LMFDB - Embedded newform 35.3.h.a.26.3

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			26.3
Root			$0.410701 + 0.711354i$ of defining polynomial
Character	$\chi$	$=$	35.26
Dual form			35.3.h.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.410701 + 0.711354i) q^{2} +(0.507487 - 0.292998i) q^{3} +(1.66265 + 2.87979i) q^{4} +(1.93649 + 1.11803i) q^{5} +0.481337i q^{6} +(1.91172 - 6.73389i) q^{7} -6.01701 q^{8} +(-4.32830 + 7.49684i) q^{9} +O(q^{10})$	\(q+(-0.410701 + 0.711354i) q^{2} +(0.507487 - 0.292998i) q^{3} +(1.66265 + 2.87979i) q^{4} +(1.93649 + 1.11803i) q^{5} +0.481337i q^{6} +(1.91172 - 6.73389i) q^{7} -6.01701 q^{8} +(-4.32830 + 7.49684i) q^{9} +(-1.59064 + 0.918354i) q^{10} +(-6.95248 - 12.0421i) q^{11} +(1.68755 + 0.974306i) q^{12} -18.3546i q^{13} +(4.00504 + 4.12552i) q^{14} +1.31033 q^{15} +(-4.17941 + 7.23895i) q^{16} +(-8.98966 + 5.19018i) q^{17} +(-3.55527 - 6.15792i) q^{18} +(24.4251 + 14.1019i) q^{19} +7.43560i q^{20} +(-1.00284 - 3.97749i) q^{21} +11.4216 q^{22} +(-4.84179 + 8.38623i) q^{23} +(-3.05355 + 1.76297i) q^{24} +(2.50000 + 4.33013i) q^{25} +(13.0566 + 7.53824i) q^{26} +10.3467i q^{27} +(22.5707 - 5.69075i) q^{28} -17.7531 q^{29} +(-0.538152 + 0.932106i) q^{30} +(25.1484 - 14.5194i) q^{31} +(-15.4670 - 26.7896i) q^{32} +(-7.05659 - 4.07412i) q^{33} -8.52645i q^{34} +(11.2307 - 10.9028i) q^{35} -28.7858 q^{36} +(-17.2496 + 29.8772i) q^{37} +(-20.0628 + 11.5833i) q^{38} +(-5.37786 - 9.31472i) q^{39} +(-11.6519 - 6.72722i) q^{40} +13.3513i q^{41} +(3.24128 + 0.920182i) q^{42} +0.607058 q^{43} +(23.1191 - 40.0434i) q^{44} +(-16.7635 + 9.67838i) q^{45} +(-3.97705 - 6.88846i) q^{46} +(-5.51096 - 3.18175i) q^{47} +4.89823i q^{48} +(-41.6907 - 25.7466i) q^{49} -4.10701 q^{50} +(-3.04142 + 5.26790i) q^{51} +(52.8575 - 30.5173i) q^{52} +(47.1578 + 81.6798i) q^{53} +(-7.36017 - 4.24939i) q^{54} -31.0925i q^{55} +(-11.5028 + 40.5179i) q^{56} +16.5273 q^{57} +(7.29121 - 12.6287i) q^{58} +(-3.99050 + 2.30392i) q^{59} +(2.17861 + 3.77347i) q^{60} +(-8.66107 - 5.00047i) q^{61} +23.8526i q^{62} +(42.2085 + 43.4782i) q^{63} -8.02607 q^{64} +(20.5211 - 35.5435i) q^{65} +(5.79629 - 3.34649i) q^{66} +(14.1007 + 24.4231i) q^{67} +(-29.8933 - 17.2589i) q^{68} +5.67454i q^{69} +(3.14325 + 12.4668i) q^{70} +115.928 q^{71} +(26.0435 - 45.1086i) q^{72} +(-54.9607 + 31.7316i) q^{73} +(-14.1688 - 24.5411i) q^{74} +(2.53744 + 1.46499i) q^{75} +93.7858i q^{76} +(-94.3811 + 23.7963i) q^{77} +8.83476 q^{78} +(2.17003 - 3.75860i) q^{79} +(-16.1868 + 9.34545i) q^{80} +(-35.9232 - 62.2208i) q^{81} +(-9.49750 - 5.48338i) q^{82} -126.336i q^{83} +(9.78699 - 9.50116i) q^{84} -23.2112 q^{85} +(-0.249319 + 0.431833i) q^{86} +(-9.00947 + 5.20162i) q^{87} +(41.8332 + 72.4572i) q^{88} +(-68.6634 - 39.6429i) q^{89} -15.8997i q^{90} +(-123.598 - 35.0888i) q^{91} -32.2008 q^{92} +(8.50833 - 14.7369i) q^{93} +(4.52671 - 2.61350i) q^{94} +(31.5327 + 54.6163i) q^{95} +(-15.6986 - 9.06359i) q^{96} -15.7307i q^{97} +(35.4374 - 19.0827i) q^{98} +120.370 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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.410701	+	0.711354i	−0.205350	+	0.355677i	−0.950244	−	0.311506i	$-0.899167\pi$
$2$	−0.410701	+	0.711354i	−0.205350	+	0.355677i	0.744894	+	0.667183i	$0.232500\pi$
$3$	0.507487	−	0.292998i	0.169162	−	0.0976659i	−0.413028	−	0.910718i	$-0.635529\pi$
$3$	0.507487	−	0.292998i	0.169162	−	0.0976659i	0.582191	+	0.813052i	$0.302196\pi$
$4$	1.66265	+	2.87979i	0.415663	+	0.719949i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$			0.481337i			0.0802229i
$7$	1.91172	−	6.73389i	0.273103	−	0.961985i
$7$	1.91172	−	6.73389i	0.273103	−	0.961985i
$8$	−6.01701			−0.752126
$9$	−4.32830	+	7.49684i	−0.480923	+	0.832983i
$10$	−1.59064	+	0.918354i	−0.159064	+	0.0918354i
$11$	−6.95248	−	12.0421i	−0.632044	−	1.09473i	−0.987133	−	0.159900i	$-0.948883\pi$
$11$	−6.95248	−	12.0421i	−0.632044	−	1.09473i	0.355089	−	0.934832i	$-0.384450\pi$
$12$	1.68755	+	0.974306i	0.140629	+	0.0811921i
$13$		−	18.3546i		−	1.41189i	−0.708266	−	0.705946i	$-0.750522\pi$
$13$		−	18.3546i		−	1.41189i	0.708266	−	0.705946i	$-0.249478\pi$
$14$	4.00504	+	4.12552i	0.286074	+	0.294680i
$15$	1.31033			0.0873551
$16$	−4.17941	+	7.23895i	−0.261213	+	0.452434i
$17$	−8.98966	+	5.19018i	−0.528804	+	0.305305i	−0.740529	−	0.672024i	$-0.765425\pi$
$17$	−8.98966	+	5.19018i	−0.528804	+	0.305305i	0.211726	+	0.977329i	$0.432092\pi$
$18$	−3.55527	−	6.15792i	−0.197515	−	0.342106i
$19$	24.4251	+	14.1019i	1.28553	+	0.742203i	0.977854	−	0.209287i	$-0.0671143\pi$
$19$	24.4251	+	14.1019i	1.28553	+	0.742203i	0.307679	+	0.951490i	$0.400448\pi$
$20$			7.43560i			0.371780i
$21$	−1.00284	−	3.97749i	−0.0477545	−	0.189404i
$22$	11.4216			0.519162
$23$	−4.84179	+	8.38623i	−0.210513	+	0.364619i	−0.951875	−	0.306486i	$-0.900847\pi$
$23$	−4.84179	+	8.38623i	−0.210513	+	0.364619i	0.741362	+	0.671105i	$0.234180\pi$
$24$	−3.05355	+	1.76297i	−0.127231	+	0.0734571i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	13.0566	+	7.53824i	0.502178	+	0.289932i
$27$			10.3467i			0.383211i
$28$	22.5707	−	5.69075i	0.806098	−	0.203241i
$29$	−17.7531			−0.612176			−0.306088	−	0.952003i	$-0.599020\pi$
$29$	−17.7531			−0.612176			−0.306088	+	0.952003i	$0.599020\pi$
$30$	−0.538152	+	0.932106i	−0.0179384	+	0.0310702i
$31$	25.1484	−	14.5194i	0.811239	−	0.468369i	−0.0361471	−	0.999346i	$-0.511508\pi$
$31$	25.1484	−	14.5194i	0.811239	−	0.468369i	0.847386	+	0.530978i	$0.178175\pi$
$32$	−15.4670	−	26.7896i	−0.483344	−	0.837176i
$33$	−7.05659	−	4.07412i	−0.213836	−	0.123458i
$34$		−	8.52645i		−	0.250778i
$35$	11.2307	−	10.9028i	0.320879	−	0.311508i
$36$	−28.7858			−0.799606
$37$	−17.2496	+	29.8772i	−0.466205	+	0.807491i	−0.999255	−	0.0385930i	$-0.987712\pi$
$37$	−17.2496	+	29.8772i	−0.466205	+	0.807491i	0.533050	+	0.846084i	$0.321046\pi$
$38$	−20.0628	+	11.5833i	−0.527969	+	0.304823i
$39$	−5.37786	−	9.31472i	−0.137894	−	0.238839i
$40$	−11.6519	−	6.72722i	−0.291297	−	0.168181i
$41$			13.3513i			0.325641i	0.986656	+	0.162821i	$0.0520592\pi$
$41$			13.3513i			0.325641i	−0.986656	+	0.162821i	$0.947941\pi$
$42$	3.24128	+	0.920182i	0.0771732	+	0.0219091i
$43$	0.607058			0.0141176			0.00705881	−	0.999975i	$-0.497753\pi$
$43$	0.607058			0.0141176			0.00705881	+	0.999975i	$0.497753\pi$
$44$	23.1191	−	40.0434i	0.525434	−	0.910078i
$45$	−16.7635	+	9.67838i	−0.372521	+	0.215075i
$46$	−3.97705	−	6.88846i	−0.0864577	−	0.149749i
$47$	−5.51096	−	3.18175i	−0.117254	−	0.0676969i	0.440226	−	0.897887i	$-0.354898\pi$
$47$	−5.51096	−	3.18175i	−0.117254	−	0.0676969i	−0.557480	+	0.830190i	$0.688232\pi$
$48$			4.89823i			0.102047i
$49$	−41.6907	−	25.7466i	−0.850830	−	0.525441i
$50$	−4.10701			−0.0821401
$51$	−3.04142	+	5.26790i	−0.0596358	+	0.103292i
$52$	52.8575	−	30.5173i	1.01649	−	0.586871i
$53$	47.1578	+	81.6798i	0.889770	+	1.54113i	0.840146	+	0.542360i	$0.182469\pi$
$53$	47.1578	+	81.6798i	0.889770	+	1.54113i	0.0496241	+	0.998768i	$0.484198\pi$
$54$	−7.36017	−	4.24939i	−0.136299	−	0.0786925i
$55$		−	31.0925i		−	0.565317i
$56$	−11.5028	+	40.5179i	−0.205408	+	0.723534i
$57$	16.5273			0.289952
$58$	7.29121	−	12.6287i	0.125711	−	0.217737i
$59$	−3.99050	+	2.30392i	−0.0676356	+	0.0390494i	−0.533436	−	0.845840i	$-0.679100\pi$
$59$	−3.99050	+	2.30392i	−0.0676356	+	0.0390494i	0.465801	+	0.884890i	$0.345766\pi$
$60$	2.17861	+	3.77347i	0.0363102	+	0.0628912i
$61$	−8.66107	−	5.00047i	−0.141985	−	0.0819749i	0.427325	−	0.904098i	$-0.359456\pi$
$61$	−8.66107	−	5.00047i	−0.141985	−	0.0819749i	−0.569310	+	0.822123i	$0.692789\pi$
$62$			23.8526i			0.384719i
$63$	42.2085	+	43.4782i	0.669975	+	0.690130i
$64$	−8.02607			−0.125407
$65$	20.5211	−	35.5435i	0.315709	−	0.546824i
$66$	5.79629	−	3.34649i	0.0878226	−	0.0507044i
$67$	14.1007	+	24.4231i	0.210458	+	0.364525i	0.951858	−	0.306539i	$-0.0991710\pi$
$67$	14.1007	+	24.4231i	0.210458	+	0.364525i	−0.741400	+	0.671064i	$0.765838\pi$
$68$	−29.8933	−	17.2589i	−0.439608	−	0.253808i
$69$			5.67454i			0.0822397i
$70$	3.14325	+	12.4668i	0.0449036	+	0.178097i
$71$	115.928			1.63279			0.816396	−	0.577492i	$-0.195969\pi$
$71$	115.928			1.63279			0.816396	+	0.577492i	$0.195969\pi$
$72$	26.0435	−	45.1086i	0.361715	−	0.626508i
$73$	−54.9607	+	31.7316i	−0.752886	+	0.434679i	−0.826736	−	0.562590i	$-0.809805\pi$
$73$	−54.9607	+	31.7316i	−0.752886	+	0.434679i	0.0738496	+	0.997269i	$0.476472\pi$
$74$	−14.1688	−	24.5411i	−0.191471	−	0.331637i
$75$	2.53744	+	1.46499i	0.0338325	+	0.0195332i
$76$			93.7858i			1.23402i
$77$	−94.3811	+	23.7963i	−1.22573	+	0.309042i
$78$	8.83476			0.113266
