LMFDB - Embedded newform 190.2.b.b.39.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(39,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("190.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.b (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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.1
Root			$1.32001 - 1.32001i$ of defining polynomial
Character	$\chi$	$=$	190.39
Dual form			190.2.b.b.39.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.12489i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} -2.12489 q^{6} -4.12489i q^{7} +1.00000i q^{8} -1.51514 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.12489i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} -2.12489 q^{6} -4.12489i q^{7} +1.00000i q^{8} -1.51514 q^{9} +(1.32001 - 1.80487i) q^{10} -2.64002 q^{11} +2.12489i q^{12} +2.51514i q^{13} -4.12489 q^{14} +(2.80487 - 3.83515i) q^{15} +1.00000 q^{16} +0.515138i q^{17} +1.51514i q^{18} -1.00000 q^{19} +(-1.80487 - 1.32001i) q^{20} -8.76491 q^{21} +2.64002i q^{22} +3.09461i q^{23} +2.12489 q^{24} +(1.51514 + 4.76491i) q^{25} +2.51514 q^{26} -3.15516i q^{27} +4.12489i q^{28} +7.79518 q^{29} +(-3.83515 - 2.80487i) q^{30} +3.67030 q^{31} -1.00000i q^{32} +5.60975i q^{33} +0.515138 q^{34} +(5.44490 - 7.44490i) q^{35} +1.51514 q^{36} -10.2498i q^{37} +1.00000i q^{38} +5.34438 q^{39} +(-1.32001 + 1.80487i) q^{40} +8.88979 q^{41} +8.76491i q^{42} +8.64002i q^{43} +2.64002 q^{44} +(-2.73463 - 2.00000i) q^{45} +3.09461 q^{46} +4.96972i q^{47} -2.12489i q^{48} -10.0147 q^{49} +(4.76491 - 1.51514i) q^{50} +1.09461 q^{51} -2.51514i q^{52} +5.48486i q^{53} -3.15516 q^{54} +(-4.76491 - 3.48486i) q^{55} +4.12489 q^{56} +2.12489i q^{57} -7.79518i q^{58} -3.15516 q^{59} +(-2.80487 + 3.83515i) q^{60} -12.6400 q^{61} -3.67030i q^{62} +6.24977i q^{63} -1.00000 q^{64} +(-3.32001 + 4.53951i) q^{65} +5.60975 q^{66} +7.40493i q^{67} -0.515138i q^{68} +6.57569 q^{69} +(-7.44490 - 5.44490i) q^{70} +11.1396 q^{71} -1.51514i q^{72} -2.70436i q^{73} -10.2498 q^{74} +(10.1249 - 3.21949i) q^{75} +1.00000 q^{76} +10.8898i q^{77} -5.34438i q^{78} -16.7493 q^{79} +(1.80487 + 1.32001i) q^{80} -11.2498 q^{81} -8.88979i q^{82} +3.28005i q^{83} +8.76491 q^{84} +(-0.679988 + 0.929759i) q^{85} +8.64002 q^{86} -16.5639i q^{87} -2.64002i q^{88} +7.60975 q^{89} +(-2.00000 + 2.73463i) q^{90} +10.3747 q^{91} -3.09461i q^{92} -7.79897i q^{93} +4.96972 q^{94} +(-1.80487 - 1.32001i) q^{95} -2.12489 q^{96} -3.93945i q^{97} +10.0147i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9} - 8 q^{14} + 8 q^{15} + 6 q^{16} - 6 q^{19} - 2 q^{20} - 20 q^{21} - 4 q^{24} + 10 q^{25} + 16 q^{26} + 16 q^{29} - 16 q^{30} + 8 q^{31} + 4 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{39} + 4 q^{41} + 18 q^{45} + 6 q^{49} - 4 q^{50} - 12 q^{51} - 4 q^{54} + 4 q^{55} + 8 q^{56} - 4 q^{59} - 8 q^{60} - 60 q^{61} - 6 q^{64} - 12 q^{65} + 16 q^{66} + 44 q^{69} - 20 q^{70} - 16 q^{71} - 28 q^{74} + 44 q^{75} + 6 q^{76} + 2 q^{80} - 34 q^{81} + 20 q^{84} - 12 q^{85} + 36 q^{86} + 28 q^{89} - 12 q^{90} + 12 q^{91} + 28 q^{94} - 2 q^{95} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9 - 8 * q^14 + 8 * q^15 + 6 * q^16 - 6 * q^19 - 2 * q^20 - 20 * q^21 - 4 * q^24 + 10 * q^25 + 16 * q^26 + 16 * q^29 - 16 * q^30 + 8 * q^31 + 4 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^39 + 4 * q^41 + 18 * q^45 + 6 * q^49 - 4 * q^50 - 12 * q^51 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 4 * q^59 - 8 * q^60 - 60 * q^61 - 6 * q^64 - 12 * q^65 + 16 * q^66 + 44 * q^69 - 20 * q^70 - 16 * q^71 - 28 * q^74 + 44 * q^75 + 6 * q^76 + 2 * q^80 - 34 * q^81 + 20 * q^84 - 12 * q^85 + 36 * q^86 + 28 * q^89 - 12 * q^90 + 12 * q^91 + 28 * q^94 - 2 * q^95 + 4 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$-1$

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
$3$		−	2.12489i		−	1.22680i	−0.789771	−	0.613402i	$-0.789801\pi$
$3$		−	2.12489i		−	1.22680i	0.789771	−	0.613402i	$-0.210199\pi$
$4$	−1.00000			−0.500000
$5$	1.80487	+	1.32001i	0.807164	+	0.590327i
$5$	1.80487	+	1.32001i	0.807164	+	0.590327i
$6$	−2.12489			−0.867481
$7$		−	4.12489i		−	1.55906i	−0.626365	−	0.779530i	$-0.715458\pi$
$7$		−	4.12489i		−	1.55906i	0.626365	−	0.779530i	$-0.284542\pi$
$8$			1.00000i			0.353553i
$9$	−1.51514			−0.505046
$10$	1.32001	−	1.80487i	0.417424	−	0.570751i
$11$	−2.64002			−0.795997			−0.397999	−	0.917386i	$-0.630295\pi$
$11$	−2.64002			−0.795997			−0.397999	+	0.917386i	$0.630295\pi$
$12$			2.12489i			0.613402i
$13$			2.51514i			0.697574i	0.937202	+	0.348787i	$0.113406\pi$
$13$			2.51514i			0.697574i	−0.937202	+	0.348787i	$0.886594\pi$
$14$	−4.12489			−1.10242
$15$	2.80487	−	3.83515i	0.724215	−	0.990231i
$16$	1.00000			0.250000
$17$			0.515138i			0.124939i	0.998047	+	0.0624697i	$0.0198977\pi$
$17$			0.515138i			0.124939i	−0.998047	+	0.0624697i	$0.980102\pi$
$18$			1.51514i			0.357121i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.80487	−	1.32001i	−0.403582	−	0.295164i
$21$	−8.76491			−1.91266
$22$			2.64002i			0.562855i
$23$			3.09461i			0.645271i	0.946523	+	0.322635i	$0.104569\pi$
$23$			3.09461i			0.645271i	−0.946523	+	0.322635i	$0.895431\pi$
$24$	2.12489			0.433740
$25$	1.51514	+	4.76491i	0.303028	+	0.952982i
$26$	2.51514			0.493259
$27$		−	3.15516i		−	0.607211i
$28$			4.12489i			0.779530i
$29$	7.79518			1.44753			0.723765	−	0.690047i	$-0.242410\pi$
$29$	7.79518			1.44753			0.723765	+	0.690047i	$0.242410\pi$
$30$	−3.83515	−	2.80487i	−0.700199	−	0.512098i
$31$	3.67030			0.659205			0.329603	−	0.944120i	$-0.393085\pi$
$31$	3.67030			0.659205			0.329603	+	0.944120i	$0.393085\pi$
$32$		−	1.00000i		−	0.176777i
$33$			5.60975i			0.976532i
$34$	0.515138			0.0883454
$35$	5.44490	−	7.44490i	0.920356	−	1.25842i
$36$	1.51514			0.252523
$37$		−	10.2498i		−	1.68505i	−0.538656	−	0.842526i	$-0.681068\pi$
$37$		−	10.2498i		−	1.68505i	0.538656	−	0.842526i	$-0.318932\pi$
$38$			1.00000i			0.162221i
$39$	5.34438			0.855786
$40$	−1.32001	+	1.80487i	−0.208712	+	0.285376i
$41$	8.88979			1.38835			0.694176	−	0.719805i	$-0.255769\pi$
$41$	8.88979			1.38835			0.694176	+	0.719805i	$0.255769\pi$
$42$			8.76491i			1.35245i
$43$			8.64002i			1.31759i	0.752322	+	0.658796i	$0.228934\pi$
$43$			8.64002i			1.31759i	−0.752322	+	0.658796i	$0.771066\pi$
$44$	2.64002			0.397999
$45$	−2.73463	−	2.00000i	−0.407655	−	0.298142i
$46$	3.09461			0.456275
$47$			4.96972i			0.724909i	0.932002	+	0.362454i	$0.118061\pi$
$47$			4.96972i			0.724909i	−0.932002	+	0.362454i	$0.881939\pi$
$48$		−	2.12489i		−	0.306701i
$49$	−10.0147			−1.43067
$50$	4.76491	−	1.51514i	0.673860	−	0.214273i
$51$	1.09461			0.153276
$52$		−	2.51514i		−	0.348787i
$53$			5.48486i			0.753404i	0.926335	+	0.376702i	$0.122942\pi$
$53$			5.48486i			0.753404i	−0.926335	+	0.376702i	$0.877058\pi$
$54$	−3.15516			−0.429363
$55$	−4.76491	−	3.48486i	−0.642500	−	0.469899i
$56$	4.12489			0.551211
$57$			2.12489i			0.281448i
$58$		−	7.79518i		−	1.02356i
$59$	−3.15516			−0.410767			−0.205384	−	0.978682i	$-0.565844\pi$
$59$	−3.15516			−0.410767			−0.205384	+	0.978682i	$0.565844\pi$
$60$	−2.80487	+	3.83515i	−0.362108	+	0.495116i
