LMFDB - Embedded newform 135.3.n.a.104.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(14,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("135.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.n (of order $18$, degree $6$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.30
Character	$\chi$	$=$	135.104
Dual form			135.3.n.a.74.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.86962 + 1.04446i) q^{2} +(-0.799738 + 2.89144i) q^{3} +(4.07967 + 3.42325i) q^{4} +(2.63957 - 4.24649i) q^{5} +(-5.31493 + 7.46205i) q^{6} +(6.76148 + 8.05802i) q^{7} +(2.02410 + 3.50585i) q^{8} +(-7.72084 - 4.62479i) q^{9} +O(q^{10})$	\(q+(2.86962 + 1.04446i) q^{2} +(-0.799738 + 2.89144i) q^{3} +(4.07967 + 3.42325i) q^{4} +(2.63957 - 4.24649i) q^{5} +(-5.31493 + 7.46205i) q^{6} +(6.76148 + 8.05802i) q^{7} +(2.02410 + 3.50585i) q^{8} +(-7.72084 - 4.62479i) q^{9} +(12.0099 - 9.42891i) q^{10} +(-13.6221 + 2.40195i) q^{11} +(-13.1608 + 9.05842i) q^{12} +(-1.13183 - 3.10967i) q^{13} +(10.9866 + 30.1856i) q^{14} +(10.1675 + 11.0282i) q^{15} +(-1.55244 - 8.80433i) q^{16} +(10.9047 - 18.8875i) q^{17} +(-17.3255 - 21.3355i) q^{18} +(6.87151 + 11.9018i) q^{19} +(25.3054 - 8.28838i) q^{20} +(-28.7067 + 13.1061i) q^{21} +(-41.5991 - 7.33504i) q^{22} +(3.41674 + 2.86699i) q^{23} +(-11.7557 + 3.04881i) q^{24} +(-11.0653 - 22.4178i) q^{25} -10.1057i q^{26} +(19.5469 - 18.6257i) q^{27} +56.0203i q^{28} +(1.10591 - 3.03846i) q^{29} +(17.6584 + 42.2664i) q^{30} +(-6.50266 - 5.45638i) q^{31} +(7.55269 - 42.8334i) q^{32} +(3.94904 - 41.3085i) q^{33} +(51.0195 - 42.8105i) q^{34} +(52.0657 - 7.44286i) q^{35} +(-15.6667 - 45.2980i) q^{36} +(6.83119 + 3.94399i) q^{37} +(7.28771 + 41.3307i) q^{38} +(9.89657 - 0.785688i) q^{39} +(20.2303 + 0.658600i) q^{40} +(-10.6450 - 29.2470i) q^{41} +(-96.0661 + 7.62668i) q^{42} +(7.24150 - 1.27687i) q^{43} +(-63.7963 - 36.8328i) q^{44} +(-40.0188 + 20.5790i) q^{45} +(6.81032 + 11.7958i) q^{46} +(-67.5050 + 56.6434i) q^{47} +(26.6987 + 2.55237i) q^{48} +(-10.7053 + 60.7126i) q^{49} +(-8.33894 - 75.8880i) q^{50} +(45.8911 + 46.6353i) q^{51} +(6.02769 - 16.5609i) q^{52} +95.8571 q^{53} +(75.5461 - 33.0329i) q^{54} +(-25.7567 + 64.1863i) q^{55} +(-14.5643 + 40.0150i) q^{56} +(-39.9087 + 10.3502i) q^{57} +(6.34708 - 7.56415i) q^{58} +(-38.6204 - 6.80982i) q^{59} +(3.72767 + 79.7975i) q^{60} +(-74.4337 + 62.4573i) q^{61} +(-12.9612 - 22.4495i) q^{62} +(-14.9377 - 93.4850i) q^{63} +(48.5308 - 84.0578i) q^{64} +(-16.1927 - 3.40189i) q^{65} +(54.4772 - 114.415i) q^{66} +(33.8519 + 93.0075i) q^{67} +(109.144 - 39.7252i) q^{68} +(-11.0222 + 7.58647i) q^{69} +(157.183 + 33.0222i) q^{70} +(-107.192 - 61.8875i) q^{71} +(0.586030 - 36.4292i) q^{72} +(-107.492 + 62.0606i) q^{73} +(15.4836 + 18.4527i) q^{74} +(73.6691 - 14.0664i) q^{75} +(-12.7094 + 72.0783i) q^{76} +(-111.461 - 93.5265i) q^{77} +(29.2201 + 8.08192i) q^{78} +(59.3719 + 21.6096i) q^{79} +(-41.4853 - 16.6472i) q^{80} +(38.2227 + 71.4145i) q^{81} -95.0462i q^{82} +(11.1780 + 4.06846i) q^{83} +(-161.979 - 44.8016i) q^{84} +(-51.4218 - 96.1614i) q^{85} +(22.1140 + 3.89930i) q^{86} +(7.90107 + 5.62763i) q^{87} +(-35.9935 - 42.8953i) q^{88} +(50.3248 - 29.0550i) q^{89} +(-136.333 + 17.2561i) q^{90} +(17.4049 - 30.1462i) q^{91} +(4.12477 + 23.3928i) q^{92} +(20.9772 - 14.4384i) q^{93} +(-252.876 + 92.0392i) q^{94} +(68.6787 + 2.23584i) q^{95} +(117.810 + 56.0936i) q^{96} +(19.8923 - 3.50756i) q^{97} +(-94.1319 + 163.041i) q^{98} +(116.283 + 44.4543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9}+O(q^{10}) $ 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9	$ 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31} + 12 q^{34} - 252 q^{35} + 324 q^{36} - 258 q^{39} + 117 q^{40} + 96 q^{41} - 666 q^{44} - 279 q^{45} - 6 q^{46} + 60 q^{49} + 48 q^{50} + 270 q^{51} + 432 q^{54} - 12 q^{55} + 294 q^{56} + 510 q^{59} + 390 q^{60} + 132 q^{61} - 486 q^{64} + 147 q^{65} - 186 q^{66} - 84 q^{69} - 141 q^{70} - 18 q^{71} - 954 q^{74} - 285 q^{75} + 84 q^{76} - 48 q^{79} - 1026 q^{81} + 198 q^{84} + 69 q^{85} - 1506 q^{86} + 792 q^{89} - 180 q^{90} - 6 q^{91} + 492 q^{94} - 543 q^{95} + 654 q^{96} + 792 q^{99}+O(q^{100}) $ 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	2.86962	+	1.04446i	1.43481	+	0.522229i	0.938307	−	0.345805i	$-0.112394\pi$
$2$	2.86962	+	1.04446i	1.43481	+	0.522229i	0.496506	+	0.868034i	$0.334616\pi$
$3$	−0.799738	+	2.89144i	−0.266579	+	0.963813i
$3$	−0.799738	+	2.89144i	−0.266579	+	0.963813i
$4$	4.07967	+	3.42325i	1.01992	+	0.855813i
$5$	2.63957	−	4.24649i	0.527914	−	0.849298i
$5$	2.63957	−	4.24649i	0.527914	−	0.849298i
$6$	−5.31493	+	7.46205i	−0.885822	+	1.24368i
$7$	6.76148	+	8.05802i	0.965926	+	1.15115i	0.988473	+	0.151399i	$0.0483780\pi$
$7$	6.76148	+	8.05802i	0.965926	+	1.15115i	−0.0225471	+	0.999746i	$0.507178\pi$
$8$	2.02410	+	3.50585i	0.253013	+	0.438232i
$9$	−7.72084	−	4.62479i	−0.857871	−	0.513865i
$10$	12.0099	−	9.42891i	1.20099	−	0.942891i
$11$	−13.6221	+	2.40195i	−1.23837	+	0.218359i	−0.754219	−	0.656623i	$-0.771984\pi$
$11$	−13.6221	+	2.40195i	−1.23837	+	0.218359i	−0.484156	+	0.874982i	$0.660873\pi$
$12$	−13.1608	+	9.05842i	−1.09673	+	0.754868i
$13$	−1.13183	−	3.10967i	−0.0870635	−	0.239205i	0.888518	−	0.458841i	$-0.151735\pi$
$13$	−1.13183	−	3.10967i	−0.0870635	−	0.239205i	−0.975582	+	0.219636i	$0.929513\pi$
$14$	10.9866	+	30.1856i	0.784760	+	2.15611i
$15$	10.1675	+	11.0282i	0.677834	+	0.735215i
$16$	−1.55244	−	8.80433i	−0.0970276	−	0.550271i
$17$	10.9047	−	18.8875i	0.641452	−	1.11103i	−0.343656	−	0.939095i	$-0.611666\pi$
$17$	10.9047	−	18.8875i	0.641452	−	1.11103i	0.985109	−	0.171932i	$-0.0550011\pi$
$18$	−17.3255	−	21.3355i	−0.962528	−	1.18530i
$19$	6.87151	+	11.9018i	0.361658	+	0.626410i	0.988234	−	0.152950i	$-0.0488774\pi$
$19$	6.87151	+	11.9018i	0.361658	+	0.626410i	−0.626576	+	0.779361i	$0.715544\pi$
$20$	25.3054	−	8.28838i	1.26527	−	0.414419i
$21$	−28.7067	+	13.1061i	−1.36698	+	0.624100i
$22$	−41.5991	−	7.33504i	−1.89087	−	0.333411i
$23$	3.41674	+	2.86699i	0.148554	+	0.124652i	0.714036	−	0.700109i	$-0.246865\pi$
$23$	3.41674	+	2.86699i	0.148554	+	0.124652i	−0.565482	+	0.824761i	$0.691310\pi$
$24$	−11.7557	+	3.04881i	−0.489821	+	0.127034i
$25$	−11.0653	−	22.4178i	−0.442614	−	0.896712i
$26$		−	10.1057i		−	0.388681i
$27$	19.5469	−	18.6257i	0.723960	−	0.689841i
$28$			56.0203i			2.00073i
$29$	1.10591	−	3.03846i	0.0381347	−	0.104774i	−0.919164	−	0.393875i	$-0.871134\pi$
$29$	1.10591	−	3.03846i	0.0381347	−	0.104774i	0.957299	+	0.289101i	$0.0933564\pi$
$30$	17.6584	+	42.2664i	0.588613	+	1.40888i
$31$	−6.50266	−	5.45638i	−0.209763	−	0.176012i	0.531853	−	0.846837i	$-0.321496\pi$
$31$	−6.50266	−	5.45638i	−0.209763	−	0.176012i	−0.741616	+	0.670825i	$0.765940\pi$
$32$	7.55269	−	42.8334i	0.236021	−	1.33854i
$33$	3.94904	−	41.3085i	0.119668	−	1.25177i
$34$	51.0195	−	42.8105i	1.50057	−	1.25913i
$35$	52.0657	−	7.44286i	1.48759	−	0.212653i
$36$	−15.6667	−	45.2980i	−0.435186	−	1.25828i
$37$	6.83119	+	3.94399i	0.184627	+	0.106594i	0.589465	−	0.807794i	$-0.299339\pi$
$37$	6.83119	+	3.94399i	0.184627	+	0.106594i	−0.404838	+	0.914388i	$0.632672\pi$
$38$	7.28771	+	41.3307i	0.191782	+	1.08765i
$39$	9.89657	−	0.785688i	0.253758	−	0.0201458i
$40$	20.2303	+	0.658600i	0.505758	+	0.0164650i
$41$	−10.6450	−	29.2470i	−0.259635	−	0.713342i	−0.999190	−	0.0402453i	$-0.987186\pi$
$41$	−10.6450	−	29.2470i	−0.259635	−	0.713342i	0.739555	−	0.673097i	$-0.235036\pi$
$42$	−96.0661	+	7.62668i	−2.28729	+	0.181588i
$43$	7.24150	−	1.27687i	0.168407	−	0.0296947i	−0.0888087	−	0.996049i	$-0.528306\pi$
$43$	7.24150	−	1.27687i	0.168407	−	0.0296947i	0.257216	+	0.966354i	$0.417195\pi$
$44$	−63.7963	−	36.8328i	−1.44991	−	0.837109i
$45$	−40.0188	+	20.5790i	−0.889307	+	0.457312i
$46$	6.81032	+	11.7958i	0.148050	+	0.256431i
$47$	−67.5050	+	56.6434i	−1.43628	+	1.20518i	−0.494393	+	0.869238i	$0.664610\pi$
$47$	−67.5050	+	56.6434i	−1.43628	+	1.20518i	−0.941883	+	0.335941i	$0.890946\pi$
$48$	26.6987	+	2.55237i	0.556224	+	0.0531743i
$49$	−10.7053	+	60.7126i	−0.218475	+	1.23903i
$50$	−8.33894	−	75.8880i	−0.166779	−	1.51776i
$51$	45.8911	+	46.6353i	0.899825	+	0.914417i
$52$	6.02769	−	16.5609i	0.115917	−	0.318480i
$53$	95.8571			1.80863			0.904313	−	0.426871i	$-0.140384\pi$
$53$	95.8571			1.80863			0.904313	+	0.426871i	$0.140384\pi$
$54$	75.5461	−	33.0329i	1.39900	−	0.611720i
$55$	−25.7567	+	64.1863i	−0.468303	+	1.16702i
$56$	−14.5643	+	40.0150i	−0.260076	+	0.714554i
$57$	−39.9087	+	10.3502i	−0.700153	+	0.181583i
$58$	6.34708	−	7.56415i	0.109432	−	0.130416i
$59$	−38.6204	−	6.80982i	−0.654583	−	0.115421i	−0.163514	−	0.986541i	$-0.552283\pi$
$59$	−38.6204	−	6.80982i	−0.654583	−	0.115421i	−0.491069	+	0.871120i	$0.663394\pi$
$60$	3.72767	+	79.7975i	0.0621278	+	1.32996i
$61$	−74.4337	+	62.4573i	−1.22022	+	1.02389i	−0.221412	+	0.975180i	$0.571066\pi$
$61$	−74.4337	+	62.4573i	−1.22022	+	1.02389i	−0.998813	+	0.0487098i	$0.984489\pi$
$62$	−12.9612	−	22.4495i	−0.209052	−	0.362089i
$63$	−14.9377	−	93.4850i	−0.237106	−	1.48389i
$64$	48.5308	−	84.0578i	0.758293	−	1.31340i
$65$	−16.1927	−	3.40189i	−0.249118	−	0.0523368i
$66$	54.4772	−	114.415i	0.825412	−	1.73356i
$67$	33.8519	+	93.0075i	0.505253	+	1.38817i	0.886083	+	0.463526i	$0.153416\pi$
$67$	33.8519	+	93.0075i	0.505253	+	1.38817i	−0.380830	+	0.924645i	$0.624362\pi$
$68$	109.144	−	39.7252i	1.60506	−	0.584194i
