LMFDB - Embedded newform 78.3.j.a.23.2

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			23.2
Root			$0.522666 - 2.95412i$ of defining polynomial
Character	$\chi$	$=$	78.23
Dual form			78.3.j.a.17.2

$q$-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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.997721	−	0.0674727i	$-0.978506\pi$
$7$	−10.8851	−	6.28452i	−1.55501	−	0.897788i	−0.557294	−	0.830315i	$-0.688160\pi$
$8$	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	0.977004	−	0.213219i	$-0.0683948\pi$
$11$	3.34234	+	5.78910i	0.303849	+	0.526282i	−0.673155	+	0.739501i	$0.735061\pi$
$12$	−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	0.843302	−	0.537440i	$-0.180609\pi$
$17$	13.5918	+	7.84721i	0.799516	+	0.461601i	−0.0437859	+	0.999041i	$0.513942\pi$
$18$	2.19557	+	12.5371i	0.121976	+	0.696507i
$19$	−8.05581	−	4.65102i	−0.423990	−	0.244791i	0.272793	−	0.962073i	$-0.412053\pi$
$19$	−8.05581	−	4.65102i	−0.423990	−	0.244791i	−0.696783	+	0.717282i	$0.745386\pi$
$20$	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	−0.989281	−	0.146025i	$-0.953352\pi$
$23$	−31.2216	+	18.0258i	−1.35746	+	0.783730i	−0.368179	+	0.929755i	$0.620019\pi$
$24$	−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	−0.309214	−	0.950992i	$-0.600066\pi$
$29$	10.4331	−	6.02355i	0.359762	−	0.207709i	0.668976	+	0.743284i	$0.266733\pi$
$30$	−22.4575	+	8.15903i	−0.748582	+	0.271968i
$31$		−	28.5613i		−	0.921332i	−0.887573	−	0.460666i	$-0.847611\pi$
$31$		−	28.5613i		−	0.921332i	0.887573	−	0.460666i	$-0.152389\pi$
$32$	−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	−0.498857	−	0.866685i	$-0.666247\pi$
$37$	0.0845745	−	0.0488291i	0.00228580	−	0.00131971i	0.501142	+	0.865365i	$0.332913\pi$
$38$			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	0.797503	−	0.603315i	$-0.206154\pi$
$41$	−5.07312	−	8.78691i	−0.123735	−	0.214315i	−0.921238	+	0.389000i	$0.872821\pi$
$42$	−52.5104	−	9.29054i	−1.25025	−	0.221203i
$43$	−34.2678	+	59.3535i	−0.796925	+	1.38032i	0.124684	+	0.992196i	$0.460208\pi$
$43$	−34.2678	+	59.3535i	−0.796925	+	1.38032i	−0.921609	+	0.388119i	$0.873125\pi$
$44$	−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	$-0.817522\pi$
$53$		−	57.4927i		−	1.08477i	0.840131	−	0.542384i	$-0.182478\pi$
$54$	−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	−0.645837	−	0.763476i	$-0.723491\pi$
$59$	19.9580	−	34.5682i	0.338271	−	0.585902i	0.984108	+	0.177573i	$0.0568246\pi$
$60$	25.8726	+	21.7354i	0.431209	+	0.362256i
$61$	5.10063	−	8.83454i	0.0836168	−	0.144829i	−0.821184	−	0.570663i	$-0.806686\pi$
$61$	5.10063	−	8.83454i	0.0836168	−	0.144829i	0.904801	+	0.425835i	$0.140019\pi$
$62$	−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	−0.904531	−	0.426407i	$-0.859779\pi$
$67$	−66.1637	+	38.1996i	−0.987517	+	0.570143i	−0.0829861	+	0.996551i	$0.526446\pi$
$68$	−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	−0.984504	−	0.175362i	$-0.943890\pi$
$71$	−24.1673	+	41.8589i	−0.340384	+	0.589562i	0.644120	+	0.764924i	$0.277224\pi$
$72$	−23.9105	−	8.73428i	−0.332090	−	0.121309i
$73$		−	8.56609i		−	0.117344i	−0.998277	−	0.0586718i	$-0.981313\pi$
$73$		−	8.56609i		−	0.117344i	0.998277	−	0.0586718i	$-0.0186866\pi$
$74$	−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	0.997851	+	0.0655307i	$0.0208740\pi$
