27261	−	5.26334i	−0.201713	−	0.169258i	−0.738049	+	0.674747i	$0.764253\pi$
$968$	7.92239	+	6.64768i	0.254635	+	0.213664i
$969$	40.7206	−	17.7291i	1.30813	−	0.569541i
$970$	−1.61975	−	0.589540i	−0.0520069	−	0.0189290i
$971$	−16.4404	−	28.4755i	−0.527596	−	0.913824i	−0.999483	−	0.0321644i	$-0.989760\pi$
$971$	−16.4404	−	28.4755i	−0.527596	−	0.913824i	0.471886	−	0.881660i	$-0.343573\pi$
$972$	−14.8557	+	4.72328i	−0.476495	+	0.151499i
$973$	−22.8593	−	10.1652i	−0.732837	−	0.325880i
$974$	1.29900	+	7.36699i	0.0416226	+	0.236054i
$975$	−5.00327	+	44.1017i	−0.160233	+	1.41239i
$976$	1.33303	−	7.56001i	0.0426694	−	0.241990i
$977$	30.3570	−	11.0491i	0.971207	−	0.353490i	0.192791	−	0.981240i	$-0.438246\pi$
$977$	30.3570	−	11.0491i	0.971207	−	0.353490i	0.778416	+	0.627749i	$0.216024\pi$
$978$	−20.6136	+	1.27073i	−0.659150	+	0.0406336i
$979$	34.9206	+	12.7100i	1.11607	+	0.406215i
$980$	−0.419113	+	1.29391i	−0.0133881	+	0.0413323i
$981$	−4.88914	−	15.9368i	−0.156098	−	0.508823i
$982$	3.65000			0.116476
$983$	3.82605	+	21.6986i	0.122032	+	0.692078i	0.983027	+	0.183464i	$0.0587309\pi$
$983$	3.82605	+	21.6986i	0.122032	+	0.692078i	−0.860995	+	0.508614i	$0.830158\pi$
$984$	−5.54499	+	5.26707i	−0.176768	+	0.167908i
$985$	0.595904	−	0.216891i	0.0189871	−	0.00691074i
$986$	−3.44607	+	19.5436i	−0.109745	+	0.622395i
$987$	−3.42506	+	18.5770i	−0.109021	+	0.591314i
$988$	20.6724	−	17.3462i	0.657676	−	0.551855i
$989$	−64.8408			−2.06182
$990$	0.138345	−	2.68927i	0.00439688	−	0.0854707i
$991$	56.1962			1.78513			0.892566	−	0.450916i	$-0.148903\pi$
$991$	56.1962			1.78513			0.892566	+	0.450916i	$0.148903\pi$
$992$	−1.28435	−	7.28392i	−0.0407782	−	0.231265i
$993$	−26.3001	−	39.6936i	−0.834607	−	1.25964i
$994$	−12.4087	+	18.4147i	−0.393580	+	0.584080i
$995$	1.95368	−	0.711080i	0.0619357	−	0.0225428i
$996$	11.3887	−	4.95845i	0.360864	−	0.157115i
$997$	−48.5834	−	17.6829i	−1.53865	−	0.560023i	−0.572929	−	0.819605i	$-0.694193\pi$
$997$	−48.5834	−	17.6829i	−1.53865	−	0.560023i	−0.965721	+	0.259582i	$0.916415\pi$
$998$	−6.60633	+	11.4425i	−0.209120	+	0.362206i
$999$	−15.4481	+	43.8251i	−0.488757	+	1.38656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.b.67.10	✓	72
7.2	even	3		378.2.w.a.121.6	yes	72
27.25	even	9		378.2.w.a.25.6	yes	72
189.79	even	9	inner	378.2.v.b.79.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.10	✓	72	1.1	even	1	trivial
378.2.v.b.79.10	yes	72	189.79	even	9	inner
378.2.w.a.25.6	yes	72	27.25	even	9
378.2.w.a.121.6	yes	72	7.2	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.58806 - 0.691418i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0337396 + 0.191347i) q^{5} +(0.772092 - 1.55044i) q^{6} +(-1.90403 - 1.83703i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.04388 - 2.19603i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.58806 - 0.691418i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0337396 + 0.191347i) q^{5} +(0.772092 - 1.55044i) q^{6} +(-1.90403 - 1.83703i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.04388 - 2.19603i) q^{9} +(0.0971494 + 0.168268i) q^{10} +(-0.802209 - 4.54955i) q^{11} +(-0.405149 - 1.68400i) q^{12} +(-0.896734 + 5.08563i) q^{13} +(-2.63939 - 0.183356i) q^{14} +(0.0787201 + 0.327199i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.45343 + 4.24947i) q^{17} +(0.154126 - 2.99604i) q^{18} +(2.61284 - 4.52557i) q^{19} +(0.182581 + 0.0664541i) q^{20} +(-4.29387 - 1.60083i) q^{21} +(-3.53892 - 2.96951i) q^{22} +(4.12504 + 3.46132i) q^{23} +(-1.39282 - 1.02959i) q^{24} +(4.66299 + 1.69719i) q^{25} +(2.58204 + 4.47223i) q^{26} +(1.72744 - 4.90061i) q^{27} +(-2.13975 + 1.55611i) q^{28} +(0.702296 + 3.98292i) q^{29} +(0.270623 + 0.200049i) q^{30} +(-1.28435 + 7.28392i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-4.41960 - 6.67031i) q^{33} +(4.61094 + 1.67825i) q^{34} +(0.415751 - 0.302350i) q^{35} +(-1.80775 - 2.39417i) q^{36} -8.94278 q^{37} +(-0.907430 - 5.14629i) q^{38} +(2.09223 + 8.69632i) q^{39} +(0.182581 - 0.0664541i) q^{40} +(0.766737 - 4.34838i) q^{41} +(-4.31829 + 1.53374i) q^{42} +(-9.22420 + 7.74002i) q^{43} -4.61973 q^{44} +(0.351244 + 0.465184i) q^{45} +5.38485 q^{46} +(-0.715807 - 4.05954i) q^{47} +(-1.72877 + 0.106571i) q^{48} +(0.250669 + 6.99551i) q^{49} +(4.66299 - 1.69719i) q^{50} +(6.83436 + 5.05207i) q^{51} +(4.85265 + 1.76622i) q^{52} +(3.60328 - 6.24106i) q^{53} +(-1.82675 - 4.86446i) q^{54} +0.897609 q^{55} +(-0.638896 + 2.56745i) q^{56} +(1.02029 - 8.99345i) q^{57} +(3.09816 + 2.59966i) q^{58} +(4.07621 - 1.48362i) q^{59} +(0.335898 - 0.0207066i) q^{60} +(1.33303 + 7.56001i) q^{61} +(3.69814 + 6.40537i) q^{62} +(-7.92578 + 0.426639i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.942865 - 0.343175i) q^{65} +(-7.67320 - 2.26889i) q^{66} +(-9.94542 - 8.34520i) q^{67} +(4.61094 - 1.67825i) q^{68} +(8.94403 + 2.64466i) q^{69} +(0.124137 - 0.498853i) q^{70} +(4.19642 - 7.26842i) q^{71} +(-2.92376 - 0.672041i) q^{72} +4.16401 q^{73} +(-6.85057 + 5.74831i) q^{74} +(8.57858 - 0.528831i) q^{75} +(-4.00310 - 3.35900i) q^{76} +(-6.83021 + 10.1362i) q^{77} +(7.19262 + 5.31691i) q^{78} +(-4.54942 + 3.81742i) q^{79} +(0.0971494 - 0.168268i) q^{80} +(-0.645082 - 8.97685i) q^{81} +(-2.20773 - 3.82390i) q^{82} +(1.24531 + 7.06248i) q^{83} +(-2.32213 + 3.95066i) q^{84} +(-0.895901 + 0.326081i) q^{85} +(-2.09096 + 11.8584i) q^{86} +(3.86915 + 5.83954i) q^{87} +(-3.53892 + 2.96951i) q^{88} +(-4.02206 + 6.96641i) q^{89} +(0.568083 + 0.130577i) q^{90} +(11.0499 - 8.03588i) q^{91} +(4.12504 - 3.46132i) q^{92} +(2.99660 + 12.4553i) q^{93} +(-3.15776 - 2.64968i) q^{94} +(0.777798 + 0.652650i) q^{95} +(-1.25581 + 1.19287i) q^{96} +(-6.79587 + 5.70241i) q^{97} +(4.68865 + 5.19774i) q^{98} +(-11.6306 - 7.53708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

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