LMFDB - Embedded newform 35.3.h.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(26,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("35.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.h (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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 19 x^{10} - 26 x^{9} + 244 x^{8} - 338 x^{7} + 1249 x^{6} - 986 x^{5} + 3532 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 19x^10 - 26x^9 + 244x^8 - 338x^7 + 1249x^6 - 986x^5 + 3532x^4 - 3618x^3 + 3579x^2 - 1386*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$1.18241 - 2.04800i$ of defining polynomial
Character	$\chi$	$=$	35.31
Dual form			35.3.h.a.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18241 - 2.04800i) q^{2} +(4.45439 + 2.57174i) q^{3} +(-0.796202 + 1.37906i) q^{4} +(-1.93649 + 1.11803i) q^{5} -12.1634i q^{6} +(-1.42520 - 6.85338i) q^{7} -5.69355 q^{8} +(8.72772 + 15.1168i) q^{9} +O(q^{10})$	\(q+(-1.18241 - 2.04800i) q^{2} +(4.45439 + 2.57174i) q^{3} +(-0.796202 + 1.37906i) q^{4} +(-1.93649 + 1.11803i) q^{5} -12.1634i q^{6} +(-1.42520 - 6.85338i) q^{7} -5.69355 q^{8} +(8.72772 + 15.1168i) q^{9} +(4.57947 + 2.64396i) q^{10} +(-6.86467 + 11.8900i) q^{11} +(-7.09319 + 4.09525i) q^{12} -6.14666i q^{13} +(-12.3505 + 11.0223i) q^{14} -11.5012 q^{15} +(9.91693 + 17.1766i) q^{16} +(-1.74292 - 1.00628i) q^{17} +(20.6395 - 35.7487i) q^{18} +(-2.08213 + 1.20212i) q^{19} -3.56072i q^{20} +(11.2767 - 34.1929i) q^{21} +32.4675 q^{22} +(-8.02550 - 13.9006i) q^{23} +(-25.3613 - 14.6423i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-12.5884 + 7.26789i) q^{26} +43.4904i q^{27} +(10.5860 + 3.49123i) q^{28} +15.9780 q^{29} +(13.5991 + 23.5544i) q^{30} +(17.9557 + 10.3667i) q^{31} +(12.0647 - 20.8967i) q^{32} +(-61.1558 + 35.3083i) q^{33} +4.75934i q^{34} +(10.4222 + 11.6781i) q^{35} -27.7961 q^{36} +(-6.51335 - 11.2814i) q^{37} +(4.92387 + 2.84279i) q^{38} +(15.8076 - 27.3796i) q^{39} +(11.0255 - 6.36558i) q^{40} -55.2974i q^{41} +(-83.3607 + 17.3354i) q^{42} +54.7172 q^{43} +(-10.9313 - 18.9336i) q^{44} +(-33.8023 - 19.5158i) q^{45} +(-18.9789 + 32.8724i) q^{46} +(61.9889 - 35.7893i) q^{47} +102.015i q^{48} +(-44.9376 + 19.5349i) q^{49} -11.8241 q^{50} +(-5.17577 - 8.96469i) q^{51} +(8.47662 + 4.89398i) q^{52} +(-33.6897 + 58.3523i) q^{53} +(89.0683 - 51.4236i) q^{54} -30.6997i q^{55} +(8.11445 + 39.0200i) q^{56} -12.3661 q^{57} +(-18.8926 - 32.7230i) q^{58} +(18.2612 + 10.5431i) q^{59} +(9.15727 - 15.8608i) q^{60} +(-22.8803 + 13.2100i) q^{61} -49.0311i q^{62} +(91.1627 - 81.3589i) q^{63} +22.2735 q^{64} +(6.87217 + 11.9029i) q^{65} +(144.623 + 83.4980i) q^{66} +(-37.2194 + 64.4659i) q^{67} +(2.77544 - 1.60240i) q^{68} -82.5581i q^{69} +(11.5934 - 35.1530i) q^{70} -66.7438 q^{71} +(-49.6916 - 86.0685i) q^{72} +(-108.278 - 62.5145i) q^{73} +(-15.4029 + 26.6787i) q^{74} +(22.2719 - 12.8587i) q^{75} -3.82851i q^{76} +(91.2699 + 30.1006i) q^{77} -74.7645 q^{78} +(49.0504 + 84.9577i) q^{79} +(-38.4081 - 22.1749i) q^{80} +(-33.2966 + 57.6714i) q^{81} +(-113.249 + 65.3844i) q^{82} +78.1877i q^{83} +(38.1755 + 42.7757i) q^{84} +4.50020 q^{85} +(-64.6983 - 112.061i) q^{86} +(71.1723 + 41.0914i) q^{87} +(39.0843 - 67.6960i) q^{88} +(38.7285 - 22.3599i) q^{89} +92.3028i q^{90} +(-42.1254 + 8.76023i) q^{91} +25.5597 q^{92} +(53.3211 + 92.3549i) q^{93} +(-146.593 - 84.6355i) q^{94} +(2.68801 - 4.65577i) q^{95} +(107.482 - 62.0548i) q^{96} -31.6777i q^{97} +(93.1423 + 68.9339i) q^{98} -239.652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{3} - 10 q^{4} - 2 q^{7} - 4 q^{8} + 14 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 6 * q^3 - 10 * q^4 - 2 * q^7 - 4 * q^8 + 14 * q^9	$ 12 q - 2 q^{2} - 6 q^{3} - 10 q^{4} - 2 q^{7} - 4 q^{8} + 14 q^{9} - 14 q^{11} + 18 q^{12} - 2 q^{14} - 20 q^{15} - 22 q^{16} + 48 q^{17} + 64 q^{18} - 30 q^{19} - 84 q^{21} - 88 q^{22} - 14 q^{23} - 36 q^{24} + 30 q^{25} + 66 q^{26} + 202 q^{28} + 64 q^{29} + 20 q^{30} + 132 q^{31} - 54 q^{32} - 192 q^{33} + 30 q^{35} + 156 q^{36} + 44 q^{37} - 300 q^{38} - 24 q^{39} - 138 q^{42} - 4 q^{43} + 6 q^{44} - 180 q^{45} - 214 q^{46} + 204 q^{47} - 24 q^{49} - 20 q^{50} - 132 q^{51} + 252 q^{52} + 196 q^{53} + 168 q^{54} - 460 q^{56} - 48 q^{57} + 158 q^{58} + 72 q^{59} + 150 q^{60} + 72 q^{61} + 536 q^{63} - 140 q^{64} + 30 q^{65} + 744 q^{66} - 138 q^{67} - 348 q^{68} + 240 q^{70} - 8 q^{71} - 196 q^{72} - 528 q^{73} + 50 q^{74} - 30 q^{75} - 176 q^{77} - 312 q^{78} - 12 q^{79} - 240 q^{80} - 310 q^{81} - 378 q^{82} - 276 q^{84} - 40 q^{86} + 138 q^{87} + 604 q^{88} + 204 q^{89} - 480 q^{91} + 732 q^{92} + 84 q^{93} - 42 q^{94} + 60 q^{95} + 540 q^{96} + 898 q^{98} - 44 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^3 - 10 * q^4 - 2 * q^7 - 4 * q^8 + 14 * q^9 - 14 * q^11 + 18 * q^12 - 2 * q^14 - 20 * q^15 - 22 * q^16 + 48 * q^17 + 64 * q^18 - 30 * q^19 - 84 * q^21 - 88 * q^22 - 14 * q^23 - 36 * q^24 + 30 * q^25 + 66 * q^26 + 202 * q^28 + 64 * q^29 + 20 * q^30 + 132 * q^31 - 54 * q^32 - 192 * q^33 + 30 * q^35 + 156 * q^36 + 44 * q^37 - 300 * q^38 - 24 * q^39 - 138 * q^42 - 4 * q^43 + 6 * q^44 - 180 * q^45 - 214 * q^46 + 204 * q^47 - 24 * q^49 - 20 * q^50 - 132 * q^51 + 252 * q^52 + 196 * q^53 + 168 * q^54 - 460 * q^56 - 48 * q^57 + 158 * q^58 + 72 * q^59 + 150 * q^60 + 72 * q^61 + 536 * q^63 - 140 * q^64 + 30 * q^65 + 744 * q^66 - 138 * q^67 - 348 * q^68 + 240 * q^70 - 8 * q^71 - 196 * q^72 - 528 * q^73 + 50 * q^74 - 30 * q^75 - 176 * q^77 - 312 * q^78 - 12 * q^79 - 240 * q^80 - 310 * q^81 - 378 * q^82 - 276 * q^84 - 40 * q^86 + 138 * q^87 + 604 * q^88 + 204 * q^89 - 480 * q^91 + 732 * q^92 + 84 * q^93 - 42 * q^94 + 60 * q^95 + 540 * q^96 + 898 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.18241	−	2.04800i	−0.591207	−	1.02400i	−0.994070	−	0.108740i	$-0.965318\pi$
$2$	−1.18241	−	2.04800i	−0.591207	−	1.02400i	0.402864	−	0.915260i	$-0.368015\pi$
$3$	4.45439	+	2.57174i	1.48480	+	0.857247i	0.999850	−	0.0172969i	$-0.00550606\pi$
$3$	4.45439	+	2.57174i	1.48480	+	0.857247i	0.484946	+	0.874544i	$0.338839\pi$
$4$	−0.796202	+	1.37906i	−0.199051	+	0.344766i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		−	12.1634i		−	2.02724i
$7$	−1.42520	−	6.85338i	−0.203600	−	0.979054i
$7$	−1.42520	−	6.85338i	−0.203600	−	0.979054i
$8$	−5.69355			−0.711693
$9$	8.72772	+	15.1168i	0.969746	+	1.67965i
$10$	4.57947	+	2.64396i	0.457947	+	0.264396i
$11$	−6.86467	+	11.8900i	−0.624061	+	1.08091i	0.364661	+	0.931140i	$0.381185\pi$
$11$	−6.86467	+	11.8900i	−0.624061	+	1.08091i	−0.988722	+	0.149765i	$0.952148\pi$
$12$	−7.09319	+	4.09525i	−0.591099	+	0.341271i
$13$		−	6.14666i		−	0.472820i	−0.971653	−	0.236410i	$-0.924029\pi$
$13$		−	6.14666i		−	0.472820i	0.971653	−	0.236410i	$-0.0759708\pi$
$14$	−12.3505	+	11.0223i	−0.882181	+	0.787310i
$15$	−11.5012			−0.766745
$16$	9.91693	+	17.1766i	0.619808	+	1.07354i
$17$	−1.74292	−	1.00628i	−0.102525	−	0.0591927i	0.447861	−	0.894103i	$-0.352186\pi$
$17$	−1.74292	−	1.00628i	−0.102525	−	0.0591927i	−0.550386	+	0.834911i	$0.685519\pi$
$18$	20.6395	−	35.7487i	1.14664	−	1.98604i
$19$	−2.08213	+	1.20212i	−0.109586	+	0.0632692i	−0.553791	−	0.832656i	$-0.686819\pi$
$19$	−2.08213	+	1.20212i	−0.109586	+	0.0632692i	0.444205	+	0.895925i	$0.353486\pi$
$20$		−	3.56072i		−	0.178036i
$21$	11.2767	−	34.1929i	0.536987	−	1.62823i
$22$	32.4675			1.47580
$23$	−8.02550	−	13.9006i	−0.348935	−	0.604373i	0.637126	−	0.770760i	$-0.280123\pi$
$23$	−8.02550	−	13.9006i	−0.348935	−	0.604373i	−0.986061	+	0.166387i	$0.946790\pi$
$24$	−25.3613	−	14.6423i	−1.05672	−	0.610097i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−12.5884	+	7.26789i	−0.484167	+	0.279534i
$27$			43.4904i			1.61075i
$28$	10.5860	+	3.49123i	0.378071	+	0.124687i
$29$	15.9780			0.550966			0.275483	−	0.961306i	$-0.411162\pi$
$29$	15.9780			0.550966			0.275483	+	0.961306i	$0.411162\pi$
$30$	13.5991	+	23.5544i	0.453305	+	0.785147i
$31$	17.9557	+	10.3667i	0.579217	+	0.334411i	0.760822	−	0.648961i	$-0.224796\pi$
$31$	17.9557	+	10.3667i	0.579217	+	0.334411i	−0.181605	+	0.983371i	$0.558129\pi$
$32$	12.0647	−	20.8967i	0.377023	−	0.653023i
$33$	−61.1558	+	35.3083i	−1.85321	+	1.06995i
$34$			4.75934i			0.139981i
$35$	10.4222	+	11.6781i	0.297777	+	0.333660i
$36$	−27.7961			−0.772114
$37$	−6.51335	−	11.2814i	−0.176036	−	0.304904i	0.764483	−	0.644644i	$-0.222994\pi$
$37$	−6.51335	−	11.2814i	−0.176036	−	0.304904i	−0.940519	+	0.339740i	$0.889661\pi$
$38$	4.92387	+	2.84279i	0.129575	+	0.0748104i
$39$	15.8076	−	27.3796i	0.405323	−	0.702041i
$40$	11.0255	−	6.36558i	0.275638	−	0.159139i
$41$		−	55.2974i		−	1.34872i	−0.738404	−	0.674358i	$-0.764420\pi$
$41$		−	55.2974i		−	1.34872i	0.738404	−	0.674358i	$-0.235580\pi$
$42$	−83.3607	+	17.3354i	−1.98478	+	0.412747i
$43$	54.7172			1.27249			0.636246	−	0.771486i	$-0.280486\pi$
$43$	54.7172			1.27249			0.636246	+	0.771486i	$0.280486\pi$
$44$	−10.9313	−	18.9336i	−0.248439	−	0.430310i
$45$	−33.8023	−	19.5158i	−0.751162	−	0.433684i
$46$	−18.9789	+	32.8724i	−0.412585	+	0.714618i
$47$	61.9889	−	35.7893i	1.31891	−	0.761475i	0.335359	−	0.942090i	$-0.391142\pi$
