LMFDB - Embedded newform 1785.2.g.f.1429.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1785,2,Mod(1429,1785)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1785, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("1785.1429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1785 = 3 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1785.g (of order $2$, degree $1$, 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:	$14.2532967608$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1429.8
Character	$\chi$	$=$	1785.1429
Dual form			1785.2.g.f.1429.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69985i q^{2} -1.00000i q^{3} -0.889490 q^{4} +(1.47723 - 1.67863i) q^{5} -1.69985 q^{6} -1.00000i q^{7} -1.88770i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.69985i q^{2} -1.00000i q^{3} -0.889490 q^{4} +(1.47723 - 1.67863i) q^{5} -1.69985 q^{6} -1.00000i q^{7} -1.88770i q^{8} -1.00000 q^{9} +(-2.85341 - 2.51107i) q^{10} -1.31823 q^{11} +0.889490i q^{12} -4.26284i q^{13} -1.69985 q^{14} +(-1.67863 - 1.47723i) q^{15} -4.98779 q^{16} -1.00000i q^{17} +1.69985i q^{18} +5.21905 q^{19} +(-1.31398 + 1.49312i) q^{20} -1.00000 q^{21} +2.24079i q^{22} +2.71209i q^{23} -1.88770 q^{24} +(-0.635573 - 4.95944i) q^{25} -7.24619 q^{26} +1.00000i q^{27} +0.889490i q^{28} +0.948665 q^{29} +(-2.51107 + 2.85341i) q^{30} -2.19047 q^{31} +4.70309i q^{32} +1.31823i q^{33} -1.69985 q^{34} +(-1.67863 - 1.47723i) q^{35} +0.889490 q^{36} +3.64278i q^{37} -8.87160i q^{38} -4.26284 q^{39} +(-3.16874 - 2.78857i) q^{40} +10.0648 q^{41} +1.69985i q^{42} -1.43751i q^{43} +1.17255 q^{44} +(-1.47723 + 1.67863i) q^{45} +4.61014 q^{46} +3.21978i q^{47} +4.98779i q^{48} -1.00000 q^{49} +(-8.43031 + 1.08038i) q^{50} -1.00000 q^{51} +3.79175i q^{52} +14.1176i q^{53} +1.69985 q^{54} +(-1.94733 + 2.21282i) q^{55} -1.88770 q^{56} -5.21905i q^{57} -1.61259i q^{58} -14.0099 q^{59} +(1.49312 + 1.31398i) q^{60} +8.36086 q^{61} +3.72347i q^{62} +1.00000i q^{63} -1.98102 q^{64} +(-7.15571 - 6.29720i) q^{65} +2.24079 q^{66} -13.6284i q^{67} +0.889490i q^{68} +2.71209 q^{69} +(-2.51107 + 2.85341i) q^{70} -6.66687 q^{71} +1.88770i q^{72} -13.0816i q^{73} +6.19219 q^{74} +(-4.95944 + 0.635573i) q^{75} -4.64229 q^{76} +1.31823i q^{77} +7.24619i q^{78} +9.12564 q^{79} +(-7.36812 + 8.37263i) q^{80} +1.00000 q^{81} -17.1086i q^{82} +6.08519i q^{83} +0.889490 q^{84} +(-1.67863 - 1.47723i) q^{85} -2.44355 q^{86} -0.948665i q^{87} +2.48842i q^{88} -0.0400448 q^{89} +(2.85341 + 2.51107i) q^{90} -4.26284 q^{91} -2.41237i q^{92} +2.19047i q^{93} +5.47315 q^{94} +(7.70974 - 8.76083i) q^{95} +4.70309 q^{96} +7.33549i q^{97} +1.69985i q^{98} +1.31823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9}+O(q^{10}) $ 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9	$ 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} - 4 q^{15} + 38 q^{16} + 12 q^{19} - 4 q^{20} - 28 q^{21} + 30 q^{24} - 8 q^{25} - 36 q^{26} - 2 q^{30} + 14 q^{31} - 6 q^{34} - 4 q^{35} + 34 q^{36} + 18 q^{39} - 62 q^{40} - 50 q^{41} - 24 q^{44} + 52 q^{46} - 28 q^{49} + 6 q^{50} - 28 q^{51} + 6 q^{54} - 14 q^{55} + 30 q^{56} + 44 q^{59} + 10 q^{60} + 26 q^{61} - 6 q^{64} + 20 q^{65} - 48 q^{66} + 38 q^{69} - 2 q^{70} + 12 q^{71} + 24 q^{74} - 16 q^{75} - 20 q^{76} - 8 q^{79} - 32 q^{80} + 28 q^{81} + 34 q^{84} - 4 q^{85} + 8 q^{86} + 84 q^{89} - 4 q^{90} + 18 q^{91} - 8 q^{94} + 4 q^{95} - 66 q^{96} - 8 q^{99}+O(q^{100}) $ 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 - 4 * q^15 + 38 * q^16 + 12 * q^19 - 4 * q^20 - 28 * q^21 + 30 * q^24 - 8 * q^25 - 36 * q^26 - 2 * q^30 + 14 * q^31 - 6 * q^34 - 4 * q^35 + 34 * q^36 + 18 * q^39 - 62 * q^40 - 50 * q^41 - 24 * q^44 + 52 * q^46 - 28 * q^49 + 6 * q^50 - 28 * q^51 + 6 * q^54 - 14 * q^55 + 30 * q^56 + 44 * q^59 + 10 * q^60 + 26 * q^61 - 6 * q^64 + 20 * q^65 - 48 * q^66 + 38 * q^69 - 2 * q^70 + 12 * q^71 + 24 * q^74 - 16 * q^75 - 20 * q^76 - 8 * q^79 - 32 * q^80 + 28 * q^81 + 34 * q^84 - 4 * q^85 + 8 * q^86 + 84 * q^89 - 4 * q^90 + 18 * q^91 - 8 * q^94 + 4 * q^95 - 66 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1785\mathbb{Z}\right)^\times$.

$n$	$596$	$766$	$1072$	$1261$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.69985i		−	1.20198i	−0.799258	−	0.600988i	$-0.794774\pi$
$2$		−	1.69985i		−	1.20198i	0.799258	−	0.600988i	$-0.205226\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.889490			−0.444745
$5$	1.47723	−	1.67863i	0.660638	−	0.750705i
$5$	1.47723	−	1.67863i	0.660638	−	0.750705i
$6$	−1.69985			−0.693961
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.88770i		−	0.667403i
$9$	−1.00000			−0.333333
$10$	−2.85341	−	2.51107i	−0.902328	−	0.794071i
$11$	−1.31823			−0.397461			−0.198731	−	0.980054i	$-0.563682\pi$
$11$	−1.31823			−0.397461			−0.198731	+	0.980054i	$0.563682\pi$
$12$			0.889490i			0.256774i
$13$		−	4.26284i		−	1.18230i	−0.806562	−	0.591149i	$-0.798674\pi$
$13$		−	4.26284i		−	1.18230i	0.806562	−	0.591149i	$-0.201326\pi$
$14$	−1.69985			−0.454304
$15$	−1.67863	−	1.47723i	−0.433419	−	0.381420i
$16$	−4.98779			−1.24695
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$			1.69985i			0.400659i
$19$	5.21905			1.19733			0.598666	−	0.800999i	$-0.295698\pi$
$19$	5.21905			1.19733			0.598666	+	0.800999i	$0.295698\pi$
$20$	−1.31398	+	1.49312i	−0.293816	+	0.333872i
$21$	−1.00000			−0.218218
$22$			2.24079i			0.477739i
$23$			2.71209i			0.565509i	0.959192	+	0.282754i	$0.0912482\pi$
$23$			2.71209i			0.565509i	−0.959192	+	0.282754i	$0.908752\pi$
$24$	−1.88770			−0.385325
$25$	−0.635573	−	4.95944i	−0.127115	−	0.991888i
$26$	−7.24619			−1.42109
$27$			1.00000i			0.192450i
$28$			0.889490i			0.168098i
$29$	0.948665			0.176163			0.0880814	−	0.996113i	$-0.471926\pi$
$29$	0.948665			0.176163			0.0880814	+	0.996113i	$0.471926\pi$
$30$	−2.51107	+	2.85341i	−0.458457	+	0.520960i
$31$	−2.19047			−0.393420			−0.196710	−	0.980462i	$-0.563026\pi$
$31$	−2.19047			−0.393420			−0.196710	+	0.980462i	$0.563026\pi$
$32$			4.70309i			0.831397i
$33$			1.31823i			0.229474i
$34$	−1.69985			−0.291522
$35$	−1.67863	−	1.47723i	−0.283740	−	0.249698i
$36$	0.889490			0.148248
$37$			3.64278i			0.598870i	0.954117	+	0.299435i	$0.0967982\pi$
$37$			3.64278i			0.598870i	−0.954117	+	0.299435i	$0.903202\pi$
$38$		−	8.87160i		−	1.43916i
$39$	−4.26284			−0.682601
$40$	−3.16874	−	2.78857i	−0.501022	−	0.440912i
$41$	10.0648			1.57185			0.785925	−	0.618321i	$-0.212187\pi$
$41$	10.0648			1.57185			0.785925	+	0.618321i	$0.212187\pi$
$42$			1.69985i			0.262293i
$43$		−	1.43751i		−	0.219218i	−0.993975	−	0.109609i	$-0.965040\pi$
$43$		−	1.43751i		−	0.219218i	0.993975	−	0.109609i	$-0.0349598\pi$
$44$	1.17255			0.176769
$45$	−1.47723	+	1.67863i	−0.220213	+	0.250235i
$46$	4.61014			0.679728
$47$			3.21978i			0.469654i	0.972037	+	0.234827i	$0.0754523\pi$
$47$			3.21978i			0.469654i	−0.972037	+	0.234827i	$0.924548\pi$
$48$			4.98779i			0.719925i
$49$	−1.00000			−0.142857
$50$	−8.43031	+	1.08038i	−1.19223	+	0.152789i
$51$	−1.00000			−0.140028
$52$			3.79175i			0.525822i
$53$			14.1176i			1.93920i	0.244701	+	0.969599i	$0.421310\pi$
$53$			14.1176i			1.93920i	−0.244701	+	0.969599i	$0.578690\pi$