$69$	−11.0222	+	7.58647i	−0.159742	+	0.109949i
$70$	157.183	+	33.0222i	2.24547	+	0.471746i
$71$	−107.192	−	61.8875i	−1.50975	−	0.871655i	−0.999935	−	0.0113712i	$-0.996380\pi$
$71$	−107.192	−	61.8875i	−1.50975	−	0.871655i	−0.509815	−	0.860284i	$-0.670286\pi$
$72$	0.586030	−	36.4292i	0.00813930	−	0.505961i
$73$	−107.492	+	62.0606i	−1.47250	+	0.850146i	−0.999522	−	0.0309305i	$-0.990153\pi$
$73$	−107.492	+	62.0606i	−1.47250	+	0.850146i	−0.472974	+	0.881076i	$0.656820\pi$
$74$	15.4836	+	18.4527i	0.209238	+	0.249360i
$75$	73.6691	−	14.0664i	0.982255	−	0.187552i
$76$	−12.7094	+	72.0783i	−0.167228	+	0.948399i
$77$	−111.461	−	93.5265i	−1.44754	−	1.21463i
$78$	29.2201	+	8.08192i	0.374616	+	0.103614i
$79$	59.3719	+	21.6096i	0.751543	+	0.273539i	0.689255	−	0.724519i	$-0.257938\pi$
$79$	59.3719	+	21.6096i	0.751543	+	0.273539i	0.0622881	+	0.998058i	$0.480160\pi$
$80$	−41.4853	−	16.6472i	−0.518566	−	0.208090i
$81$	38.2227	+	71.4145i	0.471885	+	0.881660i
$82$		−	95.0462i		−	1.15910i
$83$	11.1780	+	4.06846i	0.134675	+	0.0490176i	0.408478	−	0.912768i	$-0.366060\pi$
$83$	11.1780	+	4.06846i	0.134675	+	0.0490176i	−0.273803	+	0.961786i	$0.588282\pi$
$84$	−161.979	−	44.8016i	−1.92833	−	0.533352i
$85$	−51.4218	−	96.1614i	−0.604962	−	1.13131i
$86$	22.1140	+	3.89930i	0.257140	+	0.0453407i
$87$	7.90107	+	5.62763i	0.0908169	+	0.0646854i
$88$	−35.9935	−	42.8953i	−0.409017	−	0.487447i
$89$	50.3248	−	29.0550i	0.565447	−	0.326461i	−0.189882	−	0.981807i	$-0.560810\pi$
$89$	50.3248	−	29.0550i	0.565447	−	0.326461i	0.755329	+	0.655346i	$0.227477\pi$
$90$	−136.333	+	17.2561i	−1.51481	+	0.191735i
$91$	17.4049	−	30.1462i	0.191263	−	0.331277i
$92$	4.12477	+	23.3928i	0.0448345	+	0.254269i
$93$	20.9772	−	14.4384i	0.225561	−	0.155251i
$94$	−252.876	+	92.0392i	−2.69017	+	0.979140i
$95$	68.6787	+	2.23584i	0.722933	+	0.0235351i
$96$	117.810	+	56.0936i	1.22719	+	0.584309i
$97$	19.8923	−	3.50756i	0.205076	−	0.0361604i	−0.0701665	−	0.997535i	$-0.522353\pi$
$97$	19.8923	−	3.50756i	0.205076	−	0.0361604i	0.275242	+	0.961375i	$0.411242\pi$
$98$	−94.1319	+	163.041i	−0.960530	+	1.66369i
$99$	116.283	+	44.4543i	1.17457	+	0.449034i
$100$	31.5988	−	129.337i	0.315988	−	1.29337i
$101$	76.9560	+	91.7126i	0.761941	+	0.908045i	0.997969	−	0.0637008i	$-0.0202903\pi$
$101$	76.9560	+	91.7126i	0.761941	+	0.908045i	−0.236029	+	0.971746i	$0.575846\pi$
$102$	82.9816	+	181.757i	0.813545	+	1.78193i
$103$	−149.976	−	26.4448i	−1.45608	−	0.256746i	−0.611103	−	0.791551i	$-0.709274\pi$
$103$	−149.976	−	26.4448i	−1.45608	−	0.256746i	−0.844976	+	0.534805i	$0.820385\pi$
$104$	8.61110	−	10.2623i	0.0827990	−	0.0986760i
$105$	−20.1183	+	156.497i	−0.191603	+	1.49045i
$106$	275.074	+	100.119i	2.59504	+	0.944516i
$107$	92.8413			0.867676			0.433838	−	0.900991i	$-0.357159\pi$
$107$	92.8413			0.867676			0.433838	+	0.900991i	$0.357159\pi$
$108$	143.506	−	9.07276i	1.32876	−	0.0840071i
$109$	−20.8955			−0.191702			−0.0958510	−	0.995396i	$-0.530557\pi$
$109$	−20.8955			−0.191702			−0.0958510	+	0.995396i	$0.530557\pi$
$110$	−140.952	+	157.289i	−1.28138	+	1.42990i
$111$	−16.8670	+	16.5978i	−0.151955	+	0.149530i
$112$	60.4487	−	72.0399i	0.539720	−	0.643214i
$113$	−16.2129	+	91.9482i	−0.143477	+	0.813701i	0.825100	+	0.564987i	$0.191119\pi$
$113$	−16.2129	+	91.9482i	−0.143477	+	0.813701i	−0.968577	+	0.248714i	$0.919992\pi$
$114$	−125.333	−	11.9817i	−1.09942	−	0.105103i
$115$	21.1934	−	6.94155i	0.184290	−	0.0603613i
$116$	14.9131	−	8.61010i	0.128562	−	0.0742250i
$117$	−5.64289	+	29.2437i	−0.0482299	+	0.249946i
$118$	−103.713	−	59.8790i	−0.878928	−	0.507449i
$119$	225.927	−	39.8371i	1.89855	−	0.334766i
$120$	−18.0833	+	57.9681i	−0.150694	+	0.483067i
$121$	66.0899	−	24.0548i	0.546198	−	0.198800i
$122$	−278.831	+	101.486i	−2.28550	+	0.831853i
$123$	93.0792	−	7.38955i	0.756741	−	0.0600776i
$124$	−7.85016	−	44.5205i	−0.0633077	−	0.359036i
$125$	−124.405	−	12.1845i	−0.995238	−	0.0974757i
$126$	54.7756	−	283.869i	0.434727	−	2.25293i
$127$	8.67105	−	5.00623i	0.0682760	−	0.0394192i	−0.465473	−	0.885062i	$-0.654116\pi$
$127$	8.67105	−	5.00623i	0.0682760	−	0.0394192i	0.533749	+	0.845643i	$0.320783\pi$
$128$	93.7859	−	78.6957i	0.732702	−	0.614810i
$129$	−2.09931	+	21.9595i	−0.0162737	+	0.170229i
$130$	−42.9138	−	26.6747i	−0.330106	−	0.205190i
$131$	76.0426	−	90.6241i	0.580478	−	0.691787i	−0.393268	−	0.919424i	$-0.628656\pi$
$131$	76.0426	−	90.6241i	0.580478	−	0.691787i	0.973746	+	0.227637i	$0.0731000\pi$
$132$	157.520	−	155.006i	1.19333	−	1.17429i
$133$	−49.4433	+	135.844i	−0.371754	+	1.02139i
$134$			302.253i			2.25562i
$135$	−27.4984	−	132.170i	−0.203692	−	0.979035i
$136$	88.2889			0.649183
$137$	160.648	+	58.4710i	1.17261	+	0.426796i	0.853587	−	0.520951i	$-0.174422\pi$
$137$	160.648	+	58.4710i	1.17261	+	0.426796i	0.319025	+	0.947746i	$0.396645\pi$
$138$	−39.5534	+	10.2581i	−0.286619	+	0.0743338i
$139$	−3.65914	−	3.07039i	−0.0263248	−	0.0220891i	0.629530	−	0.776976i	$-0.283247\pi$
$139$	−3.65914	−	3.07039i	−0.0263248	−	0.0220891i	−0.655855	+	0.754887i	$0.727692\pi$
$140$	237.890	+	147.870i	1.69921	+	1.05621i
$141$	−109.795	−	240.486i	−0.778686	−	1.70558i
$142$	−242.963	−	289.552i	−1.71101	−	2.03910i
$143$	22.8871	+	39.6417i	0.160050	+	0.277214i
$144$	−28.7320	+	75.1566i	−0.199528	+	0.521921i
$145$	−9.98365	−	12.7164i	−0.0688528	−	0.0876996i
$146$	−373.282	+	65.8197i	−2.55673	+	0.450820i
$147$	−166.985	−	79.5078i	−1.13596	−	0.540870i
$148$	14.3677	+	39.4751i	0.0970794	+	0.266723i
$149$	−0.443210	−	1.21771i	−0.00297457	−	0.00817256i	0.938196	−	0.346103i	$-0.112495\pi$
$149$	−0.443210	−	1.21771i	−0.00297457	−	0.00817256i	−0.941171	+	0.337931i	$0.890273\pi$
$150$	226.094	+	36.5789i	1.50730	+	0.243860i
$151$	−3.86934	−	21.9441i	−0.0256248	−	0.145325i	0.969311	−	0.245838i	$-0.0790630\pi$
$151$	−3.86934	−	21.9441i	−0.0256248	−	0.145325i	−0.994936	+	0.100512i	$0.967952\pi$
$152$	−27.8173	+	48.1810i	−0.183009	+	0.316980i
$153$	−171.544	+	95.3953i	−1.12120	+	0.623499i
$154$	−222.165	−	384.802i	−1.44263	−	2.49871i
$155$	−40.3347	+	13.2110i	−0.260224	+	0.0852322i
$156$	43.0644	+	30.6731i	0.276054	+	0.196623i
$157$	231.652	+	40.8466i	1.47549	+	0.260169i	0.852776	−	0.522277i	$-0.174917\pi$
$157$	231.652	+	40.8466i	1.47549	+	0.260169i	0.622718	+	0.782447i	$0.286029\pi$
$158$	147.805	+	124.023i	0.935473	+	0.784955i
$159$	−76.6606	+	277.165i	−0.482142	+	1.74318i
$160$	−161.956	−	145.134i	−1.01222	−	0.907089i
$161$			46.9173i			0.291412i
$162$	35.0954	+	244.855i	0.216638	+	1.51145i
$163$		−	256.818i		−	1.57557i	−0.615951	−	0.787785i	$-0.711228\pi$
$163$		−	256.818i		−	1.57557i	0.615951	−	0.787785i	$-0.288772\pi$
$164$	56.6916	−	155.759i	0.345681	−	0.949749i
$165$	−164.992	−	125.806i	−0.999952	−	0.762461i
$166$	27.8273	+	23.3499i	0.167635	+	0.140662i
$167$	40.1788	−	227.865i	0.240592	−	1.36446i	−0.589920	−	0.807462i	$-0.700841\pi$
$167$	40.1788	−	227.865i	0.240592	−	1.36446i	0.830511	−	0.557002i	$-0.188048\pi$
$168$	−104.053	−	74.1132i	−0.619365	−	0.441150i
$169$	121.073	−	101.592i	0.716405	−	0.601136i
$170$	−47.1246	−	329.655i	−0.277204	−	1.93915i
$171$	1.98947	−	123.671i	0.0116344	−	0.723223i
$172$	33.9140	+	19.5803i	0.197175	+	0.113839i
$173$	−26.1253	−	148.164i	−0.151013	−	0.856439i	−0.962341	−	0.271847i	$-0.912366\pi$
$173$	−26.1253	−	148.164i	−0.151013	−	0.856439i	0.811327	−	0.584592i	$-0.198746\pi$
$174$	16.7953	+	24.4015i	0.0965246	+	0.140239i
$175$	105.825	−	240.742i	0.604714	−	1.37567i
$176$	42.2951	+	116.205i	0.240313	+	0.660255i
$177$	50.5764	−	106.222i	0.285742	−	0.600127i
$178$	174.760	−	30.8149i	0.981798	−	0.173117i
$179$	−48.2519	−	27.8583i	−0.269564	−	0.155633i	0.359126	−	0.933289i	$-0.383075\pi$
$179$	−48.2519	−	27.8583i	−0.269564	−	0.155633i	−0.628689	+	0.777656i	$0.716408\pi$
$180$	−233.711	−	53.0387i	−1.29839	−	0.294660i
$181$	63.8324	+	110.561i	0.352665	+	0.610834i	0.986716	−	0.162458i	$-0.0519421\pi$
$181$	63.8324	+	110.561i	0.352665	+	0.610834i	−0.634050	+	0.773292i	$0.718609\pi$
$182$	81.4320	−	68.3296i	0.447429	−	0.375437i
$183$	−121.064	−	265.170i	−0.661552	−	1.44902i
$184$	−3.13539	+	17.7817i	−0.0170402	+	0.0966396i
$185$	34.7795	−	18.5981i	0.187997	−	0.100530i
$186$	75.2770	−	19.5229i	0.404715	−	0.104962i
$187$	−103.178	+	283.480i	−0.551755	+	1.51594i
$188$	−469.303			−2.49629
$189$	282.253	+	31.5721i	1.49340	+	0.167048i
$190$	194.747	+	78.1480i	1.02498	+	0.411305i
$191$	−26.2032	+	71.9927i	−0.137190	+	0.376925i	−0.989195	−	0.146608i	$-0.953164\pi$
$191$	−26.2032	+	71.9927i	−0.137190	+	0.376925i	0.852005	+	0.523534i	$0.175387\pi$
$192$	204.236	+	207.548i	1.06373	+	1.08098i
$193$	20.9031	−	24.9113i	0.108306	−	0.129074i	−0.709168	−	0.705040i	$-0.750929\pi$
$193$	20.9031	−	24.9113i	0.108306	−	0.129074i	0.817474	+	0.575965i	$0.195374\pi$
$194$	60.7470	+	10.7113i	0.313129	+	0.0552131i
$195$	22.7863	−	44.0996i	0.116853	−	0.226152i
$196$	−251.509	+	211.041i	−1.28321	+	1.07674i
$197$	−77.6099	−	134.424i	−0.393959	−	0.682356i	0.599009	−	0.800742i	$-0.295561\pi$
$197$	−77.6099	−	134.424i	−0.393959	−	0.682356i	−0.992968	+	0.118386i	$0.962228\pi$
$198$	287.257	+	249.020i	1.45079	+	1.25767i
$199$	−76.8994	+	133.194i	−0.386429	+	0.669315i	−0.991966	−	0.126502i	$-0.959625\pi$
$199$	−76.8994	+	133.194i	−0.386429	+	0.669315i	0.605537	+	0.795817i	$0.292958\pi$
$200$	56.1961	−	84.1695i	0.280980	−	0.420847i
$201$	−295.998	+	23.4993i	−1.47263	+	0.116912i
