LMFDB - Embedded newform 78.3.j.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(17,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("78.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.j (of order $6$, degree $2$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2 x^{18} - 12 x^{17} - 51 x^{16} - 180 x^{15} + 1136 x^{14} + 144 x^{13} + 6481 x^{12} + \cdots + 3486784401 $ x^20 + 2x^18 - 12x^17 - 51x^16 - 180x^15 + 1136x^14 + 144x^13 + 6481x^12 - 16152x^11 - 55134x^10 - 145368x^9 + 524961x^8 + 104976x^7 + 7453296x^6 - 10628820x^5 - 27103491x^4 - 57395628x^3 + 86093442*x^2 + 3486784401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$0.522666 + 2.95412i$ of defining polynomial
Character	$\chi$	$=$	78.17
Dual form			78.3.j.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-0.522666 - 2.95412i) q^{3} +(-1.00000 - 1.73205i) q^{4} -5.63179 q^{5} +(3.98762 + 1.44875i) q^{6} +(-10.8851 + 6.28452i) q^{7} +2.82843 q^{8} +(-8.45364 + 3.08804i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.522666 - 2.95412i) q^{3} +(-1.00000 - 1.73205i) q^{4} -5.63179 q^{5} +(3.98762 + 1.44875i) q^{6} +(-10.8851 + 6.28452i) q^{7} +2.82843 q^{8} +(-8.45364 + 3.08804i) q^{9} +(3.98228 - 6.89751i) q^{10} +(3.34234 - 5.78910i) q^{11} +(-4.59402 + 3.85940i) q^{12} +(3.64652 - 12.4781i) q^{13} -17.7753i q^{14} +(2.94355 + 16.6370i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(13.5918 - 7.84721i) q^{17} +(2.19557 - 12.5371i) q^{18} +(-8.05581 + 4.65102i) q^{19} +(5.63179 + 9.75455i) q^{20} +(24.2545 + 28.8712i) q^{21} +(4.72678 + 8.18703i) q^{22} +(-31.2216 - 18.0258i) q^{23} +(-1.47832 - 8.35551i) q^{24} +6.71708 q^{25} +(12.7040 + 13.2894i) q^{26} +(13.5409 + 23.3591i) q^{27} +(21.7702 + 12.5690i) q^{28} +(10.4331 + 6.02355i) q^{29} +(-22.4575 - 8.15903i) q^{30} +28.5613i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-18.8486 - 6.84791i) q^{33} +22.1953i q^{34} +(61.3026 - 35.3931i) q^{35} +(13.8023 + 11.5541i) q^{36} +(0.0845745 + 0.0488291i) q^{37} -13.1551i q^{38} +(-38.7677 - 4.25038i) q^{39} -15.9291 q^{40} +(-5.07312 + 8.78691i) q^{41} +(-52.5104 + 9.29054i) q^{42} +(-34.2678 - 59.3535i) q^{43} -13.3694 q^{44} +(47.6091 - 17.3912i) q^{45} +(44.1540 - 25.4923i) q^{46} -57.8179 q^{47} +(11.2787 + 4.09767i) q^{48} +(54.4903 - 94.3800i) q^{49} +(-4.74970 + 8.22671i) q^{50} +(-30.2856 - 36.0502i) q^{51} +(-25.2592 + 6.16213i) q^{52} +57.4927i q^{53} +(-38.1837 + 0.0667479i) q^{54} +(-18.8234 + 32.6030i) q^{55} +(-30.7877 + 17.7753i) q^{56} +(17.9502 + 21.3669i) q^{57} +(-14.7546 + 8.51859i) q^{58} +(19.9580 + 34.5682i) q^{59} +(25.8726 - 21.7354i) q^{60} +(5.10063 + 8.83454i) q^{61} +(-34.9803 - 20.1959i) q^{62} +(72.6119 - 86.7406i) q^{63} +8.00000 q^{64} +(-20.5365 + 70.2740i) q^{65} +(21.7149 - 18.2426i) q^{66} +(-66.1637 - 38.1996i) q^{67} +(-27.1835 - 15.6944i) q^{68} +(-36.9319 + 101.654i) q^{69} +100.107i q^{70} +(-24.1673 - 41.8589i) q^{71} +(-23.9105 + 8.73428i) q^{72} +8.56609i q^{73} +(-0.119606 + 0.0690548i) q^{74} +(-3.51079 - 19.8431i) q^{75} +(16.1116 + 9.30205i) q^{76} +84.0200i q^{77} +(32.6185 - 44.4751i) q^{78} +37.3730 q^{79} +(11.2636 - 19.5091i) q^{80} +(61.9281 - 52.2103i) q^{81} +(-7.17448 - 12.4266i) q^{82} +52.7630 q^{83} +(25.7519 - 70.8812i) q^{84} +(-76.5460 + 44.1939i) q^{85} +96.9239 q^{86} +(12.3413 - 33.9689i) q^{87} +(9.45357 - 16.3741i) q^{88} +(49.4552 - 85.6589i) q^{89} +(-12.3650 + 70.6065i) q^{90} +(38.7260 + 158.742i) q^{91} +72.1031i q^{92} +(84.3735 - 14.9280i) q^{93} +(40.8834 - 70.8122i) q^{94} +(45.3686 - 26.1936i) q^{95} +(-12.9938 + 10.9160i) q^{96} +(43.0461 - 24.8527i) q^{97} +(77.0609 + 133.473i) q^{98} +(-10.3780 + 59.2603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	$ 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) $ 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	−0.522666	−	2.95412i	−0.174222	−	0.984706i
$3$	−0.522666	−	2.95412i	−0.174222	−	0.984706i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−5.63179			−1.12636			−0.563179	−	0.826335i	$-0.690422\pi$
$5$	−5.63179			−1.12636			−0.563179	+	0.826335i	$0.690422\pi$
$6$	3.98762	+	1.44875i	0.664604	+	0.241458i
$7$	−10.8851	+	6.28452i	−1.55501	+	0.897788i	−0.557294	+	0.830315i	$0.688160\pi$
$7$	−10.8851	+	6.28452i	−1.55501	+	0.897788i	−0.997721	+	0.0674727i	$0.978506\pi$
$8$	2.82843			0.353553
$9$	−8.45364	+	3.08804i	−0.939293	+	0.343115i
$10$	3.98228	−	6.89751i	0.398228	−	0.689751i
$11$	3.34234	−	5.78910i	0.303849	−	0.526282i	−0.673155	−	0.739501i	$-0.735061\pi$
$11$	3.34234	−	5.78910i	0.303849	−	0.526282i	0.977004	+	0.213219i	$0.0683948\pi$
$12$	−4.59402	+	3.85940i	−0.382835	+	0.321617i
$13$	3.64652	−	12.4781i	0.280502	−	0.959854i
$13$	3.64652	−	12.4781i	0.280502	−	0.959854i
$14$		−	17.7753i		−	1.26966i
$15$	2.94355	+	16.6370i	0.196236	+	1.10913i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	13.5918	−	7.84721i	0.799516	−	0.461601i	−0.0437859	−	0.999041i	$-0.513942\pi$
$17$	13.5918	−	7.84721i	0.799516	−	0.461601i	0.843302	+	0.537440i	$0.180609\pi$
$18$	2.19557	−	12.5371i	0.121976	−	0.696507i
$19$	−8.05581	+	4.65102i	−0.423990	+	0.244791i	−0.696783	−	0.717282i	$-0.745386\pi$
$19$	−8.05581	+	4.65102i	−0.423990	+	0.244791i	0.272793	+	0.962073i	$0.412053\pi$
$20$	5.63179	+	9.75455i	0.281590	+	0.487728i
$21$	24.2545	+	28.8712i	1.15498	+	1.37482i
$22$	4.72678	+	8.18703i	0.214854	+	0.372138i
$23$	−31.2216	−	18.0258i	−1.35746	−	0.783730i	−0.368179	−	0.929755i	$-0.620019\pi$
$23$	−31.2216	−	18.0258i	−1.35746	−	0.783730i	−0.989281	+	0.146025i	$0.953352\pi$
$24$	−1.47832	−	8.35551i	−0.0615968	−	0.348146i
$25$	6.71708			0.268683
$26$	12.7040	+	13.2894i	0.488616	+	0.511131i
$27$	13.5409	+	23.3591i	0.501513	+	0.865150i
$28$	21.7702	+	12.5690i	0.777507	+	0.448894i
$29$	10.4331	+	6.02355i	0.359762	+	0.207709i	0.668976	−	0.743284i	$-0.266733\pi$
$29$	10.4331	+	6.02355i	0.359762	+	0.207709i	−0.309214	+	0.950992i	$0.600066\pi$
$30$	−22.4575	−	8.15903i	−0.748582	−	0.271968i
$31$			28.5613i			0.921332i	0.887573	+	0.460666i	$0.152389\pi$
$31$			28.5613i			0.921332i	−0.887573	+	0.460666i	$0.847611\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−18.8486	−	6.84791i	−0.571171	−	0.207512i
$34$			22.1953i			0.652802i
$35$	61.3026	−	35.3931i	1.75150	−	1.01123i
$36$	13.8023	+	11.5541i	0.383397	+	0.320947i
$37$	0.0845745	+	0.0488291i	0.00228580	+	0.00131971i	0.501142	−	0.865365i	$-0.332913\pi$
$37$	0.0845745	+	0.0488291i	0.00228580	+	0.00131971i	−0.498857	+	0.866685i	$0.666247\pi$
$38$		−	13.1551i		−	0.346186i
$39$	−38.7677	−	4.25038i	−0.994043	−	0.108984i
$40$	−15.9291			−0.398228
$41$	−5.07312	+	8.78691i	−0.123735	+	0.214315i	−0.921238	−	0.389000i	$-0.872821\pi$
$41$	−5.07312	+	8.78691i	−0.123735	+	0.214315i	0.797503	+	0.603315i	$0.206154\pi$
$42$	−52.5104	+	9.29054i	−1.25025	+	0.221203i
$43$	−34.2678	−	59.3535i	−0.796925	−	1.38032i	−0.921609	−	0.388119i	$-0.873125\pi$
$43$	−34.2678	−	59.3535i	−0.796925	−	1.38032i	0.124684	−	0.992196i	$-0.460208\pi$
$44$	−13.3694			−0.303849
$45$	47.6091	−	17.3912i	1.05798	−	0.386470i
$46$	44.1540	−	25.4923i	0.959869	−	0.554181i
$47$	−57.8179			−1.23017			−0.615084	−	0.788461i	$-0.710878\pi$
$47$	−57.8179			−1.23017			−0.615084	+	0.788461i	$0.710878\pi$
$48$	11.2787	+	4.09767i	0.234973	+	0.0853681i
$49$	54.4903	−	94.3800i	1.11205	−	1.92612i
$50$	−4.74970	+	8.22671i	−0.0949939	+	0.164534i
$51$	−30.2856	−	36.0502i	−0.593835	−	0.706868i
$52$	−25.2592	+	6.16213i	−0.485754	+	0.118503i
$53$			57.4927i			1.08477i	0.840131	+	0.542384i	$0.182478\pi$
$53$			57.4927i			1.08477i	−0.840131	+	0.542384i	$0.817522\pi$
$54$	−38.1837	+	0.0667479i	−0.707106	+	0.00123607i
$55$	−18.8234	+	32.6030i	−0.342243	+	0.592782i
$56$	−30.7877	+	17.7753i	−0.549781	+	0.317416i
$57$	17.9502	+	21.3669i	0.314915	+	0.374858i
$58$	−14.7546	+	8.51859i	−0.254390	+	0.146872i
$59$	19.9580	+	34.5682i	0.338271	+	0.585902i	0.984108	−	0.177573i	$-0.0568246\pi$
$59$	19.9580	+	34.5682i	0.338271	+	0.585902i	−0.645837	+	0.763476i	$0.723491\pi$
$60$	25.8726	−	21.7354i	0.431209	−	0.362256i
$61$	5.10063	+	8.83454i	0.0836168	+	0.144829i	0.904801	−	0.425835i	$-0.140019\pi$
$61$	5.10063	+	8.83454i	0.0836168	+	0.144829i	−0.821184	+	0.570663i	$0.806686\pi$
$62$	−34.9803	−	20.1959i	−0.564199	−	0.325740i
$63$	72.6119	−	86.7406i	1.15257	−	1.37684i
$64$	8.00000			0.125000
$65$	−20.5365	+	70.2740i	−0.315945	+	1.08114i
$66$	21.7149	−	18.2426i	0.329014	−	0.276403i
$67$	−66.1637	−	38.1996i	−0.987517	−	0.570143i	−0.0829861	−	0.996551i	$-0.526446\pi$
$67$	−66.1637	−	38.1996i	−0.987517	−	0.570143i	−0.904531	+	0.426407i	$0.859779\pi$
$68$	−27.1835	−	15.6944i	−0.399758	−	0.230800i
$69$	−36.9319	+	101.654i	−0.535244	+	1.47324i
$70$			100.107i			1.43010i
$71$	−24.1673	−	41.8589i	−0.340384	−	0.589562i	0.644120	−	0.764924i	$-0.277224\pi$
$71$	−24.1673	−	41.8589i	−0.340384	−	0.589562i	−0.984504	+	0.175362i	$0.943890\pi$
$72$	−23.9105	+	8.73428i	−0.332090	+	0.121309i