$79$	2.17003	−	3.75860i	0.0274687	−	0.0475772i	−0.851964	−	0.523600i	$-0.824589\pi$
$79$	2.17003	−	3.75860i	0.0274687	−	0.0475772i	0.879433	+	0.476023i	$0.157922\pi$
$80$	−16.1868	+	9.34545i	−0.202335	+	0.116818i
$81$	−35.9232	−	62.2208i	−0.443496	−	0.768158i
$82$	−9.49750	−	5.48338i	−0.115823	−	0.0668705i
$83$		−	126.336i		−	1.52212i	−0.648679	−	0.761062i	$-0.724678\pi$
$83$		−	126.336i		−	1.52212i	0.648679	−	0.761062i	$-0.275322\pi$
$84$	9.78699	−	9.50116i	0.116512	−	0.113109i
$85$	−23.2112			−0.273073
$86$	−0.249319	+	0.431833i	−0.00289906	+	0.00502132i
$87$	−9.00947	+	5.20162i	−0.103557	+	0.0597887i
$88$	41.8332	+	72.4572i	0.475377	+	0.823377i
$89$	−68.6634	−	39.6429i	−0.771499	−	0.445425i	0.0619099	−	0.998082i	$-0.480281\pi$
$89$	−68.6634	−	39.6429i	−0.771499	−	0.445425i	−0.833409	+	0.552656i	$0.813614\pi$
$90$		−	15.8997i		−	0.176663i
$91$	−123.598	−	35.0888i	−1.35822	−	0.385592i
$92$	−32.2008			−0.350009
$93$	8.50833	−	14.7369i	0.0914874	−	0.158461i
$94$	4.52671	−	2.61350i	0.0481565	−	0.0278032i
$95$	31.5327	+	54.6163i	0.331923	+	0.574908i
$96$	−15.6986	−	9.06359i	−0.163527	−	0.0944124i
$97$		−	15.7307i		−	0.162172i	−0.996707	−	0.0810861i	$-0.974161\pi$
$97$		−	15.7307i		−	0.162172i	0.996707	−	0.0810861i	$-0.0258389\pi$
$98$	35.4374	−	19.0827i	0.361606	−	0.194721i
$99$	120.370			1.21586
$100$	−8.31325	+	14.3990i	−0.0831325	+	0.143990i
$101$	154.064	−	88.9487i	1.52538	−	0.880680i	0.525835	−	0.850586i	$-0.323753\pi$
$101$	154.064	−	88.9487i	1.52538	−	0.880680i	0.999547	−	0.0300937i	$-0.00958057\pi$
$102$	−2.49823	−	4.32706i	−0.0244924	−	0.0424222i
$103$	−137.140	−	79.1780i	−1.33146	−	0.768718i	−0.345936	−	0.938258i	$-0.612438\pi$
$103$	−137.140	−	79.1780i	−1.33146	−	0.768718i	−0.985523	+	0.169540i	$0.945772\pi$
$104$			110.440i			1.06192i
$105$	2.50497	−	8.82360i	0.0238569	−	0.0840343i
$106$	−77.4710			−0.730859
$107$	16.1203	−	27.9211i	0.150657	−	0.260945i	−0.780812	−	0.624765i	$-0.785195\pi$
$107$	16.1203	−	27.9211i	0.150657	−	0.260945i	0.931469	+	0.363821i	$0.118528\pi$
$108$	−29.7964	+	17.2029i	−0.275892	+	0.159286i
$109$	54.1126	+	93.7258i	0.496446	+	0.859870i	0.999992	−	0.00409900i	$-0.00130476\pi$
$109$	54.1126	+	93.7258i	0.496446	+	0.859870i	−0.503546	+	0.863969i	$0.667971\pi$
$110$	22.1178	+	12.7697i	0.201070	+	0.116088i
$111$			20.2164i			0.182129i
$112$	40.7565	+	41.9825i	0.363897	+	0.374844i
$113$	9.27822			0.0821082			0.0410541	−	0.999157i	$-0.486928\pi$
$113$	9.27822			0.0821082			0.0410541	+	0.999157i	$0.486928\pi$
$114$	−6.78775	+	11.7567i	−0.0595417	+	0.103129i
$115$	−18.7522	+	10.8266i	−0.163062	+	0.0941442i
$116$	−29.5172	−	51.1253i	−0.254459	−	0.440735i
$117$	137.602	+	79.4443i	1.17608	+	0.679011i
$118$		−	3.78488i		−	0.0320753i
$119$	17.7644	+	70.4576i	0.149281	+	0.592081i
$120$	−7.88424			−0.0657020
$121$	−36.1741	+	62.6553i	−0.298959	+	0.517813i
$122$	7.11421	−	4.10739i	0.0583132	−	0.0336671i
$123$	3.91190	+	6.77561i	0.0318041	+	0.0550863i
$124$	83.6260	+	48.2815i	0.674403	+	0.389367i
$125$			11.1803i			0.0894427i
$126$	−48.2634	+	12.1686i	−0.383043	+	0.0965765i
$127$	−79.8747			−0.628934			−0.314467	−	0.949268i	$-0.601826\pi$
$127$	−79.8747			−0.628934			−0.314467	+	0.949268i	$0.601826\pi$
$128$	65.1643	−	112.868i	0.509096	−	0.881780i
$129$	0.308074	−	0.177867i	0.00238817	−	0.00137881i
$130$	16.8560	+	29.1955i	0.129662	+	0.224581i
$131$	90.1744	+	52.0622i	0.688354	+	0.397422i	0.802995	−	0.595985i	$-0.203238\pi$
$131$	90.1744	+	52.0622i	0.688354	+	0.397422i	−0.114641	+	0.993407i	$0.536572\pi$
$132$		−	27.0954i		−	0.205268i
$133$	141.654	−	137.517i	1.06507	−	1.03397i
$134$	−23.1647			−0.172871
$135$	−11.5680	+	20.0363i	−0.0856886	+	0.148417i
$136$	54.0909	−	31.2294i	0.397727	−	0.229628i
$137$	−70.1719	−	121.541i	−0.512204	−	0.887163i	−0.999900	−	0.0141493i	$-0.995496\pi$
$137$	−70.1719	−	121.541i	−0.512204	−	0.887163i	0.487696	−	0.873013i	$-0.337837\pi$
$138$	−4.03661	−	2.33054i	−0.0292508	−	0.0168879i
$139$			4.55542i			0.0327728i	0.999866	+	0.0163864i	$0.00521619\pi$
$139$			4.55542i			0.0327728i	−0.999866	+	0.0163864i	$0.994784\pi$
$140$	50.0705	+	14.2148i	0.357647	+	0.101534i
$141$	−3.72899			−0.0264467
$142$	−47.6118	+	82.4661i	−0.335294	+	0.580747i
$143$	−221.027	+	127.610i	−1.54564	+	0.892378i
$144$	−36.1795	−	62.6648i	−0.251247	−	0.435172i
$145$	−34.3787	−	19.8486i	−0.237095	−	0.136887i
$146$		−	52.1287i		−	0.357046i
$147$	−28.7012	−	0.850806i	−0.195246	−	0.00578779i
$148$	−114.720			−0.775136
$149$	−70.9464	+	122.883i	−0.476151	+	0.824717i	−0.999627	−	0.0273233i	$-0.991302\pi$
$149$	−70.9464	+	122.883i	−0.476151	+	0.824717i	0.523476	+	0.852040i	$0.324635\pi$
$150$	−2.08425	+	1.20334i	−0.0138950	+	0.00802229i
$151$	−84.8300	−	146.930i	−0.561788	−	0.973045i	−0.997341	−	0.0728821i	$-0.976780\pi$
$151$	−84.8300	−	146.930i	−0.561788	−	0.973045i	0.435553	−	0.900163i	$-0.356553\pi$
$152$	−146.966	−	84.8510i	−0.966883	−	0.558230i
$153$		−	89.8588i		−	0.587312i
$154$	21.8348	−	76.9116i	0.141784	−	0.499426i
$155$	64.9329			0.418922
$156$	17.8830	−	30.9742i	0.114635	−	0.198553i
$157$	149.165	−	86.1204i	0.950095	−	0.548537i	0.0569843	−	0.998375i	$-0.481851\pi$
$157$	149.165	−	86.1204i	0.950095	−	0.548537i	0.893110	+	0.449838i	$0.148518\pi$
$158$	1.78246	+	3.08732i	0.0112814	+	0.0195400i
$159$	47.8640	+	27.6343i	0.301031	+	0.173801i
$160$		−	69.1705i		−	0.432316i
$161$	47.2159	+	48.6362i	0.293266	+	0.302088i
$162$	59.0147			0.364288
$163$	−38.6597	+	66.9605i	−0.237176	+	0.410801i	−0.959903	−	0.280333i	$-0.909555\pi$
$163$	−38.6597	+	66.9605i	−0.237176	+	0.410801i	0.722727	+	0.691134i	$0.242888\pi$
$164$	−38.4490	+	22.1985i	−0.234445	+	0.135357i
$165$	−9.11002	−	15.7790i	−0.0552122	−	0.0956304i
$166$	89.8699	+	51.8864i	0.541385	+	0.312569i
$167$			98.8292i			0.591792i	0.955220	+	0.295896i	$0.0956181\pi$
$167$			98.8292i			0.591792i	−0.955220	+	0.295896i	$0.904382\pi$
$168$	6.03412	+	23.9326i	0.0359174	+	0.142456i
$169$	−167.891			−0.993440
$170$	9.53286	−	16.5114i	0.0560756	−	0.0971258i
$171$	−211.439	+	122.074i	−1.23648	+	0.713885i
$172$	1.00932	+	1.74820i	0.00586817	+	0.0101640i
$173$	198.327	+	114.504i	1.14640	+	0.661873i	0.948007	−	0.318250i	$-0.103095\pi$
$173$	198.327	+	114.504i	1.14640	+	0.661873i	0.198390	+	0.980123i	$0.436429\pi$
$174$		−	8.54523i		−	0.0491105i
$175$	33.9379	−	8.55675i	0.193931	−	0.0488957i
$176$	116.229			0.660393
$177$	−1.35009	+	2.33842i	−0.00762760	+	0.0132114i
$178$	56.4002	−	32.5627i	0.316855	−	0.182936i
$179$	−89.0804	−	154.292i	−0.497656	−	0.861965i	0.502341	−	0.864670i	$-0.332472\pi$
$179$	−89.0804	−	154.292i	−0.497656	−	0.861965i	−0.999996	+	0.00270485i	$0.999139\pi$
$180$	−55.7435	−	32.1835i	−0.309686	−	0.178797i
$181$			141.488i			0.781702i	0.920454	+	0.390851i	$0.127819\pi$
$181$			141.488i			0.781702i	−0.920454	+	0.390851i	$0.872181\pi$
$182$	75.7223	−	73.5109i	0.416057	−	0.403906i
$183$	−5.86051			−0.0320246
$184$	29.1331	−	50.4600i	0.158332	−	0.274239i
$185$	−66.8074	+	38.5712i	−0.361121	+	0.208493i
$186$	6.98875	+	12.1049i	0.0375739	+	0.0650799i
$187$	125.001	+	72.1693i	0.668454	+	0.385932i
$188$		−	21.1606i		−	0.112556i
$189$	69.6735	+	19.7800i	0.368643	+	0.104656i
$190$	−51.8020			−0.272642
$191$	−51.1733	+	88.6348i	−0.267923	+	0.464057i	−0.968325	−	0.249692i	$-0.919671\pi$
$191$	−51.1733	+	88.6348i	−0.267923	+	0.464057i	0.700402	+	0.713748i	$0.253004\pi$
$192$	−4.07313	+	2.35162i	−0.0212142	+	0.0122480i
$193$	109.666	+	189.947i	0.568217	+	0.984180i	0.996742	+	0.0806507i	$0.0256998\pi$
$193$	109.666	+	189.947i	0.568217	+	0.984180i	−0.428526	+	0.903530i	$0.640967\pi$
$194$	11.1901	+	6.46061i	0.0576810	+	0.0333021i
$195$		−	24.0505i		−	0.123336i
$196$	4.82800	−	162.868i	0.0246326	−	0.830960i
$197$	88.1300			0.447360			0.223680	−	0.974663i	$-0.428193\pi$
$197$	88.1300			0.447360			0.223680	+	0.974663i	$0.428193\pi$
$198$	−49.4360	+	85.6256i	−0.249677	+	0.432453i
$199$	253.772	−	146.515i	1.27524	−	0.736258i	0.299267	−	0.954169i	$-0.403258\pi$
$199$	253.772	−	146.515i	1.27524	−	0.736258i	0.975969	+	0.217912i	$0.0699244\pi$
$200$	−15.0425	−	26.0544i	−0.0752126	−	0.130272i
$201$	14.3119	+	8.26295i	0.0712033	+	0.0411092i
$202$			146.125i			0.723392i
$203$	−33.9389	+	119.548i	−0.167187	+	0.588904i
$204$	−20.2273			−0.0991534
$205$	−14.9272	+	25.8547i	−0.0728156	+	0.126120i
$206$	112.647	−	65.0369i	0.546831	−	0.315713i
$207$	−41.9135	−	72.5963i	−0.202481	−	0.350707i
$208$	132.868	+	76.7114i	0.638789	+	0.368805i
$209$		−	392.172i		−	1.87642i
$210$	5.24791	+	5.40578i	0.0249900	+	0.0257418i
$211$	−96.3091			−0.456441			−0.228221	−	0.973609i	$-0.573291\pi$
$211$	−96.3091			−0.456441			−0.228221	+	0.973609i	$0.573291\pi$