$202$	125.045	+	343.558i	0.619034	+	1.70078i
$203$	31.9615	−	11.6330i	0.157446	−	0.0573056i
$204$	27.5764	+	347.353i	0.135178	+	1.70271i
$205$	−152.295	−	31.9955i	−0.742905	−	0.156075i
$206$	−402.755	−	232.530i	−1.95512	−	1.12879i
$207$	−13.1209	−	37.9373i	−0.0633861	−	0.183272i
$208$	−25.6214	+	14.7925i	−0.123180	+	0.0711180i
$209$	−122.192	−	145.623i	−0.584650	−	0.696759i
$210$	−221.187	+	428.075i	−1.05327	+	2.03845i
$211$	−12.5589	+	71.2252i	−0.0595210	+	0.337560i	−0.999997	−	0.00229880i	$-0.999268\pi$
$211$	−12.5589	+	71.2252i	−0.0595210	+	0.337560i	0.940476	+	0.339859i	$0.110379\pi$
$212$	391.066	+	328.143i	1.84465	+	1.54784i
$213$	264.670	−	260.446i	1.24258	−	1.22275i
$214$	266.420	+	96.9688i	1.24495	+	0.453125i
$215$	13.6922	−	34.1214i	0.0636848	−	0.158704i
$216$	104.864	+	30.8283i	0.485482	+	0.142723i
$217$		−	89.2917i		−	0.411483i
$218$	−59.9623	−	21.8245i	−0.275056	−	0.100112i
$219$	−93.4790	−	360.439i	−0.426845	−	1.64584i
$220$	−324.805	+	173.687i	−1.47638	+	0.789488i
$221$	−71.0760	−	12.5326i	−0.321611	−	0.0567086i
$222$	−65.7375	+	30.0126i	−0.296115	+	0.135192i
$223$	68.7753	+	81.9632i	0.308409	+	0.367548i	0.897879	−	0.440243i	$-0.145108\pi$
$223$	68.7753	+	81.9632i	0.308409	+	0.367548i	−0.589469	+	0.807791i	$0.700663\pi$
$224$	396.220	−	228.758i	1.76884	−	1.02124i
$225$	−18.2438	+	224.259i	−0.0810835	+	0.996707i
$226$	−142.561	+	246.923i	−0.630801	+	1.09258i
$227$	44.7492	+	253.785i	0.197133	+	1.11800i	0.909348	+	0.416036i	$0.136581\pi$
$227$	44.7492	+	253.785i	0.197133	+	1.11800i	−0.712215	+	0.701961i	$0.752308\pi$
$228$	−198.246	−	94.3921i	−0.869500	−	0.414000i
$229$	−5.28951	+	1.92522i	−0.0230983	+	0.00840709i	−0.353543	−	0.935418i	$-0.615023\pi$
$229$	−5.28951	+	1.92522i	−0.0230983	+	0.00840709i	0.330445	+	0.943825i	$0.392801\pi$
$230$	68.0672	+	2.21593i	0.295944	+	0.00963448i
$231$	359.566	−	247.485i	1.55656	−	1.07136i
$232$	12.8908	−	2.27300i	0.0555640	−	0.00979743i
$233$	−64.3582	+	111.472i	−0.276216	+	0.478419i	−0.970441	−	0.241338i	$-0.922414\pi$
$233$	−64.3582	+	111.472i	−0.276216	+	0.478419i	0.694226	+	0.719758i	$0.255747\pi$
$234$	−46.7368	+	78.0246i	−0.199730	+	0.333439i
$235$	62.3516	+	436.173i	0.265326	+	1.85606i
$236$	−134.247	−	159.989i	−0.568843	−	0.677920i
$237$	−109.965	+	154.388i	−0.463986	+	0.651427i
$238$	689.935	+	121.654i	2.89889	+	0.511152i
$239$	7.51579	−	8.95697i	0.0314468	−	0.0374768i	−0.750092	−	0.661334i	$-0.769991\pi$
$239$	7.51579	−	8.95697i	0.0314468	−	0.0374768i	0.781539	+	0.623857i	$0.214435\pi$
$240$	81.3118	−	106.639i	0.338799	−	0.444328i
$241$	−107.769	−	39.2248i	−0.447176	−	0.162759i	0.108610	−	0.994084i	$-0.465360\pi$
$241$	−107.769	−	39.2248i	−0.447176	−	0.162759i	−0.555785	+	0.831326i	$0.687582\pi$
$242$	214.777			0.887510
$243$	−237.059	+	53.4058i	−0.975550	+	0.219777i
$244$	−517.472			−2.12079
$245$	229.558	+	205.715i	0.936973	+	0.839653i
$246$	274.820	+	76.0121i	1.11716	+	0.308992i
$247$	29.2333	−	34.8389i	0.118353	−	0.141048i
$248$	5.96719	−	33.8416i	0.0240613	−	0.136458i
$249$	−20.7032	+	29.0668i	−0.0831453	+	0.116734i
$250$	−344.269	−	164.900i	−1.37707	−	0.659601i
$251$	35.0259	−	20.2222i	0.139546	−	0.0805667i	−0.428602	−	0.903493i	$-0.640994\pi$
$251$	35.0259	−	20.2222i	0.139546	−	0.0805667i	0.568147	+	0.822927i	$0.307660\pi$
$252$	259.082	−	432.524i	1.02810	−	1.71636i
$253$	−53.4296	−	30.8476i	−0.211184	−	0.121927i
$254$	30.1115	−	5.30946i	0.118549	−	0.0209034i
$255$	319.169	−	71.7790i	1.25164	−	0.281486i
$256$	−13.5075	+	4.91632i	−0.0527636	+	0.0192044i
$257$	−34.8884	+	12.6984i	−0.135753	+	0.0494099i	−0.409003	−	0.912533i	$-0.634123\pi$
$257$	−34.8884	+	12.6984i	−0.135753	+	0.0494099i	0.273250	+	0.961943i	$0.411901\pi$
$258$	−28.9600	+	60.8230i	−0.112248	+	0.235748i
$259$	14.4082	+	81.7130i	0.0556302	+	0.315494i
$260$	−54.4154	−	69.3103i	−0.209290	−	0.266578i
$261$	−22.5907	+	18.3448i	−0.0865546	+	0.0702867i
$262$	312.867	−	180.634i	1.19415	−	0.689442i
$263$	69.7330	−	58.5129i	0.265144	−	0.222483i	−0.500516	−	0.865727i	$-0.666857\pi$
$263$	69.7330	−	58.5129i	0.265144	−	0.222483i	0.765661	+	0.643244i	$0.222412\pi$
$264$	152.815	−	69.7679i	0.578843	−	0.264272i
$265$	253.022	−	407.056i	0.954798	−	1.53606i
$266$	−283.768	+	338.181i	−1.06680	+	1.27136i
$267$	43.7642	+	168.747i	0.163911	+	0.632013i
$268$	−180.283	+	495.324i	−0.672698	+	1.84822i
$269$			472.530i			1.75662i	0.478094	+	0.878309i	$0.341328\pi$
$269$			472.530i			1.75662i	−0.478094	+	0.878309i	$0.658672\pi$
$270$	59.1355	−	407.998i	0.219020	−	1.51111i
$271$	138.785			0.512121			0.256060	−	0.966661i	$-0.417575\pi$
$271$	138.785			0.512121			0.256060	+	0.966661i	$0.417575\pi$
$272$	−183.221	−	66.6868i	−0.673605	−	0.245172i
$273$	73.2466	+	74.4343i	0.268302	+	0.272653i
$274$	399.928	+	335.580i	1.45959	+	1.22474i
$275$	204.580	+	278.800i	0.743927	+	1.01382i
$276$	−70.9375	−	6.78154i	−0.257020	−	0.0245708i
$277$	184.029	+	219.318i	0.664366	+	0.791761i	0.988005	−	0.154420i	$-0.0493508\pi$
$277$	184.029	+	219.318i	0.664366	+	0.791761i	−0.323639	+	0.946181i	$0.604906\pi$
$278$	−7.29348	−	12.6327i	−0.0262355	−	0.0454413i
$279$	24.9714	+	72.2012i	0.0895032	+	0.258786i
$280$	131.480	+	167.469i	0.469571	+	0.598105i
$281$	−271.004	+	47.7854i	−0.964428	+	0.170055i	−0.633621	−	0.773644i	$-0.718432\pi$
$281$	−271.004	+	47.7854i	−0.964428	+	0.170055i	−0.330807	+	0.943698i	$0.607321\pi$
$282$	−63.8915	−	804.782i	−0.226566	−	2.85384i
$283$	−143.906	−	395.378i	−0.508502	−	1.39710i	−0.882783	−	0.469782i	$-0.844333\pi$
$283$	−143.906	−	395.378i	−0.508502	−	1.39710i	0.374281	−	0.927315i	$-0.377890\pi$
$284$	−225.453	−	619.427i	−0.793849	−	2.18108i
$285$	−61.3897	+	196.792i	−0.215403	+	0.690499i
$286$	24.2734	+	137.661i	0.0848720	+	0.481333i
$287$	163.697	−	283.531i	0.570372	−	0.987913i
$288$	−256.408	+	295.780i	−0.890307	+	1.02702i
$289$	−93.3245	−	161.643i	−0.322922	−	0.559317i
$290$	−15.3675	−	46.9189i	−0.0529915	−	0.161789i
$291$	−5.76677	+	60.3226i	−0.0198171	+	0.207294i
$292$	−650.982	−	114.786i	−2.22939	−	0.393102i
$293$	−237.679	−	199.436i	−0.811191	−	0.680670i	0.139701	−	0.990194i	$-0.455386\pi$
$293$	−237.679	−	199.436i	−0.811191	−	0.680670i	−0.950892	+	0.309524i	$0.899830\pi$
$294$	−396.143	−	402.567i	−1.34743	−	1.36928i
$295$	−130.859	+	146.026i	−0.443590	+	0.495004i
$296$			31.9322i			0.107879i
$297$	−221.533	+	300.672i	−0.745901	+	1.01237i
$298$		−	3.95729i		−	0.0132795i
$299$	5.04822	−	13.8699i	0.0168837	−	0.0463875i
$300$	348.699	+	194.802i	1.16233	+	0.649338i
$301$	59.2523	+	49.7186i	0.196852	+	0.165178i
$302$	11.8162	−	67.0127i	0.0391263	−	0.221896i
$303$	−326.726	+	149.168i	−1.07830	+	0.492302i
$304$	94.1198	−	78.9759i	0.309605	−	0.259789i
$305$	68.7513	+	480.942i	0.225414	+	1.57686i
$306$	−591.903	+	94.5783i	−1.93432	+	0.309079i
$307$	−10.9382	−	6.31520i	−0.0356295	−	0.0205707i	0.482079	−	0.876127i	$-0.339882\pi$
$307$	−10.9382	−	6.31520i	−0.0356295	−	0.0205707i	−0.517709	+	0.855557i	$0.673215\pi$
$308$	−134.558	−	763.115i	−0.436876	−	2.47765i
$309$	196.405	−	412.498i	0.635616	−	1.33494i
$310$	−129.544	−	4.21730i	−0.417883	−	0.0136042i
$311$	−74.8121	−	205.545i	−0.240553	−	0.660915i	−0.999947	−	0.0102838i	$-0.996727\pi$
$311$	−74.8121	−	205.545i	−0.240553	−	0.660915i	0.759394	−	0.650631i	$-0.225496\pi$
$312$	22.7862	+	33.1056i	0.0730327	+	0.106108i
$313$	66.7119	−	11.7631i	0.213137	−	0.0375818i	−0.0660599	−	0.997816i	$-0.521043\pi$
$313$	66.7119	−	11.7631i	0.213137	−	0.0375818i	0.279197	+	0.960234i	$0.409932\pi$
$314$	622.093	+	359.166i	1.98119	+	1.14384i
$315$	−436.412	−	183.328i	−1.38544	−	0.581992i
$316$	168.243	+	291.405i	0.532414	+	0.922168i
$317$	119.433	−	100.216i	0.376761	−	0.316140i	−0.434668	−	0.900591i	$-0.643134\pi$
$317$	119.433	−	100.216i	0.376761	−	0.316140i	0.811429	+	0.584451i	$0.198690\pi$
$318$	−509.474	+	715.291i	−1.60212	+	2.24934i
$319$	−7.76659	+	44.0465i	−0.0243467	+	0.138077i
$320$	−228.850	−	427.962i	−0.715156	−	1.33738i
$321$	−74.2487	+	268.445i	−0.231304	+	0.836277i
$322$	−49.0031	+	134.635i	−0.152184	+	0.418121i
$323$	299.727			0.927946
$324$	−88.5335	+	422.194i	−0.273252	+	1.30307i
$325$	−57.1878	+	59.7826i	−0.175963	+	0.183946i
$326$	268.235	−	736.971i	0.822808	−	2.26065i
$327$	16.7109	−	60.4181i	0.0511038	−	0.184765i
$328$	80.9890	−	96.5190i	0.246918	−	0.294265i
$329$	−912.867	−	160.963i	−2.77467	−	0.489250i
$330$	−342.066	−	533.343i	−1.03656	−	1.61619i
$331$	362.160	−	303.889i	1.09414	−	0.918093i	0.0971231	−	0.995272i	$-0.469036\pi$
$331$	362.160	−	303.889i	1.09414	−	0.918093i	0.997017	+	0.0771796i	$0.0245915\pi$
$332$	31.6752	+	54.8631i	0.0954074	+	0.165250i
$333$	−34.5024	−	62.0437i	−0.103611	−	0.186317i
$334$	353.294	−	611.923i	1.05777	−	1.83211i
$335$	484.310	+	101.748i	1.44570	+	0.303724i
$336$	159.956	+	232.397i	0.476059	+	0.691657i
$337$	−45.0272	−	123.711i	−0.133612	−	0.367095i	0.854786	−	0.518980i	$-0.173688\pi$
$337$	−45.0272	−	123.711i	−0.133612	−	0.367095i	−0.988398	+	0.151885i	$0.951466\pi$
$338$	453.541	−	165.075i	1.34184	−	0.488389i
$339$	−252.896	−	120.413i	−0.746007	−	0.355201i
$340$	119.401	−	568.337i	0.351179	−	1.67158i
$341$	101.686	+	58.7084i	0.298199	+	0.172165i
$342$	134.878	−	352.812i	0.394381	−	1.03161i
$343$	−115.231	+	66.5286i	−0.335950	+	0.193961i
$344$	19.1341	+	22.8031i	0.0556224	+	0.0662881i
$345$	3.12194	+	66.8308i	0.00904910	+	0.193712i
$346$	79.7812	−	452.462i	0.230582	−	1.30769i
