LMFDB - Embedded newform 1110.2.h.g.961.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 297x^{2} + 64 $ x^8 + 20x^6 + 132x^4 + 297*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.8
Root			$-2.58251i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.g.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +4.25184 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +4.25184 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.913168 q^{11} -1.00000 q^{12} +2.72857i q^{13} +4.25184i q^{14} -1.00000i q^{15} +1.00000 q^{16} -6.25184i q^{17} +1.00000i q^{18} -4.43644i q^{19} +1.00000i q^{20} +4.25184 q^{21} +0.913168i q^{22} +2.72857i q^{23} -1.00000i q^{24} -1.00000 q^{25} -2.72857 q^{26} +1.00000 q^{27} -4.25184 q^{28} -5.34961i q^{29} +1.00000 q^{30} +8.98041i q^{31} +1.00000i q^{32} +0.913168 q^{33} +6.25184 q^{34} -4.25184i q^{35} -1.00000 q^{36} +(5.43644 - 2.72857i) q^{37} +4.43644 q^{38} +2.72857i q^{39} -1.00000 q^{40} -8.98041 q^{41} +4.25184i q^{42} -3.52327i q^{43} -0.913168 q^{44} -1.00000i q^{45} -2.72857 q^{46} +6.11846 q^{47} +1.00000 q^{48} +11.0782 q^{49} -1.00000i q^{50} -6.25184i q^{51} -2.72857i q^{52} +6.25184 q^{53} +1.00000i q^{54} -0.913168i q^{55} -4.25184i q^{56} -4.43644i q^{57} +5.34961 q^{58} +5.45714i q^{59} +1.00000i q^{60} +10.6883i q^{61} -8.98041 q^{62} +4.25184 q^{63} -1.00000 q^{64} +2.72857 q^{65} +0.913168i q^{66} -13.9608 q^{67} +6.25184i q^{68} +2.72857i q^{69} +4.25184 q^{70} +12.5037 q^{71} -1.00000i q^{72} +7.77512 q^{73} +(2.72857 + 5.43644i) q^{74} -1.00000 q^{75} +4.43644i q^{76} +3.88265 q^{77} -2.72857 q^{78} +11.9608i q^{79} -1.00000i q^{80} +1.00000 q^{81} -8.98041i q^{82} +0.902234 q^{83} -4.25184 q^{84} -6.25184 q^{85} +3.52327 q^{86} -5.34961i q^{87} -0.913168i q^{88} -8.72857i q^{89} +1.00000 q^{90} +11.6015i q^{91} -2.72857i q^{92} +8.98041i q^{93} +6.11846i q^{94} -4.43644 q^{95} +1.00000i q^{96} +12.5146i q^{97} +11.0782i q^{98} +0.913168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9	$ 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{16} - 4 q^{21} - 8 q^{25} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 8 q^{30} - 4 q^{33} + 12 q^{34} - 8 q^{36} + 18 q^{37} + 10 q^{38} - 8 q^{40} - 10 q^{41} + 4 q^{44} + 2 q^{46} + 28 q^{47} + 8 q^{48} + 28 q^{49} + 12 q^{53} + 6 q^{58} - 10 q^{62} - 4 q^{63} - 8 q^{64} - 2 q^{65} + 12 q^{67} - 4 q^{70} + 24 q^{71} + 10 q^{73} - 2 q^{74} - 8 q^{75} - 32 q^{77} + 2 q^{78} + 8 q^{81} + 6 q^{83} + 4 q^{84} - 12 q^{85} + 14 q^{86} + 8 q^{90} - 10 q^{95} - 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^16 - 4 * q^21 - 8 * q^25 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 8 * q^30 - 4 * q^33 + 12 * q^34 - 8 * q^36 + 18 * q^37 + 10 * q^38 - 8 * q^40 - 10 * q^41 + 4 * q^44 + 2 * q^46 + 28 * q^47 + 8 * q^48 + 28 * q^49 + 12 * q^53 + 6 * q^58 - 10 * q^62 - 4 * q^63 - 8 * q^64 - 2 * q^65 + 12 * q^67 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 8 * q^75 - 32 * q^77 + 2 * q^78 + 8 * q^81 + 6 * q^83 + 4 * q^84 - 12 * q^85 + 14 * q^86 + 8 * q^90 - 10 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$			1.00000i			0.408248i
$7$	4.25184			1.60705			0.803523	−	0.595274i	$-0.202956\pi$
$7$	4.25184			1.60705			0.803523	+	0.595274i	$0.202956\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	1.00000			0.316228
$11$	0.913168			0.275331			0.137665	−	0.990479i	$-0.456040\pi$
$11$	0.913168			0.275331			0.137665	+	0.990479i	$0.456040\pi$
$12$	−1.00000			−0.288675
$13$			2.72857i			0.756769i	0.925648	+	0.378385i	$0.123520\pi$
$13$			2.72857i			0.756769i	−0.925648	+	0.378385i	$0.876480\pi$
$14$			4.25184i			1.13635i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$		−	6.25184i		−	1.51629i	−0.652083	−	0.758147i	$-0.726105\pi$
$17$		−	6.25184i		−	1.51629i	0.652083	−	0.758147i	$-0.273895\pi$
$18$			1.00000i			0.235702i
$19$		−	4.43644i		−	1.01779i	−0.860829	−	0.508895i	$-0.830054\pi$
$19$		−	4.43644i		−	1.01779i	0.860829	−	0.508895i	$-0.169946\pi$
$20$			1.00000i			0.223607i
$21$	4.25184			0.927829
$22$			0.913168i			0.194688i
$23$			2.72857i			0.568946i	0.958684	+	0.284473i	$0.0918186\pi$
$23$			2.72857i			0.568946i	−0.958684	+	0.284473i	$0.908181\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.00000			−0.200000
$26$	−2.72857			−0.535117
$27$	1.00000			0.192450
$28$	−4.25184			−0.803523
$29$		−	5.34961i		−	0.993398i	−0.867923	−	0.496699i	$-0.834545\pi$
$29$		−	5.34961i		−	0.993398i	0.867923	−	0.496699i	$-0.165455\pi$
$30$	1.00000			0.182574
$31$			8.98041i			1.61293i	0.591282	+	0.806465i	$0.298622\pi$
$31$			8.98041i			1.61293i	−0.591282	+	0.806465i	$0.701378\pi$
$32$			1.00000i			0.176777i
$33$	0.913168			0.158962
$34$	6.25184			1.07218
$35$		−	4.25184i		−	0.718693i
$36$	−1.00000			−0.166667
$37$	5.43644	−	2.72857i	0.893746	−	0.448574i
$37$	5.43644	−	2.72857i	0.893746	−	0.448574i
$38$	4.43644			0.719686
$39$			2.72857i			0.436921i
$40$	−1.00000			−0.158114
$41$	−8.98041			−1.40251			−0.701253	−	0.712913i	$-0.747375\pi$
$41$	−8.98041			−1.40251			−0.701253	+	0.712913i	$0.747375\pi$
$42$			4.25184i			0.656074i
$43$		−	3.52327i		−	0.537294i	−0.963239	−	0.268647i	$-0.913423\pi$
$43$		−	3.52327i		−	0.537294i	0.963239	−	0.268647i	$-0.0865766\pi$
$44$	−0.913168			−0.137665
$45$		−	1.00000i		−	0.149071i
$46$	−2.72857			−0.402306
$47$	6.11846			0.892470			0.446235	−	0.894916i	$-0.352765\pi$
$47$	6.11846			0.892470			0.446235	+	0.894916i	$0.352765\pi$
$48$	1.00000			0.144338
$49$	11.0782			1.58260
$50$		−	1.00000i		−	0.141421i
$51$		−	6.25184i		−	0.875433i
$52$		−	2.72857i		−	0.378385i
$53$	6.25184			0.858757			0.429378	−	0.903125i	$-0.358733\pi$
$53$	6.25184			0.858757			0.429378	+	0.903125i	$0.358733\pi$
$54$			1.00000i			0.136083i
$55$		−	0.913168i		−	0.123132i
$56$		−	4.25184i		−	0.568177i
$57$		−	4.43644i		−	0.587621i
$58$	5.34961			0.702438
$59$			5.45714i			0.710459i	0.934779	+	0.355230i	$0.115597\pi$
$59$			5.45714i			0.710459i	−0.934779	+	0.355230i	$0.884403\pi$
$60$			1.00000i			0.129099i
$61$			10.6883i			1.36849i	0.729250	+	0.684247i	$0.239869\pi$
$61$			10.6883i			1.36849i	−0.729250	+	0.684247i	$0.760131\pi$
$62$	−8.98041			−1.14051
$63$	4.25184			0.535682
$64$	−1.00000			−0.125000
$65$	2.72857			0.338437
$66$			0.913168i			0.112403i
$67$	−13.9608			−1.70559			−0.852793	−	0.522249i	$-0.825093\pi$
$67$	−13.9608			−1.70559			−0.852793	+	0.522249i	$0.825093\pi$
$68$			6.25184i			0.758147i
$69$			2.72857i			0.328481i
$70$	4.25184			0.508193