$89$	49.4552	+	85.6589i	0.555677	+	0.962460i	−0.442174	+	0.896929i	$0.645793\pi$
$90$	−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	0.705197	−	0.709011i	$-0.250858\pi$
$97$	43.0461	+	24.8527i	0.443775	+	0.256213i	−0.261423	+	0.965224i	$0.584192\pi$
$98$	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	−0.899152	−	0.437636i	$-0.855816\pi$
$101$	−97.9421	+	56.5469i	−0.969724	+	0.559870i	−0.0705718	+	0.997507i	$0.522482\pi$
$102$	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	−0.708843	−	0.705366i	$-0.750783\pi$
$107$	−48.4068	+	27.9477i	−0.452400	+	0.261193i	0.256443	+	0.966559i	$0.417449\pi$
$108$	26.9182	+	46.8125i	0.249243	+	0.433449i
$109$			28.3238i			0.259851i	0.991524	+	0.129926i	$0.0414738\pi$
$109$			28.3238i			0.259851i	−0.991524	+	0.129926i	$0.958526\pi$
$110$	−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	0.433540	−	0.901134i	$-0.357264\pi$
$113$	−14.7007	−	8.48743i	−0.130094	−	0.0751100i	−0.563635	+	0.826024i	$0.690597\pi$
$114$	−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	0.983306	−	0.181962i	$-0.0582447\pi$
$127$	42.4268	+	73.4854i	0.334069	+	0.578625i	−0.649236	+	0.760587i	$0.724911\pi$
$128$	−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	$-0.810976\pi$
$131$		−	146.601i		−	1.11909i	0.828801	−	0.559544i	$-0.189024\pi$
$132$	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	0.222325	+	0.974973i	$0.428636\pi$
$137$	−100.447	+	173.979i	−0.733189	+	1.26992i	−0.955513	+	0.294948i	$0.904698\pi$
$138$	−98.3851	+	117.112i	−0.712935	+	0.848639i
$139$	19.4712	−	33.7252i	0.140081	−	0.242627i	−0.787446	−	0.616384i	$-0.788597\pi$
$139$	19.4712	−	33.7252i	0.140081	−	0.242627i	0.927527	+	0.373756i	$0.121930\pi$
$140$	−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	0.244237	+	0.969716i	$0.421463\pi$
$149$	−106.934	+	185.216i	−0.717680	+	1.24306i	−0.961917	+	0.273342i	$0.911871\pi$
$150$	26.7852	−	9.73134i	0.178568	−	0.0648756i
$151$		−	39.9974i		−	0.264884i	−0.991191	−	0.132442i	$-0.957718\pi$
$151$		−	39.9974i		−	0.264884i	0.991191	−	0.132442i	$-0.0422818\pi$
$152$	−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	0.510244	−	0.860030i	$-0.329555\pi$
$163$	3.35089	+	1.93464i	0.0205576	+	0.0118689i	−0.489686	+	0.871899i	$0.662889\pi$
$164$	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	0.689995	−	0.723814i	$-0.257613\pi$
$167$	−47.0680	−	81.5242i	−0.281844	−	0.488169i	−0.971839	+	0.235646i	$0.924280\pi$
$168$	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	0.175543	−	0.984472i	$-0.443832\pi$
$173$	−101.943	−	58.8565i	−0.589263	−	0.340211i	−0.764806	+	0.644261i	$0.777165\pi$
$174$	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	−0.177172	−	0.984180i	$-0.556695\pi$
$179$	104.996	−	60.6192i	0.586567	−	0.338655i	0.763739	+	0.645525i	$0.223361\pi$
$180$	−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	0.990415	+	0.138127i	$0.0441082\pi$
$191$	306.601	+	177.016i	1.60524	+	0.926788i	0.614829	+	0.788661i	$0.289225\pi$
$192$	−4.18133	+	23.6330i	−0.0217777	+	0.123088i
$193$	−36.0550	+	20.8164i	−0.186814	+	0.107857i	−0.590490	−	0.807045i	$-0.701066\pi$
$193$	−36.0550	+	20.8164i	−0.186814	+	0.107857i	0.403676	+	0.914902i	$0.367732\pi$