$347$	28.1665	+	23.6345i	0.0811715	+	0.0681110i	0.682471	−	0.730913i	$-0.260906\pi$
$347$	28.1665	+	23.6345i	0.0811715	+	0.0681110i	−0.601299	+	0.799024i	$0.705350\pi$
$348$	12.9690	+	50.0063i	0.0372672	+	0.143696i
$349$	228.030	+	82.9963i	0.653382	+	0.237812i	0.647377	−	0.762170i	$-0.275866\pi$
$349$	228.030	+	82.9963i	0.653382	+	0.237812i	0.00600576	+	0.999982i	$0.498088\pi$
$350$	555.123	−	580.310i	1.58607	−	1.65803i
$351$	−80.0435	−	39.7034i	−0.228044	−	0.113115i
$352$			601.623i			1.70916i
$353$	−553.882	−	201.596i	−1.56907	−	0.571095i	−0.596278	−	0.802778i	$-0.703355\pi$
$353$	−553.882	−	201.596i	−1.56907	−	0.571095i	−0.972791	+	0.231683i	$0.925577\pi$
$354$	256.080	−	251.994i	0.723390	−	0.711846i
$355$	−545.746	+	291.835i	−1.53731	+	0.822069i
$356$	304.771	+	53.7394i	0.856099	+	0.150953i
$357$	−65.4961	+	685.115i	−0.183463	+	1.91909i
$358$	−109.368	−	130.340i	−0.305498	−	0.364078i
$359$	−339.767	+	196.165i	−0.946427	+	0.546420i	−0.891969	−	0.452096i	$-0.850676\pi$
$359$	−339.767	+	196.165i	−0.946427	+	0.546420i	−0.0544581	+	0.998516i	$0.517343\pi$
$360$	−153.149	−	98.6459i	−0.425415	−	0.274016i
$361$	86.0648	−	149.069i	0.238407	−	0.412933i
$362$	67.6987	+	383.939i	0.187013	+	1.06060i
$363$	16.6983	+	210.333i	0.0460008	+	0.579429i
$364$	174.204	−	63.4052i	0.478584	−	0.174190i
$365$	−20.1932	+	620.278i	−0.0553238	+	1.69939i
$366$	−70.4494	−	887.384i	−0.192485	−	2.42455i
$367$	635.805	−	112.110i	1.73244	−	0.305476i	0.783607	−	0.621257i	$-0.213378\pi$
$367$	635.805	−	112.110i	1.73244	−	0.305476i	0.948832	+	0.315781i	$0.102267\pi$
$368$	19.9376	−	34.5330i	0.0541783	−	0.0938396i
$369$	−53.0725	+	275.043i	−0.143828	+	0.745373i
$370$	119.229	−	17.0440i	0.322241	−	0.0460647i
$371$	648.136	+	772.418i	1.74700	+	2.08199i
$372$	135.006	+	12.9064i	0.362920	+	0.0346947i
$373$	450.568	+	79.4473i	1.20796	+	0.212995i	0.741135	−	0.671356i	$-0.234288\pi$
$373$	450.568	+	79.4473i	1.20796	+	0.212995i	0.466822	+	0.884351i	$0.345399\pi$
$374$	−592.166	+	705.715i	−1.58333	+	1.88694i
$375$	134.722	−	349.964i	0.359258	−	0.933238i
$376$	−335.221	−	122.010i	−0.891544	−	0.324496i
$377$	−10.7003			−0.0283827
$378$	776.983	+	385.401i	2.05551	+	1.01958i
$379$	198.451			0.523618			0.261809	−	0.965120i	$-0.415681\pi$
$379$	198.451			0.523618			0.261809	+	0.965120i	$0.415681\pi$
$380$	272.533	+	244.226i	0.717191	+	0.642700i
$381$	7.54065	+	29.0755i	0.0197917	+	0.0763136i
$382$	−150.387	+	179.224i	−0.393683	+	0.469173i
$383$	20.2158	−	114.649i	0.0527827	−	0.299345i	−0.946976	−	0.321304i	$-0.895879\pi$
$383$	20.2158	−	114.649i	0.0527827	−	0.299345i	0.999759	+	0.0219582i	$0.00699009\pi$
$384$	152.540	+	334.112i	0.397239	+	0.870083i
$385$	−691.367	+	226.446i	−1.79576	+	0.588173i
$386$	86.0028	−	49.6538i	0.222805	−	0.128637i
$387$	−61.8158	−	23.6319i	−0.159731	−	0.0610643i
$388$	93.1615	+	53.7868i	0.240107	+	0.138626i
$389$	543.225	−	95.7853i	1.39647	−	0.246235i	0.575776	−	0.817608i	$-0.304700\pi$
$389$	543.225	−	95.7853i	1.39647	−	0.246235i	0.820690	+	0.571373i	$0.193589\pi$
$390$	111.448	−	102.750i	0.285765	−	0.263461i
$391$	91.4087	−	33.2701i	0.233782	−	0.0850896i
$392$	−234.518	+	85.3576i	−0.598261	+	0.217749i
$393$	201.220	+	292.348i	0.512010	+	0.743888i
$394$	−82.3107	−	466.807i	−0.208910	−	1.18479i
$395$	248.481	−	195.082i	0.629066	−	0.493879i
$396$	322.217	+	579.424i	0.813679	+	1.46319i
$397$	−69.6526	+	40.2140i	−0.175447	+	0.101295i	−0.585152	−	0.810924i	$-0.698965\pi$
$397$	−69.6526	+	40.2140i	−0.175447	+	0.101295i	0.409705	+	0.912218i	$0.365632\pi$
$398$	−359.787	+	301.897i	−0.903989	+	0.758536i
$399$	−353.244	−	251.602i	−0.885324	−	0.630582i
$400$	−180.196	+	132.225i	−0.450489	+	0.330563i
$401$	293.307	−	349.550i	0.731440	−	0.871696i	−0.264249	−	0.964455i	$-0.585124\pi$
$401$	293.307	−	349.550i	0.731440	−	0.871696i	0.995689	+	0.0927585i	$0.0295685\pi$
$402$	−873.947	−	241.723i	−2.17400	−	0.601302i
$403$	−9.60764	+	26.3968i	−0.0238403	+	0.0655007i
$404$			637.597i			1.57821i
$405$	404.152	+	26.1911i	0.997907	+	0.0646693i
$406$	103.868			0.255832
$407$	−102.529	−	37.3173i	−0.251913	−	0.0916888i
$408$	−70.6080	+	255.282i	−0.173059	+	0.625691i
$409$	−102.869	−	86.3171i	−0.251513	−	0.211044i	0.508311	−	0.861174i	$-0.330270\pi$
$409$	−102.869	−	86.3171i	−0.251513	−	0.211044i	−0.759823	+	0.650130i	$0.774715\pi$
$410$	−403.613	−	250.881i	−0.984422	−	0.611905i
$411$	−297.541	+	417.742i	−0.723945	+	1.01640i
$412$	−521.326	−	621.292i	−1.26535	−	1.50799i
$413$	−206.257	−	357.248i	−0.499413	−	0.865008i
$414$	1.97176	−	122.570i	0.00476271	−	0.296063i
$415$	46.7818	−	36.7283i	0.112727	−	0.0885019i
$416$	−141.746	+	24.9936i	−0.340736	+	0.0600809i
$417$	11.8042	−	8.12469i	0.0283074	−	0.0194837i
$418$	−198.548	−	545.507i	−0.474996	−	1.30504i
$419$	58.8474	+	161.682i	0.140447	+	0.385876i	0.989896	−	0.141795i	$-0.0452875\pi$
$419$	58.8474	+	161.682i	0.140447	+	0.385876i	−0.849449	+	0.527671i	$0.823065\pi$
$420$	−617.805	+	569.587i	−1.47096	+	1.35616i
$421$	−39.3619	−	223.232i	−0.0934961	−	0.530243i	−0.995198	−	0.0978842i	$-0.968793\pi$
$421$	−39.3619	−	223.232i	−0.0934961	−	0.530243i	0.901702	−	0.432359i	$-0.142319\pi$
$422$	−110.431	+	191.272i	−0.261685	+	0.453252i
$423$	783.159	−	125.139i	1.85144	−	0.295836i
$424$	194.025	+	336.061i	0.457606	+	0.792597i
$425$	−544.080	−	35.4627i	−1.28019	−	0.0834416i
$426$	1031.53	−	470.946i	2.42143	−	1.10551i
$427$	−1006.56	−	177.484i	−2.35729	−	0.415654i
$428$	378.762	+	317.819i	0.884958	+	0.742568i
$429$	−132.925	+	34.4738i	−0.309849	+	0.0803585i
$430$	74.9299	−	83.6145i	0.174256	−	0.194452i
$431$		−	187.324i		−	0.434626i	−0.976102	−	0.217313i	$-0.930271\pi$
$431$		−	187.324i		−	0.434626i	0.976102	−	0.217313i	$-0.0697293\pi$
$432$	−194.333	−	143.182i	−0.449844	−	0.331441i
$433$		−	168.276i		−	0.388628i	−0.980939	−	0.194314i	$-0.937752\pi$
$433$		−	168.276i		−	0.388628i	0.980939	−	0.194314i	$-0.0622480\pi$
$434$	93.2614	−	256.234i	0.214888	−	0.590400i
$435$	44.7531	−	18.6973i	0.102881	−	0.0429823i
$436$	−85.2469	−	71.5306i	−0.195520	−	0.164061i
$437$	−10.6441	+	60.3659i	−0.0243573	+	0.138137i
$438$	108.214	−	1131.96i	0.247064	−	2.58438i
$439$	−601.654	+	504.848i	−1.37051	+	1.15000i	−0.397934	+	0.917414i	$0.630273\pi$
$439$	−601.654	+	504.848i	−1.37051	+	1.15000i	−0.972577	+	0.232582i	$0.925283\pi$
$440$	−277.162	+	39.6207i	−0.629913	+	0.0900470i
$441$	363.437	−	419.243i	0.824119	−	0.950664i
$442$	−190.871	−	110.200i	−0.431836	−	0.249321i
$443$	87.5073	+	496.279i	0.197534	+	1.12027i	0.908764	+	0.417310i	$0.137027\pi$
$443$	87.5073	+	496.279i	0.197534	+	1.12027i	−0.711231	+	0.702959i	$0.751862\pi$
$444$	−125.630	+	9.97377i	−0.282951	+	0.0224634i
$445$	9.45387	−	290.396i	0.0212447	−	0.652576i
$446$	111.752	+	307.036i	0.250565	+	0.688422i
$447$	3.87539	−	0.307667i	0.00866977	−	0.000688292i
$448$	1005.48	−	177.293i	2.24437	−	0.395743i
$449$	−168.870	−	97.4973i	−0.376103	−	0.217143i	0.300018	−	0.953933i	$-0.403007\pi$
$449$	−168.870	−	97.4973i	−0.376103	−	0.217143i	−0.676121	+	0.736790i	$0.736340\pi$
$450$	−286.582	+	624.485i	−0.636849	+	1.38774i
$451$	215.258	+	372.837i	0.477290	+	0.826691i
$452$	−380.905	+	319.618i	−0.842711	+	0.707118i
$453$	66.5445	+	6.36158i	0.146897	+	0.0140432i
$454$	−136.655	+	775.007i	−0.301002	+	1.70706i
$455$	−82.0741	−	153.483i	−0.180383	−	0.337325i
$456$	−117.066	−	118.964i	−0.256723	−	0.260886i
$457$	185.940	−	510.866i	0.406871	−	1.11787i	−0.551955	−	0.833874i	$-0.686118\pi$
$457$	185.940	−	510.866i	0.406871	−	1.11787i	0.958826	−	0.283994i	$-0.0916596\pi$
$458$	−17.1897			−0.0375321
$459$	−138.640	−	572.300i	−0.302047	−	1.24684i
$460$	110.225	+	44.2310i	0.239619	+	0.0961543i
$461$	48.9784	−	134.567i	0.106244	−	0.291902i	−0.875167	−	0.483821i	$-0.839249\pi$
$461$	48.9784	−	134.567i	0.106244	−	0.291902i	0.981411	+	0.191918i	$0.0614709\pi$
$462$	1290.31	−	334.637i	2.79287	−	0.724323i
$463$	357.463	−	426.008i	0.772059	−	0.920104i	−0.226487	−	0.974014i	$-0.572724\pi$
$463$	357.463	−	426.008i	0.772059	−	0.920104i	0.998546	+	0.0539099i	$0.0171684\pi$
$464$	−28.4684	−	5.01975i	−0.0613544	−	0.0108184i
$465$	−5.94159	−	127.191i	−0.0127776	−	0.273528i
$466$	−301.111	+	252.662i	−0.646162	+	0.542194i
$467$	175.833	+	304.551i	0.376516	+	0.652144i	0.990553	−	0.137133i	$-0.0437887\pi$
$467$	175.833	+	304.551i	0.376516	+	0.652144i	−0.614037	+	0.789277i	$0.710455\pi$
$468$	−123.130	+	99.9876i	−0.263098	+	0.213649i
$469$	−520.566	+	901.647i	−1.10995	+	1.92249i
$470$	−276.639	+	1316.78i	−0.588594	+	2.80165i
$471$	−303.367	+	637.142i	−0.644091	+	1.35274i
$472$	−54.2975	−	149.181i	−0.115037	−	0.316062i
$473$	−95.5776	+	34.7874i	−0.202067	+	0.0735463i
$474$	−476.810	+	328.183i	−1.00593	+	0.692368i
$475$	190.777	−	285.742i	0.401635	−	0.601561i
$476$	1058.08	+	610.884i	2.22286	+	1.28337i
$477$	−740.097	−	443.319i	−1.55157	−	0.929389i
$478$	30.9227	−	17.8532i	0.0646917	−	0.0373498i
$479$	−461.831	−	550.389i	−0.964157	−	1.14904i	−0.988786	−	0.149341i	$-0.952285\pi$
$479$	−461.831	−	550.389i	−0.964157	−	1.14904i	0.0246289	−	0.999697i	$-0.492160\pi$
$480$	549.169	−	352.216i	1.14410	−	0.733784i
$481$	4.53277	−	25.7066i	0.00942364	−	0.0534441i
$482$	−268.289	−	225.121i	−0.556616	−	0.467056i
$483$	−135.658	−	37.5215i	−0.280866	−	0.0776843i
$484$	351.971	+	128.107i	0.727213	+	0.264684i
$485$	37.6124	−	93.7310i	0.0775513	−	0.193260i
$486$	−736.049	−	94.3432i	−1.51450	−	0.194122i