$71$	12.5037			1.48391			0.741957	−	0.670447i	$-0.233898\pi$
$71$	12.5037			1.48391			0.741957	+	0.670447i	$0.233898\pi$
$72$		−	1.00000i		−	0.117851i
$73$	7.77512			0.910009			0.455004	−	0.890489i	$-0.349638\pi$
$73$	7.77512			0.910009			0.455004	+	0.890489i	$0.349638\pi$
$74$	2.72857	+	5.43644i	0.317190	+	0.631974i
$75$	−1.00000			−0.115470
$76$			4.43644i			0.508895i
$77$	3.88265			0.442469
$78$	−2.72857			−0.308950
$79$			11.9608i			1.34570i	0.739780	+	0.672849i	$0.234930\pi$
$79$			11.9608i			1.34570i	−0.739780	+	0.672849i	$0.765070\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$		−	8.98041i		−	0.991721i
$83$	0.902234			0.0990330			0.0495165	−	0.998773i	$-0.484232\pi$
$83$	0.902234			0.0990330			0.0495165	+	0.998773i	$0.484232\pi$
$84$	−4.25184			−0.463914
$85$	−6.25184			−0.678108
$86$	3.52327			0.379924
$87$		−	5.34961i		−	0.573538i
$88$		−	0.913168i		−	0.0973440i
$89$		−	8.72857i		−	0.925227i	−0.886560	−	0.462613i	$-0.846912\pi$
$89$		−	8.72857i		−	0.925227i	0.886560	−	0.462613i	$-0.153088\pi$
$90$	1.00000			0.105409
$91$			11.6015i			1.21616i
$92$		−	2.72857i		−	0.284473i
$93$			8.98041i			0.931226i
$94$			6.11846i			0.631071i
$95$	−4.43644			−0.455169
$96$			1.00000i			0.102062i
$97$			12.5146i			1.27067i	0.772238	+	0.635334i	$0.219137\pi$
$97$			12.5146i			1.27067i	−0.772238	+	0.635334i	$0.780863\pi$
$98$			11.0782i			1.11907i
$99$	0.913168			0.0917768
$100$	1.00000			0.100000
$101$	−7.16501			−0.712945			−0.356473	−	0.934306i	$-0.616021\pi$
$101$	−7.16501			−0.712945			−0.356473	+	0.934306i	$0.616021\pi$
$102$	6.25184			0.619025
$103$			5.33868i			0.526035i	0.964791	+	0.263018i	$0.0847178\pi$
$103$			5.33868i			0.526035i	−0.964791	+	0.263018i	$0.915282\pi$
$104$	2.72857			0.267558
$105$		−	4.25184i		−	0.414938i
$106$			6.25184i			0.607233i
$107$	−9.27143			−0.896303			−0.448151	−	0.893958i	$-0.647917\pi$
$107$	−9.27143			−0.896303			−0.448151	+	0.893958i	$0.647917\pi$
$108$	−1.00000			−0.0962250
$109$		−	13.9205i		−	1.33335i	−0.745350	−	0.666673i	$-0.767718\pi$
$109$		−	13.9205i		−	1.33335i	0.745350	−	0.666673i	$-0.232282\pi$
$110$	0.913168			0.0870672
$111$	5.43644	−	2.72857i	0.516004	−	0.258984i
$112$	4.25184			0.401762
$113$		−	1.93387i		−	0.181923i	−0.995854	−	0.0909614i	$-0.971006\pi$
$113$		−	1.93387i		−	0.181923i	0.995854	−	0.0909614i	$-0.0289940\pi$
$114$	4.43644			0.415511
$115$	2.72857			0.254440
$116$			5.34961i			0.496699i
$117$			2.72857i			0.252256i
$118$	−5.45714			−0.502370
$119$		−	26.5819i		−	2.43676i
$120$	−1.00000			−0.0912871
$121$	−10.1661			−0.924193
$122$	−10.6883			−0.967672
$123$	−8.98041			−0.809737
$124$		−	8.98041i		−	0.806465i
$125$			1.00000i			0.0894427i
$126$			4.25184i			0.378784i
$127$	−21.5623			−1.91334			−0.956672	−	0.291169i	$-0.905956\pi$
$127$	−21.5623			−1.91334			−0.956672	+	0.291169i	$0.905956\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		−	3.52327i		−	0.310207i
$130$			2.72857i			0.239311i
$131$		−	5.45714i		−	0.476793i	−0.971168	−	0.238396i	$-0.923378\pi$
$131$		−	5.45714i		−	0.476793i	0.971168	−	0.238396i	$-0.0766217\pi$
$132$	−0.913168			−0.0794811
$133$		−	18.8631i		−	1.63563i
$134$		−	13.9608i		−	1.20603i
$135$		−	1.00000i		−	0.0860663i
$136$	−6.25184			−0.536091
$137$	−16.0379			−1.37021			−0.685105	−	0.728444i	$-0.740244\pi$
$137$	−16.0379			−1.37021			−0.685105	+	0.728444i	$0.740244\pi$
$138$	−2.72857			−0.232271
$139$	17.6796			1.49957			0.749784	−	0.661683i	$-0.230158\pi$
$139$	17.6796			1.49957			0.749784	+	0.661683i	$0.230158\pi$
$140$			4.25184i			0.359346i
$141$	6.11846			0.515268
$142$			12.5037i			1.04929i
$143$			2.49164i			0.208362i
$144$	1.00000			0.0833333
$145$	−5.34961			−0.444261
$146$			7.77512i			0.643473i
$147$	11.0782			0.913713
$148$	−5.43644	+	2.72857i	−0.446873	+	0.224287i
$149$	−14.2116			−1.16426			−0.582128	−	0.813097i	$-0.697780\pi$
$149$	−14.2116			−1.16426			−0.582128	+	0.813097i	$0.697780\pi$
$150$		−	1.00000i		−	0.0816497i
$151$	3.94878			0.321347			0.160674	−	0.987008i	$-0.448633\pi$
$151$	3.94878			0.321347			0.160674	+	0.987008i	$0.448633\pi$
$152$	−4.43644			−0.359843
$153$		−	6.25184i		−	0.505432i
$154$			3.88265i			0.312873i
$155$	8.98041			0.721324
$156$		−	2.72857i		−	0.218460i
$157$	16.8998			1.34875			0.674377	−	0.738387i	$-0.264412\pi$
$157$	16.8998			1.34875			0.674377	+	0.738387i	$0.264412\pi$
$158$	−11.9608			−0.951552
$159$	6.25184			0.495804
$160$	1.00000			0.0790569
$161$			11.6015i			0.914323i
$162$			1.00000i			0.0785674i
$163$			8.07818i			0.632732i	0.948637	+	0.316366i	$0.102463\pi$
$163$			8.07818i			0.632732i	−0.948637	+	0.316366i	$0.897537\pi$
$164$	8.98041			0.701253
$165$		−	0.913168i		−	0.0710900i
$166$			0.902234i			0.0700269i
$167$			7.94878i			0.615095i	0.951533	+	0.307548i	$0.0995083\pi$
$167$			7.94878i			0.615095i	−0.951533	+	0.307548i	$0.900492\pi$
$168$		−	4.25184i		−	0.328037i
$169$	5.55491			0.427300
$170$		−	6.25184i		−	0.479495i
$171$		−	4.43644i		−	0.339263i
$172$			3.52327i			0.268647i
$173$	−25.8021			−1.96170			−0.980848	−	0.194775i	$-0.937602\pi$
$173$	−25.8021			−1.96170			−0.980848	+	0.194775i	$0.937602\pi$
$174$	5.34961			0.405553
$175$	−4.25184			−0.321409
$176$	0.913168			0.0688326
$177$			5.45714i			0.410184i
$178$	8.72857			0.654234
$179$			19.2835i			1.44131i	0.693291	+	0.720657i	$0.256160\pi$
$179$			19.2835i			1.44131i	−0.693291	+	0.720657i	$0.743840\pi$
$180$			1.00000i			0.0745356i
$181$	−17.6308			−1.31049			−0.655244	−	0.755418i	$-0.727434\pi$
$181$	−17.6308			−1.31049			−0.655244	+	0.755418i	$0.727434\pi$
$182$	−11.6015			−0.859957
$183$			10.6883i			0.790101i
$184$	2.72857			0.201153
$185$	−2.72857	−	5.43644i	−0.200608	−	0.399695i
$186$	−8.98041			−0.658476
$187$		−	5.70898i		−	0.417482i
$188$	−6.11846			−0.446235
$189$	4.25184			0.309276
$190$		−	4.43644i		−	0.321853i
$191$		−	7.29839i		−	0.528093i	−0.964510	−	0.264047i	$-0.914943\pi$
$191$		−	7.29839i		−	0.528093i	0.964510	−	0.264047i	$-0.0850573\pi$
$192$	−1.00000			−0.0721688
$193$			15.4950i			1.11536i	0.830057	+	0.557679i	$0.188308\pi$
$193$			15.4950i			1.11536i	−0.830057	+	0.557679i	$0.811692\pi$
$194$	−12.5146			−0.898498
$195$	2.72857			0.195397
$196$	−11.0782			−0.791299
$197$	12.3594			0.880569			0.440284	−	0.897858i	$-0.354878\pi$
$197$	12.3594			0.880569			0.440284	+	0.897858i	$0.354878\pi$
$198$			0.913168i			0.0648960i
$199$		−	27.3766i		−	1.94067i	−0.241757	−	0.970337i	$-0.577724\pi$
$199$		−	27.3766i		−	1.94067i	0.241757	−	0.970337i	$-0.422276\pi$
$200$			1.00000i			0.0707107i
$201$	−13.9608			−0.984721