$47$	61.9889	−	35.7893i	1.31891	−	0.761475i	0.983554	+	0.180615i	$0.0578089\pi$
$48$			102.015i			2.12532i
$49$	−44.9376	+	19.5349i	−0.917094	+	0.398671i
$50$	−11.8241			−0.236483
$51$	−5.17577	−	8.96469i	−0.101486	−	0.175778i
$52$	8.47662	+	4.89398i	0.163012	+	0.0941150i
$53$	−33.6897	+	58.3523i	−0.635655	+	1.10099i	0.350721	+	0.936480i	$0.385937\pi$
$53$	−33.6897	+	58.3523i	−0.635655	+	1.10099i	−0.986376	+	0.164507i	$0.947397\pi$
$54$	89.0683	−	51.4236i	1.64941	−	0.952289i
$55$		−	30.6997i		−	0.558177i
$56$	8.11445	+	39.0200i	0.144901	+	0.696786i
$57$	−12.3661			−0.216950
$58$	−18.8926	−	32.7230i	−0.325735	−	0.564189i
$59$	18.2612	+	10.5431i	0.309511	+	0.178696i	0.646708	−	0.762738i	$-0.276145\pi$
$59$	18.2612	+	10.5431i	0.309511	+	0.178696i	−0.337196	+	0.941434i	$0.609479\pi$
$60$	9.15727	−	15.8608i	0.152621	−	0.264347i
$61$	−22.8803	+	13.2100i	−0.375088	+	0.216557i	−0.675679	−	0.737196i	$-0.736149\pi$
$61$	−22.8803	+	13.2100i	−0.375088	+	0.216557i	0.300591	+	0.953753i	$0.402816\pi$
$62$		−	49.0311i		−	0.790824i
$63$	91.1627	−	81.3589i	1.44703	−	1.29141i
$64$	22.2735			0.348023
$65$	6.87217	+	11.9029i	0.105726	+	0.183122i
$66$	144.623	+	83.4980i	2.19126	+	1.26512i
$67$	−37.2194	+	64.4659i	−0.555513	+	0.962177i	0.442350	+	0.896843i	$0.354145\pi$
$67$	−37.2194	+	64.4659i	−0.555513	+	0.962177i	−0.997863	+	0.0653349i	$0.979188\pi$
$68$	2.77544	−	1.60240i	0.0408152	−	0.0235647i
$69$		−	82.5581i		−	1.19649i
$70$	11.5934	−	35.1530i	0.165620	−	0.502186i
$71$	−66.7438			−0.940053			−0.470027	−	0.882652i	$-0.655756\pi$
$71$	−66.7438			−0.940053			−0.470027	+	0.882652i	$0.655756\pi$
$72$	−49.6916	−	86.0685i	−0.690162	−	1.19540i
$73$	−108.278	−	62.5145i	−1.48327	−	0.856363i	−0.483446	−	0.875374i	$-0.660615\pi$
$73$	−108.278	−	62.5145i	−1.48327	−	0.856363i	−0.999819	+	0.0190109i	$0.993948\pi$
$74$	−15.4029	+	26.6787i	−0.208148	+	0.360522i
$75$	22.2719	−	12.8587i	0.296959	−	0.171449i
$76$		−	3.82851i		−	0.0503751i
$77$	91.2699	+	30.1006i	1.18532	+	0.390917i
$78$	−74.7645			−0.958520
$79$	49.0504	+	84.9577i	0.620891	+	1.07541i	0.989320	+	0.145758i	$0.0465622\pi$
$79$	49.0504	+	84.9577i	0.620891	+	1.07541i	−0.368430	+	0.929656i	$0.620104\pi$
$80$	−38.4081	−	22.1749i	−0.480101	−	0.277187i
$81$	−33.2966	+	57.6714i	−0.411069	+	0.711992i
$82$	−113.249	+	65.3844i	−1.38109	+	0.797370i
$83$			78.1877i			0.942020i	0.882128	+	0.471010i	$0.156110\pi$
$83$			78.1877i			0.942020i	−0.882128	+	0.471010i	$0.843890\pi$
$84$	38.1755	+	42.7757i	0.454471	+	0.509235i
$85$	4.50020			0.0529436
$86$	−64.6983	−	112.061i	−0.752306	−	1.30303i
$87$	71.1723	+	41.0914i	0.818072	+	0.472314i
$88$	39.0843	−	67.6960i	0.444140	−	0.769273i
$89$	38.7285	−	22.3599i	0.435151	−	0.251235i	−0.266388	−	0.963866i	$-0.585830\pi$
$89$	38.7285	−	22.3599i	0.435151	−	0.251235i	0.701539	+	0.712631i	$0.252497\pi$
$90$			92.3028i			1.02559i
$91$	−42.1254	+	8.76023i	−0.462916	+	0.0962662i
$92$	25.5597			0.277823
$93$	53.3211	+	92.3549i	0.573346	+	0.993064i
$94$	−146.593	−	84.6355i	−1.55950	−	0.900378i
$95$	2.68801	−	4.65577i	0.0282949	−	0.0490081i
$96$	107.482	−	62.0548i	1.11960	−	0.646404i
$97$		−	31.6777i		−	0.326574i	−0.986579	−	0.163287i	$-0.947790\pi$
$97$		−	31.6777i		−	0.326574i	0.986579	−	0.163287i	$-0.0522096\pi$
$98$	93.1423	+	68.9339i	0.950431	+	0.703407i
$99$	−239.652			−2.42072
$100$	3.98101	+	6.89531i	0.0398101	+	0.0689531i
$101$	−63.7153	−	36.7861i	−0.630845	−	0.364218i	0.150234	−	0.988650i	$-0.451997\pi$
$101$	−63.7153	−	36.7861i	−0.630845	−	0.364218i	−0.781079	+	0.624432i	$0.785330\pi$
$102$	−12.2398	+	21.1999i	−0.119998	+	0.207843i
$103$	23.9642	−	13.8358i	0.232663	−	0.134328i	−0.379137	−	0.925340i	$-0.623779\pi$
$103$	23.9642	−	13.8358i	0.232663	−	0.134328i	0.611800	+	0.791013i	$0.290446\pi$
$104$			34.9963i			0.336503i
$105$	16.3915	+	78.8219i	0.156110	+	0.750685i
$106$	159.341			1.50321
$107$	41.1422	+	71.2603i	0.384506	+	0.665984i	0.991701	−	0.128569i	$-0.0410384\pi$
$107$	41.1422	+	71.2603i	0.384506	+	0.665984i	−0.607194	+	0.794553i	$0.707705\pi$
$108$	−59.9759	−	34.6271i	−0.555333	−	0.320622i
$109$	16.9306	−	29.3247i	0.155327	−	0.269034i	−0.777851	−	0.628449i	$-0.783690\pi$
$109$	16.9306	−	29.3247i	0.155327	−	0.269034i	0.933178	+	0.359415i	$0.117024\pi$
$110$	−62.8731	+	36.2998i	−0.571573	+	0.329998i
$111$		−	67.0026i		−	0.603627i
$112$	103.584	−	92.4447i	0.924860	−	0.825399i
$113$	−36.7538			−0.325255			−0.162628	−	0.986688i	$-0.551997\pi$
$113$	−36.7538			−0.325255			−0.162628	+	0.986688i	$0.551997\pi$
$114$	14.6219	+	25.3258i	0.128262	+	0.222156i
$115$	31.0826	+	17.9456i	0.270284	+	0.156048i
$116$	−12.7217	+	22.0347i	−0.109670	+	0.189954i
$117$	92.9181	−	53.6463i	0.794171	−	0.458515i
$118$		−	49.8652i		−	0.422586i
$119$	−4.41238	+	13.3790i	−0.0370788	+	0.112429i
$120$	65.4825			0.545687
$121$	−33.7474	−	58.4522i	−0.278904	−	0.483076i
$122$	54.1081	+	31.2393i	0.443509	+	0.256060i
$123$	142.211	−	246.316i	1.15618	−	2.00257i
$124$	−28.5928	+	16.5080i	−0.230587	+	0.133129i
$125$			11.1803i			0.0894427i
$126$	−274.415	−	90.5014i	−2.17790	−	0.718265i
$127$	−181.035			−1.42547			−0.712737	−	0.701431i	$-0.752545\pi$
$127$	−181.035			−1.42547			−0.712737	+	0.701431i	$0.752545\pi$
$128$	−74.5954	−	129.203i	−0.582776	−	1.00940i
$129$	243.731	+	140.718i	1.88939	+	1.09084i
$130$	16.2515	−	28.1484i	0.125011	−	0.216526i
$131$	37.0813	−	21.4089i	0.283063	−	0.163427i	−0.351746	−	0.936095i	$-0.614412\pi$
$131$	37.0813	−	21.4089i	0.283063	−	0.163427i	0.634809	+	0.772669i	$0.281079\pi$
$132$		−	112.450i		−	0.851896i
$133$	11.2060	+	12.5563i	0.0842557	+	0.0944085i
$134$	176.035			1.31369
$135$	−48.6237	−	84.2187i	−0.360176	−	0.623843i
$136$	9.92340	+	5.72928i	0.0729662	+	0.0421271i
$137$	−50.5297	+	87.5200i	−0.368830	+	0.638832i	−0.989383	−	0.145332i	$-0.953575\pi$
$137$	−50.5297	+	87.5200i	−0.368830	+	0.638832i	0.620553	+	0.784165i	$0.286908\pi$
$138$	−169.079	+	97.6178i	−1.22521	+	0.707375i
$139$			132.591i			0.953895i	0.878932	+	0.476947i	$0.158257\pi$
$139$			132.591i			0.953895i	−0.878932	+	0.476947i	$0.841743\pi$
$140$	−24.4030	+	5.07475i	−0.174307	+	0.0362482i
$141$	368.164			2.61109
$142$	78.9187	+	136.691i	0.555766	+	0.962615i
$143$	73.0835	+	42.1948i	0.511073	+	0.295068i
$144$	−173.104	+	299.825i	−1.20211	+	2.08212i
$145$	−30.9413	+	17.8640i	−0.213388	+	0.123200i
$146$			295.672i			2.02515i
$147$	−250.408	−	28.5519i	−1.70346	−	0.194231i
$148$	20.7438			0.140161
$149$	−71.8152	−	124.388i	−0.481981	−	0.834816i	0.517805	−	0.855499i	$-0.326749\pi$
$149$	−71.8152	−	124.388i	−0.481981	−	0.834816i	−0.999786	+	0.0206830i	$0.993416\pi$
$150$	−52.6693	−	30.4086i	−0.351128	−	0.202724i
$151$	−73.0209	+	126.476i	−0.483582	+	0.837588i	−0.999822	−	0.0188554i	$-0.993998\pi$
$151$	−73.0209	+	126.476i	−0.483582	+	0.837588i	0.516240	+	0.856444i	$0.327331\pi$
$152$	11.8547	−	6.84430i	0.0779913	−	0.0450283i
$153$		−	35.1300i		−	0.229608i
$154$	−46.2727	−	222.512i	−0.300472	−	1.44488i
$155$	−46.3615			−0.299106
$156$	25.1721	+	43.5994i	0.161360	+	0.279483i
$157$	−172.624	−	99.6646i	−1.09952	−	0.634807i	−0.163423	−	0.986556i	$-0.552254\pi$
$157$	−172.624	−	99.6646i	−1.09952	−	0.634807i	−0.936094	+	0.351749i	$0.885587\pi$
$158$	115.996	−	200.910i	0.734149	−	1.27158i
$159$	−300.134	+	173.283i	−1.88764	+	1.08983i
$160$			53.9551i			0.337220i
$161$	−83.8279	+	74.8129i	−0.520670	+	0.464676i
$162$	157.481			0.972107
$163$	64.0489	+	110.936i	0.392938	+	0.680589i	0.992836	−	0.119488i	$-0.0381253\pi$
$163$	64.0489	+	110.936i	0.392938	+	0.680589i	−0.599897	+	0.800077i	$0.704792\pi$
$164$	76.2585	+	44.0279i	0.464991	+	0.268463i
$165$	78.9518	−	136.749i	0.478496	−	0.828779i
$166$	160.128	−	92.4501i	0.964629	−	0.556929i
$167$		−	300.506i		−	1.79944i	−0.436469	−	0.899719i	$-0.643771\pi$
$167$		−	300.506i		−	1.79944i	0.436469	−	0.899719i	$-0.356229\pi$
$168$	−64.2045	+	194.679i	−0.382170	+	1.15880i
$169$	131.219			0.776442
$170$	−5.32110	−	9.21642i	−0.0313006	−	0.0542142i
$171$	−36.3444	−	20.9834i	−0.212540	−	0.122710i
$172$	−43.5659	+	75.4584i	−0.253290	+	0.438712i
$173$	96.8042	−	55.8899i	0.559562	−	0.323063i	−0.193408	−	0.981118i	$-0.561954\pi$
$173$	96.8042	−	55.8899i	0.559562	−	0.323063i	0.752970	+	0.658055i	$0.228621\pi$
$174$		−	194.348i		−	1.11694i
$175$	−33.2390	−	10.9621i	−0.189937	−	0.0626408i
$176$	−272.306			−1.54719
$177$	54.2282	+	93.9261i	0.306374	+	0.530656i
$178$	−91.5861	−	52.8772i	−0.514529	−	0.297063i
$179$	176.173	−	305.141i	0.984207	−	1.70470i	0.338800	−	0.940858i	$-0.389979\pi$
$179$	176.173	−	305.141i	0.984207	−	1.70470i	0.645407	−	0.763839i	$-0.276688\pi$
$180$	53.8269	−	31.0770i	0.299038	−	0.172650i
$181$		−	153.980i		−	0.850718i	−0.905025	−	0.425359i	$-0.860148\pi$
$181$		−	153.980i		−	0.850718i	0.905025	−	0.425359i	$-0.139852\pi$
$182$	67.7505	+	75.9145i	0.372256	+	0.417113i
$183$	−135.891			−0.742572
$184$	45.6936	+	79.1436i	0.248335	+	0.430128i
$185$	25.2261	+	14.5643i	0.136357	+	0.0787259i
$186$	126.095	−	218.403i	0.677932	−	1.17421i
$187$	23.9292	−	13.8155i	0.127963	−	0.0738797i
$188$			113.982i			0.606288i
$189$	298.056	−	61.9826i	1.57702	−	0.327950i
$190$	−12.7134			−0.0669124