$212$	−156.814	+	271.610i	−0.739688	+	1.28118i
$213$	58.8321	−	33.9667i	0.276207	−	0.159468i
$214$	13.2412	+	22.9344i	0.0618747	+	0.107170i
$215$	1.17556	+	0.678711i	0.00546773	+	0.00315680i
$216$		−	62.2562i		−	0.288223i
$217$	−49.6957	−	197.104i	−0.229012	−	0.908312i
$218$	−88.8963			−0.407781
$219$	−18.5946	+	32.2067i	−0.0849067	+	0.147063i
$220$	89.5399	−	51.6959i	0.406999	−	0.234981i
$221$	95.2637	+	165.002i	0.431058	+	0.746614i
$222$	−14.3810	−	8.30287i	−0.0647793	−	0.0374003i
$223$			58.7156i			0.263299i	0.991296	+	0.131649i	$0.0420273\pi$
$223$			58.7156i			0.263299i	−0.991296	+	0.131649i	$0.957973\pi$
$224$	−209.967	+	52.9389i	−0.937353	+	0.236334i
$225$	−43.2830			−0.192369
$226$	−3.81057	+	6.60010i	−0.0168609	+	0.0292040i
$227$	−283.266	+	163.544i	−1.24787	+	0.720457i	−0.970684	−	0.240359i	$-0.922735\pi$
$227$	−283.266	+	163.544i	−1.24787	+	0.720457i	−0.277185	+	0.960817i	$0.589401\pi$
$228$	27.4790	+	47.5951i	0.120522	+	0.208750i
$229$	−285.472	−	164.817i	−1.24660	−	0.719726i	−0.276172	−	0.961108i	$-0.589066\pi$
$229$	−285.472	−	164.817i	−1.24660	−	0.719726i	−0.970430	+	0.241382i	$0.922399\pi$
$230$		−	17.7859i		−	0.0773301i
$231$	−40.9249	+	39.7298i	−0.177164	+	0.171990i
$232$	106.821			0.460434
$233$	107.175	−	185.633i	0.459980	−	0.796708i	−0.538980	−	0.842319i	$-0.681190\pi$
$233$	107.175	−	185.633i	0.459980	−	0.796708i	0.998959	+	0.0456108i	$0.0145234\pi$
$234$	−113.026	+	65.2556i	−0.483017	+	0.278870i
$235$	−7.11462	−	12.3229i	−0.0302750	−	0.0524378i
$236$	−13.2696	−	7.66122i	−0.0562272	−	0.0324628i
$237$		−	2.54326i		−	0.0107310i
$238$	−57.4162	−	16.3002i	−0.241244	−	0.0684881i
$239$	96.2055			0.402533			0.201267	−	0.979536i	$-0.435494\pi$
$239$	96.2055			0.402533			0.201267	+	0.979536i	$0.435494\pi$
$240$	−5.47639	+	9.48539i	−0.0228183	+	0.0395224i
$241$	95.7432	−	55.2773i	0.397275	−	0.229367i	−0.288033	−	0.957621i	$-0.593001\pi$
$241$	95.7432	−	55.2773i	0.397275	−	0.229367i	0.685307	+	0.728254i	$0.259668\pi$
$242$	−29.7134	−	51.4652i	−0.122783	−	0.212666i
$243$	−117.106	−	67.6110i	−0.481916	−	0.278234i
$244$		−	33.2561i		−	0.136296i
$245$	−51.9480	−	96.4697i	−0.212033	−	0.393754i
$246$	−6.42648			−0.0261239
$247$	258.834	−	448.314i	1.04791	−	1.81503i
$248$	−151.318	+	87.3636i	−0.610154	+	0.352273i
$249$	−37.0163	−	64.1141i	−0.148660	−	0.257486i
$250$	−7.95318	−	4.59177i	−0.0318127	−	0.0183671i
$251$			105.692i			0.421084i	0.977585	+	0.210542i	$0.0675228\pi$
$251$			105.692i			0.421084i	−0.977585	+	0.210542i	$0.932477\pi$
$252$	−55.0304	+	193.841i	−0.218375	+	0.769209i
$253$	134.650			0.532213
$254$	32.8046	−	56.8192i	0.129152	−	0.223698i
$255$	−11.7794	+	6.80083i	−0.0461937	+	0.0266699i
$256$	37.4739	+	64.9067i	0.146382	+	0.253542i
$257$	−83.5433	−	48.2337i	−0.325071	−	0.187680i	0.328580	−	0.944476i	$-0.393430\pi$
$257$	−83.5433	−	48.2337i	−0.325071	−	0.187680i	−0.653651	+	0.756796i	$0.726763\pi$
$258$			0.292200i			0.00113256i
$259$	168.213	+	173.274i	0.649472	+	0.669010i
$260$	136.477			0.524913
$261$	76.8408	−	133.092i	0.294409	−	0.509932i
$262$	−74.0694	+	42.7640i	−0.282708	+	0.163221i
$263$	−153.979	−	266.699i	−0.585470	−	1.01406i	−0.994817	−	0.101685i	$-0.967577\pi$
$263$	−153.979	−	266.699i	−0.585470	−	1.01406i	0.409347	−	0.912379i	$-0.365757\pi$
$264$	42.4596	+	24.5141i	0.160832	+	0.0928563i
$265$			210.896i			0.795835i
$266$	39.6461	+	157.245i	0.149046	+	0.591147i
$267$	−46.4611			−0.174012
$268$	−46.8891	+	81.2143i	−0.174959	+	0.303038i
$269$	86.3725	−	49.8672i	0.321087	−	0.185380i	−0.330790	−	0.943704i	$-0.607315\pi$
$269$	86.3725	−	49.8672i	0.321087	−	0.185380i	0.651877	+	0.758325i	$0.273982\pi$
$270$	−9.50193	−	16.4578i	−0.0351923	−	0.0609549i
$271$	−192.770	−	111.296i	−0.711327	−	0.410685i	0.100225	−	0.994965i	$-0.468044\pi$
$271$	−192.770	−	111.296i	−0.711327	−	0.410685i	−0.811552	+	0.584280i	$0.801377\pi$
$272$		−	86.7676i		−	0.318999i
$273$	−73.0053	+	18.4068i	−0.267419	+	0.0674241i
$274$	115.279			0.420725
$275$	34.7624	−	60.2103i	0.126409	−	0.218946i
$276$	−16.3415	+	9.43477i	−0.0592084	+	0.0341840i
$277$	256.087	+	443.556i	0.924503	+	1.60129i	0.792359	+	0.610055i	$0.208853\pi$
$277$	256.087	+	443.556i	0.924503	+	1.60129i	0.132143	+	0.991231i	$0.457814\pi$
$278$	−3.24052	−	1.87091i	−0.0116565	−	0.00672991i
$279$			251.378i			0.900997i
$280$	−67.5755	+	65.6020i	−0.241341	+	0.234293i
$281$	−128.686			−0.457959			−0.228979	−	0.973431i	$-0.573539\pi$
$281$	−128.686			−0.457959			−0.228979	+	0.973431i	$0.573539\pi$
$282$	1.53150	−	2.65263i	0.00543084	−	0.00940650i
$283$	316.557	−	182.764i	1.11858	−	0.645811i	0.177540	−	0.984114i	$-0.443186\pi$
$283$	316.557	−	182.764i	1.11858	−	0.645811i	0.941037	+	0.338303i	$0.109853\pi$
$284$	192.748	+	333.850i	0.678691	+	1.17553i
$285$	32.0049	+	18.4780i	0.112298	+	0.0648352i
$286$		−	209.638i		−	0.733000i
$287$	89.9062	+	25.5239i	0.313262	+	0.0889335i
$288$	267.783			0.929804
$289$	−90.6240	+	156.965i	−0.313578	+	0.543133i
$290$	28.2387	−	16.3036i	0.0973750	−	0.0562195i
$291$	−4.60906	−	7.98313i	−0.0158387	−	0.0274334i
$292$	−182.761	−	105.517i	−0.625893	−	0.361360i
$293$			386.006i			1.31743i	0.752394	+	0.658714i	$0.228899\pi$
$293$			386.006i			1.31743i	−0.752394	+	0.658714i	$0.771101\pi$
$294$	12.3928	−	20.0673i	0.0421524	−	0.0682560i
$295$	−10.3034			−0.0349269
$296$	103.791	−	179.771i	0.350645	−	0.607335i
$297$	124.595	−	71.9352i	0.419513	−	0.242206i
$298$	−58.2755	−	100.936i	−0.195555	−	0.338712i
$299$	153.926	+	88.8692i	0.514802	+	0.297221i
$300$			9.74306i			0.0324769i
$301$	1.16052	−	4.08786i	0.00385556	−	0.0135809i
$302$	139.359			0.461453
$303$	52.1235	−	90.2806i	0.172025	−	0.297956i
$304$	−204.165	+	117.875i	−0.671596	+	0.387746i
$305$	−11.1814	−	19.3667i	−0.0366603	−	0.0634975i
$306$	63.9214	+	36.9051i	0.208894	+	0.120605i
$307$		−	293.225i		−	0.955131i	−0.878596	−	0.477566i	$-0.841519\pi$
$307$		−	293.225i		−	0.955131i	0.878596	−	0.477566i	$-0.158481\pi$
$308$	−225.451	−	232.233i	−0.731984	−	0.754004i
$309$	−92.7959			−0.300310
$310$	−26.6680	+	46.1903i	−0.0860257	+	0.149001i
$311$	−292.937	+	169.127i	−0.941919	+	0.543817i	−0.890561	−	0.454863i	$-0.849688\pi$
$311$	−292.937	+	169.127i	−0.941919	+	0.543817i	−0.0513575	+	0.998680i	$0.516355\pi$
$312$	32.3586	+	56.0468i	0.103714	+	0.179637i
$313$	−297.997	−	172.049i	−0.952067	−	0.549676i	−0.0583447	−	0.998296i	$-0.518582\pi$
$313$	−297.997	−	172.049i	−0.952067	−	0.549676i	−0.893722	+	0.448620i	$0.851916\pi$
$314$			141.479i			0.450569i
$315$	33.1262	+	131.386i	0.105163	+	0.417097i
$316$	14.4320			0.0456709
$317$	72.7051	−	125.929i	0.229354	−	0.397252i	−0.728263	−	0.685298i	$-0.759672\pi$
$317$	72.7051	−	125.929i	0.229354	−	0.397252i	0.957617	+	0.288045i	$0.0930054\pi$
$318$	−39.3155	+	22.6988i	−0.123634	+	0.0713800i
$319$	123.428	+	213.784i	0.386922	+	0.670169i
$320$	−15.5424	−	8.97342i	−0.0485701	−	0.0280419i
$321$		−	18.8928i		−	0.0588561i
$322$	−53.9892	+	13.6123i	−0.167668	+	0.0422741i
$323$	−292.765			−0.906393
$324$	119.455	−	206.903i	0.368689	−	0.638589i
$325$	79.4777	−	45.8865i	0.244547	−	0.141189i
$326$	−31.7551	−	55.0014i	−0.0974083	−	0.168716i
$327$	54.9229	+	31.7098i	0.167960	+	0.0969717i
$328$		−	80.3349i		−	0.244923i
$329$	−31.9610	+	31.0276i	−0.0971459	+	0.0943088i
$330$	14.9660			0.0453514
$331$	96.9935	−	167.998i	0.293032	−	0.507546i	−0.681493	−	0.731824i	$-0.738669\pi$
$331$	96.9935	−	167.998i	0.293032	−	0.507546i	0.974525	+	0.224279i	$0.0720025\pi$
$332$	363.823	−	210.053i	1.09585	−	0.632690i
$333$	−149.323	−	258.635i	−0.448417	−	0.776681i
$334$	−70.3026	−	40.5892i	−0.210487	−	0.121525i
$335$			63.0603i			0.188240i
$336$	32.9842	+	9.36404i	0.0981672	+	0.0278692i
$337$	−611.186			−1.81361			−0.906803	−	0.421554i	$-0.861485\pi$
$337$	−611.186			−1.81361			−0.906803	+	0.421554i	$0.861485\pi$
$338$	68.9531	−	119.430i	0.204003	−	0.353344i
$339$	4.70858	−	2.71850i	0.0138896	−	0.00801917i
$340$	−38.5921	−	66.8435i	−0.113506	−	0.196599i
$341$	−349.688	−	201.892i	−1.02548	−	0.592060i
$342$		−	200.544i		−	0.586386i
$343$	−253.076	+	231.520i	−0.737830	+	0.674986i
$344$	−3.65267			−0.0106182
$345$	−6.34433	+	10.9887i	−0.0183894	+	0.0318513i
$346$	−162.906	+	94.0537i	−0.470826	+	0.271832i
$347$	−37.3606	−	64.7105i	−0.107667	−	0.186486i	0.807157	−	0.590336i	$-0.201005\pi$
$347$	−37.3606	−	64.7105i	−0.107667	−	0.186486i	−0.914825	+	0.403851i	$0.867672\pi$
$348$	−29.9592	−	17.2969i	−0.0860896	−	0.0497039i
$349$			439.876i			1.26039i	0.776437	+	0.630195i	$0.217025\pi$
$349$			439.876i			1.26039i	−0.776437	+	0.630195i	$0.782975\pi$
$350$	−7.85144	+	27.6561i	−0.0224327	+	0.0790176i