$54$	1.69985			0.231320
$55$	−1.94733	+	2.21282i	−0.262578	+	0.298376i
$56$	−1.88770			−0.252255
$57$		−	5.21905i		−	0.691280i
$58$		−	1.61259i		−	0.211743i
$59$	−14.0099			−1.82394			−0.911968	−	0.410262i	$-0.865437\pi$
$59$	−14.0099			−1.82394			−0.911968	+	0.410262i	$0.865437\pi$
$60$	1.49312	+	1.31398i	0.192761	+	0.169635i
$61$	8.36086			1.07050			0.535249	−	0.844694i	$-0.320218\pi$
$61$	8.36086			1.07050			0.535249	+	0.844694i	$0.320218\pi$
$62$			3.72347i			0.472881i
$63$			1.00000i			0.125988i
$64$	−1.98102			−0.247628
$65$	−7.15571	−	6.29720i	−0.887557	−	0.781072i
$66$	2.24079			0.275823
$67$		−	13.6284i		−	1.66497i	−0.554049	−	0.832484i	$-0.686918\pi$
$67$		−	13.6284i		−	1.66497i	0.554049	−	0.832484i	$-0.313082\pi$
$68$			0.889490i			0.107867i
$69$	2.71209			0.326497
$70$	−2.51107	+	2.85341i	−0.300131	+	0.341048i
$71$	−6.66687			−0.791212			−0.395606	−	0.918420i	$-0.629465\pi$
$71$	−6.66687			−0.791212			−0.395606	+	0.918420i	$0.629465\pi$
$72$			1.88770i			0.222468i
$73$		−	13.0816i		−	1.53109i	−0.643383	−	0.765544i	$-0.722470\pi$
$73$		−	13.0816i		−	1.53109i	0.643383	−	0.765544i	$-0.277530\pi$
$74$	6.19219			0.719827
$75$	−4.95944	+	0.635573i	−0.572667	+	0.0733896i
$76$	−4.64229			−0.532508
$77$			1.31823i			0.150226i
$78$			7.24619i			0.820469i
$79$	9.12564			1.02672			0.513358	−	0.858175i	$-0.328401\pi$
$79$	9.12564			1.02672			0.513358	+	0.858175i	$0.328401\pi$
$80$	−7.36812	+	8.37263i	−0.823781	+	0.936089i
$81$	1.00000			0.111111
$82$		−	17.1086i		−	1.88933i
$83$			6.08519i			0.667936i	0.942584	+	0.333968i	$0.108388\pi$
$83$			6.08519i			0.667936i	−0.942584	+	0.333968i	$0.891612\pi$
$84$	0.889490			0.0970514
$85$	−1.67863	−	1.47723i	−0.182073	−	0.160228i
$86$	−2.44355			−0.263494
$87$		−	0.948665i		−	0.101708i
$88$			2.48842i			0.265267i
$89$	−0.0400448			−0.00424474			−0.00212237	−	0.999998i	$-0.500676\pi$
$89$	−0.0400448			−0.00424474			−0.00212237	+	0.999998i	$0.500676\pi$
$90$	2.85341	+	2.51107i	0.300776	+	0.264690i
$91$	−4.26284			−0.446867
$92$		−	2.41237i		−	0.251507i
$93$			2.19047i			0.227141i
$94$	5.47315			0.564512
$95$	7.70974	−	8.76083i	0.791003	−	0.898842i
$96$	4.70309			0.480007
$97$			7.33549i			0.744806i	0.928071	+	0.372403i	$0.121466\pi$
$97$			7.33549i			0.744806i	−0.928071	+	0.372403i	$0.878534\pi$
$98$			1.69985i			0.171711i
$99$	1.31823			0.132487
$100$	0.565336	+	4.41137i	0.0565336	+	0.441137i
$101$	−2.66094			−0.264774			−0.132387	−	0.991198i	$-0.542264\pi$
$101$	−2.66094			−0.264774			−0.132387	+	0.991198i	$0.542264\pi$
$102$			1.69985i			0.168310i
$103$			8.62526i			0.849872i	0.905223	+	0.424936i	$0.139703\pi$
$103$			8.62526i			0.849872i	−0.905223	+	0.424936i	$0.860297\pi$
$104$	−8.04696			−0.789069
$105$	−1.47723	+	1.67863i	−0.144163	+	0.163817i
$106$	23.9978			2.33087
$107$		−	19.2943i		−	1.86525i	−0.360852	−	0.932623i	$-0.617514\pi$
$107$		−	19.2943i		−	1.86525i	0.360852	−	0.932623i	$-0.382486\pi$
$108$		−	0.889490i		−	0.0855913i
$109$	−4.03341			−0.386331			−0.193166	−	0.981166i	$-0.561875\pi$
$109$	−4.03341			−0.386331			−0.193166	+	0.981166i	$0.561875\pi$
$110$	3.76146	+	3.31017i	0.358641	+	0.315612i
$111$	3.64278			0.345758
$112$			4.98779i			0.471302i
$113$			18.5353i			1.74366i	0.489810	+	0.871829i	$0.337066\pi$
$113$			18.5353i			1.74366i	−0.489810	+	0.871829i	$0.662934\pi$
$114$	−8.87160			−0.830902
$115$	4.55258	+	4.00638i	0.424530	+	0.373597i
$116$	−0.843829			−0.0783475
$117$			4.26284i			0.394100i
$118$			23.8148i			2.19233i
$119$	−1.00000			−0.0916698
$120$	−2.78857	+	3.16874i	−0.254560	+	0.289265i
$121$	−9.26227			−0.842024
$122$		−	14.2122i		−	1.28671i
$123$		−	10.0648i		−	0.907509i
$124$	1.94840			0.174972
$125$	−9.26394	−	6.25935i	−0.828592	−	0.559854i
$126$	1.69985			0.151435
$127$		−	7.03516i		−	0.624269i	−0.950038	−	0.312135i	$-0.898956\pi$
$127$		−	7.03516i		−	0.624269i	0.950038	−	0.312135i	$-0.101044\pi$
$128$			12.7736i			1.12904i
$129$	−1.43751			−0.126565
$130$	−10.7043	+	12.1636i	−0.938829	+	1.06682i
$131$	−2.49412			−0.217913			−0.108956	−	0.994047i	$-0.534751\pi$
$131$	−2.49412			−0.217913			−0.108956	+	0.994047i	$0.534751\pi$
$132$		−	1.17255i		−	0.102058i
$133$		−	5.21905i		−	0.452549i
$134$	−23.1662			−2.00125
$135$	1.67863	+	1.47723i	0.144473	+	0.127140i
$136$	−1.88770			−0.161869
$137$			4.36841i			0.373218i	0.982434	+	0.186609i	$0.0597498\pi$
$137$			4.36841i			0.373218i	−0.982434	+	0.186609i	$0.940250\pi$
$138$		−	4.61014i		−	0.392441i
$139$	11.3585			0.963413			0.481707	−	0.876333i	$-0.340017\pi$
$139$	11.3585			0.963413			0.481707	+	0.876333i	$0.340017\pi$
$140$	1.49312	+	1.31398i	0.126192	+	0.111052i
$141$	3.21978			0.271155
$142$			11.3327i			0.951018i
$143$			5.61940i			0.469918i
$144$	4.98779			0.415649
$145$	1.40140	−	1.59245i	0.116380	−	0.132246i
$146$	−22.2368			−1.84033
$147$			1.00000i			0.0824786i
$148$		−	3.24022i		−	0.266345i
$149$	15.8707			1.30018			0.650090	−	0.759858i	$-0.274731\pi$
$149$	15.8707			1.30018			0.650090	+	0.759858i	$0.274731\pi$
$150$	1.08038	+	8.43031i	0.0882125	+	0.688332i
$151$	10.9078			0.887667			0.443833	−	0.896109i	$-0.353618\pi$
$151$	10.9078			0.887667			0.443833	+	0.896109i	$0.353618\pi$
$152$		−	9.85200i		−	0.799103i
$153$			1.00000i			0.0808452i
$154$	2.24079			0.180568
$155$	−3.23583	+	3.67698i	−0.259908	+	0.295342i
$156$	3.79175			0.303583
$157$			5.06290i			0.404063i	0.979379	+	0.202032i	$0.0647544\pi$
$157$			5.06290i			0.404063i	−0.979379	+	0.202032i	$0.935246\pi$
$158$		−	15.5122i		−	1.23409i
$159$	14.1176			1.11960
$160$	7.89473	+	6.94756i	0.624134	+	0.549253i
$161$	2.71209			0.213742
$162$		−	1.69985i		−	0.133553i
$163$			13.9637i			1.09372i	0.837224	+	0.546860i	$0.184177\pi$
$163$			13.9637i			1.09372i	−0.837224	+	0.546860i	$0.815823\pi$
$164$	−8.95250			−0.699073
$165$	2.21282	+	1.94733i	0.172267	+	0.151600i
$166$	10.3439			0.802843
$167$			20.0975i			1.55519i	0.628766	+	0.777595i	$0.283560\pi$
$167$			20.0975i			1.55519i	−0.628766	+	0.777595i	$0.716440\pi$
$168$			1.88770i			0.145639i
$169$	−5.17180			−0.397830
$170$	−2.51107	+	2.85341i	−0.192590	+	0.218847i
$171$	−5.21905			−0.399111
$172$			1.27865i			0.0974960i
$173$		−	9.66834i		−	0.735071i	−0.930010	−	0.367535i	$-0.880202\pi$
$173$		−	9.66834i		−	0.735071i	0.930010	−	0.367535i	$-0.119798\pi$
$174$	−1.61259			−0.122250
$175$	−4.95944	+	0.635573i	−0.374898	+	0.0480448i
$176$	6.57505			0.495613
$177$			14.0099i			1.05305i
$178$			0.0680701i			0.00510207i
$179$	−2.03325			−0.151972			−0.0759859	−	0.997109i	$-0.524210\pi$
$179$	−2.03325			−0.151972			−0.0759859	+	0.997109i	$0.524210\pi$
$180$	1.31398	−	1.49312i	0.0979385	−	0.111291i
$181$	22.0739			1.64074			0.820369	−	0.571835i	$-0.193768\pi$
$181$	22.0739			1.64074			0.820369	+	0.571835i	$0.193768\pi$
$182$			7.24619i			0.537123i
$183$		−	8.36086i		−	0.618052i
$184$	5.11960			0.377422
$185$	6.11487	+	5.38124i	0.449574	+	0.395636i
$186$	3.72347			0.273018
$187$			1.31823i			0.0963985i
$188$		−	2.86397i		−	0.208876i
$189$	1.00000			0.0727393
$190$	−14.8921	−	13.1054i	−1.08039	−	0.950766i
$191$	18.4256			1.33323			0.666614	−	0.745403i	$-0.267743\pi$
$191$	18.4256			1.33323			0.666614	+	0.745403i	$0.267743\pi$
$192$			1.98102i			0.142968i