$194$		−	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	0.920770	−	0.390105i	$-0.127561\pi$
$197$	24.1413	+	41.8139i	0.122545	+	0.212254i	−0.798226	+	0.602358i	$0.794228\pi$
$198$	−65.2404	+	54.6137i	−0.329497	+	0.275827i
$199$	177.171	−	306.870i	0.890309	−	1.54206i	0.0508035	−	0.998709i	$-0.483822\pi$
$199$	177.171	−	306.870i	0.890309	−	1.54206i	0.839505	−	0.543351i	$-0.182845\pi$
$200$	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	0.567038	−	0.823692i	$-0.308089\pi$
$211$	−90.6918	−	157.083i	−0.429819	−	0.744468i	−0.996857	+	0.0792233i	$0.974756\pi$
$212$	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	−0.574352	−	0.818609i	$-0.694746\pi$
$223$	−34.0280	+	19.6461i	−0.152592	+	0.0880989i	0.421760	+	0.906708i	$0.361412\pi$
$224$	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	−0.846603	−	0.532225i	$-0.821356\pi$
$227$	8.53945	−	14.7908i	0.0376187	−	0.0651576i	0.884222	+	0.467067i	$0.154689\pi$
$228$	19.0584	+	52.4575i	0.0835893	+	0.230077i
$229$		−	183.299i		−	0.800433i	−0.916421	−	0.400216i	$-0.868935\pi$
$229$		−	183.299i		−	0.800433i	0.916421	−	0.400216i	$-0.131065\pi$
$230$	−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	$0.132450\pi$
$233$			188.357i			0.808399i	−0.914671	+	0.404199i	$0.867550\pi$
$234$	−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	0.191907	−	0.981413i	$-0.438533\pi$
$241$	−135.458	−	78.2069i	−0.562068	−	0.324510i	−0.753975	+	0.656903i	$0.771866\pi$
$242$	−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	0.987104	−	0.160078i	$-0.0511747\pi$
$251$	336.848	+	194.479i	1.34202	+	0.774818i	0.354920	+	0.934897i	$0.384508\pi$
$252$	−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	−0.606510	−	0.795076i	$-0.707431\pi$
$257$	−56.8507	+	32.8228i	−0.221209	+	0.127715i	0.385301	+	0.922791i	$0.374098\pi$
$258$	−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	−0.552533	−	0.833491i	$-0.686339\pi$
$263$	−28.1343	+	16.2433i	−0.106975	+	0.0617618i	0.445558	+	0.895253i	$0.353005\pi$
$264$	−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	−0.142573	−	0.989784i	$-0.545538\pi$
$269$	−288.109	−	166.340i	−1.07104	−	0.618364i	−0.928465	+	0.371420i	$0.878871\pi$
$270$	215.043	+	0.375910i	0.796454	+	0.00139226i
$271$	−394.103	+	227.536i	−1.45426	+	0.839615i	−0.998719	−	0.0506017i	$-0.983886\pi$
$271$	−394.103	+	227.536i	−1.45426	+	0.839615i	−0.455537	+	0.890217i	$0.650553\pi$
$272$		−	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	−0.918276	−	0.395941i	$-0.870418\pi$
$277$	−32.1992	+	55.7707i	−0.116243	+	0.201338i	0.802033	+	0.597280i	$0.203752\pi$
$278$	−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	0.895375	−	0.445313i	$-0.146908\pi$
$283$	17.5560	+	30.4078i	0.0620352	+	0.107448i	−0.833340	+	0.552761i	$0.813574\pi$
$284$	−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	0.0183294	−	0.999832i	$-0.494165\pi$
$293$	256.388	−	444.077i	0.875045	−	1.51562i	0.856715	−	0.515790i	$-0.172501\pi$
$294$	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	$0.253234\pi$
$307$			438.552i			1.42851i	−0.699886	+	0.714254i	$0.746766\pi$
$308$	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	$0.155916\pi$
$311$			292.633i			0.940942i	−0.882416	+	0.470471i	$0.844084\pi$