$351$	189.909			0.541053
$352$	−215.068	+	372.509i	−0.610989	+	1.05826i
$353$	587.662	−	339.287i	1.66476	−	0.961152i	0.694372	−	0.719616i	$-0.255682\pi$
$353$	587.662	−	339.287i	1.66476	−	0.961152i	0.970392	−	0.241536i	$-0.0776511\pi$
$354$	−1.10896	−	1.92078i	−0.00313266	−	0.00542593i
$355$	224.494	+	129.612i	0.632378	+	0.365104i
$356$		−	263.649i		−	0.740586i
$357$	29.6591	+	30.5514i	0.0830788	+	0.0855781i
$358$	146.341			0.408775
$359$	76.4364	−	132.392i	0.212915	−	0.368779i	−0.739711	−	0.672925i	$-0.765038\pi$
$359$	76.4364	−	132.392i	0.212915	−	0.368779i	0.952626	+	0.304146i	$0.0983710\pi$
$360$	100.866	−	58.2349i	0.280183	−	0.161764i
$361$	217.225	+	376.244i	0.601731	+	1.04223i
$362$	−100.648	−	58.1092i	−0.278033	−	0.160523i
$363$			42.3957i			0.116793i
$364$	−104.451	−	414.277i	−0.286955	−	1.13812i
$365$	−141.908			−0.388789
$366$	2.40691	−	4.16890i	0.00657627	−	0.0113904i
$367$	−422.693	+	244.042i	−1.15175	+	0.664964i	−0.949313	−	0.314331i	$-0.898220\pi$
$367$	−422.693	+	244.042i	−1.15175	+	0.664964i	−0.202438	+	0.979295i	$0.564886\pi$
$368$	−40.4717	−	70.0990i	−0.109977	−	0.190486i
$369$	−100.093	−	57.7885i	−0.271254	−	0.156608i
$370$		−	63.3649i		−	0.171257i
$371$	640.175	−	161.407i	1.72554	−	0.435060i
$372$	56.5855			0.152111
$373$	−254.569	+	440.927i	−0.682491	+	1.18211i	0.291727	+	0.956502i	$0.405770\pi$
$373$	−254.569	+	440.927i	−0.682491	+	1.18211i	−0.974218	+	0.225608i	$0.927563\pi$
$374$	−102.676	+	59.2800i	−0.274535	+	0.158503i
$375$	3.27581	+	5.67388i	0.00873551	+	0.0151303i
$376$	33.1595	+	19.1447i	0.0881902	+	0.0509166i
$377$			325.851i			0.864327i
$378$	−42.6855	+	41.4389i	−0.112925	+	0.109627i
$379$	383.503			1.01188			0.505941	−	0.862568i	$-0.331145\pi$
$379$	383.503			1.01188			0.505941	+	0.862568i	$0.331145\pi$
$380$	−104.856	+	181.615i	−0.275936	+	0.477935i
$381$	−40.5354	+	23.4031i	−0.106392	+	0.0614255i
$382$	−42.0338	−	72.8048i	−0.110036	−	0.190588i
$383$	524.639	+	302.900i	1.36981	+	0.790862i	0.990904	−	0.134571i	$-0.0429657\pi$
$383$	524.639	+	302.900i	1.36981	+	0.790862i	0.378910	+	0.925434i	$0.376299\pi$
$384$		−	76.3720i		−	0.198885i
$385$	−209.373	−	59.4400i	−0.543827	−	0.154390i
$386$	−180.159			−0.466734
$387$	−2.62753	+	4.55102i	−0.00678949	+	0.0117597i
$388$	45.3012	−	26.1547i	0.116756	−	0.0674089i
$389$	−144.495	−	250.273i	−0.371453	−	0.643376i	0.618336	−	0.785914i	$-0.287807\pi$
$389$	−144.495	−	250.273i	−0.371453	−	0.643376i	−0.989789	+	0.142538i	$0.954474\pi$
$390$	17.1084	+	9.87756i	0.0438678	+	0.0253271i
$391$		−	100.519i		−	0.257082i
$392$	250.853	+	154.918i	0.639932	+	0.395198i
$393$	61.0165			0.155258
$394$	−36.1950	+	62.6916i	−0.0918656	+	0.159116i
$395$	8.40449	−	4.85233i	0.0212772	−	0.0122844i
$396$	200.133	+	346.640i	0.505386	+	0.875355i
$397$	391.345	+	225.943i	0.985755	+	0.569126i	0.904003	−	0.427527i	$-0.140615\pi$
$397$	391.345	+	225.943i	0.985755	+	0.569126i	0.0817526	+	0.996653i	$0.473948\pi$
$398$			240.696i			0.604763i
$399$	31.5955	−	111.293i	0.0791866	−	0.278929i
$400$	−41.7941			−0.104485
$401$	−169.083	+	292.861i	−0.421654	+	0.730326i	−0.996101	−	0.0882153i	$-0.971884\pi$
$401$	−169.083	+	292.861i	−0.421654	+	0.730326i	0.574447	+	0.818541i	$0.305217\pi$
$402$	−11.7558	+	6.78720i	−0.0292432	+	0.0168836i
$403$	−266.498	−	461.589i	−0.661286	−	1.14538i
$404$	512.308	+	295.781i	1.26809	+	0.732131i
$405$		−	160.653i		−	0.396675i
$406$	−71.1019	−	73.2409i	−0.175128	−	0.180396i
$407$	479.710			1.17865
$408$	18.3003	−	31.6970i	0.0448536	−	0.0776888i
$409$	−175.964	+	101.593i	−0.430231	+	0.248394i	−0.699445	−	0.714687i	$-0.746569\pi$
$409$	−175.964	+	101.593i	−0.430231	+	0.248394i	0.269214	+	0.963080i	$0.413236\pi$
$410$	−12.2612	−	21.2371i	−0.0299054	−	0.0517977i
$411$	−71.2227	−	41.1204i	−0.173291	−	0.100050i
$412$		−	526.581i		−	1.27811i
$413$	7.88562	+	31.2761i	0.0190935	+	0.0757289i
$414$	68.8556			0.166318
$415$	141.248	−	244.649i	0.340357	−	0.589516i
$416$	−491.713	+	283.890i	−1.18200	+	0.682429i
$417$	1.33473	+	2.31182i	0.00320079	+	0.00554393i
$418$	278.973	+	161.065i	0.667400	+	0.385323i
$419$		−	594.362i		−	1.41853i	−0.704944	−	0.709263i	$-0.749028\pi$
$419$		−	594.362i		−	1.41853i	0.704944	−	0.709263i	$-0.250972\pi$
$420$	29.5750	−	7.45674i	0.0704168	−	0.0177541i
$421$	22.6663			0.0538393			0.0269196	−	0.999638i	$-0.491430\pi$
$421$	22.6663			0.0538393			0.0269196	+	0.999638i	$0.491430\pi$
$422$	39.5542	−	68.5099i	0.0937303	−	0.162346i
$423$	47.7062	−	27.5432i	0.112781	−	0.0651140i
$424$	−283.749	−	491.468i	−0.669220	−	1.15912i
$425$	−44.9483	−	25.9509i	−0.105761	−	0.0610610i
$426$			55.8006i			0.130987i
$427$	−50.2302	+	48.7632i	−0.117635	+	0.114200i
$428$	107.209			0.250489
$429$	−74.7789	+	129.521i	−0.174310	+	0.301914i
$430$	−0.965608	+	0.557494i	−0.00224560	+	0.00129650i
$431$	−23.4364	−	40.5930i	−0.0543768	−	0.0941833i	0.837556	−	0.546352i	$-0.183984\pi$
$431$	−23.4364	−	40.5930i	−0.0543768	−	0.0941833i	−0.891932	+	0.452169i	$0.850651\pi$
$432$	−74.8992	−	43.2431i	−0.173378	−	0.100100i
$433$			236.997i			0.547336i	0.961824	+	0.273668i	$0.0882370\pi$
$433$			236.997i			0.547336i	−0.961824	+	0.273668i	$0.911763\pi$
$434$	160.621	+	45.5994i	0.370094	+	0.105068i
$435$	−23.2624			−0.0534767
$436$	−179.941	+	311.666i	−0.412708	+	0.714831i
$437$	−236.523	+	136.557i	−0.541242	+	0.312486i
$438$	−15.2736	−	26.4546i	−0.0348712	−	0.0603987i
$439$	−407.579	−	235.316i	−0.928426	−	0.536027i	−0.0421125	−	0.999113i	$-0.513409\pi$
$439$	−407.579	−	235.316i	−0.928426	−	0.536027i	−0.886313	+	0.463086i	$0.846742\pi$
$440$			187.084i			0.425190i
$441$	373.468	−	201.109i	0.846867	−	0.456030i
$442$	−156.499			−0.354071
$443$	−388.020	+	672.071i	−0.875892	+	1.51709i	−0.0200827	+	0.999798i	$0.506393\pi$
$443$	−388.020	+	672.071i	−0.875892	+	1.51709i	−0.855809	+	0.517291i	$0.826940\pi$
$444$	−58.2190	+	33.6127i	−0.131124	+	0.0757043i
$445$	−88.6441	−	153.536i	−0.199200	−	0.345025i
$446$	−41.7676	−	24.1146i	−0.0936494	−	0.0540685i
$447$			83.1486i			0.186015i
$448$	−15.3436	+	54.0467i	−0.0342491	+	0.120640i
$449$	−703.730			−1.56733			−0.783664	−	0.621185i	$-0.786652\pi$
$449$	−703.730			−1.56733			−0.783664	+	0.621185i	$0.786652\pi$
$450$	17.7764	−	30.7896i	0.0395031	−	0.0684213i
$451$	160.777	−	92.8247i	0.356490	−	0.205820i
$452$	15.4264	+	26.7194i	0.0341293	+	0.0591136i
$453$	−86.1002	−	49.7100i	−0.190067	−	0.109735i
$454$		−	268.670i		−	0.591784i
$455$	−200.116	−	206.136i	−0.439815	−	0.453046i
$456$	−99.4446			−0.218080
$457$	135.348	−	234.430i	0.296166	−	0.512975i	−0.679089	−	0.734056i	$-0.737625\pi$
$457$	135.348	−	234.430i	0.296166	−	0.512975i	0.975256	+	0.221081i	$0.0709584\pi$
$458$	234.487	−	135.381i	0.511980	−	0.295592i
$459$	−53.7012	−	93.0133i	−0.116996	−	0.202643i
$460$	−62.3566	−	36.0016i	−0.135558	−	0.0782644i
$461$		−	797.922i		−	1.73085i	−0.501038	−	0.865425i	$-0.667048\pi$
$461$		−	797.922i		−	1.73085i	0.501038	−	0.865425i	$-0.332952\pi$
$462$	−11.4540	−	45.4292i	−0.0247923	−	0.0983315i
$463$	110.147			0.237899			0.118949	−	0.992900i	$-0.462047\pi$
$463$	110.147			0.237899			0.118949	+	0.992900i	$0.462047\pi$
$464$	74.1975	−	128.514i	0.159908	−	0.276970i
$465$	32.9526	−	19.0252i	0.0708658	−	0.0409144i
$466$	88.0339	+	152.479i	0.188914	+	0.327208i
$467$	170.212	+	98.2720i	0.364480	+	0.210433i	0.671044	−	0.741417i	$-0.265846\pi$
$467$	170.212	+	98.2720i	0.364480	+	0.210433i	−0.306564	+	0.951850i	$0.599179\pi$
$468$			528.352i			1.12896i
$469$	191.419	−	48.2625i	0.408144	−	0.102905i
$470$	11.6879			0.0248679
$471$	50.4662	−	87.4099i	0.107147	−	0.185584i
$472$	24.0109	−	13.8627i	0.0508705	−	0.0293701i
$473$	−4.22056	−	7.31022i	−0.00892296	−	0.0154550i
$474$	1.80916	+	1.04452i	0.00381678	+	0.00220362i
$475$			141.019i			0.296881i
$476$	−173.367	+	168.304i	−0.364217	+	0.353580i
$477$	−816.454			−1.71164
$478$	−39.5117	+	68.4362i	−0.0826604	+	0.143172i
$479$	112.472	−	64.9359i	0.234806	−	0.135566i	−0.377981	−	0.925813i	$-0.623382\pi$
$479$	112.472	−	64.9359i	0.234806	−	0.135566i	0.612787	+	0.790248i	$0.290048\pi$
$480$	−20.2668	−	35.1031i	−0.0422225	−	0.0731315i
$481$	548.383	+	316.609i	1.14009	+	0.658231i
$482$			90.8097i			0.188402i
$483$	38.2117	+	10.8481i	0.0791133	+	0.0224599i
$484$	−240.579			−0.497065
$485$	17.5875	−	30.4624i	0.0362628	−	0.0628090i
$486$	96.1907	−	55.5357i	0.197923	−	0.114271i
$487$	92.6324	+	160.444i	0.190210	+	0.329454i	0.945320	−	0.326145i	$-0.105750\pi$
$487$	92.6324	+	160.444i	0.190210	+	0.329454i	−0.755110	+	0.655599i	$0.772416\pi$
$488$	52.1137	+	30.0879i	0.106790	+	0.0616555i
$489$			45.3088i			0.0926560i
$490$	89.9592	+	2.66671i	0.183590	+	0.00544227i