$202$		−	7.16501i		−	0.504129i
$203$		−	22.7457i		−	1.59644i
$204$			6.25184i			0.437717i
$205$			8.98041i			0.627219i
$206$	−5.33868			−0.371963
$207$			2.72857i			0.189649i
$208$			2.72857i			0.189192i
$209$		−	4.05122i		−	0.280229i
$210$	4.25184			0.293405
$211$	9.15408			0.630193			0.315096	−	0.949060i	$-0.397963\pi$
$211$	9.15408			0.630193			0.315096	+	0.949060i	$0.397963\pi$
$212$	−6.25184			−0.429378
$213$	12.5037			0.856739
$214$		−	9.27143i		−	0.633782i
$215$	−3.52327			−0.240285
$216$		−	1.00000i		−	0.0680414i
$217$			38.1833i			2.59205i
$218$	13.9205			0.942818
$219$	7.77512			0.525394
$220$			0.913168i			0.0615658i
$221$	17.0586			1.14749
$222$	2.72857	+	5.43644i	0.183130	+	0.364870i
$223$	−14.0270			−0.939315			−0.469657	−	0.882849i	$-0.655623\pi$
$223$	−14.0270			−0.939315			−0.469657	+	0.882849i	$0.655623\pi$
$224$			4.25184i			0.284088i
$225$	−1.00000			−0.0666667
$226$	1.93387			0.128639
$227$		−	16.3031i		−	1.08207i	−0.840999	−	0.541036i	$-0.818032\pi$
$227$		−	16.3031i		−	1.08207i	0.840999	−	0.541036i	$-0.181968\pi$
$228$			4.43644i			0.293811i
$229$	18.1345			1.19836			0.599181	−	0.800614i	$-0.295493\pi$
$229$	18.1345			1.19836			0.599181	+	0.800614i	$0.295493\pi$
$230$			2.72857i			0.179917i
$231$	3.88265			0.255459
$232$	−5.34961			−0.351219
$233$	−26.9522			−1.76570			−0.882848	−	0.469659i	$-0.844377\pi$
$233$	−26.9522			−1.76570			−0.882848	+	0.469659i	$0.844377\pi$
$234$	−2.72857			−0.178372
$235$		−	6.11846i		−	0.399125i
$236$		−	5.45714i		−	0.355230i
$237$			11.9608i			0.776939i
$238$	26.5819			1.72305
$239$		−	6.39616i		−	0.413733i	−0.978369	−	0.206867i	$-0.933673\pi$
$239$		−	6.39616i		−	0.413733i	0.978369	−	0.206867i	$-0.0663266\pi$
$240$		−	1.00000i		−	0.0645497i
$241$		−	13.0074i		−	0.837879i	−0.908014	−	0.418939i	$-0.862402\pi$
$241$		−	13.0074i		−	0.837879i	0.908014	−	0.418939i	$-0.137598\pi$
$242$		−	10.1661i		−	0.653503i
$243$	1.00000			0.0641500
$244$		−	10.6883i		−	0.684247i
$245$		−	11.0782i		−	0.707759i
$246$		−	8.98041i		−	0.572570i
$247$	12.1051			0.770232
$248$	8.98041			0.570257
$249$	0.902234			0.0571768
$250$	−1.00000			−0.0632456
$251$		−	10.6774i		−	0.673949i	−0.941514	−	0.336974i	$-0.890596\pi$
$251$		−	10.6774i		−	0.673949i	0.941514	−	0.336974i	$-0.109404\pi$
$252$	−4.25184			−0.267841
$253$			2.49164i			0.156648i
$254$		−	21.5623i		−	1.35294i
$255$	−6.25184			−0.391506
$256$	1.00000			0.0625000
$257$		−	9.23226i		−	0.575892i	−0.957647	−	0.287946i	$-0.907028\pi$
$257$		−	9.23226i		−	0.575892i	0.957647	−	0.287946i	$-0.0929724\pi$
$258$	3.52327			0.219349
$259$	23.1149	−	11.6015i	1.43629	−	0.720879i
$260$	−2.72857			−0.169219
$261$		−	5.34961i		−	0.331133i
$262$	5.45714			0.337143
$263$	−12.5146			−0.771685			−0.385842	−	0.922565i	$-0.626089\pi$
$263$	−12.5146			−0.771685			−0.385842	+	0.922565i	$0.626089\pi$
$264$		−	0.913168i		−	0.0562016i
$265$		−	6.25184i		−	0.384048i
$266$	18.8631			1.15657
$267$		−	8.72857i		−	0.534180i
$268$	13.9608			0.852793
$269$	0.517009			0.0315226			0.0157613	−	0.999876i	$-0.494983\pi$
$269$	0.517009			0.0315226			0.0157613	+	0.999876i	$0.494983\pi$
$270$	1.00000			0.0608581
$271$	−10.0931			−0.613112			−0.306556	−	0.951853i	$-0.599177\pi$
$271$	−10.0931			−0.613112			−0.306556	+	0.951853i	$0.599177\pi$
$272$		−	6.25184i		−	0.379074i
$273$			11.6015i			0.702152i
$274$		−	16.0379i		−	0.968885i
$275$	−0.913168			−0.0550661
$276$		−	2.72857i		−	0.164241i
$277$		−	0.902234i		−	0.0542100i	−0.999633	−	0.0271050i	$-0.991371\pi$
$277$		−	0.902234i		−	0.0542100i	0.999633	−	0.0271050i	$-0.00862884\pi$
$278$			17.6796i			1.06035i
$279$			8.98041i			0.537643i
$280$	−4.25184			−0.254096
$281$			23.0367i			1.37426i	0.726536	+	0.687128i	$0.241129\pi$
$281$			23.0367i			1.37426i	−0.726536	+	0.687128i	$0.758871\pi$
$282$			6.11846i			0.364349i
$283$		−	18.6088i		−	1.10618i	−0.833121	−	0.553090i	$-0.813449\pi$
$283$		−	18.6088i		−	1.10618i	0.833121	−	0.553090i	$-0.186551\pi$
$284$	−12.5037			−0.741957
$285$	−4.43644			−0.262792
$286$	−2.49164			−0.147334
$287$	−38.1833			−2.25389
$288$			1.00000i			0.0589256i
$289$	−22.0856			−1.29915
$290$		−	5.34961i		−	0.314140i
$291$			12.5146i			0.733620i
$292$	−7.77512			−0.455004
$293$	−22.3863			−1.30782			−0.653912	−	0.756571i	$-0.726873\pi$
$293$	−22.3863			−1.30782			−0.653912	+	0.756571i	$0.726873\pi$
$294$			11.0782i			0.646093i
$295$	5.45714			0.317727
$296$	−2.72857	−	5.43644i	−0.158595	−	0.315987i
$297$	0.913168			0.0529874
$298$		−	14.2116i		−	0.823254i
$299$	−7.44509			−0.430561
$300$	1.00000			0.0577350
$301$		−	14.9804i		−	0.863457i
$302$			3.94878i			0.227227i
$303$	−7.16501			−0.411619
$304$		−	4.43644i		−	0.254447i
$305$	10.6883			0.612010
$306$	6.25184			0.357394
$307$	11.6527			0.665053			0.332527	−	0.943094i	$-0.392099\pi$
$307$	11.6527			0.665053			0.332527	+	0.943094i	$0.392099\pi$
$308$	−3.88265			−0.221234
$309$			5.33868i			0.303707i
$310$			8.98041i			0.510053i
$311$		−	9.01959i		−	0.511454i	−0.966749	−	0.255727i	$-0.917685\pi$
$311$		−	9.01959i		−	0.511454i	0.966749	−	0.255727i	$-0.0823148\pi$
$312$	2.72857			0.154475
$313$			31.3926i			1.77441i	0.461371	+	0.887207i	$0.347358\pi$
$313$			31.3926i			1.77441i	−0.461371	+	0.887207i	$0.652642\pi$
$314$			16.8998i			0.953714i
$315$		−	4.25184i		−	0.239564i
$316$		−	11.9608i		−	0.672849i
$317$	6.65039			0.373523			0.186762	−	0.982405i	$-0.440201\pi$
$317$	6.65039			0.373523			0.186762	+	0.982405i	$0.440201\pi$
$318$			6.25184i			0.350586i
$319$		−	4.88509i		−	0.273513i
$320$			1.00000i			0.0559017i
$321$	−9.27143			−0.517481
$322$	−11.6015			−0.646524
$323$	−27.7359			−1.54327
$324$	−1.00000			−0.0555556
$325$		−	2.72857i		−	0.151354i
$326$	−8.07818			−0.447409
$327$		−	13.9205i		−	0.769808i
$328$			8.98041i			0.495860i
$329$	26.0148			1.43424
$330$	0.913168			0.0502682
$331$			1.68600i			0.0926712i	0.998926	+	0.0463356i	$0.0147544\pi$
$331$			1.68600i			0.0926712i	−0.998926	+	0.0463356i	$0.985246\pi$
$332$	−0.902234			−0.0495165
$333$	5.43644	−	2.72857i	0.297915	−	0.149525i
$334$	−7.94878			−0.434938
$335$			13.9608i			0.762762i
$336$	4.25184			0.231957
$337$	−27.7773			−1.51313			−0.756564	−	0.653920i	$-0.773123\pi$
$337$	−27.7773			−1.51313			−0.756564	+	0.653920i	$0.773123\pi$
$338$			5.55491i			0.302147i
$339$		−	1.93387i		−	0.105033i
$340$	6.25184			0.339054
$341$			8.20063i			0.444089i
$342$	4.43644			0.239895
$343$	17.3398			0.936261
$344$	−3.52327			−0.189962
$345$	2.72857			0.146901
$346$		−	25.8021i		−	1.38713i