$73$			8.56609i			0.117344i	0.998277	+	0.0586718i	$0.0186866\pi$
$73$			8.56609i			0.117344i	−0.998277	+	0.0586718i	$0.981313\pi$
$74$	−0.119606	+	0.0690548i	−0.00161630	+	0.000933173i
$75$	−3.51079	−	19.8431i	−0.0468105	−	0.264574i
$76$	16.1116	+	9.30205i	0.211995	+	0.122395i
$77$			84.0200i			1.09117i
$78$	32.6185	−	44.4751i	0.418186	−	0.570193i
$79$	37.3730			0.473076			0.236538	−	0.971622i	$-0.423987\pi$
$79$	37.3730			0.473076			0.236538	+	0.971622i	$0.423987\pi$
$80$	11.2636	−	19.5091i	0.140795	−	0.243864i
$81$	61.9281	−	52.2103i	0.764544	−	0.644571i
$82$	−7.17448	−	12.4266i	−0.0874937	−	0.151543i
$83$	52.7630			0.635699			0.317850	−	0.948141i	$-0.397039\pi$
$83$	52.7630			0.635699			0.317850	+	0.948141i	$0.397039\pi$
$84$	25.7519	−	70.8812i	0.306570	−	0.843824i
$85$	−76.5460	+	44.1939i	−0.900542	+	0.519928i
$86$	96.9239			1.12702
$87$	12.3413	−	33.9689i	0.141854	−	0.390447i
$88$	9.45357	−	16.3741i	0.107427	−	0.186069i
$89$	49.4552	−	85.6589i	0.555677	−	0.962460i	−0.442174	−	0.896929i	$-0.645793\pi$
$89$	49.4552	−	85.6589i	0.555677	−	0.962460i	0.997851	−	0.0655307i	$-0.0208740\pi$
$90$	−12.3650	+	70.6065i	−0.137389	+	0.784516i
$91$	38.7260	+	158.742i	0.425561	+	1.74442i
$92$			72.1031i			0.783730i
$93$	84.3735	−	14.9280i	0.907242	−	0.160516i
$94$	40.8834	−	70.8122i	0.434930	−	0.753321i
$95$	45.3686	−	26.1936i	0.477565	−	0.275722i
$96$	−12.9938	+	10.9160i	−0.135353	+	0.113709i
$97$	43.0461	−	24.8527i	0.443775	−	0.256213i	−0.261423	−	0.965224i	$-0.584192\pi$
$97$	43.0461	−	24.8527i	0.443775	−	0.256213i	0.705197	+	0.709011i	$0.250858\pi$
$98$	77.0609	+	133.473i	0.786336	+	1.36197i
$99$	−10.3780	+	59.2603i	−0.104828	+	0.598589i
$100$	−6.71708	−	11.6343i	−0.0671708	−	0.116343i
$101$	−97.9421	−	56.5469i	−0.969724	−	0.559870i	−0.0705718	−	0.997507i	$-0.522482\pi$
$101$	−97.9421	−	56.5469i	−0.969724	−	0.559870i	−0.899152	+	0.437636i	$0.855816\pi$
$102$	65.5675	−	11.6007i	0.642818	−	0.113732i
$103$	−152.226			−1.47793			−0.738963	−	0.673747i	$-0.764684\pi$
$103$	−152.226			−1.47793			−0.738963	+	0.673747i	$0.764684\pi$
$104$	10.3139	−	35.2934i	0.0991723	−	0.339359i
$105$	−136.596	−	162.597i	−1.30092	−	1.54854i
$106$	−70.4139	−	40.6535i	−0.664282	−	0.383523i
$107$	−48.4068	−	27.9477i	−0.452400	−	0.261193i	0.256443	−	0.966559i	$-0.417449\pi$
$107$	−48.4068	−	27.9477i	−0.452400	−	0.261193i	−0.708843	+	0.705366i	$0.750783\pi$
$108$	26.9182	−	46.8125i	0.249243	−	0.433449i
$109$		−	28.3238i		−	0.259851i	−0.991524	−	0.129926i	$-0.958526\pi$
$109$		−	28.3238i		−	0.259851i	0.991524	−	0.129926i	$-0.0414738\pi$
$110$	−26.6203	−	46.1077i	−0.242002	−	0.419160i
$111$	0.100043	−	0.275365i	0.000901287	−	0.00248076i
$112$		−	50.2761i		−	0.448894i
$113$	−14.7007	+	8.48743i	−0.130094	+	0.0751100i	−0.563635	−	0.826024i	$-0.690597\pi$
$113$	−14.7007	+	8.48743i	−0.130094	+	0.0751100i	0.433540	+	0.901134i	$0.357264\pi$
$114$	−38.8617	+	6.87571i	−0.340892	+	0.0603133i
$115$	175.833	+	101.517i	1.52899	+	0.882760i
$116$		−	24.0942i		−	0.207709i
$117$	7.70641	+	116.746i	0.0658668	+	0.997828i
$118$	−56.4497			−0.478387
$119$	−98.6319	+	170.835i	−0.828839	+	1.43559i
$120$	8.32561	+	47.0565i	0.0693800	+	0.392138i
$121$	38.1575	+	66.0907i	0.315351	+	0.546205i
$122$	−14.4268			−0.118252
$123$	28.6091	+	10.3940i	0.232595	+	0.0845040i
$124$	49.4696	−	28.5613i	0.398949	−	0.230333i
$125$	102.966			0.823725
$126$	54.8907	+	150.266i	0.435641	+	1.19259i
$127$	42.4268	−	73.4854i	0.334069	−	0.578625i	−0.649236	−	0.760587i	$-0.724911\pi$
$127$	42.4268	−	73.4854i	0.334069	−	0.578625i	0.983306	+	0.181962i	$0.0582447\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	−157.427	+	132.253i	−1.22036	+	1.02522i
$130$	−71.5463	−	74.8432i	−0.550356	−	0.575717i
$131$			146.601i			1.11909i	0.828801	+	0.559544i	$0.189024\pi$
$131$			146.601i			1.11909i	−0.828801	+	0.559544i	$0.810976\pi$
$132$	6.98771	+	39.4947i	0.0529372	+	0.299202i
$133$	58.4589	−	101.254i	0.439540	−	0.761306i
$134$	93.5695	−	54.0224i	0.698280	−	0.403152i
$135$	−76.2593	−	131.553i	−0.564884	−	0.974469i
$136$	38.4433	−	22.1953i	0.282672	−	0.163201i
$137$	−100.447	−	173.979i	−0.733189	−	1.26992i	−0.955513	−	0.294948i	$-0.904698\pi$
$137$	−100.447	−	173.979i	−0.733189	−	1.26992i	0.222325	−	0.974973i	$-0.428636\pi$
$138$	−98.3851	−	117.112i	−0.712935	−	0.848639i
$139$	19.4712	+	33.7252i	0.140081	+	0.242627i	0.927527	−	0.373756i	$-0.121930\pi$
$139$	19.4712	+	33.7252i	0.140081	+	0.242627i	−0.787446	+	0.616384i	$0.788597\pi$
$140$	−122.605	−	70.7862i	−0.875752	−	0.505616i
$141$	30.2195	+	170.801i	0.214322	+	1.21135i
$142$	68.3553			0.481376
$143$	−60.0491	−	62.8162i	−0.419924	−	0.439274i
$144$	6.21001	−	35.4603i	0.0431251	−	0.246252i
$145$	−58.7571	−	33.9234i	−0.405221	−	0.233955i
$146$	−10.4913	−	6.05714i	−0.0718580	−	0.0414873i
$147$	−307.290	−	111.642i	−2.09041	−	0.759467i
$148$		−	0.195317i		−	0.00131971i
$149$	−106.934	−	185.216i	−0.717680	−	1.24306i	−0.961917	−	0.273342i	$-0.911871\pi$
$149$	−106.934	−	185.216i	−0.717680	−	1.24306i	0.244237	−	0.969716i	$-0.421463\pi$
$150$	26.7852	+	9.73134i	0.178568	+	0.0648756i
$151$			39.9974i			0.264884i	0.991191	+	0.132442i	$0.0422818\pi$
$151$			39.9974i			0.264884i	−0.991191	+	0.132442i	$0.957718\pi$
$152$	−22.7853	+	13.1551i	−0.149903	+	0.0865466i
$153$	−90.6675	+	108.309i	−0.592598	+	0.707904i
$154$	−102.903	−	59.4111i	−0.668202	−	0.385786i
$155$		−	160.851i		−	1.03775i
$156$	31.4058	+	71.3980i	0.201319	+	0.457680i
$157$	102.886			0.655326			0.327663	−	0.944795i	$-0.393739\pi$
$157$	102.886			0.655326			0.327663	+	0.944795i	$0.393739\pi$
$158$	−26.4267	+	45.7724i	−0.167258	+	0.289699i
$159$	169.840	−	30.0495i	1.06818	−	0.188990i
$160$	15.9291	+	27.5900i	0.0995570	+	0.172438i
$161$	453.133			2.81449
$162$	20.1545	+	112.764i	0.124411	+	0.696076i
$163$	3.35089	−	1.93464i	0.0205576	−	0.0118689i	−0.489686	−	0.871899i	$-0.662889\pi$
$163$	3.35089	−	1.93464i	0.0205576	−	0.0118689i	0.510244	+	0.860030i	$0.329555\pi$
$164$	20.2925			0.123735
$165$	106.152	+	38.5660i	0.643343	+	0.233733i
$166$	−37.3091	+	64.6213i	−0.224754	+	0.389285i
$167$	−47.0680	+	81.5242i	−0.281844	+	0.488169i	−0.971839	−	0.235646i	$-0.924280\pi$
$167$	−47.0680	+	81.5242i	−0.281844	+	0.488169i	0.689995	+	0.723814i	$0.257613\pi$
$168$	68.6020	+	81.6601i	0.408346	+	0.486072i
$169$	−142.406	−	91.0033i	−0.842638	−	0.538481i
$170$		−	124.999i		−	0.735289i
$171$	53.7384	−	64.1947i	0.314260	−	0.375408i
$172$	−68.5356	+	118.707i	−0.398463	+	0.690158i
$173$	−101.943	+	58.8565i	−0.589263	+	0.340211i	−0.764806	−	0.644261i	$-0.777165\pi$
$173$	−101.943	+	58.8565i	−0.589263	+	0.340211i	0.175543	+	0.984472i	$0.443832\pi$
$174$	32.8767	+	39.1346i	0.188946	+	0.224911i
$175$	−73.1161	+	42.2136i	−0.417807	+	0.241221i
$176$	13.3694	+	23.1564i	0.0759623	+	0.131571i
$177$	91.6873	−	77.0259i	0.518008	−	0.435175i
$178$	69.9402	+	121.140i	0.392923	+	0.680562i
$179$	104.996	+	60.6192i	0.586567	+	0.338655i	0.763739	−	0.645525i	$-0.223361\pi$
$179$	104.996	+	60.6192i	0.586567	+	0.338655i	−0.177172	+	0.984180i	$0.556695\pi$
$180$	−77.7315	−	65.0703i	−0.431842	−	0.361502i
$181$	168.315			0.929915			0.464958	−	0.885333i	$-0.346070\pi$
$181$	168.315			0.929915			0.464958	+	0.885333i	$0.346070\pi$
$182$	−221.802	−	64.8180i	−1.21869	−	0.356143i
$183$	23.4324	−	19.6854i	0.128046	−	0.107570i
$184$	−88.3079	−	50.9846i	−0.479934	−	0.277090i
$185$	−0.476306	−	0.274996i	−0.00257463	−	0.00148646i
$186$	−41.3781	+	113.892i	−0.222463	+	0.612321i
$187$		−	104.912i		−	0.561028i
$188$	57.8179	+	100.144i	0.307542	+	0.532679i
$189$	−294.194	−	169.168i	−1.55658	−	0.895069i
$190$			74.0867i			0.389930i
$191$	306.601	−	177.016i	1.60524	−	0.926788i	0.614829	−	0.788661i	$-0.289225\pi$
$191$	306.601	−	177.016i	1.60524	−	0.926788i	0.990415	−	0.138127i	$-0.0441082\pi$
$192$	−4.18133	−	23.6330i	−0.0217777	−	0.123088i
$193$	−36.0550	−	20.8164i	−0.186814	−	0.107857i	0.403676	−	0.914902i	$-0.367732\pi$
$193$	−36.0550	−	20.8164i	−0.186814	−	0.107857i	−0.590490	+	0.807045i	$0.701066\pi$
$194$			70.2940i			0.362340i
$195$	218.332	+	23.9373i	1.11965	+	0.122755i
$196$	−217.961			−1.11205
$197$	24.1413	−	41.8139i	0.122545	−	0.212254i	−0.798226	−	0.602358i	$-0.794228\pi$
$197$	24.1413	−	41.8139i	0.122545	−	0.212254i	0.920770	+	0.390105i	$0.127561\pi$
$198$	−65.2404	−	54.6137i	−0.329497	−	0.275827i
$199$	177.171	+	306.870i	0.890309	+	1.54206i	0.839505	+	0.543351i	$0.182845\pi$
$199$	177.171	+	306.870i	0.890309	+	1.54206i	0.0508035	+	0.998709i	$0.483822\pi$
$200$	18.9988			0.0949939
$201$	−78.2647	+	215.421i	−0.389377	+	1.07175i
$202$	138.511	−	79.9694i	0.685698	−	0.395888i
$203$	−151.421			−0.745914
$204$	−32.1553	+	88.5064i	−0.157624	+	0.433855i
$205$	28.5708	−	49.4860i	0.139370	−	0.241395i
$206$	107.640	−	186.438i	0.522525	−	0.905041i
$207$	319.600	+	55.9702i	1.54396	+	0.270387i
$208$	35.9323	+	37.5881i	0.172752	+	0.180712i
$209$			62.1812i			0.297518i