$193$		−	20.9313i		−	1.50666i	−0.657640	−	0.753332i	$-0.728445\pi$
$193$		−	20.9313i		−	1.50666i	0.657640	−	0.753332i	$-0.271555\pi$
$194$	12.4692			0.895239
$195$	−6.29720	+	7.15571i	−0.450952	+	0.512431i
$196$	0.889490			0.0635350
$197$		−	16.7970i		−	1.19674i	−0.801221	−	0.598368i	$-0.795816\pi$
$197$		−	16.7970i		−	1.19674i	0.801221	−	0.598368i	$-0.204184\pi$
$198$		−	2.24079i		−	0.159246i
$199$	−17.0325			−1.20740			−0.603700	−	0.797211i	$-0.706308\pi$
$199$	−17.0325			−1.20740			−0.603700	+	0.797211i	$0.706308\pi$
$200$	−9.36193	+	1.19977i	−0.661989	+	0.0848366i
$201$	−13.6284			−0.961270
$202$			4.52320i			0.318252i
$203$		−	0.948665i		−	0.0665832i
$204$	0.889490			0.0622768
$205$	14.8680	−	16.8950i	1.03842	−	1.18000i
$206$	14.6616			1.02152
$207$		−	2.71209i		−	0.188503i
$208$			21.2621i			1.47426i
$209$	−6.87991			−0.475893
$210$	2.85341	+	2.51107i	0.196904	+	0.173280i
$211$	−10.1723			−0.700293			−0.350147	−	0.936695i	$-0.613868\pi$
$211$	−10.1723			−0.700293			−0.350147	+	0.936695i	$0.613868\pi$
$212$		−	12.5574i		−	0.862449i
$213$			6.66687i			0.456807i
$214$	−32.7974			−2.24198
$215$	−2.41304	−	2.12353i	−0.164568	−	0.144824i
$216$	1.88770			0.128442
$217$			2.19047i			0.148699i
$218$			6.85620i			0.464361i
$219$	−13.0816			−0.883974
$220$	1.73213	−	1.96828i	0.116780	−	0.132701i
$221$	−4.26284			−0.286750
$222$		−	6.19219i		−	0.415592i
$223$			2.54258i			0.170264i	0.996370	+	0.0851320i	$0.0271312\pi$
$223$			2.54258i			0.170264i	−0.996370	+	0.0851320i	$0.972869\pi$
$224$	4.70309			0.314239
$225$	0.635573	+	4.95944i	0.0423715	+	0.330629i
$226$	31.5073			2.09583
$227$		−	10.5749i		−	0.701883i	−0.936397	−	0.350942i	$-0.885862\pi$
$227$		−	10.5749i		−	0.701883i	0.936397	−	0.350942i	$-0.114138\pi$
$228$			4.64229i			0.307443i
$229$	16.7374			1.10604			0.553020	−	0.833168i	$-0.313475\pi$
$229$	16.7374			1.10604			0.553020	+	0.833168i	$0.313475\pi$
$230$	6.81024	−	7.73870i	0.449054	−	0.510275i
$231$	1.31823			0.0867332
$232$		−	1.79080i		−	0.117571i
$233$		−	5.57246i		−	0.365064i	−0.983200	−	0.182532i	$-0.941571\pi$
$233$		−	5.57246i		−	0.365064i	0.983200	−	0.182532i	$-0.0584293\pi$
$234$	7.24619			0.473698
$235$	5.40481	+	4.75637i	0.352571	+	0.310271i
$236$	12.4617			0.811187
$237$		−	9.12564i		−	0.592774i
$238$			1.69985i			0.110185i
$239$	−12.4766			−0.807041			−0.403521	−	0.914971i	$-0.632214\pi$
$239$	−12.4766			−0.807041			−0.403521	+	0.914971i	$0.632214\pi$
$240$	8.37263	+	7.36812i	0.540451	+	0.475610i
$241$	10.1786			0.655659			0.327829	−	0.944737i	$-0.393683\pi$
$241$	10.1786			0.655659			0.327829	+	0.944737i	$0.393683\pi$
$242$			15.7445i			1.01209i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.43690			−0.476099
$245$	−1.47723	+	1.67863i	−0.0943769	+	0.107244i
$246$	−17.1086			−1.09080
$247$		−	22.2480i		−	1.41560i
$248$			4.13495i			0.262569i
$249$	6.08519			0.385633
$250$	−10.6400	+	15.7473i	−0.672930	+	0.995947i
$251$	−5.67410			−0.358146			−0.179073	−	0.983836i	$-0.557310\pi$
$251$	−5.67410			−0.358146			−0.179073	+	0.983836i	$0.557310\pi$
$252$		−	0.889490i		−	0.0560326i
$253$		−	3.57515i		−	0.224768i
$254$	−11.9587			−0.750356
$255$	−1.47723	+	1.67863i	−0.0925078	+	0.105120i
$256$	17.7512			1.10945
$257$		−	18.9299i		−	1.18082i	−0.807105	−	0.590408i	$-0.798967\pi$
$257$		−	18.9299i		−	1.18082i	0.807105	−	0.590408i	$-0.201033\pi$
$258$			2.44355i			0.152129i
$259$	3.64278			0.226352
$260$	6.36494	+	5.60130i	0.394737	+	0.347378i
$261$	−0.948665			−0.0587209
$262$			4.23963i			0.261926i
$263$			4.50632i			0.277872i	0.990301	+	0.138936i	$0.0443682\pi$
$263$			4.50632i			0.277872i	−0.990301	+	0.138936i	$0.955632\pi$
$264$	2.48842			0.153152
$265$	23.6981	+	20.8549i	1.45576	+	1.28111i
$266$	−8.87160			−0.543953
$267$			0.0400448i			0.00245070i
$268$			12.1223i			0.740487i
$269$	6.65868			0.405987			0.202993	−	0.979180i	$-0.434933\pi$
$269$	6.65868			0.405987			0.202993	+	0.979180i	$0.434933\pi$
$270$	2.51107	−	2.85341i	0.152819	−	0.173653i
$271$	6.91612			0.420124			0.210062	−	0.977688i	$-0.432633\pi$
$271$	6.91612			0.420124			0.210062	+	0.977688i	$0.432633\pi$
$272$			4.98779i			0.302429i
$273$			4.26284i			0.257999i
$274$	7.42564			0.448599
$275$	0.837831	+	6.53768i	0.0505231	+	0.394237i
$276$	−2.41237			−0.145208
$277$		−	8.39750i		−	0.504557i	−0.967655	−	0.252278i	$-0.918820\pi$
$277$		−	8.39750i		−	0.504557i	0.967655	−	0.252278i	$-0.0811799\pi$
$278$		−	19.3077i		−	1.15800i
$279$	2.19047			0.131140
$280$	−2.78857	+	3.16874i	−0.166649	+	0.189369i
$281$	5.79215			0.345531			0.172765	−	0.984963i	$-0.444730\pi$
$281$	5.79215			0.345531			0.172765	+	0.984963i	$0.444730\pi$
$282$		−	5.47315i		−	0.325921i
$283$			25.7255i			1.52922i	0.644493	+	0.764610i	$0.277068\pi$
$283$			25.7255i			1.52922i	−0.644493	+	0.764610i	$0.722932\pi$
$284$	5.93012			0.351888
$285$	−8.76083	−	7.70974i	−0.518947	−	0.456686i
$286$	9.55214			0.564830
$287$		−	10.0648i		−	0.594104i
$288$		−	4.70309i		−	0.277132i
$289$	−1.00000			−0.0588235
$290$	−2.70693	−	2.38217i	−0.158957	−	0.139886i
$291$	7.33549			0.430014
$292$			11.6360i			0.680944i
$293$		−	3.51413i		−	0.205298i	−0.994718	−	0.102649i	$-0.967268\pi$
$293$		−	3.51413i		−	0.205298i	0.994718	−	0.102649i	$-0.0327318\pi$
$294$	1.69985			0.0991373
$295$	−20.6959	+	23.5174i	−1.20496	+	1.36924i
$296$	6.87648			0.399687
$297$		−	1.31823i		−	0.0764915i
$298$		−	26.9778i		−	1.56278i
$299$	11.5612			0.668600
$300$	4.41137	−	0.565336i	0.254691	−	0.0326397i
$301$	−1.43751			−0.0828565
$302$		−	18.5417i		−	1.06695i
$303$			2.66094i			0.152867i
$304$	−26.0315			−1.49301
$305$	12.3509	−	14.0348i	0.707212	−	0.803628i
$306$	1.69985			0.0971740
$307$			15.6901i			0.895481i	0.894163	+	0.447741i	$0.147771\pi$
$307$			15.6901i			0.895481i	−0.894163	+	0.447741i	$0.852229\pi$
$308$		−	1.17255i		−	0.0668124i
$309$	8.62526			0.490674
$310$	6.25031	+	5.50043i	0.354994	+	0.312403i
$311$	−33.0126			−1.87197			−0.935987	−	0.352035i	$-0.885490\pi$
$311$	−33.0126			−1.87197			−0.935987	+	0.352035i	$0.885490\pi$
$312$			8.04696i			0.455569i
$313$			1.96627i			0.111140i	0.998455	+	0.0555702i	$0.0176977\pi$
$313$			1.96627i			0.111140i	−0.998455	+	0.0555702i	$0.982302\pi$
$314$	8.60617			0.485674
$315$	1.67863	+	1.47723i	0.0945799	+	0.0832326i
$316$	−8.11717			−0.456627
$317$		−	29.0692i		−	1.63269i	−0.577564	−	0.816345i	$-0.695997\pi$
$317$		−	29.0692i		−	1.63269i	0.577564	−	0.816345i	$-0.304003\pi$
$318$		−	23.9978i		−	1.34573i
$319$	−1.25056			−0.0700179
$320$	−2.92643	+	3.32540i	−0.163593	+	0.185895i
$321$	−19.2943			−1.07690
$322$		−	4.61014i		−	0.256913i
$323$		−	5.21905i		−	0.290396i
$324$	−0.889490			−0.0494161
$325$	−21.1413	+	2.70934i	−1.17271	+	0.150287i
$326$	23.7362			1.31462
$327$			4.03341i			0.223048i
$328$		−	18.9992i		−	1.04906i
$329$	3.21978			0.177512
$330$	3.31017	−	3.76146i	0.182219	−	0.207061i
$331$	29.7790			1.63680			0.818401	−	0.574647i	$-0.194861\pi$
$331$	29.7790			1.63680			0.818401	+	0.574647i	$0.194861\pi$
$332$		−	5.41272i		−	0.297061i
$333$		−	3.64278i		−	0.199623i
$334$	34.1627			1.86930
$335$	−22.8769	−	20.1322i	−1.24990	−	1.09994i
$336$	4.98779			0.272106
$337$		−	31.8660i		−	1.73585i	−0.496694	−	0.867925i	$-0.665453\pi$