$312$	−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	0.572749	−	0.819731i	$-0.305877\pi$
$331$	49.3904	+	28.5156i	0.149216	+	0.0861498i	−0.423533	+	0.905881i	$0.639210\pi$
$332$	−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	0.544815	−	0.838556i	$-0.316600\pi$
$347$	31.5810	+	18.2333i	0.0910114	+	0.0525455i	−0.453804	+	0.891102i	$0.649933\pi$
$348$	−71.1772	−	12.5932i	−0.204532	−	0.0361874i
$349$	−298.830	+	172.530i	−0.856247	+	0.494354i	−0.862754	−	0.505625i	$-0.831262\pi$
$349$	−298.830	+	172.530i	−0.856247	+	0.494354i	0.00650692	+	0.999979i	$0.497929\pi$
$350$			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	0.671752	−	0.740776i	$-0.265542\pi$
$353$	−107.896	−	186.882i	−0.305655	−	0.529410i	−0.977407	+	0.211366i	$0.932209\pi$
$354$	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	0.873566	+	0.486706i	$0.161802\pi$
$367$	314.990	+	545.578i	0.858283	+	1.48659i	−0.0152828	+	0.999883i	$0.504865\pi$
$368$	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	−0.408571	−	0.912727i	$-0.633973\pi$
$373$	218.637	−	378.691i	0.586159	−	1.01526i	0.994730	−	0.102531i	$-0.0326941\pi$
$374$	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	−0.827977	−	0.560762i	$-0.810508\pi$
$379$	−286.650	+	165.497i	−0.756332	+	0.436669i	0.0716451	+	0.997430i	$0.477175\pi$
$380$	−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	−0.0323426	−	0.999477i	$-0.510297\pi$
$383$	325.321	−	563.472i	0.849401	−	1.47121i	0.881744	−	0.471729i	$-0.156370\pi$
$384$	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	$0.310984\pi$
$389$			644.817i			1.65763i	−0.559525	+	0.828814i	$0.689016\pi$
$390$	−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	0.451588	−	0.892226i	$-0.350858\pi$
$397$	−37.8373	−	21.8454i	−0.0953081	−	0.0550262i	−0.546897	+	0.837200i	$0.684191\pi$
$398$	−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	0.798314	−	0.602242i	$-0.205726\pi$
$401$	−49.0825	−	85.0133i	−0.122400	−	0.212003i	−0.920714	+	0.390239i	$0.872392\pi$
$402$	−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	0.774820	−	0.632181i	$-0.217840\pi$
$409$	251.431	+	145.164i	0.614745	+	0.354923i	−0.160075	+	0.987105i	$0.551174\pi$
$410$	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	−0.794408	−	0.607384i	$-0.792219\pi$
$419$	−278.887	+	161.016i	−0.665602	+	0.384285i	0.128806	+	0.991670i	$0.458885\pi$
$420$	−145.029	−	399.188i	−0.345308	−	0.950448i
$421$			798.404i			1.89645i	0.317604	+	0.948223i	$0.397122\pi$
$421$			798.404i			1.89645i	−0.317604	+	0.948223i	$0.602878\pi$
$422$	−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	0.999911	−	0.0133523i	$-0.00425030\pi$
$431$	210.497	+	364.591i	0.488392	+	0.845920i	−0.511519	+	0.859272i	$0.670917\pi$
$432$	−108.000	−	0.188791i	−0.250000	−	0.000437017i
$433$	−197.041	+	341.284i	−0.455059	+	0.788186i	−0.998692	−	0.0511377i	$-0.983715\pi$
$433$	−197.041	+	341.284i	−0.455059	+	0.788186i	0.543632	+	0.839323i	$0.317049\pi$
$434$	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	0.809637	−	0.586931i	$-0.199664\pi$
$439$	−45.4270	−	78.6819i	−0.103478	−	0.179230i	−0.913116	+	0.407701i	$0.866331\pi$
$440$	−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	$-0.845022\pi$
$443$		−	414.531i		−	0.935737i	0.883798	−	0.467868i	$-0.154978\pi$