$191$	38.4323	+	66.5667i	0.201216	+	0.348517i	0.948921	−	0.315515i	$-0.102177\pi$
$191$	38.4323	+	66.5667i	0.201216	+	0.348517i	−0.747704	+	0.664032i	$0.768844\pi$
$192$	99.2146	+	57.2816i	0.516743	+	0.298342i
$193$	−166.261	+	287.973i	−0.861456	+	1.49209i	0.00906705	+	0.999959i	$0.497114\pi$
$193$	−166.261	+	287.973i	−0.861456	+	1.49209i	−0.870523	+	0.492127i	$0.836220\pi$
$194$	−64.8759	+	37.4561i	−0.334412	+	0.193073i
$195$			70.6938i			0.362532i
$196$	8.83957	−	77.5255i	0.0450998	−	0.395538i
$197$	−122.760			−0.623146			−0.311573	−	0.950222i	$-0.600856\pi$
$197$	−122.760			−0.623146			−0.311573	+	0.950222i	$0.600856\pi$
$198$	283.367	+	490.806i	1.43115	+	2.47882i
$199$	73.5085	+	42.4402i	0.369390	+	0.213267i	0.673192	−	0.739468i	$-0.264923\pi$
$199$	73.5085	+	42.4402i	0.369390	+	0.213267i	−0.303802	+	0.952735i	$0.598256\pi$
$200$	−14.2339	+	24.6538i	−0.0711693	+	0.123269i
$201$	−331.579	+	191.437i	−1.64965	+	0.952425i
$202$			173.985i			0.861313i
$203$	−22.7719	−	109.503i	−0.112177	−	0.539426i
$204$	16.4838			0.0808031
$205$	61.8243	+	107.083i	0.301582	+	0.522356i
$206$	−56.6713	−	32.7192i	−0.275103	−	0.158831i
$207$	140.089	−	242.640i	0.676756	−	1.17218i
$208$	105.579	−	60.9560i	0.507591	−	0.293058i
$209$		−	33.0085i		−	0.157935i
$210$	142.046	−	126.770i	0.676409	−	0.603666i
$211$	142.536			0.675527			0.337763	−	0.941231i	$-0.390330\pi$
$211$	142.536			0.675527			0.337763	+	0.941231i	$0.390330\pi$
$212$	−53.6477	−	92.9205i	−0.253055	−	0.438304i
$213$	−297.303	−	171.648i	−1.39579	−	0.805858i
$214$	97.2941	−	168.518i	0.454645	−	0.787469i
$215$	−105.959	+	61.1756i	−0.492834	+	0.284538i
$216$		−	247.614i		−	1.14636i
$217$	45.4567	−	137.832i	0.209478	−	0.635171i
$218$	−80.0760			−0.367321
$219$	−321.543	−	556.928i	−1.46823	−	2.54305i
$220$	42.3369	+	24.4432i	0.192440	+	0.111105i
$221$	−6.18523	+	10.7131i	−0.0279875	+	0.0484757i
$222$	−137.221	+	79.2247i	−0.618114	+	0.356868i
$223$			229.951i			1.03117i	0.856838	+	0.515585i	$0.172425\pi$
$223$			229.951i			1.03117i	−0.856838	+	0.515585i	$0.827575\pi$
$224$	−160.408	−	52.9021i	−0.716107	−	0.236170i
$225$	87.2772			0.387898
$226$	43.4582	+	75.2719i	0.192293	+	0.333061i
$227$	297.681	+	171.866i	1.31137	+	0.757121i	0.982323	−	0.187192i	$-0.0599387\pi$
$227$	297.681	+	171.866i	1.31137	+	0.757121i	0.329048	+	0.944313i	$0.393272\pi$
$228$	9.84594	−	17.0537i	0.0431839	−	0.0747968i
$229$	0.761259	−	0.439513i	0.00332428	−	0.00191927i	−0.498337	−	0.866983i	$-0.666056\pi$
$229$	0.761259	−	0.439513i	0.00332428	−	0.00191927i	0.501661	+	0.865064i	$0.332722\pi$
$230$		−	84.8763i		−	0.369027i
$231$	329.141	+	368.802i	1.42485	+	1.59655i
$232$	−90.9716			−0.392119
$233$	−51.9301	−	89.9455i	−0.222876	−	0.386032i	0.732804	−	0.680440i	$-0.238211\pi$
$233$	−51.9301	−	89.9455i	−0.222876	−	0.386032i	−0.955680	+	0.294407i	$0.904878\pi$
$234$	−219.735	−	126.864i	−0.939039	−	0.542154i
$235$	−80.0274	+	138.611i	−0.340542	+	0.589836i
$236$	−29.0792	+	16.7889i	−0.123217	+	0.0711393i
$237$			504.580i			2.12903i
$238$	32.6175	−	6.78302i	0.137048	−	0.0285001i
$239$	−159.924			−0.669140			−0.334570	−	0.942371i	$-0.608591\pi$
$239$	−159.924			−0.669140			−0.334570	+	0.942371i	$0.608591\pi$
$240$	−114.056	−	197.552i	−0.475235	−	0.823131i
$241$	223.306	+	128.926i	0.926583	+	0.534963i	0.885729	−	0.464202i	$-0.153659\pi$
$241$	223.306	+	128.926i	0.926583	+	0.534963i	0.0408535	+	0.999165i	$0.486992\pi$
$242$	−79.8067	+	138.229i	−0.329780	+	0.571195i
$243$	42.3421	−	24.4462i	0.174247	−	0.100602i
$244$		−	42.0712i		−	0.172423i
$245$	65.1806	−	88.0709i	0.266043	−	0.359473i
$246$	−672.607			−2.73417
$247$	7.38899	+	12.7981i	0.0299149	+	0.0518142i
$248$	−102.232	−	59.0235i	−0.412225	−	0.237998i
$249$	−201.079	+	348.278i	−0.807544	+	1.39871i
$250$	22.8973	−	13.2198i	0.0915893	−	0.0528791i
$251$		−	148.025i		−	0.589740i	−0.955537	−	0.294870i	$-0.904724\pi$
$251$		−	148.025i		−	0.589740i	0.955537	−	0.294870i	$-0.0952763\pi$
$252$	39.6151	+	190.497i	0.157203	+	0.755941i
$253$	220.370			0.871026
$254$	214.059	+	370.760i	0.842750	+	1.45969i
$255$	20.0457	+	11.5734i	0.0786104	+	0.0453857i
$256$	−131.858	+	228.385i	−0.515071	+	0.892129i
$257$	59.0535	−	34.0946i	0.229780	−	0.132664i	−0.380690	−	0.924703i	$-0.624314\pi$
$257$	59.0535	−	34.0946i	0.229780	−	0.132664i	0.610471	+	0.792039i	$0.290980\pi$
$258$		−	665.549i		−	2.57965i
$259$	−68.0332	+	60.7168i	−0.262676	+	0.234428i
$260$	−21.8865			−0.0841790
$261$	139.452	+	241.537i	0.534297	+	0.925430i
$262$	−87.6909	−	50.6283i	−0.334698	−	0.193238i
$263$	−137.599	+	238.329i	−0.523191	+	0.906193i	0.476445	+	0.879204i	$0.341925\pi$
$263$	−137.599	+	238.329i	−0.523191	+	0.906193i	−0.999636	+	0.0269887i	$0.991408\pi$
$264$	348.193	−	201.030i	1.31891	−	0.761476i
$265$		−	150.665i		−	0.568547i
$266$	12.4652	−	37.7967i	0.0468618	−	0.142093i
$267$	230.015			0.861481
$268$	−59.2683	−	102.656i	−0.221151	−	0.383044i
$269$	198.847	+	114.804i	0.739207	+	0.426782i	0.821781	−	0.569803i	$-0.192981\pi$
$269$	198.847	+	114.804i	0.739207	+	0.426782i	−0.0825736	+	0.996585i	$0.526314\pi$
$270$	−114.987	+	199.163i	−0.425876	+	0.737640i
$271$	451.013	−	260.393i	1.66425	−	0.960858i	0.693607	−	0.720354i	$-0.256021\pi$
$271$	451.013	−	260.393i	1.66425	−	0.960858i	0.970648	−	0.240504i	$-0.0773128\pi$
$272$		−	39.9167i		−	0.146753i
$273$	−210.172	−	69.3141i	−0.769860	−	0.253898i
$274$	238.988			0.872219
$275$	34.3233	+	59.4498i	0.124812	+	0.216181i
$276$	113.853	+	65.7329i	0.412510	+	0.238163i
$277$	193.738	−	335.564i	0.699414	−	1.21142i	−0.269255	−	0.963069i	$-0.586778\pi$
$277$	193.738	−	335.564i	0.699414	−	1.21142i	0.968670	−	0.248352i	$-0.0798891\pi$
$278$	271.547	−	156.778i	0.976788	−	0.563949i
$279$			361.912i			1.29717i
$280$	−59.3393	−	66.4897i	−0.211926	−	0.237463i
$281$	−157.972			−0.562180			−0.281090	−	0.959681i	$-0.590696\pi$
$281$	−157.972			−0.562180			−0.281090	+	0.959681i	$0.590696\pi$
$282$	−435.322	−	753.999i	−1.54369	−	2.67376i
$283$	−39.0701	−	22.5571i	−0.138057	−	0.0797072i	0.429381	−	0.903124i	$-0.358732\pi$
$283$	−39.0701	−	22.5571i	−0.138057	−	0.0797072i	−0.567438	+	0.823416i	$0.692065\pi$
$284$	53.1415	−	92.0439i	0.187118	−	0.324098i
$285$	23.9469	−	13.8257i	0.0840242	−	0.0485114i
$286$		−	199.567i		−	0.697785i
$287$	−378.974	+	78.8099i	−1.32047	+	0.274599i
$288$	421.190			1.46247
$289$	−142.475	−	246.774i	−0.492992	−	0.853888i
$290$	73.1708	+	42.2452i	0.252313	+	0.145673i
$291$	81.4668	−	141.105i	0.279955	−	0.484896i
$292$	172.423	−	99.5484i	0.590489	−	0.340919i
$293$			54.4900i			0.185973i	0.995667	+	0.0929864i	$0.0296413\pi$
$293$			54.4900i			0.185973i	−0.995667	+	0.0929864i	$0.970359\pi$
$294$	237.612	+	546.596i	0.808203	+	1.85917i
$295$	−47.1501			−0.159831
$296$	37.0840	+	64.2314i	0.125284	+	0.216998i
$297$	−517.099	−	298.547i	−1.74107	−	1.00521i
$298$	−169.830	+	294.155i	−0.569901	+	0.987097i
$299$	−85.4420	+	49.3300i	−0.285759	+	0.164983i
$300$			40.9525i			0.136508i
$301$	−77.9830	−	374.997i	−0.259080	−	1.24584i
$302$	345.363			1.14359
$303$	−189.208	−	327.719i	−0.624450	−	1.08158i
$304$	−41.2966	−	23.8426i	−0.135844	−	0.0784296i
$305$	29.5384	−	51.1620i	0.0968472	−	0.167744i
$306$	−71.9462	+	41.5381i	−0.235118	+	0.135746i
$307$			176.942i			0.576357i	0.957577	+	0.288178i	$0.0930496\pi$
$307$			176.942i			0.576357i	−0.957577	+	0.288178i	$0.906950\pi$
$308$	−114.180	+	101.901i	−0.370714	+	0.330847i
$309$	142.328			0.460609
$310$	54.8184	+	94.9483i	0.176834	+	0.306285i
$311$	−189.438	−	109.372i	−0.609125	−	0.351678i	0.163498	−	0.986544i	$-0.447722\pi$
$311$	−189.438	−	109.372i	−0.609125	−	0.351678i	−0.772623	+	0.634865i	$0.781056\pi$
$312$	−90.0014	+	155.887i	−0.288466	+	0.499638i
$313$	132.570	−	76.5394i	0.423547	−	0.244535i	−0.273047	−	0.962001i	$-0.588031\pi$
$313$	132.570	−	76.5394i	0.423547	−	0.244535i	0.696594	+	0.717466i	$0.254698\pi$
$314$			471.379i			1.50121i
$315$	−85.5738	+	259.474i	−0.271663	+	0.823726i
$316$	−156.216			−0.494354
$317$	64.6285	+	111.940i	0.203875	+	0.353122i	0.949774	−	0.312937i	$-0.101313\pi$
$317$	64.6285	+	111.940i	0.203875	+	0.353122i	−0.745898	+	0.666060i	$0.767980\pi$
$318$	709.765	+	409.783i	2.23197	+	1.28863i
$319$	−109.684	+	189.978i	−0.343836	+	0.595542i
$320$	−43.1324	+	24.9025i	−0.134789	+	0.0778203i
$321$			423.228i			1.31847i
$322$	252.336	+	83.2198i	0.783652	+	0.258447i
$323$	4.83864			0.0149803
$324$	−53.0216	−	91.8362i	−0.163647	−	0.283445i
$325$	−26.6158	−	15.3666i	−0.0818948	−	0.0472820i
$326$	151.465	−	262.344i	0.464615	−	0.804737i
$327$	150.831	−	87.0825i	0.461258	−	0.266307i
$328$			314.838i			0.959872i
$329$	−333.624	−	373.827i	−1.01406	−	1.13625i
$330$	−373.415			−1.13156
$331$	−289.516	−	501.457i	−0.874672	−	1.51498i	−0.857112	−	0.515131i	$-0.827743\pi$
$331$	−289.516	−	501.457i	−0.874672	−	1.51498i	−0.0175606	−	0.999846i	$-0.505590\pi$
$332$	−107.826	−	62.2532i	−0.324776	−	0.187510i
$333$	113.693	−	196.922i	0.341421	−	0.591359i
$334$	−615.437	+	355.323i	−1.84262	+	1.06384i
$335$		−	166.450i		−	0.496866i
$336$	699.149	−	145.392i	2.08080	−	0.432715i
$337$	−14.2685			−0.0423397			−0.0211698	−	0.999776i	$-0.506739\pi$
$337$	−14.2685			−0.0423397			−0.0211698	+	0.999776i	$0.506739\pi$
