LMFDB - Embedded newform 350.2.m.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	350.29
Dual form			350.2.m.a.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.06039 - 1.45950i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.717612 - 2.11779i) q^{5} +(-1.45950 + 1.06039i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0786699 - 0.242121i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.06039 - 1.45950i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.717612 - 2.11779i) q^{5} +(-1.45950 + 1.06039i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0786699 - 0.242121i) q^{9} +(-1.33692 + 1.79238i) q^{10} +(1.09570 - 3.37223i) q^{11} +(1.71575 - 0.557481i) q^{12} +(4.67515 - 1.51905i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-2.32997 - 3.29304i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.75075 - 2.40971i) q^{17} +0.254581i q^{18} +(-6.68687 + 4.85829i) q^{19} +(1.82537 - 1.29153i) q^{20} +(1.45950 + 1.06039i) q^{21} +(-2.08415 + 2.86859i) q^{22} +(2.27936 + 0.740608i) q^{23} -1.80405 q^{24} +(-3.97007 - 3.03950i) q^{25} -4.91574 q^{26} +(4.71045 + 1.53052i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(-2.51202 - 1.82509i) q^{29} +(1.19833 + 3.85187i) q^{30} +(-1.04429 + 0.758719i) q^{31} -1.00000i q^{32} +(-3.75991 - 5.17507i) q^{33} +(0.920426 + 2.83278i) q^{34} +(2.11779 + 0.717612i) q^{35} +(0.0786699 - 0.242121i) q^{36} +(0.645111 - 0.209609i) q^{37} +(7.86088 - 2.55416i) q^{38} +(2.74043 - 8.43418i) q^{39} +(-2.13513 + 0.664245i) q^{40} +(0.861410 + 2.65115i) q^{41} +(-1.06039 - 1.45950i) q^{42} -10.5561i q^{43} +(2.86859 - 2.08415i) q^{44} +(-0.569216 - 0.00714273i) q^{45} +(-1.93894 - 1.40872i) q^{46} +(-2.10319 + 2.89480i) q^{47} +(1.71575 + 0.557481i) q^{48} -1.00000 q^{49} +(2.83650 + 4.11756i) q^{50} -5.37346 q^{51} +(4.67515 + 1.51905i) q^{52} +(2.94750 - 4.05689i) q^{53} +(-4.00695 - 2.91122i) q^{54} +(-6.35539 - 4.74043i) q^{55} +(0.809017 - 0.587785i) q^{56} +14.9112i q^{57} +(1.82509 + 2.51202i) q^{58} +(2.92647 + 9.00675i) q^{59} +(0.0506157 - 4.03365i) q^{60} +(-3.67180 + 11.3006i) q^{61} +(1.22763 - 0.398882i) q^{62} +(0.242121 - 0.0786699i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.137920 - 10.9911i) q^{65} +(1.97670 + 6.08366i) q^{66} +(8.79578 + 12.1064i) q^{67} -2.97856i q^{68} +(3.49793 - 2.54139i) q^{69} +(-1.79238 - 1.33692i) q^{70} +(0.363201 + 0.263881i) q^{71} +(-0.149639 + 0.205960i) q^{72} +(8.84528 + 2.87401i) q^{73} -0.678310 q^{74} +(-8.64599 + 2.57126i) q^{75} -8.26542 q^{76} +(3.37223 + 1.09570i) q^{77} +(-5.21261 + 7.17454i) q^{78} +(-1.58072 - 1.14846i) q^{79} +(2.23589 + 0.0280568i) q^{80} +(7.84660 - 5.70089i) q^{81} -2.78758i q^{82} +(6.31464 + 8.69136i) q^{83} +(0.557481 + 1.71575i) q^{84} +(-6.35961 + 1.97849i) q^{85} +(-3.26203 + 10.0395i) q^{86} +(-5.32745 + 1.73099i) q^{87} +(-3.37223 + 1.09570i) q^{88} +(4.51054 - 13.8820i) q^{89} +(0.539149 + 0.182690i) q^{90} +(1.51905 + 4.67515i) q^{91} +(1.40872 + 1.93894i) q^{92} +2.32868i q^{93} +(2.89480 - 2.10319i) q^{94} +(5.49027 + 17.6477i) q^{95} +(-1.45950 - 1.06039i) q^{96} +(0.819807 - 1.12837i) q^{97} +(0.951057 + 0.309017i) q^{98} -0.902687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.06039	−	1.45950i	0.612217	−	0.842645i	−0.384540	−	0.923108i	$-0.625640\pi$
$3$	1.06039	−	1.45950i	0.612217	−	0.842645i	0.996758	+	0.0804634i	$0.0256400\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.717612	−	2.11779i	0.320926	−	0.947104i
$5$	0.717612	−	2.11779i	0.320926	−	0.947104i
$6$	−1.45950	+	1.06039i	−0.595840	+	0.432903i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.0786699	−	0.242121i	−0.0262233	−	0.0807070i
$10$	−1.33692	+	1.79238i	−0.422772	+	0.566801i
$11$	1.09570	−	3.37223i	0.330367	−	1.01677i	−0.638592	−	0.769546i	$-0.720483\pi$
$11$	1.09570	−	3.37223i	0.330367	−	1.01677i	0.968959	−	0.247220i	$-0.0795172\pi$
$12$	1.71575	−	0.557481i	0.495294	−	0.160931i
$13$	4.67515	−	1.51905i	1.29665	−	0.421308i	0.422237	−	0.906486i	$-0.361245\pi$
$13$	4.67515	−	1.51905i	1.29665	−	0.421308i	0.874416	+	0.485178i	$0.161245\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	−2.32997	−	3.29304i	−0.601596	−	0.850260i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.75075	−	2.40971i	−0.424620	−	0.584439i	0.542088	−	0.840322i	$-0.317634\pi$
$17$	−1.75075	−	2.40971i	−0.424620	−	0.584439i	−0.966708	+	0.255882i	$0.917634\pi$
$18$			0.254581i			0.0600053i
$19$	−6.68687	+	4.85829i	−1.53407	+	1.11457i	−0.580153	+	0.814508i	$0.697007\pi$
$19$	−6.68687	+	4.85829i	−1.53407	+	1.11457i	−0.953920	+	0.300061i	$0.902993\pi$
$20$	1.82537	−	1.29153i	0.408164	−	0.288794i
$21$	1.45950	+	1.06039i	0.318490	+	0.231396i
$22$	−2.08415	+	2.86859i	−0.444343	+	0.611586i
$23$	2.27936	+	0.740608i	0.475279	+	0.154427i	0.536854	−	0.843675i	$-0.319613\pi$
$23$	2.27936	+	0.740608i	0.475279	+	0.154427i	−0.0615756	+	0.998102i	$0.519613\pi$
$24$	−1.80405			−0.368249
$25$	−3.97007	−	3.03950i	−0.794013	−	0.607901i
$26$	−4.91574			−0.964056
$27$	4.71045	+	1.53052i	0.906527	+	0.294548i
$28$	−0.587785	+	0.809017i	−0.111081	+	0.152890i
$29$	−2.51202	−	1.82509i	−0.466471	−	0.338911i	0.329594	−	0.944123i	$-0.393088\pi$
$29$	−2.51202	−	1.82509i	−0.466471	−	0.338911i	−0.796064	+	0.605212i	$0.793088\pi$
$30$	1.19833	+	3.85187i	0.218784	+	0.703252i
$31$	−1.04429	+	0.758719i	−0.187559	+	0.136270i	−0.677603	−	0.735428i	$-0.736981\pi$
$31$	−1.04429	+	0.758719i	−0.187559	+	0.136270i	0.490043	+	0.871698i	$0.336981\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.75991	−	5.17507i	−0.654516	−	0.900864i
$34$	0.920426	+	2.83278i	0.157852	+	0.485818i
$35$	2.11779	+	0.717612i	0.357972	+	0.121299i
$36$	0.0786699	−	0.242121i	0.0131116	−	0.0403535i
$37$	0.645111	−	0.209609i	0.106056	−	0.0344596i	−0.255508	−	0.966807i	$-0.582243\pi$
$37$	0.645111	−	0.209609i	0.106056	−	0.0344596i	0.361564	+	0.932347i	$0.382243\pi$
$38$	7.86088	−	2.55416i	1.27520	−	0.414339i
$39$	2.74043	−	8.43418i	0.438820	−	1.35055i
$40$	−2.13513	+	0.664245i	−0.337594	+	0.105026i
$41$	0.861410	+	2.65115i	0.134530	+	0.414039i	0.995517	−	0.0945875i	$-0.0301532\pi$
$41$	0.861410	+	2.65115i	0.134530	+	0.414039i	−0.860987	+	0.508627i	$0.830153\pi$
$42$	−1.06039	−	1.45950i	−0.163622	−	0.225206i
$43$		−	10.5561i		−	1.60980i	−0.593413	−	0.804898i	$-0.702220\pi$
$43$		−	10.5561i		−	1.60980i	0.593413	−	0.804898i	$-0.297780\pi$
$44$	2.86859	−	2.08415i	0.432456	−	0.314198i
$45$	−0.569216	−	0.00714273i	−0.0848537	−	0.00106478i
$46$	−1.93894	−	1.40872i	−0.285881	−	0.207704i
$47$	−2.10319	+	2.89480i	−0.306782	+	0.422250i	−0.934374	−	0.356293i	$-0.884041\pi$
$47$	−2.10319	+	2.89480i	−0.306782	+	0.422250i	0.627592	+	0.778542i	$0.284041\pi$
$48$	1.71575	+	0.557481i	0.247647	+	0.0804654i
$49$	−1.00000			−0.142857
$50$	2.83650	+	4.11756i	0.401141	+	0.582311i
$51$	−5.37346			−0.752435
$52$	4.67515	+	1.51905i	0.648326	+	0.210654i
$53$	2.94750	−	4.05689i	0.404871	−	0.557257i	−0.557087	−	0.830454i	$-0.688081\pi$
$53$	2.94750	−	4.05689i	0.404871	−	0.557257i	0.961958	+	0.273197i	$0.0880812\pi$
$54$	−4.00695	−	2.91122i	−0.545277	−	0.396167i
$55$	−6.35539	−	4.74043i	−0.856960	−	0.639199i
$56$	0.809017	−	0.587785i	0.108109	−	0.0785461i
$57$			14.9112i			1.97504i
$58$	1.82509	+	2.51202i	0.239646	+	0.329845i
$59$	2.92647	+	9.00675i	0.380994	+	1.17258i	0.939345	+	0.342974i	$0.111434\pi$
$59$	2.92647	+	9.00675i	0.380994	+	1.17258i	−0.558351	+	0.829605i	$0.688566\pi$
$60$	0.0506157	−	4.03365i	0.00653447	−	0.520742i
$61$	−3.67180	+	11.3006i	−0.470126	+	1.44690i	0.382294	+	0.924041i	$0.375134\pi$
$61$	−3.67180	+	11.3006i	−0.470126	+	1.44690i	−0.852420	+	0.522858i	$0.824866\pi$
$62$	1.22763	−	0.398882i	0.155909	−	0.0506581i
$63$	0.242121	−	0.0786699i	0.0305044	−	0.00991147i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.137920	−	10.9911i	0.0171069	−	1.36327i
$66$	1.97670	+	6.08366i	0.243315	+	0.748847i
$67$	8.79578	+	12.1064i	1.07458	+	1.47903i	0.865355	+	0.501159i	$0.167093\pi$
$67$	8.79578	+	12.1064i	1.07458	+	1.47903i	0.209221	+	0.977868i	$0.432907\pi$
$68$		−	2.97856i		−	0.361203i
$69$	3.49793	−	2.54139i	0.421101	−	0.305948i
$70$	−1.79238	−	1.33692i	−0.214231	−	0.159793i
$71$	0.363201	+	0.263881i	0.0431040	+	0.0313169i	0.609129	−	0.793071i	$-0.291519\pi$
$71$	0.363201	+	0.263881i	0.0431040	+	0.0313169i	−0.566025	+	0.824388i	$0.691519\pi$
$72$	−0.149639	+	0.205960i	−0.0176351	+	0.0242727i
$73$	8.84528	+	2.87401i	1.03526	+	0.336377i	0.776869	−	0.629663i	$-0.216807\pi$
$73$	8.84528	+	2.87401i	1.03526	+	0.336377i	0.258393	+	0.966040i	$0.416807\pi$
$74$	−0.678310			−0.0788519
$75$	−8.64599	+	2.57126i	−0.998353	+	0.296904i
$76$	−8.26542			−0.948109
$77$	3.37223	+	1.09570i	0.384301	+	0.124867i
$78$	−5.21261	+	7.17454i	−0.590212	+	0.812357i
$79$	−1.58072	−	1.14846i	−0.177845	−	0.129212i	0.495301	−	0.868721i	$-0.335058\pi$
$79$	−1.58072	−	1.14846i	−0.177845	−	0.129212i	−0.673146	+	0.739509i	$0.735058\pi$
