LMFDB - Embedded newform 35.3.l.a.18.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(2,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("35.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			18.4
Character	$\chi$	$=$	35.18
Dual form			35.3.l.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.585559 + 0.156900i) q^{2} +(4.00038 - 1.07190i) q^{3} +(-3.14584 - 1.81625i) q^{4} +(-4.51288 + 2.15265i) q^{5} +2.51064 q^{6} +(3.65026 + 5.97291i) q^{7} +(-3.27174 - 3.27174i) q^{8} +(7.05981 - 4.07598i) q^{9} +O(q^{10})$	\(q+(0.585559 + 0.156900i) q^{2} +(4.00038 - 1.07190i) q^{3} +(-3.14584 - 1.81625i) q^{4} +(-4.51288 + 2.15265i) q^{5} +2.51064 q^{6} +(3.65026 + 5.97291i) q^{7} +(-3.27174 - 3.27174i) q^{8} +(7.05981 - 4.07598i) q^{9} +(-2.98031 + 0.552433i) q^{10} +(-2.32026 + 4.01881i) q^{11} +(-14.5314 - 3.89367i) q^{12} +(-6.67801 - 6.67801i) q^{13} +(1.20029 + 4.07021i) q^{14} +(-15.7458 + 13.4488i) q^{15} +(5.86255 + 10.1542i) q^{16} +(-4.93904 - 18.4327i) q^{17} +(4.77346 - 1.27904i) q^{18} +(22.5268 - 13.0059i) q^{19} +(18.1066 + 1.42463i) q^{20} +(21.0047 + 19.9812i) q^{21} +(-1.98920 + 1.98920i) q^{22} +(-2.06796 + 7.71775i) q^{23} +(-16.5952 - 9.58122i) q^{24} +(15.7322 - 19.4293i) q^{25} +(-2.86259 - 4.95815i) q^{26} +(-2.48344 + 2.48344i) q^{27} +(-0.634816 - 25.4196i) q^{28} +39.4447i q^{29} +(-11.3302 + 5.40453i) q^{30} +(14.1545 - 24.5164i) q^{31} +(6.62983 + 24.7428i) q^{32} +(-4.97416 + 18.5638i) q^{33} -11.5684i q^{34} +(-29.3308 - 19.0973i) q^{35} -29.6121 q^{36} +(33.9663 + 9.10125i) q^{37} +(15.2314 - 4.08125i) q^{38} +(-33.8727 - 19.5564i) q^{39} +(21.8079 + 7.72205i) q^{40} -20.8722 q^{41} +(9.16446 + 14.9958i) q^{42} +(-14.8860 - 14.8860i) q^{43} +(14.5983 - 8.42835i) q^{44} +(-23.0859 + 33.5918i) q^{45} +(-2.42183 + 4.19473i) q^{46} +(-57.3928 - 15.3783i) q^{47} +(34.3367 + 34.3367i) q^{48} +(-22.3513 + 43.6053i) q^{49} +(12.2606 - 8.90863i) q^{50} +(-39.5160 - 68.4437i) q^{51} +(8.87901 + 33.1369i) q^{52} +(-31.9412 + 8.55863i) q^{53} +(-1.84385 + 1.06455i) q^{54} +(1.81996 - 23.1311i) q^{55} +(7.59911 - 31.4845i) q^{56} +(76.1749 - 76.1749i) q^{57} +(-6.18887 + 23.0972i) q^{58} +(36.4021 + 21.0168i) q^{59} +(73.9601 - 13.7093i) q^{60} +(19.6273 + 33.9954i) q^{61} +(12.1349 - 12.1349i) q^{62} +(50.1156 + 27.2892i) q^{63} -31.3718i q^{64} +(44.5125 + 15.7616i) q^{65} +(-5.82532 + 10.0898i) q^{66} +(-9.45259 - 35.2775i) q^{67} +(-17.9411 + 66.9570i) q^{68} +33.0905i q^{69} +(-14.1785 - 15.7846i) q^{70} +41.3839 q^{71} +(-36.4334 - 9.76231i) q^{72} +(-6.72116 + 1.80093i) q^{73} +(18.4613 + 10.6586i) q^{74} +(42.1084 - 94.5879i) q^{75} -94.4878 q^{76} +(-32.4735 + 0.810977i) q^{77} +(-16.7661 - 16.7661i) q^{78} +(-119.198 + 68.8190i) q^{79} +(-48.3155 - 33.2048i) q^{80} +(-43.9566 + 76.1350i) q^{81} +(-12.2219 - 3.27485i) q^{82} +(-37.7348 - 37.7348i) q^{83} +(-29.7867 - 101.007i) q^{84} +(61.9686 + 72.5527i) q^{85} +(-6.38103 - 11.0523i) q^{86} +(42.2807 + 157.794i) q^{87} +(20.7398 - 5.55720i) q^{88} +(106.644 - 61.5710i) q^{89} +(-18.7887 + 16.0478i) q^{90} +(15.5107 - 64.2636i) q^{91} +(20.5229 - 20.5229i) q^{92} +(30.3444 - 113.247i) q^{93} +(-31.1940 - 18.0099i) q^{94} +(-73.6638 + 107.186i) q^{95} +(53.0436 + 91.8742i) q^{96} +(-4.90063 + 4.90063i) q^{97} +(-19.9296 + 22.0265i) q^{98} +37.8293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8	$ 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8 + 14 * q^10 - 24 * q^11 - 46 * q^12 - 8 * q^13 + 52 * q^15 + 20 * q^16 - 48 * q^17 - 4 * q^18 - 72 * q^20 + 56 * q^21 + 104 * q^22 - 86 * q^23 - 16 * q^25 + 140 * q^26 + 76 * q^27 + 186 * q^28 + 64 * q^30 + 120 * q^31 + 130 * q^32 + 116 * q^33 - 240 * q^35 - 496 * q^36 + 44 * q^37 + 16 * q^38 - 158 * q^40 + 16 * q^41 - 370 * q^42 - 196 * q^43 - 104 * q^45 - 148 * q^46 - 208 * q^47 - 52 * q^48 + 580 * q^50 - 160 * q^51 - 288 * q^52 - 72 * q^53 + 208 * q^55 + 420 * q^56 + 656 * q^57 - 2 * q^58 + 262 * q^60 + 308 * q^61 + 176 * q^62 + 212 * q^63 + 132 * q^65 + 316 * q^66 + 198 * q^67 + 332 * q^68 - 200 * q^70 - 792 * q^71 + 308 * q^72 + 380 * q^73 - 450 * q^75 - 400 * q^76 - 472 * q^77 - 720 * q^78 - 324 * q^80 - 352 * q^81 - 818 * q^82 - 460 * q^83 + 144 * q^85 - 336 * q^86 - 214 * q^87 - 288 * q^88 + 120 * q^90 + 984 * q^91 + 1372 * q^92 - 68 * q^93 - 88 * q^95 + 816 * q^96 - 72 * q^97 + 482 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.585559	+	0.156900i	0.292779	+	0.0784500i	0.402219	−	0.915543i	$-0.368239\pi$
$2$	0.585559	+	0.156900i	0.292779	+	0.0784500i	−0.109440	+	0.993993i	$0.534906\pi$
$3$	4.00038	−	1.07190i	1.33346	−	0.357299i	0.479455	−	0.877566i	$-0.340834\pi$
$3$	4.00038	−	1.07190i	1.33346	−	0.357299i	0.854003	+	0.520267i	$0.174168\pi$
$4$	−3.14584	−	1.81625i	−0.786460	−	0.454063i
$5$	−4.51288	+	2.15265i	−0.902576	+	0.430530i
$5$	−4.51288	+	2.15265i	−0.902576	+	0.430530i
$6$	2.51064			0.418439
$7$	3.65026	+	5.97291i	0.521465	+	0.853273i
$7$	3.65026	+	5.97291i	0.521465	+	0.853273i
$8$	−3.27174	−	3.27174i	−0.408967	−	0.408967i
$9$	7.05981	−	4.07598i	0.784424	−	0.452887i
$10$	−2.98031	+	0.552433i	−0.298031	+	0.0552433i
$11$	−2.32026	+	4.01881i	−0.210933	+	0.365346i	−0.952007	−	0.306077i	$-0.900983\pi$
$11$	−2.32026	+	4.01881i	−0.210933	+	0.365346i	0.741074	+	0.671423i	$0.234317\pi$
$12$	−14.5314	−	3.89367i	−1.21095	−	0.324473i
$13$	−6.67801	−	6.67801i	−0.513693	−	0.513693i	0.401963	−	0.915656i	$-0.368328\pi$
$13$	−6.67801	−	6.67801i	−0.513693	−	0.513693i	−0.915656	+	0.401963i	$0.868328\pi$
$14$	1.20029	+	4.07021i	0.0857350	+	0.290730i
$15$	−15.7458	+	13.4488i	−1.04972	+	0.896584i
$16$	5.86255	+	10.1542i	0.366409	+	0.634639i
$17$	−4.93904	−	18.4327i	−0.290532	−	1.08428i	−0.944702	−	0.327931i	$-0.893649\pi$
$17$	−4.93904	−	18.4327i	−0.290532	−	1.08428i	0.654170	−	0.756348i	$-0.273018\pi$
$18$	4.77346	−	1.27904i	0.265192	−	0.0710580i
$19$	22.5268	−	13.0059i	1.18562	−	0.684520i	0.228315	−	0.973587i	$-0.426678\pi$
$19$	22.5268	−	13.0059i	1.18562	−	0.684520i	0.957309	+	0.289067i	$0.0933451\pi$
$20$	18.1066	+	1.42463i	0.905328	+	0.0712313i
$21$	21.0047	+	19.9812i	1.00023	+	0.951485i
$22$	−1.98920	+	1.98920i	−0.0904181	+	0.0904181i
$23$	−2.06796	+	7.71775i	−0.0899115	+	0.335554i	−0.996199	−	0.0871077i	$-0.972238\pi$
$23$	−2.06796	+	7.71775i	−0.0899115	+	0.335554i	0.906287	+	0.422662i	$0.138904\pi$
$24$	−16.5952	−	9.58122i	−0.691465	−	0.399217i
$25$	15.7322	−	19.4293i	0.629287	−	0.777173i
$26$	−2.86259	−	4.95815i	−0.110100	−	0.190698i
$27$	−2.48344	+	2.48344i	−0.0919792	+	0.0919792i
$28$	−0.634816	−	25.4196i	−0.0226720	−	0.907843i
$29$			39.4447i			1.36016i	0.733137	+	0.680081i	$0.238055\pi$
$29$			39.4447i			1.36016i	−0.733137	+	0.680081i	$0.761945\pi$
$30$	−11.3302	+	5.40453i	−0.377673	+	0.180151i
$31$	14.1545	−	24.5164i	0.456598	−	0.790851i	−0.542181	−	0.840262i	$-0.682401\pi$
$31$	14.1545	−	24.5164i	0.456598	−	0.790851i	0.998779	+	0.0494111i	$0.0157345\pi$
$32$	6.62983	+	24.7428i	0.207182	+	0.773214i
$33$	−4.97416	+	18.5638i	−0.150732	+	0.562540i
$34$		−	11.5684i		−	0.340247i
$35$	−29.3308	−	19.0973i	−0.838022	−	0.545637i
$36$	−29.6121			−0.822557
$37$	33.9663	+	9.10125i	0.918009	+	0.245980i	0.686734	−	0.726909i	$-0.259044\pi$
$37$	33.9663	+	9.10125i	0.918009	+	0.245980i	0.231275	+	0.972888i	$0.425710\pi$
$38$	15.2314	−	4.08125i	0.400827	−	0.107401i
$39$	−33.8727	−	19.5564i	−0.868531	−	0.501446i
$40$	21.8079	+	7.72205i	0.545197	+	0.193051i
$41$	−20.8722			−0.509078			−0.254539	−	0.967062i	$-0.581924\pi$
$41$	−20.8722			−0.509078			−0.254539	+	0.967062i	$0.581924\pi$
$42$	9.16446	+	14.9958i	0.218201	+	0.357043i
$43$	−14.8860	−	14.8860i	−0.346187	−	0.346187i	0.512500	−	0.858687i	$-0.328719\pi$
$43$	−14.8860	−	14.8860i	−0.346187	−	0.346187i	−0.858687	+	0.512500i	$0.828719\pi$
$44$	14.5983	−	8.42835i	0.331780	−	0.191553i
$45$	−23.0859	+	33.5918i	−0.513020	+	0.746483i
$46$	−2.42183	+	4.19473i	−0.0526485	+	0.0911898i
$47$	−57.3928	−	15.3783i	−1.22112	−	0.327199i	−0.410006	−	0.912083i	$-0.634473\pi$
$47$	−57.3928	−	15.3783i	−1.22112	−	0.327199i	−0.811117	+	0.584884i	$0.801140\pi$
$48$	34.3367	+	34.3367i	0.715348	+	0.715348i
$49$	−22.3513	+	43.6053i	−0.456148	+	0.889904i
$50$	12.2606	−	8.90863i	0.245211	−	0.178173i
$51$	−39.5160	−	68.4437i	−0.774824	−	1.34203i
$52$	8.87901	+	33.1369i	0.170750	+	0.637248i
$53$	−31.9412	+	8.55863i	−0.602665	+	0.161484i	−0.547235	−	0.836979i	$-0.684320\pi$
$53$	−31.9412	+	8.55863i	−0.602665	+	0.161484i	−0.0554299	+	0.998463i	$0.517653\pi$
$54$	−1.84385	+	1.06455i	−0.0341454	+	0.0197138i
$55$	1.81996	−	23.1311i	0.0330901	−	0.420565i
$56$	7.59911	−	31.4845i	0.135698	−	0.562223i
$57$	76.1749	−	76.1749i	1.33640	−	1.33640i
$58$	−6.18887	+	23.0972i	−0.106705	+	0.398227i
$59$	36.4021	+	21.0168i	0.616985	+	0.356216i	0.775694	−	0.631109i	$-0.217400\pi$
$59$	36.4021	+	21.0168i	0.616985	+	0.356216i	−0.158709	+	0.987325i	$0.550733\pi$
$60$	73.9601	−	13.7093i	1.23267	−	0.228489i
$61$	19.6273	+	33.9954i	0.321758	+	0.557302i	0.980851	−	0.194760i	$-0.0623928\pi$
$61$	19.6273	+	33.9954i	0.321758	+	0.557302i	−0.659093	+	0.752062i	$0.729059\pi$
$62$	12.1349	−	12.1349i	0.195725	−	0.195725i
$63$	50.1156	+	27.2892i	0.795486	+	0.433162i
$64$		−	31.3718i		−	0.490184i
$65$	44.5125	+	15.7616i	0.684808	+	0.242487i
$66$	−5.82532	+	10.0898i	−0.0882625	+	0.152875i
$67$	−9.45259	−	35.2775i	−0.141083	−	0.526530i	−0.999899	−	0.0142448i	$-0.995466\pi$