$210$	295.727	−	52.3224i	1.40823	−	0.249154i
$211$	−90.6918	+	157.083i	−0.429819	+	0.744468i	−0.996857	−	0.0792233i	$-0.974756\pi$
$211$	−90.6918	+	157.083i	−0.429819	+	0.744468i	0.567038	+	0.823692i	$0.308089\pi$
$212$	99.5803	−	57.4927i	0.469718	−	0.271192i
$213$	−111.025	+	93.2712i	−0.521243	+	0.437893i
$214$	68.4576	−	39.5240i	0.319895	−	0.184692i
$215$	192.989	+	334.267i	0.897623	+	1.55473i
$216$	38.2993	+	66.0694i	0.177312	+	0.305877i
$217$	−179.494	−	310.893i	−0.827161	−	1.43269i
$218$	34.6894	+	20.0279i	0.159126	+	0.0918713i
$219$	25.3052	−	4.47720i	0.115549	−	0.0204438i
$220$	75.2935			0.342243
$221$	−48.3556	−	198.214i	−0.218804	−	0.896898i
$222$	0.266510	+	0.317239i	0.00120050	+	0.00142901i
$223$	−34.0280	−	19.6461i	−0.152592	−	0.0880989i	0.421760	−	0.906708i	$-0.361412\pi$
$223$	−34.0280	−	19.6461i	−0.152592	−	0.0880989i	−0.574352	+	0.818609i	$0.694746\pi$
$224$	61.5754	+	35.5506i	0.274890	+	0.158708i
$225$	−56.7838	+	20.7426i	−0.252372	+	0.0921893i
$226$		−	24.0061i		−	0.106222i
$227$	8.53945	+	14.7908i	0.0376187	+	0.0651576i	0.884222	−	0.467067i	$-0.154689\pi$
$227$	8.53945	+	14.7908i	0.0376187	+	0.0651576i	−0.846603	+	0.532225i	$0.821356\pi$
$228$	19.0584	−	52.4575i	0.0835893	−	0.230077i
$229$			183.299i			0.800433i	0.916421	+	0.400216i	$0.131065\pi$
$229$			183.299i			0.800433i	−0.916421	+	0.400216i	$0.868935\pi$
$230$	−248.666	+	143.567i	−1.08116	+	0.624206i
$231$	248.205	−	43.9144i	1.07448	−	0.190106i
$232$	29.5093	+	17.0372i	0.127195	+	0.0734361i
$233$		−	188.357i		−	0.808399i	−0.914671	−	0.404199i	$-0.867550\pi$
$233$		−	188.357i		−	0.808399i	0.914671	−	0.404199i	$-0.132450\pi$
$234$	−148.433	−	73.1134i	−0.634330	−	0.312451i
$235$	325.618			1.38561
$236$	39.9160	−	69.1365i	0.169135	−	0.292951i
$237$	−19.5336	−	110.404i	−0.0824202	−	0.465841i
$238$	−139.487	−	241.598i	−0.586078	−	1.01512i
$239$	−388.115			−1.62391			−0.811956	−	0.583718i	$-0.801597\pi$
$239$	−388.115			−1.62391			−0.811956	+	0.583718i	$0.801597\pi$
$240$	−63.5193	−	23.0772i	−0.264664	−	0.0961551i
$241$	−135.458	+	78.2069i	−0.562068	+	0.324510i	−0.753975	−	0.656903i	$-0.771866\pi$
$241$	−135.458	+	78.2069i	−0.562068	+	0.324510i	0.191907	+	0.981413i	$0.438533\pi$
$242$	−107.926			−0.445974
$243$	−186.603	−	155.654i	−0.767914	−	0.640553i
$244$	10.2013	−	17.6691i	0.0418084	−	0.0724143i
$245$	−306.878	+	531.529i	−1.25256	+	2.16950i
$246$	−32.9597	+	27.6892i	−0.133983	+	0.112558i
$247$	28.6602	+	117.481i	0.116033	+	0.475632i
$248$			80.7836i			0.325740i
$249$	−27.5774	−	155.868i	−0.110753	−	0.625977i
$250$	−72.8077	+	126.107i	−0.291231	+	0.504426i
$251$	336.848	−	194.479i	1.34202	−	0.774818i	0.354920	−	0.934897i	$-0.384508\pi$
$251$	336.848	−	194.479i	1.34202	−	0.774818i	0.987104	+	0.160078i	$0.0511747\pi$
$252$	−222.851	−	39.0269i	−0.884330	−	0.154869i
$253$	−208.706	+	120.497i	−0.824926	+	0.476271i
$254$	60.0006	+	103.924i	0.236223	+	0.409150i
$255$	170.562	+	203.027i	0.668871	+	0.796186i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−56.8507	−	32.8228i	−0.221209	−	0.127715i	0.385301	−	0.922791i	$-0.374098\pi$
$257$	−56.8507	−	32.8228i	−0.221209	−	0.127715i	−0.606510	+	0.795076i	$0.707431\pi$
$258$	−50.6588	−	286.325i	−0.196352	−	1.10979i
$259$	−1.22747			−0.00473927
$260$	142.255	−	34.7039i	0.547133	−	0.133476i
$261$	−106.799	−	18.7032i	−0.409190	−	0.0716597i
$262$	−179.548	−	103.662i	−0.685299	−	0.395657i
$263$	−28.1343	−	16.2433i	−0.106975	−	0.0617618i	0.445558	−	0.895253i	$-0.353005\pi$
$263$	−28.1343	−	16.2433i	−0.106975	−	0.0617618i	−0.552533	+	0.833491i	$0.686339\pi$
$264$	−53.3120	−	19.3688i	−0.201939	−	0.0733667i
$265$		−	323.787i		−	1.22184i
$266$	82.6733	+	143.194i	0.310802	+	0.538325i
$267$	−278.895	−	101.326i	−1.04455	−	0.379497i
$268$			152.798i			0.570143i
$269$	−288.109	+	166.340i	−1.07104	+	0.618364i	−0.928465	−	0.371420i	$-0.878871\pi$
$269$	−288.109	+	166.340i	−1.07104	+	0.618364i	−0.142573	+	0.989784i	$0.545538\pi$
$270$	215.043	−	0.375910i	0.796454	−	0.00139226i
$271$	−394.103	−	227.536i	−1.45426	−	0.839615i	−0.455537	−	0.890217i	$-0.650553\pi$
$271$	−394.103	−	227.536i	−1.45426	−	0.839615i	−0.998719	+	0.0506017i	$0.983886\pi$
$272$			62.7777i			0.230800i
$273$	448.702	−	197.370i	1.64360	−	0.722968i
$274$	284.107			1.03689
$275$	22.4508	−	38.8859i	0.0816392	−	0.141403i
$276$	213.001	−	37.6858i	0.771744	−	0.136543i
$277$	−32.1992	−	55.7707i	−0.116243	−	0.201338i	0.802033	−	0.597280i	$-0.203752\pi$
$277$	−32.1992	−	55.7707i	−0.116243	−	0.201338i	−0.918276	+	0.395941i	$0.870418\pi$
$278$	−55.0730			−0.198104
$279$	−88.1983	−	241.447i	−0.316123	−	0.865401i
$280$	173.390	−	100.107i	0.619250	−	0.357524i
$281$	−523.068			−1.86145			−0.930725	−	0.365719i	$-0.880823\pi$
$281$	−523.068			−1.86145			−0.930725	+	0.365719i	$0.880823\pi$
$282$	−230.556	−	83.7634i	−0.817575	−	0.297033i
$283$	17.5560	−	30.4078i	0.0620352	−	0.107448i	−0.833340	−	0.552761i	$-0.813574\pi$
$283$	17.5560	−	30.4078i	0.0620352	−	0.107448i	0.895375	+	0.445313i	$0.146908\pi$
$284$	−48.3345	+	83.7178i	−0.170192	+	0.294781i
$285$	−101.092	−	120.334i	−0.354707	−	0.422224i
$286$	119.395	−	29.1271i	0.417465	−	0.101843i
$287$		−	127.529i		−	0.444350i
$288$	39.0387	+	32.6799i	0.135551	+	0.113472i
$289$	−21.3425	+	36.9663i	−0.0738495	+	0.127911i
$290$	83.0950	−	47.9749i	0.286535	−	0.165431i
$291$	−95.9166	−	114.174i	−0.329610	−	0.392350i
$292$	14.8369	−	8.56609i	0.0508113	−	0.0293359i
$293$	256.388	+	444.077i	0.875045	+	1.51562i	0.856715	+	0.515790i	$0.172501\pi$
$293$	256.388	+	444.077i	0.875045	+	1.51562i	0.0183294	+	0.999832i	$0.494165\pi$
$294$	354.019	−	297.409i	1.20415	−	1.01160i
$295$	−112.399	−	194.681i	−0.381014	−	0.659936i
$296$	0.239213	+	0.138110i	0.000808152	+	0.000466587i
$297$	180.486	−	0.315503i	0.607697	−	0.00106230i
$298$	302.456			1.01495
$299$	−338.778	+	323.854i	−1.13304	+	1.08312i
$300$	−30.8584	+	25.9239i	−0.102861	+	0.0864131i
$301$	746.017	+	430.713i	2.47846	+	1.43094i
$302$	−48.9866	−	28.2824i	−0.162207	−	0.0936505i
$303$	−115.855	+	318.888i	−0.382361	+	1.05244i
$304$		−	37.2082i		−	0.122395i
$305$	−28.7257	−	49.7543i	−0.0941825	−	0.163129i
$306$	−68.5398	−	187.631i	−0.223986	−	0.613173i
$307$		−	438.552i		−	1.42851i	−0.699886	−	0.714254i	$-0.746766\pi$
$307$		−	438.552i		−	1.42851i	0.699886	−	0.714254i	$-0.253234\pi$
$308$	145.527	−	84.0200i	0.472490	−	0.272792i
$309$	79.5635	+	449.695i	0.257487	+	1.45532i
$310$	197.002	+	113.739i	0.635490	+	0.366900i
$311$		−	292.633i		−	0.940942i	−0.882416	−	0.470471i	$-0.844084\pi$
$311$		−	292.633i		−	0.940942i	0.882416	−	0.470471i	$-0.155916\pi$
$312$	−109.652	−	12.0219i	−0.351447	−	0.0385317i
$313$	−163.079			−0.521020			−0.260510	−	0.965471i	$-0.583891\pi$
$313$	−163.079			−0.521020			−0.260510	+	0.965471i	$0.583891\pi$
$314$	−72.7516	+	126.009i	−0.231693	+	0.401304i
$315$	−408.935	+	488.505i	−1.29821	+	1.55081i
$316$	−37.3730	−	64.7319i	−0.118269	−	0.204848i
$317$	421.590			1.32994			0.664969	−	0.746871i	$-0.268445\pi$
$317$	421.590			1.32994			0.664969	+	0.746871i	$0.268445\pi$
$318$	−83.2923	+	229.259i	−0.261925	+	0.720941i
$319$	69.7420	−	40.2655i	0.218627	−	0.126224i
$320$	−45.0543			−0.140795
$321$	−57.2602	+	157.607i	−0.178381	+	0.490987i
$322$	−320.414	+	554.973i	−0.995073	+	1.72352i
$323$	−72.9951	+	126.431i	−0.225991	+	0.391428i
$324$	−152.359	−	55.0523i	−0.470244	−	0.169915i
$325$	24.4940	−	83.8164i	0.0753661	−	0.257897i
$326$			5.47198i			0.0167852i
$327$	−83.6718	+	14.8039i	−0.255877	+	0.0452718i
$328$	−14.3490	+	24.8531i	−0.0437468	+	0.0757717i
$329$	629.354	−	363.358i	1.91293	−	1.10443i
$330$	−122.294	+	102.738i	−0.370588	+	0.311328i
$331$	49.3904	−	28.5156i	0.149216	−	0.0861498i	−0.423533	−	0.905881i	$-0.639210\pi$
$331$	49.3904	−	28.5156i	0.149216	−	0.0861498i	0.572749	+	0.819731i	$0.305877\pi$
$332$	−52.7630	−	91.3883i	−0.158925	−	0.275266i
$333$	−0.865749	−	0.151615i	−0.00259985	−	0.000455300i
$334$	−66.5642	−	115.293i	−0.199294	−	0.345187i
$335$	372.620	+	215.132i	1.11230	+	0.642186i
$336$	−148.522	+	26.2776i	−0.442029	+	0.0782072i
$337$	−332.343			−0.986181			−0.493091	−	0.869978i	$-0.664133\pi$
$337$	−332.343			−0.986181			−0.493091	+	0.869978i	$0.664133\pi$
$338$	212.152	−	110.062i	0.627668	−	0.325626i
$339$	32.7564	+	38.9914i	0.0966266	+	0.115019i
$340$	153.092	+	88.3877i	0.450271	+	0.259964i
$341$	165.344	+	95.4616i	0.484881	+	0.279946i
$342$	40.6233	+	111.208i	0.118782	+	0.325170i
$343$			753.899i			2.19796i
$344$	−96.9239	−	167.877i	−0.281756	−	0.488015i
$345$	207.993	−	572.492i	0.602877	−	1.65940i
$346$		−	166.471i		−	0.481131i
$347$	31.5810	−	18.2333i	0.0910114	−	0.0525455i	−0.453804	−	0.891102i	$-0.649933\pi$
$347$	31.5810	−	18.2333i	0.0910114	−	0.0525455i	0.544815	+	0.838556i	$0.316600\pi$
$348$	−71.1772	+	12.5932i	−0.204532	+	0.0361874i
$349$	−298.830	−	172.530i	−0.856247	−	0.494354i	0.00650692	−	0.999979i	$-0.497929\pi$
$349$	−298.830	−	172.530i	−0.856247	−	0.494354i	−0.862754	+	0.505625i	$0.831262\pi$