$80$	2.23589	+	0.0280568i	0.249980	+	0.00313685i
$81$	7.84660	−	5.70089i	0.871844	−	0.633432i
$82$		−	2.78758i		−	0.307837i
$83$	6.31464	+	8.69136i	0.693122	+	0.954001i	0.999997	+	0.00225119i	$0.000716577\pi$
$83$	6.31464	+	8.69136i	0.693122	+	0.954001i	−0.306875	+	0.951750i	$0.599283\pi$
$84$	0.557481	+	1.71575i	0.0608261	+	0.187204i
$85$	−6.35961	+	1.97849i	−0.689797	+	0.214598i
$86$	−3.26203	+	10.0395i	−0.351753	+	1.08259i
$87$	−5.32745	+	1.73099i	−0.571163	+	0.185582i
$88$	−3.37223	+	1.09570i	−0.359481	+	0.116802i
$89$	4.51054	−	13.8820i	0.478116	−	1.47149i	−0.363592	−	0.931558i	$-0.618450\pi$
$89$	4.51054	−	13.8820i	0.478116	−	1.47149i	0.841708	−	0.539932i	$-0.181550\pi$
$90$	0.539149	+	0.182690i	0.0568313	+	0.0192573i
$91$	1.51905	+	4.67515i	0.159239	+	0.490089i
$92$	1.40872	+	1.93894i	0.146869	+	0.202148i
$93$			2.32868i			0.241473i
$94$	2.89480	−	2.10319i	0.298576	−	0.216928i
$95$	5.49027	+	17.6477i	0.563289	+	1.81062i
$96$	−1.45950	−	1.06039i	−0.148960	−	0.108226i
$97$	0.819807	−	1.12837i	0.0832388	−	0.114568i	−0.765367	−	0.643594i	$-0.777443\pi$
$97$	0.819807	−	1.12837i	0.0832388	−	0.114568i	0.848606	+	0.529026i	$0.177443\pi$
$98$	0.951057	+	0.309017i	0.0960712	+	0.0312154i
$99$	−0.902687			−0.0907234
$100$	−1.42528	−	4.79256i	−0.142528	−	0.479256i
$101$	−0.416855			−0.0414786			−0.0207393	−	0.999785i	$-0.506602\pi$
$101$	−0.416855			−0.0414786			−0.0207393	+	0.999785i	$0.506602\pi$
$102$	5.11046	+	1.66049i	0.506011	+	0.164413i
$103$	−8.92238	+	12.2806i	−0.879148	+	1.21004i	0.0975080	+	0.995235i	$0.468913\pi$
$103$	−8.92238	+	12.2806i	−0.879148	+	1.21004i	−0.976656	+	0.214809i	$0.931087\pi$
$104$	−3.97692	−	2.88940i	−0.389969	−	0.283329i
$105$	3.29304	−	2.32997i	0.321368	−	0.227382i
$106$	−4.05689	+	2.94750i	−0.394040	+	0.286287i
$107$			15.1814i			1.46764i	0.679343	+	0.733820i	$0.262265\pi$
$107$			15.1814i			1.46764i	−0.679343	+	0.733820i	$0.737735\pi$
$108$	2.91122	+	4.00695i	0.280132	+	0.385569i
$109$	2.45223	+	7.54720i	0.234881	+	0.722891i	0.997137	+	0.0756146i	$0.0240919\pi$
$109$	2.45223	+	7.54720i	0.234881	+	0.722891i	−0.762256	+	0.647276i	$0.775908\pi$
$110$	4.57946	+	6.47233i	0.436634	+	0.617113i
$111$	0.378145	−	1.16381i	0.0358919	−	0.110464i
$112$	−0.951057	+	0.309017i	−0.0898664	+	0.0291994i
$113$	−0.792637	+	0.257543i	−0.0745650	+	0.0242276i	−0.346062	−	0.938212i	$-0.612481\pi$
$113$	−0.792637	+	0.257543i	−0.0745650	+	0.0242276i	0.271497	+	0.962439i	$0.412481\pi$
$114$	4.60781	−	14.1814i	0.431561	−	1.32821i
$115$	3.20414	−	4.29573i	0.298788	−	0.400579i
$116$	−0.959507	−	2.95306i	−0.0890880	−	0.274185i
$117$	−0.735586	−	1.01245i	−0.0680050	−	0.0936008i
$118$		−	9.47026i		−	0.871808i
$119$	2.40971	−	1.75075i	0.220897	−	0.160491i
$120$	−1.29461	+	3.82059i	−0.118181	+	0.348770i
$121$	−1.27219	−	0.924299i	−0.115653	−	0.0840272i
$122$	6.98418	−	9.61290i	0.632318	−	0.870311i
$123$	4.78279	+	1.55402i	0.431250	+	0.140121i
$124$	−1.29081			−0.115918
$125$	−9.28600	+	6.22658i	−0.830565	+	0.556922i
$126$	−0.254581			−0.0226799
$127$	−15.0573	−	4.89242i	−1.33612	−	0.434132i	−0.448121	−	0.893973i	$-0.647906\pi$
$127$	−15.0573	−	4.89242i	−1.33612	−	0.434132i	−0.888001	+	0.459841i	$0.847906\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−15.4067	−	11.1936i	−1.35649	−	0.985545i
$130$	−3.52760	+	10.4105i	−0.309391	+	0.913062i
$131$	0.614529	−	0.446481i	0.0536916	−	0.0390093i	−0.560616	−	0.828076i	$-0.689436\pi$
$131$	0.614529	−	0.446481i	0.0536916	−	0.0390093i	0.614307	+	0.789067i	$0.289436\pi$
$132$		−	6.39674i		−	0.556765i
$133$	−4.85829	−	6.68687i	−0.421267	−	0.579825i
$134$	−4.62422	−	14.2319i	−0.399472	−	1.22945i
$135$	6.62159	−	8.87743i	0.569896	−	0.764047i
$136$	−0.920426	+	2.83278i	−0.0789259	+	0.242909i
$137$	20.4769	−	6.65336i	1.74946	−	0.568435i	0.753438	−	0.657519i	$-0.228394\pi$
$137$	20.4769	−	6.65336i	1.74946	−	0.568435i	0.996024	+	0.0890845i	$0.0283941\pi$
$138$	−4.11206	+	1.33609i	−0.350042	+	0.113736i
$139$	−2.83462	+	8.72405i	−0.240429	+	0.739964i	0.755926	+	0.654657i	$0.227187\pi$
$139$	−2.83462	+	8.72405i	−0.240429	+	0.739964i	−0.996355	+	0.0853068i	$0.972813\pi$
$140$	1.29153	+	1.82537i	0.109154	+	0.154272i
$141$	1.99476	+	6.13924i	0.167989	+	0.517017i
$142$	−0.263881	−	0.363201i	−0.0221444	−	0.0304791i
$143$		−	17.4301i		−	1.45758i
$144$	0.205960	−	0.149639i	0.0171634	−	0.0124699i
$145$	−5.66781	+	4.01023i	−0.470686	+	0.333031i
$146$	−7.52425	−	5.46669i	−0.622711	−	0.452426i
$147$	−1.06039	+	1.45950i	−0.0874596	+	0.120378i
$148$	0.645111	+	0.209609i	0.0530278	+	0.0172298i
$149$	6.36425			0.521379			0.260690	−	0.965423i	$-0.416050\pi$
$149$	6.36425			0.521379			0.260690	+	0.965423i	$0.416050\pi$
$150$	9.01739	+	0.226343i	0.736267	+	0.0184808i
$151$	−7.50750			−0.610951			−0.305476	−	0.952200i	$-0.598815\pi$
$151$	−7.50750			−0.610951			−0.305476	+	0.952200i	$0.598815\pi$
$152$	7.86088	+	2.55416i	0.637602	+	0.207169i
$153$	−0.445709	+	0.613465i	−0.0360334	+	0.0495957i
$154$	−2.86859	−	2.08415i	−0.231158	−	0.167946i
$155$	0.857414	+	2.75605i	0.0688691	+	0.221371i
$156$	7.17454	−	5.21261i	0.574423	−	0.417343i
$157$		−	9.71859i		−	0.775628i	−0.921738	−	0.387814i	$-0.873230\pi$
$157$		−	9.71859i		−	0.775628i	0.921738	−	0.387814i	$-0.126770\pi$
$158$	1.14846	+	1.58072i	0.0913668	+	0.125756i
$159$	−2.79554	−	8.60378i	−0.221701	−	0.682324i
$160$	−2.11779	−	0.717612i	−0.167426	−	0.0567322i
$161$	−0.740608	+	2.27936i	−0.0583681	+	0.179638i
$162$	−9.22423	+	2.99713i	−0.724724	+	0.235477i
$163$	−3.26214	+	1.05993i	−0.255510	+	0.0830203i	−0.433971	−	0.900927i	$-0.642888\pi$
$163$	−3.26214	+	1.05993i	−0.255510	+	0.0830203i	0.178461	+	0.983947i	$0.442888\pi$
$164$	−0.861410	+	2.65115i	−0.0672648	+	0.207020i
$165$	−13.6579	+	4.24900i	−1.06326	+	0.330784i
$166$	−3.31981	−	10.2173i	−0.257667	−	0.793017i
$167$	−15.1001	−	20.7835i	−1.16848	−	1.60828i	−0.672950	−	0.739688i	$-0.734973\pi$
$167$	−15.1001	−	20.7835i	−1.16848	−	1.60828i	−0.495532	−	0.868590i	$-0.665027\pi$
$168$		−	1.80405i		−	0.139185i
$169$	9.03228	−	6.56233i	0.694790	−	0.504795i
$170$	6.65974	+	0.0835689i	0.510779	+	0.00640944i
$171$	1.70235	+	1.23683i	0.130182	+	0.0945827i
$172$	6.20474	−	8.54009i	0.473107	−	0.651176i
$173$	−16.6195	−	5.40001i	−1.26356	−	0.410555i	−0.400798	−	0.916167i	$-0.631267\pi$
$173$	−16.6195	−	5.40001i	−1.26356	−	0.410555i	−0.862761	+	0.505611i	$0.831267\pi$
$174$	5.60161			0.424657
$175$	3.03950	−	3.97007i	0.229765	−	0.300109i
$176$	3.54577			0.267273
$177$	16.2486	+	5.27949i	1.22132	+	0.396831i
$178$	−8.57956	+	11.8087i	−0.643065	+	0.885103i
$179$	10.2927	+	7.47810i	0.769314	+	0.558939i	0.901753	−	0.432252i	$-0.142281\pi$
$179$	10.2927	+	7.47810i	0.769314	+	0.558939i	−0.132439	+	0.991191i	$0.542281\pi$
$180$	−0.456307	−	0.340355i	−0.0340111	−	0.0253686i
$181$	7.49946	−	5.44868i	0.557431	−	0.404997i	−0.273087	−	0.961989i	$-0.588045\pi$
$181$	7.49946	−	5.44868i	0.557431	−	0.404997i	0.830518	+	0.556992i	$0.188045\pi$
$182$		−	4.91574i		−	0.364379i
$183$	12.5998	+	17.3421i	0.931403	+	1.28197i
$184$	−0.740608	−	2.27936i	−0.0545983	−	0.168036i
$185$	0.0190312	−	1.51663i	0.00139920	−	0.111505i
$186$	0.719601	−	2.21471i	0.0527637	−	0.162390i
$187$	−10.0444	+	3.26362i	−0.734519	+	0.238660i
$188$	−3.40304	+	1.10571i	−0.248192	+	0.0806425i
$189$	−1.53052	+	4.71045i	−0.111329	+	0.342635i
$190$	0.231901	−	18.4806i	0.0168239	−	1.34072i
$191$	1.89075	+	5.81914i	0.136810	+	0.421058i	0.995867	−	0.0908216i	$-0.0289493\pi$
$191$	1.89075	+	5.81914i	0.136810	+	0.421058i	−0.859057	+	0.511880i	$0.828949\pi$
$192$	1.06039	+	1.45950i	0.0765272	+	0.105331i
$193$		−	14.1804i		−	1.02073i	−0.859959	−	0.510363i	$-0.829511\pi$
$193$		−	14.1804i		−	1.02073i	0.859959	−	0.510363i	$-0.170489\pi$
$194$	−1.12837	+	0.819807i	−0.0810121	+	0.0588587i
$195$	−15.8953	−	11.8561i	−1.13828	−	0.849035i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	6.09182	−	8.38467i	0.434024	−	0.597383i	−0.534847	−	0.844949i	$-0.679631\pi$
$197$	6.09182	−	8.38467i	0.434024	−	0.597383i	0.968871	+	0.247566i	$0.0796307\pi$
$198$	0.858506	+	0.278946i	0.0610114	+	0.0198238i
$199$	−11.5816			−0.821000			−0.410500	−	0.911861i	$-0.634646\pi$
$199$	−11.5816			−0.821000			−0.410500	+	0.911861i	$0.634646\pi$
$200$	−0.125464	+	4.99843i	−0.00887164	+	0.353442i
$201$	26.9962			1.90417
$202$	0.396452	+	0.128815i	0.0278943	+	0.00906340i
$203$	1.82509	−	2.51202i	0.128096	−	0.176309i
$204$	−4.34722	−	3.15844i	−0.304366	−	0.221135i
$205$	6.23273	+	0.0782106i	0.435313	+	0.00546246i
$206$	12.2806	−	8.92238i	0.855630	−	0.621652i
$207$		−	0.610143i		−	0.0424079i
$208$	2.88940	+	3.97692i	0.200344	+	0.275750i
$209$	9.05646	+	27.8729i	0.626448	+	1.92801i
$210$	−3.85187	+	1.19833i	−0.265804	+	0.0826925i
$211$	3.80332	−	11.7054i	0.261832	−	0.805835i	−0.730575	−	0.682833i	$-0.760748\pi$
$211$	3.80332	−	11.7054i	0.261832	−	0.805835i	0.992406	−	0.123002i	$-0.0392522\pi$
$212$	4.76916	−	1.54959i	0.327547	−	0.106427i