$491$	−153.060			−0.311731			−0.155866	−	0.987778i	$-0.549817\pi$
$491$	−153.060			−0.311731			−0.155866	+	0.987778i	$0.549817\pi$
$492$	−13.0082	+	22.5309i	−0.0264395	+	0.0457946i
$493$	159.594	−	92.1419i	0.323721	−	0.186900i
$494$	212.607	+	368.245i	0.430378	+	0.745436i
$495$	233.095	+	134.578i	0.470900	+	0.271874i
$496$			242.731i			0.489376i
$497$	221.622	−	780.649i	0.445920	−	1.57072i
$498$	60.8104			0.122109
$499$	41.5314	−	71.9345i	0.0832293	−	0.144157i	−0.821406	−	0.570344i	$-0.806810\pi$
$499$	41.5314	−	71.9345i	0.0832293	−	0.144157i	0.904635	+	0.426187i	$0.140143\pi$
$500$	−32.1971	+	18.5890i	−0.0643942	+	0.0371780i
$501$	28.9567	+	50.1545i	0.0577979	+	0.100109i
$502$	−75.1845	−	43.4078i	−0.149770	−	0.0864697i
$503$		−	365.831i		−	0.727298i	−0.931536	−	0.363649i	$-0.881531\pi$
$503$		−	365.831i		−	0.727298i	0.931536	−	0.363649i	$-0.118469\pi$
$504$	−253.969	−	261.609i	−0.503906	−	0.519065i
$505$	397.791			0.787704
$506$	−55.3008	+	95.7838i	−0.109290	+	0.189296i
$507$	−85.2027	+	49.1918i	−0.168053	+	0.0970252i
$508$	−132.804	−	230.023i	−0.261424	−	0.452800i
$509$	60.3516	+	34.8440i	0.118569	+	0.0684558i	0.558112	−	0.829766i	$-0.311526\pi$
$509$	60.3516	+	34.8440i	0.118569	+	0.0684558i	−0.439543	+	0.898222i	$0.644859\pi$
$510$		−	11.1724i		−	0.0219067i
$511$	108.608	+	430.761i	0.212539	+	0.842977i
$512$	459.752			0.897953
$513$	−145.908	+	252.719i	−0.284420	+	0.492630i
$514$	68.6225	−	39.6192i	0.133507	−	0.0770802i
$515$	−177.047	−	306.655i	−0.343781	−	0.595447i
$516$	1.02444	+	0.591460i	0.00198535	+	0.00114624i
$517$			88.4844i			0.171150i
$518$	−192.344	+	48.4957i	−0.371321	+	0.0936210i
$519$	134.198			0.258570
$520$	−123.475	+	213.866i	−0.237453	+	0.411280i
$521$	−195.847	+	113.072i	−0.375906	+	0.217029i	−0.676036	−	0.736869i	$-0.736303\pi$
$521$	−195.847	+	113.072i	−0.375906	+	0.217029i	0.300130	+	0.953898i	$0.402970\pi$
$522$	63.1172	+	109.322i	0.120914	+	0.209429i
$523$	−80.5280	−	46.4929i	−0.153973	−	0.0888965i	0.421034	−	0.907045i	$-0.361667\pi$
$523$	−80.5280	−	46.4929i	−0.153973	−	0.0888965i	−0.575007	+	0.818148i	$0.695001\pi$
$524$			346.245i			0.660773i
$525$	14.7159	−	14.2862i	0.0280304	−	0.0272118i
$526$	252.956			0.480906
$527$	−150.717	+	261.050i	−0.285991	+	0.495350i
$528$	58.9848	−	34.0549i	0.111714	−	0.0644979i
$529$	217.614	+	376.919i	0.411369	+	0.712512i
$530$	−150.022	−	86.6152i	−0.283060	−	0.163425i
$531$		−	39.8882i		−	0.0751191i
$532$	631.544	+	179.292i	1.18711	+	0.337015i
$533$	245.058			0.459770
$534$	19.0816	−	33.0503i	0.0357333	−	0.0618919i
$535$	62.4335	−	36.0460i	0.116698	−	0.0673757i
$536$	−84.8441	−	146.954i	−0.158291	−	0.274169i
$537$	−90.4143	−	52.2007i	−0.168369	−	0.0972080i
$538$			81.9219i			0.152271i
$539$	−20.1886	+	681.044i	−0.0374556	+	1.26353i
$540$	−76.9339			−0.142470
$541$	309.106	−	535.388i	0.571361	−	0.989626i	−0.425066	−	0.905162i	$-0.639749\pi$
$541$	309.106	−	535.388i	0.571361	−	0.989626i	0.996427	−	0.0844635i	$-0.0269177\pi$
$542$	158.341	−	91.4184i	0.292143	−	0.168669i
$543$	41.4557	+	71.8033i	0.0763456	+	0.132234i
$544$	278.086	+	160.553i	0.511188	+	0.295134i
$545$			241.999i			0.444035i
$546$	16.8896	−	59.4923i	0.0309333	−	0.108960i
$547$	231.726			0.423631			0.211815	−	0.977310i	$-0.432062\pi$
$547$	231.726			0.423631			0.211815	+	0.977310i	$0.432062\pi$
$548$	233.343	−	404.161i	0.425808	−	0.737520i
$549$	74.9755	−	43.2871i	0.136567	−	0.0788472i
$550$	28.5539	+	49.4568i	0.0519162	+	0.0899214i
$551$	−433.622	−	250.352i	−0.786973	−	0.454359i
$552$		−	34.1438i		−	0.0618546i
$553$	−21.1615	−	21.7981i	−0.0382668	−	0.0394180i
$554$	−420.701			−0.759388
$555$	−22.6026	+	39.1488i	−0.0407254	+	0.0705384i
$556$	−13.1187	+	7.57407i	−0.0235947	+	0.0136224i
$557$	51.2388	+	88.7482i	0.0919907	+	0.159333i	0.908349	−	0.418214i	$-0.137344\pi$
$557$	51.2388	+	88.7482i	0.0919907	+	0.159333i	−0.816358	+	0.577546i	$0.804010\pi$
$558$	−178.819	−	103.241i	−0.320464	−	0.185020i
$559$		−	11.1423i		−	0.0199326i
$560$	31.9867	+	126.866i	0.0571190	+	0.226546i
$561$	84.5818			0.150770
$562$	52.8516	−	91.5416i	0.0940419	−	0.162885i
$563$	32.6517	−	18.8515i	0.0579960	−	0.0334840i	−0.470722	−	0.882282i	$-0.656006\pi$
$563$	32.6517	−	18.8515i	0.0579960	−	0.0334840i	0.528718	+	0.848798i	$0.322673\pi$
$564$	−6.20000	−	10.7387i	−0.0109929	−	0.0190403i
$565$	17.9672	+	10.3734i	0.0318004	+	0.0183599i
$566$			300.246i			0.530470i
$567$	−487.663	+	122.954i	−0.860076	+	0.216851i
$568$	−697.542			−1.22807
$569$	−2.85069	+	4.93754i	−0.00501000	+	0.00867758i	−0.868520	−	0.495655i	$-0.834928\pi$
$569$	−2.85069	+	4.93754i	−0.00501000	+	0.00867758i	0.863510	+	0.504333i	$0.168261\pi$
$570$	−26.2889	+	15.1779i	−0.0461208	+	0.0266279i
$571$	−226.209	−	391.805i	−0.396162	−	0.686173i	0.597087	−	0.802177i	$-0.296325\pi$
$571$	−226.209	−	391.805i	−0.396162	−	0.686173i	−0.993249	+	0.116004i	$0.962992\pi$
$572$	−734.981	−	424.342i	−1.28493	−	0.741856i
$573$			59.9747i			0.104668i
$574$	−55.0811	+	53.4725i	−0.0959601	+	0.0931576i
$575$	−48.4179			−0.0842051
$576$	34.7393	−	60.1702i	0.0603112	−	0.104462i
$577$	−368.185	+	212.572i	−0.638102	+	0.368408i	−0.783883	−	0.620908i	$-0.786764\pi$
$577$	−368.185	+	212.572i	−0.638102	+	0.368408i	0.145781	+	0.989317i	$0.453431\pi$
$578$	−74.4387	−	128.932i	−0.128787	−	0.223065i
$579$	111.308	+	64.2637i	0.192242	+	0.110991i
$580$		−	132.005i		−	0.227595i
$581$	−850.735	−	241.520i	−1.46426	−	0.415696i
$582$	7.57178			0.0130099
$583$	655.728	−	1135.75i	1.12475	−	1.94812i
$584$	330.699	−	190.929i	0.566265	−	0.326934i
$585$	177.643	+	307.686i	0.303663	+	0.525960i
$586$	−274.587	−	158.533i	−0.468579	−	0.270534i
$587$			870.286i			1.48260i	0.671174	+	0.741300i	$0.265790\pi$
$587$			870.286i			1.48260i	−0.671174	+	0.741300i	$0.734210\pi$
$588$	−45.2699	−	84.0681i	−0.0769896	−	0.142973i
$589$	819.004			1.39050
$590$	4.23162	−	7.32939i	0.00717225	−	0.0124227i
$591$	44.7248	−	25.8219i	0.0756765	−	0.0436919i
$592$	−144.186	−	249.738i	−0.243558	−	0.421854i
$593$	−380.569	−	219.722i	−0.641769	−	0.370526i	0.143526	−	0.989646i	$-0.454156\pi$
$593$	−380.569	−	219.722i	−0.641769	−	0.370526i	−0.785296	+	0.619121i	$0.787489\pi$
$594$			118.175i			0.198948i
$595$	−44.3733	+	156.302i	−0.0745770	+	0.262692i
$596$	−471.836			−0.791672
$597$	85.8573	−	148.709i	0.143815	−	0.249094i
$598$	−126.435	+	72.9972i	−0.211430	+	0.122069i
$599$	151.024	+	261.582i	0.252127	+	0.436697i	0.964111	−	0.265498i	$-0.0855365\pi$
$599$	151.024	+	261.582i	0.252127	+	0.436697i	−0.711984	+	0.702196i	$0.752203\pi$
$600$	−15.2678	−	8.81485i	−0.0254463	−	0.0146914i
$601$		−	122.146i		−	0.203238i	−0.994823	−	0.101619i	$-0.967598\pi$
$601$		−	122.146i		−	0.203238i	0.994823	−	0.101619i	$-0.0324022\pi$
$602$	2.43129	+	2.50443i	0.00403869	+	0.00416018i
$603$	−244.129			−0.404857
$604$	282.085	−	488.586i	0.467028	−	0.808917i
$605$	−140.102	+	80.8877i	−0.231573	+	0.133699i
$606$	42.8143	+	74.1566i	0.0706507	+	0.122371i
$607$	−470.749	−	271.787i	−0.775534	−	0.447755i	0.0593113	−	0.998240i	$-0.481110\pi$
$607$	−470.749	−	271.787i	−0.775534	−	0.447755i	−0.834845	+	0.550485i	$0.814443\pi$
$608$		−	872.453i		−	1.43496i
$609$	17.8036	+	70.6129i	0.0292341	+	0.115949i
$610$	18.3688			0.0301128
$611$	−58.3998	+	101.151i	−0.0955807	+	0.165551i
$612$	258.775	−	149.404i	0.422835	−	0.244124i
$613$	−43.1213	−	74.6883i	−0.0703447	−	0.121841i	0.828708	−	0.559682i	$-0.189077\pi$
$613$	−43.1213	−	74.6883i	−0.0703447	−	0.121841i	−0.899052	+	0.437841i	$0.855743\pi$
$614$	208.587	+	120.428i	0.339718	+	0.196136i
$615$			17.4945i			0.0284464i
$616$	567.892	−	143.182i	0.921903	−	0.232439i
$617$	1023.35			1.65859			0.829295	−	0.558811i	$-0.188742\pi$
$617$	1023.35			1.65859			0.829295	+	0.558811i	$0.188742\pi$
$618$	38.1113	−	66.0107i	0.0616688	−	0.106814i
$619$	−855.637	+	494.002i	−1.38229	+	0.798065i	−0.992430	−	0.122809i	$-0.960810\pi$
$619$	−855.637	+	494.002i	−1.38229	+	0.798065i	−0.389859	+	0.920874i	$0.627476\pi$
$620$	107.961	+	186.993i	0.174130	+	0.301602i
$621$	−86.7698	−	50.0966i	−0.139726	−	0.0806708i
$622$		−	277.842i		−	0.446692i
$623$	−398.216	+	386.586i	−0.639191	+	0.620524i
$624$	89.9051			0.144079
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	244.775	−	141.321i	0.391015	−	0.225752i
$627$	−114.905	−	199.022i	−0.183262	−	0.317420i
$628$	496.018	+	286.376i	0.789837	+	0.456013i
$629$		−	358.114i		−	0.569339i
$630$	−107.067	−	30.3957i	−0.169947	−	0.0482471i
$631$	609.385			0.965746			0.482873	−	0.875691i	$-0.339593\pi$
$631$	609.385			0.965746			0.482873	+	0.875691i	$0.339593\pi$
$632$	−13.0571	+	22.6155i	−0.0206600	+	0.0357841i