$350$		−	119.398i		−	0.341138i
$351$	340.854	−	83.7848i	0.971093	−	0.238703i
$352$	−37.8143			−0.107427
$353$	−107.896	+	186.882i	−0.305655	+	0.529410i	−0.977407	−	0.211366i	$-0.932209\pi$
$353$	−107.896	+	186.882i	−0.305655	+	0.529410i	0.671752	+	0.740776i	$0.265542\pi$
$354$	29.5043	+	166.759i	0.0833456	+	0.471071i
$355$	136.105	+	235.741i	0.383394	+	0.664058i
$356$	−197.821			−0.555677
$357$	556.220	+	202.080i	1.55804	+	0.566052i
$358$	−148.486	+	85.7285i	−0.414766	+	0.239465i
$359$	−78.7412			−0.219335			−0.109667	−	0.993968i	$-0.534979\pi$
$359$	−78.7412			−0.219335			−0.109667	+	0.993968i	$0.534979\pi$
$360$	134.659	−	49.1897i	0.374053	−	0.136638i
$361$	−137.236	+	237.700i	−0.380155	+	0.658448i
$362$	−119.016	+	206.142i	−0.328775	+	0.569454i
$363$	175.296	−	147.265i	0.482910	−	0.405689i
$364$	236.223	−	225.817i	0.648965	−	0.620378i
$365$		−	48.2424i		−	0.132171i
$366$	7.54037	+	42.6183i	0.0206021	+	0.116444i
$367$	314.990	−	545.578i	0.858283	−	1.48659i	−0.0152828	−	0.999883i	$-0.504865\pi$
$367$	314.990	−	545.578i	0.858283	−	1.48659i	0.873566	−	0.486706i	$-0.161802\pi$
$368$	124.886	−	72.1031i	0.339365	−	0.195932i
$369$	15.7521	−	89.9473i	0.0426886	−	0.243760i
$370$	0.673599	−	0.388902i	0.00182054	−	0.00105109i
$371$	−361.314	−	625.814i	−0.973892	−	1.68683i
$372$	−110.230	−	131.211i	−0.296316	−	0.352718i
$373$	218.637	+	378.691i	0.586159	+	1.01526i	0.994730	+	0.102531i	$0.0326941\pi$
$373$	218.637	+	378.691i	0.586159	+	1.01526i	−0.408571	+	0.912727i	$0.633973\pi$
$374$	128.491	+	74.1842i	0.343558	+	0.198353i
$375$	−53.8166	−	304.173i	−0.143511	−	0.811127i
$376$	−163.534			−0.434930
$377$	113.207	−	108.220i	0.300284	−	0.287056i
$378$	415.214	−	240.693i	1.09845	−	0.636753i
$379$	−286.650	−	165.497i	−0.756332	−	0.436669i	0.0716451	−	0.997430i	$-0.477175\pi$
$379$	−286.650	−	165.497i	−0.756332	−	0.436669i	−0.827977	+	0.560762i	$0.810508\pi$
$380$	−90.7373	−	52.3872i	−0.238782	−	0.137861i
$381$	−239.260	−	86.9255i	−0.627978	−	0.228151i
$382$			500.678i			1.31068i
$383$	325.321	+	563.472i	0.849401	+	1.47121i	0.881744	+	0.471729i	$0.156370\pi$
$383$	325.321	+	563.472i	0.849401	+	1.47121i	−0.0323426	+	0.999477i	$0.510297\pi$
$384$	31.9010	+	11.5900i	0.0830755	+	0.0301822i
$385$		−	473.183i		−	1.22905i
$386$	50.9895	−	29.4388i	0.132097	−	0.0762664i
$387$	472.973	+	395.933i	1.22215	+	1.02308i
$388$	−86.0923	−	49.7054i	−0.221887	−	0.128107i
$389$		−	644.817i		−	1.65763i	−0.559525	−	0.828814i	$-0.689016\pi$
$389$		−	644.817i		−	1.65763i	0.559525	−	0.828814i	$-0.310984\pi$
$390$	−183.701	+	250.474i	−0.471028	+	0.642242i
$391$	−565.809			−1.44708
$392$	154.122	−	266.947i	0.393168	−	0.680987i
$393$	433.076	−	76.6231i	1.10197	−	0.194970i
$394$	34.1409	+	59.1338i	0.0866521	+	0.150086i
$395$	−210.477			−0.532853
$396$	113.020	−	41.2851i	0.285404	−	0.104255i
$397$	−37.8373	+	21.8454i	−0.0953081	+	0.0550262i	−0.546897	−	0.837200i	$-0.684191\pi$
$397$	−37.8373	+	21.8454i	−0.0953081	+	0.0550262i	0.451588	+	0.892226i	$0.350858\pi$
$398$	−501.117			−1.25909
$399$	−329.670	−	119.773i	−0.826241	−	0.300182i
$400$	−13.4342	+	23.2687i	−0.0335854	+	0.0581716i
$401$	−49.0825	+	85.0133i	−0.122400	+	0.212003i	−0.920714	−	0.390239i	$-0.872392\pi$
$401$	−49.0825	+	85.0133i	−0.122400	+	0.212003i	0.798314	+	0.602242i	$0.205726\pi$
$402$	−208.494	−	248.180i	−0.518642	−	0.617363i
$403$	356.391	+	104.149i	0.884344	+	0.258435i
$404$			226.188i			0.559870i
$405$	−348.766	+	294.037i	−0.861151	+	0.726018i
$406$	107.070	−	185.451i	0.263720	−	0.456777i
$407$	0.565354	−	0.326407i	0.00138908	−	0.000801983i
$408$	−85.6605	−	101.965i	−0.209952	−	0.249915i
$409$	251.431	−	145.164i	0.614745	−	0.354923i	−0.160075	−	0.987105i	$-0.551174\pi$
$409$	251.431	−	145.164i	0.614745	−	0.354923i	0.774820	+	0.632181i	$0.217840\pi$
$410$	40.4052	+	69.9838i	0.0985492	+	0.170692i
$411$	−461.455	+	387.665i	−1.12276	+	0.943224i
$412$	152.226	+	263.664i	0.369481	+	0.639960i
$413$	−434.489	−	250.853i	−1.05203	−	0.607391i
$414$	−294.541	+	351.852i	−0.711451	+	0.849883i
$415$	−297.151			−0.716025
$416$	−71.4439	+	17.4291i	−0.171740	+	0.0418970i
$417$	89.4512	−	75.1474i	0.214511	−	0.180210i
$418$	−76.1561	−	43.9688i	−0.182192	−	0.105188i
$419$	−278.887	−	161.016i	−0.665602	−	0.384285i	0.128806	−	0.991670i	$-0.458885\pi$
$419$	−278.887	−	161.016i	−0.665602	−	0.384285i	−0.794408	+	0.607384i	$0.792219\pi$
$420$	−145.029	+	399.188i	−0.345308	+	0.950448i
$421$		−	798.404i		−	1.89645i	−0.317604	−	0.948223i	$-0.602878\pi$
$421$		−	798.404i		−	1.89645i	0.317604	−	0.948223i	$-0.397122\pi$
$422$	−128.258	−	222.149i	−0.303928	−	0.526419i
$423$	488.772	−	178.544i	1.15549	−	0.422089i
$424$			162.614i			0.383523i
$425$	91.2971	−	52.7104i	0.214817	−	0.124024i
$426$	−35.7270	−	201.930i	−0.0838662	−	0.474014i
$427$	−111.042	−	64.1100i	−0.260051	−	0.150140i
$428$			111.791i			0.261193i
$429$	−154.181	+	210.224i	−0.359396	+	0.490033i
$430$	−545.855			−1.26943
$431$	210.497	−	364.591i	0.488392	−	0.845920i	−0.511519	−	0.859272i	$-0.670917\pi$
$431$	210.497	−	364.591i	0.488392	−	0.845920i	0.999911	+	0.0133523i	$0.00425030\pi$
$432$	−108.000	+	0.188791i	−0.250000	+	0.000437017i
$433$	−197.041	−	341.284i	−0.455059	−	0.788186i	0.543632	−	0.839323i	$-0.317049\pi$
$433$	−197.041	−	341.284i	−0.455059	−	0.788186i	−0.998692	+	0.0511377i	$0.983715\pi$
$434$	507.686			1.16978
$435$	−69.5035	+	191.306i	−0.159778	+	0.439784i
$436$	−49.0582	+	28.3238i	−0.112519	+	0.0649628i
$437$	335.353			0.767399
$438$	−12.4101	+	34.1583i	−0.0283335	+	0.0779871i
$439$	−45.4270	+	78.6819i	−0.103478	+	0.179230i	−0.913116	−	0.407701i	$-0.866331\pi$
$439$	−45.4270	+	78.6819i	−0.103478	+	0.179230i	0.809637	+	0.586931i	$0.199664\pi$
$440$	−53.2405	+	92.2153i	−0.121001	+	0.209580i
$441$	−169.193	+	966.123i	−0.383657	+	2.19075i
$442$	276.955	+	80.9355i	0.626594	+	0.183112i
$443$			414.531i			0.935737i	0.883798	+	0.467868i	$0.154978\pi$
$443$			414.531i			0.935737i	−0.883798	+	0.467868i	$0.845022\pi$
$444$	−0.576988	+	0.102085i	−0.00129952	+	0.000229922i
$445$	−278.521	+	482.413i	−0.625891	+	1.08407i
$446$	48.1228	−	27.7837i	0.107899	−	0.0622954i
$447$	−491.258	+	412.703i	−1.09901	+	0.923272i
$448$	−87.0808	+	50.2761i	−0.194377	+	0.112224i
$449$	120.474	+	208.667i	0.268316	+	0.464738i	0.968427	−	0.249297i	$-0.0801994\pi$
$449$	120.474	+	208.667i	0.268316	+	0.464738i	−0.700111	+	0.714034i	$0.746866\pi$
$450$	14.7478	−	84.2129i	0.0327730	−	0.187140i
$451$	33.9122	+	58.7377i	0.0751934	+	0.130239i
$452$	29.4013	+	16.9749i	0.0650471	+	0.0375550i
$453$	118.157	−	20.9053i	0.260833	−	0.0461485i
$454$	−24.1532			−0.0532009
$455$	−218.097	−	894.002i	−0.479334	−	1.96484i
$456$	50.7708	+	60.4347i	0.111339	+	0.132532i
$457$	491.823	+	283.954i	1.07620	+	0.621344i	0.929869	−	0.367892i	$-0.119920\pi$
$457$	491.823	+	283.954i	1.07620	+	0.621344i	0.146331	+	0.989236i	$0.453254\pi$
$458$	−224.495	−	129.612i	−0.490163	−	0.282996i
$459$	367.348	+	211.233i	0.800322	+	0.460202i
$460$		−	406.070i		−	0.882760i
$461$	42.1504	+	73.0066i	0.0914325	+	0.158366i	0.908114	−	0.418723i	$-0.137522\pi$
$461$	42.1504	+	73.0066i	0.0914325	+	0.158366i	−0.816682	+	0.577088i	$0.804189\pi$
$462$	−121.724	+	335.040i	−0.263471	+	0.725195i
$463$		−	494.207i		−	1.06740i	−0.845673	−	0.533701i	$-0.820801\pi$
$463$		−	494.207i		−	1.06740i	0.845673	−	0.533701i	$-0.179199\pi$
$464$	−41.7324	+	24.0942i	−0.0899405	+	0.0519272i
$465$	−475.174	+	84.0715i	−1.02188	+	0.180799i
$466$	230.689	+	133.188i	0.495041	+	0.285812i
$467$			489.836i			1.04890i	0.851442	+	0.524449i	$0.175729\pi$
$467$			489.836i			1.04890i	−0.851442	+	0.524449i	$0.824271\pi$
$468$	194.503	−	130.094i	0.415606	−	0.277978i
$469$	960.264			2.04747
$470$	−230.247	+	398.800i	−0.489887	+	0.848510i
$471$	−53.7751	−	303.938i	−0.114172	−	0.645304i
$472$	56.4497	+	97.7738i	0.119597	+	0.207148i
$473$	−458.139			−0.968580
$474$	149.029	+	54.1439i	0.314408	+	0.114228i
$475$	−54.1115	+	31.2413i	−0.113919	+	0.0657712i
$476$	394.528			0.828839
$477$	−177.539	−	486.022i	−0.372200	−	1.01892i
$478$	274.439	−	475.342i	0.574140	−	0.994440i
$479$	255.842	−	443.132i	0.534118	−	0.925119i	−0.465088	−	0.885265i	$-0.653977\pi$
$479$	255.842	−	443.132i	0.534118	−	0.925119i	0.999205	−	0.0398546i	$-0.0126895\pi$
$480$	73.1786	−	61.4769i	0.152456	−	0.128077i
$481$	0.917698	−	0.877273i	0.00190790	−	0.00182385i
$482$		−	221.203i		−	0.458926i
$483$	−236.837	−	1338.61i	−0.490347	−	2.77145i
$484$	76.3150	−	132.181i	0.157676	−	0.273102i
$485$	−242.427	+	139.965i	−0.499849	+	0.288588i
$486$	322.585	−	118.477i	0.663756	−	0.243780i
$487$	−700.935	+	404.685i	−1.43929	+	0.830976i	−0.997800	−	0.0662899i	$-0.978884\pi$
$487$	−700.935	+	404.685i	−1.43929	+	0.830976i	−0.441491	+	0.897265i	$0.645550\pi$
$488$	14.4268	+	24.9879i	0.0295630	+	0.0512046i
$489$	−7.46655	−	8.88776i	−0.0152690	−	0.0181754i
$490$	−433.991	−	751.695i	−0.885696	−	1.53407i