$347$		−	4.13449i		−	0.221951i	−0.993823	−	0.110976i	$-0.964602\pi$
$347$		−	4.13449i		−	0.221951i	0.993823	−	0.110976i	$-0.0353975\pi$
$348$			5.34961i			0.286769i
$349$	−7.74577			−0.414622			−0.207311	−	0.978275i	$-0.566471\pi$
$349$	−7.74577			−0.414622			−0.207311	+	0.978275i	$0.566471\pi$
$350$		−	4.25184i		−	0.227271i
$351$			2.72857i			0.145640i
$352$			0.913168i			0.0486720i
$353$			31.6796i			1.68614i	0.537806	+	0.843068i	$0.319253\pi$
$353$			31.6796i			1.68614i	−0.537806	+	0.843068i	$0.680747\pi$
$354$	−5.45714			−0.290044
$355$		−	12.5037i		−	0.663627i
$356$			8.72857i			0.462613i
$357$		−	26.5819i		−	1.40686i
$358$	−19.2835			−1.01916
$359$	−1.80447			−0.0952362			−0.0476181	−	0.998866i	$-0.515163\pi$
$359$	−1.80447			−0.0952362			−0.0476181	+	0.998866i	$0.515163\pi$
$360$	−1.00000			−0.0527046
$361$	−0.682021			−0.0358959
$362$		−	17.6308i		−	0.926654i
$363$	−10.1661			−0.533583
$364$		−	11.6015i		−	0.608081i
$365$		−	7.77512i		−	0.406968i
$366$	−10.6883			−0.558686
$367$	−9.73085			−0.507946			−0.253973	−	0.967211i	$-0.581737\pi$
$367$	−9.73085			−0.507946			−0.253973	+	0.967211i	$0.581737\pi$
$368$			2.72857i			0.142237i
$369$	−8.98041			−0.467502
$370$	5.43644	−	2.72857i	0.282627	−	0.141852i
$371$	26.5819			1.38006
$372$		−	8.98041i		−	0.465613i
$373$	−7.45714			−0.386116			−0.193058	−	0.981187i	$-0.561841\pi$
$373$	−7.45714			−0.386116			−0.193058	+	0.981187i	$0.561841\pi$
$374$	5.70898			0.295205
$375$			1.00000i			0.0516398i
$376$		−	6.11846i		−	0.315536i
$377$	14.5968			0.751773
$378$			4.25184i			0.218691i
$379$	−5.95860			−0.306073			−0.153036	−	0.988221i	$-0.548905\pi$
$379$	−5.95860			−0.306073			−0.153036	+	0.988221i	$0.548905\pi$
$380$	4.43644			0.227585
$381$	−21.5623			−1.10467
$382$	7.29839			0.373418
$383$		−	13.6428i		−	0.697117i	−0.937287	−	0.348559i	$-0.886671\pi$
$383$		−	13.6428i		−	0.697117i	0.937287	−	0.348559i	$-0.113329\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	3.88265i		−	0.197878i
$386$	−15.4950			−0.788677
$387$		−	3.52327i		−	0.179098i
$388$		−	12.5146i		−	0.635334i
$389$			19.1759i			0.972259i	0.873887	+	0.486130i	$0.161592\pi$
$389$			19.1759i			0.972259i	−0.873887	+	0.486130i	$0.838408\pi$
$390$			2.72857i			0.138167i
$391$	17.0586			0.862690
$392$		−	11.0782i		−	0.559533i
$393$		−	5.45714i		−	0.275276i
$394$			12.3594i			0.622656i
$395$	11.9608			0.601815
$396$	−0.913168			−0.0458884
$397$	−3.80447			−0.190941			−0.0954704	−	0.995432i	$-0.530436\pi$
$397$	−3.80447			−0.190941			−0.0954704	+	0.995432i	$0.530436\pi$
$398$	27.3766			1.37226
$399$		−	18.8631i		−	0.944334i
$400$	−1.00000			−0.0500000
$401$		−	0.122447i		−	0.00611470i	−0.999995	−	0.00305735i	$-0.999027\pi$
$401$		−	0.122447i		−	0.00611470i	0.999995	−	0.00305735i	$-0.000973186\pi$
$402$		−	13.9608i		−	0.696303i
$403$	−24.5037			−1.22062
$404$	7.16501			0.356473
$405$		−	1.00000i		−	0.0496904i
$406$	22.7457			1.12885
$407$	4.96439	−	2.49164i	0.246075	−	0.123506i
$408$	−6.25184			−0.309512
$409$			10.6774i			0.527961i	0.964528	+	0.263981i	$0.0850355\pi$
$409$			10.6774i			0.527961i	−0.964528	+	0.263981i	$0.914965\pi$
$410$	−8.98041			−0.443511
$411$	−16.0379			−0.791091
$412$		−	5.33868i		−	0.263018i
$413$			23.2029i			1.14174i
$414$	−2.72857			−0.134102
$415$		−	0.902234i		−	0.0442889i
$416$	−2.72857			−0.133779
$417$	17.6796			0.865775
$418$	4.05122			0.198152
$419$	25.5636			1.24886			0.624431	−	0.781080i	$-0.285331\pi$
$419$	25.5636			1.24886			0.624431	+	0.781080i	$0.285331\pi$
$420$			4.25184i			0.207469i
$421$			11.3605i			0.553679i	0.960916	+	0.276840i	$0.0892870\pi$
$421$			11.3605i			0.553679i	−0.960916	+	0.276840i	$0.910713\pi$
$422$			9.15408i			0.445614i
$423$	6.11846			0.297490
$424$		−	6.25184i		−	0.303616i
$425$			6.25184i			0.303259i
$426$			12.5037i			0.605806i
$427$			45.4449i			2.19923i
$428$	9.27143			0.448151
$429$			2.49164i			0.120298i
$430$		−	3.52327i		−	0.169907i
$431$			9.33979i			0.449882i	0.974372	+	0.224941i	$0.0722189\pi$
$431$			9.33979i			0.449882i	−0.974372	+	0.224941i	$0.927781\pi$
$432$	1.00000			0.0481125
$433$	−4.46181			−0.214421			−0.107210	−	0.994236i	$-0.534192\pi$
$433$	−4.46181			−0.214421			−0.107210	+	0.994236i	$0.534192\pi$
$434$	−38.1833			−1.83286
$435$	−5.34961			−0.256494
$436$			13.9205i			0.666673i
$437$	12.1051			0.579068
$438$			7.77512i			0.371510i
$439$		−	13.4035i		−	0.639716i	−0.947466	−	0.319858i	$-0.896365\pi$
$439$		−	13.4035i		−	0.639716i	0.947466	−	0.319858i	$-0.103635\pi$
$440$	−0.913168			−0.0435336
$441$	11.0782			0.527532
$442$			17.0586i			0.811395i
$443$	9.35471			0.444455			0.222228	−	0.974995i	$-0.428667\pi$
$443$	9.35471			0.444455			0.222228	+	0.974995i	$0.428667\pi$
$444$	−5.43644	+	2.72857i	−0.258002	+	0.129492i
$445$	−8.72857			−0.413774
$446$		−	14.0270i		−	0.664196i
$447$	−14.2116			−0.672184
$448$	−4.25184			−0.200881
$449$		−	15.5916i		−	0.735815i	−0.929862	−	0.367907i	$-0.880074\pi$
$449$		−	15.5916i		−	0.735815i	0.929862	−	0.367907i	$-0.119926\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−8.20063			−0.386152
$452$			1.93387i			0.0909614i
$453$	3.94878			0.185530
$454$	16.3031			0.765141
$455$	11.6015			0.543885
$456$	−4.43644			−0.207755
$457$			7.05748i			0.330135i	0.986282	+	0.165068i	$0.0527842\pi$
$457$			7.05748i			0.330135i	−0.986282	+	0.165068i	$0.947216\pi$
$458$			18.1345i			0.847369i
$459$		−	6.25184i		−	0.291811i
$460$	−2.72857			−0.127220
$461$			3.76020i			0.175130i	0.996159	+	0.0875650i	$0.0279086\pi$
$461$			3.76020i			0.175130i	−0.996159	+	0.0875650i	$0.972091\pi$
$462$			3.88265i			0.180637i
$463$		−	4.83499i		−	0.224701i	−0.993669	−	0.112350i	$-0.964162\pi$
$463$		−	4.83499i		−	0.224701i	0.993669	−	0.112350i	$-0.0358379\pi$
$464$		−	5.34961i		−	0.248349i
$465$	8.98041			0.416457
$466$		−	26.9522i		−	1.24854i
$467$		−	9.25651i		−	0.428340i	−0.976796	−	0.214170i	$-0.931295\pi$
$467$		−	9.25651i		−	0.428340i	0.976796	−	0.214170i	$-0.0687047\pi$
$468$		−	2.72857i		−	0.126128i
$469$	−59.3593			−2.74096
$470$	6.11846			0.282224
$471$	16.8998			0.778704
$472$	5.45714			0.251185
$473$		−	3.21734i		−	0.147934i
$474$	−11.9608			−0.549379
$475$			4.43644i			0.203558i
$476$			26.5819i			1.21838i
$477$	6.25184			0.286252
$478$	6.39616			0.292554
$479$			9.48649i			0.433449i	0.976233	+	0.216724i	$0.0695373\pi$
$479$			9.48649i			0.433449i	−0.976233	+	0.216724i	$0.930463\pi$
$480$	1.00000			0.0456435
$481$	7.44509	+	14.8337i	0.339467	+	0.676359i
$482$	13.0074			0.592470
$483$			11.6015i			0.527884i