$67$	−9.45259	−	35.2775i	−0.141083	−	0.526530i	0.858815	−	0.512286i	$-0.171201\pi$
$68$	−17.9411	+	66.9570i	−0.263839	+	0.984662i
$69$			33.0905i			0.479573i
$70$	−14.1785	−	15.7846i	−0.202550	−	0.225494i
$71$	41.3839			0.582872			0.291436	−	0.956590i	$-0.405867\pi$
$71$	41.3839			0.582872			0.291436	+	0.956590i	$0.405867\pi$
$72$	−36.4334	−	9.76231i	−0.506020	−	0.135588i
$73$	−6.72116	+	1.80093i	−0.0920706	+	0.0246702i	−0.304560	−	0.952493i	$-0.598509\pi$
$73$	−6.72116	+	1.80093i	−0.0920706	+	0.0246702i	0.212490	+	0.977163i	$0.431843\pi$
$74$	18.4613	+	10.6586i	0.249477	+	0.144036i
$75$	42.1084	−	94.5879i	0.561445	−	1.26117i
$76$	−94.4878			−1.24326
$77$	−32.4735	+	0.810977i	−0.421734	+	0.0105322i
$78$	−16.7661	−	16.7661i	−0.214949	−	0.214949i
$79$	−119.198	+	68.8190i	−1.50884	+	0.871127i	−0.508889	+	0.860832i	$0.669944\pi$
$79$	−119.198	+	68.8190i	−1.50884	+	0.871127i	−0.999947	+	0.0102950i	$0.996723\pi$
$80$	−48.3155	−	33.2048i	−0.603944	−	0.415060i
$81$	−43.9566	+	76.1350i	−0.542674	+	0.939938i
$82$	−12.2219	−	3.27485i	−0.149048	−	0.0399372i
$83$	−37.7348	−	37.7348i	−0.454637	−	0.454637i	0.442254	−	0.896890i	$-0.354179\pi$
$83$	−37.7348	−	37.7348i	−0.454637	−	0.454637i	−0.896890	+	0.442254i	$0.854179\pi$
$84$	−29.7867	−	101.007i	−0.354604	−	1.20247i
$85$	61.9686	+	72.5527i	0.729042	+	0.853561i
$86$	−6.38103	−	11.0523i	−0.0741980	−	0.128515i
$87$	42.2807	+	157.794i	0.485985	+	1.81372i
$88$	20.7398	−	5.55720i	0.235679	−	0.0631500i
$89$	106.644	−	61.5710i	1.19825	−	0.691808i	0.238083	−	0.971245i	$-0.423481\pi$
$89$	106.644	−	61.5710i	1.19825	−	0.691808i	0.960164	+	0.279436i	$0.0901476\pi$
$90$	−18.7887	+	16.0478i	−0.208763	+	0.178309i
$91$	15.5107	−	64.2636i	0.170447	−	0.706193i
$92$	20.5229	−	20.5229i	0.223075	−	0.223075i
$93$	30.3444	−	113.247i	0.326284	−	1.21771i
$94$	−31.1940	−	18.0099i	−0.331851	−	0.191594i
$95$	−73.6638	+	107.186i	−0.775409	+	1.12828i
$96$	53.0436	+	91.8742i	0.552537	+	0.957023i
$97$	−4.90063	+	4.90063i	−0.0505220	+	0.0505220i	−0.731916	−	0.681394i	$-0.761374\pi$
$97$	−4.90063	+	4.90063i	−0.0505220	+	0.0505220i	0.681394	+	0.731916i	$0.261374\pi$
$98$	−19.9296	+	22.0265i	−0.203364	+	0.224761i
$99$			37.8293i			0.382115i
$100$	−84.7795	+	32.5480i	−0.847795	+	0.325480i
$101$	38.7888	−	67.1842i	0.384048	−	0.665190i	−0.607589	−	0.794252i	$-0.707863\pi$
$101$	38.7888	−	67.1842i	0.384048	−	0.665190i	0.991637	+	0.129062i	$0.0411965\pi$
$102$	−12.4001	−	46.2779i	−0.121570	−	0.453705i
$103$	11.2015	−	41.8046i	0.108752	−	0.405870i	−0.889991	−	0.455977i	$-0.849290\pi$
$103$	11.2015	−	41.8046i	0.108752	−	0.405870i	0.998744	+	0.0501076i	$0.0159564\pi$
$104$			43.6974i			0.420167i
$105$	−137.804	−	44.9568i	−1.31242	−	0.428160i
$106$	−20.0463			−0.189116
$107$	16.7368	+	4.48460i	0.156418	+	0.0419121i	0.336178	−	0.941798i	$-0.390865\pi$
$107$	16.7368	+	4.48460i	0.156418	+	0.0419121i	−0.179760	+	0.983710i	$0.557532\pi$
$108$	12.3231	−	3.30195i	0.114102	−	0.0305736i
$109$	90.9902	+	52.5332i	0.834772	+	0.481956i	0.855484	−	0.517829i	$-0.173260\pi$
$109$	90.9902	+	52.5332i	0.834772	+	0.481956i	−0.0207114	+	0.999785i	$0.506593\pi$
$110$	4.69496	−	13.2591i	0.0426815	−	0.120537i
$111$	145.634			1.31202
$112$	−39.2505	+	72.0820i	−0.350451	+	0.643589i
$113$	−28.3157	−	28.3157i	−0.250582	−	0.250582i	0.570627	−	0.821209i	$-0.306700\pi$
$113$	−28.3157	−	28.3157i	−0.250582	−	0.250582i	−0.821209	+	0.570627i	$0.806700\pi$
$114$	56.5567	−	32.6530i	0.496111	−	0.286430i
$115$	−7.28115	−	39.2809i	−0.0633144	−	0.341573i
$116$	71.6415	−	124.087i	0.617599	−	1.06971i
$117$	−74.3650	−	19.9260i	−0.635598	−	0.170308i
$118$	18.0180	+	18.0180i	0.152695	+	0.152695i
$119$	92.0683	−	96.7846i	0.773683	−	0.813316i
$120$	95.5170	+	7.51529i	0.795975	+	0.0626274i
$121$	49.7328	+	86.1397i	0.411015	+	0.711899i
$122$	6.15903	+	22.9858i	0.0504839	+	0.188408i
$123$	−83.4967	+	22.3729i	−0.678835	+	0.181893i
$124$	−89.0558	+	51.4164i	−0.718192	+	0.414648i
$125$	−29.1729	+	121.548i	−0.233383	+	0.972385i
$126$	25.0640	+	23.8426i	0.198920	+	0.189227i
$127$	9.28220	−	9.28220i	0.0730882	−	0.0730882i	−0.669618	−	0.742706i	$-0.733542\pi$
$127$	9.28220	−	9.28220i	0.0730882	−	0.0730882i	0.742706	+	0.669618i	$0.233542\pi$
$128$	31.4415	−	117.341i	0.245637	−	0.916730i
$129$	−75.5060	−	43.5934i	−0.585318	−	0.337933i
$130$	23.5917	+	16.2134i	0.181474	+	0.124718i
$131$	76.8987	+	133.192i	0.587013	+	1.01674i	0.994621	+	0.103579i	$0.0330296\pi$
$131$	76.8987	+	133.192i	0.587013	+	1.01674i	−0.407608	+	0.913157i	$0.633637\pi$
$132$	49.3645	−	49.3645i	0.373973	−	0.373973i
$133$	159.912	+	87.0760i	1.20234	+	0.654707i
$134$		−	22.1402i		−	0.165225i
$135$	5.86148	−	16.5534i	0.0434184	−	0.122618i
$136$	−44.1479	+	76.4664i	−0.324617	+	0.562253i
$137$	−57.9286	−	216.192i	−0.422836	−	1.57805i	−0.768603	−	0.639726i	$-0.779048\pi$
$137$	−57.9286	−	216.192i	−0.422836	−	1.57805i	0.345766	−	0.938321i	$-0.387619\pi$
$138$	−5.19190	+	19.3765i	−0.0376225	+	0.140409i
$139$		−	109.554i		−	0.788160i	−0.919076	−	0.394080i	$-0.871063\pi$
$139$		−	109.554i		−	0.788160i	0.919076	−	0.394080i	$-0.128937\pi$
$140$	57.5844	+	113.349i	0.411317	+	0.809636i
$141$	−246.077			−1.74522
$142$	24.2327	+	6.49314i	0.170653	+	0.0457263i
$143$	42.3323	−	11.3429i	0.296030	−	0.0793211i
$144$	82.7770	+	47.7913i	0.574840	+	0.331884i
$145$	−84.9107	−	178.009i	−0.585591	−	1.22765i
$146$	−4.21820			−0.0288918
$147$	−42.6731	+	198.396i	−0.290293	+	1.34963i
$148$	−90.3225	−	90.3225i	−0.610287	−	0.610287i
$149$	25.2621	−	14.5851i	0.169544	−	0.0978863i	−0.412827	−	0.910810i	$-0.635459\pi$
$149$	25.2621	−	14.5851i	0.169544	−	0.0978863i	0.582371	+	0.812923i	$0.302125\pi$
$150$	39.4978	−	48.7800i	0.263318	−	0.325200i
$151$	−36.2294	+	62.7511i	−0.239930	+	0.415570i	−0.960694	−	0.277610i	$-0.910458\pi$
$151$	−36.2294	+	62.7511i	−0.239930	+	0.415570i	0.720764	+	0.693180i	$0.243791\pi$
$152$	−116.254	−	31.1501i	−0.764828	−	0.204935i
$153$	−110.000	−	110.000i	−0.718956	−	0.718956i
$154$	−19.1424	−	4.62022i	−0.124301	−	0.0300014i
$155$	−11.1025	+	141.109i	−0.0716290	+	0.910382i
$156$	71.0387	+	123.043i	0.455376	+	0.788735i
$157$	−11.5696	−	43.1782i	−0.0736916	−	0.275021i	0.919242	−	0.393693i	$-0.128803\pi$
$157$	−11.5696	−	43.1782i	−0.0736916	−	0.275021i	−0.992933	+	0.118673i	$0.962136\pi$
$158$	−80.5952	+	21.5954i	−0.510096	+	0.136680i
$159$	−118.603	+	68.4755i	−0.745931	+	0.430663i
$160$	−83.1824	−	97.3898i	−0.519890	−	0.608686i
$161$	−53.6460	+	15.8200i	−0.333205	+	0.0982608i
$162$	−37.6847	+	37.6847i	−0.232622	+	0.232622i
$163$	−61.9815	+	231.318i	−0.380255	+	1.41913i	0.465259	+	0.885175i	$0.345961\pi$
$163$	−61.9815	+	231.318i	−0.380255	+	1.41913i	−0.845513	+	0.533954i	$0.820705\pi$
$164$	65.6606	+	37.9092i	0.400370	+	0.231154i
$165$	−17.5136	−	94.4839i	−0.106143	−	0.572630i
$166$	−16.1754	−	28.0166i	−0.0974420	−	0.168774i
$167$	92.1406	−	92.1406i	0.551740	−	0.551740i	−0.375202	−	0.926943i	$-0.622427\pi$
$167$	92.1406	−	92.1406i	0.551740	−	0.551740i	0.926943	+	0.375202i	$0.122427\pi$
$168$	−3.34883	−	134.095i	−0.0199335	−	0.798186i
$169$		−	79.8084i		−	0.472239i
$170$	24.9027	+	52.2067i	0.146487	+	0.307099i
$171$	106.024	−	183.638i	0.620021	−	1.07391i
$172$	19.7923	+	73.8659i	0.115071	+	0.429453i
$173$	−26.1915	+	97.7481i	−0.151396	+	0.565018i	0.847991	+	0.530011i	$0.177812\pi$
$173$	−26.1915	+	97.7481i	−0.151396	+	0.565018i	−0.999387	+	0.0350073i	$0.988855\pi$
$174$			99.0312i			0.569145i
$175$	173.476	+	23.0449i	0.991292	+	0.131685i
$176$	−54.4105			−0.309151
$177$	168.150	+	45.0556i	0.949999	+	0.254552i
$178$	72.1068	−	19.3210i	0.405094	−	0.108545i
$179$	7.60921	+	4.39318i	0.0425095	+	0.0245429i	0.521104	−	0.853493i	$-0.325520\pi$
$179$	7.60921	+	4.39318i	0.0425095	+	0.0245429i	−0.478595	+	0.878036i	$0.658854\pi$
$180$	133.636	−	63.7445i	0.742420	−	0.354136i
$181$	−25.0328			−0.138303			−0.0691513	−	0.997606i	$-0.522029\pi$
$181$	−25.0328			−0.138303			−0.0691513	+	0.997606i	$0.522029\pi$
$182$	19.1654	−	35.1965i	0.105304	−	0.193387i
$183$	114.956	+	114.956i	0.628175	+	0.628175i
$184$	32.0163	−	18.4846i	0.174002	−	0.100460i
$185$	−172.878	+	32.0448i	−0.934475	+	0.173215i
$186$	35.5369	−	61.5517i	0.191059	−	0.330923i
$187$	85.5374	+	22.9197i	0.457419	+	0.122565i
$188$	152.618	+	152.618i	0.811795	+	0.811795i
$189$	−23.8985	−	5.76817i	−0.126447	−	0.0305194i
$190$	−59.9521	+	51.2061i	−0.315537	+	0.269506i
$191$	−178.937	−	309.927i	−0.936841	−	1.62266i	−0.771317	−	0.636451i	$-0.780402\pi$
$191$	−178.937	−	309.927i	−0.936841	−	1.62266i	−0.165524	−	0.986206i	$-0.552932\pi$
$192$	−33.6273	−	125.499i	−0.175142	−	0.653640i
$193$	224.299	−	60.1007i	1.16217	−	0.311403i	0.374338	−	0.927292i	$-0.377870\pi$
$193$	224.299	−	60.1007i	1.16217	−	0.311403i	0.787832	+	0.615890i	$0.211203\pi$
$194$	−3.63852	+	2.10070i	−0.0187552	+	0.0108283i
$195$	194.962	+	15.3396i	0.999803	+	0.0786646i
$196$	149.512	−	96.5797i	0.762815	−	0.492754i
$197$	−116.988	+	116.988i	−0.593847	+	0.593847i	−0.938668	−	0.344821i	$-0.887940\pi$
$197$	−116.988	+	116.988i	−0.593847	+	0.593847i	0.344821	+	0.938668i	$0.387940\pi$
$198$	−5.93542	+	22.1513i	−0.0299769	+	0.111875i
$199$	−232.169	−	134.043i	−1.16668	−	0.673583i	−0.213785	−	0.976881i	$-0.568579\pi$
$199$	−232.169	−	134.043i	−1.16668	−	0.673583i	−0.952896	+	0.303297i	$0.901912\pi$
$200$	−115.039	+	12.0961i	−0.575196	+	0.0604805i
$201$	−75.6278	−	130.991i	−0.376258	−	0.651698i
$202$	33.2543	−	33.2543i	0.164625	−	0.164625i