$487$			706.180i			1.45006i	0.688717	+	0.725030i	$0.258174\pi$
$487$			706.180i			1.45006i	−0.688717	+	0.725030i	$0.741826\pi$
$488$	−369.628	−	134.533i	−0.757434	−	0.275683i
$489$	742.573	+	205.387i	1.51855	+	0.420014i
$490$	443.885	+	830.089i	0.905888	+	1.69406i
$491$	−518.745	−	91.4687i	−1.05651	−	0.186291i	−0.381701	−	0.924286i	$-0.624661\pi$
$491$	−518.745	−	91.4687i	−1.05651	−	0.186291i	−0.674806	+	0.737996i	$0.735773\pi$
$492$	405.029	+	288.487i	0.823230	+	0.586355i
$493$	−45.3292	−	54.0212i	−0.0919456	−	0.109576i
$494$	120.276	−	69.4415i	0.243474	−	0.140570i
$495$	495.711	−	376.453i	1.00144	−	0.760511i
$496$	−37.9448	+	65.7223i	−0.0765016	+	0.132505i
$497$	−226.088	−	1282.21i	−0.454905	−	2.57990i
$498$	−89.7694	+	61.7873i	−0.180260	+	0.124071i
$499$	−53.0721	+	19.3167i	−0.106357	+	0.0387108i	−0.394651	−	0.918831i	$-0.629134\pi$
$499$	−53.0721	+	19.3167i	−0.106357	+	0.0387108i	0.288294	+	0.957542i	$0.406912\pi$
$500$	−465.820	−	475.577i	−0.931640	−	0.951155i
$501$	626.727	+	298.407i	1.25095	+	0.595623i
$502$	121.633	−	21.4471i	0.242296	−	0.0427233i
$503$	−287.123	+	497.312i	−0.570822	+	0.988692i	0.425660	+	0.904883i	$0.360042\pi$
$503$	−287.123	+	497.312i	−0.570822	+	0.988692i	−0.996482	+	0.0838092i	$0.973291\pi$
$504$	297.509	−	241.593i	0.590296	−	0.479351i
$505$	592.587	−	84.7111i	1.17344	−	0.167745i
$506$	−121.104	−	144.326i	−0.239336	−	0.285229i
$507$	196.921	+	431.321i	0.388403	+	0.850731i
$508$	52.5126	+	9.25940i	0.103371	+	0.0182272i
$509$	418.255	−	498.457i	0.821719	−	0.979287i	−0.178270	−	0.983982i	$-0.557050\pi$
$509$	418.255	−	498.457i	0.821719	−	0.979287i	0.999989	+	0.00469470i	$0.00149437\pi$
$510$	990.865	+	127.380i	1.94287	+	0.249764i
$511$	−1226.89	−	446.552i	−2.40096	−	0.873879i
$512$	−533.611			−1.04221
$513$	355.996	+	104.657i	0.693950	+	0.204010i
$514$	−113.380			−0.220583
$515$	−508.170	+	567.069i	−0.986738	+	1.10111i
$516$	−83.7375	+	82.4012i	−0.162282	+	0.159692i
$517$	783.506	−	933.747i	1.51549	−	1.80609i
$518$	−43.9997	+	249.534i	−0.0849414	+	0.481727i
$519$	449.301	+	42.9526i	0.865704	+	0.0827603i
$520$	−20.8492	−	63.6550i	−0.0400946	−	0.122413i
$521$	−586.933	+	338.866i	−1.12655	+	0.650414i	−0.943065	−	0.332608i	$-0.892071\pi$
$521$	−586.933	+	338.866i	−1.12655	+	0.650414i	−0.183486	+	0.983022i	$0.558738\pi$
$522$	−83.9873	+	29.0477i	−0.160895	+	0.0556470i
$523$	−46.5229	−	26.8600i	−0.0889538	−	0.0513575i	0.454863	−	0.890561i	$-0.349688\pi$
$523$	−46.5229	−	26.8600i	−0.0889538	−	0.0513575i	−0.543817	+	0.839204i	$0.683021\pi$
$524$	620.458	−	109.403i	1.18408	−	0.208785i
$525$	611.459	+	498.517i	1.16468	+	0.949556i
$526$	261.222	−	95.0769i	0.496619	−	0.180755i
$527$	−173.967	+	63.3187i	−0.330108	+	0.120149i
$528$	−369.824	+	29.3603i	−0.700424	+	0.0556066i
$529$	−88.4054	−	501.372i	−0.167118	−	0.947773i
$530$	1151.23	−	903.828i	2.17213	−	1.70534i
$531$	266.688	+	231.189i	0.502237	+	0.435383i
$532$	−666.742	+	384.944i	−1.25328	+	0.723579i
$533$	−78.9001	+	66.2051i	−0.148030	+	0.124212i
$534$	−50.6628	+	529.952i	−0.0948741	+	0.992419i
$535$	245.061	−	394.250i	0.458058	−	0.736915i
$536$	−257.551	+	306.937i	−0.480505	+	0.572643i
$537$	119.139	−	117.238i	0.221861	−	0.218321i
$538$	−493.538	+	1355.98i	−0.917356	+	2.52042i
$539$		−	852.748i		−	1.58209i
$540$	340.266	−	633.343i	0.630122	−	1.17286i
$541$	−671.816			−1.24180			−0.620902	−	0.783888i	$-0.713234\pi$
$541$	−671.816			−1.24180			−0.620902	+	0.783888i	$0.713234\pi$
$542$	398.260	+	144.955i	0.734797	+	0.267444i
$543$	−370.729	+	96.1477i	−0.682743	+	0.177068i
$544$	−726.655	−	609.736i	−1.33576	−	1.12084i
$545$	−55.1552	+	88.7326i	−0.101202	+	0.162812i
$546$	132.447	+	290.102i	0.242576	+	0.531322i
$547$	−59.9047	−	71.3916i	−0.109515	−	0.130515i	0.708502	−	0.705708i	$-0.249371\pi$
$547$	−59.9047	−	71.3916i	−0.109515	−	0.130515i	−0.818017	+	0.575194i	$0.804927\pi$
$548$	455.229	+	788.480i	0.830711	+	1.43883i
$549$	863.542	−	137.983i	1.57294	−	0.251335i
$550$	295.873	+	1013.73i	0.537951	+	1.84314i
$551$	43.7623	−	7.71648i	0.0794235	−	0.0140045i
$552$	−48.9072	−	23.2865i	−0.0886000	−	0.0421857i
$553$	227.311	+	624.533i	0.411051	+	1.12935i
$554$	299.027	+	821.570i	0.539760	+	1.48298i
$555$	25.9609	+	115.436i	0.0467764	+	0.207994i
$556$	−4.41741	−	25.0523i	−0.00794497	−	0.0450582i
$557$	−5.77288	+	9.99892i	−0.0103642	+	0.0179514i	−0.871161	−	0.490997i	$-0.836632\pi$
$557$	−5.77288	+	9.99892i	−0.0103642	+	0.0179514i	0.860797	+	0.508949i	$0.169966\pi$
$558$	−3.75260	+	233.272i	−0.00672510	+	0.418050i
$559$	−12.1668	−	21.0735i	−0.0217652	−	0.0376985i
$560$	−146.358	−	446.849i	−0.261354	−	0.797945i
$561$	−737.149	−	525.043i	−1.31399	−	0.935906i
$562$	−827.590	−	145.927i	−1.47258	−	0.259656i
$563$	137.802	+	115.629i	0.244764	+	0.205381i	0.756914	−	0.653515i	$-0.226706\pi$
$563$	137.802	+	115.629i	0.244764	+	0.205381i	−0.512150	+	0.858896i	$0.671151\pi$
$564$	375.319	−	1356.96i	0.665460	−	2.40596i
$565$	347.662	+	311.552i	0.615331	+	0.551419i
$566$		−	1284.89i		−	2.27013i
$567$	−317.017	+	790.867i	−0.559113	+	1.39483i
$568$		−	501.067i		−	0.882161i
$569$	138.908	−	381.646i	0.244126	−	0.670731i	−0.755748	−	0.654863i	$-0.772727\pi$
$569$	138.908	−	381.646i	0.244126	−	0.670731i	0.999874	−	0.0158683i	$-0.00505126\pi$
$570$	−381.706	+	500.600i	−0.669660	+	0.878246i
$571$	365.120	+	306.372i	0.639440	+	0.536554i	0.903846	−	0.427857i	$-0.140731\pi$
$571$	365.120	+	306.372i	0.639440	+	0.536554i	−0.264406	+	0.964411i	$0.585176\pi$
$572$	−42.3314	+	240.073i	−0.0740060	+	0.419709i
$573$	−187.207	−	133.340i	−0.326714	−	0.232706i
$574$	765.884	−	642.653i	1.33429	−	1.11960i
$575$	26.4641	−	108.320i	0.0460246	−	0.188383i
$576$	−763.447	+	424.552i	−1.32543	+	0.737069i
$577$	898.134	+	518.538i	1.55656	+	0.898679i	0.997582	+	0.0694957i	$0.0221390\pi$
$577$	898.134	+	518.538i	1.55656	+	0.898679i	0.558976	+	0.829184i	$0.311194\pi$
$578$	−98.9771	−	561.327i	−0.171241	−	0.971155i
$579$	55.3126	+	80.3625i	0.0955312	+	0.138795i
$580$	2.80154	−	86.0555i	0.00483024	−	0.148371i
$581$	42.7961	+	117.581i	0.0736594	+	0.202378i
$582$	−79.5529	+	167.080i	−0.136689	+	0.287079i
$583$	−1305.78	+	230.244i	−2.23976	+	0.394929i
$584$	−435.151	−	251.234i	−0.745121	−	0.430196i
$585$	109.288	+	101.153i	0.186817	+	0.172911i
$586$	−473.747	−	820.553i	−0.808441	−	1.40026i
$587$	39.9237	−	33.5000i	0.0680132	−	0.0570698i	−0.608147	−	0.793824i	$-0.708087\pi$
$587$	39.9237	−	33.5000i	0.0680132	−	0.0570698i	0.676161	+	0.736754i	$0.263643\pi$
$588$	−409.071	−	895.999i	−0.695699	−	1.52381i
$589$	20.2577	−	114.887i	0.0343933	−	0.195054i
$590$	−528.034	+	282.363i	−0.894973	+	0.478582i
$591$	450.747	−	116.900i	0.762685	−	0.197800i
$592$	24.1192	−	66.2669i	0.0407418	−	0.111937i
$593$	−826.793			−1.39425			−0.697127	−	0.716947i	$-0.745539\pi$
$593$	−826.793			−1.39425			−0.697127	+	0.716947i	$0.745539\pi$
$594$	−949.755	+	631.435i	−1.59891	+	1.06302i
$595$	427.183	−	1064.55i	0.717955	−	1.78916i
$596$	2.36038	−	6.48508i	0.00396036	−	0.0108810i
$597$	−323.622	−	328.870i	−0.542080	−	0.550871i
$598$	28.9730	−	34.5287i	0.0484498	−	0.0577402i
$599$	144.724	+	25.5188i	0.241610	+	0.0426023i	0.293141	−	0.956069i	$-0.405299\pi$
$599$	144.724	+	25.5188i	0.241610	+	0.0426023i	−0.0515320	+	0.998671i	$0.516410\pi$
$600$	198.429	+	229.801i	0.330715	+	0.383002i
$601$	182.075	−	152.779i	0.302953	−	0.254208i	−0.478619	−	0.878023i	$-0.658862\pi$
$601$	182.075	−	152.779i	0.302953	−	0.254208i	0.781572	+	0.623815i	$0.214418\pi$
$602$	118.103	+	204.560i	0.196184	+	0.339801i
$603$	168.774	−	874.654i	0.279891	−	1.45050i
$604$	59.3346	−	102.771i	0.0982361	−	0.170150i
$605$	72.3006	−	344.144i	0.119505	−	0.568834i
$606$	−1093.38	+	86.8033i	−1.80426	+	0.143240i
$607$	332.822	+	914.422i	0.548307	+	1.50646i	0.835995	+	0.548737i	$0.184891\pi$
$607$	332.822	+	914.422i	0.548307	+	1.50646i	−0.287688	+	0.957724i	$0.592887\pi$
$608$	561.693	−	204.440i	0.923837	−	0.336249i
$609$	8.07539	+	101.718i	0.0132601	+	0.167025i
$610$	−305.033	+	1451.93i	−0.500055	+	2.38022i
$611$	252.546	+	145.808i	0.413332	+	0.238637i
$612$	−1026.40	−	198.056i	−1.67713	−	0.323621i
$613$	302.798	−	174.820i	0.493960	−	0.285188i	−0.232256	−	0.972655i	$-0.574611\pi$
$613$	302.798	−	174.820i	0.493960	−	0.285188i	0.726216	+	0.687467i	$0.241277\pi$
$614$	−24.7927	−	29.5468i	−0.0403790	−	0.0481218i
$615$	214.309	−	414.765i	0.348470	−	0.674415i
$616$	102.282	−	580.072i	0.166043	−	0.941675i
$617$	−484.244	−	406.329i	−0.784836	−	0.658555i	0.159626	−	0.987178i	$-0.448971\pi$
$617$	−484.244	−	406.329i	−0.784836	−	0.658555i	−0.944461	+	0.328622i	$0.893416\pi$
$618$	994.446	−	978.577i	1.60914	−	1.58346i
$619$	−667.399	−	242.913i	−1.07819	−	0.392429i	−0.258956	−	0.965889i	$-0.583378\pi$
$619$	−667.399	−	242.913i	−1.07819	−	0.392429i	−0.819233	+	0.573461i	$0.805601\pi$
$620$	−209.777	−	84.1792i	−0.338350	−	0.135773i
$621$	120.187	−	7.59848i	0.193537	−	0.0122359i
$622$		−	667.974i		−	1.07391i
$623$	574.396	+	209.063i	0.921984	+	0.335575i
$624$	−22.2813	−	85.9130i	−0.0357072	−	0.137681i
$625$	−380.116	+	496.122i	−0.608186	+	0.793795i
$626$	203.724	+	35.9221i	0.325438	+	0.0573835i
$627$	518.781	−	236.851i	0.827401	−	0.377752i
$628$	805.238	+	959.645i	1.28223	+	1.52810i
$629$	148.984	−	86.0159i	0.236858	−	0.136750i
$630$	−1060.86	−	981.895i	−1.68391	−	1.55856i
$631$	−102.299	+	177.187i	−0.162122	+	0.280804i	−0.935630	−	0.352983i	$-0.885167\pi$