$338$	−155.155	−	268.736i	−0.459037	−	0.795076i
$339$	−163.716	−	94.5214i	−0.482938	−	0.278824i
$340$	−3.58307	+	6.20606i	−0.0105384	+	0.0182531i
$341$	−246.520	+	142.328i	−0.722933	+	0.417385i
$342$			99.2444i			0.290188i
$343$	197.925	+	280.133i	0.577041	+	0.816715i
$344$	−311.535			−0.905624
$345$	92.3027	+	159.873i	0.267544	+	0.463400i
$346$	−228.925	−	132.170i	−0.661633	−	0.381994i
$347$	94.0286	−	162.862i	0.270976	−	0.469344i	−0.698136	−	0.715965i	$-0.745987\pi$
$347$	94.0286	−	162.862i	0.270976	−	0.469344i	0.969112	+	0.246621i	$0.0793203\pi$
$348$	−113.335	+	65.4340i	−0.325676	+	0.188029i
$349$			297.734i			0.853106i	0.904463	+	0.426553i	$0.140272\pi$
$349$			297.734i			0.853106i	−0.904463	+	0.426553i	$0.859728\pi$
$350$	16.8518	+	81.0353i	0.0481479	+	0.231529i
$351$	267.320			0.761596
$352$	165.641	+	286.898i	0.470571	+	0.815052i
$353$	384.830	+	222.182i	1.09017	+	0.629410i	0.933622	−	0.358260i	$-0.116630\pi$
$353$	384.830	+	222.182i	1.09017	+	0.629410i	0.156549	+	0.987670i	$0.449963\pi$
$354$	128.240	−	222.119i	0.362261	−	0.627454i
$355$	129.249	−	74.6218i	0.364081	−	0.210202i
$356$			71.2120i			0.200034i
$357$	−54.0619	+	48.2480i	−0.151434	+	0.135148i
$358$	−833.238			−2.32748
$359$	208.158	+	360.540i	0.579827	+	1.00429i	0.995499	+	0.0947753i	$0.0302132\pi$
$359$	208.158	+	360.540i	0.579827	+	1.00429i	−0.415672	+	0.909515i	$0.636453\pi$
$360$	192.455	+	111.114i	0.534597	+	0.308650i
$361$	−177.610	+	307.629i	−0.491994	+	0.852159i
$362$	−315.351	+	182.068i	−0.871135	+	0.502950i
$363$		−	347.158i		−	0.956358i
$364$	21.4594	−	65.0684i	0.0589544	−	0.178759i
$365$	279.573			0.765955
$366$	160.679	+	278.304i	0.439013	+	0.760393i
$367$	−460.868	−	266.082i	−1.25577	−	0.725019i	−0.283521	−	0.958966i	$-0.591503\pi$
$367$	−460.868	−	266.082i	−1.25577	−	0.725019i	−0.972249	+	0.233947i	$0.924836\pi$
$368$	159.177	−	275.702i	0.432545	−	0.749191i
$369$	835.922	−	482.620i	2.26537	−	1.30791i
$370$		−	68.8840i		−	0.186173i
$371$	447.925	+	147.725i	1.20735	+	0.398180i
$372$	−169.818			−0.456499
$373$	−254.610	−	440.997i	−0.682600	−	1.18230i	−0.974185	−	0.225753i	$-0.927516\pi$
$373$	−254.610	−	440.997i	−0.682600	−	1.18230i	0.291584	−	0.956545i	$-0.405818\pi$
$374$	−56.5883	−	32.6713i	−0.151306	−	0.0873564i
$375$	−28.7530	+	49.8016i	−0.0766745	+	0.132804i
$376$	−352.937	+	203.768i	−0.938662	+	0.541937i
$377$		−	98.2114i		−	0.260508i
$378$	−479.366	−	537.130i	−1.26816	−	1.42098i
$379$	166.742			0.439953			0.219976	−	0.975505i	$-0.429402\pi$
$379$	166.742			0.439953			0.219976	+	0.975505i	$0.429402\pi$
$380$	4.28040	+	7.41387i	0.0112642	+	0.0195102i
$381$	−806.401	−	465.576i	−2.11654	−	1.22198i
$382$	90.8858	−	157.419i	0.237921	−	0.412091i
$383$	−295.194	+	170.430i	−0.770742	+	0.444988i	−0.833139	−	0.553063i	$-0.813459\pi$
$383$	−295.194	+	170.430i	−0.770742	+	0.444988i	0.0623972	+	0.998051i	$0.480125\pi$
$384$		−	767.360i		−	1.99833i
$385$	−210.397	+	43.7533i	−0.546485	+	0.113645i
$386$	786.357			2.03719
$387$	477.556	+	827.151i	1.23399	+	2.13734i
$388$	43.6855	+	25.2218i	0.112591	+	0.0650047i
$389$	14.9678	−	25.9249i	0.0384775	−	0.0666450i	−0.846145	−	0.532952i	$-0.821083\pi$
$389$	14.9678	−	25.9249i	0.0384775	−	0.0666450i	0.884623	+	0.466307i	$0.154416\pi$
$390$	144.781	−	83.5893i	0.371233	−	0.214332i
$391$			32.3035i			0.0826176i
$392$	255.854	−	111.223i	0.652690	−	0.283732i
$393$	220.233			0.560389
$394$	145.153	+	251.412i	0.368408	+	0.638102i
$395$	−189.971	−	109.680i	−0.480940	−	0.277671i
$396$	190.811	−	330.494i	0.481846	−	0.834582i
$397$	415.166	−	239.696i	1.04576	−	0.603769i	0.124300	−	0.992245i	$-0.460332\pi$
$397$	415.166	−	239.696i	1.04576	−	0.603769i	0.921459	+	0.388476i	$0.126998\pi$
$398$		−	200.727i		−	0.504340i
$399$	17.6242	+	84.7497i	0.0441710	+	0.212405i
$400$	99.1693			0.247923
$401$	304.548	+	527.492i	0.759470	+	1.31544i	0.943121	+	0.332449i	$0.107875\pi$
$401$	304.548	+	527.492i	0.759470	+	1.31544i	−0.183651	+	0.982991i	$0.558792\pi$
$402$	784.127	+	452.716i	1.95057	+	1.12616i
$403$	63.7208	−	110.368i	0.158116	−	0.273865i
$404$	101.461	−	58.5783i	0.251140	−	0.144996i
$405$		−	148.907i		−	0.367671i
$406$	−197.337	+	176.115i	−0.486052	+	0.433781i
$407$	178.848			0.439430
$408$	29.4685	+	51.0409i	0.0722266	+	0.125100i
$409$	−438.488	−	253.161i	−1.07210	−	0.618976i	−0.143344	−	0.989673i	$-0.545786\pi$
$409$	−438.488	−	253.161i	−1.07210	−	0.618976i	−0.928754	+	0.370696i	$0.879119\pi$
$410$	146.204	−	253.232i	0.356595	−	0.617640i
$411$	−450.158	+	259.899i	−1.09527	+	0.632357i
$412$			44.0643i			0.106952i
$413$	46.2300	−	140.177i	0.111937	−	0.339411i
$414$	−662.570			−1.60041
$415$	−87.4165	−	151.410i	−0.210642	−	0.364843i
$416$	−128.445	−	74.1578i	−0.308762	−	0.178264i
$417$	−340.991	+	590.613i	−0.817724	+	1.41634i
$418$	−67.6014	+	39.0297i	−0.161726	+	0.0933725i
$419$		−	600.983i		−	1.43433i	−0.696905	−	0.717163i	$-0.745440\pi$
$419$		−	600.983i		−	1.43433i	0.696905	−	0.717163i	$-0.254560\pi$
$420$	−121.751	−	40.1533i	−0.289884	−	0.0956031i
$421$	−277.147			−0.658307			−0.329153	−	0.944276i	$-0.606763\pi$
$421$	−277.147			−0.658307			−0.329153	+	0.944276i	$0.606763\pi$
$422$	−168.537	−	291.914i	−0.399376	−	0.691739i
$423$	1082.04	+	624.718i	2.55802	+	1.47687i
$424$	191.814	−	332.232i	0.452392	−	0.783565i
$425$	−8.71461	+	5.03138i	−0.0205050	+	0.0118385i
$426$			811.835i			1.90571i
$427$	123.142	+	137.981i	0.288389	+	0.323140i
$428$	−131.030			−0.306145
$429$	217.028	+	375.904i	0.505893	+	0.876232i
$430$	250.575	+	144.670i	0.582733	+	0.336441i
$431$	203.623	−	352.686i	0.472444	−	0.818296i	−0.527059	−	0.849829i	$-0.676705\pi$
$431$	203.623	−	352.686i	0.472444	−	0.818296i	0.999503	+	0.0315322i	$0.0100387\pi$
$432$	−747.018	+	431.291i	−1.72921	+	0.998359i
$433$		−	312.356i		−	0.721377i	−0.932686	−	0.360689i	$-0.882542\pi$
$433$		−	312.356i		−	0.721377i	0.932686	−	0.360689i	$-0.117458\pi$
$434$	−336.028	+	69.8792i	−0.774259	+	0.161012i
$435$	−183.766			−0.422451
$436$	26.9604	+	46.6968i	0.0618358	+	0.107103i
$437$	33.4202	+	19.2952i	0.0764764	+	0.0441537i
$438$	−760.392	+	1317.04i	−1.73606	+	3.00694i
$439$	−184.053	+	106.263i	−0.419255	+	0.242057i	−0.694758	−	0.719243i	$-0.744489\pi$
$439$	−184.053	+	106.263i	−0.419255	+	0.242057i	0.275504	+	0.961300i	$0.411155\pi$
$440$			174.790i			0.397251i
$441$	−687.509	−	508.820i	−1.55898	−	1.15379i
$442$	29.2540			0.0661855
$443$	185.709	+	321.658i	0.419208	+	0.726089i	0.995860	−	0.0909005i	$-0.0289745\pi$
$443$	185.709	+	321.658i	0.419208	+	0.726089i	−0.576652	+	0.816990i	$0.695641\pi$
$444$	92.4008	+	53.3476i	0.208110	+	0.120152i
$445$	−49.9982	+	86.5995i	−0.112356	+	0.194606i
$446$	470.940	−	271.897i	1.05592	−	0.609635i
$447$		−	738.760i		−	1.65271i
$448$	−31.7442	−	152.648i	−0.0708575	−	0.340733i
$449$	4.22975			0.00942037			0.00471018	−	0.999989i	$-0.498501\pi$
$449$	4.22975			0.00942037			0.00471018	+	0.999989i	$0.498501\pi$
$450$	−103.198	−	178.744i	−0.229328	−	0.397208i
$451$	657.483	+	379.598i	1.45783	+	0.841681i
$452$	29.2635	−	50.6859i	0.0647422	−	0.112137i
$453$	−650.527	+	375.582i	−1.43604	+	0.829099i
$454$		−	812.869i		−	1.79046i
$455$	71.7812	−	64.0617i	0.157761	−	0.140795i
$456$	70.4071			0.154402
$457$	−250.605	−	434.061i	−0.548371	−	0.949806i	−0.998386	−	0.0567855i	$-0.981915\pi$
$457$	−250.605	−	434.061i	−0.548371	−	0.949806i	0.450016	−	0.893021i	$-0.351418\pi$
$458$	−1.80025	−	1.03937i	−0.00393067	−	0.00226937i
$459$	43.7633	−	75.8003i	0.0953449	−	0.165142i
$460$	−49.4961	+	28.5766i	−0.107600	+	0.0621230i
$461$			300.121i			0.651022i	0.945538	+	0.325511i	$0.105536\pi$
$461$			300.121i			0.651022i	−0.945538	+	0.325511i	$0.894464\pi$
$462$	366.127	−	1110.16i	0.792483	−	2.40294i
$463$	571.548			1.23444			0.617222	−	0.786789i	$-0.288258\pi$
$463$	571.548			1.23444			0.617222	+	0.786789i	$0.288258\pi$
$464$	158.453	+	274.449i	0.341493	+	0.591484i
$465$	−206.512	−	119.230i	−0.444112	−	0.256408i
$466$	−122.806	+	212.706i	−0.263531	+	0.456450i
$467$	−771.238	+	445.274i	−1.65147	+	0.953478i	−0.675005	+	0.737813i	$0.735858\pi$
$467$	−771.238	+	445.274i	−1.65147	+	0.953478i	−0.976467	+	0.215665i	$0.930808\pi$
$468$			170.853i			0.365071i
$469$	494.854	+	163.202i	1.05513	+	0.347978i
$470$	378.502			0.805323
$471$	−512.623	−	887.890i	−1.08837	−	1.88512i
$472$	−103.971	−	60.0276i	−0.220277	−	0.127177i
$473$	−375.615	+	650.585i	−0.794112	+	1.37544i
$474$	1033.38	−	596.621i	2.18012	−	1.25870i
$475$			12.0212i			0.0253077i
$476$	−14.9374	−	16.7374i	−0.0313811	−	0.0351625i
$477$	−1176.14			−2.46570
$478$	189.097	+	327.525i	0.395600	+	0.685199i
$479$	−28.6660	−	16.5503i	−0.0598456	−	0.0345519i	0.469779	−	0.882784i	$-0.344334\pi$
$479$	−28.6660	−	16.5503i	−0.0598456	−	0.0345519i	−0.529624	+	0.848232i	$0.677667\pi$
$480$	−138.759	+	240.337i	−0.289081	+	0.500702i
$481$	−69.3432	+	40.0353i	−0.144165	+	0.0832335i
$482$		−	609.775i		−	1.26509i
$483$	−565.802	+	117.662i	−1.17143	+	0.243606i
$484$	107.479			0.222064
$485$	35.4167	+	61.3435i	0.0730241	+	0.126482i
$486$	−100.132	−	57.8110i	−0.206032	−	0.118953i
$487$	307.943	−	533.374i	0.632327	−	1.09522i	−0.354747	−	0.934962i	$-0.615433\pi$