$61$	−12.6400			−1.61839			−0.809195	−	0.587541i	$-0.800096\pi$
$61$	−12.6400			−1.61839			−0.809195	+	0.587541i	$0.800096\pi$
$62$		−	3.67030i		−	0.466129i
$63$			6.24977i			0.787397i
$64$	−1.00000			−0.125000
$65$	−3.32001	+	4.53951i	−0.411797	+	0.563056i
$66$	5.60975			0.690512
$67$			7.40493i			0.904656i	0.891852	+	0.452328i	$0.149406\pi$
$67$			7.40493i			0.904656i	−0.891852	+	0.452328i	$0.850594\pi$
$68$		−	0.515138i		−	0.0624697i
$69$	6.57569			0.791620
$70$	−7.44490	−	5.44490i	−0.889835	−	0.650790i
$71$	11.1396			1.32202			0.661012	−	0.750376i	$-0.270127\pi$
$71$	11.1396			1.32202			0.661012	+	0.750376i	$0.270127\pi$
$72$		−	1.51514i		−	0.178561i
$73$		−	2.70436i		−	0.316521i	−0.987397	−	0.158261i	$-0.949411\pi$
$73$		−	2.70436i		−	0.316521i	0.987397	−	0.158261i	$-0.0505886\pi$
$74$	−10.2498			−1.19151
$75$	10.1249	−	3.21949i	1.16912	−	0.371755i
$76$	1.00000			0.114708
$77$			10.8898i			1.24101i
$78$		−	5.34438i		−	0.605132i
$79$	−16.7493			−1.88444			−0.942222	−	0.334988i	$-0.891268\pi$
$79$	−16.7493			−1.88444			−0.942222	+	0.334988i	$0.891268\pi$
$80$	1.80487	+	1.32001i	0.201791	+	0.147582i
$81$	−11.2498			−1.24997
$82$		−	8.88979i		−	0.981714i
$83$			3.28005i			0.360032i	0.983664	+	0.180016i	$0.0576149\pi$
$83$			3.28005i			0.360032i	−0.983664	+	0.180016i	$0.942385\pi$
$84$	8.76491			0.956330
$85$	−0.679988	+	0.929759i	−0.0737551	+	0.100847i
$86$	8.64002			0.931678
$87$		−	16.5639i		−	1.77583i
$88$		−	2.64002i		−	0.281427i
$89$	7.60975			0.806632			0.403316	−	0.915061i	$-0.367858\pi$
$89$	7.60975			0.806632			0.403316	+	0.915061i	$0.367858\pi$
$90$	−2.00000	+	2.73463i	−0.210819	+	0.288256i
$91$	10.3747			1.08756
$92$		−	3.09461i		−	0.322635i
$93$		−	7.79897i		−	0.808715i
$94$	4.96972			0.512588
$95$	−1.80487	−	1.32001i	−0.185176	−	0.135430i
$96$	−2.12489			−0.216870
$97$		−	3.93945i		−	0.399990i	−0.979797	−	0.199995i	$-0.935907\pi$
$97$		−	3.93945i		−	0.399990i	0.979797	−	0.199995i	$-0.0640926\pi$
$98$			10.0147i			1.01164i
$99$	4.00000			0.402015
$100$	−1.51514	−	4.76491i	−0.151514	−	0.476491i
$101$	−13.7990			−1.37305			−0.686524	−	0.727107i	$-0.740864\pi$
$101$	−13.7990			−1.37305			−0.686524	+	0.727107i	$0.740864\pi$
$102$		−	1.09461i		−	0.108382i
$103$			4.57947i			0.451229i	0.974217	+	0.225614i	$0.0724389\pi$
$103$			4.57947i			0.451229i	−0.974217	+	0.225614i	$0.927561\pi$
$104$	−2.51514			−0.246630
$105$	−15.8196	−	11.5698i	−1.54383	−	1.12910i
$106$	5.48486			0.532737
$107$			10.3747i			1.00296i	0.865170	+	0.501478i	$0.167210\pi$
$107$			10.3747i			1.00296i	−0.865170	+	0.501478i	$0.832790\pi$
$108$			3.15516i			0.303606i
$109$	−3.01468			−0.288754			−0.144377	−	0.989523i	$-0.546118\pi$
$109$	−3.01468			−0.288754			−0.144377	+	0.989523i	$0.546118\pi$
$110$	−3.48486	+	4.76491i	−0.332269	+	0.454316i
$111$	−21.7796			−2.06723
$112$		−	4.12489i		−	0.389765i
$113$		−	19.2001i		−	1.80620i	−0.429435	−	0.903098i	$-0.641287\pi$
$113$		−	19.2001i		−	1.80620i	0.429435	−	0.903098i	$-0.358713\pi$
$114$	2.12489			0.199014
$115$	−4.08492	+	5.58538i	−0.380921	+	0.520839i
$116$	−7.79518			−0.723765
$117$		−	3.81078i		−	0.352307i
$118$			3.15516i			0.290456i
$119$	2.12489			0.194788
$120$	3.83515	+	2.80487i	0.350100	+	0.256049i
$121$	−4.03028			−0.366389
$122$			12.6400i			1.14437i
$123$		−	18.8898i		−	1.70324i
$124$	−3.67030			−0.329603
$125$	−3.55510	+	10.6001i	−0.317978	+	0.948098i
$126$	6.24977			0.556774
$127$		−	14.3103i		−	1.26984i	−0.772580	−	0.634918i	$-0.781034\pi$
$127$		−	14.3103i		−	1.26984i	0.772580	−	0.634918i	$-0.218966\pi$
$128$			1.00000i			0.0883883i
$129$	18.3591			1.61643
$130$	4.53951	+	3.32001i	0.398141	+	0.291184i
$131$	−6.56009			−0.573158			−0.286579	−	0.958057i	$-0.592518\pi$
$131$	−6.56009			−0.573158			−0.286579	+	0.958057i	$0.592518\pi$
$132$		−	5.60975i		−	0.488266i
$133$			4.12489i			0.357673i
$134$	7.40493			0.639689
$135$	4.16485	−	5.69467i	0.358453	−	0.490119i
$136$	−0.515138			−0.0441727
$137$			6.45459i			0.551452i	0.961236	+	0.275726i	$0.0889183\pi$
$137$			6.45459i			0.551452i	−0.961236	+	0.275726i	$0.911082\pi$
$138$		−	6.57569i		−	0.559760i
$139$	23.0596			1.95589			0.977946	−	0.208856i	$-0.0669740\pi$
$139$	23.0596			1.95589			0.977946	+	0.208856i	$0.0669740\pi$
$140$	−5.44490	+	7.44490i	−0.460178	+	0.629209i
$141$	10.5601			0.889320
$142$		−	11.1396i		−	0.934812i
$143$		−	6.64002i		−	0.555267i
$144$	−1.51514			−0.126262
$145$	14.0693	+	10.2897i	1.16839	+	0.854516i
$146$	−2.70436			−0.223814
$147$			21.2800i			1.75515i
$148$			10.2498i			0.842526i
$149$	−16.0294			−1.31318			−0.656588	−	0.754249i	$-0.728001\pi$
$149$	−16.0294			−1.31318			−0.656588	+	0.754249i	$0.728001\pi$
$150$	−3.21949	−	10.1249i	−0.262871	−	0.826693i
$151$	−14.3103			−1.16456			−0.582279	−	0.812989i	$-0.697839\pi$
$151$	−14.3103			−1.16456			−0.582279	+	0.812989i	$0.697839\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		−	0.780505i		−	0.0631001i
$154$	10.8898			0.877525
$155$	6.62443	+	4.84484i	0.532087	+	0.389147i
$156$	−5.34438			−0.427893
$157$			18.0294i			1.43890i	0.694544	+	0.719450i	$0.255606\pi$
$157$			18.0294i			1.43890i	−0.694544	+	0.719450i	$0.744394\pi$
$158$			16.7493i			1.33250i
$159$	11.6547			0.924278
$160$	1.32001	−	1.80487i	0.104356	−	0.142688i
$161$	12.7649			1.00602
$162$			11.2498i			0.883865i
$163$			2.70058i			0.211525i	0.994391	+	0.105763i	$0.0337284\pi$
$163$			2.70058i			0.211525i	−0.994391	+	0.105763i	$0.966272\pi$
$164$	−8.88979			−0.694176
$165$	−7.40493	+	10.1249i	−0.576473	+	0.788221i
$166$	3.28005			0.254581
$167$		−	8.95035i		−	0.692599i	−0.938124	−	0.346299i	$-0.887438\pi$
$167$		−	8.95035i		−	0.692599i	0.938124	−	0.346299i	$-0.112562\pi$
$168$		−	8.76491i		−	0.676227i
$169$	6.67408			0.513391
$170$	0.929759	+	0.679988i	0.0713093	+	0.0521527i
$171$	1.51514			0.115866
$172$		−	8.64002i		−	0.658796i
$173$			0.310323i			0.0235934i	0.999930	+	0.0117967i	$0.00375510\pi$
$173$			0.310323i			0.0235934i	−0.999930	+	0.0117967i	$0.996245\pi$
$174$	−16.5639			−1.25570
$175$	19.6547	−	6.24977i	1.48576	−	0.472438i
$176$	−2.64002			−0.198999
$177$			6.70436i			0.503930i
$178$		−	7.60975i		−	0.570375i
$179$	1.52982			0.114344			0.0571720	−	0.998364i	$-0.481792\pi$
$179$	1.52982			0.114344			0.0571720	+	0.998364i	$0.481792\pi$
$180$	2.73463	+	2.00000i	0.203827	+	0.149071i
$181$	−14.7493			−1.09631			−0.548154	−	0.836377i	$-0.684669\pi$
$181$	−14.7493			−1.09631			−0.548154	+	0.836377i	$0.684669\pi$
$182$		−	10.3747i		−	0.769021i
$183$			26.8586i			1.98544i
$184$	−3.09461			−0.228138
$185$	13.5298	−	18.4995i	0.994732	−	1.36011i
$186$	−7.79897			−0.571848
$187$		−	1.35998i		−	0.0994513i
$188$		−	4.96972i		−	0.362454i
$189$	−13.0147			−0.946679
$190$	−1.32001	+	1.80487i	−0.0957637	+	0.130939i
$191$	18.1249			1.31147			0.655735	−	0.754991i	$-0.272359\pi$
$191$	18.1249			1.31147			0.655735	+	0.754991i	$0.272359\pi$
$192$			2.12489i			0.153350i
$193$		−	4.56009i		−	0.328243i	−0.986440	−	0.164121i	$-0.947521\pi$
$193$		−	4.56009i		−	0.328243i	0.986440	−	0.164121i	$-0.0524789\pi$
$194$	−3.93945			−0.282836
$195$	9.64593	+	7.05464i	0.690759	+	0.505194i
$196$	10.0147			0.715334
$197$			2.14048i			0.152503i	0.997089	+	0.0762515i	$0.0242952\pi$