$631$	−102.299	+	177.187i	−0.162122	+	0.280804i	0.773507	+	0.633787i	$0.218501\pi$
$632$	44.4149	+	251.889i	0.0702767	+	0.398559i
$633$	−195.900	−	93.2749i	−0.309478	−	0.147354i
$634$	447.400	−	162.840i	0.705679	−	0.256846i
$635$	1.62892	−	50.0358i	0.00256523	−	0.0787966i
$636$	−1261.56	+	868.314i	−1.98358	+	1.36527i
$637$	200.913	−	35.4263i	0.315404	−	0.0556143i
$638$	−68.2919	+	118.285i	−0.107041	+	0.185400i
$639$	541.398	+	973.565i	0.847258	+	1.52358i
$640$	−86.6261	−	605.983i	−0.135353	−	0.946849i
$641$	488.496	+	582.166i	0.762084	+	0.908216i	0.997978	−	0.0635628i	$-0.0202463\pi$
$641$	488.496	+	582.166i	0.762084	+	0.908216i	−0.235894	+	0.971779i	$0.575802\pi$
$642$	−493.445	+	692.786i	−0.768606	+	1.07911i
$643$	−222.395	−	39.2143i	−0.345871	−	0.0609864i	−0.00198578	−	0.999998i	$-0.500632\pi$
$643$	−222.395	−	39.2143i	−0.345871	−	0.0609864i	−0.343885	+	0.939012i	$0.611743\pi$
$644$	−160.610	+	191.407i	−0.249394	+	0.297216i
$645$	87.7097	+	66.8784i	0.135984	+	0.103687i
$646$	860.102	+	313.052i	1.33143	+	0.484600i
$647$	−548.273			−0.847409			−0.423704	−	0.905801i	$-0.639270\pi$
$647$	−548.273			−0.847409			−0.423704	+	0.905801i	$0.639270\pi$
$648$	−173.002	+	278.554i	−0.266978	+	0.429867i
$649$	542.448			0.835822
$650$	−226.548	+	111.823i	−0.348535	+	0.172036i
$651$	258.182	+	71.4100i	0.396592	+	0.109693i
$652$	879.152	−	1047.73i	1.34839	−	1.60695i
$653$	−17.0770	+	96.8484i	−0.0261516	+	0.148313i	−0.995088	−	0.0989987i	$-0.968436\pi$
$653$	−17.0770	+	96.8484i	−0.0261516	+	0.148313i	0.968936	+	0.247312i	$0.0795471\pi$
$654$	111.058	−	155.923i	0.169814	−	0.238415i
$655$	−184.114	−	562.123i	−0.281091	−	0.858202i
$656$	−240.975	+	139.127i	−0.367339	+	0.212084i
$657$	1116.95	+	17.9681i	1.70007	+	0.0273487i
$658$	−2451.47	−	1415.35i	−3.72563	−	2.15100i
$659$	−1085.19	+	191.348i	−1.64672	+	0.290362i	−0.918630	−	0.395118i	$-0.870704\pi$
$659$	−1085.19	+	191.348i	−1.64672	+	0.290362i	−0.728092	+	0.685479i	$0.759593\pi$
$660$	−242.448	−	1078.06i	−0.367346	−	1.63342i
$661$	−50.7334	+	18.4654i	−0.0767524	+	0.0279356i	−0.380111	−	0.924941i	$-0.624114\pi$
$661$	−50.7334	+	18.4654i	−0.0767524	+	0.0279356i	0.303359	+	0.952876i	$0.401892\pi$
$662$	1356.66	−	493.785i	2.04934	−	0.745899i
$663$	93.0794	−	195.489i	0.140391	−	0.294855i
$664$	8.36203	+	47.4234i	0.0125934	+	0.0714208i
$665$	446.353	+	568.531i	0.671207	+	0.854934i
$666$	−34.2069	−	214.078i	−0.0513617	−	0.321439i
$667$	12.4898	−	7.21100i	0.0187254	−	0.0108111i
$668$	943.957	−	792.074i	1.41311	−	1.18574i
$669$	−291.994	+	133.310i	−0.436463	+	0.199268i
$670$	1283.52	+	797.819i	1.91570	+	1.19077i
$671$	863.926	−	1029.59i	1.28752	−	1.53441i
$672$	344.567	+	1328.59i	0.512748	+	1.97707i
$673$	127.785	−	351.087i	0.189874	−	0.521674i	−0.807829	−	0.589417i	$-0.799358\pi$
$673$	127.785	−	351.087i	0.189874	−	0.521674i	0.997703	+	0.0677430i	$0.0215798\pi$
$674$		−	402.033i		−	0.596489i
$675$	−633.841	−	232.099i	−0.939024	−	0.343851i
$676$	841.711			1.24513
$677$	−27.8116	−	10.1226i	−0.0410807	−	0.0149522i	0.321398	−	0.946944i	$-0.395847\pi$
$677$	−27.8116	−	10.1226i	−0.0410807	−	0.0149522i	−0.362479	+	0.931992i	$0.618069\pi$
$678$	−599.951	−	609.680i	−0.884884	−	0.899234i
$679$	162.766	+	136.577i	0.239714	+	0.201144i
$680$	233.045	−	374.918i	0.342713	−	0.551350i
$681$	−769.593	−	73.5721i	−1.13009	−	0.108035i
$682$	230.482	+	274.678i	0.337950	+	0.402753i
$683$	596.362	+	1032.93i	0.873151	+	1.51234i	0.858719	+	0.512447i	$0.171261\pi$
$683$	596.362	+	1032.93i	0.873151	+	1.51234i	0.0144322	+	0.999896i	$0.495406\pi$
$684$	431.474	−	497.727i	0.630810	−	0.727671i
$685$	672.337	−	527.851i	0.981515	−	0.770585i
$686$	−400.156	+	70.5582i	−0.583317	+	0.102855i
$687$	−1.33645	−	16.8340i	−0.00194534	−	0.0245036i
$688$	−22.4840	−	61.7744i	−0.0326803	−	0.0897883i
$689$	−108.494	−	298.084i	−0.157465	−	0.432632i
$690$	−60.8431	+	195.040i	−0.0881784	+	0.282667i
$691$	72.5071	+	411.208i	0.104931	+	0.595091i	0.991248	+	0.132013i	$0.0421441\pi$
$691$	72.5071	+	411.208i	0.104931	+	0.595091i	−0.886317	+	0.463078i	$0.846745\pi$
$692$	400.620	−	693.894i	0.578931	−	1.00274i
$693$	428.029	+	1237.58i	0.617647	+	1.78584i
$694$	56.1420	+	97.2408i	0.0808963	+	0.140116i
$695$	−22.6969	+	7.43402i	−0.0326575	+	0.0106964i
$696$	−3.73704	+	39.0909i	−0.00536932	+	0.0561651i
$697$	−668.483	−	117.872i	−0.959086	−	0.169113i
$698$	567.676	+	476.336i	0.813289	+	0.682430i
$699$	−270.844	−	275.236i	−0.387473	−	0.393757i
$700$	1255.85	−	619.884i	1.79408	−	0.885549i
$701$			886.684i			1.26488i	0.774608	+	0.632442i	$0.217947\pi$
$701$			886.684i			1.26488i	−0.774608	+	0.632442i	$0.782053\pi$
$702$	−188.226	−	197.536i	−0.268129	−	0.281390i
$703$			108.405i			0.154203i
$704$	−459.190	+	1261.61i	−0.652258	+	1.79206i
$705$	−1311.03	−	168.539i	−1.85962	−	0.239062i
$706$	−1378.87	−	1157.01i	−1.95308	−	1.63883i
$707$	−218.685	+	1240.23i	−0.309314	+	1.75421i
$708$	569.961	−	260.217i	0.805030	−	0.367538i
$709$	−330.910	+	277.666i	−0.466728	+	0.391631i	−0.845599	−	0.533818i	$-0.820757\pi$
$709$	−330.910	+	277.666i	−0.466728	+	0.391631i	0.378872	+	0.925449i	$0.376312\pi$
$710$	−1870.90	+	267.447i	−2.63506	+	0.376686i
$711$	−358.461	−	441.427i	−0.504165	−	0.620853i
$712$	203.725	+	117.621i	0.286131	+	0.165198i
$713$	−6.57455	−	37.2861i	−0.00922096	−	0.0522947i
$714$	−903.523	+	1897.61i	−1.26544	+	2.65772i
$715$	228.750	+	7.44697i	0.319930	+	0.0104153i
$716$	−101.486	−	278.831i	−0.141741	−	0.389429i
$717$	19.8879	+	28.8947i	0.0277376	+	0.0402994i
$718$	−1179.89	+	208.047i	−1.64330	+	0.289758i
$719$	−300.045	−	173.231i	−0.417308	−	0.240933i	0.276617	−	0.960980i	$-0.410787\pi$
$719$	−300.045	−	173.231i	−0.417308	−	0.240933i	−0.693925	+	0.720047i	$0.744120\pi$
$720$	243.311	+	320.391i	0.337933	+	0.444988i
$721$	−800.967	−	1387.32i	−1.11091	−	1.92416i
$722$	402.670	−	337.880i	0.557714	−	0.467978i
$723$	199.603	−	280.239i	0.276077	−	0.387606i
$724$	−118.063	+	669.567i	−0.163070	+	0.924816i
$725$	−80.3528	+	8.82955i	−0.110831	+	0.0121787i
$726$	−171.766	+	621.016i	−0.236592	+	0.855394i
$727$	−181.063	+	497.467i	−0.249055	+	0.684273i	0.750667	+	0.660681i	$0.229733\pi$
$727$	−181.063	+	497.467i	−0.249055	+	0.684273i	−0.999722	+	0.0235921i	$0.992490\pi$
$728$	140.918			0.193568
$729$	35.1652	−	728.151i	0.0482376	−	0.998836i
$730$	−705.801	+	1758.87i	−0.966850	+	2.40942i
$731$	54.8495	−	150.698i	0.0750334	−	0.206153i
$732$	413.842	−	1496.24i	0.565358	−	2.04404i
$733$	−597.092	+	711.587i	−0.814587	+	0.970787i	−0.999929	−	0.0118868i	$-0.996216\pi$
$733$	−597.092	+	711.587i	−0.814587	+	0.970787i	0.185342	+	0.982674i	$0.440661\pi$
$734$	1941.62	+	342.359i	2.64525	+	0.466429i
$735$	−778.399	+	499.236i	−1.05905	+	0.679232i
$736$	148.609	−	124.697i	0.201914	−	0.169426i
$737$	−684.534	−	1185.65i	−0.928812	−	1.60875i
$738$	−439.569	+	733.837i	−0.595621	+	0.994359i
$739$	237.919	−	412.087i	0.321947	−	0.557628i	−0.658943	−	0.752193i	$-0.728996\pi$
$739$	237.919	−	412.087i	0.321947	−	0.557628i	0.980890	+	0.194565i	$0.0623294\pi$
$740$	205.555	+	43.1847i	0.277777	+	0.0583577i
$741$	77.3555	+	112.388i	0.104393	+	0.151671i
$742$	1053.15	+	2893.50i	1.41934	+	3.89960i
$743$	985.780	−	358.795i	1.32676	−	0.482900i	0.421140	−	0.906996i	$-0.361630\pi$
$743$	985.780	−	358.795i	1.32676	−	0.482900i	0.905617	+	0.424096i	$0.139408\pi$
$744$	93.0789	+	44.3182i	0.125106	+	0.0595675i
$745$	−6.34088	−	1.33214i	−0.00851125	−	0.00178811i
$746$	1209.98	+	698.583i	1.62196	+	0.936438i
$747$	−67.4878	−	83.1078i	−0.0903452	−	0.111255i
$748$	−1391.36	+	803.300i	−1.86010	+	1.07393i
$749$	627.744	+	748.117i	0.838110	+	0.998821i
$750$	752.124	−	863.555i	1.00283	−	1.15141i
$751$	−12.1955	+	69.1640i	−0.0162390	+	0.0920958i	−0.991850	−	0.127410i	$-0.959333\pi$
$751$	−12.1955	+	69.1640i	−0.0162390	+	0.0920958i	0.975611	+	0.219506i	$0.0704446\pi$
$752$	603.505	+	506.401i	0.802533	+	0.673405i
$753$	30.4598	+	117.448i	0.0404512	+	0.155973i
$754$	−30.7058	−	11.1760i	−0.0407238	−	0.0148223i
$755$	−103.399	−	41.4919i	−0.136952	−	0.0549562i
$756$	1043.42	+	1095.03i	1.38018	+	1.44845i
$757$		−	1284.09i		−	1.69629i	−0.529764	−	0.848145i	$-0.677720\pi$
$757$		−	1284.09i		−	1.69629i	0.529764	−	0.848145i	$-0.322280\pi$
$758$	569.481	+	207.274i	0.751294	+	0.273449i
$759$	131.924	−	129.819i	0.173813	−	0.171039i
$760$	131.174	+	245.303i	0.172598	+	0.322767i
$761$	582.295	+	102.674i	0.765171	+	0.134920i	0.542594	−	0.839995i	$-0.317442\pi$
$761$	582.295	+	102.674i	0.765171	+	0.134920i	0.222577	+	0.974915i	$0.428553\pi$
$762$	−8.72928	+	91.3116i	−0.0114558	+	0.119832i
$763$	−141.285	−	168.376i	−0.185170	−	0.220677i
$764$	−353.350	+	204.007i	−0.462500	+	0.267024i
$765$	−47.7068	+	980.262i	−0.0623618	+	1.28139i
$766$	177.758	−	307.886i	0.232060	−	0.401940i
$767$	22.5353	+	127.804i	0.0293811	+	0.166629i
$768$	−3.41280	−	42.9878i	−0.00444375	−	0.0559738i
$769$	−128.848	+	46.8968i	−0.167552	+	0.0609841i	−0.424434	−	0.905459i	$-0.639527\pi$
$769$	−128.848	+	46.8968i	−0.167552	+	0.0609841i	0.256882	+	0.966443i	$0.417305\pi$
$770$	−2220.48	−	72.2878i	−2.88374	−	0.0938803i
$771$	−8.81491	−	111.033i	−0.0114331	−	0.144012i
$772$	170.555	−	30.0735i	0.220927	−	0.0389554i
$773$	94.2123	−	163.181i	0.121879	−	0.211100i	−0.798630	−	0.601823i	$-0.794441\pi$
$773$	94.2123	−	163.181i	0.121879	−	0.211100i	0.920509	+	0.390722i	$0.127775\pi$
$774$	−152.705	−	132.379i	−0.197294	−	0.171032i