$491$	−16.9351	−	9.77749i	−0.0344911	−	0.0199134i	0.482655	−	0.875810i	$-0.339672\pi$
$491$	−16.9351	−	9.77749i	−0.0344911	−	0.0199134i	−0.517146	+	0.855897i	$0.673006\pi$
$492$	−10.6062	−	59.9465i	−0.0215573	−	0.121842i
$493$	189.072			0.383514
$494$	−164.150	−	47.9703i	−0.332288	−	0.0971058i
$495$	58.4467	−	333.742i	0.118074	−	0.674225i
$496$	−98.9393	−	57.1226i	−0.199474	−	0.115167i
$497$	526.126	+	303.759i	1.05860	+	0.611185i
$498$	210.399	+	76.4402i	0.422488	+	0.153494i
$499$			73.9561i			0.148209i	0.997250	+	0.0741043i	$0.0236098\pi$
$499$			73.9561i			0.148209i	−0.997250	+	0.0741043i	$0.976390\pi$
$500$	−102.966	−	178.342i	−0.205931	−	0.356683i
$501$	265.433	+	96.4346i	0.529806	+	0.192484i
$502$			550.071i			1.09576i
$503$	−275.259	+	158.921i	−0.547234	+	0.315946i	−0.748006	−	0.663692i	$-0.768988\pi$
$503$	−275.259	+	158.921i	−0.547234	+	0.315946i	0.200771	+	0.979638i	$0.435655\pi$
$504$	205.378	−	245.340i	0.407495	−	0.486785i
$505$	551.590	+	318.460i	1.09226	+	0.630615i
$506$		−	340.816i		−	0.673549i
$507$	−194.404	+	468.248i	−0.383440	+	0.923566i
$508$	−169.707			−0.334069
$509$	−156.695	+	271.404i	−0.307849	+	0.533210i	−0.977892	−	0.209112i	$-0.932943\pi$
$509$	−156.695	+	271.404i	−0.307849	+	0.533210i	0.670043	+	0.742323i	$0.266276\pi$
$510$	−369.262	+	65.3328i	−0.724044	+	0.128104i
$511$	−53.8337	−	93.2428i	−0.105350	−	0.182471i
$512$	22.6274			0.0441942
$513$	−217.726	−	125.197i	−0.424417	−	0.244049i
$514$	80.3990	−	46.4184i	0.156418	−	0.0903081i
$515$	857.307			1.66467
$516$	386.496	+	140.418i	0.749023	+	0.272128i
$517$	−193.247	+	334.714i	−0.373786	+	0.647416i
$518$	0.867952	−	1.50334i	0.00167558	−	0.00290220i
$519$	227.151	+	270.388i	0.437671	+	0.520979i
$520$	−58.0859	+	198.765i	−0.111704	+	0.382240i
$521$			374.489i			0.718789i	0.933186	+	0.359395i	$0.117017\pi$
$521$			374.489i			0.718789i	−0.933186	+	0.359395i	$0.882983\pi$
$522$	98.4247	−	117.576i	0.188553	−	0.225241i
$523$	−82.6173	+	143.097i	−0.157968	+	0.273609i	−0.934136	−	0.356918i	$-0.883828\pi$
$523$	−82.6173	+	143.097i	−0.157968	+	0.273609i	0.776168	+	0.630526i	$0.217161\pi$
$524$	253.920	−	146.601i	0.484579	−	0.279772i
$525$	162.919	+	193.930i	0.310323	+	0.369391i
$526$	39.7879	−	22.9716i	0.0756424	−	0.0436722i
$527$	224.127	+	388.199i	0.425288	+	0.736620i
$528$	61.4191	−	51.5978i	0.116324	−	0.0977230i
$529$	385.358	+	667.459i	0.728464	+	1.26174i
$530$	396.556	+	228.952i	0.748219	+	0.431985i
$531$	−275.466	−	230.597i	−0.518768	−	0.434268i
$532$	−233.835			−0.439540
$533$	91.1446	+	95.3446i	0.171003	+	0.178883i
$534$	321.307	−	269.928i	0.601698	−	0.505482i
$535$	272.617	+	157.396i	0.509565	+	0.294197i
$536$	−187.139	−	108.045i	−0.349140	−	0.201576i
$537$	124.199	−	341.853i	0.231283	−	0.636598i
$538$		−	470.481i		−	0.874499i
$539$	−364.250	−	630.900i	−0.675789	−	1.17050i
$540$	−151.598	+	263.638i	−0.280737	+	0.488219i
$541$			412.712i			0.762869i	0.924396	+	0.381435i	$0.124570\pi$
$541$			412.712i			0.762869i	−0.924396	+	0.381435i	$0.875430\pi$
$542$	557.346	−	321.784i	1.02831	−	0.593698i
$543$	−87.9723	−	497.221i	−0.162012	−	0.915693i
$544$	−76.8867	−	44.3905i	−0.141336	−	0.0816003i
$545$			159.514i			0.292686i
$546$	−75.5519	+	689.107i	−0.138373	+	1.26210i
$547$	592.073			1.08240			0.541200	−	0.840894i	$-0.317970\pi$
$547$	592.073			1.08240			0.541200	+	0.840894i	$0.317970\pi$
$548$	−200.894	+	347.958i	−0.366594	+	0.634960i
$549$	−70.4002	−	58.9331i	−0.128234	−	0.107346i
$550$	31.7502	+	54.9930i	0.0577276	+	0.0999872i
$551$	−112.063			−0.203381
$552$	−104.459	+	287.520i	−0.189237	+	0.520870i
$553$	−406.809	+	234.871i	−0.735640	+	0.424722i
$554$	91.0732			0.164392
$555$	−0.563421	+	1.55080i	−0.00101517	+	0.00279423i
$556$	38.9425	−	67.4504i	0.0700404	−	0.121314i
$557$	253.100	−	438.382i	0.454398	−	0.787041i	−0.544255	−	0.838920i	$-0.683188\pi$
$557$	253.100	−	438.382i	0.454398	−	0.787041i	0.998653	+	0.0518786i	$0.0165209\pi$
$558$	358.077	+	62.7084i	0.641714	+	0.112381i
$559$	−865.577	+	211.163i	−1.54844	+	0.377751i
$560$			283.145i			0.505616i
$561$	−309.923	+	54.8341i	−0.552448	+	0.0977434i
$562$	369.865	−	640.624i	0.658122	−	1.13990i
$563$	−238.548	+	137.726i	−0.423709	+	0.244629i	−0.696663	−	0.717398i	$-0.745333\pi$
$563$	−238.548	+	137.726i	−0.423709	+	0.244629i	0.272954	+	0.962027i	$0.411999\pi$
$564$	265.617	−	223.143i	0.470951	−	0.395643i
$565$	82.7910	−	47.7994i	0.146533	−	0.0846008i
$566$	24.8279	+	43.0032i	0.0438655	+	0.0759773i
$567$	−345.977	+	957.502i	−0.610189	+	1.68872i
$568$	−68.3553	−	118.395i	−0.120344	−	0.208442i
$569$	−52.5701	−	30.3513i	−0.0923903	−	0.0533416i	0.453093	−	0.891463i	$-0.350321\pi$
$569$	−52.5701	−	30.3513i	−0.0923903	−	0.0533416i	−0.545483	+	0.838122i	$0.683654\pi$
$570$	218.861	−	38.7226i	0.383966	−	0.0679343i
$571$	520.254			0.911128			0.455564	−	0.890203i	$-0.349438\pi$
$571$	520.254			0.911128			0.455564	+	0.890203i	$0.349438\pi$
$572$	−48.7517	+	166.824i	−0.0852302	+	0.291651i
$573$	−683.178	−	813.217i	−1.19228	−	1.41923i
$574$	156.190	+	90.1763i	0.272108	+	0.157102i
$575$	−209.718	−	121.081i	−0.364727	−	0.210575i
$576$	−67.6291	+	24.7043i	−0.117412	+	0.0428894i
$577$			547.875i			0.949524i	0.880114	+	0.474762i	$0.157466\pi$
$577$			547.875i			0.949524i	−0.880114	+	0.474762i	$0.842534\pi$
$578$	−30.1828	−	52.2782i	−0.0522194	−	0.0904467i
$579$	−42.6494	+	117.391i	−0.0736604	+	0.202748i
$580$			135.694i			0.233955i
$581$	−574.331	+	331.590i	−0.988522	+	0.570723i
$582$	207.657	−	36.7403i	0.356799	−	0.0631277i
$583$	332.831	+	192.160i	0.570894	+	0.329606i
$584$			24.2286i			0.0414873i
$585$	−43.4009	−	657.489i	−0.0741896	−	1.12391i
$586$	−725.175			−1.23750
$587$	189.236	−	327.767i	0.322378	−	0.558376i	−0.658600	−	0.752493i	$-0.728851\pi$
$587$	189.236	−	327.767i	0.322378	−	0.558376i	0.980978	+	0.194117i	$0.0621843\pi$
$588$	113.921	+	643.884i	0.193743	+	1.09504i
$589$	−132.839	−	230.084i	−0.225534	−	0.390636i
$590$	317.913			0.538836
$591$	−136.141	−	49.4615i	−0.230357	−	0.0836912i
$592$	−0.338298	+	0.195317i	−0.000571450	+	0.000329927i
$593$	−307.253			−0.518134			−0.259067	−	0.965859i	$-0.583415\pi$
$593$	−307.253			−0.518134			−0.259067	+	0.965859i	$0.583415\pi$
$594$	−127.237	+	221.273i	−0.214203	+	0.372513i
$595$	555.474	−	962.110i	0.933570	−	1.61699i
$596$	−213.869	+	370.431i	−0.358840	+	0.621529i
$597$	813.929	−	683.776i	1.36337	−	1.14535i
$598$	−157.087	−	643.916i	−0.262687	−	1.07678i
$599$			129.313i			0.215881i	0.994157	+	0.107941i	$0.0344257\pi$
$599$			129.313i			0.215881i	−0.994157	+	0.107941i	$0.965574\pi$
$600$	−9.93002	−	56.1247i	−0.0165500	−	0.0935411i
$601$	−107.571	+	186.319i	−0.178987	+	0.310015i	−0.941534	−	0.336918i	$-0.890615\pi$
$601$	−107.571	+	186.319i	−0.178987	+	0.310015i	0.762547	+	0.646933i	$0.223949\pi$
$602$	−1055.03	+	609.120i	−1.75254	+	1.01183i
$603$	677.286	+	118.610i	1.12319	+	0.196700i
$604$	69.2776	−	39.9974i	0.114698	−	0.0662209i
$605$	−214.895	−	372.209i	−0.355199	−	0.615222i
$606$	−308.634	−	367.381i	−0.509297	−	0.606239i
$607$	188.519	+	326.525i	0.310575	+	0.537932i	0.978487	−	0.206308i	$-0.0661450\pi$
$607$	188.519	+	326.525i	0.310575	+	0.537932i	−0.667912	+	0.744240i	$0.732812\pi$
$608$	45.5705	+	26.3102i	0.0749515	+	0.0432733i
$609$	79.1423	+	447.314i	0.129955	+	0.734506i
$610$	81.2485			0.133194
$611$	−210.834	+	721.457i	−0.345064	+	1.18078i
$612$	278.265	+	48.7313i	0.454681	+	0.0796263i
$613$	−491.102	−	283.538i	−0.801145	−	0.462541i	0.0427262	−	0.999087i	$-0.486396\pi$
$613$	−491.102	−	283.538i	−0.801145	−	0.462541i	−0.843871	+	0.536545i	$0.819729\pi$
$614$	537.114	+	310.103i	0.874779	+	0.505054i
$615$	−161.121	−	58.5368i	−0.261985	−	0.0951818i
$616$			237.644i			0.385786i
$617$	−76.6344	−	132.735i	−0.124205	−	0.215129i	0.797217	−	0.603693i	$-0.206305\pi$
$617$	−76.6344	−	132.735i	−0.124205	−	0.215129i	−0.921422	+	0.388564i	$0.872971\pi$
$618$	−607.021	−	220.537i	−0.982235	−	0.356856i
$619$		−	659.533i		−	1.06548i	−0.846279	−	0.532741i	$-0.821162\pi$
$619$		−	659.533i		−	1.06548i	0.846279	−	0.532741i	$-0.178838\pi$
$620$	−278.603	+	160.851i	−0.449359	+	0.259438i
$621$	−1.70156	−	973.391i	−0.00274003	−	1.56746i
$622$	358.401	+	206.923i	0.576207	+	0.332673i
$623$			1243.21i			1.99552i
$624$	92.2592	−	125.794i	0.147851	−	0.201594i
$625$	−747.808			−1.19649
$626$	115.315	−	199.731i	0.184209	−	0.319058i
$627$	183.691	−	32.5000i	0.292968	−	0.0518341i
$628$	−102.886	−	178.204i	−0.163832	−	0.283765i
$629$	1.53269			0.00243671
$630$	−309.133	−	846.267i	−0.490688	−	1.34328i
$631$	474.992	−	274.237i	0.752760	−	0.434606i	−0.0739301	−	0.997263i	$-0.523554\pi$
$631$	474.992	−	274.237i	0.752760	−	0.434606i	0.826690	+	0.562657i	$0.190221\pi$
$632$	105.707			0.167258
$633$	511.443	+	185.813i	0.807967	+	0.293543i
$634$	−298.109	+	516.341i	−0.470204	+	0.814417i
$635$	−238.939	+	413.854i	−0.376282	+	0.651739i
$636$	−221.887	−	264.122i	−0.348880	−	0.415287i
$637$	−978.982	−	1024.09i	−1.53686	−	1.60768i