$213$	0.770270	−	0.250276i	0.0527780	−	0.0171486i
$214$	4.69131	−	14.4384i	0.320691	−	0.986986i
$215$	−22.3557	−	7.57521i	−1.52464	−	0.516625i
$216$	−1.53052	−	4.71045i	−0.104139	−	0.320506i
$217$	−0.758719	−	1.04429i	−0.0515052	−	0.0708908i
$218$		−	7.93560i		−	0.537466i
$219$	13.5741	−	9.86215i	0.917252	−	0.666422i
$220$	−2.35526	−	7.57069i	−0.158792	−	0.510416i
$221$	−11.8455	−	8.60625i	−0.796814	−	0.578919i
$222$	−0.719274	+	0.989996i	−0.0482745	+	0.0664442i
$223$	24.1661	+	7.85204i	1.61828	+	0.525811i	0.971535	−	0.236895i	$-0.0761297\pi$
$223$	24.1661	+	7.85204i	1.61828	+	0.525811i	0.646745	+	0.762706i	$0.276130\pi$
$224$	1.00000			0.0668153
$225$	−0.423603	+	1.20035i	−0.0282402	+	0.0800235i
$226$	0.833428			0.0554388
$227$	−14.6980	−	4.77568i	−0.975544	−	0.316973i	−0.222492	−	0.974935i	$-0.571419\pi$
$227$	−14.6980	−	4.77568i	−0.975544	−	0.316973i	−0.753052	+	0.657961i	$0.771419\pi$
$228$	−8.76458	+	12.0634i	−0.580449	+	0.798919i
$229$	9.06829	+	6.58850i	0.599250	+	0.435380i	0.845612	−	0.533797i	$-0.179236\pi$
$229$	9.06829	+	6.58850i	0.599250	+	0.435380i	−0.246363	+	0.969178i	$0.579236\pi$
$230$	−4.37478	+	3.09534i	−0.288464	+	0.204101i
$231$	5.17507	−	3.75991i	0.340495	−	0.247384i
$232$			3.10503i			0.203855i
$233$	−5.59994	−	7.70765i	−0.366864	−	0.504945i	0.585181	−	0.810903i	$-0.301023\pi$
$233$	−5.59994	−	7.70765i	−0.366864	−	0.504945i	−0.952045	+	0.305958i	$0.901023\pi$
$234$	0.386721	+	1.19020i	0.0252807	+	0.0778061i
$235$	4.62129	+	6.53146i	0.301460	+	0.426066i
$236$	−2.92647	+	9.00675i	−0.190497	+	0.586290i
$237$	−3.35237	+	1.08925i	−0.217760	+	0.0707545i
$238$	−2.83278	+	0.920426i	−0.183622	+	0.0596623i
$239$	0.0153536	−	0.0472534i	0.000993139	−	0.00305657i	−0.950559	−	0.310545i	$-0.899488\pi$
$239$	0.0153536	−	0.0472534i	0.000993139	−	0.00305657i	0.951552	+	0.307488i	$0.0994885\pi$
$240$	2.41187	−	3.23354i	0.155686	−	0.208724i
$241$	7.42612	+	22.8553i	0.478359	+	1.47224i	0.841374	+	0.540453i	$0.181747\pi$
$241$	7.42612	+	22.8553i	0.478359	+	1.47224i	−0.363016	+	0.931783i	$0.618253\pi$
$242$	0.924299	+	1.27219i	0.0594162	+	0.0817794i
$243$		−	2.63873i		−	0.169275i
$244$	−9.61290	+	6.98418i	−0.615403	+	0.447116i
$245$	−0.717612	+	2.11779i	−0.0458466	+	0.135301i
$246$	−4.06848	−	2.95593i	−0.259397	−	0.188463i
$247$	−23.8821	+	32.8709i	−1.51958	+	2.09153i
$248$	1.22763	+	0.398882i	0.0779547	+	0.0253290i
$249$	19.3811			1.22823
$250$	10.7556	−	3.05230i	0.680245	−	0.193044i
$251$	−26.8745			−1.69630			−0.848152	−	0.529754i	$-0.822284\pi$
$251$	−26.8745			−1.69630			−0.848152	+	0.529754i	$0.822284\pi$
$252$	0.242121	+	0.0786699i	0.0152522	+	0.00495574i
$253$	4.99500	−	6.87503i	0.314033	−	0.432229i
$254$	12.8085	+	9.30594i	0.803679	+	0.583907i
$255$	−3.85606	+	11.3799i	−0.241476	+	0.712634i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	3.07433i		−	0.191772i	−0.995392	−	0.0958858i	$-0.969432\pi$
$257$		−	3.07433i		−	0.191772i	0.995392	−	0.0958858i	$-0.0305684\pi$
$258$	11.1936	+	15.4067i	0.696885	+	0.959180i
$259$	0.209609	+	0.645111i	0.0130245	+	0.0400852i
$260$	6.57197	−	8.81089i	0.407576	−	0.546428i
$261$	−0.244272	+	0.751793i	−0.0151201	+	0.0465348i
$262$	−0.722422	+	0.234729i	−0.0446314	+	0.0145016i
$263$	−19.7404	+	6.41405i	−1.21725	+	0.395507i	−0.846078	−	0.533059i	$-0.821042\pi$
$263$	−19.7404	+	6.41405i	−1.21725	+	0.395507i	−0.371168	+	0.928566i	$0.621042\pi$
$264$	−1.97670	+	6.08366i	−0.121658	+	0.374423i
$265$	−6.47647	−	9.15346i	−0.397847	−	0.562293i
$266$	2.55416	+	7.86088i	0.156605	+	0.481982i
$267$	−15.4779	−	21.3035i	−0.947233	−	1.30375i
$268$			14.9643i			0.914089i
$269$	−23.6276	+	17.1664i	−1.44060	+	1.04666i	−0.452683	+	0.891672i	$0.649533\pi$
$269$	−23.6276	+	17.1664i	−1.44060	+	1.04666i	−0.987917	+	0.154985i	$0.950467\pi$
$270$	−9.04078	+	6.39675i	−0.550205	+	0.389294i
$271$	−4.40222	−	3.19840i	−0.267416	−	0.194289i	0.445994	−	0.895036i	$-0.352850\pi$
$271$	−4.40222	−	3.19840i	−0.267416	−	0.194289i	−0.713410	+	0.700747i	$0.752850\pi$
$272$	1.75075	−	2.40971i	0.106155	−	0.146110i
$273$	8.43418	+	2.74043i	0.510460	+	0.165858i
$274$	−21.5307			−1.30072
$275$	−14.5999	+	10.0576i	−0.880409	+	0.606495i
$276$	4.32368			0.260255
$277$	−7.10540	−	2.30868i	−0.426922	−	0.138715i	0.0876719	−	0.996149i	$-0.472057\pi$
$277$	−7.10540	−	2.30868i	−0.426922	−	0.138715i	−0.514594	+	0.857434i	$0.672057\pi$
$278$	5.39176	−	7.42112i	0.323376	−	0.445089i
$279$	0.265856	+	0.193155i	0.0159164	+	0.0115639i
$280$	−0.664245	−	2.13513i	−0.0396962	−	0.127598i
$281$	−24.6519	+	17.9106i	−1.47061	+	1.06846i	−0.490171	+	0.871626i	$0.663066\pi$
$281$	−24.6519	+	17.9106i	−1.47061	+	1.06846i	−0.980437	+	0.196833i	$0.936934\pi$
$282$		−	6.45518i		−	0.384400i
$283$	−3.65770	−	5.03439i	−0.217428	−	0.299264i	0.686345	−	0.727276i	$-0.259214\pi$
$283$	−3.65770	−	5.03439i	−0.217428	−	0.299264i	−0.903773	+	0.428012i	$0.859214\pi$
$284$	0.138730	+	0.426968i	0.00823213	+	0.0253359i
$285$	31.5788	+	10.7005i	1.87057	+	0.633841i
$286$	−5.38620	+	16.5770i	−0.318493	+	0.980219i
$287$	−2.65115	+	0.861410i	−0.156492	+	0.0508474i
$288$	−0.242121	+	0.0786699i	−0.0142671	+	0.00463567i
$289$	2.51175	−	7.73036i	0.147750	−	0.454727i
$290$	6.62964	−	2.06250i	0.389306	−	0.121114i
$291$	−0.777540	−	2.39302i	−0.0455802	−	0.140281i
$292$	5.46669	+	7.52425i	0.319914	+	0.440323i
$293$		−	11.4063i		−	0.666366i	−0.942862	−	0.333183i	$-0.891877\pi$
$293$		−	11.4063i		−	0.666366i	0.942862	−	0.333183i	$-0.108123\pi$
$294$	1.45950	−	1.06039i	0.0851200	−	0.0618433i
$295$	21.1745	+	0.265705i	1.23283	+	0.0154700i
$296$	−0.548764	−	0.398701i	−0.0318963	−	0.0231740i
$297$	10.3225	−	14.2077i	0.598974	−	0.824416i
$298$	−6.05276	−	1.96666i	−0.350627	−	0.113926i
$299$	11.7813			0.681333
$300$	−8.50610	−	3.00179i	−0.491100	−	0.173308i
$301$	10.5561			0.608446
$302$	7.14005	+	2.31994i	0.410864	+	0.133498i
$303$	−0.442029	+	0.608401i	−0.0253939	+	0.0349517i
$304$	−6.68687	−	4.85829i	−0.383518	−	0.278642i
$305$	21.2975	+	15.8856i	1.21949	+	0.909606i
$306$	0.613465	−	0.445709i	0.0350695	−	0.0254795i
$307$			17.7869i			1.01515i	0.861607	+	0.507576i	$0.169458\pi$
$307$			17.7869i			1.01515i	−0.861607	+	0.507576i	$0.830542\pi$
$308$	2.08415	+	2.86859i	0.118756	+	0.163453i
$309$	8.46237	+	26.0445i	0.481407	+	1.48162i
$310$	0.0362160	−	2.88611i	0.00205693	−	0.163920i
$311$	8.44402	−	25.9880i	0.478816	−	1.47364i	−0.361925	−	0.932207i	$-0.617880\pi$
$311$	8.44402	−	25.9880i	0.478816	−	1.47364i	0.840741	−	0.541437i	$-0.182120\pi$
$312$	−8.43418	+	2.74043i	−0.477491	+	0.155146i
$313$	−20.9971	+	6.82236i	−1.18682	+	0.385623i	−0.834898	−	0.550405i	$-0.814473\pi$
$313$	−20.9971	+	6.82236i	−1.18682	+	0.385623i	−0.351927	+	0.936028i	$0.614473\pi$
$314$	−3.00321	+	9.24293i	−0.169481	+	0.521609i
$315$	0.00714273	−	0.569216i	0.000402447	−	0.0320717i
$316$	−0.603782	−	1.85825i	−0.0339654	−	0.104535i
$317$	−13.9183	−	19.1569i	−0.781730	−	1.07596i	−0.995089	−	0.0989856i	$-0.968440\pi$
$317$	−13.9183	−	19.1569i	−0.781730	−	1.07596i	0.213358	−	0.976974i	$-0.431560\pi$
$318$			9.04655i			0.507305i
$319$	−8.90706	+	6.47136i	−0.498700	+	0.362326i
$320$	1.79238	+	1.33692i	0.100197	+	0.0747363i
$321$	22.1573	+	16.0982i	1.23670	+	0.898515i
$322$	1.40872	−	1.93894i	0.0785049	−	0.108053i
$323$	23.4141	+	7.60771i	1.30280	+	0.423304i
$324$	9.69893			0.538830
$325$	−23.1778	−	8.17941i	−1.28567	−	0.453712i
$326$	3.43001			0.189971
$327$	13.6155	+	4.42394i	0.752938	+	0.244645i
$328$	1.63850	−	2.25520i	0.0904709	−	0.124523i
$329$	−2.89480	−	2.10319i	−0.159595	−	0.115953i
$330$	14.3024	+	0.179472i	0.787322	+	0.00987961i
$331$	18.4215	−	13.3840i	1.01254	−	0.735651i	0.0477970	−	0.998857i	$-0.484780\pi$
$331$	18.4215	−	13.3840i	1.01254	−	0.735651i	0.964740	+	0.263206i	$0.0847799\pi$
$332$			10.7431i			0.589605i
$333$	−0.101502	−	0.139705i	−0.00556225	−	0.00765578i
$334$	7.93860	+	24.4325i	0.434381	+	1.33689i
$335$	31.9507	−	9.93995i	1.74565	−	0.543077i
$336$	−0.557481	+	1.71575i	−0.0304131	+	0.0936018i
$337$	−3.55568	+	1.15531i	−0.193690	+	0.0629337i	−0.404256	−	0.914646i	$-0.632469\pi$
$337$	−3.55568	+	1.15531i	−0.193690	+	0.0629337i	0.210566	+	0.977580i	$0.432469\pi$
$338$	−10.6181	+	3.45002i	−0.577547	+	0.187656i
$339$	−0.464620	+	1.42995i	−0.0252347	+	0.0776644i
$340$	−6.30796	−	2.13745i	−0.342097	−	0.115920i
$341$	1.41435	+	4.35291i	0.0765911	+	0.235723i
$342$	−1.23683	−	1.70235i	−0.0668801	−	0.0920525i
$343$		−	1.00000i		−	0.0539949i
$344$	−8.54009	+	6.20474i	−0.460451	+	0.334537i
$345$	−2.87198	−	9.23161i	−0.154622	−	0.497013i
$346$	14.1374	+	10.2714i	0.760032	+	0.552196i
$347$	2.50360	−	3.44591i	0.134400	−	0.184986i	−0.736512	−	0.676424i	$-0.763529\pi$
$347$	2.50360	−	3.44591i	0.134400	−	0.184986i	0.870913	+	0.491438i	$0.163529\pi$
$348$	−5.32745	−	1.73099i	−0.285581	−	0.0927910i
$349$	−16.3730			−0.876426			−0.438213	−	0.898871i	$-0.644388\pi$
$349$	−16.3730			−0.876426			−0.438213	+	0.898871i	$0.644388\pi$