$197$			2.14048i			0.152503i	−0.997089	+	0.0762515i	$0.975705\pi$
$198$		−	4.00000i		−	0.284268i
$199$	−16.5639			−1.17418			−0.587091	−	0.809521i	$-0.699727\pi$
$199$	−16.5639			−1.17418			−0.587091	+	0.809521i	$0.699727\pi$
$200$	−4.76491	+	1.51514i	−0.336930	+	0.107136i
$201$	15.7346			1.10984
$202$			13.7990i			0.970892i
$203$		−	32.1542i		−	2.25679i
$204$	−1.09461			−0.0766380
$205$	16.0450	+	11.7346i	1.12063	+	0.819582i
$206$	4.57947			0.319067
$207$		−	4.68876i		−	0.325891i
$208$			2.51514i			0.174393i
$209$	2.64002			0.182614
$210$	−11.5698	+	15.8196i	−0.798391	+	1.09165i
$211$	−15.2838			−1.05218			−0.526091	−	0.850428i	$-0.676343\pi$
$211$	−15.2838			−1.05218			−0.526091	+	0.850428i	$0.676343\pi$
$212$		−	5.48486i		−	0.376702i
$213$		−	23.6703i		−	1.62186i
$214$	10.3747			0.709197
$215$	−11.4049	+	15.5942i	−0.777810	+	1.06351i
$216$	3.15516			0.214682
$217$		−	15.1396i		−	1.02774i
$218$			3.01468i			0.204180i
$219$	−5.74645			−0.388309
$220$	4.76491	+	3.48486i	0.321250	+	0.234949i
$221$	−1.29564			−0.0871544
$222$			21.7796i			1.46175i
$223$		−	3.75023i		−	0.251134i	−0.992085	−	0.125567i	$-0.959925\pi$
$223$		−	3.75023i		−	0.251134i	0.992085	−	0.125567i	$-0.0400750\pi$
$224$	−4.12489			−0.275606
$225$	−2.29564	−	7.21949i	−0.153043	−	0.481300i
$226$	−19.2001			−1.27717
$227$			24.1542i			1.60317i	0.597878	+	0.801587i	$0.296011\pi$
$227$			24.1542i			1.60317i	−0.597878	+	0.801587i	$0.703989\pi$
$228$		−	2.12489i		−	0.140724i
$229$	13.0596			0.863005			0.431503	−	0.902112i	$-0.357984\pi$
$229$	13.0596			0.863005			0.431503	+	0.902112i	$0.357984\pi$
$230$	5.58538	+	4.08492i	0.368289	+	0.269352i
$231$	23.1396			1.52247
$232$			7.79518i			0.511779i
$233$		−	6.43899i		−	0.421832i	−0.977504	−	0.210916i	$-0.932355\pi$
$233$		−	6.43899i		−	0.421832i	0.977504	−	0.210916i	$-0.0676447\pi$
$234$	−3.81078			−0.249119
$235$	−6.56009	+	8.96972i	−0.427933	+	0.585120i
$236$	3.15516			0.205384
$237$			35.5904i			2.31184i
$238$		−	2.12489i		−	0.137736i
$239$	−22.8742			−1.47961			−0.739804	−	0.672822i	$-0.765082\pi$
$239$	−22.8742			−1.47961			−0.739804	+	0.672822i	$0.765082\pi$
$240$	2.80487	−	3.83515i	0.181054	−	0.247558i
$241$	4.96972			0.320128			0.160064	−	0.987107i	$-0.448830\pi$
$241$	4.96972			0.320128			0.160064	+	0.987107i	$0.448830\pi$
$242$			4.03028i			0.259076i
$243$			14.4390i			0.926262i
$244$	12.6400			0.809195
$245$	−18.0752	−	13.2195i	−1.15478	−	0.844563i
$246$	−18.8898			−1.20437
$247$		−	2.51514i		−	0.160034i
$248$			3.67030i			0.233064i
$249$	6.96972			0.441688
$250$	10.6001	+	3.55510i	0.670407	+	0.224844i
$251$	15.9201			1.00487			0.502433	−	0.864616i	$-0.332438\pi$
$251$	15.9201			1.00487			0.502433	+	0.864616i	$0.332438\pi$
$252$		−	6.24977i		−	0.393699i
$253$		−	8.16984i		−	0.513634i
$254$	−14.3103			−0.897910
$255$	1.97563	+	1.44490i	0.123719	+	0.0904830i
$256$	1.00000			0.0625000
$257$			1.04965i			0.0654756i	0.999464	+	0.0327378i	$0.0104226\pi$
$257$			1.04965i			0.0654756i	−0.999464	+	0.0327378i	$0.989577\pi$
$258$		−	18.3591i		−	1.14299i
$259$	−42.2791			−2.62710
$260$	3.32001	−	4.53951i	0.205898	−	0.281528i
$261$	−11.8108			−0.731069
$262$			6.56009i			0.405284i
$263$		−	11.9394i		−	0.736218i	−0.929783	−	0.368109i	$-0.880005\pi$
$263$		−	11.9394i		−	0.736218i	0.929783	−	0.368109i	$-0.119995\pi$
$264$	−5.60975			−0.345256
$265$	−7.24008	+	9.89948i	−0.444755	+	0.608120i
$266$	4.12489			0.252913
$267$		−	16.1698i		−	0.989578i
$268$		−	7.40493i		−	0.452328i
$269$	15.9394			0.971845			0.485923	−	0.874002i	$-0.338484\pi$
$269$	15.9394			0.971845			0.485923	+	0.874002i	$0.338484\pi$
$270$	−5.69467	−	4.16485i	−0.346566	−	0.253465i
$271$	1.46548			0.0890218			0.0445109	−	0.999009i	$-0.485827\pi$
$271$	1.46548			0.0890218			0.0445109	+	0.999009i	$0.485827\pi$
$272$			0.515138i			0.0312348i
$273$		−	22.0450i		−	1.33422i
$274$	6.45459			0.389936
$275$	−4.00000	−	12.5795i	−0.241209	−	0.758571i
$276$	−6.57569			−0.395810
$277$		−	32.4995i		−	1.95271i	−0.216177	−	0.976354i	$-0.569359\pi$
$277$		−	32.4995i		−	1.95271i	0.216177	−	0.976354i	$-0.430641\pi$
$278$		−	23.0596i		−	1.38303i
$279$	−5.56101			−0.332929
$280$	7.44490	+	5.44490i	0.444918	+	0.325395i
$281$	1.04965			0.0626171			0.0313085	−	0.999510i	$-0.490033\pi$
$281$	1.04965			0.0626171			0.0313085	+	0.999510i	$0.490033\pi$
$282$		−	10.5601i		−	0.628844i
$283$		−	9.34060i		−	0.555241i	−0.960691	−	0.277620i	$-0.910454\pi$
$283$		−	9.34060i		−	0.555241i	0.960691	−	0.277620i	$-0.0895458\pi$
$284$	−11.1396			−0.661012
$285$	−2.80487	+	3.83515i	−0.166146	+	0.227175i
$286$	−6.64002			−0.392633
$287$		−	36.6694i		−	2.16453i
$288$			1.51514i			0.0892804i
$289$	16.7346			0.984390
$290$	10.2897	−	14.0693i	0.604234	−	0.826179i
$291$	−8.37088			−0.490709
$292$			2.70436i			0.158261i
$293$			25.5748i			1.49409i	0.664771	+	0.747047i	$0.268529\pi$
$293$			25.5748i			1.49409i	−0.664771	+	0.747047i	$0.731471\pi$
$294$	21.2800			1.24108
$295$	−5.69467	−	4.16485i	−0.331556	−	0.242487i
$296$	10.2498			0.595756
$297$			8.32970i			0.483338i
$298$			16.0294i			0.928556i
$299$	−7.78337			−0.450124
$300$	−10.1249	+	3.21949i	−0.584561	+	0.185878i
$301$	35.6391			2.05420
$302$			14.3103i			0.823467i
$303$			29.3212i			1.68446i
$304$	−1.00000			−0.0573539
$305$	−22.8136	−	16.6850i	−1.30631	−	0.955379i
$306$	−0.780505			−0.0446185
$307$		−	9.43991i		−	0.538764i	−0.963033	−	0.269382i	$-0.913181\pi$
$307$		−	9.43991i		−	0.538764i	0.963033	−	0.269382i	$-0.0868194\pi$
$308$		−	10.8898i		−	0.620504i
$309$	9.73085			0.553569
$310$	4.84484	−	6.62443i	0.275168	−	0.376242i
$311$	−17.4655			−0.990377			−0.495188	−	0.868786i	$-0.664901\pi$
$311$	−17.4655			−0.990377			−0.495188	+	0.868786i	$0.664901\pi$
$312$			5.34438i			0.302566i
$313$		−	10.4546i		−	0.590928i	−0.955354	−	0.295464i	$-0.904526\pi$
$313$		−	10.4546i		−	0.590928i	0.955354	−	0.295464i	$-0.0954743\pi$
$314$	18.0294			1.01746
$315$	−8.24977	+	11.2800i	−0.464822	+	0.635559i
$316$	16.7493			0.942222
$317$		−	4.33348i		−	0.243393i	−0.992567	−	0.121696i	$-0.961167\pi$
$317$		−	4.33348i		−	0.243393i	0.992567	−	0.121696i	$-0.0388334\pi$
$318$		−	11.6547i		−	0.653563i
$319$	−20.5795			−1.15223
$320$	−1.80487	−	1.32001i	−0.100896	−	0.0737909i
$321$	22.0450			1.23043
$322$		−	12.7649i		−	0.711361i
$323$		−	0.515138i		−	0.0286630i
$324$	11.2498			0.624987
$325$	−11.9844	+	3.81078i	−0.664775	+	0.211384i
$326$	2.70058			0.149571
$327$			6.40585i			0.354244i
$328$			8.88979i			0.490857i
$329$	20.4995			1.13018
$330$	10.1249	+	7.40493i	0.557357	+	0.407628i
$331$	−4.56387			−0.250853			−0.125427	−	0.992103i	$-0.540030\pi$
$331$	−4.56387			−0.250853			−0.125427	+	0.992103i	$0.540030\pi$
$332$		−	3.28005i		−	0.180016i
$333$			15.5298i			0.851029i
$334$	−8.95035			−0.489741
$335$	−9.77460	+	13.3650i	−0.534043	+	0.730206i
$336$	−8.76491			−0.478165
$337$		−	13.0109i		−	0.708749i	−0.935104	−	0.354374i	$-0.884694\pi$
$337$		−	13.0109i		−	0.708749i	0.935104	−	0.354374i	$-0.115306\pi$
$338$		−	6.67408i		−	0.363022i
$339$	−40.7980			−2.21585
$340$	0.679988	−	0.929759i	0.0368775	−	0.0504233i
$341$	−9.68968			−0.524725
$342$		−	1.51514i		−	0.0819293i