$203$	−235.599	+	143.983i	−1.16059	+	0.709277i
$204$			287.084i			1.40727i
$205$	94.1938	−	44.9306i	0.459482	−	0.219174i
$206$	13.1183	−	22.7215i	0.0636810	−	0.110299i
$207$	16.8580	+	62.9148i	0.0814395	+	0.303936i
$208$	28.6599	−	106.960i	0.137788	−	0.514232i
$209$			120.708i			0.577550i
$210$	−73.6389	−	47.9463i	−0.350661	−	0.228316i
$211$	−4.70445			−0.0222960			−0.0111480	−	0.999938i	$-0.503549\pi$
$211$	−4.70445			−0.0222960			−0.0111480	+	0.999938i	$0.503549\pi$
$212$	116.027	+	31.0893i	0.547296	+	0.146647i
$213$	165.551	−	44.3593i	0.777236	−	0.208260i
$214$	9.09672	+	5.25199i	0.0425080	+	0.0245420i
$215$	99.2233	+	35.1344i	0.461504	+	0.163416i
$216$	16.2503			0.0752330
$217$	198.102	−	4.94729i	0.912911	−	0.0227986i
$218$	45.0376	+	45.0376i	0.206595	+	0.206595i
$219$	−24.9567	+	14.4088i	−0.113958	+	0.0657935i
$220$	−47.7372	+	69.4612i	−0.216987	+	0.315733i
$221$	−90.1111	+	156.077i	−0.407742	+	0.706231i
$222$	85.2771	+	22.8499i	0.384131	+	0.102928i
$223$	−167.366	−	167.366i	−0.750519	−	0.750519i	0.224057	−	0.974576i	$-0.428070\pi$
$223$	−167.366	−	167.366i	−0.750519	−	0.750519i	−0.974576	+	0.224057i	$0.928070\pi$
$224$	−123.586	+	129.917i	−0.551724	+	0.579987i
$225$	31.8726	−	201.291i	0.141656	−	0.894629i
$226$	−12.1378	−	21.0233i	−0.0537070	−	0.0930233i
$227$	−4.14740	−	15.4783i	−0.0182705	−	0.0681864i	0.956189	−	0.292751i	$-0.0945707\pi$
$227$	−4.14740	−	15.4783i	−0.0182705	−	0.0681864i	−0.974459	+	0.224565i	$0.927904\pi$
$228$	−377.987	+	101.281i	−1.65784	+	0.444216i
$229$	187.295	−	108.135i	0.817880	−	0.472204i	−0.0318045	−	0.999494i	$-0.510125\pi$
$229$	187.295	−	108.135i	0.817880	−	0.472204i	0.849685	+	0.527291i	$0.176792\pi$
$230$	1.89963	−	24.1437i	0.00825925	−	0.104972i
$231$	−129.037	+	38.0525i	−0.558601	+	0.164729i
$232$	129.053	−	129.053i	0.556262	−	0.556262i
$233$	18.2154	−	67.9809i	0.0781778	−	0.291764i	−0.915757	−	0.401732i	$-0.868408\pi$
$233$	18.2154	−	67.9809i	0.0781778	−	0.291764i	0.993935	+	0.109969i	$0.0350750\pi$
$234$	−40.4187	−	23.3357i	−0.172729	−	0.0997253i
$235$	292.111	−	54.1460i	1.24303	−	0.230409i
$236$	−76.3434	−	132.231i	−0.323489	−	0.560300i
$237$	−403.070	+	403.070i	−1.70072	+	1.70072i
$238$	69.0969	−	42.2276i	0.290323	−	0.177427i
$239$		−	33.8019i		−	0.141431i	−0.997497	−	0.0707153i	$-0.977472\pi$
$239$		−	33.8019i		−	0.141431i	0.997497	−	0.0707153i	$-0.0225282\pi$
$240$	−228.872	−	81.0424i	−0.953634	−	0.337677i
$241$	−144.912	+	250.995i	−0.601296	+	1.04147i	0.391330	+	0.920251i	$0.372015\pi$
$241$	−144.912	+	250.995i	−0.601296	+	1.04147i	−0.992625	+	0.121224i	$0.961318\pi$
$242$	15.6062	+	58.2430i	0.0644882	+	0.240673i
$243$	−86.0528	+	321.154i	−0.354127	+	1.32162i
$244$		−	142.592i		−	0.584394i
$245$	7.00158	−	244.900i	0.0285779	−	0.999592i
$246$	−52.4025			−0.213018
$247$	−237.288	−	63.5811i	−0.960680	−	0.257413i
$248$	−126.521	+	33.9012i	−0.510166	+	0.136699i
$249$	−191.401	−	110.506i	−0.768680	−	0.443798i
$250$	−36.1533	+	66.5963i	−0.144613	+	0.266385i
$251$	20.6837			0.0824054			0.0412027	−	0.999151i	$-0.486881\pi$
$251$	20.6837			0.0824054			0.0412027	+	0.999151i	$0.486881\pi$
$252$	−108.092	−	176.870i	−0.428935	−	0.701865i
$253$	−26.2179	−	26.2179i	−0.103628	−	0.103628i
$254$	6.89165	−	3.97890i	0.0271325	−	0.0156650i
$255$	325.667	+	223.814i	1.27712	+	0.877703i
$256$	−25.9218	+	44.8979i	−0.101257	+	0.175382i
$257$	−164.081	−	43.9654i	−0.638448	−	0.171072i	−0.0749479	−	0.997187i	$-0.523879\pi$
$257$	−164.081	−	43.9654i	−0.638448	−	0.171072i	−0.563500	+	0.826116i	$0.690546\pi$
$258$	−37.3734	−	37.3734i	−0.144858	−	0.144858i
$259$	69.6248	+	236.100i	0.268822	+	0.911582i
$260$	−111.402	−	130.429i	−0.428470	−	0.501652i
$261$	160.776	+	278.472i	0.616000	+	1.06694i
$262$	24.1308	+	90.0574i	0.0921023	+	0.343731i
$263$	430.997	−	115.485i	1.63877	−	0.439108i	0.682333	−	0.731041i	$-0.260965\pi$
$263$	430.997	−	115.485i	1.63877	−	0.439108i	0.956439	+	0.291934i	$0.0942987\pi$
$264$	77.0101	−	44.4618i	0.291705	−	0.168416i
$265$	125.723	−	107.382i	0.474427	−	0.405217i
$266$	79.9755	+	76.0783i	0.300660	+	0.286008i
$267$	360.618	−	360.618i	1.35063	−	1.35063i
$268$	−34.3366	+	128.146i	−0.128121	+	0.478156i
$269$	369.675	+	213.432i	1.37426	+	0.793427i	0.991461	−	0.130406i	$-0.0416281\pi$
$269$	369.675	+	213.432i	1.37426	+	0.793427i	0.382795	+	0.923833i	$0.374961\pi$
$270$	6.02948	−	8.77335i	0.0223314	−	0.0324939i
$271$	−15.9798	−	27.6778i	−0.0589660	−	0.102132i	0.835035	−	0.550196i	$-0.185447\pi$
$271$	−15.9798	−	27.6778i	−0.0589660	−	0.102132i	−0.894002	+	0.448064i	$0.852114\pi$
$272$	158.215	−	158.215i	0.581672	−	0.581672i
$273$	−6.83536	−	273.704i	−0.0250379	−	1.00258i
$274$		−	135.682i		−	0.495191i
$275$	41.5799	+	108.306i	0.151200	+	0.393839i
$276$	60.1007	−	104.098i	0.217756	−	0.377165i
$277$	11.7759	+	43.9481i	0.0425121	+	0.158657i	0.983919	−	0.178616i	$-0.0571620\pi$
$277$	11.7759	+	43.9481i	0.0425121	+	0.158657i	−0.941407	+	0.337273i	$0.890495\pi$
$278$	17.1891	−	64.1505i	0.0618312	−	0.230757i
$279$		−	230.775i		−	0.827150i
$280$	33.4813	+	158.444i	0.119576	+	0.565871i
$281$	485.686			1.72842			0.864210	−	0.503131i	$-0.167819\pi$
$281$	485.686			1.72842			0.864210	+	0.503131i	$0.167819\pi$
$282$	−144.092	−	38.6094i	−0.510966	−	0.136913i
$283$	−167.847	+	44.9744i	−0.593098	+	0.158920i	−0.542869	−	0.839818i	$-0.682662\pi$
$283$	−167.847	+	44.9744i	−0.593098	+	0.158920i	−0.0502293	+	0.998738i	$0.515995\pi$
$284$	−130.187	−	75.1636i	−0.458406	−	0.264661i
$285$	−179.790	+	507.746i	−0.630842	+	1.78157i
$286$	26.5678			0.0928943
$287$	−76.1889	−	124.668i	−0.265466	−	0.434382i
$288$	147.657	+	147.657i	0.512697	+	0.512697i
$289$	−65.0904	+	37.5800i	−0.225226	+	0.130035i
$290$	−21.7906	−	117.557i	−0.0751399	−	0.405370i
$291$	−14.3514	+	24.8573i	−0.0493175	+	0.0854204i
$292$	24.4146	+	6.54188i	0.0836117	+	0.0224037i
$293$	101.273	+	101.273i	0.345642	+	0.345642i	0.858484	−	0.512841i	$-0.171407\pi$
$293$	101.273	+	101.273i	0.345642	+	0.345642i	−0.512841	+	0.858484i	$0.671407\pi$
$294$	−56.1159	+	109.477i	−0.190870	+	0.372371i
$295$	−209.520	−	16.4851i	−0.710238	−	0.0558816i
$296$	−81.3520	−	140.906i	−0.274838	−	0.476033i
$297$	−4.21824	−	15.7427i	−0.0142028	−	0.0530056i
$298$	17.0808	−	4.57679i	0.0573182	−	0.0153584i
$299$	65.3491	−	37.7293i	0.218559	−	0.126185i
$300$	−304.262	+	221.079i	−1.01421	+	0.736930i
$301$	34.5751	−	143.251i	0.114867	−	0.475916i
$302$	−31.0601	+	31.0601i	−0.102848	+	0.102848i
$303$	83.1553	−	310.340i	0.274440	−	1.02422i
$304$	264.129	+	152.495i	0.868847	+	0.501629i
$305$	−161.756	−	111.167i	−0.530347	−	0.364480i
$306$	−47.1526	−	81.6706i	−0.154093	−	0.266898i
$307$	−170.066	+	170.066i	−0.553962	+	0.553962i	−0.927582	−	0.373620i	$-0.878116\pi$
$307$	−170.066	+	170.066i	−0.553962	+	0.553962i	0.373620	+	0.927582i	$0.378116\pi$
$308$	103.629	+	56.4288i	0.336459	+	0.183210i
$309$		−	179.241i		−	0.580068i
$310$	−28.6412	+	80.8858i	−0.0923910	+	0.260922i
$311$	−142.953	+	247.602i	−0.459657	+	0.796149i	−0.998943	−	0.0459739i	$-0.985361\pi$
$311$	−142.953	+	247.602i	−0.459657	+	0.796149i	0.539286	+	0.842123i	$0.318694\pi$
$312$	46.8392	+	174.806i	0.150125	+	0.560276i
$313$	31.8802	−	118.978i	0.101854	−	0.380123i	−0.896116	−	0.443821i	$-0.853623\pi$
$313$	31.8802	−	118.978i	0.101854	−	0.380123i	0.997969	+	0.0636978i	$0.0202894\pi$
$314$		−	27.0987i		−	0.0863015i
$315$	−284.910	−	15.2716i	−0.904476	−	0.0484811i
$316$	499.971			1.58219
$317$	−183.810	−	49.2516i	−0.579841	−	0.155368i	−0.0430349	−	0.999074i	$-0.513703\pi$
$317$	−183.810	−	49.2516i	−0.579841	−	0.155368i	−0.536806	+	0.843706i	$0.680369\pi$
$318$	−80.1928	+	21.4876i	−0.252179	+	0.0675711i
$319$	−158.520	−	91.5218i	−0.496929	−	0.286902i
$320$	67.5325	+	141.577i	0.211039	+	0.442428i
$321$	71.7603			0.223552
$322$	−33.8950	+	0.846478i	−0.105264	+	0.00262881i
$323$	−350.995	−	350.995i	−1.08667	−	1.08667i
$324$	276.561	−	159.672i	0.853582	−	0.492816i
$325$	−234.809	+	24.6896i	−0.722489	+	0.0759679i
$326$	−72.5876	+	125.725i	−0.222661	+	0.385661i
$327$	420.305	+	112.620i	1.28534	+	0.344405i
$328$	68.2884	+	68.2884i	0.208196	+	0.208196i
$329$	−117.645	−	398.937i	−0.357583	−	1.21257i
$330$	4.56925	−	58.0738i	0.0138462	−	0.175981i
$331$	−50.7585	−	87.9163i	−0.153349	−	0.265608i	0.779108	−	0.626890i	$-0.215672\pi$
$331$	−50.7585	−	87.9163i	−0.153349	−	0.265608i	−0.932457	+	0.361282i	$0.882339\pi$
$332$	50.1718	+	187.244i	0.151120	+	0.563987i
$333$	276.892	−	74.1931i	0.831509	−	0.222802i
$334$	68.4106	−	39.4969i	0.204822	−	0.118254i
$335$	118.599	+	138.855i	0.354026	+	0.414493i
$336$	−79.7522	+	330.428i	−0.237358	+	0.983415i
$337$	−456.377	+	456.377i	−1.35423	+	1.35423i	−0.473371	+	0.880863i	$0.656963\pi$
$337$	−456.377	+	456.377i	−1.35423	+	1.35423i	−0.880863	+	0.473371i	$0.843037\pi$
$338$	12.5219	−	46.7325i	0.0370471	−	0.138262i
$339$	−143.625	−	82.9220i	−0.423673	−	0.244608i
$340$	−63.1692	−	340.790i	−0.185792	−	1.00232i
$341$	65.6844	+	113.769i	0.192623	+	0.333632i
$342$	90.8958	−	90.8958i	0.265777	−	0.265777i
$343$	−342.038	+	25.6684i	−0.997196	+	0.0748349i
$344$			97.4064i			0.283158i
$345$	−71.2324	−	149.334i	−0.206471	−	0.432851i
$346$	−30.6734	+	53.1278i	−0.0886513	+	0.153549i
$347$	149.357	+	557.409i	0.430425	+	1.60637i	0.751784	+	0.659409i	$0.229194\pi$
$347$	149.357	+	557.409i	0.430425	+	1.60637i	−0.321359	+	0.946957i	$0.604140\pi$
$348$	153.585	−	573.186i	0.441335	−	1.64709i