$484$	10.1661			0.462097
$485$	12.5146			0.568260
$486$			1.00000i			0.0453609i
$487$		−	21.9769i		−	0.995866i	−0.867215	−	0.497933i	$-0.834092\pi$
$487$		−	21.9769i		−	0.995866i	0.867215	−	0.497933i	$-0.165908\pi$
$488$	10.6883			0.483836
$489$			8.07818i			0.365308i
$490$	11.0782			0.500461
$491$	−13.4852			−0.608579			−0.304290	−	0.952580i	$-0.598419\pi$
$491$	−13.4852			−0.608579			−0.304290	+	0.952580i	$0.598419\pi$
$492$	8.98041			0.404868
$493$	−33.4449			−1.50628
$494$			12.1051i			0.544636i
$495$		−	0.913168i		−	0.0410438i
$496$			8.98041i			0.403233i
$497$	53.1637			2.38472
$498$			0.902234i			0.0404301i
$499$		−	5.52216i		−	0.247206i	−0.992332	−	0.123603i	$-0.960555\pi$
$499$		−	5.52216i		−	0.247206i	0.992332	−	0.123603i	$-0.0394449\pi$
$500$		−	1.00000i		−	0.0447214i
$501$			7.94878i			0.355125i
$502$	10.6774			0.476554
$503$			39.3374i			1.75397i	0.480520	+	0.876984i	$0.340448\pi$
$503$			39.3374i			1.75397i	−0.480520	+	0.876984i	$0.659552\pi$
$504$		−	4.25184i		−	0.189392i
$505$			7.16501i			0.318839i
$506$	−2.49164			−0.110767
$507$	5.55491			0.246702
$508$	21.5623			0.956672
$509$	−7.05987			−0.312923			−0.156462	−	0.987684i	$-0.550009\pi$
$509$	−7.05987			−0.312923			−0.156462	+	0.987684i	$0.550009\pi$
$510$		−	6.25184i		−	0.276836i
$511$	33.0586			1.46243
$512$			1.00000i			0.0441942i
$513$		−	4.43644i		−	0.195874i
$514$	9.23226			0.407217
$515$	5.33868			0.235250
$516$			3.52327i			0.155104i
$517$	5.58719			0.245724
$518$	11.6015	+	23.1149i	0.509739	+	1.01561i
$519$	−25.8021			−1.13259
$520$		−	2.72857i		−	0.119656i
$521$	5.13455			0.224949			0.112474	−	0.993655i	$-0.464122\pi$
$521$	5.13455			0.224949			0.112474	+	0.993655i	$0.464122\pi$
$522$	5.34961			0.234146
$523$		−	22.1564i		−	0.968830i	−0.874838	−	0.484415i	$-0.839032\pi$
$523$		−	22.1564i		−	0.968830i	0.874838	−	0.484415i	$-0.160968\pi$
$524$			5.45714i			0.238396i
$525$	−4.25184			−0.185566
$526$		−	12.5146i		−	0.545663i
$527$	56.1442			2.44568
$528$	0.913168			0.0397405
$529$	15.5549			0.676300
$530$	6.25184			0.271563
$531$			5.45714i			0.236820i
$532$			18.8631i			0.817817i
$533$		−	24.5037i		−	1.06137i
$534$	8.72857			0.377722
$535$			9.27143i			0.400839i
$536$			13.9608i			0.603016i
$537$			19.2835i			0.832143i
$538$			0.517009i			0.0222898i
$539$	10.1162			0.435737
$540$			1.00000i			0.0430331i
$541$		−	26.0672i		−	1.12072i	−0.828250	−	0.560359i	$-0.810663\pi$
$541$		−	26.0672i		−	1.12072i	0.828250	−	0.560359i	$-0.189337\pi$
$542$		−	10.0931i		−	0.433536i
$543$	−17.6308			−0.756610
$544$	6.25184			0.268046
$545$	−13.9205			−0.596291
$546$	−11.6015			−0.496496
$547$			10.4082i			0.445023i	0.974930	+	0.222511i	$0.0714254\pi$
$547$			10.4082i			0.445023i	−0.974930	+	0.222511i	$0.928575\pi$
$548$	16.0379			0.685105
$549$			10.6883i			0.456165i
$550$		−	0.913168i		−	0.0389376i
$551$	−23.7332			−1.01107
$552$	2.72857			0.116136
$553$			50.8556i			2.16260i
$554$	0.902234			0.0383322
$555$	−2.72857	−	5.43644i	−0.115821	−	0.230764i
$556$	−17.6796			−0.749784
$557$			21.8677i			0.926566i	0.886211	+	0.463283i	$0.153329\pi$
$557$			21.8677i			0.926566i	−0.886211	+	0.463283i	$0.846671\pi$
$558$	−8.98041			−0.380171
$559$	9.61350			0.406608
$560$		−	4.25184i		−	0.179673i
$561$		−	5.70898i		−	0.241034i
$562$	−23.0367			−0.971746
$563$			20.1442i			0.848975i	0.905434	+	0.424487i	$0.139546\pi$
$563$			20.1442i			0.848975i	−0.905434	+	0.424487i	$0.860454\pi$
$564$	−6.11846			−0.257634
$565$	−1.93387			−0.0813583
$566$	18.6088			0.782188
$567$	4.25184			0.178561
$568$		−	12.5037i		−	0.524643i
$569$			38.3960i			1.60964i	0.593516	+	0.804822i	$0.297739\pi$
$569$			38.3960i			1.60964i	−0.593516	+	0.804822i	$0.702261\pi$
$570$		−	4.43644i		−	0.185822i
$571$	35.4254			1.48251			0.741254	−	0.671225i	$-0.234232\pi$
$571$	35.4254			1.48251			0.741254	+	0.671225i	$0.234232\pi$
$572$		−	2.49164i		−	0.104181i
$573$		−	7.29839i		−	0.304895i
$574$		−	38.1833i		−	1.59374i
$575$		−	2.72857i		−	0.113789i
$576$	−1.00000			−0.0416667
$577$			39.1798i			1.63108i	0.578704	+	0.815538i	$0.303559\pi$
$577$			39.1798i			1.63108i	−0.578704	+	0.815538i	$0.696441\pi$
$578$		−	22.0856i		−	0.918638i
$579$			15.4950i			0.643952i
$580$	5.34961			0.222130
$581$	3.83616			0.159151
$582$	−12.5146			−0.518748
$583$	5.70898			0.236442
$584$		−	7.77512i		−	0.321737i
$585$	2.72857			0.112812
$586$		−	22.3863i		−	0.924771i
$587$		−	15.2690i		−	0.630221i	−0.949055	−	0.315110i	$-0.897958\pi$
$587$		−	15.2690i		−	0.630221i	0.949055	−	0.315110i	$-0.102042\pi$
$588$	−11.0782			−0.456856
$589$	39.8411			1.64162
$590$			5.45714i			0.224667i
$591$	12.3594			0.508397
$592$	5.43644	−	2.72857i	0.223436	−	0.112144i
$593$	15.5123			0.637015			0.318508	−	0.947920i	$-0.396818\pi$
$593$	15.5123			0.637015			0.318508	+	0.947920i	$0.396818\pi$
$594$			0.913168i			0.0374677i
$595$	−26.5819			−1.08975
$596$	14.2116			0.582128
$597$		−	27.3766i		−	1.12045i
$598$		−	7.44509i		−	0.304453i
$599$	2.91206			0.118983			0.0594917	−	0.998229i	$-0.481052\pi$
$599$	2.91206			0.118983			0.0594917	+	0.998229i	$0.481052\pi$
$600$			1.00000i			0.0408248i
$601$	−2.46690			−0.100627			−0.0503135	−	0.998733i	$-0.516022\pi$
$601$	−2.46690			−0.100627			−0.0503135	+	0.998733i	$0.516022\pi$
$602$	14.9804			0.610556
$603$	−13.9608			−0.568529
$604$	−3.94878			−0.160674
$605$			10.1661i			0.413312i
$606$		−	7.16501i		−	0.291059i
$607$		−	18.3679i		−	0.745531i	−0.927926	−	0.372765i	$-0.878410\pi$
$607$		−	18.3679i		−	0.745531i	0.927926	−	0.372765i	$-0.121590\pi$
$608$	4.43644			0.179921
$609$		−	22.7457i		−	0.921703i
$610$			10.6883i			0.432756i
$611$			16.6947i			0.675393i
$612$			6.25184i			0.252716i
$613$	30.5698			1.23470			0.617352	−	0.786687i	$-0.288206\pi$
$613$	30.5698			1.23470			0.617352	+	0.786687i	$0.288206\pi$
$614$			11.6527i			0.470264i
$615$			8.98041i			0.362125i
$616$		−	3.88265i		−	0.156436i
$617$	−25.3409			−1.02019			−0.510093	−	0.860119i	$-0.670389\pi$
$617$	−25.3409			−1.02019			−0.510093	+	0.860119i	$0.670389\pi$
$618$	−5.33868			−0.214753
$619$	−18.9804			−0.762887			−0.381444	−	0.924392i	$-0.624573\pi$
$619$	−18.9804			−0.762887			−0.381444	+	0.924392i	$0.624573\pi$
$620$	−8.98041			−0.360662
$621$			2.72857i			0.109494i
$622$	9.01959			0.361652
$623$		−	37.1125i		−	1.48688i
$624$			2.72857i			0.109230i
$625$	1.00000			0.0400000
$626$	−31.3926			−1.25470
$627$		−	4.05122i		−	0.161790i
$628$	−16.8998			−0.674377
$629$	−17.0586	−	33.9878i	−0.680171	−	1.35518i
$630$	4.25184			0.169398