$337$		−	31.8660i		−	1.73585i	0.496694	−	0.867925i	$-0.334547\pi$
$338$			8.79128i			0.478182i
$339$	18.5353			1.00670
$340$	1.49312	+	1.31398i	0.0809759	+	0.0712608i
$341$	2.88754			0.156369
$342$			8.87160i			0.479721i
$343$			1.00000i			0.0539949i
$344$	−2.71358			−0.146306
$345$	4.00638	−	4.55258i	0.215696	−	0.245103i
$346$	−16.4347			−0.883537
$347$		−	1.62114i		−	0.0870273i	−0.999053	−	0.0435136i	$-0.986145\pi$
$347$		−	1.62114i		−	0.0870273i	0.999053	−	0.0435136i	$-0.0138552\pi$
$348$			0.843829i			0.0452340i
$349$	−24.2326			−1.29714			−0.648572	−	0.761153i	$-0.724633\pi$
$349$	−24.2326			−1.29714			−0.648572	+	0.761153i	$0.724633\pi$
$350$	1.08038	+	8.43031i	0.0577487	+	0.450619i
$351$	4.26284			0.227534
$352$		−	6.19976i		−	0.330448i
$353$		−	13.1172i		−	0.698159i	−0.937093	−	0.349080i	$-0.886494\pi$
$353$		−	13.1172i		−	0.698159i	0.937093	−	0.349080i	$-0.113506\pi$
$354$	23.8148			1.26574
$355$	−9.84851	+	11.1912i	−0.522705	+	0.593967i
$356$	0.0356195			0.00188783
$357$			1.00000i			0.0529256i
$358$			3.45621i			0.182666i
$359$	0.584856			0.0308675			0.0154338	−	0.999881i	$-0.495087\pi$
$359$	0.584856			0.0308675			0.0154338	+	0.999881i	$0.495087\pi$
$360$	3.16874	+	2.78857i	0.167007	+	0.146971i
$361$	8.23847			0.433604
$362$		−	37.5223i		−	1.97213i
$363$			9.26227i			0.486143i
$364$	3.79175			0.198742
$365$	−21.9592	−	19.3246i	−1.14940	−	1.01150i
$366$	−14.2122			−0.742884
$367$		−	20.0167i		−	1.04486i	−0.852682	−	0.522431i	$-0.825025\pi$
$367$		−	20.0167i		−	1.04486i	0.852682	−	0.522431i	$-0.174975\pi$
$368$		−	13.5273i		−	0.705160i
$369$	−10.0648			−0.523950
$370$	9.14730	−	10.3944i	0.475545	−	0.540377i
$371$	14.1176			0.732948
$372$		−	1.94840i		−	0.101020i
$373$		−	18.8646i		−	0.976774i	−0.872627	−	0.488387i	$-0.837585\pi$
$373$		−	18.8646i		−	0.976774i	0.872627	−	0.488387i	$-0.162415\pi$
$374$	2.24079			0.115869
$375$	−6.25935	+	9.26394i	−0.323232	+	0.478388i
$376$	6.07798			0.313448
$377$		−	4.04401i		−	0.208277i
$378$		−	1.69985i		−	0.0874309i
$379$	20.4953			1.05277			0.526385	−	0.850246i	$-0.323547\pi$
$379$	20.4953			1.05277			0.526385	+	0.850246i	$0.323547\pi$
$380$	−6.85774	+	7.79268i	−0.351795	+	0.399756i
$381$	−7.03516			−0.360422
$382$		−	31.3207i		−	1.60251i
$383$			13.8741i			0.708935i	0.935068	+	0.354468i	$0.115338\pi$
$383$			13.8741i			0.708935i	−0.935068	+	0.354468i	$0.884662\pi$
$384$	12.7736			0.651851
$385$	2.21282	+	1.94733i	0.112776	+	0.0992452i
$386$	−35.5800			−1.81097
$387$			1.43751i			0.0730726i
$388$		−	6.52485i		−	0.331249i
$389$	35.8144			1.81586			0.907931	−	0.419120i	$-0.137661\pi$
$389$	35.8144			1.81586			0.907931	+	0.419120i	$0.137661\pi$
$390$	12.1636	+	10.7043i	0.615930	+	0.542033i
$391$	2.71209			0.137156
$392$			1.88770i			0.0953432i
$393$			2.49412i			0.125812i
$394$	−28.5524			−1.43845
$395$	13.4807	−	15.3185i	0.678287	−	0.770760i
$396$	−1.17255			−0.0589230
$397$		−	16.1355i		−	0.809820i	−0.914357	−	0.404910i	$-0.867303\pi$
$397$		−	16.1355i		−	0.809820i	0.914357	−	0.404910i	$-0.132697\pi$
$398$			28.9527i			1.45127i
$399$	−5.21905			−0.261279
$400$	3.17010	+	24.7366i	0.158505	+	1.23683i
$401$	−10.5679			−0.527736			−0.263868	−	0.964559i	$-0.584998\pi$
$401$	−10.5679			−0.527736			−0.263868	+	0.964559i	$0.584998\pi$
$402$			23.1662i			1.15542i
$403$			9.33761i			0.465140i
$404$	2.36688			0.117757
$405$	1.47723	−	1.67863i	0.0734042	−	0.0834116i
$406$	−1.61259			−0.0800314
$407$		−	4.80203i		−	0.238028i
$408$			1.88770i			0.0934551i
$409$	−16.7929			−0.830353			−0.415177	−	0.909741i	$-0.636280\pi$
$409$	−16.7929			−0.830353			−0.415177	+	0.909741i	$0.636280\pi$
$410$	−28.7189	−	25.2733i	−1.41833	−	1.24816i
$411$	4.36841			0.215478
$412$		−	7.67208i		−	0.377976i
$413$			14.0099i			0.689383i
$414$	−4.61014			−0.226576
$415$	10.2148	+	8.98923i	0.501423	+	0.441264i
$416$	20.0485			0.982960
$417$		−	11.3585i		−	0.556227i
$418$			11.6948i			0.572012i
$419$	−15.1395			−0.739612			−0.369806	−	0.929109i	$-0.620576\pi$
$419$	−15.1395			−0.739612			−0.369806	+	0.929109i	$0.620576\pi$
$420$	1.31398	−	1.49312i	0.0641158	−	0.0728569i
$421$	17.1786			0.837236			0.418618	−	0.908162i	$-0.362515\pi$
$421$	17.1786			0.837236			0.418618	+	0.908162i	$0.362515\pi$
$422$			17.2915i			0.841735i
$423$		−	3.21978i		−	0.156551i
$424$	26.6497			1.29423
$425$	−4.95944	+	0.635573i	−0.240568	+	0.0308298i
$426$	11.3327			0.549070
$427$		−	8.36086i		−	0.404610i
$428$			17.1621i			0.829559i
$429$	5.61940			0.271307
$430$	−3.60968	+	4.10180i	−0.174074	+	0.197806i
$431$	−34.0312			−1.63922			−0.819612	−	0.572919i	$-0.805811\pi$
$431$	−34.0312			−1.63922			−0.819612	+	0.572919i	$0.805811\pi$
$432$		−	4.98779i		−	0.239975i
$433$		−	16.0610i		−	0.771842i	−0.922532	−	0.385921i	$-0.873884\pi$
$433$		−	16.0610i		−	0.771842i	0.922532	−	0.385921i	$-0.126116\pi$
$434$	3.72347			0.178732
$435$	−1.59245	−	1.40140i	−0.0763523	−	0.0671919i
$436$	3.58768			0.171819
$437$			14.1545i			0.677102i
$438$			22.2368i			1.06252i
$439$	−10.1471			−0.484293			−0.242147	−	0.970240i	$-0.577852\pi$
$439$	−10.1471			−0.484293			−0.242147	+	0.970240i	$0.577852\pi$
$440$	4.17713	+	3.67598i	0.199137	+	0.175245i
$441$	1.00000			0.0476190
$442$			7.24619i			0.344666i
$443$			20.6208i			0.979726i	0.871799	+	0.489863i	$0.162953\pi$
$443$			20.6208i			0.979726i	−0.871799	+	0.489863i	$0.837047\pi$
$444$	−3.24022			−0.153774
$445$	−0.0591554	+	0.0672202i	−0.00280424	+	0.00318654i
$446$	4.32201			0.204653
$447$		−	15.8707i		−	0.750659i
$448$			1.98102i			0.0935946i
$449$	−16.1240			−0.760940			−0.380470	−	0.924793i	$-0.624238\pi$
$449$	−16.1240			−0.760940			−0.380470	+	0.924793i	$0.624238\pi$
$450$	8.43031	−	1.08038i	0.397408	−	0.0509295i
$451$	−13.2677			−0.624750
$452$		−	16.4870i		−	0.775484i
$453$		−	10.9078i		−	0.512495i
$454$	−17.9758			−0.843646
$455$	−6.29720	+	7.15571i	−0.295217	+	0.335465i
$456$	−9.85200			−0.461362
$457$		−	8.92593i		−	0.417538i	−0.977965	−	0.208769i	$-0.933054\pi$
$457$		−	8.92593i		−	0.417538i	0.977965	−	0.208769i	$-0.0669456\pi$
$458$		−	28.4511i		−	1.32943i
$459$	1.00000			0.0466760
$460$	−4.04947	−	3.56364i	−0.188808	−	0.166155i
$461$	−15.6712			−0.729881			−0.364941	−	0.931031i	$-0.618911\pi$
$461$	−15.6712			−0.729881			−0.364941	+	0.931031i	$0.618911\pi$
$462$		−	2.24079i		−	0.104251i
$463$		−	20.0753i		−	0.932980i	−0.884526	−	0.466490i	$-0.845518\pi$
$463$		−	20.0753i		−	0.932980i	0.884526	−	0.466490i	$-0.154482\pi$
$464$	−4.73174			−0.219666
$465$	3.67698	+	3.23583i	0.170516	+	0.150058i
$466$	−9.47234			−0.438798
$467$			20.2971i			0.939239i	0.882869	+	0.469619i	$0.155609\pi$
$467$			20.2971i			0.939239i	−0.882869	+	0.469619i	$0.844391\pi$
$468$		−	3.79175i		−	0.175274i
$469$	−13.6284			−0.629299
$470$	8.08511	−	9.18737i	0.372938	−	0.423782i
$471$	5.06290			0.233286
$472$			26.4465i			1.21730i
$473$			1.89496i			0.0871306i
$474$	−15.5122			−0.712500
$475$	−3.31709	−	25.8836i	−0.152198	−	1.18762i
$476$	0.889490			0.0407697
$477$		−	14.1176i		−	0.646399i
$478$			21.2083i			0.970044i
$479$	40.7298			1.86099			0.930496	−	0.366301i	$-0.119376\pi$
$479$	40.7298			1.86099			0.930496	+	0.366301i	$0.119376\pi$