$638$			113.888i			0.178508i
$639$	333.563	+	279.231i	0.522008	+	0.436981i
$640$	31.8582	−	55.1801i	0.0497785	−	0.0862189i
$641$	−288.638	+	166.645i	−0.450293	+	0.259977i	−0.707954	−	0.706259i	$-0.750382\pi$
$641$	−288.638	+	166.645i	−0.450293	+	0.259977i	0.257661	+	0.966235i	$0.417048\pi$
$642$	−152.539	−	181.574i	−0.237600	−	0.282826i
$643$	791.041	−	456.708i	1.23023	−	0.710276i	0.263156	−	0.964753i	$-0.415237\pi$
$643$	791.041	−	456.708i	1.23023	−	0.710276i	0.967079	+	0.254477i	$0.0819033\pi$
$644$	−453.133	−	784.850i	−0.703623	−	1.21871i
$645$	886.595	−	744.823i	1.37457	−	1.15476i
$646$	−103.231	−	178.801i	−0.159800	−	0.276781i
$647$	−905.192	−	522.613i	−1.39906	−	0.807748i	−0.404766	−	0.914420i	$-0.632647\pi$
$647$	−905.192	−	522.613i	−1.39906	−	0.807748i	−0.994294	+	0.106673i	$0.965980\pi$
$648$	175.159	−	147.673i	0.270307	−	0.227890i
$649$	266.826			0.411133
$650$	85.3338	+	89.2660i	0.131283	+	0.137332i
$651$	−824.599	+	692.740i	−1.26666	+	1.06412i
$652$	−6.70178	−	3.86928i	−0.0102788	−	0.00593447i
$653$	495.462	+	286.055i	0.758748	+	0.438063i	0.828846	−	0.559477i	$-0.188998\pi$
$653$	495.462	+	286.055i	0.758748	+	0.438063i	−0.0700982	+	0.997540i	$0.522331\pi$
$654$	41.0339	−	112.945i	0.0627430	−	0.172698i
$655$		−	825.624i		−	1.26049i
$656$	−20.2925	−	35.1476i	−0.0309337	−	0.0535787i
$657$	−26.4524	−	72.4146i	−0.0402624	−	0.110220i
$658$			1027.73i			1.56190i
$659$	913.688	−	527.518i	1.38648	−	0.800482i	0.393560	−	0.919299i	$-0.371243\pi$
$659$	913.688	−	527.518i	1.38648	−	0.800482i	0.992916	+	0.118817i	$0.0379101\pi$
$660$	−39.3533	−	222.426i	−0.0596263	−	0.337009i
$661$	−636.788	−	367.649i	−0.963370	−	0.556202i	−0.0661614	−	0.997809i	$-0.521075\pi$
$661$	−636.788	−	367.649i	−0.963370	−	0.556202i	−0.897209	+	0.441607i	$0.854409\pi$
$662$			80.6543i			0.121834i
$663$	−560.275	+	246.448i	−0.845061	+	0.371717i
$664$	149.236			0.224754
$665$	−329.228	+	570.240i	−0.495080	+	0.857504i
$666$	0.797866	−	0.953114i	0.00119800	−	0.00143110i
$667$	−217.159	−	376.130i	−0.325575	−	0.563912i
$668$	188.272			0.281844
$669$	−40.2515	+	110.791i	−0.0601667	+	0.165607i
$670$	−526.964	+	304.243i	−0.786514	+	0.454094i
$671$	68.1921			0.101628
$672$	72.8373	−	200.482i	0.108389	−	0.298337i
$673$	−631.384	+	1093.59i	−0.938164	+	1.62495i	−0.169272	+	0.985569i	$0.554142\pi$
$673$	−631.384	+	1093.59i	−0.938164	+	1.62495i	−0.768892	+	0.639379i	$0.779192\pi$
$674$	235.002	−	407.035i	0.348668	−	0.603910i
$675$	90.9550	+	156.905i	0.134748	+	0.232451i
$676$	−15.2166	+	337.657i	−0.0225098	+	0.499493i
$677$		−	779.299i		−	1.15111i	−0.817764	−	0.575553i	$-0.804787\pi$
$677$		−	779.299i		−	1.15111i	0.817764	−	0.575553i	$-0.195213\pi$
$678$	−70.9168	+	12.5472i	−0.104597	+	0.0185061i
$679$	−312.374	+	541.048i	−0.460051	+	0.796831i
$680$	−216.505	+	124.999i	−0.318390	+	0.183822i
$681$	39.2304	−	32.9572i	0.0576071	−	0.0483953i
$682$	−233.832	+	135.003i	−0.342863	+	0.197952i
$683$	456.070	+	789.936i	0.667745	+	1.15657i	0.978533	+	0.206089i	$0.0660738\pi$
$683$	456.070	+	789.936i	0.667745	+	1.15657i	−0.310788	+	0.950479i	$0.600593\pi$
$684$	−164.927	−	28.8829i	−0.241121	−	0.0422265i
$685$	565.696	+	979.814i	0.825833	+	1.43039i
$686$	−923.333	−	533.087i	−1.34597	−	0.777094i
$687$	541.487	−	95.8042i	0.788191	−	0.139453i
$688$	274.142			0.398463
$689$	717.399	+	209.648i	1.04122	+	0.304279i
$690$	554.084	+	659.551i	0.803021	+	0.955871i
$691$	−143.059	−	82.5950i	−0.207031	−	0.119530i	0.392900	−	0.919581i	$-0.371472\pi$
$691$	−143.059	−	82.5950i	−0.207031	−	0.119530i	−0.599931	+	0.800052i	$0.704805\pi$
$692$	203.885	+	117.713i	0.294632	+	0.170106i
$693$	−259.457	−	710.275i	−0.374396	−	1.02493i
$694$			51.5715i			0.0743105i
$695$	−109.658	−	189.933i	−0.157781	−	0.273285i
$696$	34.9064	−	96.0786i	0.0501528	−	0.138044i
$697$			159.240i			0.228464i
$698$	422.610	−	243.994i	0.605458	−	0.349561i
$699$	−556.429	+	98.4477i	−0.796035	+	0.140841i
$700$	146.232	+	84.4273i	0.208903	+	0.120610i
$701$		−	269.009i		−	0.383751i	−0.981419	−	0.191875i	$-0.938543\pi$
$701$		−	269.009i		−	0.383751i	0.981419	−	0.191875i	$-0.0614569\pi$
$702$	−138.405	+	476.703i	−0.197158	+	0.679065i
$703$	−0.908422			−0.00129221
$704$	26.7387	−	46.3128i	0.0379812	−	0.0657853i
$705$	−170.190	−	961.916i	−0.241404	−	1.36442i
$706$	−152.588	−	264.291i	−0.216131	−	0.374350i
$707$	1421.48			2.01058
$708$	−225.100	−	81.7812i	−0.317938	−	0.115510i
$709$	−1044.51	+	603.050i	−1.47322	+	0.850564i	−0.999546	−	0.0301361i	$-0.990406\pi$
$709$	−1044.51	+	603.050i	−1.47322	+	0.850564i	−0.473674	+	0.880700i	$0.657073\pi$
$710$	−384.963			−0.542201
$711$	−315.938	+	115.409i	−0.444357	+	0.162319i
$712$	139.880	−	242.280i	0.196461	−	0.340281i
$713$	514.840	−	891.729i	0.722075	−	1.25067i
$714$	−640.804	+	538.335i	−0.897484	+	0.753970i
$715$	338.184	+	353.768i	0.472985	+	0.494780i
$716$		−	242.477i		−	0.338655i
$717$	202.855	+	1146.54i	0.282921	+	1.59908i
$718$	55.6784	−	96.4378i	0.0775465	−	0.134315i
$719$	−284.677	+	164.358i	−0.395934	+	0.228593i	−0.684728	−	0.728799i	$-0.740079\pi$
$719$	−284.677	+	164.358i	−0.395934	+	0.228593i	0.288794	+	0.957391i	$0.406746\pi$
$720$	−34.9735	+	199.705i	−0.0485743	+	0.277368i
$721$	1657.00	−	956.669i	2.29820	−	1.32686i
$722$	−194.081	−	336.158i	−0.268810	−	0.465593i
$723$	301.832	+	359.284i	0.417472	+	0.496935i
$724$	−168.315	−	291.529i	−0.232479	−	0.402665i
$725$	70.0800	+	40.4607i	0.0966621	+	0.0558079i
$726$	56.4091	+	318.825i	0.0776985	+	0.439154i
$727$	267.919			0.368527			0.184264	−	0.982877i	$-0.441010\pi$
$727$	267.919			0.368527			0.184264	+	0.982877i	$0.441010\pi$
$728$	109.534	+	448.990i	0.150458	+	0.616745i
$729$	−362.291	+	632.603i	−0.496969	+	0.867768i
$730$	59.0847	+	34.1126i	0.0809379	+	0.0467295i
$731$	−931.520	−	537.813i	−1.27431	−	0.735723i
$732$	−57.5284	−	20.9007i	−0.0785908	−	0.0285529i
$733$		−	298.597i		−	0.407363i	−0.979037	−	0.203681i	$-0.934709\pi$
$733$		−	298.597i		−	0.407363i	0.979037	−	0.203681i	$-0.0652906\pi$
$734$	445.463	+	771.564i	0.606898	+	1.05118i
$735$	1730.59	+	628.743i	2.35455	+	0.855432i
$736$			203.938i			0.277090i
$737$	−442.283	+	255.352i	−0.600113	+	0.346475i
$738$	99.0241	+	82.8947i	0.134179	+	0.112323i
$739$	−193.614	−	111.783i	−0.261995	−	0.151263i	0.363249	−	0.931692i	$-0.381667\pi$
$739$	−193.614	−	111.783i	−0.261995	−	0.151263i	−0.625244	+	0.780429i	$0.715001\pi$
$740$			1.09998i			0.00148646i
$741$	332.074	−	146.069i	0.448143	−	0.197124i
$742$	1021.95			1.37729
$743$	220.962	−	382.717i	0.297391	−	0.515097i	−0.678147	−	0.734926i	$-0.737217\pi$
$743$	220.962	−	382.717i	0.297391	−	0.515097i	0.975538	+	0.219829i	$0.0705501\pi$
$744$	238.644	−	42.2228i	0.320758	−	0.0567511i
$745$	602.232	+	1043.10i	0.808365	+	1.40013i
$746$	−618.400			−0.828954
$747$	−446.040	+	162.934i	−0.597108	+	0.218118i
$748$	−181.713	+	104.912i	−0.242932	+	0.140257i
$749$	702.551			0.937985
$750$	410.588	+	149.171i	0.547451	+	0.198895i
$751$	638.207	−	1105.41i	0.849809	−	1.47191i	−0.0315689	−	0.999502i	$-0.510050\pi$
$751$	638.207	−	1105.41i	0.849809	−	1.47191i	0.881378	−	0.472411i	$-0.156616\pi$
$752$	115.636	−	200.287i	0.153771	−	0.266339i
$753$	−750.574	−	893.442i	−0.996779	−	1.18651i
$754$	52.4927	+	215.173i	0.0696190	+	0.285375i
$755$		−	225.257i		−	0.298354i
$756$	1.18646	+	678.727i	0.00156940	+	0.897787i
$757$	−101.816	+	176.351i	−0.134499	+	0.232960i	−0.925406	−	0.378977i	$-0.876276\pi$
$757$	−101.816	+	176.351i	−0.134499	+	0.232960i	0.790907	+	0.611937i	$0.209609\pi$
$758$	405.384	−	234.049i	0.534808	−	0.308771i
$759$	465.045	+	553.564i	0.612708	+	0.729333i
$760$	128.322	−	74.0867i	0.168845	−	0.0974825i
$761$	−6.67002	−	11.5528i	−0.00876480	−	0.0151811i	0.861610	−	0.507571i	$-0.169457\pi$
$761$	−6.67002	−	11.5528i	−0.00876480	−	0.0151811i	−0.870375	+	0.492390i	$0.836123\pi$
$762$	275.644	−	231.566i	0.361737	−	0.303893i
$763$	178.001	+	308.307i	0.233291	+	0.404072i
$764$	−613.203	−	354.033i	−0.802622	−	0.463394i
$765$	510.620	−	609.976i	0.667478	−	0.797354i
$766$	−920.146			−1.20123
$767$	504.123	−	122.984i	0.657266	−	0.160344i
$768$	−36.7521	+	30.8752i	−0.0478544	+	0.0402021i
$769$	−67.7341	−	39.1063i	−0.0880808	−	0.0508535i	0.455313	−	0.890332i	$-0.349527\pi$
$769$	−67.7341	−	39.1063i	−0.0880808	−	0.0508535i	−0.543393	+	0.839478i	$0.682861\pi$
$770$	579.529	+	334.591i	0.752635	+	0.434534i
$771$	−67.2484	+	185.099i	−0.0872223	+	0.240077i
$772$			83.2656i			0.107857i
$773$	−13.8481	−	23.9855i	−0.0179147	−	0.0310292i	0.856929	−	0.515434i	$-0.172369\pi$
$773$	−13.8481	−	23.9855i	−0.0179147	−	0.0310292i	−0.874844	+	0.484405i	$0.839036\pi$
$774$	−819.360	+	299.305i	−1.05860	+	0.386698i
$775$			191.849i			0.247547i
$776$	121.753	−	70.2940i	0.156898	−	0.0905851i
$777$	0.641557	+	3.62609i	0.000825685	+	0.00466679i
$778$	789.736	+	455.954i	1.01509	+	0.586060i
$779$		−	94.3809i		−	0.121156i
$780$	−176.871	−	402.099i	−0.226758	−	0.515511i
$781$	−323.101			−0.413702