$487$	307.943	−	533.374i	0.632327	−	1.09522i	0.987075	−	0.160261i	$-0.0512335\pi$
$488$	130.270	−	75.2116i	0.266947	−	0.154122i
$489$			658.869i			1.34738i
$490$	−257.440	−	29.3536i	−0.525387	−	0.0599054i
$491$	−223.560			−0.455316			−0.227658	−	0.973741i	$-0.573107\pi$
$491$	−223.560			−0.455316			−0.227658	+	0.973741i	$0.573107\pi$
$492$	226.457	+	392.235i	0.460278	+	0.797225i
$493$	−27.8484	−	16.0783i	−0.0564877	−	0.0326132i
$494$	17.4737	−	30.2653i	0.0353718	−	0.0612658i
$495$	464.083	−	267.939i	0.937542	−	0.541290i
$496$			411.225i			0.829083i
$497$	95.1234	+	457.420i	0.191395	+	0.920363i
$498$	951.032			1.90970
$499$	410.782	+	711.496i	0.823211	+	1.42584i	0.903279	+	0.429054i	$0.141153\pi$
$499$	410.782	+	711.496i	0.823211	+	1.42584i	−0.0800672	+	0.996789i	$0.525513\pi$
$500$	−15.4184	−	8.90181i	−0.0308368	−	0.0178036i
$501$	772.825	−	1338.57i	1.54256	−	2.67180i
$502$	−303.155	+	175.026i	−0.603893	+	0.348658i
$503$			173.706i			0.345340i	0.984980	+	0.172670i	$0.0552394\pi$
$503$			173.706i			0.345340i	−0.984980	+	0.172670i	$0.944761\pi$
$504$	−519.039	+	463.221i	−1.02984	+	0.919088i
$505$	164.512			0.325767
$506$	−260.568	−	451.317i	−0.514956	−	0.891931i
$507$	584.499	+	337.460i	1.15286	+	0.665602i
$508$	144.141	−	249.659i	0.283742	−	0.491455i
$509$	−397.384	+	229.430i	−0.780715	+	0.450746i	−0.836684	−	0.547686i	$-0.815509\pi$
$509$	−397.384	+	229.430i	−0.780715	+	0.450746i	0.0559685	+	0.998433i	$0.482175\pi$
$510$		−	54.7380i		−	0.107329i
$511$	−274.117	+	831.168i	−0.536433	+	1.62655i
$512$	26.8805			0.0525010
$513$	−52.2805	−	90.5524i	−0.101911	−	0.176515i
$514$	−139.651	−	80.6278i	−0.271695	−	0.156863i
$515$	−30.9377	+	53.5857i	−0.0600732	+	0.104050i
$516$	−388.119	+	224.081i	−0.752169	+	0.434265i
$517$			982.727i			1.90083i
$518$	204.791	+	67.5397i	0.395350	+	0.130385i
$519$	574.938			1.10778
$520$	−39.1270	−	67.7700i	−0.0752443	−	0.130327i
$521$	388.712	+	224.423i	0.746089	+	0.430755i	0.824279	−	0.566184i	$-0.191581\pi$
$521$	388.712	+	224.423i	0.746089	+	0.430755i	−0.0781902	+	0.996938i	$0.524914\pi$
$522$	329.779	−	571.194i	0.631760	−	1.09424i
$523$	330.871	−	191.028i	0.632640	−	0.365255i	−0.149134	−	0.988817i	$-0.547649\pi$
$523$	330.871	−	191.028i	0.632640	−	0.365255i	0.781774	+	0.623562i	$0.214315\pi$
$524$			68.1833i			0.130121i
$525$	−119.868	−	134.312i	−0.228319	−	0.255832i
$526$	650.796			1.23726
$527$	−20.8636	−	36.1368i	−0.0395894	−	0.0685708i
$528$	−1212.96	−	700.300i	−2.29727	−	1.32633i
$529$	135.683	−	235.009i	0.256489	−	0.444252i
$530$	−308.562	+	178.148i	−0.582192	+	0.336129i
$531$			368.068i			0.693161i
$532$	−26.2382	+	5.45640i	−0.0493200	+	0.0102564i
$533$	−339.894			−0.637700
$534$	−271.973	−	471.072i	−0.509313	−	0.882156i
$535$	−159.343	−	91.9967i	−0.297837	−	0.171956i
$536$	211.910	−	367.040i	0.395355	−	0.684775i
$537$	1569.49	−	906.144i	2.92269	−	1.68742i
$538$		−	542.984i		−	1.00926i
$539$	76.2127	−	668.407i	0.141396	−	1.24009i
$540$	154.857			0.286773
$541$	−102.522	−	177.573i	−0.189504	−	0.328231i	0.755581	−	0.655055i	$-0.227355\pi$
$541$	−102.522	−	177.573i	−0.189504	−	0.328231i	−0.945085	+	0.326825i	$0.894021\pi$
$542$	−1066.57	−	615.783i	−1.96784	−	1.13613i
$543$	395.997	−	685.886i	0.729276	−	1.26314i
$544$	−42.0558	+	24.2809i	−0.0773084	+	0.0446340i
$545$			75.7161i			0.138929i
$546$	106.555	+	512.390i	0.195155	+	0.938443i
$547$	−182.754			−0.334102			−0.167051	−	0.985948i	$-0.553424\pi$
$547$	−182.754			−0.334102			−0.167051	+	0.985948i	$0.553424\pi$
$548$	−80.4637	−	139.367i	−0.146832	−	0.254320i
$549$	−399.386	−	230.586i	−0.727480	−	0.420011i
$550$	81.1688	−	140.588i	0.147580	−	0.255615i
$551$	−33.2682	+	19.2074i	−0.0603779	+	0.0348592i
$552$			470.048i			0.851536i
$553$	512.341	−	457.243i	0.926475	−	0.826840i
$554$	−916.312			−1.65399
$555$	74.9112	+	129.750i	0.134975	+	0.233784i
$556$	−182.852	−	105.570i	−0.328870	−	0.189873i
$557$	−405.832	+	702.922i	−0.728604	+	1.26198i	0.228870	+	0.973457i	$0.426497\pi$
$557$	−405.832	+	702.922i	−0.728604	+	1.26198i	−0.957473	+	0.288522i	$0.906836\pi$
$558$	741.195	−	427.929i	1.32831	−	0.766898i
$559$		−	336.328i		−	0.601659i
$560$	−97.2339	+	294.829i	−0.173632	+	0.526481i
$561$	142.120			0.253333
$562$	186.789	+	323.528i	0.332364	+	0.575672i
$563$	−275.702	−	159.176i	−0.489701	−	0.282729i	0.234749	−	0.972056i	$-0.424573\pi$
$563$	−275.702	−	159.176i	−0.489701	−	0.282729i	−0.724450	+	0.689327i	$0.757906\pi$
$564$	−293.133	+	507.721i	−0.519739	+	0.900214i
$565$	71.1735	−	41.0921i	0.125971	−	0.0727293i
$566$			106.687i			0.188494i
$567$	442.698	+	146.001i	0.780773	+	0.257497i
$568$	380.009			0.669030
$569$	−299.181	−	518.196i	−0.525801	−	0.910714i	−0.999548	−	0.0300533i	$-0.990432\pi$
$569$	−299.181	−	518.196i	−0.525801	−	0.910714i	0.473747	−	0.880661i	$-0.342901\pi$
$570$	−56.6303	−	32.6955i	−0.0993513	−	0.0573605i
$571$	−436.429	+	755.917i	−0.764324	+	1.32385i	0.176279	+	0.984340i	$0.443594\pi$
$571$	−436.429	+	755.917i	−0.764324	+	1.32385i	−0.940603	+	0.339508i	$0.889740\pi$
$572$	−116.378	+	67.1911i	−0.203459	+	0.117467i
$573$			395.352i			0.689969i
$574$	609.506	+	682.953i	1.06186	+	1.18981i
$575$	−80.2550			−0.139574
$576$	194.396	+	336.704i	0.337494	+	0.584556i
$577$	639.833	+	369.408i	1.10890	+	0.640222i	0.938543	−	0.345162i	$-0.112176\pi$
$577$	639.833	+	369.408i	1.10890	+	0.640222i	0.170353	+	0.985383i	$0.445509\pi$
$578$	−336.928	+	583.577i	−0.582921	+	1.00965i
$579$	−1481.18	+	855.161i	−2.55817	+	1.47696i
$580$		−	56.8933i		−	0.0980919i
$581$	535.850	−	111.433i	0.922289	−	0.191796i
$582$	−385.310			−0.662044
$583$	−462.538	−	801.139i	−0.793375	−	1.37417i
$584$	616.488	+	355.929i	1.05563	+	0.609468i
$585$	−119.957	+	207.771i	−0.205054	+	0.355164i
$586$	111.596	−	64.4297i	0.190436	−	0.109948i
$587$		−	149.507i		−	0.254697i	−0.991858	−	0.127349i	$-0.959353\pi$
$587$		−	149.507i		−	0.254697i	0.991858	−	0.127349i	$-0.0406467\pi$
$588$	238.750	−	322.596i	0.406038	−	0.548632i
$589$	−49.8481			−0.0846317
$590$	55.7510	+	96.5635i	0.0944931	+	0.163667i
$591$	−546.820	−	315.706i	−0.925245	−	0.534190i
$592$	129.185	−	223.755i	0.218218	−	0.377964i
$593$	−219.713	+	126.851i	−0.370511	+	0.213914i	−0.673682	−	0.739022i	$-0.735288\pi$
$593$	−219.713	+	126.851i	−0.370511	+	0.213914i	0.303171	+	0.952936i	$0.401955\pi$
$594$			1412.02i			2.37714i
$595$	−6.41370	−	30.8416i	−0.0107793	−	0.0518346i
$596$	228.718			0.383754
$597$	218.290	+	378.090i	0.365645	+	0.633316i
$598$	202.056	+	116.657i	0.337886	+	0.195078i
$599$	−261.282	+	452.554i	−0.436197	+	0.755515i	−0.997392	−	0.0721679i	$-0.977008\pi$
$599$	−261.282	+	452.554i	−0.436197	+	0.755515i	0.561196	+	0.827683i	$0.310342\pi$
$600$	−126.806	+	73.2117i	−0.211344	+	0.122019i
$601$		−	956.828i		−	1.59206i	−0.605258	−	0.796030i	$-0.706930\pi$
$601$		−	956.828i		−	1.59206i	0.605258	−	0.796030i	$-0.293070\pi$
$602$	−675.786	+	603.111i	−1.12257	+	1.00185i
$603$	−1299.36			−2.15483
$604$	−116.279	−	201.401i	−0.192514	−	0.333445i
$605$	130.703	+	75.4614i	0.216038	+	0.124730i
$606$	−447.445	+	774.998i	−0.738358	+	1.27887i
$607$	−239.609	+	138.338i	−0.394743	+	0.227905i	−0.684213	−	0.729282i	$-0.739854\pi$
$607$	−239.609	+	138.338i	−0.394743	+	0.227905i	0.289470	+	0.957187i	$0.406521\pi$
$608$			58.0128i			0.0954158i
$609$	180.180	−	546.334i	0.295862	−	0.897101i
$610$	−139.706			−0.229027
$611$	−219.985	−	381.025i	−0.360040	−	0.623608i
$612$	48.4464	+	27.9706i	0.0791608	+	0.0457035i
$613$	107.119	−	185.535i	0.174745	−	0.302668i	−0.765328	−	0.643641i	$-0.777423\pi$
$613$	107.119	−	185.535i	0.174745	−	0.302668i	0.940073	+	0.340973i	$0.110756\pi$
$614$	362.376	−	209.218i	0.590189	−	0.340746i
$615$			635.985i			1.03412i
$616$	−519.649	−	171.379i	−0.843587	−	0.278213i
$617$	1133.85			1.83769			0.918844	−	0.394620i	$-0.129124\pi$
$617$	1133.85			1.83769			0.918844	+	0.394620i	$0.129124\pi$
$618$	−168.291	−	291.488i	−0.272315	−	0.471663i
$619$	646.950	+	373.517i	1.04515	+	0.603420i	0.921289	−	0.388879i	$-0.127138\pi$
$619$	646.950	+	373.517i	1.04515	+	0.603420i	0.123865	+	0.992299i	$0.460471\pi$
$620$	36.9131	−	63.9354i	0.0595372	−	0.103122i
$621$	604.541	−	349.032i	0.973496	−	0.562048i
$622$			517.292i			0.831658i
$623$	−208.437	−	233.553i	−0.334569	−	0.374885i
$624$	627.052			1.00489
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−313.505	−	181.002i	−0.500807	−	0.289141i
$627$	84.8894	−	147.033i	0.135390	−	0.234502i
$628$	274.888	−	158.706i	0.437719	−	0.252717i
$629$			26.2169i			0.0416803i
$630$	632.586	−	131.550i	1.00410	−	0.208810i
$631$	−879.471			−1.39377			−0.696887	−	0.717181i	$-0.745432\pi$
$631$	−879.471			−1.39377			−0.696887	+	0.717181i	$0.745432\pi$
$632$	−279.270	−	483.711i	−0.441884	−	0.765365i
$633$	634.911	+	366.566i	1.00302	+	0.579093i
$634$	152.835	−	264.718i	0.241065	−	0.417537i
$635$	350.573	−	202.404i	0.552084	−	0.318746i
$636$		−	551.872i		−	0.867723i
$637$	120.074	+	276.216i	0.188500	+	0.433620i
$638$	518.766			0.813114
$639$	−582.521	−	1008.96i	−0.911613	−	1.57896i
$640$	288.907	+	166.800i	0.451417	+	0.260625i
$641$	146.735	−	254.153i	0.228916	−	0.396494i	−0.728571	−	0.684970i	$-0.759815\pi$