$444$	−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	−0.700111	−	0.714034i	$-0.746866\pi$
$449$	120.474	−	208.667i	0.268316	−	0.464738i	0.968427	+	0.249297i	$0.0801994\pi$
$450$	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	0.146331	−	0.989236i	$-0.453254\pi$
$457$	491.823	−	283.954i	1.07620	−	0.621344i	0.929869	+	0.367892i	$0.119920\pi$
$458$	−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	−0.816682	−	0.577088i	$-0.804189\pi$
$461$	42.1504	−	73.0066i	0.0914325	−	0.158366i	0.908114	+	0.418723i	$0.137522\pi$
$462$	−121.724	−	335.040i	−0.263471	−	0.725195i
$463$			494.207i			1.06740i	0.845673	+	0.533701i	$0.179199\pi$
$463$			494.207i			1.06740i	−0.845673	+	0.533701i	$0.820801\pi$
$464$	−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	$-0.824271\pi$
$467$		−	489.836i		−	1.04890i	0.851442	−	0.524449i	$-0.175729\pi$
$468$	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	0.999205	+	0.0398546i	$0.0126895\pi$
$479$	255.842	+	443.132i	0.534118	+	0.925119i	−0.465088	+	0.885265i	$0.653977\pi$
$480$	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	−0.441491	−	0.897265i	$-0.645550\pi$
$487$	−700.935	−	404.685i	−1.43929	−	0.830976i	−0.997800	+	0.0662899i	$0.978884\pi$
$488$	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	−0.517146	−	0.855897i	$-0.673006\pi$
$491$	−16.9351	+	9.77749i	−0.0344911	+	0.0199134i	0.482655	+	0.875810i	$0.339672\pi$
$492$	−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	$-0.976390\pi$
$499$		−	73.9561i		−	0.148209i	0.997250	−	0.0741043i	$-0.0236098\pi$
$500$	−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	0.200771	−	0.979638i	$-0.435655\pi$
$503$	−275.259	−	158.921i	−0.547234	−	0.315946i	−0.748006	+	0.663692i	$0.768988\pi$
$504$	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	0.670043	−	0.742323i	$-0.266276\pi$
$509$	−156.695	−	271.404i	−0.307849	−	0.533210i	−0.977892	+	0.209112i	$0.932943\pi$
$510$	−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	$-0.882983\pi$
$521$		−	374.489i		−	0.718789i	0.933186	−	0.359395i	$-0.117017\pi$
$522$	98.4247	+	117.576i	0.188553	+	0.225241i
$523$	−82.6173	−	143.097i	−0.157968	−	0.273609i	0.776168	−	0.630526i	$-0.217161\pi$
$523$	−82.6173	−	143.097i	−0.157968	−	0.273609i	−0.934136	+	0.356918i	$0.883828\pi$
$524$	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	$-0.875430\pi$
$541$		−	412.712i		−	0.762869i	0.924396	−	0.381435i	$-0.124570\pi$
$542$	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	0.998653	−	0.0518786i	$-0.0165209\pi$
$557$	253.100	+	438.382i	0.454398	+	0.787041i	−0.544255	+	0.838920i	$0.683188\pi$
$558$	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	0.272954	−	0.962027i	$-0.411999\pi$
$563$	−238.548	−	137.726i	−0.423709	−	0.244629i	−0.696663	+	0.717398i	$0.745333\pi$
$564$	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	−0.545483	−	0.838122i	$-0.683654\pi$
$569$	−52.5701	+	30.3513i	−0.0923903	+	0.0533416i	0.453093	+	0.891463i	$0.350321\pi$
$570$	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	$-0.842534\pi$
$577$		−	547.875i		−	0.949524i	0.880114	−	0.474762i	$-0.157466\pi$
$578$	−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	0.980978	−	0.194117i	$-0.0621843\pi$
$587$	189.236	+	327.767i	0.322378	+	0.558376i	−0.658600	+	0.752493i	$0.728851\pi$