$782$	400.087	−	692.971i	0.511620	−	0.886152i
$783$	0.568598	+	325.271i	0.000726178	+	0.415417i
$784$	217.961	+	377.520i	0.278012	+	0.481531i
$785$	−579.434			−0.738132
$786$	−212.387	+	584.588i	−0.270212	+	0.743750i
$787$	784.763	−	453.083i	0.997158	−	0.575709i	0.0897518	−	0.995964i	$-0.471393\pi$
$787$	784.763	−	453.083i	0.997158	−	0.575709i	0.907406	+	0.420255i	$0.138059\pi$
$788$	−96.5652			−0.122545
$789$	−33.2799	+	91.6019i	−0.0421799	+	0.116099i
$790$	148.830	−	257.780i	0.188392	−	0.326304i
$791$	106.679	−	184.773i	0.134866	−	0.233594i
$792$	−29.3534	+	167.613i	−0.0370624	+	0.211633i
$793$	128.838	−	31.4307i	0.162469	−	0.0396352i
$794$		−	61.7881i		−	0.0778187i
$795$	−956.505	+	169.232i	−1.20315	+	0.212871i
$796$	354.343	−	613.740i	0.445154	−	0.771030i
$797$	540.427	−	312.016i	0.678076	−	0.391488i	−0.121054	−	0.992646i	$-0.538627\pi$
$797$	540.427	−	312.016i	0.678076	−	0.391488i	0.799130	+	0.601158i	$0.205294\pi$
$798$	379.803	−	319.070i	0.475943	−	0.399837i
$799$	−785.848	+	453.709i	−0.983539	+	0.567847i
$800$	−18.9988	−	32.9069i	−0.0237485	−	0.0411336i
$801$	−153.559	+	876.849i	−0.191709	+	1.09469i
$802$	−69.4131	−	120.227i	−0.0865500	−	0.149909i
$803$	49.5900	+	28.6308i	0.0617559	+	0.0356548i
$804$	451.385	−	79.8625i	0.561424	−	0.0993315i
$805$	−2551.95			−3.17013
$806$	−379.563	+	362.843i	−0.470922	+	0.450177i
$807$	641.973	+	764.169i	0.795506	+	0.946926i
$808$	−277.022	−	159.939i	−0.342849	−	0.197944i
$809$	−1296.34	−	748.440i	−1.60239	−	0.925142i	−0.991007	−	0.133809i	$-0.957279\pi$
$809$	−1296.34	−	748.440i	−1.60239	−	0.925142i	−0.611386	−	0.791333i	$-0.709388\pi$
$810$	−113.506	−	635.065i	−0.140131	−	0.784031i
$811$			911.040i			1.12335i	0.827357	+	0.561677i	$0.189844\pi$
$811$			911.040i			1.12335i	−0.827357	+	0.561677i	$0.810156\pi$
$812$	151.421	+	262.268i	0.186478	+	0.322990i
$813$	−466.183	+	1283.15i	−0.573411	+	1.57829i
$814$			0.923219i			0.00113418i
$815$	−18.8715	+	10.8955i	−0.0231552	+	0.0133687i
$816$	185.453	−	32.8118i	0.227271	−	0.0402105i
$817$	552.109	+	318.760i	0.675776	+	0.390160i
$818$			410.585i			0.501938i
$819$	−817.577	−	1222.36i	−0.998262	−	1.49250i
$820$	−114.283			−0.139370
$821$	216.205	−	374.478i	0.263344	−	0.456124i	−0.703785	−	0.710413i	$-0.748508\pi$
$821$	216.205	−	374.478i	0.263344	−	0.456124i	0.967128	+	0.254289i	$0.0818414\pi$
$822$	−148.493	−	839.285i	−0.180648	−	1.02103i
$823$	−339.071	−	587.288i	−0.411993	−	0.713594i	0.583114	−	0.812390i	$-0.301834\pi$
$823$	−339.071	−	587.288i	−0.411993	−	0.713594i	−0.995108	+	0.0987966i	$0.968501\pi$
$824$	−430.561			−0.522525
$825$	−126.608	−	45.9980i	−0.153464	−	0.0557551i
$826$	614.461	−	354.759i	0.743899	−	0.429490i
$827$	−423.972			−0.512663			−0.256331	−	0.966589i	$-0.582514\pi$
$827$	−423.972			−0.512663			−0.256331	+	0.966589i	$0.582514\pi$
$828$	−222.657	−	609.534i	−0.268909	−	0.736152i
$829$	417.344	−	722.861i	0.503430	−	0.871967i	−0.496562	−	0.868001i	$-0.665404\pi$
$829$	417.344	−	722.861i	0.503430	−	0.871967i	0.999992	−	0.00396559i	$-0.00126229\pi$
$830$	210.117	−	363.934i	0.253153	−	0.438474i
$831$	−147.924	+	124.270i	−0.178007	+	0.149542i
$832$	29.1722	−	99.8248i	0.0350627	−	0.119982i
$833$		−	1710.39i		−	2.05329i
$834$	28.7848	+	162.692i	0.0345141	+	0.195075i
$835$	265.077	−	459.127i	0.317458	−	0.549853i
$836$	107.701	−	62.1812i	0.128829	−	0.0743794i
$837$	−667.165	+	386.744i	−0.797091	+	0.462060i
$838$	394.406	−	227.710i	0.470651	−	0.271731i
$839$	472.749	+	818.825i	0.563467	+	0.975953i	0.997191	+	0.0749072i	$0.0238660\pi$
$839$	472.749	+	818.825i	0.563467	+	0.975953i	−0.433724	+	0.901046i	$0.642801\pi$
$840$	−386.352	−	459.892i	−0.459943	−	0.547491i
$841$	−347.934	−	602.639i	−0.413714	−	0.716574i
$842$	977.841	+	564.557i	1.16133	+	0.670495i
$843$	273.390	+	1545.20i	0.324306	+	1.83298i
$844$	362.767			0.429819
$845$	802.000	+	512.512i	0.949112	+	0.606523i
$846$	−126.943	+	724.870i	−0.150051	+	0.856821i
$847$	−830.697	−	479.603i	−0.980752	−	0.566237i
$848$	−199.161	−	114.985i	−0.234859	−	0.135596i
$849$	−99.0042	−	35.9693i	−0.116613	−	0.0423666i
$850$			149.087i			0.175397i
$851$	−1.76037	−	3.04904i	−0.00206859	−	0.00358290i
$852$	272.575	+	99.0295i	0.319924	+	0.116232i
$853$		−	1159.07i		−	1.35881i	−0.733761	−	0.679407i	$-0.762237\pi$
$853$		−	1159.07i		−	1.35881i	0.733761	−	0.679407i	$-0.237763\pi$
$854$	157.037	−	90.6652i	0.183884	−	0.106165i
$855$	−302.643	+	361.531i	−0.353969	+	0.422843i
$856$	−136.915	−	79.0480i	−0.159948	−	0.0923458i
$857$			1427.10i			1.66523i	0.553850	+	0.832617i	$0.313158\pi$
$857$			1427.10i			1.66523i	−0.553850	+	0.832617i	$0.686842\pi$
$858$	−148.449	−	337.483i	−0.173017	−	0.393337i
$859$	545.728			0.635307			0.317653	−	0.948207i	$-0.397105\pi$
$859$	545.728			0.635307			0.317653	+	0.948207i	$0.397105\pi$
$860$	385.978	−	668.534i	0.448812	−	0.777365i
$861$	−376.735	+	66.6548i	−0.437555	+	0.0774156i
$862$	297.688	+	515.610i	0.345345	+	0.598156i
$863$	−988.979			−1.14598			−0.572989	−	0.819563i	$-0.694216\pi$
$863$	−988.979			−1.14598			−0.572989	+	0.819563i	$0.694216\pi$
$864$	76.1362	−	132.406i	0.0881206	−	0.153247i
$865$	574.119	−	331.468i	0.663721	−	0.383200i
$866$	557.315			0.643551
$867$	120.358	+	43.7272i	0.138821	+	0.0504351i
$868$	−358.988	+	621.786i	−0.413581	+	0.716343i
$869$	124.913	−	216.356i	0.143744	−	0.248971i
$870$	−185.155	−	220.398i	−0.212821	−	0.253331i
$871$	−717.926	+	686.301i	−0.824254	+	0.787946i
$872$		−	80.1117i		−	0.0918713i
$873$	−287.150	+	343.024i	−0.328924	+	0.392925i
$874$	−237.131	+	410.722i	−0.271316	+	0.469934i
$875$	−1120.79	+	647.089i	−1.28090	+	0.739530i
$876$	−33.0600	−	39.3528i	−0.0377397	−	0.0449233i
$877$	−116.509	+	67.2663i	−0.132849	+	0.0767005i	−0.564952	−	0.825124i	$-0.691105\pi$
$877$	−116.509	+	67.2663i	−0.132849	+	0.0767005i	0.432103	+	0.901824i	$0.357772\pi$
$878$	−64.2435	−	111.273i	−0.0731702	−	0.126735i
$879$	1177.85	−	989.505i	1.33999	−	1.12572i
$880$	−75.2935	−	130.412i	−0.0855608	−	0.148196i
$881$	−191.452	−	110.535i	−0.217312	−	0.125465i	0.387393	−	0.921915i	$-0.373376\pi$
$881$	−191.452	−	110.535i	−0.217312	−	0.125465i	−0.604705	+	0.796449i	$0.706709\pi$
$882$	−1063.62	−	890.370i	−1.20591	−	1.00949i
$883$	316.368			0.358287			0.179144	−	0.983823i	$-0.442667\pi$
$883$	316.368			0.358287			0.179144	+	0.983823i	$0.442667\pi$
$884$	−294.962	+	281.969i	−0.333667	+	0.318969i
$885$	−516.364	+	433.794i	−0.583462	+	0.490163i
$886$	−507.695	−	293.118i	−0.573019	−	0.330833i
$887$	−30.6083	−	17.6717i	−0.0345077	−	0.0199230i	0.482647	−	0.875815i	$-0.339675\pi$
$887$	−30.6083	−	17.6717i	−0.0345077	−	0.0199230i	−0.517155	+	0.855892i	$0.673009\pi$
$888$	0.282964	−	0.778849i	0.000318653	−	0.000877082i
$889$			1066.53i			1.19969i
$890$	−393.889	−	682.236i	−0.442572	−	0.766557i
$891$	−95.2660	−	533.013i	−0.106920	−	0.598219i
$892$			78.5842i			0.0880989i
$893$	465.770	−	268.912i	0.521579	−	0.301134i
$894$	−158.083	−	893.491i	−0.176827	−	0.999430i
$895$	−591.313	−	341.395i	−0.660685	−	0.381447i
$896$		−	142.202i		−	0.158708i
$897$	1133.77	+	831.522i	1.26396	+	0.927003i
$898$	−340.752			−0.379457
$899$	−172.041	+	297.983i	−0.191369	+	0.331460i
$900$	92.7110	+	77.6098i	0.103012	+	0.0862332i
$901$	451.157	+	781.427i	0.500730	+	0.867289i
$902$	−95.9182			−0.106340
$903$	882.460	−	2428.94i	0.977254	−	2.68986i
$904$	−41.5797	+	24.0061i	−0.0459953	+	0.0265554i
$905$	−947.913			−1.04742
$906$	−57.9461	+	159.495i	−0.0639581	+	0.176043i
$907$	135.020	−	233.862i	0.148865	−	0.257841i	−0.781943	−	0.623349i	$-0.785771\pi$
$907$	135.020	−	233.862i	0.148865	−	0.257841i	0.930808	+	0.365508i	$0.119105\pi$
$908$	17.0789	−	29.5815i	0.0188094	−	0.0325788i
$909$	1002.59	+	175.579i	1.10296	+	0.193156i
$910$	1249.14	+	365.042i	1.37268	+	0.401145i
$911$		−	836.758i		−	0.918504i	−0.888306	−	0.459252i	$-0.848117\pi$
$911$		−	836.758i		−	0.918504i	0.888306	−	0.459252i	$-0.151883\pi$
$912$	−109.917	+	19.4474i	−0.120523	+	0.0213240i
$913$	176.352	−	305.451i	0.193157	−	0.334557i
$914$	−695.543	+	401.572i	−0.760988	+	0.439357i
$915$	−131.966	+	110.864i	−0.144225	+	0.121163i
$916$	317.483	−	183.299i	0.346598	−	0.200108i
$917$	−921.314	−	1595.76i	−1.00470	−	1.74020i
$918$	−518.460	+	300.543i	−0.564772	+	0.327389i
$919$	−477.165	−	826.473i	−0.519222	−	0.899318i	−0.999750	−	0.0223393i	$-0.992889\pi$
$919$	−477.165	−	826.473i	−0.519222	−	0.899318i	0.480529	−	0.876979i	$-0.340445\pi$
$920$	497.332	+	287.135i	0.540578	+	0.312103i
$921$	−1295.54	+	229.216i	−1.40666	+	0.248878i
$922$	−119.219			−0.129305
$923$	−610.446	+	148.922i	−0.661372	+	0.161345i
$924$	−324.267	−	385.989i	−0.350938	−	0.417738i
$925$	0.568094	+	0.327989i	0.000614156	+	0.000354583i
$926$	605.278	+	349.457i	0.653648	+	0.377384i
$927$	1286.87	−	470.080i	1.38821	−	0.507098i
$928$		−	68.1487i		−	0.0734361i
$929$	698.626	+	1210.06i	0.752019	+	1.30254i	0.946843	+	0.321697i	$0.104253\pi$
$929$	698.626	+	1210.06i	0.752019	+	1.30254i	−0.194823	+	0.980838i	$0.562413\pi$