$631$			27.7602i			1.10512i	0.833474	+	0.552558i	$0.186348\pi$
$631$			27.7602i			1.10512i	−0.833474	+	0.552558i	$0.813652\pi$
$632$	11.9608			0.475776
$633$	9.15408			0.363842
$634$			6.65039i			0.264121i
$635$			21.5623i			0.855673i
$636$	−6.25184			−0.247902
$637$			30.2276i			1.19766i
$638$	4.88509			0.193403
$639$	12.5037			0.494638
$640$	−1.00000			−0.0395285
$641$	35.3621			1.39672			0.698360	−	0.715746i	$-0.253913\pi$
$641$	35.3621			1.39672			0.698360	+	0.715746i	$0.253913\pi$
$642$		−	9.27143i		−	0.365914i
$643$		−	26.8095i		−	1.05726i	−0.848852	−	0.528631i	$-0.822706\pi$
$643$		−	26.8095i		−	1.05726i	0.848852	−	0.528631i	$-0.177294\pi$
$644$		−	11.6015i		−	0.457161i
$645$	−3.52327			−0.138729
$646$		−	27.7359i		−	1.09126i
$647$			4.76996i			0.187527i	0.995595	+	0.0937633i	$0.0298897\pi$
$647$			4.76996i			0.187527i	−0.995595	+	0.0937633i	$0.970110\pi$
$648$		−	1.00000i		−	0.0392837i
$649$			4.98329i			0.195611i
$650$	2.72857			0.107023
$651$			38.1833i			1.49652i
$652$		−	8.07818i		−	0.316366i
$653$		−	15.3547i		−	0.600876i	−0.953801	−	0.300438i	$-0.902867\pi$
$653$		−	15.3547i		−	0.600876i	0.953801	−	0.300438i	$-0.0971329\pi$
$654$	13.9205			0.544336
$655$	−5.45714			−0.213228
$656$	−8.98041			−0.350626
$657$	7.77512			0.303336
$658$			26.0148i			1.01416i
$659$	7.97463			0.310648			0.155324	−	0.987864i	$-0.450358\pi$
$659$	7.97463			0.310648			0.155324	+	0.987864i	$0.450358\pi$
$660$			0.913168i			0.0355450i
$661$			0.409479i			0.0159269i	0.999968	+	0.00796345i	$0.00253487\pi$
$661$			0.409479i			0.0159269i	−0.999968	+	0.00796345i	$0.997465\pi$
$662$	−1.68600			−0.0655284
$663$	17.0586			0.662501
$664$		−	0.902234i		−	0.0350135i
$665$	−18.8631			−0.731478
$666$	2.72857	+	5.43644i	0.105730	+	0.210658i
$667$	14.5968			0.565190
$668$		−	7.94878i		−	0.307548i
$669$	−14.0270			−0.542314
$670$	−13.9608			−0.539354
$671$			9.76020i			0.376788i
$672$			4.25184i			0.164018i
$673$	−25.8682			−0.997146			−0.498573	−	0.866848i	$-0.666143\pi$
$673$	−25.8682			−0.997146			−0.498573	+	0.866848i	$0.666143\pi$
$674$		−	27.7773i		−	1.06994i
$675$	−1.00000			−0.0384900
$676$	−5.55491			−0.213650
$677$	−10.8435			−0.416751			−0.208375	−	0.978049i	$-0.566818\pi$
$677$	−10.8435			−0.416751			−0.208375	+	0.978049i	$0.566818\pi$
$678$	1.93387			0.0742697
$679$			53.2102i			2.04202i
$680$			6.25184i			0.239747i
$681$		−	16.3031i		−	0.624735i
$682$	−8.20063			−0.314018
$683$			31.3817i			1.20079i	0.799705	+	0.600393i	$0.204989\pi$
$683$			31.3817i			1.20079i	−0.799705	+	0.600393i	$0.795011\pi$
$684$			4.43644i			0.169632i
$685$			16.0379i			0.612777i
$686$			17.3398i			0.662036i
$687$	18.1345			0.691874
$688$		−	3.52327i		−	0.134324i
$689$			17.0586i			0.649881i
$690$			2.72857i			0.103875i
$691$	−25.8925			−0.984996			−0.492498	−	0.870314i	$-0.663916\pi$
$691$	−25.8925			−0.984996			−0.492498	+	0.870314i	$0.663916\pi$
$692$	25.8021			0.980848
$693$	3.88265			0.147490
$694$	4.13449			0.156943
$695$		−	17.6796i		−	0.670627i
$696$	−5.34961			−0.202776
$697$			56.1442i			2.12661i
$698$		−	7.74577i		−	0.293182i
$699$	−26.9522			−1.01942
$700$	4.25184			0.160705
$701$			13.7872i			0.520734i	0.965510	+	0.260367i	$0.0838436\pi$
$701$			13.7872i			0.520734i	−0.965510	+	0.260367i	$0.916156\pi$
$702$	−2.72857			−0.102983
$703$	−12.1051	−	24.1185i	−0.456554	−	0.909645i
$704$	−0.913168			−0.0344163
$705$		−	6.11846i		−	0.230435i
$706$	−31.6796			−1.19228
$707$	−30.4645			−1.14574
$708$		−	5.45714i		−	0.205092i
$709$		−	0.624538i		−	0.0234550i	−0.999931	−	0.0117275i	$-0.996267\pi$
$709$		−	0.624538i		−	0.0234550i	0.999931	−	0.0117275i	$-0.00373307\pi$
$710$	12.5037			0.469255
$711$			11.9608i			0.448566i
$712$	−8.72857			−0.327117
$713$	−24.5037			−0.917670
$714$	26.5819			0.994801
$715$	2.49164			0.0931822
$716$		−	19.2835i		−	0.720657i
$717$		−	6.39616i		−	0.238869i
$718$		−	1.80447i		−	0.0673421i
$719$	41.4305			1.54510			0.772548	−	0.634956i	$-0.218982\pi$
$719$	41.4305			1.54510			0.772548	+	0.634956i	$0.218982\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			22.6992i			0.845363i
$722$		−	0.682021i		−	0.0253822i
$723$		−	13.0074i		−	0.483750i
$724$	17.6308			0.655244
$725$			5.34961i			0.198680i
$726$		−	10.1661i		−	0.377300i
$727$			12.8889i			0.478023i	0.971017	+	0.239012i	$0.0768234\pi$
$727$			12.8889i			0.478023i	−0.971017	+	0.239012i	$0.923177\pi$
$728$	11.6015			0.429979
$729$	1.00000			0.0370370
$730$	7.77512			0.287770
$731$	−22.0270			−0.814697
$732$		−	10.6883i		−	0.395050i
$733$	32.8481			1.21327			0.606637	−	0.794979i	$-0.292518\pi$
$733$	32.8481			1.21327			0.606637	+	0.794979i	$0.292518\pi$
$734$		−	9.73085i		−	0.359172i
$735$		−	11.0782i		−	0.408625i
$736$	−2.72857			−0.100576
$737$	−12.7486			−0.469600
$738$		−	8.98041i		−	0.330574i
$739$	15.9339			0.586137			0.293068	−	0.956091i	$-0.405324\pi$
$739$	15.9339			0.586137			0.293068	+	0.956091i	$0.405324\pi$
$740$	2.72857	+	5.43644i	0.100304	+	0.199848i
$741$	12.1051			0.444694
$742$			26.5819i			0.975851i
$743$	33.5242			1.22988			0.614942	−	0.788572i	$-0.289179\pi$
$743$	33.5242			1.22988			0.614942	+	0.788572i	$0.289179\pi$
$744$	8.98041			0.329238
$745$			14.2116i			0.520671i
$746$		−	7.45714i		−	0.273025i
$747$	0.902234			0.0330110
$748$			5.70898i			0.208741i
$749$	−39.4207			−1.44040
$750$	−1.00000			−0.0365148
$751$	−26.9682			−0.984084			−0.492042	−	0.870572i	$-0.663749\pi$
$751$	−26.9682			−0.984084			−0.492042	+	0.870572i	$0.663749\pi$
$752$	6.11846			0.223117
$753$		−	10.6774i		−	0.389104i
$754$			14.5968i			0.531584i
$755$		−	3.94878i		−	0.143711i
$756$	−4.25184			−0.154638
$757$			22.3007i			0.810532i	0.914199	+	0.405266i	$0.132821\pi$
$757$			22.3007i			0.810532i	−0.914199	+	0.405266i	$0.867179\pi$
$758$		−	5.95860i		−	0.216426i
$759$			2.49164i			0.0904409i
$760$			4.43644i			0.160927i
$761$	7.95117			0.288230			0.144115	−	0.989561i	$-0.453967\pi$
$761$	7.95117			0.288230			0.144115	+	0.989561i	$0.453967\pi$
$762$		−	21.5623i		−	0.781119i
$763$		−	59.1880i		−	2.14275i
$764$			7.29839i			0.264047i
$765$	−6.25184			−0.226036
$766$	13.6428			0.492936
$767$	−14.8902			−0.537654
$768$	1.00000			0.0360844
$769$		−	31.4719i		−	1.13491i	−0.823406	−	0.567453i	$-0.807929\pi$
$769$		−	31.4719i		−	1.13491i	0.823406	−	0.567453i	$-0.192071\pi$
$770$	3.88265			0.139921
$771$		−	9.23226i		−	0.332492i
$772$		−	15.4950i		−	0.557679i
$773$	−19.3376			−0.695524			−0.347762	−	0.937583i	$-0.613058\pi$
$773$	−19.3376			−0.695524			−0.347762	+	0.937583i	$0.613058\pi$