$775$	−50.3658	+	206.152i	−0.0649882	+	0.266003i
$776$	52.5612	+	62.6399i	0.0677334	+	0.0807216i
$777$	−247.791	−	23.6885i	−0.318907	−	0.0304872i
$778$	1658.90	+	292.508i	2.13226	+	0.375974i
$779$	274.945	−	327.666i	0.352946	−	0.420624i
$780$	243.925	−	101.909i	0.312724	−	0.130652i
$781$	1608.84	+	585.569i	2.05997	+	0.749768i
$782$	297.058			0.379869
$783$	−34.9763	−	79.9908i	−0.0446696	−	0.102159i
$784$	551.154			0.703002
$785$	784.917	−	875.892i	0.999895	−	1.11579i
$786$	272.080	+	1049.09i	0.346158	+	1.33473i
$787$	−99.2953	+	118.336i	−0.126169	+	0.150363i	−0.825431	−	0.564503i	$-0.809068\pi$
$787$	−99.2953	+	118.336i	−0.126169	+	0.150363i	0.699262	+	0.714866i	$0.253512\pi$
$788$	143.545	−	814.085i	0.182164	−	1.03310i
$789$	113.418	+	248.424i	0.143750	+	0.314859i
$790$	916.803	−	300.284i	1.16051	−	0.380107i
$791$	−850.544	+	491.062i	−1.07528	+	0.620811i
$792$	79.5180	+	497.650i	0.100401	+	0.628346i
$793$	278.467	+	160.773i	0.351157	+	0.202740i
$794$	−241.879	+	42.6497i	−0.304633	+	0.0537150i
$795$	974.628	+	1057.13i	1.22595	+	1.32973i
$796$	−769.680	+	280.140i	−0.966934	+	0.351935i
$797$	−8.40037	+	3.05748i	−0.0105400	+	0.00383624i	−0.347285	−	0.937760i	$-0.612896\pi$
$797$	−8.40037	+	3.05748i	−0.0105400	+	0.00383624i	0.336745	+	0.941596i	$0.390674\pi$
$798$	−750.890	−	1090.95i	−0.940965	−	1.36711i
$799$	333.730	+	1892.68i	0.417685	+	2.36881i
$800$	−1043.80	+	304.652i	−1.30476	+	0.380815i
$801$	−522.923	−	8.41217i	−0.652838	−	0.0105021i
$802$	1206.77	−	696.730i	1.50470	−	0.868741i
$803$	1315.20	−	1103.59i	1.63786	−	1.37433i
$804$	−1288.02	−	917.407i	−1.60201	−	1.14105i
$805$	199.234	+	123.841i	0.247495	+	0.153840i
$806$	−55.1406	+	65.7140i	−0.0684127	+	0.0815311i
$807$	−1366.29	−	377.900i	−1.69305	−	0.468278i
$808$	−165.764	+	455.432i	−0.205153	+	0.563654i
$809$			351.841i			0.434909i	0.976071	+	0.217454i	$0.0697753\pi$
$809$			351.841i			0.434909i	−0.976071	+	0.217454i	$0.930225\pi$
$810$	1132.41	+	497.278i	1.39804	+	0.613924i
$811$	−1194.45			−1.47281			−0.736407	−	0.676538i	$-0.763479\pi$
$811$	−1194.45			−1.47281			−0.736407	+	0.676538i	$0.763479\pi$
$812$	170.215	+	61.9533i	0.209625	+	0.0762971i
$813$	−110.991	+	401.288i	−0.136521	+	0.493589i
$814$	−255.242	−	214.173i	−0.313565	−	0.263112i
$815$	−1090.57	−	677.888i	−1.33813	−	0.831765i
$816$	339.349	−	476.439i	0.415869	−	0.583871i
$817$	64.9571	+	77.4129i	0.0795069	+	0.0947526i
$818$	−205.040	−	355.140i	−0.250660	−	0.434156i
$819$	−273.800	+	152.260i	−0.334311	+	0.185910i
$820$	−511.787	−	651.877i	−0.624131	−	0.794972i
$821$	1029.30	−	181.494i	1.25372	−	0.221064i	0.492933	−	0.870067i	$-0.335925\pi$
$821$	1029.30	−	181.494i	1.25372	−	0.221064i	0.760786	+	0.649003i	$0.224814\pi$
$822$	−1290.15	+	887.992i	−1.56952	+	1.08028i
$823$	−11.4767	−	31.5320i	−0.0139449	−	0.0383134i	0.932525	−	0.361106i	$-0.117601\pi$
$823$	−11.4767	−	31.5320i	−0.0139449	−	0.0383134i	−0.946470	+	0.322792i	$0.895378\pi$
$824$	−210.856	−	579.321i	−0.255893	−	0.703060i
$825$	−969.742	+	368.564i	−1.17545	+	0.446744i
$826$	−218.750	−	1240.60i	−0.264831	−	1.50193i
$827$	−123.890	+	214.585i	−0.149807	+	0.259473i	−0.931156	−	0.364621i	$-0.881199\pi$
$827$	−123.890	+	214.585i	−0.149807	+	0.259473i	0.781349	+	0.624094i	$0.214532\pi$
$828$	76.3398	−	199.688i	0.0921978	−	0.241169i
$829$	559.323	+	968.775i	0.674696	+	1.16861i	0.976558	+	0.215256i	$0.0690584\pi$
$829$	559.323	+	968.775i	0.674696	+	1.16861i	−0.301862	+	0.953352i	$0.597608\pi$
$830$	172.607	−	56.5348i	0.207961	−	0.0681142i
$831$	−781.319	+	356.713i	−0.940215	+	0.429258i
$832$	−316.320	−	55.7757i	−0.380192	−	0.0670381i
$833$	1029.97	+	864.248i	1.23646	+	1.03751i
$834$	42.3595	−	10.9858i	0.0507908	−	0.0131725i
$835$	−861.573	−	772.086i	−1.03182	−	0.924653i
$836$		−	1012.39i		−	1.21099i
$837$	−228.736	+	14.4612i	−0.273281	+	0.0172774i
$838$			525.430i			0.627005i
$839$	−122.031	+	335.278i	−0.145448	+	0.399616i	−0.990928	−	0.134391i	$-0.957092\pi$
$839$	−122.031	+	335.278i	−0.145448	+	0.399616i	0.845480	+	0.534007i	$0.179314\pi$
$840$	−589.377	+	246.235i	−0.701640	+	0.293136i
$841$	636.234	+	533.864i	0.756521	+	0.634797i
$842$	120.203	−	681.704i	0.142759	−	0.809625i
$843$	78.5639	−	821.808i	0.0931956	−	0.974862i
$844$	−295.058	+	247.583i	−0.349595	+	0.293345i
$845$	−111.830	−	782.292i	−0.132343	−	0.925789i
$846$	2378.07	+	458.876i	2.81096	+	0.542406i
$847$	640.700	+	369.908i	0.756434	+	0.436727i
$848$	−148.813	−	843.958i	−0.175487	−	0.995234i
$849$	1258.30	−	99.8963i	1.48210	−	0.117663i
$850$	−1524.27	−	670.033i	−1.79325	−	0.788274i
$851$	12.0331	+	33.0605i	0.0141399	+	0.0388490i
$852$	1971.34	−	156.504i	2.31378	−	0.183691i
$853$	820.888	−	144.745i	0.962354	−	0.169689i	0.329668	−	0.944097i	$-0.393063\pi$
$853$	820.888	−	144.745i	0.962354	−	0.169689i	0.632687	+	0.774408i	$0.281952\pi$
$854$	−2703.09	−	1560.63i	−3.16521	−	1.82743i
$855$	−519.917	−	334.887i	−0.608090	−	0.391680i
$856$	187.920	+	325.488i	0.219533	+	0.380243i
$857$	8.13474	−	6.82586i	0.00949211	−	0.00796483i	−0.638029	−	0.770012i	$-0.720250\pi$
$857$	8.13474	−	6.82586i	0.00949211	−	0.00796483i	0.647521	+	0.762047i	$0.275806\pi$
$858$	−417.452	−	39.9079i	−0.486540	−	0.0465127i
$859$	163.139	−	925.210i	0.189918	−	1.07708i	−0.729554	−	0.683923i	$-0.760273\pi$
$859$	163.139	−	925.210i	0.189918	−	1.07708i	0.919472	−	0.393155i	$-0.128616\pi$
$860$	172.666	−	92.3321i	0.200774	−	0.107363i
$861$	688.898	+	700.069i	0.800114	+	0.813089i
$862$	195.652	−	537.549i	0.226974	−	0.623607i
$863$	−1304.97			−1.51213			−0.756065	−	0.654497i	$-0.772881\pi$
$863$	−1304.97			−1.51213			−0.756065	+	0.654497i	$0.772881\pi$
$864$	−650.171	−	977.936i	−0.752513	−	1.13187i
$865$	−698.136	−	280.148i	−0.807094	−	0.323871i
$866$	175.757	−	482.888i	0.202953	−	0.557608i
$867$	542.015	−	140.570i	0.625162	−	0.162134i
$868$	305.668	−	364.281i	0.352152	−	0.419679i
$869$	−860.676	−	151.760i	−0.990421	−	0.174638i
$870$	147.953	−	6.91150i	0.170061	−	0.00794425i
$871$	250.908	−	210.536i	0.288068	−	0.241718i
$872$	−42.2947	−	73.2566i	−0.0485031	−	0.0840099i
$873$	−169.807	−	64.9165i	−0.194510	−	0.0743603i
$874$	−93.5943	+	162.110i	−0.107087	+	0.185481i
$875$	−742.977	−	1084.84i	−0.849117	−	1.23982i
$876$	852.511	−	1790.48i	0.973186	−	2.04392i
$877$	−39.4762	−	108.460i	−0.0450128	−	0.123672i	0.915149	−	0.403115i	$-0.132072\pi$
$877$	−39.4762	−	108.460i	−0.0450128	−	0.123672i	−0.960162	+	0.279443i	$0.909850\pi$
$878$	−2253.81	+	820.321i	−2.56699	+	0.934307i
$879$	766.739	−	527.738i	0.872285	−	0.600384i
$880$	605.103	+	127.125i	0.687617	+	0.144460i
$881$	−536.832	−	309.940i	−0.609344	−	0.351805i	0.163365	−	0.986566i	$-0.447765\pi$
$881$	−536.832	−	309.940i	−0.609344	−	0.351805i	−0.772709	+	0.634761i	$0.781099\pi$
$882$	1480.81	−	823.475i	1.67892	−	0.933645i
$883$	−177.559	+	102.514i	−0.201086	+	0.116097i	−0.597162	−	0.802121i	$-0.703705\pi$
$883$	−177.559	+	102.514i	−0.201086	+	0.116097i	0.396076	+	0.918218i	$0.370372\pi$
$884$	−247.064	−	294.440i	−0.279485	−	0.333077i
$885$	−317.573	−	495.154i	−0.358839	−	0.559496i
$886$	−267.229	+	1515.53i	−0.301613	+	1.71053i
$887$	−446.951	−	375.037i	−0.503891	−	0.422815i	0.355082	−	0.934835i	$-0.384453\pi$
$887$	−446.951	−	375.037i	−0.503891	−	0.422815i	−0.858973	+	0.512020i	$0.828897\pi$
$888$	−92.3300	−	25.5374i	−0.103975	−	0.0287583i
$889$	98.9694	+	36.0219i	0.111327	+	0.0405196i
$890$	330.436	−	823.455i	0.371276	−	0.925230i
$891$	−692.208	−	881.007i	−0.776889	−	0.988785i
$892$			569.818i			0.638810i
$893$	−1138.02	−	414.205i	−1.27438	−	0.463836i
$894$	11.4423	+	3.16479i	0.0127989	+	0.00354004i
$895$	−245.664	+	131.368i	−0.274485	+	0.146779i
$896$	1268.26	+	223.629i	1.41547	+	0.249586i
$897$	36.0666	+	25.6889i	0.0402081	+	0.0286387i
$898$	−382.762	−	456.158i	−0.426239	−	0.507971i
$899$	−23.7703	+	13.7238i	−0.0264408	+	0.0152656i
$900$	−842.124	+	852.451i	−0.935694	+	0.947168i
$901$	1045.29	−	1810.50i	1.16015	−	2.00943i
$902$	228.296	+	1294.73i	0.253100	+	1.43540i
$903$	−191.145	+	131.563i	−0.211677	+	0.145695i
$904$	−355.174	+	129.273i	−0.392891	+	0.143001i
$905$	637.986	+	20.7697i	0.704957	+	0.0229499i
$906$	184.313	+	87.7583i	0.203436	+	0.0968635i
$907$	−607.332	+	107.089i	−0.669605	+	0.118069i	−0.498108	−	0.867115i	$-0.665972\pi$
$907$	−607.332	+	107.089i	−0.669605	+	0.118069i	−0.171498	+	0.985185i	$0.554861\pi$
$908$	−686.209	+	1188.55i	−0.755737	+	1.30897i
$909$	−170.014	−	1064.00i	−0.187034	−	1.17052i
$910$	−75.2154	−	526.161i	−0.0826543	−	0.578199i
$911$	−276.554	−	329.584i	−0.303572	−	0.361783i	0.592595	−	0.805501i	$-0.298104\pi$
$911$	−276.554	−	329.584i	−0.303572	−	0.361783i	−0.896166	+	0.443718i	$0.853659\pi$
$912$	153.083	+	335.302i	0.167854	+	0.367655i
$913$	−162.040	−	28.5721i	−0.177481	−	0.0312947i
$914$	1067.16	−	1271.79i	1.16757	−	1.39145i
$915$	−1445.60	−	185.837i	−1.57989	−	0.203101i
$916$	−28.1700	−	10.2530i	−0.0307533	−	0.0111933i
$917$	1244.41			1.35705
$918$	199.900	−	1787.09i	0.217756	−	1.94672i
$919$	360.453			0.392223			0.196111	−	0.980582i	$-0.437169\pi$
$919$	360.453			0.392223			0.196111	+	0.980582i	$0.437169\pi$
$920$	67.2337	+	60.2504i	0.0730801	+	0.0654896i
$921$	27.0077	−	26.5768i	0.0293244	−	0.0288564i
$922$	281.099	−	335.001i	0.304880	−	0.363341i
$923$	−71.1265	+	403.378i	−0.0770601	+	0.437029i
$924$	2314.11	+	221.226i	2.50445	+	0.239423i
$925$	12.8261	−	196.782i	0.0138660	−	0.212737i
$926$	1470.73	−	849.128i	1.58826	−	0.916985i