$349$			275.843i			0.790380i	0.918599	+	0.395190i	$0.129321\pi$
$349$			275.843i			0.790380i	−0.918599	+	0.395190i	$0.870679\pi$
$350$	97.9647	+	40.7125i	0.279899	+	0.116321i
$351$	33.1689			0.0944982
$352$	−114.820	−	30.7658i	−0.326192	−	0.0874029i
$353$	−253.997	+	68.0583i	−0.719538	+	0.192800i	−0.599966	−	0.800026i	$-0.704819\pi$
$353$	−253.997	+	68.0583i	−0.719538	+	0.192800i	−0.119572	+	0.992825i	$0.538152\pi$
$354$	91.3924	+	52.7654i	0.258171	+	0.149055i
$355$	−186.761	+	89.0852i	−0.526086	+	0.250944i
$356$	−447.313			−1.25650
$357$	264.565	−	485.863i	0.741077	−	1.36096i
$358$	3.76635	+	3.76635i	0.0105205	+	0.0105205i
$359$	−160.127	+	92.4495i	−0.446037	+	0.257519i	−0.706155	−	0.708057i	$-0.749572\pi$
$359$	−160.127	+	92.4495i	−0.446037	+	0.257519i	0.260118	+	0.965577i	$0.416238\pi$
$360$	185.435	−	34.3724i	0.515096	−	0.0954788i
$361$	157.806	−	273.328i	0.437135	−	0.757141i
$362$	−14.6582	−	3.92764i	−0.0404921	−	0.0108498i
$363$	291.283	+	291.283i	0.802432	+	0.802432i
$364$	−165.513	+	173.992i	−0.454706	+	0.477999i
$365$	26.4550	−	22.5957i	0.0724794	−	0.0619060i
$366$	49.2769	+	85.3501i	0.134636	+	0.233197i
$367$	−188.584	−	703.805i	−0.513853	−	1.91772i	−0.373526	−	0.927620i	$-0.621851\pi$
$367$	−188.584	−	703.805i	−0.513853	−	1.91772i	−0.140327	−	0.990105i	$-0.544815\pi$
$368$	−90.4913	+	24.2471i	−0.245900	+	0.0658888i
$369$	−147.354	+	85.0748i	−0.399333	+	0.230555i
$370$	−106.258	−	8.36039i	−0.287184	−	0.0225957i
$371$	−167.714	−	159.541i	−0.452058	−	0.430029i
$372$	−301.144	+	301.144i	−0.809526	+	0.809526i
$373$	−96.5404	+	360.294i	−0.258822	+	0.965935i	0.707103	+	0.707111i	$0.250002\pi$
$373$	−96.5404	+	360.294i	−0.258822	+	0.965935i	−0.965924	+	0.258824i	$0.916665\pi$
$374$	46.4911	+	26.8416i	0.124308	+	0.0717691i
$375$	13.5847	+	517.508i	0.0362259	+	1.38002i
$376$	137.460	+	238.088i	0.365586	+	0.633213i
$377$	263.412	−	263.412i	0.698706	−	0.698706i
$378$	−13.0890	−	7.12728i	−0.0346269	−	0.0188552i
$379$			94.9137i			0.250432i	0.992130	+	0.125216i	$0.0399624\pi$
$379$			94.9137i			0.250432i	−0.992130	+	0.125216i	$0.960038\pi$
$380$	426.412	−	203.399i	1.12214	−	0.535262i
$381$	27.1827	−	47.0819i	0.0713457	−	0.123574i
$382$	−56.1503	−	209.556i	−0.146990	−	0.548576i
$383$	63.9794	−	238.774i	0.167048	−	0.623432i	−0.830722	−	0.556687i	$-0.812072\pi$
$383$	63.9794	−	238.774i	0.167048	−	0.623432i	0.997770	−	0.0667443i	$-0.0212612\pi$
$384$		−	503.112i		−	1.31019i
$385$	144.803	−	73.5640i	0.376112	−	0.191075i
$386$	140.770			0.364689
$387$	−165.768	−	44.4174i	−0.428341	−	0.114774i
$388$	24.3174	−	6.51582i	0.0626736	−	0.0167934i
$389$	−100.377	−	57.9525i	−0.258038	−	0.148978i	0.365401	−	0.930850i	$-0.380932\pi$
$389$	−100.377	−	57.9525i	−0.258038	−	0.148978i	−0.623439	+	0.781872i	$0.714265\pi$
$390$	111.755	+	39.5717i	0.286550	+	0.101466i
$391$	152.473			0.389956
$392$	215.793	−	69.5376i	0.550491	−	0.177392i
$393$	450.392	+	450.392i	1.14604	+	1.14604i
$394$	−86.8587	+	50.1479i	−0.220454	+	0.127279i
$395$	389.783	−	567.164i	0.986793	−	1.43586i
$396$	68.7076	−	119.005i	0.173504	−	0.300518i
$397$	308.778	+	82.7368i	0.777778	+	0.208405i	0.625805	−	0.779980i	$-0.284771\pi$
$397$	308.778	+	82.7368i	0.777778	+	0.208405i	0.151973	+	0.988385i	$0.451437\pi$
$398$	−114.917	−	114.917i	−0.288737	−	0.288737i
$399$	733.043	+	176.928i	1.83720	+	0.443428i
$400$	289.520	+	45.8428i	0.723801	+	0.114607i
$401$	381.964	+	661.581i	0.952529	+	1.64983i	0.739925	+	0.672689i	$0.234861\pi$
$401$	381.964	+	661.581i	0.952529	+	1.64983i	0.212604	+	0.977139i	$0.431806\pi$
$402$	−23.7320	−	88.5691i	−0.0590348	−	0.220321i
$403$	−258.245	+	69.1965i	−0.640806	+	0.171703i
$404$	−244.047	+	140.900i	−0.604076	+	0.348764i
$405$	34.4785	−	438.211i	0.0851322	−	1.08200i
$406$	−160.548	+	47.3451i	−0.395439	+	0.116613i
$407$	−115.387	+	115.387i	−0.283506	+	0.283506i
$408$	−94.6440	+	353.216i	−0.231971	+	0.865726i
$409$	374.855	+	216.423i	0.916517	+	0.529151i	0.882522	−	0.470271i	$-0.155844\pi$
$409$	374.855	+	216.423i	0.916517	+	0.529151i	0.0339946	+	0.999422i	$0.489177\pi$
$410$	62.2056	−	11.5305i	0.151721	−	0.0281232i
$411$	−463.472	−	802.757i	−1.12767	−	1.95318i
$412$	−111.166	+	111.166i	−0.269820	+	0.269820i
$413$	7.34578	+	294.143i	0.0177864	+	0.712210i
$414$			39.4854i			0.0953752i
$415$	251.523	+	89.0628i	0.606079	+	0.214609i
$416$	120.959	−	209.507i	0.290767	−	0.503623i
$417$	−117.431	−	438.258i	−0.281609	−	1.05098i
$418$	−18.9391	+	70.6816i	−0.0453088	+	0.169095i
$419$			271.262i			0.647402i	0.946159	+	0.323701i	$0.104927\pi$
$419$			271.262i			0.647402i	−0.946159	+	0.323701i	$0.895073\pi$
$420$	351.858	+	391.714i	0.837757	+	0.932653i
$421$	−762.776			−1.81182			−0.905910	−	0.423470i	$-0.860812\pi$
$421$	−762.776			−1.81182			−0.905910	+	0.423470i	$0.860812\pi$
$422$	−2.75473	−	0.738129i	−0.00652780	−	0.00174912i
$423$	−467.864	+	125.364i	−1.10606	+	0.296368i
$424$	132.505	+	76.5018i	0.312512	+	0.180429i
$425$	−435.837	−	194.025i	−1.02550	−	0.456529i
$426$	103.900			0.243897
$427$	−131.407	+	241.324i	−0.307745	+	0.565161i
$428$	−44.5060	−	44.5060i	−0.103986	−	0.103986i
$429$	157.187	−	90.7518i	0.366403	−	0.211543i
$430$	52.5885	+	36.1414i	0.122299	+	0.0840498i
$431$	187.992	−	325.611i	0.436176	−	0.755479i	−0.561215	−	0.827670i	$-0.689666\pi$
$431$	187.992	−	325.611i	0.436176	−	0.755479i	0.997391	+	0.0721914i	$0.0229992\pi$
$432$	−39.7767	−	10.6581i	−0.0920756	−	0.0246716i
$433$	−179.289	−	179.289i	−0.414063	−	0.414063i	0.469089	−	0.883151i	$-0.344583\pi$
$433$	−179.289	−	179.289i	−0.414063	−	0.414063i	−0.883151	+	0.469089i	$0.844583\pi$
$434$	116.776	+	28.1852i	0.269070	+	0.0649429i
$435$	−530.482	−	621.088i	−1.21950	−	1.42779i
$436$	−190.827	−	330.522i	−0.437677	−	0.758078i
$437$	53.7914	+	200.752i	0.123092	+	0.459387i
$438$	−16.8744	+	4.52147i	−0.0385260	+	0.0103230i
$439$	−615.933	+	355.609i	−1.40304	+	0.810044i	−0.994703	−	0.102789i	$-0.967223\pi$
$439$	−615.933	+	355.609i	−1.40304	+	0.810044i	−0.408333	+	0.912833i	$0.633890\pi$
$440$	−81.6333	+	69.7245i	−0.185530	+	0.158465i
$441$	19.9387	+	398.949i	0.0452125	+	0.904645i
$442$	−77.2538	+	77.2538i	−0.174782	+	0.174782i
$443$	130.139	−	485.686i	0.293768	−	1.09636i	−0.648423	−	0.761280i	$-0.724571\pi$
$443$	130.139	−	485.686i	0.293768	−	1.09636i	0.942191	−	0.335076i	$-0.108762\pi$
$444$	−458.140	−	264.507i	−1.03185	−	0.595737i
$445$	−348.731	+	507.430i	−0.783665	+	1.14029i
$446$	−71.7428	−	124.262i	−0.160858	−	0.278615i
$447$	85.4240	−	85.4240i	0.191105	−	0.191105i
$448$	187.381	−	114.515i	0.418260	−	0.255614i
$449$		−	439.687i		−	0.979259i	−0.871930	−	0.489630i	$-0.837132\pi$
$449$		−	439.687i		−	0.979259i	0.871930	−	0.489630i	$-0.162868\pi$
$450$	50.2459	−	112.867i	0.111658	−	0.250816i
$451$	48.4289	−	83.8813i	0.107381	−	0.185990i
$452$	37.6483	+	140.505i	0.0832927	+	0.310852i
$453$	−77.6684	+	289.862i	−0.171453	+	0.639873i
$454$		−	9.71419i		−	0.0213969i
$455$	68.3392	+	323.403i	0.150196	+	0.710776i
$456$	−498.449			−1.09309
$457$	713.632	+	191.217i	1.56156	+	0.418418i	0.933157	−	0.359470i	$-0.117043\pi$
$457$	713.632	+	191.217i	1.56156	+	0.418418i	0.628402	+	0.777888i	$0.283709\pi$
$458$	126.638	−	33.9326i	0.276503	−	0.0740887i
$459$	58.0424	+	33.5108i	0.126454	+	0.0730082i
$460$	−48.4386	+	136.796i	−0.105301	+	0.297382i
$461$	−93.7144			−0.203285			−0.101643	−	0.994821i	$-0.532410\pi$
$461$	−93.7144			−0.203285			−0.101643	+	0.994821i	$0.532410\pi$
$462$	−81.5291	+	2.03607i	−0.176470	+	0.00440707i
$463$	330.338	+	330.338i	0.713472	+	0.713472i	0.967260	−	0.253788i	$-0.0816765\pi$
$463$	330.338	+	330.338i	0.713472	+	0.713472i	−0.253788	+	0.967260i	$0.581676\pi$
$464$	−400.530	+	231.246i	−0.863212	+	0.498376i
$465$	106.840	+	576.391i	0.229765	+	1.23955i
$466$	21.3324	−	36.9488i	0.0457777	−	0.0792893i
$467$	726.852	+	194.759i	1.55643	+	0.417044i	0.931531	−	0.363663i	$-0.118474\pi$
$467$	726.852	+	194.759i	1.55643	+	0.417044i	0.624898	+	0.780707i	$0.285141\pi$
$468$	197.750	+	197.750i	0.422542	+	0.422542i
$469$	176.205	−	185.231i	0.375704	−	0.394950i
$470$	179.544	+	14.1265i	0.382008	+	0.0300564i
$471$	−92.5653	−	160.328i	−0.196529	−	0.340399i
$472$	−50.3368	−	187.860i	−0.106646	−	0.398007i
$473$	94.3635	−	25.2846i	0.199500	−	0.0534559i
$474$	−299.263	+	172.780i	−0.631356	+	0.364514i
$475$	101.701	−	642.292i	0.214107	−	1.35219i
$476$	−465.417	+	137.250i	−0.977768	+	0.288340i
$477$	−190.614	+	190.614i	−0.399611	+	0.399611i
$478$	5.30352	−	19.7930i	0.0110952	−	0.0414080i
$479$	−463.131	−	267.389i	−0.966870	−	0.558222i	−0.0685891	−	0.997645i	$-0.521850\pi$
$479$	−463.131	−	267.389i	−0.966870	−	0.558222i	−0.898280	+	0.439423i	$0.855183\pi$
$480$	−437.153	−	300.433i	−0.910734	−	0.625902i
$481$	−166.049	−	287.606i	−0.345217	−	0.597933i
$482$	−124.236	+	124.236i	−0.257751	+	0.257751i
$483$	−197.647	+	120.789i	−0.409206	+	0.250081i
$484$		−	361.309i		−	0.746507i
$485$	11.5666	−	32.6653i	0.0238487	−	0.0673511i
$486$	−100.778	+	174.553i	−0.207362	+	0.359162i
$487$	−33.3158	−	124.336i	−0.0684102	−	0.255310i	0.923248	−	0.384204i	$-0.125524\pi$
$487$	−33.3158	−	124.336i	−0.0684102	−	0.255310i	−0.991658	+	0.128894i	$0.958857\pi$
$488$	47.0088	−	175.439i	0.0963296	−	0.359507i
$489$			991.797i			2.02821i
$490$	42.5246	−	142.305i	0.0867850	−	0.290418i
$491$	404.254			0.823328			0.411664	−	0.911336i	$-0.364948\pi$
$491$	404.254			0.823328			0.411664	+	0.911336i	$0.364948\pi$
$492$	303.302	+	81.2695i	0.616467	+	0.165182i