$350$	−4.11756	+	2.83650i	−0.220093	+	0.151617i
$351$	24.3470			1.29955
$352$	−3.37223	−	1.09570i	−0.179741	−	0.0584012i
$353$	3.56901	−	4.91232i	0.189959	−	0.261456i	−0.703405	−	0.710789i	$-0.748338\pi$
$353$	3.56901	−	4.91232i	0.189959	−	0.261456i	0.893365	+	0.449333i	$0.148338\pi$
$354$	−13.8219	−	10.0422i	−0.734625	−	0.533736i
$355$	0.819481	−	0.579818i	0.0434935	−	0.0307736i
$356$	11.8087	−	8.57956i	0.625862	−	0.454716i
$357$		−	5.37346i		−	0.284394i
$358$	−7.47810	−	10.2927i	−0.395230	−	0.543987i
$359$	2.06089	+	6.34277i	0.108770	+	0.334759i	0.990597	−	0.136814i	$-0.0436864\pi$
$359$	2.06089	+	6.34277i	0.108770	+	0.334759i	−0.881827	+	0.471573i	$0.843686\pi$
$360$	0.328798	+	0.464704i	0.0173292	+	0.0244920i
$361$	15.2399	−	46.9035i	0.802098	−	2.46860i
$362$	−8.81615	+	2.86454i	−0.463366	+	0.150557i
$363$	−2.69804	+	0.876645i	−0.141610	+	0.0460119i
$364$	−1.51905	+	4.67515i	−0.0796197	+	0.245044i
$365$	12.4340	−	16.6700i	0.650827	−	0.872549i
$366$	−6.62410	−	20.3869i	−0.346247	−	1.06564i
$367$	4.58400	+	6.30934i	0.239283	+	0.329345i	0.911722	−	0.410808i	$-0.134753\pi$
$367$	4.58400	+	6.30934i	0.239283	+	0.329345i	−0.672439	+	0.740153i	$0.734753\pi$
$368$			2.39666i			0.124934i
$369$	0.574131	−	0.417131i	0.0298881	−	0.0217150i
$370$	−0.486763	+	1.43652i	−0.0253056	+	0.0746810i
$371$	4.05689	+	2.94750i	0.210623	+	0.153027i
$372$	−1.36876	+	1.88394i	−0.0709671	+	0.0976778i
$373$	−0.635525	−	0.206495i	−0.0329063	−	0.0106919i	0.292518	−	0.956260i	$-0.405507\pi$
$373$	−0.635525	−	0.206495i	−0.0329063	−	0.0106919i	−0.325424	+	0.945568i	$0.605507\pi$
$374$	10.5613			0.546112
$375$	−0.759077	+	20.1556i	−0.0391986	+	1.04083i
$376$	3.57817			0.184530
$377$	−14.5165	−	4.71669i	−0.747636	−	0.242922i
$378$	2.91122	−	4.00695i	0.149737	−	0.206095i
$379$	0.792970	+	0.576127i	0.0407322	+	0.0295936i	0.607965	−	0.793964i	$-0.291986\pi$
$379$	0.792970	+	0.576127i	0.0407322	+	0.0295936i	−0.567233	+	0.823557i	$0.691986\pi$
$380$	−5.93137	+	17.5044i	−0.304273	+	0.897958i
$381$	−23.1072	+	16.7883i	−1.18382	+	0.860093i
$382$		−	6.11861i		−	0.313055i
$383$	−15.3246	−	21.0925i	−0.783050	−	1.07778i	−0.994939	−	0.100482i	$-0.967962\pi$
$383$	−15.3246	−	21.0925i	−0.783050	−	1.07778i	0.211889	−	0.977294i	$-0.432038\pi$
$384$	−0.557481	−	1.71575i	−0.0284488	−	0.0875565i
$385$	4.74043	−	6.35539i	0.241594	−	0.323900i
$386$	−4.38198	+	13.4863i	−0.223037	+	0.686436i
$387$	−2.55586	+	0.830450i	−0.129922	+	0.0422141i
$388$	1.32648	−	0.430998i	0.0673416	−	0.0218806i
$389$	−1.69569	+	5.21878i	−0.0859747	+	0.264603i	−0.984797	−	0.173711i	$-0.944424\pi$
$389$	−1.69569	+	5.21878i	−0.0859747	+	0.264603i	0.898822	+	0.438314i	$0.144424\pi$
$390$	11.4535	+	16.1877i	0.579972	+	0.819699i
$391$	−2.20594	−	6.78920i	−0.111559	−	0.343345i
$392$	0.587785	+	0.809017i	0.0296876	+	0.0408615i
$393$		−	1.37035i		−	0.0691251i
$394$	−8.38467	+	6.09182i	−0.422414	+	0.306901i
$395$	−3.56655	+	2.52349i	−0.179452	+	0.126970i
$396$	−0.730289	−	0.530586i	−0.0366984	−	0.0266629i
$397$	14.4134	−	19.8384i	0.723390	−	0.995660i	−0.276015	−	0.961153i	$-0.589014\pi$
$397$	14.4134	−	19.8384i	0.723390	−	0.995660i	0.999404	−	0.0345070i	$-0.0109861\pi$
$398$	11.0148	+	3.57892i	0.552121	+	0.179395i
$399$	−14.9112			−0.746494
$400$	1.66392	−	4.71501i	0.0831961	−	0.235751i
$401$	−27.8559			−1.39106			−0.695528	−	0.718499i	$-0.744829\pi$
$401$	−27.8559			−1.39106			−0.695528	+	0.718499i	$0.744829\pi$
$402$	−25.6750	−	8.34230i	−1.28055	−	0.416076i
$403$	−3.72966	+	5.13344i	−0.185788	+	0.255715i
$404$	−0.337243	−	0.245021i	−0.0167784	−	0.0121903i
$405$	−6.44247	−	20.7085i	−0.320129	−	1.02901i
$406$	−2.51202	+	1.82509i	−0.124670	+	0.0905777i
$407$		−	2.40513i		−	0.119218i
$408$	3.15844	+	4.34722i	0.156366	+	0.215219i
$409$	12.4701	+	38.3791i	0.616608	+	1.89772i	0.372868	+	0.927885i	$0.378375\pi$
$409$	12.4701	+	38.3791i	0.616608	+	1.89772i	0.243741	+	0.969840i	$0.421625\pi$
$410$	−5.90351	−	2.00040i	−0.291553	−	0.0987928i
$411$	12.0030	−	36.9413i	0.592062	−	1.82218i
$412$	−14.4367	+	4.69077i	−0.711246	+	0.231098i
$413$	−9.00675	+	2.92647i	−0.443193	+	0.144002i
$414$	−0.188545	+	0.580281i	−0.00926646	+	0.0285192i
$415$	22.9379	−	7.13606i	1.12598	−	0.350295i
$416$	−1.51905	−	4.67515i	−0.0744774	−	0.229218i
$417$	9.72698	+	13.3880i	0.476332	+	0.655615i
$418$		−	29.3073i		−	1.43347i
$419$	−5.18501	+	3.76713i	−0.253304	+	0.184036i	−0.707190	−	0.707024i	$-0.750037\pi$
$419$	−5.18501	+	3.76713i	−0.253304	+	0.184036i	0.453886	+	0.891060i	$0.350037\pi$
$420$	4.03365	+	0.0506157i	0.196822	+	0.00246980i
$421$	29.5757	+	21.4880i	1.44143	+	1.04726i	0.987741	+	0.156101i	$0.0498925\pi$
$421$	29.5757	+	21.4880i	1.44143	+	1.04726i	0.453690	+	0.891160i	$0.350107\pi$
$422$	−7.23435	+	9.95723i	−0.352163	+	0.484711i
$423$	0.866349	+	0.281494i	0.0421233	+	0.0136867i
$424$	−5.01459			−0.243530
$425$	−0.373702	+	14.8881i	−0.0181272	+	0.722179i
$426$	−0.809910			−0.0392402
$427$	−11.3006	−	3.67180i	−0.546876	−	0.177691i
$428$	−8.92340	+	12.2820i	−0.431329	+	0.593673i
$429$	−25.4393	−	18.4827i	−1.22822	−	0.892355i
$430$	18.9206	+	14.1127i	0.912434	+	0.680577i
$431$	−10.7363	+	7.80035i	−0.517147	+	0.375729i	−0.815528	−	0.578717i	$-0.803553\pi$
$431$	−10.7363	+	7.80035i	−0.517147	+	0.375729i	0.298381	+	0.954447i	$0.403553\pi$
$432$			4.95286i			0.238295i
$433$	1.05408	+	1.45081i	0.0506557	+	0.0697216i	0.833593	−	0.552378i	$-0.186280\pi$
$433$	1.05408	+	1.45081i	0.0506557	+	0.0697216i	−0.782938	+	0.622100i	$0.786280\pi$
$434$	0.398882	+	1.22763i	0.0191469	+	0.0589282i
$435$	−0.157163	+	12.5246i	−0.00753541	+	0.600509i
$436$	−2.45223	+	7.54720i	−0.117441	+	0.361445i
$437$	−18.8398	+	6.12144i	−0.901232	+	0.292828i
$438$	−15.9573	+	5.18484i	−0.762469	+	0.247741i
$439$	6.59731	−	20.3044i	0.314873	−	0.969078i	−0.660934	−	0.750444i	$-0.729840\pi$
$439$	6.59731	−	20.3044i	0.314873	−	0.969078i	0.975807	−	0.218634i	$-0.0701602\pi$
$440$	−0.0994831	+	7.92797i	−0.00474267	+	0.377951i
$441$	0.0786699	+	0.242121i	0.00374618	+	0.0115296i
$442$	8.60625	+	11.8455i	0.409358	+	0.563432i
$443$		−	2.55954i		−	0.121607i	−0.998150	−	0.0608036i	$-0.980634\pi$
$443$		−	2.55954i		−	0.121607i	0.998150	−	0.0608036i	$-0.0193663\pi$
$444$	0.989996	−	0.719274i	0.0469831	−	0.0341352i
$445$	−26.1624	−	19.5143i	−1.24022	−	0.925066i
$446$	−20.5569	−	14.9355i	−0.973397	−	0.707215i
$447$	6.74859	−	9.28864i	0.319197	−	0.439338i
$448$	−0.951057	−	0.309017i	−0.0449332	−	0.0145997i
$449$	23.5519			1.11148			0.555741	−	0.831355i	$-0.312435\pi$
$449$	23.5519			1.11148			0.555741	+	0.831355i	$0.312435\pi$
$450$	0.773800	−	1.01070i	0.0364773	−	0.0476450i
$451$	9.88413			0.465425
$452$	−0.792637	−	0.257543i	−0.0372825	−	0.0121138i
$453$	−7.96089	+	10.9572i	−0.374035	+	0.514815i
$454$	12.5029	+	9.08389i	0.586790	+	0.426328i
$455$	10.9911	+	0.137920i	0.515269	+	0.00646579i
$456$	12.0634	−	8.76458i	0.564921	−	0.410439i
$457$			2.51450i			0.117624i	0.998269	+	0.0588118i	$0.0187312\pi$
$457$			2.51450i			0.117624i	−0.998269	+	0.0588118i	$0.981269\pi$
$458$	−6.58850	−	9.06829i	−0.307860	−	0.423733i
$459$	−4.55874	−	14.0304i	−0.212784	−	0.654881i
$460$	5.11717	−	1.59197i	0.238589	−	0.0742259i
$461$	−2.48264	+	7.64078i	−0.115628	+	0.355866i	−0.992077	−	0.125627i	$-0.959906\pi$
$461$	−2.48264	+	7.64078i	−0.115628	+	0.355866i	0.876449	+	0.481494i	$0.159906\pi$
$462$	−6.08366	+	1.97670i	−0.283037	+	0.0919644i
$463$	−12.4700	+	4.05174i	−0.579529	+	0.188300i	−0.584090	−	0.811689i	$-0.698548\pi$
$463$	−12.4700	+	4.05174i	−0.579529	+	0.188300i	0.00456056	+	0.999990i	$0.498548\pi$
$464$	0.959507	−	2.95306i	0.0445440	−	0.137092i
$465$	4.93165	+	1.67109i	0.228700	+	0.0774949i
$466$	2.94406	+	9.06089i	0.136381	+	0.419737i
$467$	2.41338	+	3.32173i	0.111678	+	0.153711i	0.861197	−	0.508271i	$-0.169715\pi$
$467$	2.41338	+	3.32173i	0.111678	+	0.153711i	−0.749519	+	0.661983i	$0.769715\pi$
$468$		−	1.25145i		−	0.0578485i
$469$	−12.1064	+	8.79578i	−0.559020	+	0.406152i
$470$	−2.37678	−	7.63985i	−0.109633	−	0.352400i
$471$	−14.1843	−	10.3055i	−0.653579	−	0.474853i
$472$	5.56648	−	7.66160i	0.256218	−	0.352654i
$473$	−35.5977	−	11.5664i	−1.63679	−	0.531824i
$474$	3.52489			0.161904
$475$	41.3141	+	1.03701i	1.89562	+	0.0475814i
$476$	2.97856			0.136522
$477$	−1.21414	−	0.394497i	−0.0555915	−	0.0180628i
$478$	−0.0292042	+	0.0401961i	−0.00133577	+	0.00183853i
$479$	21.7384	+	15.7939i	0.993254	+	0.721641i	0.960631	−	0.277827i	$-0.0896141\pi$
$479$	21.7384	+	15.7939i	0.993254	+	0.721641i	0.0326226	+	0.999468i	$0.489614\pi$
$480$	−3.29304	+	2.32997i	−0.150306	+	0.106348i
$481$	2.69758	−	1.95991i	0.122999	−	0.0893641i
$482$		−	24.0314i		−	1.09460i
$483$	2.54139	+	3.49793i	0.115637	+	0.159161i
$484$	−0.485933	−	1.49555i	−0.0220879	−	0.0679794i
$485$	−1.80134	−	2.54591i	−0.0817947	−	0.115604i
$486$	−0.815413	+	2.50958i	−0.0369879	+	0.113837i
$487$	1.96012	−	0.636882i	0.0888216	−	0.0288599i	−0.264269	−	0.964449i	$-0.585131\pi$