$641$	146.735	−	254.153i	0.228916	−	0.396494i	0.957487	+	0.288476i	$0.0931485\pi$
$642$	866.771	−	500.431i	1.35011	−	0.779487i
$643$		−	401.514i		−	0.624439i	−0.950010	−	0.312219i	$-0.898928\pi$
$643$		−	401.514i		−	0.624439i	0.950010	−	0.312219i	$-0.101072\pi$
$644$	−36.4277	−	175.170i	−0.0565648	−	0.272003i
$645$	−629.312			−0.975677
$646$	−5.72127	−	9.90954i	−0.00885646	−	0.0153398i
$647$	−783.686	−	452.461i	−1.21126	−	0.699322i	−0.248227	−	0.968702i	$-0.579848\pi$
$647$	−783.686	−	452.461i	−1.21126	−	0.699322i	−0.963034	+	0.269380i	$0.913181\pi$
$648$	189.576	−	328.355i	0.292555	−	0.506720i
$649$	−250.714	+	144.750i	−0.386308	+	0.223035i
$650$			72.6789i			0.111814i
$651$	556.950	−	497.054i	0.855530	−	0.763525i
$652$	−203.984			−0.312858
$653$	216.459	+	374.918i	0.331484	+	0.574148i	0.982803	−	0.184657i	$-0.0591173\pi$
$653$	216.459	+	374.918i	0.331484	+	0.574148i	−0.651319	+	0.758804i	$0.725784\pi$
$654$	−356.690	−	205.935i	−0.545397	−	0.314885i
$655$	−47.8718	+	82.9163i	−0.0730867	+	0.126590i
$656$	949.823	−	548.380i	1.44790	−	0.835946i
$657$		−	2182.44i		−	3.32182i
$658$	−371.115	+	1125.28i	−0.564004	+	1.71015i
$659$	358.497			0.544002			0.272001	−	0.962297i	$-0.412315\pi$
$659$	358.497			0.544002			0.272001	+	0.962297i	$0.412315\pi$
$660$	125.723	+	217.759i	0.190490	+	0.329938i
$661$	804.899	+	464.709i	1.21770	+	0.703039i	0.964425	−	0.264355i	$-0.0851592\pi$
$661$	804.899	+	464.709i	1.21770	+	0.703039i	0.253274	+	0.967395i	$0.418492\pi$
$662$	−684.656	+	1185.86i	−1.03422	+	1.79133i
$663$	−55.1029	+	31.8137i	−0.0831114	+	0.0479844i
$664$		−	445.165i		−	0.670429i
$665$	−35.7387	−	11.7865i	−0.0537425	−	0.0177241i
$666$	−537.730			−0.807402
$667$	−128.232	−	222.104i	−0.192251	−	0.332989i
$668$	414.417	+	239.264i	0.620385	+	0.358179i
$669$	−591.375	+	1024.29i	−0.883968	+	1.53108i
$670$	−340.890	+	196.813i	−0.508791	+	0.293751i
$671$		−	362.728i		−	0.540579i
$672$	−578.468	−	648.174i	−0.860816	−	0.964545i
$673$	−853.958			−1.26888			−0.634442	−	0.772971i	$-0.718770\pi$
$673$	−853.958			−1.26888			−0.634442	+	0.772971i	$0.718770\pi$
$674$	16.8712	+	29.2218i	0.0250315	+	0.0433558i
$675$	188.319	+	108.726i	0.278991	+	0.161075i
$676$	−104.477	+	180.959i	−0.154551	+	0.267690i
$677$	321.116	−	185.396i	0.474321	−	0.273850i	−0.243726	−	0.969844i	$-0.578370\pi$
$677$	321.116	−	185.396i	0.474321	−	0.273850i	0.718047	+	0.695995i	$0.245036\pi$
$678$			447.054i			0.659371i
$679$	−217.099	+	45.1471i	−0.319734	+	0.0664905i
$680$	−25.6221			−0.0376796
$681$	883.992	+	1531.12i	1.29808	+	2.24834i
$682$	582.977	+	336.582i	0.854805	+	0.493522i
$683$	364.738	−	631.744i	0.534023	−	0.924955i	−0.465187	−	0.885212i	$-0.654013\pi$
$683$	364.738	−	631.744i	0.534023	−	0.924955i	0.999210	−	0.0397422i	$-0.0126537\pi$
$684$	57.8750	−	33.4141i	0.0846125	−	0.0488511i
$685$		−	225.976i		−	0.329892i
$686$	339.683	−	736.584i	0.495165	−	1.07374i
$687$	4.52126			0.00658116
$688$	542.626	+	939.856i	0.788701	+	1.36607i
$689$	358.672	+	207.079i	0.520568	+	0.300550i
$690$	218.280	−	378.072i	0.316348	−	0.547930i
$691$	4.35725	−	2.51566i	0.00630572	−	0.00364061i	−0.496844	−	0.867840i	$-0.665508\pi$
$691$	4.35725	−	2.51566i	0.00630572	−	0.00364061i	0.503150	+	0.864199i	$0.332174\pi$
$692$			177.999i			0.257224i
$693$	341.552	+	1642.42i	0.492860	+	2.37002i
$694$	−444.723			−0.640811
$695$	−148.242	−	256.762i	−0.213297	−	0.369442i
$696$	−405.223	−	233.955i	−0.582217	−	0.336143i
$697$	−55.6444	+	96.3790i	−0.0798342	+	0.138277i
$698$	609.759	−	352.045i	0.873581	−	0.504362i
$699$		−	534.203i		−	0.764239i
$700$	41.5824	−	37.1106i	0.0594035	−	0.0530151i
$701$	−132.748			−0.189370			−0.0946850	−	0.995507i	$-0.530184\pi$
$701$	−132.748			−0.189370			−0.0946850	+	0.995507i	$0.530184\pi$
$702$	−316.083	−	547.472i	−0.450261	−	0.779875i
$703$	27.1232	+	15.6596i	0.0385821	+	0.0222754i
$704$	−152.900	+	264.830i	−0.217187	+	0.376180i
$705$	−712.946	+	411.619i	−1.01127	+	0.583857i
$706$		−	1050.84i		−	1.48845i
$707$	−161.302	+	489.093i	−0.228149	+	0.691786i
$708$	−172.707			−0.243936
$709$	81.9066	+	141.866i	0.115524	+	0.200094i	0.917989	−	0.396606i	$-0.129812\pi$
$709$	81.9066	+	141.866i	0.115524	+	0.200094i	−0.802465	+	0.596699i	$0.796479\pi$
$710$	−305.651	−	176.468i	−0.430494	−	0.248546i
$711$	−856.195	+	1482.97i	−1.20421	+	2.08576i
$712$	−220.502	+	127.307i	−0.309694	+	0.178802i
$713$		−	332.793i		−	0.466750i
$714$	162.735	+	53.6697i	0.227921	+	0.0751677i
$715$	−188.701			−0.263917
$716$	280.539	+	485.908i	0.391814	+	0.678642i
$717$	−712.365	−	411.284i	−0.993536	−	0.573618i
$718$	492.257	−	852.615i	0.685595	−	1.18749i
$719$	1229.91	−	710.091i	1.71059	−	0.987609i	0.776827	−	0.629714i	$-0.216828\pi$
$719$	1229.91	−	710.091i	1.71059	−	0.987609i	0.933762	−	0.357895i	$-0.116505\pi$
$720$		−	774.146i		−	1.07520i
$721$	−128.976	−	144.517i	−0.178884	−	0.200440i
$722$	840.033			1.16348
$723$	663.129	+	1148.57i	0.917191	+	1.58862i
$724$	212.348	+	122.599i	0.293298	+	0.169336i
$725$	39.9451	−	69.1869i	0.0550966	−	0.0954302i
$726$	−710.980	+	410.484i	−0.979311	+	0.565405i
$727$			1115.52i			1.53441i	0.641403	+	0.767204i	$0.278353\pi$
$727$			1115.52i			1.53441i	−0.641403	+	0.767204i	$0.721647\pi$
$728$	239.843	−	49.8767i	0.329454	−	0.0685120i
$729$	850.816			1.16710
$730$	−330.571	−	572.566i	−0.452838	−	0.784338i
$731$	−95.3677	−	55.0606i	−0.130462	−	0.0753223i
$732$	108.196	−	187.402i	0.147809	−	0.256013i
$733$	−532.598	+	307.496i	−0.726600	+	0.419503i	−0.817177	−	0.576387i	$-0.804462\pi$
$733$	−532.598	+	307.496i	−0.726600	+	0.419503i	0.0905770	+	0.995889i	$0.471129\pi$
$734$			1258.48i			1.71454i
$735$	516.835	−	224.674i	0.703177	−	0.305679i
$736$	−387.302			−0.526226
$737$	−510.998	−	885.074i	−0.693348	−	1.20091i
$738$	−1976.81	−	1141.31i	−2.67860	−	1.54649i
$739$	169.560	−	293.687i	0.229446	−	0.397412i	−0.728198	−	0.685367i	$-0.759642\pi$
$739$	169.560	−	293.687i	0.229446	−	0.397412i	0.957644	+	0.287955i	$0.0929753\pi$
$740$	−40.1701	+	23.1922i	−0.0542839	+	0.0313409i
$741$			76.0103i			0.102578i
$742$	−227.093	−	1092.02i	−0.306055	−	1.47173i
$743$	−1032.93			−1.39021			−0.695105	−	0.718909i	$-0.744642\pi$
$743$	−1032.93			−1.39021			−0.695105	+	0.718909i	$0.744642\pi$
$744$	−303.586	−	525.827i	−0.408046	−	0.706757i
$745$	278.139	+	160.584i	0.373341	+	0.215548i
$746$	−602.108	+	1042.88i	−0.807115	+	1.39796i
$747$	−1181.95	+	682.400i	−1.58226	+	0.913520i
$748$			43.9997i			0.0588232i
$749$	429.738	−	383.523i	0.573749	−	0.512047i
$750$	135.991			0.181322
$751$	273.235	+	473.257i	0.363829	+	0.630170i	0.988587	−	0.150648i	$-0.0481361\pi$
$751$	273.235	+	473.257i	0.363829	+	0.630170i	−0.624759	+	0.780818i	$0.714803\pi$
$752$	1229.48	+	709.841i	1.63495	+	0.943937i
$753$	380.681	−	659.359i	0.505553	−	0.875643i
$754$	−201.137	+	116.126i	−0.266760	+	0.154014i
$755$		−	326.559i		−	0.432529i
$756$	−151.835	+	460.389i	−0.200840	+	0.608980i
$757$	191.558			0.253049			0.126524	−	0.991964i	$-0.459618\pi$
$757$	191.558			0.253049			0.126524	+	0.991964i	$0.459618\pi$
$758$	−197.158	−	341.488i	−0.260103	−	0.450511i
$759$	981.612	+	566.734i	1.29330	+	0.746685i
$760$	−15.3043	+	26.5079i	−0.0201373	+	0.0348788i
$761$	−471.813	+	272.401i	−0.619990	+	0.357952i	−0.776865	−	0.629667i	$-0.783191\pi$
$761$	−471.813	+	272.401i	−0.619990	+	0.357952i	0.156875	+	0.987618i	$0.449858\pi$
$762$			2202.01i			2.88978i
$763$	−225.103	−	74.2384i	−0.295024	−	0.0972980i
$764$	−122.400			−0.160209
$765$	39.2765	+	68.0289i	0.0513418	+	0.0889267i
$766$	698.083	+	403.038i	0.911336	+	0.526160i
$767$	64.8048	−	112.245i	0.0844912	−	0.146343i
$768$	−1174.70	+	678.211i	−1.52955	+	0.883087i
$769$			120.495i			0.156691i	0.996926	+	0.0783453i	$0.0249637\pi$
$769$			120.495i			0.156691i	−0.996926	+	0.0783453i	$0.975036\pi$
$770$	338.383	+	379.158i	0.439458	+	0.492413i
$771$	350.730			0.454903
$772$	−264.755	−	458.569i	−0.342947	−	0.594001i
$773$	−1146.74	−	662.070i	−1.48349	−	0.856495i	−0.483668	−	0.875251i	$-0.660696\pi$
$773$	−1146.74	−	662.070i	−1.48349	−	0.856495i	−0.999824	+	0.0187565i	$0.994029\pi$
$774$	1129.34	−	1956.07i	1.45909	−	2.52722i
$775$	89.7786	−	51.8337i	0.115843	−	0.0668822i
$776$			180.358i			0.232420i
$777$	−459.194	+	95.4922i	−0.590983	+	0.122899i
$778$	−70.7923			−0.0909926
$779$	66.4738	+	115.136i	0.0853323	+	0.147800i
$780$	−97.4912	−	56.2866i	−0.124989	−	0.0721623i
$781$	458.174	−	793.581i	0.586650	−	1.01611i
$782$	66.1575	−	38.1961i	0.0846004	−	0.0488441i
$783$			694.890i			0.887471i
$784$	−781.187	−	578.150i	−0.996412	−	0.737437i
$785$	445.714			0.567788
$786$	−260.406	−	451.037i	−0.331305	−	0.573838i
$787$	−1131.71	−	653.396i	−1.43801	−	0.830236i	−0.440300	−	0.897851i	$-0.645128\pi$
$787$	−1131.71	−	653.396i	−1.43801	−	0.830236i	−0.997712	+	0.0676145i	$0.978461\pi$
$788$	97.7416	−	169.293i	0.124038	−	0.214839i
$789$	−1225.84	+	707.739i	−1.55366	+	0.897008i
$790$			518.748i			0.656643i
$791$	52.3817	+	251.888i	0.0662221	+	0.318443i
$792$	1364.47			1.72281
$793$	81.1972	+	140.638i	0.102392	+	0.177349i
$794$	−981.796	−	566.840i	−1.23652	−	0.713904i
$795$	387.472	−	671.121i	0.487386	−	0.844177i