$493$	727.074	−	194.819i	1.47479	−	0.395170i
$494$	−128.970	−	74.4609i	−0.261073	−	0.150731i
$495$	−81.4334	−	170.719i	−0.164512	−	0.344888i
$496$	331.927			0.669207
$497$	151.062	+	247.182i	0.303948	+	0.497349i
$498$	−94.7384	−	94.7384i	−0.190238	−	0.190238i
$499$	419.564	−	242.235i	0.840809	−	0.485442i	−0.0167298	−	0.999860i	$-0.505326\pi$
$499$	419.564	−	242.235i	0.840809	−	0.485442i	0.857539	+	0.514418i	$0.171992\pi$
$500$	312.535	−	329.386i	0.625070	−	0.658771i
$501$	269.832	−	467.363i	0.538587	−	0.932859i
$502$	12.1115	+	3.24528i	0.0241266	+	0.00646470i
$503$	27.1976	+	27.1976i	0.0540709	+	0.0540709i	0.733625	−	0.679554i	$-0.237827\pi$
$503$	27.1976	+	27.1976i	0.0540709	+	0.0540709i	−0.679554	+	0.733625i	$0.737827\pi$
$504$	−74.6820	−	253.248i	−0.148178	−	0.502477i
$505$	−30.4251	+	386.693i	−0.0602477	+	0.765729i
$506$	−11.2385	−	19.4657i	−0.0222105	−	0.0384698i
$507$	−85.5464	−	319.263i	−0.168731	−	0.629711i
$508$	−46.0591	+	12.3415i	−0.0906676	+	0.0242943i
$509$	−96.0051	+	55.4286i	−0.188615	+	0.108897i	−0.591334	−	0.806427i	$-0.701399\pi$
$509$	−96.0051	+	55.4286i	−0.188615	+	0.108897i	0.402719	+	0.915324i	$0.368065\pi$
$510$	155.580	+	182.153i	0.305060	+	0.357164i
$511$	−35.2907	−	33.5710i	−0.0690621	−	0.0656967i
$512$	−365.823	+	365.823i	−0.714497	+	0.714497i
$513$	−23.6447	+	88.2433i	−0.0460911	+	0.172014i
$514$	−89.1810	−	51.4887i	−0.173504	−	0.100173i
$515$	39.4397	+	212.772i	0.0765819	+	0.413150i
$516$	158.353	+	274.276i	0.306886	+	0.531542i
$517$	194.969	−	194.969i	0.377115	−	0.377115i
$518$	3.72541	+	149.174i	0.00719190	+	0.287981i
$519$			419.104i			0.807522i
$520$	−94.0653	−	197.201i	−0.180895	−	0.379233i
$521$	−102.043	+	176.744i	−0.195860	+	0.339240i	−0.947182	−	0.320696i	$-0.896083\pi$
$521$	−102.043	+	176.744i	−0.195860	+	0.339240i	0.751322	+	0.659936i	$0.229416\pi$
$522$	50.4515	+	188.288i	0.0966504	+	0.360704i
$523$	71.0451	−	265.144i	0.135842	−	0.506968i	−0.864151	−	0.503232i	$-0.832144\pi$
$523$	71.0451	−	265.144i	0.135842	−	0.506968i	0.999993	−	0.00373579i	$-0.00118914\pi$
$524$		−	558.670i		−	1.06616i
$525$	718.671	−	93.7604i	1.36890	−	0.178591i
$526$	270.494			0.514247
$527$	−521.814	−	139.820i	−0.990159	−	0.265312i
$528$	−217.662	+	58.3225i	−0.412239	+	0.110459i
$529$	402.840	+	232.580i	0.761513	+	0.439660i
$530$	90.4667	−	43.1528i	0.170692	−	0.0814203i
$531$	342.656			0.645303
$532$	−344.905	−	564.367i	−0.648317	−	1.06084i
$533$	139.385	+	139.385i	0.261510	+	0.261510i
$534$	267.744	−	154.582i	0.501394	−	0.289480i
$535$	−85.1847	+	15.7899i	−0.159224	+	0.0295139i
$536$	−84.4925	+	146.345i	−0.157635	+	0.273032i
$537$	35.1487	+	9.41807i	0.0654539	+	0.0175383i
$538$	182.979	+	182.979i	0.340109	+	0.340109i
$539$	−123.380	−	191.001i	−0.228906	−	0.354362i
$540$	−48.5045	+	41.4286i	−0.0898231	+	0.0767195i
$541$	26.6437	+	46.1483i	0.0492490	+	0.0853018i	0.889599	−	0.456742i	$-0.150984\pi$
$541$	26.6437	+	46.1483i	0.0492490	+	0.0853018i	−0.840350	+	0.542044i	$0.817651\pi$
$542$	−5.01446	−	18.7142i	−0.00925177	−	0.0345281i
$543$	−100.140	+	26.8326i	−0.184421	+	0.0494154i
$544$	423.334	−	244.412i	0.778187	−	0.449286i
$545$	−523.714	−	41.2059i	−0.960942	−	0.0756071i
$546$	38.9417	−	161.342i	0.0713218	−	0.295499i
$547$	247.545	−	247.545i	0.452551	−	0.452551i	−0.443649	−	0.896200i	$-0.646316\pi$
$547$	247.545	−	247.545i	0.452551	−	0.452551i	0.896200	+	0.443649i	$0.146316\pi$
$548$	−210.426	+	785.320i	−0.383989	+	1.43307i
$549$	277.129	+	160.001i	0.504790	+	0.291440i
$550$	7.35435	+	69.9432i	0.0133716	+	0.127169i
$551$	513.013	+	888.564i	0.931058	+	1.61264i
$552$	108.264	−	108.264i	0.196130	−	0.196130i
$553$	−846.153	−	460.752i	−1.53011	−	0.833186i
$554$			27.5818i			0.0497867i
$555$	−657.227	+	313.499i	−1.18419	+	0.564862i
$556$	−198.978	+	344.640i	−0.357874	+	0.619857i
$557$	−170.804	−	637.448i	−0.306649	−	1.14443i	−0.931516	−	0.363700i	$-0.881513\pi$
$557$	−170.804	−	637.448i	−0.306649	−	1.14443i	0.624867	−	0.780731i	$-0.285153\pi$
$558$	36.2086	−	135.132i	0.0648899	−	0.242172i
$559$			198.818i			0.355668i
$560$	21.9653	−	409.790i	0.0392237	−	0.731768i
$561$	366.749			0.653742
$562$	284.398	+	76.2041i	0.506046	+	0.135595i
$563$	161.582	−	43.2957i	0.287001	−	0.0769017i	−0.112446	−	0.993658i	$-0.535869\pi$
$563$	161.582	−	43.2957i	0.287001	−	0.0769017i	0.399448	+	0.916756i	$0.369202\pi$
$564$	774.118	+	446.937i	1.37255	+	0.792442i
$565$	188.739	+	66.8316i	0.334052	+	0.118286i
$566$	−105.341			−0.186114
$567$	−615.200	+	15.3637i	−1.08501	+	0.0270965i
$568$	−135.397	−	135.397i	−0.238376	−	0.238376i
$569$	−587.768	+	339.348i	−1.03298	+	0.596394i	−0.917838	−	0.396955i	$-0.870067\pi$
$569$	−587.768	+	339.348i	−1.03298	+	0.596394i	−0.115146	+	0.993349i	$0.536734\pi$
$570$	−184.943	+	269.106i	−0.324461	+	0.472116i
$571$	−148.412	+	257.058i	−0.259917	+	0.450189i	−0.966219	−	0.257721i	$-0.917028\pi$
$571$	−148.412	+	257.058i	−0.259917	+	0.450189i	0.706303	+	0.707910i	$0.250362\pi$
$572$	−153.772	−	41.2032i	−0.268833	−	0.0720335i
$573$	−1048.02	−	1048.02i	−1.82901	−	1.82901i
$574$	−25.0527	−	84.9543i	−0.0436458	−	0.148004i
$575$	117.417	+	161.596i	0.204204	+	0.281037i
$576$	−127.871	−	221.479i	−0.221998	−	0.384512i
$577$	−31.2962	−	116.799i	−0.0542395	−	0.202425i	0.933489	−	0.358607i	$-0.116748\pi$
$577$	−31.2962	−	116.799i	−0.0542395	−	0.202425i	−0.987728	+	0.156182i	$0.950081\pi$
$578$	−44.0106	+	11.7926i	−0.0761429	+	0.0204024i
$579$	832.858	−	480.851i	1.43844	−	0.830485i
$580$	−56.1940	+	714.207i	−0.0968861	+	1.23139i
$581$	87.6449	−	363.128i	0.150852	−	0.625006i
$582$	−12.3037	+	12.3037i	−0.0211404	+	0.0211404i
$583$	39.7165	−	148.224i	0.0681243	−	0.254243i
$584$	27.8820	+	16.0977i	0.0477432	+	0.0275646i
$585$	378.494	−	70.1581i	0.646998	−	0.119928i
$586$	43.4117	+	75.1912i	0.0740813	+	0.128313i
$587$	−570.172	+	570.172i	−0.971332	+	0.971332i	−0.999600	−	0.0282686i	$-0.991001\pi$
$587$	−570.172	+	570.172i	−0.971332	+	0.971332i	0.0282686	+	0.999600i	$0.491001\pi$
$588$	494.579	−	546.616i	0.841121	−	0.929620i
$589$		−	736.369i		−	1.25020i
$590$	−120.100	−	42.5267i	−0.203559	−	0.0720791i
$591$	−342.597	+	593.395i	−0.579690	+	1.00405i
$592$	106.713	+	398.258i	0.180258	+	0.672734i
$593$	87.4970	−	326.543i	0.147550	−	0.550663i	−0.852079	−	0.523413i	$-0.824658\pi$
$593$	87.4970	−	326.543i	0.147550	−	0.550663i	0.999629	−	0.0272499i	$-0.00867500\pi$
$594$		−	9.88010i		−	0.0166332i
$595$	−207.150	+	634.968i	−0.348151	+	1.06717i
$596$	−105.961			−0.177786
$597$	−1072.45	−	287.361i	−1.79639	−	0.481341i
$598$	44.1855	−	11.8395i	0.0738887	−	0.0197984i
$599$	−288.821	−	166.751i	−0.482172	−	0.278382i	0.239149	−	0.970983i	$-0.423131\pi$
$599$	−288.821	−	166.751i	−0.482172	−	0.278382i	−0.721321	+	0.692601i	$0.756465\pi$
$600$	−447.235	+	171.699i	−0.745391	+	0.286165i
$601$	−435.153			−0.724048			−0.362024	−	0.932169i	$-0.617914\pi$
$601$	−435.153			−0.724048			−0.362024	+	0.932169i	$0.617914\pi$
$602$	42.7218	−	78.4569i	0.0709664	−	0.130327i
$603$	−210.524	−	210.524i	−0.349128	−	0.349128i
$604$	227.944	−	131.603i	0.377390	−	0.217886i
$605$	−409.867	−	281.681i	−0.677466	−	0.465588i
$606$	97.3846	−	168.675i	0.160701	−	0.278342i
$607$	−27.0211	−	7.24027i	−0.0445158	−	0.0119280i	0.236492	−	0.971633i	$-0.424002\pi$
$607$	−27.0211	−	7.24027i	−0.0445158	−	0.0119280i	−0.281008	+	0.959705i	$0.590669\pi$
$608$	471.152	+	471.152i	0.774920	+	0.774920i
$609$	−788.151	+	828.525i	−1.29417	+	1.36047i
$610$	−77.2754	−	90.4740i	−0.126681	−	0.148318i
$611$	280.573	+	485.966i	0.459203	+	0.795362i
$612$	146.255	+	545.831i	0.238979	+	0.891881i
$613$	−594.912	+	159.406i	−0.970492	+	0.260043i	−0.709036	−	0.705173i	$-0.750869\pi$
$613$	−594.912	+	159.406i	−0.970492	+	0.260043i	−0.261457	+	0.965215i	$0.584203\pi$
$614$	−126.267	+	72.9004i	−0.205647	+	0.118730i
$615$	328.649	−	280.705i	0.534389	−	0.456431i
$616$	108.898	+	103.591i	0.176783	+	0.168168i
$617$	349.281	−	349.281i	0.566095	−	0.566095i	−0.364937	−	0.931032i	$-0.618910\pi$
$617$	349.281	−	349.281i	0.566095	−	0.566095i	0.931032	+	0.364937i	$0.118910\pi$
$618$	28.1229	−	104.956i	0.0455063	−	0.169832i
$619$	103.689	+	59.8648i	0.167510	+	0.0967121i	0.581411	−	0.813610i	$-0.302501\pi$
$619$	103.689	+	59.8648i	0.167510	+	0.0967121i	−0.413901	+	0.910322i	$0.635834\pi$
$620$	291.217	−	423.742i	0.469704	−	0.683455i
$621$	−14.0309	−	24.3022i	−0.0225940	−	0.0391340i
$622$	−122.556	+	122.556i	−0.197036	+	0.197036i
$623$	757.036	+	412.225i	1.21515	+	0.661678i
$624$		−	458.601i		−	0.734938i
$625$	−129.997	−	611.331i	−0.207995	−	0.978130i
$626$	37.3354	−	64.6669i	0.0596413	−	0.103302i
$627$	129.387	+	482.877i	0.206358	+	0.770139i
$628$	−42.0265	+	156.845i	−0.0669212	+	0.249753i
$629$		−	671.044i		−	1.06684i
$630$	−164.435	−	53.6448i	−0.261009	−	0.0851504i
$631$	649.783			1.02977			0.514883	−	0.857260i	$-0.327835\pi$
$631$	649.783			1.02977			0.514883	+	0.857260i	$0.327835\pi$
$632$	615.143	+	164.827i	0.973327	+	0.260802i
$633$	−18.8196	+	5.04269i	−0.0297308	+	0.00796633i
$634$	−99.9037	−	57.6794i	−0.157577	−	0.0909770i
$635$	−21.9081	+	61.8708i	−0.0345010	+	0.0974344i
$636$	497.475			0.782193
$637$	440.459	−	141.935i	0.691458	−	0.222817i
$638$	−78.4633	−	78.4633i	−0.122983	−	0.122983i
$639$	292.163	−	168.680i	0.457219	−	0.263975i
$640$	110.703	+	597.230i	0.172974	+	0.933172i
$641$	−167.189	+	289.580i	−0.260825	+	0.451763i	−0.966461	−	0.256812i	$-0.917328\pi$