$343$			12.4352i			0.671438i
$344$	−8.64002			−0.465839
$345$	11.8683	+	8.67999i	0.638967	+	0.467315i
$346$	0.310323			0.0166831
$347$		−	13.2195i		−	0.709660i	−0.934931	−	0.354830i	$-0.884539\pi$
$347$		−	13.2195i		−	0.709660i	0.934931	−	0.354830i	$-0.115461\pi$
$348$			16.5639i			0.887917i
$349$	20.4390			1.09407			0.547037	−	0.837108i	$-0.315756\pi$
$349$	20.4390			1.09407			0.547037	+	0.837108i	$0.315756\pi$
$350$	−6.24977	−	19.6547i	−0.334064	−	1.05059i
$351$	7.93567			0.423575
$352$			2.64002i			0.140714i
$353$			10.7044i			0.569735i	0.958567	+	0.284868i	$0.0919497\pi$
$353$			10.7044i			0.569735i	−0.958567	+	0.284868i	$0.908050\pi$
$354$	6.70436			0.356333
$355$	20.1055	+	14.7044i	1.06709	+	0.780426i
$356$	−7.60975			−0.403316
$357$		−	4.51514i		−	0.238966i
$358$		−	1.52982i		−	0.0808534i
$359$	4.31410			0.227690			0.113845	−	0.993499i	$-0.463683\pi$
$359$	4.31410			0.227690			0.113845	+	0.993499i	$0.463683\pi$
$360$	2.00000	−	2.73463i	0.105409	−	0.144128i
$361$	1.00000			0.0526316
$362$			14.7493i			0.775207i
$363$			8.56387i			0.449487i
$364$	−10.3747			−0.543780
$365$	3.56978	−	4.88102i	0.186851	−	0.255484i
$366$	26.8586			1.40392
$367$			12.8099i			0.668669i	0.942454	+	0.334335i	$0.108512\pi$
$367$			12.8099i			0.668669i	−0.942454	+	0.334335i	$0.891488\pi$
$368$			3.09461i			0.161318i
$369$	−13.4693			−0.701182
$370$	−18.4995	−	13.5298i	−0.961745	−	0.703382i
$371$	22.6244			1.17460
$372$			7.79897i			0.404358i
$373$			0.704357i			0.0364702i	0.999834	+	0.0182351i	$0.00580474\pi$
$373$			0.704357i			0.0364702i	−0.999834	+	0.0182351i	$0.994195\pi$
$374$	−1.35998			−0.0703227
$375$	22.5239	+	7.55419i	1.16313	+	0.390096i
$376$	−4.96972			−0.256294
$377$			19.6060i			1.00976i
$378$			13.0147i			0.669403i
$379$	−6.12489			−0.314614			−0.157307	−	0.987550i	$-0.550281\pi$
$379$	−6.12489			−0.314614			−0.157307	+	0.987550i	$0.550281\pi$
$380$	1.80487	+	1.32001i	0.0925881	+	0.0677152i
$381$	−30.4078			−1.55784
$382$		−	18.1249i		−	0.927350i
$383$			18.6400i			0.952461i	0.879321	+	0.476230i	$0.157997\pi$
$383$			18.6400i			0.952461i	−0.879321	+	0.476230i	$0.842003\pi$
$384$	2.12489			0.108435
$385$	−14.3747	+	19.6547i	−0.732600	+	1.00170i
$386$	−4.56009			−0.232103
$387$		−	13.0908i		−	0.665444i
$388$			3.93945i			0.199995i
$389$	−13.9201			−0.705776			−0.352888	−	0.935666i	$-0.614800\pi$
$389$	−13.9201			−0.705776			−0.352888	+	0.935666i	$0.614800\pi$
$390$	7.05464	−	9.64593i	0.357226	−	0.488441i
$391$	−1.59415			−0.0806197
$392$		−	10.0147i		−	0.505818i
$393$			13.9394i			0.703152i
$394$	2.14048			0.107836
$395$	−30.2304	−	22.1093i	−1.52106	−	1.11244i
$396$	−4.00000			−0.201008
$397$			28.3784i			1.42427i	0.702041	+	0.712136i	$0.252272\pi$
$397$			28.3784i			1.42427i	−0.702041	+	0.712136i	$0.747728\pi$
$398$			16.5639i			0.830272i
$399$	8.76491			0.438794
$400$	1.51514	+	4.76491i	0.0757569	+	0.238245i
$401$	5.54920			0.277114			0.138557	−	0.990354i	$-0.455754\pi$
$401$	5.54920			0.277114			0.138557	+	0.990354i	$0.455754\pi$
$402$		−	15.7346i		−	0.784772i
$403$			9.23131i			0.459844i
$404$	13.7990			0.686524
$405$	−20.3044	−	14.8498i	−1.00893	−	0.737894i
$406$	−32.1542			−1.59579
$407$			27.0596i			1.34130i
$408$			1.09461i			0.0541912i
$409$	5.01090			0.247773			0.123886	−	0.992296i	$-0.460464\pi$
$409$	5.01090			0.247773			0.123886	+	0.992296i	$0.460464\pi$
$410$	11.7346	−	16.0450i	0.579532	−	0.792404i
$411$	13.7153			0.676524
$412$		−	4.57947i		−	0.225614i
$413$			13.0147i			0.640411i
$414$	−4.68876			−0.230440
$415$	−4.32970	+	5.92007i	−0.212537	+	0.290605i
$416$	2.51514			0.123315
$417$		−	48.9991i		−	2.39950i
$418$		−	2.64002i		−	0.129128i
$419$	15.8889			0.776222			0.388111	−	0.921613i	$-0.373128\pi$
$419$	15.8889			0.776222			0.388111	+	0.921613i	$0.373128\pi$
$420$	15.8196	+	11.5698i	0.771915	+	0.564548i
$421$	−2.38647			−0.116310			−0.0581548	−	0.998308i	$-0.518522\pi$
$421$	−2.38647			−0.116310			−0.0581548	+	0.998308i	$0.518522\pi$
$422$			15.2838i			0.744005i
$423$		−	7.52982i		−	0.366112i
$424$	−5.48486			−0.266368
$425$	−2.45459	+	0.780505i	−0.119065	+	0.0378601i
$426$	−23.6703			−1.14683
$427$			52.1386i			2.52317i
$428$		−	10.3747i		−	0.501478i
$429$	−14.1093			−0.681203
$430$	15.5942	+	11.4049i	0.752017	+	0.549995i
$431$	−2.35906			−0.113632			−0.0568160	−	0.998385i	$-0.518095\pi$
$431$	−2.35906			−0.113632			−0.0568160	+	0.998385i	$0.518095\pi$
$432$		−	3.15516i		−	0.151803i
$433$		−	0.640023i		−	0.0307576i	−0.999882	−	0.0153788i	$-0.995105\pi$
$433$		−	0.640023i		−	0.0307576i	0.999882	−	0.0153788i	$-0.00489541\pi$
$434$	−15.1396			−0.726722
$435$	21.8645	−	29.8957i	1.04832	−	1.43339i
$436$	3.01468			0.144377
$437$		−	3.09461i		−	0.148035i
$438$			5.74645i			0.274576i
$439$	25.4499			1.21466			0.607328	−	0.794451i	$-0.292241\pi$
$439$	25.4499			1.21466			0.607328	+	0.794451i	$0.292241\pi$
$440$	3.48486	−	4.76491i	0.166134	−	0.227158i
$441$	15.1736			0.722553
$442$			1.29564i			0.0616275i
$443$		−	35.6685i		−	1.69466i	−0.531067	−	0.847330i	$-0.678209\pi$
$443$		−	35.6685i		−	1.69466i	0.531067	−	0.847330i	$-0.321791\pi$
$444$	21.7796			1.03361
$445$	13.7346	+	10.0450i	0.651084	+	0.476177i
$446$	−3.75023			−0.177578
$447$			34.0606i			1.61101i
$448$			4.12489i			0.194883i
$449$	11.4399			0.539883			0.269941	−	0.962877i	$-0.412996\pi$
$449$	11.4399			0.539883			0.269941	+	0.962877i	$0.412996\pi$
$450$	−7.21949	+	2.29564i	−0.340330	+	0.108218i
$451$	−23.4693			−1.10512
$452$			19.2001i			0.903098i
$453$			30.4078i			1.42868i
$454$	24.1542			1.13361
$455$	18.7249	+	13.6947i	0.877839	+	0.642016i
$456$	−2.12489			−0.0995069
$457$		−	19.4849i		−	0.911463i	−0.890117	−	0.455732i	$-0.849378\pi$
$457$		−	19.4849i		−	0.911463i	0.890117	−	0.455732i	$-0.150622\pi$
$458$		−	13.0596i		−	0.610237i
$459$	1.62534			0.0758645
$460$	4.08492	−	5.58538i	0.190460	−	0.260420i
$461$	−29.3893			−1.36880			−0.684399	−	0.729108i	$-0.739935\pi$
$461$	−29.3893			−1.36880			−0.684399	+	0.729108i	$0.739935\pi$
$462$		−	23.1396i		−	1.07655i
$463$			12.1892i			0.566481i	0.959049	+	0.283241i	$0.0914095\pi$
$463$			12.1892i			0.566481i	−0.959049	+	0.283241i	$0.908591\pi$
$464$	7.79518			0.361882
$465$	10.2947	−	14.0761i	0.477407	−	0.652766i
$466$	−6.43899			−0.298280
$467$			17.8889i			0.827799i	0.910323	+	0.413899i	$0.135833\pi$
$467$			17.8889i			0.827799i	−0.910323	+	0.413899i	$0.864167\pi$
$468$			3.81078i			0.176153i
$469$	30.5445			1.41041
$470$	8.96972	+	6.56009i	0.413743	+	0.302595i
$471$	38.3103			1.76525
$472$		−	3.15516i		−	0.145228i
$473$		−	22.8099i		−	1.04880i
$474$	35.5904			1.63472
$475$	−1.51514	−	4.76491i	−0.0695193	−	0.218629i
$476$	−2.12489			−0.0973940
$477$		−	8.31032i		−	0.380504i
$478$			22.8742i			1.04624i
$479$	1.15894			0.0529534			0.0264767	−	0.999649i	$-0.491571\pi$
$479$	1.15894			0.0529534			0.0264767	+	0.999649i	$0.491571\pi$
$480$	−3.83515	−	2.80487i	−0.175050	−	0.128024i
$481$	25.7796			1.17545
$482$		−	4.96972i		−	0.226365i
$483$		−	27.1240i		−	1.23418i
$484$	4.03028			0.183194
$485$	5.20012	−	7.11021i	0.236125	−	0.322858i
$486$	14.4390			0.654966
$487$		−	30.6888i		−	1.39064i	−0.718700	−	0.695320i	$-0.755263\pi$