$633$	−48.8756	+	28.2183i	−0.0772127	+	0.0445787i
$634$	59.7201	+	103.438i	0.0941957	+	0.163152i
$635$	−154.677	−	89.3026i	−0.243585	−	0.140634i
$636$			183.785i			0.288969i
$637$	−472.569	+	765.215i	−0.741866	+	1.20128i
$638$	−202.768			−0.317818
$639$	−501.773	+	869.096i	−0.785247	+	1.36009i
$640$	252.380	−	145.712i	0.394344	−	0.227675i
$641$	495.827	+	858.798i	0.773522	+	1.33978i	0.935622	+	0.353005i	$0.114840\pi$
$641$	495.827	+	858.798i	0.773522	+	1.33978i	−0.162100	+	0.986774i	$0.551827\pi$
$642$	13.4395	+	7.75928i	0.0209338	+	0.0120861i
$643$		−	223.149i		−	0.347044i	−0.984830	−	0.173522i	$-0.944485\pi$
$643$		−	223.149i		−	0.347044i	0.984830	−	0.173522i	$-0.0555148\pi$
$644$	−61.5589	+	216.837i	−0.0955884	+	0.336703i
$645$	0.795444			0.00123325
$646$	120.239	−	208.260i	0.186128	−	0.322383i
$647$	89.1511	−	51.4714i	0.137792	−	0.0795540i	−0.429520	−	0.903058i	$-0.641317\pi$
$647$	89.1511	−	51.4714i	0.137792	−	0.0795540i	0.567311	+	0.823504i	$0.307984\pi$
$648$	216.150	+	374.383i	0.333565	+	0.577752i
$649$	55.4878	+	32.0359i	0.0854974	+	0.0493619i
$650$			75.3824i			0.115973i
$651$	−82.9709	−	85.4669i	−0.127451	−	0.131286i
$652$	−257.110			−0.394340
$653$	−138.978	+	240.717i	−0.212830	+	0.368633i	−0.952599	−	0.304228i	$-0.901601\pi$
$653$	−138.978	+	240.717i	−0.212830	+	0.368633i	0.739769	+	0.672861i	$0.234935\pi$
$654$	−45.1137	+	26.0464i	−0.0689812	+	0.0398263i
$655$	116.415	+	201.636i	0.177732	+	0.307841i
$656$	−96.6494	−	55.8005i	−0.147331	−	0.0850618i
$657$		−	549.376i		−	0.836188i
$658$	−8.94522	−	35.4787i	−0.0135946	−	0.0539189i
$659$	−157.660			−0.239241			−0.119621	−	0.992820i	$-0.538168\pi$
$659$	−157.660			−0.239241			−0.119621	+	0.992820i	$0.538168\pi$
$660$	30.2936	−	52.4700i	0.0458993	−	0.0795000i
$661$	275.782	−	159.223i	0.417219	−	0.240881i	−0.276668	−	0.960966i	$-0.589230\pi$
$661$	275.782	−	159.223i	0.417219	−	0.240881i	0.693887	+	0.720084i	$0.255897\pi$
$662$	79.6706	+	137.993i	0.120348	+	0.208449i
$663$	96.6902	+	55.8241i	0.145837	+	0.0841993i
$664$			760.167i			1.14483i
$665$	428.062	−	107.927i	0.643702	−	0.162296i
$666$	245.308			0.368330
$667$	85.9569	−	148.882i	0.128871	−	0.223211i
$668$	−284.608	+	164.318i	−0.426060	+	0.245986i
$669$	17.2036	+	29.7974i	0.0257153	+	0.0445403i
$670$	−44.8582	−	25.8989i	−0.0669526	−	0.0386551i
$671$			139.063i			0.207247i
$672$	−91.0446	+	88.3857i	−0.135483	+	0.131526i
$673$	607.388			0.902508			0.451254	−	0.892396i	$-0.350977\pi$
$673$	607.388			0.902508			0.451254	+	0.892396i	$0.350977\pi$
$674$	251.014	−	434.769i	0.372425	−	0.645059i
$675$	−44.8025	+	25.8667i	−0.0663741	+	0.0383211i
$676$	−279.144	−	483.492i	−0.412936	−	0.715225i
$677$	577.532	+	333.438i	0.853075	+	0.492523i	0.861687	−	0.507440i	$-0.169408\pi$
$677$	577.532	+	333.438i	0.853075	+	0.492523i	−0.00861208	+	0.999963i	$0.502741\pi$
$678$			4.46596i			0.00658695i
$679$	−105.929	−	30.0727i	−0.156007	−	0.0442897i
$680$	139.662			0.205385
$681$	−95.8359	+	165.993i	−0.140728	+	0.243748i
$682$	287.234	−	165.835i	0.421164	−	0.243159i
$683$	609.402	+	1055.52i	0.892243	+	1.54541i	0.837180	+	0.546928i	$0.184203\pi$
$683$	609.402	+	1055.52i	0.892243	+	1.54541i	0.0550632	+	0.998483i	$0.482464\pi$
$684$	−703.098	−	405.934i	−1.02792	−	0.593470i
$685$		−	313.818i		−	0.458129i
$686$	−60.7545	−	275.112i	−0.0885634	−	0.401038i
$687$	−193.164			−0.281171
$688$	−2.53714	+	4.39446i	−0.00368771	+	0.00638730i
$689$	1499.20	−	865.563i	2.17591	−	1.25626i
$690$	−5.21124	−	9.02613i	−0.00755252	−	0.0130813i
$691$	154.574	+	89.2431i	0.223696	+	0.129151i	0.607660	−	0.794197i	$-0.292108\pi$
$691$	154.574	+	89.2431i	0.223696	+	0.129151i	−0.383965	+	0.923348i	$0.625442\pi$
$692$			761.520i			1.10046i
$693$	230.113	−	810.558i	0.332054	−	1.16964i
$694$	61.3761			0.0884382
$695$	−5.09312	+	8.82154i	−0.00732822	+	0.0126929i
$696$	54.2101	−	31.2982i	0.0778880	−	0.0449687i
$697$	−69.2957	−	120.024i	−0.0994199	−	0.172200i
$698$	−312.908	−	180.657i	−0.448292	−	0.258821i
$699$		−	125.608i		−	0.179697i
$700$	81.0686	+	83.5073i	0.115812	+	0.119296i
$701$	−770.690			−1.09941			−0.549707	−	0.835357i	$-0.685261\pi$
$701$	−770.690			−1.09941			−0.549707	+	0.835357i	$0.685261\pi$
$702$	−77.9959	+	135.093i	−0.111105	+	0.192440i
$703$	−842.647	+	486.502i	−1.19864	+	0.692037i
$704$	55.8011	+	96.6504i	0.0792630	+	0.137287i
$705$	−7.22116	−	4.16914i	−0.0102428	−	0.00591367i
$706$			557.381i			0.789491i
$707$	−304.445	−	1207.49i	−0.430615	−	1.70791i
$708$	−8.97888			−0.0126820
$709$	−168.590	+	292.007i	−0.237786	+	0.411858i	−0.960079	−	0.279730i	$-0.909755\pi$
$709$	−168.590	+	292.007i	−0.237786	+	0.411858i	0.722293	+	0.691588i	$0.243088\pi$
$710$	−184.400	+	106.463i	−0.259718	+	0.149948i
$711$	18.7851	+	32.5367i	0.0264207	+	0.0457619i
$712$	413.149	+	238.531i	0.580265	+	0.335016i
$713$			281.200i			0.394391i
$714$	−33.9139	+	8.55069i	−0.0474984	+	0.0119758i
$715$	−570.689			−0.798167
$716$	296.219	−	513.066i	0.413714	−	0.716573i
$717$	48.8230	−	28.1880i	0.0680935	−	0.0393138i
$718$	62.7850	+	108.747i	0.0874443	+	0.151458i
$719$	−847.150	−	489.102i	−1.17823	−	0.680253i	−0.222628	−	0.974903i	$-0.571464\pi$
$719$	−847.150	−	489.102i	−1.17823	−	0.680253i	−0.955605	+	0.294650i	$0.904797\pi$
$720$		−	161.800i		−	0.224722i
$721$	−795.350	+	772.122i	−1.10312	+	1.07090i
$722$	−356.857			−0.494262
$723$	32.3923	−	56.1051i	0.0448026	−	0.0776004i
$724$	−407.456	+	235.245i	−0.562785	+	0.324924i
$725$	−44.3828	−	76.8732i	−0.0612176	−	0.106032i
$726$	−30.1584	−	17.4119i	−0.0415404	−	0.0239834i
$727$		−	694.151i		−	0.954816i	−0.878682	−	0.477408i	$-0.841576\pi$
$727$		−	694.151i		−	0.954816i	0.878682	−	0.477408i	$-0.158424\pi$
$728$	743.690	+	211.130i	1.02155	+	0.290014i
$729$	567.378			0.778296
$730$	58.2817	−	100.947i	0.0798379	−	0.138283i
$731$	−5.45724	+	3.15074i	−0.00746545	+	0.00431018i
$732$	−9.74397	−	16.8771i	−0.0133114	−	0.0230561i
$733$	−741.920	−	428.348i	−1.01217	−	0.584376i	−0.100343	−	0.994953i	$-0.531994\pi$
$733$	−741.920	−	428.348i	−1.01217	−	0.584376i	−0.911826	+	0.410577i	$0.865327\pi$
$734$		−	400.912i		−	0.546202i
$735$	−54.6284	−	33.7365i	−0.0743243	−	0.0459000i
$736$	299.552			0.407000
$737$	196.070	−	339.603i	0.266038	−	0.460791i
$738$	82.2162	−	47.4675i	0.111404	−	0.0643191i
$739$	−711.481	−	1232.32i	−0.962762	−	1.66755i	−0.715511	−	0.698602i	$-0.753806\pi$
$739$	−711.481	−	1232.32i	−0.962762	−	1.66755i	−0.247251	−	0.968951i	$-0.579527\pi$
$740$	−222.154	−	128.261i	−0.300209	−	0.173326i
$741$		−	303.351i		−	0.409381i
$742$	−148.103	+	521.682i	−0.199599	+	0.703075i
$743$	236.362			0.318118			0.159059	−	0.987269i	$-0.449154\pi$
$743$	236.362			0.318118			0.159059	+	0.987269i	$0.449154\pi$
$744$	−51.1947	+	88.6718i	−0.0688101	+	0.119183i
$745$	−274.774	+	158.641i	−0.368825	+	0.212941i
$746$	−209.103	−	362.178i	−0.280300	−	0.485493i
$747$	947.124	+	546.822i	1.26790	+	0.732024i
$748$			479.969i			0.641670i
$749$	−157.200	−	161.929i	−0.209880	−	0.216194i
$750$	−5.38152			−0.00717536
$751$	−449.493	+	778.545i	−0.598527	+	1.03668i	0.394512	+	0.918891i	$0.370914\pi$
$751$	−449.493	+	778.545i	−0.598527	+	1.03668i	−0.993039	+	0.117788i	$0.962420\pi$
$752$	46.0651	−	26.5957i	0.0612568	−	0.0353666i
$753$	30.9675	+	53.6373i	0.0411255	+	0.0712315i
$754$	−231.796	−	133.827i	−0.307421	−	0.177490i
$755$		−	379.371i		−	0.502478i
$756$	58.8805	+	233.533i	0.0778842	+	0.308906i
$757$	−242.213			−0.319965			−0.159982	−	0.987120i	$-0.551144\pi$
$757$	−242.213			−0.319965			−0.159982	+	0.987120i	$0.551144\pi$
$758$	−157.505	+	272.807i	−0.207790	+	0.359903i
$759$	68.3331	−	39.4521i	0.0900304	−	0.0519791i
$760$	−189.733	−	328.627i	−0.249648	−	0.432403i
$761$	1035.15	+	597.641i	1.36024	+	0.785337i	0.989656	−	0.143461i	$-0.0458230\pi$
$761$	1035.15	+	597.641i	1.36024	+	0.785337i	0.370587	+	0.928798i	$0.379156\pi$
$762$		−	38.4467i		−	0.0504549i
$763$	734.588	−	185.211i	0.962762	−	0.242741i
$764$	−340.333			−0.445463
$765$	100.465	−	174.011i	0.131327	−	0.227465i
$766$	−430.939	+	248.803i	−0.562583	+	0.324808i
$767$	42.2875	+	73.2440i	0.0551336	+	0.0954942i
$768$	38.0350	+	21.9595i	0.0495248	+	0.0285931i
$769$		−	365.727i		−	0.475587i	−0.971316	−	0.237794i	$-0.923576\pi$
$769$		−	365.727i		−	0.475587i	0.971316	−	0.237794i	$-0.0764242\pi$
$770$	128.273	−	124.527i	0.166588	−	0.161723i
$771$	−56.5295			−0.0733197
$772$	−364.672	+	631.630i	−0.472373	+	0.818174i
$773$	−445.144	+	257.004i	−0.575866	+	0.332476i	−0.759489	−	0.650520i	$-0.774551\pi$
$773$	−445.144	+	257.004i	−0.575866	+	0.332476i	0.183623	+	0.982997i	$0.441217\pi$
$774$	−2.15826	−	3.73821i	−0.00278845	−	0.00482973i