$480$	6.94756	−	7.89473i	0.317111	−	0.360344i
$481$	15.5286			0.708043
$482$		−	17.3020i		−	0.788086i
$483$		−	2.71209i		−	0.123404i
$484$	8.23870			0.374486
$485$	12.3135	+	10.8362i	0.559129	+	0.492047i
$486$	−1.69985			−0.0771068
$487$		−	28.7836i		−	1.30431i	−0.758085	−	0.652156i	$-0.773865\pi$
$487$		−	28.7836i		−	1.30431i	0.758085	−	0.652156i	$-0.226135\pi$
$488$		−	15.7828i		−	0.714453i
$489$	13.9637			0.631459
$490$	2.85341	+	2.51107i	0.128904	+	0.113439i
$491$	−5.30798			−0.239546			−0.119773	−	0.992801i	$-0.538217\pi$
$491$	−5.30798			−0.239546			−0.119773	+	0.992801i	$0.538217\pi$
$492$			8.95250i			0.403610i
$493$		−	0.948665i		−	0.0427257i
$494$	−37.8182			−1.70152
$495$	1.94733	−	2.21282i	0.0875260	−	0.0994587i
$496$	10.9256			0.490574
$497$			6.66687i			0.299050i
$498$		−	10.3439i		−	0.463522i
$499$	−11.5574			−0.517378			−0.258689	−	0.965961i	$-0.583291\pi$
$499$	−11.5574			−0.517378			−0.258689	+	0.965961i	$0.583291\pi$
$500$	8.24018	+	5.56763i	0.368512	+	0.248992i
$501$	20.0975			0.897889
$502$			9.64512i			0.430483i
$503$		−	9.99769i		−	0.445775i	−0.974844	−	0.222888i	$-0.928452\pi$
$503$		−	9.99769i		−	0.445775i	0.974844	−	0.222888i	$-0.0715483\pi$
$504$	1.88770			0.0840848
$505$	−3.93083	+	4.46673i	−0.174920	+	0.198767i
$506$	−6.07722			−0.270166
$507$			5.17180i			0.229688i
$508$			6.25770i			0.277641i
$509$	31.2809			1.38650			0.693250	−	0.720697i	$-0.256178\pi$
$509$	31.2809			1.38650			0.693250	+	0.720697i	$0.256178\pi$
$510$	2.85341	+	2.51107i	0.126351	+	0.111192i
$511$	−13.0816			−0.578697
$512$		−	4.62713i		−	0.204492i
$513$			5.21905i			0.230427i
$514$	−32.1780			−1.41931
$515$	14.4786	+	12.7415i	0.638002	+	0.561458i
$516$	1.27865			0.0562894
$517$		−	4.24442i		−	0.186669i
$518$		−	6.19219i		−	0.272069i
$519$	−9.66834			−0.424393
$520$	−11.8872	+	13.5078i	−0.521289	+	0.592358i
$521$	−5.52167			−0.241909			−0.120954	−	0.992658i	$-0.538595\pi$
$521$	−5.52167			−0.241909			−0.120954	+	0.992658i	$0.538595\pi$
$522$			1.61259i			0.0705811i
$523$			32.7457i			1.43187i	0.698167	+	0.715935i	$0.253999\pi$
$523$			32.7457i			1.43187i	−0.698167	+	0.715935i	$0.746001\pi$
$524$	2.21850			0.0969155
$525$	0.635573	+	4.95944i	0.0277387	+	0.216448i
$526$	7.66007			0.333995
$527$			2.19047i			0.0954183i
$528$		−	6.57505i		−	0.286142i
$529$	15.6446			0.680200
$530$	35.4502	−	40.2833i	1.53986	−	1.74979i
$531$	14.0099			0.607978
$532$			4.64229i			0.201269i
$533$		−	42.9044i		−	1.85840i
$534$	0.0680701			0.00294568
$535$	−32.3879	−	28.5021i	−1.40025	−	1.23225i
$536$	−25.7262			−1.11120
$537$			2.03325i			0.0877410i
$538$		−	11.3187i		−	0.487986i
$539$	1.31823			0.0567802
$540$	−1.49312	−	1.31398i	−0.0642537	−	0.0565448i
$541$	10.3254			0.443923			0.221961	−	0.975055i	$-0.428754\pi$
$541$	10.3254			0.443923			0.221961	+	0.975055i	$0.428754\pi$
$542$		−	11.7564i		−	0.504979i
$543$		−	22.0739i		−	0.947280i
$544$	4.70309			0.201643
$545$	−5.95829	+	6.77060i	−0.255225	+	0.290020i
$546$	7.24619			0.310108
$547$		−	14.0894i		−	0.602417i	−0.953558	−	0.301209i	$-0.902610\pi$
$547$		−	14.0894i		−	0.602417i	0.953558	−	0.301209i	$-0.0973901\pi$
$548$		−	3.88566i		−	0.165987i
$549$	−8.36086			−0.356833
$550$	11.1131	−	1.42419i	0.473863	−	0.0607276i
$551$	4.95113			0.210925
$552$		−	5.11960i		−	0.217905i
$553$		−	9.12564i		−	0.388062i
$554$	−14.2745			−0.606465
$555$	5.38124	−	6.11487i	0.228421	−	0.259562i
$556$	−10.1033			−0.428473
$557$		−	11.2428i		−	0.476374i	−0.971219	−	0.238187i	$-0.923447\pi$
$557$		−	11.2428i		−	0.476374i	0.971219	−	0.238187i	$-0.0765531\pi$
$558$		−	3.72347i		−	0.157627i
$559$	−6.12786			−0.259181
$560$	8.37263	+	7.36812i	0.353808	+	0.311360i
$561$	1.31823			0.0556557
$562$		−	9.84579i		−	0.415320i
$563$			22.1961i			0.935455i	0.883873	+	0.467727i	$0.154927\pi$
$563$			22.1961i			0.935455i	−0.883873	+	0.467727i	$0.845073\pi$
$564$	−2.86397			−0.120595
$565$	31.1139	+	27.3810i	1.30897	+	1.15193i
$566$	43.7294			1.83808
$567$		−	1.00000i		−	0.0419961i
$568$			12.5851i			0.528057i
$569$	−12.0342			−0.504500			−0.252250	−	0.967662i	$-0.581170\pi$
$569$	−12.0342			−0.504500			−0.252250	+	0.967662i	$0.581170\pi$
$570$	−13.1054	+	14.8921i	−0.548925	+	0.623762i
$571$	−0.950397			−0.0397729			−0.0198864	−	0.999802i	$-0.506330\pi$
$571$	−0.950397			−0.0397729			−0.0198864	+	0.999802i	$0.506330\pi$
$572$		−	4.99841i		−	0.208994i
$573$		−	18.4256i		−	0.769739i
$574$	−17.1086			−0.714098
$575$	13.4504	−	1.72373i	0.560921	−	0.0718844i
$576$	1.98102			0.0825427
$577$			11.5643i			0.481430i	0.970596	+	0.240715i	$0.0773819\pi$
$577$			11.5643i			0.481430i	−0.970596	+	0.240715i	$0.922618\pi$
$578$			1.69985i			0.0707044i
$579$	−20.9313			−0.869873
$580$	−1.24653	+	1.41647i	−0.0517594	+	0.0588158i
$581$	6.08519			0.252456
$582$		−	12.4692i		−	0.516866i
$583$		−	18.6102i		−	0.770756i
$584$	−24.6942			−1.02185
$585$	7.15571	+	6.29720i	0.295852	+	0.260357i
$586$	−5.97350			−0.246763
$587$		−	5.90911i		−	0.243895i	−0.992537	−	0.121947i	$-0.961086\pi$
$587$		−	5.90911i		−	0.243895i	0.992537	−	0.121947i	$-0.0389139\pi$
$588$		−	0.889490i		−	0.0366820i
$589$	−11.4322			−0.471054
$590$	39.9761	+	35.1799i	1.64579	+	1.44833i
$591$	−16.7970			−0.690936
$592$		−	18.1694i		−	0.746759i
$593$			42.4543i			1.74339i	0.490051	+	0.871694i	$0.336978\pi$
$593$			42.4543i			1.74339i	−0.490051	+	0.871694i	$0.663022\pi$
$594$	−2.24079			−0.0919409
$595$	−1.47723	+	1.67863i	−0.0605606	+	0.0688170i
$596$	−14.1168			−0.578249
$597$			17.0325i			0.697093i
$598$		−	19.6523i		−	0.803641i
$599$	27.1576			1.10963			0.554815	−	0.831974i	$-0.312789\pi$
$599$	27.1576			1.10963			0.554815	+	0.831974i	$0.312789\pi$
$600$	1.19977	+	9.36193i	0.0489804	+	0.382199i
$601$	25.5859			1.04367			0.521836	−	0.853046i	$-0.325247\pi$
$601$	25.5859			1.04367			0.521836	+	0.853046i	$0.325247\pi$
$602$			2.44355i			0.0995915i
$603$			13.6284i			0.554990i
$604$	−9.70241			−0.394786
$605$	−13.6825	+	15.5479i	−0.556273	+	0.632112i
$606$	4.52320			0.183743
$607$			23.6758i			0.960970i	0.877003	+	0.480485i	$0.159539\pi$
$607$			23.6758i			0.960970i	−0.877003	+	0.480485i	$0.840461\pi$
$608$			24.5457i			0.995458i
$609$	−0.948665			−0.0384419
$610$	−23.8570	−	20.9947i	−0.965941	−	0.850052i
$611$	13.7254			0.555271
$612$		−	0.889490i		−	0.0359555i
$613$		−	34.1771i		−	1.38040i	−0.723619	−	0.690199i	$-0.757523\pi$
$613$		−	34.1771i		−	1.38040i	0.723619	−	0.690199i	$-0.242477\pi$
$614$	26.6708			1.07635
$615$	−16.8950	−	14.8680i	−0.681271	−	0.599535i
$616$	2.48842			0.100261
$617$		−	39.7875i		−	1.60178i	−0.598810	−	0.800891i	$-0.704359\pi$
$617$		−	39.7875i		−	1.60178i	0.598810	−	0.800891i	$-0.295641\pi$
$618$		−	14.6616i		−	0.589778i
$619$	41.5801			1.67125			0.835623	−	0.549303i	$-0.185107\pi$
$619$	41.5801			1.67125			0.835623	+	0.549303i	$0.185107\pi$
$620$	2.87824	−	3.27064i	0.115593	−	0.131352i
$621$	−2.71209			−0.108832
$622$			56.1165i			2.25007i
$623$			0.0400448i			0.00160436i
$624$	21.2621			0.851167
$625$	−24.1921	+	6.30417i	−0.967684	+	0.252167i
$626$	3.34237			0.133588
$627$			6.87991i			0.274757i
$628$		−	4.50340i		−	0.179705i
$629$	3.64278			0.145247
$630$	2.51107	−	2.85341i	0.100044	−	0.113683i