$487$		−	30.6888i		−	1.39064i	0.718700	−	0.695320i	$-0.244737\pi$
$488$		−	12.6400i		−	0.572187i
$489$	5.73841			0.259500
$490$	−13.2195	+	18.0752i	−0.597196	+	0.816556i
$491$	3.67030			0.165638			0.0828192	−	0.996565i	$-0.473608\pi$
$491$	3.67030			0.165638			0.0828192	+	0.996565i	$0.473608\pi$
$492$			18.8898i			0.851618i
$493$			4.01560i			0.180853i
$494$	−2.51514			−0.113161
$495$	7.21949	+	5.28005i	0.324492	+	0.237320i
$496$	3.67030			0.164801
$497$		−	45.9494i		−	2.06111i
$498$		−	6.96972i		−	0.312321i
$499$	−31.3893			−1.40518			−0.702590	−	0.711595i	$-0.747973\pi$
$499$	−31.3893			−1.40518			−0.702590	+	0.711595i	$0.747973\pi$
$500$	3.55510	−	10.6001i	0.158989	−	0.474049i
$501$	−19.0185			−0.849682
$502$		−	15.9201i		−	0.710548i
$503$		−	18.1542i		−	0.809458i	−0.914437	−	0.404729i	$-0.867366\pi$
$503$		−	18.1542i		−	0.809458i	0.914437	−	0.404729i	$-0.132634\pi$
$504$	−6.24977			−0.278387
$505$	−24.9054	−	18.2148i	−1.10828	−	0.810548i
$506$	−8.16984			−0.363194
$507$		−	14.1817i		−	0.629829i
$508$			14.3103i			0.634918i
$509$	−11.5298			−0.511050			−0.255525	−	0.966802i	$-0.582248\pi$
$509$	−11.5298			−0.511050			−0.255525	+	0.966802i	$0.582248\pi$
$510$	1.44490	−	1.97563i	0.0639811	−	0.0874824i
$511$	−11.1552			−0.493475
$512$		−	1.00000i		−	0.0441942i
$513$			3.15516i			0.139304i
$514$	1.04965			0.0462982
$515$	−6.04496	+	8.26537i	−0.266373	+	0.364216i
$516$	−18.3591			−0.808213
$517$		−	13.1202i		−	0.577025i
$518$			42.2791i			1.85764i
$519$	0.659401			0.0289445
$520$	−4.53951	−	3.32001i	−0.199071	−	0.145592i
$521$	−42.5895			−1.86588			−0.932939	−	0.360035i	$-0.882765\pi$
$521$	−42.5895			−1.86588			−0.932939	+	0.360035i	$0.882765\pi$
$522$			11.8108i			0.516944i
$523$			1.21571i			0.0531594i	0.999647	+	0.0265797i	$0.00846159\pi$
$523$			1.21571i			0.0531594i	−0.999647	+	0.0265797i	$0.991538\pi$
$524$	6.56009			0.286579
$525$	−13.2800	−	41.7640i	−0.579589	−	1.82273i
$526$	−11.9394			−0.520585
$527$			1.89071i			0.0823607i
$528$			5.60975i			0.244133i
$529$	13.4234			0.583626
$530$	9.89948	+	7.24008i	0.430006	+	0.314489i
$531$	4.78051			0.207456
$532$		−	4.12489i		−	0.178836i
$533$			22.3591i			0.968478i
$534$	−16.1698			−0.699737
$535$	−13.6947	+	18.7249i	−0.592072	+	0.809550i
$536$	−7.40493			−0.319844
$537$		−	3.25069i		−	0.140278i
$538$		−	15.9394i		−	0.687198i
$539$	26.4390			1.13881
$540$	−4.16485	+	5.69467i	−0.179227	+	0.245059i
$541$	−1.92007			−0.0825503			−0.0412751	−	0.999148i	$-0.513142\pi$
$541$	−1.92007			−0.0825503			−0.0412751	+	0.999148i	$0.513142\pi$
$542$		−	1.46548i		−	0.0629480i
$543$			31.3406i			1.34495i
$544$	0.515138			0.0220864
$545$	−5.44112	−	3.97941i	−0.233072	−	0.170459i
$546$	−22.0450			−0.943437
$547$		−	10.9697i		−	0.469032i	−0.972112	−	0.234516i	$-0.924650\pi$
$547$		−	10.9697i		−	0.469032i	0.972112	−	0.234516i	$-0.0753504\pi$
$548$		−	6.45459i		−	0.275726i
$549$	19.1514			0.817361
$550$	−12.5795	+	4.00000i	−0.536390	+	0.170561i
$551$	−7.79518			−0.332086
$552$			6.57569i			0.279880i
$553$			69.0890i			2.93796i
$554$	−32.4995			−1.38077
$555$	−39.3094	−	28.7493i	−1.66859	−	1.22034i
$556$	−23.0596			−0.977946
$557$		−	23.5005i		−	0.995746i	−0.867250	−	0.497873i	$-0.834114\pi$
$557$		−	23.5005i		−	0.995746i	0.867250	−	0.497873i	$-0.165886\pi$
$558$			5.56101i			0.235416i
$559$	−21.7309			−0.919117
$560$	5.44490	−	7.44490i	0.230089	−	0.314604i
$561$	−2.88979			−0.122007
$562$		−	1.04965i		−	0.0442770i
$563$		−	7.87890i		−	0.332056i	−0.986121	−	0.166028i	$-0.946906\pi$
$563$		−	7.87890i		−	0.332056i	0.986121	−	0.166028i	$-0.0530942\pi$
$564$	−10.5601			−0.444660
$565$	25.3444	−	34.6538i	1.06625	−	1.45790i
$566$	−9.34060			−0.392615
$567$			46.4040i			1.94879i
$568$			11.1396i			0.467406i
$569$	1.09083			0.0457299			0.0228650	−	0.999739i	$-0.492721\pi$
$569$	1.09083			0.0457299			0.0228650	+	0.999739i	$0.492721\pi$
$570$	3.83515	+	2.80487i	0.160637	+	0.117483i
$571$	21.4886			0.899272			0.449636	−	0.893212i	$-0.351554\pi$
$571$	21.4886			0.899272			0.449636	+	0.893212i	$0.351554\pi$
$572$			6.64002i			0.277633i
$573$		−	38.5133i		−	1.60892i
$574$	−36.6694			−1.53055
$575$	−14.7455	+	4.68876i	−0.614931	+	0.195535i
$576$	1.51514			0.0631308
$577$			16.1055i			0.670481i	0.942133	+	0.335241i	$0.108818\pi$
$577$			16.1055i			0.670481i	−0.942133	+	0.335241i	$0.891182\pi$
$578$		−	16.7346i		−	0.696069i
$579$	−9.68968			−0.402689
$580$	−14.0693	−	10.2897i	−0.584197	−	0.427258i
$581$	13.5298			0.561311
$582$			8.37088i			0.346984i
$583$		−	14.4802i		−	0.599707i
$584$	2.70436			0.111907
$585$	5.03028	−	6.87798i	0.207976	−	0.284369i
$586$	25.5748			1.05648
$587$		−	0.480164i		−	0.0198185i	−0.999951	−	0.00990925i	$-0.996846\pi$
$587$		−	0.480164i		−	0.0198185i	0.999951	−	0.00990925i	$-0.00315426\pi$
$588$		−	21.2800i		−	0.877574i
$589$	−3.67030			−0.151232
$590$	−4.16485	+	5.69467i	−0.171464	+	0.234446i
$591$	4.54828			0.187091
$592$		−	10.2498i		−	0.421263i
$593$			40.4683i			1.66184i	0.556395	+	0.830918i	$0.312184\pi$
$593$			40.4683i			1.66184i	−0.556395	+	0.830918i	$0.687816\pi$
$594$	8.32970			0.341772
$595$	3.83515	+	2.80487i	0.157226	+	0.114989i
$596$	16.0294			0.656588
$597$			35.1963i			1.44049i
$598$			7.78337i			0.318286i
$599$	36.1698			1.47786			0.738930	−	0.673782i	$-0.235331\pi$
$599$	36.1698			1.47786			0.738930	+	0.673782i	$0.235331\pi$
$600$	3.21949	+	10.1249i	0.131435	+	0.413347i
$601$	24.3903			0.994899			0.497450	−	0.867493i	$-0.334270\pi$
$601$	24.3903			0.994899			0.497450	+	0.867493i	$0.334270\pi$
$602$		−	35.6391i		−	1.45254i
$603$		−	11.2195i		−	0.456893i
$604$	14.3103			0.582279
$605$	−7.27414	−	5.32001i	−0.295736	−	0.216289i
$606$	29.3212			1.19109
$607$		−	21.6897i		−	0.880357i	−0.897910	−	0.440178i	$-0.854915\pi$
$607$		−	21.6897i		−	0.880357i	0.897910	−	0.440178i	$-0.145085\pi$
$608$			1.00000i			0.0405554i
$609$	−68.3241			−2.76863
$610$	−16.6850	+	22.8136i	−0.675555	+	0.923698i
$611$	−12.4995			−0.505677
$612$			0.780505i			0.0315501i
$613$		−	26.2304i		−	1.05944i	−0.848174	−	0.529718i	$-0.822298\pi$
$613$		−	26.2304i		−	1.05944i	0.848174	−	0.529718i	$-0.177702\pi$
$614$	−9.43991			−0.380964
$615$	24.9348	−	34.0937i	1.00547	−	1.37479i
$616$	−10.8898			−0.438762
$617$			22.7200i			0.914671i	0.889294	+	0.457335i	$0.151196\pi$
$617$			22.7200i			0.914671i	−0.889294	+	0.457335i	$0.848804\pi$
$618$		−	9.73085i		−	0.391432i
$619$	32.9192			1.32313			0.661566	−	0.749887i	$-0.269892\pi$
$619$	32.9192			1.32313			0.661566	+	0.749887i	$0.269892\pi$
$620$	−6.62443	−	4.84484i	−0.266043	−	0.194573i
$621$	9.76399			0.391816
$622$			17.4655i			0.700302i
$623$		−	31.3893i		−	1.25759i
$624$	5.34438			0.213946
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$	−10.4546			−0.417849
$627$		−	5.60975i		−	0.224032i
$628$		−	18.0294i		−	0.719450i
$629$	5.28005			0.210529
$630$	11.2800	+	8.24977i	0.449408	+	0.328679i
$631$	17.2876			0.688209			0.344104	−	0.938931i	$-0.388183\pi$
$631$	17.2876			0.688209			0.344104	+	0.938931i	$0.388183\pi$
$632$		−	16.7493i		−	0.666252i
$633$			32.4764i			1.29082i
$634$	−4.33348			−0.172105
$635$	18.8898	−	25.8283i	0.749619	−	1.02497i
$636$	−11.6547			−0.462139