$774$	3.52327			0.126641
$775$		−	8.98041i		−	0.322586i
$776$	12.5146			0.449249
$777$	23.1149	−	11.6015i	0.829243	−	0.416200i
$778$	−19.1759			−0.687491
$779$			39.8411i			1.42746i
$780$	−2.72857			−0.0976985
$781$	11.4180			0.408567
$782$			17.0586i			0.610014i
$783$		−	5.34961i		−	0.191179i
$784$	11.0782			0.395649
$785$		−	16.8998i		−	0.603181i
$786$	5.45714			0.194650
$787$	15.7653			0.561972			0.280986	−	0.959712i	$-0.409339\pi$
$787$	15.7653			0.561972			0.280986	+	0.959712i	$0.409339\pi$
$788$	−12.3594			−0.440284
$789$	−12.5146			−0.445532
$790$			11.9608i			0.425547i
$791$		−	8.22250i		−	0.292358i
$792$		−	0.913168i		−	0.0324480i
$793$	−29.1637			−1.03563
$794$		−	3.80447i		−	0.135016i
$795$		−	6.25184i		−	0.221730i
$796$			27.3766i			0.970337i
$797$			4.41059i			0.156231i	0.996944	+	0.0781156i	$0.0248903\pi$
$797$			4.41059i			0.156231i	−0.996944	+	0.0781156i	$0.975110\pi$
$798$	18.8631			0.667745
$799$		−	38.2517i		−	1.35325i
$800$		−	1.00000i		−	0.0353553i
$801$		−	8.72857i		−	0.308409i
$802$	0.122447			0.00432374
$803$	7.09999			0.250553
$804$	13.9608			0.492360
$805$	11.6015			0.408898
$806$		−	24.5037i		−	0.863106i
$807$	0.517009			0.0181996
$808$			7.16501i			0.252064i
$809$		−	30.2983i		−	1.06523i	−0.846357	−	0.532616i	$-0.821209\pi$
$809$		−	30.2983i		−	1.06523i	0.846357	−	0.532616i	$-0.178791\pi$
$810$	1.00000			0.0351364
$811$	43.0488			1.51165			0.755823	−	0.654775i	$-0.227237\pi$
$811$	43.0488			1.51165			0.755823	+	0.654775i	$0.227237\pi$
$812$			22.7457i			0.798218i
$813$	−10.0931			−0.353980
$814$	2.49164	+	4.96439i	0.0873320	+	0.174002i
$815$	8.07818			0.282966
$816$		−	6.25184i		−	0.218858i
$817$	−15.6308			−0.546853
$818$	−10.6774			−0.373325
$819$			11.6015i			0.405388i
$820$		−	8.98041i		−	0.313610i
$821$	47.6416			1.66270			0.831351	−	0.555747i	$-0.187568\pi$
$821$	47.6416			1.66270			0.831351	+	0.555747i	$0.187568\pi$
$822$		−	16.0379i		−	0.559386i
$823$	−5.67268			−0.197737			−0.0988687	−	0.995100i	$-0.531522\pi$
$823$	−5.67268			−0.197737			−0.0988687	+	0.995100i	$0.531522\pi$
$824$	5.33868			0.185982
$825$	−0.913168			−0.0317924
$826$	−23.2029			−0.807332
$827$		−	20.2006i		−	0.702445i	−0.936292	−	0.351222i	$-0.885766\pi$
$827$		−	20.2006i		−	0.702445i	0.936292	−	0.351222i	$-0.114234\pi$
$828$		−	2.72857i		−	0.0948244i
$829$		−	36.0942i		−	1.25360i	−0.779179	−	0.626802i	$-0.784364\pi$
$829$		−	36.0942i		−	1.25360i	0.779179	−	0.626802i	$-0.215636\pi$
$830$	0.902234			0.0313170
$831$		−	0.902234i		−	0.0312981i
$832$		−	2.72857i		−	0.0945961i
$833$		−	69.2591i		−	2.39968i
$834$			17.6796i			0.612196i
$835$	7.94878			0.275079
$836$			4.05122i			0.140114i
$837$			8.98041i			0.310409i
$838$			25.5636i			0.883078i
$839$	34.6992			1.19795			0.598975	−	0.800768i	$-0.295575\pi$
$839$	34.6992			1.19795			0.598975	+	0.800768i	$0.295575\pi$
$840$	−4.25184			−0.146703
$841$	0.381668			0.0131610
$842$	−11.3605			−0.391510
$843$			23.0367i			0.793427i
$844$	−9.15408			−0.315096
$845$		−	5.55491i		−	0.191095i
$846$			6.11846i			0.210357i
$847$	−43.2248			−1.48522
$848$	6.25184			0.214689
$849$		−	18.6088i		−	0.638653i
$850$	−6.25184			−0.214436
$851$	7.44509	+	14.8337i	0.255215	+	0.508493i
$852$	−12.5037			−0.428369
$853$		−	18.0660i		−	0.618567i	−0.950970	−	0.309284i	$-0.899911\pi$
$853$		−	18.0660i		−	0.618567i	0.950970	−	0.309284i	$-0.100089\pi$
$854$	−45.4449			−1.55509
$855$	−4.43644			−0.151723
$856$			9.27143i			0.316891i
$857$		−	12.8166i		−	0.437806i	−0.975747	−	0.218903i	$-0.929752\pi$
$857$		−	12.8166i		−	0.437806i	0.975747	−	0.218903i	$-0.0702478\pi$
$858$	−2.49164			−0.0850633
$859$		−	49.7645i		−	1.69794i	−0.528439	−	0.848972i	$-0.677222\pi$
$859$		−	49.7645i		−	1.69794i	0.528439	−	0.848972i	$-0.322778\pi$
$860$	3.52327			0.120143
$861$	−38.1833			−1.30128
$862$	−9.33979			−0.318114
$863$	42.6686			1.45246			0.726229	−	0.687453i	$-0.241271\pi$
$863$	42.6686			1.45246			0.726229	+	0.687453i	$0.241271\pi$
$864$			1.00000i			0.0340207i
$865$			25.8021i			0.877297i
$866$		−	4.46181i		−	0.151618i
$867$	−22.0856			−0.750065
$868$		−	38.1833i		−	1.29603i
$869$			10.9222i			0.370512i
$870$		−	5.34961i		−	0.181369i
$871$		−	38.0931i		−	1.29074i
$872$	−13.9205			−0.471409
$873$			12.5146i			0.423556i
$874$			12.1051i			0.409463i
$875$			4.25184i			0.143739i
$876$	−7.77512			−0.262697
$877$	−19.7923			−0.668337			−0.334169	−	0.942513i	$-0.608455\pi$
$877$	−19.7923			−0.668337			−0.334169	+	0.942513i	$0.608455\pi$
$878$	13.4035			0.452347
$879$	−22.3863			−0.755072
$880$		−	0.913168i		−	0.0307829i
$881$	51.1782			1.72424			0.862118	−	0.506707i	$-0.169137\pi$
$881$	51.1782			1.72424			0.862118	+	0.506707i	$0.169137\pi$
$882$			11.0782i			0.373022i
$883$			45.0637i			1.51651i	0.651956	+	0.758257i	$0.273949\pi$
$883$			45.0637i			1.51651i	−0.651956	+	0.758257i	$0.726051\pi$
$884$	−17.0586			−0.573743
$885$	5.45714			0.183440
$886$			9.35471i			0.314277i
$887$	−30.2604			−1.01604			−0.508022	−	0.861344i	$-0.669623\pi$
$887$	−30.2604			−1.01604			−0.508022	+	0.861344i	$0.669623\pi$
$888$	−2.72857	−	5.43644i	−0.0915648	−	0.182435i
$889$	−91.6795			−3.07483
$890$		−	8.72857i		−	0.292582i
$891$	0.913168			0.0305923
$892$	14.0270			0.469657
$893$		−	27.1442i		−	0.908346i
$894$		−	14.2116i		−	0.475306i
$895$	19.2835			0.644576
$896$		−	4.25184i		−	0.142044i
$897$	−7.44509			−0.248584
$898$	15.5916			0.520300
$899$	48.0417			1.60228
$900$	1.00000			0.0333333
$901$		−	39.0856i		−	1.30213i
$902$		−	8.20063i		−	0.273051i
$903$		−	14.9804i		−	0.498517i
$904$	−1.93387			−0.0643194
$905$			17.6308i			0.586068i
$906$			3.94878i			0.131190i
$907$		−	11.0586i		−	0.367195i	−0.983002	−	0.183597i	$-0.941226\pi$
$907$		−	11.0586i		−	0.367195i	0.983002	−	0.183597i	$-0.0587742\pi$
$908$			16.3031i			0.541036i
$909$	−7.16501			−0.237648
$910$			11.6015i			0.384584i
$911$			23.7285i			0.786159i	0.919504	+	0.393080i	$0.128590\pi$
$911$			23.7285i			0.786159i	−0.919504	+	0.393080i	$0.871410\pi$
$912$		−	4.43644i		−	0.146905i
$913$	0.823891			0.0272668
$914$	−7.05748			−0.233441
$915$	10.6883			0.353344
$916$	−18.1345			−0.599181
$917$		−	23.2029i		−	0.766228i
$918$	6.25184			0.206342
$919$		−	39.0096i		−	1.28681i	−0.765527	−	0.643404i	$-0.777522\pi$
$919$		−	39.0096i		−	1.28681i	0.765527	−	0.643404i	$-0.222478\pi$
$920$		−	2.72857i		−	0.0899583i
$921$	11.6527			0.383969
$922$	−3.76020			−0.123836
$923$			34.1172i			1.12298i
$924$	−3.88265			−0.127730
$925$	−5.43644	+	2.72857i	−0.178749	+	0.0897148i
$926$	4.83499			0.158888