$588$	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	$-0.965574\pi$
$599$		−	129.313i		−	0.215881i	0.994157	−	0.107941i	$-0.0344257\pi$
$600$	−9.93002	+	56.1247i	−0.0165500	+	0.0935411i
$601$	−107.571	−	186.319i	−0.178987	−	0.310015i	0.762547	−	0.646933i	$-0.223949\pi$
$601$	−107.571	−	186.319i	−0.178987	−	0.310015i	−0.941534	+	0.336918i	$0.890615\pi$
$602$	−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	−0.667912	−	0.744240i	$-0.732812\pi$
$607$	188.519	−	326.525i	0.310575	−	0.537932i	0.978487	+	0.206308i	$0.0661450\pi$
$608$	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	−0.843871	−	0.536545i	$-0.819729\pi$
$613$	−491.102	+	283.538i	−0.801145	+	0.462541i	0.0427262	+	0.999087i	$0.486396\pi$
$614$	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	−0.921422	−	0.388564i	$-0.872971\pi$
$617$	−76.6344	+	132.735i	−0.124205	+	0.215129i	0.797217	+	0.603693i	$0.206305\pi$
$618$	−607.021	+	220.537i	−0.982235	+	0.356856i
$619$			659.533i			1.06548i	0.846279	+	0.532741i	$0.178838\pi$
$619$			659.533i			1.06548i	−0.846279	+	0.532741i	$0.821162\pi$
$620$	−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	0.826690	−	0.562657i	$-0.190221\pi$
$631$	474.992	+	274.237i	0.752760	+	0.434606i	−0.0739301	+	0.997263i	$0.523554\pi$
$632$	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	0.257661	−	0.966235i	$-0.417048\pi$
$641$	−288.638	−	166.645i	−0.450293	−	0.259977i	−0.707954	+	0.706259i	$0.750382\pi$
$642$	−152.539	+	181.574i	−0.237600	+	0.282826i
$643$	791.041	+	456.708i	1.23023	+	0.710276i	0.967079	−	0.254477i	$-0.0819033\pi$
$643$	791.041	+	456.708i	1.23023	+	0.710276i	0.263156	+	0.964753i	$0.415237\pi$
$644$	−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	−0.994294	−	0.106673i	$-0.965980\pi$
$647$	−905.192	+	522.613i	−1.39906	+	0.807748i	−0.404766	+	0.914420i	$0.632647\pi$
$648$	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	−0.0700982	−	0.997540i	$-0.522331\pi$
$653$	495.462	−	286.055i	0.758748	−	0.438063i	0.828846	+	0.559477i	$0.188998\pi$
$654$	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	0.992916	−	0.118817i	$-0.0379101\pi$
$659$	913.688	+	527.518i	1.38648	+	0.800482i	0.393560	+	0.919299i	$0.371243\pi$
$660$	−39.3533	+	222.426i	−0.0596263	+	0.337009i
$661$	−636.788	+	367.649i	−0.963370	+	0.556202i	−0.897209	−	0.441607i	$-0.854409\pi$
$661$	−636.788	+	367.649i	−0.963370	+	0.556202i	−0.0661614	+	0.997809i	$0.521075\pi$
$662$		−	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	−0.768892	−	0.639379i	$-0.779192\pi$
$673$	−631.384	−	1093.59i	−0.938164	−	1.62495i	−0.169272	−	0.985569i	$-0.554142\pi$
$674$	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	$0.195213\pi$
$677$			779.299i			1.15111i	−0.817764	+	0.575553i	$0.804787\pi$
$678$	−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	−0.310788	−	0.950479i	$-0.600593\pi$
$683$	456.070	−	789.936i	0.667745	−	1.15657i	0.978533	−	0.206089i	$-0.0660738\pi$
$684$	−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	−0.599931	−	0.800052i	$-0.704805\pi$
$691$	−143.059	+	82.5950i	−0.207031	+	0.119530i	0.392900	+	0.919581i	$0.371472\pi$
$692$	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	$0.0614569\pi$
$701$			269.009i			0.383751i	−0.981419	+	0.191875i	$0.938543\pi$