$637$		−	25.1883i		−	0.997997i
$638$			20.5795i			0.814749i
$639$	−16.8780			−0.667683
$640$	−1.32001	+	1.80487i	−0.0521780	+	0.0713439i
$641$	−9.29942			−0.367305			−0.183653	−	0.982991i	$-0.558792\pi$
$641$	−9.29942			−0.367305			−0.183653	+	0.982991i	$0.558792\pi$
$642$		−	22.0450i		−	0.870045i
$643$		−	3.40115i		−	0.134128i	−0.997749	−	0.0670642i	$-0.978637\pi$
$643$		−	3.40115i		−	0.134128i	0.997749	−	0.0670642i	$-0.0213632\pi$
$644$	−12.7649			−0.503008
$645$	33.1358	+	24.2342i	1.30472	+	0.954220i
$646$	−0.515138			−0.0202678
$647$		−	14.9348i		−	0.587146i	−0.955937	−	0.293573i	$-0.905156\pi$
$647$		−	14.9348i		−	0.587146i	0.955937	−	0.293573i	$-0.0948443\pi$
$648$		−	11.2498i		−	0.441933i
$649$	8.32970			0.326969
$650$	3.81078	+	11.9844i	0.149471	+	0.470067i
$651$	−32.1698			−1.26084
$652$		−	2.70058i		−	0.105763i
$653$			21.1202i			0.826497i	0.910618	+	0.413248i	$0.135606\pi$
$653$			21.1202i			0.826497i	−0.910618	+	0.413248i	$0.864394\pi$
$654$	6.40585			0.250489
$655$	−11.8401	−	8.65940i	−0.462633	−	0.338351i
$656$	8.88979			0.347088
$657$			4.09747i			0.159858i
$658$		−	20.4995i		−	0.799155i
$659$	−27.6547			−1.07727			−0.538637	−	0.842538i	$-0.681061\pi$
$659$	−27.6547			−1.07727			−0.538637	+	0.842538i	$0.681061\pi$
$660$	7.40493	−	10.1249i	0.288237	−	0.394111i
$661$	10.2342			0.398063			0.199032	−	0.979993i	$-0.436220\pi$
$661$	10.2342			0.398063			0.199032	+	0.979993i	$0.436220\pi$
$662$			4.56387i			0.177380i
$663$			2.75309i			0.106921i
$664$	−3.28005			−0.127291
$665$	−5.44490	+	7.44490i	−0.211144	+	0.288701i
$666$	15.5298			0.601768
$667$			24.1231i			0.934048i
$668$			8.95035i			0.346299i
$669$	−7.96881			−0.308092
$670$	13.3650	+	9.77460i	0.516334	+	0.377626i
$671$	33.3700			1.28823
$672$			8.76491i			0.338114i
$673$		−	13.4693i		−	0.519202i	−0.965716	−	0.259601i	$-0.916409\pi$
$673$		−	13.4693i		−	0.519202i	0.965716	−	0.259601i	$-0.0835911\pi$
$674$	−13.0109			−0.501161
$675$	15.0341	−	4.78051i	0.578661	−	0.184002i
$676$	−6.67408			−0.256695
$677$		−	15.1433i		−	0.582006i	−0.956722	−	0.291003i	$-0.906011\pi$
$677$		−	15.1433i		−	0.582006i	0.956722	−	0.291003i	$-0.0939890\pi$
$678$			40.7980i			1.56684i
$679$	−16.2498			−0.623609
$680$	−0.929759	−	0.679988i	−0.0356546	−	0.0260764i
$681$	51.3250			1.96678
$682$			9.68968i			0.371037i
$683$			15.8789i			0.607589i	0.952738	+	0.303795i	$0.0982536\pi$
$683$			15.8789i			0.607589i	−0.952738	+	0.303795i	$0.901746\pi$
$684$	−1.51514			−0.0579328
$685$	−8.52013	+	11.6497i	−0.325537	+	0.445113i
$686$	12.4352			0.474778
$687$		−	27.7502i		−	1.05874i
$688$			8.64002i			0.329398i
$689$	−13.7952			−0.525555
$690$	8.67999	−	11.8683i	0.330442	−	0.451818i
$691$	27.3094			1.03890			0.519449	−	0.854501i	$-0.326137\pi$
$691$	27.3094			1.03890			0.519449	+	0.854501i	$0.326137\pi$
$692$		−	0.310323i		−	0.0117967i
$693$		−	16.4995i		−	0.626766i
$694$	−13.2195			−0.501805
$695$	41.6197	+	30.4390i	1.57873	+	1.15462i
$696$	16.5639			0.627852
$697$			4.57947i			0.173460i
$698$		−	20.4390i		−	0.773627i
$699$	−13.6821			−0.517505
$700$	−19.6547	+	6.24977i	−0.742878	+	0.236219i
$701$	−20.9697			−0.792016			−0.396008	−	0.918247i	$-0.629605\pi$
$701$	−20.9697			−0.792016			−0.396008	+	0.918247i	$0.629605\pi$
$702$		−	7.93567i		−	0.299512i
$703$			10.2498i			0.386577i
$704$	2.64002			0.0994996
$705$	19.0596	+	13.9394i	0.717827	+	0.524990i
$706$	10.7044			0.402864
$707$			56.9192i			2.14067i
$708$		−	6.70436i		−	0.251965i
$709$	−37.5592			−1.41056			−0.705282	−	0.708927i	$-0.749180\pi$
$709$	−37.5592			−1.41056			−0.705282	+	0.708927i	$0.749180\pi$
$710$	14.7044	−	20.1055i	0.551845	−	0.754546i
$711$	25.3775			0.951731
$712$			7.60975i			0.285187i
$713$			11.3581i			0.425366i
$714$	−4.51514			−0.168975
$715$	8.76491	−	11.9844i	0.327789	−	0.448191i
$716$	−1.52982			−0.0571720
$717$			48.6050i			1.81519i
$718$		−	4.31410i		−	0.161001i
$719$	−3.94323			−0.147058			−0.0735288	−	0.997293i	$-0.523426\pi$
$719$	−3.94323			−0.147058			−0.0735288	+	0.997293i	$0.523426\pi$
$720$	−2.73463	−	2.00000i	−0.101914	−	0.0745356i
$721$	18.8898			0.703493
$722$		−	1.00000i		−	0.0372161i
$723$		−	10.5601i		−	0.392734i
$724$	14.7493			0.548154
$725$	11.8108	+	37.1433i	0.438641	+	1.37947i
$726$	8.56387			0.317835
$727$		−	33.2139i		−	1.23183i	−0.787811	−	0.615917i	$-0.788786\pi$
$727$		−	33.2139i		−	1.23183i	0.787811	−	0.615917i	$-0.211214\pi$
$728$			10.3747i			0.384510i
$729$	−3.06811			−0.113634
$730$	−4.88102	−	3.56978i	−0.180655	−	0.132124i
$731$	−4.45080			−0.164619
$732$		−	26.8586i		−	0.992722i
$733$		−	8.62065i		−	0.318411i	−0.987245	−	0.159205i	$-0.949107\pi$
$733$		−	8.62065i		−	0.318411i	0.987245	−	0.159205i	$-0.0508932\pi$
$734$	12.8099			0.472821
$735$	−28.0899	+	38.4078i	−1.03611	+	1.41669i
$736$	3.09461			0.114069
$737$		−	19.5492i		−	0.720104i
$738$			13.4693i			0.495811i
$739$	45.1689			1.66157			0.830783	−	0.556597i	$-0.187893\pi$
$739$	45.1689			1.66157			0.830783	+	0.556597i	$0.187893\pi$
$740$	−13.5298	+	18.4995i	−0.497366	+	0.680057i
$741$	−5.34438			−0.196331
$742$		−	22.6244i		−	0.830569i
$743$		−	24.7905i		−	0.909475i	−0.890626	−	0.454737i	$-0.849733\pi$
$743$		−	24.7905i		−	0.909475i	0.890626	−	0.454737i	$-0.150267\pi$
$744$	7.79897			0.285924
$745$	−28.9310	−	21.1589i	−1.05995	−	0.775204i
$746$	0.704357			0.0257883
$747$		−	4.96972i		−	0.181833i
$748$			1.35998i			0.0497257i
$749$	42.7943			1.56367
$750$	7.55419	−	22.5239i	0.275840	−	0.822457i
$751$	−6.76869			−0.246993			−0.123497	−	0.992345i	$-0.539411\pi$
$751$	−6.76869			−0.246993			−0.123497	+	0.992345i	$0.539411\pi$
$752$			4.96972i			0.181227i
$753$		−	33.8283i		−	1.23277i
$754$	19.6060			0.714007
$755$	−25.8283	−	18.8898i	−0.939989	−	0.687470i
$756$	13.0147			0.473339
$757$		−	45.2101i		−	1.64319i	−0.570072	−	0.821595i	$-0.693085\pi$
$757$		−	45.2101i		−	1.64319i	0.570072	−	0.821595i	$-0.306915\pi$
$758$			6.12489i			0.222466i
$759$	−17.3600			−0.630127
$760$	1.32001	−	1.80487i	0.0478819	−	0.0654696i
$761$	19.8851			0.720834			0.360417	−	0.932791i	$-0.382634\pi$
$761$	19.8851			0.720834			0.360417	+	0.932791i	$0.382634\pi$
$762$			30.4078i			1.10156i
$763$			12.4352i			0.450185i
$764$	−18.1249			−0.655735
$765$	1.03028	−	1.40871i	0.0372497	−	0.0509321i
$766$	18.6400			0.673491
$767$		−	7.93567i		−	0.286540i
$768$		−	2.12489i		−	0.0766752i
$769$	−8.07615			−0.291233			−0.145617	−	0.989341i	$-0.546517\pi$
$769$	−8.07615			−0.291233			−0.145617	+	0.989341i	$0.546517\pi$
$770$	19.6547	+	14.3747i	0.708306	+	0.518027i
$771$	2.23039			0.0803257
$772$			4.56009i			0.164121i
$773$			45.9456i			1.65255i	0.563267	+	0.826275i	$0.309544\pi$
$773$			45.9456i			1.65255i	−0.563267	+	0.826275i	$0.690456\pi$
$774$	−13.0908			−0.470540
$775$	5.56101	+	17.4886i	0.199757	+	0.628211i
$776$	3.93945			0.141418
$777$			89.8383i			3.22293i
$778$			13.9201i			0.499059i
$779$	−8.88979			−0.318510
$780$	−9.64593	−	7.05464i	−0.345380	−	0.252597i
$781$	−29.4087			−1.05233
$782$			1.59415i			0.0570067i
$783$		−	24.5951i		−	0.878956i
$784$	−10.0147			−0.357667
$785$	−23.7990	+	32.5407i	−0.849422	+	1.16143i
$786$	13.9394			0.497204
$787$			17.8439i			0.636067i	0.948079	+	0.318034i	$0.103022\pi$