$927$	1035.64	+	897.784i	1.11720	+	0.968483i
$928$	−121.795	−	70.3183i	−0.131244	−	0.0757740i
$929$	−1691.44	+	298.247i	−1.82071	+	0.321041i	−0.976590	−	0.215111i	$-0.930989\pi$
$929$	−1691.44	+	298.247i	−1.82071	+	0.321041i	−0.844122	+	0.536152i	$0.819877\pi$
$930$	115.795	−	371.195i	0.124511	−	0.399134i
$931$	−796.151	+	289.775i	−0.855157	+	0.311252i
$932$	−644.156	+	234.454i	−0.691155	+	0.251560i
$933$	654.150	−	51.9329i	0.701125	−	0.0556623i
$934$	186.483	+	1057.60i	0.199661	+	1.13233i
$935$	931.448	+	1186.41i	0.996201	+	1.26889i
$936$	−113.946	+	39.4091i	−0.121737	+	0.0421038i
$937$	−745.699	+	430.530i	−0.795837	+	0.459477i	−0.842013	−	0.539457i	$-0.818630\pi$
$937$	−745.699	+	430.530i	−0.795837	+	0.459477i	0.0461764	+	0.998933i	$0.485296\pi$
$938$	−2435.56	+	2043.68i	−2.59655	+	2.17876i
$939$	−19.3397	+	202.301i	−0.0205961	+	0.215443i
$940$	−1238.76	+	1992.89i	−1.31783	+	2.12010i
$941$	−461.605	+	550.119i	−0.490547	+	0.584611i	−0.953357	−	0.301846i	$-0.902397\pi$
$941$	−461.605	+	550.119i	−0.490547	+	0.584611i	0.462809	+	0.886458i	$0.346841\pi$
$942$	−1536.02	+	1511.51i	−1.63059	+	1.60457i
$943$	47.4795	−	130.449i	0.0503494	−	0.138334i
$944$			350.599i			0.371397i
$945$	879.096	−	1115.25i	0.930260	−	1.18015i
$946$	−310.606			−0.328336
$947$	1022.31	+	372.089i	1.07952	+	0.392913i	0.819729	−	0.572752i	$-0.194124\pi$
$947$	1022.31	+	372.089i	1.07952	+	0.392913i	0.259791	+	0.965665i	$0.416346\pi$
$948$	−977.130	+	253.416i	−1.03073	+	0.267317i
$949$	314.650	+	264.023i	0.331560	+	0.278212i
$950$	845.902	−	620.713i	0.890423	−	0.653382i
$951$	194.254	+	425.481i	0.204263	+	0.447404i
$952$	596.964	+	711.434i	0.627063	+	0.747304i
$953$	266.478	+	461.553i	0.279620	+	0.484316i	0.971290	−	0.237897i	$-0.0764582\pi$
$953$	266.478	+	461.553i	0.279620	+	0.484316i	−0.691670	+	0.722213i	$0.743125\pi$
$954$	−1660.77	−	2045.16i	−1.74085	−	2.14377i
$955$	236.551	+	301.301i	0.247698	+	0.315499i
$956$	61.3239	−	10.8131i	0.0641463	−	0.0113107i
$957$	−121.147	−	57.6823i	−0.126590	−	0.0602741i
$958$	−750.424	−	2061.77i	−0.783323	−	2.15216i
$959$	615.056	+	1689.85i	0.641352	+	1.76210i
$960$	1420.45	−	319.449i	1.47963	−	0.332759i
$961$	−154.363	−	875.438i	−0.160628	−	0.910966i
$962$	39.8568	−	69.0341i	0.0414312	−	0.0717610i
$963$	−716.813	−	429.371i	−0.744354	−	0.445868i
$964$	−305.387	−	528.946i	−0.316792	−	0.548699i
$965$	−50.6105	−	154.520i	−0.0524462	−	0.160124i
$966$	−350.099	−	249.362i	−0.362421	−	0.258139i
$967$	−46.1049	−	8.12954i	−0.0476783	−	0.00840697i	0.149758	−	0.988723i	$-0.452150\pi$
$967$	−46.1049	−	8.12954i	−0.0476783	−	0.00840697i	−0.197436	+	0.980316i	$0.563262\pi$
$968$	218.105	+	183.012i	0.225316	+	0.189062i
$969$	−239.703	+	866.641i	−0.247371	+	0.894366i
$970$	205.832	−	229.688i	0.212198	−	0.236792i
$971$		−	1134.57i		−	1.16846i	−0.811590	−	0.584228i	$-0.801397\pi$
$971$		−	1134.57i		−	1.16846i	0.811590	−	0.584228i	$-0.198603\pi$
$972$	−1149.94	−	593.633i	−1.18307	−	0.610734i
$973$		−	50.2458i		−	0.0516401i
$974$	−737.575	+	2026.47i	−0.757264	+	2.08056i
$975$	−127.122	−	213.166i	−0.130382	−	0.218631i
$976$	665.449	+	558.378i	0.681812	+	0.572109i
$977$	−4.07328	+	23.1007i	−0.00416917	+	0.0236445i	−0.986821	−	0.161813i	$-0.948266\pi$
$977$	−4.07328	+	23.1007i	−0.00416917	+	0.0236445i	0.982652	+	0.185458i	$0.0593768\pi$
$978$	1916.39	+	1364.97i	1.95950	+	1.39567i
$979$	−615.742	+	516.669i	−0.628950	+	0.527751i
$980$	232.308	+	1625.09i	0.237049	+	1.65825i
$981$	161.331	+	96.6373i	0.164456	+	0.0985090i
$982$	−1393.07	−	804.287i	−1.41860	−	0.819030i
$983$	81.6968	+	463.325i	0.0831096	+	0.471338i	0.997749	+	0.0670663i	$0.0213639\pi$
$983$	81.6968	+	463.325i	0.0831096	+	0.471338i	−0.914639	+	0.404272i	$0.867525\pi$
$984$	214.309	+	311.365i	0.217793	+	0.316428i
$985$	−775.688	−	25.2526i	−0.787500	−	0.0256371i
$986$	−73.6548	−	202.365i	−0.0747006	−	0.205238i
$987$	1195.47	−	2510.77i	1.21122	−	2.54384i
$988$	238.524	−	42.0583i	0.241421	−	0.0425691i
$989$	28.4031	+	16.3986i	0.0287191	+	0.0165810i
$990$	1815.69	−	562.529i	1.83403	−	0.568211i
$991$	106.228	+	183.992i	0.107193	+	0.185663i	0.914632	−	0.404288i	$-0.132481\pi$
$991$	106.228	+	183.992i	0.107193	+	0.185663i	−0.807439	+	0.589951i	$0.799147\pi$
$992$	−282.828	+	237.321i	−0.285109	+	0.239235i
$993$	589.042	+	1290.20i	0.593195	+	1.29929i
$994$	690.425	−	3915.60i	0.694593	−	3.93923i
$995$	362.624	+	678.126i	0.364446	+	0.681534i
$996$	−183.965	+	47.7109i	−0.184704	+	0.0479025i
$997$	341.998	−	939.631i	0.343027	−	0.942458i	−0.641484	−	0.767136i	$-0.721681\pi$
$997$	341.998	−	939.631i	0.343027	−	0.942458i	0.984511	−	0.175322i	$-0.0560967\pi$
$998$	−172.473			−0.172818
$999$	206.988	−	50.1429i	0.207196	−	0.0501931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.n.a.104.30	yes	204
3.2	odd	2		405.3.n.a.179.5		204
5.4	even	2	inner	135.3.n.a.104.5	yes	204
15.14	odd	2		405.3.n.a.179.30		204
27.7	even	9		405.3.n.a.224.30		204
27.20	odd	18	inner	135.3.n.a.74.5	✓	204
135.34	even	18		405.3.n.a.224.5		204
135.74	odd	18	inner	135.3.n.a.74.30	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.5	✓	204	27.20	odd	18	inner
135.3.n.a.74.30	yes	204	135.74	odd	18	inner
135.3.n.a.104.5	yes	204	5.4	even	2	inner
135.3.n.a.104.30	yes	204	1.1	even	1	trivial
405.3.n.a.179.5		204	3.2	odd	2
405.3.n.a.179.30		204	15.14	odd	2
405.3.n.a.224.5		204	135.34	even	18
405.3.n.a.224.30		204	27.7	even	9

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.86962 + 1.04446i) q^{2} +(-0.799738 + 2.89144i) q^{3} +(4.07967 + 3.42325i) q^{4} +(2.63957 - 4.24649i) q^{5} +(-5.31493 + 7.46205i) q^{6} +(6.76148 + 8.05802i) q^{7} +(2.02410 + 3.50585i) q^{8} +(-7.72084 - 4.62479i) q^{9} +O(q^{10})\)	\(q+(2.86962 + 1.04446i) q^{2} +(-0.799738 + 2.89144i) q^{3} +(4.07967 + 3.42325i) q^{4} +(2.63957 - 4.24649i) q^{5} +(-5.31493 + 7.46205i) q^{6} +(6.76148 + 8.05802i) q^{7} +(2.02410 + 3.50585i) q^{8} +(-7.72084 - 4.62479i) q^{9} +(12.0099 - 9.42891i) q^{10} +(-13.6221 + 2.40195i) q^{11} +(-13.1608 + 9.05842i) q^{12} +(-1.13183 - 3.10967i) q^{13} +(10.9866 + 30.1856i) q^{14} +(10.1675 + 11.0282i) q^{15} +(-1.55244 - 8.80433i) q^{16} +(10.9047 - 18.8875i) q^{17} +(-17.3255 - 21.3355i) q^{18} +(6.87151 + 11.9018i) q^{19} +(25.3054 - 8.28838i) q^{20} +(-28.7067 + 13.1061i) q^{21} +(-41.5991 - 7.33504i) q^{22} +(3.41674 + 2.86699i) q^{23} +(-11.7557 + 3.04881i) q^{24} +(-11.0653 - 22.4178i) q^{25} -10.1057i q^{26} +(19.5469 - 18.6257i) q^{27} +56.0203i q^{28} +(1.10591 - 3.03846i) q^{29} +(17.6584 + 42.2664i) q^{30} +(-6.50266 - 5.45638i) q^{31} +(7.55269 - 42.8334i) q^{32} +(3.94904 - 41.3085i) q^{33} +(51.0195 - 42.8105i) q^{34} +(52.0657 - 7.44286i) q^{35} +(-15.6667 - 45.2980i) q^{36} +(6.83119 + 3.94399i) q^{37} +(7.28771 + 41.3307i) q^{38} +(9.89657 - 0.785688i) q^{39} +(20.2303 + 0.658600i) q^{40} +(-10.6450 - 29.2470i) q^{41} +(-96.0661 + 7.62668i) q^{42} +(7.24150 - 1.27687i) q^{43} +(-63.7963 - 36.8328i) q^{44} +(-40.0188 + 20.5790i) q^{45} +(6.81032 + 11.7958i) q^{46} +(-67.5050 + 56.6434i) q^{47} +(26.6987 + 2.55237i) q^{48} +(-10.7053 + 60.7126i) q^{49} +(-8.33894 - 75.8880i) q^{50} +(45.8911 + 46.6353i) q^{51} +(6.02769 - 16.5609i) q^{52} +95.8571 q^{53} +(75.5461 - 33.0329i) q^{54} +(-25.7567 + 64.1863i) q^{55} +(-14.5643 + 40.0150i) q^{56} +(-39.9087 + 10.3502i) q^{57} +(6.34708 - 7.56415i) q^{58} +(-38.6204 - 6.80982i) q^{59} +(3.72767 + 79.7975i) q^{60} +(-74.4337 + 62.4573i) q^{61} +(-12.9612 - 22.4495i) q^{62} +(-14.9377 - 93.4850i) q^{63} +(48.5308 - 84.0578i) q^{64} +(-16.1927 - 3.40189i) q^{65} +(54.4772 - 114.415i) q^{66} +(33.8519 + 93.0075i) q^{67} +(109.144 - 39.7252i) q^{68} +(-11.0222 + 7.58647i) q^{69} +(157.183 + 33.0222i) q^{70} +(-107.192 - 61.8875i) q^{71} +(0.586030 - 36.4292i) q^{72} +(-107.492 + 62.0606i) q^{73} +(15.4836 + 18.4527i) q^{74} +(73.6691 - 14.0664i) q^{75} +(-12.7094 + 72.0783i) q^{76} +(-111.461 - 93.5265i) q^{77} +(29.2201 + 8.08192i) q^{78} +(59.3719 + 21.6096i) q^{79} +(-41.4853 - 16.6472i) q^{80} +(38.2227 + 71.4145i) q^{81} -95.0462i q^{82} +(11.1780 + 4.06846i) q^{83} +(-161.979 - 44.8016i) q^{84} +(-51.4218 - 96.1614i) q^{85} +(22.1140 + 3.89930i) q^{86} +(7.90107 + 5.62763i) q^{87} +(-35.9935 - 42.8953i) q^{88} +(50.3248 - 29.0550i) q^{89} +(-136.333 + 17.2561i) q^{90} +(17.4049 - 30.1462i) q^{91} +(4.12477 + 23.3928i) q^{92} +(20.9772 - 14.4384i) q^{93} +(-252.876 + 92.0392i) q^{94} +(68.6787 + 2.23584i) q^{95} +(117.810 + 56.0936i) q^{96} +(19.8923 - 3.50756i) q^{97} +(-94.1319 + 163.041i) q^{98} +(116.283 + 44.4543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9}+O(q^{10}) \) 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9	\( 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31} + 12 q^{34} - 252 q^{35} + 324 q^{36} - 258 q^{39} + 117 q^{40} + 96 q^{41} - 666 q^{44} - 279 q^{45} - 6 q^{46} + 60 q^{49} + 48 q^{50} + 270 q^{51} + 432 q^{54} - 12 q^{55} + 294 q^{56} + 510 q^{59} + 390 q^{60} + 132 q^{61} - 486 q^{64} + 147 q^{65} - 186 q^{66} - 84 q^{69} - 141 q^{70} - 18 q^{71} - 954 q^{74} - 285 q^{75} + 84 q^{76} - 48 q^{79} - 1026 q^{81} + 198 q^{84} + 69 q^{85} - 1506 q^{86} + 792 q^{89} - 180 q^{90} - 6 q^{91} + 492 q^{94} - 543 q^{95} + 654 q^{96} + 792 q^{99}+O(q^{100}) \) 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

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