$702$	−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	−0.473674	−	0.880700i	$-0.657073\pi$
$709$	−1044.51	−	603.050i	−1.47322	−	0.850564i	−0.999546	+	0.0301361i	$0.990406\pi$
$710$	−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	0.288794	−	0.957391i	$-0.406746\pi$
$719$	−284.677	−	164.358i	−0.395934	−	0.228593i	−0.684728	+	0.728799i	$0.740079\pi$
$720$	−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	$0.0652906\pi$
$733$			298.597i			0.407363i	−0.979037	+	0.203681i	$0.934709\pi$
$734$	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	−0.625244	−	0.780429i	$-0.715001\pi$
$739$	−193.614	+	111.783i	−0.261995	+	0.151263i	0.363249	+	0.931692i	$0.381667\pi$
$740$		−	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	0.975538	−	0.219829i	$-0.0705501\pi$
$743$	220.962	+	382.717i	0.297391	+	0.515097i	−0.678147	+	0.734926i	$0.737217\pi$
$744$	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	0.881378	+	0.472411i	$0.156616\pi$
$751$	638.207	+	1105.41i	0.849809	+	1.47191i	−0.0315689	+	0.999502i	$0.510050\pi$
$752$	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	0.790907	−	0.611937i	$-0.209609\pi$
$757$	−101.816	−	176.351i	−0.134499	−	0.232960i	−0.925406	+	0.378977i	$0.876276\pi$
$758$	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	−0.870375	−	0.492390i	$-0.836123\pi$
$761$	−6.67002	+	11.5528i	−0.00876480	+	0.0151811i	0.861610	+	0.507571i	$0.169457\pi$
$762$	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	−0.543393	−	0.839478i	$-0.682861\pi$
$769$	−67.7341	+	39.1063i	−0.0880808	+	0.0508535i	0.455313	+	0.890332i	$0.349527\pi$
$770$	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	−0.874844	−	0.484405i	$-0.839036\pi$
$773$	−13.8481	+	23.9855i	−0.0179147	+	0.0310292i	0.856929	+	0.515434i	$0.172369\pi$
$774$	−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	0.907406	−	0.420255i	$-0.138059\pi$
$787$	784.763	+	453.083i	0.997158	+	0.575709i	0.0897518	+	0.995964i	$0.471393\pi$
$788$	−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	0.799130	−	0.601158i	$-0.205294\pi$
$797$	540.427	+	312.016i	0.678076	+	0.391488i	−0.121054	+	0.992646i	$0.538627\pi$
$798$	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	−0.611386	+	0.791333i	$0.709388\pi$
$809$	−1296.34	+	748.440i	−1.60239	+	0.925142i	−0.991007	+	0.133809i	$0.957279\pi$
$810$	−113.506	+	635.065i	−0.140131	+	0.784031i
$811$		−	911.040i		−	1.12335i	−0.827357	−	0.561677i	$-0.810156\pi$
$811$		−	911.040i		−	1.12335i	0.827357	−	0.561677i	$-0.189844\pi$
$812$	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	0.967128	−	0.254289i	$-0.0818414\pi$
$821$	216.205	+	374.478i	0.263344	+	0.456124i	−0.703785	+	0.710413i	$0.748508\pi$
$822$	−148.493	+	839.285i	−0.180648	+	1.02103i
$823$	−339.071	+	587.288i	−0.411993	+	0.713594i	−0.995108	−	0.0987966i	$-0.968501\pi$
$823$	−339.071	+	587.288i	−0.411993	+	0.713594i	0.583114	+	0.812390i	$0.301834\pi$
$824$	−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	0.999992	+	0.00396559i	$0.00126229\pi$
$829$	417.344	+	722.861i	0.503430	+	0.871967i	−0.496562	+	0.868001i	$0.665404\pi$
$830$	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	−0.433724	−	0.901046i	$-0.642801\pi$
$839$	472.749	−	818.825i	0.563467	−	0.975953i	0.997191	−	0.0749072i	$-0.0238660\pi$