$631$	−28.5787			−1.13770			−0.568849	−	0.822442i	$-0.692611\pi$
$631$	−28.5787			−1.13770			−0.568849	+	0.822442i	$0.692611\pi$
$632$		−	17.2265i		−	0.685232i
$633$			10.1723i			0.404315i
$634$	−49.4133			−1.96245
$635$	−11.8094	−	10.3926i	−0.468642	−	0.412416i
$636$	−12.5574			−0.497935
$637$			4.26284i			0.168900i
$638$			2.12576i			0.0841598i
$639$	6.66687			0.263737
$640$	21.4421	+	18.8696i	0.847575	+	0.745887i
$641$	13.0074			0.513760			0.256880	−	0.966443i	$-0.417306\pi$
$641$	13.0074			0.513760			0.256880	+	0.966443i	$0.417306\pi$
$642$			32.7974i			1.29441i
$643$		−	0.285527i		−	0.0112601i	−0.999984	−	0.00563003i	$-0.998208\pi$
$643$		−	0.285527i		−	0.0112601i	0.999984	−	0.00563003i	$-0.00179211\pi$
$644$	−2.41237			−0.0950608
$645$	−2.12353	+	2.41304i	−0.0836139	+	0.0950132i
$646$	−8.87160			−0.349048
$647$		−	14.0337i		−	0.551722i	−0.961198	−	0.275861i	$-0.911037\pi$
$647$		−	14.0337i		−	0.551722i	0.961198	−	0.275861i	$-0.0889629\pi$
$648$		−	1.88770i		−	0.0741559i
$649$	18.4683			0.724944
$650$	4.60548	+	35.9370i	0.180642	+	1.40957i
$651$	2.19047			0.0858512
$652$		−	12.4206i		−	0.486427i
$653$			23.1312i			0.905193i	0.891715	+	0.452597i	$0.149502\pi$
$653$			23.1312i			0.905193i	−0.891715	+	0.452597i	$0.850498\pi$
$654$	6.85620			0.268099
$655$	−3.68440	+	4.18670i	−0.143961	+	0.163588i
$656$	−50.2009			−1.96001
$657$			13.0816i			0.510363i
$658$		−	5.47315i		−	0.213366i
$659$	20.8210			0.811072			0.405536	−	0.914079i	$-0.367085\pi$
$659$	20.8210			0.811072			0.405536	+	0.914079i	$0.367085\pi$
$660$	−1.96828	−	1.73213i	−0.0766151	−	0.0674232i
$661$	−20.3681			−0.792229			−0.396114	−	0.918201i	$-0.629642\pi$
$661$	−20.3681			−0.792229			−0.396114	+	0.918201i	$0.629642\pi$
$662$		−	50.6198i		−	1.96740i
$663$			4.26284i			0.165555i
$664$	11.4870			0.445782
$665$	−8.76083	−	7.70974i	−0.339731	−	0.298971i
$666$	−6.19219			−0.239942
$667$			2.57286i			0.0996216i
$668$		−	17.8765i		−	0.691663i
$669$	2.54258			0.0983019
$670$	−34.2218	+	38.8873i	−1.32210	+	1.50235i
$671$	−11.0215			−0.425482
$672$		−	4.70309i		−	0.181426i
$673$			11.0671i			0.426604i	0.976986	+	0.213302i	$0.0684219\pi$
$673$			11.0671i			0.426604i	−0.976986	+	0.213302i	$0.931578\pi$
$674$	−54.1674			−2.08645
$675$	4.95944	−	0.635573i	0.190889	−	0.0244632i
$676$	4.60026			0.176933
$677$		−	1.98385i		−	0.0762456i	−0.999273	−	0.0381228i	$-0.987862\pi$
$677$		−	1.98385i		−	0.0762456i	0.999273	−	0.0381228i	$-0.0121378\pi$
$678$		−	31.5073i		−	1.21003i
$679$	7.33549			0.281510
$680$	−2.78857	+	3.16874i	−0.106937	+	0.121516i
$681$	−10.5749			−0.405232
$682$		−	4.90839i		−	0.187952i
$683$			45.6910i			1.74832i	0.485641	+	0.874158i	$0.338586\pi$
$683$			45.6910i			1.74832i	−0.485641	+	0.874158i	$0.661414\pi$
$684$	4.64229			0.177503
$685$	7.33293	+	6.45315i	0.280177	+	0.246562i
$686$	1.69985			0.0649006
$687$		−	16.7374i		−	0.638573i
$688$			7.16998i			0.273353i
$689$	60.1809			2.29271
$690$	−7.73870	−	6.81024i	−0.294607	−	0.259262i
$691$	0.629981			0.0239656			0.0119828	−	0.999928i	$-0.496186\pi$
$691$	0.629981			0.0239656			0.0119828	+	0.999928i	$0.496186\pi$
$692$			8.59990i			0.326919i
$693$		−	1.31823i		−	0.0500754i
$694$	−2.75569			−0.104605
$695$	16.7791	−	19.0666i	0.636467	−	0.723239i
$696$	−1.79080			−0.0678799
$697$		−	10.0648i		−	0.381230i
$698$			41.1919i			1.55913i
$699$	−5.57246			−0.210770
$700$	4.41137	−	0.565336i	0.166734	−	0.0213677i
$701$	10.2343			0.386545			0.193272	−	0.981145i	$-0.438090\pi$
$701$	10.2343			0.386545			0.193272	+	0.981145i	$0.438090\pi$
$702$		−	7.24619i		−	0.273490i
$703$			19.0119i			0.717046i
$704$	2.61145			0.0984226
$705$	4.75637	−	5.40481i	0.179135	−	0.203557i
$706$	−22.2973			−0.839170
$707$			2.66094i			0.100075i
$708$		−	12.4617i		−	0.468339i
$709$	−7.85615			−0.295044			−0.147522	−	0.989059i	$-0.547130\pi$
$709$	−7.85615			−0.295044			−0.147522	+	0.989059i	$0.547130\pi$
$710$	19.0233	+	16.7410i	0.713933	+	0.628278i
$711$	−9.12564			−0.342238
$712$			0.0755925i			0.00283295i
$713$		−	5.94074i		−	0.222482i
$714$	1.69985			0.0636153
$715$	9.43288	+	8.30116i	0.352770	+	0.310446i
$716$	1.80855			0.0675888
$717$			12.4766i			0.465945i
$718$		−	0.994168i		−	0.0371020i
$719$	−0.739304			−0.0275714			−0.0137857	−	0.999905i	$-0.504388\pi$
$719$	−0.739304			−0.0275714			−0.0137857	+	0.999905i	$0.504388\pi$
$720$	7.36812	−	8.37263i	0.274594	−	0.312030i
$721$	8.62526			0.321221
$722$		−	14.0042i		−	0.521181i
$723$		−	10.1786i		−	0.378545i
$724$	−19.6345			−0.729710
$725$	−0.602946	−	4.70485i	−0.0223928	−	0.174734i
$726$	15.7445			0.584332
$727$			34.2680i			1.27093i	0.772129	+	0.635465i	$0.219192\pi$
$727$			34.2680i			1.27093i	−0.772129	+	0.635465i	$0.780808\pi$
$728$			8.04696i			0.298240i
$729$	−1.00000			−0.0370370
$730$	−32.8489	+	37.3273i	−1.21579	+	1.38154i
$731$	−1.43751			−0.0531681
$732$			7.43690i			0.274876i
$733$			32.0094i			1.18229i	0.806564	+	0.591147i	$0.201325\pi$
$733$			32.0094i			1.18229i	−0.806564	+	0.591147i	$0.798675\pi$
$734$	−34.0253			−1.25590
$735$	1.67863	+	1.47723i	0.0619171	+	0.0544885i
$736$	−12.7552			−0.470162
$737$			17.9653i			0.661761i
$738$			17.1086i			0.629775i
$739$	−37.4413			−1.37730			−0.688650	−	0.725094i	$-0.741796\pi$
$739$	−37.4413			−1.37730			−0.688650	+	0.725094i	$0.741796\pi$
$740$	−5.43912	−	4.78656i	−0.199946	−	0.175957i
$741$	−22.2480			−0.817299
$742$		−	23.9978i		−	0.880985i
$743$			49.8815i			1.82997i	0.403484	+	0.914987i	$0.367799\pi$
$743$			49.8815i			1.82997i	−0.403484	+	0.914987i	$0.632201\pi$
$744$	4.13495			0.151595
$745$	23.4447	−	26.6410i	0.858948	−	0.976050i
$746$	−32.0671			−1.17406
$747$		−	6.08519i		−	0.222645i
$748$		−	1.17255i		−	0.0428728i
$749$	−19.2943			−0.704997
$750$	15.7473	+	10.6400i	0.575010	+	0.388516i
$751$	27.9959			1.02158			0.510792	−	0.859704i	$-0.329352\pi$
$751$	27.9959			1.02158			0.510792	+	0.859704i	$0.329352\pi$
$752$		−	16.0596i		−	0.585633i
$753$			5.67410i			0.206776i
$754$	−6.87421			−0.250344
$755$	16.1134	−	18.3102i	0.586427	−	0.666376i
$756$	−0.889490			−0.0323505
$757$			39.6490i			1.44107i	0.693419	+	0.720534i	$0.256103\pi$
$757$			39.6490i			1.44107i	−0.693419	+	0.720534i	$0.743897\pi$
$758$		−	34.8389i		−	1.26540i
$759$	−3.57515			−0.129770
$760$	−16.5378	−	14.5537i	−0.599890	−	0.527918i
$761$	25.0189			0.906933			0.453467	−	0.891273i	$-0.350187\pi$
$761$	25.0189			0.906933			0.453467	+	0.891273i	$0.350187\pi$
$762$			11.9587i			0.433218i
$763$			4.03341i			0.146019i
$764$	−16.3894			−0.592947
$765$	1.67863	+	1.47723i	0.0606909	+	0.0534094i
$766$	23.5840			0.852123
$767$			59.7220i			2.15644i
$768$		−	17.7512i		−	0.640541i
$769$	39.9051			1.43901			0.719507	−	0.694486i	$-0.244368\pi$
$769$	39.9051			1.43901			0.719507	+	0.694486i	$0.244368\pi$
$770$	3.31017	−	3.76146i	0.119290	−	0.135553i
$771$	−18.9299			−0.681744
$772$			18.6182i			0.670082i
$773$			31.4649i			1.13171i	0.824503	+	0.565857i	$0.191455\pi$
$773$			31.4649i			1.13171i	−0.824503	+	0.565857i	$0.808545\pi$
$774$	2.44355			0.0878314
$775$	1.39220	+	10.8635i	0.0500094	+	0.390228i
$776$	13.8472			0.497086
$777$		−	3.64278i		−	0.130684i
$778$		−	60.8791i		−	2.18262i
$779$	52.5285			1.88203
$780$	5.60130	−	6.36494i	0.200559	−	0.227901i