$796$	−117.055	+	67.5819i	−0.147054	+	0.0849019i
$797$		−	263.263i		−	0.330317i	−0.986267	−	0.165159i	$-0.947186\pi$
$797$		−	263.263i		−	0.330317i	0.986267	−	0.165159i	$-0.0528136\pi$
$798$	152.728	−	136.304i	0.191389	−	0.170807i
$799$	−144.056			−0.180295
$800$	−60.3237	−	104.484i	−0.0754046	−	0.130605i
$801$	676.022	+	390.301i	0.843972	+	0.487268i
$802$	720.202	−	1247.43i	0.898007	−	1.55539i
$803$	1486.59	−	858.283i	1.85130	−	1.06885i
$804$		−	609.691i		−	0.758323i
$805$	78.6887	−	238.597i	0.0977500	−	0.296394i
$806$	−301.377			−0.373917
$807$	590.494	+	1022.77i	0.731715	+	1.26737i
$808$	362.766	+	209.443i	0.448968	+	0.259212i
$809$	296.062	−	512.795i	0.365961	−	0.633863i	−0.622969	−	0.782247i	$-0.714074\pi$
$809$	296.062	−	512.795i	0.365961	−	0.633863i	0.988930	+	0.148384i	$0.0474071\pi$
$810$	−304.961	+	176.069i	−0.376495	+	0.217370i
$811$		−	34.9609i		−	0.0431083i	−0.999768	−	0.0215542i	$-0.993139\pi$
$811$		−	34.9609i		−	0.0431083i	0.999768	−	0.0215542i	$-0.00686144\pi$
$812$	169.143	+	55.7830i	0.208304	+	0.0686983i
$813$	2678.65			3.29477
$814$	−211.472	−	366.280i	−0.259794	−	0.449976i
$815$	−248.060	−	143.218i	−0.304369	−	0.175727i
$816$	102.655	−	177.804i	0.125803	−	0.217898i
$817$	−113.928	+	65.7763i	−0.139447	+	0.0805096i
$818$			1197.37i			1.46377i
$819$	−500.085	−	560.346i	−0.610605	−	0.684183i
$820$	−196.899			−0.240120
$821$	412.442	+	714.371i	0.502365	+	0.870122i	0.999996	+	0.00273351i	$0.000870103\pi$
$821$	412.442	+	714.371i	0.502365	+	0.870122i	−0.497631	+	0.867389i	$0.665797\pi$
$822$	1064.55	+	614.616i	1.29507	+	0.747707i
$823$	−421.891	+	730.737i	−0.512626	+	0.887894i	0.487267	+	0.873253i	$0.337994\pi$
$823$	−421.891	+	730.737i	−0.512626	+	0.887894i	−0.999893	+	0.0146410i	$0.995339\pi$
$824$	−136.442	+	78.7745i	−0.165584	+	0.0956002i
$825$			353.083i			0.427980i
$826$	−341.745	+	71.0679i	−0.413735	+	0.0860387i
$827$	359.972			0.435274			0.217637	−	0.976030i	$-0.430165\pi$
$827$	359.972			0.435274			0.217637	+	0.976030i	$0.430165\pi$
$828$	223.078	+	386.382i	0.269417	+	0.466645i
$829$	−1290.05	−	744.811i	−1.55615	−	0.898446i	−0.997619	−	0.0689641i	$-0.978031\pi$
$829$	−1290.05	−	744.811i	−1.55615	−	0.898446i	−0.558534	−	0.829481i	$-0.688636\pi$
$830$	−206.725	+	358.058i	−0.249066	+	0.431395i
$831$	1725.97	−	996.487i	2.07698	−	1.19914i
$832$		−	136.907i		−	0.164552i
$833$	97.9802	+	11.1718i	0.117623	+	0.0134116i
$834$	1612.77			1.93378
$835$	335.976	+	581.928i	0.402367	+	0.696920i
$836$	45.5208	+	26.2814i	0.0544507	+	0.0314371i
$837$	−450.853	+	780.901i	−0.538654	+	0.932976i
$838$	−1230.81	+	710.610i	−1.46875	+	0.847983i
$839$			778.799i			0.928247i	0.885770	+	0.464124i	$0.153631\pi$
$839$			778.799i			0.928247i	−0.885770	+	0.464124i	$0.846369\pi$
$840$	−93.3258	−	448.776i	−0.111102	−	0.534258i
$841$	−585.703			−0.696436
$842$	327.703	+	567.597i	0.389195	+	0.674106i
$843$	−703.671	−	406.264i	−0.834722	−	0.481927i
$844$	−113.488	+	196.566i	−0.134464	+	0.232898i
$845$	−254.104	+	146.707i	−0.300715	+	0.173618i
$846$		−	2954.70i		−	3.49255i
$847$	−352.498	+	314.590i	−0.416172	+	0.371416i
$848$	−1336.40			−1.57594
$849$	−116.022	−	200.957i	−0.136658	−	0.236698i
$850$	20.6085	+	11.8983i	0.0242453	+	0.0139981i
$851$	−104.546	+	181.078i	−0.122850	+	0.212783i
$852$	473.426	−	273.333i	0.555665	−	0.320813i
$853$			496.640i			0.582228i	0.956688	+	0.291114i	$0.0940259\pi$
$853$			496.640i			0.582228i	−0.956688	+	0.291114i	$0.905974\pi$
$854$	136.980	−	415.345i	0.160398	−	0.486353i
$855$	93.8408			0.109755
$856$	−234.245	−	405.724i	−0.273650	−	0.473977i
$857$	−112.697	−	65.0654i	−0.131501	−	0.0759223i	0.432806	−	0.901487i	$-0.357523\pi$
$857$	−112.697	−	65.0654i	−0.131501	−	0.0759223i	−0.564307	+	0.825565i	$0.690857\pi$
$858$	513.234	−	888.947i	0.598175	−	1.03607i
$859$	762.753	−	440.376i	0.887954	−	0.512661i	0.0146815	−	0.999892i	$-0.495327\pi$
$859$	762.753	−	440.376i	0.887954	−	0.512661i	0.873273	+	0.487232i	$0.161993\pi$
$860$		−	194.833i		−	0.226550i
$861$	−1890.78	−	623.573i	−2.19602	−	0.724243i
$862$	−963.067			−1.11725
$863$	389.409	+	674.477i	0.451227	+	0.781549i	0.998463	−	0.0554301i	$-0.0176530\pi$
$863$	389.409	+	674.477i	0.451227	+	0.781549i	−0.547235	+	0.836979i	$0.684320\pi$
$864$	908.807	+	524.700i	1.05186	+	0.607291i
$865$	−124.974	+	216.461i	−0.144478	+	0.250244i
$866$	−639.706	+	369.334i	−0.738690	+	0.426483i
$867$		−	1465.63i		−	1.69047i
$868$	153.886	+	172.430i	0.177288	+	0.198652i
$869$	−1346.86			−1.54989
$870$	217.287	+	376.353i	0.249756	+	0.432590i
$871$	396.250	+	228.775i	0.454936	+	0.262658i
$872$	−96.3953	+	166.962i	−0.110545	+	0.191470i
$873$	478.866	−	276.474i	0.548530	−	0.316694i
$874$		−	91.2594i		−	0.104416i
$875$	76.6231	−	15.9342i	0.0875693	−	0.0182106i
$876$	1024.05			1.16901
$877$	31.3183	+	54.2449i	0.0357107	+	0.0618528i	0.883328	−	0.468755i	$-0.155297\pi$
$877$	31.3183	+	54.2449i	0.0357107	+	0.0618528i	−0.847618	+	0.530607i	$0.821964\pi$
$878$	435.253	+	251.293i	0.495732	+	0.286211i
$879$	−140.134	+	242.720i	−0.159425	+	0.276132i
$880$	527.318	−	304.447i	0.599225	−	0.345963i
$881$			1073.96i			1.21902i	0.792777	+	0.609512i	$0.208635\pi$
$881$			1073.96i			1.21902i	−0.792777	+	0.609512i	$0.791365\pi$
$882$	−229.144	+	2009.65i	−0.259800	+	2.27852i
$883$	61.5102			0.0696605			0.0348303	−	0.999393i	$-0.488911\pi$
$883$	61.5102			0.0696605			0.0348303	+	0.999393i	$0.488911\pi$
$884$	−9.84939	−	17.0597i	−0.0111418	−	0.0192982i
$885$	−210.025	−	121.258i	−0.237316	−	0.137015i
$886$	439.170	−	760.664i	0.495677	−	0.858538i
$887$	112.273	−	64.8207i	0.126576	−	0.0730786i	−0.435375	−	0.900249i	$-0.643384\pi$
$887$	112.273	−	64.8207i	0.126576	−	0.0730786i	0.561951	+	0.827171i	$0.310051\pi$
$888$			381.482i			0.429597i
$889$	258.012	+	1240.70i	0.290227	+	1.39562i
$890$	236.474			0.265701
$891$	−457.140	−	791.790i	−0.513064	−	0.888653i
$892$	−317.117	−	183.087i	−0.355512	−	0.205255i
$893$	−86.0458	+	149.036i	−0.0963559	+	0.166893i
$894$	−1512.98	+	873.520i	−1.69237	+	0.977092i
$895$			787.870i			0.880302i
$896$	−779.163	+	695.371i	−0.869602	+	0.776083i
$897$	−507.456			−0.565726
$898$	−5.00131	−	8.66252i	−0.00556938	−	0.00964646i
$899$	286.897	+	165.640i	0.319129	+	0.184249i
$900$	−69.4903	+	120.361i	−0.0772114	+	0.133734i
$901$	117.437	−	67.8023i	0.130341	−	0.0752523i
$902$		−	1795.37i		−	1.99043i
$903$	617.030	−	1870.94i	0.683311	−	2.07191i
$904$	209.260			0.231482
$905$	172.155	+	298.181i	0.190226	+	0.329482i
$906$	1538.38	+	888.185i	1.69799	+	0.980337i
$907$	700.954	−	1214.09i	0.772827	−	1.33858i	−0.163181	−	0.986596i	$-0.552175\pi$
$907$	700.954	−	1214.09i	0.772827	−	1.33858i	0.936008	−	0.351979i	$-0.114491\pi$
$908$	−474.029	+	273.681i	−0.522059	+	0.301411i
$909$		−	1284.23i		−	1.41280i
$910$	−216.073	−	71.2605i	−0.237443	−	0.0783082i
$911$	−1235.23			−1.35590			−0.677950	−	0.735108i	$-0.737132\pi$
$911$	−1235.23			−1.35590			−0.677950	+	0.735108i	$0.737132\pi$
$912$	−122.634	−	212.408i	−0.134467	−	0.232904i
$913$	−929.648	−	536.732i	−1.01823	−	0.587878i
$914$	−592.639	+	1026.48i	−0.648401	+	1.12306i
$915$	263.151	−	151.930i	0.287597	−	0.166044i
$916$			1.39977i			0.00152813i
$917$	−199.572	−	223.620i	−0.217635	−	0.243861i
$918$	−206.985			−0.225474
$919$	−341.200	−	590.976i	−0.371273	−	0.643064i	0.618488	−	0.785794i	$-0.287745\pi$
$919$	−341.200	−	590.976i	−0.371273	−	0.643064i	−0.989762	+	0.142730i	$0.954412\pi$
$920$	−176.970	−	102.174i	−0.192359	−	0.111059i
$921$	−455.048	+	788.166i	−0.494080	+	0.855772i
$922$	614.648	−	354.867i	0.666646	−	0.384889i
$923$			410.251i			0.444476i
$924$	−770.664	+	160.264i	−0.834052	+	0.173446i
$925$	−65.1335			−0.0704146
$926$	−675.805	−	1170.53i	−0.729811	−	1.26407i
$927$	418.306	+	241.509i	0.451247	+	0.260528i
$928$	192.771	−	333.888i	0.207727	−	0.359794i
$929$	109.020	−	62.9427i	0.117352	−	0.0677531i	−0.440175	−	0.897912i	$-0.645084\pi$
$929$	109.020	−	62.9427i	0.117352	−	0.0677531i	0.557527	+	0.830159i	$0.311750\pi$
$930$			563.915i			0.606360i
$931$	70.0825	−	94.6943i	0.0752766	−	0.101712i
$932$	165.387			0.177454
$933$	−562.553	−	974.371i	−0.602951	−	1.04434i
$934$	1823.84	+	1053.00i	1.95272	+	1.12740i
$935$	−30.8924	+	53.5072i	−0.0330400	+	0.0572270i
$936$	−529.033	+	305.437i	−0.565206	+	0.326322i
$937$		−	235.260i		−	0.251078i	−0.992089	−	0.125539i	$-0.959934\pi$
$937$		−	235.260i		−	0.251078i	0.992089	−	0.125539i	$-0.0400660\pi$
$938$	−250.885	−	1206.43i	−0.267468	−	1.28618i
$939$	787.358			0.838507
$940$	−127.436	−	220.725i	−0.135570	−	0.234814i
$941$	300.317	+	173.388i	0.319147	+	0.184260i	0.651012	−	0.759067i	$-0.274345\pi$
$941$	300.317	+	173.388i	0.319147	+	0.184260i	−0.331865	+	0.943327i	$0.607678\pi$
$942$	−1212.27	+	2099.71i	−1.28691	+	2.22899i
$943$	−768.665	+	443.789i	−0.815128	+	0.470614i
$944$			418.221i			0.443030i
$945$	−507.884	+	453.265i	−0.537444	+	0.479646i
$946$	1776.53			1.87794
$947$	347.003	+	601.027i	0.366424	+	0.634665i	0.989004	−	0.147892i	$-0.0472487\pi$
$947$	347.003	+	601.027i	0.366424	+	0.634665i	−0.622580	+	0.782556i	$0.713915\pi$
$948$	−695.847	−	401.747i	−0.734016	−	0.423784i
$949$	−384.255	+	665.550i	−0.404906	+	0.701317i