$487$	1.96012	−	0.636882i	0.0888216	−	0.0288599i	0.353091	+	0.935589i	$0.385131\pi$
$488$	11.3006	−	3.67180i	0.511556	−	0.166215i
$489$	−1.91217	+	5.88504i	−0.0864711	+	0.266131i
$490$	1.33692	−	1.79238i	0.0603960	−	0.0809716i
$491$	−8.82730	−	27.1676i	−0.398370	−	1.22606i	−0.926305	−	0.376773i	$-0.877034\pi$
$491$	−8.82730	−	27.1676i	−0.398370	−	1.22606i	0.527935	−	0.849285i	$-0.322966\pi$
$492$	2.95593	+	4.06848i	0.133263	+	0.183421i
$493$			9.24852i			0.416532i
$494$	32.8709	−	23.8821i	1.47893	−	1.07451i
$495$	−0.647779	+	1.91170i	−0.0291155	+	0.0859245i
$496$	−1.04429	−	0.758719i	−0.0468899	−	0.0340675i
$497$	−0.263881	+	0.363201i	−0.0118367	+	0.0162918i
$498$	−18.4325	−	5.98908i	−0.825980	−	0.268377i
$499$	9.21735			0.412625			0.206313	−	0.978486i	$-0.433854\pi$
$499$	9.21735			0.412625			0.206313	+	0.978486i	$0.433854\pi$
$500$	−11.1724	−	0.420764i	−0.499646	−	0.0188171i
$501$	−46.3457			−2.07057
$502$	25.5592	+	8.30468i	1.14076	+	0.370656i
$503$	−9.56267	+	13.1619i	−0.426379	+	0.586860i	−0.967117	−	0.254331i	$-0.918145\pi$
$503$	−9.56267	+	13.1619i	−0.426379	+	0.586860i	0.540739	+	0.841191i	$0.318145\pi$
$504$	−0.205960	−	0.149639i	−0.00917420	−	0.00666545i
$505$	−0.299140	+	0.882811i	−0.0133116	+	0.0392846i
$506$	−6.87503	+	4.99500i	−0.305632	+	0.222055i
$507$		−	20.1413i		−	0.894506i
$508$	−9.30594	−	12.8085i	−0.412884	−	0.568287i
$509$	−5.66952	−	17.4490i	−0.251297	−	0.773413i	−0.994537	−	0.104388i	$-0.966712\pi$
$509$	−5.66952	−	17.4490i	−0.251297	−	0.773413i	0.743240	−	0.669025i	$-0.233288\pi$
$510$	7.18390	−	9.63130i	0.318108	−	0.426481i
$511$	−2.87401	+	8.84528i	−0.127139	+	0.391292i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−38.9339	+	12.6504i	−1.71897	+	0.558528i
$514$	−0.950021	+	2.92386i	−0.0419036	+	0.128966i
$515$	19.6049	+	27.7084i	0.863896	+	1.22098i
$516$	−5.88484	−	18.1117i	−0.259066	−	0.797322i
$517$	7.45745	+	10.2643i	0.327978	+	0.451423i
$518$		−	0.678310i		−	0.0298032i
$519$	−25.5045	+	18.5301i	−1.11953	+	0.813383i
$520$	−8.97303	+	6.34881i	−0.393493	+	0.278414i
$521$	−15.5585	−	11.3039i	−0.681630	−	0.495233i	0.192268	−	0.981342i	$-0.438416\pi$
$521$	−15.5585	−	11.3039i	−0.681630	−	0.495233i	−0.873898	+	0.486109i	$0.838416\pi$
$522$	0.464633	−	0.639513i	0.0203364	−	0.0279907i
$523$	33.6685	+	10.9396i	1.47222	+	0.478353i	0.931778	−	0.363028i	$-0.118257\pi$
$523$	33.6685	+	10.9396i	1.47222	+	0.478353i	0.540442	+	0.841381i	$0.318257\pi$
$524$	0.759600			0.0331833
$525$	−2.57126	−	8.64599i	−0.112219	−	0.377342i
$526$	20.7563			0.905018
$527$	3.65658	+	1.18809i	0.159283	+	0.0517542i
$528$	3.75991	−	5.17507i	0.163629	−	0.225216i
$529$	−13.9604	−	10.1428i	−0.606975	−	0.440993i
$530$	3.33092	+	10.7068i	0.144686	+	0.465074i
$531$	1.95050	−	1.41712i	0.0846444	−	0.0614978i
$532$		−	8.26542i		−	0.358352i
$533$	8.05443	+	11.0860i	0.348876	+	0.480187i
$534$	8.13722	+	25.0438i	0.352132	+	1.08375i
$535$	32.1510	+	10.8944i	1.39001	+	0.471004i
$536$	4.62422	−	14.2319i	0.199736	−	0.614723i
$537$	21.8286	−	7.09255i	0.941975	−	0.306066i
$538$	27.7759	−	9.02494i	1.19750	−	0.389093i
$539$	−1.09570	+	3.37223i	−0.0471953	+	0.145252i
$540$	10.5750	−	3.28991i	0.455076	−	0.141575i
$541$	−13.4885	−	41.5135i	−0.579918	−	1.78480i	−0.618786	−	0.785559i	$-0.712375\pi$
$541$	−13.4885	−	41.5135i	−0.579918	−	1.78480i	0.0388686	−	0.999244i	$-0.487625\pi$
$542$	3.19840	+	4.40222i	0.137383	+	0.189092i
$543$		−	16.7232i		−	0.717662i
$544$	−2.40971	+	1.75075i	−0.103315	+	0.0750629i
$545$	17.7431	+	0.222647i	0.760032	+	0.00953717i
$546$	−7.17454	−	5.21261i	−0.307042	−	0.223079i
$547$	8.88392	−	12.2277i	0.379849	−	0.522817i	−0.575696	−	0.817664i	$-0.695269\pi$
$547$	8.88392	−	12.2277i	0.379849	−	0.522817i	0.955545	+	0.294847i	$0.0952687\pi$
$548$	20.4769	+	6.65336i	0.874731	+	0.284217i
$549$	3.02498			0.129103
$550$	16.9933	−	5.05370i	0.724598	−	0.215491i
$551$	25.6644			1.09334
$552$	−4.11206	−	1.33609i	−0.175021	−	0.0568678i
$553$	1.14846	−	1.58072i	0.0488376	−	0.0672192i
$554$	6.04421	+	4.39138i	0.256794	+	0.186572i
$555$	−2.19334	−	1.63600i	−0.0931022	−	0.0694441i
$556$	−7.42112	+	5.39176i	−0.314726	+	0.228661i
$557$			13.8970i			0.588836i	0.955677	+	0.294418i	$0.0951257\pi$
$557$			13.8970i			0.588836i	−0.955677	+	0.294418i	$0.904874\pi$
$558$	−0.193155	−	0.265856i	−0.00817692	−	0.0112546i
$559$	−16.0353	−	49.3515i	−0.678220	−	2.08735i
$560$	−0.0280568	+	2.23589i	−0.00118562	+	0.0944837i
$561$	−5.88772	+	18.1205i	−0.248580	+	0.765050i
$562$	28.9800	−	9.41618i	1.22245	−	0.397198i
$563$	25.3785	−	8.24597i	1.06958	−	0.347526i	0.279253	−	0.960217i	$-0.409913\pi$
$563$	25.3785	−	8.24597i	1.06958	−	0.347526i	0.790322	+	0.612691i	$0.209913\pi$
$564$	−1.99476	+	6.13924i	−0.0839945	+	0.258508i
$565$	−0.0233833	+	1.86345i	−0.000983743	+	0.0783961i
$566$	1.92297	+	5.91828i	0.0808283	+	0.248764i
$567$	5.70089	+	7.84660i	0.239415	+	0.329526i
$568$		−	0.448941i		−	0.0188371i
$569$	6.64162	−	4.82542i	0.278431	−	0.202292i	−0.439802	−	0.898095i	$-0.644951\pi$
$569$	6.64162	−	4.82542i	0.278431	−	0.202292i	0.718233	+	0.695803i	$0.244951\pi$
$570$	−26.7266	−	19.9351i	−1.11945	−	0.834990i
$571$	−4.94250	−	3.59094i	−0.206837	−	0.150276i	0.479544	−	0.877518i	$-0.340802\pi$
$571$	−4.94250	−	3.59094i	−0.206837	−	0.150276i	−0.686382	+	0.727242i	$0.740802\pi$
$572$	10.2452	−	14.1013i	0.428372	−	0.589603i
$573$	10.4980	+	3.41100i	0.438560	+	0.142497i
$574$	2.78758			0.116351
$575$	−6.79811	−	9.86837i	−0.283501	−	0.411540i
$576$	0.254581			0.0106075
$577$	10.7169	+	3.48213i	0.446150	+	0.144963i	0.523471	−	0.852043i	$-0.324637\pi$
$577$	10.7169	+	3.48213i	0.446150	+	0.144963i	−0.0773213	+	0.997006i	$0.524637\pi$
$578$	−4.77762	+	6.57584i	−0.198723	+	0.273519i
$579$	−20.6963	−	15.0367i	−0.860109	−	0.624906i
$580$	−6.94251	−	0.0871172i	−0.288272	−	0.00361734i
$581$	−8.69136	+	6.31464i	−0.360578	+	0.261976i
$582$			2.51617i			0.104299i
$583$	−10.4512	−	14.3848i	−0.432844	−	0.595758i
$584$	−2.87401	−	8.84528i	−0.118927	−	0.366020i
$585$	−2.67202	+	0.831272i	−0.110474	+	0.0343689i
$586$	−3.52475	+	10.8481i	−0.145606	+	0.448130i
$587$	4.04706	−	1.31497i	0.167040	−	0.0542747i	−0.224303	−	0.974519i	$-0.572011\pi$
$587$	4.04706	−	1.31497i	0.167040	−	0.0542747i	0.391343	+	0.920245i	$0.372011\pi$
$588$	−1.71575	+	0.557481i	−0.0707563	+	0.0229901i
$589$	3.29693	−	10.1469i	0.135848	−	0.418096i
$590$	−20.0560	−	6.79598i	−0.825693	−	0.279786i
$591$	−5.77774	−	17.7821i	−0.237665	−	0.731456i
$592$	0.398701	+	0.548764i	0.0163865	+	0.0225541i
$593$			34.6257i			1.42191i	0.703239	+	0.710954i	$0.251736\pi$
$593$			34.6257i			1.42191i	−0.703239	+	0.710954i	$0.748264\pi$
$594$	−14.2077	+	10.3225i	−0.582950	+	0.423538i
$595$	−1.97849	−	6.35961i	−0.0811103	−	0.260719i
$596$	5.14878	+	3.74081i	0.210902	+	0.153230i
$597$	−12.2811	+	16.9034i	−0.502630	+	0.691811i
$598$	−11.2047	−	3.64064i	−0.458195	−	0.148877i
$599$	−4.64845			−0.189931			−0.0949653	−	0.995481i	$-0.530274\pi$
$599$	−4.64845			−0.189931			−0.0949653	+	0.995481i	$0.530274\pi$
$600$	7.16218	+	5.48340i	0.292395	+	0.223859i
$601$	19.1953			0.782995			0.391497	−	0.920179i	$-0.371957\pi$
$601$	19.1953			0.782995			0.391497	+	0.920179i	$0.371957\pi$
$602$	−10.0395	−	3.26203i	−0.409179	−	0.132950i
$603$	2.23924	−	3.08205i	0.0911889	−	0.125511i
$604$	−6.07369	−	4.41280i	−0.247135	−	0.179554i
$605$	−2.87041	+	2.03094i	−0.116699	+	0.0825694i
$606$	0.608401	−	0.442029i	0.0247146	−	0.0179562i
$607$			1.66984i			0.0677769i	0.999426	+	0.0338884i	$0.0107891\pi$
$607$			1.66984i			0.0677769i	−0.999426	+	0.0338884i	$0.989211\pi$
$608$	4.85829	+	6.68687i	0.197030	+	0.271188i
$609$	−1.73099	−	5.32745i	−0.0701434	−	0.215879i
$610$	−15.3462	−	21.6894i	−0.621348	−	0.878177i
$611$	−5.43540	+	16.7285i	−0.219893	+	0.676761i
$612$	−0.721172	+	0.234323i	−0.0291516	+	0.00947194i
$613$	−34.8878	+	11.3357i	−1.40910	+	0.457845i	−0.912123	−	0.409916i	$-0.865558\pi$
$613$	−34.8878	+	11.3357i	−1.40910	+	0.457845i	−0.496980	+	0.867762i	$0.665558\pi$
$614$	5.49645	−	16.9163i	0.221819	−	0.682688i
$615$	6.72328	−	9.01376i	0.271109	−	0.363470i
$616$	−1.09570	−	3.37223i	−0.0441472	−	0.135871i
$617$	−4.12235	−	5.67393i	−0.165960	−	0.228424i	0.717935	−	0.696110i	$-0.245088\pi$
$617$	−4.12235	−	5.67393i	−0.165960	−	0.228424i	−0.883894	+	0.467687i	$0.845088\pi$
$618$		−	27.3848i		−	1.10158i
$619$	−25.7571	+	18.7137i	−1.03527	+	0.752166i	−0.969356	−	0.245660i	$-0.920995\pi$
$619$	−25.7571	+	18.7137i	−1.03527	+	0.752166i	−0.0659111	+	0.997825i	$0.520995\pi$
$620$	−0.926300	+	2.73366i	−0.0372011	+	0.109787i
$621$	9.60328	+	6.97719i	0.385366	+	0.279985i
$622$	−16.0615	+	22.1067i	−0.644006	+	0.886399i
$623$	13.8820	+	4.51054i	0.556171	+	0.180711i
$624$	8.86822			0.355013
$625$	6.52284	+	24.1341i	0.260914	+	0.965362i
$626$	22.0776			0.882400
$627$	50.2840	+	16.3383i	2.00815	+	0.652488i
$628$	5.71245	−	7.86251i	0.227951	−	0.313748i
$629$	−1.63453	−	1.18755i	−0.0651729	−	0.0473509i