$927$			5.33868i			0.175345i
$928$	5.34961			0.175610
$929$	−38.4594			−1.26181			−0.630906	−	0.775859i	$-0.717317\pi$
$929$	−38.4594			−1.26181			−0.630906	+	0.775859i	$0.717317\pi$
$930$			8.98041i			0.294479i
$931$		−	49.1477i		−	1.61075i
$932$	26.9522			0.882848
$933$		−	9.01959i		−	0.295288i
$934$	9.25651			0.302882
$935$	−5.70898			−0.186704
$936$	2.72857			0.0891861
$937$	48.3840			1.58063			0.790317	−	0.612698i	$-0.209916\pi$
$937$	48.3840			1.58063			0.790317	+	0.612698i	$0.209916\pi$
$938$		−	59.3593i		−	1.93815i
$939$			31.3926i			1.02446i
$940$			6.11846i			0.199562i
$941$	27.4340			0.894323			0.447161	−	0.894453i	$-0.352435\pi$
$941$	27.4340			0.894323			0.447161	+	0.894453i	$0.352435\pi$
$942$			16.8998i			0.550627i
$943$		−	24.5037i		−	0.797950i
$944$			5.45714i			0.177615i
$945$		−	4.25184i		−	0.138313i
$946$	3.21734			0.104605
$947$		−	43.6405i		−	1.41812i	−0.705146	−	0.709062i	$-0.749119\pi$
$947$		−	43.6405i		−	1.41812i	0.705146	−	0.709062i	$-0.250881\pi$
$948$		−	11.9608i		−	0.388470i
$949$			21.2150i			0.688667i
$950$	−4.43644			−0.143937
$951$	6.65039			0.215654
$952$	−26.5819			−0.861523
$953$	−35.3214			−1.14417			−0.572086	−	0.820194i	$-0.693866\pi$
$953$	−35.3214			−1.14417			−0.572086	+	0.820194i	$0.693866\pi$
$954$			6.25184i			0.202411i
$955$	−7.29839			−0.236170
$956$			6.39616i			0.206867i
$957$		−	4.88509i		−	0.157913i
$958$	−9.48649			−0.306495
$959$	−68.1906			−2.20199
$960$			1.00000i			0.0322749i
$961$	−49.6478			−1.60154
$962$	−14.8337	+	7.44509i	−0.478258	+	0.240039i
$963$	−9.27143			−0.298768
$964$			13.0074i			0.418939i
$965$	15.4950			0.498803
$966$	−11.6015			−0.373271
$967$		−	6.61759i		−	0.212807i	−0.994323	−	0.106404i	$-0.966066\pi$
$967$		−	6.61759i		−	0.212807i	0.994323	−	0.106404i	$-0.0339336\pi$
$968$			10.1661i			0.326752i
$969$	−27.7359			−0.891007
$970$			12.5146i			0.401820i
$971$	−52.8594			−1.69634			−0.848169	−	0.529725i	$-0.822295\pi$
$971$	−52.8594			−1.69634			−0.848169	+	0.529725i	$0.822295\pi$
$972$	−1.00000			−0.0320750
$973$	75.1711			2.40987
$974$	21.9769			0.704184
$975$		−	2.72857i		−	0.0873842i
$976$			10.6883i			0.342124i
$977$			22.6750i			0.725436i	0.931899	+	0.362718i	$0.118151\pi$
$977$			22.6750i			0.725436i	−0.931899	+	0.362718i	$0.881849\pi$
$978$	−8.07818			−0.258312
$979$		−	7.97065i		−	0.254743i
$980$			11.0782i			0.353879i
$981$		−	13.9205i		−	0.444449i
$982$		−	13.4852i		−	0.430330i
$983$	20.0915			0.640819			0.320410	−	0.947279i	$-0.396179\pi$
$983$	20.0915			0.640819			0.320410	+	0.947279i	$0.396179\pi$
$984$			8.98041i			0.286285i
$985$		−	12.3594i		−	0.393802i
$986$		−	33.4449i		−	1.06510i
$987$	26.0148			0.828059
$988$	−12.1051			−0.385116
$989$	9.61350			0.305692
$990$	0.913168			0.0290224
$991$		−	11.0735i		−	0.351762i	−0.984411	−	0.175881i	$-0.943723\pi$
$991$		−	11.0735i		−	0.351762i	0.984411	−	0.175881i	$-0.0562773\pi$
$992$	−8.98041			−0.285128
$993$			1.68600i			0.0535037i
$994$			53.1637i			1.68625i
$995$	−27.3766			−0.867896
$996$	−0.902234			−0.0285884
$997$		−	50.3568i		−	1.59482i	−0.603440	−	0.797408i	$-0.706204\pi$
$997$		−	50.3568i		−	1.59482i	0.603440	−	0.797408i	$-0.293796\pi$
$998$	5.52216			0.174801
$999$	5.43644	−	2.72857i	0.172001	−	0.0863281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.g.961.8	yes	8
3.2	odd	2		3330.2.h.o.2071.4		8
37.36	even	2	inner	1110.2.h.g.961.4	✓	8
111.110	odd	2		3330.2.h.o.2071.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.g.961.4	✓	8	37.36	even	2	inner
1110.2.h.g.961.8	yes	8	1.1	even	1	trivial
3330.2.h.o.2071.4		8	3.2	odd	2
3330.2.h.o.2071.8		8	111.110	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +4.25184 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +4.25184 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.913168 q^{11} -1.00000 q^{12} +2.72857i q^{13} +4.25184i q^{14} -1.00000i q^{15} +1.00000 q^{16} -6.25184i q^{17} +1.00000i q^{18} -4.43644i q^{19} +1.00000i q^{20} +4.25184 q^{21} +0.913168i q^{22} +2.72857i q^{23} -1.00000i q^{24} -1.00000 q^{25} -2.72857 q^{26} +1.00000 q^{27} -4.25184 q^{28} -5.34961i q^{29} +1.00000 q^{30} +8.98041i q^{31} +1.00000i q^{32} +0.913168 q^{33} +6.25184 q^{34} -4.25184i q^{35} -1.00000 q^{36} +(5.43644 - 2.72857i) q^{37} +4.43644 q^{38} +2.72857i q^{39} -1.00000 q^{40} -8.98041 q^{41} +4.25184i q^{42} -3.52327i q^{43} -0.913168 q^{44} -1.00000i q^{45} -2.72857 q^{46} +6.11846 q^{47} +1.00000 q^{48} +11.0782 q^{49} -1.00000i q^{50} -6.25184i q^{51} -2.72857i q^{52} +6.25184 q^{53} +1.00000i q^{54} -0.913168i q^{55} -4.25184i q^{56} -4.43644i q^{57} +5.34961 q^{58} +5.45714i q^{59} +1.00000i q^{60} +10.6883i q^{61} -8.98041 q^{62} +4.25184 q^{63} -1.00000 q^{64} +2.72857 q^{65} +0.913168i q^{66} -13.9608 q^{67} +6.25184i q^{68} +2.72857i q^{69} +4.25184 q^{70} +12.5037 q^{71} -1.00000i q^{72} +7.77512 q^{73} +(2.72857 + 5.43644i) q^{74} -1.00000 q^{75} +4.43644i q^{76} +3.88265 q^{77} -2.72857 q^{78} +11.9608i q^{79} -1.00000i q^{80} +1.00000 q^{81} -8.98041i q^{82} +0.902234 q^{83} -4.25184 q^{84} -6.25184 q^{85} +3.52327 q^{86} -5.34961i q^{87} -0.913168i q^{88} -8.72857i q^{89} +1.00000 q^{90} +11.6015i q^{91} -2.72857i q^{92} +8.98041i q^{93} +6.11846i q^{94} -4.43644 q^{95} +1.00000i q^{96} +12.5146i q^{97} +11.0782i q^{98} +0.913168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9	\( 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{16} - 4 q^{21} - 8 q^{25} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 8 q^{30} - 4 q^{33} + 12 q^{34} - 8 q^{36} + 18 q^{37} + 10 q^{38} - 8 q^{40} - 10 q^{41} + 4 q^{44} + 2 q^{46} + 28 q^{47} + 8 q^{48} + 28 q^{49} + 12 q^{53} + 6 q^{58} - 10 q^{62} - 4 q^{63} - 8 q^{64} - 2 q^{65} + 12 q^{67} - 4 q^{70} + 24 q^{71} + 10 q^{73} - 2 q^{74} - 8 q^{75} - 32 q^{77} + 2 q^{78} + 8 q^{81} + 6 q^{83} + 4 q^{84} - 12 q^{85} + 14 q^{86} + 8 q^{90} - 10 q^{95} - 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^16 - 4 * q^21 - 8 * q^25 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 8 * q^30 - 4 * q^33 + 12 * q^34 - 8 * q^36 + 18 * q^37 + 10 * q^38 - 8 * q^40 - 10 * q^41 + 4 * q^44 + 2 * q^46 + 28 * q^47 + 8 * q^48 + 28 * q^49 + 12 * q^53 + 6 * q^58 - 10 * q^62 - 4 * q^63 - 8 * q^64 - 2 * q^65 + 12 * q^67 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 8 * q^75 - 32 * q^77 + 2 * q^78 + 8 * q^81 + 6 * q^83 + 4 * q^84 - 12 * q^85 + 14 * q^86 + 8 * q^90 - 10 * q^95 - 4 * q^99

Introduction

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