$641$	−167.189	+	289.580i	−0.260825	+	0.451763i	0.705636	+	0.708574i	$0.250661\pi$
$642$	42.0199	+	11.2592i	0.0654515	+	0.0175377i
$643$	137.523	+	137.523i	0.213877	+	0.213877i	0.805912	−	0.592035i	$-0.201675\pi$
$643$	137.523	+	137.523i	0.213877	+	0.213877i	−0.592035	+	0.805912i	$0.701675\pi$
$644$	197.495	+	47.6675i	0.306669	+	0.0740178i
$645$	434.591	+	34.1937i	0.673785	+	0.0530135i
$646$	−150.457	−	260.599i	−0.232906	−	0.403404i
$647$	228.562	+	853.006i	0.353265	+	1.31840i	0.882654	+	0.470023i	$0.155754\pi$
$647$	228.562	+	853.006i	0.353265	+	1.31840i	−0.529389	+	0.848379i	$0.677579\pi$
$648$	392.908	−	105.279i	0.606340	−	0.162468i
$649$	−168.925	+	97.5286i	−0.260284	+	0.150275i
$650$	−141.368	−	22.3843i	−0.217490	−	0.0344374i
$651$	787.178	−	232.136i	1.20918	−	0.356583i
$652$	615.116	−	615.116i	0.943429	−	0.943429i
$653$	307.686	−	1148.30i	0.471189	−	1.75850i	−0.164320	−	0.986407i	$-0.552543\pi$
$653$	307.686	−	1148.30i	0.471189	−	1.75850i	0.635509	−	0.772094i	$-0.280790\pi$
$654$	228.443	+	131.892i	0.349302	+	0.201669i
$655$	−633.752	−	435.546i	−0.967560	−	0.664955i
$656$	−122.364	−	211.941i	−0.186531	−	0.323081i
$657$	−40.1095	+	40.1095i	−0.0610495	+	0.0610495i
$658$	−6.29480	−	252.059i	−0.00956657	−	0.383069i
$659$			443.971i			0.673704i	0.941558	+	0.336852i	$0.109362\pi$
$659$			443.971i			0.673704i	−0.941558	+	0.336852i	$0.890638\pi$
$660$	−116.511	+	329.040i	−0.176532	+	0.498546i
$661$	408.118	−	706.881i	0.617425	−	1.06941i	−0.372529	−	0.928021i	$-0.621509\pi$
$661$	408.118	−	706.881i	0.617425	−	1.06941i	0.989954	−	0.141391i	$-0.0451574\pi$
$662$	−15.9280	−	59.4441i	−0.0240604	−	0.0897948i
$663$	−193.180	+	720.956i	−0.291372	+	1.08742i
$664$			246.917i			0.371863i
$665$	−909.107	−	48.7293i	−1.36708	−	0.0732772i
$666$	173.778			0.260927
$667$	−304.424	−	81.5702i	−0.456408	−	0.122294i
$668$	−457.210	+	122.509i	−0.684447	+	0.183397i
$669$	−848.924	−	490.127i	−1.26895	−	0.732626i
$670$	47.6601	+	99.9160i	0.0711345	+	0.149128i
$671$	−182.161			−0.271477
$672$	−355.133	+	652.189i	−0.528472	+	0.970519i
$673$	398.004	+	398.004i	0.591387	+	0.591387i	0.938006	−	0.346619i	$-0.112670\pi$
$673$	398.004	+	398.004i	0.591387	+	0.591387i	−0.346619	+	0.938006i	$0.612670\pi$
$674$	−338.841	+	195.630i	−0.502732	+	0.290252i
$675$	9.18163	+	87.3214i	0.0136024	+	0.129365i
$676$	−144.952	+	251.064i	−0.214426	+	0.371397i
$677$	−614.195	−	164.573i	−0.907230	−	0.243092i	−0.225112	−	0.974333i	$-0.572275\pi$
$677$	−614.195	−	164.573i	−0.907230	−	0.243092i	−0.682119	+	0.731241i	$0.738941\pi$
$678$	−71.0905	−	71.0905i	−0.104853	−	0.104853i
$679$	−47.1596	−	11.3825i	−0.0694544	−	0.0167636i
$680$	34.6286	−	440.119i	0.0509244	−	0.647233i
$681$	−33.1823	−	57.4735i	−0.0487259	−	0.0843957i
$682$	20.6118	+	76.9241i	0.0302225	+	0.112792i
$683$	673.375	−	180.430i	0.985907	−	0.264173i	0.270377	−	0.962755i	$-0.412852\pi$
$683$	673.375	−	180.430i	0.985907	−	0.264173i	0.715530	+	0.698582i	$0.246185\pi$
$684$	−667.066	+	385.131i	−0.975243	+	0.563057i
$685$	726.812	+	850.950i	1.06104	+	1.24226i
$686$	−204.311	−	38.6355i	−0.297829	−	0.0563199i
$687$	633.340	−	633.340i	0.921892	−	0.921892i
$688$	63.8861	−	238.426i	0.0928577	−	0.346550i
$689$	270.459	+	156.149i	0.392538	+	0.226632i
$690$	−18.2803	−	98.6200i	−0.0264932	−	0.142927i
$691$	−161.282	−	279.349i	−0.233404	−	0.404268i	0.725403	−	0.688324i	$-0.241653\pi$
$691$	−161.282	−	279.349i	−0.233404	−	0.404268i	−0.958808	+	0.284056i	$0.908320\pi$
$692$	259.930	−	259.930i	0.375621	−	0.375621i
$693$	−225.951	+	138.087i	−0.326048	+	0.199259i
$694$			349.830i			0.504078i
$695$	235.832	+	494.405i	0.339327	+	0.711375i
$696$	377.928	−	654.591i	0.543000	−	0.940504i
$697$	103.089	+	384.732i	0.147903	+	0.551983i
$698$	−43.2797	+	161.522i	−0.0620053	+	0.231407i
$699$		−	291.474i		−	0.416987i
$700$	−503.873	−	387.572i	−0.719818	−	0.553674i
$701$	−877.436			−1.25169			−0.625846	−	0.779947i	$-0.715246\pi$
$701$	−877.436			−1.25169			−0.625846	+	0.779947i	$0.715246\pi$
$702$	19.4223	+	5.20419i	0.0276671	+	0.00741338i
$703$	883.524	−	236.740i	1.25679	−	0.336756i
$704$	126.077	+	72.7906i	0.179087	+	0.103396i
$705$	1110.51	−	529.717i	1.57520	−	0.751372i
$706$	−159.408			−0.225791
$707$	542.874	−	13.5575i	0.767856	−	0.0191760i
$708$	−447.140	−	447.140i	−0.631554	−	0.631554i
$709$	631.373	−	364.523i	0.890512	−	0.514137i	0.0164019	−	0.999865i	$-0.494779\pi$
$709$	631.373	−	364.523i	0.890512	−	0.514137i	0.874110	+	0.485728i	$0.161446\pi$
$710$	−123.337	+	22.8619i	−0.173714	+	0.0321998i
$711$	−561.011	+	971.699i	−0.789045	+	1.36667i
$712$	−550.356	−	147.467i	−0.772971	−	0.207117i
$713$	159.940	+	159.940i	0.224320	+	0.224320i
$714$	231.150	−	242.991i	0.323739	−	0.340323i
$715$	−166.623	+	142.316i	−0.233040	+	0.199043i
$716$	−15.9582	−	27.6405i	−0.0222880	−	0.0386040i
$717$	−36.2322	−	135.220i	−0.0505331	−	0.188592i
$718$	−108.269	+	29.0106i	−0.150793	+	0.0404048i
$719$	726.775	−	419.604i	1.01081	−	0.583594i	0.0993843	−	0.995049i	$-0.468313\pi$
$719$	726.775	−	419.604i	1.01081	−	0.583594i	0.911430	+	0.411455i	$0.134979\pi$
$720$	−476.441	−	37.4864i	−0.661723	−	0.0520645i
$721$	290.583	−	85.6919i	0.403028	−	0.118851i
$722$	135.290	−	135.290i	0.187382	−	0.187382i
$723$	−310.662	+	1159.41i	−0.429685	+	1.60361i
$724$	78.7491	+	45.4658i	0.108769	+	0.0627981i
$725$	766.383	+	620.551i	1.05708	+	0.855932i
$726$	124.861	+	216.266i	0.171985	+	0.297886i
$727$	−34.3820	+	34.3820i	−0.0472929	+	0.0472929i	−0.730358	−	0.683065i	$-0.760647\pi$
$727$	−34.3820	+	34.3820i	−0.0472929	+	0.0472929i	0.683065	+	0.730358i	$0.260647\pi$
$728$	−261.001	+	159.507i	−0.358517	+	0.219103i
$729$			585.757i			0.803507i
$730$	19.0362	−	9.08031i	0.0260770	−	0.0124388i
$731$	−200.868	+	347.913i	−0.274785	+	0.475941i
$732$	−152.844	−	570.422i	−0.208803	−	0.779265i
$733$	−260.501	+	972.204i	−0.355391	+	1.32634i	0.524602	+	0.851348i	$0.324214\pi$
$733$	−260.501	+	972.204i	−0.355391	+	1.32634i	−0.879992	+	0.474988i	$0.842452\pi$
$734$		−	441.708i		−	0.601782i
$735$	−234.499	−	987.197i	−0.319046	−	1.34312i
$736$	−204.669			−0.278083
$737$	163.706	+	43.8649i	0.222125	+	0.0595182i
$738$	−99.6326	+	26.6965i	−0.135003	+	0.0361741i
$739$	−744.283	−	429.712i	−1.00715	−	0.581477i	−0.0967929	−	0.995305i	$-0.530858\pi$
$739$	−744.283	−	429.712i	−1.00715	−	0.581477i	−0.910355	+	0.413827i	$0.864192\pi$
$740$	602.047	+	213.182i	0.813578	+	0.288083i
$741$	−1017.39			−1.37300
$742$	−73.1742	−	119.735i	−0.0986175	−	0.161368i
$743$	−259.321	−	259.321i	−0.349020	−	0.349020i	0.510725	−	0.859744i	$-0.329377\pi$
$743$	−259.321	−	259.321i	−0.349020	−	0.349020i	−0.859744	+	0.510725i	$0.829377\pi$
$744$	−469.794	+	271.235i	−0.631443	+	0.364564i
$745$	−82.6081	+	120.201i	−0.110883	+	0.161344i
$746$	−113.060	+	195.826i	−0.151555	+	0.262501i
$747$	−420.207	−	112.594i	−0.562527	−	0.150729i
$748$	−227.459	−	227.459i	−0.304090	−	0.304090i
$749$	34.3073	+	116.337i	0.0458042	+	0.155323i
$750$	−73.2424	+	305.163i	−0.0976566	+	0.406884i
$751$	−416.133	−	720.764i	−0.554106	−	0.959739i	−0.997973	−	0.0636465i	$-0.979727\pi$
$751$	−416.133	−	720.764i	−0.554106	−	0.959739i	0.443867	−	0.896093i	$-0.353606\pi$
$752$	−180.313	−	672.936i	−0.239777	−	0.894861i
$753$	82.7427	−	22.1709i	0.109884	−	0.0294434i
$754$	195.573	−	112.914i	0.259380	−	0.149753i
$755$	28.4175	−	361.178i	0.0376391	−	0.478381i
$756$	64.7045	+	61.5515i	0.0855880	+	0.0814173i
$757$	−504.353	+	504.353i	−0.666252	+	0.666252i	−0.956846	−	0.290594i	$-0.906147\pi$
$757$	−504.353	+	504.353i	−0.666252	+	0.666252i	0.290594	+	0.956846i	$0.406147\pi$
$758$	−14.8920	+	55.5775i	−0.0196464	+	0.0733213i
$759$	−132.984	−	76.7786i	−0.175210	−	0.101158i
$760$	591.695	−	109.677i	0.778546	−	0.144312i
$761$	−595.614	−	1031.63i	−0.782673	−	1.35563i	−0.930380	−	0.366597i	$-0.880523\pi$
$761$	−595.614	−	1031.63i	−0.782673	−	1.35563i	0.147707	−	0.989031i	$-0.452811\pi$
$762$	23.3042	−	23.3042i	0.0305830	−	0.0305830i
$763$	18.3614	+	735.236i	0.0240648	+	0.963612i
$764$			1299.98i			1.70154i
$765$	733.210	+	259.626i	0.958445	+	0.339380i
$766$	74.9274	−	129.778i	0.0978164	−	0.169423i
$767$	−102.743	−	383.444i	−0.133955	−	0.499927i
$768$	−55.5710	+	207.394i	−0.0723581	+	0.270044i
$769$			598.803i			0.778678i	0.921095	+	0.389339i	$0.127296\pi$
$769$			598.803i			0.778678i	−0.921095	+	0.389339i	$0.872704\pi$
$770$	96.3330	−	20.3564i	0.125108	−	0.0264369i
$771$	−703.513			−0.912468
$772$	−814.767	−	218.316i	−1.05540	−	0.282793i
$773$	−1450.36	+	388.622i	−1.87627	+	0.502746i	−0.876500	+	0.481402i	$0.840128\pi$
$773$	−1450.36	+	388.622i	−1.87627	+	0.502746i	−0.999772	+	0.0213434i	$0.993206\pi$
$774$	−90.0977	−	52.0179i	−0.116405	−	0.0672066i
$775$	−253.655	−	660.709i	−0.327297	−	0.852528i
$776$	32.0672			0.0413237
$777$	531.600	+	869.857i	0.684170	+	1.11951i
$778$	−49.6837	−	49.6837i	−0.0638608	−	0.0638608i
$779$	−470.185	+	271.461i	−0.603575	+	0.348474i
$780$	−585.457	−	402.355i	−0.750586	−	0.515840i
$781$	−96.0214	+	166.314i	−0.122947	+	0.212950i
$782$	89.2819	+	23.9230i	0.114171	+	0.0305921i
$783$	−97.9584	−	97.9584i	−0.125107	−	0.125107i
$784$	−573.813	+	28.6781i	−0.731905	+	0.0365793i
$785$	145.160	+	169.953i	0.184917	+	0.216501i
$786$	193.065	+	334.398i	0.245629	+	0.425442i
$787$	25.7763	+	96.1983i	0.0327526	+	0.122234i	0.980367	−	0.197183i	$-0.0631794\pi$
$787$	25.7763	+	96.1983i	0.0327526	+	0.122234i	−0.947614	+	0.319418i	$0.896513\pi$
$788$	580.505	−	155.546i	0.736681	−	0.197393i