$630$	−0.182690	+	0.539149i	−0.00727856	+	0.0214802i
$631$	−16.0674	+	11.6737i	−0.639633	+	0.464721i	−0.859724	−	0.510758i	$-0.829365\pi$
$631$	−16.0674	+	11.6737i	−0.639633	+	0.464721i	0.220091	+	0.975479i	$0.429365\pi$
$632$			1.95388i			0.0777212i
$633$	−13.0511	−	17.9633i	−0.518735	−	0.713977i
$634$	7.31729	+	22.5203i	0.290607	+	0.894396i
$635$	−21.1664	+	28.3774i	−0.839965	+	1.12612i
$636$	2.79554	−	8.60378i	0.110850	−	0.341162i
$637$	−4.67515	+	1.51905i	−0.185236	+	0.0601869i
$638$	10.4709	−	3.40219i	0.414546	−	0.134694i
$639$	0.0353181	−	0.108698i	0.00139716	−	0.00430002i
$640$	−1.29153	−	1.82537i	−0.0510520	−	0.0721539i
$641$	−4.44139	−	13.6692i	−0.175424	−	0.539901i	0.824228	−	0.566258i	$-0.191609\pi$
$641$	−4.44139	−	13.6692i	−0.175424	−	0.539901i	−0.999653	+	0.0263570i	$0.991609\pi$
$642$	−16.0982	−	22.1573i	−0.635346	−	0.874479i
$643$			4.50981i			0.177849i	0.996038	+	0.0889247i	$0.0283431\pi$
$643$			4.50981i			0.177849i	−0.996038	+	0.0889247i	$0.971657\pi$
$644$	−1.93894	+	1.40872i	−0.0764048	+	0.0555113i
$645$	−34.7618	+	24.5955i	−1.36875	+	0.968447i
$646$	−19.9172	−	14.4707i	−0.783633	−	0.569343i
$647$	−2.27030	+	3.12481i	−0.0892549	+	0.122849i	−0.851309	−	0.524664i	$-0.824191\pi$
$647$	−2.27030	+	3.12481i	−0.0892549	+	0.122849i	0.762054	+	0.647513i	$0.224191\pi$
$648$	−9.22423	−	2.99713i	−0.362362	−	0.117739i
$649$	33.5794			1.31811
$650$	19.5158	+	14.9414i	0.765473	+	0.586050i
$651$	−2.32868			−0.0912681
$652$	−3.26214	−	1.05993i	−0.127755	−	0.0415101i
$653$	−5.18140	+	7.13159i	−0.202764	+	0.279081i	−0.898274	−	0.439436i	$-0.855178\pi$
$653$	−5.18140	+	7.13159i	−0.202764	+	0.279081i	0.695510	+	0.718516i	$0.255178\pi$
$654$	−11.5820	−	8.41484i	−0.452893	−	0.329046i
$655$	−0.504560	−	1.62184i	−0.0197148	−	0.0633707i
$656$	−2.25520	+	1.63850i	−0.0880508	+	0.0639726i
$657$		−	2.36773i		−	0.0923738i
$658$	2.10319	+	2.89480i	0.0819910	+	0.112851i
$659$	1.12103	+	3.45017i	0.0436691	+	0.134400i	0.970514	−	0.241045i	$-0.0774901\pi$
$659$	1.12103	+	3.45017i	0.0436691	+	0.134400i	−0.926845	+	0.375444i	$0.877490\pi$
$660$	−13.5469	−	4.59038i	−0.527314	−	0.178680i
$661$	1.86743	−	5.74735i	0.0726345	−	0.223546i	−0.908148	−	0.418648i	$-0.862504\pi$
$661$	1.86743	−	5.74735i	0.0726345	−	0.223546i	0.980783	+	0.195103i	$0.0625040\pi$
$662$	−21.6558	+	7.03638i	−0.841675	+	0.273477i
$663$	−25.1217	+	8.16254i	−0.975646	+	0.317007i
$664$	3.31981	−	10.2173i	0.128833	−	0.396508i
$665$	−17.6477	+	5.49027i	−0.684350	+	0.212903i
$666$	0.0533625	+	0.164233i	0.00206776	+	0.00636390i
$667$	−4.37411	−	6.02045i	−0.169366	−	0.233113i
$668$		−	25.6899i		−	0.993970i
$669$	37.0856	−	26.9443i	1.43381	−	1.04173i
$670$	−33.4585	−	0.419850i	−1.29262	−	0.0162202i
$671$	34.0852	+	24.7643i	1.31584	+	0.956016i
$672$	1.06039	−	1.45950i	0.0409055	−	0.0563016i
$673$	48.3829	+	15.7205i	1.86502	+	0.605982i	0.993239	+	0.116091i	$0.0370366\pi$
$673$	48.3829	+	15.7205i	1.86502	+	0.605982i	0.871784	+	0.489891i	$0.162963\pi$
$674$	3.73866			0.144008
$675$	−14.0488	−	20.3937i	−0.540738	−	0.784953i
$676$	11.1645			0.429404
$677$	−12.8302	−	4.16878i	−0.493104	−	0.160219i	0.0519005	−	0.998652i	$-0.483472\pi$
$677$	−12.8302	−	4.16878i	−0.493104	−	0.160219i	−0.545005	+	0.838433i	$0.683472\pi$
$678$	0.883760	−	1.21639i	0.0339406	−	0.0467152i
$679$	1.12837	+	0.819807i	0.0433028	+	0.0314613i
$680$	5.33872	+	3.98210i	0.204731	+	0.152707i
$681$	−22.5558	+	16.3878i	−0.864341	+	0.627980i
$682$		−	4.57692i		−	0.175259i
$683$	1.12279	+	1.54538i	0.0429622	+	0.0591324i	0.829958	−	0.557826i	$-0.188365\pi$
$683$	1.12279	+	1.54538i	0.0429622	+	0.0591324i	−0.786995	+	0.616959i	$0.788365\pi$
$684$	0.650240	+	2.00123i	0.0248625	+	0.0765190i
$685$	0.604083	−	48.1404i	0.0230808	−	1.83935i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	19.2319	−	6.24882i	0.733742	−	0.238407i
$688$	10.0395	−	3.26203i	0.382752	−	0.124364i
$689$	7.61740	−	23.4440i	0.290200	−	0.893143i
$690$	−0.121309	+	9.66728i	−0.00461814	+	0.368027i
$691$	3.95473	+	12.1714i	0.150445	+	0.463022i	0.997671	−	0.0682105i	$-0.0217289\pi$
$691$	3.95473	+	12.1714i	0.150445	+	0.463022i	−0.847226	+	0.531233i	$0.821729\pi$
$692$	−10.2714	−	14.1374i	−0.390461	−	0.537424i
$693$		−	0.902687i		−	0.0342902i
$694$	−3.44591	+	2.50360i	−0.130805	+	0.0950354i
$695$	16.4415	+	12.2636i	0.623663	+	0.465185i
$696$	4.53180	+	3.29255i	0.171777	+	0.124804i
$697$	4.88037	−	6.71725i	0.184857	−	0.254434i
$698$	15.5716	+	5.05953i	0.589395	+	0.191506i
$699$	−17.1875			−0.650090
$700$	4.79256	−	1.42528i	0.181142	−	0.0538703i
$701$	−41.8257			−1.57974			−0.789868	−	0.613277i	$-0.789851\pi$
$701$	−41.8257			−1.57974			−0.789868	+	0.613277i	$0.789851\pi$
$702$	−23.1554	−	7.52363i	−0.873943	−	0.283961i
$703$	−3.29543	+	4.53577i	−0.124289	+	0.171070i
$704$	2.86859	+	2.08415i	0.108114	+	0.0785495i
$705$	14.4331	+	0.181112i	0.543581	+	0.00682106i
$706$	−4.91232	+	3.56901i	−0.184878	+	0.134321i
$707$		−	0.416855i		−	0.0156774i
$708$	10.0422	+	13.8219i	0.377408	+	0.519458i
$709$	8.19141	+	25.2106i	0.307635	+	0.946802i	0.978681	+	0.205387i	$0.0658452\pi$
$709$	8.19141	+	25.2106i	0.307635	+	0.946802i	−0.671046	+	0.741416i	$0.734155\pi$
$710$	−0.958547	+	0.298207i	−0.0359736	+	0.0111915i
$711$	−0.153712	+	0.473075i	−0.00576463	+	0.0177417i
$712$	−13.8820	+	4.51054i	−0.520251	+	0.169040i
$713$	−2.94221	+	0.955983i	−0.110187	+	0.0358019i
$714$	−1.66049	+	5.11046i	−0.0621423	+	0.191254i
$715$	−36.9133	−	12.5081i	−1.38048	−	0.467775i
$716$	3.93147	+	12.0998i	0.146926	+	0.452191i
$717$	−0.0526857	−	0.0725157i	−0.00196758	−	0.00270815i
$718$		−	6.66918i		−	0.248892i
$719$	6.06749	−	4.40829i	0.226279	−	0.164401i	−0.468869	−	0.883267i	$-0.655339\pi$
$719$	6.06749	−	4.40829i	0.226279	−	0.164401i	0.695149	+	0.718866i	$0.255339\pi$
$720$	−0.169104	−	0.543563i	−0.00630214	−	0.0202574i
$721$	−12.2806	−	8.92238i	−0.457353	−	0.332287i
$722$	−28.9879	+	39.8985i	−1.07882	+	1.48487i
$723$	41.2319	+	13.3971i	1.53343	+	0.498242i
$724$	9.26985			0.344511
$725$	4.42552	+	14.8810i	0.164360	+	0.552667i
$726$	2.83688			0.105287
$727$	−24.4915	−	7.95778i	−0.908340	−	0.295138i	−0.182665	−	0.983175i	$-0.558472\pi$
$727$	−24.4915	−	7.95778i	−0.908340	−	0.295138i	−0.725675	+	0.688037i	$0.758472\pi$
$728$	2.88940	−	3.97692i	0.107088	−	0.147394i
$729$	19.6886	+	14.3046i	0.729206	+	0.529799i
$730$	−16.9768	+	12.0118i	−0.628339	+	0.444577i
$731$	−25.4372	+	18.4812i	−0.940828	+	0.683552i
$732$			21.4360i			0.792299i
$733$	26.9272	+	37.0621i	0.994579	+	1.36892i	0.928593	+	0.371100i	$0.121019\pi$
$733$	26.9272	+	37.0621i	0.994579	+	1.36892i	0.0659858	+	0.997821i	$0.478981\pi$
$734$	−2.40995	−	7.41707i	−0.0889529	−	0.273769i
$735$	2.32997	+	3.29304i	0.0859423	+	0.121466i
$736$	0.740608	−	2.27936i	0.0272992	−	0.0840182i
$737$	50.4630	−	16.3964i	1.85883	−	0.603970i
$738$	−0.674931	+	0.219299i	−0.0248446	+	0.00807249i
$739$	2.44969	−	7.53938i	0.0901134	−	0.277341i	−0.895836	−	0.444385i	$-0.853422\pi$
$739$	2.44969	−	7.53938i	0.0901134	−	0.277341i	0.985949	+	0.167044i	$0.0534223\pi$
$740$	0.906848	−	1.21579i	0.0333364	−	0.0446934i
$741$	22.6508	+	69.7121i	0.832099	+	2.56094i
$742$	−2.94750	−	4.05689i	−0.108206	−	0.148933i
$743$		−	50.3686i		−	1.84785i	−0.382578	−	0.923923i	$-0.624964\pi$
$743$		−	50.3686i		−	1.84785i	0.382578	−	0.923923i	$-0.375036\pi$
$744$	1.88394	−	1.36876i	0.0690686	−	0.0501813i
$745$	4.56706	−	13.4781i	0.167324	−	0.493801i
$746$	0.540610	+	0.392776i	0.0197931	+	0.0143806i
$747$	1.60759	−	2.21266i	0.0588186	−	0.0809568i
$748$	−10.0444	−	3.26362i	−0.367259	−	0.119330i
$749$	−15.1814			−0.554716
$750$	6.95033	−	18.9345i	0.253790	−	0.691390i
$751$	29.6545			1.08211			0.541053	−	0.840988i	$-0.318026\pi$
$751$	29.6545			1.08211			0.541053	+	0.840988i	$0.318026\pi$
$752$	−3.40304	−	1.10571i	−0.124096	−	0.0403212i
$753$	−28.4975	+	39.2234i	−1.03851	+	1.42938i
$754$	12.3484	+	8.97167i	0.449704	+	0.326729i
$755$	−5.38747	+	15.8993i	−0.196070	+	0.578635i
$756$	−4.00695	+	2.91122i	−0.145731	+	0.105880i
$757$		−	52.1250i		−	1.89452i	−0.320473	−	0.947258i	$-0.603842\pi$
$757$		−	52.1250i		−	1.89452i	0.320473	−	0.947258i	$-0.396158\pi$
$758$	−0.576127	−	0.792970i	−0.0209259	−	0.0288020i
$759$	−4.73747	−	14.5804i	−0.171959	−	0.529237i
$760$	11.0502	−	14.8148i	0.400834	−	0.537389i
$761$	2.87132	−	8.83702i	0.104085	−	0.320342i	−0.885429	−	0.464774i	$-0.846136\pi$
$761$	2.87132	−	8.83702i	0.104085	−	0.320342i	0.989515	+	0.144432i	$0.0461356\pi$
$762$	27.1641	−	8.82616i	0.984052	−	0.319738i
$763$	−7.54720	+	2.45223i	−0.273227	+	0.0887768i
$764$	−1.89075	+	5.81914i	−0.0684050	+	0.210529i
$765$	0.979345	+	1.38415i	0.0354083	+	0.0500440i
$766$	8.05661	+	24.7957i	0.291097	+	0.895905i
$767$	27.3634	+	37.6625i	0.988034	+	1.35991i
$768$			1.80405i			0.0650979i
$769$	−6.02297	+	4.37594i	−0.217194	+	0.157800i	−0.691063	−	0.722795i	$-0.742857\pi$
$769$	−6.02297	+	4.37594i	−0.217194	+	0.157800i	0.473869	+	0.880595i	$0.342857\pi$