$840$	−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	$0.237763\pi$
$853$			1159.07i			1.35881i	−0.733761	+	0.679407i	$0.762237\pi$
$854$	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	$-0.686842\pi$
$857$		−	1427.10i		−	1.66523i	0.553850	−	0.832617i	$-0.313158\pi$
$858$	−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	0.432103	−	0.901824i	$-0.357772\pi$
$877$	−116.509	−	67.2663i	−0.132849	−	0.0767005i	−0.564952	+	0.825124i	$0.691105\pi$
$878$	−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	−0.604705	−	0.796449i	$-0.706709\pi$
$881$	−191.452	+	110.535i	−0.217312	+	0.125465i	0.387393	+	0.921915i	$0.373376\pi$
$882$	−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	−0.517155	−	0.855892i	$-0.673009\pi$
$887$	−30.6083	+	17.6717i	−0.0345077	+	0.0199230i	0.482647	+	0.875815i	$0.339675\pi$
$888$	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	0.930808	−	0.365508i	$-0.119105\pi$
$907$	135.020	+	233.862i	0.148865	+	0.257841i	−0.781943	+	0.623349i	$0.785771\pi$
$908$	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	$0.151883\pi$
$911$			836.758i			0.918504i	−0.888306	+	0.459252i	$0.848117\pi$
$912$	−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	0.480529	+	0.876979i	$0.340445\pi$
$919$	−477.165	+	826.473i	−0.519222	+	0.899318i	−0.999750	+	0.0223393i	$0.992889\pi$
$920$	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	−0.194823	−	0.980838i	$-0.562413\pi$
$929$	698.626	−	1210.06i	0.752019	−	1.30254i	0.946843	−	0.321697i	$-0.104253\pi$
$930$	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	0.965718	−	0.259593i	$-0.0835885\pi$
$947$	244.368	+	423.258i	0.258045	+	0.446946i	−0.707673	+	0.706540i	$0.750255\pi$
$948$	−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	0.127751	−	0.991806i	$-0.459224\pi$
$953$	−635.939	−	367.160i	−0.667302	−	0.385267i	−0.795054	+	0.606539i	$0.792557\pi$
$954$	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	$-0.849637\pi$
$967$		−	879.981i		−	0.910011i	0.890489	−	0.455006i	$-0.150363\pi$
$968$	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	0.887821	−	0.460189i	$-0.152218\pi$
$971$	906.134	+	523.156i	0.933196	+	0.538781i	0.0453752	+	0.998970i	$0.485552\pi$
$972$	−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	0.657383	−	0.753556i	$-0.271663\pi$
$977$	−316.457	−	548.120i	−0.323907	−	0.561024i	−0.981291	+	0.192532i	$0.938330\pi$
$978$	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	−0.995602	−	0.0936866i	$-0.970135\pi$
$991$	−573.725	−	993.722i	−0.578936	−	1.00275i	0.416666	−	0.909060i	$-0.363199\pi$
$992$	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	−0.927302	−	0.374313i	$-0.877879\pi$
$997$	−139.068	+	240.873i	−0.139486	+	0.241598i	0.787816	+	0.615911i	$0.211212\pi$
$998$	−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.23.2	yes	20
3.2	odd	2	inner	78.3.j.a.23.10	yes	20
13.4	even	6	inner	78.3.j.a.17.10	yes	20
39.17	odd	6	inner	78.3.j.a.17.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.j.a.17.2	✓	20	39.17	odd	6	inner
78.3.j.a.17.10	yes	20	13.4	even	6	inner
78.3.j.a.23.2	yes	20	1.1	even	1	trivial
78.3.j.a.23.10	yes	20	3.2	odd	2	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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