$950$	24.6193	−	14.2140i	0.0259151	−	0.0149621i
$951$			664.831i			0.699086i
$952$	25.1221	−	76.1742i	0.0263887	−	0.0800149i
$953$	1530.11			1.60557			0.802786	−	0.596267i	$-0.203350\pi$
$953$	1530.11			1.60557			0.802786	+	0.596267i	$0.203350\pi$
$954$	1390.68	+	2408.73i	1.45774	+	2.52487i
$955$	−148.848	−	85.9373i	−0.155861	−	0.0899867i
$956$	127.332	−	220.546i	0.133193	−	0.230696i
$957$	−977.149	+	564.157i	−1.02105	+	0.589506i
$958$			78.2774i			0.0817091i
$959$	671.823	+	221.566i	0.700545	+	0.231038i
$960$	−256.171			−0.266845
$961$	−265.562	−	459.966i	−0.276339	−	0.478633i
$962$	163.985	+	94.6765i	0.170462	+	0.0984164i
$963$	−718.154	+	1243.88i	−0.745747	+	1.29167i
$964$	−355.594	+	205.302i	−0.368874	+	0.212969i
$965$		−	743.542i		−	0.770510i
$966$	909.983	+	1019.64i	0.942011	+	1.05552i
$967$	66.4870			0.0687560			0.0343780	−	0.999409i	$-0.489055\pi$
$967$	66.4870			0.0687560			0.0343780	+	0.999409i	$0.489055\pi$
$968$	192.142	+	332.800i	0.198494	+	0.343802i
$969$	21.5532	+	12.4437i	0.0222427	+	0.0128418i
$970$	83.7544	−	145.067i	0.0863447	−	0.149553i
$971$	−527.453	+	304.525i	−0.543206	+	0.313620i	−0.746377	−	0.665523i	$-0.768208\pi$
$971$	−527.453	+	304.525i	−0.543206	+	0.313620i	0.203171	+	0.979143i	$0.434875\pi$
$972$			77.8565i			0.0800993i
$973$	908.699	−	188.969i	0.933915	−	0.194213i
$974$	−1456.47			−1.49534
$975$	−79.0381	−	136.898i	−0.0810647	−	0.140408i
$976$	−453.806	−	262.005i	−0.464965	−	0.268448i
$977$	635.780	−	1101.20i	0.650748	−	1.12713i	−0.332194	−	0.943211i	$-0.607789\pi$
$977$	635.780	−	1101.20i	0.650748	−	1.12713i	0.982942	−	0.183917i	$-0.0588777\pi$
$978$	1349.36	−	779.056i	1.37972	−	0.796581i
$979$			613.973i			0.627143i
$980$	69.5584	+	160.010i	0.0709779	+	0.163276i
$981$	591.063			0.602511
$982$	264.340	+	457.851i	0.269186	+	0.466243i
$983$	147.832	+	85.3509i	0.150389	+	0.0868270i	0.573306	−	0.819341i	$-0.305661\pi$
$983$	147.832	+	85.3509i	0.150389	+	0.0868270i	−0.422917	+	0.906168i	$0.638994\pi$
$984$	−809.683	+	1402.41i	−0.822848	+	1.42521i
$985$	237.723	−	137.250i	0.241343	−	0.139340i
$986$			76.0448i			0.0771245i
$987$	−524.707	−	2523.16i	−0.531618	−	2.55640i
$988$	−23.5325			−0.0238183
$989$	−439.133	−	760.600i	−0.444017	−	0.769060i
$990$	−1097.48	−	633.628i	−1.10856	−	0.640028i
$991$	11.7052	−	20.2740i	0.0118115	−	0.0204581i	−0.860059	−	0.510194i	$-0.829574\pi$
$991$	11.7052	−	20.2740i	0.0118115	−	0.0204581i	0.871871	+	0.489736i	$0.162907\pi$
$992$	433.262	−	250.144i	0.436756	−	0.252161i
$993$		−	2978.25i		−	2.99924i
$994$	824.322	−	735.673i	0.829298	−	0.740113i
$995$	−189.798			−0.190752
$996$	−320.198	−	554.600i	−0.321484	−	0.556827i
$997$	1576.72	+	910.318i	1.58146	+	0.913057i	0.994647	+	0.103336i	$0.0329516\pi$
$997$	1576.72	+	910.318i	1.58146	+	0.913057i	0.586815	+	0.809721i	$0.300382\pi$
$998$	971.429	−	1682.56i	0.973376	−	1.68594i
$999$	490.634	−	283.268i	0.491125	−	0.283551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.h.a.31.2	yes	12
3.2	odd	2		315.3.w.c.136.5		12
4.3	odd	2		560.3.bx.c.241.1		12
5.2	odd	4		175.3.j.b.24.10		24
5.3	odd	4		175.3.j.b.24.3		24
5.4	even	2		175.3.i.d.101.5		12
7.2	even	3		245.3.h.c.166.2		12
7.3	odd	6		245.3.d.a.146.10		12
7.4	even	3		245.3.d.a.146.9		12
7.5	odd	6	inner	35.3.h.a.26.2	✓	12
7.6	odd	2		245.3.h.c.31.2		12
21.5	even	6		315.3.w.c.271.5		12
28.19	even	6		560.3.bx.c.481.1		12
35.12	even	12		175.3.j.b.124.3		24
35.19	odd	6		175.3.i.d.26.5		12
35.33	even	12		175.3.j.b.124.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.h.a.26.2	✓	12	7.5	odd	6	inner
35.3.h.a.31.2	yes	12	1.1	even	1	trivial
175.3.i.d.26.5		12	35.19	odd	6
175.3.i.d.101.5		12	5.4	even	2
175.3.j.b.24.3		24	5.3	odd	4
175.3.j.b.24.10		24	5.2	odd	4
175.3.j.b.124.3		24	35.12	even	12
175.3.j.b.124.10		24	35.33	even	12
245.3.d.a.146.9		12	7.4	even	3
245.3.d.a.146.10		12	7.3	odd	6
245.3.h.c.31.2		12	7.6	odd	2
245.3.h.c.166.2		12	7.2	even	3
315.3.w.c.136.5		12	3.2	odd	2
315.3.w.c.271.5		12	21.5	even	6
560.3.bx.c.241.1		12	4.3	odd	2
560.3.bx.c.481.1		12	28.19	even	6

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18241 - 2.04800i) q^{2} +(4.45439 + 2.57174i) q^{3} +(-0.796202 + 1.37906i) q^{4} +(-1.93649 + 1.11803i) q^{5} -12.1634i q^{6} +(-1.42520 - 6.85338i) q^{7} -5.69355 q^{8} +(8.72772 + 15.1168i) q^{9} +O(q^{10})\)	\(q+(-1.18241 - 2.04800i) q^{2} +(4.45439 + 2.57174i) q^{3} +(-0.796202 + 1.37906i) q^{4} +(-1.93649 + 1.11803i) q^{5} -12.1634i q^{6} +(-1.42520 - 6.85338i) q^{7} -5.69355 q^{8} +(8.72772 + 15.1168i) q^{9} +(4.57947 + 2.64396i) q^{10} +(-6.86467 + 11.8900i) q^{11} +(-7.09319 + 4.09525i) q^{12} -6.14666i q^{13} +(-12.3505 + 11.0223i) q^{14} -11.5012 q^{15} +(9.91693 + 17.1766i) q^{16} +(-1.74292 - 1.00628i) q^{17} +(20.6395 - 35.7487i) q^{18} +(-2.08213 + 1.20212i) q^{19} -3.56072i q^{20} +(11.2767 - 34.1929i) q^{21} +32.4675 q^{22} +(-8.02550 - 13.9006i) q^{23} +(-25.3613 - 14.6423i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-12.5884 + 7.26789i) q^{26} +43.4904i q^{27} +(10.5860 + 3.49123i) q^{28} +15.9780 q^{29} +(13.5991 + 23.5544i) q^{30} +(17.9557 + 10.3667i) q^{31} +(12.0647 - 20.8967i) q^{32} +(-61.1558 + 35.3083i) q^{33} +4.75934i q^{34} +(10.4222 + 11.6781i) q^{35} -27.7961 q^{36} +(-6.51335 - 11.2814i) q^{37} +(4.92387 + 2.84279i) q^{38} +(15.8076 - 27.3796i) q^{39} +(11.0255 - 6.36558i) q^{40} -55.2974i q^{41} +(-83.3607 + 17.3354i) q^{42} +54.7172 q^{43} +(-10.9313 - 18.9336i) q^{44} +(-33.8023 - 19.5158i) q^{45} +(-18.9789 + 32.8724i) q^{46} +(61.9889 - 35.7893i) q^{47} +102.015i q^{48} +(-44.9376 + 19.5349i) q^{49} -11.8241 q^{50} +(-5.17577 - 8.96469i) q^{51} +(8.47662 + 4.89398i) q^{52} +(-33.6897 + 58.3523i) q^{53} +(89.0683 - 51.4236i) q^{54} -30.6997i q^{55} +(8.11445 + 39.0200i) q^{56} -12.3661 q^{57} +(-18.8926 - 32.7230i) q^{58} +(18.2612 + 10.5431i) q^{59} +(9.15727 - 15.8608i) q^{60} +(-22.8803 + 13.2100i) q^{61} -49.0311i q^{62} +(91.1627 - 81.3589i) q^{63} +22.2735 q^{64} +(6.87217 + 11.9029i) q^{65} +(144.623 + 83.4980i) q^{66} +(-37.2194 + 64.4659i) q^{67} +(2.77544 - 1.60240i) q^{68} -82.5581i q^{69} +(11.5934 - 35.1530i) q^{70} -66.7438 q^{71} +(-49.6916 - 86.0685i) q^{72} +(-108.278 - 62.5145i) q^{73} +(-15.4029 + 26.6787i) q^{74} +(22.2719 - 12.8587i) q^{75} -3.82851i q^{76} +(91.2699 + 30.1006i) q^{77} -74.7645 q^{78} +(49.0504 + 84.9577i) q^{79} +(-38.4081 - 22.1749i) q^{80} +(-33.2966 + 57.6714i) q^{81} +(-113.249 + 65.3844i) q^{82} +78.1877i q^{83} +(38.1755 + 42.7757i) q^{84} +4.50020 q^{85} +(-64.6983 - 112.061i) q^{86} +(71.1723 + 41.0914i) q^{87} +(39.0843 - 67.6960i) q^{88} +(38.7285 - 22.3599i) q^{89} +92.3028i q^{90} +(-42.1254 + 8.76023i) q^{91} +25.5597 q^{92} +(53.3211 + 92.3549i) q^{93} +(-146.593 - 84.6355i) q^{94} +(2.68801 - 4.65577i) q^{95} +(107.482 - 62.0548i) q^{96} -31.6777i q^{97} +(93.1423 + 68.9339i) q^{98} -239.652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{3} - 10 q^{4} - 2 q^{7} - 4 q^{8} + 14 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 6 * q^3 - 10 * q^4 - 2 * q^7 - 4 * q^8 + 14 * q^9	\( 12 q - 2 q^{2} - 6 q^{3} - 10 q^{4} - 2 q^{7} - 4 q^{8} + 14 q^{9} - 14 q^{11} + 18 q^{12} - 2 q^{14} - 20 q^{15} - 22 q^{16} + 48 q^{17} + 64 q^{18} - 30 q^{19} - 84 q^{21} - 88 q^{22} - 14 q^{23} - 36 q^{24} + 30 q^{25} + 66 q^{26} + 202 q^{28} + 64 q^{29} + 20 q^{30} + 132 q^{31} - 54 q^{32} - 192 q^{33} + 30 q^{35} + 156 q^{36} + 44 q^{37} - 300 q^{38} - 24 q^{39} - 138 q^{42} - 4 q^{43} + 6 q^{44} - 180 q^{45} - 214 q^{46} + 204 q^{47} - 24 q^{49} - 20 q^{50} - 132 q^{51} + 252 q^{52} + 196 q^{53} + 168 q^{54} - 460 q^{56} - 48 q^{57} + 158 q^{58} + 72 q^{59} + 150 q^{60} + 72 q^{61} + 536 q^{63} - 140 q^{64} + 30 q^{65} + 744 q^{66} - 138 q^{67} - 348 q^{68} + 240 q^{70} - 8 q^{71} - 196 q^{72} - 528 q^{73} + 50 q^{74} - 30 q^{75} - 176 q^{77} - 312 q^{78} - 12 q^{79} - 240 q^{80} - 310 q^{81} - 378 q^{82} - 276 q^{84} - 40 q^{86} + 138 q^{87} + 604 q^{88} + 204 q^{89} - 480 q^{91} + 732 q^{92} + 84 q^{93} - 42 q^{94} + 60 q^{95} + 540 q^{96} + 898 q^{98} - 44 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^3 - 10 * q^4 - 2 * q^7 - 4 * q^8 + 14 * q^9 - 14 * q^11 + 18 * q^12 - 2 * q^14 - 20 * q^15 - 22 * q^16 + 48 * q^17 + 64 * q^18 - 30 * q^19 - 84 * q^21 - 88 * q^22 - 14 * q^23 - 36 * q^24 + 30 * q^25 + 66 * q^26 + 202 * q^28 + 64 * q^29 + 20 * q^30 + 132 * q^31 - 54 * q^32 - 192 * q^33 + 30 * q^35 + 156 * q^36 + 44 * q^37 - 300 * q^38 - 24 * q^39 - 138 * q^42 - 4 * q^43 + 6 * q^44 - 180 * q^45 - 214 * q^46 + 204 * q^47 - 24 * q^49 - 20 * q^50 - 132 * q^51 + 252 * q^52 + 196 * q^53 + 168 * q^54 - 460 * q^56 - 48 * q^57 + 158 * q^58 + 72 * q^59 + 150 * q^60 + 72 * q^61 + 536 * q^63 - 140 * q^64 + 30 * q^65 + 744 * q^66 - 138 * q^67 - 348 * q^68 + 240 * q^70 - 8 * q^71 - 196 * q^72 - 528 * q^73 + 50 * q^74 - 30 * q^75 - 176 * q^77 - 312 * q^78 - 12 * q^79 - 240 * q^80 - 310 * q^81 - 378 * q^82 - 276 * q^84 - 40 * q^86 + 138 * q^87 + 604 * q^88 + 204 * q^89 - 480 * q^91 + 732 * q^92 + 84 * q^93 - 42 * q^94 + 60 * q^95 + 540 * q^96 + 898 * q^98 - 44 * q^99

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