$770$	−6.47233	+	4.57946i	−0.233247	+	0.165032i
$771$	−4.48700	−	3.26000i	−0.161595	−	0.117406i
$772$	8.33501	−	11.4722i	0.299984	−	0.412892i
$773$	−5.72245	−	1.85934i	−0.205822	−	0.0668757i	0.204291	−	0.978910i	$-0.434511\pi$
$773$	−5.72245	−	1.85934i	−0.205822	−	0.0668757i	−0.410114	+	0.912034i	$0.634511\pi$
$774$	2.68739			0.0965963
$775$	6.45201	+	0.161950i	0.231763	+	0.00581742i
$776$	−1.39474			−0.0500682
$777$	1.16381	+	0.378145i	0.0417514	+	0.0135659i
$778$	3.22539	−	4.43936i	0.115636	−	0.159159i
$779$	−18.6402	−	13.5429i	−0.667854	−	0.485224i
$780$	−5.89067	−	18.9348i	−0.210920	−	0.677975i
$781$	1.28783	−	0.935661i	0.0460821	−	0.0334806i
$782$			7.13859i			0.255275i
$783$	−9.03942	−	12.4417i	−0.323042	−	0.444630i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−20.5819	−	6.97418i	−0.734601	−	0.248919i
$786$	−0.423462	+	1.30328i	−0.0151044	+	0.0464865i
$787$	−16.1901	+	5.26048i	−0.577114	+	0.187516i	−0.583007	−	0.812467i	$-0.698124\pi$
$787$	−16.1901	+	5.26048i	−0.577114	+	0.187516i	0.00589311	+	0.999983i	$0.498124\pi$
$788$	9.85677	−	3.20266i	0.351133	−	0.114090i
$789$	−11.5712	+	35.6126i	−0.411947	+	1.26784i
$790$	4.17179	−	1.29786i	0.148426	−	0.0461756i
$791$	−0.257543	−	0.792637i	−0.00915719	−	0.0281829i
$792$	0.530586	+	0.730289i	0.0188535	+	0.0259497i
$793$			58.4098i			2.07419i
$794$	−19.8384	+	14.4134i	−0.704038	+	0.511514i
$795$	−20.2271	−	0.253817i	−0.717382	−	0.00900197i
$796$	−9.36973	−	6.80751i	−0.332101	−	0.241286i
$797$	−24.9545	+	34.3469i	−0.883934	+	1.21663i	0.0913816	+	0.995816i	$0.470872\pi$
$797$	−24.9545	+	34.3469i	−0.883934	+	1.21663i	−0.975316	+	0.220815i	$0.929128\pi$
$798$	14.1814	+	4.60781i	0.502016	+	0.163115i
$799$	10.6578			0.377045
$800$	−3.03950	+	3.97007i	−0.107463	+	0.140363i
$801$	−3.71597			−0.131297
$802$	26.4925	+	8.60793i	0.935483	+	0.303957i
$803$	19.3836	−	26.6793i	0.684033	−	0.941491i
$804$	21.8404	+	15.8680i	0.770252	+	0.559621i
$805$	4.29573	+	3.20414i	0.151404	+	0.112931i
$806$	5.13344	−	3.72966i	0.180818	−	0.131372i
$807$			52.6877i			1.85470i
$808$	0.245021	+	0.337243i	0.00861981	+	0.0118642i
$809$	−0.825590	−	2.54090i	−0.0290262	−	0.0893334i	0.935494	−	0.353343i	$-0.114955\pi$
$809$	−0.825590	−	2.54090i	−0.0290262	−	0.0893334i	−0.964520	+	0.264009i	$0.914955\pi$
$810$	−0.272121	+	21.6858i	−0.00956136	+	0.761960i
$811$	6.41459	−	19.7421i	0.225247	−	0.693239i	−0.773020	−	0.634382i	$-0.781255\pi$
$811$	6.41459	−	19.7421i	0.225247	−	0.693239i	0.998266	−	0.0588564i	$-0.0187454\pi$
$812$	2.95306	−	0.959507i	0.103632	−	0.0336721i
$813$	−9.33616	+	3.03350i	−0.327433	+	0.106390i
$814$	−0.743227	+	2.28742i	−0.0260501	+	0.0801740i
$815$	−0.0962352	+	7.66914i	−0.00337097	+	0.268638i
$816$	−1.66049	−	5.11046i	−0.0581288	−	0.178902i
$817$	51.2848	+	70.5875i	1.79423	+	2.46954i
$818$		−	40.3542i		−	1.41095i
$819$	1.01245	−	0.735586i	0.0353778	−	0.0257035i
$820$	4.99641	+	3.72678i	0.174482	+	0.130145i
$821$	24.1772	+	17.5658i	0.843791	+	0.613050i	0.923427	−	0.383774i	$-0.125376\pi$
$821$	24.1772	+	17.5658i	0.843791	+	0.613050i	−0.0796364	+	0.996824i	$0.525376\pi$
$822$	−22.8310	+	31.4242i	−0.796322	+	1.09604i
$823$	28.4531	+	9.24496i	0.991811	+	0.322259i	0.759589	−	0.650404i	$-0.225400\pi$
$823$	28.4531	+	9.24496i	0.991811	+	0.322259i	0.232222	+	0.972663i	$0.425400\pi$
$824$	15.1797			0.528808
$825$	−0.802560	+	31.9736i	−0.0279416	+	1.11318i
$826$	9.47026			0.329513
$827$	−17.0359	−	5.53531i	−0.592398	−	0.192482i	−0.00255080	−	0.999997i	$-0.500812\pi$
$827$	−17.0359	−	5.53531i	−0.592398	−	0.192482i	−0.589847	+	0.807515i	$0.700812\pi$
$828$	0.358633	−	0.493616i	0.0124634	−	0.0171544i
$829$	−23.4051	−	17.0048i	−0.812894	−	0.590602i	0.101774	−	0.994808i	$-0.467548\pi$
$829$	−23.4051	−	17.0048i	−0.812894	−	0.590602i	−0.914668	+	0.404205i	$0.867548\pi$
$830$	−24.0204	−	0.301417i	−0.833762	−	0.0104624i
$831$	−10.9040	+	7.92225i	−0.378257	+	0.274820i
$832$			4.91574i			0.170423i
$833$	1.75075	+	2.40971i	0.0606600	+	0.0834914i
$834$	−5.11378	−	15.7386i	−0.177076	−	0.544983i
$835$	−54.8512	+	17.0644i	−1.89820	+	0.590536i
$836$	−9.05646	+	27.8729i	−0.313224	+	0.964005i
$837$	−6.08029	+	1.97561i	−0.210166	+	0.0682870i
$838$	6.09534	−	1.98050i	0.210560	−	0.0684151i
$839$	13.2568	−	40.8003i	0.457677	−	1.40858i	−0.410287	−	0.911956i	$-0.634572\pi$
$839$	13.2568	−	40.8003i	0.457677	−	1.40858i	0.867964	−	0.496627i	$-0.165428\pi$
$840$	−3.82059	−	1.29461i	−0.131823	−	0.0446681i
$841$	−5.98220	−	18.4113i	−0.206283	−	0.634873i
$842$	−21.4880	−	29.5757i	−0.740525	−	1.01925i
$843$			54.9718i			1.89333i
$844$	9.95723	−	7.23435i	0.342742	−	0.249017i
$845$	−7.41597	−	23.8377i	−0.255117	−	0.820041i
$846$	−0.736960	−	0.535433i	−0.0253372	−	0.0184086i
$847$	0.924299	−	1.27219i	0.0317593	−	0.0437129i
$848$	4.76916	+	1.54959i	0.163774	+	0.0532133i
$849$	−11.2263			−0.385286
$850$	4.95609	−	14.0440i	0.169993	−	0.481704i
$851$	1.62568			0.0557275
$852$	0.770270	+	0.250276i	0.0263890	+	0.00857431i
$853$	4.68526	−	6.44871i	0.160420	−	0.220800i	−0.721239	−	0.692686i	$-0.756427\pi$
$853$	4.68526	−	6.44871i	0.160420	−	0.220800i	0.881659	+	0.471887i	$0.156427\pi$
$854$	9.61290	+	6.98418i	0.328947	+	0.238994i
$855$	3.84097	−	2.71765i	0.131358	−	0.0929418i
$856$	12.2820	−	8.92340i	0.419790	−	0.304996i
$857$		−	50.4068i		−	1.72186i	−0.508720	−	0.860932i	$-0.669881\pi$
$857$		−	50.4068i		−	1.72186i	0.508720	−	0.860932i	$-0.330119\pi$
$858$	18.4827	+	25.4393i	0.630990	+	0.868483i
$859$	−13.2785	−	40.8672i	−0.453058	−	1.39437i	−0.873400	−	0.487004i	$-0.838090\pi$
$859$	−13.2785	−	40.8672i	−0.453058	−	1.39437i	0.420342	−	0.907366i	$-0.361910\pi$
$860$	−13.6335	−	19.2688i	−0.464899	−	0.657061i
$861$	−1.55402	+	4.78279i	−0.0529609	+	0.162997i
$862$	12.6212	−	4.10088i	0.429881	−	0.139677i
$863$	19.2509	−	6.25501i	0.655309	−	0.212923i	0.0375556	−	0.999295i	$-0.488043\pi$
$863$	19.2509	−	6.25501i	0.655309	−	0.212923i	0.617754	+	0.786372i	$0.288043\pi$
$864$	1.53052	−	4.71045i	0.0520693	−	0.160253i
$865$	−23.3625	+	31.3215i	−0.794348	+	1.06496i
$866$	−0.554161	−	1.70553i	−0.0188312	−	0.0579564i
$867$	−8.61905	−	11.8631i	−0.292718	−	0.402892i
$868$		−	1.29081i		−	0.0438129i
$869$	−5.60489	+	4.07219i	−0.190133	+	0.138140i
$870$	4.01979	−	11.8630i	0.136284	−	0.402195i
$871$	59.5117	+	43.2378i	2.01648	+	1.46506i
$872$	4.66443	−	6.42003i	0.157957	−	0.217410i
$873$	−0.337695	−	0.109724i	−0.0114293	−	0.00371359i
$874$	19.8094			0.670062
$875$	−6.22658	−	9.28600i	−0.210497	−	0.313924i
$876$	16.7785			0.566893
$877$	0.500490	+	0.162619i	0.0169004	+	0.00549126i	0.317455	−	0.948273i	$-0.397172\pi$
$877$	0.500490	+	0.162619i	0.0169004	+	0.00549126i	−0.300555	+	0.953765i	$0.597172\pi$
$878$	−12.5488	+	17.2720i	−0.423503	+	0.582901i
$879$	−16.6476	−	12.0952i	−0.561509	−	0.407961i
$880$	2.54449	−	7.50920i	0.0857748	−	0.253135i
$881$	−8.45789	+	6.14502i	−0.284954	+	0.207031i	−0.721075	−	0.692857i	$-0.756352\pi$
$881$	−8.45789	+	6.14502i	−0.284954	+	0.207031i	0.436122	+	0.899888i	$0.356352\pi$
$882$		−	0.254581i		−	0.00857219i
$883$	−10.8960	−	14.9970i	−0.366679	−	0.504691i	0.585315	−	0.810806i	$-0.300971\pi$
$883$	−10.8960	−	14.9970i	−0.366679	−	0.504691i	−0.951995	+	0.306115i	$0.900971\pi$
$884$	−4.52457	−	13.9252i	−0.152178	−	0.468355i
$885$	22.8410	−	30.6225i	0.767793	−	1.02936i
$886$	−0.790940	+	2.43426i	−0.0265722	+	0.0817807i
$887$	−19.8434	+	6.44752i	−0.666277	+	0.216487i	−0.622578	−	0.782558i	$-0.713914\pi$
$887$	−19.8434	+	6.44752i	−0.666277	+	0.216487i	−0.0436997	+	0.999045i	$0.513914\pi$
$888$	−1.16381	+	0.378145i	−0.0390549	+	0.0126897i
$889$	4.89242	−	15.0573i	0.164087	−	0.505007i
$890$	18.8516	+	26.6438i	0.631909	+	0.893102i
$891$	−10.6272	−	32.7070i	−0.356023	−	1.09573i
$892$	14.9355	+	20.5569i	0.500076	+	0.688296i
$893$		−	29.5751i		−	0.989692i
$894$	−9.28864	+	6.74859i	−0.310659	+	0.225707i
$895$	23.2232	−	16.4314i	0.776267	−	0.549243i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	12.4928	−	17.1949i	0.417124	−	0.574121i
$898$	−22.3992	−	7.27793i	−0.747470	−	0.242868i
$899$	4.00800			0.133674
$900$	−1.04825	+	0.722119i	−0.0349417	+	0.0240706i
$901$	−14.9363			−0.497599
$902$	−9.40036	−	3.05436i	−0.312998	−	0.101699i
$903$	11.1936	−	15.4067i	0.372501	−	0.512704i
$904$	0.674257	+	0.489876i	0.0224255	+	0.0162930i
$905$	−6.15745	−	19.7923i	−0.204681	−	0.657919i
$906$	10.9572	−	7.96089i	0.364029	−	0.264483i
$907$		−	43.6714i		−	1.45008i	−0.688705	−	0.725042i	$-0.741820\pi$
$907$		−	43.6714i		−	1.45008i	0.688705	−	0.725042i	$-0.258180\pi$
$908$	−9.08389	−	12.5029i	−0.301460	−	0.414923i
$909$	0.0327939	+	0.100929i	0.00108770	+	0.00334761i
$910$	−10.4105	−	3.52760i	−0.345105	−	0.116939i
$911$	−12.6714	+	38.9987i	−0.419824	+	1.29208i	0.488041	+	0.872821i	$0.337712\pi$
$911$	−12.6714	+	38.9987i	−0.419824	+	1.29208i	−0.907865	+	0.419264i	$0.862288\pi$
$912$	−14.1814	+	4.60781i	−0.469593	+	0.152580i