$930$	233.033	−	641.414i	0.250573	−	0.689693i
$931$			1013.74i			1.08888i
$932$	−326.244	+	188.357i	−0.350047	+	0.202100i
$933$	−864.472	+	152.949i	−0.926551	+	0.163933i
$934$	−599.924	−	346.366i	−0.642316	−	0.370842i
$935$			590.844i			0.631919i
$936$	21.7970	+	330.207i	0.0232874	+	0.352786i
$937$	63.1645			0.0674114			0.0337057	−	0.999432i	$-0.489269\pi$
$937$	63.1645			0.0674114			0.0337057	+	0.999432i	$0.489269\pi$
$938$	−679.009	+	1176.08i	−0.723891	+	1.25382i
$939$	85.2360	+	481.756i	0.0907732	+	0.513052i
$940$	−325.618	−	563.988i	−0.346403	−	0.599987i
$941$	−729.679			−0.775430			−0.387715	−	0.921779i	$-0.626735\pi$
$941$	−729.679			−0.775430			−0.387715	+	0.921779i	$0.626735\pi$
$942$	410.272	+	149.056i	0.435532	+	0.158233i
$943$	316.782	−	182.894i	0.335930	−	0.193949i
$944$	−159.664			−0.169135
$945$	1656.84	+	952.719i	1.75327	+	1.00817i
$946$	323.953	−	561.103i	0.342445	−	0.593132i
$947$	244.368	−	423.258i	0.258045	−	0.446946i	−0.707673	−	0.706540i	$-0.750255\pi$
$947$	244.368	−	423.258i	0.258045	−	0.446946i	0.965718	+	0.259593i	$0.0835885\pi$
$948$	−171.692	+	144.237i	−0.181110	+	0.152149i
$949$	106.888	+	31.2364i	0.112633	+	0.0329151i
$950$		−	88.3638i		−	0.0930145i
$951$	−220.351	−	1245.43i	−0.231704	−	1.30960i
$952$	−278.973	+	483.196i	−0.293039	+	0.507558i
$953$	−635.939	+	367.160i	−0.667302	+	0.385267i	−0.795054	−	0.606539i	$-0.792557\pi$
$953$	−635.939	+	367.160i	−0.667302	+	0.385267i	0.127751	+	0.991806i	$0.459224\pi$
$954$	720.793	+	126.229i	0.755548	+	0.132316i
$955$	−1726.72	+	996.920i	−1.80808	+	1.04390i
$956$	388.115	+	672.235i	0.405978	+	0.703175i
$957$	−155.401	−	184.981i	−0.162383	−	0.193292i
$958$	361.816	+	626.683i	0.377678	+	0.654158i
$959$	2186.75	+	1262.52i	2.28024	+	1.31650i
$960$	23.5484	+	133.096i	0.0245296	+	0.138642i
$961$	145.252			0.151147
$962$	0.425525	+	1.74427i	0.000442334	+	0.00181317i
$963$	495.517	+	86.7778i	0.514556	+	0.0901119i
$964$	270.917	+	156.414i	0.281034	+	0.162255i
$965$	203.055	+	117.234i	0.210419	+	0.121486i
$966$	1806.92	+	656.475i	1.87052	+	0.679580i
$967$			879.981i			0.910011i	0.890489	+	0.455006i	$0.150363\pi$
$967$			879.981i			0.910011i	−0.890489	+	0.455006i	$0.849637\pi$
$968$	107.926	+	186.933i	0.111494	+	0.193112i
$969$	411.645	+	149.555i	0.424814	+	0.154340i
$970$		−	395.881i		−	0.408125i
$971$	906.134	−	523.156i	0.933196	−	0.538781i	0.0453752	−	0.998970i	$-0.485552\pi$
$971$	906.134	−	523.156i	0.933196	−	0.538781i	0.887821	+	0.460189i	$0.152218\pi$
$972$	−82.9982	+	478.860i	−0.0853891	+	0.492655i
$973$	−423.893	−	244.735i	−0.435656	−	0.251526i
$974$		−	1144.62i		−	1.17518i
$975$	−260.406	−	28.5502i	−0.267083	−	0.0292822i
$976$	−40.8050			−0.0418084
$977$	−316.457	+	548.120i	−0.323907	+	0.561024i	−0.981291	−	0.192532i	$-0.938330\pi$
$977$	−316.457	+	548.120i	−0.323907	+	0.561024i	0.657383	+	0.753556i	$0.271663\pi$
$978$	16.1649	−	2.86002i	0.0165285	−	0.00292436i
$979$	−330.592	−	572.603i	−0.337684	−	0.584885i
$980$	1227.51			1.25256
$981$	87.4648	+	239.439i	0.0891588	+	0.244076i
$982$	23.9499	−	13.8275i	0.0243889	−	0.0140809i
$983$	512.383			0.521244			0.260622	−	0.965441i	$-0.416072\pi$
$983$	512.383			0.521244			0.260622	+	0.965441i	$0.416072\pi$
$984$	80.9188	+	29.3987i	0.0822346	+	0.0298767i
$985$	−135.959	+	235.487i	−0.138029	+	0.239074i
$986$	−133.694	+	231.566i	−0.135593	+	0.234853i
$987$	−1402.34	−	1669.27i	−1.42081	−	1.69126i
$988$	174.823	−	167.122i	0.176947	−	0.169152i
$989$			2470.81i			2.49830i
$990$	367.420	+	307.573i	0.371132	+	0.310680i
$991$	−573.725	+	993.722i	−0.578936	+	1.00275i	0.416666	+	0.909060i	$0.363199\pi$
$991$	−573.725	+	993.722i	−0.578936	+	1.00275i	−0.995602	+	0.0936866i	$0.970135\pi$
$992$	139.921	−	80.7836i	0.141050	−	0.0814351i
$993$	−110.053	−	131.001i	−0.110829	−	0.131925i
$994$	−744.055	+	429.580i	−0.748546	+	0.432173i
$995$	−997.793	−	1728.23i	−1.00281	−	1.73691i
$996$	−242.394	+	203.634i	−0.243368	+	0.204452i
$997$	−139.068	−	240.873i	−0.139486	−	0.241598i	0.787816	−	0.615911i	$-0.211212\pi$
$997$	−139.068	−	240.873i	−0.139486	−	0.241598i	−0.927302	+	0.374313i	$0.877879\pi$
$998$	−90.5774	−	52.2949i	−0.0907589	−	0.0523997i
$999$	0.00460926	+	2.63677i	4.61388e−6	+	0.00263941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.j.a.17.2	✓	20
3.2	odd	2	inner	78.3.j.a.17.10	yes	20
13.10	even	6	inner	78.3.j.a.23.10	yes	20
39.23	odd	6	inner	78.3.j.a.23.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.j.a.17.2	✓	20	1.1	even	1	trivial
78.3.j.a.17.10	yes	20	3.2	odd	2	inner
78.3.j.a.23.2	yes	20	39.23	odd	6	inner
78.3.j.a.23.10	yes	20	13.10	even	6	inner

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.522666 - 2.95412i) q^{3} +(-1.00000 - 1.73205i) q^{4} -5.63179 q^{5} +(3.98762 + 1.44875i) q^{6} +(-10.8851 + 6.28452i) q^{7} +2.82843 q^{8} +(-8.45364 + 3.08804i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-0.522666 - 2.95412i) q^{3} +(-1.00000 - 1.73205i) q^{4} -5.63179 q^{5} +(3.98762 + 1.44875i) q^{6} +(-10.8851 + 6.28452i) q^{7} +2.82843 q^{8} +(-8.45364 + 3.08804i) q^{9} +(3.98228 - 6.89751i) q^{10} +(3.34234 - 5.78910i) q^{11} +(-4.59402 + 3.85940i) q^{12} +(3.64652 - 12.4781i) q^{13} -17.7753i q^{14} +(2.94355 + 16.6370i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(13.5918 - 7.84721i) q^{17} +(2.19557 - 12.5371i) q^{18} +(-8.05581 + 4.65102i) q^{19} +(5.63179 + 9.75455i) q^{20} +(24.2545 + 28.8712i) q^{21} +(4.72678 + 8.18703i) q^{22} +(-31.2216 - 18.0258i) q^{23} +(-1.47832 - 8.35551i) q^{24} +6.71708 q^{25} +(12.7040 + 13.2894i) q^{26} +(13.5409 + 23.3591i) q^{27} +(21.7702 + 12.5690i) q^{28} +(10.4331 + 6.02355i) q^{29} +(-22.4575 - 8.15903i) q^{30} +28.5613i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-18.8486 - 6.84791i) q^{33} +22.1953i q^{34} +(61.3026 - 35.3931i) q^{35} +(13.8023 + 11.5541i) q^{36} +(0.0845745 + 0.0488291i) q^{37} -13.1551i q^{38} +(-38.7677 - 4.25038i) q^{39} -15.9291 q^{40} +(-5.07312 + 8.78691i) q^{41} +(-52.5104 + 9.29054i) q^{42} +(-34.2678 - 59.3535i) q^{43} -13.3694 q^{44} +(47.6091 - 17.3912i) q^{45} +(44.1540 - 25.4923i) q^{46} -57.8179 q^{47} +(11.2787 + 4.09767i) q^{48} +(54.4903 - 94.3800i) q^{49} +(-4.74970 + 8.22671i) q^{50} +(-30.2856 - 36.0502i) q^{51} +(-25.2592 + 6.16213i) q^{52} +57.4927i q^{53} +(-38.1837 + 0.0667479i) q^{54} +(-18.8234 + 32.6030i) q^{55} +(-30.7877 + 17.7753i) q^{56} +(17.9502 + 21.3669i) q^{57} +(-14.7546 + 8.51859i) q^{58} +(19.9580 + 34.5682i) q^{59} +(25.8726 - 21.7354i) q^{60} +(5.10063 + 8.83454i) q^{61} +(-34.9803 - 20.1959i) q^{62} +(72.6119 - 86.7406i) q^{63} +8.00000 q^{64} +(-20.5365 + 70.2740i) q^{65} +(21.7149 - 18.2426i) q^{66} +(-66.1637 - 38.1996i) q^{67} +(-27.1835 - 15.6944i) q^{68} +(-36.9319 + 101.654i) q^{69} +100.107i q^{70} +(-24.1673 - 41.8589i) q^{71} +(-23.9105 + 8.73428i) q^{72} +8.56609i q^{73} +(-0.119606 + 0.0690548i) q^{74} +(-3.51079 - 19.8431i) q^{75} +(16.1116 + 9.30205i) q^{76} +84.0200i q^{77} +(32.6185 - 44.4751i) q^{78} +37.3730 q^{79} +(11.2636 - 19.5091i) q^{80} +(61.9281 - 52.2103i) q^{81} +(-7.17448 - 12.4266i) q^{82} +52.7630 q^{83} +(25.7519 - 70.8812i) q^{84} +(-76.5460 + 44.1939i) q^{85} +96.9239 q^{86} +(12.3413 - 33.9689i) q^{87} +(9.45357 - 16.3741i) q^{88} +(49.4552 - 85.6589i) q^{89} +(-12.3650 + 70.6065i) q^{90} +(38.7260 + 158.742i) q^{91} +72.1031i q^{92} +(84.3735 - 14.9280i) q^{93} +(40.8834 - 70.8122i) q^{94} +(45.3686 - 26.1936i) q^{95} +(-12.9938 + 10.9160i) q^{96} +(43.0461 - 24.8527i) q^{97} +(77.0609 + 133.473i) q^{98} +(-10.3780 + 59.2603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9	\( 20 q - 20 q^{4} + 18 q^{7} - 4 q^{9} + 8 q^{10} - 42 q^{13} + 60 q^{15} - 40 q^{16} - 84 q^{19} + 260 q^{25} - 36 q^{27} - 36 q^{28} + 4 q^{30} - 258 q^{33} - 8 q^{36} - 192 q^{37} + 46 q^{39} - 32 q^{40} + 32 q^{42} + 26 q^{43} + 180 q^{45} + 144 q^{46} + 264 q^{49} - 188 q^{51} + 12 q^{52} + 324 q^{54} - 120 q^{55} - 168 q^{58} - 98 q^{61} + 252 q^{63} + 160 q^{64} + 144 q^{66} - 498 q^{67} - 146 q^{69} - 144 q^{72} - 556 q^{75} + 168 q^{76} - 220 q^{78} + 492 q^{79} + 212 q^{81} + 16 q^{82} + 168 q^{84} + 540 q^{85} + 302 q^{87} - 512 q^{90} + 10 q^{91} + 750 q^{93} + 48 q^{94} - 498 q^{97}+O(q^{100}) \) 20 * q - 20 * q^4 + 18 * q^7 - 4 * q^9 + 8 * q^10 - 42 * q^13 + 60 * q^15 - 40 * q^16 - 84 * q^19 + 260 * q^25 - 36 * q^27 - 36 * q^28 + 4 * q^30 - 258 * q^33 - 8 * q^36 - 192 * q^37 + 46 * q^39 - 32 * q^40 + 32 * q^42 + 26 * q^43 + 180 * q^45 + 144 * q^46 + 264 * q^49 - 188 * q^51 + 12 * q^52 + 324 * q^54 - 120 * q^55 - 168 * q^58 - 98 * q^61 + 252 * q^63 + 160 * q^64 + 144 * q^66 - 498 * q^67 - 146 * q^69 - 144 * q^72 - 556 * q^75 + 168 * q^76 - 220 * q^78 + 492 * q^79 + 212 * q^81 + 16 * q^82 + 168 * q^84 + 540 * q^85 + 302 * q^87 - 512 * q^90 + 10 * q^91 + 750 * q^93 + 48 * q^94 - 498 * q^97

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