$781$	8.78847			0.314476
$782$		−	4.61014i		−	0.164858i
$783$			0.948665i			0.0339025i
$784$	4.98779			0.178135
$785$	8.49872	+	7.47908i	0.303332	+	0.266940i
$786$	4.23963			0.151223
$787$			3.16406i			0.112787i	0.998409	+	0.0563933i	$0.0179601\pi$
$787$			3.16406i			0.112787i	−0.998409	+	0.0563933i	$0.982040\pi$
$788$			14.9408i			0.532243i
$789$	4.50632			0.160429
$790$	−26.0392	−	22.9152i	−0.926434	−	0.815284i
$791$	18.5353			0.659041
$792$		−	2.48842i		−	0.0884223i
$793$		−	35.6410i		−	1.26565i
$794$	−27.4280			−0.973384
$795$	20.8549	−	23.6981i	0.739648	−	0.840486i
$796$	15.1502			0.536986
$797$			53.2495i			1.88619i	0.332519	+	0.943097i	$0.392102\pi$
$797$			53.2495i			1.88619i	−0.332519	+	0.943097i	$0.607898\pi$
$798$			8.87160i			0.314051i
$799$	3.21978			0.113908
$800$	23.3247	−	2.98916i	0.824653	−	0.105683i
$801$	0.0400448			0.00141491
$802$			17.9639i			0.634326i
$803$			17.2446i			0.608549i
$804$	12.1223			0.427520
$805$	4.00638	−	4.55258i	0.141206	−	0.160457i
$806$	15.8725			0.559087
$807$		−	6.65868i		−	0.234396i
$808$			5.02306i			0.176711i
$809$	−44.4117			−1.56143			−0.780716	−	0.624886i	$-0.785145\pi$
$809$	−44.4117			−1.56143			−0.780716	+	0.624886i	$0.785145\pi$
$810$	−2.85341	−	2.51107i	−0.100259	−	0.0882301i
$811$	12.0589			0.423445			0.211723	−	0.977330i	$-0.432093\pi$
$811$	12.0589			0.423445			0.211723	+	0.977330i	$0.432093\pi$
$812$			0.843829i			0.0296126i
$813$		−	6.91612i		−	0.242559i
$814$	−8.16273			−0.286103
$815$	23.4398	+	20.6276i	0.821060	+	0.722553i
$816$	4.98779			0.174607
$817$		−	7.50242i		−	0.262476i
$818$			28.5453i			0.998064i
$819$	4.26284			0.148956
$820$	−13.2249	+	15.0279i	−0.461834	+	0.524797i
$821$	34.5235			1.20488			0.602440	−	0.798165i	$-0.294195\pi$
$821$	34.5235			1.20488			0.602440	+	0.798165i	$0.294195\pi$
$822$		−	7.42564i		−	0.258999i
$823$			7.07375i			0.246576i	0.992371	+	0.123288i	$0.0393438\pi$
$823$			7.07375i			0.246576i	−0.992371	+	0.123288i	$0.960656\pi$
$824$	16.2819			0.567207
$825$	6.53768	−	0.837831i	0.227613	−	0.0291695i
$826$	23.8148			0.828621
$827$		−	26.2151i		−	0.911589i	−0.890085	−	0.455795i	$-0.849355\pi$
$827$		−	26.2151i		−	0.911589i	0.890085	−	0.455795i	$-0.150645\pi$
$828$			2.41237i			0.0838358i
$829$	−21.0062			−0.729577			−0.364788	−	0.931090i	$-0.618859\pi$
$829$	−21.0062			−0.729577			−0.364788	+	0.931090i	$0.618859\pi$
$830$	15.2803	−	17.3636i	0.530389	−	0.602698i
$831$	−8.39750			−0.291306
$832$			8.44479i			0.292770i
$833$			1.00000i			0.0346479i
$834$	−19.3077			−0.668571
$835$	33.7362	+	29.6886i	1.16749	+	1.02742i
$836$	6.11961			0.211651
$837$		−	2.19047i		−	0.0757137i
$838$			25.7348i			0.888995i
$839$	33.1058			1.14294			0.571469	−	0.820624i	$-0.306374\pi$
$839$	33.1058			1.14294			0.571469	+	0.820624i	$0.306374\pi$
$840$	3.16874	+	2.78857i	0.109332	+	0.0962148i
$841$	−28.1000			−0.968967
$842$		−	29.2011i		−	1.00634i
$843$		−	5.79215i		−	0.199492i
$844$	9.04821			0.311452
$845$	−7.63994	+	8.68151i	−0.262822	+	0.298653i
$846$	−5.47315			−0.188171
$847$			9.26227i			0.318255i
$848$		−	70.4154i		−	2.41808i
$849$	25.7255			0.882895
$850$	1.08038	+	8.43031i	0.0370567	+	0.289157i
$851$	−9.87954			−0.338666
$852$		−	5.93012i		−	0.203163i
$853$		−	30.3394i		−	1.03880i	−0.854531	−	0.519401i	$-0.826155\pi$
$853$		−	30.3394i		−	1.03880i	0.854531	−	0.519401i	$-0.173845\pi$
$854$	−14.2122			−0.486332
$855$	−7.70974	+	8.76083i	−0.263668	+	0.299614i
$856$	−36.4218			−1.24487
$857$			21.2155i			0.724708i	0.932041	+	0.362354i	$0.118027\pi$
$857$			21.2155i			0.724708i	−0.932041	+	0.362354i	$0.881973\pi$
$858$		−	9.55214i		−	0.326105i
$859$	9.64903			0.329221			0.164610	−	0.986359i	$-0.447363\pi$
$859$	9.64903			0.329221			0.164610	+	0.986359i	$0.447363\pi$
$860$	2.14637	+	1.88886i	0.0731907	+	0.0644096i
$861$	−10.0648			−0.343006
$862$			57.8479i			1.97031i
$863$		−	15.2145i		−	0.517906i	−0.965890	−	0.258953i	$-0.916622\pi$
$863$		−	15.2145i		−	0.517906i	0.965890	−	0.258953i	$-0.0833776\pi$
$864$	−4.70309			−0.160002
$865$	−16.2295	−	14.2824i	−0.551821	−	0.485616i
$866$	−27.3013			−0.927735
$867$			1.00000i			0.0339618i
$868$		−	1.94840i		−	0.0661330i
$869$	−12.0297			−0.408080
$870$	−2.38217	+	2.70693i	−0.0807630	+	0.0917737i
$871$	−58.0955			−1.96849
$872$			7.61388i			0.257838i
$873$		−	7.33549i		−	0.248269i
$874$	24.0605			0.813860
$875$	−6.25935	+	9.26394i	−0.211605	+	0.313178i
$876$	11.6360			0.393143
$877$		−	53.5867i		−	1.80949i	−0.425949	−	0.904747i	$-0.640060\pi$
$877$		−	53.5867i		−	1.80949i	0.425949	−	0.904747i	$-0.359940\pi$
$878$			17.2485i			0.582109i
$879$	−3.51413			−0.118529
$880$	9.71288	−	11.0371i	0.327421	−	0.372059i
$881$	−24.1273			−0.812870			−0.406435	−	0.913680i	$-0.633228\pi$
$881$	−24.1273			−0.812870			−0.406435	+	0.913680i	$0.633228\pi$
$882$		−	1.69985i		−	0.0572369i
$883$		−	41.1894i		−	1.38614i	−0.720873	−	0.693068i	$-0.756259\pi$
$883$		−	41.1894i		−	1.38614i	0.720873	−	0.693068i	$-0.243741\pi$
$884$	3.79175			0.127531
$885$	23.5174	+	20.6959i	0.790529	+	0.695685i
$886$	35.0523			1.17761
$887$			13.5093i			0.453599i	0.973942	+	0.226799i	$0.0728261\pi$
$887$			13.5093i			0.453599i	−0.973942	+	0.226799i	$0.927174\pi$
$888$		−	6.87648i		−	0.230760i
$889$	−7.03516			−0.235952
$890$	0.114264	+	0.100555i	0.00383015	+	0.00337062i
$891$	−1.31823			−0.0441624
$892$		−	2.26160i		−	0.0757241i
$893$			16.8042i			0.562331i
$894$	−26.9778			−0.902274
$895$	−3.00357	+	3.41306i	−0.100398	+	0.114086i
$896$	12.7736			0.426737
$897$		−	11.5612i		−	0.386017i
$898$			27.4084i			0.914631i
$899$	−2.07802			−0.0693059
$900$	−0.565336	−	4.41137i	−0.0188445	−	0.147046i
$901$	14.1176			0.470324
$902$			22.5530i			0.750934i
$903$			1.43751i			0.0478372i
$904$	34.9892			1.16372
$905$	32.6082	−	37.0538i	1.08393	−	1.23171i
$906$	−18.5417			−0.616006
$907$			47.6075i			1.58078i	0.612603	+	0.790391i	$0.290123\pi$
$907$			47.6075i			1.58078i	−0.612603	+	0.790391i	$0.709877\pi$
$908$			9.40630i			0.312159i
$909$	2.66094			0.0882579
$910$	12.1636	+	10.7043i	0.403221	+	0.354844i
$911$	22.5367			0.746674			0.373337	−	0.927696i	$-0.378214\pi$
$911$	22.5367			0.746674			0.373337	+	0.927696i	$0.378214\pi$
$912$			26.0315i			0.861989i
$913$		−	8.02168i		−	0.265479i
$914$	−15.1727			−0.501870
$915$	−14.0348	−	12.3509i	−0.463975	−	0.408309i
$916$	−14.8878			−0.491906
$917$			2.49412i			0.0823632i
$918$		−	1.69985i		−	0.0561034i
$919$	−21.8566			−0.720982			−0.360491	−	0.932763i	$-0.617391\pi$
$919$	−21.8566			−0.720982			−0.360491	+	0.932763i	$0.617391\pi$
$920$	7.56284	−	8.59390i	0.249339	−	0.283333i
$921$	15.6901			0.517006
$922$			26.6387i			0.877299i
$923$			28.4198i			0.935449i
$924$	−1.17255			−0.0385742
$925$	18.0662	−	2.31525i	0.594012	−	0.0761251i
$926$	−34.1251			−1.12142
$927$		−	8.62526i		−	0.283291i
$928$			4.46166i			0.146461i
$929$	34.2174			1.12264			0.561318	−	0.827600i	$-0.310294\pi$
$929$	34.2174			1.12264			0.561318	+	0.827600i	$0.310294\pi$
$930$	5.50043	−	6.25031i	0.180366	−	0.204956i
$931$	−5.21905			−0.171047
$932$			4.95665i			0.162360i
$933$			33.0126i			1.08078i
$934$	34.5021			1.12894
$935$	2.21282	+	1.94733i	0.0723668	+	0.0636846i
$936$	8.04696			0.263023