$787$			17.8439i			0.636067i	−0.948079	+	0.318034i	$0.896978\pi$
$788$		−	2.14048i		−	0.0762515i
$789$	−25.3700			−0.903194
$790$	−22.1093	+	30.2304i	−0.786613	+	1.07555i
$791$	−79.1983			−2.81597
$792$			4.00000i			0.142134i
$793$		−	31.7914i		−	1.12895i
$794$	28.3784			1.00711
$795$	21.0353	+	15.3843i	0.746044	+	0.545626i
$796$	16.5639			0.587091
$797$			37.3326i			1.32239i	0.750215	+	0.661194i	$0.229950\pi$
$797$			37.3326i			1.32239i	−0.750215	+	0.661194i	$0.770050\pi$
$798$		−	8.76491i		−	0.310274i
$799$	−2.56009			−0.0905696
$800$	4.76491	−	1.51514i	0.168465	−	0.0535682i
$801$	−11.5298			−0.407386
$802$		−	5.54920i		−	0.195949i
$803$			7.13957i			0.251950i
$804$	−15.7346			−0.554918
$805$	23.0390	+	16.8498i	0.812020	+	0.593878i
$806$	9.23131			0.325159
$807$		−	33.8695i		−	1.19226i
$808$		−	13.7990i		−	0.485446i
$809$	38.6950			1.36044			0.680221	−	0.733007i	$-0.261884\pi$
$809$	38.6950			1.36044			0.680221	+	0.733007i	$0.261884\pi$
$810$	−14.8498	+	20.3044i	−0.521770	+	0.713424i
$811$	13.3444			0.468585			0.234292	−	0.972166i	$-0.424723\pi$
$811$	13.3444			0.468585			0.234292	+	0.972166i	$0.424723\pi$
$812$			32.1542i			1.12839i
$813$		−	3.11399i		−	0.109212i
$814$	27.0596			0.948440
$815$	−3.56479	+	4.87420i	−0.124869	+	0.170736i
$816$	1.09461			0.0383190
$817$		−	8.64002i		−	0.302276i
$818$		−	5.01090i		−	0.175202i
$819$	−15.7190			−0.549268
$820$	−16.0450	−	11.7346i	−0.560314	−	0.409791i
$821$	−37.3482			−1.30346			−0.651730	−	0.758451i	$-0.725956\pi$
$821$	−37.3482			−1.30346			−0.651730	+	0.758451i	$0.725956\pi$
$822$		−	13.7153i		−	0.478374i
$823$		−	51.5630i		−	1.79737i	−0.438593	−	0.898686i	$-0.644523\pi$
$823$		−	51.5630i		−	1.79737i	0.438593	−	0.898686i	$-0.355477\pi$
$824$	−4.57947			−0.159533
$825$	−26.7299	+	8.49954i	−0.930617	+	0.295916i
$826$	13.0147			0.452839
$827$			48.5639i			1.68873i	0.535767	+	0.844366i	$0.320022\pi$
$827$			48.5639i			1.68873i	−0.535767	+	0.844366i	$0.679978\pi$
$828$			4.68876i			0.162946i
$829$	−0.325919			−0.0113196			−0.00565982	−	0.999984i	$-0.501802\pi$
$829$	−0.325919			−0.0113196			−0.00565982	+	0.999984i	$0.501802\pi$
$830$	5.92007	+	4.32970i	0.205489	+	0.150286i
$831$	−69.0578			−2.39559
$832$		−	2.51514i		−	0.0871967i
$833$		−	5.15894i		−	0.178747i
$834$	−48.9991			−1.69670
$835$	11.8146	−	16.1542i	0.408860	−	0.559041i
$836$	−2.64002			−0.0913071
$837$		−	11.5804i		−	0.400277i
$838$		−	15.8889i		−	0.548872i
$839$	17.1202			0.591055			0.295527	−	0.955334i	$-0.404505\pi$
$839$	17.1202			0.591055			0.295527	+	0.955334i	$0.404505\pi$
$840$	11.5698	−	15.8196i	0.399195	−	0.545826i
$841$	31.7649			1.09534
$842$			2.38647i			0.0822432i
$843$		−	2.23039i		−	0.0768188i
$844$	15.2838			0.526091
$845$	12.0459	+	8.80986i	0.414391	+	0.303069i
$846$	−7.52982			−0.258880
$847$			16.6244i			0.571222i
$848$			5.48486i			0.188351i
$849$	−19.8477			−0.681171
$850$	0.780505	+	2.45459i	0.0267711	+	0.0841916i
$851$	31.7190			1.08731
$852$			23.6703i			0.810931i
$853$		−	24.9092i		−	0.852874i	−0.904517	−	0.426437i	$-0.859769\pi$
$853$		−	24.9092i		−	0.852874i	0.904517	−	0.426437i	$-0.140231\pi$
$854$	52.1386			1.78415
$855$	2.73463	+	2.00000i	0.0935225	+	0.0683986i
$856$	−10.3747			−0.354598
$857$			11.6509i			0.397988i	0.980001	+	0.198994i	$0.0637674\pi$
$857$			11.6509i			0.397988i	−0.980001	+	0.198994i	$0.936233\pi$
$858$			14.1093i			0.481683i
$859$	5.35998			0.182880			0.0914400	−	0.995811i	$-0.470853\pi$
$859$	5.35998			0.182880			0.0914400	+	0.995811i	$0.470853\pi$
$860$	11.4049	−	15.5942i	0.388905	−	0.531756i
$861$	−77.9182			−2.65545
$862$			2.35906i			0.0803499i
$863$		−	41.0790i		−	1.39835i	−0.714953	−	0.699173i	$-0.753552\pi$
$863$		−	41.0790i		−	1.39835i	0.714953	−	0.699173i	$-0.246448\pi$
$864$	−3.15516			−0.107341
$865$	−0.409630	+	0.560094i	−0.0139278	+	0.0190438i
$866$	−0.640023			−0.0217489
$867$		−	35.5592i		−	1.20765i
$868$			15.1396i			0.513870i
$869$	44.2186			1.50001
$870$	−29.8957	−	21.8645i	−1.01356	−	0.741276i
$871$	−18.6244			−0.631065
$872$		−	3.01468i		−	0.102090i
$873$			5.96881i			0.202014i
$874$	−3.09461			−0.104677
$875$	43.7240	+	14.6644i	1.47814	+	0.495747i
$876$	5.74645			0.194154
$877$		−	45.9532i		−	1.55173i	−0.630899	−	0.775865i	$-0.717314\pi$
$877$		−	45.9532i		−	1.55173i	0.630899	−	0.775865i	$-0.282686\pi$
$878$		−	25.4499i		−	0.858892i
$879$	54.3435			1.83296
$880$	−4.76491	−	3.48486i	−0.160625	−	0.117475i
$881$	−6.90917			−0.232776			−0.116388	−	0.993204i	$-0.537132\pi$
$881$	−6.90917			−0.232776			−0.116388	+	0.993204i	$0.537132\pi$
$882$		−	15.1736i		−	0.510922i
$883$			48.5213i			1.63287i	0.577435	+	0.816437i	$0.304054\pi$
$883$			48.5213i			1.63287i	−0.577435	+	0.816437i	$0.695946\pi$
$884$	1.29564			0.0435772
$885$	−8.84983	+	12.1005i	−0.297484	+	0.406754i
$886$	−35.6685			−1.19831
$887$		−	23.7990i		−	0.799091i	−0.916713	−	0.399546i	$-0.869168\pi$
$887$		−	23.7990i		−	0.799091i	0.916713	−	0.399546i	$-0.130832\pi$
$888$		−	21.7796i		−	0.730875i
$889$	−59.0284			−1.97975
$890$	10.0450	−	13.7346i	0.336708	−	0.460386i
$891$	29.6997			0.994976
$892$			3.75023i			0.125567i
$893$		−	4.96972i		−	0.166305i
$894$	34.0606			1.13916
$895$	2.76113	+	2.01938i	0.0922943	+	0.0675003i
$896$	4.12489			0.137803
$897$			16.5388i			0.552213i
$898$		−	11.4399i		−	0.381755i
$899$	28.6107			0.954219
$900$	2.29564	+	7.21949i	0.0765214	+	0.240650i
$901$	−2.82546			−0.0941298
$902$			23.4693i			0.781441i
$903$		−	75.7290i		−	2.52010i
$904$	19.2001			0.638586
$905$	−26.6206	−	19.4693i	−0.884900	−	0.647180i
$906$	30.4078			1.01023
$907$		−	17.9726i		−	0.596770i	−0.954446	−	0.298385i	$-0.903552\pi$
$907$		−	17.9726i		−	0.596770i	0.954446	−	0.298385i	$-0.0964479\pi$
$908$		−	24.1542i		−	0.801587i
$909$	20.9073			0.693453
$910$	13.6947	−	18.7249i	0.453974	−	0.620726i
$911$	19.5592			0.648024			0.324012	−	0.946053i	$-0.394968\pi$
$911$	19.5592			0.648024			0.324012	+	0.946053i	$0.394968\pi$
$912$			2.12489i			0.0703620i
$913$		−	8.65940i		−	0.286584i
$914$	−19.4849			−0.644502
$915$	−35.4537	+	48.4764i	−1.17206	+	1.60258i
$916$	−13.0596			−0.431503
$917$			27.0596i			0.893588i
$918$		−	1.62534i		−	0.0536443i
$919$	−35.4948			−1.17087			−0.585433	−	0.810720i	$-0.699076\pi$
$919$	−35.4948			−1.17087			−0.585433	+	0.810720i	$0.699076\pi$
$920$	−5.58538	−	4.08492i	−0.184144	−	0.134676i
$921$	−20.0587			−0.660957
$922$			29.3893i			0.967886i
$923$			28.0175i			0.922209i
$924$	−23.1396			−0.761236
$925$	48.8392	−	15.5298i	1.60582	−	0.510617i
$926$	12.1892			0.400563
$927$		−	6.93853i		−	0.227891i
$928$		−	7.79518i		−	0.255889i
$929$	−17.9532			−0.589026			−0.294513	−	0.955648i	$-0.595157\pi$
$929$	−17.9532			−0.589026			−0.294513	+	0.955648i	$0.595157\pi$
$930$	−14.0761	−	10.2947i	−0.461575	−	0.337577i
$931$	10.0147			0.328218
$932$			6.43899i			0.210916i
$933$			37.1122i			1.21500i
$934$	17.8889			0.585342
$935$	1.79518	−	2.45459i	0.0587088	−	0.0802735i
$936$	3.81078			0.124559
$937$			5.66652i			0.185117i	0.995707	+	0.0925585i	$0.0295045\pi$
$937$			5.66652i			0.185117i	−0.995707	+	0.0925585i	$0.970495\pi$
$938$		−	30.5445i		−	0.997313i
$939$	−22.2148			−0.724953