$775$	125.742	+	72.5972i	0.162248	+	0.0936738i
$776$			94.6518i			0.121974i
$777$	136.135	+	38.6480i	0.175206	+	0.0497400i
$778$	237.377			0.305112
$779$	−188.278	+	326.107i	−0.241692	+	0.418623i
$780$	69.2605	−	39.9876i	0.0887955	−	0.0512661i
$781$	−805.990	−	1396.01i	−1.03200	−	1.78747i
$782$	71.5047	+	41.2833i	0.0914383	+	0.0527919i
$783$		−	183.686i		−	0.234593i
$784$	360.621	−	194.191i	0.459976	−	0.247693i
$785$	385.142			0.490627
$786$	−25.0595	+	43.4043i	−0.0318823	+	0.0552218i
$787$	489.379	−	282.543i	0.621828	−	0.359013i	−0.155752	−	0.987796i	$-0.549780\pi$
$787$	489.379	−	282.543i	0.621828	−	0.359013i	0.777580	+	0.628784i	$0.216447\pi$
$788$	146.529	+	253.796i	0.185951	+	0.322076i
$789$	−156.284	−	90.2308i	−0.198079	−	0.114361i
$790$			7.97142i			0.0100904i
$791$	17.7373	−	62.4786i	0.0224240	−	0.0789868i
$792$	−724.267			−0.914478
$793$	−91.7816	+	158.970i	−0.115740	+	0.200467i
$794$	−321.451	+	185.590i	−0.404850	+	0.233740i
$795$	61.7921	+	107.027i	0.0777260	+	0.134625i
$796$	843.868	+	487.207i	1.06014	+	0.612070i
$797$		−	1.99923i		−	0.00250845i	−0.999999	−	0.00125422i	$-0.999601\pi$
$797$		−	1.99923i		−	0.00250845i	0.999999	−	0.00125422i	$-0.000399232\pi$
$798$	66.1923	+	68.1836i	0.0829478	+	0.0854431i
$799$	66.0556			0.0826728
$800$	77.3350	−	133.948i	0.0966687	−	0.167435i
$801$	594.393	−	343.173i	0.742063	−	0.428430i
$802$	−138.885	−	240.556i	−0.173174	−	0.299945i
$803$	764.227	+	441.226i	0.951714	+	0.549473i
$804$			54.9536i			0.0683503i
$805$	37.0561	+	146.973i	0.0460325	+	0.182575i
$806$	437.804			0.543181
$807$	29.2219	−	50.6139i	0.0362106	−	0.0627186i
$808$	−927.002	+	535.205i	−1.14728	+	0.662383i
$809$	−270.408	−	468.360i	−0.334250	−	0.578937i	0.649091	−	0.760711i	$-0.275150\pi$
$809$	−270.408	−	468.360i	−0.334250	−	0.578937i	−0.983340	+	0.181774i	$0.941816\pi$
$810$	114.281	+	65.9804i	0.141088	+	0.0814573i
$811$			1225.35i			1.51091i	0.655200	+	0.755456i	$0.272584\pi$
$811$			1225.35i			1.51091i	−0.655200	+	0.755456i	$0.727416\pi$
$812$	−400.701	+	101.029i	−0.493474	+	0.124419i
$813$	−130.438			−0.160440
$814$	−197.017	+	341.244i	−0.242036	+	0.419218i
$815$	−149.728	+	86.4456i	−0.183716	+	0.106068i
$816$	−25.4227	−	44.0334i	−0.0311553	−	0.0539626i
$817$	14.8275	+	8.56064i	0.0181487	+	0.0104781i
$818$		−	166.897i		−	0.204031i
$819$	798.025	−	774.719i	0.974389	−	0.945933i
$820$	−99.2748			−0.121067
$821$	16.1781	−	28.0213i	0.0197054	−	0.0341307i	−0.856005	−	0.516968i	$-0.827061\pi$
$821$	16.1781	−	28.0213i	0.0197054	−	0.0341307i	0.875710	+	0.482838i	$0.160394\pi$
$822$	58.5024	−	33.7764i	0.0711708	−	0.0410905i
$823$	423.664	+	733.808i	0.514781	+	0.891626i	0.999853	+	0.0171521i	$0.00545995\pi$
$823$	423.664	+	733.808i	0.514781	+	0.891626i	−0.485072	+	0.874474i	$0.661207\pi$
$824$	825.174	+	476.415i	1.00143	+	0.578173i
$825$		−	40.7412i		−	0.0493833i
$826$	−25.4870	−	7.23563i	−0.0308559	−	0.00875984i
$827$	30.1624			0.0364721			0.0182361	−	0.999834i	$-0.494195\pi$
$827$	30.1624			0.0364721			0.0182361	+	0.999834i	$0.494195\pi$
$828$	139.375	−	241.405i	0.168327	−	0.291551i
$829$	92.4071	−	53.3513i	0.111468	−	0.0643562i	−0.443229	−	0.896408i	$-0.646167\pi$
$829$	92.4071	−	53.3513i	0.111468	−	0.0643562i	0.554698	+	0.832052i	$0.312834\pi$
$830$	116.022	+	200.955i	0.139785	+	0.242115i
$831$	259.922	+	150.066i	0.312782	+	0.180585i
$832$			147.315i			0.177062i
$833$	508.415	+	15.0712i	0.610342	+	0.0180927i
$834$	−2.19270			−0.00262913
$835$	−110.494	+	191.382i	−0.132329	+	0.229200i
$836$	1129.37	−	652.044i	1.35093	−	0.779957i
$837$	150.228	+	260.203i	0.179484	+	0.310876i
$838$	422.802	+	244.105i	0.504537	+	0.291295i
$839$		−	372.216i		−	0.443642i	−0.975087	−	0.221821i	$-0.928800\pi$
$839$		−	372.216i		−	0.443642i	0.975087	−	0.221821i	$-0.0712001\pi$
$840$	−15.0725	+	53.0917i	−0.0179434	+	0.0632044i
$841$	−525.827			−0.625241
$842$	−9.30908	+	16.1238i	−0.0110559	+	0.0191494i
$843$	−65.3067	+	37.7048i	−0.0774693	+	0.0447269i
$844$	−160.128	−	277.350i	−0.189725	−	0.328614i
$845$	−325.120	−	187.708i	−0.384758	−	0.222140i
$846$			45.2480i			0.0534847i
$847$	352.760	+	363.372i	0.416481	+	0.429010i
$848$	−788.368			−0.929679
$849$	107.099	−	185.501i	0.126147	−	0.218494i
$850$	36.9206	−	21.3161i	0.0434360	−	0.0250778i
$851$	−167.038	−	289.318i	−0.196284	−	0.339974i
$852$	195.634	+	112.950i	0.229618	+	0.132570i
$853$		−	740.832i		−	0.868502i	−0.900792	−	0.434251i	$-0.857013\pi$
$853$		−	740.832i		−	0.868502i	0.900792	−	0.434251i	$-0.142987\pi$
$854$	−14.0584	−	55.7585i	−0.0164618	−	0.0652910i
$855$	−545.933			−0.638518
$856$	−96.9957	+	168.002i	−0.113313	+	0.196263i
$857$	−648.162	+	374.216i	−0.756315	+	0.436659i	−0.827971	−	0.560771i	$-0.810505\pi$
$857$	−648.162	+	374.216i	−0.756315	+	0.436659i	0.0716563	+	0.997429i	$0.477172\pi$
$858$	−61.4235	−	106.389i	−0.0715892	−	0.123996i
$859$	−29.5865	−	17.0817i	−0.0344429	−	0.0198856i	0.482680	−	0.875797i	$-0.339664\pi$
$859$	−29.5865	−	17.0817i	−0.0344429	−	0.0198856i	−0.517123	+	0.855911i	$0.672997\pi$
$860$			4.51384i			0.00524865i
$861$	53.1047	−	13.3893i	0.0616779	−	0.0155508i
$862$	38.5014			0.0446651
$863$	67.3566	−	116.665i	0.0780493	−	0.135185i	−0.824359	−	0.566067i	$-0.808464\pi$
$863$	67.3566	−	116.665i	0.0780493	−	0.135185i	0.902408	+	0.430882i	$0.141797\pi$
$864$	277.184	−	160.032i	0.320815	−	0.185223i
$865$	256.039	+	443.472i	0.295998	+	0.512684i
$866$	−168.589	−	97.3346i	−0.194675	−	0.112396i
$867$			106.211i			0.122503i
$868$	484.992	−	470.828i	0.558746	−	0.542428i
$869$	−60.3484			−0.0694458
$870$	9.55386	−	16.5478i	0.0109815	−	0.0190204i
$871$	448.277	−	258.813i	0.514669	−	0.297145i
$872$	−325.596	−	563.949i	−0.373390	−	0.646731i
$873$	117.931	+	68.0873i	0.135087	+	0.0779923i
$874$		−	224.335i		−	0.256677i
$875$	75.2872	+	21.3737i	0.0860425	+	0.0244270i
$876$	−123.665			−0.141170
$877$	−93.9312	+	162.694i	−0.107105	+	0.185512i	−0.914596	−	0.404368i	$-0.867491\pi$
$877$	−93.9312	+	162.694i	−0.107105	+	0.185512i	0.807491	+	0.589880i	$0.200825\pi$
$878$	334.786	−	193.289i	0.381305	−	0.220147i
$879$	113.099	+	195.893i	0.128668	+	0.222859i
$880$	225.077	+	129.948i	0.255769	+	0.147668i
$881$			1388.35i			1.57588i	0.615749	+	0.787942i	$0.288853\pi$
$881$			1388.35i			1.57588i	−0.615749	+	0.787942i	$0.711147\pi$
$882$	−10.3238	+	348.264i	−0.0117050	+	0.394857i
$883$	−496.627			−0.562432			−0.281216	−	0.959645i	$-0.590738\pi$
$883$	−496.627			−0.562432			−0.281216	+	0.959645i	$0.590738\pi$
$884$	−316.780	+	548.680i	−0.358349	+	0.620679i
$885$	−5.22886	+	3.01888i	−0.00590831	+	0.00341117i
$886$	−318.720	−	552.040i	−0.359729	−	0.623070i
$887$	−961.181	−	554.938i	−1.08363	−	0.625635i	−0.151758	−	0.988418i	$-0.548493\pi$
$887$	−961.181	−	554.938i	−1.08363	−	0.625635i	−0.931874	+	0.362783i	$0.881827\pi$
$888$		−	121.642i		−	0.136984i
$889$	−152.698	+	537.867i	−0.171764	+	0.605025i
$890$	145.625			0.163623
$891$	−499.511	+	865.178i	−0.560618	+	0.971019i
$892$	−169.089	+	97.6236i	−0.189562	+	0.109443i
$893$	−89.7373	−	155.430i	−0.100490	−	0.174053i
$894$	−59.1481	−	34.1492i	−0.0661612	−	0.0381982i
$895$		−	398.380i		−	0.445117i
$896$	−635.464	−	654.581i	−0.709224	−	0.730559i
$897$	104.154			0.116114
$898$	289.022	−	500.602i	0.321851	−	0.557463i
$899$	−446.462	+	257.765i	−0.496621	+	0.286724i
$900$	−71.9646	−	124.646i	−0.0799606	−	0.138496i
$901$	−847.866	−	489.516i	−0.941028	−	0.543303i
$902$			152.493i			0.169061i
$903$	−0.608784	−	2.41457i	−0.000674179	−	0.00267394i
$904$	−55.8272			−0.0617557
$905$	−158.188	+	273.990i	−0.174794	+	0.302752i
$906$	70.7228	−	40.8319i	0.0780605	−	0.0450683i
$907$	−265.494	−	459.848i	−0.292716	−	0.506999i	0.681735	−	0.731599i	$-0.261226\pi$
$907$	−265.494	−	459.848i	−0.292716	−	0.506999i	−0.974451	+	0.224600i	$0.927892\pi$
$908$	−941.945	−	543.832i	−1.03738	−	0.598934i
$909$			1539.99i			1.69416i
$910$	228.823	−	57.6931i	0.251454	−	0.0633990i
$911$	861.264			0.945405			0.472703	−	0.881222i	$-0.343278\pi$
$911$	861.264			0.945405			0.472703	+	0.881222i	$0.343278\pi$
$912$	−69.0742	+	119.640i	−0.0757392	+	0.131184i
$913$	−1521.35	+	878.351i	−1.66632	+	0.962050i
$914$	111.175	+	192.561i	0.121636	+	0.210679i
$915$	−11.3488	−	6.55225i	−0.0124031	−	0.00716092i
$916$		−	1096.13i		−	1.19665i
$917$	522.970	−	507.697i	0.570305	−	0.553650i
$918$	88.2205			0.0961008
$919$	361.705	−	626.491i	0.393585	−	0.681710i	−0.599334	−	0.800499i	$-0.704568\pi$
$919$	361.705	−	626.491i	0.393585	−	0.681710i	0.992920	+	0.118789i	$0.0379012\pi$
$920$	112.832	−	65.1436i	0.122644	−	0.0708083i
$921$	−85.9143	−	148.808i	−0.0932838	−	0.161572i
$922$	567.605	+	327.707i	0.615624	+	0.355431i