$937$			31.9632i			1.04419i	0.852887	+	0.522095i	$0.174849\pi$
$937$			31.9632i			1.04419i	−0.852887	+	0.522095i	$0.825151\pi$
$938$			23.1662i			0.756402i
$939$	1.96627			0.0641669
$940$	−4.80753	−	4.23074i	−0.156804	−	0.137992i
$941$	−7.31089			−0.238328			−0.119164	−	0.992875i	$-0.538021\pi$
$941$	−7.31089			−0.238328			−0.119164	+	0.992875i	$0.538021\pi$
$942$		−	8.60617i		−	0.280404i
$943$			27.2965i			0.888896i
$944$	69.8785			2.27435
$945$	1.47723	−	1.67863i	0.0480544	−	0.0546057i
$946$	3.22116			0.104729
$947$		−	19.7154i		−	0.640664i	−0.947305	−	0.320332i	$-0.896205\pi$
$947$		−	19.7154i		−	0.640664i	0.947305	−	0.320332i	$-0.103795\pi$
$948$			8.11717i			0.263633i
$949$	−55.7649			−1.81020
$950$	−43.9982	+	5.63855i	−1.42749	+	0.182939i
$951$	−29.0692			−0.942635
$952$			1.88770i			0.0611807i
$953$			36.8324i			1.19312i	0.802569	+	0.596560i	$0.203466\pi$
$953$			36.8324i			1.19312i	−0.802569	+	0.596560i	$0.796534\pi$
$954$	−23.9978			−0.776956
$955$	27.2188	−	30.9297i	0.880781	−	1.00086i
$956$	11.0978			0.358928
$957$			1.25056i			0.0404248i
$958$		−	69.2346i		−	2.23687i
$959$	4.36841			0.141063
$960$	3.32540	+	2.92643i	0.107327	+	0.0944502i
$961$	−26.2018			−0.845221
$962$		−	26.3963i		−	0.851051i
$963$			19.2943i			0.621749i
$964$	−9.05373			−0.291601
$965$	−35.1358	−	30.9203i	−1.13106	−	0.995360i
$966$	−4.61014			−0.148329
$967$		−	24.8807i		−	0.800109i	−0.916491	−	0.400054i	$-0.868991\pi$
$967$		−	24.8807i		−	0.800109i	0.916491	−	0.400054i	$-0.131009\pi$
$968$			17.4844i			0.561969i
$969$	−5.21905			−0.167660
$970$	18.4199	−	20.9312i	0.591429	−	0.672060i
$971$	−37.8289			−1.21399			−0.606993	−	0.794707i	$-0.707625\pi$
$971$	−37.8289			−1.21399			−0.606993	+	0.794707i	$0.707625\pi$
$972$			0.889490i			0.0285304i
$973$		−	11.3585i		−	0.364136i
$974$	−48.9279			−1.56775
$975$	2.70934	+	21.1413i	0.0867685	+	0.677063i
$976$	−41.7022			−1.33485
$977$			59.8958i			1.91624i	0.286374	+	0.958118i	$0.407550\pi$
$977$			59.8958i			1.91624i	−0.286374	+	0.958118i	$0.592450\pi$
$978$		−	23.7362i		−	0.758999i
$979$	0.0527883			0.00168712
$980$	1.31398	−	1.49312i	0.0419737	−	0.0476960i
$981$	4.03341			0.128777
$982$			9.02276i			0.287928i
$983$		−	40.5495i		−	1.29333i	−0.762775	−	0.646664i	$-0.776164\pi$
$983$		−	40.5495i		−	1.29333i	0.762775	−	0.646664i	$-0.223836\pi$
$984$	−18.9992			−0.605674
$985$	−28.1959	−	24.8131i	−0.898396	−	0.790610i
$986$	−1.61259			−0.0513553
$987$		−	3.21978i		−	0.102487i
$988$			19.7894i			0.629583i
$989$	3.89864			0.123970
$990$	−3.76146	−	3.31017i	−0.119547	−	0.105204i
$991$	−38.2772			−1.21591			−0.607957	−	0.793970i	$-0.708011\pi$
$991$	−38.2772			−1.21591			−0.607957	+	0.793970i	$0.708011\pi$
$992$		−	10.3020i		−	0.327088i
$993$		−	29.7790i		−	0.945008i
$994$	11.3327			0.359451
$995$	−25.1609	+	28.5912i	−0.797655	+	0.906401i
$996$	−5.41272			−0.171508
$997$		−	27.4621i		−	0.869732i	−0.900495	−	0.434866i	$-0.856796\pi$
$997$		−	27.4621i		−	0.869732i	0.900495	−	0.434866i	$-0.143204\pi$
$998$			19.6458i			0.621876i
$999$	−3.64278			−0.115253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1785.2.g.f.1429.8	✓	28
5.2	odd	4		8925.2.a.cw.1.10		14
5.3	odd	4		8925.2.a.cv.1.5		14
5.4	even	2	inner	1785.2.g.f.1429.21	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1785.2.g.f.1429.8	✓	28	1.1	even	1	trivial
1785.2.g.f.1429.21	yes	28	5.4	even	2	inner
8925.2.a.cv.1.5		14	5.3	odd	4
8925.2.a.cw.1.10		14	5.2	odd	4

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:	\( N \)	\(=\)	\( 1785 = 3 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1785.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.69985i q^{2} -1.00000i q^{3} -0.889490 q^{4} +(1.47723 - 1.67863i) q^{5} -1.69985 q^{6} -1.00000i q^{7} -1.88770i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.69985i q^{2} -1.00000i q^{3} -0.889490 q^{4} +(1.47723 - 1.67863i) q^{5} -1.69985 q^{6} -1.00000i q^{7} -1.88770i q^{8} -1.00000 q^{9} +(-2.85341 - 2.51107i) q^{10} -1.31823 q^{11} +0.889490i q^{12} -4.26284i q^{13} -1.69985 q^{14} +(-1.67863 - 1.47723i) q^{15} -4.98779 q^{16} -1.00000i q^{17} +1.69985i q^{18} +5.21905 q^{19} +(-1.31398 + 1.49312i) q^{20} -1.00000 q^{21} +2.24079i q^{22} +2.71209i q^{23} -1.88770 q^{24} +(-0.635573 - 4.95944i) q^{25} -7.24619 q^{26} +1.00000i q^{27} +0.889490i q^{28} +0.948665 q^{29} +(-2.51107 + 2.85341i) q^{30} -2.19047 q^{31} +4.70309i q^{32} +1.31823i q^{33} -1.69985 q^{34} +(-1.67863 - 1.47723i) q^{35} +0.889490 q^{36} +3.64278i q^{37} -8.87160i q^{38} -4.26284 q^{39} +(-3.16874 - 2.78857i) q^{40} +10.0648 q^{41} +1.69985i q^{42} -1.43751i q^{43} +1.17255 q^{44} +(-1.47723 + 1.67863i) q^{45} +4.61014 q^{46} +3.21978i q^{47} +4.98779i q^{48} -1.00000 q^{49} +(-8.43031 + 1.08038i) q^{50} -1.00000 q^{51} +3.79175i q^{52} +14.1176i q^{53} +1.69985 q^{54} +(-1.94733 + 2.21282i) q^{55} -1.88770 q^{56} -5.21905i q^{57} -1.61259i q^{58} -14.0099 q^{59} +(1.49312 + 1.31398i) q^{60} +8.36086 q^{61} +3.72347i q^{62} +1.00000i q^{63} -1.98102 q^{64} +(-7.15571 - 6.29720i) q^{65} +2.24079 q^{66} -13.6284i q^{67} +0.889490i q^{68} +2.71209 q^{69} +(-2.51107 + 2.85341i) q^{70} -6.66687 q^{71} +1.88770i q^{72} -13.0816i q^{73} +6.19219 q^{74} +(-4.95944 + 0.635573i) q^{75} -4.64229 q^{76} +1.31823i q^{77} +7.24619i q^{78} +9.12564 q^{79} +(-7.36812 + 8.37263i) q^{80} +1.00000 q^{81} -17.1086i q^{82} +6.08519i q^{83} +0.889490 q^{84} +(-1.67863 - 1.47723i) q^{85} -2.44355 q^{86} -0.948665i q^{87} +2.48842i q^{88} -0.0400448 q^{89} +(2.85341 + 2.51107i) q^{90} -4.26284 q^{91} -2.41237i q^{92} +2.19047i q^{93} +5.47315 q^{94} +(7.70974 - 8.76083i) q^{95} +4.70309 q^{96} +7.33549i q^{97} +1.69985i q^{98} +1.31823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9}+O(q^{10}) \) 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9	\( 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} - 4 q^{15} + 38 q^{16} + 12 q^{19} - 4 q^{20} - 28 q^{21} + 30 q^{24} - 8 q^{25} - 36 q^{26} - 2 q^{30} + 14 q^{31} - 6 q^{34} - 4 q^{35} + 34 q^{36} + 18 q^{39} - 62 q^{40} - 50 q^{41} - 24 q^{44} + 52 q^{46} - 28 q^{49} + 6 q^{50} - 28 q^{51} + 6 q^{54} - 14 q^{55} + 30 q^{56} + 44 q^{59} + 10 q^{60} + 26 q^{61} - 6 q^{64} + 20 q^{65} - 48 q^{66} + 38 q^{69} - 2 q^{70} + 12 q^{71} + 24 q^{74} - 16 q^{75} - 20 q^{76} - 8 q^{79} - 32 q^{80} + 28 q^{81} + 34 q^{84} - 4 q^{85} + 8 q^{86} + 84 q^{89} - 4 q^{90} + 18 q^{91} - 8 q^{94} + 4 q^{95} - 66 q^{96} - 8 q^{99}+O(q^{100}) \) 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 - 4 * q^15 + 38 * q^16 + 12 * q^19 - 4 * q^20 - 28 * q^21 + 30 * q^24 - 8 * q^25 - 36 * q^26 - 2 * q^30 + 14 * q^31 - 6 * q^34 - 4 * q^35 + 34 * q^36 + 18 * q^39 - 62 * q^40 - 50 * q^41 - 24 * q^44 + 52 * q^46 - 28 * q^49 + 6 * q^50 - 28 * q^51 + 6 * q^54 - 14 * q^55 + 30 * q^56 + 44 * q^59 + 10 * q^60 + 26 * q^61 - 6 * q^64 + 20 * q^65 - 48 * q^66 + 38 * q^69 - 2 * q^70 + 12 * q^71 + 24 * q^74 - 16 * q^75 - 20 * q^76 - 8 * q^79 - 32 * q^80 + 28 * q^81 + 34 * q^84 - 4 * q^85 + 8 * q^86 + 84 * q^89 - 4 * q^90 + 18 * q^91 - 8 * q^94 + 4 * q^95 - 66 * q^96 - 8 * q^99

Introduction

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