$913$	36.2283	−	11.7713i	1.19898	−	0.389572i
$914$	0.777024	−	2.39144i	0.0257017	−	0.0791017i
$915$	45.7687	−	14.2388i	1.51307	−	0.470719i
$916$	3.46378	+	10.6604i	0.114446	+	0.352230i
$917$	0.446481	+	0.614529i	0.0147441	+	0.0202935i
$918$			14.7524i			0.486902i
$919$	−26.3152	+	19.1191i	−0.868059	+	0.630682i	−0.930065	−	0.367394i	$-0.880250\pi$
$919$	−26.3152	+	19.1191i	−0.868059	+	0.630682i	0.0620066	+	0.998076i	$0.480250\pi$
$920$	−5.35867	−	0.0672425i	−0.176670	−	0.00221692i
$921$	25.9600	+	18.8611i	0.855413	+	0.621494i
$922$	4.72226	−	6.49963i	0.155519	−	0.214054i
$923$	2.09886	+	0.681962i	0.0690849	+	0.0224471i
$924$	6.39674			0.210437
$925$	−3.19824	−	1.12865i	−0.105158	−	0.0371099i
$926$	13.1117			0.430878
$927$	3.67531	+	1.19418i	0.120713	+	0.0392221i
$928$	−1.82509	+	2.51202i	−0.0599115	+	0.0824611i
$929$	16.8628	+	12.2516i	0.553251	+	0.401960i	0.828983	−	0.559274i	$-0.188920\pi$
$929$	16.8628	+	12.2516i	0.553251	+	0.401960i	−0.275732	+	0.961235i	$0.588920\pi$
$930$	−4.17388	−	3.11326i	−0.136867	−	0.102088i
$931$	6.68687	−	4.85829i	0.219153	−	0.159224i
$932$		−	9.52718i		−	0.312073i
$933$	−28.9756	−	39.8815i	−0.948620	−	1.30566i
$934$	−1.26879	−	3.90493i	−0.0415160	−	0.127773i
$935$	−0.296316	+	23.6139i	−0.00969058	+	0.772258i
$936$	−0.386721	+	1.19020i	−0.0126404	+	0.0389030i
$937$	−18.3457	+	5.96087i	−0.599326	+	0.194733i	−0.592940	−	0.805247i	$-0.702033\pi$
$937$	−18.3457	+	5.96087i	−0.599326	+	0.194733i	−0.00638646	+	0.999980i	$0.502033\pi$
$938$	14.2319	−	4.62422i	0.464687	−	0.150986i
$939$	−12.3079	+	37.8797i	−0.401652	+	1.23616i
$940$	−0.100392	+	8.00039i	−0.00327442	+	0.260944i
$941$	14.3464	+	44.1537i	0.467680	+	1.43937i	0.855581	+	0.517669i	$0.173200\pi$
$941$	14.3464	+	44.1537i	0.467680	+	1.43937i	−0.387901	+	0.921701i	$0.626800\pi$
$942$	10.3055	+	14.1843i	0.335772	+	0.462150i
$943$			6.68087i			0.217559i
$944$	−7.66160	+	5.56648i	−0.249364	+	0.181174i
$945$	8.87743	+	6.62159i	0.288783	+	0.215400i
$946$	30.2812	+	22.0006i	0.984528	+	0.715301i
$947$	29.7855	−	40.9962i	0.967899	−	1.33220i	0.0247984	−	0.999692i	$-0.492106\pi$
$947$	29.7855	−	40.9962i	0.967899	−	1.33220i	0.943101	−	0.332507i	$-0.107894\pi$
$948$	−3.35237	−	1.08925i	−0.108880	−	0.0353772i
$949$	45.7188			1.48409
$950$	−38.9716	−	13.7530i	−1.26441	−	0.446207i
$951$	−42.7185			−1.38524
$952$	−2.83278	−	0.920426i	−0.0918109	−	0.0298312i
$953$	27.3101	−	37.5891i	0.884660	−	1.21763i	−0.0904479	−	0.995901i	$-0.528830\pi$
$953$	27.3101	−	37.5891i	0.884660	−	1.21763i	0.975108	−	0.221729i	$-0.0711701\pi$
$954$	1.03281	+	0.750378i	0.0334384	+	0.0242944i
$955$	13.6805	+	0.171668i	0.442692	+	0.00555506i
$956$	0.0401961	−	0.0292042i	0.00130004	−	0.000944531i
$957$			19.8621i			0.642049i
$958$	−15.7939	−	21.7384i	−0.510277	−	0.702337i
$959$	6.65336	+	20.4769i	0.214848	+	0.661234i
$960$	3.85187	−	1.19833i	0.124319	−	0.0386759i
$961$	−9.06465	+	27.8981i	−0.292408	+	0.899939i
$962$	−3.17120	+	1.03038i	−0.102244	+	0.0332209i
$963$	3.67573	−	1.19432i	0.118449	−	0.0384864i
$964$	−7.42612	+	22.8553i	−0.239179	+	0.736118i
$965$	−30.0310	−	10.1760i	−0.966734	−	0.327577i
$966$	−1.33609	−	4.11206i	−0.0429880	−	0.132303i
$967$	−26.5584	−	36.5545i	−0.854060	−	1.17551i	−0.982953	−	0.183854i	$-0.941142\pi$
$967$	−26.5584	−	36.5545i	−0.854060	−	1.17551i	0.128893	−	0.991658i	$-0.458858\pi$
$968$			1.57251i			0.0505424i
$969$	35.9316	−	26.1058i	1.15429	−	0.838640i
$970$	0.926448	+	2.97795i	0.0297465	+	0.0956162i
$971$	−45.9767	−	33.4041i	−1.47546	−	1.07199i	−0.978984	−	0.203939i	$-0.934626\pi$
$971$	−45.9767	−	33.4041i	−1.47546	−	1.07199i	−0.496480	−	0.868048i	$-0.665374\pi$
$972$	1.55101	−	2.13478i	0.0497486	−	0.0684731i
$973$	−8.72405	−	2.83462i	−0.279680	−	0.0908736i
$974$	−2.06099			−0.0660385
$975$	−36.5154	+	25.1547i	−1.16943	+	0.805595i
$976$	−11.8822			−0.380340
$977$	−43.7189	−	14.2051i	−1.39869	−	0.454462i	−0.489924	−	0.871765i	$-0.662975\pi$
$977$	−43.7189	−	14.2051i	−1.39869	−	0.454462i	−0.908767	+	0.417303i	$0.862975\pi$
$978$	3.63716	−	5.00612i	0.116303	−	0.160078i
$979$	−41.8711	−	30.4212i	−1.33821	−	0.972265i
$980$	−1.82537	+	1.29153i	−0.0583092	+	0.0412563i
$981$	1.63442	−	1.18747i	0.0521830	−	0.0379131i
$982$			28.5657i			0.911569i
$983$	18.1886	+	25.0344i	0.580125	+	0.798474i	0.993709	−	0.111992i	$-0.0357231\pi$
$983$	18.1886	+	25.0344i	0.580125	+	0.798474i	−0.413584	+	0.910466i	$0.635723\pi$
$984$	−1.55402	−	4.78279i	−0.0495404	−	0.152470i
$985$	−13.3854	−	18.9181i	−0.426494	−	0.602782i
$986$	2.85795	−	8.79586i	0.0910156	−	0.280117i
$987$	−6.13924	+	1.99476i	−0.195414	+	0.0634939i
$988$	−38.6421	+	12.5556i	−1.22937	+	0.399446i
$989$	7.81796	−	24.0612i	0.248597	−	0.765101i
$990$	1.20682	−	1.61796i	0.0383553	−	0.0514222i
$991$	−10.9850	−	33.8083i	−0.348949	−	1.07396i	−0.959435	−	0.281929i	$-0.909026\pi$
$991$	−10.9850	−	33.8083i	−0.348949	−	1.07396i	0.610486	−	0.792027i	$-0.290974\pi$
$992$	0.758719	+	1.04429i	0.0240893	+	0.0331561i
$993$		−	41.0785i		−	1.30359i
$994$	0.363201	−	0.263881i	0.0115200	−	0.00836979i
$995$	−8.31112	+	24.5275i	−0.263480	+	0.777572i
$996$	15.6796	+	11.3919i	0.496828	+	0.360966i
$997$	−18.8783	+	25.9838i	−0.597883	+	0.822915i	−0.995512	−	0.0946311i	$-0.969833\pi$
$997$	−18.8783	+	25.9838i	−0.597883	+	0.822915i	0.397630	+	0.917546i	$0.369833\pi$
$998$	−8.76623	−	2.84832i	−0.277490	−	0.0901620i
$999$	3.35957			0.106292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.29.3	✓	24
25.12	odd	20		8750.2.a.bb.1.11		12
25.13	odd	20		8750.2.a.z.1.2		12
25.19	even	10	inner	350.2.m.a.169.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.29.3	✓	24	1.1	even	1	trivial
350.2.m.a.169.3	yes	24	25.19	even	10	inner
8750.2.a.z.1.2		12	25.13	odd	20
8750.2.a.bb.1.11		12	25.12	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.06039 - 1.45950i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.717612 - 2.11779i) q^{5} +(-1.45950 + 1.06039i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0786699 - 0.242121i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.06039 - 1.45950i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.717612 - 2.11779i) q^{5} +(-1.45950 + 1.06039i) q^{6} +1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0786699 - 0.242121i) q^{9} +(-1.33692 + 1.79238i) q^{10} +(1.09570 - 3.37223i) q^{11} +(1.71575 - 0.557481i) q^{12} +(4.67515 - 1.51905i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-2.32997 - 3.29304i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.75075 - 2.40971i) q^{17} +0.254581i q^{18} +(-6.68687 + 4.85829i) q^{19} +(1.82537 - 1.29153i) q^{20} +(1.45950 + 1.06039i) q^{21} +(-2.08415 + 2.86859i) q^{22} +(2.27936 + 0.740608i) q^{23} -1.80405 q^{24} +(-3.97007 - 3.03950i) q^{25} -4.91574 q^{26} +(4.71045 + 1.53052i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(-2.51202 - 1.82509i) q^{29} +(1.19833 + 3.85187i) q^{30} +(-1.04429 + 0.758719i) q^{31} -1.00000i q^{32} +(-3.75991 - 5.17507i) q^{33} +(0.920426 + 2.83278i) q^{34} +(2.11779 + 0.717612i) q^{35} +(0.0786699 - 0.242121i) q^{36} +(0.645111 - 0.209609i) q^{37} +(7.86088 - 2.55416i) q^{38} +(2.74043 - 8.43418i) q^{39} +(-2.13513 + 0.664245i) q^{40} +(0.861410 + 2.65115i) q^{41} +(-1.06039 - 1.45950i) q^{42} -10.5561i q^{43} +(2.86859 - 2.08415i) q^{44} +(-0.569216 - 0.00714273i) q^{45} +(-1.93894 - 1.40872i) q^{46} +(-2.10319 + 2.89480i) q^{47} +(1.71575 + 0.557481i) q^{48} -1.00000 q^{49} +(2.83650 + 4.11756i) q^{50} -5.37346 q^{51} +(4.67515 + 1.51905i) q^{52} +(2.94750 - 4.05689i) q^{53} +(-4.00695 - 2.91122i) q^{54} +(-6.35539 - 4.74043i) q^{55} +(0.809017 - 0.587785i) q^{56} +14.9112i q^{57} +(1.82509 + 2.51202i) q^{58} +(2.92647 + 9.00675i) q^{59} +(0.0506157 - 4.03365i) q^{60} +(-3.67180 + 11.3006i) q^{61} +(1.22763 - 0.398882i) q^{62} +(0.242121 - 0.0786699i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.137920 - 10.9911i) q^{65} +(1.97670 + 6.08366i) q^{66} +(8.79578 + 12.1064i) q^{67} -2.97856i q^{68} +(3.49793 - 2.54139i) q^{69} +(-1.79238 - 1.33692i) q^{70} +(0.363201 + 0.263881i) q^{71} +(-0.149639 + 0.205960i) q^{72} +(8.84528 + 2.87401i) q^{73} -0.678310 q^{74} +(-8.64599 + 2.57126i) q^{75} -8.26542 q^{76} +(3.37223 + 1.09570i) q^{77} +(-5.21261 + 7.17454i) q^{78} +(-1.58072 - 1.14846i) q^{79} +(2.23589 + 0.0280568i) q^{80} +(7.84660 - 5.70089i) q^{81} -2.78758i q^{82} +(6.31464 + 8.69136i) q^{83} +(0.557481 + 1.71575i) q^{84} +(-6.35961 + 1.97849i) q^{85} +(-3.26203 + 10.0395i) q^{86} +(-5.32745 + 1.73099i) q^{87} +(-3.37223 + 1.09570i) q^{88} +(4.51054 - 13.8820i) q^{89} +(0.539149 + 0.182690i) q^{90} +(1.51905 + 4.67515i) q^{91} +(1.40872 + 1.93894i) q^{92} +2.32868i q^{93} +(2.89480 - 2.10319i) q^{94} +(5.49027 + 17.6477i) q^{95} +(-1.45950 - 1.06039i) q^{96} +(0.819807 - 1.12837i) q^{97} +(0.951057 + 0.309017i) q^{98} -0.902687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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