$789$	1600.36	−	923.969i	2.02834	−	1.17106i
$790$	317.229	−	270.951i	0.401556	−	0.342976i
$791$	65.7676	−	272.487i	0.0831449	−	0.344484i
$792$	123.768	−	123.768i	0.156272	−	0.156272i
$793$	95.9506	−	358.093i	0.120997	−	0.451567i
$794$	167.826	+	96.8945i	0.211368	+	0.122033i
$795$	387.837	−	564.333i	0.487846	−	0.709852i
$796$	486.912	+	843.356i	0.611698	+	1.05949i
$797$	672.137	−	672.137i	0.843333	−	0.843333i	−0.145957	−	0.989291i	$-0.546626\pi$
$797$	672.137	−	672.137i	0.843333	−	0.843333i	0.989291	+	0.145957i	$0.0466263\pi$
$798$	401.480	+	218.616i	0.503108	+	0.273955i
$799$			1133.86i			1.41910i
$800$	585.038	+	260.446i	0.731298	+	0.325557i
$801$	501.925	−	869.359i	0.626622	−	1.08534i
$802$	119.860	+	447.325i	0.149452	+	0.557761i
$803$	8.35724	−	31.1896i	0.0104075	−	0.0388414i
$804$			549.437i			0.683379i
$805$	208.043	−	186.875i	0.258439	−	0.232143i
$806$	−162.074			−0.201085
$807$	1707.62	+	457.554i	2.11600	+	0.566982i
$808$	−346.716	+	92.9023i	−0.429104	+	0.114978i
$809$	274.028	+	158.210i	0.338724	+	0.195562i	0.659708	−	0.751522i	$-0.270680\pi$
$809$	274.028	+	158.210i	0.338724	+	0.195562i	−0.320984	+	0.947085i	$0.604013\pi$
$810$	88.9446	−	251.189i	0.109808	−	0.310110i
$811$	825.207			1.01752			0.508759	−	0.860909i	$-0.330105\pi$
$811$	825.207			1.01752			0.508759	+	0.860909i	$0.330105\pi$
$812$	1002.67	−	25.0401i	1.23481	−	0.0308376i
$813$	−93.5930	−	93.5930i	−0.115121	−	0.115121i
$814$	−85.6699	+	49.4616i	−0.105246	+	0.0607636i
$815$	−218.232	−	1177.34i	−0.267770	−	1.44458i
$816$	463.329	−	802.509i	0.567805	−	0.983467i
$817$	−528.941	−	141.729i	−0.647419	−	0.173475i
$818$	185.543	+	185.543i	0.226825	+	0.226825i
$819$	−152.435	−	516.910i	−0.186123	−	0.631148i
$820$	−377.924	−	29.7351i	−0.460883	−	0.0362623i
$821$	241.583	+	418.433i	0.294254	+	0.509663i	0.974811	−	0.223032i	$-0.0715955\pi$
$821$	241.583	+	418.433i	0.294254	+	0.509663i	−0.680557	+	0.732695i	$0.738262\pi$
$822$	−145.438	−	542.780i	−0.176931	−	0.660317i
$823$	45.9972	−	12.3249i	0.0558897	−	0.0149756i	−0.230766	−	0.973009i	$-0.574123\pi$
$823$	45.9972	−	12.3249i	0.0558897	−	0.0149756i	0.286656	+	0.958034i	$0.407456\pi$
$824$	−173.422	+	100.125i	−0.210464	+	0.121511i
$825$	282.428	+	388.694i	0.342337	+	0.471144i
$826$	−41.8496	+	173.391i	−0.0506654	+	0.209916i
$827$	−80.3234	+	80.3234i	−0.0971262	+	0.0971262i	−0.754000	−	0.656874i	$-0.771878\pi$
$827$	−80.3234	+	80.3234i	−0.0971262	+	0.0971262i	0.656874	+	0.754000i	$0.271878\pi$
$828$	61.2367	−	228.538i	0.0739573	−	0.276013i
$829$	−1277.48	−	737.553i	−1.54099	−	0.889690i	−0.998777	−	0.0494476i	$-0.984254\pi$
$829$	−1277.48	−	737.553i	−1.54099	−	0.889690i	−0.542211	−	0.840242i	$-0.682413\pi$
$830$	133.307	+	91.6154i	0.160611	+	0.110380i
$831$	94.2157	+	163.186i	0.113376	+	0.196373i
$832$	−209.501	+	209.501i	−0.251804	+	0.251804i
$833$	914.159	+	196.627i	1.09743	+	0.236047i
$834$		−	275.051i		−	0.329797i
$835$	−217.473	+	614.166i	−0.260447	+	0.735529i
$836$	219.236	−	379.728i	0.262244	−	0.454220i
$837$	25.7330	+	96.0368i	0.0307443	+	0.114739i
$838$	−42.5609	+	158.840i	−0.0507887	+	0.189546i
$839$		−	1180.75i		−	1.40733i	−0.710534	−	0.703663i	$-0.751547\pi$
$839$		−	1180.75i		−	1.40733i	0.710534	−	0.703663i	$-0.248453\pi$
$840$	303.773	+	597.947i	0.361635	+	0.711842i
$841$	−714.883			−0.850039
$842$	−446.650	−	119.680i	−0.530464	−	0.142137i
$843$	1942.93	−	520.606i	2.30478	−	0.617563i
$844$	14.7995	+	8.54447i	0.0175349	+	0.0101238i
$845$	171.800	+	360.166i	0.203313	+	0.426231i
$846$	−293.632			−0.347082
$847$	−332.967	+	611.482i	−0.393114	+	0.721938i
$848$	−274.163	−	274.163i	−0.323306	−	0.323306i
$849$	−623.242	+	359.829i	−0.734090	+	0.423827i
$850$	−224.766	−	181.996i	−0.264430	−	0.214113i
$851$	−140.482	+	243.322i	−0.165079	+	0.285925i
$852$	−601.365	−	161.135i	−0.705828	−	0.189126i
$853$	920.396	+	920.396i	1.07901	+	1.07901i	0.996598	+	0.0824123i	$0.0262624\pi$
$853$	920.396	+	920.396i	1.07901	+	1.07901i	0.0824123	+	0.996598i	$0.473738\pi$
$854$	−114.810	+	120.691i	−0.134438	+	0.141325i
$855$	−83.1625	+	1056.97i	−0.0972661	+	1.23622i
$856$	−40.0858	−	69.4307i	−0.0468293	−	0.0811107i
$857$	412.809	+	1540.63i	0.481691	+	1.79770i	0.594520	+	0.804081i	$0.297342\pi$
$857$	412.809	+	1540.63i	0.481691	+	1.79770i	−0.112829	+	0.993614i	$0.535991\pi$
$858$	106.281	−	28.4779i	0.123871	−	0.0331911i
$859$	−1009.08	+	582.590i	−1.17471	+	0.678219i	−0.954785	−	0.297298i	$-0.903914\pi$
$859$	−1009.08	+	582.590i	−1.17471	+	0.678219i	−0.219924	+	0.975517i	$0.570581\pi$
$860$	−248.328	−	290.742i	−0.288753	−	0.338072i
$861$	−438.415	−	417.051i	−0.509193	−	0.484380i
$862$	161.169	−	161.169i	0.186971	−	0.186971i
$863$	215.164	−	803.004i	0.249321	−	0.930480i	−0.721841	−	0.692059i	$-0.756704\pi$
$863$	215.164	−	803.004i	0.249321	−	0.930480i	0.971162	−	0.238421i	$-0.0766297\pi$
$864$	−77.9121	−	44.9826i	−0.0901761	−	0.0520632i
$865$	−92.2185	−	497.507i	−0.106611	−	0.575152i
$866$	−76.8539	−	133.115i	−0.0887458	−	0.153712i
$867$	−220.104	+	220.104i	−0.253869	+	0.253869i
$868$	−632.182	−	344.239i	−0.728320	−	0.396589i
$869$		−	638.712i		−	0.734996i
$870$	−213.180	−	446.916i	−0.245034	−	0.513697i
$871$	−172.459	+	298.708i	−0.198001	+	0.342949i
$872$	−125.821	−	469.571i	−0.144290	−	0.538499i
$873$	−14.6226	+	54.5724i	−0.0167499	+	0.0625114i
$874$			125.992i			0.144156i
$875$	−832.484	+	269.435i	−0.951410	+	0.307926i
$876$	104.680			0.119498
$877$	900.602	+	241.316i	1.02691	+	0.275160i	0.732680	−	0.680574i	$-0.238269\pi$
$877$	900.602	+	241.316i	1.02691	+	0.275160i	0.294233	+	0.955734i	$0.404936\pi$
$878$	−416.460	+	111.590i	−0.474328	+	0.127096i
$879$	513.685	+	296.576i	0.584398	+	0.337402i
$880$	245.548	−	117.127i	0.279032	−	0.133099i
$881$	1060.28			1.20350			0.601749	−	0.798685i	$-0.294471\pi$
$881$	1060.28			1.20350			0.601749	+	0.798685i	$0.294471\pi$
$882$	−50.9197	+	236.736i	−0.0577321	+	0.268408i
$883$	−622.595	−	622.595i	−0.705090	−	0.705090i	0.260408	−	0.965499i	$-0.416143\pi$
$883$	−622.595	−	622.595i	−0.705090	−	0.705090i	−0.965499	+	0.260408i	$0.916143\pi$
$884$	566.950	−	327.329i	0.641346	−	0.370281i
$885$	−855.829	+	158.638i	−0.967039	+	0.179251i
$886$	152.408	−	263.979i	0.172018	−	0.297944i
$887$	−1248.03	−	334.409i	−1.40703	−	0.377011i	−0.526163	−	0.850383i	$-0.676370\pi$
$887$	−1248.03	−	334.409i	−1.40703	−	0.377011i	−0.880863	+	0.473372i	$0.843037\pi$
$888$	−476.475	−	476.475i	−0.536571	−	0.536571i
$889$	89.3242	+	21.5593i	0.100477	+	0.0242512i
$890$	−283.818	+	242.414i	−0.318897	+	0.272375i
$891$	−203.981	−	353.306i	−0.228935	−	0.396527i
$892$	222.527	+	830.484i	0.249470	+	0.931036i
$893$	−1492.89	+	400.018i	−1.67177	+	0.447948i
$894$	63.4238	−	36.6178i	0.0709439	−	0.0409595i
$895$	−43.7964	−	3.44591i	−0.0489345	−	0.00385018i
$896$	815.639	−	240.529i	0.910311	−	0.268447i
$897$	220.979	−	220.979i	0.246353	−	0.246353i
$898$	68.9870	−	257.463i	0.0768229	−	0.286707i
$899$	967.041	+	558.321i	1.07568	+	0.621047i
$900$	−465.862	+	575.342i	−0.517625	+	0.639269i
$901$	315.518	+	546.493i	0.350186	+	0.606541i
$902$	41.5189	−	41.5189i	0.0460299	−	0.0460299i
$903$	−15.2368	−	610.118i	−0.0168735	−	0.675656i
$904$			185.283i			0.204960i
$905$	112.970	−	53.8868i	0.124829	−	0.0595435i
$906$	−90.9588	+	157.545i	−0.100396	+	0.173891i
$907$	−375.031	−	1399.63i	−0.413485	−	1.54315i	−0.787852	−	0.615865i	$-0.788807\pi$
$907$	−375.031	−	1399.63i	−0.413485	−	1.54315i	0.374367	−	0.927281i	$-0.377860\pi$
$908$	−15.0654	+	56.2250i	−0.0165919	+	0.0619218i
$909$		−	632.410i		−	0.695721i
$910$	−10.7253	+	200.094i	−0.0117860	+	0.219883i
$911$	−158.132			−0.173581			−0.0867903	−	0.996227i	$-0.527661\pi$
$911$	−158.132			−0.173581			−0.0867903	+	0.996227i	$0.527661\pi$
$912$	1220.08	+	326.918i	1.33780	+	0.358463i
$913$	239.203	−	64.0944i	0.261997	−	0.0702020i
$914$	387.872	+	223.938i	0.424367	+	0.245009i
$915$	−766.243	−	271.322i	−0.837424	−	0.296527i
$916$	−785.599			−0.857640
$917$	−514.846	+	945.495i	−0.561447	+	1.03107i
$918$	28.7294	+	28.7294i	0.0312956	+	0.0312956i
$919$	916.425	−	529.098i	0.997198	−	0.575733i	0.0897800	−	0.995962i	$-0.471384\pi$
$919$	916.425	−	529.098i	0.997198	−	0.575733i	0.907418	+	0.420229i	$0.138050\pi$
$920$	−104.695	+	152.339i	−0.113799	+	0.165586i
$921$	−498.036	+	862.623i	−0.540755	+	0.936616i
$922$	−54.8753	−	14.7038i	−0.0595177	−	0.0159477i
$923$	−276.362	−	276.362i	−0.299417	−	0.299417i
$924$	475.042	+	114.656i	0.514115	+	0.124087i
$925$	711.195	−	516.760i	0.768860	−	0.558660i
$926$	141.602	+	245.262i	0.152918	+	0.264862i
$927$	−91.3143	−	340.790i	−0.0985052	−	0.367626i
$928$	−975.974	+	261.511i	−1.05170	+	0.281801i
$929$	−833.885	+	481.444i	−0.897616	+	0.518239i	−0.876426	−	0.481537i	$-0.840079\pi$
$929$	−833.885	+	481.444i	−0.897616	+	0.518239i	−0.0211899	+	0.999775i	$0.506745\pi$
$930$	−27.8743	+	354.274i	−0.0299724	+	0.380940i
$931$	63.6216	+	1272.99i	0.0683368	+	1.36733i
$932$	−180.773	+	180.773i	−0.193963	+	0.193963i
$933$	−306.462	+	1143.73i	−0.328470	+	1.22587i
$934$	395.057	+	228.086i	0.422973	+	0.244204i
$935$	−435.358	+	80.6985i	−0.465624	+	0.0863086i
$936$	178.110	+	308.496i	0.190288	+	0.329589i
$937$	140.324	−	140.324i	0.149759	−	0.149759i	−0.628251	−	0.778011i	$-0.716229\pi$
$937$	140.324	−	140.324i	0.149759	−	0.149759i	0.778011	+	0.628251i	$0.216229\pi$
$938$	132.241	−	80.8173i	0.140982	−	0.0861592i
$939$		−	510.131i		−	0.543270i
$940$	−1017.28	−	360.212i	−1.08221	−	0.383204i