$923$		−	2127.82i		−	2.30533i
$924$	−182.457	−	51.7987i	−0.197465	−	0.0560592i
$925$	−172.496			−0.186482
$926$	−45.2375	+	78.3536i	−0.0488526	+	0.0846151i
$927$	1187.17	−	685.413i	1.28066	−	0.739388i
$928$	274.587	+	475.599i	0.295891	+	0.512499i
$929$	1268.22	+	732.209i	1.36515	+	0.788168i	0.990304	−	0.138919i	$-0.0443629\pi$
$929$	1268.22	+	732.209i	1.36515	+	0.788168i	0.374844	+	0.927088i	$0.377696\pi$
$930$			31.2546i			0.0336071i
$931$	−655.225	−	1216.78i	−0.703786	−	1.30696i
$932$	712.780			0.764785
$933$	−99.1077	+	171.660i	−0.106225	+	0.183987i
$934$	−139.812	+	80.7208i	−0.149692	+	0.0864248i
$935$	161.376	+	279.511i	0.172594	+	0.298942i
$936$	−827.950	−	478.017i	−0.884562	−	0.510702i
$937$		−	526.823i		−	0.562245i	−0.959672	−	0.281122i	$-0.909293\pi$
$937$		−	526.823i		−	0.562245i	0.959672	−	0.281122i	$-0.0907067\pi$
$938$	−44.2844	+	155.989i	−0.0472115	+	0.166299i
$939$	−201.640			−0.214739
$940$	23.6582	−	40.9773i	0.0251683	−	0.0435929i
$941$	−138.148	+	79.7597i	−0.146810	+	0.0847606i	−0.571605	−	0.820529i	$-0.693679\pi$
$941$	−138.148	+	79.7597i	−0.146810	+	0.0847606i	0.424796	+	0.905289i	$0.360346\pi$
$942$	41.4530	+	71.7986i	0.0440053	+	0.0762194i
$943$	−111.967	−	64.6442i	−0.118735	−	0.0685517i
$944$		−	38.5161i		−	0.0408009i
$945$	112.808	+	116.201i	0.119373	+	0.122964i
$946$	6.93354			0.00732933
$947$	−367.974	+	637.350i	−0.388568	+	0.673020i	−0.992257	−	0.124200i	$-0.960364\pi$
$947$	−367.974	+	637.350i	−0.388568	+	0.673020i	0.603689	+	0.797220i	$0.293697\pi$
$948$	7.32405	−	4.22854i	0.00772579	−	0.00446049i
$949$	582.420	+	1008.78i	0.613720	+	1.06299i
$950$	−100.314	−	57.9164i	−0.105594	−	0.0609646i
$951$		−	85.2098i		−	0.0896002i
$952$	−106.889	−	423.944i	−0.112278	−	0.445319i
$953$	−1266.14			−1.32858			−0.664290	−	0.747475i	$-0.731266\pi$
$953$	−1266.14			−1.32858			−0.664290	+	0.747475i	$0.731266\pi$
$954$	335.318	−	580.788i	0.351486	−	0.608792i
$955$	−198.194	+	114.427i	−0.207532	+	0.119819i
$956$	159.956	+	277.052i	0.167318	+	0.289803i
$957$	125.276	+	72.3284i	0.130905	+	0.0755782i
$958$			106.677i			0.111354i
$959$	−952.595	+	240.177i	−0.993321	+	0.250446i
$960$	−10.5168			−0.0109550
$961$	−58.8720	+	101.969i	−0.0612611	+	0.106107i
$962$	−450.443	+	260.063i	−0.468236	+	0.270336i
$963$	139.547	+	241.702i	0.144908	+	0.250989i
$964$	318.375	+	183.814i	0.330264	+	0.190678i
$965$			490.441i			0.508229i
$966$	−23.4104	+	22.7268i	−0.0242344	+	0.0235267i
$967$	721.006			0.745611			0.372806	−	0.927910i	$-0.378396\pi$
$967$	721.006			0.745611			0.372806	+	0.927910i	$0.378396\pi$
$968$	217.660	−	376.998i	0.224855	−	0.389460i
$969$	−148.574	+	85.7795i	−0.153328	+	0.0885237i
$970$	14.4464	+	25.0218i	0.0148932	+	0.0257957i
$971$	1137.58	+	656.779i	1.17155	+	0.676395i	0.954045	−	0.299664i	$-0.0968746\pi$
$971$	1137.58	+	656.779i	1.17155	+	0.676395i	0.217506	+	0.976059i	$0.430208\pi$
$972$		−	449.653i		−	0.462606i
$973$	30.6757	+	8.70868i	0.0315270	+	0.00895034i
$974$	−152.177			−0.156239
$975$	26.8893	−	46.5736i	0.0275788	−	0.0477678i
$976$	72.3963	−	41.7980i	0.0741766	−	0.0428259i
$977$	−583.442	−	1010.55i	−0.597177	−	1.03434i	−0.993236	−	0.116116i	$-0.962956\pi$
$977$	−583.442	−	1010.55i	−0.597177	−	1.03434i	0.396059	−	0.918225i	$-0.370378\pi$
$978$	−32.2306	−	18.6083i	−0.0329556	−	0.0190269i
$979$			1102.47i			1.12611i
$980$	191.442	−	309.995i	0.195348	−	0.316321i
$981$	−936.863			−0.955009
$982$	62.8618	−	108.880i	0.0640141	−	0.110876i
$983$	1426.30	−	823.472i	1.45096	−	0.837713i	0.452425	−	0.891802i	$-0.350559\pi$
$983$	1426.30	−	823.472i	1.45096	−	0.837713i	0.998536	+	0.0540892i	$0.0172255\pi$
$984$	−23.5379	−	40.7689i	−0.0239207	−	0.0414318i
$985$	170.663	+	98.5323i	0.173262	+	0.100033i
$986$			151.371i			0.153520i
$987$	−7.12878	+	25.1106i	−0.00722267	+	0.0254414i
$988$	1721.40			1.74231
$989$	−2.93925	+	5.09093i	−0.00297194	+	0.00514755i
$990$	−191.465	+	110.542i	−0.193399	+	0.111659i
$991$	275.595	+	477.344i	0.278097	+	0.481679i	0.970912	−	0.239437i	$-0.0769629\pi$
$991$	275.595	+	477.344i	0.278097	+	0.481679i	−0.692814	+	0.721116i	$0.743630\pi$
$992$	−777.940	−	449.144i	−0.784214	−	0.452766i
$993$		−	113.675i		−	0.114477i
$994$	464.297	+	478.265i	0.467100	+	0.481152i
$995$	655.236			0.658529
$996$	123.090	−	213.198i	0.123585	−	0.214055i
$997$	469.250	−	270.922i	0.470662	−	0.271737i	−0.245855	−	0.969307i	$-0.579069\pi$
$997$	469.250	−	270.922i	0.470662	−	0.271737i	0.716517	+	0.697570i	$0.245735\pi$
$998$	34.1140	+	59.0871i	0.0341823	+	0.0592055i
$999$	−309.130	−	178.476i	−0.309439	−	0.178655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.h.a.26.3	✓	12
3.2	odd	2		315.3.w.c.271.4		12
4.3	odd	2		560.3.bx.c.481.3		12
5.2	odd	4		175.3.j.b.124.5		24
5.3	odd	4		175.3.j.b.124.8		24
5.4	even	2		175.3.i.d.26.4		12
7.2	even	3		245.3.d.a.146.8		12
7.3	odd	6	inner	35.3.h.a.31.3	yes	12
7.4	even	3		245.3.h.c.31.3		12
7.5	odd	6		245.3.d.a.146.7		12
7.6	odd	2		245.3.h.c.166.3		12
21.17	even	6		315.3.w.c.136.4		12
28.3	even	6		560.3.bx.c.241.3		12
35.3	even	12		175.3.j.b.24.5		24
35.17	even	12		175.3.j.b.24.8		24
35.24	odd	6		175.3.i.d.101.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.h.a.26.3	✓	12	1.1	even	1	trivial
35.3.h.a.31.3	yes	12	7.3	odd	6	inner
175.3.i.d.26.4		12	5.4	even	2
175.3.i.d.101.4		12	35.24	odd	6
175.3.j.b.24.5		24	35.3	even	12
175.3.j.b.24.8		24	35.17	even	12
175.3.j.b.124.5		24	5.2	odd	4
175.3.j.b.124.8		24	5.3	odd	4
245.3.d.a.146.7		12	7.5	odd	6
245.3.d.a.146.8		12	7.2	even	3
245.3.h.c.31.3		12	7.4	even	3
245.3.h.c.166.3		12	7.6	odd	2
315.3.w.c.136.4		12	21.17	even	6
315.3.w.c.271.4		12	3.2	odd	2
560.3.bx.c.241.3		12	28.3	even	6
560.3.bx.c.481.3		12	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.410701 + 0.711354i) q^{2} +(0.507487 - 0.292998i) q^{3} +(1.66265 + 2.87979i) q^{4} +(1.93649 + 1.11803i) q^{5} +0.481337i q^{6} +(1.91172 - 6.73389i) q^{7} -6.01701 q^{8} +(-4.32830 + 7.49684i) q^{9} +O(q^{10})\)	\(q+(-0.410701 + 0.711354i) q^{2} +(0.507487 - 0.292998i) q^{3} +(1.66265 + 2.87979i) q^{4} +(1.93649 + 1.11803i) q^{5} +0.481337i q^{6} +(1.91172 - 6.73389i) q^{7} -6.01701 q^{8} +(-4.32830 + 7.49684i) q^{9} +(-1.59064 + 0.918354i) q^{10} +(-6.95248 - 12.0421i) q^{11} +(1.68755 + 0.974306i) q^{12} -18.3546i q^{13} +(4.00504 + 4.12552i) q^{14} +1.31033 q^{15} +(-4.17941 + 7.23895i) q^{16} +(-8.98966 + 5.19018i) q^{17} +(-3.55527 - 6.15792i) q^{18} +(24.4251 + 14.1019i) q^{19} +7.43560i q^{20} +(-1.00284 - 3.97749i) q^{21} +11.4216 q^{22} +(-4.84179 + 8.38623i) q^{23} +(-3.05355 + 1.76297i) q^{24} +(2.50000 + 4.33013i) q^{25} +(13.0566 + 7.53824i) q^{26} +10.3467i q^{27} +(22.5707 - 5.69075i) q^{28} -17.7531 q^{29} +(-0.538152 + 0.932106i) q^{30} +(25.1484 - 14.5194i) q^{31} +(-15.4670 - 26.7896i) q^{32} +(-7.05659 - 4.07412i) q^{33} -8.52645i q^{34} +(11.2307 - 10.9028i) q^{35} -28.7858 q^{36} +(-17.2496 + 29.8772i) q^{37} +(-20.0628 + 11.5833i) q^{38} +(-5.37786 - 9.31472i) q^{39} +(-11.6519 - 6.72722i) q^{40} +13.3513i q^{41} +(3.24128 + 0.920182i) q^{42} +0.607058 q^{43} +(23.1191 - 40.0434i) q^{44} +(-16.7635 + 9.67838i) q^{45} +(-3.97705 - 6.88846i) q^{46} +(-5.51096 - 3.18175i) q^{47} +4.89823i q^{48} +(-41.6907 - 25.7466i) q^{49} -4.10701 q^{50} +(-3.04142 + 5.26790i) q^{51} +(52.8575 - 30.5173i) q^{52} +(47.1578 + 81.6798i) q^{53} +(-7.36017 - 4.24939i) q^{54} -31.0925i q^{55} +(-11.5028 + 40.5179i) q^{56} +16.5273 q^{57} +(7.29121 - 12.6287i) q^{58} +(-3.99050 + 2.30392i) q^{59} +(2.17861 + 3.77347i) q^{60} +(-8.66107 - 5.00047i) q^{61} +23.8526i q^{62} +(42.2085 + 43.4782i) q^{63} -8.02607 q^{64} +(20.5211 - 35.5435i) q^{65} +(5.79629 - 3.34649i) q^{66} +(14.1007 + 24.4231i) q^{67} +(-29.8933 - 17.2589i) q^{68} +5.67454i q^{69} +(3.14325 + 12.4668i) q^{70} +115.928 q^{71} +(26.0435 - 45.1086i) q^{72} +(-54.9607 + 31.7316i) q^{73} +(-14.1688 - 24.5411i) q^{74} +(2.53744 + 1.46499i) q^{75} +93.7858i q^{76} +(-94.3811 + 23.7963i) q^{77} +8.83476 q^{78} +(2.17003 - 3.75860i) q^{79} +(-16.1868 + 9.34545i) q^{80} +(-35.9232 - 62.2208i) q^{81} +(-9.49750 - 5.48338i) q^{82} -126.336i q^{83} +(9.78699 - 9.50116i) q^{84} -23.2112 q^{85} +(-0.249319 + 0.431833i) q^{86} +(-9.00947 + 5.20162i) q^{87} +(41.8332 + 72.4572i) q^{88} +(-68.6634 - 39.6429i) q^{89} -15.8997i q^{90} +(-123.598 - 35.0888i) q^{91} -32.2008 q^{92} +(8.50833 - 14.7369i) q^{93} +(4.52671 - 2.61350i) q^{94} +(31.5327 + 54.6163i) q^{95} +(-15.6986 - 9.06359i) q^{96} -15.7307i q^{97} +(35.4374 - 19.0827i) q^{98} +120.370 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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