$940$	6.56009	−	8.96972i	0.213967	−	0.292560i
$941$	−24.7044			−0.805339			−0.402670	−	0.915345i	$-0.631918\pi$
$941$	−24.7044			−0.805339			−0.402670	+	0.915345i	$0.631918\pi$
$942$		−	38.3103i		−	1.24822i
$943$			27.5104i			0.895863i
$944$	−3.15516			−0.102692
$945$	−23.4899	−	17.1795i	−0.764125	−	0.558850i
$946$	−22.8099			−0.741613
$947$		−	13.5904i		−	0.441628i	−0.975316	−	0.220814i	$-0.929129\pi$
$947$		−	13.5904i		−	0.441628i	0.975316	−	0.220814i	$-0.0708713\pi$
$948$		−	35.5904i		−	1.15592i
$949$	6.80183			0.220797
$950$	−4.76491	+	1.51514i	−0.154594	+	0.0491576i
$951$	−9.20815			−0.298595
$952$			2.12489i			0.0688679i
$953$			24.7375i			0.801326i	0.916225	+	0.400663i	$0.131220\pi$
$953$			24.7375i			0.801326i	−0.916225	+	0.400663i	$0.868780\pi$
$954$	−8.31032			−0.269057
$955$	32.7131	+	23.9251i	1.05857	+	0.774197i
$956$	22.8742			0.739804
$957$			43.7290i			1.41356i
$958$		−	1.15894i		−	0.0374437i
$959$	26.6244			0.859748
$960$	−2.80487	+	3.83515i	−0.0905269	+	0.123779i
$961$	−17.5289			−0.565448
$962$		−	25.7796i		−	0.831167i
$963$		−	15.7190i		−	0.506539i
$964$	−4.96972			−0.160064
$965$	6.01938	−	8.23039i	0.193771	−	0.264946i
$966$	−27.1240			−0.872699
$967$			35.6897i			1.14770i	0.818960	+	0.573851i	$0.194551\pi$
$967$			35.6897i			1.14770i	−0.818960	+	0.573851i	$0.805449\pi$
$968$		−	4.03028i		−	0.129538i
$969$	−1.09461			−0.0351639
$970$	−7.11021	−	5.20012i	−0.228295	−	0.166966i
$971$	16.4995			0.529495			0.264748	−	0.964318i	$-0.414711\pi$
$971$	16.4995			0.529495			0.264748	+	0.964318i	$0.414711\pi$
$972$		−	14.4390i		−	0.463131i
$973$		−	95.1184i		−	3.04935i
$974$	−30.6888			−0.983331
$975$	8.09747	+	25.4655i	0.259327	+	0.815548i
$976$	−12.6400			−0.404597
$977$		−	49.8501i		−	1.59485i	−0.603420	−	0.797423i	$-0.706196\pi$
$977$		−	49.8501i		−	1.59485i	0.603420	−	0.797423i	$-0.293804\pi$
$978$		−	5.73841i		−	0.183494i
$979$	−20.0899			−0.642076
$980$	18.0752	+	13.2195i	0.577392	+	0.422281i
$981$	4.56766			0.145834
$982$		−	3.67030i		−	0.117124i
$983$		−	5.19014i		−	0.165540i	−0.996569	−	0.0827698i	$-0.973623\pi$
$983$		−	5.19014i		−	0.165540i	0.996569	−	0.0827698i	$-0.0263766\pi$
$984$	18.8898			0.602185
$985$	−2.82546	+	3.86330i	−0.0900267	+	0.123095i
$986$	4.01560			0.127883
$987$		−	43.5592i		−	1.38650i
$988$			2.51514i			0.0800172i
$989$	−26.7375			−0.850203
$990$	5.28005	−	7.21949i	0.167811	−	0.229451i
$991$	−32.4272			−1.03008			−0.515042	−	0.857165i	$-0.672224\pi$
$991$	−32.4272			−1.03008			−0.515042	+	0.857165i	$0.672224\pi$
$992$		−	3.67030i		−	0.116532i
$993$			9.69771i			0.307748i
$994$	−45.9494			−1.45743
$995$	−29.8957	−	21.8645i	−0.947757	−	0.693152i
$996$	−6.96972			−0.220844
$997$		−	10.1992i		−	0.323012i	−0.986872	−	0.161506i	$-0.948365\pi$
$997$		−	10.1992i		−	0.323012i	0.986872	−	0.161506i	$-0.0516351\pi$
$998$			31.3893i			0.993612i
$999$	−32.3397			−1.02318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.b.b.39.1	✓	6
3.2	odd	2		1710.2.d.d.1369.4		6
4.3	odd	2		1520.2.d.j.609.5		6
5.2	odd	4		950.2.a.n.1.1		3
5.3	odd	4		950.2.a.i.1.3		3
5.4	even	2	inner	190.2.b.b.39.6	yes	6
15.2	even	4		8550.2.a.ck.1.3		3
15.8	even	4		8550.2.a.cl.1.1		3
15.14	odd	2		1710.2.d.d.1369.1		6
20.3	even	4		7600.2.a.cd.1.1		3
20.7	even	4		7600.2.a.bi.1.3		3
20.19	odd	2		1520.2.d.j.609.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.1	✓	6	1.1	even	1	trivial
190.2.b.b.39.6	yes	6	5.4	even	2	inner
950.2.a.i.1.3		3	5.3	odd	4
950.2.a.n.1.1		3	5.2	odd	4
1520.2.d.j.609.2		6	20.19	odd	2
1520.2.d.j.609.5		6	4.3	odd	2
1710.2.d.d.1369.1		6	15.14	odd	2
1710.2.d.d.1369.4		6	3.2	odd	2
7600.2.a.bi.1.3		3	20.7	even	4
7600.2.a.cd.1.1		3	20.3	even	4
8550.2.a.ck.1.3		3	15.2	even	4
8550.2.a.cl.1.1		3	15.8	even	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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.12489i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} -2.12489 q^{6} -4.12489i q^{7} +1.00000i q^{8} -1.51514 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.12489i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} -2.12489 q^{6} -4.12489i q^{7} +1.00000i q^{8} -1.51514 q^{9} +(1.32001 - 1.80487i) q^{10} -2.64002 q^{11} +2.12489i q^{12} +2.51514i q^{13} -4.12489 q^{14} +(2.80487 - 3.83515i) q^{15} +1.00000 q^{16} +0.515138i q^{17} +1.51514i q^{18} -1.00000 q^{19} +(-1.80487 - 1.32001i) q^{20} -8.76491 q^{21} +2.64002i q^{22} +3.09461i q^{23} +2.12489 q^{24} +(1.51514 + 4.76491i) q^{25} +2.51514 q^{26} -3.15516i q^{27} +4.12489i q^{28} +7.79518 q^{29} +(-3.83515 - 2.80487i) q^{30} +3.67030 q^{31} -1.00000i q^{32} +5.60975i q^{33} +0.515138 q^{34} +(5.44490 - 7.44490i) q^{35} +1.51514 q^{36} -10.2498i q^{37} +1.00000i q^{38} +5.34438 q^{39} +(-1.32001 + 1.80487i) q^{40} +8.88979 q^{41} +8.76491i q^{42} +8.64002i q^{43} +2.64002 q^{44} +(-2.73463 - 2.00000i) q^{45} +3.09461 q^{46} +4.96972i q^{47} -2.12489i q^{48} -10.0147 q^{49} +(4.76491 - 1.51514i) q^{50} +1.09461 q^{51} -2.51514i q^{52} +5.48486i q^{53} -3.15516 q^{54} +(-4.76491 - 3.48486i) q^{55} +4.12489 q^{56} +2.12489i q^{57} -7.79518i q^{58} -3.15516 q^{59} +(-2.80487 + 3.83515i) q^{60} -12.6400 q^{61} -3.67030i q^{62} +6.24977i q^{63} -1.00000 q^{64} +(-3.32001 + 4.53951i) q^{65} +5.60975 q^{66} +7.40493i q^{67} -0.515138i q^{68} +6.57569 q^{69} +(-7.44490 - 5.44490i) q^{70} +11.1396 q^{71} -1.51514i q^{72} -2.70436i q^{73} -10.2498 q^{74} +(10.1249 - 3.21949i) q^{75} +1.00000 q^{76} +10.8898i q^{77} -5.34438i q^{78} -16.7493 q^{79} +(1.80487 + 1.32001i) q^{80} -11.2498 q^{81} -8.88979i q^{82} +3.28005i q^{83} +8.76491 q^{84} +(-0.679988 + 0.929759i) q^{85} +8.64002 q^{86} -16.5639i q^{87} -2.64002i q^{88} +7.60975 q^{89} +(-2.00000 + 2.73463i) q^{90} +10.3747 q^{91} -3.09461i q^{92} -7.79897i q^{93} +4.96972 q^{94} +(-1.80487 - 1.32001i) q^{95} -2.12489 q^{96} -3.93945i q^{97} +10.0147i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9} - 8 q^{14} + 8 q^{15} + 6 q^{16} - 6 q^{19} - 2 q^{20} - 20 q^{21} - 4 q^{24} + 10 q^{25} + 16 q^{26} + 16 q^{29} - 16 q^{30} + 8 q^{31} + 4 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{39} + 4 q^{41} + 18 q^{45} + 6 q^{49} - 4 q^{50} - 12 q^{51} - 4 q^{54} + 4 q^{55} + 8 q^{56} - 4 q^{59} - 8 q^{60} - 60 q^{61} - 6 q^{64} - 12 q^{65} + 16 q^{66} + 44 q^{69} - 20 q^{70} - 16 q^{71} - 28 q^{74} + 44 q^{75} + 6 q^{76} + 2 q^{80} - 34 q^{81} + 20 q^{84} - 12 q^{85} + 36 q^{86} + 28 q^{89} - 12 q^{90} + 12 q^{91} + 28 q^{94} - 2 q^{95} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9 - 8 * q^14 + 8 * q^15 + 6 * q^16 - 6 * q^19 - 2 * q^20 - 20 * q^21 - 4 * q^24 + 10 * q^25 + 16 * q^26 + 16 * q^29 - 16 * q^30 + 8 * q^31 + 4 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^39 + 4 * q^41 + 18 * q^45 + 6 * q^49 - 4 * q^50 - 12 * q^51 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 4 * q^59 - 8 * q^60 - 60 * q^61 - 6 * q^64 - 12 * q^65 + 16 * q^66 + 44 * q^69 - 20 * q^70 - 16 * q^71 - 28 * q^74 + 44 * q^75 + 6 * q^76 + 2 * q^80 - 34 * q^81 + 20 * q^84 - 12 * q^85 + 36 * q^86 + 28 * q^89 - 12 * q^90 + 12 * q^91 + 28 * q^94 - 2 * q^95 + 4 * q^96 + 24 * q^99

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