$941$	918.461	−	1590.82i	0.976048	−	1.69057i	0.299616	−	0.954060i	$-0.403141\pi$
$941$	918.461	−	1590.82i	0.976048	−	1.69057i	0.676432	−	0.736505i	$-0.263525\pi$
$942$	−29.0470	−	108.405i	−0.0308354	−	0.115079i
$943$	43.1630	−	161.086i	0.0457720	−	0.170823i
$944$			492.847i			0.522084i
$945$	120.268	−	25.4142i	0.127268	−	0.0268933i
$946$	59.2225			0.0626031
$947$	−1268.75	−	339.960i	−1.33975	−	0.358986i	−0.483411	−	0.875393i	$-0.660602\pi$
$947$	−1268.75	−	339.960i	−1.33975	−	0.358986i	−0.856343	+	0.516407i	$0.827269\pi$
$948$	2000.07	−	535.917i	2.10978	−	0.565314i
$949$	56.9106	+	32.8573i	0.0599690	+	0.0346231i
$950$	160.327	−	360.143i	0.168766	−	0.379098i
$951$	−788.100			−0.828707
$952$	−617.878	+	15.4306i	−0.649031	+	0.0162086i
$953$	−334.114	−	334.114i	−0.350591	−	0.350591i	0.509738	−	0.860330i	$-0.329742\pi$
$953$	−334.114	−	334.114i	−0.350591	−	0.350591i	−0.860330	+	0.509738i	$0.829742\pi$
$954$	−141.523	+	81.7085i	−0.148347	+	0.0856483i
$955$	1474.69	+	1013.48i	1.54417	+	1.06123i
$956$	−61.3928	+	106.335i	−0.0642184	+	0.111230i
$957$	−732.244	−	196.204i	−0.765145	−	0.205020i
$958$	−229.237	−	229.237i	−0.239287	−	0.239287i
$959$	1079.84	−	1135.16i	1.12601	−	1.18369i
$960$	421.911	+	493.973i	0.439491	+	0.514556i
$961$	79.7981	+	138.214i	0.0830366	+	0.143824i
$962$	−52.1062	−	194.463i	−0.0541645	−	0.202145i
$963$	136.437	−	36.5583i	0.141680	−	0.0379629i
$964$	911.742	−	526.394i	0.945790	−	0.546052i
$965$	−882.858	+	754.065i	−0.914879	+	0.781414i
$966$	−134.686	+	39.7182i	−0.139426	+	0.0411162i
$967$	−121.148	+	121.148i	−0.125283	+	0.125283i	−0.766968	−	0.641685i	$-0.778235\pi$
$967$	−121.148	+	121.148i	−0.125283	+	0.125283i	0.641685	+	0.766968i	$0.278235\pi$
$968$	119.114	−	444.540i	0.123052	−	0.459235i
$969$	−1780.34	−	1027.88i	−1.83730	−	1.06076i
$970$	11.8981	−	17.3127i	0.0122661	−	0.0178481i
$971$	587.626	+	1017.80i	0.605176	+	1.04820i	0.992024	+	0.126052i	$0.0402307\pi$
$971$	587.626	+	1017.80i	0.605176	+	1.04820i	−0.386847	+	0.922144i	$0.626436\pi$
$972$	854.004	−	854.004i	0.878605	−	0.878605i
$973$	654.358	−	399.901i	0.672516	−	0.410998i
$974$		−	78.0333i		−	0.0801164i
$975$	−912.859	+	350.459i	−0.936266	+	0.359445i
$976$	−230.131	+	398.599i	−0.235790	+	0.408401i
$977$	−112.253	−	418.933i	−0.114895	−	0.428796i	0.884384	−	0.466761i	$-0.154579\pi$
$977$	−112.253	−	418.933i	−0.114895	−	0.428796i	−0.999279	+	0.0379651i	$0.987912\pi$
$978$	−155.613	+	580.755i	−0.159113	+	0.593819i
$979$			571.442i			0.583700i
$980$	−466.826	+	757.699i	−0.476353	+	0.773163i
$981$	856.498			0.873087
$982$	236.715	+	63.4275i	0.241054	+	0.0645901i
$983$	−1503.35	+	402.822i	−1.52935	+	0.409788i	−0.922807	−	0.385262i	$-0.874111\pi$
$983$	−1503.35	+	402.822i	−1.52935	+	0.409788i	−0.606543	+	0.795050i	$0.707444\pi$
$984$	346.377	+	199.981i	0.352010	+	0.203233i
$985$	276.118	−	779.787i	0.280323	−	0.791662i
$986$	456.311			0.462790
$987$	−898.243	−	1469.79i	−0.910074	−	1.48915i
$988$	630.991	+	630.991i	0.638654	+	0.638654i
$989$	145.670	−	84.1028i	0.147291	−	0.0850383i
$990$	−20.8982	−	112.743i	−0.0211093	−	0.113882i
$991$	560.438	−	970.706i	0.565527	−	0.979522i	−0.431473	−	0.902126i	$-0.642006\pi$
$991$	560.438	−	970.706i	0.565527	−	0.979522i	0.997000	−	0.0773962i	$-0.0246606\pi$
$992$	700.447	+	187.684i	0.706096	+	0.189198i
$993$	−297.290	−	297.290i	−0.299386	−	0.299386i
$994$	49.6727	+	168.441i	0.0499725	+	0.169458i
$995$	1336.30	+	105.140i	1.34302	+	0.105669i
$996$	401.412	+	695.266i	0.403024	+	0.698058i
$997$	−54.5324	−	203.518i	−0.0546964	−	0.204130i	0.933170	−	0.359435i	$-0.117031\pi$
$997$	−54.5324	−	203.518i	−0.0546964	−	0.204130i	−0.987867	+	0.155305i	$0.950364\pi$
$998$	283.686	−	76.0134i	0.284255	−	0.0761658i
$999$	−106.956	+	61.7509i	−0.107063	+	0.0618127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.l.a.18.4	yes	24
3.2	odd	2		315.3.ca.a.298.3		24
5.2	odd	4	inner	35.3.l.a.32.3	yes	24
5.3	odd	4		175.3.p.c.32.4		24
5.4	even	2		175.3.p.c.18.3		24
7.2	even	3	inner	35.3.l.a.23.3	yes	24
7.3	odd	6		245.3.g.b.148.3		12
7.4	even	3		245.3.g.c.148.3		12
7.5	odd	6		245.3.m.b.128.3		24
7.6	odd	2		245.3.m.b.18.4		24
15.2	even	4		315.3.ca.a.172.4		24
21.2	odd	6		315.3.ca.a.163.4		24
35.2	odd	12	inner	35.3.l.a.2.4	✓	24
35.9	even	6		175.3.p.c.93.4		24
35.12	even	12		245.3.m.b.177.4		24
35.17	even	12		245.3.g.b.197.3		12
35.23	odd	12		175.3.p.c.107.3		24
35.27	even	4		245.3.m.b.67.3		24
35.32	odd	12		245.3.g.c.197.3		12
105.2	even	12		315.3.ca.a.37.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.l.a.2.4	✓	24	35.2	odd	12	inner
35.3.l.a.18.4	yes	24	1.1	even	1	trivial
35.3.l.a.23.3	yes	24	7.2	even	3	inner
35.3.l.a.32.3	yes	24	5.2	odd	4	inner
175.3.p.c.18.3		24	5.4	even	2
175.3.p.c.32.4		24	5.3	odd	4
175.3.p.c.93.4		24	35.9	even	6
175.3.p.c.107.3		24	35.23	odd	12
245.3.g.b.148.3		12	7.3	odd	6
245.3.g.b.197.3		12	35.17	even	12
245.3.g.c.148.3		12	7.4	even	3
245.3.g.c.197.3		12	35.32	odd	12
245.3.m.b.18.4		24	7.6	odd	2
245.3.m.b.67.3		24	35.27	even	4
245.3.m.b.128.3		24	7.5	odd	6
245.3.m.b.177.4		24	35.12	even	12
315.3.ca.a.37.3		24	105.2	even	12
315.3.ca.a.163.4		24	21.2	odd	6
315.3.ca.a.172.4		24	15.2	even	4
315.3.ca.a.298.3		24	3.2	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.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.585559 + 0.156900i) q^{2} +(4.00038 - 1.07190i) q^{3} +(-3.14584 - 1.81625i) q^{4} +(-4.51288 + 2.15265i) q^{5} +2.51064 q^{6} +(3.65026 + 5.97291i) q^{7} +(-3.27174 - 3.27174i) q^{8} +(7.05981 - 4.07598i) q^{9} +O(q^{10})\)	\(q+(0.585559 + 0.156900i) q^{2} +(4.00038 - 1.07190i) q^{3} +(-3.14584 - 1.81625i) q^{4} +(-4.51288 + 2.15265i) q^{5} +2.51064 q^{6} +(3.65026 + 5.97291i) q^{7} +(-3.27174 - 3.27174i) q^{8} +(7.05981 - 4.07598i) q^{9} +(-2.98031 + 0.552433i) q^{10} +(-2.32026 + 4.01881i) q^{11} +(-14.5314 - 3.89367i) q^{12} +(-6.67801 - 6.67801i) q^{13} +(1.20029 + 4.07021i) q^{14} +(-15.7458 + 13.4488i) q^{15} +(5.86255 + 10.1542i) q^{16} +(-4.93904 - 18.4327i) q^{17} +(4.77346 - 1.27904i) q^{18} +(22.5268 - 13.0059i) q^{19} +(18.1066 + 1.42463i) q^{20} +(21.0047 + 19.9812i) q^{21} +(-1.98920 + 1.98920i) q^{22} +(-2.06796 + 7.71775i) q^{23} +(-16.5952 - 9.58122i) q^{24} +(15.7322 - 19.4293i) q^{25} +(-2.86259 - 4.95815i) q^{26} +(-2.48344 + 2.48344i) q^{27} +(-0.634816 - 25.4196i) q^{28} +39.4447i q^{29} +(-11.3302 + 5.40453i) q^{30} +(14.1545 - 24.5164i) q^{31} +(6.62983 + 24.7428i) q^{32} +(-4.97416 + 18.5638i) q^{33} -11.5684i q^{34} +(-29.3308 - 19.0973i) q^{35} -29.6121 q^{36} +(33.9663 + 9.10125i) q^{37} +(15.2314 - 4.08125i) q^{38} +(-33.8727 - 19.5564i) q^{39} +(21.8079 + 7.72205i) q^{40} -20.8722 q^{41} +(9.16446 + 14.9958i) q^{42} +(-14.8860 - 14.8860i) q^{43} +(14.5983 - 8.42835i) q^{44} +(-23.0859 + 33.5918i) q^{45} +(-2.42183 + 4.19473i) q^{46} +(-57.3928 - 15.3783i) q^{47} +(34.3367 + 34.3367i) q^{48} +(-22.3513 + 43.6053i) q^{49} +(12.2606 - 8.90863i) q^{50} +(-39.5160 - 68.4437i) q^{51} +(8.87901 + 33.1369i) q^{52} +(-31.9412 + 8.55863i) q^{53} +(-1.84385 + 1.06455i) q^{54} +(1.81996 - 23.1311i) q^{55} +(7.59911 - 31.4845i) q^{56} +(76.1749 - 76.1749i) q^{57} +(-6.18887 + 23.0972i) q^{58} +(36.4021 + 21.0168i) q^{59} +(73.9601 - 13.7093i) q^{60} +(19.6273 + 33.9954i) q^{61} +(12.1349 - 12.1349i) q^{62} +(50.1156 + 27.2892i) q^{63} -31.3718i q^{64} +(44.5125 + 15.7616i) q^{65} +(-5.82532 + 10.0898i) q^{66} +(-9.45259 - 35.2775i) q^{67} +(-17.9411 + 66.9570i) q^{68} +33.0905i q^{69} +(-14.1785 - 15.7846i) q^{70} +41.3839 q^{71} +(-36.4334 - 9.76231i) q^{72} +(-6.72116 + 1.80093i) q^{73} +(18.4613 + 10.6586i) q^{74} +(42.1084 - 94.5879i) q^{75} -94.4878 q^{76} +(-32.4735 + 0.810977i) q^{77} +(-16.7661 - 16.7661i) q^{78} +(-119.198 + 68.8190i) q^{79} +(-48.3155 - 33.2048i) q^{80} +(-43.9566 + 76.1350i) q^{81} +(-12.2219 - 3.27485i) q^{82} +(-37.7348 - 37.7348i) q^{83} +(-29.7867 - 101.007i) q^{84} +(61.9686 + 72.5527i) q^{85} +(-6.38103 - 11.0523i) q^{86} +(42.2807 + 157.794i) q^{87} +(20.7398 - 5.55720i) q^{88} +(106.644 - 61.5710i) q^{89} +(-18.7887 + 16.0478i) q^{90} +(15.5107 - 64.2636i) q^{91} +(20.5229 - 20.5229i) q^{92} +(30.3444 - 113.247i) q^{93} +(-31.1940 - 18.0099i) q^{94} +(-73.6638 + 107.186i) q^{95} +(53.0436 + 91.8742i) q^{96} +(-4.90063 + 4.90063i) q^{97} +(-19.9296 + 22.0265i) q^{98} +37.8293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8	\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8 + 14 * q^10 - 24 * q^11 - 46 * q^12 - 8 * q^13 + 52 * q^15 + 20 * q^16 - 48 * q^17 - 4 * q^18 - 72 * q^20 + 56 * q^21 + 104 * q^22 - 86 * q^23 - 16 * q^25 + 140 * q^26 + 76 * q^27 + 186 * q^28 + 64 * q^30 + 120 * q^31 + 130 * q^32 + 116 * q^33 - 240 * q^35 - 496 * q^36 + 44 * q^37 + 16 * q^38 - 158 * q^40 + 16 * q^41 - 370 * q^42 - 196 * q^43 - 104 * q^45 - 148 * q^46 - 208 * q^47 - 52 * q^48 + 580 * q^50 - 160 * q^51 - 288 * q^52 - 72 * q^53 + 208 * q^55 + 420 * q^56 + 656 * q^57 - 2 * q^58 + 262 * q^60 + 308 * q^61 + 176 * q^62 + 212 * q^63 + 132 * q^65 + 316 * q^66 + 198 * q^67 + 332 * q^68 - 200 * q^70 - 792 * q^71 + 308 * q^72 + 380 * q^73 - 450 * q^75 - 400 * q^76 - 472 * q^77 - 720 * q^78 - 324 * q^80 - 352 * q^81 - 818 * q^82 - 460 * q^83 + 144 * q^85 - 336 * q^86 - 214 * q^87 - 288 * q^88 + 120 * q^90 + 984 * q^91 + 1372 * q^92 - 68 * q^93 - 88 * q^95 + 816 * q^96 - 72 * q^97 + 482 * q^98

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